B 428181

!
1
ARTES
1837
SCIENTIA
LIBRARY
VERITAS
OF THE
UNIVERSITY OF MICHIGAN
PLURIBUS UNUM
!
SI QUAERIS PENINSULAM AMOENAM
CIRCUMSPICE
DEPARTMENT
OF
ENGINEERING
TA
145
R98

40
A
GENERAL TEXT BOOK,
FOR
ARCHITECTS, ENGINEERS, SURVEYORS,
SOLICITORS,
AUCTIONEERS, LAND AGENTS, STEWARDS,
COUNTRY GENTLEMEN, AND OTHERS.
。
3744

A
GENERAL TEXT BOOK.
FOR THE
CONSTANT USE AND REFERENCE
OF
CF TRE
ARCHITECTS, ENGINEERS, SURVEYORS,
SOLICITORS,
AUCTIONEERS, LAND AGENTS, AND STEWARDS,
IN ALL THEIR SEVERAL AND VARIED PROFESSIONAL OCCUPATIONS;
܀
AND FOR THE
ASSISTANCE AND GUIDANCE
OF
COUNTRY GENTLEMEN AND OTHERS
ENGAGED IN THE
TRANSFER, MANAGEMENT, OR IMPROVEMENT OF LANDED PROPERTY :
CONTAINING
THEOREMS, FORMULE, RULES, AND TABLES
IN
GEOMETRY, MENSURATION, AND TRIGONOMETRY;
LAND MEASURING, SURVEYING, AND LEVELLING; RAILWAY AND HYDRAULIC ENGINEERING;
TIMBER MEASURING; THE VALUATION OF ARTIFICERS' WORK,
ESTATES, LEASEHOLDS, LIFEHOLDS, ANNUITIES, TILLAGES, FARMING STOCK, & TENANT RIGHT :
THE ASSESSMENT OF PARISHES, RAILWAYS, GAS AND WATER WORKS;
THE LAW OF DILAPIDATIONS AND NUISANCES, APPRAISEMENTS AND AUCTIONS,
LANDLORD AND TENANT, AGREEMENTS AND LEASES.
TOGETHER WITH EXAMPLES OF VILLAS AND COUNTRY HOUSES.
BY
EDWARD RYDE,
CIVIL ENGINEER AND LAND SURVEYOR, AUTHOR OF SEVERAL PROFESSIONAL WORKS.
TO WHICH AKE ADDED SEVERAL CHAPTERS ON
AGRICULTURE AND LANDED PROPERTY.
BY
PROFESSOR DONALDSON,
AUTHOR OF SEVERAL WORKS ON AGRICULTURE.
LONDON:
JOHN WEALE, 59, HIGH HOLBORN, MDCCCLIV.
LONDON:
PRINTED BY GEORGE PHIPPS, RANELAGH Street,
EATON SQUARE.
10-5-39
Reclass
1 b m
W
1
PREFACE.
THE design of this Book is not entirely due to me, but
was suggested by the eminent Professional Publisher
whose name appears at the foot of the title page. The
necessity for its production became apparent from the
many enquiries made of him for a work of this character,
and when he did me the favor to consult me on the
subject, it at once occurred to my mind that the Book
should be one which if placed in the hands of my pupils
would afford them the materials for the nucleus of that
professional knowledge that should govern their pursuits
in after-life; a volume to which men of all professions
collateral to my own might constantly refer for assistance
and information; a volume which would guide the pos-
sessor or agent of real property, alike in the transfer as in
the improvement or management of his estates; and
finally, a volume that would be found acceptable on the
table and desk of every practical man and student
throughout the kingdom.
In the preparation of such a work, an attempt at
vi
PREFACE.
complete originality would be as futile as it is unne-
cessary; so many matters of scientific detail, having long
since become in a great measure common property; I
have therefore in the first five chapters which treat of
Arithmetic, Geometry, Mensuration, and Trigonometry,
consulted established authorities, but especially I should
mention Mr. LAWS' Edition of "Dr. Gregory's Mathe-
matics for Practical Men." There are also a few other
instances of very minor importance, in which having
found material ready to my hand, I have not hesitated
to transcribe it (I hope honorably) to these pages, having
acknowledged each instance as it occurs. The remaining
matter, forming the great bulk of the work, has been an
undertaking of immense labour; has occupied the leisure
time of several years; and will I trust be found to answer
the purposes for which it is intended.
If it may sometimes appear to competent persons that
too great an importance has been given to trivial things,
they must bear in mind that I have been writing for the
benefit of all parties; alike for those who may be assumed
to know but very little of the subjects treated of, as for
those who are well informed upon them. On the other
hand I must claim indulgence if any of my observations
are not sufficiently in detail for the comprehension of the
less skilled portion of my readers, both on account of the
PREFACE.
vii
very limited space at my command for the disposition of
so many subjects, and the great difficulty an efficient per-
son experiences in describing such things as appear to
him so simple that he imagines every one must know them.
It is presumed that a very important feature of the
work will be found in the numerous Tables with which
its pages are interspersed. To the practical man Tables
on many of the subjects which are herein contained are of
unknown value, by affording much facility for calculation,
and by greatly diminishing the chances of error.
The chapters upon Engineering, Surveying, Hydrau-
lics, and Valuations are extended to a length commen-
surate only with the importance of the matters considered,
and the necessity of expounding the many and varied
rules by which operations of that kind are directed.
The Builders' Prices are intended to represent such
a scale as will serve to remunerate the master tradesman
for the outlay of his capital, his superintendence, and
skill; and, although they are published at a time when
unfortunately prices are influenced by a variety of oper-
ating causes, it is believed they will be found fair expo-
nents of average charges. With this view they have been,
in some instances, submitted to artificers themselves, for
confirmation of my opinions; and the assistance rendered
me in this particular by Mr. Powell, a plumber, painter,
viii
PREFACE.
and glazier, and Mr. Hopwood, an ironmonger, both of
Pimlico, and men who have my confidence, and such
patronage as is at my disposal in their respective busi-
nesses, has been such as to merit my acknowledgment
here.
The chapters on Dilapidations and Nuisances, with
the Law of Auction and Appraisements, were origi-
nally intended to be supplied by a barrister of emi-
nence; but it appeared as the work progressed, that
the printed authorities of which the publisher of this
book is sole proprietor, aided by that knowledge and
experience which fortune has enabled me to acquire, by
the exercise of general professional business from a very
early age, was sufficient to produce all that could be
desired.
The examples of Villas and Country Houses are
obtained from auxiliary sources: and the chapters on
Landed Property, by Professor Donaldson, convey their
own description of that gentleman's assistance on the
work.
I should now conclude, but that I feel the aid
of subordinates, when willingly and assiduously accorded
in any undertaking, should meet with courteous acknow-
ledgment. The names of my assistants, Mr. William Eve
and Mr. Frank Harrow, have been already mentioned in
PREFACE.
ix
the book in connection with one of the most useful tables;
but, in addition to the services there referred to, upon
one or other of them has devolved the tedious and irksome
task of reading for the correction of the press; (very often
after the ordinary business of the day had been disposed
of) so that I feel great pleasure in expressing the sense
I entertain of this additional help.
I have only to add, that, if any errors are found, and
the person who makes the discovery will be at the trouble
of communicating with me, the correction shall be made
in all future editions, the preparation of which I reserve
to myself.
UPPER BELGRAVE PLACE,
EATON SQUARE, London.
1ST DECEMBER, 1853.
EDWARD RYDE.
ARITHMETIC
SECT. 1
CONTENTS.
Notation
CHAPTER I.
2 Proof of the First Four Rules
3 Vulgar Fractions
4
Decimals
•
5
Duodecimals
6
Powers and Roots.
7 Properties of Numbers
8 Logarithms and Mathematical Tables
PAGE
1 to 171
1
2
1 07 ∞ co
3
6
8
9
10
13 to 171
CHAPTER II.
PLANE AND SOLID GEOMETRY
172 to 191
SECT. 1
Definitions
172
2
Of Angles and Right Lines, and their Rectangles
173
3
Of Triangles
174
4 Of Quadrilaterals and Polygons
176
5 Of the Circle, and Inscribed and Circumscribing
Figures
178
6 Of Planes and Solids
183
•
7 Practical Geometry
186
CHAPTER III.
MENSURATION
SECT. 1 Comparison of English and French Weights and
Measures
2 Mensuration of Superfices
3 Mensuration of Solids
192 to 199
192
194
197
TRIGONOMETRY
SECT. 1
CHAPTER IV.
Definitions and Trigonometrical formulæ
2 General Propositions
3 Solution of the Cases of Plane Triangles
CHAPTER V.
CONIC SECTIONS
200 to 215
200
201
203
216 to 218
xii
CONTENTS.
LAND MEASURING
CHAPTER VI.
PAGE
219 to 256
226
230 to 256
Table of Decimals of an Acre
Table of Land Measure, by dimensions taken in
yards
•
CHAPTER VII.
LAND SURVEYING
257 to 296
SECT. 1 Parish and Estate Surveying
2 Trigonometrical Surveying
258
271
3 Traverse Surveying .
280
4 Field Instruments-the Prismatic Compass
283
the Box Sextant
286
the Theodolite
290
CHAPTER VIII.
Levelling .
296 to 315
Levelling Instruments-the Spirit Level
299
the Y Level
301
Troughton's Level
307
Mr. Gravatt's Level
308
Levelling Staves
309
Examples in Levelling
314
CHAPTER IX.
PLOTTING
The Circular Protractor
The T Square and Semi-circular Protractor
Plotting Sections
316 to 326
319
320
326
CHAPTER X.
COMPUTATION OF AREAS
326 to 334
The Pediometer
326
The Computing Scale
Computing Tables
328
330 to 334
CHAPTER XI.
COPYING MAPS
335 to 338
The Pentagraph
336
CHAPTER XII.
RAILWAY SURVEYING
338 to 423
SECT. 1 Exploration and Trial Levels
Standing Orders
338
339
CONTENTS.
xiii
SECT. 2 Proceedings subsequent to the passing of the Act
Tables for Setting out Curves
Tables for Setting out Slopes
Tables of Relative Gradients
•
PAGE
350
360
375 to 378
379
392 to 419
420 to 423
Specification of Works to be executed in the con-
struction of a Railway .
Form of Tender
COLONIAL SURVEYING
CHAPTER XIII.
424 to 439
CHAPTER XIV.
HYDRAULICS IN CONNECTION WITH DRAINAGE, SEWERAGE, AND
WATER SUPPLY
Synopsis of Ryde's Hydraulic Tables
Specifications-Iron Pipes and Castings
Stone Ware Drain Pipes
Pipe Laying
Reservoir
440 to 491
443
468
473
477
485
CHAPTER XV.
TIMBER MEASURING
491 to 540
Timber Tables-Solid Measure
496 to 515
Unequal Sided Timber
518 to 527
Superficial Measure
529 to 540
CHAPTER XVI.
ARTIFICERS' WORK.
541 to 577
SECT. 1 Bricklayers' and Excavators'
2 Slaters'
3 Carpenters' and Joiners'
4 Sawyers'
5
Stonemasons'
6 Plasterers'
7 Ironmongers'
8 Painters'
9 Glaziers'
•
10 Paper Hangers'.
541
549
551
566
566
571
573
573
575
576
VALUATION OF ESTATES
CHAPTER XVII.
577 to 624
Tables for the Purchasing of Freehold, Copyhold, or Leasehold
Estates, Annuities, and Advowsons, and for Renewing Leases
for Terms of Years certain and for Lives
589 to 615
xiv
CONTENTS.
CHAPTER XVIII.
PAGE
VALUATION OF TILLAGES AND TENANT RIGHT.
Tables for Measuring and Valuing Hay Ricks
625 to 646
638 to 646
CHAPTER XIX.
VALUATION OF PARISHES
647 to 659
CHAPTER XX.
BUILDERS' PRICES.
660 to 706
SECT. 1 Carpenters' and Joiners'
2 Masons'
3 Bricklayers'
4 Plasterers'
5 Ironmongers'
6 Drainers'
660
674
676
676
677
686
7 Plumbers'
689
8 Painters'
694
9
Paper Hangers' and Decorators'
697
10
Glaziers'
699
11
Zinc Workers'
703
12 Coppersmiths'
705
13 Wireworkers'
706
CHAPTER XXI.
DILAPIDATIONS AND NUISANCES
707 to 748
SECT. 1 General Definitions
707
счна со до
2
Dilapidations by Tenants for Life and Years
714
•
3
by Mortgagee or Mortgagor
737
4
5
of Party Walls and Fences
of Highways and Bridges
738
740
6 Nuisances
746
CHAPTER XXII.
THE LAW RELATING TO APPRAISERS AND AUCTIONEERS
SECT. 1 The Law relating to Appraisements
•
749 to 765
749
752
2
of Auction
CHAPTER XXIII.
LANDLORD AND TENANT
SEOT. 1 Agreements and Leases
2 Notice to Quit
3 Distress
4 Recovery of Possession
765 to 786
765
773
775
782
·
CONTENTS.
XV
CHAPTER XXIV.
TABLES.
Of Natural Sines and Cosines
For Reducing Links into Feet
Decimals of a Pound Sterling
STAMP LAWS .
Stamp Duties
Customs' Duties
PAGE
787 to 808
788 to 802
803 to 806
807 to 808
CHAPTER XXV.
809 to 832
809
823
EXAMPLES OF VILLAS AND COUNTRY HOUSES
833 to 855
ON LANDED PROPERTY,
BY.
PROFESSOR DONALDSON.
CHAPTER I.
LANDLORD AND TENANT-THEIR POSITION AND CONNECTIONS
857
CHAPTER II.
LEASE OF LAND, CONDITIONS, AND RESTRICTIONS; CHOICE OF
TENANT AND ASSIGNATION OF THE DEED
877
CHAPTER III.
CULTIVATION OF LAND, AND ROTATION OF CROPS .
CHAPTER IV.
BUILDINGS NECESSARY ON CULTIVated Lands-DWELLING HOUSES,
FARMERIES, AND COTTAGES FOR LABOURERS
CHAPTER V.
LAYING OUT FARMS, ROADS, FENCES, AND GATES
•
•
•
CHAPTER VI.
PLANTATIONS-YOUNG AND OLD TIMBER .
•
898
921
941
953
xvi
CONTENTS.
CHAPTER VII.
MEADOWS AND EMBANKMENTS, BEDS OF RIVERS, Water Courses,
AND FLOODED GROUNDS.
CHAPTER VIII.
LAND DRAINING, OPEN AND COVERED-PLAN, EXECUTION, AND
ARRANGEMENT BETWEEN LANDLORD AND TENANT
•
CHAPTER IX.
MINERALS-WORKING AND VALUE
CHAPTER X.
EXPENSES OF AN ESTATE-REGULATIONS OF DISBURSEMENTS—AND
RELATION OF THE APPROPRIATE EXPENDITURES
CHAPTER XI.
VALUATION OF LANDED PROPERTY; OF THE SOIL, OF HOUSES, OF
WOODS, OF MINERALS, OF MANORIAL RIGHTS, OF ROYALTIES,
AND OF FEE FARM RENTS
•
PAGE
963
975
988
1003
1013
CHAPTER XII.
LAND STEWARD AND FARM BAILIFF: QUALIFICATIONS AND DUTIES 1024
CHAPTER XIII.
MANOR BAILIFF, WOODREEVE, GARDENER, AND GAMEKEEPER—
THEIR POSITION AND DUTIES
CHAPTER XIV,
FIXED DAYS OF AUDIT-HALF-YEARLY PAYMENTS OF RENTS-
FORM OF NOTICES, RECEIPTS, AND OF CASH BOOKS, GENERAL
MAP OF ESTATES, AND OF EACH SEPARATE FARM-CONCLUDING
OBSERVATIONS
1048
1058
A
GENERAL TEXT BOOK,
ETC., ETC.
CHAP. I.
ARITHMETIC.
SECT. I.-Notation.
ARITHMETIC is the science of numbers.
To the head of notation we may refer the explanation of the principal
symbols or characters employed to express operations or results in com-
putation. Thus,
The sign+ (plus) belongs to addition, and indicates that the numbers
between which it is placed are to be added together. Thus, 5 + 7
expresses the sum of 5 and 7, or that 5 and 7 are to be added together.
The sign — (minus) indicates that the number which is placed after it
is to be subtracted from that which precedes it. So, 9-3 denotes that
3 is to be taken from 9.
The sign denotes difference, and is placed between two quantities
when it is not immediately evident which of them is the greater.
The sign x (into), for multiplication, indicates the product of two
numbers between which it is placed. Thus 8 x 5 denotes 8 times 5
or 40.
The sign÷(by), for division, indicates that the number which pre-
cedes it is to be divided by that which follows it; and the quotient that
results from this operation is often represented by placing the first num-
ber over the second with a small bar between them. Thus, 158
denotes that 15 is to be divided by 8, and the quotient is expressed
thus 15.
The sign, two equal and parallel lines placed horizontally, is that
of equality. Thus, 2 + 3 + 4 = 9, means that the sum of 2, 3, and 4,
is equal to 9.
Inequality is represented by two lines so drawn as to form an angle,
and placed between two numbers, so that the angular point turns towards
the least. Thus, 7 > 4, and A > B, indicate that 7 is greater than 4,
and the quantity represented by A greater than the quantity represented
by B; and, on the other hand, 3 < 5 and C < D indicate that 3 is less
than 5, and C less than D
B
2
PROOF OF THE FIRST FOUR RULES OF ARITHMETIC.
Colons and double colons are placed between quantities to denote their
proportionality. So, 3:5:: 9:15, signifies that 3 are to 5 as 9 are to
15, or 3=15 9
The extraction of roots is indicated by the sign, with a figure occa-
sionally placed over it to express the degree of the root; or by a fraction
(having unity for its numerator, and the figure expressing the degree of
the root for its denominator) placed above and to the right of the quantity
to have its root extracted; thus,√4 or 4³, signifies the square root of 4;
3/27, or 27, the cube root of 27; 16 or 16, the fourth or biquadrate
root of 16.
4
The raising of powers is expressed by a whole number similarly placed,
the figure denoting the power to which the quantity is to be raised; thus,
62, signifies the square of 6; 83, the cube of 8; and 34, the fourth power
of 3. The figures thus used to indicate the power, whether whole or
fractional numbers, are termed indices or exponents.
When both operations are to be successively performed upon a quan-
tity, that is, when some root is to be extracted, and then that root to be
raised to some different power, the operation is very simply expressed by
a fraction placed as before, the denominator of which indicates the root to
be extracted, and the numerator the power to which that root is to be
afterwards raised. Thus, 273, denotes that the cube root of 27 is to be
extracted, and that the root so obtained is to be squared, or raised to the
second power. It is immaterial which operation is first performed, for
the result would be the same whether we first extracted the cube root, as
above, and then squared it, or whether we squared the number first, and
then extracted the cube root of the power so obtained.
SECT. II.-Proof of the first four Rules of Arithmetic.
Simple as these four rules are, it is not unusual to commit errors in
working them: it is, therefore, useful to possess modes of proof.
1. Now, addition may be proved by adding
downwards, as well as upwards, and observing
whether the two sums agree; or, by dividing
the numbers, to be added into two portions,
finding the sum of each, and then the sum of
those two separate amounts. Thus, in the
margin, the sum of the four numbers is 7355;
the sum of the two upper ones 5857, of the
two lower ones 1498, and their sum is 7355,
the same as before.
2758
2758
3099
3099
469
1029
5857
7355
469
1029
1498
7355
2. The proof of subtraction is effected by adding the remainder to the
subtrahend; if their sum agrees with the minuend the work is right,
otherwise not.
VULGAR FRACTIONS.
3
3. Multiplication and division reciprocally prove each other.
There is also another proof for multiplication, known technically by the
phrase casting out the nines. Add together the numbers from left to
right in the multiplicand, dropping 9 whenever the sum exceeds 9, and
carry on the remainder, dropping the nines as often as the amount is be-
yond them; and note the last remainder. Do the same with the multi-
plier and with the product; then multiply the first two remainders and
cast the nines out of their product; 'if the remainder is equal to the last
remainder, this is regarded as a test that the work is right. Thus, taking
an example in multiplication, assume the figures in the multiplicand to
amount to 6 above two nines, those in the multiplier to 6 above three
nines, those in the product to 0 above six nines; the product 6 x 6 of the
two first excesses is 36, or 0 above four nines: the coincidence of the two
O's is the proof. It is plain, however, that the proof will be precisely the
same so long as the figures in the product be the same, whatever be their
order: the proof, therefore, though ingenious, is defective*.
A similar proof applies to division.
SECT. III.-Vulgar Fractions.
Common or Vulgar Fractions are so denominated to distinguish them
from another kind, hereafter to be mentioned, called Decimal Fractions.
A fraction is an expression for the value of any part of an integer, or
whole number, such number being considered as unity. Thus, if a pound
sterling be the unit, then a shilling will be the twentieth part of that unit,
and four pence will be four-twelfths of that twentieth part. These, re-
presented according to the usual notation of vulgar fractions, will be
and of, respectively.
ΤΣ
The lower number of a fraction thus represented (denoting the number
of parts into which the integer is supposed to be divided) is called the
denominator; and the upper figure (which indicates the number of those
parts expressed by the fraction) the numerator. Thus, in the fractions
5, 1, 7 and 15 are denominators, 5 and 8 numerators.
Vulgar fractions are divided into proper, improper, mixed, simple,
compound, and complex.
Proper fractions have their numerators less than their denominators,
as 2, §, &c.
5
Improper fractions have their numerators equal to, or greater than,
their denominators, as 4, 12, &c.
81 M N +
* The correctness of this proof, with the exception above specified, may be shewn
algebraically, thus:-put M and N the number of nines in the multiplicand and
multiplier respectively, m and n their excesses; then, 9 M+ m = the multiplicand,
and 9 N + n
the multiplier, and the product of those factors will be
9 Mn+ 9 Nm = m n; but the three first terms are each a precise number of nines ;
because one of the factors in each is so; these, therefore, being neglected, there re-
mains m n to be divided by nine; but m n is the product of the two former excesses :
therefore the truth of the method is evident.
Q. E. D.
4
VULGAR FRACTIONS.
Mixed fractions, or numbers, are those compounded of whole numbers
and fractions, as 7, 12, &c.
Simple fractions are expressions for parts of whole numbers, as
,, &c.
as
Compound fractions are expressions for the parts of given fractions, as
of, of, &c.
Complex fractions have either one or both terms fractional numbers,
5 12 69
24' 143' 123'
&c.
The value of a fraction is not altered by multiplying or dividing
both its numerator and denominator by the same number; thus,
1, 4, 11, 114, are all equal, although successively multiplied by 2, 6,
2
and 12.
2
288,
Any number which will divide two or more numbers without re-
mainder, is called their common measure.
REDUCTION OF VULGAR FRACTIONS.
This consists principally in changing them into a more commodious
form for the operations of addition, subtraction, &c.
CASE I.-To reduce fractions to their lowest terms.
Rule.-Divide the numerator and denominator of a fraction by any
number that will divide them both, without a remainder; the quotient
again, if possible, by any other number: and so on, till 1 is the greatest
divisor.
Thus, 1178=214 == 11 = 3, where 5, 3, 7, 7, respectively,
2205
are the divisors.
98
147
Or, 1470 = 2, by dividing at once by 735.
2205
Note. This number 735 is called the greatest common measure of the
terms of the fraction: it is found thus-Divide the greater of the two
numbers by the less; the last divisor by the last remainder, and so on till
nothing remains: the last divisor is the greatest common measure
required.
CASE II. To reduce an improper fraction to its equivalent whole or
mixed number.
Rule.—Divide the numerator by the denominator, and the quotient will
be the answer: as is evident from the nature of division.
CASE III. To reduce a mixed number to its equivalent improper
fraction; or a whole number to an equivalent fraction having any as-
signed denominator.
Rule. This is, evidently, the reverse of Case II.; therefore multiply
the whole number by the denominator of the fraction, and add the nume-
rator to obtain the numerator of the fraction required.
Ex.-Reduce 2211 to an improper fraction, and 20 to a fraction whose
denominator shall be 274.
(22 × 43) + 11 - 957 new numerator, and 257 the 1st fraction.
20 × 274 = 5480 new numerator, and 5480 the 2nd fraction.
CASE IV. To reduce a compound fraction to an equivalent simple one.
VULGAR FRACTIONS.
5
Rule.-Multiply all the numerators together for the numerator, and all
the denominators together for the denominator, of the simple fraction re-
quired.
If part of the compound fraction be a mixed or a whole number, reduce
the former to an improper fraction, and make the latter a fraction by
placing 1 under the numerator.
When like factors are found in the numerators and denominators, cancel
them both.
Ex.-Reduce of of of off to a simple fraction.
& 2 5 7
1 × 5 × 4 20
1 × 9 × 11¯99
2 × 3 × 5 × 7 x 8 2 × 5 × 8 1 × 5 × 8
3 × 4 × 7 × 9 × 11 ‍4 × 9 × 11 2 × 9 × 11
Here the 3 and 7 common to numerator and denominator are first cancelled;
then the fraction is divided by 2; and then by 2 again.
CASE V. To reduce fractions of different denominators to equivalent
fractions having a common denominator.
Rule.-Multiply each numerator into all the denominators except its
own, for new numerators; and all the denominators together for a common
denominator.
Ex.-Reduce, %, and 5, to equivalent fractions having a common
denominator.
2 x 7 x 9 = 126
6 × 3 × 9 = 162
the numerators.
5 × 3 × 7 = 105
x
3 × 7 × 9 = 189, the common denominator.
189,
162
42 54
Hence the fractions are 126, 183, 185, or 43, 53, 35, when divided by 3.
Hence, also, it appears that exceed, and that exceed.
ADDITION AND SUBTRACTION OF FRACTIONS.
Rule. If the fractions have a common denominator, add or subtract the
numerators, and place the sum or difference as a new numerator over the
common denominator.
If the fractions have not a common denominator, they must be reduced
to that state before the operation is performed.
In addition of mixed numbers, it is usually best to take the sum of the
integers, and that of the fractions, separately; and then their sum, for the
result required.
MULTIPLICATION AND DIVISION OF FRACTIONS.
Rule 1. To multiply a fraction by a whole number, multiply the nume-
rator by that number, and retain the denominator :-Or, divide the de-
nominator by the same number, (if a multiple of it,) and retain the nume-
rator.
2. To divide a fraction by a whole number, multiply the denominator
by that number, and retain the numerator :-Or, divide the numerator by
the same number, (if a multiple of it,) and retain the denominator.
6
DECIMALS.
3. To multiply two or more fractions is the same as to take a fraction
of a fraction; and is, therefore, effected by taking the product of the
numerators for a new numerator, and of the denominators for a new de-
nominator. (The product is evidently smaller than either factor when
each is less than unity.)
4. To divide one fraction by another, invert the divisor, and proceed as
in multiplication. (The quotient is always greater than the dividend
when the divisor is less than unity.)
SECT IV. Decimals.
The embarrassment and loss of time occasioned by the computation of
quantities expressed in vulgar or ordinary fractions, have inspired the
idea of fixing the denominator so as to know what it is without actually
expressing it. Hence originate two dispositions of numbers, decimal
fractions and complex numbers. Of the latter, such, for example, as when
we express lineal measures in yards, in feet (or thirds of a yard), and
inches (or twelfths of a foot), we shall treat in the following section, and
shall here confine ourselves to the former.
Decimal fractions, or substantively decimals, are fractions always having
some power of ten for their denominator; but for the sake of brevity only
the numerator is expressed, being written as a whole number with a dot
placed on its left hand, which dot determines the value of the denominator,
the number of cyphers in the denominator being always equal to the
number of figures to the right of the dot, or as it is termed decimal point;
if the number of significant figures in the numerator is not sufficient,
cyphers are added to the left hand. It is evident that the values of
decimals decrease in the same tenfold proportion from the point towards
the right hand, as those of integers increase towards the left: thus
The vulgar fraction,
0
is written
•1
100
•01
""
""
тобо
""
""
""
10000
·001
·0001
""
7
""
""
10
.7
""
43
""
""
100
•43
""
125
">
10000
•0125
""
The vulgar fraction,
10
7,3% is written
7.3
""
42.85
""
""
57.217
""
100
1000
42.85
""
57.217
""
&c.
&c.
The value of a decimal fraction is not altered by cyphers on the right
hand: for 500 or 500, is in value the same as, or 5, that is 1.
1000
When decimals terminate after a certain number of figures, they are
called finite, as 1251851, 958058237.
∙125
1000
=
1000
When one or more figures in the decimal become repeated, it is called
a repeating or circulating decimal; and a dot is placed over the figure to
}
DECIMALS.
7
be repeated, if only one, or if more than one, over the first and last
figures; thus-
•333333, &c.
is written ⚫3
•666666, &c.
==
.6
•428571428571, &c.
= 3
•428571
""
•29504504, &c.
131
4 4 4
""
-29504
When the circulating portion of the decimal is preceded by other figures
which do not circulate, (as in the last example,) it is called a mixed
circulate.
Rules for the management of this latter kind of decimals are given by
several authors; but, in general, it is more simple and commodious to
perform the requisite operations by means of the equivalent vulgar frac-
tions, the method of obtaining which is given in Case III.
Reduction of Decimals is a rule by which the known parts of given
integers are converted into equivalent decimals, and vice versa.
CASE I.—To reduce a given vulgar fraction to an equivalent decimal.
Rule.-Annex as many cyphers to the numerator as may be necessary
then divide by the denominator, and point off in the quotient as many
places of decimals as the number of cyphers added to the numerator; if
the quotient does not contain so many figures, the deficiency must be made
up by cyphers placed on the left hand.
CASE II.-Any decimal being given to find its equivalent vulgar frac-
tion; or to express its value by integers of lower denominations.
Rule.-When the equivalent vulgar fraction is required, place under the
decimal as a denominator a unit, with as many cyphers as there are figures
in the proposed decimal; and let the fraction so constituted be reduced to
its lowest terms.
Or, if the value of the decimal be required in lower denominations,
multiply the given decimal by the number of parts in the next less de-
nomination contained in its integer; and point off, from right to left, as
many figures of the product as there were places in the given decimal.
Multiply the decimal last pointed off by the value of its integer, in the
next inferior order, pointing off the same number of decimals as before;
and thus continue the process to the lowest integer, or until the decimals
cut off become all cyphers; then will the several numbers on the left of
the separating points, together with the remaining decimal, if any, express
the required value of the given decimal.
CASE III.—To reduce a circulating decimal to its equivalent vulgar
fraction.
Rule.-Take the figures in the decimal and place them as a whole
number for the numerator, and under them for a denominator as many 9's
as there are figures in the circulate, and the fraction thus formed will be
equivalent in value to the given decimal.
If the decimal is a mixed circulate, subtract the finite part (or the
figures which are not repeated) from the whole mixed circulate, (both
considered as whole numbers,) for the numerator; and for the denomi-
nator, take as many 9's as there are figures in the circulating portion of
8
DUODECIMALS.
the decimal, with as many cyphers to the right as there are figures in the
finite portion of the same.
Examples.
The circulate
.3
91
06
6
"
99
•549
549
>>
999
7-630
2
33
61
TIT
7630
999
7770
=
TTT
The mixed circulate ·6409
6409-64
141
9900
220
5.29504
= 529504-29
""
= 51
131
444.
99900!
SECT. V.-Duodecimals.
Fractions whose denominators are multiples of 12, as 144, 1728, &c.,
are called duodecimals; and the division and sub-division of the integer
are understood without being expressed, as in decimals. The method of
operating by this class of fractions is principally in use among artificers,
in computing the contents of work, of which the dimensions are taken in
feet, inches, and twefths of an inch.
Rule.—Set down the two dimensions to be multiplied together, one
under the other, so that feet shall stand under feet, inches under inches,
&c. Multiply each term in the multiplicand, beginning at the lowest, by
the feet in the multiplier, and set the result of each immediately under its
corresponding term, observing to carry 1 for every 12, from the inches to
the feet. In like manner, multiply all the multiplicand by the inches of
the multiplier, and then by the twelfth parts, setting the result of each
term one place removed to the right hand when the multiplier is inches,
and two places when the parts become the multiplier. The sum of these
successive products will be the answer required.
Or, instead of multiplying by the inches, &c., take such parts of the
multiplicand as these are of a foot.
Examples.
1. Multiply 12 ft. 7 ins. by 7 ft. 3 ins.
ft. ins. 1
12 7 4
7 3 9
88
3 4
ins.
3
1 10 0
3
9 5 6 0
9'
92 2 7 6 0
or,
ft. ins.
12 7 4
1
7 ft.
14 14
of 1 ft.
of 3 ins.
92 2 7
88 3 4
3 110
9 512
POWERS AND ROOTS.
9
2. Multiply 35 ft. 4 ins. into 12 ft. 3½ ins.
ft. ins.
35 4 6
12 3 4
424 6 0
ins.
8 10 1 6
3
11 9
6 0
4'
or,
||
ft. ins.
35 4 6
12 ft.
424 6
0
1 of 1 ft.
of 3 ins.
8 10 11
11 91
434 3 11
434 3 11 0 0
The feet in the answers are square feet, but the numbers standing in
the place of inches are not square inches, but twelfth parts of square feet,
each part being equal to 12 square inches; and the numbers in the third
place being twefth parts of these are square inches; in like manner, if the
operation be carried further, every successive place will be a twelfth part
of that preceding it.
SECT. VI.-Powers and Roots.
1.—To Extract the Square Root.
Rule.-Divide the given number into periods of two figures each, by
setting a point over the place of units, another over the place of hundreds,
and so on over every second figure, both to the left hand in integers, and
to the right hand in decimals. Find the greatest square in the first period
on the left hand, and set its root on the right hand of the given number,
after the manner of a quotient figure in division. Subtract the square thus
found from the said period, and to the remainder annex the two figures
of the next following period, for a dividend. Double the root above-
mentioned for a divisor; and find how often it is contained in the said
dividend, exclusive of its right-hand figure; and set that quotient figure.
both in the quotient and divisor. Multiply the whole augmented divisor
by this last quotient figure, and subtract the product from the said divi-
dend, bringing down to it the next period of the given number, for a new
dividend. Repeat the same process, viz., find another new divisor, by
doubling all the figures now found in the root; from which, and the last
dividend, find the next figure of the root as before; and so on through all
the periods, to the last.
Note.-The best way of doubling the root, to form the new divisors, is
by adding the last figure always to the last divisor, as appears in the fol-
lowing Example.-Also, after the figures belonging to the given number
are all exhausted, the operation may be continued into decimals at plea-
sure, by adding any number of periods of cyphers, two in each period.
10.
PROPERTIES OF NUMBERS.
Example.
Find the square root of 17-3056
17-3056(4·16 the root: in which the number of
16
decimal places is the same as the
number of decimal periods into which
the given number was divided.
81
130
1 |
81
826
4956
6
4956
2.-To Extract Cube and higher Roots.
The rules for extracting the cube and higher roots, are very tedious.
in practice: on which account it is advisable to work by means of
logarithms.
SECT. VII.-Properties of Numbers.
To render these intelligible, we shall here collect a few definitions.
Def. 1. A unit, or unity, is the representation of any thing considered
individually, without regard to the parts of which it is composed.
2. An integer is either a unit or an assemblage of units; and a fraction
is any part or parts of a unit.
3. A multiple of any number is that which contains it some exact num-
ber of times.
4. One number is said to measure another, when it divides it without
leaving any remainder.
5. And if a number exactly divides two, or more numbers, it is then
called their common measure.
6. An even number, is that which can be halved, or divided into two
equal parts.
7. An odd number, is that which cannot be halved, or which differs
from an even number by unity.
8. A prime number, is that which can only be measured by 1, or unity.
9. One number is said to be prime to another when unity is the only
number by which they can both be measured.
10. A composite number, is that which can be measured by some num-
ber greater than unity.
11. A perfect number, is that which is equal to the sum of all its divi-
sors, or aliquot parts:—thus 6 = § + § + §.
Prop. 1. The sum or difference of any two even numbers is an èven
number.
PROPERTIES OF NUMBERS.
11
2. The sum or difference of any two odd numbers is even; but the sum
of three odd numbers is odd.
3. The sum of any even number of odd numbers is even; but the sum
of any odd number of odd numbers is odd.
4. The sum or difference of an even and an odd number is odd.
5. The product of any number of even numbers is even; and any power
of an even number is even.
6. The product of any number of odd numbers is odd; and every power
of an odd number is odd.
7. The product of any number of even numbers, by any number of odd
numbers, is even.
8. An odd number cannot be divided by an even number, without a
remainder.
9. If an odd number divides an even number, it will also divide the
half of it.
10. If a number consist of many parts, and each of those parts have a
common divisor d, then will the whole number, taken collectively, be
divisible by d.
11. Neither the sum nor the difference of two fractions, which are in
their lowest terms, and of which the denominator of the one contains a
factor not common to the other, can be equal to an integral number.
12. If a square number be either multiplied or divided by a square, the
product or quotient is a square; and conversely, if a square number be
either multiplied or divided by a number that is not a square, the product
or quotient is not a square.
13. The product arising from two different prime numbers cannot be a
square number.
14. The product of no two different numbers prime to each other can
make a square, unless each of those numbers be a square.
15. The square root of an integral number, that is not a complete
square, can neither be expressed by an integer nor by any rational
fraction.
16. The cube root of an integer that is not a complete cube cannot be
expressed by either an integer or a rational fraction.
17. Every prime number greater than 2, is of one of the forms 4 n + 1,
or 4n — 1.
18. Every prime number greater than 3, is of one of the forms 6 n + 1
or 6 n 1.
19. No algebraical formula can contain prime numbers only.
20. The number of prime numbers is infinite.
21. The first twenty prime numbers are 1, 2, 3, 5, 7, 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47, 53, 59, 61, and 67.
22. A square number cannot terminate with an odd number of
cyphers.
23. If a square number terminate with a 4, the last figure but one
(towards the right hand) will be an even number.
24. If a square number terminate with 5, it will terminate with 25.
12
PROPERTIES OF NUMBERS.
25. If a square number terminate with an odd digit, the last figure but
one will be even; and if it terminate with any even digit, except 4, the
last figure but one will be odd.
26. No square number can terminate with two equal digits, except two
cyphers or two fours.
27. No number whose last, or right-hand digit is 2, 3, 7, or 8, is a
square number.
28. If a cube number be divisible by 7, it is also divisible by the cube
of 7.
29. The difference between any integral cube and its root is always
divisible by 6.
30. Neither the sum nor the difference of two cubes can be a cube.
31. A cube number may end with any of the natural numbers 1, 2, 3,
4, 5, 6, 7, 8, 9 or 0.
32. If any series of numbers, beginning from 1, be in continued geo-
metrical proportion, the 3rd, 5th, 7th, &c. will be squares; the 4th, 7th,
10th, &c. cubes; and the 7th, of course, both a square and a cube.
33. All the powers of any number that end with either 5 or 6, will end
with 5 or 6, respectively.
34. Any power, n, of the natural numbers, 1, 2, 3, 4, 5, 6, &c. has as
many orders of differences as there are units in the common exponent of
all the numbers; and the last of those differences is a constant quantity,
and equal to the continual product 1 x 2 x 3 x 4 x
x n con-
tinued till the last factor, or the number of factors be n, the exponent of
the powers. Thus,
The 1st powers 1, 2, 3, 4, 5, &c., have but one order of
differences 1 1 1 1 &c., and that difference is 1.
The 2nd powers 1, 4, 9, 16, 25, &c., have two orders of
differences 357 9
2 2 2
of which the last is constantly 2=1 x 2.
The 3rd powers 1, 8, 27, 64, 125, &c., have three orders of
differences 7 19 37 61
12 18 24
6 6
of which the last is 6 = 1 × 2 × 3.
In like manner, the 4th, or last, differences of the 4th powers, are
each=24=1×2×3×4; and the 5th, or last differences of the 5th
powers, are each 125=1×2×3×4×5.
35. If unity be divided into any two unequal parts, the sum of the
square of either of those parts added to the other is the same. Thus, of
the two parts and ‡, † + (‡)² = 1 + (1)² = 2}; so, again, of the parts
2 and 3, % + (3)² = 3 + (?)² = 18.
3
2
19
25'
21
For the demonstrations of these and a variety of other properties of
numbers, those who wish to pursue this curious line of inquiry may con-
sult Legendre "Sur la Théorie des Nombres," the "Disquisitiones Arith-
LOGARITHMS.
13
metica" of Gauss, or Barlow's "Elementary Investigation of the Theory
of Numbers."
Also, for the highly interesting properties of Circulating Decimals, and
their connexion with prime numbers, consult the curious works of the late
Mr. H. Goodwyn, entitled "A First Centenary," and "A Table of the
Circles arising from the Division of a Unit by all the Integers from 1 to
1024."
SECT. VIII.-Logarithms.
As Logarithms are so fully described in most elementary treatises on
Arithmetic, and as a knowledge of their nature and properties is unnecessary
to their application to the purposes of calculation, we shall here only
explain the manner of using the accompanying tables.
By an inspection of Table II., which contains the logarithms of all
numbers from 1 to 100, it will be seen that each logarithm consists of two
distinct parts, separated by a decimal point; thus, the logarithm of 13 is
1·113943; the number to the left of the decimal point (or 1 in the above
example) is called the index or characteristic*, and its value depends only
upon the number of digits in the quantity whose logarithm it is, without
any regard to the value of that quantity, and it is always 1 less than that
number of digits; thus, in the example, the characteristic of the logarithm
of 13, which contains two digits, is 1, or one less than that number; and
it will be seen from the Table, that 1 is the characteristic of all the loga-
rithms from 10 to 99, but that, for numbers below 10, the index is 0, and
for 100 is 2, in each case 1 less than the number of digits in the quantity
of whose logarithm it is the characteristic. The characteristic, therefore,
of the logarithms of all numbers
equal to or greater than
1 and less than
10 is 0.
10
""
100
""
""
""
100,, 1.
1000,, 2.
1000
""
""
""
10000,, 3.
""
""
10000
&c.
""
100000 4.
&c.
&c.
When the quantity is less than unity, the characteristic of its logarithm
becomes negative, and its value is determined by the number of cyphers
which occur between the decimal point and the first significant figure (the
fraction being decimally expressed), and is always 1 greater than such
number of cyphers; or it is equal to the difference in the number of
figures in the numerator and decimal denominator; thus, the characteristic
of the logarithm of
* In order to avoid confusion from the use of the word index to signify two things,
we shall throughout this work employ the term characteristic when speaking of logar-
ithms, and index when speaking of roots or powers.
14
LOGARITHMS.
·1 or
•01
""
·001
·0001
&c.
""
Too
тобо
is T•*
2.
""
3.
""
10000,, 4·
&c. &c.
The decimal part of the logarithm, or that lying to the right of the
decimal point, is called the mantissa, and depends entirely on the relative
value of the figures composing the quantity whose logarithm it is, and
not at all upon the actual numerical value of that quantity; thus, in the
example already given, the decimal part of the logarithm of 13 is
∙113943, which is also the decimal part of the logarithm of 1.3, or 130, or
1300, for in each case the 1 and the 3 have the same relative value. So
that the decimal portion of a logarithm is always the same for the same
figures, and is not altered by the addition of any number of cyphers either
to the right or to the left hand of those figures, or what is equivalent, by
the multiplication or division of the quantity by 10, or any power of 10;
it is only the characteristic of the logarithm which alters its value, 1
being added to the characteristic for every 10 by which the quantity is
multiplied, or subtracted from it for every 10 by which the quantity is
divided. Thus,
the logarithm of 745800
that of 74580
""
13
""
""
""
"9
being 5.872622
is
4.872622
7458
3.872622
745.8
2.872622
74.58
1.872622
""
7.458
0.872622
.7458
1-872622
""
•07458
2-872622
•007458
3.872622
""
It must be borne in mind, that in the logarithm of a fractional quantity,
it is only the characteristic which has a negative value, and that the
decimal part of a logarithm is always positive. It is, however, sometimes
convenient to have the whole logarithm expressed, negatively, both cha-
racteristic and decimal; for which purpose, subtract the last right hand
figure in the decimal portion from 10, and all the others from 9, and the
result will be what is termed the arithmetical complement of the decimal,
to which prefix the former characteristic less 1, and the result will be a
negative logarithm, equivalent in value to the original logarithm having
only a negative characteristic; for example, the logarithm of 07458, as
above, is 2-872622, which is equivalent to 1.127378. It is also fre-
quently convenient to take the arithmetical complement of the whole
logarithm, and this is obtained by subtracting the right hand figure of the
decimal from 10, and all the others from 9, including the characteristic
* The negative sign (—) is always placed above the characteristic, thus 2, instead of
before it, in order to avoid its being misunderstood for the sign of subtraction.
USE OF THE TABLES.
15
when positive, but if negative it must be added to 9. Thus, the arithme-
tical complement
of 3.146128 is 6.853872
2-076276 11.923714
""
""
5-322839 4.677161
""
""
I-986772 10.013228
""
USE OF THE TABLES.
To find the logarithm of any given number.
If the number is less than 100, its logarithm will be found in Table II.,
with its proper characteristic prefixed; but if the number contains more
than two figures, its logarithm may be found from Table I. as follows :—
If there are only three figures in the number, look for that number in the
first column of the table, and on the same line in the next column to the
right, under 0, will be found the decimal portion of the required logarithm,
to which the proper characteristic must be prefixed, according to the rules
which we have just explained. If the quantity contains four figures, look
for the first three figures in the first column as before, and the four last
figures of the logarithm of the required number will be found on the same
line with those three figures, and in that column which has at its head the
fourth figure of the given number; the two first figures of the logarithm
will be found in the second column (headed O), and which figures being
common to all the logarithms inclosed by each pair of horizontal lines, it
is unnecessary to repeat. Where these first figures change their value in
the middle of a line, the same is indicated by a break in the horizontal
line, thus, 139879 | 0194, which shews that the two first figures (13) have
changed to 14, and the right hand logarithm is therefore 140194.
Examples.
Required the logarithm of 734.
In Table I., on the same line with 734 and under O, are found 5696,
the four last figures of the logarithm, to which the common figures 86 and
the proper characteristic 2 being prefixed, we obtain 2.865696, the
logarithm required.
Find the logarithm of 3476.
Here, on the same line with 347 and under 6, will be found 1080,
which, with the two first figures and the characteristic prefixed, is
3.541080, the logarithm required.
The log. of
5·84 is 0·766413
0932,, 2-969416
""
10.24,, 1·010300
""
""
3708,, 3.569140
When the quantity whose logarithm is required contains more than four
figures, proceed as follows:-Find the logarithm for the first four figures
as above, then look in the first column of the Table of Proportional Parts, at
16
LOGARITHMS.
the lower part of each page, for the first four figures, and on the same line
in the column having at its head the fifth figure will be found the quantity
which must be added to the logarithm already taken out, to give the
logarithm of the quantity first required. If the first four figures are not
found in the first column of the table, then take the line containing the
next less number to it. If the number whose logarithm is required con-
tains more than five figures, proceed as above to obtain the logarithm of
the first five figures, then, on the same line of the Table of Proportional
Parts that the number added to the logarithm for the fifth figure was
found, and in the column having at its head the sixth figure, will be found
a quantity which, divided by 10 (or what is the same, having its right
hand figure taken away*), and added to the logarithm already found, will
give the logarithm of the first six figures; again, on the same line and in
the column having at its head the seventh figure, will be found a quantity
which, divided by 100 (or having two figures cut off from the right hand),
and added, will give the logarithm for seven figures.
Examples.
Required the logarithms of 11488, 621547, 768654, 7642-179.
Log. of the first four figures from Tab. I.
From Table of Proportional Parts on line with 1148
4.059942
and under 8
}
302 4
Logarithm of 11488, as required
= 4.060244
Log. of 6215
From Table of Proportional Parts, on line with 6160,
the next less No. in the table to 6215, and under 4.
On same line under 7
Logarithm of 621547 = 5·793474
5.793441
28
4 9
Log. of 7686 .
5.885700
From Table of Proportional Parts on same line with
7686 and under 5
}
28
On same line under 4
2 2
Logarithm of 768654 = 5·885730
Log. of 7642
= 3.883207
From Table of Proportional Parts on same line with
7552 and under 1
}
57
On same line under 7
3 99
On same line under 9
513
Logarithm of 7642·179 = 3·883217
* If the figure thus cut off exceeds five, one must be added to the last right hand
figure left.
USE OF THE TABLES.
17
To find the number answering to any given logarithm.
Look in the upper portion of Table I. for the given logarithm, or the
next less in value to it that can be found, then on the same line, in the
first column, will be found the first three figures, and at the head of the
column in which the logarithm was found, the fourth figure of the number
sought. If the given logarithm is found exactly in the table, the figures
thus obtained will be the required number, care being taken to point off
one more figure to the left hand than there are units in the characteristic
of the given logarithm, cyphers being attached to the right hand of the
number, if requisite. If, however, the given logarithm is not found ex-
actly in the table, subtract from it the next less logarithm found, calling
the remainder the first difference; then look in the Table of Proportional
Parts on the same line with the four figures already obtained from Table
I. (or the next less figures which can be found) for this difference, and at
the head of the column in which it is found will be the fifth figure of the
number sought. If the first difference is not found exactly in the table,
look for the next less number to it, which subtract from the first differ-
ence for the second difference; then add a cypher to this second difference,
and look for it on the same line of the Table of Proportional Parts, as
before, and the figure at the head of the column containing the nearest
number to it, either greater or less, will be the sixth figure of the number
required.
Examples.
Required the number answering to the logarithm 3·241756.
= 3·241756
3.241546 = the log of
Given log.
Next less log. in Table I.
In Table of Prop. Parts
on same line with the
next less No. to 1744
On the same line
1744.
210 first dif.
199 is found in col. 8
.8
110 second dif.
99 is found in col. 4
⚫04
The No. required
= 1744·84
In this example the next less logarithm which can be found in Table I.
is 3-241546, the number answering to which, 1744, is the first four figures
of the number sought; then subtracting this logarithm from the given logar-
ithm, we obtain for the first difference 210, and looking in the Table of
Proportional Parts on a line with 1740 (the next less number to 1744), for
the next less number to 210, we find 199, at the head of the column
containing which is 8, the fifth figure required; then, subtracting 199
from 210, we obtain the second difference, 11, and adding a cypher, the
nearest number which we find on the same line is 99, at the head of the
column containing which is 4, the sixth figure required.
C
18
DESCRIPTION OF THE
Required the numbers answering to the following logarithms:
3.510009, 2.475771, 5-871624.
The number answering to the logarithm 3.510009 is found at once to
be 3236.
Given log.
Next less log.
2-475771
2.475671 = the log. of 299-0
100 = 1st dif.
From Table of Proportional Parts 87
.06
130 = 2nd dif.
130
•009
No. required = 299.069
Given log. = 5·871624
Next less log. — 5·871573
= the log. of 744000·
51 = 1st dif.
From Table of proportional parts
46.
80.
50
52 ..
9.
The No. required
=744089.
It should be observed here, that the number of figures which may be
depended upon in any result obtained by logarithms, will be equal to the
number of decimal places in the logarithms employed; thus, in using the
tables appended to this work, the results obtained will be accurate to six
figures, except towards the end of the tables, in which only five figures
should be trusted.
Mathematical Tables.
TABLES III., IV., and V.
Mathematicians have computed the lengths of the sines, tangents, and
secants (assuming unity for the radius) corresponding to arcs from 1
minute of a degree, through all the gradations of magnitude, up to a quad-
rant, or 90°; and the results of the computations are arranged for use in
tables called Trigonometrical Tables. As, however, these quantities have
to be carried to several places of decimals in order to obtain sufficiently
accurate results, their use in calculations is attended with much labour,
and therefore it is usual to employ their logarithms instead; but in this
case the assumed radius is taken as 10,000,000,000 instead of unity, since
with the latter most of the quantities would be fractional, and therefore
MATHEMATICAL TABLES.
19
have negative characteristics, the use of which would be inconvenient, and
is superseded by taking the radius as above.
Table V. is such a table of the logarithms of the sines, cosines, tangents,
cotangents, secants, and cosecants, for every minute from 1 minute to 90
degrees, calculated to a radius of 10,000,000,000 as above. It will be
observed that the headings of the columns run along the tops of the pages
as far as the 45th degree, after which they return along the bottoms of
the pages in contrary order, as below:-

Sin D.
Cosec Tan D.
Cot Sec
D.
Cos
Cos
D.
Sec
Cot D.
Tan
Cosec D.
Sin
The reason of this will be apparent, if we only consider that the cos, cot,
or cosec of an arc is the sin, tan, or sec of the complement of that arc.
The intermediate columns headed D, contain the differences of the con-
secutive logarithms in the contiguous columns on either side; it will be
seen that the same difference is common to the sin and cosec, the tan and
cot, and the sec and cos; since, from Table XXI.,
1
1
sin=
=
or 1 sin. cosec;
tan= or 1 tan. cot;
cot'
cosec
1
cos'
COS
sec= or 1 sec. cos; and consequently, log sin + log
cosec = log tan + log cot = log sec + log cos = 2 log rad = 20; there-
fore as the sin, tan, or sec increases, so must the corresponding cosec, cot,
or cos diminish, and their differences must be equal. The differences of
the sines and tangents are not inserted on the two first pages, for the
reason explained at page 21.
USE OF TABLE V.
To find the logarithmic sine, tangent, &c., of a given arc.
If the arc contains only degrees and minutes, its sin, tan, &c., will be
found simply by inspection, by looking along the top or bottom of the
tables for the degrees, and then in the first or last vertical column for the
minutes, according as the number of degrees is less or greater than 45°;
and on the same line, in the column having for its title (either at the top
or bottom, according as the degrees were found) the name of the trigono-
metrical quantity required, its log will be found.
If the arc contains seconds as well, the logarithm must be found as
above for the degrees and minutes; then take the number in the con-
tiguous column headed D on the same line, multiply it by the number of
seconds, and divide by 100 (which is done by cutting off the two last
figures); the quotient must then be added to or subtracted from the log
20
DESCRIPTION OF THE
already taken out, according as the same would be increased or decreased
by an increase in the arc.
Examples.
1. Find the log sin of 37° 47′.
As the arc is less than 45°, by looking along the top of the table for the
degrees, and in the first column for the minutes, we find in the column
having at its top the word sine the figures 9.787232, which is the log sine
of the arc required.
2. Find the log tan of 75° 34'.
Here, as the arc is greater than 45°, looking at the bottom of the tables
for the degrees, and in the last column for the minutes, we find in the
column having tan at the bottom, 10-589431, the tan of 75° 34′.
3. Find the log sin of 31° 45′ 5″.
The log sin of 31° 45′ is
9.721162
The No. in col. D is 340 x 5" 100 = +
100
17
... The log sin of 31° 45′ 5″ =
9.721179
4. Find the log cos of 25° 1′ 47″.
The log cos of 25° 1′ is
9.957217
The No. in col. D is 98 x 47" 100
100
47
... The log cos of 25° 1′ 47″ =
9.957170
To find the arc corresponding to any given log sin, tan, &c. :-
Look in Table V. for the given log sin, &c., or the next less log thereto,
and on the same line will be found the minutes, and at the top or bottom
of the page the degrees, of the arc required; if the log thus found is less
than the given log, subtract the former from the latter, add two cyphers
to the right of the remainder, and divide it by the number found in the
contiguous column headed D; the quotient will be the number of seconds
to be added to the degrees and minutes in the arc already obtained.
Examples.
1. Find the arc whose log tan is 10-577537.
Here the arc is found by inspection to be 75° 11′.
2. Find the arc corresponding to the log sin 9-395401.
Given log = 9.395401
Next less log = 9.395166
log tan 14° 23'
23500820 29 seconds;
... 9.395401 is the log tan of 14° 23′ 29″.
MATHEMATICAL TABLES.
21
In the sines and tangents of arcs less than about 5°, the differences
between any two successive values are so great (as will be seen by an in-
spection of column D in the table) that the method above given for finding
the intermediate values for seconds will not be sufficiently correct; and
the same remark applies to the cosines and tangents of arcs greater than
about 85°. It will also be observed, that in the cosines and secants of
arcs less than 5º, and in the sines and cosecants of arcs greater than 85°,
the differences are too small to enable us to calculate accurately the value
of any arc from them.
The first of these difficulties may be removed by the rules given below
for determining the values of the sines and tangents of small arcs, and the
tangents of large arcs, and conversely the arcs from the sines and tangents.
A table has also been given (Table IV.) of the logarithmic sines for every
tenth of a minute as far as a degree and a half, and of the cosines for every
tenth of a minute from 88° 29′ to the end of the quadrant. The second
difficulty, however, could only be got over by extending the tables to more
decimal places, but as this would also require all other quantities employed
in the same calculations to be taken to an equal number of decimals, much
additional trouble would be occasioned; and it is therefore better for de-
termining the value of an arc when near 90°, to employ some other func-
tion than its sine, as, for instance, its cosine. In order to render this
clearer to those who are not familiar with the use of logarithms, we sub-
join an example of such a substitution of the cosine for the sine.
For instance, let it be desired from the formula.
P₁: P₂ :: sin ß : sin ♪
1
to determine the value of the angle §, when P₁ = 600·1; P₂ = 669; and
the angle ß = 63° 45′.
First by multiplying the means and extremes, and dividing both sides
by P₁, we obtain
sin d=
2
P₁
1
P₂ sin ß .
Then from Table XXI.
•
(a.)
sin ♪ = √1 — (cos §)²
P₂ sin ẞ
P₁
=√1
= √ 1 — (cos d)²;
squaring both sides
P₂ sin ß
P₁
B) = 1 — (cos d')³,
transposing, and extracting the square root.
cos d =
2
2
P₁
- (P, sing).. (b.)
1 -
We have, therefore, two equations, (a) and (b), from either of which
we can obtain the value of the angle d, by substituting the values of the
known quantities; but in doing so we shall find that the second equation
will give the value of & much more exactly than the first.
22
DESCRIPTION OF THE
Thus, by substituting the known quantities in equation (a), we have
669 × sin 63° 45′
600.1
=
sin d.
Whence by logarithms,
Log sin 63° 45'
9.952731
Log 669
2.825426
12-778157
Log 600.1
2.778224
Log sin &
9.999933
·. ♪ = 88° 59′ 25″.
Proceeding in a similar manner with equation (b), we have

669 × sin 63° 45′\²
1 – (669
600.1
= cos d.
Whence by logarithms, taking the radius as unity, for the reasons ex-
plained at page 25.
Log sin 63° 45′ =
1.952731
Log 669
2.825426
2-778157
Log 600-1
2.778224
1.999933
2
Log ⚫99969
Then 1
•99969 =
1.999866
·00031, the log of which
4-491362 ÷ 2 2.245681 = cos &;
or restoring the radius of the tables,
4-491362, and
cos ♪ = 8·245681 =
8-245681 = sin of the complement of §;
therefore, by the rule given below for finding a small arc from its
sin, we have
8.245681
5.314425
22
3.560128 = 3631.86 seconds = 1° 0′ 31″·86;
♪ = 88° 59′ 28″-14,
whence we see that the former value of d obtained from equation (a) is
upwards of three seconds too small.
MATHEMATICAL TABLES.
23
To find accurately the log sin of an arc less than 5º.
Reduce the arc to seconds, and find the log of that number from Table
I., to which add 4.685575 (the log sin of 1"), and subtract one-third of
the decimal portion of the log sec of the arc taken from Table V.; the
remainder is the log sin of the arc required.
Examples.
Find the log sines of 13′ and of 1° 3′.
Log (13′ × 60) = 780″ = 2.892095
4.685575
7.577670
Log sec of 13' = '000003 ÷ 3 = '000001
Log sin of 13′ = 7·577669
Log (63' x 60)=3780" 3.577492
4.685575
8.263067
Log sec of 1° 3′ = '000073 ÷ 3 = ·000024
Log sin of 1° 3′ = 8·263043
To find accurately the log tan of an arc less than 5°.
To the log of the number of seconds in the arc add 4.685575, and two-
thirds of the decimal portion of its log sec; the sum is the log tan of the
arc required.
Examples.
Find the log tans of 24' and 1° 15′.
Log (24′ × 60) = 1440′′ = 3·158362
4.685575
Log sec of 24′ = ·000011 × 3: = '000007
Log tan of 24′ = 7·843944
Log (75′ × 60) = 4500″ = 3.653213
Log sec of 1° 15′ =·000103 ×
4.685575
= 000068
Log tan of 1° 15′ = 8·338856
24
DESCRIPTION OF THE
To find accurately the log tan of an arc greater than about 85º.
Add to the log of the number of seconds that the arc is less than 90°,
two-thirds of the decimal portion of the log cosec, and subtract the sum
from 15-314425; the remainder will be the log tan required.
Examples.
1. Find the log tan of 89° 5′ 13″.
90° 0' 0"
89 5 13
0° 54′ 47″ = 3287 seconds.
Constant log
Log of 3287
= 15·314425
= 3.516800
Log cosec of 89° 5′ 13″ = '000057 × 1/ = .000038
3.516838
Log tan of 89° 5′ 13″ — 11·797587
2. Find the log tan of 88° 51′ 10″.
90° 0' 0"
88 51 10
1° 8′ 50″ = 4130 seconds.
Constant log
= 15·314425
Log of 4130
= 3.615950
Log cosec of 88° 51′ 10″ = '000087 × 3
•000058
3.616008
Log tan of 88° 51′ 10″ = 11·698417
To find accurately an arc of not more than 5° from its log sine.
To the given log sin, add 5·314425, and one-third of the decimal por-
tion of the secant of the nearest arc to that whose log sin is given, the sum,
rejecting 10 from the characteristic, will be the logarithm of the number
of seconds in the arc.
Example.
Required the arc whose log sin is 8-314719.
Given log sin
= 8.314719
Constant log
= 5·314425
Log sec of nearest arc = '000093 ÷ 3 =
·000093÷ 3 = 000031
Arc required 1° 10′ 58″ = 4258″ = 3.629175
MATHEMATICAL TABLES.
25
To find accurately an arc of not more than 5° from its log tan.
To the given log tan add 5·314425, and from the sum subtract two-
thirds of the decimal portion of the log sec of the arc whose log tan is
nearest to that given, and the remainder, rejecting 10 from the character-
istic, will be the log of the number of seconds in the arc.
Example.
Required the arc whose long tan is 8-231461
Given log tan
8.231461
Constant log
Log sec of nearest arc = '000063 ×
5.314425
13.545886
•000042
Required arc = 58′ 34″ = 3514"
= 13.545844
To find accurately an arc greater than 85° from its log tan.
Add to the given log tan two-thirds of the decimal portion of the log
cosec of the nearest arc to that whose log tan is given, and subtract the
sum from 15.314425; the remainder is the log of the number of seconds
that the arc is less than 90º.
Example.
Required the arc whose log tan is 11.695900.
Constant log
15.314425
Given log tan
11.695900
Log cosec of nearest arc '000088 ×
•000059
11.695959
3.618466
Required arc = 1° 9′ 14″ = 4154″ .
In extracting the root or raising the power of any trigonometrical
quantity by means of its logarithm, it will always be found most conve-
nient to reduce the assumed radius to unity, by subtracting 10 from the
characteristic of the logarithm, which will frequently then become nega-
tive; it must, however, be borne in mind that the decimal part of the
logarithm is always positive; and, therefore, if it is required to multiply a
logarithm with a negative characteristic by any number (as the index of
a power), first multiply the decimal part of the logarithm, pointing off as
many decimal figures in the product as there were in the logarithm, then
multiply the characteristic, and subtract from the product the number (if
any) pointed off to the left in the first product: the result will be the ne-
gative characteristic, and the decimals pointed off in the first product will
be the decimal part of the required logarithm. To divide a logarithm
with a negative characteristic by any number: if the characteristic is a
26
DESCRIPTION OF THE
mutiple of that number, that is, if it is divisible by it without remainder,
proceed as in ordinary division; if not, separate the characteristic from the
decimal, and add to the characteristic a number which will make it divi-
sible, and prefix to the decimal the same number, then divide both by the
given divisor, and the quotients will be the characteristic and decimal of
the logarithm required. An example of this alteration of the characteristic
is given at page 22.
Although Table V. only purports to give the sines, tangents, &c., of
angles less than, or equal to 90°, any of these functions of angles greater
than 90° may readily be obtained, since any function of an angle greater
than 90° is equal to the same function of the supplement of that angle; due
regard being had to changing the sign, if requisite, according to Table
III., which exhibits the value of each trigonometrical line at the com-
mencement of each quadrant, and also the sign with which it is effected in
passing through the same. Thus, the log sin of 141° 15' is 9-796521, the
same as the sin of its supplement 38° 45'; the log sec of 95° 43′ is
11.001701, or the sec of 84° 17′ with its sign changed; the log cosec of the
same is 10-002165, or the cosec of 84° 17', the sign remaining the same;
and the log tan of 173° 4′ is 9.084947, or the tan of 6° 56' with its
sign altered.
TABLE VI.
Meridional Parts.
In nautical charts, drawn according to Mercator's projection of the
sphere, the meridional lines are drawn parallel to each other, or equidis-
tant in every latitude, as shewn in fig. 1, so that the distance between any
two meridians being assumed as true at the equator would be too great in
every other latitude; for whereas the length of a degree of latitude really
decreases as we approach the poles, here it is represented as though its
length were everywhere the same. If, therefore, the parallels of latitude
were drawn at equal distances in representing any country situated in a
high latitude, its form would become so much distorted from its breadth
being thus increased without its length, that the country would hardly be
recognised, and very erroneous views would be occasioned of its form and
relative extent. Thus, in the latitude of 60°, a degree of longitude is only
half what it is at the equator, and therefore all dimensions east and west
would be twice as great as they should be, if drawn to the same scale as
those north and south. To correct this distortion, therefore, and preserve
the true form of the countries, the distance between the parallels of lati-
tude is increased precisely in the same proportion as that between the
meridians; so that on a Mercator's chart the relative magnitude of a
degree of latitude and longitude is everywhere truly preserved; the
parallels of latitude being drawn more and more distant as we leave the
equator, as shewn in fig. 1.
MATHEMATICAL TABLES.
27
Fig. 1.

D
Now, the numbers in the table of meridional parts are nothing more
than the distances of the several parallels of latitude from the equator, as
shewn on a Mercator's chart, expressed in minutes of longitude at the
equator. In using the table the degrees of latitude must be sought at the
top of the table, and the minutes in the side column, the meridional parts.
will then be found at their intersection; thus the meridional parts of
27° 25′ are 1712, and of 76° 3' are 7222.
The great use of this table for nautical purposes is to determine the
latitude and longitude of a ship at sea, when the course and distance that
she has run are known. By the course of a ship is meant the direction in
which she sails, estimated by the angle which that direction makes with
the meridian. When the course makes the same angle with every meri-
dian crossed, it is termed a rhumb, and this course is that usually adopted
by navigators, in consequence of the facilities which it affords in ascer-
taining the position of their vessels.
On a Mercator's chart any rhumb is obviously a straight line, because
no other than a straight line would on such a chart cross every meridian
at the same angle. Thus, if A and B, figure 1, are any two places between
which a vessel sails, then the straight line A B is the rhumb upon which
the vessel would sail to preserve the same course or make the same angle
with every meridian crossed; A C is the difference of latitude, C B the
difference of longitude, and A B the nautical distance run. If now we set
off from A towards C, a distance A D equal to the actual difference of
latitude measured in degrees at the equator, and draw a line D E parallel
to the equator, then will the line A E, measured on the equator, be the
true nautical distance, and, being multiplied by 60 (the number of nautical
* It is hardly necessary to state that a minute is the 60th part of a degree, and a
second the 60th part of a minute.
28
DESCRIPTION OF THE
miles in a degree), will give the distance run by the ship, and the line
DE is termed the departure or distance run either to the east or west.
By inspecting the diagram, we see that A E: rad :: A D: cos < A,
or the nautical distance is to radius as the actual difference of latitude is
to the cosine of the course; and also A B: rad :: BC: tan ◄ A, or the
meridional difference of latitude is to radius as the difference of longitude
is to the tangent of the course.
If we put d for the nautical distance, c for the course, 7 for the difference
of the latitude, λ for the meridional difference of latitude, and L for the
difference of longitude, we have, from the above proportions,
rad. l = d cos c,
And rad. L=λ tan c.
From which formulæ either two of the four quantities d, c, l, and L being
known, the others may be easily found.
For example, a vessel leaving latitude 25° 34′ N. and longitude
61° 24′ w. sails 543 nautical miles on a rhumb line, whose course is N.
42° 5′ E., what latitude and longitude is she then in ?
Log cos c (= 42° 5′): = 9.870504
Log d (= 543)
Rad.
= 2.734800
12.605304
=10·000000
2.605304 = = log of 403 =
= 1,
then 403 ÷ 60 = 6° 43′ = the ship's difference of latitude to the north;
therefore, 25° 34′ + 6° 43′ = 32° 17′ N. is the latitude she is now in.
Again,
Meridional parts for 32° 17′ = 2048
""
for 25 34 = 1588
Meridional difference of latitude = λ = 560
Log tan c (= 42° 5′) = 9.955707
..
Log λ (= 560)
Rad
= 2.748188
12.703895
= 10.000000
2-703895 — log of 505·7 — L,
then 505·7 ÷ 60 = 8° 25′ 42″ = the ship's difference of longitude to the
east; therefore, 61° 24'-8° 25′ 42″ 52° 58′ 28" w. is the longitude
she is now in.
Example 2.-A vessel sails from latitude 41° 20′ N., and
49° 50′ w., to latitude 64° 25′ N., and longitude 10° 13′ 6″ w.,
her course and nautical distance?
longitude
what was
MATHEMATICAL TABLES.
29
Meridional parts for 64° 25′ = 5097
for 41 20 = 2728
""
""
23 5 2369 =λ =
60
Meridional
difference
of latitude.
Difference of lat. = 7 = 1385
49° 50′ 0″
10 13 6
39 36 54
60
Log L (2376.9)
Rad.
Log λ (2369).
Log (1385)
Rad.
•
3.376010
= 10.000000
13.376010
= 3.374565
10·001445 = log tan 45° 5′ 44″ = c.
= 3·141450
=10·000000
Log cos c ( = 45° 5′ 44″)
13.141450
9-848757
3·292693 = log of 1962 = d.
TABLE VII.
Length of a Degree of Longitude on each Parallel of Latitude.
This table requires no explanation; it exhibits the length of a degree
of Longitude in nautical miles (each of which equals 6075.6 feet) at every
degree of latitude from the Equator to the Poles.
TABLES VIII. AND IX.
Dip of the Horizon.
The latitude and longitude of a vessel is determined by observations
made on the heavenly bodies, which observations consist principally in
measuring their altitudes or the angle which they make with the horizon.
The altitudes thus taken being compared with certain altitudes given in
30
DESCRIPTION OF THE
the "Nautical Almanac," enable the observer to determine both his latitude
and longitude. It is, however, requisite to make certain corrections in
the observed altitudes in order to obtain the true altitudes.
H
A
K
1
G
F
F
If, in fig. 2, G C D F is a section of the
earth, and B the place of an observer, then
GE F is the rational horizon, and H CI
the sensible horizon. Also, if A is the
place of a heavenly body, the angle A E F
is its true altitude, A CI its apparent alti-
tude, and A B D its observed altitude.
If the observer had been on the surface
of the earth as C, then the observed altitude
would have coincided with the apparent
altitude, but when raised above the same,
as is always the case at sea when the ob-
servations are made from the vessel's deck, the horizon dips, or becomes
depressed, as shewn by the line B D, and the observed altitude A B D
becomes greater than the apparent altitude A B K or A C I* by the angle
K B D: the magnitude of this angle (termed the dip of the horizon) de-
pends upon the height of the observer above the surface of the earth; its
values for all heights between 1 and 140 feet are given in Table VIII.
The angle found in the second column must be subtracted from the ob-
served altitude to obtain the apparent altitude.
The dip given in Table VIII. supposes that the view of the sea horizon
is perfectly unobstructed. Should, however, any object intervene, as a
coast, the margin of the sea where it meets the shore must then be taken
as the horizon; and in this case the angle to be subtracted from the ob-
served altitude will be found in Table IX. under the proper height, and
on a line with the distance of the object from the observer, which may
always be judged of with sufficient precision by an experienced eye.
Thus, if the vessel is about 2 miles from the shore and the observer is 20
feet above the surface of the sea, the angle to be subtracted for the dip
will be 6 minutes.

TABLE X.
Reduction of the Moon's Horizontal Parallax.
The difference between the apparent altitude of a heavenly body, or
the angle which it makes with the sensible horizon, and its true altitude,
or the angle which it forms with the rational horizon, is termed its
parallax. The parallax of a body is greatest when it is in the horizon,
and it decreases as its altitude increases, until, when it attains the zenith,
* The distance B C of the observer above the earth's surface is so inconsiderable, as
compared with в A, the distance of the body, that these two angles may be considered
as equal without any appreciable error.
MATHEMATICAL TABLES.
31
its parallax becomes nothing. Thus, in fig. 3 the parallax at C is greater
than that at E, and is nothing at the zenith F.

B
D
The amount of the horizontal parallax depends upon the distance of the
body A C and upon the earth's radius A B. The nearer the object, that
is, the less A C is, the greater is the angle A C B or the parallax. The
moon being much nearer to the earth than any other of the heavenly
bodies, its parallax is much greater, and as its distance from the earth
varies, so also does its parallax; the amount of its parallax is given in the
“Nautical Almanac" for every day throughout the year. The parallax
there given is, however, calculated for the earth's greatest or equatorial
radius; and since, from the proximity of the moon, the decrease of the
earth's radius in higher latitudes diminishes the parallax to such an ex-
tent as to require correction, we have given in Table X. the amount to be
subtracted from the equatorial parallax to give the true parallax in any
given latitude. For example, let the earth's equatorial parallax on any
given day, as found in the "Nautical Almanac," be 58 minutes, what will
it be for the same day in latitude 52°? Here under 58', and on a line
with 52°, we find 7-"2, which must be subtracted from 58', giving
57′ 52″8 for the moon's parallax in that latitude.
TABLE XI.
Augmentation of the Moon's Semidiameter.
In making an observation, it is the position of the centre of the object
which is required, but as it would not be easy in practice to judge with
sufficient precision of its position, it is usual to measure to the nearest
edge (or limb, as it is termed) of the object, and to add the angular value
of its semidiameter. In the case of the moon, its apparent semidiameter
varies considerably according to its distance from the earth, and also from
its great proximity its semidiameter is sensibly increased by the parallax ;
for, as her altitude increases, she approaches nearer to the observer, and
the apparent semidiameter becomes greater. The value of her horizontal
32
DESCRIPTION OF THE
semidiameter for every day is given in the "Nautical Almanac;" and
Table XI. shews the augmentation of the same occasioned by an increased
altitude. Thus, when the moon's horizontal semidiameter is 15′ 30″, her
apparent semidiameter, with an altitude of 51°, will be 15' 42".
TABLE XII. AND XIII.
Longitude and Time.
As the sun apparently revolves round the earth once in every twenty-
four hours, with an equal rate, it arrives at each meridian at a different
time. And it is on this principle that the longitude of a place is de-
termined by the interval of time between the sun's passing the meridian
of that place and the meridian of Greenwich. As the whole 360° are
equal to an interval of 24 hours, any lesser number of degrees are equal
to a proportionate interval of time, and these two tables are for facilitating
the conversion of longitude into time, or vice versa. As an example of
their use, let it be required to find the interval of time corresponding with
a difference of longitude of 43° 13′ 10″.
H. M. S.
From 2nd column, Table XII. 40° = 2 40
1st
""
""
""
1st
3° =
10′ =
12
""
""
1st
3'
40
12
""
""
3rd
10" =
0.667
""
""
2 52 52.667
The time is therefore
Again, if it were required to know the difference of longitude cor-
responding with an interval of 4 hours, 31 minutes, and 6 seconds; we
have
From 1st column of Table XIII. 4 hours
60° 0' 0"
""
2nd
2nd
30 mins.
7 30 0
""
""
""
1 min.
0 15 0
""
""
""
""
2nd
""
6 secs.
: 0 1 30
""
""
Which gives for the diff. of longitude. 67 46 30
TABLE XIV.
Parallax in altitude of the Sun and Planets.
The horizontal parallax of the sun and planets depends upon their dis-
tance from the earth, and is given for every day in the "Nautical Almanac.”
The parallax for any altitude is, as already explained, less than when the
object is in the horizon; and Table XIV. is intended to give the amount
of parallax for any apparent altitude when the amount of the horizontal
parallax is known. In using the Table look for the horizontal parallax
at the head of the Table, and in the column at the head of which it stands,
MATHEMATICAL TABLES.
33
and on the same line with the apparent altitude, will be found the parallax
required. For example, if the sun's horizontal parallax is 9", what is
her parallax with an apparent altitude of 48°? Here, in the column
having 9″ at its head, and on the same line with 48°, will be found 6",
which is the sun's parallax at the time.
TABLES XV. and XVI.
Refraction of the Sun and Stars.
There is another correction rendered necessary in order to reduce the
observed altitude of a heavenly body to its apparent altitude; in conse-
quence of the optical property of the atmosphere termed refraction. While
the effect of the parallax is to make the object appear lower than its true
place, that of refraction is to make its altitude appear greater. The effect
of refraction is greatest when the object is in the horizon, and it gradually
diminishes until at the zenith it becomes nothing; it is not, however, al-
ways constant for the same altitude, but varies with the temperature and
density of the atmosphere. Table XV. gives the refraction for every ten
minutes of apparent altitude, calculated for a mean temperature of 50°
Fahr., and a mean pressure of 29.6 ins.; and Table XVI. contains the
correction requisite to be made for any other temperature and pressure.
For example, what is the refraction of any heavenly body whose observed
altitude is 31° 20′ when the temperature is 72°, and the barometer 30-35?
In this case we first find, from Table XV., the refraction for a mean state
of the atmosphere to be 1′ 35.5", we then find, from Table XVI., that at
the temperature of 72° we must subtract 5", and with the barometer at
30-35, that we must add 1", after which we have 1′ 31.5″ for the required
refraction. It must be observed, that when the temperature is below the
mean, the correction must be added, and when above, the mean subtracted;
also, when the barometer is below the mean the correction must be sub-
tracted, but when above the same it must be added. The correction for
the thermometer is found in the column having the temperature at its
head, while that for the barometer is found in that having the pressure at
its foot.
TABLE XVII.
Correction of the Moon's Altitude.
As already explained, the effect of the refraction is to raise the object,
while that of parallax is to depress it; the parallax, however, being
always the greater, the apparent altitude is always less than the true
altitude. Table XVII. contains the difference of the refraction and
parallax for the moon, which is therefore the correction to be added to the
apparent altitude to obtain her true altitude. In using the table, the cor-
rection will be found in the column having at its head the moon's hori-
zontal parallax, and opposite to the apparent altitude. Should these not
be found exactly in the table, we must take the next less values, and to the
number thus found we must add or subtract (as the case may be) a pro-
D
34
DESCRIPTION OF THE
portional part for the requisite number of minutes or seconds wanting,
which are given for the altitudes in the left-hand column, and for the
parallax in the right-hand column. For example, let the correction be
required when the apparent altitude is 29° 37′, and the moon's horizontal
parallax is 56′ 24″. In this case the next less numbers to these in the
Table are 29° 30′ and 56'.
Under 56', and opposite 29° 30', we find 47′
Add proportional parts for parallax 20″
1"
18
4"
3.5
""
""
>>
47 22.5
Subtract prop. parts for altitude
7'
3
47 19.5
Correction required
The moon's true altitude therefore equals 30° 24′ 19″·5.
Ex. 2. What is the moon's true altitude when its apparent altitude is
9° 53', and its horizontal parallax is 58′ 20″?
Under 58′ and opposite 9° 50' we find .
Add proportional parts for parallax 20″
""
51′ 44″
20
for altitude 3'
2
52 6
Correction.
Therefore the moon's true altitude equals 10° 45′ 6″.
TABLE XVIII.
Logarithms for finding the Horary Angle or Apparent Time.
as
The use of this Table is to facilitate the calculation of the Apparent
Time at any place, from observations made on the altitude of some
known celestial body. The logarithms in the Table are twice the sine of
half the arc of longitude corresponding with the number of hours and
minutes at which it stands*. The use of the Table is as follows:
having obtained this logarithm, look in the table for it, or for the next
less logarithm to it, and take out the time in hours and minutes
found (if the altitude is decreasing) at the top and in the left-hand column,
(but if increasing) at the bottom, and in the right-hand column. Then
subtract the logarithm taken in the table from the given logarithm, and
having added to the right of the difference thus obtained two cyphers,
divide it by the nearest number in the contiguous column headed Diff.,
and the quotient will be the number of seconds to be added to the hours
and minutes already obtained, when the altitude is decreasing, and to
be subtracted when increasing. For example, what is the apparent
* The manner of performing the calculation by which this logarithm is derived
from the observed altitude is fully explained in a Treatise on Navigation, by James
Greenwood, B.A.-Weale, Holborn.
MATHEMATICAL TABLES.
35
time corresponding to the logarithm 9.649321 when the altitude was
decreasing?
Given log
9.649321
Next less log in Table 9-648913
= log of 5 H. 35 M.
40800 ÷ 3516 = 11 seconds.
Therefore, the apparent time required is 5 H. 35 M. 11 s.
Ex. 2. What is the apparent time corresponding with the logarithm
9.215630, when the altitude was increasing?
Given log
9.215630
Next less log in table 9.214358 = 20 H. 49 M.
127200 7114 18 seconds.
Therefore the apparent time is 20 H. 48 м. 42 s.
TABLE XIX.
Common and Hyperbolic Logarithms.
The object of this Table is to facilitate the conversion of common
logarithms, into hyperbolic, and vice versa. Its use is as follows:-To
convert common logarithms into hyperbolic, write the common logarithm,
as shewn in the first example below, and then take from the second column
of the Table the equivalent value of each figure in hyperbolic logarithms,
taking care that the latter are each moved as many places to the right as
the corresponding numbers in the common logarithm are; the sum of the
whole will be the hyperbolic logarithm required.
To convert hyperbolic logarithms into common, proceed in a similar
manner, writing the hyperbolic logarithm as in the second example
below, and taking its equivalent value in common logarithms from the
fourth column of the Table.
Ex. 1. What is the hyperbolic logarithm of 3156?
By reference to Table I. we find the common logarithm of 3156 is
3.499137; then-
Hyp. Log.
6.907755 | 3
Com. Log.

3.
·4.
•921034
0
*09
•207232 7
⚫009
⚫020723 3
•
•0001.
⚫000230 3
⚫00003
•000069 1
·000007 .
•000016 1
8.057061
Ex. 2. What is the common logarithm of the number whose hyperbolic
logarithm is 5·160731?
36
DESCRIPTION OF THE
Hyp. Log.
Com. Log.

5.
2.171472
4
•1.
⚫043429
⚫06
•026057
·0007.
•000304
•00003
⚫000001
•000013 0
•000000 4
2-241277
TABLE XX.
Curvature of the Earth and Refraction.
This table is of use in Geodesical operations. Practically, a level line
on the earth's surface is a line everywhere equally distant from its centre.
It is obviously, therefore, not a straight line, but is a portion of a circle,
having the same radius as the earth. When a level, theodolite, or other
instrument has the axis of its telescope so adjusted as to be truly level, the
prolongation of that axis is not a level line, but is a tangent to that line,
coinciding with it only at the point where the instrument stands, and being
above it everywhere else. The height of this line above the true level line,
if there were no refraction, would be equal to the ver sine of an arc whose
radius equalled that of the earth, and whose length was equal to the dis-
tance from the instrument: these heights for various distances up to 30
miles are given in the second column of the Table. The effect, however,
of the refraction of the atmosphere is to curve the visual ray passing
through the centre or axis of the telescope, so that the optical axis is really
a curved line which approximates very nearly to a circle, having a radius
seven times greater than that of the earth. The heights in the second
column require to be reduced by a seventh part, and the numbers thus
obtained are given in the third column. To exemplify its use, let us sup-
pose that an instrument, placed in an elevated position, has its telescope
directed to a church tower 3 miles distant, and that when its telescope is
perfectly level the horizontal wires are found to cut a point in one of the
windows, which, on direct measurement, is found to be 95 feet from the
ground, it is required to ascertain the real difference of level of the two
spots.
Now, on reference to the Table, we find the correction for 3 miles
is 5·14, which, being subtracted from 95 feet, gives 89.86 feet for the
actual height of the instrument above the ground on which the tower
stands. In taking a series of consecutive observations, as in the ordinary
operation of levelling by back and fore sights, to ascertain the relative
level of two distant places, so long as no great difference in the range or
length of the sights occurs, no correction for curvature or refraction need
be made, for when the sights are actually equal no error arises in the
ultimate result.
MATHEMATICAL TABLES.
37
TABLES XXI., XXII., XXIII., AND XXIV.
Trigonometrical Expressions.
These Tables require no particular explanation. Table XXI. contains
equivalent expressions for sin a, cos a, tan a, cot a, sec a, cosec a, ver sin a,
and will be found of considerable use in reducing formulæ containing
trigonometrical expressions. Table XXII. contains expressions, the sin,
cos, tan, and cot, of mutiple arcs. Table XXIII. contains a variety of
formulæ relating to the trigonometrical functions of two angles or arcs.
And Table XXIV. contains expressions for the sin, cos, tan, and cot, in
terms of the arc, and for the arc in terms of the sin and tan, and also ex-
pressions for the powers of the sin and cos.
Fig. 4.
B
C
α
TABLE XXV.
The formulæ given in this Table are intended to
enable all the six parts of a plane rectilineal triangle to
be determined when three of those parts were pre-
viously known. When either a side or angle is wanted
it will only be necessary to make A or ẞ the side or
angle as the case may be, and to insert in the formulæ
the proper values of those letters which are known, which will then ex-
press the value wanted. For example, in a triangle, two of whose sides
are 23 and 35 feet in length, and the angle included between is 51°, what
is the length of the third side? In this case we have given B, C and a,
and want to find A, we must, therefore, select a formulæ containing only
those letters; we find, accordingly, No. 7 gives
A = √(B² + C2-2 B. C. cos a.)
We have B = 23, C35, cos 51° 62932; inserting these values,
we have
A =√(23² + 352-2 x 23 x 35 x 62932) = 27.217, which is the
length of the side required.

TABLE XXVI.
The formulæ given in this Table are to facilitate the solution of quad-
ratic and cubic equations, in order to which it is only necessary to substi-
tute for
p and զ their known values in the formule when the value of x
will be determined. By way of example, let it be required to find the
value of x in the cubic equation x³ + 3x-536 = 0. We see by reference
in the Table, p being
to the Table that this corresponds with equation (6)
equal to 3, and q to 536. Then, if we substitute these values in the
second expression, it becomes.
Tan a =
3
3 × 536
100
3
2
2
3 = 536
therefore, a = 0° 12′ 36″, and ½ a =
: 0° 6' 18";
38
DESCRIPTION OF THE
then,
Tan ẞtan (6′ 18″);
therefore, 67° 1' 5", and 26 14° 2′ 10″,
and
x=2
3. cot (14° 2′ 10″) = 8,
which is the true value of x.
TABLE XXVII.
This Table contains the differential coefficients of some of the most fre-
quently-occurring functions of u, and will be found to include all the rules
for simple differentiation.
TABLE XXVIII.
This table contains a variety of constant numbers of frequent use in
general calculations; it also contains their logarithms to seven places of
decimals, and the arithmetical complements of the same. The latter will
be found of use in cases where it is required to divide by the numbers in
the Table.
TABLE XXIX.
To reduce the Sun's Declination to any given Meridian, and to any time
under that Meridian.
In the "Nautical Almanac" the sun's declination is given for each day
at noon at Greenwich; it is, however, necessary for the purposes of navi-
gation to ascertain its declination at any other meridian, either at noon or
at any other time of the day. In either of these cases, having obtained
the declination from page II. of the month, in the "Nautical Almanac,"
the correction to be either added or subtracted therefrom, according to the
directions given below, may be found in the following manner.
I. If the sun's declination is required for some other meridian at noon,
reckon the difference of longitude between that meridian and Greenwich,
then look for this difference in the first left-hand column of the table, and
on the line on which the same is found, and in the vertical column having
at its head the nearest number to the declination already taken from the
“Nautical Almanac," will be found the correction required. It will be
seen in the "Nautical Almanac," whether the sun's declination is in-
creasing or decreasing; when decreasing, add the correction in east lon-
gitude, and subtract it in west longitude; but when the declination is
increasing, subtract the correction in east longitude, and add it in west
longitude.
Example.
What was the sun's declination at noon, on the 13th of November, 1850,
in longitude 175° w.?
MATHEMATICAL TABLES.
39
Here we find, from the "Nautical Almanac," that the sun's declination
at noon at Greenwich was 17° 58′ 1″ south, and that it was increasing.
We next look in the first column of the table for the given difference of
longitude, viz., 175°, but the nearest number that we find is 170°, which
is 5º too small, and we must, therefore, add together the corrections found
in the proper vertical column on both the lines having 5° and 170° in the
first column. Thus, in the present instance, in the column having at its
head 18° (the nearest to 17° 58′ 1″,) and on the same line with 5° we find
13″, and on the same line with 170° we find 7′ 22″; these being added
together give 7′ 35″ for the required correction, which, as the sun's decli-
nation is increasing and the difference of longitude is westerly, has to be
added to 17° 58′ 1″, making 18° 5′ 36″ for the sun's declination at noon in
longitude 175° west.
II. If the sun's declination is required for Greenwich at any other hour
than noon, reckon the interval between that time and noon; then look for this
interval in the last right-hand column of the table, and on the same line
in which it is found, and in the vertical column having at its head the
nearest number to the sun's declination (from the "Nautical Almanac "),
will be found the required correction, which, when the sun's declination is
increasing, is to be added, if the time is after noon, and subtracted if before
noon; but when the declination is decreasing must be subtracted if the
time is after noon, and added if before noon.
Examples.
What was the sun's declination at Greenwich on the 4th of July, 1850,
at 7 h. 28 m.?
From the "Nautical Almanac " we find the sun's declination at noon to
have been 22° 54′ 58″ north, and to have been decreasing. Then looking
in the last column of the table for the nearest number to 7h. 28 m., we
find 7 h. 20 m., and on the same line in the column headed with 23° (the
nearest number to 22° 54′ 58″,) we find 1′ 30″, and in the same vertical
column on the same line with 8 m. we find 2", therefore the correction is
1′ 32″, which, as the sun's declination was decreasing, and the time after
noon has to be subtracted from 22° 54′ 58″, leaving 22° 53′ 26″ north for
the sun's declination at the hour required.
What was the sun's declination at Greenwich on the 24th of August,
1850, at 20 h. 12 m. ?
In this instance the time given, viz., 20 h. 12 m. on the 24th is equi-
valent to 3 h. 48 m. before noon on the 25th, for which day the sun's
declination is found in the "Nautical Almanac" to have been 10° 48′ 56″
north, and to have been decreasing. Looking then in the column of the
table having at its head 11° (the nearest to 10° 48′ 56″,) and on the same
line with 3 h. 20 m. we find 2′ 56″, and on the same line with 28 m. we
find 25″; adding these two together, we obtain 3′ 21″ for the correction,
which, as the sun's declination is decreasing, and the time before noon,
40
MATHEMATICAL TABLES.
must be added to 10° 48′ 56″, making 10° 52′ 17″ north for the sun's
declination at the time required.
III. If the sun's declination is required for some other meridian than
Greenwich, at any other hour than noon, we must first make the necessary
correction for the difference of longitude in the manner already explained,
and then the correction for time according to rule II.
Examples.
What was the sun's declination on the 17th of May, 1850, at 5 h. 40 m.,
in longitude 128° E. ?
Sun's declination (increasing) at Greenwich, at noon
Subtract correction for 120°
Subtract correction for 8°
Add correction for 5 h. 20 m.
19° 18′ 38″ N.
4′ 46″
0 19
'}
0 5 5
19 13 33
3' 11"
0 12 J
0 3 23
19 16 56 N.
Add correction for 0h. 20 m.
Sun's declination at the time and place required
What was the sun's declination on the 3rd of June, 1850, at 17 h. 20 m.,
in longitude 79° w.?
17h. 20 m. on the 3rd, is equivalent to 6 h. 40 m. on the 4th.
Sun's declination (increasing) at Greenwich, at noon 22° 25′ 47″ N.
Add correction for 70°
Add correction for 9°
1' 41" }
0 12
} 0 1 53
Subtract correction for 6 h. 40 m.
Sun's declination at the time and place required
22 27 40
. 0 2 24
22 25 16 n.
When the sun is near either of the equinoxes its declination may be
less than the correction, in which case, when the correction is subtractive,
the declination must be subtracted from it, and the remainder will be the
sun's declination of a contrary name to that which it was before.
Example.
What was the sun's declination at noon on the 23rd of September, 1850,
in longitude 164° E ?
The sun's declination (increasing) at noon, at Greenwich
Subtract correction for 160° at noon
Subtract correction for
4° .
Sun's declination at the place required
0° 1′ 57″ s.
10′ 25″
0 16
0 10 41
0 8 44 N.
MATHEMATICAL TABLES.
41

No. 100 L. 000.]
N.
Ι
2
LOGARITHMS OF NUMBERS.
3
4
6
7
[No. 109
8
L. 040.
9
N.
5
1000000000434 0868 | 13011734 2166 | 2598 | 3029 | 3461 3891 100
4321 4751 5181 5609 6038 6466 6894 7321 7748 8174
2 8600 9026 9451 9876 0300 0724 1147 1570 1993 2415
I
3 012837 3259 3680 4100 4521 4940 5360 5779 6197 6616
4 7033 7451 7868 8284 8700
6
9116 9532 9947
3252 3664 | 4075
7350 77578164
1408 1812 2216
I
2 3 4 noo
61976616
0361 0775
4486 | 4896
8571 8978 6
2619 3021
5 021189 1603 2016 2428 2841
5306 5715 6125 6533 6942
9384 9789 0195 0600 1004
8033424 3826 4227 4628 5029 5430 5830 6230 6629 7028
7426 7825 8223 8620 9017 9414 9811
7
9
PROPORTIONAL PARTS.
|
I
2
4
5
| |
|
5
78
0207 0602 | 0998
9
6
7
8
9
|
00
N.
3
1000 434 86.8 | 130°2 173⋅6 | 217′0 | 260°4 3038 347°2 390.6
1002 43.3 86.6 129.9 173.2 216.5 259.8 3031 3464 389.7
| |
1004 432 864 129.6 172.8 2160 2592 3024 3456 388-8
|
1006 43.1 86.2 129°3 172.4 2155 258.6 3017 3448 3879
1009 430 86.0 129.0 172.0 2150 258.0 3010 3440 387.0
1011 429 85.8 128.7 1716 214'5 2574 300'3 3432 386.1
| |
1014 42.8 85.6 1284 1712 2140 256-8 299.6 3424 385°2
1016 427 85°4 128°1 | 170·8 213.5 256.2 2989 341.6 3843
| |
1018 42.6 85.2 127.8 1704 2130 255.6 298.2 3408 3834
1020 425 850 1275 1700 212.5 2550 297°5 3400 382.5
1023 424 848 1272 169.6 2120 2544 296.8 3392 381.6
|
1026 42.3 84.6 1269 1692 2115 253-8 296.1 3384 380.7
| |
1028 42.2 84.4 126.6 168.8 2110 2532 2954 3376 | 379.8
1030 42.1 84.2 126.3 168.4 2105 252.6 2947 336.8 378-9
| |
1033 420 840 1260 1680 2100 2520 2940 336.0 378.0
| |
| |
1035 419 83.8 125.7 167·6 2095 2514 2933 3352 3771
| |
| | |
1038 418 83.6 125°4 167.2 2090 250.8 292.6 3344 376.2
| |
|
1040 417 83.4 1251 166.8 208.5 250°2 2919 333.6 375'3
1043 41.6 83.2 124.8 1664 2080 2496 2912 332-8 3744
| | | |
1045 415 830 124°5 1660 2075 249'0 2905 3320 373'5
1048 414 82.8 124°2 1656 | 207′0 248′4 289.8 3312 372-6
| | | |
1050 41.3 82.6 123′9 1652 206.5 247.8 2891 3304 3717
| |
1053 412 824 1236 1648 2060 247.2 288.4 329.6 370.8
1055 411 822 123 3 1644 2055 246-6 287.7 328.8 369.9
| | |
1058 410 820 1230 1640 2050 2460 2870 3280 369.0
| |
1060 409 81.8 122.7 163.6 204 5 2454 286.3 327.2 368.1
| |
1063 40.8 81.6 1224 1632 2040 244.8 285.6 326-4 367.2
| |
1066 407 814 122.1 162.8 2035 244 2 2849 325-6 366.3
1068 40.6 812 121.8 1624 2030 243.6 2842 3248 3654
| | |
1071 405 810 121.5 1620 202.5 243.0 2835 3240 364 5
| | |
1074 404 808 1212 161·6 | 202′0 | 242°4 | 282·8 | 323°2 | 363.6
| |
1076 403 806 1209 161-2 2015 241-8 2821 3224 362.7
1079 402 804 1206 160.8 2010 241-2 2814 321-6 361-8
1082 401 802 120°3 1604 2005 240·6 280.7 3208 360·9
1084 400 800 1200 1600 2000 2400 2800 3200 360.0
1087 399 79.8 119.7 1596 1995 2394 2793 3192 359°1
| | |
| | |
1090 39.8 79.6 1194 1592 199.0 238.8 278.6 3184 358·2
| |
| |
1093 397 794 1191 158.8 198.5 238.2 2779 317-6 357 3
| | |
1095 39.6 79.2 118.8 1584 1980 2376 277 2 316.8 3564
| | |
1098 39.5 79.0 118.5 1580 1975 2370 276.5 316.03555
|
|
|
|
E
42
MATHEMATICAL TABLES.

No. 110 L 041.]
LOGARITHMS OF NUMBERS.
[No. 119 L. 078.
N. о
I
2
3
4 5 6 7
8 9 N.
I
I
110 041393 1787 2182 2576 2969 3362 3755 4148 4540 4932 110
5323 5714 6105 6495 6885 7275 7664 8053 8442 8830
2 9218 9606 9993 0380 0766 1153 1538
3 053078 3463 3846 4230 4613 4996 5378
4
6905 7286 7666
5060698 1075 1452
8046 8426 8805 9185
1829 2206 2582 2958
1924 2309 2694
5760 6142 6524
9563 | 9942 0320
3333 3709 4083
4458 4832 5206 5580 5953 6326 6699 7071 7443 7815
7 8186 8557 8928 9298 9668 0038 0407 0776
8071882 2250 2617| 2985 3352 3718 4085 4451
5547 5912 6276 6640 70047368 7731 8094
6
91
PROPORTIONAL PARTS.
2
23 to
4
5
6
70
1145 1514
4816 | 5182 8
8457 8819 9
5
6
7
8
9
N. I
3 4
1101 394 78.8 1182 157.6 1970 2364 2758 3152 354-6
1104 39.3 78.6 1179 1572 1965 235.8 275°1 3144 353'7
1106 392 784 117.6 156.8 1960 2352 2744 313-6 352-8
| | | | |
1109 39.1 78.2 117.3 15641955 2346 | 2737 312-8 351*9
1112 390 780 1170 1560 1950 2340 2730 3120 3510
1115389 77-8 1167 155.6 1945 2334 272-3 311°2 350°1
II18 38.8 77.6 1164 155.2 1940 232.8 2716 3104 349°2
38-877-6
| | | | |
1121 387 77°4 | 116′1 | 1548 1935 232°2 270°9 309.6 | 348°3
1124 38.6 77.2 | 115·8 | 154°4 1930 231.6 | 270°2 | 308.8 | 3474
| | |
1127 385 770 1155 1540 192.5 2310 269.5 308.0346.5
1129 384 768 1152 153.6 1920 2304 268-8 3072 345.6
113238.3
1132 38.3 76.6 1149 1532 191.5 229.8 268.1 3064 3447
1135 382 764 114.6 152.8 1910 229°2 2674 305.6 343.8
| | | |
1138 381 762 114.3 1524 1905 228.6 266.7 3048 3429
1141 380 760 1140 1520 1900 2280 266.0 3040 3420
1144 379 758 1137 151-6 189.5 2274 | 265.3 3032 341*I
1148 378 756 1134 1512 189.0 226.8 2646 3024 340°2
1151 377 754 1131 150-8 188.5 2262 263 9 301-6 339°3
1154 376 752 112.8 1504 1880 225.6 263 2 3008 338.4
| |
1157 375 750 1125 1500 187.5 2250 262-5 3000 337.5
|
|
1160 374 748 | 112′2 | 149-6 | 187′0 | 224′4 | 261.8 | 299.2 336-6
1163 373 74-6 1119 1492 186.5 223.8 2611 2984 335'7
1166 372 744 1116 148-81860 223.2 2604 2976 3348
1169 371 742 1113 148 4 185.5 222.6 259.7 296.8 333'9
| |
1172 370 740 1110 1480 1850 2220 259.0 2960 3330
|
1175 369 738 1107 1476 1845 2214 258.3 2952 332.1
1178 36.8 73.6 110'4 147°2 1840 2208 2576 2944 331°2
1182 367 734 1101 146-8 183.5 220 2 2569 293.6 3303
1185 36.6 73.2 109.8 1464 1830 219.6 256.2 2928 3294
|
| |
1188 36.5 730 109'5 146'0 182.5 2190 2557 2920 328.5
|
| | |
1192 364 72-8 | 109.2 145.6 1820 2184 2548 | 2912 327.6
F195 36.3 72.6 108.9 145 2 1815 217-8 2541 2904 326-7
| | |
1198 362 724 108.6 1448 1810 217-22534 289.6 | 325.8
1202 361 72-2 108-3 1444 1805 216.6 252 7 288.8 3249
1205 360 720 1080 1440 1800 2160 252.0 2880 324.0
1208 359 71.8 107.7 143-6 179°5 2154 251°3 2872 323.1
1212 35.8 71.6 | 107′4 | 1432 1790 2148 250·6 2864 | 322°2
1215 357 714 1071 142.8 178.5 2142 249′9 285.6 321°3
1218 35.671-2 106·8 | 142°4 1780 213.6 249.2 284.8 3204
MATHEMATICAL TABLES.
43

No. 120 L. 079.]
LOGARITHMS OF NUMBERS.
I
2.
3
[No. 134 L. 130.
6
7
9 N.
N.I о
4
! 5 1
ら
​120 079181 9543 9904 0266 | 0626 | 0987 1347 1707 2067 | 2426|120
1082785 3144 3503 3861 4219 4576 49345291 5647 6004 I
6360 6716 7071 7426 77818136 8490 8845 9198 9552
|
9905 0258 0611 0963 1315 1667 2018 2370 2721 3071
|
4 093422 3772 4122 4471 4820 5169 5518 5866 6215 6562
8298 8644 8990 9335 9681 0026
23
5
71
78
|
2091 2434 2777 3119 3462
| | | |
5510 5851 6191 6531 6871
8903 9241 9579 9916
0253
2270 2605 2940 3275 3609
| |
2
34
56
7
8
9
6910 7257 7604 7951
|
6100371 0715 1059 1403 1747
|
38044146 4487 4828 5169
7210 7549 7888 8227 8565
9 110590 0926 | 1263 | 1599 | 1934
3943 4277 4611 4644 5278 5611
|
I 7271 7603 7934 8265 85958926 9256|9586|9915 0245 I
2 120574 0903 1231 1560 1888 2216 2544 2871 3198 3525
|
3852 4178 4504 4830 5156 5481 5806 6131 6456 6781
7105 7429 7753 8076 8399 8722 9045 9368 9690
|
130
3
4
PROPORTIONAL PARTS.
2
4
5943 6276 | 6608 | 6940 130
| |
7
2
3
0012 4
N. I
3
5
6
8
9
1222 355 71°0 106.5 142′0 1775 2130 248.5 | 2840 3195
1225 354 70.8 1062 141.6 1770 212 4 2478 283.2 318.6
|
1228 35.3 70.6 1059 141°2 176.5 211.8 2471 2824 3177
| |
1231 352 70'4 105.6 140·8 1760 2112 2464 281-6 316.8
35:2704105.6 |
1235 351 70'2 105°3 1404 175'5 2106 245 7 280.8 315'9
1239 350 700 1050 1400 1750 2100 2450 2800 3150
1243 349 698 1047 139.6 1745 2094 244°3 2792 3141
| | | |
1247 348 69.6 1044 1392 1740 208.8 2436 278.4 3132
1250 347 694 1041 138.8 1735 2082 2429 277·6 312.3
|
| | |
1253 346 692 103.8 1384 173′0 207·6 | 2422 276.8 3114
| |
1257 345 690 103.5 1380 172.5 2070 241°5 276·0 | 310′5
1261 344 68.8 1032 137.6 172′0 2064 240.8 2752 309.6
|
1264 343 68.6 1029 1372 1715 205.8 240°1 2744 308.7
1268 342 684 1026 136.8 1710 2052 2394 2736 307.8
|
1272 341 682 102.3 1364 170°5 2046 238.7 272.8 306-9
| |
1276 340 680 102'0 136.0 1700 2040 238.0 2720 306·0
1279 339 67.8 1017 1356 169.5 2034 237 3 2712 305.1
1283 33.8 67.6 1014 1352 1690 202-8 236.6 2704 304.2
1287 337 674 101°1 1348 168.5 2022 2359 269.6 303.3
IOII | | |
100-8 1344 168.0 2016 2352 268.8 302 4
| | |
1291 336 672
1295 335 670
1298 334 66.8
1302 333 66.6
1306 332 664
1310 33166.2
1314 330 66.0
1318 329 658
1322 32.8 65.6
1326 327 654
1330 32.6 65.2
1334 325 65.0
1338 324 64.8
1343 323 64.6
1347 32-264-4
|
|
|
100'5 1340 1675 2010 2345 2680 3015
|
1002 133.6 167′0 2004 233.8 2672 300-6
999 1332 166·5 | 199·8 | 233′1 | 2664 2997
99.6 132.8 166.0 1992 2324 265.6 298.8
993 1324 1655 1986 2317 2648 2979
| |
990 1320 1650 1980 2310 2640 297.0
|
| |
987 1316 1645 1974 230°3 263.2 296.1
|
| | |
984 1312 1640 196.8 229.6 262.4 295 2
981 130-8 163.5 1962 228.9 261.6 2943
9781304 163′0 195.6 228.2 260·8 293'4
| | | |
97.5 1300 1625 1950 227.5 2600 292.5
972 | 129.6 | 162′0 | 1944 | 226·8 | 259′2 | 291-6
96.9 1292 1615 1938 226.1 2584 290.7
96·6 128.8 1610 1932 2254257·6 | 289.8
| |
44
MATHEMATICAL TABLES.

No. 135 L. 130.]
56 7R
8
140
I
3
5
6
9
I
2
2
LOGARITHMS OF NUMBERS.
4
[No. 149 L. 175.
7
8
9
N.
6
9
1
3815 4120
9868 0168
4424 4728 | 5032
7457 7759 8061
|
0469 0769 1068
2
3
2863 3161
5838 6134
3460 3758 4055
6430 6726 7022
00
456 7
8
9
9
N.
3
5
6
135 130334 0655 0977 1298 1619 1939 2260 2580 2900 3219 135
|
3539 3858 4177 4496 4814 5133 5451 5769 6086 6403
51335451 |
6721 7037 7354 7671 7987 8303 8618 8934 9249 9564 7
9879 0194 0508 0822 1136 1450 1763 2076 2389 2702 8
9 143015 33273639 3951 4263 4574 4885 5196 5507 5818
||
6128 6438 6748 7058 7367 7676 7985 | 8294 8603 8911 140
9219 9527 9835 0142 0449 0756 1063 1370 1676 1982
2152288 2594 2900 3205 3510
5336 56405943 6246 6549 68527154
4 8362 8664 8965 9266 9567
161368 1667 1967|| 2266|| 2564
4353 4650 4947 5244 5541
7 7317 7613 7908 8203 8497 8792 9086 9380 9674 9968
8 170262 0555 0848 11411434 1726 2019 2311 2603 2895
3186 34783769 4060 4351 4641 4932 5222 5512 5802
| |
N. I
3 4 5
6
7
8
1351 321 642 96.3 1284 1605 1926 2247 256.8 288.9
1355 320 640 960 1280 1600 1920 2240 2560 288.0
1359 319 63·8
957 127.6 1595 1914 2233 2552 287-1
|
954 127.2 1590 190 8 222.6 2544 286-2
951 126.8 158.5 1902 2219 2536 285-3
948 1264 1580 189.6 2212 252.8 284-4
945 1260 157.5 189.0 2205 2520 283.5
942 125.6 1570 1884 219.8 2512 282-6
939 1252 156.5 187.8 2191 2504 2817
|
93.6 1248 1560 1872 2184 249.6 280.8
|
933 1244 1555 186-6 2177 248.8 279°9
930 1240 1550 1860 2170 248.0 279'0
927 123.6 1545 1854 216.3 247.2 278.1
| |
| | 278′1
924 1232 1540 184-8 215.6 246·4 | 277'2
122.8 1535 184-2 2149 245.6 | 276·3
1224 1530 183.6 2142 2448 275°4
|
122.0 | 152°5 1830 213.5 2440 2745
|
121.6 1520 1824 212.8 243.2 273.6
PROPORTIONAL PARTS.
1364 318 63.6
1368 317 634
1372 316 632
1376 315 630
1381 314 62.8
1385 313 62.6
1390 312 624
1394 311 62.2
1398 310 62.0
|
1403 309 61.8
1412 307 614 92.1
| |
1417 30.6 61.2
1422 305 610
1426 304 60.8
918
91.5
912
|
1431 303 60·6
90'9
1436 302 604
90'6
1441 301 60°2
90.3
1446 300 600
1446300
90'0
897
1408 308 61.6
1818 | 212°1 | 242°4 | 272°7
1812 2114 2416 | 271.8
|
121°2 1515
120.8 1510
1204 150°5 180.6 2107 240.8 270.9
1200 1500 1800 2100 2400 270°0
1450 29.9 59.8 119.6 1495 1794 2093 2392 269.1
| |
1455 29.8 59.6 894 1192 1490 178.8 208.6 238.4 268.2
1460 297 594 891 118-8 148.5 178.2 2079 237.6 267.3
|
|
1465 29.6 59:2 88.8 1184 148.0 177.6 2072 236.8 266-4
1470 29'5 59°0 88.5 1180 147.5 1770 206·5 | 236·0 265′5
1475 294 58.8 88.2 117.6 1470 176.4 205.8 2352 264·6
1480 29.3 58.6 117-2 146.5 175.8 2051 2344 2637
1485 292 584 87.6 116.8 1460 175.2 2044 233.6 262.8
1490 291 58.2 87.3 116.4 145.5 174.6 2037 232.8 2619
| | | |
1495 290 580 870 116.0 1450 1740 2030 232.0 2610
1500 28.9 57.8 86.7 115.6 144'5 1734 2023 2312 260.1
|
1505 28.8 57.6 864 1152 1440 172.8 2016. 2304 2592
1511287 57'4 8611148 143.5 172-2 2009 229.6 258.3
1516 | 28-6 | 57°2 | 85·8 | 114°4 | 143·0 | 171·6 | 200·2 | 228·8 | 257:4
879
MATHEMATICAL TABLES.
45

No. 150 L. 176.]
LOGARITHMS OF NUMBERS.
N.
о
I
2
3
4
5
[No. 169 L. 230.
6
7
8
9
N.
8113 8401 8689 150
I
150 176091 6381 6670 6959 72487536 || 7825
I
234 56 D∞
7
8
|
8977 9264 9552 9839 0126 0413 0699 0986 1272 1558
2 3
4
5
6
7
8
9
2 181844 2129 2415 2700 2985 3270 3555 3839 4123 4407
4691 4975 5259 5542 5825 6108 6391 6674 6956 7239
7521 7803 8084 8366 8647 8928 9209 9490 9771 0051
|
190332 0612 0892 1171 1451 1730 2010 2289 2567 2846
3125 3403 3681 3959 4237 4514 4792 5069 5346 5623
| |
5900 6176 6453 6729 7005 7281 7556 7832 8107 8382
| |
8657 8932 9206 9481 9755 0029 0303 0577 0850 1124
9 201397 1670 1943 2216 | 2488 | 2761 | 3033 | 3305 | 3577 3848
| 27613033 | |
4120 4391 4663 4934 5204 5475 5746 6016 6286 6556 160
|
6826 7096 7365 7634 7904 8173 8441 8710 8979 9247
9515 9783
|
2
0051 0319 0586 0853 1121 1388 1654 1921
3 212188 2454 2720 2986 3252 3518 3783 4.049 4314 4579
|
|
4844 5109 5373 5638 5902 6166 6430 6694 6957 7221
7484 7747 8010 8273 8536 8798 9060 9323 9585 9846
| |
6220108 0370 0631 | 0892 | 1153 1414 1675 1936 2196| 2456
|
2716 2976 3236 3496 3755 4015 4274 4533 4792 5051
5309 5568 5826 6084 6342 6600 6858 7115 7372 7630
7887 8144 8400 8657 89139170 | 9426 | 9682|9938
7887 8144 8400 8657
160
I
2
4
5
7
8
୨
.00 a
PROPORTIONAL Parts.
I
2
4
이
​7
I
3
4
5
6
78
0193
8
9
9
00
6
5
1140 142.5 1710 1995 2280 256.5
113.6 1420 1704 198.8 227.2 255.6
1132 141-5 169.8 1981 226 4 2547
112.8 1410 1692 1974 225.6 253.8
| | |
1124 1405 168.6 196.7 224-8 252.9
1120 1400 1680 1960 2240 252.0
1116 139.5 1674 1953 2232 251'1
|
1112 1390 166-8 1946 222 4 250°2
110.8 138.5 166.2 1939 221-6 249°3
1104 138.0 165.6 1932 220.8 248.4
|
N.
3
1521 285 570 85.5
1527 28.4 56.8 85.2
1532 28.3 56.6 84.9
1537 28.2 56.4 84.6
1543 281 562 843
1548 280 560 840
1554 279 558 83.7
1559 278 556 834
1565 277 554 831
1570 27.6 55.2 82.8
1576 275 550 82.5 1100 137.5 165.0 192.5 | 2200 247′5
| |
1582 274 548 82.2 109.6 1370 1644 1918 2192 246·6
| | |
| |
1587 273 546 819 109°2 136.5 163.8 1911 2184 245'7
| | | | |
1593 272 544 81.6 108.8 136.0 163.2 1904 217.6 244.8
272544
1599
27.1 542 813 1084 135°5 162.6 189.7 216.8 243'9
1605 270 540 810 1080 1350 1620 1890 2160 2430
1611 269 53.8 80.7 107.6 1345 1614 1883 2152 242 1
1617 26.8 536 804 1072 1340 1608 187.6 2144 241-2
1623 267 534 801 106.8 133.5 1602 1869 2136 240*3
|
1629 26.6 532 79.8 106.4 1330 1596 1862 212-8 239°4
1635 26.5 530 79′5 | 1060 | 132.5 | 1590 | 185.5 2120 238.5
1641 264 52.8 79.2 105.6 | 132′0 158.4 184-8 2112 237.6
1648 26.3 52.6 78.9 1052 1315 157-8 1841 2104 236.7
165426.252.4 | |
1654 262 52.4 78.6 1048 1310 1572 1834 209.6 | 235·8
|
1660 261 52.2 78.3 1044 1305 156-6 182.7 208-8234'9
| |
1667 260 52·0 | 78′0 | 104°0 1300 1560 182.0 2080 234°0
1673 259 51.8 77.7 103.6 129.5 1554 1813 2072 2331
| |
1680 25.8 51.6 77.4 103.2 129.0 1548 180·6 206·4 | 232°2
1686 257 514 771 102-8 128.5 1542 1799 2056 231°3
|
|
1693 256 512 768 1024 1280 1536 1792 2048 2304
| |
|
1699 25.5 51.0 76.5 102.0 | 127.5 | 1530 | 178.5 | 2040 | 229.5
| | |
|
46
MATHEMATICAL TABLES.

I
2
3
5
7
No. 170 L. 230.]
N.
O
LOGARITHMS OF NUMBERS.
I
2
3
4
5
6
7
170 230449 0704 0960 1215 1470 1724
2996 3250 3504 3757 4011 4264
5528 5781 6033 6285 6537 6789
8046 8297 8548 8799 9049 9299
1979
[No. 189 L. 278.
89
N.
2234 | 2488 | 2742170
4517 4770 5023 5276 I
7041 7292 7544 7795
9550 9800
| | |
0050 0300
2541 2790
2
3456
9
180
4 240549 0799 1048 1297 1546 1795 2044 2293
3038 3286 3534 3782 4030 4277 4525 4772 5019 5266
5513 5759 | 6006 | 6252,
6499 6745 6991 7237 7482 7728
7973 8219 8464 8709 8954 9198 9443 9687 9932 0176
8 250420 0664 0908 1151 1395 1638 1881 2125 2368 2610
2853 3096 3338 3580 3822 4064 4306 4548 4790 5031 9
|
7
|
8
5273 5514 5755 5996 6237 6477 6718 6958 7198 7439180
7679 7918 8158 8398 8637 8877 9116 9355 9594 9833
I
I
2 3+ in
5
2 260071 0310 0548 0787 1025 1263 1501 1739 1976 2214
2451 2688 2925 3162 3399 3636 3873 4109 4346 4582
| | |
4818 5054 5290 5525 5761 5996 6232 6467 6702 6937
7172 7406 7641 7875 8110 8344 8578 8812 9046 9279
|
9513 9746 9980 0213 0446 0679 0912 1144 1377 1609
7 271842 2074 2306 2538 2770 3001 32333464 3696 3927
41584389 4620 4850 5081 5311 5542 5772 6002 6232
6462 66926921 7151 7380 | 76097838 8067 8296 8525
|
789
9
2 3
4
5
6
78
9
9
7
8
177·8 203′2 | 228.6
177°1 2024 227°7
176.4 2016 226.8
175°7 2008 225'9
N. 1 | 2 3
4
5
6
1706 254 50·8 | 76°2 | 101·6 | 127′0 | 152°4
1713 253 50·6 | 75′9 | 101°2 | 126.5 151.8
1719 252 504 75.6 100-8 126.0 1512
1726 251 502 75°3 1004 125°5 150-6
1733 250 500 750 | 1000 | 1250 1500 1750 2000 225.0
1740 249 49.8 747 99.6 1245 1494 174 3 1992 224*1
1747 248 49.6 | 74:4 992 1240 148.8 1736 1984 223.2
1754 247 49′4 | 74'1 98.8 123.5 148.2 1729 1976 222°3
|
1761 246 49.2 73.8 984 123′0 147.6 1722 196.8 2214
|
1769 245 490 735 980 122.5 1470 171′5 196′0 | 220′5
PROPORTIONAL PARTS.
960
1776 244 48.8 | 73°2 97′6 | 122′0 | 146′4 | 170·8 | 1952 | 219′6
1783 243 48.6 | 72°9 972 121°5 1458 170°1 | 1944 2187
1790 242 484 72.6 96.8 1210 1452 169'4 1936 217.8
1798 241 482 723 964 120°5 1446 1687 192.8 216'9
1805 240 480 720
1200 1440 1680 1920 216.0
|
| |
1813 239 47-8 717 95.6 1195 1434 167.3 1912 | 215°1
1820 23.8 47.6 714 952 1190 142.8 166.6 1904 || 214°2
1828 237 474 71'I
|
948 118.5 142°2 | 165'9
1836 23.6 47.2 70.8 944 1180 141-6 1652
1844 235 470 70'5 940 117.5 1410 1645
189.6| 213.3
188-8 | 2124
1880 2115
|
1852
234 46.8 70.2 93.6 1170 140°4 163.8 187.2 2106
1859
23.3 46.6 69.9 93.2 116.5 139.8 | 163.1 | 1864 209'7
1867 23.2 464 69.6 92.8 116-0 139.2 162.4 185.6 208.8
| |
1876 23′1 46.2 69.3
23.146.2
924 115.5 138.6 1617 1848 2079
1884 230460 690 920 1150 1380 1610 1840 207.0
1892 229 458 68.7 916 1145 1374 1603 183.2 206.1
| |
1900 22.8 456 684 912 1140 136-8 159.6 1824 205.2
| | |
1908 227 45°4 | 68·1 90.8 1135 136.2 158.9 181.6 2043
1917 226 45.2 67.8
90°4 1130 135.6 158.2 180.8 2034
45.2 67.8
MATHEMATICAL TABLES.
47

No. 190 L. 278.]
N. о
I
2
LOGARITHMS OF NUMBERS.
[No. 214 L. 332.
3
4
5 6 7
8
9 N.
2 3 4 5 6 7∞
8
I
3804
6007
I
1234 SO DO0
5
6
7
8
9
I
2547 2764 2980 200
4706 4921 5136
6854 7068 7282
8991 9204 9417
92049417
|190| 278754 | 8982|9211|9439|9667 | 9895|0123 0351 0578 | 0806 |190
1 281033 1261 1488 1715 1942 2169 2396 2622 2849 3075
3301 3527 3753 3979 4205 4431 4656 4882 5107 5332
5557 5782 6007 6232 6456 6681 6905 7130 7354 7578
7802 8026 8249 8473 8696 8920 9143 9366 9589 9812
290035 0257 0480 0702 0925 11471369 1591 1813 2034
2256 2478 2699 2920 3141 3363 3584 4025 4246
4466 4687 4907 5127 5347 5567 5787 6226 6446
6665 6884 7104 7323 7542 7761 7979 8198 8416 8635
9 8853 9071 9289 | 9507 | 9725 9943 0161 0378 0595 0813
| |
200 301030 1247 1464| 1681 | 1898 2114 2331
3196 3412 3628 3844 4059 4275 4491
5351 5566 5781 5996 6211 6425 6639
7496 7710 7924 8137 8351 8564 8778
9630 9843 0056 0268 0481 0693 0906 1118 1330 1542
311754 1966 2177 2389 2600 2812 3023 3234 3445 3656
3867 4078 4289 | 4499 4710 4920 5130 5340 5551 5760
5970 6180 6390 6599 6809 7018 7227 7436| 7646| 7854
8 8063 8272 8481 8689 8898 9106 9314 9522 9730 9938
9320146 0354 0562 0769 0977 1184 1391 1598 1805| 2012
| |
2219 2426 2633 2839 3046 3252 3458 3665 3871 4077 210
4282 4488 4694 4899 5105 5310 5516 5721 5926 6131
6336 6541 6745 6950 7155 7359 7563 7767 7972 8176
| |
8380 8583 8787 8991 9194 9398 9601 9805 0008 0211
4330414 0617 | 0819 | 1022 | 1225 | 1427 | 1630 | 1832 | 2034 | 2236
4
23+ iO 7∞
6
210
I
2 3 4
PROPORTIONAL PARTS.
I
ΙΙΙΟ
|
23 456 78
9
I
2
3
4
8
9
N.
3 4
1 | 2
6
5
7
1925 225 450 67.5 900 112.5 1350 1575 1800 202.5
1934 224 448 67.2 89.6 1120 134′4 156·8 179°2 201·6
1943
22.344.6 66.9 89.2 111'5 133.8 156·1 | 178'4 2007
| |
1952 22'2 444 66.6 88.8 1110 1332 1554 177.6 199.8
|
1961 22.I 442 66.3 884 110.5 132.6 1547 176.8 1989
| |
1969 22.0 440 66.0 88.0 1100 1320 1540 176.0 1980
1978 219 43.8 65.7 87.6 109.5 1314 1533 175°2 1971
1987 218 43.6 654 87′2 1090 1308 | 152.6 1744 | 196-2
1996 217 434 651 86.8 108.5 1302 1519 1736 195'3
| |
2005 21.6 43.2 64.8 86.4 1080 129.6 1512 172-8 194'4
2015
215 430 64.5 86.0 107.5 1290 150'5 1720 1935
2024 214 428 642 85.6 1070 128.4 149.8 1712 192.6
2034
213 42-6 639 85.2 106.5 127.8 1491 1704 1917
2043
21.2 424 63.6 84.8 1060 1272 1484 169.6 190-8
| |
|
2053
211 42 2 633 844 105'5 126.6 147.7 1688 189.9
2063 21'0 42.0 630 840 1050 1260 1470 1680 189.0
2073
20.9 41.8 62.7 83.6 104.5 1254 146.3 1672 188.1
2082 20.8 41.6 62.4 83.2 1040 1248 145.6 166.4 187.2
2092 207 414 62.1 82.8 103.5 1242 1449 165.6 186.3
|
2103 20.6 41.2 61.8 82.4 1030 123.6 144°2 | 164·8 | 185′4
2113
20.5 400 61.5 82.0 102.5 1230 143.5 1640 1845
2123 204 408 61.2 81.6 102'0 1224 142.8 163.2 183.6
2134 20.3 40.6 60.9 81.2 101.5 121.8 142°1 1624 182.7
2144 20'2 404 60.6 80.8 1010
121°2 | 1414 | 161.6 | 181-8
48
MATHEMATICAL TABLES.

No. 215 L. 332.]
LOGARITHMS OF NUMBERS.
[No. 239 L. 380.
N.
о
I
2
3
4
5
6
7
8
9
N.
6
6
557
215 332438 2640 2842 3044 3246 3447 3649 3850 4051 4253 215
4454 4655 4856 5057 5257 5458 5658 5859 6059 6260
6460 6660 6860 7060 7260 7459 7659 7858 8058 8257
8456 8656 8855 9054 9253 9451 9650 9849 0047 0246
78
220
8
9 340444 0642 0841 1039 1237 1435 1632 1830 | 2028 2225 9
2423 2620 2817 3014 3212 3409 3606 3802 3999 4196 220
4392 4589 4785 4981 5178 5374 5570 5766 5962 | 6157
6353 6549 6744 6939 7135 7330 7525 7720 7915 8110
8305 8500 8694 8889 9083 9278 94729666 | 9860
1 2 3
56 78 9
I
0054
I
2
3456 78
4 350248 0442 0636 0829 1023 1216 1410 1603| 1796 | 1989
2183 2375 2568 | 2761 | 2954 3147 3339 3532 3724 3916
4108 4301 4493 4685 4876 5068 5260 5452 5643 5834
6026 6217 6408 6599 6790 6981 7172 7363 7554 7744
7935 81258316 8506 8696 8886 9076 9266 9456| 9646
9835
0025 0215 0404 0593 0783 0972 1161 1350 1539 9
230 361728 1917 2105 2294 2482 2671 2859 3048 3236 3424 230
3612 3800 3988 4176 4363 4551 4739 4926 5113 5301 I
5488 5675 5862 6049 6236 6423 6610 6796 6983 7169
7356 7542 7729 7915 8101 8287 8473 8659 8845 9030
9216 9401 9587 9772 9958 0143 0328 0513 0698 0883
5 371068 1253 1437 1622 1806 1991 2175 2360 2544 2728
| |
2912 3096 3280 3464 3647 3831 4015 4198 4382 4565
4748 4932 5115 5298 5481 5664 5846 6029 6212 6394
6577 6759 6942 7124 7306 7488 7670 7852 8034 8216
8398 8580 8761 8943 91249306 94879668|9849
0030 9
1234 6 789
PROPORTIONAL PARTS.
I
2
3 4
in
5
6
7
8
9
2 3 456 78
N.
2155
20'I 402 603 804 100.5 120.6 1407 160·8 1809
2166
20'0 400 600 800 100.0 1200 1400 1600 180.0
2176 19'9 398 59'7 79.6 99.5 1194 1393 159°2 179°1
39-8597
| | |
2187 19.8 39.6 594 79°2 99'0 118.8 138.6| 1584 178.2
2198 197 394 59°1 78:8 98.5 118.2 137′9 1576 1773
|
118-21379
19.6 392 58.8 78.4 980 117.6 137.2 156.8 176.4
2221 19.5 390 58.5 78.0 97.5 1170 136.5 1560 1755
2232 194 38-8 582 77.6 970 1164 135-8 1552 1746
2210
2244
19.3 38-6 579 772
|
2256 192 384 57.6 76.8
2267 191 382 573 764
2279 19'0 380 57.0 76.0
2291 18.9 37.8 56.7 75.6
2303
18.8 37.6 564 752
18.7 374 56°1 | 74-8
18.6 37.2 55.8 744
2316
2328
2341
18.5370 55°5 | 740
2353
18.4 36.8 552 | 73.6
2366 18.3 36.6 549 732
|
2379 18.2 364 546 | 72-8
2392 18.1 36.2 543 724
2406
18.0 36.0 540 720
2419 179 35.8 537 716
| |
96.5 115·8 | 135°1 | 1544 1737
960 1152 1344 153.6 172.8
|
955 114-6 1337 152·8 | 171-9
950 1140 1330 1520 1710
94'5 1134 | 132°3 | 151*2 | 170*1
940 112.8 131.6 1504 | 169°2
935 112.2 1309 149.6 168.3
930 1116 130′2 | 148.8 | 167°4
925 1110 129.5 1480 166.5
920 1104 128.8 147.2 165.6
915 109.8 128.1 1464 1647
910 109.2 1274 145.6 163.8
90.5 108.6 126.7 144-8 162-9
900 1080 1260 1440 162.0
89.5 1074 1253 1432 1611
MATHEMATICAL TABLES.
49

No. 240 L. 380.]
LOGARITHMS OF NUMBERS.
[No. 269 L. 431.
N.
I
2
3
4
5
6
7
8 9 N.
123
5070
I
2
240 380211 0392 0573 0754 0934 1115 1296 1476 1656 1837 240
2017 2197 2377 2557 2737 2917 3097 3277
3815 3995 4174 4353 45334712 4891
5606 5785 5964 6142 6321 6499 6677 6856
7390 7568 7746 7924 8101 8279 8456 8634
9166 9343 9520 9698 9875 0051 0228 0405
||
| | |
3456 3636
5249 5428
7034 7212
8811 8989
0582 0759
a 3 + iO DOO a
4
4
5
5
7
8
9
6 390935 1112 1288|| 1464 1641 1817 1993 2169 2345 2521
2697 2873 3048 3224 3400 3575 3751 3926 4101 4277
4452 4627 4802 4977 5152 5326 5501 5676 5850 6025
6199 6374 6548 6722 6896 7071 7245 7419 7592 7766
6
7
8
9
250
9328 9501 250
1056| 1228
Ι
2 3 4 56
7940 8114 8287 8461 8634 | 8808 8981 9154
I 9674 9847 0020 0192 0365 0538 0711 0883
2 401401 1573 1745 1917 2089 2261 2433 2605 2777 2949
3121 3292 3464 3635 3807 3978 4149 4320 4492 4663
4834 5005 5176 5346 5517 5688 5858 6029 61996370
6540 6710 6881 7051 7221 7391 7561 7731 7901 8070
8240 8410 8579 8749 8918 9087 9257 9426 9595 9764
9933 0102 0271 0440 | 0609 0777 0946 1114 1283 1451
8 411620 1788 1956 2124 2293 2461| 2629 2796 | 2964 3132
3300 3467 3635 3803 3970 4137 4305 4472 4639 4806
7
9
260
23 +
23456
78 9
I
OHN
2
4973 5140 5307 5474 5641 5808 5974 6141 6308 6474 260
I 6641 6807 6973 7139 7306 7472 7638 7804 7970 8135
8301 8467 8633 8798 89649129 | 9295 | 9460 | 9625 | 9791
9956
0121 0286 0451 0616 0781 0945 1110 1275 1439
|
4 421604 1768 1933 2097 2261 2426 2590 2754 2918 3082
3246 3410 3574 3737 3901 4065 4228 4392 4555 4718
4882 5045 5208 5371 5534 5697 5860 6023 6186 6349
6511 6674 6836 6999 7161 7324 7486 7648 7811 7973
8135 8297 8459 8621 8783 894491069268 | 9429|9591
975299140075|0236|0398 | 0559 | 0720 | 0881 | 1042 | 1203
5
6
78
9
PROPORTIONAL PARTS.
I
2
3456 78
9
9
N.
3 4 5
6
7
8
2433 17.8 35.6 534 71°2 890 106.8 124.6 1424 160°2
2446 17.7 354 531 70.8 88.5 106.2 123'9 1416 1593
2460 17.6 352 52.8 704 88.0 105.6 123.2 140·8 158.4
2474 17.5 350 525 70°0 | 87°5 | 105′0 | 122°5 | 140°0 | 157°5
2488 17.4 348 52.2 69.6 | 87·0 | 1044 | 121.8 | 139′2 | 156·6
2503 17.3
346 519 69.2 86.5 103.8 121°1 1384 155'7
2517 17.2 344 51.6 68.8 86.0 103.2 1204 1376 | 154.8
2532 17.1 342 513 68.4 85.5 102.6 119.7 136.8 1539
2547 17.0 340 510 68.0 85.0 1020 1190 1360 | 153.0
2562 169 33.8 50.7 67.6 84.5
2577
16.8 33.6 504 67.2 84.0
2592 16.7
33°4501
50.1 66.8 83.5
2608 16.6 332 49.8 66.4 83.0
2624 16.5 330 495 66.0 82.5
264c 16.4 32.8 49.2 65.6 82.0
2656 16.3 32.6 48.9 65.2 81.5
2672 16.2 32.4 48.5 64.8 81.0
2689
16.1 322 483 644 805
1014 118.3 1352 152.1
100.8 117.6 1344 1512
| |
1002 116.9 133.6 150*3
996 116.2 132.8 149°4
990 115.5 1320 148.5
984 114.8 131.2 147.6
978 114 11304 146.7
972 1134 129.6 | 145.8
96.6 1127 128.8 1449
|
50
MATHEMATICAL TABLES.

No. 270 L 431.]
I
2
3
4
5
6
440909 1066|| 1224
1381
7
2480 2637 2793 2950 3106 3263
8
4045 4201 4357 4513
N. о
LOGARITHMS OF NUMBERS.
[No. 299 L. 476.
I
2
3
4
5
6
7
270 431364 1525 1685 1846 2007 2167 2328 2488
|
2969 3130 3290 3450 3610 3770 3930 4090
4569 4729 4888 5048 5207 5367 5526 5685
6163 6322 6481 6640 6799 6957 7116 7275
7751 7909 8067 8226 8384 8542 8701 8859
9333 9491 9648 9806 9964 0122
I
2
8 9 N.
2649 2809 |270.
4249 4409
5844 6004
7433 7592
9017 9175
0594 0752
4
3+ 5 78
|
0279
0437
|
1538 | 1695
1852
2009
2166| 2323
6
3419
| |
3576 3732 3889
4669 4825
4981
5137 5293 5449
9
6537
| |
6692 6848 7003
9
280
8088
|
8242 8397 8552 280
9633
I
2
23456 7
3
4
5
6
7
8
9787 9941 0095
1172 1326 1479 1633
2706 2859 3012 3165
4235 4387 4540 4692
| |
5758 5910 6062 6214
7428 7579 7731
|
5604 5760 5915 6071 6226 6382
7158 7313 7468 7623 7778 7933
I 8706 8861 9015 9170 9324 9478
2 450249 0403 0557 0711 0865 1018
| | |
1786 1940 2093 2247 2400 2553
3318 3471 3624 3777 3930 4082
| | | |
4845 4997 5150 5302 5454 5606
6366 6518 6670 6821 6973 7125 7276
7882 8033 8184 8336 8487 8638 8789 8940 | 9091 | 9242
8 9392 9543 9694 9845 9995 0146 0296 0447 0597 0748
9460898 1048 1198 1348 | 1499 | 1649 | 1799 1948 2098 2248 9
290 2398 2548 2697 2847 2997 3146 3296 3445 3594 3744 290
|
I 3893 4042 4191 4340 4490 4639 4788 4936 5085 5234
|
2345
7
8
9
5383 5532 5680 5829 5977 6126 6274 6423 6571 6719
6868 7016 7164 7312 7460 7608 7756 7904 8052 8200
|
I
2
4. 8347 8495 8643 8790 8938 9085 9233 9380 9527 9675
9822 9969 0116 0263
6471292 1438 1585 1732
2756 2903 3049 3195
4216 4362 4508 4653
56715816 5962 | 6107
|
N.
2705 16.0 32°0
2722 15'9 31.8
2740 15.8 31.6
2757 15'7 314
2775 15.6 31.2
2792 15.5 31.0
2810 154 30.8
2833 15.3 30.6
2847 15.2 30°4
2866 15'1 30°2
2885 15.0 30.0
2904 14.9 29.8
2924 14.8 29.6
2944 14'7 29'4
2964 14.6 29.2
2984 14.5 29.0
3005 14'4 28.8
3026 14:3 28.6
3047
142 284
3069 14'I 28.2
3091 14'0 28.0
PROPORTIONAL PARTS.
I
234 no
5
6
7
8
9
78
0410 0557 0704 0851 0998 1145
1878 2025 2171 2318 2464 2610
3341 3487 3633 3779 3925 4071
4799 4944 5090 5235 5381 5526
62526397 | 6542 | 6687 | 6832|6976
3 4 5 6
7
8
9
480 640 800 96′0 | 1120 1280 | 1440
47.7 63.6 79.5 954 111.3 1272 143 1
474 632 790 948 110.6 1264 1422
47.1 62.8 78.5 94′2 109′9 | 125.6 | 141′3
46.8 62.4 78.0 93.6 109.2 | 1248 | 140°4
46.5 620 775 930 108.5 1240 139 5
46.2 61.6 77.0 924 107.8 | 123′2 | 138.6
459 61.2 76.5 91.8 1071 1224 1377
45.6 60.8 76.0 91.2 106.4 1216 136.8
453 604 755 90.6 105.7 120.8 135'9
450 600 750 900 1050 | 120′0 | 135°0
447 596 74'5 89'4 104°3 | 119′2 | 134°1
444 592 740 88.8 103.6 1184 133°2
441 58.8 73.5 88.2 | 102.9 117·6 | 132°3
43.8 58.4 73.0 87.6 102.2 116.8 1314
43.5 58.0 72.5 87.0 101.5 116.0 1305
432 576 72.0 864 100-8 1152 129.6
429 572 71.5 85.8 1001 1144 128.7
42.6 56.8 710 | 852
42.3 564 70.5 84.6
42°056·0 700 840
|
994 113.6 127.8
98.7 1128 126.9
98.0 1120 126′0
MATHEMATICAL TABLES.
51

No. 300 L. 477-]
LOGARITHMS OF NUMBERS.
N. о
I
2
3
4
1 6
5
}
[No. 339 L. 531.
78
9 N.
300 477121 7266 7411 7555 7700 7844 7989 8133 8278 8422 300
I
23 456 7∞
8
9
I
123456
9575 9719 9863 I
1012
1156 | 1299
2445
2588 2731
|
3872
4015 4157
5295
5437 5579
6714
6855 6997
8127
8269 8410
9537
23 456 78
9
9677 | 9818
1081 | 1222
2481 2621 310
38764015
I
OH 2m
3
4
5
8566 8711 8855 8999 9143 9287 9431
2 480007 0151 0294 0438 0582 0725 0869
1443 1586 1729 1872 2016 2159 2302
2874 3016 3159 3302 3445 3587 3730
4300 4442 4585 4727 4869 5011 5153
5721 5863 6005 6147 6289 6430 6572
7138 7280 7421 7563 7704 7845 7986
7280|7421 | |
8551 8692 8833 8974 9114 9255 9396
9958
0099 0239 0380 0520 0661 0801 0941
310 491362 1502 1642 1782 1922 2062 2201| 2341
|
2760 2900 3040 3179 3319 | 3458 3597 3737
4155 4294 4433 4572 4711 4850 4989 5128 5267 5406
5544 5683 5822 5960 6099 6238 6376 6515 6653 6791
6930 7068 7206 7344 7483 7621 7759 7897 8035 8173
8311 8448 8586 8724 8862 8999 9137 9275 9412 9550
9687 9824 9962 0099 0236 0374 0511 0648 0785 0922
|
7 501059 1196 1333 1470 1607 1744 1880 2017 2154 2291
2427 2564 2700 2837 2973 3109 3246 3382 3518 3655
| |
3791 3927 4063 4199 4335 4471 4607 4743 4878 5014
5150 5286 5421 5557 5693 5828 5964 6099 6234 6370 320
6505 6640 6776 6911 7046 7181 7316 7451 7586 7721
7856 79918126 8260 8395 85308664 8799 | 8934 | 9068
9203 9337 9471 9606 9740 9874 0009 0143 0277 0411
| |
| |
4 510545 0679 0813 0947 1081 1215 1349 1482 1616 1750
| | |
1883 2017 2151 2284 2418 2551 2684 2818 2951 3084
|
3218 3351 3484 3617 3750 3883 4016 4149 4282 4415
4548 4681 4813 4946 5079 5211 5344 5476 5609 5741
5874 6006 6139 6271 6403 6535 6668 6800 6932 7064
| |
|
7196 7328 7460 7592 7724 7987 8119 8251 8382 9
8514 8646 8777 8909 9040 9171 9303 9434 9566 9697 330
I 9828 9959 009002210353
0090 0221 0353 0485 0615 0745 0876 1007
07450876 |
2 521138 1269 1400 1530 1661 1792 1922 2053 2183 2314
8
9
320
I
O123 +56 7∞
8
9
330
4
~ 3 + in6 78
|
7855
2444 2575 2705 2835 2966 3096 3226 3356 3486 3616
3746 3876 4006 4136 4266 4396 4526 4656 4785 4915
5045 5174 5304 5434 5563 5693 5822 5951 6081 6210
6339 6469 6598 6727 6856 6985 7114 7243 7372 7501
| | |
|
7630 7759 7888 8016 8145 8274 8402 8531 8660 8788
8917 9045 9174 9302 9430 9559 9687 9815 9943 0072
9 5302000328 0456 0584 0712 0840
953020003280456|0584 | |
PROPORTIONAL PARTS.
|
N.
3113 13.9 27.8 41.7
13.8 27.6 414
6 78 a
9
I
2
3456 7.00
8
Ι
23456 7∞
8
0968 1096 1223 1351
9
I
2
3
4
5 6 7
3135
8
9
55.6 69.5 834 97°3 | 1112 | 125°1
552 690 82-8 96.6 1104 124°2
3158
13.7
27.4 41'1
548
3181
13.6
27°2 40·8
544
3205
13'5
27.0 40'5
540
3228
13'4
26.8 40°2
3253 13°3
3277 13.2
68.5 82.2 959 | 109.6 | 123°3
680 81.6 95.2 108.8 | 122′4
67.5 81.0 94.5 1080 121.5
536 670 80.4 93.8 107.2 120.6
532 66.5 79.8 93.1 106.4 1197
52.866.0 792 | 92°4 | 105.6 | 118.8
52.4 65.5 78.6 91.7 1048 | 1179
520 650 78.0 91.0 1040 1170
25.838.7
387 516645 774903 | 103.2 | 116-1
26.6 39.9
26.4 39.6
39.6
3302 13°1
26.2 39°3
3327 13.0 26.0 39°0
3353 12.9
}
52
MATHEMATICAL TABLES.

No. 340 L. 531.]
I
2
3456
LOGARITHMS OF NUMBERS.
[No. 379 L. 579-
I
2
3
4
5
6
7
8
|
1
2
3
4
5
6
N. о
9 N.
340 531479 1607 1734 1862 1990 2117 2245 2372 2500 2627 1340
| |
2754 2882 3009 3136 3264 3391 3518 3645 3772 3899
4026 4153 4280 4407 4534 4661 4787 4914 5041 5167
5294 5421 5547 5674 5800 5927 6053 6179 6306 6432
6558 6685 6811 6937 7063 7189 7315 7441 7567 7693
7819 7945 8071 8197 8322 8448 8574 8699 8825 8951
9076 9202 9327 9452 9578 9703 9829 9954 0079 0204
| | | |
7 540329 0455 0580 0705 0830 0955 1080 1205 1330 1454
1579 1704 1829 1953 2078 | 2203 | 2327 2452 2576 2701
2825 2950 3074 3199 3323 3447 3571 3696 3820 | 3944
4068 4192 4316 4440 4564 4688 4812 4936 5060 5183 350
5307 5431 5555 5678 5802 5925 6049 6172 6296 6419
6543 6666 6789 6913 7036 7159 7282 7405 7529 7652
7775 7898 8021 8144 8267 8389 8512 8635 8758 8881
8
9
350
I
2
3
56 7∞
8
9
|360
7
8
9
I
2 3 4 5 to
6
7
8
4 9003 9126 9249 9371 9494 9616 9739 9861 9984 0106
5550228 0351 0473 0595 0717 0840 0962 1084 1206 1328
1450 1572 1694 1816 1938 2060 | 2181| 2303 2425 2547
2668 2790 2911 3033 3155 3276 3398 3519 3640 3762
3883 4004 4126 4247 4368 4489 4610 4731 4852 4973
5094 5215 5336 5457 5578 5699 5820 5940 6061 6182 9
6303 6423 6544 6664 6785| 6905 7026| 7146 7267 7387 360
I 7507 7627 7748 7868 7988 8108 8228 8349 84698589
8709 8829 8948 90689188 9308 94289548 | 9667 | 9787
9907 0026 0146 0265 0385 0504 c624 0743 0863 0982
|
5
2 3 4 SO 7∞ a
8
9
370
I
1
2
3456 7∞ a
8
9
I
4 561101 1221 1340 1459 1578 1698 1817 1936 2055 2174
2293 2412 2531 2650 2769 2887 3006 3125 3244 3362
3481 3600 3718 3837 3955 4074 4192 4311 4429 4548
4666 4784 4903 5021 5139 5257 5376 5494 5612 5730
|
5848 5966 6084 6202 6320 6437 6555 6673 6791 6909
7026 7144 7262 7379 7497 7614 7732 7849 7967 8084
8202 8319 8436 8554 8671 8788 8905 9023 9140 9257 370
9374 9491 9608 9725 9842 9959 0076 0193 0309 0426
2570543 0660 0776 0893 1010 1126 1243 1359 1476 1592
1709 1825 1942 2058 2174 2291 2407 2523 2639 2755
2872 2988 3104 3220 3336 3452 3568 3684 3800 3915
40314147 4263| 4379 | 4494 4610 | 4726 | 4841 | 4957 | 5072
5188 5303 5419 5534 5650 5765 5880 5996 6111 6226
6341 6457 6572 6687 6802 6917 7032 7147 7262 7377
7492 7607 7722 7836 7951 8066 8181 8295 8410 8525
8639 8754 88688983 90979212 | 9326|9441! 9555 | 9669
N.
5 6 7 89
3379 12.8 25.6 384 512 640 76.8 89.6 1024 1152
| |
3406
12.7 25°4 381 508 63.5 76.2 88.9 101.6 1143
3433 12.6 25°2 37.8
630 75.6 88.2 100-8 1134
3460 12.5 25.0
62.5 750 87.5 1000 112.5
23456 7∞ a
8
9
PROPORTIONAL PARTS.
I
2
ક્ષે
3
4
504
37.5
500
3488
12.4 24.8
372
496 62.0
49.6
62.0 74.4 86.8
3516
12.3 24.6
36.9 49°2
3545
2 3 4 SO 700
5
8
9
99.2111.6
98.4 | 110°7
976 | 109-8
96·8 | 108.9
96.0 108.0
12.2 24.4
3574 12.1 24°2
3604 12'0 24.0
3634 11.9 23.8
36.6 48.8
61.5 73.8 86.1
610 732 854
610 732 854
36.3 484 60.5 72.6 84.7
60·572-6847 |
360 480 600 720 840
35747-659-5714 83.3
95'2 107.1
F
MATHEMATICAL TABLES.
53

No. 380 L. 579.]
N.
LOGARITHMS OF NUMBERS.
I
2
3 451 6
7
[No. 414 L. 617.
|
N.
I
8 9
0583 | 0697 | 0811380
1722 1836 1950
2972 3085
4105 4218
41054218
5235 5348
380 579784 9898 0012 0126 0241 0355 0469
1580925 1039 1153 1267 1381 1495 1608
| | |
2063 2177 2291 2404 2518 2631 2745 2858
3199 3312 3426 3539 3652 3765 3879 3992
|
4331 4444 4557 4670 4783 4896 50095122
|
5461 5574 5686 5799 5912 6024 6137 6250 6362 6475
6587 6700 6812 6925 7037 7149 7262 7374 7486 7599 6
7711 7823 7935 8047 8160 8272 8384 8496 8608 8720
4
1 2 3 +56 7∞
|
8 8832 8944 9056 9167 9279 9391 9503 9615| 9726 9838
9950 co61 0173 0284 0396 0507 0619 0730 0842 0953
9
I
1 2 3 4 no 7∞•a
5
8
I
390 591065 1176 1287 1399 1510 1621 1732 1843 1955 2066 390
2177 2288 2399 2510 2621 2732 2843 2954 3064 3175
| |
3286 3397 3508 3618 3729 3840 3950 4061 4171 4282
| |
4393 4503 4614 4724 4834 4945 5055 5165 5276 5386
5496 5606 5717 5827 5937 6047 6157 6267 6377 6487
6597 6707 6817 6927 7037 7146 7256 7366 7476 7586
7695 7805 7914 8024 8134 8243 8353 8462 8572 8681
8791 8900 9009 9119 9228 9337 9446 9556 9665 9774
| |
9883 9992 OIOI 0210 0319 0428 0537 0646 | 0755|0864
9 600973 1082 1191 1299 1408 1517 1625 1734 1843 1951
| |
234567∞
8
400
I
2 3 4 56
78 9
10
|
2 3 456 78
9
I
2 3 4 no 78
2060 2169 2277 2386 2494 2603 2711 2819 2928 3036 400
3144 3253 3361 3469 3577 3686 3794 3902 4010 4118
|
4226 4334 4442 4550 4658 4766 4874 4982 5089 5197
5305 5413 5521 5628 5736 5844 5951 6059 6166 6274
6381 6489 6596 6704 6811 6919 7026 7133 7241 7348
7455 75627669 7777 7884 7991 8098 8205 8312 8419
8526 8633 8740 8847 8954 9061 9167 9274 9381 9488
9594 9701 9808 9914 0021 0128 0234 0341 0447 0554
8 610660 0767 0873 0979 1086 1192 1298 1405 1511 1617
| | |
1723 1829 1936 2042 2148 2254 2360 2466 2572 2678 9
27842890 2996 3102 3207 3313 3419 3525 3630 3736 410
3842 3947 4053 4159 4264 4370 4475 4581 4686 4792
4897 5003 5108 5213 5319 5424 5529 5634 5740 5845 2
5950 6055 6160 6265 6370 6476 6581 6686 | 6790|6895 3
7000 7105 7210 7315 7420 7525 7629 7734 7839 7943
| |
5
6 7
8
9
590 70.8 82.6 944 106.2
58-570°2 | 81.9 | 93⋅6 | 105.3
58.0
580 69.6 81-2 92.8 1044
57.5 690 80.5 920 103.5
570 68.4 79.8 91.2 102.6
56.567.8791 90'4 101'7
56.0
56.0 67.2 78.4 89.6 100-8
I
1 2 3 +
4
PROPORTIONAL PARTS.
N.
3665 11.8 23.6
3696 11'7 23.4
3727 11.6 23°2
I
2
3760
11.5 23.0
3792 11:4 22.8
· 3 4
35.4 47°2
35°1 46.8
34.8464
34'5 46'0
34°2 45'6
3826
33'9 45'2
3860
3895
3930
II'I 22.2
ΙΙΟ 22.0
11.3 22.6
II*2 224 33.6 44.8
33.6448
33°3 44'4
33°0 44'0
3966 IC'9 21.8 32°7 43.6
4002 10.8 21.6
4039 10.7 214
32.4 43°2
32°I 42.8
4077 10.6 21'2 31.8 42'4
4116
21'0 31.5 42.0
10'5
|
1
4
99'9
98.1
55.5 66.6 77.7 88.8
550 66.0 77.0 88.0 99'0
54-5 65.4 76.3 87.2
540 64.8 75.6 86.4
535 642 749 85.6
530 63.6 742 84.8
52.5 630 735 840
97.2
96.3
95'4
94'5
54
MATHEMATICAL TABLES.

No. 415 L. 618.]
N. о
I
LOGARITHMS OF NUMBERS.
[No. 459 L. 662.
2
3
4 5 6
7
8 9 N.
415 618048 8153 8257 8362 8466 8571 8676 8780 8884 8989 415
| |
9093 9198 9302 9406 9511 9615|9719 9824
6
78 9
420
I
1 2 3 +6
4
8
9
430
123456
4
|
6135 6238
|
7058 7161 7263
8082 8185 8287
9104 9206 | 9308
0224 0326
6
7
8
9
2
3456
78
|
0123
1139
||
1241 1342
2153
| |
2255 2356
3266 3367
9
|
I
2 3
4
6
5678
9928 0032
7 620136 0240 0344 0448 0552 0656 0760 | 0864 0968 || 1072
| | | |
1176 1280 1384 1488 1592 1695 1799 1903 2007 2110
|| |
|
2214 2318 2421 2525 2628 2732 2835 2939 3042 3146
|
3249 3353 3456 3559 3663 3766 3869 3973 4076 4179 420
4282 4385 4488 4591 4695 4798 4901 5004 5107 5210 I
5312 5415 5518 5621 5724 5827 5929 6032
6340 6443 6546 6648 6751 6853 6956
7366 7468 7571 7673 7775 7878 7980
5 8389 8491 8593 8695 8797 8900 9002
9410 9512 9613 9715 9817 9919 0021
7630428 0530 0631 0733 0835 0936 1038
1444 1545 1647 1748 1849 1951 2052
2457 2559 2660 2761 2862 2963 3064 3165
3468 3569 3670 3771 3872 3973 4074 4175 4276 4376 430
I 4477 4578 4679 4779 4880 4981 5081 5182 5283 5383
| |
5484 5584 5685 5785 5886 5986 6087 6187 6287 6388
6488 6588 6688 6789 6889 6989 7089 7189 7290 7390
7490 7590 7690 7790 7890 7990 8090 8190 8290 8389
8489 8589 8689 8789 8888 8988 9088 9188| 9287 | 9387
9486 9586 9686 9785 9885 9984 0084 0183 0283 0382
|
7640481 0581 0680 0779 0879 0978 1077 1177 1276| 1375
| | |
| |
1474 1573 1672 1771 1871 1970 2069 2168 2267 2306
2465 2563 2662 2761 2860 2959 3058 3156 3255 3354
3453 3551 3650 3749 3847 3946 4044 4143 | 4242 | 4340 440
|
4439 4537 4636 4734 4832 4931 5029 5127 5226 5324
|
5422 5521 5619 5717 5815 5913 6011 6110 6208 6306
6404 6502 6600 6698 6796 | 6894 | 6992 | 7089 7187 7285
|
7383 7481 7579 7676 7774 7872 7969 8067 8165 8262
|
8360 8458 8555 8653 8750 8848 8945 9043 9140 9237
|
9335 9432 9530 9627 9724 9821 9919 0016 0113 0210
|
7650308 0405 0502 0599 0696 0793 0890 0987 1084 1181
1278 1375 1472 1569 1666 1762 1859 1956 2053 2150
2246 2343 2440 2536 2633 2730 2826 2923 3019 3116
3213 3309 3405 3502 3598 3695 3791 3888 3984 4080 450
4177 4273 4369 4465 4562 4658 4754 4850 4946 5042
5138 5235 5331 5427 5523 5619 | 5715 5810 5906 6002
6098 6194 6290 6386 6482 6577 6673 6769 6864 6960
| |
7056 7152 7247 7343 7438 7534 7629 7725 7820 7916
| |
8011 8107 8202 8298 8393 8488 8584 8679 8774 8870
|
896590609155 9250 9346 9441 9536 9631| 9726 | 9821
9916 0011 0106 0201 0296 0391 0486 0581 0676 0771
8 660865 0960 1055 1150 1245 1339 1434 1529 1623 1718
1813 1907 2002 2096 2191 2286 2380 2475 2569 2663
N.
3 4
78 9
440
1234 in 1 ∞o a
6
8
450
I
2345678
9
PROPORTIONAL
PARTS.
in
་
9
I
2
3
4
5
6
7
78 9
9
I
2
3
456
78
9
I
2
5
6
7
8
9
4155 10'4 20.8 31.2 41.6 52.0
4196 10'3 20.6 30.9 41'2 51.5
4237 10'2 20.4 30.6 40.8 51.0
4278 ΙΟΙ 20'2 30.3 40°4 50.5
4321
20.0
10'0
4364
9.9 | 19.8
30.0 40.0
29.7 | 39.6
500
49'5
62.4 72.8 832 | 93.6
61.8 721 824 927
|
612 714 81.6 91-8
60.670.7 80.8 90.9
600 700 800 900
59469.3 79.2 89.1
MATHEMATICAL TABLES.
55

No. 460 L. 662.]
I
234
5
7
LOGARITHMS OF NUMBERS.
[No. 499 L. 698.
I
2
3
4
5 6
| 6
7
8
9
N.
I
23456
78
N. о
460 662758 2852 2947 3041 3135 3230 3324 3418 3512 3607460
3701 3795 3889 3983 4078 4172 4266 4360 4454 4548
4642 4736 4830 4924 5018 5112 5206 5299 5393 5487
5581 5675 5769 5862 5956 6050 6143 6237 6331 6424
6518 6612 6705 6799 6892 6986 7079 7173 7266 7360
7453 7546 7640 7733 7826 7920 8013 8106 8199 8293
8386 8479 8572 8665 8759 8852 8945 9038| 9131 9224
9317 9410 9503 9596 9689 9782 9875 9967 0060 0153
8670246 0339 0431 0524 0617 0710 0802 0895 0988 1080 8
9 1173 1265 1358 1451 1543 1636 1728 1821 1913 2005 9
2098 2190 2283 2375 2467 2560 2652 2744 2836 2929 470
I 3021 3113 3205 3297 3390 3482 3574 3666 3758 3850
3942 4034 4126 4218 4310 4402 4494 4586 4677 4769
4861 4953 5045 5137 5228 5320 5412 5503 5595 5687
5778 5870 5962 6053 6145 6236 6328 6419 6511 6602
6694 6785 6876 6968 7059 7151 7242 7333 7424 7516
7607 7698 7789 7881 7972 8063 8154 8245 8336 8427
8518 8609 8700 8791 8882 8973 9064 9155 9246 9337
9428 9519 9610 9700 9791 9882 9973 0063 0154 0245
680336 0426 0517 0607 0698 0789 0879 0970 1060 1151
470
23456 700
8
9
480
I
23456 DO
7
8
9
I
I
2
3456
7
8
9
I
2
3
456
78
7
8
9
1241 1332 1422 1513 1603 1693 1784 1874 1964 2055 480
2145 2235 2326 2416 2506 2596 2686 2777 2867 2957
3047 3137 3227 3317 3407 3497 3587 3677 3767 3857
3947 4037 4127 4217 4307 4396 4486 4576 4666 4756
4845 4935 5025 5114 5204 5294 5383 5473 5563 5652
5742 5831 5921 6010 6100 6189 6279 6368 6458 6547
6636 6726 6815 6904 6994 7083 7172 7261 7351 7440
7529 7618 7707 7796 7886 7975 8064 8153 8242 8331
8420 8509 8598 8687 8776 8865 8953 9042 9131 9220
|
9309 9398 9486 9575 9664 9753 9841 9930 0019 0107
490 690196 0285 0373 0462 0550 0639 0728 0816 0905 0993 490
1081 1170 1258 1347 1435 1524 1612 | 1700 1789 1877
1965 2053 2142 2230 2318 2406 2494 2583 2671 2759
2847 2935 3023 3111 3199 3287 3375 3463 3551 3639
3727 3815 3903 3991 4078 4166 4254 4342 4430 4517
4605 4693 4781 4868 4956 5044 5131 5219 5307 5394
5482 5569 5657 5744 5832 5919 6007 6094 6182 6269
6356 6444 6531 6618 6706 6793 6880 6968 70557142
7229 7317 7404 7491 7578 7665 7752 7839 7926 8014
|
8
8100 8188 8275 8362 8449 8535 8622 8709 8796 8883 9
N. 1 2 3
I
4 5 6789
4410 98 19.6 29'4
39°2 49'0 58.8 68.6 78.4 88.2
4454 9'7 19'4 29'I 38-8 485
4500 9.6 19.2
28.8 384
23456 78
9
PROPORTIONAL PARTS.
I
2
23
4
5
58-2
58.2 67.9 77.6 87.3
480
57.6
67.2 76.8 86.4
4547 9.5 19.0
28.5 38.0 47'5
57'0
66.5 76.0 85.5
4595 9'4 18.8 28.2 37.6 47'0
56.4
65.8752 84.6
4644 9'3
18.6 27.9
372
465
46.5
55.8
558
651 | 744 83.7
4695 9.2
18.4 27.6
36.8
46.0
55.2
64.4 73.6 82.8
4746 9.I
4798 9.0 18.0 27.0 36.0 45'0 54:0
18.2 27.3 36.4
45'5
546
63.7 72.8 81.9
4852 8.9 17.8
26.7 35.6
4907 8.8 17.6
44'5 53°4
264 352 44.0 52·8
63.0 72.0 81.0
62-371-280*1
61.67041 79°2
56
MATHEMATICAL TABLES.

No. 500 L. 698.]
N.
о
I
2
LOGARITHMS OF NUMBERS.
[No. 544 L. 736.
3
4
5
6
7
8
9 N.
500 698970 9057 | 9144 | 92319317|94049491 9578 9664 9751 500
9838 9924 0011 0098 0184 0271 0358 0444 0531 0617 I
I
23456 7∞ a
2 3 4 5 DOO a
6
2 700704 0790 0877 0963| 1050 1136 1222 1309 1395 1482
1568 1654 1741 1827 1913 1999 2086 2172 2258 2344
2431 2517 2603 2689 2775 2861 2947 3033 3119 3205
3291 3377 3463 3549 3635 3721 3807 3893 3979 4065
4151 4236 4322 4408 4494 4579 4665 4751 4837 4922
5008 5094 5179 5265 5350 5436 5522 5607 5693 5778 7
5864 5949 6035 6120 6206 6291 6376 6462 | 6547 6632
6718 6803 6888 6974 7059 7144 7229 7315 7400 7485
7570 7655 7740 7826 7911 7996 8081 8166 8251 8336 510
8421 8506 8591 8676 8761 8846 8931 9015 9100 9185 Ι
927093559440 9524 9609 9694 9779 9863 9948 0033
8
510
I
2
3456 78
520
I
3 710117 0202 | 0287 0371 0456 0540 | 0625 0710 0794 0879
0963 1048 1132 1217 1301| 1385 1470 1554 1639 1723
1807 1892 1976 2060 2144 2229 2313 2397 2481 | 2566
2650 2734 2818 2902 2986 3070 3154 3238 3323 3407
| | |
3491 3575 3659 3742 3826 3910 3994 4078 4162 4246
4330 4414 4497 4581 4665 4749 4833 4916 5000 5084
9 5167 5251 5335 5418 5502 5586 5669 5753 5836 5920
4
0123 & in 78 9
6
530
I
8
9
23456 7∞ a
8
I
23 456 7∞ a
8
9
I
6003 6087 6170 6254 6337 6421 6504 6588 | 6671 | 6754 520
6838 6921 7004 7088 7171 7254 7338 7421 7504 7587
7671 7754 7837 7920 8003 8086 8169 8253 8336 8419
8502 8585 8668 8751 88348917 9000 9083 9165 9248
9331 9414 9497 9580 9663 9745 9828 9911 9994 0077
720159 0242 0325 0407 0490 0573 0655 0738 0821 0903
0986 1068 1151 1233 1316 1398 1481 1563 1646 1728
| | | |
1811 1893 1975 2058 2140 2222 2305| 2387|2469 | 2552
2634 2716 2798 2881 2963 3045 3127 3209 3291 3374
3456 3538 3620 3702 3784 3866 3948 4030 4112 4194
4276 4358 4440 4522 4604 4685 4767 4849 4931 5013 530
5095 5176 5258 | 5340 5422 5503 5585 5667 5748 5830
5912 5993 6075 6156 6238 6320 6401 6483 6564 6646
6727 6809 6890 6972 7053 7134 7216 7297 7379 7460
7541 7623 7704 7785 7866 7948 8029 8110 8191 8273
8354 8435 8516 8597 8678 8759 8841 8922 9003 9084
9165 9246 9327 9408 9489 9570 9651 9732 9813 9893
9974 0055 0136 0217 0298 0378 0459 0540 0621 | 0702
8 730782 0863 0944 1024 1105 1186 1266 1347 1428 1508
1589 1669 1750 1830 1911 1991 2072 2152 2233 2313
2394 2474 2555 2635 2715 2796 2876 2956 3037 3117 540
3197 3278 3358 3438 3518 3598 3679 3759 3839 3919
3999 4079 4160 4240 4320 4400 4480 4560 4640 4720
4800 4880 4960 5040 5120 5199 5279 5359 5439 5519
5599 | 5679 | 5759583859185998 6078 6157 6237 6317
23456 7∞ a
9
540
1234
PROP. PARTS.
N.
I
2
3
4
5
6
7
4963
5020
5079
5139
3.
23456
7∞ a
8
9
123 +
4
8 9
8.7 17'4 26.1 34.8 43'5 52.2 609 69.6 78.3
8.6 17.2 25·8 34'4 43°0 51.6
68.8 77'4
60.2
17.0 25'5 34:0 42'5 510 59'5 68.076·5
16.8 25.2 33.6 42.0 50'4 58.8 672175.6
8.5
8:4
MATHEMATICAL TABLES.
57

No. 545 L. 736.]
LOGARITHMS OF NUMBERS.
[No. 584 L. 767.
N. O
I
2
3
4
5
6
7
8
9 N.
6
78 9
I
123456 176 9
560
I
2
4
6
78
70
9
I
23456 78
9
I
545 736397 6476 6556 6635 67156795 6874 6954 7034 7113 545
7193 7272 7552 7431 7511 7590 7670 7749 7829 7908
7987 8067 8146 8225 8305 8384 8463 8543 8622 8701
8781 8860 8959 9018 9097 9177 9256 9335 9414 9493
9572 9651 9731 9810 9889 9968 0047 0126 0205 0284
550 740363 0442 0521 0600 0678 0757 0836 0915 0994 1073 550
1152 1230 1309 | 1388 | 1467 1546| 1624 1703 1782 1860
1939 2018 2096 2175 2254 2332 2411 2489 2568 | 2647
2725 2804 2882 2961 3039 3118 3196 3275 3353 3431
3510 3588 3667 3745 3823 3902 3980 4058 4136 4215
4293 4371 4449 4528 4606 4684 4762 4840 4919 4997
5075 5153 5231 5309 5387 5465 5543 5621 5699 5777
5855 5933 6011 6089 6167 6245 6323 6401 6479 6556
6634 6712 6790 6868 | 6945 7023 7101 7179 7256 7334
7412 7489 7567 7645 7722 7800 7878 7955 8033 8110
8188 8266 8343 8421 8498 8576 8653 8731 8808 8885 560
8963 90409118 9195 9272 9350 9427 9504 9582 | 9659
9736 9814 9891 9968 0045 0123 0200 0277 0354 0431
3750508 0586 0663 0740 | 0817 0894 0971 1048 1125 1202
1279 1356 1433 1510 1587 1664 1741 1818 1895 1972
2048 2125 2202 2279 | 2356| 2433 2509|2586|| 2663 2740
2816 2893 2970 3047 3123 3200 3277 3353 3430 3506
3583 3660 3736 3813 3889 3966 4042 4119 4195 4272
4348 4425 4501 4578 4654 4730 4807 4883 4960 5036
5112 5189 5265 5341 5417 5494 5570 5646 5722 5799
5875 5951 6027 6103 61806256 | 6332 | 6408 | 6484| 6560 570
| 61036180 6256|6332|6408
6636 6712 6788 6864 6940 7016 7092 7168 7244 7320
7396 74727548 7624 7700 7775 7851 7927 8003 8079
8155 8230 8306 8382 8458 8533 8609 8685 8761 8836
8912 8988 9063 9139 9214 9290 9366 9441 9517 9592
9668 9743 9819 9894 9970 0045 0121 0196 0272 | 0347
6760422 0498 0573 0649 0724 07990875 0950 | 1025 1101
1176|| 1251 1326 1402 1477 1552 1627 1702 1778 1853
8 1928 2003 2078 2153 2228 2303 2378 2453 2529 2604
2679 2754 2829 | 2904 | 2978 | 3053 | 3128 3203 3278 3353
580 3428 3503 3578 3653 3727 3802 3877 3952 4027 4101 580
4176 4251 4326 4400 4475 4550 4624 4699 4774 4848
4923 4998 5072 5147 5221 | 5296 | 5370 5445 5520 5594
5669 5743 5818 5892 5966 6041 6115 6190 6264 6338
6413 6487 6562 6636 | 6710 6785 6859 6933 7007 7082
6
3tno 7∞ a
8
9
570
I
2
23
7
9
1234
2 3 4 5 6 7OO a
8
9
I
234 56 700 a
8
I
1234
PROPORTIONAL PARTS.
N.
I
2
3
4
5201
8.3
16.6
5
6
415 498
7
5264 8.2
5328 8.1
16.4
16.2
24933°2
246 32.8 41′0 49°2 574 65.6 73.8
8 9
581 664 74'7
24 3
32.4
40.5 48.6 56-7 648 729
5394 8.0 16.0
24 0
32.0
400 480
560 640 72.0
5462 79 15.8
237
31-6
39.5 47'4
55.3 63.2 71'1
5532
7.8
15.6
23.4
31.2
5603 7'7 15'4
23 I
30.8
5677 7.6 15.2
22.8
30.4
5752 7.5 15.0 22.5 30.0
5829 7'4 14.8 22.2
46.8 54.6 62.4 70°2
38.5 46.2 53.9 61.6 69.3
38.0 45.6 53.2 608 68.4
45'0 52.5 600 67.5
29.6 37.0 44.4 51.8 592 66.6
390
37.5
F
58
MATHEMATICAL TABLES.

LOGARITHMS OF NUMBERS.
No. 585 L. 767.]
N. O
23
I
6
56 78
590
I
1 2 3 456 7∞ a
8
9
600
1 2
[No. 629 L. 799.
4 5
6
7
8
9
N.
6
7
8
9
I
23 +6 7OO
5
8
9
I
585 767156 7230 7304 7379 7453 7527 7601 7675 7749|7823|585
7898 7972 8046 8120 8194 8268 8342 8416 8490 8564
8638 8712 8786 8860 8934 9008 9082 9156 9230 9303
9377 9451 9525 9599 9673 9746 9820 9894 9968 0042
9 770115 0189 0263 0336 0410 0484 0557 0631 0705 0778
03360410 | 05570631 |
0852 0926 0999 1073 1146 | 1220 | 1293 | 1367 1440 1514 590
1587 1661 1734 1808 1881 1955 2028 2102 2175 2248
| |
2322 2395 2468 2542 2615 2688 2762 2835 2908 2981
3055 3128 3201 3274 3348 3421 | 3494 3567 3640 | 3713
3786 3860 3933 4006 4079 4152 4225 4298 4371 4444 4
4517 4590 4663 4736 4809 4882 4955 5028 5100 5173
5246 5319 5392 5465 5538 5610 5683 5756 5829 5902
5974 6047 6120 6193 6265 6338 6411 6483 6556 6629
670167746846
6701 6774 6846 6919 6992 7064 7137 7209 7282 7354
7427 7499 7572 7644 7717 7789 7862 7934 8006 8079
8151 8224 8296 8368 8441 8513 8585 8658 8730 8802 600
8874 8947 9019 9091 9163 9236 9308 9380 9452 9524
9596 9669 9741 9813 9885 9957 0029 0101 0173 9245
780317 0389 046105330605 0677 0749 0821 0893 0965
1037 1109 1181 | 1253 | 1324 1396 1468 1540 1612 1684
1755 1827 1899 1971 2042 2114 2186| 2258|| 2329 | 2401
2473 2544 2616 2688 2759 2831 2902 2974 3046 3117
| | |
3189 3260 3332 3403 3475 3546 3618 3689 3761 3832
3904 3975 4046 | 4118 | 4189 4261 4332 4403 4475 4546
4617 4689 4760 4831 4902 4974 5045 5116 | 5187 | 5259
5330 5401 5472 5543 5615 5686 5757 5828 5899 5970 610
6041 6112 6183 6254 6325 6396 6467 6538 6609 6680 I
6751 6822 6893 6964 7035 7106 7177 7248 7319 7390
7460 7531 7602 7673 7744 7815 7885 7956 8027 8098
8168 8239 8310 8381 8451 8522 8593 8663 8734 8804
85228593 | 87348804
8875 8946 9016 9087 | 9157 9228| 9299 9369 | 9440 | 9510
93699440 |
9581 9651 9722 9792 9863 9933 0004 0074 0144 0215
790285 0356 0426 0496 0567 0637 0707 0778 0848 0918
0988 1059 1129 1199 1269 1340 1410 1480 1550 1620
1691 1761 1831 1901 1971 2041 2111 2181 2252 2322
| |
| |
4
mtino 78 9
610
I
123456
78 9
620
1
|
|
23456 7∞ a
8
H2
3
4
56 76 a
8
9
2392 2462 2532 2602 2672 2742 2812 2882 2952 3022 620
3092 3162 3231 3301 3371 3441 3511 3581 3651 3721
|
3790 3860 3930 4000 4070 4139 4209 4279 | 4349 | 4418
4488 4558 4627 46974767 4836 4906 4976 5045 5115
5185 5254 5324 5393 5463 5532 5602 5672 5741 5811
5880 5949 6019 6088 6158 6227 6297 6366 6436 6505
6574 6644 6713 6782 6852 6921 6990 7060 7129 7198
|
7268 7337 7406 | 7475 7545 7614 7683 7752 7821 7890
7960 8029 8098 8167 8236 8305 8374 8443 8513 8582
|
9 8651 8720 8789
8651 8720 8789 8858 | 8927 | 8996 | 9065913492039272
234no too a
7
8
PROP. PARTS.
N. I
2
3
+4
|
5
29.2
6
7
1234 SO NO0 a
5
7
8
8 9
36.543.8 511 584 65'7
28.8 36.0 43°2 504 57.6 64.8
28.4 35.5 42.6 49.7 56.8 63.9
5908 7:3
14.6 | 21°9
5990 7'2
21.6
14'4
6074 7'1 14.2 21°3
6160
7.0 14.0 21.0
28.0
6248 | 69 | 13.8
13.8 207 27-6
35°0 42'0
34.5
49°056.0 63.0
414 483 55°2 | 62°1
MATHEMATICAL TABLES.
59

i
No. 630 L. 799.]
LOGARITHMS OF NUMBERS.
[No. 674 L. 829.
N. O
I
2
3
4
5 16 7
8 ŷ N.
234
78 9
2637 2705
3321 3389
4003 4071
4685 4753
5365 5433
I
2 3 4 16 7∞ a
630 799341 9409 9478 9547 9616 9685 9754 9823 9892 9961 630
1800029 0098 0167 02360305 0373 0442 0511 0580 0648
0717 0786 0854 0923 0992 IC61 1129 1198 1266 1335
1404 1472 1541 1609 1678 1747 1815 1884 1952 2021
2089 2158 2226 2295 2363 2432 2500 2568
2774 2842 2910 2979 3047 3116 3184 3252
3457 3525 3594 3662 3730 3798 3867 3935
4139 4208 4276 4344 4412 4480 4548 4616
4821 4889 4957 5025 5093 5161 5229 5297
5501 5569 5637 5705 5773 5841 5908 5976 6044 6112
640 806180 6248 6316 6384 6451 6519 6587 6655 6723 6790 640
I 6858 6926 6994 7061 7129 7197 7264 7332 7400 7467
7535 7603 7670 7738 7806 7873 7941 8008 8076 8143
| |
8211 8279 8346 8414 8481 8549 8616 8684
8886 8953 9021 9088 9156 9223 9290 9358
5 9560 9627 9694 9762 9829 9896 9964 0031
6810233 0300 | 0367 0434 | 0501 0569 0636 0703
| | |
2
2 3
7
8
9
650
I
23456 7∞ a
8
9
660
8
9
I
8751 8818
9425 9492
0098 0165
07700837
4
5
6
7
8
23+ SO DOO a
I
23456 TO
7
8
0904 0971 1039 1106 11731240 1307 1374 1441 1508
|
1575 1642 1709 1776 1843 1910 1977 2044 2111 2178
2245 2312 2379 2445 2512 2579 2646 2713 2780 2847
2913 2980 3047 3114 3181 3247 3314 3381 3448 3514 650
35813648 3714 3781 3848 3914 3981 4048 4114 4181
4248 4314 4381 4447 4514 4581 4647 4714 4780 4847
4913 4980 5046 5113 5179 5246 5312 5378 5445 5511
5578 5644 5711 5777 5843 5910 5976 6042 6109 6175
6241 6308 6374 6440 6506 6573 6639 6705 6771 6838
67716838
6904 6970 7036 7102 7169 7235 7301 7367 7433 7499
7565 7631 7698 7764 7830 7896 7962 8028 8094 8160
|
8226 8292 8358 8424 8490 8556 8622 8688 8754 8820
|
88858951 9017 9083 9149 9215 9281 9346 9412 9478 9
9544 9610 9676 9741 9807 9873 9939 0004 0070 0136 660
|
1820201 0267 0333 0399 0464 0530 0595 0661 0727 0792
|
0858 0924 0989 1055 1120 1186 1251 1317| 1382 1448
|
|
1514 1579 1645 1710 1775 1841 1906 1972 2037 2103
2168 2233 2299 2364 2430 2495 2560 2626| 2691| 2756
2822 2887 2952 3018 3083 3148 3213 3279 3344 3409
3474 3539 3605 3670 3735 3800 3865 3930 3996 4061
4126 4191 4256 4321 4386 4451 4516 4581 4646 4711
4776 4841 4906 4971 5036 5101 5166 5231 5296|| 5361
5426 5491 5556 5621 5686 5751 5815 5880 5945 6010
| |
6075 6140 6204 6269 6334 6399 6464 6528 6593 6658 670
6723 6787 6852 6917 6981 7046 71117175 7240 7305
7369 7434 7499 7563 7628 7692 7757 7821 7886 7951
| |
8015 8080 8144 8209 8273 8338 8402 8467 8531 8595
| |
8660 8724 8789 8853 8918 8982 9046 91119175 9239
|
23456 too a
7
8
670
I
2
3
4
PROP. PARTS.
1
23456 78
9
2
3
4
8 9
6
7
40.8 47.6 544 61.2
402 | 469 53.6 60.3
39.646.252.8 594
N. I
6340 6.8
6433 6.7
6.6
2
13.6
6530
6630 6.5
6733 6.4 12.8
13'4 20'I
13.2 19.8
13.0 19'5
19.2
3
20'4 27.2 340
26.8 33°5
4
5
26.4 33°0
26.0
32.5
25.6 32.0
39°0
384
45'5 52.0 58.5
448 51°2 57.6
57
60
MATHEMATICAL TABLES.

No. 675 L. 829.]
LOGARITHMS OF NUMBERS.
[No. 719 L. 857.
N. о
I
2
3
4 5
6
7
8
9 N.
78 9
680
I
12345 7∞ a
8
9
690
I
4
23+36 7∞ a
8
9
700
I
|
678 a
9.
I
1.2 3456 700 a
8
9
I
123456 N∞ a
7
8
675 829304 9368 9432 9497 9561 9625 9690 9754 9818 9882 675
6 9947 0011 0075 0139 0204 0268 0332 0396 0460 0525
78305890653 0717 0781 0845 0909 0973 1037 1102 1166
1230 1294 1358 1422 1486 1550 1614 1678 1742 1806
1870 1934 1998 2062 2126 2189 2253 2317 2381 2445
2509 2573 2637 2700 2764 2828 2892 2956 3020 3083 680
3147 3211 3275 3338 3402 3466 3530 3593 3657 3721
3784 3848 3912 3975 4039 4103 4166 4230 4294 4357
4421 4484 45484611 | 4675 4739 | 4802 | 4866 | 4929|4993
5056 5120 5183 5247 5310 5373 5437 5500 5564 5627
5691 5754 5817 5881 5944 6007 6071 6134 6197 6261
6324 6387 6451 6514 6577 6641 6704 6767 6830 6894
6957 7020 7083 7146 7210 7273 7336 7399 7462 7525
7588 7652 7715 7778 7841 7904 7967 8030 8093 8156
8219 8282 8345 8408 8471 8534 8597 8660 8723 8786
8849 8912 8975 9038 9101 9164 9227 9289 9352 9415 690
9478 9541 9604 9667 9729 9792 9855 9918 9981 0043
2840106 0169 0232 | 0294 03570420 0482 0545 0608 0671
0733 0796 0859 0921 0984 1046 1109 1172 1234 1297
1359 1422 1485 1547 1610 1672 1735 1797 1860 1922
1985 2047 2110 2172 2235 2297 2360 2422 2484 2547
2609 2672 2734 2796 2859 2921 2983 3046 3108 3170
3233 3295 3357 3420 3482 3544 3606 3669 3731 3793
3855 3918 3980 4042 4104 4166| 4229 4291 4353 4415
4477 4539 4601 4664 4726 4788 4850 4912 4974 5036 9
5098 5160 5222 5284 5346 5408 5470 5532 5594 5656 700
5718 5780 5842 5904 5966 6028 6090 6151 6213 6275
6337 6399 6461 6523 6585 6646 6708 6770 6832 6894
6955 7017 7079 7141 7202 7264 7326 7388 7449 7511
7573 7634 7696 7758 7819 7881 7943 8004 8066 8121
8189 8251 8312 8374 8435 8497 8559 8620 8682 8743
8805 8866 8928 8989 9051 9112 9174 9235 9297 9358
94199481 9542 9604 9665 9726 9788 9849 9911 9972
88500330095 0156 0217 0279 0340 0401 0462 05240585
0646 0707 0769 | 0830 | 0891 0952 1014 1075 1136 1197 9
1258 1320 1381 1442 1503 1564 1625 1686 1747 1809 710
| || |
1870 1931 1992 2053 2114 2175 2236 2297 2358 2419
2480 2541 2602 2663 2724 2785 2846 2907 2968 3029
3090 3150 3211 3272 3333 3394 3455 3516 3577 3637
3698 3759 3820 3881 39414002 4063 4124 4185 4245
4306 4367 4428 4488 4549 4610 4670 4731 4792 4852
4913 4974 5034 5095 5156 5216 5277 5337 5398 5459
5519 5580 5640 5701 5761 5822 5882 5943 6003 6064
6124 6185 6245 6306 6366 6427 6487 6548 6608 6668
6729 67896850 6910 6970 703170917152 | 7212 | 7272
N. I
6839 6.3 12.6
6948 6.2
12.4
7061 6.1 12.2
7178❘ 6.0
123456 7∞ a
OH 23 †SO 78 a
9
710
I
4
9
PROP.
PARTS.
9
I
23 456 7∞
8
I
1234 ISO 7∞0 a
6
441504 56.7
434 49.6 55.8
2
12.0
3 4 5
6
189 25°2 31'5
37.8
18.6 24.8 31'0 37°2
18.3 244 30.5 36.6
18.0 24'0 30.0 36.0
7 8
8
42.7 48.8 549
420 480 54'0
|
MATHEMATICAL TABLES.
61

No. 720 L. 857.]
LOGARITHMS OF NUMBERS.
[No. 764 L. 883.
N. о
I
2
3
4
5
6
7
៖
9
N.
I
2
1 2 3 4 56
41
78
9
730
I
2
3456 78
0757
0218 0278
0817 0877
1415 1475
2012 2072
2608 2668
3204 3263
I
4
1 2 3 & 56 78 a
9
I
23 +46 78
5
720857332 7393 7453 7513 7574 7634 7694 7755 7815 7875 720
7935 7995 8056 8116 8176 8236 8297 8357 8417 8477
|
85378597
8537 8597 8657 8718 8778 8838 8898 8958 9018 9078
9138 9198 9258 9318 9379 9439 9499 9559 9619 9679
9739 9799 9859 9918 9978 0038 0098 0158
5860338 0398 0458 0518 0578 0637 0697
| |
0937 1996 1056 1116 1176 1231 1295 1355
|
1534 1594 1654 1714 1773 1833 1893 1952
2131 2191 2251 | 2310 | 2370 | 2430 2489 2543
2728 2787 2847 2906 2966 3025 3085 3144
3323 3382 3442 3501 3561 3620 3680 3739 3799 3858 730
3917 3977 4036 4096 4155 4214 4274 4333 4392 4452
4511 4570 4630 4689 4748 4808 4867 4926 4985 5045
5104 5163 5222 | 5282 | 5341 5400 5459 5519 5578 5637
5696 5755 5814 5874 5933 5992 6051 6110 6169 6228
6287 6346 6405 6465 6524 6583 6642 6701 6760 6819
6878 6937 6996 7055 7114 7173 7232 7291 7350 7409
7467 7526 7585 7644 7703 7762 7821 7880 7939 7998
|
8056 8115 8174 8233 8292 8350 8409 8468 8527 8586
9 8644 8703 8762 8821 8879 8938 8997 9056 9114 9173 9
9232 9290 9349 9408 9466 | 9525 9584 9642 9701 9760 740
9818 9877 9935 9994 0053 0111 0170 0228 0287 0345
2870404 0462 0521 0579 0638 0696 0755 0813 0872 0930
0989 1047 1106 1164 1223 1281 1339 1398 1456| 1515
1573 1631 1690 1748 1806 1865 1923 1981 2040 2098
2156 2215 2273 2331 2389 2448 2506 2564 2622 2681
2739 2797 2855 2913 2972 3030 3088 3146 3204 3262
3321 3379 3437 3495 3553 3611 3669 3727 3785 3844
3902 3960 4018 4076 4134 4192 4250 4308 4366 4424
4482 4540 4598 | 4656 | 4714 4772 4830 4888 4945 5003
5061 5119 5177 5235 5293 5351 5409 5466 5524 5582 750
5640 5698 5756 5813 5871 5929 5987 6045 6102 6160
2 6218 6276 6333 6391 6449 6507 6564 6622 6680 6737
3 6795 6853 6910 6968 7026 7083 7141 7199 7256 7314
7371 7429 7487 7544 7602 7659 7717 7774 7832 7889
7947 8004 8062 8119 8177 8234 8292 | 8349 8407 8464
8522 8579 8637 8694 8752 8809 8866 8924 8981 9039
9096 9153 9211 9268 9325 9383 9440 9497 9555 9612
9669 9726 9784 9841 9898 9956 0013 0070 0127 0185
|
|
8
9 880242 0299 0356 0413 0471 0528 0585 0642 0699 0756 9
740
I
23 456 78
9
750
I
78
8
760
I
234
I
123456 700
9
I
2
3
4
6
I
2
0814 0871 0928 0985 1042 1099 1156 1213 1271 1328 760
1385 1442 1499 1556 1613 1670 1727 1784 1841 1898
1955 2012 2069|2126 | 2183 2240 2297 2354 2411 2468
2525 2581 2638 2695 2752 | 2809 | 2866 2923 2980 3037
3093 3150 3207 3264 3321 3377 3434 3491 3548 3605 4
|
3
PROP.
PARTS.
N.
I
2
3
4
5
6
་
7
8 9
7299
5'9
7423 5.8
7552 5'7
86
11.8 17.7
114
23.6 29.5
11.6 17.4 23.2
17.1 22.8
29.0
41.3472 53.1
34.8 40.6 464 52.2
28.5 34°2 39.9 45.6 51.3
35°4
62
MATHEMATICAL TABLES.

No. 765 L. 883.]
LOGARITHMS OF NUMBERS.
[No. 809 L. 908.
N.
O
I
2
3
4
5
6 7
8
9 N.
6
78
56 7∞ 9
7
4682 4739
5248 5305
5813 5870 8
6378 6434
765 883661 3718 3775 3832 3888 3945 4002 4059 4115 4172 765
4229 4285 4342 4399 4455 4512 4569 4625
4795 4852 49094965 | 5022 5078 5135 5192
5361 5418 5474 5531 5587 5644 5700 5757
5926 5983 6039 6096 6152 6209 6265 6321
| |
6491 6547 6604 6660 6716 6773 6829 6885
9
770
I
2 3 4 iO
8
9
780
I
|
|
|
6942 6998 770
I
2
7505 7561
7054 7111 7167 7223 7280 7336 7392 7449
| |
7617 7674 7730 7786 7842 7898 7955 8011 8067 8123
8179 8236 8292 8348 8404 8460 8516 8573 8629 8685 3
8741 8797 8853 8909 8965 9021 9077 9134 9190 9246 4
9302 9358 9414 9470 9526 9582 9638 9694 9750 9806 5
9862 9918 9974 0030 0086 0141 0197 0253 0309 0365
679
8
I
7 890421 0477 0533 0589 0645 0700 0756 0812 0868 0924
0980 1035 1091 11471203 1259 1314 1370 | 1426 | 1482
1537 1593 1649 1705 1760 1816 1872 1928 1983 2039 9
2095 2150 2206 | 2262 | 2317 | 2373 2429 2484 2540 2595 780
2651 2707 2762 2818 2873 2929 2985 3040 3096 3151
3207 3262 3318 3373 3429 3484 3540 3595 3651 3706
3762 3817 3873 3928 3984 4039 4094 4150 4205 | 4261
4316 4371 4427 4482 4538 4593 4648 4704 4759 4814
| | |
4870 4925 4980 5036 5091 5146 5201 5257 5312 5367
| |
5423 5478 5533 5588 5644 5699 5754 5809 5864 5920
5975 6030 6085 6140 6195 6251 6306 6361 6416 6471
| |
6526 6581 6636 6692 | 6747 6857 6912 6967 7022
7077 7132 7187 7242 7297 7352 7407 | 7462 7517 | 7572
1234 SO T∞
7
8
9
790
I
3
4
2mt no 7∞ a
6
8
1800
I
123+ SO DO
8
9
PROP.
PARTS.
6802
1 2 3 4 5 7∞ a
6
8
I
2 3 4 no 700 a
5
6
8
9
7627 7682 7737 7792 7847 7902 7957 8012 8067 8122 790
8176 8231 8286 8341 8396 8451 8506 8561 8615 8670
8725 8780 8835 8890 8944 8999 9054 9109 9164 9218
9273 9328 9383 9437 9492 9547 9602 9656 9711 9766
9821 9875 9930 9985 0039 0094 0149 0203 0258 0312
|
900367 0422 0476 0531 0586 0640 0695 0749 0804 0859
05310586
|
091309681022 1077 1131 1186| 1240 1295 1349|| 1404
| |
1458 1513 1567 1622 1676 1731 1785 1840 1894 1948
2003 2057 2112 2166| 2221 22752329 2384 2438 2492
|
23842438
2547 2601 2655 2710 2764 2818 2873 2927| 2981 3036
3090 3144 3199 3253 3307 3361 3416 3470 3524 3578 800
| |
3633 3687 3741 | 3795 | 3849 | 3904 | 3958 | 4012 | 4066 | 4120 I
4174 4229 4283 4337 439 4445 44994553 4607 4661
4716 4770 4824 | 4878 | 4932 4986 5040 5094 5148 5202
5256 5310 5364 5418 5472 5526 5580 5634 5688 5742
56345688
5796 5850 5904 5958 6012 6066 6119 6173 6227 6281
6335 6389 6443 6497 6551 6604 6658 6712 6766 | 6820
| |
6874 6927 6981 7035 7089 7196 7250 7304 7358
7411 7465 7519 7573 7626 7734 7787 7841 7895
7949 8002 8056 8109 8163
8270 8324 8378 8431
82708324 | |
7143
7680
8217
N. I
2
3
7686 5.6
7825 5'5 II O
7968 5'4 10.8
II.2
16.8
4 5
22.4 28.0
6
33-6
|
1234 NO 78 a
9
7
8 9
392 448 504
16.5 22'0 27.5 33°0 38.5 440 49'5
16.2
21.6
27.0 32.4
37.8432 48.6
MATHEMATICAL TABLES.
63

No. 810 L. 908.]
N.
I
2
LOGARITHMS OF NUMBERS.
[No. 854 L. 931.
5
6
7
8
9
N.
3
4
810 908485 8539 8592 8646 | 86998753 8807 8860 8914 8967 810
| |
I 9021 9074 9128 9181 9235 9289 9342 9396 9449 9503
9556 9609 9663 9716 9770 9823 9877 9930 6984 0037
2
3456 7∞ a
8
9
820
I
I
2
4
5
6
7
8
9
~ 3+nO DO GO Ham +56 7∞ a o
I
2
3 910091 0144 0197 025103040358 | 0411 0464 | 0518 0571
0624 0678 0731 0784 0838 0891 0944 0998 1051 1104
|
| |
1158 1211 1264 1317 1371 1424 1477 1530 15841637
1690 1743 1797 1850 1903 1956 2009 2063 2116 2169
2222 2275 2328 2381 2435 2488 2541 2594 2647 2700
2753 2806 2859 2913 2966 | 3019 | 3072 3125 3178 3231
3284 3337 3390 3443 3496 3549 3602 3655 3708 3761
3814 3867 3920 3973 4026 4079 4132 4184 4237 4290 820
4343 4396 4449 4502 4555 4608 4660 4713 4766 4819
4872 4925 4977 5030 5083 5136 5189 | 5241 | 5294 5347
| |
|
5400 5453 5505 5558 5611 5664 5716 5769 5822 5875
| | |
| |
5927 59806033 6085 6138 | 6191 | 6243 6296 6349 6401
| | |
6454 6507 6559 6612 6664 6717 6770 6822 6875 6927
|
6980 7033 7085 7138 7190 7243 7295 7348 7400 7453
7506 7558 7611 7663 7716 7768 7820 78737925 7978
|
|
8030 8083 8135 8188 8240 8293 8345 8397 8450 8502
8555 8607 8659 8712 8764 8816 8869 8921 8973 9026
|
9078 913091839235928793409392 | 9444 9496 9549 830
9601 9653 9706 9758 9810 9862 9914 9967 0019 0071
2 3 4 5O Z∞ a
7
8
9
830
I
HO
8
9
840
I
23456 7oo a OH 2 m +6 78 9
|
3
4
8
I
1234 SO ZO0 a
6
7
8
9
I
2 920123 0176 0228 0280 0332 0384 0436 0489 0541 0593
0645 0697 0749 0801 0853 0906 0958 1010 1062 1114
1166 1218 1270 1322 1374 1426 1478 1530 1582 1634
1686 1738 1790 1842 1894 1946 1998 2050 2102 2154
2206 2258 2310 2362 2414 2466 2518 2570 2622 2674
2725 2777 2829 2881 29332985 3037 3089 3140 3192
3244 3296 3348 3399 34513503 355536073658 3710
3762 3814 3865 3917 3969 | 4021 | 4072 | 4124 4176 4228
4279 4331 4383 4434 4486 4538 4589 4641 4693 4744 840
4796 4848 4899 4951 5003 5054 5106 5157 5209 5261
5312 5364 5415 5467 5518 5570 5621 5673 5725 5776
5828 5879 5931 5982 6034 6085 6137 6188 6239 6291
|
6342 6394 6445 6497 6548 6600 6651 6702 6754 6805
| |
6857 6908 6959 70117062 7114 7165 7216 7268 7319
7370 7422 7473 7524 7576 7627 7678 7730 7781 7832
| |
|
7883 7935 7986 8037 8088 8140 8191 | 8242 | 8293 | 8345
8396 8447 8498 8549 8601 8652 8703 8754 8805 8857
8908 8959 9010 9061 9112 9163 9215 9266 9317 9368
|
|
9419 9470 9521 9572 9623 9674 9725 9776 9827 9879 850
9930 9981
0032 0083 0134
2930440 0491 0542 0592 0643
| | |
0949 1000 1051 1102 1153
1458 1509 1560 1610 1661
3
4
5
850
I
234
PROP.
PARTS.
123456 7∞ 9
8
I
0185 0236 0287 0338 0389
2
0694 0745 0796 0847 0898
069407450796 | |
1203 1254 1305 1356 1407
| |
3
1712 1763 1814 1864 1915 4
8
6
7
37°1
31.8
9
42.4 47.7
36.441-646-8
4
3
5
21.2
15'9
26.5
5.2 10'4 15.6 20.8 26.0 31.2
N.
I
2
8117
5:3
10.6
8271
8432
5'I
10.2 | 15°3 20'4 25.5 30.6
35.7 40.8 459
64
MATHEMATICAL TABLES.

No. 855 L. 931.]
6
78 9
860
1234 36 700
8
2
456 7∞
LOGARITHMS OF NUMBERS.
[No. 899 L. 954-
I
2
3
4
5
6
7
8
9 N.
2322
2829
3335
2372 2423 855
2879 2930
3386 3437
|
3892 3943
| |
4397 4448
678 a
I
2 3 4 i 70 a
8
I
23456 7∞ a
N. о
855 931966 2017 2068 2118 2169 2220 2271
2474 2524 2575 2626 2677 2727 2778
2981 3031 3082 3133 3183 3234 3285
3487 3538 3589 | 3639 3690 3740 3791 3841
|
3993 4044 4094 4145 4195 4246 4296 4347
4498 4549 4599 4650 4700 4751 4801 4852 4902 4953 860
5003 5054 5104 5154 5205 5255 5306 5356 5406 5457
5507 5558 5608 5658 5709 5759 5809 5860 5910 5960
6011 6061 6111 6162 6212 6262 6313 6363 6413 6463
6514 6564 6614 6665 6715 6765 6815 6865| 6916 6966
7016 7066 7116 7167 7217 7267 7317 7367 7418 7468
7518 7568 7618 7668 7718 7769 7819 7869 | 7919 | 7969
|
8019 8069 8119 8169 8219 8269 8319 8370 8420 8470
8520 8570 8620 8670 8720 8770 8820 8870 8920 8970
9 9020 9070 9120 9170 9220 9270 9319 9369 9419 9469
870
9519 9569 9619|9669|9719|9769 9819 9869||9918|9968|870
1940018 0068 0118 0168 0218 0267 0317 0367 0417 0467
0516 0566 0616 0666 0716 0765 0815 0865 0915 0964
1014 1064 1114 1163 1213 1263 1313 1362 | 1412 || 1462
1511 1561 1611 1660 1710 1760 1809 1859 1909 1958
2008 2058 2107 2157 2207 2256 2306 2355 2405 2455
2504 2554 2603 2653 2702 2752 2801 2851 2901 2950
3000 3049 3099 3148 3198 3247 3297 3346 3396 3445
3495 3544 3593 3643 3692 3742 3791 3841 3890 3939
3989 4038 4088 4137 4186 4236 4285 4335 4384 4433
4483 4532 4581 4631 | 4680 4729 4779 4828 4877 4927 880
4976 5025 5074 5124 5173 5222 5272 5321 5370 5419
| | |
5469 5518 5567 5616 5665 5715 5764 5813 5862 5912
5961 6010 6059 6108 6157 6207 6256 6305 6354 6403
6452 6501 6551 6600 6649 6698 6747 6796 | 6845 6894
|
6943 6992 7041 7090 7139 7189 7238 7287 7336 7385
7434 7483 7532 7581 7630 7679 7728 7777 7826| 7875
7924 7973 8022 8070 8119 8168 8217 8266 8315 8364
8413 8462 8511 8560 8608 8657 8706 8755 8804 8853
8902 8951 8999 9048 9097 9146 9195 9244 9292 | 9341
9390 9439 9488 9536 9585 9634 9683 9731 9780 9829 890
I 9878 9926 9975 0024 0073 0121 0170 0219 0267 0316
2 950365 0414 0462 0511|0560 | 0608 | 0657 0706 0754 0803
3 0851 0900 0949 | 0997 1046 1095 1143 1192 1240 1289
4 1338 1386 1435 1483 1532 1580 1629 1677 1726 1775
1823 1872 1920 1969 2017 2066 2114 2163 2211 2259
2308 2356 2405 2453 2502 2550 2599 2647|| 2696| 2744
2792 2841 2889 2938 2986 3034 3083 3131 3180 3228
| |
3276 3325 3373 3421 3470 3518 3566 3615 3663 3711
3760 3808 3856 39053953 4001 4049 4098 4146 | 4194
8
9
880
Ι
1234 ISO 70 a
6
9
890
6
8
PROP.
PARTS.
8
I
23456 7OO
8
9
I
2
5
346 7∞
8
9
N. I 2
3
4
5
8599
8773 49
8954 4.8 9.6
5'0 ΙΟ
9.8
15.0
147 | 19.6
14'4 192
20'0
6
7
25.0 30°0 35°0
24'5 29.4 34°3
24.0 28.8
33.6
8
9
400 450
39°244'1
38.443.2
MATHEMATICAL TABLES.
65

I
.2
23 456 78
9
910
I
2
4
56
78
L. 954.]
I
LOGARITHMS OF NUMBERS.
|
|
[No. 944 L. 975-
I
2
HN 34 no 7∞
6
8
23456 7∞ a
No. 900
N.
i | 2
3 4 5
6 ! 7
8
9 IN.
900 954243 4291 4339 4387 4435 4484 4532 | 4580 | 4628 4677 900
4725 4773 4821 4869 4918 4966 5014 5062 5110 5158
5207 5255 5303 5352 5399 5447 5495 5543 5592 5640
| |
| | | |
5688 5736 5784 5832 5880 5928 5976 6024 6072 6120
6168 6216 6265 6313 6361 6409 6457 6505 65536601
6649 6697 6745 6793 6840 6888 6936 6984 7032 7080
7128 7176 7224 7272 7320 7368 7416 7464 7512 7559
7607 7655 7703 7751 7799 78477894 7942 7990 8038
8086 8134 8181 8229 8277 8325 8373 8421 8468 8516
|
8564 8612 8659 8707 8755 8803 8850 8898 8946 8994 9
9041 9089 9137 9185 9232 9280 9328 9375 9423 9471 910
9518 9566 9614 9661 9709 9757 9804 9852 9900 9947 I
9995 0042 0090 01380185 0233 0281 0328 0376 | 0423
3960471 0518 0566 0613 0661 0709 0756 0804 0851 0899
0946 0994 1041 1089 1136 1184 1231 1279 13261374
1421 1469 1516 1563| 1611 1658 1706 1753 1801 1848
1895 1943 1990 2038 2085 2132 2180 2227 2275 2322
2369 2417 2464 2511 2559 2606 2653 2701 2748 2795
2843 2890 2937 2985 3032 3079 3126 3174 3221 3268
3316 3363 3410 3457 3504 3552 3599 3646 3693 3741
| |
3788 3835 3882 3929 3977 4024 4071 4118 4165 4212 920
4260 4307 4354 4401 4448 4495 4542 4590 4637 4684
|
4731 4778 4825 4872 4919 4966 5013 5060 5108 5155
5202 5249 5296 5343 5390 5437 5484 | 5531 5578 5625
5672 5719 5766 5813 5860 5907 5954 6001 6048 6095
6142 6189 6236 6283 6329 6376 6423 6470 6517 6564
6611 6658 6705 6752 6799 6845 6892 6939 6986 7033
7080 7127 7173 7220 7267 7314 7361 7408 7454 7501
7548 7595 7642 7688 7735 7782 7829 7875 7922 7969
80168062 8109 8156 8203 8249 8296 8343 8389 8436
8483 8530 8576 8623 8670 8716 8763 8810 8856 8903 930
8950 8996 9043 9090 9136 9183 9229 9276 9323 9369
9416 9463 9509 95569602 9649 9695 9742 9789 9835
9882 9928 9975 0021 0068 0114 0161 0207 0254 0300
4970347 0393 0440 0486 05330579 0626 0672 0719 0765
0812 0858 0904 0951 0997 1044 1090 1137 1183 1229
1276 1322 1369 1415 1461 1508 1554 1601 1647 1693
1740 17861832 | 1879 | 1925 1971 2018 2064 2110 2157
8 2203 2249 2295 2342 2388 2434 2481 2527 2573 2619
2666 2712 2758 2804 2851| 2897 2943 2989 3035 3082
8
9
920
I
2
3456
7
8
9
930
I
2 3
456 7∞
9
1940
I
-
8
9
I
2345O DOO a
6
7
8
1
2
4
5
6
3tno 78 9
3128 3174 3220 3266 3313 3359 3405 3451 3497 3543 940
3590 3636 3682 3728 3774 3820 3866 3913 3959 4005
I
3
4
2 4051 4079 4143 | 4189 4235 4281 4327 4374 4420 4466
4512 4558 4604 4650 4696 4742 4788 4834 4880 4926
4972 5018 5064 | 5110 5156 | 5202 | 5248 | 5294 5340 5386
2
3
4
N.
I
2
PROP.
PARTS.
9143
4.7
9'4
9339
4.6 9.2
9544 4.5 9'0
3 4
18.8
14'1
13.8
13.5
18.0
5
6
28.2
23'5
18.4 23.0 27.6 32.2
22.5 27.0 31.5
7
8
9
32.9
37.6 42.3
36.8 414
36.0 40.5
66
MATHEMATICAL TABLES.

No. 945 L. 975.]
N.
O
LOGARITHMS OF NUMBERS.
[No. 989 L. 995-
I
2
3
4
5
6
7
8
9 N.
6
78 9
950
I
2 3 4 5 6 7∞ a
960
8
I
23456 too a
7
1184
6
7
8
9
I
2 3 4 SO DO a
5
6
7
8
9
I
3
5
6
2 3 4 SO 7∞ a
945 975432-5478 5524 5570 5616 5662 5707 5753 5799 5845 945
5891 5937 5983 6029 6075 6121 6167 6212 6258 6304
6350 6396 6442 6488 6533 6579 6625 6671 | 6717 | 6763
|
6808 6854 6900 6946 6992 7037 7083 7129 7175 7220
7266 7312 7358 7403 7449 7495 7541 7586 7632 7678
7724 7769 7815 7861 7906 7952 7998 8043 8089 8135 950
8181 8226 8272 8317 8363 8409 8454 8500 8546 8591
8637 8683 8728 8774 8819 8865 8911 8956 9002 9047
9093 913891849230 | 9275 9321 | 9366 | 9412 9457 9503
9548 9594 9639 9685 9730 9776 9821 9867| 9912 | 9958
5980003 0049 0094 0140 0185 0231 0276 0322 | 0367 | 0412
0458 050305490594 0640 0685 0730 0776 0821 0867
0912 0957 1003 1048 1093 1139 1229|| 1275 1320
1366 1411 1456 1501 1547 1592 1637 1683 1728 1773
1819 1864 1909 1954 2000 2045 2090 2135 2181 2226
2271 2316 2362 2407 2452 2497 2543 2588 | 2633 | 2678 960
2723 2769 2814 2859 2904 2949 2994 3040 3085 3130
3175 3220 3265 3310 3356 3401 3446 3491 3536 | 3581
3626 3671 3716 3762 3807 3852 3897 3942 3987 4032
4077 4122 4167 4212 4257 4302 4347 4392 4437 4482
4527 4572 4617 4662 4707 4752 4797 4842 4887 4932
4977 5022 5067 5112 5157 5202 5247 5292 5337 5382
5426 5471 5516 5561 5606 5651 5696 5741 5786 5830
5875 5920 5965 6010 6055 6100 6144 6189 6234 6279
6324 6369 6413 6458 6503 6548 6593 6637 6682 6727
6772 6817 6861 6906 6951 6996 7040 7085 7130 7175 970
7219 7264 7309 7353 7398 7443 7488 7532 7577 7622
7666 7711 7756 7800 7845 7890 7934 7979 8024 8068
8113 8157 8202 8247 8291 8336 8381 8425 8470 8514
8559 8604 8648 8693 8737 8782 8826 8871 8916 8960
9005 9049 9094 9138 9183 9227 9272 9316 9361 9405
9450 9494 9539 9583 9628 9672 9717 9761 9806 9850
9895 9939 9983 0028 0072 0117 0161 0206 0250 0294
8990339 0383 0428 0472 0516 0561 0605 | 0650 0694 0738
0783 0827 0871 0916 0960 1004 1049 1093 1137 1182 9
1226 1270 1315 1359 1403 1448 1492 1536 1580 | 1625 980
1669 1713 1758 1802 1846 1890 1935 1979 2023 2067
|
2111 2156 2200 2244 2288 2333 2377 2421 2465 2509
2554 2598 2642 2686 2730 2774 2819 2863 2907 2951
29953039 3083 | 3127 | 3172 | 3216 | 3260 3304 3348 3392
3436 3480 3524 3568 3613 3657 3701 3745 3789 3833
3877 3921 3965 4009 4053 4097 4141 4185 4229 4273
4317 4361 4405 4449 4493 4537 4581 4625 4669 4713
4757 4801 4845 4889 4933 4977 5021 5065 5108 5152
5196 5240 5284 5328 | 5372 5416 5460 | 5504 | 5547 | 5591
8
970
I
23 456 7∞
9
980
I
23 tinO DOO a
8
9
I
24456
78
I
2 3 4 56
-7
8
9
PROP.
PARTS.
N.
I
2
3
4
9759
4:4
8.8
9983 4.3 8.6
5
6
13.2 17.6 22.0 26.4 30.8
12.9 17.2 21.5 25.8 30'I
7
*8
9
35.2 39.6
34'4 38.7
MATHEMATICAL TABLES.
67

No. 990 L. 995]
N.
I
23456 too a
LOGARITHMS OF NUMBERS.
I
2
3
4
[No. 999
L. 999.
ŷ
N.
CO
I
23 456 78
56 7
990 995635 5679 5723 5767 5811 5854 | 5898 5942 5986 6030 990
58545898 6030990
6074 6117 6161 6205 6249 6293 6337 6380 6424 6468
6512 6555 6599 6643 6687 6731 6774 6818 6862 6906
|
6949 6993 7037 7080 7124 7168 7212 7255 | 7299 | 7343
7386 7430 7474 7517 7561 7605 7648 7692 7736 7779
| || | |
7823 7867 7910 7954 7998 8041 8085 8129 8172 8216
8259 8303 8347 8390 8434 8477 8521 8564 8608 8652
8695 8739 8782 8826 8869 8913 8956 9000 9043 9087
9130 9174 9218 9261 9305 9348 9392 9435 9479 9522
9565 9609 9652 9696 97399783|9826|9870 | 9913 | 9957
TABLE II.—LOGARITHMS OF NUMBERS FROM I TO 100.
Log. N. Log. N.
7
8
9
N.
Log. N. Log. N.
41
I 0·000000 [21 | 1*322219 161278461 1785330
2 0·301030 ||22| 1°342423 42 1623249|| 62 | 1*792392
30477121|23| 1°361728 || 43 1633468 | 63 1799341
4 0.602060 24 1380211 44 1643453 64 1.806180
50-698970 25 1397940 45 1653213 65 1812913
60-778151 ||26| 1414973 46 1.662758 || 66 | 1819544
70845098 27 1431364 47 1672098 67 1.826075
8 090309028 1447158 48 1.681241 68 1-832509
90954243|29| 1462398|| 49 1690196 69 1-838849
IO 1'000000 30 1'477121 50 1.698970 70 1.845098
11 104139331 1491362 || 51 1707570 71 1-851258
|
12 107918132 1.505150 || 52 1716003 72 1-857332
13 1113943 33 1'518514 53 1724276 || 731-863323
14 114612834 1531479 54 1732394|| 74 1.869232
15 117609135 1544068 55 1740363 75 1875061
16 120412036 1.556302|| 56 1748188|| 76 1.880814
17 1230449 37 1568202 57 1755875 77 1.886491
18 1255273 38 1579784 58 1763428 781-892095
19 1278754 39 1-591065 59 1770852 79 1.897627
20 130103040 1.602060 60 1778151
|| |
|
Log.
9
81 1-908485
82 1-913814
83 1-919078
84 1924279
85 1.929419
86 1.934498
87 1939519
88 1-944483
89 1949390
90 1'954243
91 1'95904.1
92 1-963788
93 1.968483
94 1973128
95 1977724
|
96 1-982271
97 1-986772
98 1991226
991-995635
80 1.903090 || 100
2'000000
TABLE III.
Sign Value Sign Value Sign Value
| |
in-2nd at in 3rd at in 4th at
at 90°. Quad. 180º.
Quad. 270°. Quad. 360°.
Value
at oº.
Sign
in ist
Value
Quad.
Ꭱ
R
Sin....
Tan....
Sec
Versin
Cos....
Cot.....
Cosec..
++
R 8 8 ROOF
OOROR 8 8
Ꭱ
+11 +11+
Ꭱ
2 R
R
1 +1 +1 +1
A 8 8 ROOR
Ꭱ
| 1+++1 |
K signifies equal to rad; ∞ signifies infinite; O signifies evanescent.
OOROR 8 8
68
MATHEMATICAL TABLES.

TABLE IV.—LOGARITHMIC SINES.
•I
$2
*3
'4
*5
O。
5
6 241877 249056
256118
5°463726 5.764756 5'940847 6·065786 | 6·162696 89 59
1 6.463726 6.505119 6.542907 6.577669
2 764756 785945 806149 825454
3
609854 639817 58
843937 861666
57
56
940847 955088 968876 982240 995205 7007794
47.065786 7.076510 | 7·086975 7097194 7107179 116938 55
162696 171296 179729 188002 196120
204089 54
263066|| 269906|| 276639 53
7
308824 314984
8 366816 372211 377540
321058
327049 332958 338787 52
382804 388005
393145 89 51
O
ΙΟ
II
9 7417968 7422767 | 7°427513 7°432208 7°436853 | 7441449
463725 468047 472326 476563 480759 484915
505118 509048 512943 516804 520630 524423
50
49
48
12
542906 546511
550085 553630 557147
560635 47
13
577668 580996
584299
587577
590830
594059
46
14
609853 612944
616013
619061
622087
625093 45
15
639816 642702
645568
648416
651245
654056 44
16
667845 670550
673239
675912
678568
681208 43
17
694173 696720 699253 701770
704273 706762 89 42
1 2 2 2 2 2 2 2
2 2 2 3 3
20
21
22
0 18 7.718997 7·721403 | 7723795 | 7-726175
19 742477 744757 747025 749281
764754 766920
766920 769075 771220
785943 788006 790059 792103 794137
806146 808115 810076 812028
7728542 | 7·730896
41
751525 753758
40
773354 775477
39
796162
38
813971
815905 37
23
825451 827335
829211
831079
832939
834791 36
24 843934
843934 845740
847538 849329
851112
852888 35
25
861662 863396 865123 866843 868556
870262 34
26 878695 880362
882023 883678 885326
886968 89 33
28 910879 912428
29
30
31
926119 927614 929104
940842 942287 943727
955082 956481
957875
32 968870 970225
971576
0 277-8950857-8966917-8982917-899884 7.901472 7.903054 32
918566
930589 932068 933543 30
945163 946594
948020 29
959264 | 960650
28
962031
972922 974265 975603 27
33 982233 983547 984857 986164 987466 988764 26
34 995198 996473 997745 9990138.000277 8.001538 25
35 8.007787 8.009026 8010261 8011493 012722 013947 89 24
o 36 8.020021 8021225 8.022427 8.023625 8.024819 8.026011
913970 915508 917039
31
23
38
39
40
4I
37 031919 033092 034261 035426 036589
043501 044642 045781 046916 048048
054781 055893 057003 058109 059213
065776 066861
076500 077558
037749
22
049178
21
42 086965 087997
090056
060314
067942 069021 070098 071171
078613 079666 080716 081764 18
089028
20
19
091081
092104 17
43
097183 098192
099198
100203
101204 102204
16
44
107167 108153
109136
110118
45
116926 117890 118852 119812
111097
120769
112074 15
121725 89 14
ΙΟ
*9
.8
'7
.6
5
Log. Cosines.
MATHEMATICAL TABLES.
69

TABLE IV.-LOGARITHMIC SINES.
•6
.8
*9
I'O
6-241877
6.308824
6-366816
6-417969
6463726 89 59
|
I
667846
694175
718999
742480
764756
58
23456 7O
878699
895090
910884
926124
940847
57
7020028
7031928
7043510
7'054791
7.065786
56
126484
135824
144967
153922
162696
55
211914
219601
227154
234578
241877
54
283270
289801 296235
302575
308824
53
344539 350217 355820
361353
366816
52
8
398224 403245 408208
413116
417968 89 51
9
7'445998
7*450497
7'454952
7°459361
7463725
50
10
489031
493109 497149
501152
505118
49
I I
528183
531911 535607
539272
542906
48
12
564096
567529
570935
574315
577668 47
13
597264
600445
603604
606740
609853
46
14
628078
631042
633986
636911
639816
45
15
656849
659624
662382
665122
667844
44
16
683832
68644I
689034
691611
694173
43
17
709237
711697
714144
716577
718997 89 42
o 18
7'733237
7'735566
7737882
7°740186
7'742477
41
19
755980
758190
760389
762577
764754
40
20
777591
779694 781787
783870
785943
39
21
798177 800183 802180
804167 806146
38
22
817831
819749
821658
823558
825451
37
23
836635
838471
840300 842120
843934
36
24
854657
856419
858174
859922
861662
35
o 27
2 2
2 2 2 33
25
871962
873655
875342
877022
878695
34
26
888603
890233
891856
893474
895085
89 33
7.904630 | 7906201 | 7907766 | 7°909326
7.909326
7910879
32
28
920087
921603
923113
924619
926119
31
29
935012
936477
937937 939392
940842
30
30
949442
950859
952271
953679
955082
29
31
963407 964779
966147
967511 968870
28
32
976937 978267
979593
980915
982233
27
33
990058 991349
992636
993919
995198
26
34
8.002795
8.004048
8.005298
8.006544
8.007787
25
35
015168 016386
017601
018813
020021
89 24
0 36
8-0271998-028384 | 8:029566 | 8·030744
8.030744
8.031919
23
41
42
43
44
45
£ £ £ £ £ £ www.
37
038905
040059 041209
042356
043501
22
38
050304
051428
052549
053666
054781
061412
062507 063599
064689
065776
40
072242 073310
082809
093125
103201
074376
083851 084892
094143 095159
104196 105188
075439 076500
085929 086965
113049
114021
122678
123629
114992
124579
096172 097183
106179 107167
115960 116926
125526
126471
89 14
2 2 HHHHHH
21
20
19
18
17
16
15
4
*3
*2
*I
Ο
Log. Cosines.
70
MATHEMATICAL TABLES.

00
TABLE IV.-LOGARITHMIC SINES.
'O
'I
$2
'3
'4
*5
45 8.116926 8117890 8-118852 8.119812 8.120769 8-121725 89 14
46| 126471 127414 128355 129294 130231 131166 13
47 135810 136733 137654 138574 139491 140406 12
48
144953
145857
146759 147659
148557
149453 II
49
153907
I 54793
50
162681
163548
51
171280
172131
155676 156558
164414
172980
157438
158316
ΙΟ
165279
166141 167002
173827
174673
175517
52 179713 180547 181380 182211
183041
183868
in in
55 204070
53 187985 188803 189620 190436
54 8.196102 8.196905 8.197707 8.198508 8.199307 8-200104
204859 205646 206432
191250
192062 89 6
98 76
5
207217 208000
4
56
211895 212670 213443 214215 214986
215755
3
57
219581
220342
221102 221861
222618
223374
58
227134 227882
228628
229374
230118
230861
59
234557 235292
236026
236759
237491
238221 89
ར
I
2
I
OHN
241855 242578
243300
24402 I
24474I
245459
I
249033 249744 250455
251164
251871
252578
2 10 000
in in
I
59
58
9
IO
II
3456 7∞ ao -
256094 256794 257492
38·263042 8·263731 | 8·264419 8-265105 | 8.265791 | 8·266475
269881 270559 271236
258190 258887 259582 89 57
56
271912 272587 273260
55
276614 277281 277948
278613
279278
27994I
54
283243 283901
284557
285213
285867
286521 53
289773 290421
291068
291713
292358
293002
52
8
296207 296845
297482
298118 298754
299388
51
302546 303174
303803 304430
305056
305681
50
308794 309414
310033 310651 311268
311885 49
314954 315565
316175| 316784 317393 318001 89 48
I 12 8 321027 8.321629 8.322231 | 8.322832 | 8.323433 | 8.324032
13
14
HH
15
16
17
18
2 346 NO
47
327016 327611 | 328204
328204
332924 333511
338753
33933I
344504 345075
350181
355783
328797 329389 329980
334096 334681
339909 340486
345645 346215
350744 351307 351869
356340 | 356895 357450
19 361315 361864 362413 362961
20 3.66777 367319
367319 367861 368402 368943
1 21 8-372171 8.372707 8.373242 8.373776 8.374310 8.374843
46
335265
335848
341063 341638 44
346784 347352 43
45
352430 352991 42
358004
358558 41
363508
364054 40
369482 88 39
38
23
29
WNNNNNN
24
25
26
27
403199
28
408161
22 377499 378028 378557 379084
382762 383285 383807 384329
387962 388479 388995
393101 393611 394121 394631
398179 398684 399188 399691
403698 404196
408654 409147
379612
380138 37
384850 385370 36
389510
390025 390539 35
395139 395647 34
400194 400696 33
404694
405191 405687 32
409639
410130 410621 31
413068
30
417919
413555 414042
418401 418883 419364
414529
415015
419844
415500 30
420324 88 29
ΙΟ
*9
.8
'7
.6
'5
Log. Cosines.
MATHEMATICAL TABLES.
71
}

'7
·6
TABLE IV.-LOGARITHMIC SINES.
·8
*9
ΙΟ
45
8.122678
8.123629
8:124579
8-125526
8.126471
89 14
46
I 32099
133030
133959
134885
135810
13
47
141319
142231
143140
144048
144953
12
48
150348
151241
152131
153020
153907
I I
49
159193
160067
160940
161811
162681
10
50
167861
168718
169574
*70428
171280
51
176359 177200
178039
$78877
179713
52
184695 185520
186343
187165
187985
53
192873
193683
194491
195297
196102
89 6
98. 76
• 54
8.200900
8.201695
8.202488
8.203280
8.204070
5
55
208782
209562
210341
211119
211895
4
56
216523
217289
218055
218819
219581
3
57
224128 224881
225634
226384
227133
2
58
231603 232343
233082
233820
234557
I
59
238951
239679
240405
241131
241855 89
I о
246176
246892
247607
248321
249033
59
I
253284
253988
254691
255393
256094 58
2
260276
260970
261662
262352
263042 88 57
I
3
8.267158
4
273933
8.267841 8.268522
274605
8.269202
8.269881
56
275275
275945
276614
55
56 780
280604 281265
281925
282585 283243
54
287173 287825 288475
293645 294287
289125 289773
53
294928
295568
296207
52
300021
300654
301286
301916
302546
51
9
306306 306929
307552
308173
308794
IO
312500 313115
313729 314342
314954
I I
318608
319214 319819
320423
321027
88 48
I 12
8-324630
8-3252288-325825
8.326421 | 8.327016
13
330571
331160 331749
332337
332924
14
33643I 337012
337593
338174
338753
15
342213 342787
343360
343933 344504
16
347919 348485
349051
349616 350180
43
17
353551 354110
354669
355226 355783
18
359111 359663
360214
360765 361315
4I
19
364600
365145
365690
366234
366777
is good fo4$ 7 7 7 !
50
49
47
46
45
44
42
40
20
370021
370560
371095
371635 372171
88 39
I 21
8-375375
8-375907
8-376438
8.376969
8.377499
38
22
380664 381190
381714
382239 382762
37
23
385889 386409
386927
387445 387962
36
24
25
26
28
29
2 2 2 2
+ no no a
391053 391566
392078
392590
393101
35
396155 396662
397168
401198 401699 402200
27.
406183
406679
411112
411601
397674 398179
402700
407173 407668 408161
4.12091 412579
34
403199
33
32
413068
3I
415985
416469
416953
417436
417919
30
30
420804
421283
422762
422239
422717
88 29
4
*3
*2
•I
Ο
Log. Cosines.
72
MATHEMATICAL TABLES.

0 Deg.
TABLE V.-LOG. SINES, ETC.
Sine
Cosec.
Tang. Cotang. Sec. D. Cosine
10'00
0000
o0.000000 Infinite. ooooooo Infinite.
16·463726|13·536274 6·463726 13.536274 0000
2 764756 235244 764756 235244 0000
3 940847 059153 940847 059153 0000
47.065786 12.934214 7065786 12'934214 0000
5 162696 837304 162696
6 241877 758123 241878
7 308824 691176 308825
8 366816 633184 366817
O
0000
0000
02 Deg.
10'000000
60
O
0000
59
58
о
0000
57
о
0000
56
о
8373040000
758122 0001
691175 0001
633183 0001
55
о
9'999999
54
I
9999
53
I
9999
89 52
I
o 97417968 12.582032 7°417970 12.582030 0001
10 463725 536275 463727
II 505118 494882 505120
12 542906 457094-
13 577668 422332
14 609853 390147 609857
15 639816 360184 639820
16 667845 332155 667849
17 694173 305827 694179
9'999999
SI
I
536273 0002
9998
50
I
494880 0002
9998
49
I
542909
4570910003
9997
48
577672
422328 0003
I
9997
47
I
390143 0004
9996
360180 0004
I
9996
I
332151 0005
9995
I
305821 0005
9995 89 43
I
o 187718997 12:281003 7.719003
19 742477 257523
12:2809970006
9*999994
742484
257516 0007
I
9993
4I
20 764754 235246
I
764761
235239 0007
9993
21 785943 214057
I
785951
214049 0008
9992
22 806146 193854
I
806155
193845 0009
9991
24 843934 156066
23 825451 174549
825460
I
174540 0010
9990
I
843944
156056 0011
9989
25 861662 138338
861674
2
138326 0011
9989
26 878695 121305 878708
121292 | 0012
2 2
33 982233 017767 982253
29 926119 073881 926134
30 940842 059158
31 955082 044918
32 968870 031130 968889
0 277.895085 12-104915 7-895099 12 104901 0013
28 910879 089121 910894
35
9988 89
9*999987
2
089106 0014
9986
073866 0015
2
9985
2
940858
059142 0017
9983
30
2
955100
0449000018
9982
2
0311110019
9981
28
2
0177470020
9980
27
~~wwwwwwwwwww A‡‡ ‡‡‡÷:
46
45
44
42
40
39
38
37
36
34
32
34 995198
004802
995219 004781 0021
2
9979
26
35 8.007787 11-992213 8.007809 11992191 0023
0 36 8.020021 11.979979 8.020045 11'979955 0024
2
9977 89 25
2
9*999976
24
Cosine
40 065776
934224 065806
41 076500 923500
42 086965 913035 086997
43 097183 902817 097217
44 107167 892833
45 116926
90 Deg.
107202
883074 116963
Secant Cotang.
37 031919
38 043501 956499 043527
39 054781 945219 054809
2
968081
031945
968055 0025
9975
23
956473 0027
2
9973
22
945191 0028
2
9972
21
2
934194 0029
9971
20
076531
923469 0031
2
9969
19
2
9130030032
9968
18
2
902783 0034
9966
17
2
892798 0036
9964
3
883037 0037
Tang. Cos. D.
16
9963 89 15
76
Sine
891 Deg.
MATHEMATICAL TABLES.
73

0 Deg.
TABLE V.-LOG. SINES, ETC.
Sine Cosec. Tang. Cotang. Sec. D.
10'00
0458-116926 11.883074 8.116963 11-883037 0037
46
126471
873529
47 135810 864190 135851
33
1 Deg.
Cosine
9*999963
15
126510
873490 0039
3
9961
14
864149 0041
9959
13
48 144953
49 153907
855047 144996
846093 153952
•
855004 0042
3
9958
12
846048 0044
3
9956
I I
50 162681
837319 162727
837273 0046
3
9954
ΙΟ
51 171280
I
758145 241921
750967 249102
828720 171328
820287 179763
52 179713]
53 187985 812015 188036
o 54 8.196102 11.803898 8.196156
55 204070 795930 204126
56 211895 788105 211953
57 219581 780419 219641
58 227134 772866
59 234557 765443 234621
1 o 241855
249033
2 256094 743906
743906 256165
11.803844 0054
8.263042 11.736958 8.263115 11736885 | 0073
828672 0048 3
9952
820237 0050
811964 0052
3
9950
ܣܗ
9
8
33
9948 89 7
9*999946
6
795874 0056
788047 0058
780359 0060
227195
772805 0062
765379 0064
758079 0066
9932
59
9929 88 58
I
9'999927
57
4 269881 730119 269956
7300440075
9925
56
7 289773
8 296207
9 302546
10 308794
5 276614 723386 276691
6 283243 716757 283323
710227 289856
703793 196292
723309 0078
9922
55
716677 0080
9920
710144 0082
703708 0085
4
54
9918
697454 302634
697366 0087
+4
53
9915
52
9913
691206
691206 308884
691116 0090
4
51
9910
50
I I 314954
685046 315046
684954 0093
9907 88 49
750898 0068
743835 0071
3344++++++++
0044
5
9942
4
9940
3
9938
2
9936
I
9934 89 O
1 128.32102711-678973 8.321122 11678878 0095
13 327016 672984 327114
14 332924
15 338753
16 344504
667076 333025
661247 338856
655496 344610
17 350181 649819 350289
18 355783 644217 355895
19 361315 638685 361430
20 366777 633223 366895
1 21 8.37217111*627829 8.372292 11627708 0121
22 377499 622501 377622
672886 0098
666975 0101
661144 0103
655390 0106
649711 0109
644105 0112
638570 0115
633105 0118
+44 + in in in in in ini
9'999905 48
9902
47
4
9899
46
5
9897 45
9894
44
9891
43
9888
42
9885
4I
9882 88 40
9*999879
39
5
622378 0124
9876
23 382762 617238 382889
617111 0127
9873
38
37
24 387962
612038 388092
611908 0130
9870
36
***70 000 NO
333 M
25 393101 606899 393234
606766 0133
9867
35
26 398179
601821 398315
601685 0136
9864
34
27 403199
596801 403338
596662 0139
9861
33
28 408161 591839 408304
591696 0142
9858 32
29 413068
586932
586932 413213
586787 0146
30 417919
Cosine
582081 418068
Secant Cotang.
5
581932 0149
Tang. Cos. D.
9854 31
9851 88 30
Sine
891 Deg.
88 Deg.
G
74
MATHEMATICAL TABLES.

1 Deg.
Sine
D.
TABLE V.-LOG. SINES, ETC.
Cosec. Tang. D.
Cot. Sec. D. Cos.
21 Deg.
8.
II*
8.
II* 10'00
9'99
58 535523 6106
6158
59 539186
20542819
I 546422
2549995
3553539
1 30 417919
31422717
32 427462 7909
7823
33 432156
34 436800 7740
35441394
36445941
37 450440
38 454893
I 39459301
40463665
41 467985
42 472263
43 476498
44 480693
45 484848
46 | 488963
47 493040
I 48 497078
49 501080
50 505045
51 508974
52 512867
53 516726
54 520551
55 524343
56 528102
I 57 531828
7996
8002
7914
7828
7745
7657
7663
7577
7499
7422
7346
7583
7273
7200
7129
7505
7428
7352
7279
7206
582081 418068
577283 422869
572538 427618
567844 432315 567685 0159
563200 436962
558606 441560
554059 446110
549560 450613 549387 0173 9827
545107 455070 544930 01776
540699 459481
536335 463849
532015 468172
581932 0149
6 9851
577131 0152
6
9848
572382 0156
6
9844
2 2 2
30
29
28
6
9841
27
563038 0162
558440 0166
69838
26
6/9834
25
553890 0169
6 9831
24
6
23
9823 88 22
540519 0180
536151 0184
6
9820
21
7060
7135
7066
531828 0188 6 9812
6
9816
20
19
6991
6924
6931
6859
6865
6794
6731
6801
6738
527737 472454
523502 476693
519307 580892 519108 01996
515152 585050
511037 589170
506960 593250
527546 0191
6
6998 523307 0195
6
9809
18
9805
17
9801
16
514950 0203
9797
15
7
510830 0207
9793
14
506750 0210
7
9790 88
13
7
6669
6608
6548
6489
6432
6375
6319
6264
6211
502922 597293 6676
498920 501298
494955 505267
491026 509200
502707 0214
9786
12
6615
498702 0218
7
9782
ΓΙ
7
6555
6496
6439
6382
6326
6272
494733 0222
9778
10
490800 0226 9774
7
6055
6004
5 560540
4 557054 5811
5955
5906
5858
460814 539447 6062
457181 543084 6012
453578 546691
450005 550268
446461 553817
464477 535779 6113
486902 0231
487133 513098|
483274 516961
479449 520790
475657 524586 475414 0243 9757
471898 528349 6218 471651 0247 9753
468172 532080 6165 467920 0252
7
9769
483039 0235
7
9765
479210 0239
7
7
7
9761
88
98 76 54
7
9748
3
464221 0256
9740
460553 0260
7
7
9744
2
I
456916 0265
7
9735 88 O
5962
453309 0269
7
9731
59
449732 0274
9726
58
442946 557336
5914
5866
5765
439460 560828
5819
446183 0278
442664 0283
439172 0287
8
9722
57
N
6 563999
7 567431
8 570836
9 574214
5773
∞ ∞
9717
8
56
8
9713 87 55
436001 564291
5719
5674
5630
10 577566 5587
II 580892
12 584193
13 587469
14 590721
15 593948
432569 567727
429164 571137
425786 574520
422434 577877
5544
5552
419108 581208
5502
5510
415807 584514
5460
5468
412531 587795
5419
4427
409279 591051
5379
5387
406052 594283
Cos. D. Sec. Cot. D.
5727
5682
5638
435709 0292
432273 0296
428863 0301
8
9708
54
9704
53
9699
52
5595
425480 0306
422123 031I
9694
51
9689
50
418792 0315 9685
415486 0320 9680
8
412205 0325 9675 47
8
408949 0330 9670
49
48
88 Deg.
46
405717 0335 9665 87 45
Tang. Cos. D. Sine
87 Deg.
MATHEMATICAL TABLES.
75

21 Deg.
Sine D.
8.
Cosco. Tang. D.
TABLE V.-LOG. SINES, ETC.
Cot. Sec. ID. Cos.
3 Deg.
II'
8.
1 I'
10'00
9'99
215 593948|
16 597152
17 600332
18 603489
19 606623
20 609734
21 612823
22 615891
23 618937
2 24 621962
25624965
26 627948
27 630911
28 633854
29 636776
30 639680
31 642563
32 645428
2 33 648274
34 651102
35 653911
36 656702
37 659475
38 662230
39 664968
40 667689
41 670393
2 42. 673080
43 675751
44 678405
45 681043
46 683665
47 686272
48 688863
49 691438
50 693998
2 51 696543
52699073
53 701589
54 704090
55 706577
56 709049
57 711507
58 713952
59 716383
60 718800
5339
5300
5261
5223
5186
406052 594283
402848 597492
399668 600677
396511 603839
393377 606978
390266 610094
5347
5308
405717 0335
402508 0340
399323 0345
5270
∞ ∞ ∞
8
9665
8
9660
なま
​45
44
8
9655
43
5232
396161 0350
9650
42
8
393022 0355
9645
41
5194
5149
387177 613189
5158
389906 0360
9
9640
40
5112
5076
5041
384109 616262
381063 619313
5121
386811 0365
9635
39
5085
383738 0371
9629 38
380687 0376
5050
9624 87 37
9
5006
4972
4938
4904
4871
4839
4806
4775
4743
378038622343
375035 625352
372052 628340
369089 631308
366146 634256|
363224 637184
360320 640093
357437 642982
354572 645853
377657 0381
9619
36
5015
4981
4947
4913
4880
4848
4816
4784
4753
374648 0386 9614
371660 0392 9608
9
368692 0397 9603
9
365744 0403 9597
9
362816 0408 9592
9
359907 0414 9586
9
357018 0419
9
9
9
35
9
34
33
32
31
30
9581
29
351726 648704
4712
4682
4652
4622
4592
4563
4535
4506
4479
445I
Cos. D.
872 Deg.
348898 651537
346089 654352
343298 657149
340525 659928
337770 662689
335032 665433
332311 668160
329607 670870
326920 673563
324249 676239
4424
321595 678900
4397
318957 681544
4370
316335 684172
4344
313728 686784
4318
311137 689381
4292
308562 691963
4267
306002 694529
4242
303457 697081
4217
300927 699617
4192
298411 702139
4168
295910 704646
4144
293423 707140
4121
290951 709618
4097
288493 712083
4074 286048 714534
4051
283617 716972
4029
281200 719396
Sec. Cot. D.
4722
4691
348463 0436
354147 0425 9575 87 28
351296 0430
86∞
9570
27
9564
26
4661
345648 0442
9558
25
4631
342851 0447
9553
24
IO
46c2
I
4573
I
4544
4517
4488
4461
4434
4407
4380
4354
4328
4303
4277
4252
4228
4203
4179
321100 0494
318456 0500 9500
315828 0507 9493
313216 0513 9487
310619 0519
3080370525
ΙΟ
IO
ΙΟ
IO
IO
340072 0453 9547
337311 0459
334567 0465 9535
331840 0471 .9529
329130 0476 952487 19
326437 0482
9518
323761 0488 9512
23
954I
22
21
10
20
IO
18
17
9506
16
15
14
13
ΙΟ
9481
12
IO
9475
II
ΙΟ
305471 0531
9469 87 10
302919 0537 9463
300383 0544 9456
297861 0550 9450
4062
4040
295354 0557 9443
4155 292860 0563
9437
4132
|290382 0569 9431
4108
287917 0576 9424
4085
285466 0582
IO
II
II
II
II
II
II
II
98 76
4
3
283028 0589
II
II
9418
9411
2
I
280604 0596 9404 87 O
Tang. Cos. D. Sine
87 Deg.
76
MATHEMATICAL TABLES.

о
3 Deg.
Sine D.
8.
TABLE V.-LOG. SINES, ETC.
Cosec. Tang. D. Cot.
32 Deg.
Sec. D. Cos.
I I'
8.
II' 10.00
9'99
3 0 718800
6
7735354
8737667
I 721204
2 723595
3725972
4728337
5 730688
733027 3877
4006
3984
281200 719396
278796 721806 4017
3995
276405 724204
3962
280604 0596
9404 870
278194 0602
3941
3919
3898
3857
274028 726588
271663 728959
269312 731317 3930
266973 733663
264646 735996
3974
3952
275796 0609 9391
273412 0616 9384
II
II
II
9398
59
58
II
57
3909
271041 0622
268683 0629
9378
56
II
266337 0636
3889
II
11 9371
55
9364
12
54
3 9 739969
10 742259
262333 738317
3836
260031 740626
3816
3868
3848
264004 0643
261683 0650
9357
12
53
9350 86
12
52
3827
259374 0657
9343
12
51
II 744536 3796
257741 742922
3756
12 746802 3776 255464 745207
3807
257078 0664
9336
12
50
253198 747479
3787
254793 0671
9329
16
13 749055
3737
14751297
3749
248703 751989
3717
15 753528 246472 754227
3698
755747 3678 244253 756453
17 757955 3661 242045 758668
250945 749740
3768 252521 0678
12
49
9322
48
12
250260 0685
9315
12
47
248011 0692
9308
3729
12
46
3710
245773 0699
9301
45
3692 243547 0706 9294
3673
241332 0714 9286 86 43
12
12
12
44
3 18 760151
19 762337
20 764511
21 766675
22768828
23 770970
24 77310I
25 775223
26
777333
3 27 779434
3642
3624
239849 760872
237663 763065
3655
3606
3588
3570
3553
3535
3518
3501
235489 765246
233325 767417
231172 769578
229030 771727|
3636
239128 0721
236935 0728
12
9279
9272
42
3618
234754 0735 9265
3600
3583
3484
3467
3451
3418
3354
3323
3308
D.
28 781524
29 783605
30 785675
31 787736 3434
32 789787
33 791828 3402
3386
34 793859
35 795881 3370
3 36 797894
37 799897 3339
38 801892
39 803876
40 805852 3293
3278
41 807819
42 809777
43 811726 3249
44 813667 3234
45 815599 3219
Cos.
87 Deg.
186333 814589 3248
184401 816529 3233
Sec. Cot. D.
Tang.
224777 775995
222667 778114
220566 780222
226899 773866 3565
3548
3531
3514
218476| 782320| 3497 217680 0795
216395 784408
214325 786486
212264 788554 3447
210213 790613
208172 792662 3415
206141 794701
204119 796731
202106 798752
200103 800763
198108 802765 3337
196124 804758 3322
194148 806742 3307
192181 808717
3263
190223 810683
188274 812641
12
12
232583 0743 9257
12
230422 0750 9250
13
228273 0758 9242
226134 0765 13
9235
13
224005 0773 9227 35
13
221886 0780
9220 86 34
13
219778 0788 9212
13
4I
40
ww
39
38
37
36
333
33
3480
3464
9205
343 I
3399
3383
3368
215592 0803
213514 0811 9189
13
211446 0819
209387 0826 9174
207338 0834
13
9197
13
33 3
32
31
30
9181
29
13
28
13
9166
27
205299 0842
203269 0850
13
9158
26
13
9150 86 25
13
201248 0858
3352
9142
24
199237 0866
13
9134
23
197235 0874
13
9126
22
195242 0882
13
9118
21
3292
3277
3262
13
193258 0890
9110
20
13
191283 0898 9102
13
189317 0906 9094
14
187359 0914 9086
14
185411 0923 9077
14
183471 0931 9069 86 15
Cos. D. Sine
19
18
17
16
861 Deg.
MATHEMATICAL TABLES.
77

3 Deg.
Sine
8.
D.
Cosec.❘ Tang.
TABLE V.—LOG. SINES, ETC.
Sec. D. Cos.
4 Deg
D. Cot.
II'
8.
I I' 10'00
9.99
3 45 815599
46 817522
47 819436
48 821343 3177
3205
3191
49 823240
50 825130
51 827011
52 828884
53 830749
3 54 832607
55 834456
56836297
57 838130
58 839956
59 841774
3163
3149
3135
3122
3108
3095
184401 816529
182478 818461
180564 820384
178657 822298
176760 824205
174870 826103
3219
183471 0931 9069
15
3205
3191
181539 0939
179616 0947 14
14
9061
14
9053
13
3177
3163
3150
171116 829874
169251 831748
172989 827992 3136 172008 0981 9019
14
177702 0956 9044
175795 0964 9036
173897 0973
12
14
I I
14
14
9027
10
9
3123
3108
3082
3069
3056
167393 833613
165544 835471
163703 837321
161870 839163
3096
3083
3070
3043
3057
160044 840998
3030
158226 842825
3045
40843585 3017
I 845387 3005
2 847183
2992
156415 844644
154613 846455
152817 848260
2980
3032
3019
3007
170126 0990 14
168252 0998 14
166387 1007 8993
14
164529 1016
162679 1024
160837 1033
159002 1042
157175 1050
155356 1059
153545 1068
151740 1077
9010
9002 86
14
In4m2 = 0 G8 76
HH
++
8984
14
8976
14 8967
5
15
8958
15 8950
15
15 8941 86
8932
59
15 8923
58
2995
15
4321
o non
0
4 3
3 848971
2967
4
5
850751
852525
6 854291 2943
7 856049
8 857801
9859546
10 861283
II 863014
4 12 864738
2955
2931
2919
2908
2896
2884
2873
151029 850057
149249851846
147475 853628
145709 855403
143951857171
142199 858932
140454 860686
138717 862433
136986 864173
2970
2958
149943 1086
2982
148154 1095
146372 1104
8914
15
15
2861
14
23
13 866455 2850
868165
15 869868
16 871565 2817
17 873255
18 874938
19 876615
20 878285
4 21 879949
22 881607
883258
24 884903
25 886542
26 888174
27 889801
28 891421
29 893035
30 894643
Cos.
2839
2828
2806
2795
2783
2773
135262 865906
133545 867632
131835 869351
130132 871064
128435 872770
126745 874469
125062 876162
123385 877849
121715 879529
120051 881202
2763
2946
2935
860686 2923
2911
2900
2888
2877
2866
2854
144597 1113 8887
142829 1122
141068 1131
139314 1140
15
15
15
15
137567 1149 8851
135827 1159
15
15
15
1 in 5 in 10 10 10 in 5
8905
8896
10 10 10
57
56
55
54
8878
53
8869
52
8860
51
50
8841 85 49
2843
2832
134094 1168
132368 1177
130649 1187
16
128936 1196
127230| 1205
8832
48
15
566
H H
16
8823
47
8813
46
16
8804
45
8795
16
44
2821
2811
2800
2789
2779
125531 1215 8785
16
123838 1224 8776
16
43
122151 1234 8766
16
42
41
16
120471| 1243 8757 85 40
2752
2742
2731
2721
2711
110199 891112
2700
108579 892742
2690
106965 894366
2680
105357 895984
D. Sec. Cot. D.
118393 882869
116742 884530
115097 886185
113458 887833
2737
111826 889476
118798 1253
117131 1262
2768
2758
2747
16
8747
39
8738
16
2727
2717
2707
2697
115470 1272
113815 1282
112167 1292
110524 1301 8699
108888 131I 8689
16
8728
8718
98 76
m co m m
38
37
36
16
8708
16
16
16
107258 1321 8679
6
I
105634 1331
8669
31
17
104016 1341 8659 85 30
Tang. Cos. D. Sine
35
34
33
32
861 Deg.
85 Deg.
78
MATHEMATICAL TABLES.

4 Deg.
O
Sine
8.
TABLE V.-LOG. SINES, ETC.
D. Cosec. Tang.
51 Deg.
D.
Cot. Sec. D. Cos.
II'
8.
I I'
9'99
4 30 894643
31 896246
32 897842
33 899432
34 901017 2631
35 902596
2670
2660
2651
2641
105357 895984
103754 897596
102158 899203
100568 900803
2687
104016 1341
8659
17
2677
2667
102404 135I
100797 1361
8649
097404 903987
2622
098983 902398 2648
2658
099197 1371
2638
097602 1381 8619
096013 139F
17
17
17 8629
8639
M2 2 2 2
30
29
28
27
26
860
17
8609
25
36 904169 2612
37 905736
38 907297
4 39 908853
40 910404
41 911949
42 913488
43 915022
44 916550
45 918073
46 919591
47 921103
4 48 922610
49 924112
50 925609
51 927100
52 928587
53 930068
54 931544
55 933015
092703 908719
094264 907147 2620 092853 1411
2603
2629
095831 905570 |094430 1401 8599
17
24
17
8589
23
2610
091281 1422 8578 85 22
17
2593
17
2584
2575
2566
2556
2547
2538
2529
2520
2512
2503
2494
2486
2477
2469
2460
2452
2435
2427
56 934481 2443 065519 936093 2461
091147 910285
089596 911846
088051 913401
086512 914951
084978 916495
083450 918034
081927 919568
080409 921096
078897 922619
077390 924136
075888 925649
074391 927156
072900 928658
071413 930155
069932 931647
068456 933134
066985 934616
2601
2583
2592 086599 1452
089715 1432
088154 1442 8558
8568
21
17
20
17
8548
19
2574
2565
085049 1463 8537
083505 1473
17
18
17
8527
17
2556
081966 1484
080432 1494 8506
17
18
8516
16
98 76
2547
2538
2530
2521
2512
2503
2495
2486
2478
2470
078904 1505 8495
077381 1515 8485 85 13
18
18
18
15
14
1590
5
2411
2403
2394
2387
2379
2371
059704 941952
058262 943404
056826 944852
055394 946295)
053966 947734
052544 949168
2363
063907 1612 8388 85
4 57 935942 064058 937565 062435 1623 8377
062602 939032
18
58 937398
060968 1634
59 938850 2419 061150 940494 059506 1645
o 940296
1941738
2 943174
3 944606
4 946034
5 947456
075864 1526 8474
18
0743511536 8464
18
072844 1547 8453
18
071342 1558 8442
18
069845 1569 8431
18
068353 1579 8421
18
066866
18
18
12
II
ΙΟ
8410
065384 1601 8399
2453
2445
2437
2430
2421
2413
18
8366
987654
3 2
2
18
18
8355
I
058048 1656
8344
8 о
056596 1667
19
8333
59
19
055148 1678
8322
58
2405
053705 1689
19
8311
57
2397
19
052266 1700
5
6 948874
7950287
8 951696
9 953100
10 954499
II 955894
12 957284
13 958670
14 960052
15 961429
051126 950597
049713 952021
048304 953441
046900 954856
045501 956267
044106 957674
2335
042716 959075
041330 960473
039948 961866
038571 963255
2355
2348
2340
2332
2325
2317
2310
2302
2295
Cos. D. Sec. Cot. D. Tang. Cos. D. Sine
2329
2321
2314
2390
050832 1711
2382
049403 1723
2374
2366047979 1734
046559 1745
2358
045144 1757
2351
043733 1768
2344
042326 1780
040925 1791
039527 1803
038134 1814
036745 1826 8174 84 45
8300 56
19
8289 84 55
19
8277 54
198266
53
19
8255
52
19 8243
51
19
8232
50
19
8220
19
8209
goog
49
48
19
8197
47
19
19
8186
46
85 Deg.
84 Deg.
MATHEMATICAL TABLES.
79

51 Deg.
O
Sine D.
TABLE V.-LOG. SINES, ETC.
Cosec. Tang. D.
D. Cot. Sec. D. Cos.
6 Deg.
8.
II'
8.
II' 10'00
9'99
5 15961429
16 962801
17 964170
18 965534
19 966893
20 968249
21 969600
22 970947
23 972289
5 24 973628
25 974962
26 976293
27 977619
28 978941
29 980259
30 981573 2183
31 982883
32 984189
5 33985491
34 986789
35 988083
36 989374
37 990660
38991943
39 993222
40 994497
41 995768
5 42 997036
43 998299
44 999560
45 000816
46 002069
47 003318
48 004563
49005805 2064
50 007044
5 51008278
52 009510
53 010737
54 011962
55 013182
56 014400
57 015613
58 016824
59 018031
60 019235
2288
038571963255 036745 1826
037199 964639
2280
2273
2266
2259
2252
2245
2238
2231
2224
2217
2210
2203
2197
2190
2307
2300
2293
2286
2279
2271
2265
2257
2251
2244
2237
2230
2223
035361 1837
2217
2210
2204
035830 966019 033981 1849 8151
034466 967394 032606 1861
033107 968766
031234 1872 8128
031751 970133
029867 1884 8116
030400 971496 028504 1896 8104
029053 972855 027145 1908 8092
027711 974209
025791 1920 8080 84 37
026372 975560
025038 976906 |023094| 1944 8056
023707 978248
022381 979586
021059 980921
019741 982251
018427 983577
017117 984899
19
198163
8174
45
44
43
19
20
20
20
20
20
20
8139
42
41
40
39
38
024440 1932 8068
20
36
35
021752 1956 8044
020414 1968 8032
019079 1980 8020
017749 1992 8008
016423 2004
20
20
20
20
34
33
32
3I
20
7996
30
2177
015811 986217
2197
015101 2016 7984
013783 2028
20
29
20
2170
2163
2157
2150
2144
2191
20
7972 84 28
014509 987532
2131
2125
2119
2112
2106
013211 988842
011917 990149
010626 991451
009340 992750
2138
008057 994045
006778 995337
005503 996624
004232 997908
002964 999188
001701 000465
2100
2184
012468 2041
7959
27
2178
011158 2053
20
7947
26
20
009851 2065
7935
25
2171
2127
008549 2078
2165
|007250 209o 7910
2158
005955 2103 7897
2152 004663 2115
7885
2146
003376 2128 7872 20
2140
002092 2140 7860 84 19
2134
000812 2153 7847
21
7922
24
21
21
21
21
21
21
21
23
22
21
18
2094
2070
2058
2052
2046
204.0
2034
2029
2023
2017
2012
2006
Cos. D.
842 Deg.
000440 001738
999184 003007
2088
997931 004272
2082
996682 005534
2076
995437 006792
994195 008047
992956 009298
991722 010546
990490 011790
989263 013031
988038 014268
986818 015502|
985600 016732
984387 017959
983176 019183
981969 020403
980765 021620
Sec. Cot. D.
2121
2115
9995352165 7835
998262 2178
17
21
7822
16
2109
2103
996993 2191
995728 2203
21
7809
15
21
7797
14
2097
2091
2085
994466 2216 7784
993208 2229
21
13
21
991953 2242
990702 2255
2080
21
7771
7758
12
II
21
7745 84 10
21
2074
2068
2062
2056
2051
989454 2268
988210 2281
7732
21
7719
96
8
2045
2040
986969 2294
985732 2307
984498 2320
983268 2333
982041 2346 22
21
7706
7
21
22
7693
6
7680
5
22
7667
4
7654
3
2033
2028
980817 2359 7641
979597 2372
22
22
22
2
7628
978380 2386 7614 84
Tang. Cos. D. Sine
84 Deg.
80
MATHEMATICAL TABLES.

6 Deg.
Sine
O
D.
62 Deg.
TABLE V.-LOG. SINES, ETC.
Cosec. Tang. D. Cot.
Sec. D. Cos.
9°
ΙΟ
9°
IO* 10'00
9'99
6
ΙΙ
0 019235
I 020435
2021632
3022825
4024016
51025203
6 026386
7027567
8 028744
6 9029918
10 031089
II 032257
12 033421
13 034582
14 035741
15 036896
16 038048
17 039197
6 18 040342
2000
1995
1989
1984
1978
1973
1967
1962
1957
1951
1946
1941
1936
1930
1925
1920
1915
1910
1905
980765 021620
979565 022834
978368 024044
977175 025251 2006
975984026455
974797 027655
973614 028852
972433 030046
2023
2017
2011
2000
971256 031237 968763 2493
970082 032425 967575 2507
968911 033609 |966391|2520
967743 034791
966579 035969
965418 037144
964259 038316|
963104 039485
961952 040651
960803 041813
1995
1990
1985
1979
1974
1969
978380 2386 7614
977166 2399 7601
975956 2412 7588
974749 2426 7574
973545 2439 7561
972345 2453 7547
971148 2466 7534
23
969954 2480
60
22
22
59
58
22
2.2
57
56
76
22
22
55
54
7520
53
23
23
33
7507 83 52
7493
51
1964
1958
1953
19 041485 1899
20042625 1895
959658 042973 957027 2631
958515 044130
21 043762
22 044895 1884 955105 047582 1908 952418 2687
23046026 1879
953974 048727
957375 045284 954716 2659
956238 046434
1889
1948
1943
1938
1933
1928
1923
1918
1913
23
965209 2534 7466
23
964031 2548 7452
23
962856 2561 7439
23
961684 2575 7425
23
960515 2589
959349 2603
958187 2617
אא
23
7480
50
49
48
47
46
7411
45
23
7397
44
23
7383 83 43
23
7369
42
955870 2645
23
7355
41
23
7341
953566 2673
23
7327¹
24
7313
1903
24 047154
1875
25 048279 1870
26 049400 1865
1889
6 27 050519 1860 949481053277 1884
28 051635 1855
29 052749 1850
30 053859 1845
31 054966
1841
32 056071
1836
33 057172 1831
34 058271
35 059367
1822
952846 049869 1898 950131 2715 7285
951721 051008 1893
950600 052144
24
951273 2701 7299
24
24
948992 2729
947856 2743
7271
24
24
7257183 34
946723 2758
7242
948365054407
947251 055535
946141 056659
945034 057781
943929 058900
942828 060016
1879
1874
945593 2772
944465 2786 24
24
7228
wwwwwwww £ £ £
40
1870
1865
942219 2815
943341 280124 7199
7214
31
24
1827 941729 061130
1855
7170
1860 941100 2830
939984 2844
7185
24
24
24
1851
940633 062240
938870 2859
1846 937760 2873
7156
7141
24
7127 83 25
2 HO 9∞
765
332
222
30
29
28
27
26
24
6 36 060460
37 061551
38 0626391808
39 063724
1804
40 064806
41 065885
42 066962
1817
1813
938449 064453
939540 063348 1842
936652 2888
7112
24
1799
1794
43 068036 1786
44 069107
45 070176
Cos.
84 Deg.
1781
1790
937361 065556 934444 2917
1833
936276 066655 1828 933345 2932
25
935194 067752 932248 2947 7053
1824
25
934115 068846
1819 931154 2961 7039
25
933038 069938 930062 2976
1815
25
931964 071027 1810 928973 2991
930893 0721131806 927887 3006
929824 073197
926803 3021
1837 935547 2902
24
7098
23
24
7083
22
25
7068
21
20
19
7024
18
7009
17
25
6994
16
25
6979 83 15
98 765
D.
Sec. Cot. D.
Tang. Cos. D. Sine
831 Deg.
MATHEMATICAL TABLES.
81

62 Deg.
•
Sine
D.
TABLE V.-LOG. SINES, ETC.
Cosec. Tang. D. Cot.
Sec. D. Cos.
7 Deg.
IO'
9'
7
6 45 070176
46 071242
47 072306
48 073366
49 074424]
50 075480
51 076533
52 077583
53 078631
6 54 079676
55 080719
56 081759
57 082797
58 083832
59 084864
0085894
I 086922
2087947
7 3 088970
4 089990
5 091008
6092024
7093037
8094047
9095056
10 096062
11 097065
7 12 098066
13 099065
14 100062
1777
1772
1768
1763
1759
1755
1750
9*
929824 073197
928758 074278
927694 075356
926634 076432
925576 077505
924520 078576
923467 079644
922417 080710
1746
921369 081773
10°
10.00
9'99
1802
1797
1793
926803 3021 6979
15
925722 3036 6964
25
924644 3051 6949
25
14
13
923568 3066
25
6934
12
1789
25
1784
922495 3081
6919
II
125
1780
921424 3096
920356 3111
1776
125 6889
6904
IO
9
919290 3126
1772
1742
1738
1733
1729
1725
1721
1717
1713
1709
1704
1700
1696
1692
1688
1684
1680
1676
1673
1668
1767
918227 3142 25 6858 83 7
25 6874
8
25
1665
1661
1657
920324 082833
919281 083891
918241 084947
917203.086000
916168 087050
915136 088098
914106 089144
913078 090187
912053 091228
911030 092266
910010 093302
908992 094336
907976 095367
906963 096395
905953 097422
904944 098446
903938 099468
902935 100487
901934 101504
1763
917167 3157
916109 3172
6843
6
25 6828
5
1759
1755
1751
915053 3188
914000 3203 6797
25 6812
4
26
1747
1743
1738
1735
1731
2 2
26
3
26
26
26
2 2
26
26
1727
1722
2 2 2
1719
912950 3218
911902 3234 6766
910856 3249 6751 83 о
909813 3265 6735 59
908772 3280
907734 3296 6704
906698 3312
905664 3327
904633 3343
6782
2
I
6720 82 58
26
57
6688
56
26
26
6673
55
26
6657
54
1715
1711
1707
1703
1699
1695
903605 3359 664I
26
53
902578 3375
901554 3390
900532 3406
26
6625
52
6610
26
5I
26
6594
50
27
899513 3422 657882 49
898496 3438
6562
48
1691
27
15 101056
16 102048
17 103037
1653
1649
1645
900935 102519
899938 103532
898944 104542
897952 105550
896963 106556
18 104025 1642 894990 108560
895975 107559
19 105010
1638
20 105992 1634
7 21 106973 1630
1687
897481 3454
6546
47
27
1684
896468 3470
6530
46
1680
895458 3486
27
1676
894450 3502
27
6514
1672
893444 3518
27
6498
6482
22 107951
23 108927
24 109901
25110873
26 111842
27 112809
1627
1623
1619
1616
1612
1608
28 113774 1605
29 114737
30 115698
1601
Cos.
D.
1669
1665
894008 109559 1661
893027 110556
892049 111551
891073 112543
890099 113533
889127 114521
888158 115507
887191 116491
886226 117472
885263 118452
884302 119429.
Sec. Cot. D.
892441 3535
891440 3551
27
27
6465
6449
1658
1654
1650
1643
890441 3567 6433 82
889444 3583
888449 3600
887457 3616
1647 885479 3649
886467 3632
27
27
64.17
2 2 2 2 2
27
6400
27
27
སས
6384
6368
27
6351
wwwww.f£ £ £ £ ££
40
39
38
37
36
98 76
35
1639
1636
1632
1629
884493 3665
883509 3682
27
882528 3698
27
6335
34
27
6318
33
6302
32
881548 3715
28
28
6285
31
880571 3731
6269 82 30
Tang. Cos. D. Sine
831 Deg.
822 Deg.
82
MATHEMATICAL TABLES.

7 Deg.
Sine
D.
Cosec. | Tang.
D.
TABLE V.-LOG. SINES, ETO.
Cot.
Sec. D. Cos.
81 Deg.
W N Hot
9
7 30 115698
31 116656
32 117613
33 118567
10°
9°
10°
10'00
9'99
1597
1594
34 119519 1583
35 120469
36 121417
37 122362
38 123306
7 39 124248
40 125187
41 126125
42 127060
43 127993
44 128925
45 129854
46 130781
47 131706
7 48 132630
49❘ 133551
50134470
51 135387
52 136303
53 137216
54 138128
55 139037
56 139944
7 57 140850
58 141754
59 142655
8 143555
I 144453
2145349
3 146243
4 147136
5 148026
884302 119429
1625
883344 120404 1622
882387 121377 1618
1590 881433 122348
1587 880481 123317
880571 3731
6269
1615
1611
879531 124284
1580
1608
879596 3748 6252
878623 3765 6235
877652 3781
876683 3798
875716 3815
28
30
28
29
28
1576
878583 125249 1604
877638 126211
874751 3832
873789 3849
1573
1601
876694 127172
872828 3866
1569
1597
2 2 2 2 2 2 2
28
28
∞ ∞
6219
27
6202
26
28
∞
28
28
∞
6185
25
6168
∞
24
28
∞
6151
23
28
∞
6134 82 22
1566
875752 128130
871870 3883
6117
21
1594
28
1562
1559
1556
874813 129087
873875 130041
872940 130994
870913 3900
1591
28
∞ ∞
6100
20
1587
869959 3917
6083
19
1552
1545
872007 131944
871075 132893
1549 870146 133839
1584
869006 3934
29 6066
18
96
1581
868056 3951
29 6049
17
867107 3968
29
6032
16
96
1577 866161 3985
29 6015
15
I 542
1532
1529
1525
1522
1519
1516
1512
1509
1506
869219 134784
868294 135726
1539
867370 136667
1535 866449 137605
865530 138542
864613 139476
863697 14.0409|
862784 141340
861872 142269
860963 143196
860056 144121
1574
1571
865216 4002 5998
1567
864274 4020 5980
29
29
29
14
82 13
1564
1561
863333 4037
862395 4054
5963
12
1558
861458 4072
1551
860524 4089
29
1555 859591 4106
2 2 2 2 2
29
5946
II
29
5928
ΙΟ
29
5911
5894
96
8
1548
858660 4124
29
5876
7
1545
1542
1539
855879 4177
857731 4141
856804 4159 5841
29
5859
6
29
5
29
29
582382
4
859150 145044
1503
1500
1496
1493
1490
1487
1484
1481
858246 145966
857345 146885)
856445147803
855547 148718
854651 149632)
853757 150544|
852864 151454
851974 152363
1529
1532 853115
1535 854034 4212
854956 4194 5806
1526
1523
1520
1517
1514
1511
wwwwww
853115 4229 5771 82 I
852197 4247 5753
851282 4265 5735
850368 4283
849456 4301
848546 4319
847637 4336
29
29
5788
2
3 2
29
о
30
59
30
30
30
5717
5699
58
57
30
30
5681 56
5664 81 55
76
8 6 148915
7 149802
8 150686
9151569
ΙΟ
10 152451
II 153330
12 154208
13 155083
14 155957
15 156830
Cos.
82 Deg.
1478
1475
1472
1469
1466
1463
1460
1457
1454
D. Sec. Cot. D.
851085 153269
850198 154174
849314 155077
848431 155978
847549 156877
846670 157775
845792 158671
844917 159565
1508
1505
846731 4354 5646
8458264372 5628
1502
1499
1496
1493
1490
1487
840435 4481 5519
844043 160457
843170 161347
1484
839543 4499 5501
30
30
844923 4390 5610
30
844022 4409
5591
30
843123 4427 5573
130
842225 4445 5555
30
841329 4463 5537
30
30
31
838653 4518 5482 81 45
Tang. Cos. D. Sine
54
53
52
51
50
49
48
47
46
812 Deg.
MATHEMATICAL TABLES.
83

81 Deg.
TABLE V.—LOG SINES, ETC.
Sine D. Cosec. Tang. D. | Cot. | Sec. D.|_Cos.
9'99
9 Deg
9°
815156830
16 157700
17 158569
18 159435
19 160301
20 161164
21 162025
22 162885
23 163743
8 24 164600
25 165454
26 166307
27 167159
28 168008
29 168856
30 169702
31170547
32 171389
10'
9'
IO' 10'00
1451
1448
1445
1442
1439
1436
1433
1430
1427
843170 161347
842300 162236
841431 163123 1476
840565 164008
839699 164892
838836 165774
837975 166654
837115 167532
1481
1479
1473
1470
1467
1464
1461
1458
836257 168409 831591 4666 31 5534
834226 4610 31
833346 4628 31
832468 4647
838653 4518 5482
837764 4536
836877 4554
835992 4573 31
835108 4591
45
333
31
5464
44
31
5446
43
5427
42
31
5409
41
5390
40
mmm m
5372
39
31
5353
38
81 37
835400 189284
1424
1422
1419
1416
1413
1410
1407
1405
833693 171029
832841 171899
831992 172767
831144 173634
830298 174499
829453 175362
828611 176224
834546 170157 1455
1453
1450
1447
1444
1442
1439
1436
830716 4684 5316
829843 4703 5297
828971 4722 5278
828101 4740
827233 4759 5241
826366 4778 5222
825501 4797
824638 4816
31
36
31
31
31
31
32
32
32
32
35
34
5260
33
32
823776 4835 5165
1402
1433
32
2 2 2 2 2
31
5203
30
5184
29
81 28
8 33 172230
34 173070|
35 173908
36 174744
37 175578
38 176411
39 177242
40 178072
41 178900
8 42 179726
43 180551
44 181374
45 182196
46 183016
47 183834
48 184651
49 185466
50 186280
1399
1396
1394
1391
1388
1386
1383
1380
1377
1369
1366
1364
1361
1359
1356
8 51 187092
52 187903
53 188712
54 189519
55 190325
56 191130
57 191933
58 192734
59 193534
60 194332
1353
1351
1348
1346
827770 177084
826930 177942
826092 178799
825256 179655
824422 180508
823589 181360 1420
822758 182211
821928 183059
821100 183907
820274 184752
1374
819449 185597
1372 818626 186439
817804 187280
816984 188120
816166 188958
815349 189794
814534 190629
813720 191462
812908 192294
812097 193124
811288193953
810481 194780|
1431
1428
1425
1423
1417
822916 4854 5146
32
822058 4873 5127
32
821201 4892
32
820345 4911 5089
32
819492 4930 5070
818640 4949
27
26
5108
25
24
23
32
5051
22
817789 4968
32
5032
21
1415
1412
1409
1407
1404
1402
1399
1396
32
816941 4987 5013
32
816093 5007 4993
32
815248 5026 4974
32
814403 5045 4955
32
813561 5065 4935
32
812720 5084 4916
33
811880 5104
20
81 19
18
17
16
15
1393
1391
1389
1343
1341
1338
1336
1333
1330
808870 196430
808067 197253 1371
1369
807266 198074
806466 198894
805668 199713
1386
1384
1381
1379
1376
1374
33
809371 5162 4838
33
808538 5182 4818 81 10
33
807706 5202 4798
33
806876 5221 4779
33
806047 5241 4759
805220 5261 33
809675 195606 804394 5281 33
811042 5123
810206 5143 4857
4896
33 4877
14
13
33
12
II
4739
4719
1366
1364
33
803570 5300 4700
33
802747 5320 4680
801926 5340 33 4660
801106 5360 33 4640
800287 5380 33 4620 81
98 76 54
3
2
I
Cos. D. Sec. Cot. D. Tang. Cos. D. Sine
81 Deg.
81 Deg.
84
MATHEMATICAL TABLES.

9 Deg.
TABLE V.-LOG. SINES, ETC.
•
Sine D.
Cosec. Tang. | D.
Cot.
93 Deg.
Sec. D. Cos.
9°
10*
9°
1328
1326
1323
1321
90 194332 805668 199713
10* 10.00 9'99
6
9 9 201451
1306
IO 202234
II 203017
12 203797
I304
1299
1294
1280
1278
1275
1273
1271
1268
1264
1259
1257
1255
1253
1250
14205354
15 206131
16 206906 1292
1289
793094 212611
17 207679
1287
792321 213405
9 18 208452 791548 214198
1285
19 209222 1282 790778 214989
20 209992
21 210760
22 211526
23212291
24213055
25 213818
26 214579 1266
9 27 215338.
28 216097
29 216854
30 217609
31 218363
32 219116
33 219868
I 195129
804871 200529
2195925
804075 201345
3 196719 803281 202159
4197511
802489 202971
1318
5 198302 801698 203782
1316
199091
800909 204592
1313
800121 205400
7 199879
8200666 1311
1308 799334 206207
798549 207013
797766| 207817
796983 208619
1301
796203209420
13204577 1296 795423 210220
794646 211018
1361
1359
1356
800287 5380 4620
60
1354
1352
1349
33
33
797841 5440 4560
797029 5460 34
34
796218 5481 4519
799471 5400
798655 5420 4580
33 4600
59
58
4540
1347
1345
34
795408 5501 4499
34
794600 5521 4479
34
1342
793793 5541
34 4459 80 52
1340
792987 5562
4438
1338
1335
1333
34
792183 5582 4418
791381 5603
34
790580 5623
34
4397
4377
789780 5643
34
1331
4357
793869 211815 1328
1326
788982 5664
788185 5684
34
4336
34
1324
1321
1319
34
787389 5705 4295
34
35
785802 5746
4316 45
786595 5726 4274 80 43
4254
42
1317
790008 215780
789240 216568
788474 217356 1312
787709 218142
786945 218926
786182 219710
785421 220492
784662 221272
1261 783903 222052
783146 222830!
782391 223606
781637 224382
780884 225156
785011 5767 35
4233
4.I
1315
1310
1308
1305
1303
1301
1299
784220 5788 35
783432 5809
35
782644 5829 4171
4212
35
4191
38
1297
1294
1292
1290
1246
1244
1242
1239
1237
1235
1233
1231
1228
35 221367
9 36 222115
37 222861
38 223606
39224349
40 225092
41225833
42 226573
43 22731I 772689 233586
44 228048 1226 771952 234345
45 228784
771216 235103
34 220618 1248 779382 226700
780132 225929
778633 227471
772529 6104
777885 228239
777139 229007
776394 229773
775651 230539
774908 231302
774167 232065
771761 6125
36
770993 6146
36
1273
770227 6168 3832
769461 6189 36
35
781858 5850 4150
35
781074 5871 4129
35
780290 5892 4108
35
779508 5913 4087 80 34
35
778728 5934 4066
35
777948 5955 4045
35
777170 5976 4024
35
776394 5997 4003
35
775618 6019 3981
35
1288 774844 6040
35
1286 774071 6061
1284
1281
1279
1277
1275
36
35
32
30
29
28
3960
33 M
35
136
56
26
3918
773300 6082 35
3939
27
3896 80 25
~ ~ ~ ~ wwwwwwwwwww ✡ ‡ ‡ ‡‡££££✡ue aumen
57
56
55
54
49
48
47
46
44
40
3875
24
3854
23
22
3811
21
768698 6211
36
1271
1269
767935 6232
36
3789
20
773427 232826
1267
1265
1262
765655 6297
36
766414 6275
36
767174 6254
3768
19
3746
18
36
3725
17
764897 6319
36
3703
16
3681 80 15
98 765
Cos. D.
Sec. Cot.
D. Tang. Cos. D. Sine
81 Deg.
801 Deg.
MATHEMATICAL TABLES.
85

9°
ΙΟ
9 45 228784|
46 229518
47 230252
48 230984
49 231714
50 232444
51233172
52 233899
53 234625
9 54 235349
55 236073
56 236795
57 237515
58 238235
59 238953
100 239670
1240386
2 241101
10 3 241814
4 242526
5243237
6 243947
244656
8245363
9246069
10 246775
11 247478
10 12 248181
1224
1222
1220
1218
1216
1214
1212
1209
1207
1205
1203
1201
I 199
1197
1195
1193
1191
1189
770482 235859
769748 236614
769016 237368
768286 238120
767556 238872
766828 239622
766101 240371
765375 241118
93 Deg.
Sine
TABLE V.-LOG. SINES, ETC.
D. Cosec. Tang. D. Cot.
୨
10/1/2 Deg.
Sec. D. Cos.
9*99
771216 235103 1260 764897 6319 3681
10° ΤΟ ΟΝ
1258
1256
1254
12:52
1250
1248
1246
764141 6340 36
36
763386 6362 3638
762632 6384 36
761880 6406 36
761128 6428 37
760378 6450 37
759629 6472 37
wwwww
3660
15
14
13
3616
12
3594
II
3572
10
764651 241865
763927 242610
1232
1230
14 249583
15 250282
16 250980
17 251677
18 252373
19 253067
20 253761
10 21 254453
22 255144
23 255834
24 256523
25 257211
26 257898
27 258583
28 259268
29 259951
30 260633
Cos.
80 Deg.
13 248883 1167
1185
1183
1181
1179
1177
1175
1173
1171
1169
757474 249264
756763 249998
756053 250730
755344 251461
754637 252191
1224
1222
1220
1218
1217
762485 244097
761765 244839
761047 245579
754421 6626 37
760330 246319 753681 6649 37
759614 247057
1228 752943 6671 3329
758899 247794 1226 752206 6693 3307
758186 248530
1187
1244
1242
1240
1238
758882 6494 37 3506 80 7
3550
3528
96
9
8
371
763205 243354 756646 6560 37
758135 6516 3484
37
757390 6538 3462
6
5
1234
37
755903 6582
1236
755161 6604 37
3440
4
3418
3
3396
2
3374
I
3351 80 o
751470 6715 3285
750736 6738 3262
750002 6760 3240
749270 6783 3217
748539 6805 38
747809 6828
753931 252920
753225 253648
752522 254374
1215
751819 255100
751117 255824
1165 750417 256547
1163
1161
1159
1158
1156
1154
749718 257269
749020 257990
748323 258710
747627 259429
746933| 260146|
746239 260863
1213
121 I
1209
1207
1205
1203
1201
1200
747080 6851
746352 6873
745626 6896
744900 6919
744176 6941
38
745547 261578
744856 262292
744166| 263005
1152
1150
1148
736283 7194
743477 263717
1146
742789 264428
1144
742102 265138
1142
741417 265847
1141
740732 266555
1139
740049 267261
1137
739367 267967
D. Sec. Cot. D.
1198
1196
1194
1192
1190
1189
1187
1185
1183
1181
1179
1178
1176
743453 6964
742731 6987
38
742010 70IO
741290 7033
740571 7056
7398547079
739137 7102
38
38
∞ ∞
∞
∞
∞ ∞
MM MM MM MM M
3
3
3
m
m
M
37
37
37
37
37
59
79 58
57
56
37
55
54
38
3195
53
38
3172
52
38
3149
51
38
3127
50
38
3104 79 49
3081
48
383059
47
3036
46
3013
45
382990
44
2967
43
∞ ∞ ∞0
MM M
38
2944
42
38
2921
4I
38
2898 79 40
738422 7125
38
737708 7148
736995 7171
391
735572 7217
39
734862 7241 2759
39
ww www W
38
∞ ∞
2875
39
2852
38
2829
39
37
2806
36
2783
35
34
734153 7264 2736
39
733445 7287 2713
39
732739 7310 2690
39
732033 7334 2666 79 30
Tang. Cos. D. Sine
33
32
31
791 Deg.
86
MATHEMATICAL TABLES.

10 Deg.
Sine
TABLE V.-LOG. SINES, ETC.
11 Deg.
D. | Cosec. Tang. D. Cot.
Sec. ID. Cos.
9'
IO'
9*
10°
10'00
9'99
1135
1133
1131
1130
1128
1126
1124
1122
II20
1119
1117
1115
1113
IIII
IIIO
1108
1106
1105
1103
4 283190
5 283836
II
1084
1082
1081
1079
1077
1076
1074
6284480
1072
7 285124
1071
8 285766 714234 294017
1069
9286408
713592 294684
1067
10 287048 1066 712952 295349
11 287687 712313 296013
1064
12 288326 711674 296677
1063
13 288964
711036 297339
1061
14 289600
710400 298001
1059
15290236
709764 298662
Cos. D. Sec. Cot.
38 266051
10 39 266723 733277 274269
40 267395 732605 274964
41 268065 731935 275658
42268734 731266 276351
43 269402
730598 277043
44 270069 729931 277734
45 270735 729265 278424
46271400
728600 279113
47 272064 727936 279801
10 48 272726
727274 280488
726612 281174
49 273388
ΙΙΟΙ
50 274049 725951 281858 718142 7810 40
1099
51 274708
725292 282542
1098
52 275367
724633 283225
1096
53 276024 723976 283907
1094
54 276681
723319 284588
1092
55277337 722663 285268
1091
56 277991
722009 285947
1089
10 57 278644 721356 286624
1087
58 279297 1086 720703 287301
59 279948 720052 287977
11 0 280599
719401 288652
I 281248 |718752 289326|
2 281897 718103 289999
3282544 |717456 290671
10 30 260633 739367 267967
39
31 261314 738686 268671 731329 7357 2643
39
32 261994 738006 269375 730625 7381 2619
39
33262673 737327 270077
729923 7404 2596
39
34 263351 736649 270779
2572
729221 7428
39
35 264027 735973 271479
728521 7451 2549
39
36 264703 735297 272178 727822 7475 2525
39
37 265377 734623 2728761162 727124 7499 2501
II74
1172
1170
1169
1167
1165
1164
733949 273573 1160 726427 7522 2478 79 22
732033 7334
2666
30
29
28
27
26
25
24
23
39
40
1158
1157.
1155
725731 7546
1153
1151
1150
1148
1147
1145
1143
1141
1140
1138
1136
2454
40
725036 7570 2430 20
140
|724342 7594 2406
723649 7618 2382
722957 7641 2359
722266 7665 2335
721576 7689 2311
720887 7713 2287
40
720199 7737 2263 79 13
21
b ‡ ‡ ‡ ÷ ÷ ÷
19
40
18
40
17
40
16
40
15
40
14
40
719512 7761
718826 7786
2239
12
40
2214
II
2190
ΙΟ
717458 7834
716775 7858 2142
716093 7883 2117
1135
1133
1131
1130
1128
1126
1125
1123
716810 291342
716164 292013|
715520 292682
714876 293350
I 122
II20
1118
1117
710001 8103
709329 8127 1873 57
708658 8152
707987 8177 1823 78 55
1115
1114
II 12
IIII
1109
1107
1106
1104
1103
ΙΙΟΙ
701999 8401 1599
79 Deg.
42
42
42
42
42
42
47
$6
701338 8426 1574 78 45
D. Tang. Cos. D. Sine
707318 8201 1799 54
706650 8226
705983 8251
705316 8276
704651 8301
40
40
40
41
715412 7907 2093
41
714732 7931 2069
41
714053 7956 2044 79 4
4I
713376 7980
41
712699 8004 1996
41
712023 8029
41
711348 8053
141
710674 8078 1922
41
41
4.I
41
4I
2166
98 76 in t
5
2020
1971
1947 79
321
3
2
I
O
1897
59
58
1848 56
41
1774
53
42
1749
52
42
1724
51
1699 50
1674
703987 8326
1649
703323 8351
1624
702661 8376
49
48
782 Deg.
MATHEMATICAL TABLES.
87

111 Deg.
Sine
D.
TABLE V.-LOG. SINES, ETC.
Cosec. Tang. D. Cot.
Sec. D. Cos.
12 Deg.
ŷ'
IO*
1058
9
709764 298662
10*
ΙΟΟΟ
9'99
1056
1054
1053
1051
1050
1048
1046
1045
1043
1042
1040
1039
1037
1036
1034
1031
ΙΙ
1029
1028
1026
1025
1023
1022
1020
1019
1017
698486 310398
697868 311042
697252 311685
696636 312327
696021 312967
695407 313608
694793 314247 1064
694181 314885
693570 315523 1061
1014
1013
ΙΟΙΙ
ΙΟΙΟ
1008
1007
11 15 290236
701338 8426 1574
42
16 290870 709130 299322 700678 8451 1549
42
17 291504 708496 299980 700020 8476 1524
42
18 292137
707863 300638 699362 8502 1498
42
19 292768
707232 301295
698705 8527 1473
42
20 293399
706601 301951
698049 8552 1448
42
21294029
705971 302607 697393 8578 1422
42
22 294658 705342 303261| 696739 8603 1397
42
23295286
|704714 303914 696086 8628 1372
43
II 24 295913 704087 304567 1086 695433 8654 1346
43
25 296539 703461 305218 694782 8679 1321
1084
43
26 297164 702836 305869 694131 8705
1083
43
27 297788
702212 306519. 1081 693481 8730 1270
43
28 298412
701588 307168) 692832 8756 1244
143
29 299034
700966 307815 692185 8782
43
30 299655 700345 308463 691537 8807 1193
143
31 300276
699724 309109 690891 8833 1167
1032 699105 309754 1074
1075
143
32 300895
II 33 301514
34 302132
35 302748
36 303364
37 303979
38 304593
39 305207
40 305819
41 306430
II 42 307041 1016 692959 316159 1060
43 307650 692350 316795
45
1100
44
1098
1096
43
42
1095
1093
1092
1090
4I
40
39
38
1089
1087
78 37
36
35
1295
34
33
32
1080
1078
1218
31
30
1077
29
143
1073
1070
1071 688315 8936 143
690246 8859 1141 78 28
689602 8885 1115
688958 8910
27
43
1090
26
1064
25
1068
687673 8962 143 1038
24
1067
1065
687033 8988
686392 9014
143
IO12
23
43
0986
22
685753 9040
43
0960
21
685115 9066
1062
143
0934
20
684477 9092 0908 78 19
44
44
683841 9118 0882
18
1058
683205 9145
44
0855
17
44 308259
45 308867
46 309474
47 310080
48 310685
49 311289 1005 688107 321222 1048
50311893 1004
691741 317430
691133 318064
690526 318697
689920 319329
689315 319961
688711 320592
682570 9171
44
0829
16
1057
1055
1054
1053
1051
1050
681936 9197
44
0803
15
44
681303 9223 0777
44
680671 9250 0750
44
680039 9276 0724
44
679408 9303 06971
14
13
12
I I
678778 9329
44 0671 78 10
44
II 51 312495
52 313097
53 313698
54 314297
55 314897
56 315495
57 316092
58 316689
59 317284
1003
ΙΟΟΙ
IOOO
998
997
996
994
993
60 317879
687505 321851
686903 322479
686302 323106
685703 323733
685103 324358
684505 324983
683908 325607
683311 326231
682716 326853
991 682121 327475
1047
678149 9356 0644
677521 9382 [44] 0618
1045
1044
1043
1041
1040
1039
1037
1036
44
676894 9409 0591
44
676267 9435
0565
44
675642 9462 0538
44
675017 9489 0511
45
674393 9515 0485
45
673769 9542
45
673147 9569
98 765+
4
3
0458
0431
2
I
145
672525 9596 0404 78 O
Cos. D. Sec. Cot. D.
Tang. Cos. D. Sine
78 Deg.
78 Deg.
88
MATHEMATICAL TABLES.

12 Deg.
122 Deg.
TABLE V.-LOG. SINES, ETC.
Sine D. Cosec. Tang. D. Cot. Sec. D. Cos.
9°3
12 0 17879
990
988
986
984
983
982
980
10.6 9°
82121 327474
I 18473 81527 328095
2 19066 80934 328715
987
3 19658
80344 329334
420249 79751 329953
520840
79160 330570
78570 331187 1026
621430
7 22019 77981 331803
8 22607
77393 332418
IO*
ΙΟ
1035
1033
1032
1030
1029
1028
1025
979
1024
12
923194
10 23780
II 24366 976
76806 333033
977
12 24950
13 25534
972
14 26117
970
15 26700
969
16 27281
968
17 27862
12 18 28442
1929021
20 29599
21 30176
22 30753
23 31329
24 31903
25 32478
26 33051
12 27 33624
975
76220 333646
75634 334259.
1021
1023 666354 09866
45
9'9
672526 09596 90404
45
671905 09622 90378 59
145
671285 09649 90351
45
670666 09676 90324
45
670047 09703 90297
45
669430 09730 90270
668813 09757
145
90243
45
668197 09785 90215
45
667582 09812 90188 77 52
45
666967 09839
60
90161
90134
1020
665741 09893
45
973
75050 334871
74466 335482
73883 336093
73300 336702
1017
1019 664518 09948
665129 09921 90079
46 90107
ུ༦ལྦུ༦པཉྩ་
58
57
56
55
54
53
51
50
49
46
48
1016
72719| 337311
966
666aa
965
964
962
961
72138 337919
71558 338527
70979 339133
70401 339739
1012
1015 662689 10030
1013 662081 10058
663907 09975 90025
663298 10003
4690052
47
46
46
46
89997
45
46
89970
44
46
89942 77 43
IOII
661473 10085 89915
660867 10113
46
42
69824 340344| 659656 10168
960
958
957
956
69247 340948|
68671 341552
68097 342155
67522 342757
66949 343358
ΙΟΙΟ
1008
1007
1006
660261 10140
46
89887
4.I
46
89860
40
659052 10196
46
89832
39
1004
658448 10223
46
89804
38
1003
1002
954
1000
657845 10251
657243 10279
656642 10307
46
89777
37
89749
47
47 89721
36
35
28 34195
29 34766
30 35337
31 35906
3236475
3337043
34 37610
35 38176
12 36 38742
37 39306
38 39871
39 40434
40 40996
41 41558
42 42119
43 42679
44 43239
45 43797
953
952
950
949
948
946
66376 343958
65805 344558
65234 345157
64663 345755
998
64094 346353
996
654843 10391 89609
997 654245 10418
656042 10335 89665
999 655442 10363 147 89637
47
89693 77 34
33
32
47
31
63525 346949
994
62957 347545
993
945
62390 348141
944
992 651859 10531
653647 10447
653051 10475 89525
652455 10503 89497
47
47
47 89553
89582
30
29
28
47
27
47
61824 348735
943
990
991 651265 10559 47
89469
26
47
89441 77 25
941
940
939
937
936
935
934
932
931
61258 349329
60694 349922
60129 350514
59566 351106 986
59004 351697
58442 352287
57881 352876
988
987
985
983
982
57321 353465
981
Cos. D.
56761 354053
56203 354640
Sec. Cot.
980
979
650671 10587 89413
650078 10616 47 89384
47
649486 10644 89356
47
648894 10672 89328
47
648303 10700 89300
47
647713 10729
89271
47 89243
647124 10757
646535 10786
645947 10814
645360 10843
D. Tang. Cos. D.
24
23
22
21
20
19
18
47
47 89186
47 89214
17
16
89157 77 15
Sine
78 Deg.
771 Deg.
MATHEMATICAL TABLES.
89

12 Deg.
o
Sine
9°
10°
12 45 | 343797
46 344355
47 344912
48 345469
49 346024
50 346579
51 | 347134
52 347687
53 348240
930
929
927
926
D. Cosec. Tang. D. Cot
9°
656203 354640
655645 355227
655088 355813
654531 356398
TABLE V.-LOG. SINES, ETC.
132 Deg.
Sec. D. Cos.
10*
ΙΟΟΙ 9.98
977
976
975
653976 356982
974
645360 0843 9157
644773 0872
644187 0900
643602 0929
15
47
48 9100
48 9128
14
13
925
653421 357566
973
643018 0958
642434 0986
48
9071
12
48
9042
II
924
652866 358149
971
922
921
652313 358731
651760 359313
970
641851 1015 8985
48 9014
IO
969
920
968
641269 1044
640687 1073
48
48
8956
96
8
48
8927 77 7
12 54 348792
651208 359893
919
55 349343
56 349893
57 350443
58 350992
59 351540
13 0352088|
I 352635
2 353181
13 3 353726
4 354271
5 354815
6 355358
7 355901
8356443
9 356984
650657 360474
967
640107 1102 8898
6
917
916
650107 361053
966
649557 361632
965
915
649008 362210
963
639526 1131
638947 1160 48
638368 1189
48
8869
5
78
8840
4
8811
914
648460 362787
962
913
961
637790 1218 8782
6372131247 8753
3
49
2
911
910
647912 363364
647365 363940
646819 364515
49
49
909
66a
960
959
958
908
907
905
904
903
902
901
10 357524
II 358064
899
644099 367382 953
643557 367953
643016 368524
642476 369094
646274 365090
645729 365664
645185 366237 955
644642 366810
957
954
952
951
898
641936 369663
13 12 358603
| 897 | 640859| 370799
639785 371933
892
891
890
889
888
638713 373064
638178 373629
637644 374193
637111 374756 939
887
885
883
634454 377563
633925 378122 932
633396 378681 931
632869 379239 930
877
Cos.
D.
641397 370232
13 359141 896 640322 371367
14 359678
895
15 360215 893 | 639248| 372499||
16360752
17 361287
18 361822
19 362356
20 362889
13 21 363422
22 363954
636578 375319
636046 375881
23.364485 635515 376442
24 365016 634984 377003
25 365546
26 366075
27 366604
28 367131
884
882
881
880
879
29 367659 632341 379797
30 368185
771 Deg.
631815 380354)
929
Sec. Cot. D.
Tang. Cos. D. Sine
950
949
948
634910 1364 8636
634336 1393 8607
633763 1422 8578
633190 1452 8548
632618 1481 8519
632047 1511 8489
631476 1540 8460
630906 1570 8430
630337 1599 49 8401
636636 1276 8724 77 0
49 8695
636060 1305
59
635485 1334
I
49 8666
149
76 58
57
49
49
49
49
49
49
49
56
55
54
53
52
51
50
946 629768 1629
49
8371
76 49
48
945
49
629201 1658 8342
47
944
628633 1688
628067 1718 50
49
8312
46
8282
45
943
942
941
940
938
50
627501 1748 8252
626936 1777
50
626371 1807
625807 1837
625244 1867
44
10 10 10
50
8223
50 8193
43
42
8163
41
50
8133 76 40
50
937
624681 1897
624119 1927
8103
39
50
935
934
933
623558 1957
622997 1987 8013
150
8073
38
96
8043
37
50
36
622437 2017
621878 2047 150
621319 2078
50
7983
35
7953
34
50
7922
33
928
620761 2108
620203 2138 50
619646 2168 50
50
7892
32
7862
31
7832 76 30
76 Deg.
H
90
MATHEMATICAL TABLES.

13 Deg.
Sine
9°
TABLE V.-LOG. SINES, ETC.
D. Cosec. | Tang. | D. Cot.
10°
141 Deg.
Sec. D. Cos.
10° ΙΟΟΙ
9.98
876
875
874
873
871
13 30 368185
31 368711
32 369236
33 369761
34 370285 872
35 370808
36 371330 870
37 371852 869
38 372373 867
13 39 372894 866
40 373414 865
41 373933 864
42 374452 863
43 374970 862
44 375487 624513 388084
45376003 623997 388631
861
860
9*
631815 380354
631289 380910
630764 381466|
630239 382020
629715 382575
629192 383129
628148 384234
628670 383682
627627 384786 920
927
926
925
924
923
617425 2290 51
619646 2168
619090 2199 7801
618534 2229
617980 2260
7832
922
921
919
616871 2321 7679
616318 2351
615766 2382
615214 2412
627106 385337
626067 386438
626586 385888
625548 386987
625030 387536
918
614663 2443
614112 2474
917
915
914
913
912
856
852
46 376519 859
47 377035 858
13 48 377549 857 621937 390815
622451 390270
49 378063
50 378577 854 620911 391903
621423 391360
51379089 853 620399 392447
622965 389724
911
910
909
613562 2504 7496
613013 2535 7465
612464 2566 51
7434
51
611916 2597 7403
52
611369 2623 7372
52
610822 2659
623481 389178
LA LA LA Ln in in in in in 20 in in
51
29
51
7771
2
28
3000
51
7740
27
7710
26
51
25
51
7649
24
51
7618
23
51
7588
76 22
51
7557
21
51
7526
20
51
19
51
18
96
17
16
15
908
907
906
851
850
618866 394073
52 379601
53 380113
54 380624 619376 393531 606469.2908
905
619887 392989 904
848
845
1384182
2 384687
3 385192
843
842
841
5 386201
839
14
9 388210
6386704
838
7387207 837 612291 401058
8 387709 836 611790 401591
835 611289 402124
613296 399990
615313 397846|
614808 398383 601617 3191 6809
4385697 840 613799 399455
614303 398919
55 381134 849 618357 394614
52
605927 2939 7061
56 381643
605386 2970 7030 76 4
13 57 382152 847 617339 395694
617848 395154 604846 3002 6998
58382661
846 616832 396233
59 383168
140 383675 844 615818 397309
604306 3033
603767 3064
616325 396771 603229 3096
903
902
901
900
899
610276 2690 52 7310 76 13
52
609730 2721 7279
52
609185 2752
7248
52
608640 2783 7217
52
608097 2814 7186
52
607553 2845 7155
52
607011 2876 7124
52
7341
14
12
II
IO
7092
52
52
52
898
897
52
52
6967
6936
896
896
12 389711
13 390210
14 390708
15 391206
833
831
832 609790 403718 885
830
609292 404249
608794 404778
53
53
601081 3222
53
600545 3254
53
600010 3286
612793 400524 599476 3317
598942 3349
53
598409 3381
10 388711
597876 3413
834
53
II 389211 610789 402656 597344 3445
610289 403187 596813 3477
53
6491
596282 3509
53
595751 3541 6459
53 6427 75 45
595222 3573
895
602691 3127
602154 3159
6904 76 0
52 6873
53 6841
59
58
57
894
6778
56
892
893
6746 75 55
6714 54
891
53 6683
53
890
889
888
887
886
53 6651
52
6619
5I
53 6587
6555
153 6523
49
48
47
884
883
a∞ to int mano ao non mi to go to
9
8
7
6
5
3
2
I
50
46
Cos. D.
Sec. Cot. D. Tang. Cos. D. Sine
/
761 Deg.
75 Deg.
MATHEMATICAL TABLES.
91

15 Deg.
141 Deg.
Sine
TABLE V.-LOG. SINES, ETO.
D. Cosec. Tang. D. Cot.
Sec. D. Cos.
10*
IO*
ΙΟΟΙ
9°
9*
9'98
14 15 391206
828
16391703
17 392199 826
18 392695
827
825
19 393191 824
20 393685
21 394179
22 394673
23395166
608794 404778
608297 405308
607801 405836
607305 406364
606809 406892
882
881
880
879
878
823
606315 407419
877
595222 3573 6427
594692 3605 6395
594164 3637 6363
593636 3669 6331
593108 3701 6299
54 6266
592581 3734
45
53
44
53
43
54
4.2
54
822
605821 407945
876
592055 3766
54
6234
605327 408471
821
820
604834 408997
875
874
591529 3798
5910033831
54 6202
54 6169 75 37
54
14 24 395658
819
25 396150
26 396641
817
814
813
14 33 400062
34 400549 810
35401035)
36 401520 808
37402005]
807
38402489
39402972
40403455
41 403938
∞ ∞ ∞ 00 00 00 00 ∞ ∞
811
27 397132 817
28 397621 816
29 398111
30 398600
31 399088 600912 413179
32 399575 812
600425 413699
599938 414219 865
604342j 409521
603850 410045
818
603359 410569
602868 411092
874
873
872
602379 411615
871
590479 3863
589955 3896
589431 3928
54
588908 3961
6137
54 6104
54 6072
wwwwww B B
41
40
6039
33
870
588385 3993
54 6007
32
868
601889 412137 587863 4026 5974
815 601400 412658 869
54
31
867
866
54
587342 4058 5942
54
586821 4091
55
5863014124 5876
55
585781 4157 5843
30
5909
29
75 28
809
806
598965 415257 864
598480 415775
597995 416293
597511 416810
597028 417326
864
599451 414738 5852624189 5811
55
55
584743 4222
5778
2277
26
25
55
863
584225 4255
5745
24
862
583707 4288
55
5712
23
861
805
860
804
596545 417842
596062 418358
583190 4321 5679
582674 4354 5646
582158 4387
55
22
55
21
803
00 00
859
858
581642 4420 5580 75 19
14 42 404420 802
801
800
799
798
797
796
795
794
794
793
791
790
789
788
787
786
595580 418873
43404901 595099 419387
594618 419901
44 405382
45 405862 594138 420415
46406341 593659 420927
47 406820
593180 421440
48 407299
592701 421952
49 407777 592223422463
50 408254
14 51 408731
52 409207
53 409682
54 410157
55 410632
56 411106
57 411579
58 412052
59 4125241
60 412996
857
581127 4453
55
55
55
5547
5613
20
18
856
855
155
580613 4486 5514
5800994520
17
55
5480
16
855
579585 4553
55
5447
15
854
853
578560 4620
579073 4586 55 5414
14
56
5380
13
852
578048 4653
56
851
591746 422974
850
но
10 10 10
577537 4686
56
5347
12
577026 4720 5280
56 5314
II
591269 423484
590793423993.
590318 424503
792 589843 425011
849
576007 4787
848
575497 4820
848
156
576516 4753 5247
75 10
156
5213
156
5180
847
574989 4854
589368 425519
588894 426027
588421 426534
574481 4887
156
56
5146
846
573973 4921
(56) 5113
845
56
5079
98765+
4
844
573466 4955
56
5045
3
587948 427041
843
572959 4989
56
5011
2
587476 427547
572453 5022
4978
I
843
587004 428052
571948 5056 4944 75 o
56
Cos. D. Sec. Cot.
D.
Tang. Cos. D. Sine
75 Deg.
75 Deg.
92
MATHEMATICAL TABLES.

15 Deg.
Sine
TABLE V.-LOG. SINES, ETC.
D. | Cosec. | Tang. | D. | Cot.
15 Deg
Sec. D. Cos.
9'
IO'
9°
10°
ΙΟΟΙ
9'98
15
784
783
783
782
781
6
780
779
778
777
776
775
774
773
773
772
0412996 587004 428052
785
I 413467 586533 428557
2 413938
3 414408
4 414878
5415347
41581
7 416283
8 416751
15 9 417217
10 417684
11 418150
12 418615
13 419079
14 419544
15 420007
16 420470
17 420933
3/
586062 429062
585592 429566
585122 430070
584653 430573
584185 431075
583717 431577
583249 432079 835
582783432580
582316 433080
581850 433580
00 00 00 00 00 00 00 00 00
842
571948 5056
4944
84I
571443 5090
57
4910
570938 5124
840
57
4876
www)
839
838
838
0100 00
837
836
765
570434 5158 4842
569930 5192
569427 5226
568925 5260 57
568423 5294 57
57
57
4808
57
4774
4740
4706
581385 434080
580921 434579
580456 435078
∞ ∞ ∞ 00 00 00
834
833
832
832
831
830
770
579993 435576
579530 436073
771
579067 436570
829
828
828
564424 5568 57
563927 5603
563430 5637 58
567921 5328 4672
567420 5363
566920 5397 57
566420 5431 57
565920 5465 57
565421 5500
564922 5534 57 4466
57
57
74 52
4637
4603
4569
4535
57
4500
58
15 18 421395 769
19 421857
20 422318 767
768
21 422778
22 423238
23 423697
24 424156
25 424615
26 425073 762
15 27 425530 761
28 425987 760
29 426443
760
30 426899
31427354
32 427809
33428263
34 428717
35429170
15 36 429623
767
766
578605 437067
578143 437563 826
577682 438059
577222 438554
576762 439048
827
825
58
562933 5672 4328
58
562437 5706 4294
561941 5741 58
4432
4397
4363 74 43
45
42
41
824
765
764
763
576303 439543
575844 440036 822
575385 440529 821
574927 441022
574470 441514
574013 442006
573557 442497 818
573101 442988
823
823
560457 5845
4190
4155
58
559964 5880 4120
4259
58
561446 5776 4224
58
560952 5810
40
39
58
38
37
559471 5915
58
36
4085
820
558978 5950
158
58
∞ ∞
4050 74 34
819
558486 5985
557994 6019
819
759
757
572646 443479 816
572191 443968
571737 444458
756
557012 6089
817
4015
3981
58
557503 6054 3946
58
33
32
58
31
556521 6125
758
58
3911
30
8 7+7+7 77 mmmmmmmmm
бо
59
58
56
55
54
51
49
48
47
46
44
58
816 556032 6160
3875
29
3840
28
755
571283 444947
815
555542 6195
59
3805
2.7
814
555053 6230
59
754
813
570830 445435 554565 6265 59
3770
26
3735 74 25
59
753
37430075
38430527
39 430978
40 | 431429
41 431879
42432329
43432778
44433226
45 433675
Cos. D.
752
752
570377 445923
569925 446411
569473 446898
812
553589 6336 59
812 554077 6300 3700
24
3664
23
811
751
569022 447384
810
553102 6371
552616 6406 59
59
3629
22
3594
21
750
568571 447870
749
568121 448356
809
749
748
567671 448841
809
552130 6442
59
551644 6477
59
3558
20
3523
19
551159 6513
808
59
3487
18
567222 449326 ·550674 6548 59
747
566774 449810
807
806 550190 6584
59
566325 450294 549706 6619 59 3381 74 15
Sec. Cot. D. Tang. Cos. D. Sine
3452
3416
17
16
98 765
75 Deg.
741 Deg.
MATHEMATICAL TABLES.
93

15 Deg.
O
TABLE V.-LOG. SINES, ETC.
Sine D. Cosec.
16 Deg.
Cosec. Tang. D.
Cot.
Sec. ID. Cos.
9°
IO'
9*
IO'
ΙΟ ΟΙ
9'98
46 434122
47 434569
48435016
49 435462
50 435908
51 436353
52 436798
53437242
746
15 45 433675 566325 450294 806
549706 6619
3381
15
745
744
744
565878 450777
565431 451260
805
549223 6655
59
3345
14
564984 451743
804
548740 6691
59
3309
13
743
564538 452225
803
548257 6727
59
60
3273
12
547775 6762
802
60
3238
II
564092 452706
742
802
547294 6798
563647 453187
60
3202
ΙΟ
741
546813 6834
801
563202 453668
60
3166
9
740
800
5463326870
740
562758 454148
60
3130
8
545852 6906 3094 74 7
799
60
15 54 437686
562314 454628
16
55 438129
56438572
57 439014
58 439456
59 439897
0440338
I 440778
2 441218
739
545372 6942
738
737
736
561871 455107
561428 455586
560986 456064
799
798
544893 6978
60 3058
6
603022
5
797
736
560544 456542 796
735
734
560103 457019
559662 457496
796
544414 7014
543936 7050
543458 7086
60 2986
4
733
732
559222 457973
558782 458449
795
794
793
793
60 2950
60 2914
542981 7122 2878
60
542504 7158 2842 74 0
60
542027 7195 2805
60
61
3
2
I
59
541551 7231 276973 58
6
16 3 441658
4 442096
5 442535
442973
7 443410 728
8 443847
9 444284
10 444720 726
II 445155
16 12 445590
731
558342 458925
792
731
730
729
791
790
790
789
727
788
727
788
61
557904 459400
61
557465 459875 540125 7340 2660
61
557027 460349 539651 7376 2624
61
556590 460823 539177 7413 2587
556153 461297
555716 461770
541075 7267 2733
540600 7304 2696
57
56
55
54
61
53
538703 7449
538230 7486
61
2551
52
555280 462242
554845 462714
725
61
2514
51
787
537758 7523
786
537286 7559
61
2477
50
724
723
721
720
720
719
717
715
714
713
713
712
711
Cos. D.
20449054 718 550946 466945
16 21 449485 550515 467413
22 449915 716 550085 467880
23450345 716 549655 468347
777
776
775
775
774
773
Cot. D. Tang. Cos. D. Sine
533992 7817 2183
62
533524 7854
62
533055 7891
532587 7928
532120 7965
531653 8002
24450775
549225 468814 531186 8039
25 451204 548796 469280 530720 8076
26 451632
548368 469746|
530254 8114
27 452060
547940 470211 529789 8151
28 452488
547512 470676|
529324 8188
29 452915 547085 471141
528859 8226
30 453342 546658 471605 528395 8263
Sec.
554410 463186
13 446025 553975 463658
14 446459 553541 464129
723
535871 7669 61 2331
15 446893 553107 464599
722
535401 7706
783
16 447326 552674 465069 534931 7743
17 447759 552241 465539 534461 7780 2220
782
18 448191
551809 466008
781
19448623
551377 466476|
780
61
244
73 49
785
785
536814 7596
536342 7633
66
61
2404
48
61
2367
47
784
46
61
2294
45
783
61
2257
44
62
43
42
2146
41
780
2109 73 4C
62
779
62
*2072
778
778
62
62
2035
1998
1961
333 m
38
A www B B
37
62
36
66
62
1924
35
1886
62
34
62
1849
33
1812
62
32
62
1774
31
1737 73 30
741 Deg.
731 Deg.
94
MATHEMATICAL TABLES.

16 Deg.
TABLE V.-LOG. SINES, ETO.
171 Deg.
Sine
IO*
9°
16 30 453342
31 453768
32 454194
33 454619
34455044
35 455469
36 455893
37 456316
38 456739
710
710
709
708
D. | Cosec. | Tang. | D.
9°
546658 471605
546232 472068
545806 472532
545381 472995
544956 473457
Cot.
Sec.
D. Cos.
10°
ΙΟΟΙ
9*98
773
772
771
771
528395 8263 1737
527932 8301 1699
527468 8338 1662
527005 8375 1625
526543 8413
62
63
63
63
26
1587
~ N N N W
30
29
28
27
707
770
707
706
705
544531 473919
544107 474381
543684 474842
543261 475303
769
769
526081 8451 1549
525619 8488
63
63
25
768
525158 8526
63
1512
24
704
767
524697 8564 63
63
1474
23
1436
73 22
542838 475763
704
542416 476223
703
541994 476683
702
541573 477142
701
701
700
699
698
698
697
696
688
687
686
16 39 457162
40 457584
41 458006
42 458427
43 458848
541152 477601
5223998753
540732 478059
44 459268
521941 8791 63
45 459688
521483 8829 63
540312 478517
46460108 539892 478975
5210258867 1133
47 460527
520568 8905
539473 479432
16 48 460946 539054 479889
49 461364 538636 480345
50 461782 538218 480801
695
51 462199 537801 481257
695
52 462616 537384 481712
694
53 463032 536968 482167
693
54 463448 536552 482621
693
55 463864 536136 483075
692
56 464279 691 535721 483529
16 57 464694 535306 483982
690
58 465108 600 534892 484435
59 465522 534478 484887
689
17 0 465935 688 534065 485339
I 466348 533652 485791
2 466761
533239 486242
3467173 532827 486693
767
524237 8601
766
523777 8639
631
399
21
63
1361
20
765
523317 8677
765
522858 8715 63
63
1323
19
1285
18
764
63
1247
17
1209
16
763
1171
15
763
14
762
64
761
64
1095
73 13
9∞ 70 in t~
520111 8943 64
761
1057
12
760
759
519655 8981 1019
64
519199 9019 64
II
0981
ΙΟ
759
758
518743 9058 0942
518288 9096 0904
517833 9134
64
9
8
64
0866
757
64
7
517379 9173
0827
6
757
64
756
755
516925 9211 64
516471 9250 64
0789
5
0750 73
4
516018 9288
755
515565 9327
64
0712
754
515113 9365
64
0673
753
514661 9404
64
0635
32 1
I
753
64
0596 73
0
752
514209 9442 64
0558
59
513758 9481
751
65
0519
58
513307 9520
0480
751
65
57
4 467585
5 467996
685
532415 487143
512857 9558
0442
56
685
532004 487593
750
65
512407 9597
749
65
0403 72 55
17
7468817 683
6468407 684
531593 488043
749
531183 488492
748
511957 9636
511508 9675
65
0364 54
8 469227 683
530773 488941
682
9469637 530363 489390
747
511059 9714
510610 9753
65 0286
0325
53
65
52
0247
|
10 470046
529954 489838
681
II 470455 680 529545 490286
12 470863 680
747
746 510162 9792
65
51
0208
50
746
509714 9831
65
0169
49
65
13 471271
14 471679
15 472086
679
529137 490733
528729 491180
509267 9870
745
508820 9909
65
0130
48
0091
47
744
65
678
744
Cos. D.
528321 491627
527914 492073
Sec. Cot. D. Tang. Cos. D. Sine
508373 9948
0052
46
507927 9988 001272 45
65
731 Deg.
72 Deg.
MATHEMATICAL TABLES.
95

171 Deg.
TABLE V.—LOG SINES, ETO.
Sine D. Cosec. Tang. D. Cot. Sec. D.¦ Cos.
18 Deg.
9'4
17 15 72086
678
16 72492
17 72898
677
676
2274923
672
30 78142
667
10'5 9°
27914 492073
27508 492519
27102 492965
1873304
26696 493410
676
1973710 26290 493854
675
20 74115 25885 494299
674
21 74519 25481 494743
674
25077 495186
673
23 75327 672
24673 495630
17 24 75730 24270 496073
25 76133 671
23867 496515
737
26 76536 23464 496975
670
736
27 76938 23062 497399
669
736
28 7734.0
22660 497841
669
29 77741 668
22259 498282 735
734
21858 498722
IO*
10'0
9'9
507927 19988
80012
45
743
65
507481 20027 79973
44
743
742
741
507035 20066
506590 20105
65
740
740
740
739
738
66
66
506146 20145 79855
66
505701 20184 79816
66
505257 20224 79776
66
504814 20263 79737
66
504370 20303 79697
66
79934
79895
43
42
41
40
39
38
72 37
737
503927 20342
503485 20382 79618
66
503043 20421 66 79579
502601 20461 79539
66
502159 20501 66 79499
501718 20541
66
501278 20580
66
79658
36
35
34
33
32
79459
3I
79420
31 78542 667
21458 499163
734
665
32 78942 666 21058 499603
17 33 79342 20658 500042
733
500837 20620 79380
66
66
733
500397
499958 20700
20660
66
79340
72
79300
732
67
34 79741
35 80140
665
36 80539 663
664
40
38 81334 662
39 81731 661
82128
37 80937 663
20259 500481
19860 500920
19461 501359
19063 501797
499519 20740
79260
76
M32 2
2 2
30
29
28
27
26
18269 502672
17872 503109
661
41 82525 660 17475 503546)
731
731
730
730
729
728
728
727
67
499080 20780 79220
67
498641 20820 79180
67
498203 20860 79140
67
18666 502235 497765 20900 79100
25
24
23
22
67
497328 20941 79059
67
496891 20981 79019
67
496454 21021 78979 72 19
67
21
20
17 42 82921
43 83316
659
659
657
657
656
655
50 86075 654
1751 86467
52 86860
655
17079 503982
16684 504418 727
44 83712
16288 504854
658
45 84107 15893 505289
46 84501
47 84895
48 85289
49 85682
726 495582 21102
496018 21061 78939
18
67
78898
17
67
495146 21142
78858
16
725
67
494711 21183
78817
1.5
14318 507027
13925 507460
725
724
724
723
722
67
15499 505724
15105 506159 493841 21264
14711 506593
494276 21223
78777
14
67
78736
13
67
493407 21304
78696
12
68
492973 21345
68
78655
II
653
53 87251
54 87643
653
652
55
88034
651
651
57
88814
650
56 88424 11576 510054 489946 21630
650
649
11186 510485
58 89204 10796 510916
648
59 89593 10407 511346|
6089982
10018 511776
Cos. D. Sec. Cot. D.
722
721
721
720
719
719
718
718
717
716
492540 21385
13533 507893
492107 21426 68
13140 508326 491674 21467
12749 508759 491241 21507 68
12357 509191 490809 21548
11966 509622 490378 21589
78615 72 10
68
78574
68
78533
78493
78452
489515 21671
489084 21712 78288
68
68
68
68
68
78411
78370
78329
98 76 in + m 2
5
4
3
488654 21753 68
488224 21794 78206 72 o
Tang. Cos. D. Sine
78247
I
72 Deg.
72 Deg.
MATHEMATICAL TABLES.
96

5491922
6492308
645
18
8 493081
9 493466
10 493851
II 494236
12 494621
7492695 644
644
643
642
fff
508078 513921
507692 514349
507305 514777
506919 515204
18 Deg.
Sine
9°
18 0 489982
I 490371
2 490759
TABLE V.-LOG. SINES, ETC.
D. | Cosec. | Tang. | D. Cot.
698998
IO'
9°
510018 511776
716
509629| 512206 716
509241 512635
647
3 491147 646 508853 513064
4491535 508465 513493
646
Sec.
18 Deg.
D. Cos.
10* 10°02 9'97
488224 1794
487794 1835 8165
68
68
487365 1876
715
486936 1917 8083
69 8042
714
486507 1958
714
486079 1999 69
8206
68
60
59
8124
58
57
56
69 8001
55
713
713
485651 2041 7959
69
54
712
712
485223 2082 7918
484796 2123 7877
69
53
69
71 52
642
641
506534 515631
506149 516057
505764 516484
641
505379 516910
13495005 640
14 495388
639
504995 517335
504612 517761
639
638
637
504228 518185
15 495772
16 496154
503846 518610
17 496537 503463 519034
18 18 496919 637
503081 519458
19 497301 636 502699 519882
20 497682
21 498064
635
633
632
632
28500721
18 27 500342 499658 523259
631
631
499279 523680
29 501099
37 504110
38504485
39504860
40 505234
41 505608
42 505981
625
625
624
495890 527451
495515 527868
495140 528285
479272 2665 70
70
478849 2707 7293
70
478427 2749 7251
70
478005 2791 7209
70
477583 2833 7167
70
477162 2875 7125
70
476741 2917 7083
70
476320 2959 7041
70
498901 524100
630
475900 300I 6999
30 501476 498524 524520
70
629
6957
475480 3043
31 501854 498146 524939
629
475061 3086 70 6914
32 502231 628 497769 525359 474641 3128 70 6872
698
33 502607 628 497393 525778
698 474222 3170
34 502984 497016 526197
627
697 473803 3213
35 503360
496640 526615
626
473385 3255
697
18 36 503735 626 496265 527033 696 472967 3298
483943 2206 7794
483516 2248 7752
69
483090 2289 7711
69
482665 2331 7669
69
4822392372 7628
69
481815 2414
69
481390 2456 7544
70
480966 2497
706
7503
70
480542 2539 7461
480118 2581 70
636 502318 520305 479695 2623 70
501936 520728
22 498444 634
501556 521151
23 498825
634
501175 521573
24 499204 500796 521995
25 499584 500416 522417
26 | 499963
500037 522838
484369 2165 7835
51
711
69
50
710
69
49
710
48
709
47
709
46
708
7586
708
45
44
707
71 43
706
705
705
704
703
703
703
42
7419
4.I
7377
40
7335
39
38
37
36
702
35
71 34
702
701
701
33
32
31
700
30
699
29
699
28
71 6830
27
71
6787
26
71
6745 71 25
71
6702
24
696
695
695
623
494766 528702
694
623
43 506354 622 493646 529950
44 506727 621 493273 530366
494392 529119
622 494019 529535
693
472549 3340
472132 3383
471715 3426 6574
471298 3468 6532
470881 3511
71
6660
23
71 6617
22
171
21
71
20
71
6489
19
71
693
470465 3554
6446
18
693
470050 3596
71
6404
17
692
469634 3639
45 507099
Cos. D. Sec. Cot.
492901 530781 469219 3682 6318 71 15
D. Tang. Cos. D. Sine
71
171
6361
16
72 Deg.
711 Deg.
MATHEMATICAL TABLES.
97

18 Deg.
Sine D. Cosec.
Cosec. Tang. D.
Tang. D.
Cot.
TABLE V.-LOG. SINES, ETC.
19 Deg.
Sec. ID. Cos.
9°
10'
9*
IO'
10°02
9'97
18 45 507099 620
619
619
616
46 507471 620
47 507843
48 508214
49508585
491415 532439
618
50 508956 491044 532853
618
51 509326 490674 533266
617
52 509696
616 490304 533679 688
53 510065 489935 534092
492901530781
492529 531196
492157 531611
491786 532025
691
691
690
690
467975 3811 72
469219 3682 6318
468804 3725 6275
468389 3768
15
71
14
71
6232
13
6189
12
689
689
688
467561 3854 6146
72
467147 3897
466734 3940
466321 3983 6017
72
II
6103
72 6060
ΙΟ
72
0 900
9
8
72
687
465908 4026
5974 71 7
72
55 510803
56 511172
615
615
614
613
613
612
612
611
611
18 54 510434 489566 534504
489197 534916
488828 535328
57 511540 488460 535739 685
687
465496 4070
5930
6
686
465084 4113
72
5887
5
686
464672 4156
72
5844
464261 4200
72
5800
608
605
58 511907
463850 4243
488093 536150
59512275 487725 536561
19 0 512642 487358 536972
I 513009 486991 537382
2 513375
19 3 513741 610
486259 538202 682
4 514107 485893 538611 682
609
485528 539020681
5514472
609
6
514837 608
485163 539429 681
7 515202
484798 539837 680
8 515566 607
484434 540245 680
9515930 484070 540653
607
10 516294 606
483706 541061 679
II 516657 483343 541468
72
685
684
684
683
462208 4417
486625 537792 683
463439 4286 72
463028 4330
462618 4373
72
5757
5714
5670 71
432 = O
I
73
5627
59
73
5583 70 58
73
678
461798 4461 5539
73
461389 4504
73
460980 4548 5452
73
460571 4592 5408
73
460163 4635
73
459755 4679 5321
73
679 459347 4723 5277
73
458939 4767 5233
73
458532 4811
5496 56
765
in in in
57
55
54
5365
53
52
51
50
5189 70 49
73
567
19 12 517020
13 517382
14 517745
15 518107
16 518468
17 518829
482980 541875
605
604
604
603
603
602
601
601
600
600
599
599
598
598
18 519190
19 519551
20 519911
19 21 520271 479729 545524 454476 5252
22 520631 479369 545928
23520990 479010 546331
24521349 478651 546735
25 521707 478293 547138
674
482618 542281 677
482255 542688
677
457312 4943 5057
73
481893 543094 456906 4987
676
481532 543499
676
456501 5031
481171 543905 456095 5075
675
480810 544310 455690 5120
675
480449 544715 674
480089 545119
458125 4855
678
5145
48
73
457719 4899
5101
47
73
46
5013
45
73
4969
74
4925
74
4880
455285 5164 4836
454881 5208
74
41
74
4792
70 40
74
4748
673
741
673
454072 5297
4703
597
596
596
595
Cos. D.
74
74
452862 5430 4570
74
26 522066 477934 547540 671
452460 5475 4525
74
27 522424 477576 547943 452057 5519
670
74
28 522781
477219 548345 451655 5564
670
74
29523138 476862 548747 451253 5609
669
74
30.523495 476505 549149 450851 5653 4347 70 30
672
672
453669 5341 4659
453265 5386
74
4614
wwww . # £ £ £
44
43
42
39
38
37
36
35
671
34
4481
33
4436
32
4391
31
Sec. Cot. D. Tang. Cos. D. Sine
711 Deg.
704 Deg.
98
MATHEMATICAL TABLES.

19 Deg.
TABLE V.-LOG. SINES, ETO.
201 Deg.
Sine
D. Cosec. Tang. | D.
Cot.
Sec.
D. Cos.
9°
10*
9°
10°
10.02
9'97
19 30 523495
31523852
32 524208
33 524564
34 524920
35 525275
36 525630
37 525984
38526339
595
594
594
593
593
592
591
591
590
590
476505 549149 669
476148 549550 668
475792 549951 668
475436 550352
475080 550752
474725 551152 666
474370551552 666
474016 551952
473661 552351 665
473307 552750
589
589
588
588
587
587
586
471190 555139 662
470839 555536
586
470487 555933 661
585
49 530215
50 530565
51 5309151
52 531265
53 531614
54 531963
55 532312
56 532661
585
584
470136 556329 660
469785 556725 660
469435 557121
450851 5653 4347
75
450450 5698 4302
75
450049 5743 4257
75
449648 5788
667
4212
175
449248 5833 4167
75
448848 5878 4122
75
448448 5923 4077
75
448048 5968 4032
75
447649 6013 3987
75
19 39 526693
447250 6058
665
3942
75
40 527046 472954 553149 664
446851 6103 3897
41 527400
75
472600 553548 446452 6148
664
75
42 527753 472247 553946 446054 6193 3807
663
43 528105 471895 554344 445656 6239
663
44 528458 471542 554741 662
445259 6284
45 528810
444861 6329 3671
46 529161
47 529513
19 48 529864
30
29
28
27
667
26
25
24
665
23
70 22
21
20
3852
19
18
86
75
3761
17
75
3716
16
176
661
444464 6375
444067 6420
76
15
66
77
76
76
3625
3580 70 13
14
584
469085 557517 442483 6602
659
443671 6465 3535
76
443275 6511 3489
442879 6556
12
II
76
76
3444
IO
583
468735 557913
582
582
581
467339 559491
581
468037 558702 441298 6739
467688 559097 657
442087 6648
468386 558308 441692 6693
659
76
3398
659
76
3352
658
76
3307
658
440903 6785
76
657
580
466991 559885
580
I | 534399 465601 561459)
2534745 465255 561851
579
578
577
577
577
576
3 535092 464908 562244
4 535438 464562 562636
5535783 576 464217 563028 653
19 57 533009
440115 6876
76
58 533357 466643 560279 656 439721 6922 3078
76
59 533704 466296 560673 4393276968
77
200534052 465948 561066
2986 70 °
438934 7014
77
438541 7060 2940
77
440509 6831 76 3169 70 4
76
3261
3215
656
3124
655
3032
655
654
59
653
653
437756 7152
437364 7198
436972 7245
654 438149 7106 2894
58
77
2848
57
77
2802
56
77
2755 69 55
a∞ not mano ao noin
9
8
7
6
5
3
2
I
575
574
574
573
573
7 536474 463526 563811
20 6536129 463871 563419 436581 7291
77
652
2709
54
8 536818 463182 564202
9 537163 462837564592
652
436189 7337
77
2663
53
651
435798 7383
77
2617
52
462493 564983
572
572
461806 565763
571
571
10 537507
11 537851
12 538194
13 538538
14 538880
15 539223
Cos. D.
70 Deg.
461462 566153 649
461120 566542
460777 566932
Sec. Cot. D.
433068 7709
229169 45
Tang. Cos. D. Sine
69 Deg.
4354087430
435017 7476
462149 565373 434627 7522
177
651
2570
51
77
650
2524
50
77
650
2478
49
649
78
433847 7615
77
434237 7569 2431
48
649
2385
78
433458 7662
78 2338
47
46
MATHEMATICAL TABLES.
99

201 Deg.
TABLE V.-LOG. SINES, ETO.
21 Deg.
Sine
D.
Cosec. Tang. D.
|
Cot.
Sec. D. Cos.
9°
10°
10°
10.02
9°
9'97
2015 539223
565
570
570
569
569
460777 566932 433068 7709
16 539565 460435 567320 648
17 539907 460093 567709
18 540249 459751 568098
21 541272
22 541613
*9 540590 568 459410 568486 646
20 540931 568 459069 568873 646
458728 569261
567
567 458387.569648
23 541953 566 458047 570035 645
644
566 457707 570422
20 24542293
25 542632 457368 570809
2291
648
647
647
432680 7755
432291 7802
431902 7849
178
45
78
78
645
645
431514 7895
431127 7942
430739 7989
430352 8036
178
429965 8083
429578 8130
78
78
78
178
644
565
564
26 542971
27 543310 456690 571581
457029 571195
643
564
563
563
562
28 543649 456351 571967
643
429191 8177 1823
428805 8224
428419 8271
78
78
78
00 00 00 00 00 00 00 00
∞ ∞ ∞
2245
44
2198
43
2151
42
2105
41
2058
40
2011
39
1964
78 1917 69 37
1870
38
36
35
1776
34
1729
33
30 544325 455675 572738|
29 543987 456013 572352 642 427648 8365 1635
642
428033 8318
79
1682
32
79
427262 8412
79
1588
31 544663 455337 573123
642
641
426877 8460
79
1540
32 545000
20 33 545338 561 454662 573892
34 545674
35 546011
562 455000573507
64.I
426493 8507
79
1493
69 28
MMN 2
31
30
29
79
426108 8554
1446
27
640
559
559
558
558
557
38 547019 452981 575810
39547354 452646 576193
40 547689
41 548024
561
560 453989 574660
36 546347 560 453653 575044
37 546683 453317 575427
454326 574276
640
425724
79
8602
1398
26
639
425340 8649
79
1351
25
639
424956 8697
79
1303
24
639
424573 8744
79
1256
23
638
424190 8792
79 1208
22
638
423807 8839
79 1161
21
452311 576576
637
451976 576958
637
423424 8887
423042 8934 80
79
1113
20
79 1066 69 19
20 42 548359
43 548693
44 549027
451641 577341
557
636
422659 8982
1018
18
556
556
555
555
554
554
553
553
552
552
552
551
551
550
550
451307 577723
450973 578104
45 549360 450640 578486
46 549693 450307 578867
47 550026
449974 579248
48 550359 449641 579629
449308 580009
49 550692
50 551024 448976 580389
636
636
635
422277 9030 80
421896 9078
421514 9126
∞ ∞
∞
80
80
∞
80
635
634
634
634
633
421133 9173
420752 9221
420371 9269
419991 9317
419611 9365
∞
80
∞ ∞ ∞ ∞
80
O
O
O
O
O
0970
17
0922
16
0874
15
0827
14
0779
13
80
0731
12
80
0683
II
80
0635 69 10
549
549
Cos. D.
20 51 551356 448644 580769|
52 551687 448313 581149
53 552018 447982 581528
54552349 447651 581907
55 552680
447320 582286
56 553010 446990 582665
57 553341 446659 583043
58 553670 446330 583422
446000 583800
59 554000
60 554329
445671 584177
Sec. Cot. D. Tang. Cos. D. Sine
633
632
632
632
631
631
630
630
629
419231 9414
418851 9462
418472 9510
418093 9558
417714 9606
417335 9655
416957 9703
416578 9751
416200 9800
415823 9848
0586
80
80
80
81
81
O O O O
∞∞
∞
∞ ∞ ∞ ∞ ∞ ∞
0538
80
0490
0442
80
0394
0345
0297
0249
98 76543 N
2
81
0200
I
81
0152 69 o
69 Deg.
69 Deg.
Uorm
100
MATHEMATICAL TABLES.

21 Deg.
21 Deg.
TABLE V.-LOG. SINES, ETC.
Sine D. Cosec.] Tang. D. Cot. Sec. D. Cos.
10*
ΙΟ Ο
9'5
10'4
9*
9'9
548
548
547
547
546
44357 585686 627
21
545
545
544
544
543
543
543
542
542
54I
54I
540
540
539
539
957280 42720 587566
628
2154329 45671 584177 415823 29848
I 54658 45342 584555 41544529897
254987 45013 584932 628 415068 29945 81 70055
3 55315 44685 585309
414691 29994 70006
4 55643
414314 30043 69957
5❘ 55971
413938 30091
44029 586062
546
627
6 56299 43701 586439 627
7 56626
43374 586815 626
8 56953 43047:587190 626
629
629
81 70152
81 70103
60
59
58
57
81
56
69909
413561 30140 69860
413185 30189
∞ ∞ ∞
81
81
81
81
81
55
54:
69811
53
412810 30238 69762 68 52
538
537
537
536
536
37532 593542
536
535
535
534
534
533
533
532
532
531
531
531
530
530
529
43
528
528
28 63433
495344 31223
29 63755 36245 595027 404973 31272
30 64075 35925 595398 404602 31322
31 64396 35604 595768 404232 31372
32 64716
35284 596138 403862 31422
33 65036
34964 596508 616 403492 31472
34 65356
34644 596878
35 65676 34324 597247
21 36 65995 34005 597616
37 66314 33686 597985
3866632 33368 598354
39 66951 33049 598722
40 67269
41 67587 32413 599459
42 67904 32096 599827
529
68222
613
31778 600194 612
44 68539 31461| 600562 399438 32023
612
45 68856 31144 600929 399071 32073
10 57606 42394 587941
11 57932 42068 588316
12 58258 41742 588691
13 58583 41417 589066
14 58909 41091 589440
15 59234 40766 589814
16 59558
40442 590188
17 59883 40117 590562
21 18 60207 39793 590935 409065 30728 69272
19 60531 39469 591308 408692 30777 69223
20 60855 39145 591681
21 61178
538
22 61501
23 61824
24 62146
25 62468
26 62790
21 27 63112
625
412434 30286 69714
51
81
412059 30335
69665
50
625
81
625
411684 30384 82
69616
49
411309 30433
69567
48
624
82
624
410934 30482
69518
47
82
410560 30531
69469
46
623
82
410186 30580
69420
45
623
82
623
409812 30630
69370
44
82
622
622
622
621
409438 30679
69321 68 43
33
82
42
618
618
37210 593914 406086 31123 83
36888 594285
36567 594656 618
617
617
617
616
620
40
39
38
408319 30827 69173
38822 592054 621 407946 30876
38499 592426 407574 30925 82
38176 592798 407202 30975 69025
37854 593171 406829 31024 68976
406458 3107483 68877 68 34
68926 35
620
619
619
82
82
37
36
82
82
82
82
69124
69075
+ + mm mm m
4I
98 765+
405715 31173 83 68777
68827
33
.∞ ∞ ∞ ∞ ∞ ∞
183
68728
321
333
32
31
83
68678
30
83
68628
29
83
68578
28
83
616
615
615
615
403122 31521
402753 31571
402384 31621
402015 31671
68528
83 68479
27
83
83 68429
68 25
765
2 2 2
26
68379
24
83
8368329
23
401646 31722
68278
22
614
83
401278 31772
68228
21
614
84
32731 599091
613
400909 31822
68178
20
84
613
400541 31872
400173 31922
399806 31973
68128
19
84
68078
18
84
68027
17
84
16
97977
84
67927 68 15
98 765
Cos. D. Sec. Cot.
D. Tang.
Cos. D.
Sine
681 Deg.
69 Deg.
MATHEMATICAL TABLES.
101

50 570435
51 570751
52 571066
53 571380
2r 54 571695
55 572009
56 572323
57 572636
58 572950
59 573263
22573575
I 573888
2 574200
525
525
524
524
48 569804 526 430196 602029
49 570120 526 429880 602395 610
429565 602761
429249 603127
428934 603493
428620 603858
O
21 Deg.
Sine
9*
TABLE V.—LOG. SINES, ETC.
22 Deg.
D. | Cosec. | Tang. | D. | Cot. | Sec. [D.| Cos. |
528
IO'
9°
21 45 568856| 431144 600929 611
46 569172 430828 601296
47 569488
430512 601662
527
527
ΙΟ 10.03 9'96
398704 2124
611
399071 2073 7927
84
15
7876
14
611
3983382174 7826
84
13
84
610
397971 2225
610
397605 2275 7725
3972392326
7775
12
84
II
84
7674
IO
609
609
396873 2376 7624
396507 2427 7573
396142 2478
84
84
84
609
85
7522 68 7
523
523
523
428305 604223 608
427991 604588
427677 604953
427364 605317
608
522
607
427050 605682
522
521
521
520
426737 606046
426425 606410
426112 606773 606
425800 607137
607
395047 2630
607
394683 2681
3943182732
395777 2529
395412 2579 85 7421
7471
9876
85
85
606
393954 2783
606
393590 2834
393227 2885
392863 2936
520
605
∞
∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞
5555555 in
5
7370
7319
4
3
85
7268
7217
2
I
7166 68 0
7115
7064 67 58
85
22
519
519
3 574512 425488 607500!
4574824 425176 607863
5 575136
605
392500 2987
6
518
518
517
575447 424553 608588
391775 309o
519 424864 608225
604
604
517
516
516
18
19 579470
516
515
515
514
514
513
513
513
512
512
511
511
511
510
510
509
509
509
420530 613281
20 579777 420223 613641
22 21 580085 419915 614000
22580392 419608 614359
23 580699 419301 614718
24 581005 418995 615077
25 581312 418688 615435
26 581618 418382 615793
27 581924 418076 616151
28 582229
417771 616509
29582535 417465 616867
417160 617224
30 582840
Cos. D. Sec. Cot. D.
7 575758 424242 608950
8 576069 423931 609312
9 576379 423621 609674.
10 576689
423311610036 389964 3347
II 576999
423001 610397 602 389603 3398
22 12 577309 422691 610759 602 389241 3450
13 577618
422382 611120
388880 3501
14 577927 422073 611480 601 388520 3553
15 578236 421764 611841 388159 3605
16 578545 421455 612201 387799 3656
86
17 578853 421147 612561 387439 3708 6292
86
579162 420838 612921
387079 3760 6240
86
386719 3812 6188
86
386359 3864 6136 67 40
86
386000 3915 6085
604
392137 3039 6961
391412 3141
603
391050 3192
390688 3244
603
390326 3295
603
602
601
∞ ∞ ∞ ∞ 00 00 00 00 00
∞ ∞
7013
85
85
6910
85
85 6808
6859
85
86
86
6756
6705
6653
86
86
86
6602 67
6550
ེ⊕ ུསྶསྶཔºོ པུ
56
54
49
48
86
6499
47
86
6447
46
601
600
86
6395
45
6344
44
600
43
600
42
41
599
599
39
598
598
598
597
597
597
596
596
596
87
385641 3967 6033
87
385282 4019 5981
87
3849234072 5928
87
384565 4124 5876
87
384207 4176 5824
87
383849 4228 5772
87
383491 4280 5720
87
383133 4332 5668 31
87
382776 4385 5615 67 30
Tang. Cos. D. Sine
38
37
36
35
100 76 in
34
33
32
681 Deg.
67 Deg.
102
MATHEMATICAL TABLES.

22 Deg.
Sine
D. Cosec. Tang. | D.
TABLE V.-LOG. SINES, ETC.
Cot.
234 Deg.
Sec. ID. Cos.
9*
22 30 582840 417160 617224
10*
9'
ΙΟ
10.03 9'96
508
508
507
507
505
505
31 583145 416855 617582
32 583449 416551 617939
33 583754 416246 618295
34 584058
506 415942 618652
35 584361 415639 619008
506
36 584665
506 415335 619364
37 584968 415032 619721
38 585272 414728 620076
595
595
595
382776 4385 5615
382418 4437 5563
87
3820614489
87
30
29
594
594
381705 4542 5458
87
381348 4594
87
5511
28
27
5406
26
594
593
593
593
504
504
503
503
503
502
502
501
501
22 39 585574 414426 620432)
40 585877 414123 620787
41 586179 413821 621142
42 586482 413518 621497
43 586783 413217 621852
44 587085 412915 622207
45 587386 412614 622561
46 587688 412312 622915
47 587989 412011 623269
592
379924 4805 5195
379568 4857
3809924647 5353
88
380636 4699 5301
88
380279 4752 5248
88
87
25
24
23
67 22
88
88
5143
21
592
592
591
591
590
590
590
379213 4910 5090
378858 4963 5037
378503 5016
378148 5069
377793 5121 88
377439 5174 4826
88
377085 5227 4773
20
88
88
19
4984
18
188
88
4931
17
4879
16
15
88
14
376731 5281
589
88
4719
67 13
22 48 588289|
49 588590
50 588890
51 589190
52 589489
53 589789
54 590088
55 590387
56 590686
22 57 590984
501
411711 623623
411410 623976
376377 5334
589
4666
12
89
500
411110 624330
500
589
376024 5387
410810 624683
499
499
410511 625036 374964 5546
588 375317 5493
588 375670 5440 89
89
4613
II
4560
ΙΟ
4507
89
588
499
410211 625388
409912 625741
498
587 374612 5600
89
4454
4400
498
409613 626093
587
374259 5653
89
4347
98 76
89
409314 626445
587
373907 5706
4294
5
89
497
409016 626797
497
497
496
496
58 591282
408420 627501
59 591580
23 591878 408122 627852
408718 627149
555
586
373555 5760
4240 67 4
189
586 373203 5813
4187
586
372851 5867
89
3
4133
2
89
585
372499 5920
4080
I
89
495
495
495
494
494
I 592176 407824 628203
2592473 407527 628554
585
89
585
3 592770 407230 628905
4 593067 406933 629255
5 593363 406637 629606
585
3919
371446 6081
89
4026 67
372148 5974
371797 6028
67 °
3972
59
584
371095 6135
89
58
3865
584
370745 6189
90
3811
57
56
23
7 593955
493
6593659 406341 629956|
493 406045 630306
583
370394 6243
90
3757
66 55
190
9 594547
493
492
492
491
491
8594251 405749 630656
405453 631005
10 594842 405158 631355
II 595137 404863 631704
00 00 00 00 00 00
10
10
10
10
10
583
370044 6296
3704
54
583
369694 6350 3650
90
53
583
582
582
491
490
12 595432 404568 632053
13 595727 404273 632401
14 596021 403979 632750
15 596315 403685 633098
582
581
581
581
369344 6404 3596
190
368995 6458 3542
90
3686456512 3488
90
368296 6566 3434
190
367947 6621 3379
190
367599 6675 3325
190
367250 6729 3271
190
190
52
51
50
49
48
47
46
Cos. D. Sec. Cot. D.
67 Deg.
366902 6783 3217 66 45
Tang. Cos. D. Sine
662 Deg.
MATHEMATICAL TABLES.
103

234 Deg.
24 Deg.
TABLE V.-LOG. SINES, ETO.
Sine D. Cosec. | Tang. | D. | Cot.
Sec. [D. Cos.
9'
älú
IO*
9*
IO'
10.03 9'96
23 15 596315
16 596609
17 596903
18 597196
19 597490
20 597783
21 598075
22 598368
23 598660
490
489
489
489
488
403685 633098
403391 633447
403097 633795
402804 634143
580
580
580
579
579
488
579
487
578
487
578
578
366902 6783 3217
366553 6837 3163
90
366205 6892 3108
91
365857 6946 3054
365510 7001
402510 634490
402217 634838
401925 635185
401632 635532
401340 635879
487
90
45
44
43
42
23 24 598952
486
577
25 599244
26 599536
27 599827
28 600118
486
485
485
485
484
484
484
399300 638302
399010 638647
483
398720 638992
483
398430 639337
482
398140 639682
482
397850 640027
482
397561 640371
481
397272 640716
481
481
396983 641060
396695 641404
480 396406 641747
480
396118 642091
395830 642434
362389 7492
399882 637611
29 600409 399591 637956
30 600700
31 600990
32 601280
23 33 601570
34601860
35 602150
36 602439
37 602728
38 603017
39 603305
40 603594
41 603882
23 42 604170
577
577
577
576
365162 7055 2945
364815 7110
364468 7164 2836
364121 7219
363774 7273 2727
401048 636226
400756 636572
363428 7328 2672
400464 636919
363081 7383 2617
362735 7438
400173 637265
91
91
91
91
91
191
91
91
91
2999
4I
40
2890
2781 66 37
96
33
39
38
36
35
34
2562
91
33
2508
479
395543 642777
479
479
478
477
477
476
476
475
475
392678 646199
392393 646540
392108 646881
474
474
474
473
473
Cos. D. Sec. Cot. D.
662 Deg.
476
392964 645857
394108 644490
49 606179 393821 644832
50 606465 393535 645174
23 51 606751
52 607036
53 607322
54 607607
55 607892
56 608177
93
57 608461 391539 647562
567 352438 9101
93
58 608745 391255 647903 352097 9157 0843
567
94
390971 648243
59 609029
351757 9214 0786
567
194
60 609313 390687 648583 351417 9270 0730 66 O
Tang. Cos. D. Sine
91
92
92
361008 7712 2288 66 28
192
360663 7767 2233
92
360318 7822
92
359973 7877 2123
92
359629 7933 2067
92
359284 7988 2012
92
358940 8043 1957
92
358596 8098 1902
92
358253 8154 1846
92
357909 8209
1791
92
357566 8265 1735
43 604457
357223 8320
44 604745
356880 8376
395255 643120
45 605032
356537 8431
478 394968 643463
46 605319
478 394681 643806
47 605606 394394 644148
48 605892
576 362044 7547
191
32
2453
31
576
575
361698 7602 2398
361353 7657
30
2343
29
575
575
574
2178
206
27
26
574
25
574
24
573
23
573
22
573
21
20
572
572
66 19
18
572
572
571
92
92
93
2 2 3
1680
17
1624
16
571
1569
15
571
570
570
570
569
555
393249 645516 569 354484 8765
93
356194 8487 1513
93
3558528542 1458
93
355510 8598 1402
93
355168 8654 1346
93
354826 8710 1290
93
14
13
12
II
66 10
1235
569
354143 8821
569 353801 8877
568 353460 8933
93
1179
93
1123
93
1067
98 76
391823 647222 568 352778 9045
568
353119 8989
93
IOII
5
193
0955
4
0899
3
2
I
66 Deg.
104
MATHEMATICAL TABLES.

242 Deg.
24 Deg.
TABLE V.-LOG. SINES, ETC.
Sine D. Cosec. Tang. D.
| Cot. Sec. D. Coş.
9.6
240 09313
I 09597
2 09880
3 10164
410447
5 10729
6 11012
711294
8 11576
24 9
473
472
472
472
471
47I
10'3 9°
90687 648583
90403 648923
90120 649263
89836 649602
89553 649942
89271 650281 565
ΙΟ
10'0
9'9
566
351417 39270 60730
60
566 351077 39326
566 350737 39382
566 350398 39439
350058 39495
470
470
88706 650959
88424 651297
565
88988 650620 349380 39608 60392
565 349719 39552
94
94 60448
94 60505
94
60674
94 60618
94 60561
59
58
57
28 7
56
55
564
470
564
11858
469
IO 12140
II 12421
12 12702
13 12983
14 13264
469
469
468
468
467
467
17 14105
15 13545 86455 653663|
16 13825 467 86175 654000
88142 651636
87860 651974
87579 652312
87298 652650
87017 652988 563
86736 653326 563
564
563
563
562
562
466
85895 654337
562
561
24 18 14385
19 14665
20 14944
466
466
85615 654674
345663 40232 195
349041 39665
348703 39721 60279
348364 39778 60222
94 60165
348026 39835
94
347688 39891 60109
95 60052
347350 39948
195
347012 40005 59995
95
346674 40062 59938
95
346337 40118 59882
346000 40175 195
94
94 60335
54
53
65 52
94
51
50
49
48
47
46
45
95
44
59825
59768
65 43
465
85335 655011 561
85056 655348 561
561
24
26 16616
465
465
23 15781 84219 656356
464
16060 83940 656692
464
25 16338 83662 657028
464
21 15223 84777 655684 560 344316 40461 59539
22 15502 84498 656020
345326 40289 59711
344989 40346 59654
344652 40404 59596
42
95
195
95
41
40
559
463
83384 657364
559
559
28 17172
29 17450
30 17727
31 18004
32 18281
24 27 16894
463
462
59482
95
59425
195
343308 40632 59368
95
342972 40690 59310
96
342636 40747 59253
196
83106 657699 342301 40805
82828 658034 559
560 343980 40518
560 343644 40575
95
39
38
96
37
36
35
65 34
462
82550 658369. 558
462
461
461
461
460
460
4.60
4221038
43 21313
459
459
459
458
458
457
457
457
D.
33 18558
34 18834
35 19110
24 36 19386
37 19662
80062 661377
38 19938
39 20213 79787 661710
40 20488 79512 662043
41 20763 79237 662376
557
80614 660710
80338 661043
557
557
556
556
556
81719 659373 340627 41092
81442 659708 340292 41150
81166 660042 557
558
558
82273 658704 341296 40977
81996 659039
558 341966 40862
341631 40919
340961 41035
aaa a
96
96
96
96
339958 41208
80890 660376 339624 41266
966 a
96
96
96
196
666OOOOO6
59195
33
96 59138
59081
59023
58965
HO
3332
32
31
30
29
58908
28
58850 27
58792 26
5873465 25
339290 41323
338957 41381
555
555
555
554
554
554
78962 662709
78687 663042
44 21587 78413 663375 336625 41787 58213 16
4521861
78139 663707 336293 41846 58154 65 15
Cos.
Sec. Cot. D. Tang. Cos. D. Sine
338623 41439
338290 41497
337957 41555
337624 41613
337291 41671
336958 41729 197
aaa aa a
96
58677
24
96
58619
23
96
58561
22
58503
21
1971
58445
20
97
197
58387 19
58329 18
58271
96
17
197
97
96
66 Deg.
651 Deg.
MATHEMATICAL TABLES.
105

24 Deg.
о
Sine
D.
9°
IO'
456
456
456
455
455
455
454
454
454
453
453
453
452
452
374594 668013
452
374323 668343
I
1 626219
2626490
451
374052 668672
2445 621861 378139 663707 336293 1846 8154
46 622135 377865 664039 335961 1904 8096
47 622409 377591 664371 335629 1962
48 622682
49 622956
50 623229
51 623502
52 623774
53 624047
24 54 624319
55 624591
56 624863
57 625135
58 625406
59 625677
25 o 625948
TABLE V.-LOG. SINES, ETC.
25 Deg.
Cosec. Tang. D. Cot. | Sec. D. | Cos.
9°
IO' 10'04
9'95
377318 664703 335297 2021
377044 665035 334965 2079
376771 665366 334634 2137
376498 665697 334303 2196
376226 666029 333971 2254
375953 666360 333640 2313
375681 666691
375409 667021
375137 667352
374865 667682
554
553
553
553
553
552
552
552
551
97
15
14
97
8038
13
97
7979
12
97
7921
I I
97
7863
10
97
7804
97
7746
98
98
7687 65 7
987
บ
551
551
551
333309 2372
332979 2430
98
332648 2489 7511
332318 2548
98
7628
7570
6
98
550
550
550
373781 669002
550
451
45I
373510 669332
549
25 3 626760
4 627030
5 627300
6 627570
7 627840
8 628109 449
9 628378 448
10 628647
11 628916
25 12 629185
549
450
450
450
449
373240 669661
372970 669991
372700 670320
372430 670649
372160 670977.
331987 2607 7393
98
331657 2665 7335
98
331328 2724 7276 65 o
98
330998 2783 7217
98
330668 2842 7158 64 58
98 7452
5432 - O
I
59
98
330339 2901
549
98
7099
57
548
330009 2960
548
329680 3019 6981
98
7040
56
98
55
371891 671306
449
371622 671634
448
447
13 629453
14 629721
15 629989
16 630257
17 630524
18 630792
19 631059 445
20 631326 445
25 21 631593
22 631859
23 632125
24 632392
25 632658
26 632923 443
27 633189
28 633454 442
29 633719
30633984
447
447
446
446
446
446
445
444
444
444
443
443
442
442
547
547
370815 672619. 327381 3434
546
370547 672947
546 327053 3494
326726 3553
370279 673274
546
370011 673602 326398 3613
546
369743 673929 326071 3673
545
369476 674257. 325743 3732
545
369208 674584 325416 3792
545
368941 674910 325090 3852
544
368674 675237 324763 3911
544
368407 675564
544
368141 675890
544
367875 676216
543
367608 676543
543
367342 676869
543
367077 677194
543
366811 677520
542
366546 677846
542
366281 678171
542
366016 678496
329023 3138
328694 3197
328366 3256
371353 671963
328037 3316
371084 672291 327709 3375
548
329351 3079
6921
99
54
6862
548
547
99
99 6803
53
52
547
99
6744
51
99
99 6625 64 49
6684 50
99
99
99
100
99 6208
6387 45
6327 44
99 6268
6506 47
99 6447
6566 48
46
43
42
6148 41
100
100
6089 64 40
324436 3971 6029 39
324110 4031 5969
38
323784 4091 5909
323457 4151 5849
323131 4211 5789
322806 4271 5729
322480 4331 5669
322154 4391 5609
321829 4452
100
100
100
100
100
100
1ΟΟ
100
100
37
36
35
34
33
32
5548
31
Cos. D.
651 Deg.
Sec. Cot. D.
321504 4512 5488 64 30
Tang. Cos. D. Sine
644 Deg.
I
106
MATHEMATICAL TABLES.

261 Deg.
25/ Deg.
O
Sine
TABLE V.-LOG. SINES, ETC.
D. Cosec. Tang. | D. | Cot.
Sec. D. Cos.
9°
ΙΟ
9*
IO'
10'04
9'95
441
438
25 30 633984 366016 678496 321504 4512
31 634249 365751 678821 321179 4572
441
32 634514 365486 679146| 320854 4632
440
33 634778 365222 679471 320529 4693
440
34 635042 364958 679795 320205 4753
440
35 635306 364694 680120
439
36 635570 364430 680444
439
37 635834 364166 680768
439
38 636097 363903 681092
438
25 39 636360
438 363640 681416 539
318584 5056
40636623 363377 681740 318260 5117
539
5488
542
100
54I
54I
54I
541
540
540
540
540
5428
ΙΟΙ
5368
32 2
30
29
28
319880 4814 5186
319556 4874 5126
319232 4935 5065
318908 4995 5005
ΙΟΙ
ΙΟΙ
ΙΟΙ
ΙΟΙ
ΙΟΙ
ΙΟΙ
ΙΟΙ
5307
27
5247
26
25
24
23
64 22
4944
2 I
ΙΟΙ
4883
20
437
437
437
437
436
436
436
435
435
435
434
434
434
41 636886 363114 682063 317937 5177 4823
539
42 637148 362852 682387 317613 5238
539
43 637411 362589 682710
538 317290 5299
44637673 362327 683033 316967 5360
45 637935 362065 683356 316644 5421
46 638197
47 638458
25 48 638720 361280 684324 315676 5604
49638981 361019 684646 315354 5665
[IOI
19
ΙΟΙ
4762
18
ΙΟΙ
538
538
100 00 00
4701
17
98 7
ΙΟΙ
4640
16
ΙΟΙ
4579
15
538
537
361803 683679 316321 5482
361542 684001 315999 5543 4457
IOI
4518
14
102
64 13
102
4396
12
537
102
433
433
433
432
432
432
431
431
431
430
430
430
537
50 639242 360758 684968
315032 5726
537
51 639503 360497 685290 314710 5787
536
52 639764 360236 685612
536 314388 5848
53 640024 359976 685934 314066 5910
54 640284 359716 686255 313745 5971
55 640544 359456 686577 313423 6032
56 640804 359196 686898 313102 6094
25 57 641064 358936 687219 312781 6155
58 641324 358676 687540 312460 6217 3783
59 641584 358416 687861
3722
312139 6278
26 641842 358158 688182 311818 6340
I 642101 357899 688502 311498 6401
2 642360 357640 688823 311177 6463 3537
3 642618 357382 689143
4335
II
102
4274
ΙΟ
102
4213
9
102
4152
8
102
536
4090
7
102
536
535
535
4029
6
102
3968
5
102
3906 64 4
102
3845
3
430
429
429
429
428
427
427
Cos.
D.
64 Deg.
310857 6525
4 642877 357123 689463 310537 6587
5 643135 356865 689783
310217 6648
26 6643393 356607 690103 309897 6710
7 643650 356350 690423 309577 6772 3228
8 643908
356092 690742 309258 6834 3166
9 644165 355835 691062 308938 6896 3104
10 644423 355577 691381 308619 6958 3042
II 644680
428 355320 691700 531
428 355064 692019 531
12 644936
13 645193 354807 692338
14 645450 354550 692656
15 645706 354294 692975 307025 7269 2731 63 45
Sec. Cot. D. Tang. Cos. D. Sine
535
535
534
534
534
534
533
533
533
533
533
532
532
102
102
103
103
103
2
I
3660 64 0
3599
59
58
103
103
103
103
33
3475
57
3413 56
3352 63 55
3290
54
103
103
103
103
532
531
531
308300 7020
307981 7082
307662 7145
307344 7207
103
wwwww
53
52
51
50
2980
49
104
2918
48
104
2855
47
104
2793 46
104
63 Deg
MATHEMATICAL TABLES.
107

26 Deg.
TABLE V.-LOG SINES, ETC.
27 Deg
Sine | D. Cosec. Tang. | D.
9.6
Cot. Sec. | D.
Cos.
26 15 45706|
16 45962 427
1746218
18 46474
1946729
426
10'3 9°
54294 692975
54038 693293
426 53782 693612
426 53526 693930
10°
ΙΟΟ
9'9
531
530
425
425
425
424
424
424
3049527
424
423
423
423
422
422
422
422
421
26 24 48004 51996 695836 304164 47832 52168
25 48258 51742 696153 303847 47894
26 48512
51488 696470 303530 47957
104
104
104
104
104
104
20 46984 53016 694566 305434 47581 52419
21 47240 52760 694883 305117 47644 52356
22 47494 52506 695201 304799 47706 52294
2347749 52251 695518
530
530
530
529
307025 47269
306707 47331
306388 47394 52606
104
306070 47456 52544
305752 47519
53271 694248
52731
45
104
104
52669
44
43
42
52481
41
40
49713 698685
49461 699001
421
|49208 699316
421
48956 699632
420
420
420
419
419
419
418
48703 699947
3851549 48451 700263
50473 697736 302264 48209
31 49781 50219 698053 301947 48272
32 50034 49966 698369
26 33 50287
34 50539
35 50792
36 51044
37 51297
28 49020
50980697103 30289748083
2949274 50726 697420 302580 48145
27 48766 51234 696787 30321348020 51980
529
529
529
529
528
528
528
528
527
527
527
39
38
304482 47769 52231
63 37
36
105
105
105
52106
35
52043
34
33
105
51917
32
105
51854
31
105
51791
30
105
51728
29
301631 48335
105
51665
63 28
527
105
526
301315 48398
51602
27
526
526
39 51800 48200 700578 299422 48778
418
417
417
417
416
297534 49159
297220 49222
46192 703095
47 53808
296905 49286
48 54059 45941 703409 296591 49350
49 54309 45691 703723 296277 49414 50586
526
525
525
47948 700893
4052052
525
41 52304 47696 701208
51096 63 19
524
26 42 52555
47445 701523 298477 48968 51032
524
43 52806
298163 49032
47194 701837
524
.44 53057
46943 702152 297848 49095
46692 702466 524
45 53308 418
524
46442 702780
46 53558 418
523
523
523
523
| 526/300368 48588
300999 48461
300684 48524
105
105
105 51476
51539
26
25
51412
24
300053 48651
105
51349
106
23
299737 48714
51286
22
106
51222
21
299107 48841
298792 48904
106
51159
20
416
416
416
60 57047
415
415
415
414
414
414
413
Cos. D. Sec. Cot. D.
26 51 54808 |45192 704350 295650 49542
522
52 55058 44942 704663
522
44693 704977
53 55307
522
54 55556 44444 705290
522
55 55805 44195 705603 294397 49798
521
56 56054 43946 705916. 294084 49862
521
57 56302 43698 706228 293772 49926
521
5856551 43449 706541 293459 49990
521
59 56799 43201 706854 293146 50055
42953 707166 521
292834 50119
Tang. Cos.
522
50 54558 45442 704036 295964 49478 50522 63 10
106
106
106
106
106
106
106
106
106
106
18
50968
17
50905
16
50841
15
50778
14
50714
13
50650
12
I I
107
50458
295337 49606
107
50394
295023 49670
294710 49734
107
50330
107
50266
107
50202
107
50138
107
50074
107
50010
107
49945
98 765432 H
107
49881 63 O
|
D. Sine
633 Deg.
63 Deg.
108
MATHEMATICAL TABLES.

413
413
412
412
412
7
411
410
410
410
409
409
409
408
339009 712146
408
661726
19
20 661970
21 662214
22 662459
408
6 658531 341469 709037 290963 0506
658778 341222 709349 290651 0571
8659025 411
519
340975 709660 290340 0636
27 9 659271 340729 709971
10 659517 340483 710282 289718 0765
11 659763
340237 710593 289407 0830 9170
12 660009 339991 710904
13 660255
339745 711215
14 660501 339499 711525
15 660746 339254 711836
16 660991 409
17 661236
27 18 661481
27 Deg.
Sine
9°
TABLE V.-LOG. SINES, ETC.
D. Cosec. | Tang. D. Cot.
9°
IO*
270 657047 342953 707166
272 Deg.
Sec. D. Cos.
9'94
10° 10*05
292834 0119 9881
I 657295 342705 707478
2 657542 342458 707790 292210 0248
107
107
108
108
3 657790 342210 708102 291898 0312 9688
4 658037 341963 708414 291586 0377 9623
658284 341716 708726| 291274 0442
412
411
520
520
520
520
519
519
519
292522 0184 9816
107
9752 58
108 9558
108 9494
108 9429
519
518
518
518
518
518
517
✪ ∞ ∞ ∞ ∞ ∞ t
108
9364 62 52
290029 0700
407
407
4.07
406
405
405
405
404
27 27 663677
28 663920 405
29 664163
30 664406
31 664648
32 664891
33 665133 334867 717401 282599 2269
338519 712766| 287234 1285 8715
338274 713076
407
516
286614 1416109 8584
337786 713696
286304 1481
337541 714005 285995 1546 8454
516
23 662703 337297 714314 285686 161219 8388
406
24 662946
25 663190
26663433 406
515
515
109
337054 714624 285376 1677 8323
336810 714933 285067 1743
336567 715242 515
515
284758 1808
336323 715551 284449 1874
336080 715860 514
338764 712456 287544 1220
ни
517
338030 713386| 516 |286924| 1350 |
517
517
516
289096 0895 9105
|288785 0960 9040
288475 1025 8975
288164 1090 108 8910
287854 1155 108
1155108
108
108
108
108
108
108
9300
9235
45
8845
44
109
8780 62 43
109 8650
42
516
109 8519
109
40
39
38
37
109 8257
36
8126
109 8192 62 34
109
35
44 667786
404
404
403
665375
34
403
35 665617
403
27 36 665859
37 666100 402
402
38 666342
402
39 666583
402
40 666824
401
41 667065
401
42 667305 332695 720169 279831 2864
401
43 667546 332454 720476 279524 2930
401
332214 720783 279217 2996
400
45 668027 331973 721089 278911 3063
Cos. D. Sec. Cot. D. Tang. Cos. D.
63 Deg.
284140 1940
335837 716168 283832 2005
335594 716477 283523 2071
335352 716785 283215 2137
335109 717093 282907 2203
334625 717709 282291 2335
514
514
514
514
513
513
513
513
513
512
512
512
512
512
511 I
511
II
5II
334141 718325 281675 2467 7533
333900 718633| 281367 2533 7467
333658 718940
281060 2599
333417 719248 280752 2665 7335
333176 719555 280445 2731 7269
332935 719862
280138 2797 7203
334383 718017 281983 2400 7600 62 25
O
109 8060
109
110
IIO
IIO
IIO
IIO
II
33
wwwwwww↑‡‡ £$£At Abuu muo
59
57
56
49
48
47
46
32
7995
❤
7929
7863
7797
7731
7665 26
980 76
MM2 2
2 2 2
31
30
29
28
27
IIO
24
IIO
IIO
ΙΙΟ
110
IIO
23
7401
22
21
20
19
IIO
III
7136
18
7070
17
III
III
7004
16
6937 62 15
Sine
621 Deg.
MATHEMATICAL TABLES.
109

400
400
399
399
399
399
398
398
398
397
397
397
397
396
396
396
395
395
395
395
394
394
394
394
393
393
393
55 670419 329581 724149 275851 3730
56 670658 329342 724454 275546 3797 6203
57 670896 329104 724759 275241 3864
58 671134 328866 725065| 274935 3931 6069
59 671372
328628 725369 274631 3998
28 0 671609 328391 725674
1 671847 328153 725979 274021 4132
2 672084 327916 726284 273716 4200
28 3 672321 327679 726588 273412 4267
4 672558 327442 726892 273108 4334
27 Deg.
Sine
9°
TABLE V.-LOG. SINES, ETC.
28 Deg.
D. | Cosec. Tang. D. Cot. Sec. D. Cos.
IO*
9°
IO'
10.05
III
III
9'94
2745 668027 331973 721089 278911 3063 6937
46 668267 331733 721396 278604 3129 6871
47 668506 331494 721702 278298 3196 6804
48 668746 331254 722009 277991 3262
49 668986 331014 722315
50 669225 330775 722621
51 669464 330536 722927
52 669703 330297 723232
53 669942 330058 723538
27 54 670181 329819 723844 276156 3663 6337
15
14
98 76
511
511
510
510
510
13
277685 3329 6671
III
III
6738
12
II
III
277379 3396
510
6604
ΙΟ
III
510
277073 3462
6538
509
276768 3529
III
6471
276462 3596
III
6404 62 7
509
III
509
III
6270
509
5
509
508
508
508
508 274326 4065
112
I12
112
112
4
6136
3
2
6002
I
112
5935 62 0
112
508
112
5868 59
507
112
5800 61 58
392
113
113
10 673977
113
326023 728716 271284 4739 5261
113
11 674213 325787 729020 270980 4807
113
28 12 674448 325552 729323 270677 4875
5672795 327205 727197
6 673032 326968 727501 272499 4469 5531
7 673268 326732 727805 272195 4536 5464
8 673505 326495 728109 271891 4604
9673741 326259 728412 271588 4672 5328
392
392
392
391
391
391
391
390
13 674684 325316 729626 270374 4942
14 674919 325081 729929 270071 5010
113
15 675155 324845 730233 269767 5078 4922
113
16 675390
324610 730535 269465 5146 4854
17 675624
113
324376 730838 269162 5214 4786
18 675859
113
324141 731141 268859 5282 4718
19 676094 323906 731444 268556 5350
20 676328 323672 731746 268254 5418
507
507
507
507
506
506
506
506
506
505
5733
112
5666
272803 4402
112
II2
112
5598
5396
5193 61 49
ི་ྲུྨཨºོ༢༦
56
55
54
53
50
5125
48
113
5058
390
390
390
389
389
389
388
388
388
28 21 676562 323438 732048 267952 5486 4514
22 676796 323204 732351
267649 5554 4446
23 677030 322970 732653 267347 5623 4377
24 677264 322736 732955 267045 5691 4309
25 677498 322502 733257
26 677731
322269 733558
27 677964 322036 733860 503
28 678197
321803 734162
29 678430 321570 734463
30 678663 321337 734764
505
505
505
505
504
504
504
504
504
503
503
113
4990
113
113
114
4650
4582 61
114
114
114
503
503
502
266743 5759 4241
266442 5828
266140
266140 5896
114
114
wwwww.f££££££
47
46
44
42
40
39
38
37
36
35
98 765
114
4172
4104
34
265838| 5964
114
33
4036
502
265537 6033
114
32
502
Cos. D. Sec. Cot. D.
265236 6101 3899 61 30
Tang. | Cos. D. Sine
114
3967 31
621 Deg.
61 Deg.
110
MATHEMATICAL TABLES.

291 Deg.
28 Deg.
Sine
TABLE V.-LOG. SINES, ETC.
D. Cosec. Tang. D. Cot.
Sec. D. Cos.
9°
IO*
9*
IO* 10.05
9'94
28 30 678663
32
33
34
679128
679360
679592
35 679824
36 680056
37 680288
38 680519
∞ ∞ ∞ ∞
∞
∞
∞
∞
∞
mmm
en
en
en
M
M M
388
387
387
387
387
386
སསསས བ
386
385
41681213
42
43
Www W
∞ ∞ ∞0
385
383
382
382
382
382
381
33
381
381
∞ ∞
28 39 680750 319250 737471 262529 6721 3279
40 680982 319018 737771 262229 6790 3210
385
318787 738071 261929 6859 3141
385
681443
318557 738371 261629 6928
384
681674 |318326 738671 261329 6997 3003
384
318095 738971
44 681905
384
45 682135 317865 739271
384
46 682365 317635 739570
383
47 682595 317405 739870
383
28 48 682825 317175 740169
383
49 683055 316945 740468
50 683284
316716 740767
51 683514 316486 741066
52 683743 316257 741365
53 683972 316028 741664
54 684201
315799 741962
55 684430 315570 742261
56 684658
321337 734764
265236 6101 3899
31 678895 321105 735066 264934 6170 3830
320872 735367 264633 6239
320640 735668 264332 6307 3693
115
320408 735969| 264031 6376
115
320176 736269 263731 6445 3555
115
319944 736570 263430 6514 3486
115
263129 6583 3417
386 319712 736871
115
319481 737171 262829 6652 3348
115
30
502
502
502
114
29
114
3761
28
114
27
501
501
501
501
501
500
3624
26
25
24
23
61 22
2I
500
115
20
500
500
500
499
499
499
115
19
115
3072
18
499
499
499
498
59
28 57 684887
58685115
685343
29 685571
I
2
685799
686027
W W W W W
380
380
380
3 686254
380
379
379
379
379
378
29
9
377
377
377
377
376
376
312384 746429
312157 746726
6 686936 313064 745538 254462 8602
378
7 687163 312837 745835 254165 8672
378
8 687389
687616 378 312611 746132
315113 742858 257142 7971
314885 743156 256844 8041
314657 743454 256546 8111
314429 743752 256248 8181
314201 744050 255950 8251
255652 8321
313973 744348
313746 744645 255355 8391
4 686482 313518 744943 255057 8461
5 686709 313291 745240 254760 8531
498
498
498
498
497
497
497
497
497
115
115
261029 7066
115
260729 7136 2864
115
260430 7205 2795
116
260130 7274
2726
116
259831 7344 116
2656
259532 7413 116 2587
259233 7483 116 2517
258934 7552 116 2448
258635 7622 2378
258336 7692 2308
258038 7761 2239
257739 7831 2169
17
2934
16
15
14
61 13
12
II
ΙΟ
116
116
116
116
315342 742559 257441 7901 116 2099 61 4
98 76 5t
116
2029
116
1959
3
2
1889
497
496
496
496
496
LO LO LO
117
117
117
1819 61 0
1749
496
117
117
117 1609
1679
57
1539
56
495
117
1469 60 55
1398
༦ºོཀྵུ་༠ *
59
58
54
495
117
D.
495
495
495
495
494
494
494
494
Sec. Cot. D.
10 687843
II 688069 311931 747023 252977 8954 1046
12 688295 311705 747319
252681 9025
13 688521
252384 9095
311479 747616
14 688747 311253 747913 252087 9166
15 688972 311028 748209 251791 9237
Cos.
Tang. Cos. D.
253868 8742
253571 8813
253274 8883
117
1328 53
1258
52
117
1187
51
117
II 17
50
117
118
49
118
118
118
0975
48
0905
47
0834
46
0763 60 45
Sine
61 Deg.
602 Deg.
MATHEMATICAL TABLES.
111

291 Deg.
TABLE V.-LOG. SINES, ETC.
| Sine D. Cosec. Tang, D. Cot. Sec. D. Cos.
30 Deg.
9.6
374
373
373
373
373
372
372
372
371
22 90548 09452 750281
23 90772 |09228 750576
29 24 90996
09004 750872
25 91220 08780 751167
376
376
375
375
375
375
374
374
374
10'3 9°
29 15 88972
11028 748209 251791 59237 40763
16 89198 10802 748505 251495 59307
17 89423 10577 748801 251199 59378
18 89648 10352 749097
19 89873 10127 749393 250607 59520
20 90098 09902 749689
250311 59591
21 90323 09677 749985 250015 59662
IO'
10'0
9'9
494
493
493
493
493
493
118
118
40693
250903 59449
118
118
40622
40551
40480
118
41
77777
45
44
43
42
493
11840409
118 40338
40
39
27 91668 08332 751757
26 91444 08556 751462|
248538 60018 39982
248243 60089 39911
28 91892 08108 752052
247948 60160
29 92115 07885 752347 247653 60232 39768
492
492
492
492
249719 59733 40267
249424 59804 40196
249128 59875 40125
248833 59946 40054
3092339 07661 752642 247358 60303 39697
3994342
371
371
371
370
370
370
05658 755291
370
40 94564 05436 755585
369
41 94786
31 92562 07438 752937 247063 60375 39625
3292785 |07215] 753231 246769 60446 39554
29 33 93008 06992 753526 246474 60518
34 93231 06769 753820 246180 60590
3593453
06547 754115 245885 60661
36 93676 06324 754409 245591 60733
37 93898 06102 754703 245297 60805
38 94120 05880 754997 245003 60877
29 42 95007
3 3
369
368
368
368
367
50 96775 367
367
03446 758224
04993 756172 243828 61164
43 95229 04771 756465
369
44 95450 04550 756759
368
45 95671
46 95892
47 96113
48 96334
49 96554
369 05214 755878 244122 61092
492
492
491
491
491
491
491
491
490
490
490
490
490
490
489
489
489
489
489
|04329| 757052 489 242948 61381
04108 757345 242655 61453
03887 757638
118
118
119
119
119
38
60
60 37
36
35
34
33
119
119
39840
32
31
119
30
119
119
119
29
60 28
39482
27
119
39410
26
119
39339
119
25
39267
24
120
39195
120
23
39123
22
120
244709 60948
244415 61020
39052
21
120
38980
20
120
38908
120
60 19
38836
18
120
243535 61237
243241 61309
38763
17
120
38691
16
120
38619
15
120
488
38547
14
120
488
03666 757931 242069 61598
488 242362 61525
38475
13
120
38402
I2
488 241776 61670
121
38330
II
121
03225 758517
488 241483 61742
38258 60 10
121
29 51 96995 03005 758810
367
488 241190 61815
38185
121
366
54 97654
366
52 97215
5397435 02565 759395
02785 759102
487
240898 61887
38113
86
8
121
366 02346 759687|
487
365
57 98313 01687 760564 487 239436 62251
58 98532 01468 760856
55 97874 02126 759979 487 240021 62105
366
56 98094 01906 760272
365
365
5998751 01249 761148
365
486 238852 62396
60 98970 01030 761439 238561 62469
Cos. D. Sec. Cot. D. Tang. Cos. D. Sine
487
240605 61960
240313 62033
38040
121
37967
121
121
37895
487
239728 62178
37822
121
486 239144 62324
121
37749
37676
76543
2
121
121
37604
3753160 O
I
602 Deg.
60 Deg.
112
MATHEMATICAL TABLES.

30 Deg.
Sine
9°
TABLE V.—LOG. SINES, ETC.
D. Cosec. Tang. | D. Cot.
30 Deg.
Sec. D.
Cos.
IO*
9'
IO* 10'06
9'93
364
364
300 698970 301030 761439
1 699189 300811 761731
486
364
364
363
2 699407
3 699626 300374 762314
4 699844 300156 762606
486
238561 2469
238269 2542
7531
60
121
300593 762023
486
486 237977 2615
237686 2688
122
122
7458 59
7385 58
7312
363
363
362
362
362
361
361
298198 765224
14 702019 297981 765514
15 702236 297764 765805
361
16 702452 297548 766095
361
30 18 702885
8 700716
30 9700933 299067 764061
235939 3128
10 701151 298849 764352 235648 3201
II 701368 298632 764643
12 701585 298415 764933
362
13 701802
237394 2762
5 700062 299938 762897 237103 2835
363
6 700280 299720 763188 236812 2908
363
485
7 700498 299502 763479 236521 2981
299284 763770 485
|236230 3054
122
485
122
485
122
7238
7165
7092
122
7019
122
485
122
6946 59 52
485
6872
122
484
6799
484
484 235357 3275
235067 3348
122
122
6725
484
484 234776 3422
234486 3495
484
17 702669 360 297331 766385. 483
484
234195 3569
233905 3643
233615 3716
123 6505
123 6431
123 6578
6652
123 6357
19 703101
360
360
359
359
359
359
359
296899 766965
20 703317 296683 767255
232745 3938 123 6062
21 703533 296467 767545 232455 4012
22 703749 296251 767834 232166 4086123
23 703964 296036 768124 231876 4160 5840
24704179 295821 768413 231587 4234
360 297115 766675 233325 3790
123
123 6284 59 43
6210
483
483
483
483
483
233035 3864
123 6136
123
5988
5914
123
482
123
25 704395 295605 768703
26 704610
28 705040
29 705254
30 705469
31 705683 357
32705898
33 706112
34 706326
30 27 704825 358 295175 769281
358 295390 768992 231008 4382
358
358
357
357
357
294960 769570
294746 769860
294531 770148
294317 770437
294102 770726
293888 771015
35 706539 356
30 36 706753
37 706967
38707180 356
356
356
39 707393
40 707606 355
355
41 707819
42 708032 355
43 708245 354
354
44 708458
354
45 708670
Cos. D.
355
482
482
482
482
482
481
481
481
481
481
481
481
480
480
480
480
480
5766
ww ww f ‡ ‡ £££££££4 Jun
56
55
48
46
44
4.2
4.I
40
37
36
231297 4308
124
5692
35
124
124 5618 59 34
291968 773608 480
291755 773896
293247 771880
293033 772168
292820 772457
292607 772745
|292394 773033 226967 5426 125
292181 773321 226679 5501 125
226392 5576 125
226104 5651
291542 774184 225816 5726 125 4274
291330 774471 225529 5801
Sec. Cot.
230719 4457
230430 4531
230140 4605 5395
229852 4680 124
229563 4754
229274 4829
228985 4903
293674 771303 228697 4978
293461 771592
228408 5052
228120 5127
5543
33
124
124
5469
5320
124
124
124
5246
5171
5097
124
5022
124
4943 59
210 9∞
765
3332
2
2 2 2
32
31
30
29
28
27
26
25
124
4873
24
227832 5202
124
4798
23
125
|227543 5277
227255 5351
4723
22
125
4649
4574
4499
479
479
479
125
D. Tang. Cos. D. Sine
125
4424
4349
4199 59 15
0 000 7 5
2 2 H H
21
20
19
18
17
16
60 Deg.
591 Deg
MATHEMATICAL TABLES.
113

30 Deg.
TABLE V.-LOG. SINES, ETC.
31 Deg.
Sine
D. | Cosec. Tang. D.
| Cot.
Cot
Sec.D. | Cos. |
9*
ΙΟ
9°
10° 10'06
9'93
354
353
353
353
353
353
352
352
352
35I
351
351
351
350
350
350
350
30 45 708670 291330 774471
46 708882
291118 774759
47 709094 290906 775046
224954 5952 4048
48 709306 290694 775333 224667 6027 3973
49 709518 290482 775621
224379 6102 125
50 709730 290270 775908 224092 6178
5I 709941
290059 776195
52 710153
53 710364
30 54 710575
55 710786
56 710997
57 711208
58 711419
289847 776482 478 223805 6253
289636 776769
352
479
479
479
479
478
478
225529 5801
225241 5877 4123
4199
125
15
14
125
125
13
12
126
3898
II
6
349
349
349
349
349
348
348
348
348
4 712679
287321 779918 476 220368 7162
220082 7238
5 712889 287111 780203
713098 286902 780489
7 713308 286692 780775
8 713517
9713726
10 713935
II 714144
223518 6329
478
478 223231 6404
289425 777055 222945 6480
3520
478
289214 777342 222658 6555 3445
289003 777628 222372 6631 3369
288792 777915 222085 6707 3293
288581 778201 221799 6783
59 711629 288371 778487 221513 6859 3141
31 0 711839 288161 778774 221226 6934 3066 59 0
I 712050 287950 779060 220940 7010
2 712260 287740 779346 477
31 3 712469 287531 779632
126 3822
126
126
IO
3747
3671
96
8
126 3596 59 7
6
478
477
477
477
477
477
126
126
126
126
126
126
5
4
3
3217
2
I
126
2990
476 220654 7086
127
59
127
2914
58 58
2838
127
57
476
2762
56
476 219797 7315
127
2685
476 219511 7391
127
55
2609
476
476
475
475
475
286483 781060 218940 7543
286274 781346
218654 7620 2380
286065 781631 218369 7696 2304
285856 781916 218084 7772
219225 7467
127
54
2533
127
127
127
127
127
53
2457
52
51
50
2228
58 49
347
347
347
347
347
346
31 12 714352| 285648 782201 217799 7849 2151
13 714561 285439 782486 217514 7925
14714769 285231 782771 217229 8002
15 714978 285022 783056 216944 8079 1921
16 715186 284814 783341 216659 8155 1845
17 715394 284606 783626 216374 8232
346
346
18 715602 284398 783910
216090 8309
19 715809 284191 784195 215805 8386
20 716017 346 283983 784479
215521 8463
345
345
345
345
345
344
344
344
344
Cos. D. Sec. Cot.
591 Deg.
31 21 716224 283776 784764 215236 8540
22 716432 283568 785048 214952 8617
23716639 283361 785332
214668 8694
24 716846 283154 785616 214384 8771
25717053 282947 785900 214100 8848
26 717259 282741 786184 213816 8925
27 717466 282534 786468 213532 9002
28 717673 282327 786752 213248 9079
29717879 282121 787036 212964 9157
30 718085 281915 787319
212681 9234 0766 58 30
Tang. Cos. D. Sine
475
475
475
475
475
474
474
474
474
474
474
473
473
473
473
473
473
473
48
127
128
2075
47
128
1998
46
128
45
128
44
1768
128
128
128
128
1691
1614
1537 58 40
1460
128
128
128
1383
1306
1229
wwwwf+++
43
42
39
38
37
36
98 76
129
1152
35
129
1075
34
129
0998
33
129
129
129
0921
32
0843
31
D.
581 Deg.
114
MATHEMATICAL TABLES.

31 Deg.
TABLE V.-LOG. SINES, ETC.
321 Deg.
Sine D. Cosec. Tang. | D. Cot. Sec. D. Cos.
9'7
10'2 9'
10'
ΙΟ
9'9
31 30 18085 81915 787319 212681 69234 30766
343
343
35 19114
36 19320
37 19525
341
46 21366 340
78634 791846
340
78430 792128
58 23805 76195 795227
5924007 75993 795508
320 24210| 75790 795789
I 24412 75588 796070
4 25017
337
337
337
337
468 203930 71658
337
2 24614 75386 796351 203649 71737
336
3 24816 336 75184 796632
336 74983 796913
340
339
339
339
339
339
53 22791
338
54 22994
338
5523197
338
5623400
338
31 57 23603 76397 794945 205055 71343 28657
469
4721570
31 48 21774 78226 792410
207590 70636 29364
49 21978 78022 792692 207308 70714 29286
50 22181 77819 792974 207026 70793 29207
51 22385 77615 793256 206744 70871 29129
52 22588 77412 793538
206462 70950 29050
206181 71028
77209 793819
28972
77006 79410I 205899 71107 28893
76803794383 205617 71185
76600 794664
31 18291 81709 787603 212397 69312 30688
472
343 81503 787886
32 18497
129
212114 69389
33 18703 81297 788170 211830 69467
343
34 18909 81091 788453 211547 69544
343
472
80886 788736 211264 69622
342 80680 789019
210981 69700
342
130
210698 69777
80475 789302
342
38 19730 80270 789585 210415 69855 30145
342
31 39 19935 80065 789868 210132 69933
40 | 20140 79860 790151 209849 70011 29989
341
41 20345 79655 790433 209567 70089 29911
341
42 20549 79451 790716 209284 70167 29833
341
43 20754 79246 790999 |209001| 70245
4420958 340
79042 791281
208719 70323
340
4521162
78838 791563 208437 70401
208154 70479
207872 70558 29442
472
30
129
29
472
472
129
66
30611
28
30533
27
129
30456
26
129
30378
472
472
471
471
471
471
471
471
471
129
25
30300
24
30223
23
130
58 22
130
30067
21
130
130
130
20
19
18
471
130
130
130
29755
17
29677
16
470
29599
15
130
29521
14
470
130
58 13
470
470
130
12
470
470
470
469
469
469
469
469 205336 71264
HHH
131
131
131
131
131
131
131
131
II
IO
9
8
7
6
28815
28736 58
131
5
58 4
4444
469
468
468
204773 71422
204492 71501
204211 71580
131
131
28578
28499
321
I
131
132
132
28420 58 o
28342
59
468
28263
58
468
203368 71817
132
28183
57
336
32
ΙΟ
I I
13 26827
14 27027
1527228
Cos.
335
335
335
335
335
334
334
334
334
D.
468
468
468
467
525219
74781 797194
6 25420 74580 797475
7 25622 74378 797755
8 25823 74177 798036, 201964 72213
9 26024
201684 72292
73976 798316
467
10 26225 73775 798596 |201404 72371
467
11 26426
73574 798877 201123 72451
467
12 26626
73374 799157
200843 72530
467
73173 799437 200563 72610 27390
467
72973 799717 200283 72690 27310
467
72772 799997 200003 72769 27231 57 45
Sec. Cot. D. Tang. Cos. D. Sine
468 203087 71896 |
202806 71975
132
28104
56
132
132
28025 57 55
|202525 72054
|202245 72133
27946
54
132
27867
53
132
27787
52
132
27708
51
132
27629
50
132
132
133
133
133
27549
49
27470
48
47
46
58 Deg.
572 Deg.
MATHEMATICAL TABLES.
115

321 Deg.
Sine.
9'
D. Cosec.
TABLE V.-LOG. SINES, ETO.
Cosec. Tang. | D. Cot. Sec. D. Cos.
33 Deg.
IO'
9'
10° 10.07
9'92
32 15 727228
34731009
328
328
328
267413 807527
45733177
47 733569
48 733765
49 73396
50 734157
327
327
334
333
133
333
133
333
133
333
133
6831
333
133
21 728427 271573 801675 466 198325 3249 6751
133 6671
332
22 728626 271374 801955 198045 3329
332
23 728825 271175 802234 197766 3409 6591
332
465
32 24 | 729024 270976 802513 197487 3489
332
465
25729223 270777 802792 197208 3569
331
26729422 270578 803072 196928 3649
331
27 729621 270379 803351 196649 3730
331
465
28729820 270180 803630 196370 3810
465
29 730018 331
269982 803908 196092 3890
330
465
30 730216 269784 804187 195813 3971
330
31 730415 269585 804466 195534 4051
330
32 730613 269387 804745 195255 4132 5868
330
32 33 730811 269189 805023 194977 4212
330
194698 4293
268991 805302
329
35 731206 268794 805580 194420 4374 5626
329
36 731404 268596 805859 464194141 4455
329
37 731602 268398 806137 193863 4535
329
268201 806415
38731799
193585 4616
329
39 731996 268004 806693
328
40 732193 267807 806971
328
41732390 267610 807249
32 42 732587
267216 807805
43 732784
44 732980 267020 808083
327 266823 808361 463
46 733373 266627 808638 463
272772 799997 200003 2769
466
16 727428
272572 800277 199723 2849 7151
466 19972
17 727628 272372 800557 199443 2929
466
18 727828
272172 800836 199164 3009 6991
466
19 728027 271973 801116 198884 3089 6911
466
20 728227 271773 801396 198604 3169
466
7231
133
45
44
7071
43
42
4I
40
39
466
38
465
133
133
134 6431
134
57 37
6511
36
35
98765
465
134 6270
6351
34
134
33
6190
32
134 6110
31
134
465
6029
30
134
464
5949
29
134
464
57 28
134
464
464
464
5788
134
5707
2 2
27
26
134
25
134
135
5545
24
464
5465
23
463
135 5384
22
463
193307 4697
135
5303
21
463
193029 4778
135
5222
20
463
192751 4859
135
5141
57 19
135
463
463
192473 4940
192195 5021
191917 5103 4897
135
191639 5184 4816
5060
18
135
4979
135
17
16
15
327
462 191362 5265
266431 808916 191084 5346
266235 809193
135
136
4735
14
462
327
326
266039 809471
136
462 190807 5428 4572
4654
326
265843 809748
462 190529 5509
462 190252 5591
136
13
12
136
449I
II
136 4409
57 10
326
326
325
325
325
325
325
324
324
32 51734353
52734549 265451 810302
53734744 265256 810580
265647 810025 189975 5672
55 735135 264865 811134
189698 5754
189420 5836
54734939 265061 810857 189143 5917
|264670 811410
56 735330
188590 6081
57 735525 264475 811687 188313 6163
58 735719 264281 811964 188036 6245
59 735914 264086 812241 187759 6327
60 736109 263891 812517 187483 6409
462
462
462
462
461
461
461
461
461
1364328
136
4246
86
9
136
4164
7
188866 5999
333 MM M
136
4083
4001
136
136
3919
654
136
3837
3
3755
2
137
3673
I
137
3591 57 o
Cos. D. Sec. Cot. D. Tang. Cos. D. Sine
572 Deg.
57 Deg.
}
116
MATHEMATICAL TABLES.

33 Deg.
Sine
9'7
33 Deg.
TABLE V.-LOG. SINES, ETC.
D. Cosec. Tang. D. Cot. Sec. D. Cos.
321
321
321
321 60602 817209
320
320
320
320
320
319
319
319
319
319
19 39783 60217 817759
20 39975 60025 818035 181965 78060 21940
21 40167
181690 78143
59833 818310
22 40359 59641 818585 181415 78226
23 40550
59450 818860
181140 78309
2440742
180865 78393
59258 819135
25 40934 59066 819410
180590 78476
26 41125
58875 819684 180316 78559
33 27 41316 58684 819959 180041 78643
318
31
318
32 42271
317
317
317
317
317
57920 821057
33 42462 318 57729 821332
40 43792
3743223 56777 822703 177297 79480
3843413
39 43602 316 56587 822977
316 56398 823250
41 43982 316 56208 823524
316 56018 823798||
179217 78893 21107
178943 78977 21023
178668 79061 20939
140 20856
57538 821606
178394 79144
34 42652
178120 79228
57348 821880
20772
35 42842 57158 822154
177846 79312
33 36 43033 56967 822429 177571 79396
28 41508 58492 820234 179766 78726 21274
318
29 41699 58301 820508 179492 78810 21190
30 41889
42080 318 58111 820783
459
459
459
459
459
459
458
458
458
458
458
458
458
458
10°2
9°
330 36109 63891 812517
324
324
324
323
323
5 37080
6 37274
323
323
9'9
187483 76409 23591
I 36303 63697 812794 187206 76491 23509
236498 63502 813070 186930 76573 23427
3 36692 63308 813347 186653 76655
4 36886 63114 813623 186377 76737 23263
137
186101 76819
62920 813899
23181
323 62726 814175
137
185825 76902 23098
7 37467 62533 814452 185548 76984 23016
IO'
10*0
461
461
461
460
460
460
460
460
60
137
137
137
137
59
58
23345
57
56
322
460
322
322
322
322
33 9
10 38048 61952 815279
II 38241 61759 815555
12 38434 61566 815831
460
4.60
459
459
137
137
137
137
184721 77232 22768
138
184445 77314 22686
138
184169 77397 22603
13 38627 61373 816107 183893 77480 138
321 61180 816382 459
837661 62339 814728 185272 77067 22933 56 52
9 37855 62145 815004 184996 77149 22851 51
138
14 38820
138
183618 77562 22438
15 39013 |60987 816658 183342 77645 22355
16 39206 60794 816933 183067 77728 138
17 39398
138
33 18 39590 60410 817484 182516 77894 22106
55
54
53
00 00 00 00 00 00
50
49
48
22520
47
46
45
138
182791 77811 22189
22272
44
5643
182241 77977
139
139
139
138
138
138
139
21774
139 21691
139 21607
21524
42
22023
4I
40
21857
333
39
38
37
36
35
2144156 34
21357
33
458
457
457
457
139
139
139
139
139
333 N
32
31
30
29
28
457
457
457
457
27
140
140
140
26
20688 56 25
20604
457
24
140
457
20520
23
456 177023 79564
140
20436
22
456
176750 79648
140
456
176476 79732
140
20352
20268
21
20
44 44550
315
315
Cos. D.
57 Deg.
456
456
456
42 44171
43 44361 316 (55829 824072||
175928 79901 20099
55639 824345 175655 79985 20015
55450 824619 175381 80069 19931
45 44739 55261 824893 175107 80154 19846 56 15
Sec. Cot. D. Tang. Cos. D.
Sine
561 Deg.
456 176202 79816 140
140
20184 19
18
140
140
141
17
16
98 76
MATHEMATICAL TABLES.
117

315
315
315
314
314
314
314
314
313
313
313
313
313
312
312
253941 826805
312
312
312
311
311
311
311
311
310
310
310
310
33 Deg.
TABLE V.-LOG. SINES, ETC.
Sine D. Cosec.
D. Cosec. Tang. D.
Tang. D. Cot.
9*
IO*
9*
34 Deg.
Sec. D. Cos.
IO* 10.08
9'91
33 45 744739 255261 824893 175107 0154 9846
12
456
46 744928 255072 825166
456 174834 0238
47 745117 254883 825439 174561 0323 9677
48745306 254694 825713 174287 0407 9593
49|745494 254506 825986 174014 0492 9508
50 745683 254317 826259 173741 0576
51 745871 254129 826532 173468 0661
52 746059
53 746248 253752 827078 172922 0831 9169 56 7
543N HO9∞ 76
8
33 54 746436
55 746624 253376 827624 172376 1000 9000
56 746812 253188 827897 172103 1085 8915
57 746999 253001 828170
171830 1170
58 747187 252813 828442 171558 1255
59 747374 252626 828715 171285 1341
340 747562 252438 828987 171013 1426
I 747749 252251 829260
170740 1511
2 747936 252064 829532 170468 1596
34 3 748123 251877 829805
170195 1682
4 748310 251690 830077 169923 1767
5 748497 251503 830349 169651 1853
6 748683 251317 830621 169379 1938
7 748870 251130 830893 169107 2024
8 749056 250944 831165 168835 2109
9 749243 250757 831437 168563 2195 7805
IO 749429 250571 831709 168291 2281 7719
II 749615 250385 831981 168019 2366 7634 55 49
15
455
455
455
455
455
455
455
455
173195 0746
253564 827351 172649 0915 9085
455
454
454
454
454
454
454
454
454
454
453
453
453
453
453
141
141
141
141
141
141
141
141
141
141
14I
142
8830
142 8745
142 8659
9762
14
13
I I
9424
ΙΟ
9339
9254
5
4
3
2
I
142
142 8489
8574 56 °
59
142
142
8404 55 58
8318
57
142 8233
56
142 8147
55
142 8062
54
142
7976
53
453
143
143
143
143
7891
52
51
50
453
143
310
309
309
309
309
309
308
308
308
34 12 749801 250199 832253
13749987 250013 832525
14 750172 249828 832796
15750358 249642 833068
453
453
453
16 750543 249457 833339
17 750729 249271 833611
18
750914 249086 833882
19 751099
248901834154
20 751284 248716 834425
34 21 751469.
22 751654 248346 834967
23 751839 308 248161 835238
452
452
452
452
452
308 248531 834696
308
452
452
452
26
307
307
307
307
307
306
24 7520231 247977 835509
25 752208 247792 835780
752392 247608 836051
27 752576 247424 836322
28 752760
247240 836593
29 752944 247056 836864
246872 837134
30753128
452
452
45I
45I
451
45I
143
167475 2538 7462
143
167204 2624 7376
143
166932 2710 7290
166661 2796 143
7204
143
166389 2882 7118
144
166118 2968 7032
144 6946
165846 3054
165575 3141
165304 3227
165033 3313
164762 3400
164491 3486
164220 3573
163949 3659
163678 3746
163407 3833
163136 3919
451 162866 4006 145
167747 2452 7548
48
47
46
45
44
43
42
4I
144
144 6859 55 40
144 6341
144 6427
6773
144 6687
144 6600
144 6514
333 m
39
38
37
36
98 76
35
34
144 6167
144 6254
33
32
145 6081
31
321
5994 55 30
Cos. D. Sec. Cot. D. Tang. Cos. D. Sine
561 Deg.
55 Deg.
118
MATHEMATICAL TABLES.

84 Deg.
TABLE V.-LOG. SINES, ETC.
351 Deg.
Sine
9°
3430 753128
IO*
D. | Cosec. | Tang. | D.
9'
Cot.
Sec. | D. | Cos.
10'
10.08
9'91
www w
306
306
306
306
50 756782 303
246872 837134
31 753312 246688 837405
32 753495
246505 837675
33 753679 246321 837946 162054 4267 5733
246138 838216
34 753862
161784 4354
305
145
35 754046 245954 838487
161513 4441 5559
305
36754229
145
161243 4528
245771 838757
5472
305
145
37 754412 245588 839027 160973 4615 5385
305
145
38 754595 245405 839297
160703 4703 5297
305
145
34 39 754778
160432 4790
245222 839568
304
40 754960
160162 4877
245040 839838
304
41 755143 244857 840108 450
1598924965 5035
304
42 755326 244674 840378
43 755508 304
244492 840647
44 755690 304
159083 5227
244310 840917
146
45 755872 304
244128 841187 158813 5315 4685
303
46 756054
146
158543 5402
243946 841457
303
47 756236
146 4598
158274 5490
243764 841726
303
34 48 756418 243582 841996 158004 5578 4422
49 756600 303
157734 5666
243400 842266
243218 842535
162866 4006
451
5994
30
45I
162595 4093
145
5907
29
162325 4180
145
451
5820
28
145
451
45I
450
450
450
450
450
27
145
5646
26
25
24
23
55 22
5210
21
145
146
5123
20
450
450
159622 5052
146
19
146
4948
18
159353 5140
4860
302
302
450
449
449
449
449
449
449
449
449
146
17
4773
16
76
15
14
1464510 55 13
543
157465 5754
146
146
147
147
12
4334
4246
II
IO
301
301
301
301
300
300
300
300
300
9
299
7 759852 240148 847107
299
148
8 760031 239969 847376
299
148
760211
39789 847644 152356 7434 2566
299
148
10 760390 239610 847913 152087 7523 2477
299
148
11 760569
151819 7612
239431 848181
298
148
12 760748 239252 848449
151551 7701 2299
298
149
13 760927
151283 7790 2210
149
14 761106 298 239073 848717
238894 848986 151014 7879 2121
298
15 761285 238715 849254 150746 7969
Cos. D. Sec. Cot. D. Tang. Cos. D.
55 Deg.
51 756963 243037 842805 157195 5842 4158
52757144 242856 843074 156926 5930 4070
449
53 757326 242674 843343 156657 6018 147 3982
302
302
54757507 242493 843612
55 757688 302
242312 843882
301
56 757869 242131 844151
301
34 57 758050 241950 844420
449
156388 6106
449
448 156118 6194
448 155849 6282 147
448 155580 6370
58 758230 241770 844689 155311 6459
59 758411 241589 844958 155042 6547
35758591 241409 845227
I 758772 241228 845496
2 758952 241048 845764
3 759132 240868 846033
4759312 240688 846302 448
5 759492 240508 846570
35 6759672 240328 846839
147
147
3894
3806
147
3718 55 4
98 765+
3630
448
147
147
3
354I
2
448
3453
I
448
448
448
154773 6635
154504 6724
154236 6813
147
147
3365 55 0
3276
147
59
448
447
447
447
152893 7256 2744
148
153967 6901 3099
148
153698 6990 3010
148
153430 7078 2922
148
153161 7167 2833
3187
58
57
56
54 55
65
148
54
447
152624 7345 2655
53
52
447
51
44.7
50
447
2388
49
48
447
447
447
47
46
149
2031 54 45
Sine
3
542 Deg.
MATHEMATICAL TABLES.
119

58 68871
59 69045
35 Deg
TABLE V.—LʊG. SINES, ETC.
D. Cosec. Tang. D. Cot.
Sine
9'7
35 15
61285
298
17
298
2 2
oo oo
296
296
10'2
9°
445
Sec. D. Cos.
IO'
10'0
149
38715 849254 447 150746 87969 12031
16 61464 38536 849522 447 150478 88058 11942
149 11853
61642
38358 849799 446 150210 88147
297
149
18 61821
38179 850058 446 149942 88237 11763
297
149
19 61999
38001 850325 446 149675 88326 11674
297
149
20 62177 37823 850593 446 149407 88416 11584
297
149
2162356 37644 850861 446 149139 88505 11495
297
149
22 62534 37466 851129 446 148871 88595 11405
296
149
23 62712 296 37288 851396 446 148604 88685 11315
150
35 24 62889 37111 851664 446 148336 88774 11226
150
25 63067 36933 851931 446 148069 88864 11136
150
2663245 296 36755 852199 446 147801 88954 11046
150
27 63422 36578 852466 446 147534 89044 10956
28 63600 296
150
36400 852733 445 147267 89134 10866
150
29 63777
36223 853001 445 146999 89224 10776
150 10686
30 63954 36046 853268 146732 89314
445
150
31 64131 35869 853535 445 146465 89404 10596
150
32 64308
35692 853802 445146198 89494 10506
150
35 33 64485 35515 854069 445 145931 89585 10415
150
34 64662
35338 854336 145664 89675 10325
151
35 64838
35162 854603 445 145397 89765 10235
151
36 65015 34985 854870 445 145130 89856 10144
151
37 65191 34809 855137 445 144863 89946 10054
151
38 65367 34633 855404 445 144596 90037 c9963
151
39 65544 34456 855671 444 144329 90127 09873
151
40 65720
34280 855938
09782
144062 90218
444
151
41 65896 34104 856204 444 143796 90309 09691
151
35 42 66072
33928 856471 444 143529 90399 09601
151
43 66247
33753 856737 444 143263 90490 09510
151
4466423
33577 857004 444 142996 90581 09419
151
45 66598 33402 857270 444 142730 90672 09328
152
46 66774 33226 857537 142463 90763
152
47 66949 33051 857803 444 142197 90854 09146
152
48 67124 32876 858069 444 141931 90945 09055
152
4967300
141664 91036
32700 858336
444
50 67475
141398 91127
32525 858602
291
443
35 51 67649 32351 858868
141132 91219
443
52 67824 32176 859134
140866 91310
53 67999 32001 859400
140600 91401
54 68173 31827 859666 140334 91493
55 68348
31652 859932 140068 91584
56 68522 31478 860198 139802 91676
57 68697 31303 860464 139536 91767
295
295
295
295
295
294
294
294
294
294
294
293
293
293
293
293
293
292
292
292
292
292
444
36 Deg.
9'9
45
44
43
42
41
40
39
38
54 37
36
35
34
33
32
31
30
29
54 28
210 a∞
765
2 2 2
27
26
25
24
23
22
21
20
54 19
18
17
16
15
092.37
14
13
12
08964
II
152 08873 54 10
9856 5 4 3 2 10
152
60 69219
54 Deg.
291
291
291
291
290
290
290
139270 91859
31129 860730
290
30955 860995
290
30781 861261
Cos. D. Sec. Cot.
08781
152
08690
443
443
443
443
443
443
443
443
152
08599
152
152
08507
08416
139005 91951
153
153
153
153
153 08324
98 765+
4
08233
3
08141
2
08049
I
138739 92042 07958 54 0
D. Tang. Cos. D. Sine
54 Deg.
120
MATHEMATICAL TABLES.

286
|
25 773533 285
285
285
28 774046 285
36 27 773875 285 226125 868416
26 773704 226296 868152
36 Deg.
Sine
290
289
289
289
289
ΙΟ
Sec. D. Cos.
TABLE V.-LOG. SINES, ETC.
D. Cosec. Tang.. D. Cot.
9°
9*
36 0 769219 230781 861261
230607 861527
I 769393
2769566 230434 861792
3 769740 230260 862058
4 769913 230087 862323
5 770087
137411| 2502
289 229913 862589
6 770260
137146 2594
229740 862854
7 770433 288 229567 863119 136881 2686 153
154
8 770606 288 229394 863385
136615 2778 7222
154
36 9 770779 288 229221 863650
10 770952 288 229048 863915
II 771125 288 228875 864180
12 771298 228702 864445
287
13 771470 287
228530 864710
228357 864975 442
14771643 287
288
15 771815 287 228185 865240 441
16 771987 228013 865505
287
17 772159287
227841 865770
36 18 772331 286 227669 866035
19 772503 286 227497 866300
20 772675 286 227325 866564
21 772847 286 227153 866829
22 773018 226982 867094
226810 867358 441
23 773190286
24 773361 226639 867623
226467 867887
in in initi
362 Deg.
ΙΟ 10'09
9'90
443
138739 2042 7958
60
138473 2134
I53 7866
443
59
138208 2226
153
7774
442
58
442
137942 2318
137677 2410 153
153 7682
57
7590
442
56
153
7498
442
153
55
7406
442
54
442
7314
53
442
53 52
136350 2871 7129
442
442
442
442
51
441
136085 2963 7037
154
135820 3055 6945
154
135555 3148
135290 3240
135025 3333
134760 3425
154
50
49
6852
154 6760
48
154 6667
47
46
154 6575
134495 3518
44I
154 6482
45
44
134230 3611
154 6389
44.I
441
133965 3704 6296
155
53 43
42
441
441
133700 3796 6204
133436 3889155 6111
133171 3982
155
4I
40
155 6018
44I
132906 4075 155
5925
132642 4168
155
5832
44I
132377 4261
155
5739
44I
155
132113 4355
5645
44I
www ww
39
38
37
36
9∞ 76
35
131848 4448
155
440
155
5552❘ 53 34
131584 4541
225954 868680
440
5459
29|774217
30 774388
285
284
225783 868945
225612 869209
31 774558 284 225442 869473
32 774729 284
35 775240 284
36 36 775410 283
37 775580
284
156
156
156
130527 4915 5085
130263 5008
225271 869737
33 774899 284
225101 870001
34 775070 224930 870265
224760 870529
440
131320 4634 5366
155
33
32
131055 4728
5272
440
130791 4821
5179
33
31
440
440
440
440
440
30
156
29
129999 5102 4898
156 4992
28
283
283
282
44 776768 282 223232 872903 127097 6136 3864 16
45 776937 223063 873167
Cos. D. Sec. Cot.
54 Deg.
439
157
157
126833 6230 3770 53 15
D. Tang. Cos. D. Sine
531 Deg.
156 4711 53 25
224590 870793 129207 5383 4617
156
128943 5477
224420 871057
156 4523
38 775750
128679 5571
224250 871321
39 775920 224080 871585
283
40 776090
223910 871849
283
41 776259 283
223741 872112
42 776429
43 776598 282 223402 872640
129735 5196
129471 5289
440
156
27
156
4804
26
440
24
440
440
440
439
439
439
439
23
157
128415 5665 4335
157
128151 5759
4241
157
127888 5853 4147
157
127624 5947
223571 872376|
4429
22
21
20
19
127360 6041 157 3959
4053
18
17
98 76 5
MATHEMATICAL TABLES.
121

282
281
281
281
281
281
281
280
O
279
279
279
279
23937 097271
23674 097366
23411 097461
59 79295 20705 76851 23149 097556
37 79463
36 Deg.
TABLE V.-LOG. SINES, ETC.
Sine D. Cosec. Tang., D. | Cot. Sec.
9'7
10*2 9.8
36 45 76937 282 23063 73167 26833 096230 903770
46 77106
47 77275
48 77444
49 77613
50 77781 22219 74484 25516 096702 158
22725 73694 26306 096419 903581
22556 73957 26043 096513
22387 74220 25780 096608
51 77950 |22050| 74747
52 78119 21881 75010
53 78287 21713 75273
280
36 54 78455 280 21545 75536
55 78624 280 21376 75800 438
5678792 21208 76063
57 78960
280 21040 76326
58 79128 20872 76589 438
280
37 Deg.
D.
Cos.
ΙΟΙ
10°
9'
439
439
439
439
439
22894 73430 26570 096324
157
15
903676
157
14
157
13
903487
12
57
903392
II
439
439
25253 096797 158
903298
ΙΟ
439
438
24990 096892
24727 096986
158
903203
158 903108
158
903014 53
24464 097081
438
24200 097176
158 902919
98 76
158
902824
5
438
158
902729
4
158
902634
3
20537 77114 22886 097651
I 79631 20369 77377 22623 097747
2 79798 20202 77640 22360 097842
438
438
438
438
438
159
902539
2
159
902444
I
159
902349 53 0
159
902253
59
37 3
456 7∞
80467
80634
279
4 80133 19867 78165
279
80300
278
278 19533 78691
3 79966 20034 77903 438 22097 097937
159
902158 52 58
278
19366 78953
278
278
278
277
13 81634
14 81800
56 78
277
277
277
277
277
276
276
276
159
159
£59
21309 098224
159
21047 098319 901681
8 80801
159
19199 79216 20784 098415 901585
159
9 80968
19032 79478 20522 098510
159
10 81134
18866 7974I
20259 098606
160 901394
11 81301 18699 80003
29997 098702 901298
37 12 81468 18532 80265 29735 098798
902063
438
15 81966 18034 81052 18948 099086
276
16 82132 17868 81314 18686 099182
17 82298
17702 81576
18 82464 17536 81839
19 82630 17370 82101
20 82796 17204 82363
438
437
437
437
437
437
437
437
437
437
437
437
438
19700 78428 21572 098128 901872
57
21835 098033 901967
56
55
901776
54
53
52
901490
51
50
18366 80528 19472 098894
18200 80790
19210 098990
437
18424 099278
18161099374 900626
160
160 901202
160 901106
160
160 900914
160 900818
52 49
48
47
901010
46
45
44
437
37 21 82961
276
275
275
275
27 83953
28 84118
275
275
274
275 16047 84196
436
15882 84457
276 17039 82625 17375 099663
22 83127 16873 82887 17113 099760
2383292 16708 83148
24 83458 16542 83410 16590 099953 900047
25 83623 16377 83672
26 83788 16212 83934
436
17899 099471
17637 099567
160 900722
160
160 900529
43
42
4I
436
161 900433
161900337
52 40
436
436
16852 099856
436
436
436
29 84282 15718 84719 15281 100436 899564
436
30 84447 15553 84980
15020 100533 899467 52 30
Cos. D. Sec. Cot. D. Tang. Cos. ID. Sine
16328 100049 899951
16066 100146 899854
15804 100243 899757
43615543| 100340 899660
38
161 900240
161 900144
161
161
161
161
161
161
39
37
36
35
34
33
32
31
531 Deg.
K
52 Deg.
122
MATHEMATICAL TABLES.

37 Deg.
Sine
TABLE V.-LOG. SINES, ETC.
D. Cosec. Tang. | D. Cot.
38 Deg.
Sec. D. Cos.
9°
IO'
9*
IO*
ΙΟ ΙΟ 9.89
274
274
274
274
274.
273
273
273
273
273
272
272
272
272
272
272
37 30 784447 215553 884980
215388 885242
31 784612
215224 885503
32784776
33 784941 215059 885765
34 785105 214895 886026
35 785269 214731 886288
36 785433 273 214567 886549 113451 1116
37 785597 214403 886810 113190 1213 8787
38 785761 214239 887072 112928 1311 8689
436
436
436
436
436
436
435
435
115020 0533 162 9467
30
435
114758 0630
162 9370
114497 0727 162 9273
1629273
114235 0824 9176
162
113974 0922 162 9078
113712 1019 8981
162
162
162
162
29
28
27
26
25
8884
24
23
52 22
271
271
37 39 785925 214075 887333
40 786089 213911 887594
41 786252 213748 887855
42 786416
213584 888116
43 786579 213421 888377
44 786742
213258 888639
45 786906 213094 888900
46 787069 212931 889160
47 787232 212768 889421
212605 889682
37 48 787395
49 787557
50 787720
435
435
435
435
435
112667 1408
112406 1506
112145 1603
111884 1701
111623 1798
111361 1896
66
162
163
163
163
163
435
163
435
III100 1994
110840 2092
163
435
163
110579 2190
435
163
271
271
271
271
271
270
270
270
212443 889943
212280 890204
435
435
268
268
268
267
D.
51 787883 212117 890465 109535 2582
52 788045 211955 890725
53 788208 211792 890986
54 788370 211630 891247
55 788532 211468 891507
56 788694 211306 891768
37 57 788856 211144 892028
107972 3172
270
164
58 789018 210982 892289 107711 3271
270
164
59 789180 210820 892549.
6631
107451 3369
270
38789342 210658 892810,
269
107190 3468
I 789504 210496 893070 106930 3567
269
2789665
106669 3665
210335 893331
269
3789827
106409 3764
210173 893591
269
434 106149 3863
4 789988 210012 893851
269
209851 89411I
5 790149
269
38 6790310 209690 894371
268
7 790471 268 209529 894632
8 790632 209368 894892
9 790793 268 209207 895152
10 790954 209046 895412
11 791115 208885 895672
12 791275 208725 895932
267
13791436 208564 896192
267
14 791596 208404 896452
15 791757 208243 896712
Cos.
Sec. Cot.
110318 2288
110057 2386
109796 2484
163
163
2 mm en en MMM en
69666 66
8592
8494
21
20
8397
19
8299
18
8202
17
8104
16
8006
15
7908
14
7810 52 13
76 54 m
7712
12
7614
II
434
163
7516
IO
7418
434
434
434
434
109275 2680
164
109014 2778 7222
164
434 108753 2877
164
108493 2975 7025
164
164
7320
7123
434
108232 3074 6926 52 4
98 76 54
164
6828
434
434
434
434
434
6729
2
32 K
I
164
6532 52 0
434
434
105889 3962
6 6 6 6 6 1
164
165
6433
59
165
6335
58
165
6236
57
165
6137
56
434
165
6038 51 55
434
433
433
105629 4061 5939
165
105368 4160 5840
105108 4259 5741
104848 4359
54
165
53
165
52
433
433
433
104588 4458 5542
165
104328 4557 166 5443
165
5641
51
50
49
104068 4657
433
166 5343
48
103808 4756
433
166 5244
47
103548 4855 5145
46
433
166
103288 4955 5045 51 45
D.
Tang. Cos. D. Sine
52 Deg.
512 Deg.
123
MATHEMATICAL TABLES.

266
265
265
265
265
265
4646
166
101990 5454
166 4546
101730 5554 4446
167
101470 5654
4346
167
23793035 266
206965 898789 101211 5754 4246
167
38 24 793195 206805 899049 100951 5854
25 793354 206646 899308 100692 5954 4046
26 793514
100432 6054
206486 899568
27793673 206327 899827
100173
28 793832 206168 900086 099914 6255 3745
267
16 791917 267
208083 896971 103029 5055 166 4945
17 792077
102769 5154
207923 897231
267
166
18 792237 266 207763 897491 102509 5254 4746
166
19 792397 266 207603 897751 102249 5354
20 792557 266 207443 898010
21 792716 207284 898270
22 792876 266 207124 898530
38 Deg.
Sine
9'
TABLE V.-LOG. SINES, ETC.
D. Cosec. Tang. | D. Cot.
39 Deg.
Sec. D. Cos.
IO'
9°
3815791757 208243 896712
ΙΟ
ΙΟΙΟ
9.89
103288 4955 166 5045
433
433
433
433
455
44
4846
43
42
41
433
40
433
433
433
433
432
51 37
167
4146
333
98 76
39
38
36
35
264
264
|
37 795259
38795417
39 795575
204741 902419
263
263
262
262
262
262
261
261
261
261
261
260
260
260
55 798091 261 201909 907077 431
56 798247
57 798403
58 798560
59 798716
60 798872
Cos. D.
201753 907336
201597 907594
201440 907852)
201284 908111
201128 908369
Sec. Cot. D.
29 793991 265
|
206009 900346| 099654 6355
30 794150 205850 900605 099395 6456
31 794308 205692 900864 099136 6556 3444
168
32 794467 205533 901124 098876 6657
264
168
38 33 794626
098617 6757
264
205374 901383
168 3243
34 794784
098358 6858
205216 901642
264
168
35 794942 264
205058 901901 098099 6959
168 3041
36 795101 204899 902160 097840 7060 2940
264
168
097581 7161 2839
263
168
097321 7261
204583 902679
263
168 2739
2638
097062 7362
204425 902938
263
168
096803 7464 2536
40 795733 263 204267 903197 431
168
41 795891 204109 903455 096545 7565 2435 51 19
263
169
38 42 796049
096286 7666
203951 903714
203794 903973
43 796206
096027 7767
203636 904232
44 796364
095768 7868
45 796521
095509 7970
203479 904491
46 796679 203321 904750
095250 8071
47 796836 203164 905008
094992 8173
48 796993
094733 8274
203007 905267
262
49 797150 202850 905526 094474 8376
202693 905784 094216 8477
50 797307
202536 906043.
38 51 797464
093957 8579
52 797621
093698 8681
202379 906302
53 797777 261 202223 906560 093440 8783
54 797934 261
202066 906819 093181 8885
1013
092923 8987
|092664 9089
092406 9191
092148 9293
432
432
432
432
432
432
432
432
432
432
432
432
432
432
432
167
167
167
6154 3846
3946
34
33
32
167
3645
31
167
167
3544
30
29
3343
51 28
27
3142
26
25
24
23
22
2I
20
431
431
431
431
431
431
431
431
431
431
431
431
431
431
2334
18
169
2233
17
169
2132
16
169
2030
15
169
1929
14
8173169
169
1827
13
1726
12
169
1624
II
169
1523 51 10
170
1421
431
431
431
430
170
170
170
170
170
170
170
1319
1217
1115
OGII
0809
98 7ont m
6
5
4
3
0707
2
091889 9395
091631 9497 0503 51 o
Tang. Cos. D. Sine
170 0605
I
170
51 Deg.
51 Deg.
124
MATHEMATICAL TABLES.

39 Deg.
O
TABLE V.-LOG. SINES, ETC.
Sine D. Cosec. Tang.| D. Cot. Sec. D. Cos.
9*
10° 9'9
10'0 ΙΟΙ
39 798872 260 201128 08369 91631 09497 90503
39 Deg.
9.8
60
260
259
259
259
259
259
259
258
258
14
15
258
257
257
257
257
257
257
256
256 197718 14044
23 802436 256 197564 14302
24 802589
25 802743
19 801819 198181 13271
20 801973 198027 13529 86471 11556
21 802128 197872 13787
22 802282
7 799962
8 800117
39 9
800272 199728 10693
10 800427
199573 10951
II 800582 199418 11209
12 800737 258
88533 10729
199263 11467
258
13 800892
172
88276 10832
|199108 11724
258
801047
198953 11982 88018 10936 89064
801201 258
172
87760 11039
198799 12240
88961
16 801356 198644 12498
172
87502 11142 88858
17 801511
172
87244 11245
198489 12756
39 18 801665 198335 13014 86986 11349
430
430
430
I 799028 260 200972 08628
91372 09600 90400
430
200816 08886
2 799184
91114 09702 90298
200661 09144
430
3 799339
|90856 09805
430
4 799495 200505 09402 90598 09907
430
5799651 200349 09660
90340 10010 89990 55
430
6799806 200194 09918 90082 10112 89888
430
200038 10177
171
89823 10215 89785
170
59
171
171
171
171
171
58
90195
57
90093
56
54
53
199883 10435 89565 10318 89682 50 52
430
430
430
430
430
430
430
430
430
429
429
89307 10421 89579
89049 10523 89477
171
171
171
171
88791 10626 89374
49
172
89271
89168
48
47
172
172
86729 11452
172
172 88548
88755 50 43
88651
429
86213 11659
429
429
429
197411 14560
26 802897
39 27 803050 196950 15332
256
256
256
255
255
255
255
255
255
254
254
254
254
197103 15075
429
429
429
85183 12074
256 197257 14817
85956 11763 88237
85698 11866173 88134
173 88030
85440 11970
88444
173 88341
173
£ £ £ £ ‡‡ A+ AAYU one
50
46
45
44
42
4I
40
39
38
37
36
173
87926
35
84925 12178
173
87822 50 34
173
84668 12282
87718
33
195877 17134
40 805039
41 805191
42 805343
43 805495
253
44 805647
253
45 805799
Cos. D.
254
254
253
28 803204 196796 15590
29 803357 196643 15847
30 803511 196489 16104
31 803664 196336 16362
32 803817 196183 16619
33803970 196030 16877
34 804123
35 804276 195724 17391
39 36 804428 195572 17648
37 804581
195419 17905
38 804734 195266 18163
39804886 195114 18420
254 194961 18677 428
194809 18934 428
81066 13743
194657 19191 80809 13848
194505 19448 80552 13953
194353 19705) 80295 14058
194201 19962 80038 14163 85837 50 15
Sec. Cot. D. Tang. Cos. D. Sine
429
84410 12386
173
87614
32
429
84153 12490
173
87510
31
429
429
173
83896 12594
87406
30
83638 12698
174
87302
29
429
174
83381 12802
87198
28
429
429
83123 12907
82866 13011
174
174 87093
27
429
429
174
82609 13115 174 86885 50 25
86989 26
429
82095 13324
429
428
81837 13429 86571
81580 13534
174
81323 13638
174
174
82352 13220 86780 24
86676
23
22
174
428
428
428
428
175 86152
86466 21
86362 20
175 86257
19
18
175 86047
17
175
175
85942
16
51 Deg.
501 Deg.
MATHEMATICAL TABLES.
125

39 Deg
Sine
D.
TABLE V.-LOG. SINES, ETC.
Cosec. Tang. | D. Cot. Sec. D. Cos.
40 Deg.
9°
10°
9°
10°
IO II
9.88
253
253
253
253
252
252
252
252
252
252
252
251
251
251
251
251
251
251
192535 922787
192385 923044
192234 923300
192083 923557
191933 923813
191782 924070
39 45 805799 194201 919962
080038 4163
46 805951 194049 920219 0797814268
193897 920476
47 806103
48 806254 193746 920733
428 079267 4478 |
49 806406 193594 920990 079010 4584
50 806557
175
078753 4689
193443 921247
51806709 193291 921503 078497 4795
52 806860
078240 4900
193140 921760
192989 922017
53 807011
077983 5006
39 54 807163
192837 922274
55 807314
56 807465
57 807615
58 807766
59 807917
400 808067
I 808218
428
428
428
5837
175
15
5732
079524 4373 5627
175
14
175
13
5522
12
175
428
5416
II
428
428
428
428
5311
IO
7
76
17
5205
77
176
5100
98
176 4994 50 7
192686 922530 428
077726 5111
428
428
077470 5217
077213 5323
176 4889
6
428
076956 5428 176
176 4783
4677
5
4
428
2 808368 191632 924327 427 075673 5958 177
250
250
250
250
250
250
249
249
249
249
249
249
177
4254 50 O
59
4042 49 58
40 3 808519 191481 924583 075417 6064 3936
4 808669 191331 924840 075160 6171
5808819 191181 925096 074904 6277
6808969
191031 925352 074648 6383
7 809119 190881 925609 074391 6490
8 809269
190731 925865
9 809419 190581 926122
10 809569 190431 926378
11 809718 190282 926634
427
427
076700 5534
076443 5640
076187 5746
177
075930 5852 4148
176 4572
3
176 4466
176 4360
2
I
427
427
427
427
427
427
427
177
57
3829
177
56
3723
177
55
3617
177
54
3510
074135 6596 3404
073878 6703
177
53
177
52
427
073622 6809
178 3297
51
427
248
248
248
248
248
248
40 12 809868 190132 926890
13 810017 189983 927147
072853 7129
14 810167
189833 927403 072597 7236
15 810316 189684 927659
248
072341 7343
16 810465 189535 927915 0720857450
17 810614 189386 928171 071829 7557
18 810763 189237 928427 071573 7664
19 810912 189088 928683 071317 7771
188939 928940 427 071060 7879
427
073366 6916 178
3191
50
178 3084
49 49
073110 7023
427
427
427
427
427
427
427
178
2977
48
178
178
178
178
178
∞ ∞ ∞ ∞ ∞ ∞
2871
47
2764
46
2657
45
2550
44
2443
43
247
247
247
187900 930731
187752 930987
187604 931243
20 811061
40 21 811210
22 811358
23 811507
24 811655
25 811804
26 811952
27 812100
188196 930220
247 188048 930475
247
28 812248 247
29 812396
30 812544
247
246
Cos. D.
501 Deg.
187456 931499
068501 8954
Sec. Cot. D. Tang. Cos. D. Sine
179
179
2336 42
2229
4I
2121
188790 929196 070804 7986
188642 929452
188493 929708
188345 929964
427
427
427
427
49 40
古
​179
179
070548 8093
2014
1907
39
38
070292 8201
426 070036 8308
179
426
426
426
426
426
069780 8416
069525 8523
069269 8631
069013| 8739
068757 8847
179
179
180
179 1261
179 1584
1477
1369
179 1692
1799
37
36
35
34
33
32
1153
180
31
1046 49 30
494 Deg.
126
MATHEMATICAL TABLES.

40 Deg.
TABLE V.-LOG. SINES, ETC.
Sine. D. Cosec. Tang. D. Cot. Sec.
9.8
ΙΟΙ
9°
4030 | 12544 87456 931499
IO'
411 Deg.
D.
Cos.
ΙΟΙ
9.8
245
245
245
245
42 14313
245
244
244
244
244
244
244
244
243
243
243
243
243
242
242
242
242
242
242
242
241
241
41 6 17813 82187 940694 059306 22880
241
7 17958 82042 940949 |059051| 22990
241
8 18103
81897 941204 058796 23101
241
9 18247 81753 941458 |058542 23211
241
10 18392
81608 941714 058286 23322
241
II 18536 |81464 941968 058032 23432
240
12 18681 81319 942223 057777 23543
240
1318825 81175 942478 057522 23653
240
14 18969
240
15 19113
Cos. D.
22660
059817
517668 82332 940438| 059562 22770
246
31 12692 87308 931755 068245 19062 80938
246
87160 932010
32 12840
067990 19170
246
33 12988 87012 932266 067734 19278
246
86865 932522
34 13135
|067478 19387
246
35 13283 86717 932778 067222 19495 80505
246
36 13430 86570 933033 |066967 19603
37 13578 245 86422 933289 066711 19711
86275 933545
38 13725
066455 19820 80180
86128 933800 066200 19928
40 39 13872
40 14019 85981 934056
41 14166 85834 934311
245 85687 934567
43 14460 85540 934823
44 14607 85393 935078
45 14753 85247 935333
46 14900 85100 935589
47 15046 84954 935844
40 48 15193 84807 936100
49 15339 84661 936355
50 15485 84515 936610
51 15632 84368 936866 063134 21234 78766
52 15778 84222 937121 062879 21344 78656
53 15924 243 83931 937632
84076 937376 062624 21453 78547
54 16069
062368 21562 78438
55 16215 243 83639 938142
83785 937887 062113 21672 78328
56 16361
061858 21781 78219 49
40 57 16507 83493 938398 061602 21891
58 16652 83348 938653 061347 22001
59 16798 83202 938908 061092 22110
41 0 16943 83057 939163 060837 22220
I 17088 82912 939418 060582 22330
217233 82767 939673 060327 22440
3 17379 82621 939928 060072 22550 77450
4 17524 82476 940183
426
426
426
426
426
426
426
426
426
426
426
426
426
068501 18954 81046
180
30
29
180
180
80830
28
180
80722
27
180
80613
26
98 76
180
25
426
426
426
426
426
426
426
426
425
425
425
425
425
425
425
425
425
425
425
425
425
425
425
425
425
425
425
425
425
425
425
425
80072
065944 20037 79963
065689 20145 79855
065433 20254
79746
065177 20363 79637
064922 20471 79529
064667 20580 79420
064411 20689
79311
064156 20798 79202
063900 20907
063645 21016 78984
063390 21125
180
181
181
181
181
181
181
181
181
181
181
182
182
182
182
182
182
182
182
182
80397
24
80289
23
49 22
21
20
19
18
17
16
15
98 765
14
49 13
79093
12
II
78875
ΙΟ
10 900 DO 54
8
7
6
4
183
78109
3
∞ ∞
183
183
77999
2
77890
I
183
183 77780 49 0
77670
59
183
183
77560
58
57
183
183
77340
56
184
77230 48 55
77120
54
184
77010
53
184
76899
52
184
76789
51
184
76678
50
184
184
76568 49
184
76457
48
76347
47
81031 942733 057267 23764
80887 942988 057012 23875
184
76236
46
185
76125 4845
Sec. Cot. D. Tang. Cos.
D.
Sine
49 Deg.
48 Deg.
MATHEMATICAL TABLES.
127
i

41 Deg.
O
Sine
9
TABLE V.-LOG. SINES, ETO.
42 Deg.
D. Cosec. Tang. D.
|
Cot. Sec. D. Cos.
10'
9*
IO*
10'12
9.87
41 15 819113
16 819257
17 819401
18 819545
19 819689
20 819832
21 819976
22 820120
2 2
238
238
∞ ∞ ∞ ∞ ∞ ∞
179021 946299
237
237
237
237
237
237
237
31 821407
32 821550
41 33 821693
178307 947572 052428 5879
34 821835 178165 947826 052174 5991
35 821977 178023 948081 424
051919 6104
36 822120 177880 948336 051664 6216
37 822262 177738 948590 051410 6328
38 822404 177596 948844 051156 6440
39 822546 177454 949099 050901 6552
40 822688
236 177312 949353 050647 6665
41 822830 177170 949607
236
28 820979
238
29 821122 238 178878 946554 053446 5432
30 821265 238 178735 946808
240
240
240
239
239
239
239
239
239
41 24 820406
179594 945281 054719 4874 5126
239
25 820550 179450 945535
238
26 820693
238 179307 945790
27 820836 238 179164 946045
23 820263 179737 945026 054974 4763 5237 48 37
425
425
425
425
425
425
425
424
424
180311 944007 055993 4318
180168 944262 055738 4429
055483 4541
180024 944517
185
179880 94477! 055229 4652 5348
180887 942988
180743 943243
180599 943498
180455 943752 056248 4207 5793
185
057012 3875 6125
185
056757 3986 6014
185
056502 4096
185
∞ ∞ ∞
5904
42
7777
45
44
43
185
5682
4I
185
5571
40
5459
39
38
185
185
424
186
36
054465 4986
424
1865014
35
054210 5097
424
186 4903
34
053955 5209
424
186 4791
33
(053701| 5320
424
178593 947063 052937 5656
424
424
424
424
424
186
1864568
4680
32
3I
053192 5544
186 4456
30
186 4344
178450 947318 052682 5768 4232
187
29
48 28
187
4121
27
187
4009
26
236
236
236
235
235
235
235
236177028 949862 050138 6890
424
424
41 42 822972
43 823114 176886 950116 049884 7002
44 823255 176745 950370 |049630 7115 2885
176603 950625
236
188 3110
188
188
45 823397
049375 7228
188 2772
46 823539
176461 950879 049121 7341 2659
188
47 823680
176320 951133 048867 7453
188 2547
48 823821 176179 951388 048612 7566 2434
188
49 823963 176037 951642 048358 7679
188 2321
50 824104 175896 951896| 048104 7792
2208
188
41 51 824245 175755 952150 047850 7905 2095
235
52 824386 175614 952405 047595 8019 1981
235
53 824527 175473 952659 047341 8132
235
54 824668 175332 952913 047087 8245
234
55 824808 175192 953167 046833 8359
234
56 824949 175051 953421 046579 8472
234
57 825090 174910 953675 046325 8586
234
189
58 825230 174770 953929 046071 8699
234
189
174629 954183 045817 8813 1187
234
189
174489 954437 045563 8927 1073 48 0
Cos. D. Sec. Cot. D. Tang. Cos. D. Sine
59 825371
60 825511
483 Deg.
98 76543
424
424
424
424
424
424
4.24
187
3896
25
187
3784
24
187
3672
23
187
3560
22
187
3448
21
050393 6777
187
3335
20
187
3223 48 19
18
2998
17
16
424
424
424
424
424
424
424
424
189
424
424
424
423
423
423
423
423
189
189
1868
189
189
1755
1641
189
1528
1414
1301
2
I
15
14
13
12
II
48 10
48 Deg.
128
MATHEMATICAL TABLES.

42 Deg.
TABLE V.-LOG. SINES, ETC.
42 Deg.
O
Sine | D. Cosec.
D. Cosec. Tang.| D.
9.8
Cot. Sec.
D.
Cos.
42 25511
I 25651
225791
325931
4 26071
5 26211
626351
7 26491
826631
10'I 9'9
74489 54437
10°0 ΙΟΙ
9.8
45563 28927
71073
60
234
423
74349 54691
190
45309 29040
70960
233
423
190
233
74209 54945
74069 55200
45055 29154
70846 58
423
44800 29268
190
70732
233
423
73929 55454
44546 29382
190
70618
གགག་
59
57
56
233
423
73789 55707
233
423
44293 29496
190
70504
55
73649 55961
233
233
73509 56215
423
423
44039 29610
43785 29724
190
190 70276
70390
54
53
190
73369 56469
4353 29839
70161
47 52
233
423
190
42 9 26770
232
73230 56723
43277 29953
70047
51
423
232
232
232
232
232
232
10 26910
II 27049
12 27189
1327328
14 27467 72533 57993
15 27606 72394 58246
73090 56977
423
43023 30067
191
69933
50
191
72951 57231
42769 30182
69818
49
423
191
72811 57485
42515 30296
69704
48
72672 57739
423
42261 30411
191 69589
47
423
42007 30526
191
69474
46
423
191
41754 30640
69360
45
423
191
16 27745
17 27884
72255 58500
41500 30755
69245
44
232
423
72116 58754
41246 30870
191 69130
47 43
231
423
191
42 18 28023
231
71977 59008
423
40992 30985
69015
42
192
19
28162
71838 59262
40738 31100
68900
4I
231
25 28993
26
29131
71007 60784
70869 61038
42 27 29269 70731 61291
231
231
231
231
230
230
230
230
230
230
230
229
229
229
229
229
229
20 28301 71699 59516
21 28439 71561 59769
22 28578
71422 60023
71284 60277
23 28716
2428855 71145 60531
423
192
40484 31215
68785
40
423
192
40231 31330
68670
423
192
39977| 31445
68555
423
423
39723 31560
192
68440
39469 31676
192
68324
28 76
mmm m
39
38
37
36
423
192
39216 31791
68209
35
423
192
423
38962 31907
68093 47 34
192
31 29821
70179 62306
32 29959
70041 62560
33 30097 69903 62813
34 30234 69766 63067
69628 63320
35 30372
42 36 30509 69491 63574
37 30646
38 30784
39 30921
2829407
2929545 70455 61799
3029683 70317 62052
70593 61545
423
38709 32022
67978
33
38455 32138
193 67862
32
423
193
423
38201 32253
67747
31
37948 32369
19367631
30
423
193
37694 32485
67515
29
423
37440 32601
193
67399
28
423
423
37187 32717
193 67283
27
36933 32833
19367167
26
423
423
36680 32949
193
67051 47 25
193
229
229
228
69354 63827
69216 64081
69079 64335
41 31195 228
42 31332 228
43 31469
228
44 31606
228
45 31742
36426 33065
36173 33181
35919 33297
35665 33414
40 31058 228 68942 64588 35412 33530
68805 64842 35158 33647
68668 65095
423
194 66819
66935 24
23
423
423
423
422
422
422
422
422
194
194 66586
66.703
22
21
194
66470
20
194 66353
19
Cos. D.
34905 33763
68531 65349 34651 33880
68394 65602 34398 33996
6825865855 34145 34113
Sec. Cot. D. Tang. Cos.
194
66237
18
194 66120
17
194 66004
16
195
65887 47 15
D.
Sine
48 Deg.
471 Deg.
MATHEMATICAL TABLES.
129

422 Deg.
TABLE V.-LOG. SINES, ETC.
434 Deg.
Sine
9-8
D. | Cosec. Tang.] D. Cot. Sec.
D.
Cos.
10'1 9'9
IO'O
ΙΟΙ
9.8
42 45 | 31742
46 31879
47 32015
48 32152
49 32288
50 32425
51 32561
52 32697
53 32833
42 54 32969 226
228
228
422
422
227
67848 66616
422
68258 65855 34145 34113
68121 66109
67985 66362
65887
15
33891 34230
195
65770
14
33638 34347
195
65653
13
195
33384 34464
65536
12
227
227
227
67712 66869
422
33131 34581
195
65419
II
67575 67123
422
32877 34698
195
65302
10
67439 67376
422
227
67303 67629
422
32624 34815
195
65185
195
32371 34932
65068
98
227
422
67167 67883
195
32117 35050
227
422
195
64950 47 7
O
55 33105 226
56 33241 226
57 33377 226
58 33512
59 33648
43 33783
67031 68136
66895 68389
66759 68643
66623 68896
422
31864 35167 64833
6
422
31611 35284 64716
196
196
5
422
31357 35402
31104 35519
196
64598
4
226
66488 69149
422
196
64481
3
30851 35637
226
66352 69403
422
196
64363
2
226
66217 69656
30597 35755
422
196
64245
I 33919
66081 69909
422
30344 35873
196
64127 47 0
30091 35990
234054 225
225
65946 70162
422
196
64010 59
29838 36108
63892 46 58
422
197
6
10 35134
17 36075
43 12 35403 64597 72694
13 35538 64462 72948
14 35672 64328 73201
15 35807 64193 73454
16 35941 224 63925 73960
64059 73707
225
225
225
225
225
225
224
224
224
43 334189 65811 70416
434325 65675 70669
422
29584 36226
63774
422
29331 36344
197
63656
༄༦༦༠༥
5 34460 65540 70922
29078 36462
197
63538
55
422
197
34595 65405 71175
28825 36581
9 34999 65001 71935
64866 72188
II 35269 64731 72441
7 34730 65270 71429
834865 65135 71682
422
28571 36699
197
63419
54
63301
53
422
28318 36817
197
63183
52
422
28065 36936
197
63064
51
422
197
27812 37054
422
198
62946
50
27559 37173
422
198
62827 46 49
224
224
224
224
422
27306 37291
198
62709
48
27052 37410
422
198
62590 47
422
26799 37529
198
62471
46
422
26546 37647
198
62353
45
26293 37766
422
198
62234
44
223
20 36477 223
223
43 21 36611
22 36745
2336878
24 37012
25 37146
26 37279
27 37412
28 37546
2937679
30 37812
18 36209 223 63791 74213
25787 38004
1936343 63657 74466 25534 38123
26040 37885
422
422
422
422
198
62115
43
198
61996
42
63523 74719 25281 38242
198
61877 4I
61758 46 40
199
223
223
223
63122 75479
62988 75732
222
222
222
222
222
222
62188 77250
24521 38600
24268 38720
62854 75985 2401538839
62721 76238 23762 38959
62588 76491
23509 39078
62454 76744 23256 39198
62321 76997
23003 39318
22750 39438
Cos. D. Sec. Cot. D. Tang. Cos.
422
422
422
422
422
422
422
422
422
63389 74973 25027 38362
63255 75226 24774 38481
199 61400
199 61519
61638 39
38
37
199 61280
36
199 61161
35
199
199
61041
34
60922 33
199 60802
199
32
60682
31
200
60562 46 30
D.
Sine
471 Deg.
461 Dog.
130
MATHEMATICAL TABLES.

43 Deg.
TABLE V.-LOG. SINES, ETO.
Sine D. Cosec. | Tang. D. Cot. Sec.
44 Deg.
D.
Cos.
9.8
43 30 37812
ΙΟΙ 9'9
62188 77250
10'0
ΙΟΙ
9.8
31 37945
32 38078
33 38211
222
222
221
221
62055 77503
61922 77756
422
22750 39438
60562
30
200
422
22497 39558
60442
29
200
2224439678
61789 78009
422
60322
28
200
21991 39798
60202
27
34 38344
61656 78262
422
21738 39918
200
60082
26
221
35 38477
61523 78515
422
200
221
21485 40038
59962
36 38610
61390 78768
422
25
200
221
21232 40158
59842
24
37 38742
3838875
221
61258 79021
422
200
20979 40279
59721
221
61125 79274
422
23
422
20726 40399
201
59601
46 22
201
48 39 39007
221
40 39140
220
41 39272
220
6099379527
60860 79780
60728 80033
20473 40520
59480
21
422
201
20220 40640
59360
20
422
201
19967 40761
59239
19
4239404
60596 80286
422
201
220
19714 40881
59119
18
86
43 39536
220
60464 80538
422
201
19462 41002
58998
17
44 39668
4539800
60332 80791
422
201
46 39932
47 40064
43 48 40196
220
220
220
219
60200 81044
421
19209 41123
58877
16
201
60068 81297
42 I
18956 41244
58756
15
202
18703 41365
59936 81550
421
58635
14
202
18450 41486
42I
58514 46 13
202
59804 81803
219
18197 41607
49 40328
5040459
59672 82056
42I
58393
12
202
219
17944 41728
58272
II
59541 82309
421
202
219
17691 41849
51 40591
219
59409 82562
421
58151
10
202
52 40722
53 40854 59146 83067
5440985 5901583320
55 41116 58884 83573
56 41247 58753 83826
43 57 41378 218 58622 84079
58 41509 218 58491 84331
59 41640
44 0 | 41771
59278 82814
421
17438 41971
58029
202
219
219
219
218
218
421
1718642092
57908
202
421
16933 42214
57786
42I
16680 42335
202
57665
421
16427 42457
203
57543
42 I
16174 42578
203
57422 46 4
98 7654
203
15921 42700
421
57300
3
1566942822
203
218
218
58360 84584
421
57178
2
I 41902 218
58229 84837
58098 85090
421
15416 42944
203
57056
I
15163 43066
203
421
56934 46 o
218
5 42424
217
217
217
242033 57967 85343
3 42163 57837 85596
4 42294 57706 85848
421
14910 43188
203
56812
421
14657 43310
203
56690
204
14404 43432
421
56568
in in in
59
58
57
204
57576 86101
421
14152 43554
56446
56
421
13899 43677
204
204
56323 45 55
44
642555
742685
217
57445 86354
8 42815
217
57315 86607
42 I
13646 43799
56201
54
204
13393 43922
Cos. D.
942946 57054 87112
10 43076 56924 87365
11 43206 216 56794
56794 87618
12 43336
13 43466
14 43595 216
15 43725
46 Deg.
217
57185 86860
421
56078
53
204
421
13140 44044
55956
52
217
217
12888-44167
204
421
55833
51
421
12635 44289
204
55711
50
216
216
56664 87871
56534 88123
56405 88376
56275 88629
421
12382 44412
205
55588
49
12129 44535
205
42 I
421
421
55465
48
11877 44658
205
55342
47
205
205
11624 44781
11371 44904 55096 45 45
55219
46
Sec. Cot. DTang. Cos. D. Sine
45 Deg.
MATHEMATICAL TABLES.
131

441 Deg.
TABLE V.-LOG. SINES, ETC.
45 Deg.
Sine D. Cosec. Tang.
D. | Cot. Sec.
D.
Cos.
ΙΟΙ
216
17 3984
9.84
44 15 3725 56275 9.988629 11371 44904
16 3855 216 56145 9988882 11118 45027
216 56016 9989134
IO'O ΙΟΙ
9.8
19 4243
31 5790
215
215
215
215
215
215
215
215
215
214
214
214
214
214
214
214
214
214
213
213
213
213
213
213
213
213
212
212
212
212
212
212
212
212
211
211
211
211
211
211
211
51909 9'997221
51782 9997473
44 51 8345 51655 9997726
52 8472
51528 9997979
53 8599 51401 9998231
54 8726
55 8852
56 8979
57 9106
58 9232
59 9359
45 7582 52418 9996210 03790 48628
46 7709 52291 9996463 03537 48754
477836 52164 9996715 03285 48879
48 7964 52036 9*996968 03032 49004
49 8091
50 8218
18 4114 55886 9989387 10613 45273
55757 9989640 10360 45397
20 4372 55628 9989893 10107 45520
21 4502 55498 9990145 09855 45644
22 4631 55369 9990398. 09602 45767
23 4760 55240 9990651 09349 45891
44 244889
55111 9990903 09097 46014
25 5018
08844 46138
54982 9991156
26 5147 54853 9991409 08591 46262
27 5276 54724 9991662 08338 46386
28 5405
54595 9'991914
08086 46510
29 5533 54467 9992167 |07833 46634
30 5662 54338 9992420 07580 46758
54210 9992672 07328 46882
32 5919 54081 9992925 07075 47006
44 33 6047 53953 9993178
06822 47131
34 6175
53825 9993430
06570 47255
35 6304 53696 9993683 06317 47380
36 6432 53568 9993936 06064 47504
37 6560
53440 9994189 05811 47629
38 6688
05559 47753
53312 9994441
39 6816
53184 9994694 05306 47878
40 6944
53056 9994947 05053 48003
41 7071
04801 48128
52929 9995199
44 42 17199
52801 9995452 04548 48253
43 7327 52673 9995705 04295 48378
447454 52546 9995957 04043 48503
421
42I
421
421
421
42I
421
421
421
421
421
421
421
421
421
421
421
421
421
421
421
421
421
421
421
421
421
55096
45
205
54973
44
10866 45150
205
54850
43
205
206
54727
42
206
54603
41
206
54480
40
206
54356
39
206
54233
38
206
54109 45 37
206 53986
36
206
206 53738
53862
35
34
53614
33
207
53490
32
207
53366
31
207
53242
30
207
207
53118 29
52994 45 28
207
207
52869 27
52745
26
207
52620
25
207
208
52496
24
208
52371
23
208
52247
22
208
52122
21
208
208
51997
20
51873 45 19
02779 49130
0252749255
02274 49381
C2021 49507
01769 49632
51274 9998484 01516 49758
51148 9998737 01263 49884
51021 9998989 01011 50010
60 9485
211
50894 9999242 00758 50136
50768 9.999495 00505 50262
50641 9999747 00253 50389
421
50515 10.000000
00000 50515
421
421
42 I
421
421
421
421
421
421
421
421
421
421
421
421
421
421
208
51747
18
208
51622
17
51497
16
209
51372
15
209
51246
14
209
51121
13
209
50996
12
209
50870
II
209
50745 45 10
209
50619
209
210
210
210
210
50493
50368
50242
98 76
50116
5
49990
4
210
49864
3
210
49738
2
210
49611
210
49485 45
Cos. D. Sec. Cot. D. Tang. Cos.
45 Deg.
D. Sine
45 Deg.
132
MATHEMATICAL TABLES.
TABLE VI.—MERIDIONal Parts.

4
7
8
9
0×23 + no t∞ αlo Hamt SO N∞ a
O
I I
0
2
C
2
O
O
I I 12
2
3456 78 9
6° 17° | 8° 9
13° | 14° |15" | 16° | 17° | 18° | 19° | 20° | 21° | 22° | 23° | 24°
60 120 180 240 300 361 421 482 542 603 664 725 787 848 910 973 1035 1098 1161 1225 1289 1354 1419 1484
1 61121181 788850911
61 121 181 241 301 362 422 483 543 604 665 726 788 850 911 974 1036 1099 1163 1226 1290 1355 1420 1485
62 122 182 242 302 363 423 484 544 605 666 727 789 851 913 975 1037 1100 1164 1227 1291 1356 1421 1486
63 123 183 243 303 364 424 485 545 606 667 728 790 852 914 976 1038 1101 1165 1228 1292 1357 1422 1487|
64 124 184 244 304 365 425 486 546 607 668 729 791 853 915 977 10391102 1166|1229 1293 13581423 1488
65 125 185 245 305 366 426 487 547 608 669 730 792 854 916 978 1041 1103 1167 1230 1295 1359 1424 1490
6 66 126 186246 306 367 427 488 548 609 670 731 793 855 917 979 1042 1105 1168 1232|1296|1360|1425|1491
7|67|127187|247|307|368|428|489|549|610|671|732
67127 187 247 307 368 428 489 549 610|671 732 794 856 918 980 1043 1106 1169|1233 1297 1361|1426|1492
8 795857
68 128 188 248 308 369 429 490 550 611 672 734 795 857 919 981 10441107 1170 1234 1298 1362 1427 1493
9|69|129|189249309 370 430 491 551 612 673 735 796 858 920 982 1045 1108 11711235 1299 1363 14281494
10 70 130 190 250 310 371 431 492 552 613 674 736 797 859 921 983 1046 1109 1172 1236 1300 1364 1430 1495 10
11 71131191 251 311 372 432 493 553 614 675 737 798 860 922 984 1047 11101173 1237 1301 1366 1431 1496 II
12 72132192 252 312 373 433 494 554 615 676 738 799 861 923 985 1048 11111174 1238 1302 1367 1432 1497 12
13 73 133 193 253 313 374 434 495 555 616 677 739 800 862 924 986 1049 11121175 1239 1303 1368 1433 1498 13
14 74134194 254 314 375435 496 556 617 678 740 801 863 925 987 1050 1113 1176 1240 1304|1369|1434|1499|| 14
618679 741802
15 75 135 195 255 315 376 436 497 557 618 679 741 802 864 926 988 1051 1114 1177 1241 1305 1370 14351500 15
16 76136196 256 316 377 437 498 558 619 680 742 803 865 927 989 1052 1115 1178 1242 1306 1371 1436 1502 16
17 77 137 197 257 317 378 438 499 559 620 681 743 804 866 928 9901053 1116 1179 1243 1307 1372 1437 1503 17
18 78 138 198 258 318 379 439 500 560 621 682 744 805 867 929 991|1054 1117 1181 1244 1308 1373 1438 1504 18
19 79 139 199 259 319 380 440 501 561 622|683745|806|868|930| 993 10551118 1182 1245 1310 1374 1439 1505 19
80 140 200 260 320 381 441 502 562 623 684 746 807 869 931 994 10561119 1183 1246 13111375 1440 1506 20
21 81141 201|261|321 382 442 503 564 624 685 747 808 870 932 995 1057 1120 1184|1248|1312|1376|1441|1507 21
22 82 142 202 262 322 383 443 504 565 625 687 748 809 871 933 996 1058 1121 1185 1249 1313 1377 1443 1508 22
23 83143203263 323 384 444 505 566 626 688 749 810 872 934 997 1059 1122 1186 1250 1314 1379 14441509 23
24 84 144 204 264 324 385 445 506 567 627 689 750 811 873 935 998 1060 1123 1187 1251 1315 1380 1445 1510 24
25 85 145 205 265 325 386 446 507 568 628 690 751 812 874 936 999 1061 1125 1188 1252 1316 1381 1446 1511 25
26 86 146 206 266 326 387 447 508 569 629 691 752 813 875 937 1000 1063 1126 1189 1253 1317 1382 1447 1513
1126|1189|1253|13171382 26
27 87 147 207 267 327 388 448 509 570 631 692 753 815 876 938 1001| 1064 1127 1190 1254 13181383 1448 1514 27
28 88 148 208 268 328 389 449 510 571 632 693 754 816 877 939 1002 1065 1128 1191 1255 1319 1384 1449 1515 28
29 89149209269 330 390 450 511 572 633 694 755817878|941 1003|1066|1129|1192 1256 1320 1385 1450 1
1516 29
ΙΟ
II
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
2 2 2 2 2 2 2
20
22
MATHEMATICAL TABLES.
133
TABLE
VI.-MERIDIONAL PARTS.

w
30
31
32
wwwwwww
a
40
4I
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
3456 7∞
37
•
I I 12
I 3
220
2° | 3° | 4° | 5° | 6° | 7° | 8° | 9° | 10
14° | 15° | 16° | 17° | 18° | 19° | 20° | 21° 23° 24°
30 90150210270 331 391 451 512 573 634 695 756 818 879 942 1004 1067 11301193 1257 1321 1386 1451 1517 30
31 91151211271 332 392 452 513 574 635 696 757 819 880 943 1005 1068 1131 1194 1258 1322 1387 1452 1518 31
32 92152212272 333 393 453 514 575 636 697 758 820 882 944 1006 1069 1132 1195 1259 1324 1388 1453 1519 32
33 93153213 273 334 394 454 515 576 637 698 759 821 883 945 1007 1070 1133 1196 1260 1325 1389 14551520 33
34 94154214274 335 395 455 516 577 638 699 760 822 884 946 1008 1071 1134 1198 1261 1326 1390 1456 1521 34
95|155|215|275|336|396|456|517578|639|700
35 95 155 215 275 336 396 456 517 578 639 700 761 823 885 947 1009 1072 1135 1199 1262 1327 1392 1457 1522 35
36 96156 216 276 337 397 457 518 579 640 701 762 824 886 948 1010 1073 1136 1200 1264 1328 1393 1458 1524 36
97 157 217 277 338 398 458 519 580 641 702 763 825 887 949 1011 1074 1137 1201 1265|1329 1394 1459 1525 37
38 98 158 218 278 339 399 459 520 581 642 703 764 826 888 950 1012 1075 1138 1202 1266 1330 1395 1460 1526 38
39 99 159 219 279 340 400 460 521 582 643 704 765 827 889 951 1013 1076 1139|1203|1267 1331 1396 1461 1527 39
40 100 160 220 280 341 401 461 522 583 644 705 766 828 890 952 1014 1077 1140 1204 1268 1332 1397 1462|1528| 40
41 101 161 221 281 342 402 462 523 584 645 706 767 829 891 953 1015 1078 1141 1205 1269 1333 1398 1463|1529 41
42|102 162 222 282 343 403 463 524 585 646 707 768 830 892 954 1016 1079 1142 1206 1270 1334 1399 1464 1530 42
43 103 163|223 283 344 404 464 525 586 647 708 769 831 893 955 1018 1080 11441207 12711335 1400 1465 1531 43
44 104 164 224 284 345 405 465 526 587 648 709 770 832 894 956 1019 1081 1145 1208 1272 1336 1401|1467|1532|| 44
45 105 165 225 285 346 406 466 527 588 649 710 771 833 895 957 1020 1082 1146 1209 1273 1338 1402 1468 1533 45
46 106 166 226 286 347 407 467 528 589 650 711 772834 896 958 1021 1084 1147|1210 1274 1339 1403 1469 1535 46
47 107 167 227 287 348 408 468 529 590 651 712 773 835 897 959 1022 1085 1148 1211 1275 1340 1405 1470 1536 47
48 108 168 228 288 349 409 469 530 591 652 713 774 836|898 960 1023 1086 1149|1212 1276 1341 1406 1471 1537 48
49 109 169 229 289 350 410 470 531 592 653 714 775 837 899 961 IC24 1087 1150 12131277 1342 1407 1472 1538 49
50 110 170 230 290 351 411 471 532 593 654 715 777 838 900 962 1025 1088 1151 1215 1278 1343 1408 1473 1539 50
51|111|171231 291 352 412 472 533 594 655 716 778839 901|963|1026|1089 1152 1216 1280 1344 1409 1474 1540 51
52|112|172|232|292|353 413 473 534 595 656 717 779 840|902|964|1027 1090|1153|12171281 1345 141014751541 52
53113173 233 293354414474 535 596 657 718 780 841 903|965|1028 1091 1154 1218|1282|1346 1411|1476|1542 53
54 114 174234294355 415 476 536 597 658 719 781 842|904|966|1029|1092|1155|1219|1283|1347 1412 1477 1543 54
55 115 175 235 295 356 416 477 537 598 659 720 782 843 905 968 1030 1093 1156 1220 1284 1348 1413 1479 1544 55
56| 116 176 236 296 357 417 478 538 599 660 721 783 844 906 969 1031 1094 1157 1221 1285 1349 1414 1480|1546 56
57 117 177 237 297 358 418 479 539 600 661 722 784 845 907 970 1032 1095 1158 1222 1286 1350 1415 14811547 57
58 118 178 238 298 359 419 480 540 601 662 723 785 846 908 971 1033 1096 1159 1223 1287 1352 1416 1482 1548 58
59|119179|239|299|360|420|481|541|602|663|724|786|847|909 972 1034|1097|1160|1224|1288│1353│141814831549 59
134
MATHEMATICAL. TABLES.
TABLE VI.-MERIDIONAL PARTS.

I
OH2M+no z∞ al
6
7
8
I I
25° 26° 27° 28° | 29° | 30º | 31° | 32° | 33° | 34° | 35° | 36° | 37° | 38° | 39° | 40° | 41′
I
0×2M to 78 a
9
ΙΟ
II
12
13
42° | 43° | 44° | 45°
1550 1616 1684 1751 1819 1888 1958 2028 2100 2171224423182393 2468 2545 2623 2702 2782 2863|2946 3030
1551 1618 1685 1752 1821 1890 1959 2030 2101 2173 2246 2319 2394 2470 2546 2624 2703 2783 2864 2947 3031
1552 1619 1686 1753 1822 1891 1960 2031 2102 2174 2247 2320 2395 2471 2548 2625 2704 2784 2866 2949 3033
3 1553 1620 1687 1755 1823 1892 1962 2032 2103 2175 2248 2322 2396 2472 2549 2627 2706 2786 2867 2950 3034
4
1554 1621 1688 1756 1824 1893 1963 2033 2104 2176 2249 2323 2398 2473 2550 2628 2707 2787 2869 2951 3036
5 1556 1622 1689 1757 1825 1894 1964 2034 2105 2178 2250 2324 2399 2475 2551 2629 2708 2788 2870 2953 3037
1557 1623 1690 1758 1826 1895 1965 2035 2107 2179 2252 2325 2400 2476 2553 2631 27102790 2871 2954 3038
1558 1624 1691 1759 1827 1896 1966 2037 2108 2180 2253 2327 2401 2477 2554 2632 2711 2791 28732956 3040
1559 1625 1693 1760 1829 1898 1967 2038 2109 2181 22542328|2403 2478 2555 2633 2712 2792 2874 2957 3041
9 1560 1626 1694 1761 1830 1899 1969 2039 2110 2182|2255 2329|2404|2480|2557 2634 2714 2794 2875 2958 3043
IO 1561 1628 1695 1762 1831 1900 1970 2040 2111 21842257 2330 2405 2481 2558 2636 27152795 2877 2960 3044
1562 1629 1696 1764 1832 1901 1971 2041 2113 2185 2258|2332 2406 2482 2559 2637 2716 2797 2878 2961|3046
12 1563 1630 1697 1765 1833 1902 1972 2043 2114 2186 22592333 2408 2484 2560 2638 2718 2798 2880 2963 3047
13 1564 1631 1698 1766 1834 1903 1973 2044 2115 2187 2260 23342409 2485 2562 2640 2719 2799 28812964 3048
141565 1632| 1699|1767|1835 1905 1974 2045 2116 2188 2261|2335 2410 2486 2563|2641 2720 2801 2882 2965 3050
15 1567 1633 1700 1768 1837 1906 1976 2046 2117 2190 2263 2337 2411 2487 2564 2642 2722 2802 2884 2967 3051
16 1568 1634 1701 1769 1838 1907 1977 2047 2119 2191 2264|2338|2413|2489|2566|2644|2723 2803 2885 2968 3053
17 1569 1635 1703 1770 1839 1908 1978 2048 2120 2192 2265 2339 2414 2490 2567 2645 2724 2805 2886 2970 3054
1570 1637 1704 1772 1840 1909 1979 2050 2121 2193 2266| 2340 2415 2491 2568 2646 2726| 2806 2888 2971 3055
1571 1638 1705 1773 1841 1910 1980 2051 2122 2194 2268 2342 2416|2492|2569 2648 2727 2807 2889 2972 3057 19
1572 1639 1706 1774 1842 1912 1981 2052 2123 2196 2269 2343 2418 24942571 2649 2728 2809 2891 2974 3058
1573 1640 1707 1775 1843 1913 1983 2053 2125 2197 2270 2344 2419 2495 2572 2650 2729 2810 2892 2975 3060
1574 1641 1708 1776 1845 1914 1984 2054 2126 2198 22712345 2420 2496 2573 2651 2731 2811 2893 2976 3061
23 1575 1642 1709 1777 1846 1915 1985 2056 2127 21992272|2346|2422 2498 2575 2653 2732 2813 2895 2978 3063 23
24 1577 1643 1711 1778 1847 1916 1986 2057 2128 2200 22742348 2423|2499 2576 2654 2733 2814 2896 2979 3064 24
25 1578 1644 1712 1780 1848 1917 1987 2058 2129 2202 22752349 242425002577 2655 2735 2815 2897 2981 3065 25
26 1579 1645 1713 1781 1849 1918 1988 2059 2131|2203|2276|2350|2425|2501 2578 2657 27362817|28992982 3067|| 25
1580 1647 1714 1782 1850 1920 1990 2060|2132|2204|22772351 2427 2503 2580 2658 2737 2818 2900 2983 3068 27
1581 1648 1715 1783 1852 1921 1991 2061 2133 2205 22792353 2428 25042581 2659 2739 2820 2902 2985 3070 28
29 | 1582| 1649| 1716|1784|1853|1922|1992|2063|2134|2207|2280|2354|2429|2505|2582|2661|27402821|2903|2986|3071 29
18
19
20
21
22
56 7∞
27
28
14
15
16
17
18
20
21
MATHEMATICAL TABLES.
135
TABLE VI.—MERIDIONAl Parts.

32
33
34
39
40
41
4.4
30
33
43
25° 26° 27° 28° 29° 30° 31° 32° 33° | 34° 35° | 36°
35° | 36° | 37° | 38° | 39° 40° 41° 42° | 43° | 44° | 45°
2135|2208|2281 25842662
30 1583 1650 1717 1785 1854 1923 1993 2064 2135 2208 2281 2355 2430 2506 2584 2662 2742 2822 2904 2988 3073
31 1584 1651 1718 1786 1855 1924 1994 2065 2137|2209|22822356 2432 2508 2585 2663 2743 2824 2906 2989 3074 31
1585 1652 1720 1787 1856 1925 1995 2066 2138 2210 2283 2358 2433 25092586 2665 2744 2825 2907 2991 3075 32
1586 1653 1721 1789 1857 1927 1997 2067 2139 2211 2285 2359 2434 2510 2588 2666 2746 2826 2908 2992 3077
1588 1654 1722 1790 1858 1928 1998 2069 2140 2213 2286 2360 2435 2512 2589|2667|2747 2828 2910 2993 3078 34
2513|2590|2669|2748|2829|2911|29953080 ||
35 1589 1656 1723 1791 1860 1929 1999 2070 2141 22142287 2361 2437 2513 2590 2669 2748 2829 2911 2995 3080 35
36 1590 1657 1724 1792 1861 1930 2000 2071 2143 2215 2288 2363 2438 2514 2591 2670 2750 2830 2913 2996 3081 36
37 1591| 1658 1725 1793|1862|1931 2001 2072 2144 2216 2290 2364 2439 2515 2593 2671 2751 2832 2914 2998 3083 37
38 1592 1659 1726 1794 1863 1932 2002 2073 2145 2217 22912365 2440 2517 2594 2673 2752 2833 2915 2999 3084 38
1593 1660 1727 1795 1864 1934 2004 2075 2146 2219 2292|2366 2442 25182595 2674 2754 2834 2917 3000 3085 39
1594 1661 1729 1797 1865 1935 2005 2076 2147 2220 2293|2368 2443 2519 2597 2675 2755 2836 2918 3002 3087 40
1595 1662 1730 1798 1866 1936 2006 2077 2149 2221 2295 2369 2444 2521 2598 2676 2756 2837 2919 3003 3088 | 41
42 1596 1663| 1731|1799|1868 1937 2007 2078 2150 22222296 2370 2445 2522 2599 2678 2758 2839 2921 3005 3090 42
43 1598 1664 1732 1800 1869 1938 2008 2079 2151 2224 2297 2371 2447 2523 2601 2679 2759 2840 2922 3006 3091
1599 1666 1733 1801 1870 1939 2010 2080 2152 2225 2298 2373 2448 2524 2602 2680 2760 2841 2924 3007 3093
1600 1667 1734 1802 1871 1941 2011 2082 2153|2226 2299 23742449 2526 2603 2682 2762 2843 2925 3009 3094 45
1601 1668 1735 1803 1872 1942 2012 2083 2155 2227 2301 2375 2451 2527 2604 2683 2763 2844 2926 3010 3095 46
1602 1669 1736 1805 1873 1943 2013 2084 2156|2228 2302|2376 2452 2528|2606|2684 2764 2845 2928|3012 3097 47
48 1603 1670 1738 1806 1875 1944 2014 2085 2157 2230 2303 2378 2453 2530 2607 2686 2766 2847 2929|3013 3098 48
1604 1671 1739 1807 1876 1945 2015 2086 2158 22312304 2379 2454 2531 2608 2687 2767 2848 293130143100
50 1605 1672 1740 1808 1877 1946 2017 2088 21592232 2306 2380 2456 2532 2610 2688 2768 2849 2932 30163101
1606 1673 1741 1809 1878 1948 2018 2089|2161 2233 2307 2381 2457 2533 2611 2690 2770 2851 2933 3017 3103
1608 1675 1742 1810 1879 1949 2019 2090 2162 2235 2308 2383 2458 25352612 2691 2771 2852 2935 3019 3104 52
53 1609 1676 1743 1811 1880 1950 2020 2091 2163 2236 2309 23842459 2536 2614 2692 2772 2854 2936 30203105 53
54 1610 1677 1744 1813 1881 1951 2021 2092 2164 2237 2311 2385 2461 2537 2615 2694 2774 28552937 3021 3107
55 1611 1678 1746 1814 1883 1952 2022 2094 2165 2238 2312 2386 2462 2538 2616 2695 2775 2856 2939 3023 3108 55
56 1612 1679 1747 1815 1884 1953 2024 2095 2167 2239 2313 2388 2463 25402617 2696 2776 2858 2940 3024 3110
2167|2239|2313|2388|2463|2540|2617|2696|2776|2858 56
57 1613 1680 1748 1816 1885 1955 2025 2096 2168 2241 2314 2389|2464 2541 2619 2698 2778 2859 2942 3026 311I
58 1614 1681 1749 1817 1886 1956 2026 2097 2169 2242 2316 2390 2466 2542 2620 2699 2779 2860 2943 3027 3113 58
59 1615 1682 1750 1818 1887 1957 2027 2098 2170|2243|2317|2391|2467|2544 2621 2700 2780 2862|2944 3029|3114
45
46
47
49
51
52
44
49
50
51
54
57
59
136
MATHEMATICAL TABLES.
TABLE VI.—MERIDIONAL Parts.

I
2
6
8
II
12
∞ ∞ | ∞ ∞
•
I
2
9
II
12
46° 47° 48° | 49° | 50°
50° | 51 52° | 53° | 54°
54 | 55° | 56° | 57°
57° 58° 59° | 60° | 61° 62° | 63° | 64° | 65° | 66°
3116 3203 3292 3382 3474 3569 3665 37643865 3968 40744183 42944409 4527 4649 4775 4905 5039 5179 5324
41844296
3117 3204 3293 3384 3476 3570 3667 3765 3866 397040764184 4296|4411 4529 4651 4777 4907 5042 5181 5326
3118 3206 3295 3385 3478 3572 3668 3767 3868 3971 4077 4186 4298 4413 4531 4653 4779 4909 5044 5184 5328
3 3120 3207 3296 3387 3479 3574 3670 3769 3870 3973 4079 4188 4300441545334655 4781 4912 50465186 5331
4 3121 3209 3298 3388 3481 3575 3672 3770 3871 3975 4081 4190 4302 4417 4535 4657 4784 4914 5049 5188 5333
3123 3210 3299 3390 3482 3577 3673 3772 3873 3977 4083 4192 4304 4419 4537 4660 4786 4916 5051 5191 5336
3124 3212 3301 3391 3484 3578 3675 3774 3875 3978 4085 4194 4306 4421 4539 4662 4788 4918 5053 5193 5338
7 3126 3213 3302 3393 3485 3580 3677 3775 3877 39804086 4195 4308 4423 4541 4664 4790 4920 5055 5195 5341
3127 3214 3303 3394 3487 3582 3678 3777 3878 3982 4088|4197|4309|4425 4543 4666 4792 4923 5058 5198 5343
93129 3216 3305 3396 348835833680 3779 3880 3984 40904199 4311 4427 4545|4668|4794 4925 5060|5200 5346
10 3130 3217 3306|3397 3490 3585 3681 3780 3882|39854092 4201 4313 4429 4547 4670 4796 4927|5062|5203|5348 | 10
3131 3219 3308 3399 3492 3586 3683 3782 3883 3987 4094 4203 4315 4431 4549 4672 4798 4929|5065 5205 5351
3133 3220 3309 3400 3493 3588 3685 3784 3885 3989 4095420543174433 4551 4674 4801 4931 5067|5207 5353
13 3134 3222 3311 3402 3495 3590 36863785 3887 3991 4097 4207 4319 4434 4553 4676 4803 4934 5069 5210 5356 13
14 3136 3223 3312 3403|3496 3591|3688 3787 3889 3992|4099|4208 4321 4436 4555 4678 48054936|5071 5212 5358
15 3137 3225 3314 3405 3498 3593 3690 3789 3890 3994 4101 4210 4323 4438 4557 46804807 4938 5074 5214 5361 15
16|3139 3226 3316 3407 3499 3594 3691 3790 3892 3996 4103 42124325 4440 4559 4682 4809 4940 5076 5217 5363 16
17 3140 3228 3317 3408 3501 3596 3693 3792|3894 3998|410442144327 4442 4562 4684 4811 4943 5078 5219 5366 | 17
4106|4216
||
3142 3229 3319 3410 3503 3598 3695 3794 3895 3999 4106 4216 4328 4444|4564 4687|4814 4945 5081 5222 5368 | 18
3143 3231 3320 3411 3504 3599 3696 3795 3897 4001 4108 4218 4330 4446 4566 4689 4816 4947 5083 52245371
3144 3232 3322 3413 3506 3601 3698 3797 3899 4003 411042204332 4448 4568 4691 4818 4949 5085 5226 5373
3146 3234 3323 3414 3507 3602 3699 3799 3901 4005 4112 4221 4334 4450 4570 4693 4820 4951 5088 5229 5376 21
3147 3235 3325 3416 3509 3604 3701 3800 39024006 41134223 4336 4452 4572 4695 4822 49545090 5231 5378 22
3149 3237 3326 3417 3510 3606 3703 3802|3904 4008 4115 4225 4338 4454 4574 4697 4824 4956 5092 52345380 23
3150 3238 3328 3419 3512 3607 3704 3804 3906 4010 4117 4227 4340 4456 4576 4699 4826 4958 5095 5236|5383 | 24
3152 3240 3329 3420 3514 3609 3706 3806 390740124119 4229 4342 4458 4578 4701 4829 4960 5097 5238 5385 25
3153 3241 3331 3422 3515 3610 3708 3807 3909 40144121 4231 4344 4460 4580 4703 4831 4963 5099 5241 5388|| 26
27 3155 3242 3332 3423 3517 3612 3709 3809 3911 4015 4122 4232 4346 4462 4582 4705 4833 49655102 5243 5390 27
28 3156 3244 3334 3425 3518 3614 3711 3811 3913 4017 4124 4234 4347 4464 4584 4707 4835 4967 5104 5246 5393 28
293157 3245 3335 3427 35203615 3713|3812 3914 4019 4126 4236 4349 4466 4586 47104837 4969 51065248 5395 | 29
18
19
20
21
22
23
24
25
26
14
19
20
MATHEMATICAL TABLES.
137
TABLE VI.-MERIDIONAL I ARTS.

30
31
33
35
39
40
4I
46° | 47° | 48° | 49° | 50° | 51° | 52° | 53° 54° | 55° | 56° | 57° | 580 | 59° | 60° | 61° | 62° | 63° 64° | 65° | 66°
31
32
34
35
36
16 78
37
3159 3247 3337 3428 3521 3617 3714 3814 3916 4021 4128 4238 4351 4468 4588 4712 4839 4972 5108 5250 5398 30
3160 3248 3338 3430 35233618 3716 3816 3918 40224130 4240 4353 4470 4590 4714 4842 4974 5111 52535401
32 3162 3250 3340 3431 35253620 3717 38173919 40244132 42424355 4472 4592 4716 48444976 5113 5255 5403
33 3163 3251 3341 3433 3526 3622 3719 3819 3921 4026 4133 4244 4357 4474 4594 4718 4846 4978 5115 5258 5406 33
34 3165 3253 3343 3434 3528 3623 3721 3821 3923 4028 4135 4246 4359 4476 4596 4720 4848 4981 5118 5260 5408
3166 3254 3344 3436 3529 3625 3722 3822 3925 40294137 4247 4361 4478 4598 4722 4850 4983 5120 5263 5411
36 3168 3256 3346 3437 3531 3626 3724 3824 3926 4031 4139 4249 4363 4480 4600 4724 4852 4985 5122 5265 5413
37 3169 3257 3347 3439 3532 3628 3726 3826 3928 4033 4141 4251 4365 4482 4602 4726 4855 4987 5125 5267 5416
383171 3259 3349 3440 3534 3630 3727 3827 3930 4035 41 42 4253 4367 44844604 4728 4857 4990 5127 5270 5418 38
3172 3260 3350 3442 3536 3631 3729|3829|3932 4037 4144 4255 4369 4486 4606 4731 4859 4992 5129 5272 5421 | 39
3173 3262 3352 3443 3537 3633 3731 3831 3933 4038 4146|4257 4370 4488 4608 4733 4861 4994 5132 5275 5423 40
3175 3263 3353 3445 3539 3634 3732 3832 3935 4040 4148 4259 4372 4490 4610 4735 4863 4996 5134 5277 5426 41
42 3176 3265 3355 3447 3540 3636 3734 3834 3937 4042 4150 4260 4374 4492 4612 4737 4865 4999 5136 5280 5428 42
43 3178 3266 3356 3448 3542 3638 3736 3836 3938 40444152 4262 4376 4494 4614 4739 4868 5001 5139 5282 5431 43
44 3179 3268 3358 3450 3543 3639 3737 3838 3940 4045 4153 4264 4378 4495 4616 4741 4870 5003 5141 5284 5433 44
45 3181 3269 3359 3451 3545 3641 3739 3839 3942 4047 4155 4266 4380 4497 4618 4743 4872 5005 5143 5287 5436 45
46 3182 3271 3361 3453 3547 3643 3741 3841 3944 4049 4157 4268 4382 4499 4620 4745 4874 5008 5146 5289 5438 46
47 3184 3272 3362 3454 3548 3644 3742 3843 3945 4051 4159 4270 4384 4501 4623 4747 4876 50105148 5292 5441 47
48 3185 3274 3364 3456 3550 3646 37443844 3947 4052 4161 4272 4386 4503 4625 4750 4879 5012 5151 5294 5443 48
49 3187 3275 3365 3457 3551 3647 3746 3846 3949 4054 4162 4274 4388 4505 4627 4752 4881 5014 5153 5297 5446| 49
318832773
50 3188 3277 3367 3459 3553 3649 3747 3848 3951 4056 4164 4275 4390 4507 4629 47 54 4883 5017 5155 5299 5448 50
3190 3278 3368 3460 3555 3651 3749 3849 3952 4058 41664277 4392 4509 4631 4756 4885 5019 5158 5301 5451
3191 3280 3370 3462 3556 3652 3750 3851 3954 40604168 4279 4394 4511 4633 4758 4887 5021 5160 5304 5454 52
3192 3281 3371 3464 3558 3654 3752 3853 3956 4061 4170 4281 4396 4513 4635 4760 4890 5023 5162 5306 5456 53
3194 3283 3373 3465 3559 3655 3754 3854 3958 4063 4172 4283 4398 4515 4637 4762 4892 5026 5165 5309 5459
3195 3284 3374 3467 3561 3657 3755 3856 3959 4065 4173 4285 4399 4517 4639 4764 4894 5028 5167 5311 5461
56 3197 3286 3376 3468 3562 3659 3757 3858 3961 4067 4175 4287 4401 4519 4641 4766 4896 5030 5169 5314 5464 56
57 3198 3287 3378 3470 3564 3660 3759 3860 3963 4069 4177 4289 4403 4521 4643 4769 4898 5033 5172 5316 5466
3200 3289 3379 3471 3566 3662 3760 3861 3964 4070 4179 4291 4405 4523 4645 4771 4901 50355174 5319 5469 | 58
3201 3290 3381|3473 3567|3664|3762|3863|3966|4072 4181 4292 4407 4525 4647 4773 4903 5037 5176 5321 5471
51
52
53
54
55
5555 in in in in
58
59
51
54
55
57
59
L
138
MATHEMATICAL TABLES.
TABLE VI.-MERIDIONAL PARTS.

O
I
2345O ZO a
8
10
I I
I 2
80°
67° 68° | 69°
69° 70° 71° 72° 73° 74° 75° | 76° | 77° | 78° | 79°
81° 82°
5474 5631 5795 5966 6146 6335 6534 6746 6970 7210 7467 7745 8046 8375 8739 9145
5477 5633 5797 5969 6149 6338 6538 6749 6974 7214 7472 7749 8051 8381 8745 9153
5479 5636 5800 5972 6152 6341 6541 6753 6978 7218 7476 7754 8056 8387 8752 9160
5482 5639 5803 5975 6155 6345 6545 6757 6982 7222 7481 7759 8061 8393 8758 9167
5484 5642 5806 5978 6158 6348 6548 6760 6986 7227 7485 7764 8067 8398 8765 9174
5487 5644 5809 5981 6161 6351 6552 6764 6990 7231 7490 7769 8072 8404 8771 9182
5489 5647 5811 5984 6164 6354 6555 6768 6994 7235 7494 7774 8077 8410 8778 9189
7 5492 5650 5814 5986 6167 6358 6558 6771 6997 7239 7498 7778 8083 8416 8784 9196
5495 5652 5817 5989 6170 6361 6562 6775 7001 7243 7503 7783 8088 8422 8791 9203
9 5497 5655 5820 5992 6173 6364 6565 6779 7005 7247 7507 7788 8093 8427 8797 9211
5500 5658 5823 5995 6177 6367 6569 6782 7009 7252 7512 7793 8099 8433 8804 9218
5502 5660 5825 5998 6180 6371 6572 6786| 7013 7256 7516 7798 8104 8439 8810 9225
5505 5663 5828 6001 6183 6374 6576 6790 7017 7260 7521 7803 8109 8445 8817 9233
13 5507 5666 5831 6004 6186 6377 6579 6793 7021 7264 7525 7808 8115 8451 8823 9240
5510 5668 5834 6007 6189 6380 6583 6797 7025 7268 7530 7813 8120 8457 8830 9248
5513 5671 5837 6010 6192 6384 6586 6801 7029 7273 7535 7817 8125 8463 8836 9255
5515 5674 5839 6013 6195 6387 6590 6804 7033 7277 7539 7822 8131 8469 8843 9262
5518 5676 5842 6016 6198 6390 6593 6808 7037 7281 7544 7827 8136 8474 8849 9270
5520 5679 5845 6019 6201 6394 6597 6812 7041 7285 7548 7832 8141 8480 8856 9277
19 5523 5682 5848 6022 6205 6397 6600 6815 7045 7289 7553 7837 8147 8486 8863 9285
5526 5685 5851 6025 6208 6400 6603 6819 7048 7294 7557 7842 8152 8492 8869 9292
5528 5687 5854 6028 6211 6403 6607 6823 7052 7298 7562 7847 8158 8498 8876 9300
5531 5690 5856 6031 6214 6407 6610 6826 7056 7302 7566 7852 8163 8504 8883 9307
5533 5693 5859 6034 6217 6410 6614 6830 7060 7306 7571 7857 8168 8510 8889 9315
24 5536 5695 5862 6037 6220 6413 6617 6834 7064 7311 7576 7862 8174 8516 8896 9322
25 5539 5698 5865 6040 6223 6417 6621 6838 7068 7315 7580 7867 8179 8522 8903 9330
26 5541 5701 5868 6043 6226 6420 6624 6841 7072 7319 7585 7872 8185 8528 8909 9337
5544 5704 5871 6046 6230 6423 6628 6845 7076 7323 7589 7877 8190 8534 8916 9345
28 5546 5706 5874 6049 6233 6427 6631 6849 7080 7328 7594 7882 8196 8540 8923 9353
5549 5709 5876 6052 6236 6430 6635 6853 7084 7332 7599 7887 82018546 8930 9360
14
456
15
16
17
18
78
20
21
22
23
27
29
I
0×23 +SO zo a
7
8
83° 84° 85°
9606 10137 10765
9614 10146 10776
9622 1015610788
9631 10166|10799
9639 10175 10811
9647 10185 10822
9655 10195 10834
9664 10205 10846|
9672 10214 10858
9680 10224 10869
9689|10234 10881 ΙΟ
9697 10244 10893 II
9706 10254 10905 12
9714 10264 10917 13
9723 10273 10929 14
9731 10283 10941 15
9740 10293 10953 16
9748 10303 10965 17
9757 10314 10978 18
9765 10324 10990 19
9774 10334 11002
9783 10344 11014 21
9791 10354 11027 22
9800 10364 11039 23
9809 1037411052 24
9817 1038511064 25
9826 10395 11077 26
9835 10405 11089 27
9844 10416 11102 28
9852 1042611115 29
20
MATHEMATICAL TABLES.
139
TABLE VI.-MERIDIONAL PARTS.

Он
333
30
31
32
33
39
83° 84° 85°
9861 10437 11127 30
9870 1044711140 31
9879 10457 11153 32
9888 10468 11166 33
9897 10479 11179 34
9906 10489 11192 35
9915 10500 11205 36
99241051c11218 37
993310521 11231 38
9942 10532 11244 39
99511054211257 40
9960 1055311270 41
9969 10564 11284 42
9978 10575 11297 43
9987 1058611310 44
9996 10597 11324 45
67° 68° 69° 70° 710 72° 73° 74° 75° | 76° | 77° 78° 79° 80° 81° 82°
5552 5712 5879 6055 6239 6433 6639 6856 7088 7336| 7603 7892| 8207 8552 8936 9368
5554 5715 5882 6058 6242 6437 6642 6860 7092 7341 7608 7897 8212 8558 8943 9376
5557 5717 5885 6061 6245 6440 6646 6864 7096 7345 7612 7902 8218 8565 8950 9383
5559 5720 5888 6064 6249 6443 6649 6868 7100 7349 7617 7907 8223 8571 8957 9391
34 5562 5723 5891 6067 6252 6447 6653 6871 7104 7353 7622 7912 8229 8577 8963 9399
35 5565 5725 5894 6070 6255 6450 6656 6875 7108 7358 7626 7917 8234 8583 8970 9407
36 5567 5728 5896 6073 6258 6453 6660| 6879 7112 7362 7631 7922 8240 8589 8977 9414
37
5570 5731 5899 6076 6261 6457 6663 6883 7116 7366 7636 7927 8245 8595 8984 9422
38 5573 5734 5902 6079 6264 6460 6667 6886 7120 7371 7640 7932 8251 8601 8991 9430
5575 5736 5905 6082 6268 6463 6670 6890 7124 7375 7645 7937 8256 8607 8998 9438|
40 5578 5739 5908 6085 6271 6467 6674 6894 7128 7379 7650 7942 8262 8614 9005 9445
41 5580 5742 5911 6088 6274 6470 6677 6898 7132 7384 7654 7948 8267 8620 9012 9453
42 5583 5745 5914 6091 6277 6473 6681 6901 7136 7388 7659 7953 8273 8626 9018 9461
43 5586 5747 5917 6094 6280 6477 6685 6905 7140 7392 7664 7958 8279 8632 9025 9469
44 5588 5750 5919 6097 6283 6480 6688 6909 7145 7397 7668 7963 8284 8638 9032 9477
45 5591 5753 5922 6100 6287 6483 6692 6913 7149 7401 7673 7968 8290 8644 9039 9485
46 5594 5756 5925 6103 6290 6487 6695 6917 7153 7406 7678 7973 8295 8651 9046 9493|10005 10608 11337 46
47 5596 5758 5928 6106 6293 6490 6699 6920 7157 7410 7683 7978 8301 8657 9053 9501 1001510619 11351 47
48 5599 5761 5931 6109 6296 6494 6702 6924 7161 7414 7687 7983 8307 8663 9060 9509 10024 10630 11365 48
49 5602 5764 5934 6112 6299 6497 6706 6928 7165 7419 7692 7989 8312 8669 9067 9517 10033 10641 11378 49
50 5604 5767 5937 6115 63036500 6710 6932 7169 7423 7697 7994 8318 8676 9074 9525 10043 10652 11392 50
51 5607 5770 5940 6118 6306 6504 6713 6936 7173 7427 7702 7999 8324 8682 9081 9533 10052 10663 11406 51
52 5610 5772 5943 6121 6309 6507 6717 6940 7177 7432 7706 8004 8329 8688 9088 9541 10061 10674 11420 52
53 5612 5775 5946 6124 6312 6511 6720 6943 7181 7436 7711 8009 8335 8695 9096 9549 10071 10685 11434 53
54 5615 5778 5948 6127 6315 6514 6724 6947 7185 7441 7716 8014 8341 8701 9103 9557 10080 10696 11448 54
55 5617 5781 5951 6130 6319 6517 6728 6951 7189 7445 7721 8020 8347 8707 9110 9565 10089 10708 11462 55
56 5620 5783 5954 6133 6322 6521 6731 6955 7194 7449 7725 8025 8352 8714 9117 9573 10099 10719 11476 56
5623 5786 5957 6136 6325 6524 6735 6959 7198 7454 7730 8030 8358 8720 9124 9581 10108 10730 11490 57
58 5625 5789 5960 6140 6328 6528 6738 6963 7202 7458 7735 8035 8364 8726 9131 9589 10118 10742 11504 58
59 5628 5792 5963 6143 6332| 6531| 6742| 6966| 7206| 7463| 7740| 8040| 8369| 8733| 9138| 9598|10127|10753 11518| 59
57
|
140
MATHEMATICAL TABLES.

TABLE VII.-LENGTH OF
DEGREE OF LONGITUDE ON EACH
PARALLEL OF LATITUDE.
Latitude.
Nautical miles. Latitude. Nautical miles. Latitude. Nautical miles.
о
I
59'99
2
59'96
3
59'92
4
59.85
5
59'77
6
59.67
w w w w w w
31
51°43
61
29.09
32
50.88
62
28.17
33
50°32
63
27.74
34
49'74
64
26.30
35
49'15
65
25°36
36
48.54
66
24.40
78
59'55
37
47'92
67
23.44
9
59'42
59.26
IO
59°09
II
58.89
12
58.69
13
58.46
∞ 2 g 7 q 2
38
47°28
68
22.48
39
46.63
69
21.50
40
45'96
70
20°52
41
45°28
71
19'53
42
44'59
72
18.54
43
43.88
73
17'54
14
58.22
44
43°16
74
16.54
15
57.95
45
42°43
75
15°53
16
57.67
46
41-68
76
14.52
17
57-38
47
40.92
77
13.50
18
57:06
48
40.15
78
12:48
19
56.73
20
56.38
21
56.01
22
55-63
23
55°23
24
54.81
25
54:38
26
53.93
27
53:46
28
52'97
29
52:48
30
51.96
a = = * M * 4 5 6
49
39°36
79
11:45
50
38.57
80
10.42
51
37.76
81
9°38
52
36.94
82
8.35
53
36.11
83
7°31
54
35°27
84
6.27
55
34.4I
85
5°23
56
33°45
86
4.18
57
32.68
87
3.14
3179
88
2.09
59
30°90
89
1'05
60
30.00
90
0'00
MATHEMATICAL TABLES.
141

TABLE VIII.
DIP OF HORIZON, CORRECTED
FOR REFRACTION.
TABLE IX.
DIP OF THE HORIZON AT VARIOUS
DISTANCES FROM IT.
Distance in
miles.
HEIGHT OF Eye.
feet. I feet. I feet. I feet. | feet. | feet.
5
10 15
20 25 30
II
22
34
45
56 68
6++mm
OOHHH
II
17 22 28 34
4
4
3
3
12
15 19
23
9 12 15
17
7
6
86
9
12
14
IO
12
2186 54
ΙΟ
66
5
5
3
4
4
3
4
4
3 4
4
876 in in in
8
7
6
6
5
6
5
5
5
5
5
in in 4 4
33
3
3
2 2 2 2 2 2 2
Ca
2233 +no
feet.
feet.
"1
IO
1234 SO Z∞ ao
• 59
41
6 18
I 24
42
623
1 42
43
627
I 58
4.4
632
5
2 12
45
6 37
6
225
47
6 45'
7
2 36
48
6
50
8
2 47
6 58
9
2 57
53
3 7
56
7 10
7 22
2}}
II
12
13
HH
123456 76 O
инин
X 2
3 16
59
7 34
4
3 25
62
3.49
3 56
14
15
16
17
18
3 33
3 41
4 4 77
4 II
19 4 17
20
4 24
4 31
80
83
86
8
58
9 17
65
7 45
7 56
5
6
68
8
7
71
8 18
74
8 28
78∞∞
8 38
8
48
TABLE X.-REDUCTION OF
MOON'S EQUATORIAL PARALLAX.
HORIZONTAL PARALLAX.
Lat.
9
8
54
56 58 60
6 | 62
"
"1
//
21
89
22
4 37
90
9 22
23
24
25
26
27
28
3456 78
4 43
92
9 26
12
4 49
4 55
a a
95
98
50
9 36
16
48 26
O'I
ΟΙ
ΟΙ
ΟΙ
ΟΙ
O'2
0'2
0*2
O'2
0'2
0'4
0'5 0'5 0.5
0'5
0.8
0.8
0°9 0'9
0'9
9 45
20
1'3
5 I 100
9 52
24
1.8
300
1.3 1'4 1'4 1'5
1'9
1.9 2.0
2.0
5 7 ΙΟΙ
9 54
5 13 104 10 2
29
5 18
107
IO II
30
5 24
ΙΙΟ
10 19
wwww wwwww
31
5 29
32
5 34
113 10 28
116
44
10 36
33
5 39
119
10 44
52
34
5 44
122
10 52
35
36
37
38
56 7∞
5 49
6
39
40
125 II о
5 54 128 II
5 59 131 II 16
4 134 II 24
6 9 137 II 31
6 14
140 II 39
8
5666 778
68
72
OON OF OUT* A www
2'4
3°0
3'I
2.5 2.6 2.6 2.7
3.3 3.4 3'5
3°7
4'5
96
on of
3'9
4.0 4.I
4'3
4.6
4.8 5.0
5'1
683
5°2
6.0 6.2
6.7
ino
420
5'4
7.0
7'4 7.7
60 8.1 8.4 8.7
632 O
7∞∞
5.6
6.3
7°2
457
5.8
6.0
6.6
6.8
7'4 7.6
8.0
8.2
8.5
9.0 9'3
64
8.7
9'3
76
10'2
73∞ N
9'1 9'4
9.8 IO'I 104 10.8
10.6 10.9 11.3
10'0
9'7
9.6 10.0 10'3 10.6
II.2
11'7
80 105 10˚9 II.2 11.6 12'0
142
MATHEMATICAL TABLES.

Altitude.
TABLE XI.
AUGMENTATION OF THE MOON'S
SEMIDIAMETER.
TABLE XII.
FOR CONVERTING LONGITUDE
INTO TIME.
HORIZONTAL SEMIDIAMETER.
"/
14 30 15 0 15 30 16 0 16 30 17 0
30/15
Long.
Time.
H. M.
M. S.
Long.
H. M.
M. S.
Time.
Long.
Time.
Secs.
NOT
23
1 2 3
NOHH 22
"/
I
O
I
I
3
3
4
4
4
4
5
5
5
6
mt in iO
3
1 2 3 +SO N∞
48
30
2 O
40
2 40
I 067
2133
O 12
50
3 20
3 $200
4
o 16
60
4 о
5
O 20
70
4 40
6
O 24
80
5 20
4
7 10 28
80 32
90 36
90
6
O
100
6 40
86 2er f
4/267
5 333
6.400
7467
8533
200j13 20
9.600
5
ΙΟ
10 0 40
300 20
010-667
5
20 I 20
6
Ι
I
I
NOH122
I
I
I
I
"
NOHH 2 2
O
O
122
8
0246∞
33445
78 9
6 78 a
8
67∞ ∞ a
66 78 9
56 77∞
166 ^~
I2
14
16 4
18
21
24
27
233
4
5
30 7
3
3
4
4
5
8
233 ++
02 46 ∞
IO
8
9
9
33
7
9
10
ΙΟ
36
39
4.2
45
48
ΙΟ
∞aaoo
8
9
9 ΙΟ
ΙΟ
II
TABLE XIII.
FOR CONVERTING TIME INTO
9
9
ΙΟ
II
I I
12
IO
IO
I I
12
13
LONGITUDE.
ΙΟ
I I
12
13
13
II
12
12
13
14
Time. Long.
Time. Long.
Min.
Time.
Long.
51
I I
ΙΙ
12
13
14
54
I I
12
13 13
14
57
I I
12
13
14
++ in
15
15
16
15
60 12
13
63 12 13
14
14 15
14 15 16
16 17
66 12
13
14
15
16 17
69 13
72
75
250
13 14
15
14 15 16
16 17
17 18
18
78 13
13 14 15 16
14 15 16 17
17
18
H.
556 6
34
1 2 3 456 7∞
78∞ ∞ ∞
H.
Sec.
Sec.
=
18 8 120 8
9 135
1 2 3 +SO 7∞ a
∞ ∞ ∞
81
14 14
87
84 14
14
90
14
HHHH
15
16 18
15
16
56
17
19
18 19
ΙΙ
I 15
30
45
I
бо 4
75 5
90 6
105
O 1501
15
0 30 02 30
0 45 03 45
I o 0.4 6:0
1505 7.5
I 30 0.6 9.0
I 45|| 0:710'5
2 o 0.8 12.0
2 15 0913'5
ΙΟ 150 ΙΟ 2 30
11 165 20
5
15
16
17
15
16
17
77
18
19
12 180 30
7 30
18
19
16 240
40 10 о
20 300
50 12 30
MATHEMATICAL TABLES.
143

TABLE XIV.
PARALLAX IN ALTITUDE OF THE SUN AND PLANETS.
HORIZONTAL PARALLAX IN SECONDS.
App.
Alt. I 3
5
7 9 II 13 15
17|19|21 23
25|27|29
29 | 31
3
"
I
1 3
//
5
= 5
//
"1
//
//
#1
7
9
II 13 15 17 19 21
23
252729
29 31
6
I
3
5 7 9
11 13 15
17 19 21
23
2527
25 27 29 31
9
I 3
5 7
9
II 13 15
17 19 21
23
2527 29 31
29
12 1 3 5 7 9 11
II
13 15
17
19 21
|
22
24 26 28 30
15 I
3
มา
5
7
II
9
13 14
26 28
22 24 26 28 30
18 1 3 5 7 9 10 12 14 16 18 20 22 24 26 28 29
16
18 20
21
I
3
5 7
8
ΙΟ
12
16 18 20 21
14
24. I
3
5
6
8
ΙΟ
I2
14
16 17 19
212325
23 25 27
27 29
212325
27
I
3
46
8
ΙΟ
12
13 15 17 19
20
301 3 4 6 8 10 11 13 15
II
16 18
33
I
2 4
8
13
9 II
14 16
18
19
2628
22 24 26 28
20 22 23 25 27
21 23 24
19 21 23
24 26
36
I 2
4
6
7
9 II
I 2
14 15 17
19 20
19
2223
2325
39
I 2 4
5
7
9 10
12
13 15 16
18 19 21
23 24
42
I
2
4
5
7
8 10
II
13 14 16
17
17 19 20
22 23
45
I
2
4
5
6
8
9 II
I2 13 15
16 18 19
21
22
48
I 2
3
5
6
7
9 10
I I
13 14
15
51
54
57
60
63
66
I
2
3
4
6
7
8
9
I I
12
13
+58
I
2
3
4
6
8
9
IO II
12
I
2
3
4 5
6
7
8
9
ΙΟ
12
II
14 15
15 17 18 19 21
14 16 17
14 15 16 17 18
17
16 17
18 19
18 20
I
2
3
4
5
5
7
8
9|10
12
II
13 14 15
15 16
I
2.
3
4
5
6
7
8
9 10
ΙΟ
I I
12
13 14
о
I
2
3 4 4
5
6
7
8
9
9 10
II
12 13
69
I
2
3
3
4
5
5
6
7
8 8
9
10
IO
I I
72
I
2 2
3
3
4
5
5
6
6
7
8
8
9 10
75
I
I
2 2
3
3
4
4
5
5
6
6
7
8 8
78
I
I
I
2
2
3
3
4
4
4
In
5
6
6
6
81
84
87
'90
I I
I
2
2
2
3 3
4
3
4 4
5
5
O
I I
I
I
I 2
2
2
2 2
3
3 3
3
I
I
I
I I
I
I
I
I 2 2
O
O
о
O
о
O
O
144
MATHEMATICAL TABLES.

TABLE XV.-REFRACTION OF THE SUN AND STARS.
App.
Alt.
Refrac-
App. | Refrac- App. Refrac- App. Refrac- App.
tion.
Alt. tion.
Alt. tion.
Alt. tion.
Alt.
Refrac-
tion.
I
10 23
0 24 21′2
9.6
IO
0 5 19.819
02 47.7 28
OI 49°237
OI 17.2
10 5 15°1
102 46°3
10 I 48.4
10 I 16.7
20 22 3.4
205 104
20 2 44.8
20 I 47.6
20 I 16.2
30 21
1.9
305
5'7
302 43°3
30 I 46.9
30 I 15.8
40 20
4.8
40 5 ΙΟ
402 41.8
40 I 46.2
40 I 15'3
50 19 11'5
2 o 18 22.2
10 17 36.3
20 16 53°2
30 16 13:4
II 04 517 || 20
IC 4 47'7
20 4 43'7
50 4 56.3
502 403
304 39 7
10 2 374
20 2 36.0
302 34.6
30 I 42'7
40 15 36.0
404 35.7
402 332
50 15 09
504 31-8
(~)
3
0 14 28.112
04 279 21
10 13 57.3
20 13 28.5
30 13 13
40 12 35.6
10 4 24.5
204 21.1
30 4 17.7
40 4 14.3
50 12 11'3
4
1.5
50 10 10.9
5
6
011 48.313
IO II 26.6
20 II 6.1
30 10 46.7
40 10 28.3
O 9 543 14
938.4
IO
O O
9 23.4
50 4 10.5
04 7522
10 4 4.5
20 4
30 3 58.6
40 3 55'7
503 52.7
0 3 49.8 ||23
10 3 47°2
203 44.6
15 0 3 34°3 | 24
02 16.5 32
10 2 15'4
02 10:233
IO 2
9'2
OI 33141
10 I 32.5 10 I
50 I 30°2
OI
0 1 29.642
10 I 29'0
20 I
5'7
30 I
40 I 5'3
50 I 4'9
OI 4.6
ΟΙ
ΙΟ Ι 4.2
20 I 3.8
30 I
3'5
5 180
50 2 319
02 30.630
10 2 29.3
20 2 28.1
302 26.9
40 2 25.6
502 244
02 23.231
IO] 2 22′I
202 209
0238.829
50 I 45'5
0 I 44.838
01
10 I 44'1
20 1 43'4
I
40 I 42.0
50 I 413
01 40.639
IO I 39'9
20 I 39°3
I
50 1 14.8
0 I 144
IO I 14'0
20 1 13.5
301 13'1
40 I 12'7
50 I 12.2
OI 11.8
10 I 11.3
20 I 10.9
30 I 38.6
40 I 38.0
50 I 37°3
30 I 10'5
40 I 10'I
50 I
9'7
01 36.740
10 I 36.1
20 I 35°5
O I
9'3
10 I
8.9
20 1
I
8.5
30 2 19.8
30 I 34'9
30 I
8.1
402 18.7
40 I 34'3
40 I
7'7
50 2 17.6
50 I 337
50 I
7.3
I
01 6.9
6.5
20
202 14:4
30 9 40
303 42.0
30 2 13.3
20 I 31.9
30 I 31.3
40
8 553
40 3 39:4
40 2 12.3
40 I 30'7
50
ΙΟ
8 42.3
8 29.9
8 18.2
50 3 36.8
50 2 11.2
20 8 6.6
10 3 32.1
20 3 29.8
30
7 55.6
30 3 27.5
20 2 8.2
302 7.2
20 I 28.4
4.0 7 44'9
403 25'2
50 7 347
503 22.9
402
502
6.2
5°2
2 2
7
ΙΟ
O
ง
7 247 16 0 3 20725
O 2
4.3 34
7 15:3
10 3 18.5
20
7 6.3
20 3 16.5
10 2 3.4
20 2 2.5
30 I 27.8
40 I 27°3
501 26.7
01 26.243
10 1 25.6
40 I 3.I
50 I
O I
IO I
2.8
2:4
2'0
30
6 57'7
30 3 14.5
40
6 49.6
40 3 12.5
302
402
1.6
56
20 I 25'1
20 I
1'7
30 I 24.6
30 I
1°3
0'7
50
8
1 2 3
ΙΟ
20
30
O O O
OO
6
41.9
50 3 10.5
50 I 59.8
о
6 34417
6 27 I
6. 20.0
03 8.5 26
IO 3 6.6
20 3
4.8
6
13'1
303
3.0
01 58.935
10 I 58.0
20 I 57°2
30 I 56.4
40 I 24.1
50 I 23.6
OI 231 44
10 I 22.6
20 I 22'I
40 I
ΙΟ
50 I
0.6
ΟΙ 0'3
ΙΟ Ι O'O
30 1 21.6
40 6 64
40 3
1.2
40 I 55.6
40 I 21'I
50
9
O
10
30 5 35'9
50 5 25.1
5 59'9
5 53.5 18
5 47'4
20 5 41'5
40 5 30'4
502 59°4 50 I 547
02 57-627 01 53-936
102 55'9
202 543
302 52.6
40 2 51°0
502 49°3
50 I 20.6
10 I 53.2
20 I 52.4
OI 20145
10 I 19.6
200 59.6
300 59°2
400 58.9
500 58.5
00 58.2
10 0 57.8
20 I 19°1
200 57'5
301 51.6
40 I 50.8
501 1 500ll
50 1 17.6
30 I 18.6
40 I 18.1
300 57*2
400 56.9
500 56.5
6.1
MATHEMATICAL TABLES.
145

TABLE XV.-REFRACTION OF THE SUN AND STARS.
App.
Alt.
Refrac-
tion.
App. | Refrac-
Alt. tion.
App. Refrac- App. Refrac- App.
Alt. tion. Alt.
Refrac-
tion.
Alt.
tion.
"/
100 55.8
100 40°5
200 55°5
200 40°3
46 0 56.255 00 40864 00 284 73
10 0 28.2
200 28.0
0 17.8 82
10 0 17.6 IO O
200 17:4
20
888
8.2
8.1
7'9
300 55°2
300 40°0
300 27.8
300 17.2
300
7.8
96
400 549
400 39.8
400 27.6
500 54-6
500 39°5
47
054-356
100 54'0
200 53.6
39365
500 27°4
00 272 74
400 17.0
500 16.8
00 16.7 83
400 7.6
50 0 7.4
00
7°2
10 0 39°0
100 26.9
10 0 16.5
200 38.8
200 26.7
200 16.3
ΙΟ Ο 7:0
200 6·9
30 53°3
300 38.5
300 26.5
300 16.1
400 53°0
400 38.
48
500 52.7
100 52.1
500 38.0
00 524157
0 37.8 66
10 0 37.6
200 51.8
200 37°3
200 25.5
400 26.3
500 26.1
00 25.9 75
100 25.7
400 16.0
500 15.8
00 15.6|84
10 O 154
200 15.2
300 6.7
40 o
6.5
500 6.3
IO O
6.1
5'9
200 5.8
300 51.5
300 37°1
300 25°3
300 15.0
300 5.6
40 51.2
50
O 50°9
400 36·9
50
400 25.1
400 14.8
40 0
5.5
36.6
500 24'9
500 14.7
50
5'3
49
00 50.658
100 50'4
0036.4
36467
ΙΟ 36.2
IO O
67
00 247 76
0 0 14 585 0
5'1
100 24.5
100 14:3
ΙΟ
4'9
200 50.1
20
36.0
200 24°3
200 14°2
300 49.8
300 35'7
300 24'1
40
o 49°5
400 35'5
400 23.9
50
O 49°2
500 35°2
500 23.7
50 O 48.959
100 48.6
200 48.3
00 35068
10 0 34.8
ΙΟ
20 O
34-6
OO 23'577
IO O 23'4
200 23.2
300 14.0
400 13.8
500 13.7
0 13.5 86
10 0 13°4
200 13.2
20 O
300 4.6
400 4.5
500 4.3
4'I
IO O 3'9
4.8
20 O
3'7
30 O 48.1
300 34°3
300 23.0
300 13.0
30
3.6
40
0 47.8
400 34'1
400 22.8
400 12.8
40
3'4
50
° 47'5
500 33.8 500 22.6
500 12.6
50
SI
oO 47°260
100 46.9
10 O 33'4
IO
200 46.6
200 33 I
300 46.3
300 32.9
40° 46'1
400 32.7
50 • 45.8
52
IO O 45°2
200 45°C
30 0 44.6
400 444
500 44'1
500 31.2
53
O °
0 43.962
100 43.6
200 43°3
300 43°1
300 304
400 42.8
400 30°2
500 42.6
500 30.0
54
0042.363
100 42.0
200 41.8
oO 29°772
10 O 29'4
200 29.2
300 41.5
400 41.3
500 410
300 29.0
400 28.8
500 28.6
00 45.661
00 33.669 0 0 224 78
500 32.5
00 32.3 70
100 32.0
200 31.8
300 31.6
400 31'4
00 31071
10 0 30.8
200 30.6
IO O 22*2
20 O 22'0
300 21.8
400 21.6
500 21'4
OO 212 79
IO O 21°O|
200 20.8
300 20.6
400 204
500 20°2
00 20.080
10 0 19.8
200 19.6
300 19:4
400 19:2
500 19.0
00 18.9 81
10 o 18.8
200 18.6
20 O 12*0
300 11'9 300
400 II 7
400
50 0 11.5 500
OO 11.3 88
IO O II'2
20 O II'O
300 10.8
4º O 10.7
ΙΟ Ο ΙΟΙ
20 0 10°O]
300 9.8
400 9.6 400 0'3
500 94
300 18.4 300 8.7
oo 12.4 87
IO O 12.2|
IO O
200
IO O
M32 2 2 2 2 2 -
3'3
3'I
2'9
2.8
2.6
2.4
2.2
2.0
1'9
20 O
I'7
300
I'5
40 0
1'3
50 0 10.5 500
I'I
0 0 10.389
00
ΙΟ
ΙΟ Ο
0'9
200
0.7
300 0'5
500 ΟΙ
O O
9.2
10 0
ΙΟ Ο
9.0
200
8.9
40 0 18.2
500 18.0
40
5010
00 00 00
8.6
8.4
146
MATHEMATICAL TABLES.

80
6503622 7 7
348 34 21 7 6
046 32 20 7 6
57 44 31 18 6
55 42 30 17 6
o Apparent
altitude.
TABLE XVI.-CORRECTION FOR TABLE OF REFRACTION.
о
20
24
28
+ +
+
=
I OI 591 43 I 251
101 531 381 211
201 481 33|1 17|1
30 431 291 14|1
401 391 251 110
501 351 211
HEIGHT OF THE THERMOMETER.
32136 40 44 48 52|56|60|64
+++++
44|48|52|56|60|64
"
•2+1=
に
​に
​68
=
1800
72
800
761
3 I 17 I 30 I 43
13 1 26| 1 38
91 211 33
6 I 18 1 29
953 38 238 7 2136501
20 34 48 1 OI
19 32 450 57 I
18 31 430 54 I
18 30 410 52 1
4 I 15 I 25
6
6
17 28 390 50 1
I I II I 21
2
01 311 181
50 53 39 29 17 6
5
16 27 370 480 58 I
81 18
20 I 231 III
oo 48 37 26 16 5
5 1525350 440 54 I
3 I II
401 17 1
60 550 44 34 24 14 5
5
14 23 320 410 500
58 1
I 6
3
ΟΙ ΙΙΙ
10 510 41 32 22 13 4
4
13 21 300 380 46 54 I I
201
60 570 470 38 29 21 13 4
4
12 20 280 350 430 500 57
40I
20 530 440 36 28 20 12 4
4
11 18 260 33 0 400 470 53
4
4
10 17 240 310 370 440 50
3
10 16 220 300 350 410 46
3 3 9 15 21 0 280 330 38
olo
00 580 490 410 33 26 18 11 4
200 540 460 390 31 24 17 10 3
400 510 430 370 29 23 16 10
5 00 480 410 350 28 22 16 9
300 450 380 320 26 20 149
00 410 350 300 24 19 13
300 340 290 240 2015 II
8 00 320 270 230 19 15 10
14
15
16
56
3
43
3 3 9 14200 260 310 360 40
33813 190 24 0 290 340 38
2 7 12 170 220 260 310 35
2711150 200 240 290 33
26 10 140 19 0 230 27 0 31
269 130 17 0 21 0 250 29
259130 16 0 20 0 240 27
258 110 14 0 18 0 210 24
14 7 100 13 0 16 0 19 0 22
147 90 12 0 15 0 18 0 20
120 150
90 110 13 0 16 0 18
a a∞ Z NO66
6
8
30
380 330 280 22 17 12
7
2
7
00 360 310 260 21|16| 12
7
2
62
6
2
9
oo 280 240 200 16139
2
ΙΟ
I I
13
o 260 220 180 15 12 8
00 230 200 170 14 11 8 5
[2 00 210 180 150 13 10 7
74 I
974
864
863
5
2
2
I 46
I I 3
6
I I 35
7
I
I 35 7
8
90
8
753 I
53 I I
4 3 I
I 35
I34
24
I
24
9 7
42 I I 24
Ο ΙΙΟ ΙΟ Ο
80
7
2 2 2 3M44 in
O
235
23
26
28
Ο
60
4
40
70
17
18
19
20
22
24
30
35
40
45
50
55
60
65
70
70
80
00 200 170 140 12 9 7
00 180 160 130 11 8 6
00 170 150 120 10 8 6
00 160 140 120 975 3 I
00 150 130 110
140 120 100
0 130 110
00 130 II O
00
O O
O
O O O O O O O O
O O O O O O O O O O O O O O O O O O O O O O
55+3M N N 2 -
665 &
บา บา
O 100 120 150 17
O II O 140 16
00
O
O
30
20
ini in 44mMM2 2 2
2 2 2 H
24
I
3
I O I
100
90
4/2
90 70 6 32
80 70 6
90 70 60
80 70
70 60
4
30 30
30 30 20
30 20 20
20 210 20
20 IO ΙΟ
IO 10
432
43
I I
I I
I I 2 3
2 I о
432
32 I I о I
43
33
32 I O о I2
322
22 I I
2 I I I
HOOOS1.6z
HEIGHT
OF
O
O
O
I
O O
I
O
2 2 I I
о O I
O
I
20
I I
I
O O I
I
O
O
I I I
O
O
ΙΟ
I I
I
о
O
о
28.26
OM
28.560 H
28.850
29°45
9
90 110 130 15
80 10 0 12 0 14
80 90 110 13
70
9 0 10 0 12
8 0 10 0 II
9 O II
8'0 10
7
6
80
6
7
6 8 o
6
7
6
985
5 6
7
4
6
3 3
20 3
4
2 21
2
2
2
ΙΟ 2
O O O O O O O O O O O O O O O O O
3
3
3
20
2
2
I O I O
ΙΟ ΙΟ I O ΙΟ I
I O ΙΟ
I
+29.750
+30°050
+30·3500 =
+ 30.64 0
O
+ 30°93
THE
BAROME-
TER.
MATHEMATICAL TABLES.
147

TABLE XVII.—CORRECTION OF THE MOON'S ALTITUDE.
MOON'S Horizontal Parallax.
P. P. (Moon's
for App.
Alt. Alt.
54
55'
56'
57' 58'
60'
59'
61'
P. P.
for
Par.
I
2
//
2
+
4
7H
3 II
4 15
5 18 3
6 22
7 26
8 29
9 33
I
7 2
2
2
4
3 5
4 7
4
=
=
//
=
//
=
"1
0 35 36 36 36 37 36 38 36 39 36 40 36 41 36 42 36
10 36 22 37 22 38 22 39 22 40 22 41 22 42 22 43 22|,
20 37 438 439 440 441 442 443 444 41 I'O
30 37 44 38 44 39 44 40 44 41 44 42 44 43 44 44 44 2 2.0
4038
40 38 2039 2040 2041 2042 2043 2044 2045 20 3 3.0
50 38 55 39 55 40 55 41 55 42 55 43 55 44 55 45 554 40
039 28 40 27 41 27 42 27 43 27 44 27 45 27 46 27 5 50
10 39 58 40 58 41 58 42 58 43 58 44 58 45 58 46 586 6.0
20 40 26 41 26 42 26 43 25 44 25 45 25 46 25 47 25 7 7:0
30 40 53 41 53 42 53 43 52 44 52 45 52 46 52 47 528 8.0
40 41 1742 1743 1744 1745 1746 1747 1748 179 90
50 41 42 42 42 43 41 44 41 45 41 46 41 47 41 48 41
0 42 443 444 445 446 447 448 349 3
10 42 25 43 24 44 24 45 24 46 24 47 24 48 23 49 23,
20 42 45 43 44 44 44 45 44 46 44 47 44 48 44 49 44 1 10
30 43 344 345 346 247 2 48 249 250 22 2.0
40 43 21 44 21 45 21 46 21 47 21 48 2049 2050 203 3.0
50 43 38 44 37 45 37 46 37 47 36 48 36 49 36 50 364 4.0
5 95 43 53 44 53 45 53 46 53 47 53 48 53 49 52 50 52 5 5.0
10 44 9 45 9 46 8 47 8 48 8 49 8 50
851 76 6.0
20 44 23 45 23 46 23 47 22 48 22 49 2150 21 51 217 70
30 44 36 45 36 46 35 47 35 48 35 49 35 50 34 51 348 8.0
40 44 49 45 49 46 49 47 48 48 48 49 48 50 48 51 479 9*0
50 45 1 46 I 47 I 48 049 49 59 50 59 51 59
6 II
7 12
8 14
9 16
=
་
LO
6
50 11 51 10
52 IC
50 22 51 21
52 21/
50 31
51 31
52 311 10
50 41
51 41
52 412 20
50 51
51 50
52 503 30
0 45 12 46 12 47 11 48 11 49 11
10 45 23 46 23 47 23 48 22 49 22
20 45 33 46 33 47 33 48 32 49 32
30 45 43 46 43 47 42 48 42 49 42
40 45 53 46 53 47 52 48 52 49 52
50 46 247 248 I 49 I 50 051 51 59 52 594 40
0 46 11 47 10 48 10 49 10 50 951 952 8
57
53 8 5 5.0
10 46 20 47 19 48 19 49 18 50 18 51 17 52 17 53 166 6.0
|
20 46 28 47 27 48 26 49 26 50 26 51 25 52 25 53 247 70
30 46 34 47 34 48 33 49 33 50 32 51 32 52 31 53 318 8.0
353
40 46 41 47 41 48 40 49 39 50 39 51 38 52 38 53 379 90
50 46 48 47 47 48 47 49 46 50 46 51 45 52 44 53 44
I I
2 2
3 3
4 4
5
6 6
7 7
8 8
9 9
I I
I
2 2
1 2 3 4 5 78 9
8
46 54 47 54 48 53 49 53 50 52 51 52 52 51 53 51
IO 47
47
20 47 6 48
59 48 59 49 58 50 58 51 57 52 56 53 56
549 5 50 4 51
"/
352 353 254 21 IO
853
9 52
754 72 2°0
14 52 14 53 13 54 123 30
30 47 12 48 11 49 10 50 9 51
40 47 17 48 16 49 16 50 15 51
50 47 22 48 21 49 20 50 1951 1952 18 53 17
1853 1754 174 40
047
47 26 48 25 49 25 50 24 51 23 52 22 53 22 54 215 50
10 47 32 48 31 49 30 50 29 51 29 52 28 53 27 54 266 6.0
20 47 35 48 34 49 34 50 33 51 32 52 31 53 31
47.35
353 354 307 7'0
36 52 35 53 35 54 348 8.0
51 41 52 40 53 39 54
54 389 90
51 44 52 43 53 42 54 41
2
5 39
6
3
7
4
4
30 47 40 48 39 49 38 50 37 51 36 52 35 53 35
3949
9 5
40 47 44 48 43 49 42
50 41
50 47 48 48 46 49 46 50 45
.
148
MATHEMATICAL TABLES.

TABLE XVII-CORRECTION OF THE MOON'S ALTITUDE.
MOON'S HORIZONTAL PARALLAX.
P. P. Moon's
for App.
Alt. Alt.
54'
55'
56′ | 57′
58'
59'
60'
61'
о
=
//
P. P.
for
Par.
+
123456 7∞ a
I
о
20 47 57 48 57
30 48 I 49
4048
40 48
449 3 50
251
I
50
5 48
6 49 5 50
4 51
//10
47 51 48 50 49 49 50 48 51
10 47 54 48 53 49 52 50 52 51
49 55 50 55 51
49 59 50 58.51
47 52 46 53 45 54 44
50 52 49 53 49 54 47
54 52 52 53 52 54 511 10
57 52 56 53 55 54 542 2.0
052 59 53 58 54 573 2.9
054 594 3'9
152
352
253
I 54
ΙΙΙ
48
9 49 7 50
651
552
4 53 3 54
2 55
5 49
I
10 48 11 49 10 50
8 51
7 52
6 53 5 54
653
4 55
3
6
5'9.
I
20 48 13 49 12
50
11 51
9 52
853 7 54
655
55
57 6.9
8
2 2
30 48 15 49 14
50
13 51 12 52
10 53 9 54
855
7 8 7.9
14 51 13 52
II
12 53 11 54 10 55
898.8
50
17 51 15 52
I
3
о
4 с
2 m ti6 DOO
8
9
12
113
40 48 17 49 16 50
50 48 19 49 18
1949
048 21 49 20
10 48 23 49 22
20 48 24 49 23
30 48 26 49 25
40 48 27 49 26
50 48 28 49 27
048 29 49 27
10 48 31 49 29
20 48 31 49 30
30 48 33 49 30
14 53 13 54 11 55 10
54
50 1951 17 52 16 53 15 54 13 55 12
50 20 51 19 52 18 53 16 54 15 55 14
50 22 51 20 52 19 53 17
50 23 51 22 52 21 53 19
50 24 51 23 52 21 53 20
50 25 51 24 52 22 53 21
50 26 51 24 52 23 53 21
50 28 51 26 52 25 53 23
50 28 51 27 52 25 53 24
=
54 16 55 151 10
54 17 55 16 2 20
1755 16|2
1855 17 3 29
54 19 55 18 4 3'9
54 20 55 195 49
54 21 55 19 5'9
54 22 55 207 6.9
6
50 29 51 27 52 26 53 24 54 22 55 208 79
I
7
I
I
I
40 48 32 49 31
50 48 33 49 31
50
50
14
1
23456
789
་
I
2345W ZOO a
о
//
O
о
15
16
117
29 51 28 52 26 53 24
30 51 28 52 26 53 24
048 34 49 32 50 30 51 29 52 27 53 25
10 48 34 49 33 50 31 51 29 52 27 53 26
20 48 34 49 32 50 31 51 29 52 27 53 25
30 48 35 49 33 50 31 51 29 52 27 53 25
40 48 35 49 34 50 32 51 29 52 28 53 26
50 48 35 49 33 50 31 51 29 52 27 53 25
048 36 49 34 50 31 51 30 52 27 53 25
10 48 35 49 33 50 31 51 29 52 27 53 25
20 48 35 49 33 50 31 51 29 52 26 53 24
30 48 35 49 33 50 31 51 28 52 26 53 24
40 48 34 49 33 50 30 51 28 52 26 53 24
50 48 34 49 32 50 30 51 27 52 25 53 23
54 22 55 219 8.8
54 23 55 21
22/
54 23 55 21
54 24 55 22
54 24 55 221 10
54 24 55 22 2 19
54 23 55 223 29
54 23 55 21 4 39
54 23 55 215 48
54 23 55 216 5.8
54 22 55 20 7 6.8
54 22 55 208 77
54 21 55 199 87
54 20 55 18
=
048 34 49 31 50 29 51 26 52 24 53 22 54 20 55 17
10 48 33 49 31 50 28 51 26 52 24 53 21 54 19 55 16/
20 48 32 49 30 50 27 51 25 52 23 53 20 54 1855 151 10
30 48 32 49 29 50 26 51 24 52 22 53 1954 17 55 14 2 19
40 48 31 49 28 50 26 51 24 52 21 53 1854 1655 13 3 29
50 48 30 49 27 50 25 51 23 52 20 53 17 54 15 55 124 3'9
048 29 49 27 50 24 51 22 52 19 53 16 54 14 55 11 5 48
10 48 28 49 26 50 24 51 21 52 18 53 15 54 13 55 106 5.8
50 23 51 20 52 17 53 14 54 12 55
50 22 51 1952 1653 13 54 10 55
50 21 51 18 52 15 53 12 54 9 55
20 48 28 49 25
6
I
7
I
8
I
9
I
40 48 26 49 24
30 48 27 49 24
50 48 26 49 23
97 6-8
88 77
6
8.6
50 20 51 17 52 14 53 11 54 8 55 5
MATHEMATICAL TABLES.
149

I
I
5
6
I
7
1234 So to a
2 2 2
8
2 2 2 2
8
1 2 3 4 5 6 7∞ a
TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE.
P. P. Moon's
MOON'S HORIZONTAL Parallax.
P. P.
Alt.
Alt.
for App. 54' 55′
for
56'
57'
58′ 59′ 60' 61'
Par.
=
//
་
"1
"/18
I
O
23456 7∞ a
048 24 49 21
10 48 23 49 20
20 48 22 49 19
3048 2049 17 50
40 48 19 49 16 50 12 51
50 1851 15 52 12 53
954
655 3
50
17 51 14 52 11 53
854
5 55
2
"/
50
16 51 13 52 10 53
7 54
355
14 51
10 52
753
4 54
01 0.9
154 582 19
952
6 53
353 59 54 563 2.8
I
50 48 1849 15 50
11 51
8 52
453
3·8
119
048 16 49 12 50
9 51
51
5 52
I
10 48 15 49 11 50
I
20 48 12 49 9 50
8
I
9
I
30 48 11 498 50
4048
40 48 9 49 5 50
50 48 8 49
4 50
20
I
I
I21
048 549
IO 48
ΙΟ
2048
349
o
851
5 51
4 52
I 53 58 54 554 3.8
2 52 59 53 56 54 535 47
1 52 58 53 54 54 516 57
I
251 59 52 55 53 52 54 497 6.7
4 51 I 51 57 52 54 53 51 54 478 7.6
2 50 58 51 55 52 52 53 48 54 449 8.5
I 50 57 51 54 52 50 53 46 54 43
"/
2 49 58 50 55 51 51 52 47 53 44 54 40
49 56 50 53 51 48 52 45 53 42 54 38
2 48 58 49 55 50 51 51 47 52 43 53 40 54 361 09
30 48 048 56 49 52 50 48 51 45 52 41 53 37 54 332 1°9
40 47 58 48 54 49 50 50 46 51 42 52 38 53 34 54 303 2.8
50 47 56 48 52 49 48 50 44 51 41 52 36 53 32 54 284 37
047 54 48 50 49 46.50 42 51 38 52 34 53 30 54 265 47
6 5.6
10 47 53 48 48 49 44 50 40 51 35 52 32 53 27 54 23
20 47 50 48 46 49 42 50 37 51 34 52 30 53 25 54 217 6.6
30 47 47 48 43 49 39 50 35 51 31 52 27 53 22 54 198 7:5
40 47 45 48 41 49 36 50 32 51 28 52 24 53 20 54 159 84
50 47 44 48 39 49 35 50 31 51 26 52 22 53 1854 13
22
I
123
047 41 48 37 49 32 50 28 51 24 52
10 47 39 48 34 49 30 50 25 51 21 52
20 47 36 48 31 49 27 50 22 51 18 52
30 47 33 48 29 49 24 50 20 51 15 52
40 47 31 48 26 49 21 50 16 51
50 47 28 48 23 49 19 50 14 51
47 26 48 21 49 16 50 11 51
10 47 24 48 19 49 14 50 9 51 4 5
20 47 21 48 16 49 11 50 6 51 2 51
30 47 18 48 13 49 9 50 3 50 58 51
40 47 16 48 10 49
10 49 5 50 I 50 55 51
50 47 13 48 849 2 49 57 50 52 51
19 53
16 53
15 54 11
12 54
י7
13 53
954
4I 0'9
11 53
654
12 52
653
22 1.8
253 573 2.8
952
5 53 53 554 3.8
652
2 52 57 53 52 5 47
59 52 54 53 50 6 5.6
56 52 51 53 477 65
54 52 48 53 43 8 7'4
50 52 45 53 409
47 52 42 53 37
in Noo
8:3
654 m
24
549
I
3.
5
6
7
8
33
23 + no too a
I
I
4 I
2
2
225
047 10 48
049 54 50 49 51 44 52 39 53 34
10 47 7 48 2 56 49 51 50 46 51 41 52 35 53 30
20 47 4 47 59 48 54 49 48 50 43 51 38 52 32 53 271 0.9
3047 I 47 56 48 5149
49 46 50 41 51 35 52 29 53 23 2 1.8
40 46 58 47 53 48 47 49 42 50 37 51 31 52 25 53 203 27
50 46 56 47 50 48 44 49 39 50 33 51 27 52 22 53 174 3.6
O 46 52 47 47 48 41 49 36 50 30 51 24 52 19 53 135 45
10 46 49 47 44 48 38 49 32 50 26 51 21 52 15 53 106 54
20 46 46 47 40 48 34 49 28 50 22 51 17 52 11 53 57 64
28 7.2
30 46 42 47 36 48 30 49 25 50 1951 13 52 753
40 46 39 47 33 48 27 49 22 50 16 51 10 52 4 52 589 8.2
58 46 36 47 30 48 24 49 18 50 12 51 6 520 52 54
150
MATHEMATICAL TABLES.

TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE.
P. P. Moon's!
I
for
Alt.
MOON'S HORIZONTAL PARALLAX.
App.
Alt.
54' 55'
56' 57'
"26
I
I
I
10
2 3 4 5 ZOO a
5
6
7
8
"1
46 33 47 27 48 21 49
10 46 30 47 24 48 1849
20 46 27 47 20 48 14 49
30 46 24 47 1748 11 49
40 46 20 47 13 48 6 49
50 46 16 47 10 48 3 48
227
46 13 47
10 46 9 47
20 46 6 47
30 46 2 46 56
40 45 59 46 52
50 45 55 46 48
2 2 2 3 3
9 3
=
་
58' 59' 60' 61'
=
་
P. P.
for
Par.
=
15 50 9 51 3 51 57 52 51
12 50 6 50 59 51 53 52 47'
8 50 2 50 56 51 49 52 431 0.9
549 59 50 52 51 46 52 392 1.8
49 54 50 47 51 41 52 353 27
57 49 50 50 44 51 37 52 314 35
7 480 48 53 49 47 50 40 51 34 52 27 5 44
3 47 56 48 50 49 43 50 36 51 30 52 23 6 5°3
47 5348 46 49 39 50 33 51 26 52 19 7 6.3
47 48 48
48 42 49 35 50 28 51 21 52 15 8 7'1
47 45 48 38 49 31 50 24 51 17 52 11 19 8.0
47 41 48 34 49 27 50 20 51 14 52 6
MM HO
28
"1
I
2
I
1
045 52 46 45
47 38 48 31 49 24 50
10 45 49 46 42 47 35 48 28 49 21 50
20 45 45 46 38 47 30 48 23 49 16 50
30 45 41 46 34 47 27 48 19 49 12 50
40 45 37 46 31 47 23 48 16 49 8 50
50 45 33 46 26 47 19 48
2/29
045 29 46 21 47 14 48
10 45 25 46 1847 10 48 2 48
16 51
14 51
10 52
3
751 59'
951
2 51 541 0'9
5 50 58 51 512 1-8
I 50 54 51 463 2.6
20 45 22 46
30 45 17 46
40 45 1346
50 45 946
11 49 4 49
6 48
14 47 6 47 58 48 51 49 43 50 36
947 147 54 48
56
50 49 51
414 35
59 49 51
55 49 47
50 44 51
365 44
50 39
51
32 6 5'3
51
28 7 6.2
46 49 38 50 30
51
23 8
7°C
46
18 9 7'9
46
14
30
91
2 2 2 3 3 +
4
8
9
3456 7∞ a
I
2345 Doo a
O
5 46 58 47 50 48 42 49 34 50 26 51
246 54 47 46 48 38 49 31 50 22 51
4/
45 5 45 57 46 49 47 41 48 33 49 25 50 17 51
IO 45 45 53 46 45 47 37 48 28 49 21 50 12 51
20 44 58 45 49 46 41 47 33 48 25 49 16 50 851
OI 0.9
I 30 44 53 45 44 46 36 47 28 48 19 49 11 50 3 50 55 2 1*7
46 32 47 24 48 15 49 7 49 59 50 503 2.6
46 27 47 18 48 10 49
I
2
231
6
3
7 3
8
41
9
4
I
2 3 tiO ZOO a
O
H
I
2
32
233
3
4
5
6
7 3
8
4
9
4
40 44 49 45 41
50 44 44 45 36
044 40 45 31
2 49 53 50 45 4 34
46 23 47 15 48 6 48 57 49 49 50 40 5 43
10 44 36 45 27 46 18 47
948 I 48 52 49 43 50 356 52
20 44 31 45 23 46 14 47 5 47 56 48 48 49 39 50 307 6.1
30 44 27 45 1946 10 47 I 47 52 48 44 49 35 50 268 6.8
40 44 24 45 15 46
6 46 57 47 48 48 39 49 30 50 219 7'7
50 44 19 45 10 46 46 52 47 43 48 34 49 25 50 16
I
=
OI 0.8
044 14 455 45 56 46 47 47 38 48 29 49 20 50 11
10 44 10 45 I 45 51 46 42 47 33 48 23 49 14 50 5
20 44 6 44 56 45 47 46 38 47 29 48 19 49 10 50
30 44 044 51 45 42 46 33 47 23 48 14 49 449 552 17
40 43 57 44 47 45 37 46 28 47 19 48 9 49 049 50 3 2:5
50 43 51 44 42 45 32 46 22 47 13 48 3 48 54 49 454 33
043 47 44 38 45 28 46 18 47 8 47 59 48 49 49 405 42
10 43 43 44 33 45 24 46 14 47 4 47 54 48 44 49 356 50
20 43 39 44 29 45 19 46 9 47 047 49 48 40 49 307 59
30 43 34 44 24 45 14 46 4 46 54 47 44 48 34 49 248 6.7
40 43 29 44 20 45 10 45 59 46 49 47 39 48 29 49 199 75
50 43 25 44 14 45 4 45 54 46 44 47 34 48 23 49 13
MATHEMATICAL TABLES.
151

TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE.
MOON'S HORIZONTAL PARALLAX.
P. P. Moon's
for App.
Alt.
Alt.
54'
55'
56' 57'
58'
59' 60 | 61'
P. P.
for
Par.
"34
1
I
I
4 2
1 2 2 334+ in
1 2 3 456 7∞ a
5 335
8
9 5
"
I I
I
2
4
2
5
3
7 4
4
H23+56 78 a
8
9
36
3 37
5
=
I
I
38
=
Our ŏ =
044
་
//
11
"1
11
=
12 49
=
//
2/
8 48 571 0.8
248 512 1.6
57 48 46
463 24
13 47 2 47 51 48 404 3:3
8 46 57 47 46 48 355 41
246 51 47 40 48 29
6 5.0
043 20 44 10 45 0 45 50 46 39 47 29 48 1849 8
10 43 15 44 544 54 45 44 46 33 47 23 48
20 43 10 44 44 49 45 39 46 28 47 18 48
30 43 5 43 55 44 44 45 34 46 23 47 12 48
4043
143 50 44 40 45 29 46 18 47 8 47
50 42 55 43 45 44 34 45 23 46
42 51 43 40 44 29 45 18 46
10 42 45 43 35 44 24 45 13 46
20 42 41 43 30 44 19 45 8 45 57 46 46 47 35 48 247 5.8
30 42 36 43 25 44 13 45 245 51 46 40 47 29 48 18 8 6.5
40 42 31 43 20 44 9 45 58 45 46 46 35 47 24 48 139 74
50 42 26 43 14 44 3 45 52 45 40 46 29 47 1748
I
12 48
6
I
042 21 43 9 43 58 44 47 45 35 46 24 47
10 42 15 43 4 43 53 44 41 45 29 46 18 47 6 47 55.
20 42 11 42 59 43 48 44 36 45 24 46 13 47
147 491 0·8
30 42 6 42 54 43 42 44 30 45 18 46 7 46 55 47 432 1.6
4042 1 42 49 43 37 44 25 45 13 46 46 50 47 383 24
50 41 55 42 43 43 31 44 19 45 7 45 55 46 43 47 314 32
041 51 42 39 43 26 44 14 45 2 45 50 46 38 47 26 5 40
265
10 41 45 42 33 43 21 44 8 44 56 45 44 46 32 47 206 48
20 41 40 42 28 43 16 44 3 44 51 45 39 46 27 47 147 5.6
30 41 34 42 22 43 10 43 57 44 45 45 33 46 20 47 78 6·4
40 41 30 42 17 43
14 47 29 72
50 41 24 42 11 42
8 46 56
846
0 41 19 42
10 41 14 42
20 41
I 30 41
5 43 52 44 40 45 27 46
59 43 46 44 34 45 21 46
6 42 54 43 41 44 28 45 15 46 3 46 51
042 48 43 35 44 22 45 9 45 56 46 44'
8 41 54 42 42 43 29 44 16 45 3 45 50 46 371 08
241 48 42 36 43 23 44 9 44 56 45 44 46 30 2 1.6
4 44 51 45 38 46 253 2.3
58 44 45 45 31 46 184 3*1
19 43 6 43 52 44 39 45 26 46 13 5 39
13 42 59 43 46 44 33 45 19 46
40 40 57 41 43 42 30 43 18 44
50 40 51 41 37 42 24 43 11 43
3139 040 46 41 32 42
2 2 3 3445
2 3456 7∞ a
7 4
8
9 5
་
40
I
I
2
I
2
4
2
5 3141
3+no 7 9
10 40 40 41 26 42
20 40 35 41 21 42
30 40 29 41 15 42
40 40 24 41 10 41
50 40 1841 441
5
6 47
842 54 43 41 44 27 45 14 46 07 5.5
242 48 43 34 44 21 45
7 45 538 6.2
57 42 43 43 29 44 15 45 I 45 489 70
50 42 36 43 22 44 944 54 45 30
0 40 13 40 59 41 45 42 31 43 17 44
30 39 55 40 40 41 26 42
344 49 45 35
10 40 740 53 41 38 42 25 43 10 43 56 44 42 45 28
20 40 I 40 47 41 32 42 1843 4 43 49 44 35 45 211 0·8
11 42 57 43 43 44 28 45 142 15
40 39 49 40 35 41 21 42 6 42 51 43 37 44 23 45 83 23
50 39 44 40 29 41 14 42 042 45 43 30 44 16 45 14 3°C
039 38 40 24 41 9 41 54 42 39 43 25 44 10 44 555 3.8
10 39 32 40 17 41 3 41 48 42 33 43 18 44 344 486 45
20 39 27 40 12 40
5741 42 42 27 43 12 43 57 44 427 5*3
5 40 50 41 35 42 20 43 5 43 50 44 35 8 6.0
6
4
7 4
8
5
30 39 21 40
9
5
40 39 15 40
50 39 9 39 54 40 39 41 23| 42
040 45 41 30 42
543 358
15 42 59 43 44 44 299 6.8
8 42 53 43 38 44 22
152
MATHEMATICAL TABLES.

P. P. Moon's
TABLE XVII. CORRECTION OF THE MOON'S ALTITUDE.
MOON'S HORIZONTAL PARALLAX.
for
Alt.
App.
P. P.
for
Alt.
54' 55'
56′
57 1
58'
59′
60'
61'
Par.
O
"1
/
"/
"1
་
"/
I
SIHH2mm+nno
123456 78 9
"142
42 0 39 3 39 47
10 38 56 39 41
40
26 41
20 38 51 39 36
40
Ι 30 38 45 39 29 40
40 38 40 39 25
40
3
5 343
39
4
४
5
6
40 32 41 17 42 I 42 46 43 30 44 15
8"
II 0.7
13 40 57 41 42 42 26 43 10 43 542 15
840 52 41 36 42 20 43
50 38 33 39 17 40 I 40 45 41 29|42 13| 42 57 43 414 29
038 27 39 11 56 40 39 41 23 42 742 51 43 355 3.6
10 38 21 39 5 39 48 40 32 41 16 42 0 42 44 43 276 44
20 38 15 38 59 39 42 40 26 41 941 53 42 36 43 207 51
30 38 8 38 52 39 35 40 19 41 241 46 42 29 43 138 5.8
40 38 3 38 46 39 30 40 13 40 57 41 40 42 23 43 79 6.6
2343
50 37 56 38 39 39 23 40 6 40 49 41 33 42 16 42 59
10 41 54 42 39 43 23 44
20 41 441 49 42 33 43 17 44
4 43 48 3 22
44
2
~Ham4no 78 9
I
I
037 50 38 34 39
10 37 44 38 27 39
20 37 38 38 20 39
1740
10 39
040
53 40
43 41 26 42
10 42 53
36 41 19 42
3641 1942
4 39 46 40
I
30 37 31 38 14 38
3
2
4
3
5 3145
6
4
7
5
39 40 40
40 37 26 38 8 38 51 39 33 40
50 37 18 381 38 44 39 26 40
37 13 37 55 38 38 39 21 40
10 37 7 37 49 38 31 39 14 39
20 37 37 42 38 24 39 6 39
56
2 42 46
29 41 12 41 55 42 38 1 07
22 41 5 41 48 42 31
312 I'4
16 40 59 41 41 42 243 21
9 40 51 41 34 42 174 2.8
340 45 41 28 42 10 5 35
56 40 39 41 21 42
36 4.2
48 40 31 41 13 41 557 49
5
30 36 53 37 35 38 17 38 59 39 41 40 23 41
6
96 3
I
I
I
23++ no 6
23&io zoo a
541
5 41 48 8 5.6
40 36 47 37 29 38 11 38 53 39 35 40 17 40 59 41 419 6.3
50 36 40 37 22 38 4 38 46 39 28 40 10 40 51 41 33
32 14
15 40 57 3 20
8 40 494 27
46 0 36 35 37 17 37 58 38 40 39 21 40 3 40 45 41 26
10 36 28 37 9 37 51 38 33 39 14 39 56 40 37 41 19
20 36 21 37 3 37 44 38 26 39 7 39 48 40 30 41 III 0°7
30 36 14 36 56 37 37 38 18 38 59 39 41 40 22 41
40 36 9 36 49 37 31 38 12 38 53 39 34 40
50 361 36 43 37 24 38 5 38 46 39 27 40
35 56 36 37 37 17 37 58 38 40 39 20 40
10 35 49 36 29 37 10 37 51 38 32 39 13 39 53 40 34 6 4'1
20 35 42 36 23 37 3 37 44 38 25 39 5 39 46 40 267 48
30 35 35 36 16 36 56 37 37 38 17 38 58 39 38 40 19 8 5.5
40 35 29 36 9 36 50 37 30 38 11 38 51 39 32 40 129 6.2
37 22 38 3 38 44 39 24 40 4
4 3
5
447
6
4
7
8
6
9
I
I
4 3
〃
I
2344 no 6
1234 6 7∞ a
50 35 22 36 2 36 42
48 35 16 35 56 36 36 37
449
5
6 4
8 6
9
140 425 34
16 37 57 38 37 39 17 39 57
10 35 9 35 49 36 29 37 9 37 49 38 29 39 939 49/
2035 235 42 36 22 37 I 37 42 38 21 39 139 411 06
30 34 55 35 34 36 15 36 54 37 34 38 13 38 54 39 33 2 13
40 34 49 35 28 36 8 36 47 37 28 38 7 38 47 39 24 3 19
50 34 42 35 21 36 I 36 40 37 20 37 59 38 39 39 18 4 2.6
0 34 35 35 14 35 53 36 33 37 12 37 52 38 31 39 10 5 32
10 34 28 35 7 35 46 36 25 37 4 37 44 38 23 39
26 39
20 34 21 35 35 39 36 18 36 58 37 37 38 16 38 557 46
30 34 14 34 53 35 32 36 11 36 50 37 29 38 8 38 478 5.2
34 46 35 26 36 4 36 43 37 22 38
138 409 5'9
134 40 35 18 35 57 36 36 37 15 37
40 34
50 34
53 38 32
MATHEMATICAL TABLES.
153

"1 /
"/
37 6 37 45 38 24
36 58 37 37 38 15
36 52 37 30 38 81 0·6
36 44 37 22 38 02 1.2
36 36 37 14 37 523 19
36 29 37 6 37 454 2.5
36 21 36 59
for
Alt.
App.
Alt.
54
55'
56'
TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE.
P. P. Moon's
MOON'S HORIZONTAL PARALLAX.
59'
60' 61'
P. P.
for
Par.
57' 58′
་
"50
1
4
5
1 2 2 m t in SO Z
23 456 78 a
I
3
451
5
5
6
9 7
33 54 34 32 35 11 35 49 36 28
10 33 46 34 25 35 3 35 42 36 20
20 33 40 34 19 34 57 35 35 36 13
30 33 33 34 II 34 49 35 28 36 5
40 33 26 34 4 34 41 35 20 35 58
50 33 19 33 57 34 35 35 13 35 51
33 12 33 50 34 27 35 5 35 43
10 33 5 33 42 34 20 34 57 35 35
20 32 58 33 36 34 13 34 51 35 28 36
30 32 51 33 28 34 6 34 43 35 21
40 32 43 33 21 33 57 34 35 35
50 32 36 33 13 33 51 34 27 35
36
52
I
I
2
2
3 2
4 3
453
5
6 5
7
5
8 6
9 7
37 365 31
13 36 51 37 28
286 3·8
6 36
36 43 37 217 45
35 58 36 35 37 128 51
35 49 36 27 37 49 57
435 42 36 19 36 56
12
032 29 33 6 33 43 34 19 34 57 35 33 36 10 36 48
10 32 21 32 58 33 35 34 12 34 49 35 25 36 2 36 40
20 32 15 32 52 33 28 34 5 34 41 35 18 35 55 36 321 06
30 32 7 32 44 33 20 33 57 34 34 35 10 35 47 36 23 2 12
4032 032 36 33 13 33 49 34 25 35 235 39 36 143 18
5031 53 32 30 33 6 33 42 34 18 34 54 35 31 36 74 24
031 46 32 22 32 58 33 34 34 11 34 47 35 23 35 59 5 30
10 31 38 32 14 32 50 33 26 34 34 38 35 14 35 506 3.6
7 32 43 33 19 33 55 34 31 35 735 437 42
032 36 33 11 33 47 34 22 34 58 35 34 8 4.8
40 31 16 31 52 32 28 33 3 33 39 34 15 34 50 35 259 54
50 31 10 31 46 32 21 32 56 33 32 34 7 34 43 35 18
20 31 32 32
30 31 24 32
54
I
I 20 30 47 31
30 30 40 31
HN
2
3
4 3
5 455
2 2 3 4566 7
7
8
6
9 7
4 3
1223 to 6 2
1234 SO Z∞0 a
5
2
0 31 2 31 38 32 13 32 48 33 23 33 59 34 34 35 9
10 30 55 31 30 32 5 32 40 33 15 33 50 34 26 35 I/
22 31 57 32 32 33 7 33 43 34 17 34 521 0·6
14 31 49 32 24 32 59 33 34 34
731 41 32 16 32 50 33 25 34
40 30 32 31
50 30 25 31
30 17 30 52
31 34 32
31 26 32
9 32 44 33
032 35 33
10 30 9 30 44 31 18 31 53 32 27 33
20 30 3 30 37 31 11 31 45 32 19
30 29 55 30 29 31 331 37 32 11
18 33 53
834 432 1.2
34 353 1'7
34 274 2°3
9 33 44 34 185 29
I 33 35 34 9 6 34
32 54 33 28 34 2740
32 45 33 19 33 538 46
40 29 48 30 21 30 55 31 29 32 3 32 37 33 10 33 449 5'1
50 29 41 30 14 30 48 31 22 31 55 32 29 33 3 33 37
56 0 29 33 30 7 30 40 31
457
5
7
6
8
6
9
7
//
13 31 47 32 20 32 54 33 28
10 29 25 29 58 30 32 31 531 38 32 12 32 46 33 19 /
20 29 17 29 50 30 23 30 57 31 30 32 4 32 37 33 101 0'5
30 29 9 29 43 30 16 30 49 31 22 31 55 32 28 33 I2 I'I
40 29 I 29 34 30 7 30 41 31 13 31 46 32 19 32 523 16
50 28 54 29 27 30 0 30 33 31 6 31 39 32 11 32 444 2'1
0 28 47 29 20 29 52 30 24 30 57 31 30 32 3 32 35 5 27
10 28 39 29 11 29 44 30 17 30 49 31 21 31 54 32 266 32
20 28 32 29 4 29 37 30 9 30 41 31 14 31 46 32 18 7 37
30 28 24 28 56 29 28 30 I 30 33 31 5 31 37 32 108 42
40 28 16 28 48 29 20 29 52 30 24 30 57 31 28 32 19 4.8
50 28 9 28 41 29 13 29 45 30 17 30 49 31 20 31 53
M
154
MATHEMATICAL TABLES.

TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE.
P. P. Moon's]
MOON'S HORIZONTAL PARALLAX.
for
Alt.
App.
Alt.
54'
55'
"1
56' 57′ 58'
59
60'
61'
P. P.
for
Par.
//
"/
//
//
//
"/
o 28 128 33 29 5 29 37 30 8 30 40 31 12 31 44
10 27 53 28 25 28 56 29 28 29 59 30 31 31 331 34'
8
20 27 45 28 16 28 48 29 19 29 51 30 22 30 54 31 251 0*5
28 40 29 11 29 42 30 14 30 45 31 162 10
028 3129 2 29 34 305 30 36 31 73 15
28 24 28 55 29 26 29 57 30 28 30 594 21
o 27 14 27 45 28
IO 27 627 36 28
20 26 58 27 29 28
58
I
3
4
5
6
2334 56 77
1 2 3 4 SO N∞ a
I
30 27 37 28
3
40 27 29 28
3
50 27 22 27
459
7
8
H
60
I
2
3
4 3
61
8
8
~mmt 56 7∞
23 456 7OO a
1234 +56 78
1 2 3 4 56 7∞ a
I
I
4 4
8
62
4/63
53
15 28 47 29
17 29 48 30 19 30 505 2.6
728 38 29
9 29 39 30 10 30 416 3.1
028 30 29 129 31 30 230 337 3.6
30 26 51 27 21 27 51 28 22 28 52 29 22 29 53 30 248 41
40 26 42 27 13 27 43 28 13 28 43 29 14 29 44 30 159 46
50 26 34 27 4 27 34 28 4 28 35 29 5 29 35 30 5
026 26 26 56 27 26 27 56 28 26 28 56 29 26 29 56
10 26 18 26 48 27 18 27 48 28 17 28 47 29 17 29 47'
20 26 11 26 40 27 10 27 40 28 10 28 39 29 9 29 38 1 05
30 26 2 26 32 27 2 27 31 28
I 28 30 29 0 29 29 2 I'O
40 25 54 26 23 26 53 27 22 27 52 28 21 28 50 29 203 14
50 25 47 26 16 26 45 27 15 27 44 28 13 28 42 29 124 19
025 39 26 8 26 37 27
826
6 27 35 28 4 28 33 29
25 2.4
10 25 30 25 59 26 29 26 57 27 26 27 55 28 24 28 53 6 29
20 25 22 25 51 26 20 26 48 27 17 27 46 28 15 28 447 34
30 25 14 25 42 26 11 26 40 27
927 37 28 6 28 358 3.8
40 25 6 25 34 26
625
226 31 27
027 28 27 57 28 259 43
50 24 58 25 27 25 55 26 24 26 52 27 20 27 48 28 16
7
024 50 25 18 25 46 26 15
10 24 42 25 10 25 38 26 6
20 24 34 25 225 30 25 58
30 24 26 24 54 25 22 25 49
40 24 17 24 45 25 13 25 40 26 8 26 35 27 3 27 313 13
50 24 10 24 37 25 4 25 32 25 59 26 26 26 53 27 214 18
o 24
124 28 24 55 25 23 25 50 26 17 26 44 27 11 5 22
IC 23 53 24 20 24 47 25 14 25 41| 26
8 26 35 27 26 27
20 23 45 24 12 24 39 25 6 25 33 26
30 23 36 24 3 24 30 24 57 25 24 25 51
26 43 27 11 27 39 28
26 34 27
3427 2 27 30 27 58,
26 26 26 54 27 22 27 49 1 0‘4
26 17 26 44 27 12 27 402 0.9
26 27 26 547 31
26 17 26 448 3.6
40 23 28 23 55 24 21 24 48 25 15 25 41 26 826 359 4:0
50 23 2123 47 24 14 24 40 25 725 3326
64 0 23 12 23 39 24
I I
3 3
4 4
23456 to a
23446 N∞
5
7
8 7
9 8
026 26
24 58 25 24 25 50 26 16
24 48 25 16 25 41 26 7
24 3925 5 25 31 25 571 04
5 24 31
10 23 4 23 30 23 56 24 22
20 22 55 23 21 23 48 24 13
30 22 47 23 13 23 39 24 4 24 30 24 56 25 22 25 482 0.8
40 22 39 23 4 23 30 23 55 24 21 24 47 25 12 25 38 3 12
50 22 31 22 56 23 22 23 47 24 13 24 38 25 4 25 294 1*7
65 0 22 22 22 47 23 13 23 38 24 4 24 29 24 55 25 205 2.1
IO 22 14 22 3923 4 23 29 23 55 24 20 24 45 25 106 2.5
20 22 5 22 30 22 55 23 20 23 46 24 10 24 35 25 17 2.9
30 21 56 22 22 22 46 23 11 23 36 24 124 26 24 518 33
40 21 48 22 13 22 37 23 223 27 23 52 24 16 24 419 37
50 21 41 22 5 22 30 22 54 23 18 23 43 24 8 24 32
MATHEMATICAL TABLES.
155

TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE.
P. P. Moon's
for
Alt.
MOON'S HORIZONTAL PARALLAX.
App.
Alt.
54 1 55'
56′ | 57'
=
//
P. P.
for
58'
59'
60'
61'
Par.
I I
2 3 4 5 ISO 70
1234 no too a
"66
4
4
5
567
67
6
5
7 6
8
9 8
I
I
→
//
"1
་་
021 32 21 56 22 21 22 45 23 9 23 34 23 58 24 23
10 21 23 21 48 22 12 22 36 23 0 23 24 23 48 24 13/
20 21 16 21 40 22 4
16|23
22 28 22 52 23 16 23 40 24 41 04
30/21
721 31 21 55 22 19 22 43 23 723 31 23 542 0.8
40 20 58 21 22 21 46 22 10 22 33 22 57 23 21 23 453 1'1
50 20 49 21 13 21 37 22
022 24 22 48 23 11 23 354 15
0 20 41 21 4 21 28 21 51 22 15 22 38 23 1 23 255 19
10 20 32 20 55 21 19 21 42 22 6 22 29 22 52 23 156 2.3
20 20 25 20 48 21 11 21 34 21 57 22 20 22 43 23 77 27
30 20 16 20 39 21 2 21 25 21 48 22 11 22 34 22 568 3.0
40/20
7 20 30 20 53 21 16 21 38 22 I 22 24 22 479 34
50 19 58 20 21 20 44 21 7 21 29 21 52 22 14 22 37
I
81 04
68 o 19 50 20 12 20 35 20 57 21 20 21 42 22 5 22 27
10 19 41 20
3 20 26 20 48 21 11 21 32 21 55 22 17
20 19 33 19 56 20 18 20 39 21 2 21 24 21 46 22
30 19 24 19 47 20 8 20 30 20 53 21 14 21 36 21 592 07
40 19 15 19 38 19 59 20 21 20 43 21
321 25 21 49|3 I'I
50 19
8 19 30 19 51 20 13 20 34 20 56 21 18 21 404 1'5
o 18 59 19 21 19 42 20 4 20 25 20 46 21 8 21 305 1.8
10 18 51 19 12 19 33 19 54 20 16 20 36 20 58 21 19
21 196 2.2
319 24 19 45 20 6 20 27 20 49 21
18 54 19 15 19 36 19 57 20 18 20 39 21
40 18 24 18 45 19 6 19 27 19 46 20 8 20 29 20 5019 3.3
50 18 16 18 37 18 58
5
4 4
69
234 SO
78
=23&SO N∞ a
6 6
7 6
8
LO
7
8
70
//
I
I
234566
123456 7∞ a
78
8
I
I
2
3
571
23456 78
30
20 18 42 19
18 33
107 25
082.9
19
18 19 39
19
59 20 20 20 41
18 48
19
9
19 29
19 50 20 10 20 31
18 39 18
59 19 20
1 18 20 18 41 19
19 40 20 I 20 21
o 18 7 18 28
10 17 58 18 19
20 17 49 18 10 18 30 18 50 19 10 19 31 19 50 20 111 03
30 17 41 18
I 19 20 19 41 20 1/2 0.7
40 17 33 17 53 18 12 18 32 18 52 19 12 19 32 19 513 10
50 17 24 17 44 18 3 18 23 18 42 19 2 19 22 19 424 13
o 17 15 17 35 17 54 18 14 18 33 18 53 19 12 19 325 17
10 17 6 17 25 17 45 18 4 18 23 18 43 19 2 19 21 2.0
20 16 57 17 16 17 35 17 54 18 14 18 33 19 117 23
30 16 48 17 7 17 26 17 45 18 4 18 23 18 42 19 28 2.6
40 16 40 16 59 17 18 17 37 17 55 18 15 18 33 18 529 30
50 16 31 16 50 17 9 17 27 17 46 18 5 18 24 18 42
72 0 16 22 16 41
10 16 13 16 31
18 52
16 59 17 18 17 36 17 55 18 13 18 32
16 50 17 9 17 27 17 45 18 3 18 22/
1/2 0.6
2016 4 16 22 16 41 16 59 17 17 17 36 17 54 18 121 0.3
30 15 55 16 13 16 31 16 49 17 7 17 25 17 43 18
40 15 47 16 5 16 23 16 41 16 59 17 17 17 35 17 523 09
50 15 38 15 56 16 14 16 31 16 49 17 7 17 25 17 424 12
o 15 29 15 47 16 4 16 22 16 40 16 57 17 14 17 325 15
10 15 20 15 38 15 55 16 13 16 30 16 47 17 5 17 22 6 1.8
20 15 11 15 28 15 46 16 3 16 20 16 37 16 55 17 127 21
573
6
7
8
9
9
40 14 54 15 11
15 28 15 45 16
50 14 45 15
2
15 18 15 35 15 52 16
9 16 26 16 42
30 15 2 15 19 15 36 15 53 16 10 16 28 16 44 17
2
2824
16 18 16 35 16 529 27
156
MATHEMATICAL TABLES.

TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE.
P. P. Moon's
for App.
Alt. Alt.
54
55'
MOON'S HORIZONTAL PARALLAX.
་
56′
=
57′
P. P.
58′
59' 60' |
61'
Par.
=
"
//
=
"174
I
I
2
2
3
3
5
4 4
5 75
6
7 7
8 8
9 9
..
ـر
I
I
2
3 3
4
4
1234 io n∞ à
12 0.5
15 523 0.8
14 36 14 53 15 9 15 26 15 42 15 59 16 15 16 32
10 14 27 14 44| 15 O 15 16 15 32 15 49 16 5 16 21
20 14 18 14 34 14 50 15 6 15 23 15 39 15 55 16 III 0°3
615
15 13 15 29 15 45 16
15 4 15 20 15 36
14 54 15 10 15 26 15 424 I'I
14 45 15 O 15 16 15 315 13
14 35 14 50 15 6 15 21 6 1.6
14 25 14 40 14 55 15 107 1.8
08 2.1
14 15 14 30 14 45 15
14 7 14 22 14 36 14 519 24
13 57 14 11 14 26 14 41
30 14 9 14 25
40 14
114 16
50 13 52 14 7
13 43 13 58
10 13 33 13 49
20 13 24 13 40
30 13 15 13 30
40 13 7 13 22
50 12 58 13 13
14 41 14 57
14 33 14 48
14 23 14 39
14 13 14 29
14 4 14 19
13 55 14 10
13 45 14 0
13 37 13 52
13 28 13 42
4
13
13 47 14 1
76 0 12 49 13
18 13 32
14 16 14 31
10 12 40 12 54 13 8 13 23 13 37 13 52 14 6 14 20
20 12 31 12 44 12 59 13 13 13 27 13 41 13 56 14 101 0'2
30 12 22 12 35 12 49 13 4 13 17 13 31 13 46 13 592 05
40 12 13 12 27 12 41 12 55 13 9 13 23 13 36 13 503 07
50 12 4 12 18 12 32 12 45 12 59 13 12 13 26 13 394 09
0 11 55 12 8 12 22 12 35 12 49 13 2 13 16 13 29 5 1'1
10 11 45 11 59 12 12 26 12 40 12 53 13
II
26 12 40 12 53 13 7 13 206 1'4
12 3 12 16 12 30 12 43 12 57 13 107 1.6
08 1.8
12 21 12 34 12 47 13
577
20 II 37 II 51
12
6
6
7 7
8
8
30 11 28 II 41
9 9
II 54 12
II II
7
58
12 11 12 24 12 37 12 499 21
12 1 12 14 12 26 12 39
78
=
//
I
I
2 2
10 58 11
10
3 3
10 49 II
4 4
10 39 10
51
5
579
10 30 10 41
6
6
9
10 21 10 32
7
7
20
O
10 11 10 22
8 8
30 9 39 9 50
10 2 10 13
9 9
40
9 319 42
9 5210 3
50
9 22 9 33
80
་
=
123456 Zoo a
123456 7∞ a
10
123
O O
I I
20
30
3 3 40
4 4 50 8 27
81
8 18
IO 8 9 8 18
7 7 20
8 8 30
8 0 8 9
750 7 59
9 9 40 7 41 7 50
50 7 32 7 41
9 13 9 23
9 39 14
8 54 9 4
9 33 9 44
8 45
9 24 9 34
9 15 9 25
9 5 9 15
8 36
8 56 9 5
40 II 19 11 32 11 45 II
50 II II II 23 II 36 II 49
I
*
81 0.2
O II 2 II 14 11 26 11 39 11 51 12 4 12 16 12 29
6 12 19/
10 10 52 II 5 II 17 II 29 II 42 11 54 12
20 10 43 10 55 II 8 11 20 11 32 11 44 II 56 12
30 10 34 10 46
11 22 11 34 11 46 11 582 04
40 10 26 10 38
II 12 II 24 11 36 11 483 0.6
50 10 17 10 28
II 3 II 14 11 26 11 384 0.8
O 10 7 10 18
10 53 11 4 II 16 11 275 10
ΙΟ 9 58 10
10 43 10 54 II 611 176 12
9 48 10
10 33 10 44 10 56 11
77 14
10 24 10 35 10 46 10 578 1.6
10 14 10 25 10 35 10 469 1.8
10 4 10 15 10 25 10 36
O
O O O
8 55
46
9 43 9 53
9 54 10 5 10 15 10 25
9 44 9 55 10 5 10 15
9 35 9 45
9 25 9 35
9 15 9 25
//
=
9 55 10 51 0.2
9 45 9 552 03
9 34
9 443 0'5
8 37
8 46 8 56
8 27
8 37 8 46
8 27 8 36
9 5 9 15
8 559 5
9 24
9 14
9 344 0.6
9 245 0.8
8 45 8 55
9
4
9 136 10
8 18
8
27
8 36 8 45
8
54
8 8
8
17
8 26 8 35
8 44
9 37 I'I
8 528 13
7 59
8
7
8 16
8 25
8 33
8 429 15
7 49 7 58
8 6
8 15
8 23
8 32
MATHEMATICAL TABLES.
157

TABLE XVII. CORRECTION OF THE MOON'S ALTITUDE.
P. P. Moon's
MOON'S HORIZONTAL PARALLAX.
for
Alt.
App.
Alt.
54′ | 55′ | 56′
57' 58'
59' 60'
61'
P. P.
for
Par.
=
1182
0723
7 31
7 40
7 48
7 56
8 58 13
10 7 14
7 22
7 30
7 38
7 46
7 55
8
3
- ∞ ∞ ∞
9
123 + 50 No a
123456
I I
20 7 5
7 13
7 21
7 29
7 37
7 45 7 53
30
655
7
3
7 II
7 19
7 27
7 357 42
40
6 46
6 54
7
2
7
9
7 17
7 25 7 32
4 4
50 6 37
6 45
652
52
7 O
7 7
7 14 7 22
83
o 6 28
6 35
6 42
6 50
6 57
7 47 12
10 6 19
6 26
6 33
6 40
6
47
6 54 7 2
8 21
8 II
8
ΙΙ ΟΙ
7 50 2 0.3
7 40
7 40 3 04
7 294 05
7 19 5 0.6
96 0.8
7 9
7 7
20 6
6 16
9
623
6
30
6 37
6
6
44
51
6 587 09
8 8
30 6
O
6
7
6 14
6 21
6 27
6
6
34 41
6 48 8 10
9
40 5 51
5 58
6 4
6 II
6 18
6 24
6 31
6 37 9 12
50 5 42
5 48
5 55
6 I
6
8
6 14
6 21
6 27
84
0533
5 39 5 45
5 52
5 58
6 4
4
6 10
6 17
→
10 5 23
5 30
5 36
5 42 5 48
5 54 6
6
61 "/
I
5
6
7
2 3 4 5 NO a
1 2 3 + SO Noo a
I
20 5 14
5 20 5 26
5 32
5 38
5 44 5 50
5 561 O'I
3º 5 5
5 11
5 17
5 22 5 28
5 34 5 40
5 452 0°2
3 3
40 4 56
5 I
5 7
5 13 5 18
5 24 5 29
5 35 3 03
4 4
50 4 47
4 52
4 57
5
3 5 8
5 14 5 19
5 244 04
85
이 ​4 37
4 43
4 48
4 53
4 58
5 45 9
5 14 15 05
IO 4 28
4 33
4 38
4 43
4 48
4 53 4 59
5 4
46 0.6
7
20 4 19
4 24
4 29
4 34
4 38
4 43
4 48
4 53 7 0.6
8 8
9
9
304 10
4 14
4 19
4 24 4 29
4 33
4 38
4 38
4 438 0.7
404 0
4 5
4 10
4 14 4 19
4 23 4 28
4 329 0·8
50 3 51
3 56
4
4
44
9
4 13 4 17
4 22
86
0342
3 46
3 50
I I
10 3 33
20 3 24
3 37
3 41
6 61
7 7
20 228
2 2
3 3
4 4
5 587
30 3 14
40 3 5
50 2 56
0246
10 2 37
IO 237
3 27 3 31
3 18
3 22
393 12
2 59 3 2
2 50 2 53
240
2 31
243
2 34
3 55 3 59
3.49
3 45
3 35 3 39
325 3 29
3 16 3 19
3 639
256
2 56 2 59
259
2 46 249
4 3 34
3 53 3 57
3 43 3 47
3 33 3 36
4 7
4 II
4
I
3 50 I 0.1
3 40 2 0°I
3 23
3 26
3 303 0.2
3 12
3 16
3 19 4 0°2
3 2 3 5
3 950*3
252
2 55
2 58 6 04
2 362 39
2 42
2 45
2 48704
8 8
30 2 19
2 21
9 9
40 2 10
2 12
50 2
2
123
224
2 14
2
2 27 2 29
232
2 35
2 17
2 19
2 22
2 24
5
2
7
2 9
2 12
2 14
88
o
1 51
I 53
I 55
I 57 I 59
ΙΟ
I 42
I 44
I 46
I 48 I 50
I 51
21
2 2 2 4
I 53
2 1
I
23456 too a
1 2 3 4 SO 7∞ a
I
20
I 33
I
34
I 36 I 38 I 40
I 41
I 43
2378 0.5
227905
2 16
6
I 55'
I 45 I 0.0
30 I 23
I 25
I 26
I 28
I 30
I 31
I 33
I 342 O'I
40 I 14
I
15
I 17
1 18
89
50 I 5
0 0 56
ΤΟ 0 46
I
6 I 7
I
∞ ∞
I 20 I 21
I 22
I 243 OI
8
I 10
I II
I 12 Ι 13 4 ΟΙ
• 57 0 58
O 59
I O
I I
I
2
I 35 O'I
47 • 48
O
49
0 50
0 51
0 52
O 52 6 0.2
20 0 37
0 38
0 38
0
39
0 40
0 41
0 41
O 42 7 0.2
8 8
9 9
30 0 28 O 28
40 0 18
0 29
O 29
50 O 9
O 19
O 9
0 19
Ο ΙΟ
O 20
0 30
O 20
0 30
O 20
Ο ΙΟ
Ο ΙΟ
O IO
Ο ΙΟ
0 31 0 318 0.2
O 21
O 21 9 O'2
Ο ΙΟ
158
MATHEMATICAL TABLES.
Min. 2 Hours.
Diff.
3 Hours. Diff.
4 Hours. Diff. 5 Hours.
Hours.
Diff.
Diff.
6 Hours.
6 Hours.
Diff.
Diff. 7 Hours.
Diff.
4
0 × 23 t
8.825992
9*165679
I
833034
11737
7602
9*397940
9*568894
9.698970
9*798933
60
5457
840015
11635
170240
401214
7555
5428
571358
4107
174773
404471
573811
4088
700861
3152
3138
800384
2418
59
702743
801828
2407
846936
11535
179278
7509
5401
4070
407713
576253
704618
3124
803266
2396
8
9
56 7∞ a
853798
58.860602
11437
183756
7463
410938
5375
578684.
4052
3110
706484
804697
2385
56
11340
7418
5348
4033
3097
2375
9.188207
9'414147
9 581104
9.708342
867349
11245
192631
7373
5322
417340
874040
11152
11061
197028
7329
5296
583513
4015
3083
9.806122
710192
807540
2364
55
54
3997
3070
420517
880676
7285
585911
201399
423679
5270
588299
3980 712034
808952
2353
887258
10970
7241
10880
205745
426825
5243
3962
713868
3057
810357
2342
52
590676
715694
3043
811756
2332
7198
5217
3944
3030
2321
10 8.893785
9'210064
II
10792
900261
12
13
14
234
906684
10706
214358
7156
9'429955
9'593042
9'717512
9.813149
50
5192
433070
10620
218627
7114
436170
5167
595398
3927
3017
719322
814535
2311
49
3910
3005
597744
913055
10536
222870
7073
5142
3892
721124
815915
2300
48
2992
2289
439255
600078
722919
7032
5117
3875
2978
817289
47
919377
227089
10453
6991
442325
602403
5092
3857
724705
2965
818656
2279
2268
46
15 8.925648
9.231284
16 931871
10371
235454
6950 9445379
10290
17
18
78
938045
239600
6910
448419
5067
9.604717
607021
3840
9*726484
9.820017
5043
10210
6870
451445
5018
609315
3823
728255
2952
821372
2258
45
2939
2248
3806
730018
822721
2926
43
944171
243722
10132
6831
454455
611598
731774
824063
2237
42
4993
19
20
950251
956284
247821
10055
251897
6792
457451
4969
613872
3790
2913
733522
825399
2227
41
460433
616135
3772
735262
2900
826729
2217
40
21 Hours.
Diff.
20 Hours. Diff. 19 Hours. Diff. 18 Hours. Diff. 17 Hours. Diff. 16 Hours. Diff. Min.
TABLE XVIII.
LOGARITHMS FOR FINDING THE HORARY ANGLE OR APPARENT TIME.

o ammo ime nga no 4 $
MATHEMATICAL TABLES.
159
TABLE XVIII.
Logarithms FOR FINDING THE HORARY ANGLE OR APPARENT TIME.

Min. 2 Hours.
Diff.
3 Hours. Diff. 4 Hours. Diff. 5 Hours. Diff. 6 Hours. Diff.
7 Hours.
Diff.
208.956284
9*251897
21
962271
9979
6753
9'460433
9.616135
9°735262
9.826729
255949
22
968213
9904
6715
463400
4945
618388
3756
2887
2206
40
736994
259978
4921
9830
6678
466354
620632
3740
2875
828053
2196
39
23
974111
263985
4898
738719
24
979965
9757
6640
469293
9684
267969
6602
472218
4875
622865
3721
2863
829370
2186
4852
625089 3707
740437
830682
2850
2176
3690
742147
2837
831987
2166
38
37
36
333 en
98 76
45 8.985775
26
9612 9'271930
991543
275870
6566 9'475129
4828 .9.627303
478026
629507
3674 9'743849
2825
9.833287
35
27
997269
9543
279788
0530
4805
28 9002953
9474
283684
6493
480909
631701
4782
3658
745544
834580
2155
2813
29
008596
9405
9338
287558 6457
483779
4760
633886
3642
747232
2800
835867
2145
33
6422
486635
636061
748912
3626
4738
3610
750585
2788
837148
2135
www.g
34
32
2776
838424
2125
31
2115
wwwww
30 9014198
9'291412
019761
9272
6387
9*489478
9.638227
4715
025284
9206
295244
6352
492307
4693
640383
3593
753909
9*752251 2763 9'839693
30
2105
840956
29
299055
030768
914.1
302845
6317
495123
036213
9077
306615
6283
497926
4672
642529
3577
9013
6249
500716
4650
644666
3562
755560
2750
2095
842213
28
2738
2085
757203
843464
4628
646794
3547
2727
2076
27
758840
844710
26
3532
2715
2066
ww ww
36
37
38
no no no
35 9'041621
046991
8950
310364 6216 9'503492
9.648913
4607
8888
314094
052323
057619
8827
317803 6148
6182
506256
651022
3516 9*760469
9.845949
762091
2703
2056
25
4585
509007
4563
653122
3500
39 062879
40 068103
8767
321492
6115
511745
655213
3485
8707
325161
4542
6083
514470
657294
3469
765314
763706 2680
2692
847183
2046
24
848410
2036
23
2668
849632
22
2027
766914
850848
21
328811
517183
4521
659367
3455
768508
2657
2017
852058
20
21 Hours. Diff.
20 Hours. Diff. 19 Hours. Diff. 18 Hours. Diff. 17 Hours. Diff. 16 Hours. Diff. Min.
|
160
MATHEMATICAL TABLES.
Min. 2 Hours.
Diff.
3 Hours. Diff. Hours. Diff. 5 Hours. Diff. 6 Hours. Diff.
4
7
Hours. Diff.
TABLE XVIII.
LOGARITHMS FOR FINDING THE HORARY ANGLE OR APPARENT TIME.

40 9.068103
8648
9°328811
9°517183
9.659367
6052
9*768508
41
073292
42
078446
8590
332442
6019
519883
4500
661430
3440
2645
9.852058
4479
43 083565
8532
336053
522570
5987
44
088651
8477
339645
4458
663485
3425
771674
770094 2633
853263
2007
525245
5956
8419
343219
527908
4438
665530
3409
2622
854461
1998
1988
773247
5924
4418
667567
3395
2610
855654
774812
1979
3379
2598
856841
20
19
18
17
16
24H
9∞
HH
26
1969
45 9093702
46
098720
8363
9'346773
5893
9'530559
9.669594
4397
47
103706
8308
350309
533197
671613
3365
9*776371
2586 9.858022
777922
48
108658
8254
353827
5863
859198
1959
HK
15
14
8201
357326
5832
535823
4377
673623
3350
49
113579
8148
360807
5802
538437
4357
4338
675621
3336
779467
2575
781005
2563
860367
1949
13
861532
1940
12
541040
5772
4318
677617
3322
782536
2552
1931
862690
II
3307
2541
1921
509*118468
8095
9.364270
9*543630
51 123325
52
128151
8043
367715
5742
546208
4298
9.679601
9'784061
9.863843
ΙΟ
5712
4278
681576
3292
371142
548775
53
132946
7992
5683
4258
683543
3278
785578
2530
1912
374552
551330
7942
5654
685501
3263
787089
2518
864990
9
54
137711
7892
377945
553874
4239
5625
687450
3249
788593 2507
866131
1903
8
2495
790090
4220
3235
2484
868397
867267 1884
1893
o a∞ 76
1874
55 9°142446
56
7842
9*381320
9*556406
9.689391
9'791580
9.869522
147151
384678
5597
57
151826
7793
388018
5568
558926
4.200
561435
4182
691324
3221
793064
2473
870641
1865
5
58
156473
7744
5540
7696
391342
563933
4163
693248
3207
2462
794541
695163
3193
796012
2451
872862
871754 1846
1856
4
59
161090
бо
7648
394650
5512
566419
4144
697071
3179
797476
2440
165679
5484
397940
568894
4125
698970
3165
2428
873964
1837
1828
798933
875061
In+m2 10
21 Hours. Diff. 20 Hours. Diff. 19 Hours. Diff. 18 Hours. Diff. 17 Hours. Diff. 16 Hours. Diff. Min.
MATHEMATICAL TABLES.
161

TABLE XIX.
COMMON AND HYPERBOLIC LOGARITHMS.
Common
Logarithms.
Hyp. Logarithmus
Hyperbolic Com. Logarithms.
Logarithms.
I'
2'
: ☹ m + in ☺ i ∞ å
3°
4*
6.
9*
2*3025851
4.6051702
6.9077553
9°2103404
11.5129255
13.8155106
16.1180957
18.4206807
20.7232658
I'
i i in it in ó Å öö ä
9'
*4342945
·8685890
1.3028834
I*7371779
2.1714724
6.
2.6057669
7'
3*0400614
8.
3*4743559
3·9086503
TABLE XX.
CURVATURE OF THE EARTH AND REFRACTION.
Distance
in
Chains.
Curvature
Distance
Curvature.
and
Refraction.
in
Miles.
Curvature.
Curvature
and
Refraction.
I
123&56 NO
Feet.
*OOOIC
Feet.
*00009
Feet.
Feet.
*00042
*00036
*00094
*00080
4
*00167
*00143
•00261
*00223
•00375
*00322
*00511
*00438
8
•00667
*00572
9
•00844
*00724
123456 7∞0 a
I
•67
*57
2.67
2:29
6.00
5'14
10.67
9:15
16.67
14.29
24.00
20.57
32.68
28.01
8
42.69
36.60
54.02
46.30
10
*01042
*00893
ΙΟ
66.70
57'17
II
01261
*01081
II
80.71
69.18
12
•01501
*01286
12
96.05
72°33
13
•01761
01510
13
112.72
96.62
14
⚫02043
01751
14
130'73
112.05
15
⚫02345
*02010
15
150.08
128.64
16
*02668
*02287
16
170*75
146.36
17
03012
*02582
17
192'77
165.23
18
*03377
*02894
18
216.10
185°23
19
*03762
*03225
19
240.80
206.40
20
*04169
*03573
20
266.80
228.68
198
40
•16685
*14302
25
416.88
357°32
60
*37519
32173
30
600.30
514-83
162
MATHEMATICAL TABLES.

TABLE XXI.—TRIGONOMETRICAL EQUIVALENTS.
(Arc c = half the arc a.)
(1.) Sin a= cos a. tan a =
cos a
cot a
I
√1 — (cos α)²
Совес а
I
tan a
- 2 sinc.cos C
√ 1 + (cot α)²
I
cos 2 a
2
cot a + tan c
I
√1+ (tan α)²
2 tan c
I + (tan c)²
cot c + tan c
= 2 {sin (45°+c)}² — I = I — 2 { sin (⁄ 5° — c) }²
{tan (45° - c)}²
1 + {tan (45° — c) }²
sin a
(2.) Cos a =
sin a. cot a =
tan a
I
✓ I + (tan a)²
= 1 − 2 (sin c)²
I
-
(tan c)2
I + (tan c)²
-
sin (60° + a) — sin (60° — a).
√ 1 — (sin a)²
I -
cot a
√1+ (cota) 2
= 2 (cos c)² - I =
cot c tan c
cote+tan c
X
sec a
(cos c)2- (sin c)?
I
I + cos 2 a
2
I + tan a. tan c
(3.) Tan &=
sin a
cos a
I
I
I =
√(sec a)² I
cot a
(cos a)2
sec a
cosec a
2 tan c
NI
2 cot c
sin a
(sin a)2
sin a. cos a
√ I — (cos α)²
cos a
cot a
2
I
CON 2 a
I
Ap
(tan c)2
(cot c)2
I
cot c
tan c
sin 2 a
sin 2 a
C08 2 a
=cot a 2 cot 2 α =
I + cos 2 a
I + cos 2 a
(4.) Cot a =
✔ (cosec a)²
- I
cos a
sin a
1
tan a
= the reciprocals of the above
expressions for the tangent.
I
cos a
the reciprocals of the above
tan a
sin a
expressions for the cosine.
(5.) Sec a =
√1 + (tana)³
(6.) Cosec a =
I
√1+ (cota) 2
sec a
= sec a. cot a
tan a
I
the recipro-
sin a
cals of the above expressions for the sine.
(sin a)2
(7.) Versin a =
I + cos a
| (8.) Coversin a =
(cos a)2
I + sin a
MATHEMATICAL TABLES.
163

TABLE XXII.-EXPRESSIONS FOR MULTIPLE ABOS.
(1.) Sin a=.
α
cos a
2
(2.) Sin 2 a 2 sin a. cos a.
(3.) Sin 3 α= 3 sin a 4 (sin a)³.
(4) Sin 4 a = cos a {4 sin a—8 (sin a)³}.
(5.) Sin 5 a = 5 sin a — 20 (sin a)³ + 16 (sin a)5.
sin (3
(6.) Sin na = 2 sin ẞ. sin
•
(8 + 1). sin (6+2)+ &c
n 2
I
(2 sin a)”−3.
n—1
(7.)
= cos a { (2 sin a)
(n-3). (n-4)
+
I.2
(2 sin a) "-5
(n−4). (n-5). (n − 6)
(2 sin a)”—' + &c.
78-7
1.2.3
(8.) Cos &a=
I + cos a
2
(9.) Cos 2 a=2 (cos a)³ — I.
(10.) Cos 3 α=4 (cos a)3-3 cos a.
(11.) Cos
4
4 a = 8 (cos a)¹ — 8 (cos a)²+ 1.
(12.) Cos 5 a = 16 (cos a)5 — 20 (cos a)³+5 cos a.
(13.) Cos na={{(2 sin a)” — n (2 sin a)
N-2
**+ n (n − 3)
(2 sin a)”~4
n (n
4). (n − 5)
I.2.3
(2 sin a) 7.
n-6
I 2
•
+ &c.}.
(14.) Tan
α
2
(15.) Tan 2 α=
(16.) Tan 3 α =
tan a
I+ √1+ (tan a)
I
2 tan a
1 — (tan a)²º
3 tan a (tan a)3
I
3 (tan a)²
(17.) Tan 4a=
4 tan a
4 (tan a)³
I
(18.) Tan 5α=
a
(19.) Cot 2
2
(20.) Cot 2 α =
(21.) Cot 3 a =
(22.) Cot 4 α =
(23.) Cot 5 a =
6 (tan a)² + (tan a)*
5 tan a
I
1 — 10
10 (tan a)³ + (tan a)5
(tan a)² + 5 (tan a)ª¯
I
√ 1+ (cot a)² — cot a
(cot a)2 - I
2 cot a
(cot a)³ — 3 cot a
3 (cot a)² - I
(cot a) - 6 (cot a)²+1.
4 (cot a)3-4 cot a
(cot a)5 - 10 (cot a)3 + 5 cot a
5 (cot a) 10 (cot a)²+1
164
MATHEMATICAL TABLES.

TABLE XXIII.-FORMULA RELATING TO TWO ARCS OR ANGLES.
(1.) Sin (a+ß) sin a. cos ẞ+cos a. sin ß.
=
-cos a. sin ß.
(2.) Sin (a -ß) = sin a. cos ß
cos ẞ - cos a
(3.) Cos (a+ß) = cos a. cos ẞ — sin a. sin ß.
(4.) Cos (a —ß) =
(5.) Tan (a+b)
(6.) Tan (a -ß):
(7.) Cot (a+ß)
(8.) Cot (a-B)
cos a. cos ẞ+ sin a . sin ß.
tan a+tan ẞ
I tan a. tan ẞ
tan a-tan B
I tan a. tan ẞ
cot a. cot ẞ — I
cot ẞ+ cot a
cot a. cot ẞ + I
cot ẞ- cot a
(9.) Sin (a+ß). sin (a — ß) = (sin a)² - (sin ẞ)² = (cos 6)² — (cos a)².
(10.) Cos (a+ß). cos (a — ß) = (cos a)² — (sin ß)² = (cos ß)² — (sin a)².
·
Sin (a+B)
tan atan B
cot ẞ+cot a
(11.)
Sin (a-ß)
tan a tan B
cot ẞ-cot a
Cos (a + B)
cot ẞ tan a
cot a- tan 3
(12.)
Sin (a — ß)
cot ẞ+tan a
cot a+tan B
-
(13.) Sin a+ sin 3 = 2 sin § (a+ß) . cos § (a — ß).
(14.) Sin a- sin ß = 2 sin § (a− ß) . cos § (a + B).
(15.) Cos a+cos B = 2 cos & (a + B). cos (a — ß).
(16.) Cos acos B = 2 sin § (a — B). sin § (a +ß).
(17.) Tan a+tan ß :
sin (a+B)
cos a. cos B
(18.) Tan a
sin (a-ß)
-tan B
(19.) Cot a+cot ß
(20.) Cot a- cot B
(21.) 2 sin a.
(22.) 2 cos a
(23.) 2 cos a.
(24.) 2 sin a
a.
cos ß
.
=
:
-
cos a . cos ẞ
sin (a+B)
sin a. sin ẞ
sin (a -ß)
sin a. sin B
sin (a+ẞ) + sin (a —ß).
-
sin ß = sin (a + ß) — sin (a — ß).
cos B = cos (a+B) + cos (a -B).
sin B
— cos (a — ß) — cos (a+B).
=
(25.) Tan (a+B+g)
If a+ß+y=x.
=
I
tan (a+ẞ)+tan y
I-tan (a + B). tan y
tan atan ẞ +tan y tan a. tan ẞ. tan y
tan a. tan ẞ-tan a. tan ß- tan ß. tan y
=
(26.) Tan a+tan ẞ+tan y tan a. tan ß. tan y.
MATHEMATICAL TABLES.
165

TABLE XXIV.-TRIGONOMETRICAL EXPRESSIONS.
Expressions for the sin, cos, tan, and cot, in terms of the arc a.
a5
a7
I.2.3 I.2.3.4.5
a³
(1.) Sin a = a
+
= a(
(z.) Cosa
= 1
(3.) Tan a
I
a2
I 2
•
+
a²
= (1 - 402)
I
(4.) Cot a = =
8 a
4a²
a
g-2
·
•
I 3.4.5.6.
+ &c.
7
a²
I
I
4
a
I.2.3.4 I
-)·(1
+
2 a
a2
I
I g²
8
a
a?
•
&c.
92
q8
.2.3.4.5.6
402). (1-
972
8 a
+ &c.
27).
&c.
+
25 x² - 4 a²
+ &c.
4 Ju²
&c.
α
a²
4a²
2 a
Expressions for the arc in terms of the sin and tan.
(sin a)3 I. 3. (sin a)5
I
Ι
•
(5.) Arca = sin a +
+
+ &c.
•
I 2.3
2.3.4.5
(tan a)³
3
(tan a)
+
&c.
5
(6.) Arc a = tan a
Expressions for the powers of the sin and cos.
(7.) 2 (sin a)2
(8.) 4 (sina)3 =
(9.) 8 (sin a)4
(10.) 16 (sina)5
cos 2 a,
3 sin a
sin 3 a,
4 cos 2a + cos 4a,
3
sin 5 a
2" (sin a)" = ± 2 sin na
(II.) 2n
5 sin 3a +10 sin a,
2n. sin (n − 2) a +
2n (n
I)
sin (n—4) a
I 2
•
2n (n
+
1). (n 2)
I 2.3
sin (n
<
6) a + &c.
(12.) Or, 27 (sin a)"
-
±2cosna+2n.cos (n − 2) a±
— 2 n (n − 1). (n − 2)
+
I.2.3
2n (n-1)
cos (n—4) a
I.2
cos (n
6) a + &c.
When n is of the form 4m + 1, use series (11) with the upper signs.
N
n
""
""
n
99
4m I,
""
4m,
""
(II)
(12)
lower signs.
upper signs.
""
2
(13.) 2 (cosa)² =
(14.) 4 (cos a a)3
cos 2a + 1,
cos 3 a + 3 cos a,
4m + 2,
(12)
lower signs.
(15.) 8 (cos a)4
cos 4a + 4 cos 2a + 3,
(16.) 16 (cos a)5
(17.)
2" (cos a)"
cos 5a + 5 cos 3 a + 10 cos a.
= 2 cosna + 2n. cos (n − 2) a +
2 n (n
I 2
•
· 1) cos (n — 4) a
Game
2n (n 1). (n − 2)
+
cos (n
6) a + &c.
1.2.3
2n (n - 1). (n
The formula ending in
· 2). &c.
I.2.3. &c.
cos (n — n) a, or in
2 n (n − 1). (n
I
2.3
3. &c.
1). (n-2). &c.
cos a, according as n is an even or an odd number,
and in the former case half the expression is to be taken for the last term.
166
MATHEMATICAL TABLES.

TABLE XXV. FORMULA FOR SOLVING ALL THE CASES
OF A RECTILINEAL TRIANGLE, OF WHICH THREE PARTS ARE KNOWN.
Value of any side, as A.
B. sin a
(1.) A
--
sin ẞ
C. sin a
(2.)
(3.)
sin y
B
+
C
(4.)
cos y sin y. cot a
cos ẞ+ sin ẞ. cot a
(5.)
==
B. cos y
B. sin y. cot ß.
y.cot B.
(6.)
= C. cons ß +
C. sin B. cot y
(7.)
✔ (B² + C²
2 B. C. cos α).
(8.)
= B. cosy {C² - B². (sin y)}.
± √
(9.)
= C. cos ß ± √ {B² — C². (sin ß)²}
Value of the sin of any angle, as ß.
B. sin a
A
(10.) Sin B
(II.)
B. sin y
C
(12.)
= sin (y + a).
(13.)
=
sin y.
.cos a + cos y sin a.
B. sin a
(14.)
✔ B² + C²
2 B. C. cos a)
(15.)
(16.)
(17.)
B. sin y
✓ (B² + A² — 2 B. A. cos y)
I =
A² C²
+ 07 - B²) ?
2A.C
sin a {C. cos a± √ò
C¹³ . (sin a²) }
A
(18.)
siny {A.cosy± √ ѳ
A². (sin y)}
C
a
B
MATHEMATICAL TABLES.
167

TABLE XXVI.-TRIGONOMETRICAL FORMULA FOR THE SOLUTION OF QUADRATICS AND CUBICS.
(1.) x²+px=q.
Let tan a=
Root = √q. tan § a,
2nd Root = √q. cot & a.
(5.) x³+px+q=0.
P
Let tan a =
39
Let tan 6 = ³/ tan § a,
=³/
Only real root x = — 2,
. cot 2 B.
EQUATIONS OF THE SECOND DEGREE.
√q. tan § a,
2.8
´(2.) x·³ —px= q.
(3.) x²+p
I
- ..
2
Tan a =
Sin α =
P
P
✔g. tana,
X
√q. cotta.
√q. cota.
EQUATIONS OF THE THIrd Degree.
(6.) x³ + px − q =o.
P
Tan a = 2
Tanak
39
tan ß = ³/tan ½ a,
x = ;
p
cot 2 ẞ.
3
(7.) x³−px+q=0.
P
Sin a=
p
2
39
3
3
tan α =
✓ tana,
P
2
3
sin 2 B
z is imaginary.
If p² <49,
When 4p³ <27 q².
(4.) x² -px
— px = — q.
-√
Sin a=
T =
Ρ
√q. tan § a,
x = √ q. cot § a.
(8.) x³-px-q=0.
Sin a =
P
39
tan a = ³/ tan } a,
2
3
3
(9.) x³ − px + q = 0.
39
Let sin 3 α=
Ρ
When 4p³ > or
= 27q², the fol-
lowing will be the solution of the two
last cases.
I
P
213
+3 =
(10.) x³
39
Sin 3 α =
P
X
2
- 2
sin 2 ß
= xp -q=0.
I
量
​P. sin a.
3
3
sin (60° — a).
√. sin (60° + a).
Root x = 2
sin a.
3
P
2nd root x = 2
sin (60°—a).
3
3rd root = - 2
x
P. sin (60°+a).
x = 2 V
168
MATHEMATICAL TABLES.

TABLE XXVII.-DIFFERENTIAL COEFFICIENTS.
Value of u
(1.) x.
(2.) nx
(3.) x¹.
I.
n.
du
Value of
dz
m
(4.) log, x.
(5.) log z.
(6.) ax.
in which m is the modulus of the
{in
system of logarithms.
I
[= 2.7182818.]
I
ar
log, a.
(7.) sin x.
(8.) cos x.
COS X.
sin z.
I
(9.) tan x.
(cos x)2
(Io.) cot2.
(11.) (sin x)2.
(12.) (cos x)2.
(13.) (tan x)².
(14.) (cot x)2.
(15.) sin-1 x.
(16.) cos-1x.
I
(sin x)2
2 sin z. cos X.
2 sin z.cos X.
2 tan x
(cos x)2
2 cot z
(sin x)2
I
I
(17.) tan-¹x.
-VI-2
I
I + 2.2
(18.) px ± 4x.
d (px)
dx
d (4x)
dx
d (ø x)
d (4x)
4x.
ФХ
a x
d x
(19.)
4 x
(x)2
d (fx)
(20.) fx. Qx. 4 x.
Qx. 4 x
+fx.4x.
dx
d (ø x)
dx
+fx.qx
•
d (4 x)
d x
(21.) v, in which
d. (4 x)
dx (ø v)
v = 4 x.
d x
a v
MATHEMATICAL TABLES.
169

TABLE XXVIII.
USEFUL NUMBERS, WITH THEIR LOGARITHMS.
Circumference of a circle
whose dia. I
Number.
3.1415927
Logarithm. Complement
Logarithm. of Logarithm.
0'49714999*5028501
Area of the same
•
0-7853982 1-8950899 10*1049101
4
Diameter of a
whose area
circle
I
•} = √
Surface of a sphere whose
dia. I
•
Solidity of the same
Diameter of a sphere
whose solidity=1
+16
216
1*1283792
0.0524551 9'9475449
3.1415927
0'4971499 9*5028501
05235988 17189986 10-281CO14
Length of arc 2"= sin 2″ (rad.
being unity)
1*2407010
0.0936672 9.9063328
Length of arc 1″=sin 1″ (rad.
being unity)
Į
0000004848 6-6855749 15.3144251
0*000009696 6·9866049 15.0133951
Length of arc 3"— sin 3″ (rad.
being unity)
=0'000014544 5·1626961 14.8373039
0000290888 44637261 13'5362739
Length of arc 1′= sin 1′ (rad.
being unity)
Length of arc 1° (rad being unity)=0017453293 22418774 117581226
Length of sin 1° (rad being unity)
Radius reduced to seconds
""
•
to minutes
·
to degrees
•
0.017452406 22418553 117581447
206264.8
5*3144251 4.6855749
3437 74677
35362739 | 6·4637261
57°295780
17581226 8.2418774
360 degrees expressed in seconds
12 hours expressed in seconds
24 hours expressed in seconds
No. whose hyperbolic loga- }
rithm is I
Modulus of common logarithms
1296000
6.1126050 3.8873940
46354837 53645163
86400 49365137 50634863
43200
==2718281829 04342944 9'5437056
= *434294482 | 1·6377843 10-3622157
I'949040 02898127 97101873
2*1315308 0*3286916 9.6713084
No. of French metres in a toise
No. of English yards in a French
toise
No. of English feet in a French
toise
No. of English yards in a French
metre.
No. of English feet in a French
metre
No. of English inches in a French
metre.
= 6·394592508058128 | 9*1941872
No. of English feet in a French foot =
No. of English acres in a French are =
No. of imp. lbs. Troy in a French
gramme
•
1093633100388716 9-8611284
3.2808992 05159929 94840071
39°37079 15951742 84048258
10657654 00276616 | 9′9723384
0'02471143 23928978 11.6071022
0.00268098 3.4282936 |12:5717064
N
170
MATHEMATICAL TABLES.

TABLE XXVIII.
USEFUL NUMBERS, WITH THEIR LOGARITHMS.
No. of imp. lbs. Avoird. in a
French gramme
No. of English cwts. in a French
kilogramme
·
No. of imp. gallons in a French
litre
No. of Sexagesimal degrees in a
Centesimal degree.
Number.
Logarithm. of Logarithm.
Complement
} 0*00220606 3*3436173 12·6563827
0'0196969
2*2943979 117056021
022009687 13426137 10.6573863
0'9
19542425100457575
No. of Sexagesimal minutes in a
Centesimal minute
0'54
1-7323938 19:2676062
No. of Sexagesimal seconds in a
Centesimal second
C'324
15105450 104894540
Weight of a cubic foot of pure
water in lbs. Avoird. the Bar.
being 30, and the Ther. 62°
Length in inches of a pendulum
which vibrates seconds in the
latitude of Greenwich
62.3210606 17946348 8.2053652
39°1393
15926130 8.4073860
Velocity (in feet per second)
acquired in a second by a
body falling in vacuo in
g=
32.19084
1*5077222 | 8·4922778
the lat. of Greenwich
No. of cubic inches in an im-
perial gallon
277*274
•
No. of feet in a statute mile
5280
2'4429092
3.7226339 6·2773661
7*5570908
No. of feet in a geographical or
nautical mile
6075.6
37835892 | 6·2164108
235*9093
2*3727441
8.6272559
Diurnal acceleration of stars
(=3m 55°•9093) expressed in
mean solar seconds
Sidereal day (=23h 56m 48.09)
expressed in mean solar days
Mean solar day
•
(=24h3m 56°5554)
expressed in sidereal days
Sidereal revolution of Earth ex-
pressed in mean solar days
Tropical revolution of Earth ex-
pressed in mean solar days.
Earth's equatorial radius ex-
pressed in feet.
Earth's polar radius expressed in
feet
Compression of the Earth
Length of a degree of latitude in
feet at the Equator
Length of a degree of latitude in
feet in latitude 45°
•
}
099726967 1-9988127 10'0011873
100273791 0.0011874 9.9988126
365·25636
2.5625978 74374022
365-242242-5625910| 74374080
20921665 73205963 2.6794037
20852394
7'3191559
2.6808441
I
3'5199931 12:4800069
302
362732
5'5595859 44404141
364543'5
5'5617494 44382506
MATHEMATICAL TABLES.
171
1ABLE XXIX.

Long.
O
I
2
O
%
40
8 0
O
40
4°
6° 8°
〃
.
SUN'S DECLINATION.
13° | 14° | 15°
10° 11°
12°
40 40
4 0
41°
Ο
=
=
40 310 30 310
Time
from
16° | 17° | 18° | 19°
|
20° | 21° | 22°
23° 23° 15′ Noon.
h
*
!
".
"
36
310
30 30 310
60 60 60 510 510
20
410
20
410 310
510 4/0
ΙΟ
I O 1
O
6
223+ TO 77∞
O
I
O 8
4∞
2
O 12
2
O 16
3
20
4
o 24
0 28
O 32
8 o 8 O 80 80 70 70 70 70 610
30 12 O 12
12 O II O II O II Ο ΙΙ Ο ΙΟΟ ΙΟΟ 910 910 910 80 80 70 6/0
40
4 0 160 16 0 16 0 15 0 15 0 14 0 14 0 140 130 120 120 120 110 100 100 80 80 60
50 20 O 20 O 20 0 190 190 180 18 0 170 160 150 150 150 140 130 120 110 910 710 4
60 240 24 0 240 23
0 240 230 230 22 O 21 0 200 200 180 180 180 160 160 140 130 100 80
4
O 270 260 26 0 250 250 240 230 220 210 210 190 190 170 150 130 100
0 310 300 300 290 290 270 270 260 240 240 220 210 190 170 150 110
70 270 27
80 310 31
9 350 35
10 390
0 39 39
20 I 19 I 18
30 I 58 57
40 2 37 2 36
50 3 16 3 15
60 3 55 3 54
70 4 351 4 33
80 5 14 5 12
35 34
O
39 38
I 17 I 16
O
O
•
°
56
I 14 I 12 Ι ΙΟ I 81 6I 4 Ι 20 590 560 520 480 430 370 290 16 O II
I 481 451 431 391 361 321 281 231 181 III 40 550 430 250 17
I
340 320 320 310 300 280 270 270 240 240 210 190 160 120
37 36 35 340 330 320 310 290 280 260 240 210 180 140 8
3 35 3 3
I
ΙΟ
4 12
I 561 54 51
2 35 2 32 2 28
2 24 2 20 2 17 2 132 82
3 13 3 10 3 6
3 O 256 2 512 462 412
3 52
3 52 3 48 3 43
3 25 3 193 133
4 31 4 264 20
4 6
3 593 533 453
5 10 5 4 4 57
4 48
4 41
4 344 264 174
90 5 531 5 521
5 48 5 42
5 34
5 23
5
5 16
5
100 6 32 6
31
6 27 6 21 6 11
II
5 59
5 51
H
0 36
6
0 40
I 20
2
130 580 33
580 330 22
311 120 410 28
491 260 49 0 34
2 40
3 20
81 410 58 • 39
4 40
6044
5 20
50
6
• 56
6 40
I
I
I
7
7 20
୪ о
8 40
31 571 511 441 351 251
342 272 192 101 591 471
52 562 472 362 23 2 81
363 253 153 22 47 2 29/2
73 553 433 283 112 512 261 551
84 594 494 37 4 254 103 543 343 122 442 91 14
5 5 5 425 325 215 94 534 384 203 583 33 3 3 2 241 22
IIO 7 II 7 10 7 6 6 6 48 6
6 59
6 26 6 166 55 535 40 5 235 6
64
35
4 464 233 553 212 381 30
120 7 51 7 49
I 6 51
7 44 7 37 7 25 7 II 7
6 396 256 105 535 345 124 464 163 392 531 39
130 8 30 8 27 8 23 8 15 8 27 477 36 7 257 12 6 57 6 416 216
25 38
Ι
114 37 3 583 71 47 I 12
140 9 9 9
91 9 7
79 2 8 53 8 40 8 23 8 12 7 59 7 457 307 126 516 306 45 34 4 59 163 211 55 1 18
150 9 48 9 45 9 40 9 30 9 17 8 58 8 47 8 338 188 27 427 216 576 305 57 5 204 333 352 4 I 24
160 10 28 10 25 10 20 10
348 13
8 137 497 256 566 215 414 523 502 12
170 II 611 410 58 10 47 10
68 458 197 53
8 197 537 226 466 25 114 52 22
180 11 46 11 4311 37 11 25|11
389 15 8 49 8 21 7 48 7 9/6 245 29|4 192 28
9 9 54 9 35 9 22 9 88 528
31 10 II 9 57 9 429 259
8/10 32|10
10 46 10 32 10 169 589
O
9 20
10 O
I 29 10 40
I 34 II 20
I 40 12
O
ז'
172
GEOMETRICAL DEFINITIONS.
CHAP. II.
PLANE AND SOLID GEOMETRY.
SECT. I.-Definitions.
1. GEOMETRY is that department of science, by means of which we de-
monstrate the properties, affections, and measures of all sorts of magnitude.
2. Magnitude is a term used to denote the extension of any thing, and
is of three kinds; as the magnitude of a line, which is only in one direc-
tion, viz., length; the magnitude of a surface, which is in two directions,
viz., length and breadth; and the magnitude of a solid, which is in three
directions, viz., length, breadth and depth.
3. A point has no parts or magnitude; neither length, breadth, nor
thickness, and serves only to assign position.
4. A line has length without breadth or thickness, and indicates direc-
tion and distance.
Cor. The extremities of a line are, therefore, points.
5. A right line is that which lies evenly, or in the same direction, be-
tween two points. A curve line continually changes its direction.
Cor. Hence there can only be one species of right lines, but there is an
infinite variety in the species of curves.
6. An angle is the inclination of two lines to one another, meeting in
a point, called the angular point. When it is formed by two right lines,
it is a plane angle, as A; if by curve lines, it is a curvilineal angle, as B.
(Fig. 1.)
7. A right angle is that which is made by one right line A B falling
upon another C D, and making the angles on each side equal, that is,
A B C A B D: so that the line A B does not incline more to one side
than another: it is then said to be perpendicular to the line C D. All
other angles are called oblique angles. (Fig. 2.)
8. An obtuse angle is greater than a right angle, as R. (Fig. 3.)
9. An acute angle is less than a right angle, as S. (Fig. 3.)
10. Contiguous or adjacent angles, are the two angles formed by one
line falling upon another, as R, S. (Fig. 3.)
11. Vertical or opposite angles, are those made on contrary sides of
two lines intersecting one another, as A E C, DE B. (Fig. 4.)
12. A surface has length and breadth, but no thickness, and shews
extension. The area of a figure is the quantity of space which its sur-
face occupies.
Cor. The boundaries or limits of a surface are lines.
13. A plane is that surface which lies perfectly even between its ex-
tremes; or which, being cut by another plane in any direction, its section
would be a straight line.
ANGLES, AND RIGHT LINES, AND THEIR RECTANGLES.
173
14. A solid is a magnitude extended every way, or which has length,
breadth, and depth.
Cor. The boundaries or extremes of a solid are surfaces.
15. The square of a right line is the space included by four right lines
equal to it, set perpendicular to one another.
16. The rectangle of two lines is the space included by four lines equal
to them, set perpendicular to one another, the opposite ones being equal.
17. One right line is said to be parallel to another, when both lines,
being extended to any length, will never meet, but always preserve the
same distance between them.
SECT. II.—Of Angles, and Right Lines, and their Rectangles.
PROP. I. If to any point C in a right line A B, several other right
lines D C, E C are drawn on the same side; all the angles formed at the
point C, taken together, are equal to two right angles; thus, A C D +
DCE + ECB the two right angles ACP + PCB. (Fig. 5.)
[Euclid, Book I. Prop. 13.]
Cor. 1. All the angles made about one point in a plane, being taken
together, are equal to four right angles.
Cor. 2. If all the angles at C, on one side of the line A B, are found
to be equal to two right angles; then A C B is a straight line. (Fig. 5.)
[Euc. B. I. Prop. 14.]
II. If two right lines, A B, C D, cut one another, the opposite angles
CE B and A E D will be equal. (Fig. 4.) [Euc. B. I. Prop. 15.]
III. A right line, B I, which is perpendicular to one of two parallels,
is perpendicular to the other. (Fig. 6.)
IV. If a right line C G, intersects two parallels A D, F H; the
alternate angles, A B E, and B E H, will be equal. (Fig. 6.) [Euc. B.
I. Prop. 29.]
Cor. 1. The two internal angles D BE and BEH on the same side
are equal to two right angles. (Fig. 6.)
Cor. 2. The external angle C B D, is equal to the internal angle on
the same side B E H. (Fig. 6.) [Euc. B. I. Prop. 28.]
V. Right lines, parallel to the same right line, are parallel to one
another. [Euc. B. I. Prop. 30.]
VI. If a right line A C be divided into two parts A B, B C; the
square of the whole line is equal to the squares of both the parts, and
twice the rectangle of the parts; or A C² = A B² + B C² + 2 A B ×
BC. (Fig. 7.) [Euc. B. II. Prop. 4.]
VII. The square of the difference of two lines A C, B C, is equal to
the sum of their squares, wanting twice their rectangle; or A B² = A C²
+BC2 2 ACX B C. Or A B² + 2 A C × B C = A C² + B C²
(Fig. 7.) [Euc. B. II. Prop. 7.]
VIII. The square of the sum of two lines is equal to the sum of their
squares, together with their rectangle.
174
TRIANGLES.
IX. The rectangle of the sum and difference of two lines is equal to
the difference of their squares.
X. The square of the sum, together with the square of the difference of
two lines, is equal to twice the sum of their squares.
SECT. III.—Of Triangles.
DEFINITIONS.
1. A triangle is a plane figure bounded by three right lines, called the
sides of the triangle.
2. An equilateral triangle is one in which all the three sides are equal.
3. An isosceles triangle has only two sides equal.
4. A scalene triangle has all its three sides unequal.
5. An equiangular triangle is one which has three equal angles; and
two triangles are said to be equiangular, when the angles in the one are
respectively equal to those in the other.
6. A right-angled triangle is that which has one of its angles a right
angle. The side opposite to the right angle is called the hypothenuse, and
the other two sides the legs.
7. An oblique angled triangle has all its angles oblique.
8. An obtuse angled triangle has one of its angles obtuse.
9. An acute angled triangle has all its angles acute.
10. In a triangle, the lowest side, as A B, is called the base, and the
opposite angle C the vertex: the altitude of a triangle is the perpendicular
height (CD) from the base, or its extension to the vertex. (Fig. 8.)
11. Similar triangles are those whose angles or sides are respectively
equal, each to each. And homologous sides are those lying between equal
angles.
PROPOSITIONS.
PROP. I. In any triangle A B C, if one side B C be produced or drawn
out; the external angle A C D will be equal to the two internal opposite
angles A B C and B A C. (Fig. 9.) [Euc. B. I. Prop. 32.]
II. In any triangle, the sum of the three internal angles is equal to
two right angles. [Euc. B. I. Prop. 32.]
Cor. 1. If two angles in one triangle be equal to two angles in another:
the third will also be equal to the third.
Cor. 2. If one angle of a triangle be a right angle, the sum of the other
two will be equal to a right angle.
III. The angles at the base of an isosceles triangle, are equal. [Euc.
B. I. Prop. 5.]
Cor. 1. An equilateral triangle is also equiangular; and the contrary.
Cor. 2. The line which is perpendicular to the base of an isosceles
triangle, bisects both it and the vertical angle.
IV. In any triangle, the greatest side is opposite to the greatest angle,
and the least to the least. [Euc. B. I. Prop. 18.]
TRIANGLES.
175
V. In any triangle A B C, the sum of any two sides B A, A C, is
greater than the third B C, and their difference is less than the third side.
(Fig. 10.) [Euc. B. I. Prop. 20.]
VI. If two triangles A B C, a b c, have two sides, and the included
angle equal in each; these triangles, and their correspondent parts, shall
be equal. (Fig. 11.) [Euc. B. I. Prop. 4.]
VII. If two triangles A B C and a b c, have two angles and an in-
cluded side equal, each to each; the remaining parts shall be equal, and
the whole triangles equal. (Fig. 11.) [Euc. B. I. Prop. 26.]
VIII. Triangles of equal bases and heights are equal. [Euc. B. I.
Prop. 37.]
IX. Triangles of the same height, are in proportion to one another as
their bases. [Euc. B. VI. Prop. 1.]
X. If a line D E be drawn parallel to one side B C, of a triangle; the
segments of the other sides will be proportional; that is, A D: DB::
A E: EC. (Fig. 12.) [Euc. B. VI. Prop. 2.]
Cor. 1. If the segments be proportional, A D : DB::AE:EC; then
the line D E is parallel to the side B C. (Fig. 12.)
Cor. 2. If several lines be drawn parallel to one side of a triangle, all
the segments will be proportional.
Cor. 3. A line drawn parallel to any side of a triangle, cuts off a
triangle similar to the whole.
XI. In similar triangles, the homologous sides are proportional; that
is, A B: AC::DE: DF. (Fig. 13.) [Euc. B. VI. Prop. 4.]
XII. Like triangles are in the duplicate ratio, or as the squares of,
their homologous sides. [Euc. B. VI. Prop. 19.]
XIII. In any triangle, the difference of the squares of the two legs A B
and A C, is equal to twice the rectangle contained by the base B C, and
the distance D 0, of its middle point from the perpendicular D A.
(Fig. 14.)
XIV. In a right-angled triangle B A C, if a perpendicular be let fall
from the right angle upon the hypothenuse, it will divide it into two
triangles, similar to one another and to the whole, A B D, A D C. (Fig.
14.) [Euc. B. VI. Prop. 8.]
Cor. 1. The rectangle of the hypothenuse and either segment is equal
to the square of the adjoining side.
XV. The distance A O of the right angle, from the middle of the
hypothenuse is equal to half the hypothenuse. (Fig. 14.)
XVI. In a right-angled triangle, the square of the hypothenuse is
equal to the sum of the squares of the two sides. [Euc. B. I. Prop. 47.]
XVII. If the square of one side of a triangle be equal to the sum of the
squares of the other two sides; then the angle comprehended by them is
a right angle. [Euc. B. I. Prop. 48.]
XVIII. If an angle A, of a triangle B A C be bisected by a right line.
A D, which cuts the base; the segments of the base will be proportional
to the adjoining sides of the triangle; that is, BD:DC::AB: A C.
(Fig. 10.) [Euc. B. VI. Prop. 3.]
176
QUADRILATERALS AND POLYGONS.
XIX. If the sides be as the segments of the base, the line A D bisects
the angle A. (Fig. 10.) [Euc. B. VI. Prop. A.]
XX. Three lines drawn from the three angles of a triangle to the
middle of the opposite sides, all meet in one point.
XXI. Three perpendicular lines erected on the middle of the three
sides of any triangle, all meet in one point.
XXII. The point of intersection of the three perpendiculars, will be
equally distant from the three angles; or, it will be the centre of the cir-
cumscribing circle.
XXIII. Three perpendiculars drawn from the three angles of a
triangle, upon the opposite sides, all meet in one point.
XXIV. Three lines bisecting the three angles of a triangle, all meet
in one point.
XXV. If D be any point in the base of a scalene triangle, A BC: then
is A B² x D C + A C² × B D = A D² × B C + B C × B D × D C.
(Fig. 10.)
SECT. IV.-Of Quadrilaterals and Polygons.
DEFINITIONS.
1. A quadrangle or quadrilateral, is a plane figure bounded by four
right lines.
2. A parallelogram is a quadrangle whose opposite sides are parallel,
as AG BH. The line A B drawn to the opposite corners is called the
diameter or diagonal. And if two lines be drawn parallel to the two
sides, through any point of the diagonal, they divide it into several others,
and then C and D are called parallelograms about the diameter; and E
and F the complements; and the figure E D F a gnomon. (Fig. 15.)
3. A rectangle is a parallelogram whose sides are perpendicular to one
another.
4. A square is a rectangle of four equal sides and four equal angles.
5. A rhombus is a parallelogram, whose sides are equal, and all its
angles oblique.
6. A rhomboid is a parallelogram in which only the opposite sides are
equal, and all its angles oblique.
7. A trapezoid is a quadrangle, having only two sides parallel, as
Fig. 16.
8. A trapezium is a quadrangle that has no two sides parallel, as
Fig. 17.
9. A polygon is a plane figure enclosed by many right lines. If all
the sides and angles are equal, it is called a regular polygon, and denomi-
nated according to the number of sides or angles, as a pentagon having
five sides, a hexagon, having six sides, a heptagon, having seven sides, &c.
10. The diagonal of a quadrangle or polygon is a line drawn between
any two opposite corners of the figure, as A B. (Fig. 15.)
QUADRILATERALS AND POLYGONS.
177
11. The height of a figure is a line drawn from its vertex, perpendicular
to the base, or opposite side on which it stands.
12. Like or similar figures, are those whose several angles are equal to
one another, and the sides about the equal angles proportional.
13. Homologous sides of two like figures are those between two angles,
respectively equal.
14. The perimeter or circumference of a figure, is the compass of it, or
sum of all the lines that enclose it.
15. The internal angles of a figure are those on the inside, made by the
lines that bound the figure, as A B C, D C B, &c. (Fig. 18.)
16. The external angles of a figure are the angles made by each side of
a figure, and the adjoining side drawn out, as B A F, A E G. (Fig. 18.)
PROPOSITIONS.
PROP. I. In any parallelogram the opposite sides and angles are equal;
and the diagonal divides it into two equal triangles. [Euc. B. I. Prop. 34.]
II. The diagonals of a parallelogram intersect each other in the middle
point of both.
III. Any line B C passing through the middle of the diagonal of a
parallelogram P, divides the area into two equal parts. (Fig 19.)
IV. Any right line BC drawn through the middle point P of the
diagonal of a parallelogram, is bisected in that point; or BP = P C.
(Fig. 19.)
V. In any parallelogram A G H B, the complements E and F are equal.
(Fig. 15.) [Euc. B. I. Prop. 43.]
VI. Parallelograms of equal bases and heights are equal. [Euc. B. I.
Prop. 36.]
VII. The area of a parallelogram is double the area of a triangle having
the same base and height. [Euc. B. I. Prop. 41.]
VIII. Parallelograms of the same height are to one another as their
bases. [Euc. B. VI. Prop. 1.]
IX. Parallelograms of equal bases are as their heights.
X. Parallelograms are to one another, as their bases and heights.
XI. In any parallelogram the sum of the squares of the diagonals is
equal to the sum of the squares of all the four sides.
XII. The sum of the four internal angles of any quadrilateral figure, is
equal to four right angles.
XIII. If two angles of a quadrangle be right angles, the sum of the
other two amounts to two right angles.
XIV. The sum of all the internal angles of a polygon is equal to twice
as many right angles, abating four, as the polygon has sides.
Cor. Hence all right-lined figures of the same number of sides, have
the sum of all the internal angles equal.
XV. The sum of the external angles of any polygon is equal to four
right angles.
Cor. All right-lined figures have the sum of their external angles
equal.
178
CIRCLES, ETC.
XVI. In two similar figures A C, PR; if two lines B E, Q T, be
drawn after a like manner, as suppose, to make the angle C B E=RQT;
then these lines have the same proportion as any two homologous sides of
the figure; viz.,
BEQT BO: QR: AB: PQ:: AD: PS. (Fig. 20.)
XVII. All similar figures are to one another as the squares of their
homologous sides.
XVIII. Any figure described on the hypothenuse of a right-angled
triangle, is equal to two similar figures described the same way upon the
two legs; that is, B F CALC+AG B. (Fig. 21.) [Euc. B. VI.
Prop. 31.]
XIX. Any regular figure A BCDE, is equal to a triangle whose base
is the perimeter ABCDEA; and height the line O P, drawn from the
centre, perpendicular to one side. (Fig. 22.)
XX. Only three sorts of regular figures can fill up a plane surface, that
is, the whole space round an assumed point, and these are six triangles,
four squares, or three hexagons.
SECT. V. Of the Circle, and Inscribed and Circumscribed Figures.
DEFINITIONS.
1. A circle is a plane figure described by a right line moving about a
fixed point, as A C about C: or it is a figure bounded by a curved line,
every part of which is equidistant from a fixed point. (Fig. 23.)
2. The centre of a circle is the fixed point about which the line moves,
as C. (Fig. 23.)
3. The radius is the line that describes the circle, as C A. (Fig. 23.)
Cor. All the radii of a circle are equal.
4. The circumference is the line described by the extreme end of the
moving line, as ABDEA. (Fig. 23.)
5. The diameter is a line drawn through the centre, from one side to the
other, as A D. (Fig. 23.)
6. A semicircle is half the circle, cut off by the diameter, as A B D.
7. A quadrant, or quarter of a circle, is the part between two radii per-
pendicular to one another, as CDE. (Fig. 23.)
8. An arc is any part of the circumference, as A B. (Fig. 24.)
9. A sector is a part bounded by two radii, and the arc between them,
as A CB. (Fig. 24.)
10. A chord is a right line drawn through the circle, as D F.
11. A segment is a part cut off by a right line, or chord, as DEF, or
DABF. (Fig. 24.)
12. Angle at the centre is that whose angular point is at the centre
ACB. (Fig. 24.)
13. Angle at the circumference is when the angular point is in the cir-
cumference, as BA D, or B C D. (Fig. 25.)
CIRCLES, ETC.
179
14. Angle in a segment, is the angle made by two lines drawn from
some point of the arc of that segment to the ends of the base; as B CD
is an angle in the segment B CD. (Fig. 25.)
15. Angle upon a segment is the angle made in the opposite segment,
whose sides stand upon the base of the first; as B A D, which stands upon
the segment B C D. (Fig. 25.)
16. A tangent is a line touching a circle, which, produced, does not cut
it, as G A F. (Fig. 23.)
17. Circles are said to touch one another, which meet, but do not cut
one another.
18. Similar arcs, or similar sectors, are those bounded by radii that
make the same angle.
19. Similar segments are those which contain similar triangles, alike
placed.
20. A figure is said to be inscribed in a circle, or a circle circumscribed
about a figure, when all the angular points of the figure are in the circum-
ference of the circle. (Fig. 26.)
21. A circle is said to be inscribed in a figure, or a figure circumscribed
about a circle, when the circle touches all the sides of the figure. (Fig. 27.)
22. One figure is inscribed in another, when all the angles of the in-
scribed figure are in the sides of the other. (Fig. 28.)
PROPOSITIONS.
PROP. I. The radius C R, bisects any chord at right angles, which does
not pass through the centre, as A B. (Fig. 29.) [Euc. B. III. Prop. 3.]
Cor. 1. If a line bisects a chord at right angles, it passes through the
centre of the circle.
Cor. 2. The radius that bisects the chord also bisects the arc.
II. In a circle equal chords are equally distant from the centre. [Euc.
B. III. Prop. 14.]
III. If several lines be drawn through a circle, the greatest is the
diameter, and those that are nearest the centre are greater than those that
are farther off. [Euc. B. III. Prop. 15.]
IV. If from any point three equal right lines can be drawn to the cir-
cumference, that point is the centre. [Euc. B. III. Prop. 9.]
V. No circle can cut another in more than two points. [Euc. B. III.
Prop. 10.]
VI. There can be only two equal lines drawn from any exterior point,
to the circumference of a circle.
VII. In any circle, if several radii be drawn making equal angles, the
arcs and sectors comprehended thereby will be equal; that is, if the angle
A C B = BCD, then, the arc A B = BD, and the sector ACB = B CD.
(Fig. 30.) [Euc. B. III. Prop. 26.]
VIII. In the same or equal circles, the arcs, and also the sectors, are
proportional to the angles intercepted by the radii.
IX. The circumferences of circles are to one another as their diameters.
180
CIRCLES, ETC.
X. A right line, perpendicular to the diameter of a circle, at the ex-
treme point, touches the circle in that point, and lies wholly without the
circle; or is a tangent to the circle.
XI. If two circles touch one another, either inwardly or outwardly, the
line passing through their centres shall also pass through the point of
contact. [Euc. B. III. Prop. 11 and 12.]
XII. In a circle the angle at the centre is double the angle at the cir-
cumference, standing upon the same arc; or B D C = 2 BAC. (Fig. 31.)
[Euc. B. III. Prop. 20.]
XIII. All angles in the same segment of a circle are equal, as DAC
= DBC, and D G C DHC. (Fig. 32.) [Euc. B. III. Prop. 21.]
•
—
· XIV. If two right lines D C, A B, be drawn from the extremities of
two equal arcs DA, BC, they will be parallel. (Fig. 32.)
XV. The angle ABC in a semicircle is a right angle. (Fig. 33.) [Euc.
B. III. Prop. 31.]
XVI. The angle F BG, in a greater segment FABCG, is less than a
right angle; and the angle DBE, in a less segment DBE, is greater
than a right angle. (Fig. 33.) [Euc. B. III. Prop. 31.]
XVII. If two lines cutting a circle, intersect one another in A; and
there be made at the centre,▲ ECF = ▲ BAD; then the arc BD +
GH = 2 EF, if A is within the circle; or the arc BDG H = 2 EF,
if A is without. (Fig. 34.)
XVIII. If from a point without, two lines, A B, AD be drawn to cut a
circle; the angle made by them is equal to the angle at the centre, standing
on half the difference of the two arcs of the circumference GH, BD.
(Fig. 34.)
XIX. The angle A= ▲ BHD + HD G, when A is within; or A =
BHD-HD G, when A is without the circle. (Fig. 34.)
XX. In a circle, the angle made at the point of contact between the
tangent and any chord, is equal to the angle in the alternate or opposite.
segment; ECF = E BC, and E CA=EGC. (Fig. 35.) [Euc. B. III.
Prop. 32.]
XXI. A tangent to the middle point of an arc, is parallel to the chord
of it.
XXII. If from any point B in a semicircle, a perpendicular B D be let
fall upon the diameter, it will be a mean proportional between the seg-
ments of the diameter; that is, A D:DB::DB: DC. (Fig 36.) [Euc.
B. VI. Prop. 13.]
XXIII. The chord is a mean proportional between the adjoining seg-
ment and the diameter, from the similarity of the triangles: that is, A D :
AB::AB: AC; and CD: CB:: CB: CA. (Fig. 36.)
XXIV. In a circle, if the diameter AD be drawn, and from the ends of
the chords AB, AC, perpendiculars be drawn upon the diameter; the
squares of the chords will be as the segments of the diameter; that is,
AE:AF: A B2: A C². (Fig. 37.)
B²
XXV. If two circles touch one another in P, and the line PDE be
drawn through their centres; and any line PA B is drawn through that
}
CIRCLES, ETC.
181
point to cut the circles, that line will be divided in proportion to the
diameters; that is, PA: P B :: PD: PE. (Fig. 38.)
XXVI. If through any point F in the diameter of a circle, any chord,
C F D be drawn, the rectangle of the segments of the chord is equal to
the rectangle of the segments of the diameter; CF × F D = AF ×
FB also G F x F E. (Fig. 39.) [Euc. B. III. Prop. 35.]
XXVII. If through any point F out of the circle in the diameter B A
produced, any line F C D be drawn through the circle: the rectangle of
the whole line and the external part is equal to the rectangle of the whole
line passing through the centre, and the external part; D F x FC=
AFX FB also F Ex F G. (Fig. 40.)
XXVIII. Let H F be a tangent at H; then the rectangle C F × F D
= square of the tangent F H. (Fig. 40.) [Euc. B. III. Prop. 36.]
XXIX. If from the same point F, two tangents be drawn to the circle,
they will be equal; that is, F H = FI. (Fig. 40.)
XXX. If a line P F C be drawn perpendicular to the diameter A D of
a circle; and any line drawn from A to cut the circle and the perpen-
dicular; then the rectangle of the distances of the sections from A, will
be equal to the rectangle of the diameter and the distance of the perpen-
dicular from A; that is, A B x A CAP x A D.
Also, A BACA K². (Fig. 41.)
(Fig. 41.)
XXXI. In a circle E D F whose centre is C, and radius C E, if the
points B, A, be so placed in the diameter produced, that C B, C E, CA
be in continual proportion, then two lines B D, A D drawn from these
points to any point in the circumference of the circle will always be in
the given ratio of B E to A E. (Fig. 42.)
XXXII. In a circle, if a perpendicular D B be let fall from any point
D, upon the diameter C I, and the tangent D O drawn from D, then
A B, A C, A O, will be in continual proportion. (Fig. 43.)
XXXIII. If a triangle B D F be inscribed in a circle, and a perpen-
dicular D P let fall from D on the opposite side B F, and the diameter
D A drawn; then, as the perpendicular is to one side including the angle
D, so is the other side to the diameter of the circle; that is, D P : DB::
DF: DA. (Fig. 44.)
XXXIV. The rectangle of any two sides of an inscribed triangle is
equal to the rectangle of the diameter, and the perpendicular on the third
side; that is, BD X D F = AD × DP. (Fig. 44.)
XXXV. If a triangle B A C be inscribed in a circle, and the angle A
bisected by the right line A E D, then as one side is to the segment of
the bisecting line within the triangle, so is the whole bisecting line to
the other side; that is, A B: A E:: A D : A C; and A B × A C =
BE. ECA E2. (Fig. 45.)
XXXVI. If a quadrilateral A B C D be inscribed in a circle, the sum
of two opposite angles is equal to two right angles; that is, A DC+
A B C two right angles. (Fig. 46.) [Euc. B. III. Prop. 22.]
182
CIRCLES, ETC.
XXXVII. If a quadrangle be inscribed in a circle, the rectangle of the
diagonals is equal to the sum of the rectangles of the opposite sides; or
CAX BD CBX DA+ CD x A B. (Fig. 46.)
XXXVIII. A circle is equal to a triangle whose base is the circum-
ference of the circle; and height, its radius.
XXXIX. The area of a circle is equal to the rectangle of half the cir-
cumference and half the diameter.
XL. Circles (that is, their areas) are to one another as the squares of
their diameters, or as the squares of the radii, or as the squares of the
circumferences. [Euc. B. XII. Prop. 2.]
XLI. Similar polygons inscribed in circles, are to one another as the
circles wherein they are inscribed.
XLII. A circle is to any circumscribed rectilineal figure, as the circle's
periphery to the periphery of the figure.
XLIII. If an equilateral triangle A B C be inscribed in a circle; the
square of the side thereof is equal to three times the square of the radius;
that is, A B² = 3 A D². (Fig. 47.)
XLIV. If from any point D in the circumference of a circle, having
inscribed in it an equilateral triangle, chords be drawn to the three angles
A, B, C; the longest chord A D, is equal to the sum of the two lesser
chords, B D and C D. (Fig. 48.)
XLV. A square inscribed in a circle, is equal to twice the square of
the radius.
XLVI. The side of a regular hexagon inscribed in a circle, is equal to
the radius of the circle.
XLVII. If two chords in a circle mutually intersect at right angles,
the sum of the squares of the segments of the chords is equal to the
square of the diameter of the circle; that is, A P² + P B² + P C² +
P D² = diam.² (Fig. 49.)
XLVIII. If the diameter P Q be divided into two parts at any point
R, and if R S be drawn perpendicular to P Q; also R T applied equal to
the radius, and T R produced to the circumference at V: then,
RT=
RV =
PR+RQ; or RT is the arithmetical mean,
2
; or RV is the harmonical mean,
between the
two segments
of the diame-
ter PR, QR
(Fig. 50.)
RS =√ PRX RQ; or RS is the geometrical mean,
2 X PRX RQ
PR+RQ
XLIX. If the arcs P Q, Q R, R S, &c., be equal, and there be drawn
the chords PQ, P R, P S, &c., then it will be P Q: PR:: PR: P Q
+PS:: PS: PR+PT::PT:PS+P V, &c. (Fig. 51.)
L. If the arcs PQ, QR, RS, &c., be equal, the angles Q P R, R P S,
SP T, &c., will be equal; or in equal circles, equal angles stand upon
equal arcs, whether they be at the centres or circumferences. (Fig. 51.)
[Euc. B. III. Prop. 26.]
LI. The centre of a circle being O, and P a point in the radius, or in
the radius produced; if the circumference be divided into as many equal
PLANES AND SOLIDS.
183
parts A B, B C, C D, &c., as there are units in 2n, and lines be drawn
from P to all the points of division; then shall the continual product of
all the alternate lines, viz., P A PCX PE, &c., be = r² xn when
P is within the circle, or = x ™ when P is without the circle; and the
product of the rest of the lines, viz., P B × PD × P F, &c., = p² +
x²: where r = A O the radius, and x = 0 P the distance of P from the
centre. (Fig. 52.)
—
SECT. VI.-Of Planes and Solids.
DEFINITIONS.
1. THE common section of two planes, is the line in which they meet,
or cut each other.
2. A line is perpendicular to a plane, when it is perpendicular to every
line in that plane which meets it.
3. One plane is perpendicular to another, when every line of the one,
which is perpendicular to the line of their common section, is perpen-
dicular to the other.
4. The inclination of one plane to another, or the angle they form be-
tween them, is the angle contained by two lines, drawn from any point
in the common section, and at right angles to the same, one of these lines
in each plane.
5. Parallel Planes are such as being produced ever so far in any direc-
tion, will never meet, or which are everywhere at an equal perpendicular
distance.
6. A solid angle is that which is made by three or more plane angles,
meeting each other in the same point.
7. Similar solids, contained by plane figures, are such as have all their
solid angles equal, each to each, and are bounded by the same number of
similar planes, alike placed.
8. A prism is a solid whose ends are parallel, equal, and like plane
figures, and its sides, connecting those ends, are parallelograms. (Fig.
53 and 54.)
9. A prism takes particular names according to the figure of its base
or ends, whether triangular, square, rectangular, pentagonal, hexa-
gonal, &c.
10. A right or upright prism, is that which has the planes of the sides
perpendicular to the planes of the ends or base. (Fig. 53.) When such
is not the case it is called an oblique prism. (Fig. 54.)
11. A parallelopiped, or parallelopipedon, is a prism bounded by six
parallelograms, every opposite two of which are equal, alike, and parallel.
(Fig 55.)
12. A rectangular parallelopipedon is that whose bounding planes are
all rectangles, which are perpendicular to each other. (Fig. 56.)
13. A cube is a square prism, being bounded by six equal square sides
or faces, which are perpendicular to each other. (Fig. 57.)
184
PLANES AND SOLIDS.
14. A cylinder is a round prism having circles for its ends; and is
conceived to be formed by the rotation of a right line about the circum-
ferences of two equal and parallel circles, always parallel to the axis.
(Fig. 58.)
15. The axis of a cylinder is the right line A B joining the centres of
the two parallel circles, about which the figure is described.
16. A pyramid is a solid whose base is any right-lined plane figure,
and its sides triangles, having all their vertices meeting together in a
point above the base, called the vertex of the pyramid. (Fig. 59.)
17. Pyramids, like prisms, take particular names from the figure of
their base.
18. A cone is a round pyramid having a circular base, and is conceived
to be generated by the rotation of a right line about the circumference of
a circle, one end of which is fixed at a point above the plane of that circle.
(Fig. 60.)
19. The axis of a cone is the right line, A B, joining the vertex, or
fixed point, and the centre of the circle about which the figure is de-
scribed.
20. When the axis of a cone or pyramid is perpendicular to the base,
it is called a right cone or pyramid; but if inclined it is called oblique.
21. Similar cones and cylinders, are such as have their altitudes and
the diameters of their bases proportional.
22. A sphere is a solid bounded by one curve surface, which is every-
where equally distant from a certain point within, called the centre.
It
is conceived to be generated by the rotation of a semi-circle about its
diameter, which remains fixed. (Fig. 61.)
23. The axis of a sphere is the right line about which the semi-circle
revolves, and the centre is the same as that of the revolving semi-circle.
24. The diameter of a sphere is any right line passing through the
centre, and terminated both ways by the surface.
25. The altitude of a solid is the perpendicular drawn from the vertex
to the opposite side or base.
PROPOSITIONS.
PROP. I. If any prism be cut by a plane parallel to its base, the section
will be equal and like to the base.
II. If a cylinder be cut by a plane parallel to its base, the section will
be a circle, equal to the base.
III. All prisms and cylinders, of equal bases and altitudes, are equal to
each other. [Euc. B. XI. Prop. 31.]
IV. Rectangular parallelopipedons, of equal altitudes, are to each other
as their bases. [Euc. B. XI. Prop. 32.]
V. Rectangular parallelopipedons, of equal bases, are to each other as
their altitudes.
VI. Because prisms and cylinders are as their altitudes, when their
bases are equal: and, as their bases when their altitudes are equal. There-
PLANES AND SOLIDS.
185
fore, universally, when neither are equal, they are to one another as the
product of their bases and altitudes: hence, also, these products are the
proper numeral measures of their quantities or magnitudes.
VII. Similar prisms and cylinders are to each other as the cubes of
their altitudes, or of any like linear dimensions. [Euc. B. XI., Prop. 33.]
VIII. In any pyramid a section parallel to the base is similar to the
base; and these two planes are to each other as the squares of their dis-
tances from the vertex.
IX. In a right cone, any section parallel to the base is a circle; and
this section is to the base as the squares of their distances from the vertex.
X. All pyramids and cones of equal bases and altitudes are equal to one
another.
XI. Every pyramid is the third part of a prism of the same base and
altitude. [Euc. B. XII., Prop. 10.]
XII. If a sphere be cut by a plane, the section will be a circle.
XIII. Every sphere is two-thirds of its circumscribing cylinder.
XIV. A cone, hemisphere, and cylinder of the same base and altitude
are to each other as the numbers 1, 2, 3. [Euc. B. XII., Prop. 10.]
XV. AH spheres are to each other as the cubes of their diameters; all
these being like parts of their circumscribing cylinders. [Euc. B. XII.,
Prop. 18.]
XVI. There are only three sorts of regular plane figures which can be
joined together, so as to form a solid angle; viz., three, four, or five
triangles, three squares, and three pentagons: thus giving five different
species of solid angles, which are those of the five regular or Platonic
bodies; viz. :-
1. The tatraedon, (Fig. 62,) bounded by four equilateral triangles,
each solid angle of which is formed by three triangles.
2. The hexaedron, or cube, (Fig. 57,) contained by six squares, each
solid angle of which is formed by three squares.
3. The octaedron, (Fig. 63,) bounded by eight triangles, each solid
angle of which is formed by four triangles.
4. The dodecaedron, (Fig. 64,) bounded by twelve pentagons, each
solid angle of which is formed by three pentagons.
5. The icosaedron, (Fig. 65,) bounded by twenty triangles, each solid
angle of which is formed by five triangles.
XVII. Only one sort of the foregoing five regular bodies, joined at
their angles, can completely fill a solid space, without leaving any vacuity;
viz., eight hexaedrons, or cubes.
XVIII. A sphere is to any circumscribing solid B F, (all whose planes
touch the sphere,) as the surface of the sphere to the surface of the solid.
(Fig. 66.)
XIX. All bodies circumscribing the same sphere, are to one another
as their surfaces.
XX. The sphere is the greatest or most capacious of all bodies of equal
surface.
186
PRACTICAL GEOMETRY.
SECT. VII.-Practical Geometry.
It is not intended in this place to present a complete collection of
Geometrical Problems, but merely a selection of the most useful, espe-
cially in reference to the employments of Mechanics and Engineers.
The instruments for the purposes of geometrical construction, are too
well known to require any description here; and their use is much easier
learned by an examination of the instruments themselves, than by any
written explanation.
PROB. I. From a given point B in a given straight line A C, to draw a
line perpendicular to the same.
From B as a centre, with any radius, describe arcs cutting A C in a and
c, then from a and c with any larger radius describe arcs cutting each
other in d and e; then the straight line d Be will be perpendicular to
AC. (Fig. 67.)
PROB. II. To erect a perpendicular at the end of a given line.
With any radius, and from a point somewhere above A B, describe a
semicircular arc passing through the point B, at which the perpendicular
is to be erected, and also cutting A B in C; then, through C and the centre
of the arc produce the right line CD, cutting the arc in D, and a line
joining D and B will be the perpendicular required. (Fig. 68.)
PROB. III. To bisect any given angle A C B.
From C as a centre, with any radius, describe an arc cutting the sides
in D and E; then from D and E, as centres with the same radius, describe
arcs cutting each other in F; then the straight line joining C and F will
bisect the angle ACB. (Fig. 69.)
PROB. IV. To bisect a given angle B A P; then to bisect its half; and
so on.
Through any point B draw B E parallel to AP, and upon B E set off
the distance B C equal to B A; then join A. C, and it will bisect the angle
ВАР.
Again, set off, upon BE, from C, CD = CA; join A D, and it will
bisect CA P, or quadrisect BA P.
Again, set off, upon BE, DE = DA; join EA; and E A P will be
of BA P: and so on. (Fig. 70.)
PROB. V. At a given point A in a given line AB, to make an angle
equal to a given angle C.
From the centres A and C, with the same radius, describe the arcs
DE, FG. Then, with radius D E, and centre F, describe an arc, cutting
FG in G. Through G draw the line A G; and it will form the angle
required. (Fig. 71.)
PROB. VI. To divide any given angle ABC into three equal parts.
From B, with any radius, describe the circle ACDA. Bisect the
angle A B C by BE, and produce A B to D. On the edge of a ruler mark
off the length of the radius A B. Lay the ruler on D, and move it till
PRACTICAL GEOMETRY.
187
one of the marks on the edge intersects B E, and the other the arc A Cin
G. Set off the distance C G from G to F: and draw the lines BF, and
BG, they will trisect the angle ABC. (Fig. 72.)
PROB. VII. To divide a given line A B into any proposed number of
equal parts.
1st Method. Draw any other line A C, forming any angle with the given
line A B; on which set off as many of any equal parts, A D, D E, E F,
FC, as the line A B is to be divided into. Join BC; parallel to which
draw the other lines FG, EH, DI: then these will divide A B in the
manner required. (Fig. 73.)
2nd Method, without drawing parallel lines. Let A B be the line
which is to be divided into n equal parts. Through one extremity A
draw any right line AD, upon which set off n + 1 equal parts, the
point D being at the termination of the (n + 1)th part. Join D B
and produce it until the prolongation B E = B D. Let F be the
termination of the (n - 1)th part. Join F E, and the right line of
junction will cut the given line A B in the point P, such that
BP = A B; and of course n distances each equal to BP set off
1
-
n
upon BA, will divide it, as required*. (Fig. 74.)
PROB. VIII. To cut off from a given line A B, supposed to be very
short, any proportional part.
Suppose, for example, it were required to find the,,, &c., of
the line A B, fig. 75. From the ends A and B draw A D, B C, perpen-
dicular to A B, and divide A D into twelve equal parts; then through
these divisions 1, 2, 3, &c., draw lines 1 f, 2 g, &c., parallel to A B. Draw
the diagonal A C, and 1 d will be the of AB; 2 c,, and so on. The
12
same method is applicable to any other part of a given line.
PROB. IX. To make a diagonal scale, say, of feet, inches, and tenths of
an inch.
Draw an indefinite line A B, on which set off from A to B the given
length for one foot, any required number of times; and from these divi-
sions A, C, H, B, draw A D, C E, &c., perpendicular to A B. On A D and
BF set off any length ten times, and through these divisions draw lines
parallel to A B; then divide A C and D E into twelve equal parts, each
of which will be one inch. Draw the lines A 1, g 2, &c., and they will form
the scale required; viz., each of the larger divisions from E to G, G to F,
&c., will represent a foot; each of the twelve divisions between D and E,
an inch; and the several horizontal lines parallel to R C in the triangle
ECR, will be equal to fo, fo, fo, &c., of an inch. (Fig. 76.)
Note.-If the scale be meant to represent feet, or any other unit, and
tenths and hundredths, then D E must be divided into ten instead of twelve
equal parts.
* The truth of this method is easily demonstrated.
point of division, on a D, between F and D, draw IB.
DIIF, IB is parallel to F P. Consequently, BP: BA::
Through 1 the intermediate
Then, because D B — B E, and
IF:IA::1: n, by construction.
188
PRACTICAL GEOMETRY.
PROB. X. To find the centre of a circle.
Draw any chord A B, and bisect it perpendicularly with the line R D.
Then bisect R D in C, which will be the centre required. (Fig. 29.)
PROB. XI. To divide a given circle into any number of concentric parts,
equal to each other in area.
Draw the radius A B, and on it describe the semicircle Aƒ e d B.
Divide A B into the proposed number of equal parts, 1, 2, 3, &c., and
erect the perpendiculars 1 d, 2 e, 3f, &c., meeting the semicircle in d, e, f,
&c. Then from the centre B, and with radii Bd, Be, &c., describe cir-
cles; so shall the given circle be divided into the proposed number of
equal concentric parts. (Fig. 77.)
PROB. XII. To divide a given circle into any number of parts, equal both
in area and perimeter.
Divide the diameter QR into the proposed number of equal parts at the
points S, T, V, &c.; then, on one side of the diameter describe semicircles
on the diameters QS, QT, QV, and on the other side of it describe semi-
circles on RV, RT, RS; so shall the parts 17, 35, 53, 71, be all equal,
both in area and perimeter. (Fig. 78.)
PROB. XIII. To describe the circumference of a circle through three
given points, A, B, C.
From the middle point B draw chords B A, B C, to the two other points,
and bisect these chords perpendicularly by lines meeting in O, which will
be the centre. Then from the centre O, at the distance of any of the points,
as O A, describe a circle, and it will pass through the two other points
BC, as required. (Fig. 79.)
The same method may be employed for finding the centre of a circular
arc, by taking any three points in the same, as A, B, and C.
PROB. XIV. To describe mechanically the circumference of a circle
through three given points, A, B, C, when the centre is inaccessible; or the
circle too large to be described with compasses.
Place two rulers MN, RS, cross ways, touching the three points, A, B, C.
Fix them in V by a pin, and by a transverse piece T. Hold a pencil in A,
and describe the arc BA C, by moving the angle RAN, so as to keep the
outside edges of the rulers against the pins B C. Remove the instrument
R.V N, and on the arc described mark two points, D, E, so that their dis-
tance shall be equal to the length B C. Apply the edges of the instrument
against D E, and with a pencil in G describe the arc B C, which will com-
plete the circumference of the circle required. (Fig. 80.)
Otherwise. Let an axle of 12 or 15 inches long carry two unequal
wheels A and B, of which one, A, shall be fixed, while the other, B, shall
be susceptible of motion along the axle, and being placed at any assigned
distance, A B, upon the paper or plane on which the circle is to be de-
scribed. Then will A and B be analogous to the ends of a conic frustum,
the vertex of the complete cone being the centre (0) of the circle (CDEF)
which will be described by the rim, or edge, of the wheel A, as it rolls
upon the proposed plane. Then it will be, as the diameter of the wheel
A is to the difference of the diameters of A and B, so is the radius of the
PRACTICAL GEOMETRY.
189
circle proposed to be described by A, to the distance, A B, at which the
two wheels must be asunder, measured upon the plane on which the circle
is to be described.
The wheel B will evidently describe, simultaneously, another circle
(GHIK) whose radius will be less than that of the former by A B.
(Fig. 81.)
PROB. XV. On a given chord A B to describe mechanically an arc of a
large circle that shall contain any number of degrees.
Place two rulers, forming an angle A CB, equal to the supplement of
half the given number of degrees, and fix them in C. Place two pins at
the extremities of the given chord, and hold a pencil in C; then move the
edges of this instrument against the pins, and the pencil will describe the
arc required. (Fig. 82.)
Suppose it is required to describe an arc of 50 degrees on the given
chord A B; subtract 25 degrees (which is half the given angle,) from 180,
and the difference, 155 degrees, will be the supplement. Then form an
angle A C B of 155 degrees with the two rulers, and proceed as has been
shewn above.
PROB. XVI. To describe the segment of a circle of large radius, of
which the chord A B and versine CD are given.
Through D draw H I parallel to A B; then join A D and D B, and
draw A H perpendicular to A D and BI perpendicular to B D, also draw
A d and B d perpendicular to A B. Then divide A C, B C, H D, and
I D, into any number of equal parts, 1, 2, 3, &c., and draw lines joining
the corresponding numbers in HI and A B; also divide A d, B d, into the
same number of equal parts, a, b, c, &c., and draw lines from the point D
to these last divisions, then will the points where the lines a D, b D, c D,
&c., cut the lines 11, 22, 33, &c., be so many points in the required seg-
ment. (Fig. 83.)
PROB. XVII. To find the length of any given arc of a circle, A B.
From A and B, as centres, with radius equal to a quarter of the chord of
the arc A B, describe arcs cutting the given arc in C, and its chord in D;
join C D, which will equal half the length of the arc A B nearly.
(Fig. 84.)
PROB. XVIII. To draw a straight line equal in length to any given
portion of the circumference of a circle.
Let A BCD be the circle, and let A a, a b, b B, be the portions of the
circumference of which the length is required; draw the two diameters
BD and AC at right angles to each other, and at the end of the latter draw
the tangent line A e; then divide the radius EC into four equal parts, and
set off three of them from C to F on the diameter produced; then draw
lines from F through the points a, b, B, cutting the tangent line A e, in
c, d, e; so shall the lines A c, cd, de, be equal in length to the arcs A a,
ab, b B, and the whole line A e equal to the quadrant A B. (Fig. 85.)
PROB. XIX. To bisect any given triangle A BC.
Upon any one of the sides, as A B, describe a semicircle, which bisect
in the point D; then from B as a centre with radius BD describe an arc
190
PRACTICAL GEOMETRY.
cutting A B in E, through which point draw the line EF parallel with
the side AC; then will the line EF bisect the given triangle A B C.
(Fig. 86.)
PROB. XX. To reduce a given rectilinear figure, ABCDEFGA,
of any number of sides, to a triangle of equal area.
Join any two alternate angles, as A C, and through the intermediate
angle B, draw BH parallel to A C, cutting one of the adjoining sides in H,
and join C H, then will the triangle C B a, added to the figure, be equal
to the triangle a A H taken out of the same; in like manner join H D, and
draw GI parallel to the same through the intermediate point G, producing
it to cut the side A G (also produced) in I, and join ID. Next join D F,
and through E draw a line parallel thereto, cutting the side G F produced
in K, and join D K; lastly, join D G, and draw parallel to the same
through the point K a line cutting the side A G produced in L, then join
D L, and the triangle ID L will be equal in area to the given rectilinear
figure ABCDEFGA. (Fig. 87.)
PROB. XXI. To form a rectangle of the largest area, in a given
triangle, A B C.
Bisect any two sides A B and B C in D and E, and from those points
draw lines D F and E G perpendicular to the third side AC and join D E,
then will the rectangle D E F G be the largest which can be inscribed in
the given triangle. (Fig. 88.)
PROB. XXII. To form a square equal in area to a given triangle,
A BC.
On the longest side produced set off CD, equal half the perpendicular
height BE; and at C erect the perpendicular C F; then on A D describe
a semicircle cutting C F in G, and on C G form the square C G H I, which
will be equal in area to the given triangle. (Fig. 89.)
PROB. XXIII. To find the side of a square equal in area to a given
rectangle, A B CD.
Produce the lesser side A B of the rectangle till A E equal the longer
side A D; then describe upon A E a semicircle cutting B C in F, and join
A F, which will be the side of the square required. (Fig. 90.)
PROB. XXIV. To find the side of a square equal to the difference be-
tween two given squares.
Let the sides of the two given squares be A and B. Then draw the
line C D equal to the lesser line B, and at one of its extremities erect the
indefinite perpendicular D E; then with radius equal to A, and from Cas
a centre, describe an arc cutting this perpendicular in E; then D E will
equal the side of the square required. (Fig. 91.)
PROB. XXV. To find the side of a square equal in area to any number
of given squares.
Let the lines A, B, and C, be the sides of the given squares. Draw D E
equal to A, and at the end of it erect the perpendicular E F equal to B;
join D F and perpendicular to it, from the point F, erect the perpendicular
G F equal to C; then join D G, which will be equal to the side of a square
equal in area to the three squares on A, B, and C. (Fig. 92.)
PRACTICAL GEOMETRY.
191
PROB. XXVI. To find the side of a square nearly equal in area to a
given circle, A BCD.
Draw the two diameters, A C, BD, at right angles to each other; then
bisect the radius E C in F, and through D and F produce the straight line
D G cutting the circle in G, then will D G equal the side of the square
required. (Fig. 93.)
PROB. XXVII. Given the side of a regular polygon of any number of
sides (not exceeding twelve), to find the radius of the circle in which it may
be inscribed.
Multiply the given side of the polygon by the number which stands in
column b, opposite its proper name in the annexed Table of Polygons; the
product will be the radius required.
Thus, suppose the polygon was to be an octagon, and each side 12, then
1.3065628 × 12 = 15.6687536 would be the radius sought. Take 15.67
as a radius from a diagonal scale, describe a circle, and from the same
scale, taking off 12, it may be applied as the side of an octagon in that circle.
PROB. XXVIII. Given the radius of a circle, to find the side of any
regular polygon (not having more than twelve sides) inscribed in it.
Multiply the given radius by the number in column c, standing opposite
the number of sides of the proposed polygon; the product is the length of
the side required,
Thus, suppose the radius of the circle to be 5, then 5 × 1·732051 =
8-66025, will be the side of the inscribed equilateral triangle.
Table of Polygons.

No.
of
Names.
sides.
Multipliers
for areas.
(a.)
Radius of
circum. cir.
Factors
for sides.
(ხ.)
(c.)
3 Trigon
0.4330127
0.5773503
1.732051
4
Tetragon, or Square
1.0000000
0.7071068
1.414214
5 Pentagon
1.7204774
0.8506508
1.175570
6
Hexagon
2.5980762 1.0000000
1.000000
7 Heptagon
3.6339124 1.1523824 0.867767
8
Octagon
4-8284271
1.3065628 0.765367
9 Nonagon
6.1818242
1.4619022 0.684040
10 Decagon
7.6942088
1.6180340 0.618034
11
Undecagon
9.3656399
1.7747324
0.563465
12 Dodecagon
11.1961524
1.9318517
0.517638
192
WEIGHTS AND MEASURES.
CHAP. III.
MENSURATION.
SECT. I.-Comparison of English and French Weights and Measures.
THE following is a comparative Table of the Weights and Measures of
England and France, which was published by the Royal and Central
Society of Agriculture of Paris, in the Annuary for 1829, and founded
on a Report, made by Mr. Mathieu, to the Royal Academy of Sciences of
France, on the bill passed the 17th of May, 1824, relative to the Weights
and Measures termed "Imperial," which are now used in Great Britain.
Measures of Length.
ENGLISH.
1 Inch (1-36th of a yard)
1 Foot (1-3rd of a yard)
Yard Imperial
Fathom (2 yards)
Pole, or perch (5½ yards)
Furlong (220 yards)
Mile (1760 yards)
1 Millimetre
1 Centimetre
FRENCH.
1 Decimetre
1 Metre
Myriametre
1 Yard square
ENGLISH.
1 Rod (square perch)
1 Rood (1210 yards square)
1 Acre (4840 yards square)
FRENCH.
1 Metre square
1 Are
1 Hectare
Il ti
|| ||
FRENCH.
2.539954 centimetres.
3.0479449 decimetres.
0-91438348 metre.
1-82876696 metre.
5.02911 metres.
201.16437 metres.
1609-3149 metres.
ENGLISH.
0.03937 inch.
0.393708 inch.
3.937079 inches.
39.37079 inches.
3.2808992 feet.
1.093633 yard.
6.2138 miles.
Square Measures.
ENGLISH.
1 Pint (1-8th of a gallon)
1 Quart (1-4th of a gallon)
1 Gallon imperial
•
Solid Measures.
FRENCH.
0.836097 metre square.
25.291939 metres square.
10-116775 ares.
0.404671 hectare.
ENGLISH.
1.196033 yard square.
0.098845 rood.
2.473614 acres.
FRENCH.
0.567932 litre.
1.135864 litre.
4.54345794 litres.
WEIGHTS AND MEASURES.
193
ENGLISH.
1 Peck (2 gallons)
1 Bushel (8 gallons)
1 Sack (3 bushels)
1 Quarter (8 bushels) .
1 Chaldron (12 sacks)
•
FRENCH.
1 Litre
1 Decalitre
1 Hectolitre
||
FRENCH.
9-0869159 litres.
36-347664 litres.
1.09043 hectolitre.
2.907813 hectolitres.
13.08516 hectolitres.
{
ENGLISH.
1.760773 pint.
0-2200967 gallon.
2.2009667 gallons.
. 22.009667 gallons.
ENGLISH TROY.
Weights.
FRENCH.
0.06477 gramme.
1.55456 gramme.
1 Grain (1-24th of a pennyweight)
1 Pennyweight (1-20th of an ounce)
1 Ounce (1-12th of a pound troy)
1 Pound troy imperial
ENGLISH AVOIRDUPOIS.
1 Drachm (1-16th of an ounce)
1 Ounce (1-16th of a pound)
1 Pound avoirdupois imperial
1 Hundred-weight (112 pounds)
1 Ton (20 hundred-weight
1 Gramme
1 Kilogramme
FRENCH.
31.0913 grammes.
0-3730959 kilogramme.
FRENCH.
1.7712 gramme.
28.3384 grammes.
0.4534148 kilogramme.
50-78246 kilogrammes.
1015-649 kilogrammes.
ENGLISH.
15.438 grains troy.
0-643 pennyweight.
0.03216 ounce troy.
{{
2.68027 pounds troy.
Angular Measure.
2.20548 do. avoirdupois.
In France, the centesimal division of the circle is frequently employed,
in which the whole circumference is divided into 400 degrees, each de-
gree into 100 minutes, each minute into 100 seconds, &c.
1 Degree
CENTESIMAL.
1 Minute
1 Second
1 Degree
1 Minute
1 Second
ENGLISH.
|| ||
ENGLISH.
54 minutes.
32.4 seconds.
•324 second.
CENTESIMAL.
14 degree.
1.85185 minute.
3.08641 seconds.
194
MENSURATION OF SUPERFICIES.
SECT. II.-Mensuration of Superficies.
TRIANGLES.
Let b, c, and d, represent the three sides of a triangle (see fig. 95);
ß, y, and ♪, the angles opposite those sides respectively; and h the per-
pendicular height from the vertex to the base b; then the
area= = bh,
or = 1 bc. sins = 1 c d. sin ß = db. sin y.
d² — c² b) 2 b
Or, = ✓ d² - (d²
26
the least.
+
where b is the greatest side and c
2
If half the sum of the three sides or
log of area =
area=
b + c + d
b+c+
2
=s, then the
√ s (s — b). (s — c) . (s — d), and the
{log s + log (s — b) + log (s — c) + log (8 — d) }.
QUADRILATERALS, OR FOUR-SIDED FIGURES.
Square, Rectangle, Rhombus and Rhomboid:-To obtain the area,
multiply the perpendicular height (h, fig. 96) by the base (b) on which
it falls.
The area of a Trapezium is best found by dividing it into two triangles
(as fig. 17), the areas of which may be found by the foregoing rules.
The area of a Trapezoid (fig. 16) may either be found in the same way,
or by multiplying half the sum of the two parallel sides (a + b) by the
perpendicular distance between them (h).
POLYGONS.
To obtain the area of any regular polygon, having less than twelve
sides, multiply the square of one of the sides by the number found in
column a, of the Table of Polygons, page 191. Or, generally, if the
length of one of the equal sides, and n the number of them; then the
area=12 tan.
The area of an irregular
into triangles, as in fig. 97.
it, by Prob. XX., page 190.
n
4
n
(90 On - 180).
N
polygon may be determined by dividing it
Or by forming one triangle equal in area to
CIRCLES.
Let d represent the diameter, c the circumference, a the area, and p =
3.14159; then the
с
Diameter = d
4 a
<=2
a
Ρ
с
p
4 a
Circumference = c =
c = pd
Area = a=
p d²
4
d
= 2√ pa.
c²
dc
= '7854 d².
4p
4
с
4 a
c²
and P
p =-
•
d2
4 a
MENSURATION OF SUPERFICIES.
195
Circular Arcs.-If r represents the radius, and d the diameter of the
circlè; s the sine, and v₁ the versed sine of the arc; c the chord of half
the arc, v, the versed sine of half the arc; and m the measure in degrees
of the whole arc; then
the length of the arc 0174533 r m ;
or = 2 d
✓ 3
3v₁
nearly;
3 d
V2
5 v1
or
· Z { 5 d
+4√ dv₂} nearly;
5d-3 v₂
8c-2s
or =
nearly.
3
And the following relations between the several quantities, from which
any one of them may be obtained, will be found useful, viz. :—
V₁ = r
√ p² — s²
c = √ s² +
8 = √ r²
d =
$2
01
+21
v
v₂ ²
1
2
...
(r — v₁)²
(1.)
(2.)
(3.)
(4.)
Circular Sectors.-Let d represent the diameter of the circle, 7 the
length of the arc of the sector, and m its measure in degrees; then the
area = Zrl.
or = ·00218 d² m.
Circular Segments.-Let d represent the diameter of the circle, v the
versed sine, c₁ the chord of the whole arc, and c₂ the chord of half the
arc; then the
area = {√ (dv — v²) + √ dv} nearly;
or = v(dv -
v²) nearly;
or=&v (c₁ + c₂) nearly;
2
or = √(c+v²) nearly.
V
Or the area of any segment, as fig. 98, may be obtained by finding the
area of the sector A B C D, and subtracting from it the area of the
triangle A C D.
The area of a circular zone, as E F G H, may be found by subtracting
the area of the segment G H I from the area of the segment E GIH F.
PARABOLA.
The area of a parabola is equal to two-thirds of the product of the base
x the perpendicular height.
Parabolic Arcs.-Let x be the abscissa a b, fig. 99, measured from the
vertex a, and y the corresponding right ordinate cb; then the length of
the arc c a d is
= 2√ (y² + $x²) nearly;
or = } { √ (y² + # x²)
y² + z x²
y
}
Parabolic Frustum, or Zone.-The word zone is here used to denote
the space c d e g (fig. 99), contained between the two parallel double ordi-
196
MENSURATION OF SUPERFICIES.
nates c d and e g.
Let y₁ = the length of the double ordinate c d, and
y2 = the length of eg, and d = the perpendicular distance between them
bf; then the
Y2
area of the zone =
f d Y 2³ — y i
Y ₂² — Yı
3
3
2
2
ELLIPSE.
The area is equal to the product of the transverse diameter x the con-
jugate diameter x 785398.
The periphery or circumference is equal to the sum of the transverse
and conjugate diameters x 1.57079.
The foregoing is only an approximation to the periphery, although suf-
ficiently near the truth for ordinary purposes; but where greater accuracy
is required the following series may be employed. Let t represent the
C2
transverse axis, c the conjugate, p = 3.14159, &c., and d = 1 – ; then
d
3 d²
pt {1
22
22.42
will be the periphery.
32.5 ď³
22.42.62
32.52.7 dt
22. 42. 62. 82
&c.}
Elliptic Segments-To find the area of the elliptic segment abc (fig.
100), find the area of the corresponding circular segment, dbe, described
on the same axis (bƒ) to which the cutting line or base of the segment a c
is perpendicular. Then, as this axis (bf): the other axis (gh): the
circular segment (dbe): the elliptic segment (abc).
Elliptic Arcs.-Let t represent the semi-transverse, and c the semi-
conjugate diameters of the ellipse, and d the distance of the ordinate from
the centre, then the length of the arc contained between the ordinate and
the parallel semi-axis will be
=d{1+ ď² +
c?
4t2 c²
2
d+ +
6 t
40 to
+2
c²
or make
8 tª c² — 4t² ct + co
112 t¹2
=r; then the
d® + &c.}
12
t² — fr d²
length of the arc = d
nearly.
t2
ť² - d²
HYPERBOLA.
The area of an hyperbola or hyperbolic segment may be found as
follows:-let t and c represent the semi-transverse and semi-conjugate
diameters, 2y the double ordinate which cuts off the segment, and x its
abcissa; also q =
area = 2 x y {3-325
{}}
X
2t+x
; then the
9
92
3.5.7
93
3.5.7.9
&c.}
or
4 cx
15
{4√ (2tx + & x²) + √2tx} nearly.
Hyperbolic Arcs.-The notation being the same, the following approx-
imation may be employed to obtain the length of an hyperbolic arc.
120 ct + (19² + 21 c²) 4 x
Arc
+y, nearly.
120 c² t +(91² + 21 c²) 4 x
MENSURATION OF SOLIDS.
197
SECT. III.-Mensuration of Solids.
PARALLELOPIPEDON, PRISM, OR CYLINDER.
Surface. Multiply the perimeter of one end by the length or per-
pendicular height, to which add the area of the two ends, the sum will be
the surface.
Solidity = the area of the base x the perpendicular height.
PYRAMID OR CONE.
Surface. Multiply half the perimeter by the slant height, to which
add the area of the base, the sum is the surface.
Solidity the area of the base x one-third the perpendicular height.
Frustum of a Pyramid or Cone. Surface.-Multiply half the sum of
the perimeters of the two ends by the perpendicular height.
Solidity.—Add a diameter or side of the greater end to one of the less,
and from the square of the sum subtract the product of the said two
diameters or sides; then multiply the remainder by one-third of the
height, and this product by 785398 for circles, or by the proper multi-
plier for polygons; the last product will be the capacity.
That is, let D equal the greater diameter, d the less, h the perpendicu-
lar height, and p=785398 for cones, or for any pyramid the proper
multiplier from column (a) in the table at page 191, then
Solidity=ph (D² + D d + d²).
SPHERE.
Surface the diameter x the circumference,
the square of the
diameter × 3.14159, — the square of the circumference × 3183.
Solidity = the cube of the diameter × ·5236, the cube of the cir-
cumference x ·01688.
Spherical Segment.-Let d equal the diameter of the aphere, r the
radius of the base of the segment, and h its height; then the curved sur-
face = 3.14159 d h.
Solidity=0·5236 h² (3d-2 h);
or = 0·5236 h (3r² + h²).
The surface and solidity of a spherical zone may be obtained by taking
the difference between the two segments.
CONOIDS.
A conoid is the solid generated by the revolution of a conic section
about one of its axis, and is called a spheroid, paraboloid, or hyperboloid,
according to the section from which it is produced.
Spheroids. When the ellipse revolves about its transverse axis, it is
called an oblong or prolate spheroid; when about its conjugate axis, an
oblate spheroid; and when about any other of its diameters, a universal
spheroid, in which latter case its figure is somewhat resembling a heart.
To obtain the solidity of a spheroid, multiply the square of the revolving
axis by the fixed axis, and the product by 0-5236.
198
MENSURATION OF SOLIDS.
Paraboloid.-Let y be the radius of the circular base, and x the alti-
tude of the solid; then
Surface
0·5236y {(y² + 4x²)* — y³} .
х2
Solidity = 1.5708 y² x.
Hyperboloid. Let t equal the transverse axis, r the radius of the base,
a the altitude, and p the parameter; then the
Solidity = p²
1
t + // a
t + a
THE REGULAR OR PLATONIC SOLIDS.
The regular or Platonic bodies are five in number, and have already
been described at page 185.
1. To find either the surface or the solid content of any of the regular
bodies. Multiply the proper tabular area or surface (taken from column
(a) in the following table,) by the square of the linear edge of the solid,
for the superficies. And
Multiply the tabular solidity in column (b) of the table by the cube of
the linear edge for the solid content.
Surfaces and Solidities of Regular Bodies, the side being unity or 1.

No. of
sides.
Name.
Surface.
(a)
Solidity.
(6)
46
Tetraedron
1.7320508
0.1178513
Hexaedron
6.0000000
1.0000000
8
Octaedron
3.4641016
0.4714045
12
Dodecaedron
20.6457288
7-6631189
20
Icosaedron
8.6602540
2.1816950
2. The diameter of a sphere being given, to find the side of any of the
Platonic bodies, that may be either inscribed in the sphere, or circum-
scribed about the sphere, or that is equal to the sphere.-Multiply the
given diameter of the sphere by the proper or corresponding number, in
the following table, answering to the thing sought, and the product will
be the side of the Platonic body required.

The diam. of a
sphere being 1;
That may be
inscribed in the
sphere, is
That is equal to
to the sphere, is
the side of a
That may be cir-
cumscribed about
the sphere, is
Tetraedron
0.8164966
2.4494897
1.6439480
Hexaedron
0.5773503 1.0000000
0.8059958
Octaedron
0.7071068 1-2247447
1.0356300
Dodecaedron 0.3568221 0.4490279
0-4088190
Icosaedron
0.5257309 0.6615845
0-6214433
MENSURATION OF SOLIDS.
199
3. The side of any of the five Platonic bodies being given, to find the
diameter of a sphere, that may either be inscribed in that body, or circum-
scribed about it, or that is equal to it.-As the respective number in the
table above, under the title inscribed, circumscribed, or equal, is to 1, so
is the side of the given Platonic body to the diameter of its inscribed, cir-
cumscribed, or equal sphere.
4. The side of any one of the five Platonic bodies being given, to find
the side of the other four bodies, that may be equal in solidity to that of
the given body.—-As the number under the title equal in the last column
of the table above, against the given Platonic body, is to the number
under the same title, against the body whose side is sought, so is the side
of the given Platonic body to the side of the body sought.
Besides these there are thirteen demiregular bodies, called Solids of
Archimedes. They are described in the Supplement to Lidonne's Tables
de tous les Diviseurs des Nombres, &c., Paris, 1808; twelve of them were
described by Abraham Sharp, in his Treatise on Polyedra.
TO FIND THE CONTENTS OF SURFACES AND SOLIDS NOT REDUCIBLE TO ANY
KNOWN FIGURE, BY THE EQUIDISTANT ORDINATE METHOD.
The general rule is included in this proposition, viz. :-If any right
line be divided into any even number of equal parts, 1, 2, 3, 4, &c., (fig.
101,) and at the points of division be erected perpendicular ordinates 1 A,
2 B, 3 C, &c., terminated by any curve A C G: then, if a be put for the
sum of the first and last ordinates, 1 A, 7 G, e for the sum of the even
ordinates, 2 B, 4 D, 6 F, &c., viz., the second, fourth, sixth., &c., and o for
the sum of all the rest, 3 C, 5 E, &c., viz., the third, fifth, &c., or the odd
ordinates, excepting the first and last: then, the common distance 1, 2,
2, 3, &c., of the ordinates being multiplied into the sum arising from the
addition of s, four times e, and twice o, one third of the product will be the
area 1 A, G 7, very nearly.
That is,
s + 4e + 2o
3
D=
D = area, D being = A C = CE, &c.
The same theorem will equally serve for the contents of all solids, by
using the sections perpendicular to the axis instead of the ordinates. The
proposition is quite accurate, for all parabolic and right lined areas as
well as for all solids generated by the revolutions of conic sections or right
lines about axes, and for pyramids and their frustums. For other areas
and solidities it is an excellent approximation.
The greater the number of ordinates, or of sections, that are taken, the
more accurately will the area or the capacity be determined. But in a
great majority of cases five equidistant ordinates, or sections, will lead to a
very accurate result.
200
TRIGONOMETRY.
CHAP. IV.
TRIGONOMETRY.
SECT. I.-Definitions and Trigonometrical Formulœ.
1. Plane Trigonometry is that branch of mathematics by which we
learn how to determine or compute the unknown parts of a plane, or
rectilinear triangle, from those which are known, when that is possible.
Every triangle consists of six parts, viz., three sides, and three angles
opposite those sides. And any three of these being given (excepting only
when the three angles are given,) the others may always be determined
from them.
The determination of the mutual relation of the sines, tangents, secants,
&c., of the sums, differences, multiples, &c., of arcs or angles; or the in-
vestigation of the connected formulæ, is also usually classed under plane
trigonometry.
2. Let A C B (fig. 102,) be a rectilinear angle: if about C as a centre,
with any radius C A, a circle be described, intersecting C A, C B, in
A, B, the arc A B is called the measure of the angle A C B.
3. The circumference of a circle is supposed to be divided or to be
divisible into 360 equal parts, called degrees; each degree into 60 equal
parts, called minutes; each of these into 60 equal parts, called seconds;
and so on to the minutest possible subdivisions. Of these, the first is
indicated by a small circle, the second by a single accent, the third by a
double accent, &c. Thus, 47° 18′ 34" 45"", denotes 47 degrees, 18
minutes, 34 seconds, and 45 thirds. The number of degrees, minutes,
seconds, &c., contained in the arc A B of the circle described from the
angular point C, and which is contained between the two legs A C, A B,
is called the measure of the angle A C B, which is then said to be an
angle of so many degrees, minutes, seconds, &c. Thus, since a quadrant
or quarter of a circle, contains 90 degrees, and a quadrantal arc is the
measure of a right angle, a right angle is said to be one of 90 degrees.
4. The complement of an arc is its difference from a quadrant, as B E;
and the complement of an angle is its difference from a right angle, as
EC B.
5. The supplement of an arc is its difference from a semicircle, as
A' E B; and the supplement of an angle is its difference from two right
angles, as A' C B.
6. The sine of an arc is a perpendicular let fall from one extremity
upon a diameter passing through the other, as B D.
7. The versed sine or versine of an arc is that part of the diameter
which is intercepted between the foot of the sine and the arc, as D A.
1
PLANE TRIGONOMETRY.
201
8. The tangent of an arc is a right line which touches it in one extre-
mity, and is limited by a right line drawn from the centre of the circle
through the other extremity, as A T.
9. The secant of an arc is the radial line which thus limits the tangent,
as CT.
10. These are also, by way of accommodation, said to be the sine, tan-
gent, &c., of the angle measured by the aforesaid arc, to its determinate
radius.
11. The cosine of an arc or angle, is the sine of the complement of that
arc or angle, as GB: the cotangent of an arc or angle is the tangent of the
complement of that arc or angle, as E M. And the co-versed sine E G, and
cosecant C M, are similarly the versed sine and secant of the complement.
12. The suversine of an arc is the versed sine of its supplement, as A D.
Note.-The following contractions are employed to express the fore-
going terms, viz. :—
For the radius of the arc A B we write rad A B,
sine
tangent
ditto
sin A B,
ditto
tan AB,
secant
ditto
sec A B,
versine.
ditto
versin A B,
cosine
ditto
cos AB,
cotangent...
ditto
cot A B,
cosecant
ditto
cosec A B,
coversine....
ditto
covers A B.
SECT. II.-General Propositions.
I. The chord of any arc is a mean proportional between the versed sine
of that arc and the diameter of the circle.
II. As radius is to the cosine of any arc, so is twice the sine of that arc
to the sine of double the arc.
III. The secant of any arc is equal to the sum of its tangent, and the
tangent of half its complement.
IV. The sum of the tangent and secant of any arc, is equal to the tan-
gent of an arc exceeding that by half its complement. Or, the sum of the
tangent and secant of an arc is equal to the tangent of 45° plus half the arc.
V. The chord of 60° is equal to the radius of the circle; the versed sine
and cosine of 60° are each equal to half the radius, and the secant of 60° is
equal to double the radius.
VI. The tangent of 45° is equal to the radius.
VII. The square of the sine of half any arc or angle is equal to a rect-
angle under half the radius and the versed sine of the whole arc; and the
square of its cosine is equal to a rectangle under half the radius and the
versed sine of the supplement of the whole arc or angle.
VIII. The rectangle under the radius and the sine of the sum or the
difference of two arcs is equal to the sum or the difference of the rectangles
under their alternate sines and cosines.
Р
202
PLANE TRIGONOMETRY.
IX. The rectangle under the radius and the cosine of the sum or the
difference of two arcs, is equal to the difference or the sum of the rect-
angles under their respective cosines and sines.
X. As the difference or sum of the square of the radius and the rectangle
under the tangents of two arcs, is to the square of the radius; so is the
sum or difference of their tangents, to the tangent of the sum or difference
of the arcs.
XI. As the sum of the sines of two unequal arcs, is to their difference;
so is the tangent of half the sum of those two arcs to the tangent of half
their difference.
XII. Of any three equidifferent arcs, it will be as radius is to the
cosine of their common difference, so is the sine of the mean arc, to half
the sum of the sines of the extremes; and, as radius is to the sine of the
common difference, so is the cosine of the mean arc to half the difference
of the sines of the two extremes.
(A.) If the sine of the mean of three equidifferent arcs (radius being
unity) be multiplied into twice the cosine of the common difference, and
the sine of either extreme be deducted from the product, the remainder
will be the sine of the other extreme.
(B.) The sine of any arc above 60°, is equal to the sine of another arc
as much below 60°, together with the sine of its excess above 60°.
Cor. From this latter proposition, the sines below 60° being known,
those of arcs above 60° are determinable by addition only.
XIII. In any right-angled triangle, the hypothenuse is to one of the
legs, as the radius is to the sine of the angle opposite to that leg; and one
of the legs is to the other as the radius is to the tangent of the angle oppo-
site to the latter.
XIV. In any plane triangle, as one of the sides is to another, so is the
sine of the angle opposite to the former to the sine of the angle opposite to
the latter.
XV. In any plane triangle it will be, as the sum of the sides about the
vertical angle is to their difference, so is the tangent of half the sum of the
angles at the base, to the tangent of half their difference.
XVI. In any plane triangle it will be, as the cosine of the difference of
the angles at the base, is to the cosine of half their sum, so is the sum of
the sides about the vertical angles to the third side. Also, as the sine of
half the difference of the angles at the base, is to the sine of half their sum,
so is the difference of the sides about the vertical angle to the third side,
or base*.
XVII. In any plane triangle it will be, as the base is to the sum of the
two other sides, so is the difference of those sides to the difference of the
segments of the base made by a perpendicular let fall from the vertical
angle.
* These propositions were first given by Thacker in his Mathematical Miscellany, pub-
lished in 1743; their practical utility has been subsequently shown by Professor
Wallace, in the Edinburgh Philosophical Transactions.
PLANE TRIGONOMETRY.
203
XVIII. In any plane triangle it will be, as twice the rectangle under
any two sides, is to the difference of the sum of the squares of those two
sides and the square of the base, so is the radius to the cosine of the angle
contained by the two sides.
Cor. When unity is assumed as radius, then if A C, A B, B C, are
the sides of a triangle, and C the angle opposite the side A B, this
A C² + BC2 A B2
: and similar expressions for
Prop. gives cos C=
the other angles.
2CB.CA
XIX. As the sum of the tangents of any two unequal angles is to their
difference, so is the sine of the sum of those angles to the sine of their
difference.
XX. As the sine of the difference of any two unequal angles is to the
difference of their sines, so is the sum of those sines to the sine of the sum
of the angles.
These and other propositions are the foundation of various formulæ, for
which the reader who wishes to pursue the inquiry may consult the best
treatises on Trigonometry.
SECT. III.—Solution of the Cases of Plane Triangles.
Although the three sides and three angles of a plane triangle, when
combined three and three, constitute twenty varieties, yet they furnish
only three distinct cases in which separate rules are required.
CASE I.
When a side and an angle are two of the given parts.
The solution may be effected by Prop. XIV. of the preceding section,
wherein it is affirmed that the sides of plane triangles are respectively.pro-
portional to the sines of their opposite angles.
In practice, if a side be required, begin the proportion with a sine,
and say,
As the sine of the given angle,
Is to its opposite side;
So is the sine of either of the other angles,
To its opposite side.
If an angle be required, begin the proportion with a side, and say,
As one of the given sides,
Is to the sine of its opposite angle;
So is the other given side,
To the sine of its opposite angle.
The third angle becomes known by taking the sum of the two former
from 180°.
Note. It is usually best to work the proportions in trigonometry by
means of the logarithms, taking the logarithm of the first term from the
204
PLANE TRIGONOMETRY.
sum of the logarithms of the second and third, to obtain the logarithm of the
fourth term. Or, adding the arithmetical complement of the logarithm of
the first term to the logarithms of the other two, to obtain that of the fourth.
CASE II.
When two sides and the included angle are given.
The solution may be effected by means of Props. XV. and XVI. of the
preceding section.
Thus: take the given angle from 180°, the remainder will be the sum of
the other two angles.
Then say,
As the sum of the given sides,
Is to their difference;
So is the tangent of half the sum of the remaining angles;
To the tangent of half their difference.
Then, secondly say,
Or,
As the cosine of half the said difference,
Is to the cosine of half the sum of the angles;
So is the sum of the given sides,
To the third, or required side.
As the sine of half the diff. of the angles,
Is to the sine of half their sum;
So is the difference of the given sides,
To the third side.
Example.—In the triangle A B C (Fig. 9) are given A C = 450, B C
540, and the included angle C = 80°; to find the third side, and the
two remaining angles. Then,
Log (BC-AC
90)
Log tan (A + B =
50°)
=
1.954243
='10.076187
12.030430
Log (BO+AC
990)
2.995635
Log tan (½ A – B = 6°11′)
9.034795
Then, Log cos († A + B = 50°)
Log (BC+A C
9.808068
990)
2.995635
12.803703
Log cos († A – B = 6°11′)
9.997466
Log (AB
640·08) = 2.806237
(A
Also, ½ (A + B) + † (A — B) = 56° 11′ = A; and † (A + B) — 1
B)
= 43° 49′ = B.
Here, much time will be saved in the work by taking log cos (A + B)
from the tables, at the same time with log tan (A + B); and log cos
PLANE TRIGONOMETRY,
205
(A — B) as soon as log tan ½ (A - B) is found. Observe, also, that the
log of B C + AC is the same in the second operation as in the first,
Thus the tables need only be opened in five places for both operations.
Another solution to Case II.
.
Supposing C to be the given angle, and C A, CB, the given sides; then
the third side may be found by this theorem, viz. :—
C²
AB=√ (A C² + BC-2AC. CB. cos C).
Thus, taking A C='450, BC = 540, C = 80°, its cos 1736482
AB=√(450 +5402 - 2 x 450 x 540 × 1736482)
={902 (52 + 622 × 5 × 6 × 1736482)}
X
90 ✓ 50.58118 = 90 × 7·112 = 640·08, as before.
CASE III.
When the three sides of a plane triangle are given, to find the angles.
1st Method.—Assume the longest of the three sides as base, then say,
conformably with Prop. XVI., last section,
As the base,
Is to the sum of the two other sides;
So is the difference of those sides,
To the difference of the segments of the base.
Half the base added to the said difference gives the greater segment,
and made less by it gives the less; and thus, by means of the perpendicular
from the vertical angle, divides the original triangle into two, each of which
falls under the first case.
2nd Method.—Find any one of the angles by means of Prop. XVIII.
of the preceding section; and the remaining angles either by a repe-
tition of the same rule, or by the relation of the sides to the sines of
their opposite angles, viz. :—
cos C =
A C²+ BC2 - A B²
; cos B =
2 AC. BC
BA² + AC² - BC2
A B² + BC² - A C²
2 AB. BC
and cos A
2AB.AC
RIGHT-ANGLED PLANE TRIANGLES.
Right-angled triangles may (as well as others,) be solved by means of
the rule to the respective case under which any specified example falls;
and it will then be found, since a right angle is always one of the data,
that the rule usually becomes simplified in its application.
When two of the sides are given, the third may be found by means of
the property in Geom., Prop. XVI., Sect. II.
Hypoth. =√(base² + perp.²)
Base =√(hyp.2 — perp.²) = √ (hyp. + perp.). (hyp. — perp.)
Perp. (hyp.2 - base2)=√(hyp. + base).. (hyp. - base.)
There is another method for right-angled triangles, known by the
phrase making any side radius; which is this.
206
PLANE TRIGONOMETRY.
"To find a side. Call any one of the sides radius, and write upon it
the word radius; observe whether the other sides become sines, tangents,
or secants, and write those words upon them accordingly. Call the word
written upon each side the name of each side: then say,
As the name of the given side,
Is to the given side;
So is the name of the required side,
To the required side."
"To find an angle. Call either of the given sides radius, and write
upon
it the word radius; observe whether the other sides become sines,
tangents, or secants, and write those words on them accordingly. Call the
word written upon each side the name of that side. Then say,
As the side made radius,
Is to radius ;
So is the other given side,
To the name of that side,
which determines the opposite angle.”
When the numbers which measure the sides of the triangle are either
under 12, or resolvable into factors which are each less than 12, the
solution may be obtained, conformably with this rule, easier without
logarithms than with them. For,
Let A BC (Fig. 103) be a right-angled triangle, in which A B, the
base, is assumed to be radius; BC is the tangent of A, and A C its secant,
to that radius; or, dividing each of these by the base, we shall have the
tangent and secant of A respectively, radius being unity. Tracing in like
manner the consequences of assuming BC (as fig. 104), and AC (as fig.
105), each for radius, we shall readily obtain these expressions.
1. perp.
base
= tan angle at base. (Fig. 103.)
2.
hyp.
= sec angle at base. (Fig. 103.)
base
base
3.
tan angle at vertex. (Fig. 105.)
perp.
hyp.
4.
sec angle at vertex. (Fig. 105.)
perp.
5.
perp.
= sin angle at base. (Fig. 104.)
hyp.
base
6.
sin angle at vertex. (Fig. 104.)
hyp.
SECT. IV.—On the application of Trigonometry to measuring Heights
and Distances.
Trigonometry receives its principal practical application in the opera-
tions of surveying, and measuring heights and distances; as, however, the
methods of its application (depending on the peculiar circumstances of
PLANE TRIGONOMETRY.
207
each case) are exceedingly various, we cannot lay down any general rules,
but must content ourselves with giving a selection of such examples
as are most likely to occur; and the principles developed in which
will be sufficient to guide any person in its further application to other
cases.
Example 1.
In order to find the distance between two trees, A and B (Fig. 9),
which could not be directly measured because of a pool which occupied
much of the intermediate space, I measured the distance of each of them
from a third object, C, viz., A C588, B C 672, and then at the point
=
C took the angle ACB between the two trees 55° 40. Required
their distance.
This is an example to Case II. of plane triangles, in which two sides,
and the included angle, are given. The work, therefore, may exercise the
student: the answer is 593.8.
Example 2.
Wanting to know the distance between two inaccessible objects, C and
D (fig. 106), which lay in a direct line from the bottom of a tower on
whose top I stood, I took the angles of depression of the two objects, viz.,
of the most remote 2510, of the nearest 57°. What is the distance between
them, the height of the tower A B being 120 feet.
HAD = 25° 30′, hence B A D=BAH-HAD = 64° 30′.
HAC 57° C, hence BAC =BAH
BAH-HAC = 33° 0.
Hence the following calculation, by means of the natural tangents.
For, if A B be regarded as radius, BD and BC will be the tangents of
the respective angles BAD, BA C, and C D the difference of those tan-
gents. It is, therefore, equal to the product of the difference of the
natural tangents of those angles into the height A B.
Thus, nat. tan 64° 30′ =
nat. tan 33°
difference
2.0965436
0.6494076
1.4471360
120
multiplied by height,
gives distance CD=173.6563200
* *The natural sines, tangents, &c., are easily obtained from Table IV.
by subtracting 10 from the characteristics, and then finding the natural
number answering to the logarithms with their characteristics so altered.
208
PLANE TRIGONOMETRY.
Example 3.
Standing at a measurable distance A B (Fig. 103), on a horizontal plane,
from the bottom of a tower, I took the angle of elevation of the top (C);
it is required from thence to determine the height of the tower.
In this case there would be given A B and the angle A, to find BC=
ABX tan A.
By logarithms, when the numbers are large, it will be log BC=
log A B + log tan A.
Note.-If angle A = 11° 19′ then BC
A B very nearly.
BC= AB
""
A=16 42
BC=AB
""
A=21 48
""
"}
""
A=26 34
BC = 1 A B
""
A=30 58
"7
""
A35 0
""
""
A 38 40
BC
""
""
""
A=45
= 45 0
BC
""
BC= & AB
BC=7AB
10
AB
A B, exactly.
To save the time of computation, therefore, the observer may set the
instrument to one of these angles, and advance or recede, till it accords
with the angle of elevation of the object; its height above the horizontal
level of the observer's eye will at once be known, by taking the appro-
priate fraction of the distance A B.
Example 4.
Wanting to know the height of a church steeple, to the bottom of
which I could not measure on account of a high wall between me and the
church, I fixed upon two stations at the distance of 93 feet from each
other, on a horizontal line from the bottom of the steeple, and at each of
them took the angle of elevation of the top of the steeple, that is, at the
nearest station 55° 54', at the other 33° 20′.
steeple.
Required the height of the
Recurring to figure 106, we have given the distance CD, and the
angles of elevation at C and D. The quickest operation is by means of
the natural tangents, and the theorem A B
CD
cot D-cot C
Thus cot D=cot 33° 20′ = 1·5204261
C=cot 55 54 = 6770509
Their difference = ·8433752
Hence A B =
93
-8433752
=110.27 feet.
Example 5.
Wishing to know the height of an obelisk standing at the top of a
regularly sloping hill, I first measured from its bottom a distance of 36
PLANE TRIGONOMETRY.
209
feet, and there found the angle formed by the inclined plane and a line
from the centre of the instrument to the top of the obelisk 41°; but after
measuring on downward in the same sloping direction 54 feet farther, I
found the angle formed in like manner to be only 23° 45'. What was the
height of the obelisk, and what the angle made by the sloping ground with
the horizon?
there are given in the
to find BC. It will be
B-A): A B (= 54)
The figure being constructed (see fig. 107),
triangle A CB, all the angles and the side A B,
obtained by this proportion, as sin C (= 17° 15'
:: sin A (= 23° 45′): BC = 73-3392. Then, in the triangle D B C are
known BC as above, BD=36, CBD 41°; to find the other angles
and the side CD. Thus, first, as CB+BD: CB-BD : : tan ½ (D+C)
= ½ (139°) : tan † (D — C) — 42° 24. Hence 69° 30′ + 42° 241
1
112° 541 = CD B, and 69° 30' 42° 24127° 5 BCD. Then,
=
sin B CD: BD :: sin C BD: CD = 51·86 height of the obelisk.
The angle of inclination D A E=HDA=CD B-90° = 22° 541'.
Remark. If the line B D cannot be measured, then the angle DAE of
the sloping ground must be taken, as well as the angles CA B and C B D.
In that case D A E + 90° will be equal to CD B: so that, after C B is
found from the triangle A CB, CD may be found in the triangle CBD,
by means of the relation between the sides and the sines of their opposite
angles.
Example 6.
Being on a horizontal plane, and wanting to ascertain the height of a
tower standing on the top of an inaccessible hill, I took the angle of ele-
vation of the top of the hill 40°, and of the top of the tower 51°, then
measuring in a direct line 180 feet farther from the hill, I took in the
same vertical plane the angle of elevation of the top of the tower 33° 45′.
Required from hence the height of the tower.
The figure being constructed (see fig. 108), there are given, A B = 180,
C A B = 33° 45′, A C B = CBE-CA E = 17° 15′, C B D = 11°,
BDC 180° — (90° — D B E) = 130°. And CD may be found from
=
the expression C D . rad¹ = A B. sin A. sin C B D. cosec A C B . sec.
D BE.
Or, using logarithms,
log A B = 180°
+ log sin A
+ log sin CBD =
+ log cosec A CB =
+log sec DBE
2.255273
9.744739
9.280599
33° 45'
11° 0′ =
17° 15′ = 10·527914
40° 0′ = 10·115746
41.924271
- log rad = 40.000000
log CD = 83.9983
1.924271
210
PLANE TRIGONOMETRY.
*
Example 7.
In order to determine the distance between two inaccessible objects A
and B (Fig. 108), on a horizontal plane, we measured a convenient base,
CD, of 536 yards, and at the extremities C and D took the following
angles, viz., DCB = 40° 16′, BC A = 57° 40′, CD A = 42° 22′, A D B
= 71° 7'. Required the distance A B.
First, in the triangle CD A are given all the angles, and the side C D
to find A. D. So, again, in the triangle CD B, are given all the angles,
and CD to find D B. Lastly, in the triangle D A B are given the two
sides AD, BD, and the included angle A D B, to find A B = 939-52
yards.
Remark.-In like manner the distances taken two and two, between
any number of remote objects posited around a convenient station line,
may be ascertained.
Example 8.
Suppose that in carrying on an extensive survey, the distance between
two spires A and B (Fig. 109) has been found equal to 6594 yards, and
that C and D are two eminences conveniently situated for extending the
triangles, but not admitting of the determination of their distance by actual
admeasurement: to ascertain it, therefore, we took at C and D the fol-
lowing angles, viz. :—
s
ACB=85° 46'
BCD = 23° 56′
Required CD from these data.
ADC=31° 48'
ADB= 68° 2′
In order to solve this problem, construct a similar quadrilateral A c db,
assuming cd equal to 1, 10, or any other convenient number: compute
Ab from the given angles, according to the method of the preceding ex-
ample. Then, since the quadrilaterals Acdb, A C D B, are similar, it
will be, as Ab :cd::AB:CD; from which CD is found to be equal to
4694 yards.
Example 9.
Given the angles of elevation of any distant object, taken at three places
in a horizontal right line, which does not pass through the point directly
below the object; and the respective distances between the stations; to
find the height of the object, and its distance from either station.
Let AEC (Fig. 110) be the horizontal plane, FE the perpendicular
height of the object above that plane, A, B, C, the three places of obser-
vation, FA E, F BE, FCE, the angles of elevation, and A B, B C, the
given distances. Then, since the triangles AEF, BEF, CEF, are all
right angled at E, the distances A E, BE, CE, will manifestly be as the
cotangents of the angles of elevation at A, B, and C.
*"hine are two big to be tu
PLANE TRIGONOMETRY.
211
Put ABD, B Cd, E F = x, and then express algebraically
the theorem given in Geom., which in this case becomes,
A E². BC+C E². A B = BE². AC + AC. A B.BC.
The resulting equation is
dx² (cot A)² + D x² (cot C)² = (D + d) x² (Cot B)² + (D + d) D d.
From which is readily found

x =
✓
(D + d) D d
-
d (Cot A)² + D (cot C)² (D + d) (cot B)² *
Thus E F becoming known, the distances A E, BE, CE, are found, by
multiplying the cotangents of A, B, and C, respectively, by E F.
Remark. When D = d, or D + d 2D = 2d, that is, when the point
B is midway between A and C, the algebraic expression becomes,
x=d÷√(cot A)² + (cot C)² — (cɔt B)²,
which is tolerably well suited for logarithmic computation. The rule
may, in that case, be thus expressed.
Double the log cotangents of the angles of elevation of the extreme sta-
tions, find the natural numbers answering thereto, and take half their sum ;
from which subtract the natural number answering to twice the log cotan-
gent of the middle angle of elevation: then half the log of this remainder
subtracted from the log of the measured distance between the first and
second, or the second and third stations, will be the log of the height of
the object.
The distance from either station will be found as above.
Note.—The case explained in this example, is one that is highly useful,
and of frequent occurrence. An analogous one is when the angles of
elevation of a remote object are taken from the three angles of a triangle
on a horizontal plane, the sides of that triangle being known, or measurable :
but the above admits of a simpler computation, and may usually be employed.
Example 10.
From a convenient station P (Fig. 111), where could be seen three
objects, A, B, and C, whose distances from each other were known (viz.
A B 800, A C600, BC= 400 yards), I took the horizontal angles
APC = 33° 45', BPC = 22° 30′. It is hence required to determine
the respective distances of my station from each object.
Here it will be necessary, as preparatory to the computation, to describe
the manner of
Construction.-Draw the given triangle A B C from any convenient
scale. From the point A draw a line AD to make with AB an angle
equal to 22° 30′, and from B a line BD to make an angle DBA =
33° 45'. Let a circle be described to pass through their intersection D,
and through the points A and B. Through C and D draw a right line to
meet the circle again in P: so shall P be the point required. For, drawing
PA, PB, the angle APD is evidently = A B D, since it stands on the
212
PLANE TRIGONOMETRY.
same arc AD: and for a like reason BPD=BAD. So that P is the
point where the angles have the assigned value.
The result of a careful construction of this kind, upon a good-sized
scale, will give the values of PA, PC, P B, true to within the 200th
part of each.
Manner of Computation.-In the triangle ABC, where the sides are
known, find the angles. In the triangle A B D, where all the angles are
known, and the side AB, find one of the other sides AD. Take BAD
from BAC, the remainder, D A C, is the angle included between the two
known sides, AD, AC; from which the angles ADC and ACD may be
found, by Case II., p. 204. The angle C A P=180° (A PC+ACD).
—
Also, BCP BCA-ACD; and PBC=ABC+PBA=ABC
+ sup. A DC. Hence the three required distances are found by these
proportions. As sin APC: AC :: sin PAC: PC:: sin PCA: PA;
and lastly, as sin BPC: BC:: sin BPC: BP. The results of the com-
putation are, PA = 709.33, P C = 1042·66, P B = 934 yards.
*** The computation of problems of this kind, however, may be a
little shortened by means of an analytical investigation. Those who wish
to pursue this department of trigonometry may consult the treatises by
Bonnycastle, Gregory, and Woodhouse.
Note. If C had been nearer to P than A B, the general principles of
construction and computation would be the same; and the modification in
the process very obvious.
DETERMINATION OF HEIGHTS AND DISTANCES BY APPROXIMATE MECHANICAL
METHODS.
1. For Heights.
1. By shadows, when the sun shines.-Set up vertically a staff of
known length, and measure the length of its shadow upon a horizontal or
other plane; measure also the length of the shadow of the object whose
height is required. Then it will be, as the length of the shadow of the
staff, is to the length of the staff itself; so is the length of the shadow of
the object, to the object's height.
2. By two rods or staves set up vertically.-Let two staves, one, say, of
6 feet, the other of 4 feet long, be placed upon horizontal circular or square
feet, on which each may stand steadily. Let A B (Fig. 112) be the object,
as a tower or steeple, whose altitude is required, and AC the horizontal
plane passing through its base. Let CD and E F, the two rods, be placed
with their bases in one and the same line C A, passing through A, the foot
of the object; and let them be moved nearer to, or farther from, each other,
until the summit B of the object is seen, in the same line as D and F, the
tops of the rods. Then by the principle of similar triangles, it will be, as
DH (=CE): FH:: DG (CA): BG; to which add A GCD, for
the whole height A B.
PLANE TRIGONOMETRY.
213
3. By reflection.-Place a vessel of water upon the ground, and recede
from it, until you see the top of the object reflected from the smooth sur-
face of the liquid. Then, since by a principle in optics, the angles of inci-
dence and reflection are equal, it will be as your distance measured
horizontally from the point at which the reflection is made, is to the
height of your eye above the reflecting surface; so is the horizontal
distance of the foot of the object from the vessel to its altitude above the
said surface*.
4. By means of a portable barometer and thermometer.-Observe the
altitude B, of the mercurial column, in inches, tenths, and hundredths, at
the bottom of the hill, or other object whose altitude is required; observe,
also, the altitude, b, of the mercurial column at the top of the object; ob-
serve the temperatures on Fahrenheit's thermometer, at the times of the
two barometrical observations, and take the mean between them.
Then 55000 ×
B-b
B+b
height of the hill, in feet for the temperature
440
of 55° on Fahrenheit. Add 10 of this result for every degree which
the mean temperature exceeds 55°; subtract as much for every degree
below 55°.
This will be a good approximation when the height of the hill is less
than 2000 feet; and it is easily remembered, because 55°, the assumed tem-
perature, agree with 55, the significant figures in the co-efficient; while
the significant figures in the denominator of the correcting fraction are
two fours.
5. By an extension of the principle of page 208.-Set the sextant, or
other instrument, to the angle 45°, and find the point C (Fig. 103) on the
horizontal plane, where the object A B has that elevation: then set the
instrument to 26° 34', and recede from C, in direction B C D, till the object
has that elevation.
The distance CD between the two stations will be
= A B.
So, again, if C = 40°, D = 24° 31, CD will be =
if C =
35°, D = 22° 23′, CD
if C = 30°, D = 20° 6'′, CD
or,
""
or,
""
or,
""
or, generally, if cot D
if C = 20°, D
A B.
A B.
""
A B.
""
A B.
""
cot C = rad, C D
= A B.
= 14° 56′, CD
6. For deviation from level.-Let E represent the elevation of the tan-
gent line to the earth above the true level, in feet and parts of a foot, D
the distance in miles: then E = ½ D².
first
* Leonard Digges, in his curious work, the Pantometria, published in 1571,
proposed a method for the determination of altitudes by means of a geometrical
square and plummet, which has been described by various later authors, as Ozanam,
Donn, Hutton, &c. But, as it does not seem preferable to the methods above given,
I have not repeated it here.
214
PLANE TRIGONOMETRY.
This gives 8 inches for a distance of one mile; and is a near approxima-
tion when the distance does not exceed 2 or 3 miles.
2. For Distances.
1. By means of a rhombus set off upon a horizontal plane.-Suppose O
(Fig. 113) the object, and O B the required distance. With a line or
measuring tape, whose length is equal to the side of the intended rhombus,
say 50 or 100 feet, lay down one side BA in the direction BO towards
the object, and BC another side in any convenient direction (for whether
B be a right angle, or not, is of no consequence); and put up rods or arrows
at A and C. Then fasten two ends of two such lines at A and C, and ex-
tend them until the two other ends just meet together at D; let them lie
thus stretched upon the ground, and they will form the two other sides of
the rhombus AD, CD. Fix a mark or arrow at R, directly between C
and O, upon the line A D; and measure R D, R A upon the tape. Then
it will be as RD:DC::CB: BO, the required distance.
Otherwise. To find the length of the inaccessible line Q R.
At some convenient point B (Fig. 114) lay down the rhombus B ADC,
so that two of its sides, BA, BC, are directed to the extremities of
the line QR. Mark the intersections, O and P, of A R, CQ, with the
sides of the rhombus (as in the former method): then the triangle
ODP will be similar to the triangle R B Q; and the inaccessible
distance R Q will be found
Thus, if B A B C, &c. =
=
OP=13 ft. 7 ins., then Q R
2
OP × BA² *
OD X DP
100 ft., OD=9 ft. 5 ins., DP11 ft. 10 ins.,
10000 × 1372
=
9_5 × 1110100
12
= 1219 feet.
2. By means of a micrometer attached to a telescope.-Portable in-
struments for the purpose of measuring extremely small angles, have
been invented by Martin, Cavallo, Dollond, Brewster, and others. In
employing them for the determination of distances, all that is necessary in
practice is to measure the angle subtended by an object of known dimen-
sions, placed either vertically or horizontally, at the remoter extremity of
the line whose length we wish to ascertain. Thus, if there be a house, or
other erection, built with bricks, of the usual size; then four courses in
height are equal to a foot, and four in length equal to a yard: and distances
measured by means of these will be tolerably accurate, if care be taken
while observing the angle subtended by the horizontal object, to stand
directly in front of it. A man, a carriage-wheel, a window, a door, &c.,
at the remoter extremity of the distance we wish to ascertain, may serve
for an approximation. But in all cases where it is possible, let a foot, a
*For PD: DA::AB: BR:
A B2
PD
and OD: OP::BR:RQ
A B2. O P
OD.DP'
PLANE TRIGONOMETRY.
215
yard, or a six-feet measure, be placed vertically, at one end of the line to
be measured, while the observer with his micrometer stands at the other.
Then, if h be the height of the object,
either h× cotangle subtended
or hx cot angle
will give the distance, according as the eye of the observer is horizontally
opposite to the middle, or to one extremity of the object whose angle is
taken.
When a table of natural tangents is not at hand, a very near approxi-
mation for all angles less than half a degree, and a tolerably near one up
to angles of a degree, will be furnished by the following rules.
If the distant object whose angle is taken be 1 foot in length, then
3437·73 ÷ the angle in minutes will give the distance in
or 206264 ÷ the angle in seconds
}
feet.
If the remote object be 3, 6, 9, &c., feet in length, multiply the former
result by 3, 6, 9, &c., respectively.
Ex. 1. What is the distance of a man 6 feet high, when he subtends an
angle of 30 seconds?
206264 × 6÷ 30= 206264 ÷ 5= 41252.8 feet 13750.9 yards,
the distance required.
Ex. 2. In order to ascertain the length of a street, I put up a foot mea-
sure at one end of it, and standing at the other found that measure to
subtend an angle of 2 minutes: required the length of the street.
3437·73 ÷ 2 = 1718.86 feet = 572.95 yards.
3. By means of the velocity of sound.-Let a gun be fired at the re-
moter extremity of the required distance, and observe, by means of a
chronometer that measures tenths of seconds, the interval that elapses
between the flash and the report: then estimate the distance for one
second by the following rule, and multiply that distance by the observed
interval of time; the product will give the whole distance required.
At the temperature of freezing, 32°, the velocity of sound is 1100 feet
per second; for lower temperatures deduct, or for higher temperatures
add, half a foot per second for every degree of difference from 32° on
Fahr. thermometer; the result will shew the velocity of sound, very
nearly, at all such temperatures.
Thus, at the temperature of 50° the velocity of sound is,
1100 × (50 — 32) = 1109 feet.
1 :
At temperature 60°, it is 1100 + ½ (60 −32) = 1114 feet.
216
CONIC SECTIONS.
CHAP. V.
CONIC SECTIONS.
SECT. I.-Definitions.
1. Conic Sections are the figures made by a plane cutting a cone.
2. According to the different positions of the cutting plane there arise
five different figures or sections, viz., a triangle, a circle, an ellipse, an
hyperbola, and a parabola: of which the three last are peculiarly called
Conic Sections.
3. If the cutting plane pass through the vertex of the cone, and any
part of the base, the section will be a triangle, as A B. (Fig. 115.)
4. If the plane cut the cone parallel to the base, or make no angle with
it, the section will be a circle, as A B. (Fig. 116.)
5. The section is an ellipse when the cone is cut obliquely through both
sides, or when the plane is inclined to the base in a less angle than the
side of the cone is, as A B C D. (Fig. 120.)
6. The section is a parabola when the cone is cut by a plane parallel to
the side, or when the cutting plane and the side of the cone make equal
angles with the base, as P₁ A P₂. (Fig. 138.)
7. The section is an hyperbola when the cutting plane makes a greater
angle with the base than the side of the cone makes, as P₁ A P₂. (Fig.
130.)
Note. In all the above definitions the cone is supposed to be a right
cone.
8. If all the sides of the cone be continued through the vertex, forming
an opposite equal cone, and the plane be also continued to cut the opposite
cone, this latter section is called the opposite hyperbola to the former, as
S, B S. (Fig. 130.)
9. And if there be two other cones, with their axes in the same plane
and their sides touching the sides of the former cones, then will the same
plane cut all the cones and form four hyperbolas, as P, A P₂, R, C R2, S₁
B S2, Q1 D Q₂ (fig. 118), each opposite pair of which are similar; these
hyperbolas are said to be conjugate to each other, and the figure thus
formed is called the figure of the conjugate hyperbolas, as fig. 118.
Note.—In the following definitions, the letters refer to fig. 117 for the
ellipse; fig. 118 for the hyperbola; and fig. 119 for the parabola.
10. The vertices of any section are the points where the cutting plane
meets the opposite sides of the cone, as A and B.
Cor. Hence the ellipse and the opposite hyperbolas have each two
vertices; but the parabola only one; unless we consider the other as at
an infinite distance.
11. The major axis, or transverse diameter of a conic section, is the
line or distance A B between the vertices.
CONIC SECTIONS.
217
Cor. Hence the axis of a parabola is infinite in length, A B being only
a part of it.
12. The centre O is the middle of the axis.
Cor. Hence the centre of a parabola is infinitely distant from the vertex.
And of an ellipse, the axis and centre lie within the curve: but of an
hyperbola, without.
13. The minor or conjugate axis, is the line C D, drawn through the
centre perpendicular to the transverse axis, and bounded each way by the
curve.
Cor. Hence the parabola has not any conjugate axis, unless we suppose
it at an infinite distance, and infinite in length.
14. A tangent to a curve at any point, is a line as A, T₁, which touches
the curve in that point; but being produced either way does not cut it.
15. A diameter is any right line, as A, B₁, drawn through the centre,
and terminated on each side by the curve; and the extremities of the
diameter, or its intersections with the curve, as A, and B₁, are its vertices
Cor. Hence all the diameters of a parabola are parallel to the axis, and
infinite in length. Hence, also, every diameter of the ellipse and hyper-
bola has two vertices; but of the parabola, only one; unless we consider
the other as at an infinite distance.
16. The conjugate to any diameter is the line drawn through the centre,
and parallel to the tangent of the curve at the vertex of the diameter.
So, C₁ D₁, parallel to the tangent at A₁, is the conjugate to A₁ B₁.
17. An ordinate to any diameter is a line parallel to its conjugate, or to
the tangent at its vertex, and terminated by the diameter and curve. So,
K I and K₂ A, are ordinates to the axis A B; and K, I and E₁ I, ordi-
nates to the diameter A, B₁.
1
Cor. Hence the ordinates of the axes are perpendicular to it; but of
other diameters, the ordinates are oblique to them.
18. An abscissa is a part of any diameter, contained between its vertex
and an ordinate to it; as A K or B K, and A, E, or B, E₁.
Cor. Hence, in the ellipse and hyperbola, every ordinate has two
abscissæ; but in the parabola only one; the other vertex of the diameter
being infinitely distant.
19. The vertex from which the abscissæ are measured is called the origin
of those abscissæ, and any abscissa and its ordinate are called co-ordinates,
as A K and K I.
20. The parameter of any diameter is that double ordinate which is a
third proportional to the transverse and conjugate axes in the ellipse or
hyperbola, and to any abscissa and its ordinate in the parabola. The
parameter of the transverse axis is called the principal parameter, or the
latus rectum; thus, if A, B, C, D₁ :: C, D, : I, I, then I, I, is the para-
meter of A₁ B₁; and if A B : C D : : C D : I½ I3, then I, I, is the latus rectum.
21. The point where the parameter cuts the transverse axis is called
the focus, as E, F; and the distance of the focus from the nearest vertex
of the same axis is called the focal distance, as A E, B F.
1
1
Cor. Hence, the ellipse and hyperbola have each two foci, but the
218
CONIC SECTIONS.
parabola only one.
The foci (or burning points) were so called because
all rays are united or reflected into one of them, which proceed from the
other focus, and are reflected from the curve.
22. The point E is also frequently called the pole; and a line drawn
from any point in the curve to the pole, is called the radius vector as
E I. And the angle B E I, contained between the radius vector and the
transverse axis, is called the traced angle.
23. The directrix is a right line drawn perpendicular to the transverse
axis of a conic section, through an assignable point in the prolongation of
that axis; such that lines drawn from any points in the curve parallel to
the axis to meet the directrix, shall be to lines drawn from the same
points to the focus, in a constant ratio for the same curve.
2
Thus, if A E: AT:: EI₂: I½y : : E 1: I, x:: EI:IX, then X Y
is the directrix.
In the ellipse A E is less than A T.
In the parabola A E is equal to A T.
In the hyperbola A E is greater than A T.
24. The subtangent to any point in a curve, is that portion of the trans-
verse axis which is contained between the tangent and ordinate to the
same point, as K₂ T1.
25. A normal at any point is a line drawn from that point perpen-
dicular to the tangent, to meet the transverse axis, as A, L.
26. The Radius of Curvature of a conic section or other curve, is the
radius of that circle which is precisely of the same curvature as the curve
itself, at any assigned point, or the radius of the circle which fits the curve
and coincides with it, at a small distance on each side of the point of con-
tact. The circle itself is called the osculatory circle, or the equicurve
circle; and if the curve be of incessantly varying curvature, each point
has a distinct equicurve circle, the radius of which is perpendicular to the
tangent at the point of contact.
27. An asymtote is a right line towards which a certain curve line ap-
proaches continually nearer and nearer, yet so as never to meet, except
both be produced indefinitely. The hyperbola has two asymptotes, as
U V, W Z.
LAND MEASURING.
219
CHAPTER VI.
LAND MEASURING.
We cannot enter upon any calculation connected with Land
that is not more or less dependent upon the admeasurement of its
surface, or, in more technical terms, its "superficial area;" how
much more important then, than is ordinarily supposed, does it be-
come that the very simple operations necessary to arrive at a
correct result should be properly understood by those who affect
to practise this particular branch of science. No extraordinary
ability or power of genius, nothing out of the common way in
point of education and mental attainments, no laborious application
to study, nor any great amount of previous practice, is requisite to
produce a competent "Land Measurer." I do not mean to say
that all these are not advantages which will give a man possessing
them superiority over another who does not possess them; but
they are not at all indispensable; and I will endeavour to expound
in simple language the rules requisite to be understood to enable
any person, though of mean ability, who can perform the four
fundamental rules of arithmetic, (or by the aid of Tables I pub-
lished ten years since, or the Tables I will annex to this article,
addition only), to measure accurately any piece of land that may
come in his way although he may not be able to do it quickly, so
as to turn to profitable pecuniary account the knowledge he has
thus acquired.
I must not here be misunderstood. While all I have said above
applies to “ Land Measuring,” not one word is applicable to "Land
Surveying;" that is a totally different branch of science, requiring
long practice and a thoroughly perfect scientific education.
By "Land Surveying" I mean the admeasurement, by an infinity
of instrumental and other contrivances, of the geographical and
physical features of the earth's surface, embracing in their widest
scope the operations of " Surveying, Mapping, and Levelling.”
In extensive operations, land is generally measured with a chain
of 100 links, known as Gunter's Chain, from the name of its in-
ventor, the Rev. Edward Gunter, who was born in 1680, and died
in 1726, so that it must have been in use upwards of 125 years.
The chief advantage of the use of this chain is the facility it affords
in squaring or casting the dimensions, 100,000 square links, or 10
square chains, being equal to one statute acre. If, however, the
220
LAND MEASURING.
results of operations in other measures are conveniently tabulated,
this advantage of Gunter's Chain is superseded, and the non-pro-
fessional "Land Measurer" is at liberty to take the dimensions in
that measure with which he is most familiar. Country gentlemen,
farmers, and indeed all classes of the community, being more gene-
rally acquainted with the standard yard, it is my intention to lay
down the principles of Land Measuring without reference to any
particular kind of measure used, and then to annex thereto a cor-
rectly computed Table of results, in statute acres, of dimensions
taken in yards. These Tables will, as I have previously stated,
entirely obviate the necessity of all calculation in cases when the
pieces of land do not exceed 100 yards square, and will render dimen-
sions in yards equally as convenient as those in chains and links.
RULES.
1. If the piece of land to be measured is in the form of a square
or rectangle, that is, having four right angles, and all its sides
parallel, its area is found by multiplying its length by its width.
(Vide Mensuration of Superficies.)
2. If the piece of land to be measured is triangular, the length
of the base multiplied by one-half the perpendicular, or one-half
of the base multiplied by the perpendicular, will give the area;
or, what is the same thing, the full base multiplied by the perpen-
dicular, will give twice the area of the triangle. (Vide Mensuration
of Superficies.)
3. If the piece of land has two of its sides parallel and at right
angles with the base, add the two parallel sides together, and
multiply one-half their sum by the base or side running at right
angles to them, the product will be the area; or multiply the sum
of the two sides by the base, and take half the product for the
area.
Example 1.
A square piece of land is 4 long and 4 wide, what is its area?
(Fig. 125.)
4 long
multiplied by 4 wide
gives
. 16 superficial area.
I have endeavoured to render this result plainly apparent by
dividing the figure into squares and numbering them, from which
it will at once be seen that the area of the figure must be 16 squares
of whatever measure the dimensions were taken in.
LAND MEASURING.
221
Ex. 2.-What is the content of the triangular piece of land
whose base is 8 and perpendicular 4? (Fig. 126.)
8 base
multiplied by 2 half perpendicular
gives 16 superficial content.
or 8 base
4 perpendicular
2)32 twice area
gives 16 required area.
or 4 half base
4 perpendicular
16 area.
This is also rendered clearly apparent on the figure, by which
it is shewn that the triangle ABC contains 12 perfect squares
and 8 half-squares. It also shews that the two triangles wanting
to form a rectangle of the same dimensions contain, in the aggre-
gate, the same number of squares and half-squares as the triangle;
thus illustrating, in the plainest manner, that one-half the area
of the rectangle is the area of the triangle.
Ex. 3.—Required the area of the rhomboid whose base is 4, and
its parallel sides 4 and 8 respectively. (Fig. 127.)
added to.
4 height of one side
8 height of opposite side
divided by 2) 12
gives
6 mean height
multiplied by 4 base
gives
. 24 area.
or,
added to .
4
8
12 sum of the sides
multiplied by 4 base
divided by 2)48
gives
24 area.
The figures shew that 6 must be the mean height, the square A
and the two half squares a a, rejected, being equal to the square
B, and the two half squares b b, taken in.
The previous rules form the fundamental ones for measuring
land, but it is very unusual indeed to meet with just such figures
222
LAND MEASURING.
in practice; it does not unfrequently happen that a four-sided
field is met with, but then it scarcely ever occurs that the sides
are parallel to each other, or if so, that the angles are right angles;
even should that be the case, it is not possible to be certain of the
fact, without verifying it by some process that would take as much
time as would be required to measure the field; the rule then is
to divide the field into several imaginary mathematical figures,
and to take such dimensions as may be required to produce the
area. The triangle will be found to be the most useful of all
others for this purpose, or a trapezium divided into two triangles
by the "diagonal," which thus becomes a base common to both tri-
angles, and will consequently give the area of the trapezium if mul-
tiplied into half the sum of the two perpendiculars of the triangle.
Ex. 4.-Required the Content of the Field in the form of a
Trapezium, whose dimensions in Links are as given in Fig. 128.
Note.-In measuring the base AB, it was found that the first
perpendicular to the corner E, sprang at the point C 422 links
from A, and a mark was there left until the perpendicular could be
measured; (it is very dangerous to the accuracy of the work to dis-
continue measuring on one line, to measure another, before the
first line is completed; the insertion of the figures in the wrong
places, and mixing the arrows which denote the number of chains,
are among the most fruitful sources of error to an unpractised
person in such cases.) Continuing the diagonal the perpendicular
to the corner, F was found to spring at the point D 830 links from
A*. Continuing the total length, the base A B was found to be
1142 links. The chain was then taken to F, and the perpendicular
FD was measured, equal 460 links; and then the perpendicular
from C to E, and found to be 480 links, which completed the
operation.
add
{
460
480
Calculation.
divide by 2) 940 sum of perpendiculars
470 half sum of perpendiculars.
* The insertion of the distances on the diagonal at which the perpendiculars rise are
not at all required in the computation of the area, but it is always worth while to enter
them in the Field Book, as they enable an approximate plot of the field to be drawn, if
at any future time such may be desirable. I once measured field by field the parish
of Walton-upon-Thames, containing 7300 acres, and by attending to this particular in
keeping the Field Notes, I was enabled some two or three years subsequently, at my
leisure, to plot a very tolerable map of that parish.-E. R.
LAND MEASURING.
223
multiply
by
acres
1142 diagonal
470 half sum of perpendiculars
79940
4568
5,36740 product in square links
4
rood
1,46960
40
perches 18,78400
The area 536740 square links is reduced into acres, roods, and
perches, by dividing by 100,000 the number of square links in an
acre; this is readily done by cutting off the five right-hand figures;
the figure 5 remaining on the left-hand being acres, and those
on the right decimals of an acre, which by multiplying by 4 (the
number of roods in an acre) and again cutting off five figures,
leaves one rood on the left of the decimal dot-the decimals of a
rood being multiplied by 40 (the number of perches in a rood), and
the five decimals again pointed off, leave 18 perches and 78400
decimals of a perch.
The answer, therefore, is 5A. 1R. 18.7r.
To facilitate this reduction of square links, a Table is annexed,
shewing the several roods and perches in any decimal of an acre.
It is very easy to reduce them mentally by committing the fol-
lowing particulars to memory.
.00625 is 1 perch
•01250 is 2
•02500 is 4
•05000 is 8
"
وو
وو
•10000 is 16
•20000 is 32
•25000 is 1 rood
•50000 is 2 roods
75000 is 3 roods
In our previous example, this is the
kind of mental calculation we should
have to carry on.
We see that the given decimal
•36740 is more than one rood; there-
fore, we set down one rood, and at
a glance we discover we have left
•11740 10000 of which we know to
be ..
16
•01250
2
and the remainder nearly 1
19 percs nearly
By the assistance of some Tables published by me in 1842,
224
LAND MEASURING.
under the title of "Ryde's Pocket Companion and Ready Reckoner,"
the calculation of the previous example would have been as under.
The Tables rising in value, every separate link up to 1000, the
half of the diagonal or odd number would have been taken (to
bring it within the scope of the Tables, and thus save one line of
addition,) and the sum of the perpendiculars. Thus,
at page 115
A. R. P.
1142
571 by 900 = 5 0
22.2
2
وو
by 40 = 0
0
36.5
5 1 18.7
otherwise it would have stood
at page 94
470 by 1100 = 5_0_27·2
by 40 = 0 0 30.
وو
by
2 = 0 0 1.5
5 1 18.7
The only advantage of the former arrangement over the latter
being, the saving of one line, effected in the addition of the quantities.
Ex. 5.-What is the Content of the piece of Land whose
dimensions are marked upon figure 129?
AB
First, we have the diagonal A B = 1034, and the two perpen-
diculars CE and D F = 411 and 395 respectively; then on the
line BE, between it and the curved fence, we have, first, a triangle
BIK, whose base BI is 100, and perpendicular I K 66; next
a rhomboid HIKL, whose base IH is the difference between
300 and 100, and whose perpendiculars HL and IK are 6 and 20
respectively; then a rectangle G H L M, whose base HG is the
difference between 700 and 300, and whose perpendiculars HL and
GM are 20; and lastly, we have a triangle EG M, whose base
GE is the difference between 960 and 700, and whose perpen-
dicular G M is 20.
Calculation.
1034
2
517 × (411 + 395
806)
2) 100
50 half-base
6 perp.
300 Tri. BIK.
LAND MEASURING.
225
400 base
20
6
20 perp.
2) 26
8000
13 1-perp.
200
260
2600
2600
10 1-perp.
517 -diagonal.
806 sum of perp.
3102
41360
4.16702 area of trapezium AEBF.
300 Triangle BIK.
2600 Rhomboid HIK L.
8000 Rectangle G H L M.
2600 Triangle E G M.
4.30202 Total area of field.
At
By the Table of Decimals of an acre ·30052 = lr. 8p.
Answer 4a. 1r. 8p.
By "Ryde's Pocket Companion and Ready Reckoner."
page 104, 517 by 806
وو
وو
P.
26.6 Trap. A E B F.
A. B.
=
4 0
10, 50
6 0
=
0
0.4 Tri. BIK.
""
3, 13
80, 400
200 = 0
0
4.1 Rhom. HIKL.
39
20 = 0
0
12.8 Rec. G HLM.
52, 260
10 = 0
0
وو
4.1 Tri. E G M.
Answer 4 1 8.
Other Examples might be added, with all the fences crooked,
but it is considered unnecessary, as every distinct fence would
have to be treated in a similar manner to the fence BKL ME,
in our last Example.
226
DECIMALS OF AN ACRE.

R. P.
Dec.
R. P.
Dec.
R. P.
Dec.
R. P.
Dec.
0 1
.00625
1 1
.25625
2 1
.50625
3 1
.75625
0 2
.01250
1 2
.26250
2 2
.51250
3 2
.76250
0 3
.01875
1 3
.26875
2 3
.51875
3 3
.76875
0 4
.02500
1 4
.27500
2 4
.52500
3 4
.77500
0 5
.03125
1 5
.28125
2 5
.53125
3 5
.78125
0 6
.03750
1 6
.28750
2 6
.53750
3 6
.78750
0 7
.04375 1 7
.29375
2 7
.54375
3 7
.79375
08
.05000 1 8
.30000
2 8
.55000
3 8
.80000
09
.05625 1 9
.30625
2 9
.55625
3 9
.80625
0 10
.06250
1 10
.31250
2 10
.56250
3 10
.81250
0 11
.06875
1 11
.31875
2 11
.56875
3 11
.81875
0 12
.07500
1 12
.32500
2 12
.57500
3 12
.82500
0 13
.08125
1 13
.33125
2 13
.58125
3 13
.83125
0 14
.08750
1 14
.33750
2 14
.58750
3 14
.83750
0 15
.09375
1 15
.34375
2 15
.59375
3 15
.84375
0 16
.10000
1 16
.35000
2 16
.60000
3 16
.85000
0 17
.10625
1 17
.35625
2 17
.60625
3 17
.85625
0 18
.11250
1 18
.36250
2 18
.61250
3 18
.86250
0 19
.11875
1 19
.36875
2 19
.61875
3 19
.86875
0 20
.12500
1 20
.37500
2 20
.62500
3 20
.87500
0 21
.13125
1 21
.38125
2 21
.63125
3 21
.88125
0 22
.13750
1 22
.38750
2 22
.63750
3 22
.88750
0 23
.14375
1 23
.39375
2 23
.64375
3 23
.89375
0 24
.15000
1 24
.40000
2 24
.65000
3 24
.90000
0 25
.15625
1 25
.40625
2 25
.65625
3 25
.90625
0 26
.16250
1 26
.41250
2 26
.66250
3 26
.91250
0 27 .16875
1 27
.41875
2 27
.66875
3 27
.91875
0 28 .17500
1 28
.42500
228
.67500
328
.92500
0 29
.18125
1 29
.43125
2 29
.68125
3 29
.93125
0 30
.18750
1 30
.43750
2 30
.68750
3 30
.93750
0 31
.19375
1 31
.44375
2 31
.69375
3 31
.94375
0 32
.20000
1 32
.45000
2 32
.70000
3 32
.95000
0 33
.20625
1 33
.45625
2 33
.70625
3 33
.95625
0 34
.21250
1 34
.46250 2 34
.71250
3 34
.96250
0 35
.21875
135
.46875 2 35
.71875
3 35
.96875
0 36
.22500
1 36
.47500 2 36
.72500
336
.97500
0 37 .23125
038 .23750 1 38
0 39 .24375
1 0 .25000
1 37
.48125 2 37
.73125
3 37
.98125
.48750
2 38
.73750
3 38
.98750
1 39
.49375
2 39
.74375
3 39
.99375
20
.50000
30
.75000
LAND MEASURING.
227
Required the content of the field whose dimensions in yards are
as shewn upon fig. 130.
Yards.
14
= 7 1-perp.
198
2
99 half-base
37 = base.
2
88 perp.
259 Tri. B.
792
792
198
2
160
38
8712 Triangle A.
= 19=-base
2
259 Tri.
B.
19
361 Tri.
C.
1932 Rhom. D.
171
1026 Tri.
E.
27+ 19 46
2
2
19
361 Tri. C.
23-perp.
160—76 = 84 base
12290 area in square yards.
4840) 12290 (2 acres.
9680
2610
4
92
184
1932 Rhomboid D.
4840) 10440 (2 roods.
9680
760
40
76
=38-base
4840) 30400 (6.28 perches
2
29040
27 perp.
13600
266
9680
76
39200
1026 Tri. E.
By the new Tables:-
88 yards by 99 = 1
7
37=0
0 8.56
19=0 0 11.93
38720
480
A. R. P.
3 8
19
""
23
840 1 23.87
دو
38
Answer
27=0 0 33.92
2 2 6.28
228
LAND MEASURING.
Note.-The reduction of square yards into acres, roods, and
perches is given in this case to illustrate the method of doing it by
figures; for the future we shall only employ the Tables.
Required the Area of the Field whose dimensions in yards are
as marked upon fig. 131.
By the Tables.
198
× 116 + 46 = 99 × 162*
2
99 × 100 = 2
99 × 62 = 1
1
0 7·27
2.91
Trap. A.
186
× 127 + 68 = 93 × 195*
2
93 × 100 = 1
93 × 95 = 1
2+8
× 55 =
3 27·44
3 12·07
5 × 55 = 0 0 9.09
Trap. B.
9.09 Rhom. C.
2
8+4
× 134 – 55 – 6 × 79 = 0 0 15.67
Rhom. D.
2
7+5
+
× 27 =
6 × 27 = 0 0 5.36
Rhom. E.
2
66
× 11 =
33 × 11 = 0 0 12.10
0 12.10 Tri. F.
2
157-87
70
×4=35 × 4 = 0 0 4.63
Tri. G.
2
2
Total Contents . . 7 1 16.54
What are the respective quantities of four pieces of Harvest
Work, whose dimensions in yards are severally, as marked on
fig. 132?
Note.-We may here remark, that in narrow slips of land, such
as is represented in this field, it is sufficiently accurate for ordinary
purposes, if the mean length is ascertained by measuring up the
middle of the slip, and the width is taken as near to either end as
possible, about at right angles with the centre length, and averaged
for a mean width.
* The Tables being limited to 100 yards in extent an extra line in the casting is
required in each of these two figures.
†This figure is not strictly a mathematical one; it will be observed, the mean
length is taken and the mean width: the field represented, is an actual field, in the
parish of Walton.
Here is another little irregularity of small importance; the 11 yards may not be
quite at right angles with the base, but not sufficiently at variance to produce any
practical consequence.
LAND MEASURING.
229
By the Table.
A. R.
P.
= 28 × 97 = 0 2 9.79 Trap. A.
25 + 31
56
2
2
33 + 43
76
38 × 94 = 0 2 38·08 Trap. B.
2
2
48 + 46
2
94
2
32 + 34
2
66
=
33 × 97 = 0
2
= 47 × 96 = 0 3 29.16 Trap. C.
Total Contents
2 25·82
= 0 2 25·82 Trap. D.
2 3 22.85
The little instrument used for erecting perpendiculars is called
a Cross. The most simple one that can be constructed, and the
most convenient because the most portable, consists of a round
piece of box-wood, about four inches in diameter, and three-quar-
ters of an inch in thickness; it has a hole in the centre, through
which it may be slipped on to the offset rod, to a suitable height
when stuck in the ground for a man's eye to look into. Two
grooves at right angles with each other are cut into it, as shewn on
Fig. 133; a thin piece of vernier is stuck on to the top of it, and
when on the staff it appears as Fig. 134. To prove the accuracy
of the Cross, look into groove AB, Fig. 135, and direct an assistant
to set up a stick C; look through the other groove D E, and have
another stick set up at F: twist the Cross round on the offset
rod until the stick at F can be seen through the groove A B; then
if the stick at C is seen through the groove D E, the Cross is
obviously correct.
Tables of Land Measure, by dimensions taken in yards.

Dimensions.
Statute content. Dimensions.
Statute content.
Dimensions.
Statute content.
Yards.
A. R. P.
Yards.
A. B. P.
Yards.
A. R. P.
1 by 1
0 0
0.03
1 by 65
0 0
2.15
2 by 30
0 0 1.98
2
0 0
0.07
66
0 0
2.18
31
0 0
2.05
3
0 0
0.1
67
0 0
2.21
32
0 0
2.12
4
0 0
0.13
68
0 0
2.25
33
0
0
2.18
5
0 0
0.16
69
0 0
2.28
34
0 0
2.25
67
0
0
0.2
70
0 0
2.31
35
0
0
2.31
0 0
0.23
71
0 0
2.35
36
0 0
2.38
8
0 0
0.26
72
0 0 2.38
37
0 0
2.45
9
0 0
0.3
73
0 0
2.41
38
0 0 2.51
10
0 0
0.33
74
0 0
2.45
39
0 0
2.58
11
0 0
0.36
75
0 0
2.48
40
0 0
2.64
12
0 0
0.4
76
0 0
2.51
41
0 0
2.71
13
0 0
0.43
77
0 0
2.55
42
0 0
2.78
14
0 0
0.46
78
0 0
2.58
43
0 0
2.84
15
0 0
0.5
79
0 0 2.61
44
0
0
2.91
16
0 0
0.53
80
0 0 2.64
45
0 0
2.98
17
0 0
0.56
81
0 0 2.68
46
0 0
3.04
18
0 0
0.6
82
0 0
2.71
47
0 0 3.11
19
0 0
0.63
83
0 0
2.74
48
0 0
3.17
20
0 0
0.66
84
0 0 2.78
49
0 0 3.24
21
0 0
0.69
85
0 0 2.81
50
0 0
3.31
22 0 0
0.73
86
0 0 2.84
51
0 0
3.37
23
0
0
0 0.76
87
0 0 2.88
52
0 0 3.44
24
0
0
0 0.79
88
0 0 2.91
53
0 0
3.50
25
0
0
0 0.83
89
0 0 2.94
54
0
0
3.57
26
0 0 0.86
90
0 0 2.98
55
0 0
3.64
27 0 0 0.89
91
0 0 3.01
56
0 0
3.7
28 0 0 0.93
92
0 0 3.04
57
0 0
3.77
29 0 0 0.96
93
0 0 3.07
58
0
0
3.83
30 0 0 0.99
94
0 0 3.11
59
0 0 3.9
31 0 0 1.02
95
0 0 3.14
60
0 0 3.97
32
0 0 1.06
96
0 0 3.17
61
0
0 4.03
33
0 0 1.09
97
0 0 3.21
62
0 0 4.1
34
0 0
1.12
98
0 0 3.24
63
0 0 4.17
35
0 0 1.16
99
0 0 3.27
64
0 0 4.23
36
0 0 1.19
100
0 0 3.31
65
0 0 4.3
37
0 0
1.22
2 by 2
0 0 0.13
66
0 4.36
38 0 0 1.26
3
0 0 0.2
67
0 0 4.43
39
0 0
0 1.29
4
0 0 0.26
68
0 0 4.5
40
0
0
0 1.32
0 0 0.33
69
0 0 4.56
41
0
0
0 1.36
6
0 0 0.4
70
0 0 4.63
42
0
0 0 1.39
7
0 0 0.46
71
0 0 4.69
43
0 0 1.42
8
0 0 0.53
72
0 0 4.76
44
0 0 1.45
9
0 0 0.6
73
0 0 4.83
45 0 0 1.49
10
0 0 0.66
74
0 0 4.89
46 0 0 1.52
11
0 0 0.73
75
0 0 4.96
47
0 0
0 1.55
12
0 0 0.79
76
0 0 5.02
48
0 0 1.59
13
0 0 0.86
77
0 5.09
49 0 0 1.62
14
0 0 0.93
78
0 0 5.16
50 0 0 1,65
15
0 0 0.99
79
0
0 5.22
51
0 0 1.69
16
0 0 1.06
80
0 0 5.29
52
0 0 1.72
17
0 0 1.12
81
0 0 5.36
53
0 0 1,75
18
0 0
0 1.19
82
0 0 5.42
54 0 0 1,79
19
0 0 1.26
83
0 0 5.49
55
0 0 1.82
56
0 0 1,85
57
0 0 1.88
58
0 0 1,92
59
0 0 1,95
22222
20
0 0 1.32
84
0 0 5.55
21
0 0 1.39
85
0 5.62
0 0 1.45
86
0 5.69
23
0 0 1.52
87
0 5,75
24
0 0 1.59
88
0
0 5.82
60
0 0 1.98
25
0 0 1.65
89
0 0 5.88
61
0 0 2.02
26 0 0 1.72
90
0 0 5.95
62
0 0 0 2.05
27
0 0 1,79
91
0 0 6.02
63
0 0
0 2,08
64
0 0 2.12
88888
28
0 0 1.85
92
0 0 6.08
29 0 0 1.92
93
0 0 6.15
TABLES OF LAND MEASURE.
231

Dimensions.
Statute content.
Dimensions. Statute content.
Dimensions.
Yards.
A. R.
P.
Yards.
A. R.
P.
Yards.
Statute content.
A. R. P.
2 by 94
0 0
6.21
3 by 60
0 0
5.95
4 by 27
0 0 3.57
95
0 0
6.28
61
0 0
6.05
28
0 0
3.7
96
0 0
6.35
62
0
0
6.15
29
0 0
3.83
97
0 0
6.41
63
0
0
6.25
30
0
0
3.97
98
0 0 6.48
64
0
0
0
6.35
31
0 0 4.1
99
0 0 6.55
65
0
0
0 6.45
32
0 4.23
100
0 0 6.61
66
0
0
0 6.55
33
0 0
4.36
3 by 3
0 0 0.3
67
0
0 0
6.64
34
0 0
4.5
4
0 0 0.4
68
0
0
0
6.74
35
0
0 4.63
0 0 0.5
69
0
0
0
6.84
36
0 0 4.76
6
0 0
0.6
70
0 0 6.94
37
0
0
4.89
7
0 0 0.69
71
0 0
7.04
38
0 0 5.02
8
0 0 0.79
72
0 0 7.14
39
0
0 5.16
9
0 0 0.89
73
0 0 7.24
40
0
0
5.29
10
0 0 0.99
74
0 0
7.34
41
0 0
5.42
11 0 0
1.09
75
0 0 7.44
42
0 0
5.55
12
0 0 1.19
76
0 0 7.54
43
0 0
5.69
13
0 0
1.29
77
0 0 7.64
44
0
0
5.82
14 0 0
1.39
78
0 0 7.74
45
0 0
5.95
15 0 0 1.49
79
0 0 7.83
46
0
0
6.08
16 0 0 1.59
80
0 0 7.93
47
0
6.21
17
0 0 1.69
81
0 0
0 8.03
48
0 0
6.35
18
0 0 1.79
82
0
0
0 8.13
49
0 0
6.48
19
0 0 1.88
83
0
0
0
8.23
50
0 0
6.61
20 0 0 1.98
84
0
0
0 8.33
51
0 0
6.74
21
0 0 2.08
85
0
0
0 8.43
52
0
0
6.88
22 0 0 2.18
86
0
0
0
8.53
53
0 0 7.01
23 0 0 2.28
87
0
0
0
8.63
54
0 0 7.14
24
0 0 2.38
88
0
0
0
8.73
55
0 0
7.27
25 0 0 2.48
89
0
0
0
8.83
56
0 0
7.4
26
0 0 2.58
90
0
0
0
8.93
57
0 0 7.54
27
0 0 2.68
91
0
0
0 9.02
58
0 0 7.67
28
0 0 2.78
92
0
0
0
9.12
59
0
0 7.8
29
0 0 2.88
93
0
0
0 9.22
60
0 0 7.93
ུ
30 0 0 2.98
94
0
0
0
9.32
61
0
0 8.07
31 0 0 3.07
95
0 0
0 9.42
62
0 0 8.2
32 0 0 3.17
96
0
0
0 9.52
63
0 0 8.33
33
0 0 3.27
97
0
0
0 9.62
64
0 0 8.46
34 0 0 3.37
98
0
0
0 9.72
65
0 0 8.6
35 0 0 3.47
99
0
0
0 9.82
66
0 0 8.73
36 0 0 3.57
100
0 0
0 9.92
67
0 0 8.86
37 0 0 3.67
4 by 4
38 0 0 3.77
39 0 0 3.87
456
0 0
0 0.53
68
0 0 8.99
0 0 0.66
69
0 0 9.12
0 0
0 0.79
70
0 0 9.26
40 0 0 3.97
7
0
0
0 0.93
71
0 0 9.39
41 0 0 4.07
8
0
0
0 1.06
72
0 0 9.52
42 0 0 4.17
9
0
0
0 1.19
73
0 0 9.65
43 0 0 4.26
10
0 0
0 1.32
74
0 0 9.79
44 0 0 4.36
11
0 0 0
1.45
75
0 0 9.92
45 0 0 4.46
12
0 0 1.59
76
0 0 10.05
46 0 0 4.56
13
0 0 1.72
77
0 0 10.18
47
0 0 4.66
14
0 0 1.85
78
0 0 10.31
48 0 0 4.76
15
0 0 1.98
79
0 0 10.45
49 0 0 4.86
16
0 0 2.12
80
0
0 10.58
50 0 0 4.96
17
0 0 2,25
81
0
0 10.71
51
0 0 5.06
18
0 0 2,38
82
0 0 10.84
52 0 0 5.16
19
0 0 2.51
83
0 0 10.98
53
0 0 5.26
20
0 0 2.64
84
0 0 11.11
54 0 0 5.36
21
0 0 2.78
85
0 0 11.24
55
0 0 5.45
22
0 0 2,91
86
0
0 11.37
56 0 0 5.55
23
0 0 3.04
87
0
0 11.5
57
0 0 5.65
24
0 0 3.17
88
0
0 11.64
58
0 0 5.75
25
0 0 3.31
89
0 0 11.77
59
0 0 5.85
26
0 0
0 3.44
90
0 0 11.9
232
TABLES OF LAND MEASURE.

Dimensions.
Yards.
Statute content.
A. R. P.
Dimensions. Statute content.
Dimensions. Statute content.
Yards.
4 by 91
0 0 12.03
5 by 59
92
0
0 12.17
60
A. R. P.
0 0 9.75
0 0 9.92
Yards.
A. R. P.
6 by 28
0 0 5.55
29
0 0
5.75
93
0
0 12.3
61
0 0 10.08
30
0 0 5.95
94
0 0 12.43
62
0 0 10.25
31
0 0 6.15
95
0 0 12.56
63
0 0 10.41
32
0 0
6.35
96
0 0 12.69
64
0
0 10.58
33
0 0
6.55
97
0 0 12.83
65
0
0 10.74
34
0
6.74
98
0
0 12.96
66
0
0 10.91
35
0 0
6.94
99
0 0 13.09
67
0
0 11.07
36
0 0
7.14
100
0 0 13.22
68
0 0 11.24
37
0 0 7.34
5 by 5
0 0 0.83
69
0 0 11.4
38
0 0
7,54
6
0 0 0.99
70
0 0 11.57
39
0 0
7.74
7
0 0
1.16
71
0 0 11.74
40
0 0
7,93
8 0 0
1.32
72
0
0 11.9
41
0 0
8.13
11
13
15
17
POHERCRONO
9 0 0
1.49
73
0 0 12.07
42
0 0
8.33
10 0 0
1.65
74
0
0 12.23
43
0 0
8.53
0 0
1.82
75
0 0 12.4
44
0 0 8.73
12 0 0
1.98
76
0
0 12.56
45
0 0
8.93
0 0 2.15
77
0 0 12.73
46
0 0 9.12
14 0 0
2.31
78
0
0 12.89
47
0 0
9.32
0 0 2.48
79
0
0 13.06
48
0 0
9.52
16 0 0
2.64
80
0
0 13.22
49
0 0
9.72
0 0 2.81
81
0
0 13.39
50
0 0 9.92
18 0 0 2.98
82
0
0 13.55
51
0 0 10.12
19
0 0 3.14
83
0
0 13.72
52
0
0 10.31
20 0 0
3.31
84
0
0 13.88
53
0 0 10.51
21
0 0 3.47
85
0
0 14.05
54
0 0 10.71
22 0 0 3.64
86
0
0 14.21
55
0 0 10.91
23
0 0 3.8
87
0
0 14.38
56
0 0 11.11
24 0 0 3.97
88
0
0 14.55
57
0 0 11.31
25
0 0 4.13
89
0
0 14.71
58
0 0 11.5
26
0 0 4.3
90
0 0 14.88
59
0 0 11.7
27 0 0 4.46
91
0 0 15.04
60
0 0 11.9
28
0 0 4.63
92
0 0 15.21
61
0 0 12.1
29
0 0 4,79
93
0 0 15.37
62
0 0 12.3
30
0 0 4.96
94
0 0 15.54
63
0 0 12.5
31
0 0 5.12
95
0 0 15.7
64
0 0 12.69
32
0 0 5.29
96
0 0 15.87
65
0 0 12.89
33 0 0 5.45
97
0 0 16.03
66
0 0 13.09
34
0 0 5.62
98
0
0 16.2
67
0 0 13.29
35
0 0 5.79
99
0 0 16.36
68
0 0 13.49
36
0 0
5.95
100
0 0 16.53
69
0 0 13.69
37
0 0 6.12
6 by 6
0 0 1.19
70
0 0 13.88
38
0 0 6.28
7
0 0 1.39
71
0 0 14.08
39 0 0 6.45
8
0 0 1.59
བ
72
0 0 14.28
40 0 0 6.61
9
0 0 1.79
73
0 0 14.48
41
0 0 6.78
10
0 0
1.98
74
0 0 14.68
42 0 0 6.94
11
0 0
2.18
75
0 0 14.88
43
0 0 7.11
12
0 0 2.38
76
0 0 15.07
44
0 7.27
13
0 0 2.58
77
0 0 15.27
45
0 0 7,44
14
0 0 2.78
78
0 0 15.47
46
0 7.6
15
0 2.98
79
0 0 15.67
47
0 0 7.77
16
0 0 3.17
80
0 0 15.87
48 0 0 7.93
17
0 0 3.37
81
0 0 16.07
49 0 0 8.10
18
0 0 3.57
82
0 0 16.26
50 0 0 8.26
19
0 0 3.77
83
0 0 16.46
51
0 0 8.43
20
0 0 3.97
84
0 0 16.66
52
0 0 8.6
21
0 0 4.17
85
0 0 16.86
53
0 0 8.76
22
0 0 4.36
86
0 0 17.06
54 0 0 8.93
23
0 0 4.56
87
0 0 17.26
55
0 0 9.09
24
0 0 4.76
88
0 0 17.45
56
0 0 9.26
25
0 4.96
89
0 0 17.65
57 0 0 9.42
26
0 0
5.16
90
0 0 17.85
58
0 0 9.59
27
0 0
0 5.36
91
0 0 18.05
TABLES OF LAND MEASURE.
233

Dimensions.
Statute content.
Yards.
A. R. P.
Dimensions.
Yards.
Statute content.
Dimensions.
Statute content,
A. R. P.
Yards.
A. R. P.
6 by 92
0 0 18.25
7 by 62
0 0 14.35
8 by 33
0 0
0 8.73
93
0 0 18.45
63
0 0 14.58
34
0 0
0
8.99
94
0 0 18.64
64
0 0 14.81
35
0
0
9.26
95
0 0 18.84
65
0 0 15.04
36
0 0
0 9.52
96
0 0 19.04
66
0 0 15.27
37
0 0 9.79
97
0 0 19.24
67
0 0 15.5
38
0 0 10.05
98
0 0 19.44
68
0
0 15.74
39
0 0 10.31
99
0
0 19.64
69
0
0 15.97
40
0
0 10.58
100
0
0 19.83
70
0
0 16.2
41
0 0 10.84
7 by 7
0 0 1.62
71
0
0 16.43
8
0 0
1.85
72
0
0 16.66
9
0 0
2.08
73
0
0 16.89
***
42
0 0 11.11
43
0
0 11.37
44
0
0 11.64
10
0 0
2.31
74
0
0.17.12
45
0
0 11.9
11 0 0 2.55
75
0
0 17.36
46
0 0 12.17
12
0 0 2.78
76
0
0 17.59
47
0
0 12.43
13
0
0
0
3.01
77
0
0 17.82
48
0
0 12.69
14
0
0
0
3.24
78
0
0 18.05
49
0 0 12.96
15
0 3.47
79
0
0 18.28
50
0
0 13.22
16
0 0 3.7
80
0
0 18.51
51
0
0 13.49
17
0 0 3.93
81
0
0 18.74
52
0
0 13.75
18
0 0
4.17
82
0
0 18.98
53
0
0 14.02
19
0 0 4.4
83
0
0 19.21
54
0
0 14.28
20
0 0 4.63
84
0 0 19.44
55
0
0 14.55
21
0 0
4.86
85
0
0 19.67
56
0
0 14.81
22 0 0 5.09
86
0
0 19.9
57
0 0 15.07
23 0 0 5.32
87
0 0 20.13
58
0
0 15.34
24 0 0 5.55
88
0 0 20.36
59
0
0 15.6
25
0 0 5.79
89
0
0 20.6
60
0 0 15.87
26 0 0 6.02
90
0 0 20.83
61
0
0 16.13
27
0 0 6.25
91
0 0 21.06
62
0
0 16.4
28
0 0 6.48
92
0
0 21.29
63
0
0 16.66
29
0 0 6.71
93
0 0 21.52
64
0
0 16.93
30
0 0 6.94
94
0 0 21.75
65
0 0 17.19
31
0 0
0 7.17
95
0 0 21.98
66
0
0 17.45
32
0 0 7.4
96
0 0 22.21
67
0
0 17.72
33
0 0 7.64
97
0 0 22.45
68
0
0 17.98
34
0 0 7.87
98
0
0 22.68
69
0 0 18.25
35
0 0 8.1
99
0 0 22.91
70
0
0 18.51
36
0 0 8.33
100
0 0 23.14
71
0 0 18.78
37
0 0 8.56
8 by 8
0 0 2.12
72
0
0 19.04
38
0 0 8.79
9
0 0 2.38
73
0 0 19.31
39 0 0 9.02
10
0 0 2.64
74
0
0 19.57
40
0 0 9.26
11
0 0 2.91
75
0
0 19.83
41 0 0 9.49
12
0 0 3.17
76
0
0 20.1
*****
42
0 0
0 9.72
13
0 0
3.44
77
0
0 20.36
43
0 0 9.95
14
0 0 3.7
78
0 0 20.63
44 0 0 10.18
15
0 0 3.97
79
0 0 20.89
45
0 0 10.41
16
0 0
4.23
80
0 0 21.16
46
0 0 10.64
17
0 0
4.5
81
0 0 21.42
47
0 0 10.88
18
0 0
4.76
82
0 0 21.69
48
0 0 11.11
19
0
0.5.02
83
0 0 21.95
49
0 0 11.34
20
0 0
5.29
84
0 0 22.21
50
0 0 11.57
21
0 0 5.55
85
0 0 22.48
51
0 0 11.8
22
0 0 5.82
86
0 0 22.74
52
0 0 12.03
23
0 0 6.08
87
0 0 23.01
53
0 0 12.26
24
0 0 6.35
88
0 0 23.27
54
0 0 12.5
25
0 0 6.61
89
0
0 23.54
55
0 0 12.73
26
0 0 6.88
90
0
0 23.8
56
0 0 12.96
27
0 0 7.14
91
0 24.07
57
0
0 13.19
28
0 0 7.4
92
0 0 24.33
58
0
0 13.42
29
0 0 7.67
93
0
0 24.6
59
0 0 13.65
30
0
0
0 7.93
94
0 0 24.86
60
0 0 13.88
31
0 0 0 8.20
95
0 0 25.12
61
0 0 14.12
32
0 0 8.46
96
0 0 25.39
Ꭱ
R
234
TABLES OF LAND MEASURE.

Dimensions.
Statute content.
Dimensions. Statute content.
Dimensions.
Statute content.
Yards,
A. R. P.
Yards.
+
A. R. P.
Yards.
8 by 97
0
0 25.65
9 by 69
0 0 20.53
10 by 42
A. R. P.
0 0 13.88
98
0
0 25.92
70
0 0 20.83
43
0 0 14.21
99
0 26.18
71
0 0 21.12
44
0 0 14.55
100
0
0 26.45
72
0 0 21.42
45
0 0 14.88
9 by 9
0 0 2.68
73
0 0 21.72
46
0 0 15.21
10
0 0
2.98
74
0 0 22.02
47
0 0 15.54
11
0 0
3.27
75
0 0 22.31
48
0 0 15.87
12
0 0
3.57
76
0 0 22.61
49
0
0 16.2
13
0 0
3.87
77
0 0 22.91
50
0
0 16.53
14
0 0 4.17
78
0 0 23.21
51
0
0 16.86
15
0
4.46
79
0 0 23.5
52
0 0 17.19
16
0 4.76
80
0 0 23.8
53
0 0 17.52
17
0 0 5.06
81
0 0 24.1
54
0 0 17.85
18
0 0 5.36
82
0 0 24.4
55
0 0 18.18
19
0 0 5.65
83
0 0 24.69
56
0
0 18.51
20
0 0 5.95
84
0 0 24.99
57
0 0 18.84
21
0 0 6.25
85
0 0 25.29
58
0
0 19.17
22 0 0 6.55
86
0 0 25.59
59
0 0 19.5
23
0 0 6.84
87
0 0 25.88
60
0
0 19.83
24
0 0
7.14
88
0
0 26.18
61
0 0 20.17
25 0 0 7.44
89
0 0 26.48
62
0 20.5
26
0 0 7.74
90
0 0 26.78
63
0 20.83
27
0 0 8.03
91
0
0 27.07
64
0 21.16
28
0 0
8.33
92
0 0 27.37
65
0
0 21.49
29
0 0 8.63
93
0
0 27.67
66
0
0 21.82
30
0 0 8.93
94
0
0 27.97
67
0
0 22.15
31
0 0 9.22
95
0 0 28.26
68
0
0 22.48
32
0 9.52
96
0 0 28.56
69
0 0 22.81
33
0 9.82
97
0 0 28.86
70
0 23.14
34
0
0 10.12
98
0 0 29.16
71
0 0 23.47
35
0 10.41
99
0 0 29.45
72
0 0 23.8
36
0
0 10.71
100
0 0 29.75
73
0
0 24.13
37
0 0 11.01
10 by 10
0 0 3.31
74
0
0 24.46
38
0 0 11.31
11
0 0 3.64
75
0
0 24.79
39
0 0 11.6
12
0 0 3.97
76
0 25.12
40
0 0 11.9
13
0 0 4.3
77
0 25.45
41
0 0 12.2
14
0 0 4.63
78
0
0 25.79
42
0 0 12.5
15
0 0 4.96
79
0 0 26.12
43
0 0 12.79
16
0 0 5.29
80
0 0 26.45
44
0
0 13.09
17
0 0 5.62
81
0 0 26.78
45
0
0 13.39
18
0 0 5.95
82
0 0 27.11
46
0 0 13.69
19
0 0 6.28
83
0 0 27.44
47
0 0 13.98
20
0 0 6.61
84
0 0 27.77
48
0 0 14.28
21
0 0 6.94
85
0 0 28.1
49
0
0 14.58
22
0 0 7.27
86
0
0 28.43
50
0
0 14.88
23
0
0.7.6
87
0
0 28.76
51
0
0 15.17
24
0 0 7.93
88
0
0 29.09
52
0
0 15.47
25
0 0
8.26
89
0 0 29.42
53
0 0 15.77
26
0 0
8.6
90
0
0 29.75
54
0 0 16.07
27
0 0 8.93
91
0 0 30.08
55
0 0 16.36
28
0 0 9.26
92
0 0 30.41
56
0 0 16.66
29
0 0 9.59
93
0
0 30.74
57
0 0 16.96
30
0 0 9.92
94
0
0 31.07
58
0 0 17.26
31
0 0 10.25
95
0
0 31.4
59
0 0 17.55
32
0 0 10.58
96
0
0 31.74
60
0
0 17.85
33
0 0 10.91
97
0
0 32.07
61
0
0 18.15
34
0 0 11.24
98
0
0 32.4
62
0 0 18.45
35
0 0 11.57
99
0
0 32.73
63
0 0 18.74
36
0 0 11.9
100
0 0 33.06
64
0 0 19.04
37
0 0 12.23
11 by 11
0
0 4.
65
0 0 19.34
38
0 0 12.56
12
0
0 4.36
66
0 0 19.64
39
0
0 12.89
13
0
0 4.73
67 0 0 19.93
40
0 0 13.22
14 0 0 5.09
68
0 0 20.23
41
0 0 13.55
15
0 0 5.45
TABLES OF LAND MEASURE.
235

Dimensions. Statute content.
Yards.
A. R. P.
Dimensions.
Yards.
Statute content.
Dimensions.
A. R. P.
Yards.
Statute content.
A. R. P.
11 by 16
0 0
5.82
11 by 80
0
0 29.19
12 by 55
0 0 21.82
17
0
0
0
6.18
81
0 0 29.56
56
0 0 22.21
18
0 0
6.55
82
0 0 29.92
57
0 0 22.61
19
0 0
0
6.91
83
0
0 30.28
58
0 0 23.01
20
0
0
7.27
84
0
0 30.65
59
0 0 23.4
21
0
0
0
7.64
85
0
0 31.01
60
0 0 23.8
22
0 8.
86
0
0 31.37
61
0
0 24.2
23
0
8.36
87
0 0 31.74
62
0
0 24.6
24
0
8.73
88
0
0 32.1
63
0 0 24.99
25
0 9.19
89
0
0 32.46
64
0
0 25.39
26
0
0 0
9.56
90
0
0 32.83
65
0 0 25.79
27
0 0 9.92
91
0
0 33.19
66
0 0 26.18
28
0 0 10.28
92
0
0 33.56
67
0 0 26.58
29
0 0 10.65
93
0
0 33.92
68
0 0 26.98
30
0 0 11.01
94
0
0 34.28
69
0
0 27.37
31
0 0 11.37
95
0
0 34.65
70
0 0 27.77
32
0 0 11.74
96
0
0 35.01
71
0 0 28.17
33
0 0 12.1
97
0
0 35.37
72
0 0 28.56
34
0 0 12.46
98
0 0 35.74
73
0 0 28.96
35
0 0 12.83
99
0 0 36.1
74
0 0 29.36
36
0 0 13.19
100
0 0 36.46
75
0 0 29.75
37
0 0 13.56
12 by 12
0 0 4.76
76
0 0 30.15
38
0 0 13.92
13
0 0 5.16
77
0 0 30.55
39
0 0 14.28
14
0 0 5.55
78
0 0 30.94
40
0 0 14.65
15
0 0 5.95
79
0 0 31.34
41
0 0 15.01
16
0 0 6.35
80
0
0 31.74
42
0 0 15.37
17
0 6.74
81
0 0 32.13
43
0 0 15.74
18
0 0 7.14
82
0 0 32.53
44
0 0 16.1
19
0 7.54
83
0 0 32.93
45
0 0 16.46
20
0 0 7.93
84
0 0 33.32
46
0
0 16.83
21
0 0 8.33
85
0 0 33.72
47
0
0 17.19
22
0
0 8.73
86
0 0 34.12
48
0
0 17.56
23
0 9.12
87
0 0 34.51
49
0 0 17.92
24
0 0 0 9.52
88
0 0 34.91
50
0 0 18.28
25
0
0 9.92
89
0 0 35.31
51
0 0 18.65
26
0 0 10.31
90
0 0 35.7
52
0 0 19.01
27
0 0 10.71
91
0
0 36.1
53
0 0 19.37
28
0 0 11.11
92
0 0 36.5
54
0 0 19.74
29
0 0 11.5
93
0 0 36.89
55
0 0 20.1
30
0 0 11.9
94
0 0 37.29
56
0 0 20.46
31
0 0 12.3
95
0 0 37.69
57
0 0 20.83
32
0 0 12.69
96
0 0 38.08
58
0 0 21.19
33
0 0 13.09
97
0 0 38.48
59
0 0 21.56
34
0 0 13.49
98
0 0 38.88
60
0 0 21.92
35
0 0 13.88
99
0 0 39.27
61
0
0 22.28
36
0
0 14.28
100
0 0 39.67
62
0
0 22.65
37
0 0 14.68
13 by 13
0 0
5.59
63
0
0 23.01
38
0
0 15.07
14
0
6.02
64
0
0 23.37
39
0
0 15.47
15
0 0
6.45
65
0 0 23.74
40
0 0 15.87
16
0 0
6.88
66
0 0 24.1
41
0
0 16.26
17
0
0
0
7.31
67
0 0 24.46
42
0 0 16.66
18
0 0
0
7.73
68
0
0 24.83
43
0 0 17.06
19
0
0
0 8.17
69
0
0 25.19
44
0 0 17.45
20
0 0 0
8.6
70
0 25.56
45
0 0 17.85
21
0 0 0 9.02
222
71
0 25.92
46
0 0 18.25
22
0 0
9.45
72
0
0 26.28
47
0 0 18.64
23
0 0
9.88
73
0
0 26.65
48
0 0 19.04
24
0 0 10.31
74
0
0 27.01
49
0 0 19.44
25
0 0 10.74
75
0 0 27.37
50
0 0 19.83
26
0 0 11.17
76
0 0 27.74
51
0 0 20.23
27
0 0 11.6
77
0 0 28.1
52
0 0 20.63
78
0 0 28.46
53
0
0 21.02
79
0
0 28.83
54
0 0 21.42
888
28
0 0 12.03
29
0 0 12.46
30
0 0 12.89
236
TABLES OF LAND MEASURE.

Dimensions.
Yards.
Statute content.
Dimensions. Statu e content. Dimensions.
Statute content.
A. R. P.
Yards.
A. R.
P.
Yards.
A. R. P.
13 by 31
0 0 13.32
13 by 95
0 1
0.83
14 by 72
0 0 33.32
32
0 0 13.75
96
0 1
1.26
73
0
0 33.79
33
0 0 14.18
97
0 1
1.69
74
0 0 34.25
34
0 0 14.61
98
0 1
2.12
75
0
0 34.71
35
0 0 15.04
99
0 1
2.55
76
0 0 35.17
36
0 0 15.47
100
0 1
2.98
77
0
0 35.64
37
0 0 15.9
14 by 14
0 0
6.48
78
0
0 36.1
38
0 0 16.33
15
0 0
6.94
79
0
0 36.56
39
0 0 16.76
16
0 0
7.4
80
0
0 37.02
40
0 0 17.19
17
0 0
7.87
81
0
0 37.49
41
0
0 17.62
18
0 0
8.33
82
0
0 37.95
42
0
0 18.05
19
0
0 8.79
83
0
0 38.41
43
0
0 18.48
20
0 0 9.26
84
0
0 38.88
44
0
0 18.91
21
0 0 9.72
85
0 0 39.34
45
0
0 19.34
22
0
0 10.18
86
0 0 39.8
46
0
0 19.77
23
0
0 10.64
87
0
1
1 0.26
47
0 0 20.2
24
0 0 11.11
88
0
1
1
0.73
48
0
0 20.63
25
0 0 11.57
89
0
1
1.19
49
0 21.06
26
0
0 12.03
90
0 1
1.65
50
0 21.49
27
0 0 12.5
91
0 1 2.12
51
0 21.92
28
0
0 12.96
92
0 1
2.58
52
0
0 22.35
29
0
0 13.42
93
0
1 3.04
53
0
0 22.78
30
0
0 13.88
94
0
1
1 3.5
54
0
0 23.21
31
0
0 14.35
95
0
1 1 3.97
55
0
0 23.64
32
0 0 14.81
96
0
1
4.43
56
0
0 24.07
33
0 0 15.27
97
0 1
4.89
57
0 0 24.5
34
0
0 15.74
98
0 1
5.36
58
0 0 24.93
35
0 16.2
99
0 1
5.82
59
0 0 25.36
36
0 0 16.66
100
0 1 6.28
60
0 0 25.79
37
0
0 17.12
15 by 15
0 0
7.44
61
0 0 26.21
38
0
0 17.59
16
0 0
7.93
62
0 0 26.64
39
0
0 18.05
17
0 0
8.43
63
0 0 27.07
40
0 18.51
18
0 0 8.93
64
0 0 27.5
41
0
0 18.98
19
0 0 9.42
65
0
0 27.93
42
0
0 19.44
20
0 0 9.92
66
0
0 28.36
43
0
0 19.9
21
0 0 10.41
67
0
0 28.79
44
0 0 20.36
22
0
0 10.91
68
0
0 29.22
45
0
0 20.83
23
0
0 11.4
69
0
0 29.65
46
0
0 21.29
24
0
0 11.9
70
0
0 30.08
47
0
0 21.75
25
0
0 12.4
71
0
0 30.51
48
0
0 22.21
26
0
0 12.89
72
0
0 30.94
49
0 0 22.68
27
0
0 13.39
73
0
0 31.37
50
0 0 23.14
28
0 0 13.88
74
0
0 31.8
51
0 23.6
29
0 0 14.38
75
0
0 32.23
52
0 0 24.07
30
0 0 14.88
76
0
0 32.66
53
0 24.53
31
0 0 15.37
77
0
0 33.09
54
0 0 24.99
32
0 0 15.87
78
0
0 33.52
55
0
0 25.45
33
0 0 16.36
79
0 0 33.95
56
0
0 25.92
34
0 0 16.86
80
0 0 34.38
57
0
0 26.38
35
0 0 17.36
81
0 0 34.81
58
0
0 26.84
36
0 0 17.85
82
0 0 35.24
59
0 27.31
37
0 0 18.35
83
0 0 35.67
60
0
O 27.77
38
0 0 18.84
84
0 0 36.1
61
0 28.23
39
0 0 19.34
85
0 0 36.53
62
0
0 28.69
40
0 0 19.83
86
0 0 36.96
63
0
0 29.16
41
0 0 20.33
87
0 0 37.39
64
0
0 29.62
42
0 0 20.83
88 0 0 37.82
65
0
0 30.08
43
0 0 21.32
89
0 0 38.25
66
0
0 30,55
44
0 0 21.82
90
0
0 38.68
67
0
0 31.01
45
0 0 22.31
91
0 0 39.11
68
92
0
0 39.54
93 0 0 39.97
94
0 1 0.4
71
228:
0
0 31.47
46
0 0 22.81
69
0
0 31.93
47
0 0 23.31
70
0
0 32.4
48
0 0 23.8
0
0 32.86
49
0 0 24.3
TABLES OF LAND MEASURE.
237

Dimensions.
Statute content.
Yards.
A. R. P.
Dimensions.
Yards.
Statute content.
Dimensions.
Statute content.
A. R.
P.
Yards.
A. R.
P.
15 by 50
0
0 21.79
16 by 29
0 0 15.34
16 by 93
0 1
9.19
51
0
0 25.29
30
0 0 15.87
94
0 1
9.72
52
0
0 25.79
31
0 0 16.4
95
0 1 10.25
53
0
0 26.28
32
0 0 16.93
96
0 1 10.78
54
0
0 26.78
33
0
0 17.45
97
0 1 11.31
55
0
0 27.27
34
0
0 17.98
98
0 1 11.83
56
0
0 27.77
35
0
0 18.51
99
0 1 12.36
57
0
0 28.26
36
0
0 19.04
100
0 1 12.89
58
0
0 28.76
37
0
0 19.57
17 by 17
0
0
9.55
59
0
0 29.26
38
0
0 20.1
18
0
0 10.12
60
0
0 29.75
39
0
0 20.63
19
0
0 10.68
61
0
0 30.25
40
0
0 21.16
20
0
0 11.24
62
0
0 30.74
41
0
0 21.69
21
0
0 11.8
63
0
0 31.24
42
0
0 22.21
22
0
0 12.36
64
0
0 31.74
43
0
0 22.74
23
0
0 12.93
65
0
0 32.23
44
0
0 23.27
24
0
0 13.49
66
0
0 32.73
45
0
0 23.8
25
0 14.05
67
0
0 33.22
46
0
0 24.33
26
0
0 14.61
68
0
0 33.72
47
0
0 24.86
27
0
0 15.17
69
0
0 34.21
48
0
0 25.39
28
0
0 15.74
70
0
0 34.71
49
0
0 25.92
29
0 0 16.3
71
0
0 35.21
50
0 26.45
30
0
0 16.86
72
0
0 35.7
51
0
0 26.98
31
0
0 17.42
73
Ꮳ
0 36.2
52
0
0 27.5
32
0
0 17.98
74
0
0 36.69
53
0
0 28.03
33
0
0 18.55
75
.0
0 37.19
54
0
0 28.56
34
0
0 19.11
76
0
0 37.69
55
0
0 29.09
35
0
0 19.67
77
0
0 38.18
56
0
0 29.62
36
0
0 20.23
78
0
0 38.68
57
0
0 30.15
37
0
0 20.79
79
0
0 39.17
58
0
0 30.68
38
0
0 21.36
80
0
0 39.67
59
0
0 31.21
39
0
0 21.92
81
0 1 0.17
60
0
0 31.74
40
0
0 22.48
82
0 1 0.66
61
0
0 32.26
41
0
0 23.04
83
0 1 1.16
62
0
0 32.79
42
0
0 23.6
84
0 1 1.65
63
0
0 33.32
43
0 24.17
85
0 1 2.15
64
0
0 33.85
44
0
0 24.73
85
86 0 1 2.64
65
0
0 34.38
45
0 25.29
87
0 1 3.14
66
0
0 34.91
46
0
0 25.85
88
0 1 3.64
67
0
0 35.44
47
0 0 26.41
89
0 1 4.13
68
0
0 35.97
48
0
0 26.98
90
0 1 4.63
69
0
0 36.5
49
0
0 27.54
91
0 1 5.12
70
0
0 37.02
50
0 28.1
92
0 1 5.62
71
0
0 37.55
51
0
0 28.66
93
0 1 6.12
72
0
0 38.08
52
0
0 29.22
94
0 1 6.61
73
0
0 38.61
53
0
0 29.79
95
0 1 7.11
74
0
0 39.14
54
0
0 30.35
96
0 1 7.6
75
0 0 39.67
55
0 30.91
97
0 1 8.1
76
0 1 0.2
56
0
0 31.47
98
0
1 8.6
77
0 1 0.73
57
0 32.03
99
0 1 9.09
78
0 1 1.26
58
0
0 32.6
100
0 1 9.59
79
0 1 1.79
59
0
0 33.16
16 by 16
0 0 8.46
80
0 1 2.31
60
0
0 33.72
17
0 0 8.99
81
0
1 2.84
61
0
0 34.28
18
0
0 9.52
82
0 1 3.37
62
0
0 34.84
19
0
0 10.05
83
0 1 3.9
63
0
0 35.4
20
0
0 10.58
84
0 1
4.43
64
0
0 35.97
21
0 0 11.11
85
0 1
4.96
65
0
0 36.53
22
0
0 11.64
86
0 1
5.49
66
0 0 37.09
23
0
0 12.17
87
0 1
1 6.02
67
0
0 37.65
24
0
0 12.69
88
0 1 1 6.55
68
0 38.21
25
0
0 13.22
89
0 1
1 7.07
26
0
0 13.75
90
0 1 7.6
27
0
0 14.28
91
0 1 1 8.13
28
0
0 14.81
92
0 1 8.66
SCEN
69
0 0 38.78
70
0 0 39.34
0 0 39.9
72
0 1 0.46
TABLES OF LAND MEASURE.
238

Dimensions.
Statute content.
Dimensions. Statute content.
Dimensions.
Statute content.
Yards.
A. R.
P.
Yards.
A. R. P.
Yards.
A. R. P.
17 by 73
0 1
1.02
18 by 54
0 0 32.13
19 by 36
0 0 22.61
74
0 1
1.59
55
0 0 32.73
37
0
0 23.24
75
0 1
2.15
56
0 0 33.32
38
0
0 23.87
76
0 1
2.71
57
0 0 33.92
39
0
0 24.5
77
0 1
3.27
58
0
0 34.51
40
0
0 25.12
78
0 1
3.83
59
0
0 35.11
41
0 0 25.75
79
0 1
4.4
60
0
0 35.7
42
0
0 26.38
80
0 1
4.96
61
0
0 36.3
43
0
0 27.01
81
0 1
5.52
62
0
0 36.89
44
0 0 27.64
82
0 1
6.08
63
0
0 37.49
45
0
0 28.26
83
0 1
6.64
64
0
0 38.08
46
0
0 28.89
84
0 1
7.21
65
0
0 38.68
47
0
0 29.52
85
0 1
7.77
66
0
0 39.27
48
0
0 30.15
86
0 1
8.33
67
0
0 39.87
49
0
0 30.78
87
0 1
8.89
68
0 1 0.46
50
0
0 31.4
88
0 1 9.45
69
1
1.06
51
0
0 32.03
89
0 1 10.02
70
0
1
1.65
52
0
0 32.66
90
0 1 10.58
71
0
1
2.25
53
0
0 33.29
91
0 1 11.14
72
0
1
2.84
54
0
0 33.92
92
0 1 11.7
73
0 1
3.44
55
0
0 34.55
93
0 1 12.26
74
0 1
4.03
56
0
0 35.17
94
0 1 12.83
75
0 1
4.63
57
0
0 35.8
95
0 1 13.39
76
0 1
5.22
58
0
0 36.43
96
0 1 13.95
77
0
1
5.82
59
0
0 37.06
97
0 1 14.51
78
0
1
6.41
60
0
0 37.69
98
0 1 15.07
79
0 1
7.01
61
0
0 38.31
99
0 1 15.64
80
0 1
7.6
62
0
0 38.94
100
0
1 16.2
81
0
1
8.2
63
0 0 39.57
18 by 18
0
0 10.71
82
0 1
8·79
64
0
1 0.2
19
0 11.31
83
0 1 9.39
65
0 1 0.83
20
0 0 11.9
84
0 1 9.98
66
0 1
1.45
21
0 0 12.5
85
0
1 10.58
67
0 1
2.08
22
0 0 13.09
86
0
1 11.17
68
0 1
2.71
23
0 0 13.69
87
0 1 11.77
69
0 1
3.34
24
0 0 14.28
88
0 1 12.36
70
0 1
3.97
25
0 0 14.88
89
0
1 12.96
71
0
1
4.6
26
0 0 15.47
90
0 1 13.55
72
0 1
5.22
27
0 0 16.07
91
0 1 14.15
73
0 1
5.85
28
0 0 16.66
92
0
1 14.74
74
0 1
6.48
29
0 0 17.26
93
0 1 15.34
75
0 1
7.11
30
0 0 17.85
94
0
1 15.93
76
0 1
7.74
31
0 0 18.45
95
0
1 16.53
77
0 1
8.36
32
0 0 19.04
96
0 1 17.12
78
0 1 8.99
33
0 0 19.64
97
0 1 17.72
79
0
1 1 9.62
34
0 0 20.23
98
0
1 18.31
80
0
1 10.25
35
0 0 20.83
99
0
1 18.91
81
0
1 10.88
36
0 0 21.42
100
0
1 19.5
82
0 1 11.5
37
0
0 22.02 19 by 19
0 0 11.93
83
0 1 12.13
38
0 0 22.61
20
0
0 12.56
84
0 1 12.76
39
0 0 23.21
21
0 0 13.19
85
0 1 13.39
40 0 0 23.8
22
0 0 13.82
86
0 1 14.02
41
0 0 24.4
23
0
0 14.45
87
0 1 14.64
42
0 0 24.99
24
0
0 15.07
88
0 1 15.27
43
0 0 25.59
25
0
0 15.7
89
0
1 15.9
44
0 0 26.18
26
0
0 16.33
90
0
1 16.53
45
0 0 26.78
27
0
0 16.96
91
0 1 17.16
46
0 0 27.37
28
0
0 17.59
92
0 1 17.79
47
0 0 27.97
29
0' 0 18.21
93
0 1 18.41
48
0 0 28.56
30
0 18.84
94
0 1 19.04
49
0 0 29.16
31
0 19.47
95
0 1 19.67
50
0 0 29.75
32
0
0 20.1
96
0 1 20.3
51
0 0 30.35
33
0
0 20.73
97
0 1 20.93
52
0 0 30.94
34
0
0 21.36
98
0 1 21.55
53
0 0 31.54
35
0 0 21.98
99
0 1 22.18
TABLES OF LAND MEASURE.
239

Dimensions.
Statute content.
Dimensions. Statute content.
Dimensions.
Statute content.
iards.
A. R. P.
Yards.
A. R. P.
Yards.
A. R.
P.
19 by 100
20 by 20
0
1 22.81
20 by 83
0 1 14.88
21 by 67
0 1 6.51
0 0 13.22
84
0 1 15.54
68
0 1
7.21
21
0
0 13.88
85
0
1 16.2
69
0 1
7.9
22
0
0 14.55
86
0 1 16.86
70
0 1
8.6
23
0 0 15.21
87
0 1 17.52
71
0 1
9.29
24
0
0 15.87
88
0
1 18.18
72
0 1 9.98
25
0 0 16.53
89
0 1 18.84
73
0
1 10.68
26
0 0 17.19
90
0
1 19.5
74
0 1 11.37
27
0
0 17.85
91
0
1 20.17
75
0 1 12.07
28
0
0 18.51
92
0
1 20.83
76
0 1 12.76
29
0
0 19.17
93
0
1 21.49
77
0 1 13.45
30
0
0 19.83
94
0
1 22.15
78
0 1 14.15
31
0
0 20.5
95
0 1 22.81
79
0 1 14.84
32
0 0 21.16
96
0 1 23.47
80
0 1 15.54
33
0
0 21.82
97
0
1 24.13
81
0 1 16.23
34
0
0 22.48
98
0
1 24.79
82
0 1 16.93
35
0
0 23.14
99
0
1 25.45
83
0 1 17.62
36
0
0 23.8
100
0
1 26.12
84
0 1 18.31
37
0
0 24.46
21 by 21
0
0 14.58
85
0 1 19.01
38
0 0 25.12
22
0
0 15.27
86
0 1 19.7
39
0
0 25.79
23
0
0 15.97
87
0 1 20.4
40
0
0 26.45
24
0
0 16.66
88
0
1 21.09
41
0 0 27.11
25
0
0 17.36
89
0 1 21.79
42
0 0 27.77
26
0
0 18.05
90
0
1 22.48
43
0
0 28.43
27
0
0 18.74
91
0
1 23.17
44
0
0 29.09
28
0
0 19.44
92
0 1 23.87
45
0
0 29.75
29
0
0 20.13
93
0 1 24.56
46
0 0 30.41
30
0 0 20.83
94
0 1 25.26
47
0 0 31.07
31
0
0 21.52
95
0
1 25.95
48
0 0 31.74
32
0
0 22.21
96
0 1 26.64
49
0 0 32.4
33
0 0 22.91
97
0
1 27.34
50
0 0 33.06
34
0
0 23.6
98
0
1 28.03
51
0
0 33.72
35
0 0 24.3
99
0
1 28.73
52
0 0 34.38
36
0
0 24.99
100
0
1 29.42
53
0 0 35.04
37
0
0 25.69
22 by 22
0 0 16.
54
0 0 35.7
38
0
0 26.38
23
0 0 16.73
55
0 0 36.36
39
0
0 27.07
24
0 0 17.45
56
0 0 37.02
40
0 0 27.77
25
0 0 18.18
57
0 37.69
41
0
0 28.46
26
0 0 18.91
58
0 0 38.35
42
0
0 29.16
27
0 0 19.64
59
0 0 39.01
43
0 0 29.85
28
0 0 20.36
60
0
0 39.67
44
0 0 30.55
29
0 0 21.09
61
0 1
1
0.33
45
0
0 31.24
30
0 0 21.82
62
0 1 1
0.99
46
0 0 31.93
31
0 0 22.55
63
0 1 1.65
47
0
0 32.63
32
0
0 23.27
64
0 1
2.31
48
0 0 33.32
33
0 0 24.
65
0 1 2.98
49
0
0 34.02
34
0 0 24.73
66
0 1 3.64
50
0
0 34.71
35
0
0 25.45'
67
0 1 4.3
51
0 0 35.4
36
0 0 26.18
68
0 1 4.96
52
0
0 36.1
37
0 0 26.91
69
0 1 5.62
53
0 0 36.79
38
0
0 27.64
70
0 1 6.28
54
0
0 37.49
39
0 28.36
71
0 1 6.94
55
0
0 38.18
40
0 29.09
72
0 1 7.6
56
0 0 38.88
41
0
0 29.82
73
0 1 8.26
57
0 0 39.57
42
0
0 30.55
74
0 1 8.93
58
0 1 0.26
43
0
0 31.27
75
0 1 9.59
59
0 1 0.96
44
0
0 32.
76
0 1 10.25
60
0 1 1.65
45
0
0 32.73
77
1 10.91
61
0 1 2.35
46
0
0 33.45
78
0 1 11.57
62
0 1 3.04
47
0 0 34.18
79
0 1 12.23
80
0 1 12.89
81
0 1 13.55
65
82
0 1 14.21
66
3+38
63
0 1 3.74
48
0 0 34.91
64
0 1
4.43
49
0 0 35.64
0 1 5.12
50
0 0 36.36
0 1 5.82
51
0
0 37.09
240
TABLES OF LAND MEASURE.

Dimensions. Statute content.
Dimensions. Statute content.
Dimensions.
Statute content.
Yards.
A. R. P.
Yards.
A. R. P.
Yards.
A. R. P.
22 by 52
0 0 37.82
23 by 38
0 0 28.89
24 by 25
0 0 19.83
53
0 0 38.55
39
0 0 29.65
26
0
0 20.63
54
0 0 39.27
40
0 0 30.41
27
0 0 21.42
55
0
1 0.
41
0 0 31.17
28
0 0 22.21
56
0 1 0.73
42
0
0 31.93
29
0 0 23.01
57
0 1
1
1.45
43
0 0 32.69
30
0 0 23.8
58
0 1
2.18
44
0
0 33.45
31
0
0 24.6
59
0 1
2.91
45
0
0 34.21
32
0
0 25.39
60
0 1
3.64
46
0
0 34.98
33
0
0 26.18
61
0
1
4.36
47
0
0 35.74
34
0
0 26.98
62
0 1 1
5.09
48
0 0 36.5
35
0
0 27.77
63
0 1 5.82
49
0 0 37.26
36
0 0 28.56
64
0 1 6.55
50
0
0 38.02
37
0
0 29.36
65
66
67
68
70
71
72
88508RENOLE
0 1 1
7.27
51
0
0 38.78
38
0
0 30.15
0 1 8.
52
0
0 39.54
39
0
0 30.94
0 1
8.73
53
0 1 1 0.3
40
0
0 31.74
0 1 9.45
54
0 1
1.06
41
0 0 32.53
69 0 1 10.18
55
0 1
1.82
42
0
0 33.32
0
1 10.91
56
0 1
2.58
43
0
0 34.12
0
1 11.64
57
0 1
3.34
44
0
0 34.91
0 1 12.36
58
0 1 4.1
45
0
0 35.7
73
0
1 13.09
59
0
1
4.86
46
0
0 36.5
74
0
1 13.82
60
0 1 5.62
47
0
0 37.29
75
0
1 14.55
61
0 1 6.38
48
0
0 38.08
76
0
1 15.27
62
0 1
7.14
49
0 0 38.88
77
0 1 16.
63
0 1
7.9
50
0
0 39.67
78
0 1 16.73
64
0 1 8.66
51
0
1
1 0.46
79
0 1 17.45
65
0 1 9.42
52
0
1
1 1.26
80
0
1 18.18
66
0 1 10.18
53
0 1
2.05
81
0 1 18.91
67
0 1 10.94
54
0 1
2.84
82
0 1 19.64
68
0 1 11.7
55
0 1 1 3.64
83
0 1 20.36
69
0 1 12.46
56
0
1
1 4.43
84
0 1 21.09
70
0 1 13.22
57
0
1
1 5.22
85
0 1 21.82
71
0
1 13.98
58
0
1
1 6.02
86
0 1 22.55
72
0 1 14.74
59
0
1
1 6.81
87
0 1 23.27
73
0 1 15.5
60
0
1
1 7.6
88
0 1 24.
74
0 1 16.26
61
0
1
1
8.4
89
0 1 24.73
75
0
1 17.02
62
0
1 9.19
90
0 1 25.45
76
0 1 17.79
63
0 1
1 9.98
31
0 1 26.18
77
0
1 18.55
64
0
1 10.78
92
0 1 26.91
78
0
1 19.31
65
0
1 11.57
93
0
1 27.64
79
0
1 20.07
66
0
1 12.36
94
0 1 28.36
80
0
1 20.83
67
0
1 13.16
95
0
1 29.09
81
0
1 21.59
68
0 1 13.95
96
0
1 29.82
82
0
1 22.35
69
0 1 14.74
97
0 1 30.55
83
0
1 23.11
70
0 1 15.54
98
0 1 31.27
84
0
1 23.87
71
0 1 16.33
99
0
1 32.
85
0 1 24.63
72
0 1 17.12
100
0
1 32.73
86
0 1 25.39
73
0 1 17.92
23 by 23
0
0 17.49
87
0
1 26.15
74
0 1 18.71
24
0
0 18.25
88
0 1 26.91
75
0 1 19.5
25
0 0 19.01
89
0 1 27.67
76
0
1 20.3
26
0
0 19.77
90
0 1 28.43
77
0 1 21.09
27
0 0 20.53
91
0 1 29.19
78
0
1 21.88
28
0
0 21.29
92
0 1 29.95
79
0 1 22.68
29
0
0 22.05
93
0 1 30.71
80
0 1 23.47
30
0 0 22.81
94
0 1 31.47
81
0 1 24.26
31 0 0 23.57
95
0 1 32.23
82
0 1 25.06
32
0 0 24.33
96
0 1 32.99
83
0 1 25.85
33
0 0 25.09
97
0 1 33.75
84
0 1 26.64
34
0 0 25.85
98
0 1 34.51
85
0 1 27.44
35
0 0 26.61
99
0 1 35.27
86
0 1 28.23
36
0 0 27.37
100
0
1 36.03
87
0 1 29.02
37
0 0 28.13 24 by 24
0 0 19.04
88
0
1 29.82
TABLES OF LAND MEASURE.
241
•

Dimensions.
Yards.
Statute content.
A. R. P.
Dimensions.
Yards.
Statute content.
Dimensions.
Statute content.
24 by 89
0 1 30.61
25 by 77
A. R. P.
0 1 23.64
Yards.
A, R. P.
26 by 66
0 1 16.73
90
0 1 31.4
78
0
1 24.46
67
0 1 17.59
91
0 1 32.2
79
0 1 25.29
68
0 1 18.45
92
0 1 32.99
80
0 1 26.12
69
0 1 19.31
93
0 1 33.79
81
0 1 26.94
70
0 1 20.17
94
0 1 34.58
82
0 1 27.77
71
0 1 21.02
95
0 1 35.37
83
0
1 28.6
72
0
1 21.88
96
0 1 36.17
84
0
1 29.42
73
0 1 22.74
97
0 1 36.96
85
0 1 30.25
74
0 1 23.6
98
0
1 37.75
86
0 1 31.07
75
0
1 24.46
99
0
1 38.55
87
0
1 31.9
76
0 1 25.32
100
0
1 39.34
88
0
1 32.73
77
0
1 26.18
25 by 25
0
0 20.66
89
0
1 33.55
78
0 1 27.04
26
0
0 21.49
90
0
1 34.38
79
0
1 27.9
27
0
0 22.31
91
0
1 35.21
80
0
1 28.76
28
0
0 23.14
92
0
1 36.03
81
0
1 29.62
29
0
0 23.97
93
0
1 36.86
82
0
1 30.48
30
0
0 24.79
94
0
1 37.69
83
0
1 31.34
31
0
0 25.62
95
0
1 38.51
84
0
1 32.2
32
0
0 26.45
96
0
1 39.34
85
0
1 33.06
33
0 0 27.27
97
0
2 0.17
86
0
1 33.92
34
0 0 28.1
98
0 2 0.99
87
0
1 34.78
35
0 0 28.93
99
0 2 1.82
88
0
1 35.64
36
0 0 29.75
100
0 2 2.64
89
0
1 36.5
37
0 0 30.58
26 by 26
0 0 22.35
90
0
137.36
38 0 0 31.4
27
0
0 23.21
91
0 1 38.21
39
0 0 32.23
28
0
0 24.07
92
0
1 39.07
40
0 0 33.06
29
0
0 24.93
93
0 1 39.93
41
0 0 33.88
30
0
0 25.79
94
0.2 0.79
42
0 0 34.71
31
0
0 26.64
95
0 2 1.65
43 0
0 35.54
32
0
0 27.5
96
2
2.51
44
0 0 36.36
33
0
0 28.36
97
0
2 3.37
45
0 0 37.19
34
0
0 29.22
98
0
2 4.23
46
0
0 38.02
35
0
0 30.08
99
0 2 5.09
47
0 0 38.84
36
0
0 30.94
100
0 2 5.95
48
0 0 39.67
37
0
0 31.8
27 by 27
0 0 24.1
49
0 1 0.5
38
0
0 32.66
28
0 0 24.99
50
0 1 1.32
39
0
0 33.52
29
0
0 25.88
51
0 1 2.15
40
0
0 34.38
30
0 0 26.78
52
0 1
2.98
41
0
0 35.24
31
0
0 27.67
53
0 1
3.8
42
0
0 36.1
32
0 0 28.56
54
0 1 4.63
43
0
0 36.96
33
0 0 29.45
55
0 1
5.45
44
0
0 37.82
34
0 0 30.35
56
0 1
6.28
45
0
0 38.68
35
0 0 31.24
57
0 1 7.11
46
0
0 39.54
36
0 0 32.13
58 0 1 7.93
47
0
1 0.4
37
0
0 33.02
59
0 1 8.76
48
0 1
1.26
38
0
0 33.92
60 0 1 9.59
49
0 1 2.12
39
0 34.81
61
0 1 10.41
50
0 1 2.98
40
0
0 35.7
62 0 1 11.24
51
0
1 3.83
41
0
0 36.6
63
0 1 12.07
52
0 1 1 4.69
42
0
0 37.49
64
0 1 12.89
53
0 1 5.55
43
0
0 38.38
65
0 1 13.72
54
0 1 6.41
44
0
0 39.27
66
0 1 14.55
55
0 1 7.27
45
0 1 0.17
67 0 1 15.37
56
0 1 8.13
46
0 1 1.06
68
0 1 16.2
57
0 1 8.99
47
0 1 1.95
69
0 1 17.02
58
0 1 9.85
48
0 1 2.84
70
0 1 17.85
59
0 1 10.71
49
0 1 3.74
71
0 1 18.68
60
0
1 11.57
50
0 1 4.63
72
0 1 19.5
61
73
0 1 20.33
74 0 1 21.16
75
0 1 21.98
76
0 1 22.81
UNI15
0 1 12.43
51
0 1 5.52
62
0 1 13.29
52
0 1 6.41
63
0
1 14.15
53
0 1 7.31
64
0
1 15.01
54
0 1 8.2
65
0
1 15.87
55
0 1 9.09
242
TABLES OF LAND MEASURE.

Dimensions.
Statute content.
Dimensions.
Statute content.
Dimensions.
Statute content.
Yards.
A. R.
P.
Yards.
A. R.
P.
Yards.
A. R. P.
27 by 56
0 1
9.98
28 by 47
0 1
3.5
29 by 39
0 0 37.39
57
0 1 10.88
48
0 1
4.43
40
0
0 38.35
58
0 1 11.77
49
0 1
5.36
41
0 0 39.31
59
0 1 12.66
50
0 1
6.28
42
0 1 1
0.26
60
0 1 13.55
51
0 1
7.21
43
0
1
1.22
61
0 1 14.45
52
0
1 8.13
44
0 1
2.18
62
0 1 15.34
53
0 1 9.06
45
0 1 1
3.14
63
0 1 16.23
54
0
1 9.98
46
0
1
4.1
64
0 1 17.12
55
0
1 10.91
47
0
1
5.06
65
0 1 18.02
56
0
1 11.83
48
0 1
6.02
66
0 1 18.91
57
0
1 12.76
49
0 1
7.98
67
0 1 19.8
58
0 1 13.69
50
0 1
8.93
68
0 1 20.69
59
0
1 14.61
51
0 1 9.89
69
0
1 21.59
60
0 1 15.54
52
0 1 10.85
70
0
1 22.48
61
0 1 16.46
53
0
1 11.81
71
0
1 23.37
62
0
1 17.39
54
0 1 12.77
72
0 1 24.26
63
0
1 18.31
55
0 1 13.73
73
0 1 25.16
64
0
1 19.24
56
0 1 14.69
74
0 1 26.05
65
0
1 20.17
57
0 1 15.64
75
0 1 26.94
66
0
1 21.09
58
0 1 16.6
76
0 1 27.83
67
0
1 22.02
59
0 1 17.56
77
0 1 28.73
68
0
1 22.94
60
0 1 18.52
78
0 1 29.62
69
0
1 23.87
61
0 1 19.48
79
0 1 30.51
70
0
1 24.79
62
0 1 20.44
80
0 1 31.4
71
0
1 25.72
63
0 1 21.4
81
0 1 32.3
72
0
1 26.64
64
0 1 22.36
82
0 1 33.19
73
0 1 27.57
65
0 1 23.31
83
0 1 34.08
74
0
1 28.5
66
0 1 24.27
84
0 1 34.98
75
0
1 29.42
67
0 1 25.23
85
0 1 35.87
76
0
1 30.35
68
0 1 26.19
86
0 1 36.76
77
0
1 31.27
69
0 1 27.15
87
0
137.65
78
0
1 32.2
70
0 1 28.11
88
0 1 38.55
79
0
1 33.12
71
0 1 29.07
89
0 1 39.44
80
0
1 34.05
72
0 1 30.02
90
0 2 0.33
81
0 1 34.98
73
0 1 30.98
91
0 2 1.22
82
0
1 35.9
74
0 1 31.94
92
0 2 2.12
83
0 1 36.83
75
0 1 32.9
93
0 2 3.01
84
0 1 37.75
76
0 1 33.86
94 0 2 4.9
85
0 1 38.68
77
0 1 34.82
95
0 2 4.79
86
0 1 39.6
78
0 1 35.78
96 0 2
2
5.69
87
0 2 0.53
79
0 1 36.74
97
0 2 6.58
88
0 2 1.45
80
0 1 37.69
98
0 2 2
7.47
89
0 2 2.38
81
0 1 38.65
99
0 2
2 8.36
90
0
2 3.31
82
0 1 39.61
100
0
2
2 9.26
91
0 2 4.23
83
0 2 0.57
28 by 28
0
0 25.92
92
0 2 5.16
84
0 2 1.53
29
0
0 26.84
93
0
2 6.08
85
0 2 2.49
30
0
0 27.77
94
0 2 7.01
86
0 2 3.45
31
0
0 28.69
95
0 2 7.93
87
0 2 4.4
32
0
0 29.62
96
0 2 8.86
88
0 2 5.36
33
0 0 30.55
97
0 2 9.79
89
0 2 6.32
34
0 0 31.47
98
0 2 10.71
90
0 2 7.28
35
0 0 32.4
99
0 2 11.64
91
0 2 8.24
36
0 0 33.32
100
0 2 12.56
92
0 2 9.2
37
0 0 34.25
29 by 29
0
0 27.8
93
0 2 10.16
38
0 0 35.17
30
0 0 28.76
94
0 2 11.12
39
0 0 36.1
31
0 0 29.72
95
0 2 12.07
40
0 0 37.02
32
0
0 30.68
96
0 2 13.03
41
0 0 37.95
33
0
0 31.64
97
0 2 13.99
42
0 0 38.88
34
0 0 32.6
98
0 2 14.95
43
0 0 39.8
35
0
0 33.55
99
0 2 15.91
44
0 1 0.73
36
0
0 34.51
100
0 2 16.87
45
0 1 1 1.65
37
0
0 35.47
30 by 30
0 0 29.75
46
0 1 2.58
38
0 0 36.43
31
0 0 30.74
TABLES OF LAND MEASURE.
243

Dimensions.
Statute content.
Dimensions. Statute content.
Dimensions.
Yards.
30 by 32
A. R. P.
0 0 31.74
Yards.
A. R. P.
Yards.
Statute content.
A. R. P.
96
0 2 15.21
31 by 90
0 2 12.23
33
0
0 32.73
97
0 2 16.2
91
0 2 13.26
34
0
0 33.72
98
0 2 17.19
92
0 2 14.28
35
0 0 34.71
99
0 2 18.18
93
0 2 15.31
36
0 0 35.7
100
0
2 19.17
94
0 2 16.33
37
0 0 36.69
31 by 31
0
0 31.77
95
0 2 17.36
38
0
0 37.69
32
0
0 32.79
96
0 2 18.38
39
0
0 38.68
33
0
0 33.82
97
0 2 19.4
40
0
0 39.67
34
0 0 34.84
98
0 2 20.43
41
0 1 0.66
35
0 0 35.87
99
0 2 21.45
42
0 1 1.65
36
0
0 36.89
100
0 2 22.48
43
0 1 2.64
37
0 0 37.92
32 by 32
0 0 33.85
44
0 1 3.64
38
0
0 38.94
33
0 0 34.91
45
0 1
4.63
39
0 0 39.97
34
0 0 35.97
46
0 1
5.62
40
0 1 0.99
35
0 0 37.02
47
0 1
6.61
41
0 1
2.02
36
0 0 38.08
48
0 1
7.6
42
0 1
3.04
37
0
0 39.14
49
0 1 8.6
43
0 1
4.07
38
0
1 0.2
50
0 1 9.59
44
0 1
5.09
39
0
1
1.26
51
0 1 10.58
45
0 1
6.12
40
0
1
1
2.31
52
0 1 11.57
46
0 1
7.14
41
0
1
3.37
53
0 1 12.56
47
0 1 8.17
42
0
1
1
4.43
54
0 1 13.55
48
0 1 9.19
43
0
1
5.49
55
0 1 14.55
49
0 1 10.21
44
0
1
6.55
56
0 1 15.54
50
0 1 11.24
45
0 1
7.6
57
0 1 16.53
51
0 1 12.26
46
0 1
8.66
58
0 1 17.52
52
0 1 13.29
47
0
1
9.72
59
0 1 18.51
53
0 1 14.31
48
0 1 10.78
60
0 1 19.5
54
0 1 15.34
49
0 1 11.83
61
0 1 20.5
55
0 1 16.36
50
0
1 12.89
62
0 1 21.49
56
0 1 17.39
51
0 1 13.95
63
0 1 22.48
57
0 1 18.41
52
0 1 15.01
64
0 1 23.47
58
0 1 19.44
53
0 1 16.07
65
0
1 24.46
59
0 1 20.46
54
0
1 17.12
66
0
1 25.45
60
0 1 21.49
55
0 1 18.18
67
0
1 26.45
61
0 1 22.51
56
0 1 19.24
68
0
1 27.44
62
0
1 23.54
57
0 1 20.3
69
0 1 28.43
63
0 1 24.56
58
0 1 21.36
70
0 1 29.42
64
0 1 25.59
59
0
1 22.41
71
0 1 30.41
65
0
1 26.61
60
1 23.47
72
0 1 31.4
66
0
1 27.64
73
0 1 32.4
67
0
1 28.66
74
0
1 33.39
68
0
1 29.69
75
0 1 34.38
69
0
1 30.71
76
0 1 35.37
70
0
1 31.74
77
0
1 36.36
71
0 1 32.76
78
0 1 37.36
72
0 1 33.79
79
0
1 38.35
73
0 1 34.81
80
0
1 39.34
74
0 1 35.83
81
0
2 0.33
75
0
1 36.86
888
82
0 2 1.32
76
0
1 37.88
83
0 2 2.31
77
0
1 38.91
84
0 2 3.31
78
0 1 39.93
INNJ88RRARIS2
1 24.53
62
0 1 25.59
63
0
1 26.64
64
0 1 27.7
65
0
1 28.76
0 1 29.82
67
0
1 30.88
0
1 31.93
69
0 1 32.99
70
0
1 34.05
71
0
1 35.11
0
1 36.17
73
0
1 37.22
85
0 2 4.3
79
0 2 2 0.96
74
0 1 38.28
86
0 2 5.29
80
02 1.98
75
0 1 39.34
87
0 2 6.28
81
0 2
2 3.01
76
0 2 0.4
88
0 2 7.27
82
0 2 4.03
77
0 2 1.45
89
0 2 8.26
83
0 2 5.06
78
0 2 2.51
91
2UNKHA
90
0 2 9.26
84
0 2 6.08
79
0 2 3.57
0 2 10.25
92
0 2 11.24
93
0 2 12.23
87
94
0 2 13.22
95
0 2 14.21
168888888
85
0 2 7.11
80
0 2 4.63
0 2 8.13
81
0 2 5.69
0 2 9.16
82
0 2
2 6.74
0 2 10.18
83
0
2
2
7.8
89
0 2 11.21
84
0 2
8.86
244
TABLES OF LAND MEASURE.

Dimensions.
Yards.
Statute content.
Dimensions.
Statute content.
Dimensions.
Statute content.
A. R. P.
Yards.
A. R. P.
Yards.
A. R. P.
32 by 85
0 2 9.92
33 by 81
0 2
8.36
34 by 78
0 2
7.67
86
0 2 10.98
82
0 2 9.45
79
2 8.79
87
0 2 12.03
83
0 2 10.55
80
2 9.92
88
0 2 13.09
84
0 2 11.64
81
0
2 11.04
89
0 2 14.15
85
0 2 12.73
82
0
2 12.17
90
0 2 15.21
86
0 2 13.82
83
0
2 13.29
91
0 2 16.26
87
0 2 14.91
84
0
2 14.41
92
0 2 17.32
88
0 2 16.
85
0 2 15.54
93
0 2 18.38
89
0 2 17.09
86
0 2 16.66
94
0 2 19.44
90
0 2 18.18
87
0 2 17.79
95
0 2 20.5
91
0 2 19.27
88
0 2 18.91
96
0 2 21.55
92
0 2 20.36
89
0 2 20.03
97
0
2 22.61
93
0 2 21.45
90
0 2 21.16
98
0 2 23.67
94
0 2 22.55
91
0 2 22.28
99
0
2 24.73
95
0
2 23.64
92
0
2 23.4
100
0 2 25.79
96
0 2 24.73
93
0
2 24.53
33 by 33
0
0 36.
97
0 2 25.82
94
0
2 25.65
34
0 0 37.09
98
0 2 26.91
95
0 2 26.78
35
0 0 38.18
99
0 2 28.
96
0
2 27.9
36
0 0 39.27
100
0 2 29.09
97
0 2 29.02
37
0 1
0.36
34 by 34
0 0 38.21
98
0
2 30.15
38
0 1
1.45
35
0 0 39.34
99
0
2 31.27
39
0 1
2.55
36
0
1 0.46
100
0
2 32.4
40
0 1
3.64
37
0 1
1.59
35 by 35
0
1 0.5
41
0 1
4.73
38
0 1
2.71
36
0 1
1.65
42
0 1 1 5.82
39
0 1
3.83
37
0 1
2.81
43
0 1 6.91
40
0 1
4.96
38
0 1
3.97
44
0 1 8.
41
0 1
6.08
39
0 1
5.12
45
0 1 9.09
42
0 1 7.21
40
0 1
6.28
46
0 1 10.18
43
0 1
8.33
41
0 1
7.44
47
0 1 11.27
44
0 1 9.45
42
0 1
8.6
48
0 1 12.36
45
0 1 10.58
43
0 1 9.75
49
0 1 13.45
46
0 1 11.7
44
0
1 10.91
50
0 1 14.55
47
0 1 12.83
45
0
1 12.07
51
0 1 15.64
48
0 1 13.95
46
0
1 13.22
52
0 1 16.73
49
0 1 15.07
47
0
1 14.38
53 0 1 17.82
50
0 1 16.2
48
0
1 15.54
54
0 1 18.91
51
0 1 17.32
49
0
1 16.69
55
0 1 20.
52
0 1 18.45
50
1 17.85
56
0 1 21.09
53
0 1 19.57
51
0
1 19.01
57
0 1 22.18
54
0 1 20.69
52
0
1 20.17
58 0 1 23.27
55
0 1 21.82
53
0
1 21.32
59
0 1 24.36
56
0 1 22.94
54
0
1 22.48
60 0 1 25.45
57
0 1 24.07
55
0
1 23.64
61
0 1 26.55
58
0 1 25.19
56
0
1 24.79
62
0
1 1 27.64
59
0 1 26.31
57
0
1 25.95
63 0 1 28.73
60
0 1 27.44
58
0
1 27.11
64
0 1 29.82
61
0 1 28.56
59
0
1 28.26
65
0 1 30.91
62
0 1 29.69
66
0 1 32.
63
0 1 30.81
67
0 1 33.09
64
0 1 31.93
68
0 1 34.18
65
0 1 33.06
69
0
135.27
66
0 1 34.18
70
0 1 36.36
67
0 1 35.31
71
0 1 37.45
68
0 1 36.43
72
0 1 38.55
69
0 1 37.55
73
0 1 39.64
70
0 1 38.68
74
0 2 0.73
71
0 1 39.8
75 0 2 1.82
72
0 2 0.93
76 0 2 2.91
73
2 2.05
77
0 2 4.
74
0 2 3.17
78
2 5.09
75
0 2 4.3
79
0 2 6.18
76
0 2
5.42
80
0 2 7.27
77
0 2
6.55
JFINIJ:****FCC28
0
1 29.42
0
1 30.58
62
0
1 31.74
0
1 32.89
0
1 34.05
0
1 35.21
0
1 36.36
0
1 37.52
0 1 38.68
69
0
1 39.83
70
0
2 0.99
0 2 2.15
72
0
2 3.31
0
2 4.46
2 5.62
0
2 6.78
TABLES OF LAND MEASURE.
245

Statute content.
Dimensions. Statute content.
Dimensions. Statute content.
Dimensions.
Yards
A. R. P.
Yards.
A. R. P.
Yards.
A. R. P.
35 by 76
0 2
7.93
36 by 75
0 2
2
9.26
37 by 75
0 2 11.74
77
0 2
9.09
76
0 2 10.45
76
0 2 12.96
78
0 2 10.25
77
0
2 11.64
77
0 2 14.18
79
0 2 11.4
78
0 2 12.83
78
0 2 15.4
80
0 2 12.56
79
0 2 14.02
79
0 2 16.63
81
0 2 13.72
80
0
2 15.21
80
0 2 17.85
82
0
2 14.88
81
0 2 16.4
81
0 2 19.07
83
0
216.03
82
0 2 17.59
82
0 2 20.3
84
0
2 17.19
83
0 2 18.78
83
0 2 21.52
85
0
2 18.35
84
0
2 19.97
84
0 2 22.74
86
0 2 19.5
85
0
2 21.16
85
0 2 23.97
87
0 2 20.66
86
0 2 22.35
86
0 2 25.19
88
0 2 21.82
87
0
2 23.54
87
0 2 26.41
89
0
2 22.98
88
0 2 24.73
88
0 2 27.64
90
0
2 24.13
89
0
2 25.92
89
0
2 28.86
91
0
2 25.29
90
0 2 27.11
90
0 2 30.08
92
0
2 26.45
91
0 2 28.3
91
0 2 31.31
93
0 2 27.6
92
0 2 29.49
92
0 2 32.53
94
0 2 28.76
93
0 2 30.68
93
0 2 33.75
95
0 2 29.92
94
0 2 31.87
94
0 2 34.98
96
0 2 31.07
95
0 2 33.06
95
0
2 36.2
97
0 2 32.23
96
0 2 34.25
96
0 2 37.42
98
0 2 33.39
97
0 2 35.44
97
0
2 38.64
99
0
234.55
98
0 2 36.63
98
0 2 39.87
100
0 2 35.7
99
0 2 37.82
99
0 3 1.09
36 by 36
0 1 2.84
100
0 2 39.01
100
0 3
2.31
37
0 1
4.03
37 by 37
0 1 5.26
38 by 38
0 1
7.74
38
0 1 5.22
38
0 1 6.48
39
0 1 8.99
39
0 1
1
6.41
39
0 1 7.7
40
0 1 10.25
40
0
1
1 7.6
40
0 1 8.93
41
0
1 11.5
41
0 1
8.79
41
0 1 10.15
42
0 1 12.76
42
0 1 9.98
42
0 1 11.37
43
0 1 14.02
43
0 1 11.17
43
0 1 12.6
44
0 1 15.27
44
0 1 12.36
44
0 1 13.82
45
0 1 16.53
45
0 1 13.55
45
0 1 15.041
46
0 1 17.79
46
0 1 14.74
46
0 1 16.26
47
0
1 19.04
47
0 1 15.93
47
0 1 17.49
48
0
1 20.3
48
0 1 17.12
48
0 1 18.71
49
0 1 21.55
49
0 1 18.31
49
0 1 19.93
50
0
1 22.81
50
0 1 19.5
50
0 1 21.16
51
0 1 24.07
51
0 1 20.69
51
0 1 22.38
52
0 1 25.32
52
0 1 21.88
52
0 1 23.6
53
0 1 26.58
53
0 1 23.07
53
0 1 24.83
54
0 1 27.83
54
0 1 24.26
54
0 1 26.05
55
0 1 29.09
55
0 1 25.45
55
0 1 27.27
56
0
1 30.35
56
0 1 26.64
56
0 1 28.5
57
0 1 31.6
57
0 1 27.83
57
0 1 29.72
58
0 1 32.86
58
0 1 29.02
58
0 1 30.94
59
0 1 34.12
59
0 1 30.21
59
0 1 32.17
60
0 1 31.4
60
0 1 33.39
61
61
0 1 32.6
61
0 1 34.61
62
62
0 1 33.79
62
0 1 35.83
63
0 1 34.98
63
0 1 37.06
64
0 1 36.17
64
0 1 38.28
65
0 1 37.36
65
0 1 39.5
66
0 1 38.55
66
0 2 0.73
67
0 1 39.74
67
0 2 1.95
68
68
0 2 0.93
68
0 2 3.17
8UNIHUS583
60
0 1 35.37
0 1 36.63
0 1 37.88
63
0 1 39.14
64
0 2 0.4
65
0 2 1.65
66
0 2
2
2.91
67
0 2 4.17
0 2 5.42
69
0 2
6.68
69
0 2 2.12
69
0 2 4.4
70
0 2 7.93
70
0 2 3.31
70
0 2 5.62
71
0 2 9.19
71
0 2 4.5
71
0 2
6.84
72
0 2 10.45
72
0 2 5.69
72
0 2
8.07
73
0 2 11.7
73 0 2 6.88
73
0 2 9.29
74
0 2 12.96
74
0 2 8.07
74
0 2 10.51
75
0 2 14.21
246
TABLES OF LAND MEASURE.

Dimensions. Statute content.
Dimensions.
Statute content. Dimensions.
Statute content.
Yards.
A. R. P.
Yards.
A. R. P.
Yards.
A. R. P.
38 by 76
0 2 15.47
39 by 78
0 2 20.56
40 by 81
0 2 27·11
77
0
2 16.73
79
0 2 21.85
82
0 2 28.43
78
0 2 17.97
80
0 2 23.14
83
0 2 29.75
79
0 2 19.24
81
0 2 24.43
84
0 2 31.07
80
0 2 20.5
82
0 2 25.72
85
0
232.4
81
0 2 21.75
83
0 2 27.01
86
0
2 33.72
82
0 2 23.01
84
0 2 28.3
87
0 2 35.04
83
0 2 24.26
85
0 2 29.59
88
0 2 36.36
84
0 2 25.52
86
0 2 30.88
89
0 2 37.69
85
0
2 26.78
87
0 2 32.17
90
0 2 39.01
86
0 2 28.03
88
0 2 33.45
91
0 3 0.33
87
0 2 29.29
89
0
2 34.74
92
0 3 1.65
88
0 2 30.55
90
0 2 36.03
93
0 3 2.98
89
0 2 31.8
91
0
2 37.32
94
0 3
4.3
90
0 2 33.06
92
0 2 38.61
95
0 3
5.62
91
0 2 34.31
93
0 2 39.9
96
0
3
6.94
92
0 2 35.58
94
0 3 1.19
97
3 8.26
93
0 2 36.83
95
0 3
2.48
98
3 9.59
94
0 2 38.08
96
0
3
3.77
99
0
3 10.91
95
0 2 39.34
97
0
3 3
5.06
100
0
3 12.23
96
0 3 0.6
98
0
3
6.35
41 by 41
0
1 15.57
97
0 3
1.85
99
0
3 3
7.64
42
0
1 16.93
98
0 3 3.11
100
0
3 8.93
43
0 1 18.28
99
0 3 4.36
40 by 40
0
1 12.89
44
0
1 19.64
100
0 3 5.62
41
0 1 14.21
45
0 1 20.99
39 by 39
0 1 10.28
42
0 1 15.54
46
0
1 22.35
40
0
1 11.57
43
0
1 16.86
47
0 1 23.7
41
0 1 12.86
44
0 1 18.18
48
0
1 25.06
42 0 1 14.15
45
0 1 19.5
49
0 1 26.41
43
0 1 15.44
46
0 1 20.83
50
0 1 27.77
44
0 1 16.73
47
0 1 22.15
51
0 1 29.12
45 46 47 48
0 1 18.02
48
0 1 23.47
52
0
1 30.48
0 1 19.31
49
0 1 24.79
53
0 1 31.83
0 1 20.6
50
0
1 26.12
54
0 1 33.19
0 1 21.88
51
0 1 27.44
55
0
1 34.55
49
0 1 23.17
52
0
1 28.76
56
0
1 35.9
50
0 1 24.46
53
0 1 30.08
57
0 1 37.26
51
0 1 25.75
54
0 1 31.4
58
1 38.61
52
0 1 27.04
55
0 1 32.73
59
0
1 39.97
53
0 1 28.33
56
0 1 34.05
60
0
2 1.32
54
0 1 29.62
57
0
1 35.37
61
0 2 2.68
55
0 1 30.91
58
0 1 36.69
62
0 2 4.03
56
0 1 32.2
59
0 1 38.02
63
0 2 5.39
57
0 1 33.49
60
0 1 39.34
64
0 2 6.74
58
0 1 34.78
61
0 2 0.66
65
0 2 8.1
59
0 1 36.07
62
0 2 1.98
66
0 2 9.45
60
0
1 37.36
63
0 2
3.31
67
0 2 10.81
61
0 1 38.64
64
0 2
4.63
68
0
2 12.17
62
0 1 39.93
65
0 2
5.95
69
0 2 13.52
63
0 2 1.22
66
0 2
7.27
70
0
2 14.88
64
0 2 2.51
67
0 2
8.6
71
0
216.23
65
0 2 3.8
68
0 2
9.92
72
0
2 17.59
66
0 2 5.09
69
2 11.24
73
0
2 18.94
67
0 2 6.38
70
2 12.56
74
0
2 20.3
68 0 2 7.67
71
0 2 13.88
75
0
2 21.65
69
0 2 8.96
72
0 2 15.21
76
0
2 23.01
70
0 2 10.25
73
0 2 16.53
77
0
2 24.36
71
0 2 11.54
74
0 2 17.85
78
0 2 25.72
72
0 2 12.83
75
0 2 19.17
79
0
2 27.07
73
0 2 14.12
76
0 2 20.5
80
0
2 28.43
74
0 2 15.4
77
0 2 21.82
81
0 2 29.79
75
0 2 16.69
78
0 2 23.14
82
0 2 31.14
76
0 2 17.98
79
0
2 24.46
83
0 2 32.5
77
0 2 19.27
80
0 2 25.79
84
0 2 33.85
TABLES OF LAND MEASURE.
247

Dimensions. Statute content. Dimensions. Statute content.
Dimensions.
Statute content.
Yards.
A. R. P.
Yards.
A. R. P.
Yards.
A. R. P.
41 by 85
0 2 35.21
42 by 90
0 3
4.96
43 by 96
0 3 16.46
86
0
236.56
91
0 3
6.35
97
0
3 17.88
87
0
237.92
92
0 3
7.74
98
0
3 19.31
88
0 2 39.27
93
0
3
9.12
99
0
•
3 20.73
89
0 3 0.63
94
0 3 10.51
100
0
3 22.15
90
0 3
1.98
95
0
3 11.9
44 by 44
0
1 24.
91
0 3
3.34
96
0
3 13.29
45
0 1 25.45
92
0 3
4.69
97
0 3 14.68
46
0
1 26.91
93
0 3
6.05
98
0 3 16.07
47
0
1 28.36
94
0 3 7.4
99
0 3 17.45
48
0
1 29.82
95
0 3 8.76
100
0 3 18.84
49
0 1 31.27
96
0 3 10.12
43 by 43
0 1 21.12
50
0 1 32.73
97
0
3 11.47
44
0 1 22.55
51
0 1 34.18
98
0
3 12.83
45
0 1 23.97
52
0
1 35.64
99
0
3 14.18
46
0 1 25.39
53
0
1 37.09
100
0
3 15.54
47
0 1 26.81
54
0
1 38.55
42 by 42
0
1 18.31
48
0 1 28.23
55
0
2
2 0.
43
0
1 19.7
49
0 1 29.65
56
0
2
2
1.45
44
0
1 21.09
50
0 1 31.07
57
0
2
2 2.91
45
0 1 22.48
51
0 1 32.5
58
0
2
2 4.36
46
0 1 23.87
52
0 1 33.92
59
0
2
5.82
47
0 1 25.26
53
0 1 35.34
60
0
2
2
7.27
48
0 1 26.64
54
0 1 36.76
61
0
2 8.73
49
0 1 28.03
55
0 1 38.18
62
0
2 10.18
50
0 1 29.42
56
0 1 39.6
63
0
2 11.64
51
0 1 30.81
57
0 2 1.02
64
0
2 13.09
52
0 1 32.2
58
0 2 2.45
65
0 2 14.55
53
0 1 33.59
59
0 2 3.87
66
0
2 16.
54
0 1 34.98
60
0 2 5.29
67
0 2 17.45
55
0 1 36.36
61
0 2
6.71
68
0
2 18.91
56
0 1 37.75
62
0 2 8.13
69
0 2 20.36
57
0 1 39,14
63
0 2 9.55
70
0 2 21.82
58
0 2 0,53
64
0 2 10.98
71
0 2 23.27
59 0 2 1.92
65
0 2 12.4
72
0 2 24.73
60
0 2 3.31
66
0 2 13.82
73
0
2 26.18
61
0 2 4.69
67
0 2 15.24
74
0 2 27.64
62
0 2 6.08
68
0 2 16.66
75
0
2 29.09
63
0 2 7.47
69
0 2 18.08
76
0
2 30.55
64
0 2 8,86
70
0 2 19.5
77
0
2 32.
65
0 2 10.25
71
0 2 20.93
78
2 33.45
66
0
2 11.64
72
0 2 22.35
79
0
2 34.91
67
0
213,02
73
0 2 23.77
80
0
2 36.36
68
0 2 14.41
74
0 2 25.19
81
0
2 37.82
69
0 2 15,8
75
0 2 26.61
82
0 2 39.27
70
0 2 17.19
76
0 2 28.03
83
0
3 0.73
71
0 2 18,58
77
0 2 29.45
84
0 3
2.18
72
0 2 19.97
78
0 2 30.88
85
0 3 3 3.64
73
0 2 21,36
79
0
2 32.3
86
0
3 5.09
74
0
2 22.74
80
0
233.72
87
0
3 6.55
75
0
2 24,13
81
0
2 35.14
88
0 3 8.
76
0
2 25.52
82
0
2 36.56
89
0 3 9.45
77
0 2 26.91
83
0 2 37.98
90
0 3 10.91
78
0 2 28,3
84
0 2 39.4
91
0 3 12.36
79
0 229.69
85
0 3 0.83
92
0
3 13.82
80
0 2 31.07
86
0 3 2.25
93
0
3 15.27
81
0 2 32.46
87
0 3 3.67
94
0
3 16.73
82
0 2 33.85
88
0 3 5.09
95
0
3 18.18
83
0 2 35.24
89
0 3
6.51
96
0
3 19.64
84
0 2 36.63
90
0 3 7.93
97
0 3 21.09
85
0 2 38.02
91
0 3
3 9.36
98
0
3 22.55
86
0 2 39.4
92
0 3 10.78
99
0
3 24.
87
0 3 0.79
93
0 3 12.2
100
0
3 25.45
88
0 3 2.18
94
0 3 13.62
45 by 45
0
1 26.94
89
0 3 3·57
95
0 3 15.04
46
0 1 28.43
248
TABLES OF LAND MEASURE.

Dimensions.
Yards.
Statute content.
Dimensions.
Statute content.
Dimensions.
A. R. P.
Yards.
A. R.
P.
Yards.
A. R.
Statute content.
P.
45 by 47
0 1 29.92
46 by 56
0 2
5.16
47 by 66
0
222.55
48
0 1 31.4
57
0 2
6.68
67
0
2 24.1
49
0
1 32.89
58
0 2 8.2
68
0 2 25.65
50
0 1 34.38
59
0 2
9.72
69
0 2 27.21
51
0 1 35.87
60
0 2 11.24
70
0 2 28.76
52
0
1 37.36
61
0 2 12.76
71
0 2 30.31
53
0 1 38.84
62
0 2 14.28
72
0 2 31.87
54
0 2 0.33
63
0 2 15.8
73
0 2 33.42
55
0 2
1.82
64
0 2 17.32
74
0
2 34.98
56
0 2
3.31
65
0 2 18.84
75
0
2 36.53
57
0 2 4.79
66
0 2 20.36
76
0
2 38.08
58
0 2 6.28
67
0 2 21.88
77
0
2 39.64
59
0 2 7.77
68
0 2 23.4
78
3 1.19
60
0 2 9.26
69
0 2 24.93
79
3 2.74
61
0 2 10.74
70
0 2 26.45
80
3 4.3
62
0
2 12.23
71
0 2 27.97
81
3 5.85
63
0
2 13.72
72
0 2 29.49
82
0
3 7.4
64
0 2 15.21
73
0 2 31.01
83
0 3 8.96
65
0 2 16.69
74
0 2 32.53
84
0 3 10.51
66
0 2 18.18
75
0 2 34.05
85
0 3 12.07
67
0 2 19.67
76
0 2 35.57
86
0 3 13.62
68
0
2 21.16
77
0 2 37.09
87
0 3 15.17
69
0
222.64
78
0 2 38.61
88
0 3 16.73
70
0 2 24.13
79
0 3 0.13
89
0 3 18.28
71
0 2 25.62
80
0 3 1.65
90
0
3 19.83
72
0 2 27.11
81
0 3 3.17
91
0
3 21.39
73
0 2 28.6
82
0 3 4.69
92
0
3 22-94
74
0 2 30.08
83
0 3 6.21
93
0
3 24.5
75
0 2 31.57
84
0 3 7.74
94
0
3 26.05
76
0
2 33.06
85
0 3 9.26
95
0
3 27.6
77
0
234.55
86
0 3 10.78
96
0 3 29.16
78
0 2 36.03
87
0 3 12.3
97
0 3 30.71
79
0 2 37.52
88
0 3 13.82
98
0 3 32.26
80 0 2 39.01
89
0 3 15.34
99
0 3 33.82
81
0 3 0.5
90
0 3 16.86
100
0 3 35.37
82
0 3 1.98
91
0 3 18.38
48 by 48
0 1 36.17
83
0 3 3.47
92
0 3 19.9
49
0 1 37.75
84
0 3 4.96
93
0 3 21.42
50
0 1 39.34
85
0 3 6.45
94
0 3 22.94
51
0 2 0.93
86
0 3 7.93
95
0 3 24.46
52
0 2 2.51
87
0 3 9.42
96
0 3 25.98
53
0 2
4.1
88
0 3 10.91
97
0 3 27.5
54
0 2 5.69
89
0 3 12.4
98
0 3 29.02
55
2 7.27
90
0 3 13.88
99
0 3 30.55
56
0
2 8.86
91
0 3 15.37
100
0 3 32.07
57
0
92
0 3 16.86
47 by 47
0
1 33.02
93
0 3 18.35
48
0 1 34.58
94
0 3 19.83
49
0 1 36.13
95
0 3 21.32
50
0 1 37.69
96
0 3 22.81
51
0 1 39.24
97
0 3 24.3
52
0 2 0.79
98
0 3 25.79
53
0 2 2.35
99
0 3 27.27
54
0 2 3.9
100
0 3 28.76
55
0 2 5.45
46 by 46
0 1 29.95
56
0 2 7.01
47
0 1 31.47
57
0 2 8.56
48
0 1 32.99
58
0 2 10.12
49
0 1 34.51
59
0 2 11.67
50 0 1 36.03
60
0 2 13.22
51
0 1 37.55
61
0
2 14.78
52
0 1 39.07
62
0
2 16.33
53 0 2 0.6
63
0 2 17.88
54
0 2 2.12
64
0 2 19.44
55
0 2 3.64
65
0 2 20.99
ZZZZZZZIXARAC*****:
0
212.03
59
0
2 10.45
2 13.62
60
0
2 15.21
0
2 16.79
62
0 2 18.38
63
0 2 19.97
64
0
2 21.55
65
0
2 23.14
66
0
2 24.73
67
0
2 26.31
68
0
2 27.9
0
2 29.49
70
0
2 31.07
71
0
2 32.66
72
0
2 34.25
73
0
2 35,83
74
0 2 37.42
75
0 2 39.01
76
0 3 0.6
TABLES OF LAND MEASURE.
249

Dimensions. Statute content.
Yards.
A. R. P.
Dimensions.
Yards.
Statute content. Dimensions.
Statute content.
A. R. P.
Yards.
48 by 77
0
3
2.18
49 by 89
0 3 24.17
51 by 52
A. R. P.
0 2 7.67
78
0 3
3
3.77
90
0 3 25.79
53
0 2 9.36
79
0 3
3
5.36
91
0 3 27.4
54
2 11.04
80
0
3
3 6.94
92
0 3 29.02
55
0 2 12.73
81
0
3
3
8.53
93
0 3 30.64
56
0 2 14.41
82
0
3 10.12
94
0 3 32.26
57
0 2 16.1
83
0 3 11.7
95
0 3 33.88
58
0 2 17.79
84
0 3 13.29
96
0 3 35.5
59
0 2 19.47
85
0
3 14.88
97
0 3 37.12
86
0
3 16.46
98
0 3 38.74
87
0
3 18.05
99
1 0 0.36
88
0 3 19.64
100
1 0
1.98
89
0 3 21.22
50 by 50
0 2
2.64
90
0 3 22.81
51
0 2
4.3
91
0
3 24.4
52
0 2 5.95
92
0
3 25.98
53
0 2 7.6
93
0
3 27.57
54
0 2
9.26
94
0
3 29.16
55
0 2 10.91
95
0
3 30.74
56
0
2 12.56
96
0 3 32.33
57
0
2 14.21
71
97
0 3 33.92
58
0
2 15.87
98
0 3 35.5
59
0 2 17.52
99
0 3 37.09
60
0 2 19.17
100
0
3 38.68
61
0
2 20.83
49 by 49
0
1 39.37
62
0 2 22.48
50
0
2 0.99
63
0
2 24.13
IZLAFIZZJOBRPAR3828:
0 2 21.16
61
0 2 22.84
0 2 24.53
0 2 26.21
0 2 27.9
0 2 29.59
66
0 2 31.27
67
0
2 32.96
0
2 34.64
0
2 36.33
70
0
2 38.02
0
2 39.7
72
0 3 1.39
0 3
3.07
74
0 3 4.76
0 3 6.45
0
3 8.13
77
0
3
3
9.82
51
0
2 2 2.61
64
0 2 25.79
78
0
3 11.5
52
0
2 2 4.23
65
0 2 27.44
79
0
3 13.19
53
0
2
2 5.85
66
0 2 29.09
80
0 3 14,88
54
0 2 7.47
67
0 2 30.74
81
0
3 16.56
55
0 2
2
9.09
68
0 2 32.4
82
0
3 18.25
56
0 2 10.71
69
0 2 34.05
83
0
3 19.93
57
0 2 12.33
70
0 2 35.7
84
0 3 21.62
58
0 2 13.95
71
0 2 37.36
85
0
3 23.31
59
0 2 15.57
72
0 2 39.01
86
0 3 24.99
60
0 2 17.19
73
0 3 0.66
87
0
3 26.68
61
0 2 18.81
74
0 3 2.31
88
0 3 28.36
62
0 2 20.43
75
0 3 3.97
89
0
3 30.05
63
0 2 22.05
76
0 3 5.62
90
0 3 31.74
64
0 2 23.67
77
3 7.27
91
0
3 33.42
65
0
2 25.29
78
0 3 8.93
92
0 3 35.11
66
0 2 26.91
79
0 3 10.58
93
0
3 36.79
67
0 2 28.53
80
0
3 12.23
94
0
3 38.48
68
0 2 30.15
81
0 3 13.88
95
1 0 0.17
69
0 2 31.77
82
0 3 15.54
96
1 0 1.85
70
0
2 33.39
83
0 3 17.19
97
1 0
3.54
71
0
2 35.01
84
0 3 18.84
98
1 0
5.22
72
0 2 36.63
85
0 3 20.5
99
1 0 6.91
73
0 2 38.25
86
0 3 22.15
100
1 0 8.6
74
0 2 39.87
87
0 3 23.8
52 by 52
0
2 9.39
75
0 3 1.49
88
0 3 25.45
53
0 2 11.11
76 0 3 3.11
89
0 3 27.11
54
0 2 12.83
77
0 3 4.73
90
0 3 28.76
55
0 2 14.55
78
0 3 6.35
91
0
3 30.41
56
0 2 16.26
79
0 3 7.97
92
0 3 32.07
57
0 2 17.98
80
0 3 9.59
93
0 3 33.72
58
0
2 19.7
81
0 3 11.21
94
0 3 35.37
59
0 2 21.42
82
0 3 12.83
95
0 3 37.02
60
0 2 23.14
83
0
3 14.45
96
0
3 38.68
61
0 2 24.86
84
0
3 16.07
97
1 0 0 0.33
62
0 2 26.58
85
0 3 17.69
98
1 0 1.98
63
0
2 28.3
86
0 3 19.31
99
1 0 3.64
64
0
2 30.02
87
0 3 20.93
100
1 0 5.29
65
0 2 31.74
88
0 3 22.55 51 by 51
0 2 5.98
66
0 2 33.45
S
250
TABLES OF LAND MEASURE.

Dimensions. Statute content.
Yards.
A. R. P.
Dimensions.
Yards.
Statute content.
Dimensions.
Statute content.
A. R. P.
Yards.
A. R. P.
52 by 67
0 2 35.17
53 by 83
0 3 25.42
54 by 100
1
0 18.51
68
0 2 36.89
84
0
3 27.17
55 by 55
0 2 20.
69
0 2 38.61
70 0 3 0.33
71
0 3 2.05
72
0 3
3.77
∞ ∞ ∞ ∞
85
0
3 28.93
56
0 2 21.82
86
0
3 30.68
57
0 2 23.64
87
0
3 32.43
58
0 2 25.45
88
0
3 34.18
59
0
2 27.27
73
0 3
5.49
89
0 3 35.93
60
0 2 29.09
74
0 3
7.21
90
0 3 37.69
61
0
2 30.91
75
0 3 8.93
91
0 3 39.44
62
0
2 32.73
76
0 3 10.64
92
1 0 1.19
63
0 2 34.55
77
0 3 12.36
93
1 0
2.94
64
0 2 36.36
78
0 3 14.08
94
1
0
4.69
65
0 2 38.18
7.9
0 3 15.8
95
1 0
6.45
66
0 3 0.
80
0 3 17.52
96
1 0
8.2
67
0 3 1.82
81
0 3 19.24
97
1
0 9.95
68
0 3 3.64
82
0 3 20.96
98
1 0 11.7
69
0
3
3 5.45
83
0 3 22.68
99
1
0 13.45
70
0 3 7.27
84
0 3 24.4
100
1
0 15.21
71
0 3 9.09
85
0 3 26.12
54 by 54
0 2 16.4
72
0 3 10.91
86
0 3 27.83
55
0
2 18.18
73
0
3 12.73
87
0 3 29.55
56
0 2 19.97
74
0 3 14.55
88
0 3 31.27
57
0 2 21.75
75
0 3 16.36
89
0 3 32.99
58
0
2 23.54
76
0 3 18.18
90
0 3 34.71
59
0
225.32
77
0
3 20.
91
0 3 36.43
60
0 2 27.11
78
0 3 21.82
92
0
3.38.15
61
0 2 28.89
79
0 3 23.64
93 0 3 39.87
62
0 2 30.68
80
0 3 25.45
94 1 0 1.59
63
0 2 32.46
81
0 3 27.27
95
1 0 3.31
64
0
2 34.25
82
0 3 29.09
96 1 0 5.02
65
0
236.03
83
0 3 30.91
97
1 0 6.74
66
0
2 37.82
84
0 3 32.73
98
1 0 8.46
67
0
239.6
85
0 3 34.55
99
1 0 10.18
68
0
3
1.39
86
0
3 36.36
100
1
0 11.9
69
3 3.17
87
0 3 38·18
53 by 53
0
2 12.86
70
3 4.96
88
1 0 0.
54
0
2 14.61
71
3 6.74
89
1
0
0 1.82
55
0
2 16.36
72
0 3 8.53
90
1
0
0 3.64
56
0 2 18.12
73
0 3 10.31
91
1 0 5.45
57
0 2 19.87
74
0 3 12.1
92
1
0 7.27
58
0 2 21.62
75
0 3 13.88
93
1
0 9.09
59
0 2 23.37
76
0 3 15.67
94
1 0 10.91
60
0
2 25.12
77
0 3 17.45
95
1
0 12.73
61
0
2 26.88
78
0 3 19.24
96
1 0 14.55
62
0
2 28.63
79
0 3 21.02
97
1 0 16.36
63
0
2 30.38
80
0 3 22.81
98
1
0 18.18
64
0
2 32.13
81
0 3 24.6
99
1
0 20.
65
0
2 33.88
82
0 3 26.38
100
1
0 21.82
66
0 2 35.64
83
0 3 28.17
56 by 56
0
2 23.67
67
0 2 37,39
84
0 3 29.95
57
0 2 25.52
68
0 2 39.14
85
0 3 31.74
58
0 2 27.37
69
0 3 0.89
86
0 3 33.52
59
0 2 29.22
70
0 3 2.64
87
0 3 35.31
60
0 2 31.07
71
0 3 4.4
88
0 3 37.09
61
0 2 32.93
72
0 3 6.15
89
0 3 38.88
62
0 2 34.78
73
0 3 7.9
90
1 0
0 0.66
63
0 2 36.63
74
0 3 9.65
91
1 0 2.45
64
0 2 38.48
75
0 3 11.4
92
1 0 4.23
65
0 3 0.33
76
0 3 13.16
93
1
0 6.02
66
0 3 2.18
77
0 3 14.91
94
1 0 7.8
67
0 3 4.03
78
0 3 16.66
95
1 0 9.59
68
0 3 5.88
79
0 3 18.41
96
1 0 11.37
69
0 3 7.74
80
0
3 20.17
97
1 0 13.16
70
0 3
3 9.59
81
0 3 21.92
98
1 0 14.94
71
0 3 11.44
82
0 3 23.67
99
1 0 16.73
72
0 3 13.29
TABLES OF LAND MEASURE.
251

Dimensions.
Yards.
Statute content.
A. R. P.
Dimensions.
Yards.
Statute content.
Dimensions.
Statute content.
A. R. P.
Yards.
A. R. P.
56 by 73
0 3 15.14
57 by 93
1 0 15.24
59 by 72
0 3 20.43
74
0 3 16.99
94
1
0 17.12
73
0 3 22.38
75
0
3 18.84
95
1
0 19.01
74
0 3 24.33
76
0
3 20.69
96
1
0 20.89
75
0 3 26.28
77
0
3 22.55
97
1
0 22.78
76
0 3 28.23
78
0
3 24.4
98
1
0 24.66
77
0 3 30.18
79
0
3 26.25
99
1
0 26.55
78
0 3 32.13
80
0 3 28.1
100
1
0 28.43
79
0
3 34.08
81
0 3 29.95
58 by 58
0
2 31.21
80
0 3 36.03
82
0 3 31.8
59
0
2 33.12
81
0 3 37.98
83
0 3 33.65
60
0 2 35.04
82
0 3 39.93
84
0 3 35.5
61
85
0 3 37.36
86
0 3 39.21
87
1
0 1.06
88
1
0 2.91
89
1
0 4.76
90
1
0 6.61
91
1
0 8.46
68
92
1
0 10.31
69
93
1
0 12.17
NOBRARA382
0
2 36.96
83
1 0 1.88
62
0 2 38.88
84
1 0 0
3.83
63
0
3 0.79
85
1
0
5.79
64
0 3
3 2.71
86
1 0
7.74
65
0
3 4.63
87
1
0 9.69
66
0
3
3 6.55
88
1
0 11.64
67
0
3
3 8.46
89
1
0 13.59
0
3 10.38
90
1
0 15.54
0
3 12.3
91
1
0 17.49
70
0 3 14.21
92
1
0 19.44
94
1
0 14.02
71
0 3 16.13
93
1 0 21.39
95
1
0 15.87
72
0 3 18.05
94
1
0 23.34
96
1
0 17.72
73
0 3 19.97
95
1
0 25.29
97
1 0 19.57
74
0 3 21.88
96
1
0 27.24
98
1
0 21.42
75
0 3 23.8
97
1
0 29.19
99
1
0 23.27
76
0 3 25.72
98
1
0 31.14
100
1
0 25.12
77
0 3 27.64
99
1 0 33.09
57 by 57
0
2 27.4
78
0 3 29.55
100
1 0 35.04
58
0
2 29.29
79
0 3 31.47
60 by 60
0 2 39.01
59
0
2 31.17
80
0 3 33.39
61
0 3 0.99
60
0
2 33.06
81
0 3 35.31
62
0 3 298
61
0
234.94
82
0 3 37.22
63
0 3 4.96
62
0
2 36.83
83
0 3 39.14
64
0 3 3 6.94
63
0 2 38.71
84
1 0 1.06
65
0 3 8.93
64
0 3 0.6
85
1 0
0 2.98
66
0 3 10.91
65
0 3 2.48
86
1
0
0 4.89
67
0 3 12.89
66
0 3 4.36
87
1
0 6.81
68
0 3 14.88
67
0 3 6.25
88
1 0 8.73
69
0 3 16.86
68
0 3 8.13
89
1
0 10.64
70
0 3 18.84
69
0 3 10.02
90
1 0 12.56
71
0 3 20.83
70
0 3 11.9
91
1 0 14.48
72
0 3 22.81
71
0 3 13.79
92
1
0 16.4
73
0 3 24.79
72
0 3 15.67
93
1
0 18.31
74
0 3 26.78
73
0 3 17.55
94
1
0 20.23
75
0 3 28.76
74
0 3 19.44
95
1
0 22.15
76
0 3 30.74
75
0 3 21.32
96
1
0 24.07
77
0 3 32.73
76
0 3 23.21
97
1
0 25.98
78
0 3 34.71
77
0 3 25.09
98
1
0 27.9
79
0 3 36.69
78
0 3 26.98
99
1 0 29.82
80
0 3 38.68
79
0 3 28.86
100
1
0 31.74
81
1 0 0.66
80
0 3 30.74
59 by 59
0
2 35.07
82
1 0 2.64
81
0 3 32.63
60
0
2 37.02
83
1 0 4.63
82
0 3 34.51
61
0 2 38.98
84
1 0 6.61
83
0 3 36.4
62
0 3 0.93
85
1
0
0 8.6
84
0 3 38.28
63
0 3 2.88
86
1
0 10.58
85
1
0 0.17
64
0 3 4.83
87
1
0 12.56
86
1 0 2.05
65
0 3 6.78
88
1
0 14.55
87
1 0 3.93
66
0 3 8.73
89
1
0 16.53
88
1 0 5.82
67
0 3 10.68
90
1
0 18.51
89
1 0 7.7
68
0 3 12.63
91
1
0 20.5
90
1 0 9.59
69
0 3 14.58
92
1
0 22.48
91
1
0 11.47
70
0 3 16.53
93
1
0 24.46
92
1
0 13.36
71
0 3 18.48
94
1
0 26.45
252
TABLES OF LAND MEASURE:

Dimensions. Statute content. Dimensions. Statute content.
Dimensions.
Statute content.
Yards.
A. R. P.
Yards.
A. R. P.
Yards.
A. R. P.
60 by 95
1 0 28.43
62 by 80
1 0
3.97
64 by 69
0 3 25.98
96
1
0 30.41
81
1 0
6.02
70
0 3 28.1
97
1
0 32.4
82
1
0 8.07
71
0
3 30.21
98
1 0 34.38
83
1
0 10.12
72
0
3 32.33
99
1
0 36.36
84
1
0 12.17
73
0
3 34.45
100
1
0 38.35
85
1
0 14.21
74
0 3 36.56
61 by 61
0
3 3.01
86
1
0 16.26
75
0 3 38.68
62
0 3
5.02
87
1
0 18.31
76
1
0 0.79
63
0 3
7.04
88
1
0 20.36
77
1 0 2.91
64
0 3 9.06
89
1
0 22.41
78
1 0 5.02
65
0 3 11.07
90
1
0 24.46
79
1 0 7.14
66
0
3 13.09
91
1
0 26.51
80
1
0 9.26
67
0
3 15.11
92
1
0 28.56
81
1
0 11.37
71
IIIIIFINIJ88:
0
3 17.12
93
1
0 30.61
82
1
0 13.49
0
3 19.14
94
1
0 32.66
83
1
0 15.6
70
0
3 21.16
95
1
0 34.71
84
1
0 17.72
0
3 23.17
96
1
0 36.76
85
1
0 19.83
72
0
3 25.19
97
1
0 38.81
86
1
0 21.95
73
0
3 27.21
98
1
1 0.86
87
1
0 24.07
74
0
3 29.22
99
1 1 2.91
88
1
0 26.18
75
0 3 31.24
100
1
1 4.96
89
1
0 28.3
76
0
3 33.26
63 by 63
0
3 11.21
90
1
0 30.41
77
0
3 35.27
64
0
3 13.29
91
1
0 32.53
78
0 3 37.29
65
0
3 15.37
92
1
0 34.64
0
3 39.31
66
0
3 17.45
93
1
0 36.76
80
1 0 1.32
67
0
3 19.54
94
1
0 38.88
81
1 0 3.34
68
0
3 21.62
95
1
1 0.99
82
1 0
5.36
69
0
3 23.7
96
1
1 3.11
83
1 0 7.37
70
0
3 25.79
97
1
1 5.22
84 1 0 9.39
71
0
3 27.87
98
1 1 7.34
85
1
0 11.4
72
0 3 29.95
99
1
1 9.45
86
1
0 13.42
73
0 3 32.03
100
1
1 11.57
87
1
0 15.44
74
0 3 34.12
65 by 65
0
3 19.67
88
1
0 17.45
75
0
3 36.2
66
0
3 21.82
89
1
0 19.47
76
0 3 38.28
67
0
3 23.97
90
1
0 21.49
77
1 0 0.36
68
0
3 26.12
91
1
0 23.5
78
1 0 2.45
69
0
3 28.26
92
1
0 25.52
79
1 0 4.53
70
0
3 30.41
93
1
0 27.54
80
1 0 6.61
71
0
3 32.56
94
1
0 29.55
81
1
0 8.69
72
0 3 34.71
95
1
0 31.57
82
1
0 10.78
73
0
3 36.86
96
1
0 33.59
83
1
0 12.86
74
0
3 39.01
97
1
0 35.6
84
1
0 14.94
75
1
0 1.16
98
1
0 37.62
85
1
0 17.02
76
1
0 3.31
99
1
0 39.64
86
1
0 19.11
77
1
0 5.45
100
1 1 1.65
87
1
0 21.19
78
1 0 7.6
62 by 62
0 3 7.07
88
1
0 23.27
79
1
0 9.75
63
0 3 9.12
89
1
0 25.36
80
1
0 11.9
64
0 3 11.17
90
1
0 27.44
81
1
0 14.05
65
0 3 13.22
91
1
0 29.52
82
1
0 16.2
66
0 3 15.27
92
1
0 31.6
83
1
0 18.35
67
0 3 17.32
93
1
0 33.69
84
1
0 20.5
68
0 3 19.37
94
1
0 35.77
85
1
0 22.64
69
0 3 21.42
95
1
0 37.85
86
1
0 24.79
70
0 3 23.47
96
1
0 39.93
87
1
0 26.94
71
0 3 25.52
97
1
1
2.02
88
1
0 29.09
72
0 3 27.57
98
1 1 4.1
89
1
0 31.24
73
0 3 29.62
99
1 1 6.18
90
1
0 33.39
74
0 3 31.67
100
1 1 8.26
91
1
0 35.54
75
0 3 33.72 64 by 64
0 3 15.4
92
1
0 37.69
76
0 3 35.77
65
0 3 17.52
93
1
0 39.83
77
0 3 37.82
66
0 3 19.64
94
1 1 1.98
78
0 3 39.87
67
0 3 21.75
95
1 1 4.13
79
1 0 1.92
68
0 3 23.87
96
1 1 6.28
TABLES OF LAND MEASURE.
253

Dimensions. Statute content.
Yards.
A. R.
P.
Dimensions.
Yards.
Statute content. Dimensions.
Statute content.
A. R. Ρ
Yards.
A. R. P.
65 by 97
1 1 8.43
67 by 92
1 1
3.77
69 by 91
1 1 7.57
98
1
1 10.58
93
1 1
5.98
92
1
1 9.85
99
1
1 12.73
94
1
1 8.2
93
1 1 12.13
100
1
1 14.88
95
1
1 10.41
94
1 1 14.41
66 by 66
0
3 24.
96
1
1 12.63
95
1 1 16.69
78
CIZIJAF≈≈NJ882
67
0
3 26.18
97
1
1 14.84
96
1 1 18.98
3 28.36
98
1
1 17.06
97
1 1 21.26
3 30.55
99
1
1 19.27
98
1 1 23.54
70
0
3 32.73
100
1
1 21.48
99
1
1 25.82
0 3 34.91
68 by 68
0 3 32.86
100
1 1 28.1
0 3 37.09
69
0
3 35.11
70 by 70
1 0 1.98
0
3 39.27
70
0
3 37.36
71
1 0
4.3
74
1 0 1.45
71
0 3 39.6
72
1 0
6.61
1
0 3.64
72
1
0 1.85
73
1 0 8.93
76
1
0 5.82
73
1 0 4.1
74
1 0 11.24
77
1
0 8.
74
1
0
0 6.35
75
1
0 13.55
1
0 10.18
75
1
0 8.6
76
1
0 15.87
1
0 12.36
76
1
0 10.84
77
1
0 18.18
80
1
0 14.55
77
1
0 13.09
78
1
0 20.5
81
1
0 16.73
78
1
0 15.34
79
1
0 22.81
82
1
0 18.91
79
1
0 17.59
80
1 0 25.12
83
1
0 21.09
80
1
0 19.83
81
1
0 27.44
84
1
0 23.27
81
1
0 22.08
82
1 0 29.75
85
1
0 25.45
82
1
0 24.33
83
1
0 32.07
86
1 0 27.64
83
1
0 26.58
84
1
0 34.38
87
1 0 29.82
84
1
0 28.83
85
1
0 36.69
88
1
0 32.
85
1
0 31.07
86
1
0 39.01
89
1
0 34.18
86
1
0 33.32
87
1
1
1.32
90
1
0 36.36
87
1
0 35.57
88
1 1
3.64
91
1
0 38.55
88
1
0 37.82
89
1
1
5.95
92
1 1 0.73
89
1
1 0.07
90
1 1
8.26
93
1 1
1 2.91
90
1
1 2.31
91
1 1 10.58
94
1
1
1 5.09
91
1
1 4.56
92
1
1 12.89
95
1
1 7.27
92
1 1 6.81
93
1 1 15.21
96
1
1 9.45
93
1 1 9.06
94
1 1 17.52
97
1
1 11.64
94
1
1 11.51
95
1 1 19.83
98
1
1 13.82
95
1
1 13.55
96
1 1 22.15
99
1
1 16.
96
1
1 15.8
97
1 1 24.46
100
1
1 18.18
97
1
1 18.05
98
1 1 26.78
67 by 67
0 3 28.4
98
1
1 20.3
99
1 1 29.09
68
0 3 30.61
99
1
1 22.55
100
1 1 31.4
69
0 3 32.83
100
1
1 24.79
71 by 71
1 0 6.64
70
0 3 35.04
69 by 69
0
3 37.39
72
1 0 8.99
71
0 3 37.26
70
0
3 39.67
73
1 0 11.34
72
0 3 39.47
71
1 0 1.95
74
1
0 13.69
73
1 0 1.69
72
1 0 4.23
75
1 0 16.03
74 1 0 3.9
73
1 0 6.51
76
1 0 18.38
75
1 0 6.12
74
1
0 8.79
77
1
0 20.73
76
1 0 8.33
75
1 0 11.07
78
1 0 23.07
77
1 0 10.55
76
1 0 13.36
79
1 0 25.42
78
1
0 12.76
77
1
0 15.64
80
1 0 27.77
79
1
0 14.98
78
1
0 17.92
81
1 0 30.12
80
1 0 17.19
79
1
0 20.2
82
1
0 32.46
81
1 0 19.4
80
1
0 22.48
83
1 0 34.81
82
1 0 21.62
81
1
0 24.76.
84
1
0 37.16
83
1 0 23.83.
82
1
0 27.04
85
1
0 39.5
84
1
0 26.05
83
1
0 29.32
86
1 1 1.85
85
1
0 28.26
84
1
0 31.6
87
1
1.4.2
86
1
0 30.48
85
1
0 33.88
88
1 1 6.55
87
1
0 32.69
86
1
0 36.17
89
1
1 8.89
88
1 0 34.91
87
1 0 38.45
90
1
1 11.24
89
1
0 37.12
88
1
1 0.73
91
1 1 13.59
90
1
0 39.34
89
1
1 3.01
92
1 1 15.93
91
1 1 1 1.55
90
1 1 5.29
93
1 1 18.28
254
TABLES OF LAND MEASURE.

Dimensions.
Statute content.
Dimensions. Statute content.
Dimensions.
Statute content.
Yards.
A. R. P.
71 by 91
1 1 20.63
Yards.
74 by 74
A. R. P.
Yards.
A. K. P.
1 0 21.02
76 by 87
1 1 18.58
95
1 1 22.98
75
1
0 23.47
88
1
1 21.09
96
1
1 25.32
76
1
0 25.92
89
1
1 23.6
97
1 1 27.67
77
1
0 28.36
90
1
1 26.12
98
1 1 30.02
78
1
0 30.81
91
1
1 28.63
99
1 1 32.36
79
1
0 33.26
92
1
1 31.14
100
1
1 34.71
80
1
0 35.7
93
1
1 33.65
72 by 72
1
0 11.37
81
1
0 38.15
94
1
1 36.17
73
1
0 13.75
82
1
1 0.6
95
1
1 38.68
74
1
0 16.13
83
1
1
3.04
96
1
2
1.19
75
1
0 18.51
84
1
1
5.49
97
1
2 3.7
76
1
0 20.89
85
1 1 7.93
98
1 2 6.21
77
1
0 23.27
86
1
1 10.38
99
1
2 8.73
78
1
0 25.65
87
1
1 12.83
100
1
2 11.24
79
1
0 28.03
88
1
1 15.27
77 by 77
1
0 36.
80
1
0 30.41
89
1
1 17.72
78
1
0 38.55
81
1 0 32.79
90
1
1 20.17
79
1
1
1.09
82
1
0 35.17
91
1
1 22.61
80
1 1 3.64
83
1 0 37.55
92
1
1 25.06
81
1 1 6.18
84
1 0 39.93
93
1
1 27.5
82
1 1 8.73
85
1 1 2.31
94
1 1 29.95
83
1
1 11.27
86
1
1 4.69
95
1.1 32.4
84
1
1 13.82
87
1 1 7.07
96
1 1 34.84
85
1
1 16.36
88
1
1 9.45
97
1
1 37.29
86
1
1 18.91
89
1
1 11.83
98
1
1 39.74
87
1
1 21.45
90
1 1 14.21
99
1 2 2.18
88
1
1 24.
91
1 1 16.6
100
1
2 4.63
89
1 1 26.55
92
1
1 18.98
75 by 75
1
0 25.95
90
1
1 29.09
93
1 1 21.36
76
1
0 28.43
91
1
1 31.64
94
1 23.74
77
1
0 30.91
92
1
1 34.18
95
1 1 26.12
78
1
0 33.39
93
1
1 36.73
96. 1 1 28.5
79
1
0 35.87
94
1
1 39.27
97
1 1 30.88
80
1
0 38.35
95
1
2 1.82
98
1
1 33.26
81
1
1 0.83
96
1 2 4.36
99
1
1 35.64
82
1
1
3.31
97
1 2 6.91
100
1
1 38.02
83
1
1 5.79
98
1
2 9.45
73 by 73
1
0 16.17
84
1 1 8.26
99
1
2 12.
74
1
0 18.58
85
1
1 10.74
100
1
2 14.55
75
1
0 20.99
86
1
1 13.22
78 by 78
1
1 1.12
76
1
0 23.4
87
1
1 15.7
79
1 1 3.7
77
1
0 25.82
88
1
1 18.18
80
1
1 6.28
78
1
0 28.23
89
1
1 20.66
81
1 1 8.86
79
1
0 30.64
90
1
1 23.14
82
1
1 11.44
80
1
0 33.06
91
1
1 25.62
83
1
1 14.02
81
1
0 35.47
92
1 1 28.1
84
1
1 16.6
82
1
0 37.88
93
1
1 30.58
85
1
1 19.17
83
1
1 0.3
94
1
1 33.06
86
1
1 21.75
84
1 1 2.71
95
1
1 35.54
87
1
1 24.33
85
1 1 5.12
96
1 1 38.02
88
1
1 26.91
86
1 1 7.54
97
1 2 0.5
89
1
1 29.49
87
1
1 9.95
98
1 2 2.98
90
1 1 32.07
88
1
1 12.36
99
1 2 5.45
91
1 1 34.64
89
1 1 14.78
100
1 2 7.93
92
1 1 37.22
90
1 1 17.19 76 by 76
1
0 30.94
93
1 1 39.8
91
1 1 19.6
77
1
0 33.45
94
1
2 2.38
92
1
1 22.02
78
1 0 35.97
95
1 2 4.96
93
1 1 24.43
79
1 0 38.48
96
1 2 7.54
94
1
1 26.84
80
1
1 0.99
97
1 2 10.12
95
1
1 29.26
81
1 1 3.5
98
1
2 12.69
96
1
1 31.67
82
1 1 6.02
99
1
2 15.27
97
1
1 34.08
83
1
1 8.53
100
1
2 17.85
98
1 1 36.5
84
1
1 11.04
79 by 79
1
1 6.31
99
1
1 38.91
85
1
1 13.55
80
1
1 1 8.93
100
1 2
2 1.32
86
1 1 16.07
81
1
1 11.54
TABLES OF LAND MEASURE.
255

Dimensions.
Statute content.
1 ards.
A. R. P.
Dimensions.
Yards.
Statute content.
Dimensions.
Statute content.
A. R. P.
Yards.
A. R. P.
79 by 82
1 1 14.15
82 by 86
1 1 33.12
85 by 99
1 2 38.18
83
1 1 16.76
87
1
1 35.83
100
1 3
0.99
84
1 1 19.37
88
1
1 38.55
86 by 86
1 2
4.5
85
1 1 21.98
89
1 2 1.26
87
1 2 7.34
86
1 1 24.6
90
1
2 3.97
88
1 2 10.18
87
1 1 27.21
91
1
2 6.68
89
1
2 13.02
88
1 1 29.82
92
1
2 9.39
90
1 2 15.87
89
1
1 32.43
93
1
2 12.1
91
1
2 18.71
90
1
1 35.04
94
1
2 14.81
92
1
2 21.55
91
1
1 37.65
95
1
2 17.52
93
1
2 24.4
92
1 2 0.26
96
1
2 20.23
94
1
2 27.24
93
1 2 2.88
97
1
2 22.94
95
1
2 30.08
94
1
2
5.49
98
1
2 25.65
96
1
2 32.93
95
1 2
2
8.1
99
1
2 28.36
97
1 2 35.77
96
1
2 10.71
100
1
2 31.07
98
1
2 38.61
97
1 2 13.32
83 by 83
1
1 27.74
99
1 3 1.45
98
1 2 15.93
84
1
1 30.48
100
1 3 3
4.3
99
1 2 18.55
85
1
1 33.22
87 by 87
1
2 10.21
100
1
2 21.16
86
1
1 35.97
88
1
2 13.09
80 by 80
1
1 11.57
87
1
1 38.71
89
1 2 15.97
81
1
1 14.21
88
82
1 1 16.86
89
83
1
1 19.5
90
84
1
1 22.15
91
1 2
NNNN
1 2 1.45
90
1 2 18.84
1 2 4.2
91
1 2 21.72
1 2 6.94
92
1
2 24.6
2
9.69
93
1 2 27.47
85
1
1 24.79
92
1
2 12.43
94
1 2 30.35
86
1
1 27.44
93
1 2 15.17
95
1 2 33.22
87
1 1 30.08
94
1
2 17.92
96
1
2 36.1
88
1
1 32.73
95
1
2 20.66
97
1 2 38.98
89
1
1 35.37
96
1 2 23.4
98
1 3 1.85
90
1 1 38.02
97
1
2 26.15
99
1 3 4.73
91
1 2 0.66
98
1
2 28.89
100
1 3 7.6
92
1
2 3.31
99
1 2 31.64
88 by 88
1 2 16.
93
1 2 5.95
100
1
2 34.38
89
1
2 18.91
94
1 2 8.6
84 by 84
1 1 33.26
90
1 2 21.82
95
1 2 11.24
85
1 1 36.03
91
1
2 24.73
96
1 2 13.88
86
1
1 38.81
92
1 2 27.64
97
1 2 16.53
87
1
2 1.59
93
1
2 30.55
98 1
2 19.17
88
1 2 4.36
94
1 2 33.45
99
1
2 21.82
89
1 2 7.14
95
1
2 36.36
100
1
2 24.46
90
1 2 9.92
96
1 2 39.27
81 by 81
1
1 16.89
91
1
2 12.69
97
1
3 2.18
82
1
1 19.57
92
1
2 15.47
98
1 3 5.09
83
1
1 22.25
93
1
2 18.25
99
1 3 8.
84 1
1 24.93
94
1
2 21.02
100
1 3 10.91
85
1
1 27.6
95
1
2 23.8
89 by 89
1
2 21.85
86 1
1 30.28
96
1
2 26.58
90
1
2 24.79
87
1 1 32.96
97
1 2 29.36
91
1
2 27.74
88 1
1 35.64
98
1 2 32.13
92
1 2 30.68
89
1 1 38.31
99
1 2 34.91
93
1 2 33.62
90
1 2 0.99
100
1
2 37.69
94
1 2 36.56
91
1 2 3.67
85 by 85
1 1 38.84
95
1 2 39.5
92
1 2 6.35
86
1 2 1.65
96
1 3 2.45
93
1 2 2 9.02
87
1 2 4.46
97
1 3 5.39
94
1 2 11.7
88
1 2 7.27
98
1 3 8.33
95
1
2 14.38
89
1 2 10.08
99
1 3 11.27
96
1 2 17.06
90
1
2 12.89
100
1 3 14.21
97
1 2 19.74
91
1 2 15.7
90 by 90
1 2 27.77
98
1 2 22.41
92
1 2 18.51
91
1 2 30.74
99
1 2 25.09
93
1
2 21.32
92
1 2 33.72
100
1
2 27.77
94
1 2 24.13
93
1 2 36.69
82 by 82
1
1 22.28
95
1 2 26.94
94
1 2 39.67
83
1 1 24.99
96
1 2 29.75
95
1 3 2.64
84
1
1 27.7
97
1 2 32.56
96
1 3 5.62
85
1
1 30.41
98
1 2 35.37
97
1 3 8.59
256
TABLES OF LAND MEASURE.

Dimensions.
Yards.
Statute content.
Dimensions.
Statute content.
Dimensions.
Statute content.
A. R. P.
Yards.
90 by 98
1 3 11.57
92 by 99
A. R. P.
1 3 21.09
Yards.
A. R. P.
95 by 98
1 3 27.77
99
1
3 14.55
100
1
3 24.13
99
1 3 30.91
100
1
3 17.52
93 by 93
1 3 5.92
100
1 3 34.05
91 by 91
1
2 33.75
94
1 3 8.99
96 by 96
1 3 24.66
92
1
2 36.76
95
1
3 12.07
97
1
3 27.83
93
1
2 39.77
96
1 3 15.14
98
1
3 31.01
94
1
3 2.78
97
1
3 18.21
99
1
3 34.18
95
1 3 5.79
98
1
3 21.29
100
1.3 37.36
96
1
3 8.79
99
1
3 24.36
97 by 97
1 3 31.04
97
1
3 11.8
100
1
3 27.44
98
1 3 34.25
98
1
3 14.81
94 by 94
1
3 12.1
99
1 3 37.45
99
1 3 17.82
95
1
3 15.21
100
2
0 0.66
100
1
3 20.83
96
1
3 18.31
98 by 98
1 3 37.49
92 by 92
1
2 39.8
97
1
3 21.42
99
2 0 0.73
93
1 3 2.84
98
1
3 24.53
100
2 0 3.97
94
1 3 5.88
99
1
3 27.64
99 by 99
2 0 4.
95
1
3 8.93
100
1
3 30.74
100
2 0 7.27
96
1 3 11.9795 by 95
1
3 18.35
100 by 100
20 10.58
97
1
3 15.01
96
1
3 21.49
98
1 3 18.05
97
1
3 24.63
THESE TABLES have been computed by my Assistants, MR. A. R.
SOWDON and MR. W. EVE, and the proofs from the press most carefully
examined by MR. W. EVE and MR. FRANK HARROW, whose assistance
I have much pleasure in acknowledging.
LAND SURVEYING.
257
CHAPTER VII.
LAND SURVEYING.
UNLIKE Land Measuring, the Science of Land Surveying, to
be practised successfully, requires that the person who uses it
should be well educated in the several branches of Arithmetic,
Algebra, Logarithms, Trigonometry, and Geometry; and to carry
on Surveys of extensive and varied character, several years of
previous practice is necessary.
Under the heading of Land Surveying, is properly included
every description of Mapping and Levelling, in whatever manner
performed.
As great, if not greater improvements have been effected in this
particular science within the last few years than in any other, and
many costly works have been published, but as I believe, with
very few exceptions, those works, while they profess to do every-
thing, contain nothing, comparatively speaking, of the practical
methods adopted by skilful surveyors of the present day. The
little work in Mr. Weale's Rudimentary Treatises* is written by
a practical Surveyor, and contains many very useful remarks,
which will, doubtless, conduce to promote its circulation; but with
this exception, I am not acquainted with any Treatise exclusively
penned by a practical man. They are, for the most part, the pro-
duction of schoolmasters and other mere theorists; and some of
them are but enlarged editions of original works, written previous
to the introduction of those improvements into the practice of
Surveying of which I have spoken.
Perhaps the greatest stimulant Civil Surveying ever received
was, the passing of the Tithe Commutation Act in 1836, under
which all titheable lands in England and Wales were required to be
surveyed and mapped. In accordance with the provisions of that
Act and the new Poor-Law Assessment Act of a previous session,
I, in my own personal practice, surveyed and mapped parishes to
an aggregate extent of about sixty thousand acres within a period
of ten years. It has long been my desire to publish fully the
practical knowledge experience has taught me in that and subse-
quent works; but a want of time, coupled with the very great
expense of such a publication, and its usually unprofitable cha-
racter (at all events to an author) has deterred the intention.
* Land and Engineering Surveying, by T. Baker, C.E.
258
LAND SURVEYING.
The following Synopsis is intended to contain such information
as will afford an insight into the best principles of the science, in
character with the nature of the present work.
SEC. 1.-Parish and Estate Surveying.
The first step in the practice of Surveying is to learn to chain a
line with accuracy and dispatch; the former of which being ac-
quired, the latter will be sure to follow, with practice. An active
man who has a good eye is invaluable to a surveyor as a chain-
man: such a one is very difficult to be obtained, and is not often
to be met with in a purely agricultural district. Many of the most
active men being wholly incapable of sticking out a straight line,
while on the contrary, men with excellent eyes are frequently too
cloddy in their motions to get across a country. A little attention
in the selection of a chain-man will amply repay the trouble.
The best way to direct a chain is for the person who follows it
to stand perfectly upright behind the arrow which has been left in
the ground; his heels touching each other, his toes pointed out on
either side of the arrow, and his feet forming something like an
angle of 30 degrees with the chain line. His chain-man should also
stand erect, and so soon as he is placed nearly in his position,
should take care that his heels touch, and that his feet form the
reverse position of his director, who is then enabled, by the motion
of the thumb of the right-hand in which he holds the handle of the
chain, to bring him into an exact line between himself and the fore
mark, which, if of good size and well chosen, will then appear to
rise directly above the centre of the man's head. The man, if he
understand his business, will at the same time discover if any par-
ticular object which he may have noticed to have been either in a
direct line with the chain, or bearing a relative position therewith
in former sets, still occupies the same position, and thus becomes a
guarantee that no mistake has been made in the foremark. He
will then be careful to tighten the chain so soon as the director has
his handle to the arrow; when he has so done, will stick his arrow
down between his feet, and will then be ready to proceed on his
line when directed. The director of the chain having the handle
in his right-hand, will stoop down as soon as his chain-man is in the
right direction; and putting his thumb through the bow or eye of
the arrow, will cause the handle of the chain to touch the arrow ;
and seeing that while in that position his chain-man places his ar-
row properly in the ground, will, as soon as that is accomplished,
close his hand without withdrawing his thumb, and in rising will
LAND SURVEYING.
259
way be very
draw the arrow up with him. Five arrows can in this
conveniently carried, their points always sticking out to the right,
the obvious consequence of the hand being closed upon them, and
the back of the hand being kept in a perfectly horizontal position,
otherwise the points will be found to be sticking in the ground
when the attempt is made to put the thumb through the eye of the
arrow. According to the height of the person directing a chain
will be the distance from the arrow at which his feet will require
to be placed, so that when he stoops to touch the wire with the
handle, the chain may exactly reach the required spot without sub-
sequently requiring to be moved either backwards or forwards: this
also is one of those mechanical performances in which practice will
produce the greatest proficiency.
The chain-man should carry the arrows in his left hand, the
chain in his right, and while walking along should draw one arrow
out of the bundle with his right hand in readiness for use at the
termination of the chain. He should also pay attention to the length
of a chain, so as to judge approximately the point at which he will
have to stop, that no sudden jerk may be experienced by the chain
(which does it great harm) and that the operation of turning round
and getting in line be effected as quickly as possible; to which end
he should be instructed to be always on the look out for his back
mark, and by moving about to place himself as nearly as he can do
in the same relative position with it and the director (who is
standing at the last arrow) as he occupied in setting the previous
chains. A chain-man's attention should be called to the necessity
of observing, as soon as the first chain on a line is set, the position
of some one or more objects to serve as a back mark; it will save
much loss of valuable time, and no end of trouble, and there are
seldom cases when something cannot be noticed, at all events, if
not directly in line, so little removed from it that its position can
be approximately determined.
Before commencing to chain a line, the director of the chain
should stand at the point at which the line commences, and look-
ing at the most distant fore mark, should observe if any remark-
able object, a green spot in a field, a gap or a bush in a hedge, a
tree, a bough, or a thistle, is directly in his line; if so, he should
frequently notice while traversing the line, that his position with
reference to it becomes unaltered; and by the exercise of care in
this manner, a line 30 or 40 chains in length, may be chained with
perfect straightness without any artificial setting out. But if there
is no intervening object, and the line is a long one with off-sets, it
will be better to direct one or two sticks to be stuck up at inter-
260
LAND SURVEYING.
mediate distances, for the best men will sometimes wind a line if
they have but a single mark at the end of it to guide them.
Very competent surveyors vary in their practice as to the num-
ber of arrows they use. I have had experience in the several
methods, both from necessity (caused by the occasional loss of an
arrow) and design, and have no hesitation in recommending the
number ten as the most practical, surest, and best. The chain-man
proceeds with his eleventh chain precisely in the same manner as
though he had a handful of arrows, the only difference in his opera-
tion being, instead of sticking down that of which he has none left,
he lays his handle of the chain on the ground and places his foot.
upon it, in which position he remains until the ten wires are
brought up to him by the director, of whom he takes them, imme-
diately places one in the ground, and then proceeds on his way.
The pointed end of the swivel in the centre of the chain should
always determine the end which should go first; if attention is not
paid to this, the abrupt angles at the other end of the swivel hang
in the bushes in passing through hedges, and frequently meet with
other obstructions which jerk and stretch the chain, and which are
passed harmless if the other end is driven first.
To ensure expedition, a surveyor's field staff should include a
man to draw and another to follow the chain, a boy to carry sticks
and make marks and stations; and if the work is very thick, a com-
petent person to measure the offsets, himself keeping the book; if
not very close work, he can save the offset man by using the rod
himself: the great desideratum being (always assuming the prac-
tice is followed for a profit) to keep the chain continually moving.
Throughout the course of every line an infinity of marks should
be made at intervals, certainly not exceeding ten chains, and if at
five the better. These marks will be found exceedingly useful in
determining the position of other lines falling near them, and in
the detection of an error, an event which will happen occasionally
to the most careful.
This induces a notice of a few of the most fruitful sources of
error to young surveyors. First may be mentioned, want of at-
tention to the change of arrows at the end of ten chains; then the
omission in long naked lines to make any note in the book of the
number of changes as they successively occur; the mistake of the
40 brass mark for 60; the 20 for 80; the confusion of the fore
mark with some other object similar, but out of direction; cases in
which it is impossible to set an arrow down at the end of the chain
that perhaps occurs in the centre of a pond or a deep ditch, in con-
sequence of which several parts of a chain are obliged to be used,
LAND SURVEYING.
261
and require to be set to rights when the obstruction is passed; and
last, though not of least importance, the too common practice of
allowing a chain-man to hold his own handle of the chain to the
point which terminates the line, instead of hauling beyond it, by
which means the chain is frequently read from the wrong end, or
an offset is booked at the wrong place.
The best marks to be made on a line in grass lands are such as
can be cut out with a small spade in one of the forms of fig. 136,
and if many of them are made in one piece of ground, they should
be distinguished from one another, as shewn in the fig., where
the different position of the detached diamond, which is entered
in the book as marked on the land, readily effects it. In arable
land nothing more can be done than driving in a peg; but every
fence should be marked, either by a race mark on a quickset or
bough, or in any ready way which may present itself. All pale
fences should be rased on passing, and every post which may be
in line.
The length of the offset rod in most general favour is ten links,
but fifteen links will be found preferable; and the one used by me
is twenty links. It is made of a straight piece of ground-ash. It
has no figures on it; but the links are marked by characteristic
colouring; an arrangement which allows either end to be used
without chance of error.
In "sticking out a line," particular care should be taken that at
least three (as many more as possible) of the ranging rods or
pickets are seen at the time of planting a fresh one; an obvious
precaution against a deviation of the line, which the slightest inac-
curacy would produce if only two were used. In crossing the
sharp apex of a hill great care is also required to preserve the
straightness of a line, and in many cases which occur in large sur-
veys, the use of an instrument, if not absolutely indispensable is
very desirable. It sometimes happens that a line may be ranged
across a series of hills, from apex to apex, and the intermediate
spaces across the valleys subsequently managed, but no regular
rule can be laid down; generally, the great consideration is, to get
some permanent and very prominent back and fore mark, if pos-
sible, beyond the limits of the work. As an illustration of this
method, in conducting a survey of the parish of Horsell, in Surrey,
about two years since, I found the church, in the heart of the vil-
lage, to occupy a very prominent position on a hill; and I imme-
diately obtained permission to use the tower (a square one) as a
station. Upon the top of this I erected a large flag pole, and from
that pole laid out a line towards every remarkable object on the
262
LAND SURVEYING.
surrounding hills, regardless of where it would terminate, and then
connected them by base lines. These lines were all patterns of
straightness-houses and farm buildings offered small obstacles
with such a mark behind and before; and although it frequently
happened that for eight or ten fields we could see neither, no in-
stance occurred in which the end of our line was not proved beyond
doubt as being in the same direction in which we started.
A knowledge of the principles of what is technically called
"taking up the details" of a survey, next claims our attention.
This is done by means of what are called "offsets," or short lines
measured from any given point on a chain line to an angle or point
in a hedge, fence, or building, to fix the position of that point upon
the plan. These offsets are measured with the offset rod already
spoken of, and are generally taken at right angles with the chain
line, simply because that is an angle that may be very approxi-
mately determined upon the ground and as readily upon the plan,
without the aid of an instrument in either case; short distances.
only being used. It is not however at variance with sound prin-
ciples if a sextant or any angular instrument is used, if these off-
sets are made to take any other angle which special circumstances
may require; but then it involves the noting of the angle, and so
forth, and occasions an inconvenience and trouble to the surveyor,
which he will always avoid if he can. All offsets not specially de-
noted by any angle are understood to be right angles, whether
under a variety of circumstances that may have occurred in the
field they are so drawn in the book or not.
There is another species of offsets called "opposites," and dis-
tinguished from the ordinary offsets by the letters "op" annexed
to them. They are such as these: supposing two chain lines A B
and A C, (fig. 137,) to pass on either side the house D, and that in
chaining those lines the points a and d, at which the line of the
front of the building b c would, if produced, intersect, had been
noticed; then would the distance a b become an "op." at the point a
on the line A C to the corner of the house D, and the distance c d
would become an op" at the point d on line A B to the same
house D, the position of which, if the points are correctly taken, a
proof of which is afforded by measuring bc, must be obviously
better fixed than by any other method of offsetting.
When the distance between any two points on a given line of
fence or building is taken, it is called an "along," and is entered
in the book with an "a" attached to the figures, thus 24 a placed
on a line between two points denotes it is 24 along that line from
point to point.
LAND SURVEYING.
263
The accuracy of an offset depends upon the care with which it
is taken; but after all it is generally little more than an approxi-
mation to truth, and becomes more and more liable to error as it is
increased in length; for it may be measured on the ground with a
little inclination from the perpendicular in one direction, and
plotted on the paper with an inclination in the opposite direction.
Slight inaccuracies may also occur in measuring with the rod;
hence, what is of but trifling importance in small operations in-
creases with a significant ratio, and renders it necessary to sub-
scribe a limit to the length of the offset. This limit has been
usually fixed by writers on the subject at "one chain;" but that is
too much, except for very small scales, and as applied to the scale
of 44 feet to an inch, adopted by the General Board of Health for
all plans made under the "Public Health Act 1848," totally im-
practicable. To that scale two lengths of the rod used is quite as
long as any offset can be safely taken, and then great care is re-
quired to make them plot nicely, as every half link makes a percep-
tible difference. The length of the offset must therefore be a dis-
cretionary point with the surveyor, as ranging from about 30 to 80
or 100 links, according to circumstances; special points and sharp
angles being as much as possible fixed by short offsets, while fences
running nearly parallel to the chain line in which a departure from
the perpendicular will neither affect the length of the offset nor the
position of the fence on the paper, may form exceptions for the
exercise of a little indulgence.
To illustrate the method of taking up the details, we will con-
sider the fence A abcd B (fig. 138), is to be taken up by the offset
line A B. Looking along the fence from the point A, we discover
that a bend occurs at the point a, and therefore in chaining along
the line from A towards B, we carry the point a in our mind's eye,
and determine when we arrive at the point a', from which the per-
pendicular d'a arises; noting the distances A a and a'a, we proceed
to measure until we arrive at b', where we note the respective dis-
tances A b and b'b, and chain on to c; here the chain line touches
the fence, and therefore we have only one distance to denote, viz.,
Ac; hence, we go on to d, noting in a similar manner the dis-
tances A d' and d'd, and complete our work by entering the length
of the line AB. A little consideration and study will convey to
the mind of the enquirer the application of this principle to every
crooked fence which can possibly occur in a survey. Had there
been a fence on the opposite side of the line in fig. 138, as in fig.
139, offsets would have been required, as there shewn; and again,
if one line had been insufficient to take up the fence, more must
264
LAND SURVEYING.
have been taken, as shewn in Figures 140 and 141; the several
ends of the lines being fixed by triangulation, as hereafter to be
spoken of.
We now come to the consideration of the method of laying out the
fundamental lines of a survey. In order to do this effectually, the
surveyor must acquaint himself with the boundary of the land to
be surveyed, and if he can make one triangle encompass the whole
without going too far out of the work, of course that is the best
method that can be adopted; because if he can only get the sides of
that triangle accurately set out and measured, all other lines within
it may be made to depend thereon, and the chances of error are
consequently confined to the internal detail thereof, which is easily
detected and rectified.
A large triangle, comprising the boundary of an estate, is gene-
rally sufficiently proved by the secondary lines that traverse it from
side to side in every possible direction; but it is a very great ad-
vantage where it can be done to take the angles formed by the
several sides of the triangle. This enables the straightness of the
sides to be tested by casting the internal angles together and ascer-
taining if they amount to 180 degrees, as the sum of the internal
angles of all triangles should do. It also enables a surveyor to run
a proof line from any one of the points of the triangle, so as to fall
at a right angle on the opposite side. For instance, let us suppose
the angles of the triangle represented in fig. 142 were taken, and
that the angle B A C is 38 degrees, we require to let fall the proof
line BD, so that the angles BD A and B DC may be each right
angles. Taking the angle B A D=38° and the angle B DA = 90°,
we know of course that the angle ABD must be such as will
make when cast with the two known angles 180 degrees; hence,
in this case, we have to lay off 52 degrees at B as the measure of
the angle A B D. If any one of the sides is not straight, the
aggregate sum of the observed angles will be either greater or less
than 180 degrees, according to the nature of the error. (See fig.
143.) It is hardly to be supposed, with the irregular shapes which
boundaries of fields and landed properties assume, that many
estates exist which can be enclosed in one triangle, as above stated,
although it does sometimes happen, and has within my experience.
The estate alluded to is situate on Sunbury Common, between
three roads. It is now divided among several owners, but twenty
years ago it formed one property, it is represented in fig. 144.
When an estate cannot be entirely encompassed by one triangle,
then the desideratum is to enclose as much of it as possible within
the triangle, leaving the outskirts to be provided for by secondary
LAND SURVEYING.
265
constructions. In the estate represented by fig. 145, having laid
out the primary triangle A B C, and the proof line B D, the lines
CE, EF, and FG, are severally determined on as necessary, as
fundamental lines for that corner of the estate, and to fix their
*position beyond all doubt with reference to the large triangle the
line F G is produced to H, a line is taken from E through G to K,
and from C through I to F. To provide for the remaining portion
of the estate, a line is run from B to O, from 0 to M, and from
M to N, and then their positions are securely fixed by the lines
PLM, BQM, and LQ O. The great beauty of the method of
construction just described is, that if any one of the lines be wrong,
the remaining lines are sufficient not only to detect the mistake,
but to point out beyond doubt the line in error, and to plot the
work accurately without its aid. For example, suppose an error
had been contained in either of the lines CE or E F, by plotting
the lines CIF, F G H, and EIGK, it would have been apparent
at once which was in error, as the other would scale the measured
length.
It may be as well to observe, that the constructions herein re-
commended for estates or blocks of land containing many enclo-
sures, apply equally to single fields of similar proportions, examples
of which our space will not admit.
When the limits of the estate to be surveyed assume other
forms than those of a triangle, it is generally desirable to divide it
into two principal triangles, and provide for the outskirts as most
expedient. Fig. 146 is an illustration of my meaning. Here
A B C and C D A are the two principal triangles, and the accu-
racy of the two opposite points B and D is securely tested by the
proof line BED; then by using E as a common point, and laying
out E FG, HIE, AG, G H, and HD, AEG becomes a triangle
with AF as a proof line; E G H a triangle with F I a proof line;
and E HD is a triangle with DI as a proof line; while the lines
A G, G H, and HD, severally act as proofs to each other and the
whole work.
Sufficient having been said to enunciate a principle so far as
theory is concerned, it is now proposed to see by a reference to
an instance of actual practice, how far this principle can be carried
out in practice; for it must be remembered, that in all professions,
mere theories, when attempted to be put in practice, are assailed
by an infinity of difficulties. Hence, it is totally impossible to
prescribe a rule from which no deviation shall be made; the only
practical mode is to point out correct tenets, and require as close
an approximation thereto as possible.
T
266
LAND SURVEYING.
►
Plate 5 represents a reduced plan of the parish of Sunbury,
surveyed by me about five years since. Several difficulties pre-
sented themselves during the laying out of the fundamental lines,
of which the close proximity of the River Thames to the village,
on the south side of the parish, the number of houses and gardens *
scattered about its area, and the very flat nature of the country,
formed some of the most prominent. Advantage was first of all
taken of the straight piece of road from F to M, and a line ranged
down it to A; a second line was then laid out from B to R,
escaping as much as possible of the village of Sunbury, but en-
countering a great portion of the Thames and the tributary
streams; a third line was then laid out from R to M, avoiding the
villages of Halliford and Charlton, but extending some distance
beyond the parish to meet the main line. These three lines
formed the fundamental triangle B M R.
The next step was to lay out the proof line R I, about which
the only difficulty encountered was at Y. A line was then found
practicable from D to W, and at W another line was laid off
to fall on the base at right angles at H. A line down the straight
road from X through Y to P, completed the principal lines within
the large triangle. Lines were then started from R and O,
and from their interception at the point c, a tie-line was laid out
so as to fall at right angles on the base of the triangle at Q.
From Q a line was laid out through a to l, and from Q through f
and h to i; 10 and 7b being joined the triangles ROc and Ob l
became fundamental triangles, well and securely fixed and proved.
The small triangle dek, with the lines kh and ig completed the
boundary on the south-west. The triangle T t B, with proof lines
tV and s U, and the triangle Sn R, with lines R M Q, no, op,
np, p q, qr, r S, and r T (some of which were obliged to be calcu-
lated) completed the fundamental lines for the survey of the
boundary on the river side; and the triangles A Cu, CG w,
G K 3, G3 w, w Cu; with proof lines Cv; Ex; Fy; F1; z5;
1, 4, 9; 2,3; and tie and secondary lines 6,7; 7,5; 7,8; 8, 9;
9,3; 10, 12: and 11, 12, 13 formed all the lines necessary for the
triangulation of the parish.
Upon examination, theory might suggest that the triangles to
the north of the line A M, should have been fewer in number, and
that at all events the line between points u and 3 should have been
one continuous one; but the local difficulties intervening would
have caused a far greater loss of time than any advantage gained
* The houses and gardens are not shewn in detail on the plan owing to the diminu-
tive size of the scale; it has been thought better to block in the sites built upon.
LAND SURVEYING.
267
would justify, and therefore the attention was chiefly directed to
the formation of a series of triangles, the sides of which would
check one another, and be useful as offset lines, in the which we
were very successful. It was not deemed expedient to extend c Q
into the large triangle, the safety of the triangle R o C being per-
fectly secure without it. The lines in the south corner are such
as it were possible to obtain; the theodolite being used in all cases
where it became necessary to compute the sides of triangles by
means of the contained angles. On the whole, the triangulation of
this parish is offered as a good practical illustration of the best
principles of surveying, carried out without the smallest view to the
purposes to which it is now about to be applied; executed, moreover,
to produce professional remuneration under the influence of a very
bad bargain; and now selected by chance from a number of others
equally good, but with less convenient dimensions for the size of
our intended work.
Note.-It should be here stated that the lines, and not the sta-
tions, were all numbered in the actual survey. The lettering has
been adopted in the plate as offering greater facility of reference.
Having laid out the fundamental lines of a survey, and chained
them, the next process requiring attention is what is technically
termed “filling in ;" that is, laying out, and chaining such a num-
ber of internal or secondary lines, as may be required, with the
offsets upon them, to take up all the fences, houses, buildings, and
other features upon the land. Here it must be observed, that the
lines taken for this purpose should be what are called "through
lines," that is, lines running from any one already fixed line to
another line already fixed, so that no distortion of the internal
features of the survey, with reference to the external ones can
take place. It is not imperatively necessary to the accuracy of
the map that these lines are to follow consecutively from one fixed
line to another; they may be taken in this way: Let A B,
B C, and C A (fig. 147) be the lines of a triangle, already
fixed; and a line is required from D to E to take up the neigh-
bouring fence, which at the point E turns to the right. A line is
then run from F, crossing E to G, where the fence again deviates
its course; and lastly, the line from H, through G to I, completes
the filling in of the fence. This is manifestly as correct an opera-
tion as though the order of the lines had been reversed (as they
will be when they come to be plotted), and H I had been first
chained, then G F, and then E D, and equally so as though the
line D E had been extended to e, that a line had then been car-
ried from E to f, and then from G to i. The position and direc-
268
LAND SURVEYING.
tion of these secondary lines entirely depend upon local circum-
stances; it is often more expeditious to run two or three lines on
the ground, than encounter the local difficulties of laying out one
line which would look best upon paper. It is desirable that as
many lines as possible should proceed from one station, by reason
of the excellent check they become to each other.
I will here notice a few of the methods by which obstructions
in the admeasurement of chain lines may be overcome; but it
must not for a moment be understood that the plans here sug-
gested are the only efficient ones; on the contrary, an infinite
number will present themselves to the mathematician, who will of
course adopt that one that may be best suited to the special cir-
cumstances for which some expedient is required.
In figure 148 the chain line A B crosses a river, and it is to be
premised that the surveyor has no instrument for taking angles
with him, he is therefore desirous of getting the inaccessible dis-
tance c d, in the readiest manner possible. Let the points a c re-
present the extremities of the last perfect chain before arriving at
the river, and let b be a mark at the centre link of that chain,
then let one handle of the chain be held at a, and the other at b ;
and by laying hold of the centre of the chain, let the point ƒ of the
equilateral triangle a bƒ be marked in a similar manner set out
the triangle b c e, then will fe⇒ a bor b c = 50 links; let the
lines d e and bf be made to intersect in g; and let the distance
fg be accurately measured in links, and tenths of links by reason
of its shortness; then say as the side f g of the triangle ƒge is to
the side fe, so is the side e c of the similar triangle c d e to the
required side cd; for example, let ƒg = 22.6 links; then fg =
22·6 : ƒ e = 50 : : e c = 50 : c d = 110 links.
=
:
Suppose A B C D, fig. 149, to be the site of a house crossed
by the chain line E F G H, which has been previously laid out,
either from high ground or by means of good back and fore marks.
Measure the distance F D, and set off the same from D to I: in
like manner set off C K equal to C G, then will the distance I K
equal the required distance F G. Had FD and G C been equal,
the line would have crossed the house at right angles, and the
width D C would consequently have been equal to the required
distance.
Fig. 150 represents a house crossed by the chain line E F G H
in a different manner. In this case make D I equal F D, and
then because the triangles GDI and F D G are similar and
equal, the side G I will be equal to the required side G F. Rec-
tangular hay and corn ricks are generally so nearly right angled
LAND SURVEYING.
269
as to admit of this process with sufficient approximation to
truth.
If the obstruction is a pond, lay off a b (Fig. 151) and c d, each
equal 50 links on the chain line on either side of the pond; con-
struct the equilateral triangles a be, a b f, c d g, and c d h, by
holding the handles of the chain at the points a b and c d, and
marking the points e f g h, with the centre of the chain in manner
described in the first example; produce a e, and g d to k, and a f
and d h to i; then because all the triangles are similar and equi-
lateral the sides a k, k d, di, and i a, are all similar to the re-
quired side a d. If the pond is small the operations need only be
carried on on one side of it, which even then affords a check upon
the accuracy of the work, inasmuch as a k and k d should exactly
correspond; but if the equilateral triangles, whose sides are 50
links are very disproportioned to the required side; it is better to
repeat the work on both sides, and average the length of the four
sides (supposing they do not quite agree) for the length of the
required side.
If the surveyor had with him, as every surveyor should have
when filling in a survey, a pocket sextant, he would have set out
the angles ka d, k da, i ad, i da, each equal 60 degrees with
the sextant.
Some surveyors, in matters of this kind, lay off the angle d a k
= 60 degrees, and then walking along the line a k lay off the
angle a k d therefrom, also equal 60 degrees. This practice is
open to grave objection-for if the slightest inaccuracy is com-
mitted in laying off the first angle, it is not only repeated but in
all probability increased in the second; whereas in the plan herein
recommended, each angle depends solely upon the base line.
One great advantage in the use of a sextant over the chain
only, for purposes of this kind, is, that the operations are not re-
quired to be of quite such large dimensions, and consequently the
liability to error is proportionately diminished; for instance, in
the example we have quoted the angles might have been taken
at b and c, the equilateral triangle confined to the actual unknown
distance bc, and the lines to be measured been reduced to b l, l c,
c m, and m b.
If an instrument is at hand, when the obstruction of a river (or
any other feature) impedes the admeasurement of a line, it is easily
overcome in this way-let A and B (fig. 152) be known points
in the chain line already measured, and noted in the field book in
ordinary course. At B erect a perpendicular, upon which at any
point D observe the angle AD B; lay off the angle B D C equal
270
LAND SURVEYING.
thereto; then because the triangles A B D and BCD are similar
and equal; the unknown base B C equals the known base A B.
The method of keeping a Field Book is varied by different
surveyors to a great extent; but in the course of my practice I
have made a trial of most methods, and think I may safely chal-
lenge all others to a comparison with the one used by myself which
is herein recommended.
Fig. 153 illustrates one page of this Field Book, and Fig. 154
the lines therein referred to.
13, at the foot of the column,
signifies that line 13 is the one referred to by the notes. 1636-12,
placed at the foot of the page, on the left hand, represents that
line 13 starts from the point denoted by the admeasurement 1636,
on line 12; and the position of those figures illustrates approxi-
mately the relative positions of the two lines. 1290--11, on the
right hand side of the page, denotes the point to which line 13
proceeds, and again illustrates, by the position of the figures, the
relative positions of the lines 13 and 11. The theodolite bearing
is entered to shew the mode of doing it. The correct bearing of
the line is entered at top, the opposite bearing beneath it. The
offsets to the neighbouring fence speak for themselves: at zero
it is two links to the right of the chain line; at 210, on the line,
it is twelve to the right; at 280, the line crosses it; at 430, it is
16 to the left; at 520, 10 to the left; at 680, the line crosses it
again; and at the same point on the line, it is 59, opposite to the
corner of the house, the dimensions of which are given; but to
positionise which an op. on another line is required: at 730
another fence, running to the corner of the house is crossed, at
19 a, or 19 along which the first fence terminates: at 1050 a
point is crossed, which represents zero on line 6 (or 0-6), the posi-
tion of which line is also relatively shewn: at 1115, the line is
opposite the straight portion of another fence, to which is noted an
op. of 230: at 1136 it crosses that fence wihch proceeds 3 a, and
then turns; and at 1250 the line terminates.
If the actual starting point of line 13 had not been known when
12 was measured, so that when 13 was chained, it had become ne-
cessary to measure from any given known point on 12 to ascer-
tain such starting point, such distance would have to be expressed
in the Field Book, and added to or subtracted from the given
point, as the case might be. Fig. 155 illustrates this: 1600-12 is
the known point, beyond which 36 links had to be measured to
the starting point of—13, and being measured beyond the known
point on the given line had to be added thereto. 1350-11 is the
nearest known point to which the line proceeds; and falling on
TRIGONOMETRICAL SURVEYING.
271
that line between the known point and zero the remeasured dis-
tance 60 had to be subtracted from the known quantities, leaving
1290 as the point of junction. The point to which a line proceeds
cannot generally be filled in until the line is measured.
By a strict observance to this mode of entering the field notes,
and trusting nothing whatever to memory, it becomes as easy to
plot the work ten years subsequent to the survey as at the time.
I surveyed in or about the year 1842 a parish containing upwards
of fourteen thousand acres, and did not lay down a line of it until
the work was completed, and I had returned to my office-a cir-
cumstance necessitated by the impossibility of getting a room
sufficiently large for the map (which was eighteen feet by twelve
feet) within the parish surveyed. And as a further proof of the
excellence of this kind of Field Book-requiring very recently a
replot of this very survey, I placed the Field Books in the hands
of two of my pupils, who produced, notwithstanding the circum-
stances that they had never seen the parish, and knew nothing of
the survey, as good a map as my own plot; indeed the operation
of plotting from such a Field Book is perfectly mechanical
SECT. II.-Trigonometrical Surveying.
In very extensive surveys, such as the Survey of the United
Kingdom, now being carried on by the scientific branch of the
Ordnance Corps, or (to illustrate a case within my practice) the
Survey of the Island of Guernsey, which I am conducting, the
methods previously described would not be at all applicable. It
would neither be possible to lay out the lines of construction, nor
to measure them with a sufficient degree of accuracy. It there-
fore becomes necessary to adopt some more certain mode of opera-
tion by an extended system of triangulation, on the data of one
very correctly measured base, and the sides calculated therefrom,
and the angles trigged at the vertices of the respective triangles.
In such a system the first attention must be turned to the
selection of the base, which should be as long as it possibly can
be, in proportion to the extent of the country, and should be
situate in a level plain, from either end of which some suitable
trigonometrical points can be seen. In the Survey of the Island
of Guernsey the base line was chosen in a straight level road.
In cases requiring more than ordinary accuracy, glass, deal, and
platinum rods have been used, laid in a level trough purposely
erected for the occasion, and brought into contact by the most deli-
272
TRIGONOMETRICAL SURVEYING.
cate and careful operations; but for all ordinary purposes, a careful
admeasurement by the chain, taken twice in contrary directions,
will produce results, the mean of which may be very safely taken
as the correct length of the base.
I have said that the base should be measured in a level
plain, but I do not intend to imply that no other will do. So that
the site chosen for the base does not contain irregularities and
undulations of surface, a gentle fall in either direction can ob-
viously cause no other inconvenience than to require the base to
be levelled, and from the hypothenusally measured base, and its
perpendicular height at one end above the other, the true hori-
zontal base can be readily obtained by any of the Rules of Right
Angled Triangles. AC (fig. 103,) being the line measured;
A B being the base whose length is required; B C the ascer-
tained height of C above A: or the angle of elevation or depres-
sion can be taken with the theodolite from each end of the base,
and the calculation will resolve itself into the case of a right
angled triangle, in which the hypothenuse and the angles are
given to find the base. But the base so found evidently requires
some further reduction to render it mathematically correct, ac-
cording to the degree of elevation at which it is situated above
the level of the sea.
The annexed figure will serve to illustrate the nature of this
reduction.
a b is the level of the sea, or an arc of the
earth's circumference. A B is the reduced level
base or a parallel arc, the distance between which
is the height above the level of the sea, to which
the base has already been reduced.
a
A
B

b
Now, the length of the arc A B being known,
though obviously longer than it should be, at
the level of the sea, and the radius of the
earth a C being assumed as 21,008,000 feet;
it is evident that by ascertaining the height
of a above A the correct length of ab may be
ascertained; from which as a base, we can calcu-
late the sides of a number of triangles, and from the sides of these
triangles, forming so many fresh bases, can safely determine other
trigonometrical points, until the whole country to be surveyed is
covered with a net work of triangles, which can be correctly
delineated upon paper in their true geographical positions.
C
The following is the formulæ for making this correction :—
From the sum of the log of the altitude A a, and the log of the
TRIGONOMETRICAL SURVEYING.
273
base A B, subtract the log of the sum of the radius and altitude
(a C + A a) and the remainder will be the log of a number of feet,
(all the dimensions being taken in feet) to be subtracted from the
base AB, to produce the true base a b.
This correction will not be required in ordinary surveys, unless
the base measured is at great elevation.
It sometimes happens that the length of a base, or distance
between two points eminently qualified as stations to form the
extremities of a base, cannot be entirely ascertained by actual
admeasurement. The base used for the Ordnance Survey of Ire-
land was lengthened two miles by calculation beyond the mea-
sured distance. I will shew how this can be done, and at the
same time be made to test the accuracy of the measured base.
Let A and B (fig. 156,) be two elevated positions, which it is
desirable to constitute extremities to the base, and let it be pos-
sible to ascertain by admeasurement the length of the line
C D E.
First the line between A and B is correctly staked out by the
theodolite or transit instrument, and permanent marks are made
at C D E F and G.
Secondly, the line is measured from C to D, and from D to E;
and lastly, the following angles are taken :-
At A. FA B and B A G.
At C.
ACF; FCB; BCG; and G C A.
At D.
ADF; FDB; BDG; and G D A.
At E.
AEF; FEB; BEG; and GE A.
At B.
ABF; and A B G.
At F.
AFC; CFD; DFE; and EF B.
And at G. AGC; CGD; DGE; and E G B.
Now by calculation we have first the triangle C D F, in which
are given the base C D, and all the angles, to find the sides C F
and D F.
Secondly, the triangle D E F; given the base D E, and all the
angles, to find the sides D F and F E.
Thirdly, the triangle C E F; given the base CE, and all the
angles, to find the sides C F and E F.
Now the side D F being common to the first and second
triangles, if the admeasurement of the base and angles have been
correctly taken, the result in each case should correspond.
And the side C F being common to the first and third triangles,
and the side E F to the second and third, the results of the cal-
culations should also correspond, and if they do the admeasure-
ment of the two sections of the base C E is proved to be correct.
374
TRIGONOMETRICAL SURVEYING.
The same operation takes place on the opposite side of the base
with the several triangles C DG; DEG; and CE G.
And thus we obtain lots of data for the calculation of the per-
fect base AB.
First, we have the triangle C F A, with base C F, and all the
angles known, to find A C.
Secondly-The triangle D FA, with base DF, and all the
angles, to find A D.
Thirdly-The triangle E F A, with base E F, and all the
angles, to find E A.
Fourthly-The triangle EF B, with base EF, and all the
angles, to find E B.
And fifthly-The triangle AF B, with base AF, and all the
angles, to find A B.
It will be obvious that the calculations and tests can be carried
on through several other triangles, on the same side of the base,
and a corresponding number on the opposite side; but sufficient
has been said to elucidate the principle, and if A D, as found in
the second triangle, is equal to the measured length CD, plus
A C, as found in the first triangle; and A E, as found in the
third triangle, is equal to the measured length C E, plus A C,
there can be no doubt as to the accuracy of either A C; CD; or
DE. And if the length A B, as found by the fifth triangle, is
equal to E B, as found by the fourth, plus A C, plus C D, plus
DE, there is sufficient proof of the accuracy of the whole base
without reference to other triangles.
The best triangles in the example before us, from which to
compute the base, would have been ADF and ADG for the
length AD; and D F B, and D G B for the length D B, the sides
D F and D G being taken as the mean result of the calculations of
the triangles CDF and C D G, and DEF and DE G.
Those who would pursue the subject of bases, beyond these re-
marks, will find the accounts of the admeasurement of the base
lines for the Ordnance Surveys of England and Ireland very in-
teresting. The account of the former operation was published in
1801; and of the latter very recently by Captain Yolland, Royal
Engineers.
Detailed accounts of the methods adopted at various times upon
the Continent may be found in many standard works-" Recueil
des Observations Géodesiques, par Biot et Arago." "Puissant,
Traité de Géodesie.” "Base du Système Métrique Decimal ;" and
the works of Cassini, Colonel Lampton, &c.
TRIGONOMETRICAL SURVEYING.
275
Triangulation.
The second process in a trigonometrical survey is to select a
number of conspicuous stations on the highest hills as trigonome-
trical points, which may either consist of prominent objects such
as churches, windmills, towers, and trees, or they may be artificial
erections of poles, flag staves, &c. ; the latter possessing the advan-
tage, if the points are intended as theodolite stations, from which
to trig other angles, inasmuch as they can be moved to allow the
theodolite to be placed over the exact point; but the former are
preferable as the stations of scondary triangles, in which it is not
considered necessary to trig the third angle. The nearer the
triangles are equilateral the less will be the error produced by any
fault in taking the angles; and as the base is generally shorter than
it is desirable to retain the sides of the principal triangles, they
should be enlarged gradually in the following manner, until they
attain a length in proportion to the nature of the work and the
power of the instruments employed.
Fig. 157 is an illustration. A B is the base from which the
several sides of the triangles ABD and ABC are computed.
From B D and B C, and the contained angle, we obtain CD, as
well as from A D and A C, and the contained angles. The mean
of these results is taken as a new base for the triangles C D E and
C D F, and in like manner E F is obtained. From EF we pro-
ceed to find G H, which has now acquired a length sufficient to
take a place as a side of one of the main triangles GHI. Upon
HI is built I K, and so the work proceeds.
It is always desirable, but of course not necessary, to take all the
angles of each triangle; therefore, while the theodolite is in use at
any station, all objects that can be intersected should be trigged;
they will be found of infinite service in "filling in," and can never
be more accurately fixed in position.
Fig. 158 will represent my meaning. ABC and ABD are
two triangles, and A B C D are stations, at which the theodolite
will be placed for the angles of those triangles. EFGHIK and
L are objects visible from two, and some of them from three, of
these stations, which are readily fixed in position by arranging
them in triangles and taking the angles. Where objects are thus
taken from three stations, the distances obtained become a check
upon each other.
It frequently happens that the objects best adapted to form
points in a triangle are inaccessible, and the theodolite cannot be
placed over the centre of the station. It then becomes necessary
276
TRIGONOMETRICAL SURVEYING:
“to reduce the angles taken to the centre." Cases of this nature are
of three kinds :—First, when the nearest point at which the theo-
dolite can be placed is within the triangle; secondly, when it is with-
out; and thirdly, when it is on one of the sides of the triangle.
Fig. 159 represents the first case. ABC is the triangle, A is
the angle required, and D is the nearest point at which it can be
approached by the instrument. Measure A D, and take the angle
BDA, BDC, and CD A.
Now the angle BDC the <BAC+ < ABD + AC D.
Suppose A B, whose length is known, to be the base of the triangle
ABC. Then in the triangle ABD we have the sides A B and
AD and < A D B to find the remaining angles, and the side B D.
Deduct the angle ABD from A B C, and we have in the triangle
BCD the side B D, and the angles DBC and BDC to find the side
DC. And lastly, in the triangle CDA we have the sides AD
and D C, and the contained angle to find the remaining angles.
From the angle BDC subtract the angle ABD, plus A CD,
and the remainder is the angle B A C, which should also equal the
angle B A D, plus D A C.
Case 2 is illustrated by Fig. 160. ABC is again the triangle,
of which AB is the base. D is the theodolite station. The angle
BEC equals the angle BDC plus the angle D BA; and the
angle B E C equals the angle B A C plus the angle E CA. Hence
we must find the angles DB A, B E C, and E CA, and from these
the angle B A C is attainable.
Case 3 is when the position of the theodolite is upon one of the
sides of the triangle, which is the most simple case of the three.
The distance AD (fig. 161) being measured, the remaining
distance of the base is known; and the angle BDC being equal
to the angle B A C plus the angle A CD, we have only to find
the latter angle, and subtract it from BD C, and it will give the
angle B A C required.
It is not always possible to ascertain A D, or the distance of
the theodolite from the centre of the station by actual admeasure-
ment;
in such cases a short base must be measured from the theo-
dolite in any direction, and the distance found by a small triangle
DE A, (fig. 162.)
If the triangles and the instruments made use of are very large,
a correction for spherical excess becomes necessary; but in smaller
instruments this correction is too minute to be noticed, in com-
parison with the unavoidably greater errors of observation to which
they are subject.
In the conduct of a trigonometrical survey, it not unfre-
TRIGONOMETRICAL SURVEYING.
277
quently becomes necessary to visit the same theodolite station
a number of times, sometimes after the lapse of a consider-
able interval; and although every care may have been taken
to mark the station well, it may from some cause or other be lost;
hence it is desirable that a ready and a certain method of finding a
lost station should be known to the surveyor.
Let A B C and D, (fig. 163,) be trigonometrical points, whose
distances from each other have been previously determined. Let
A be the lost station, and B C and D conspicuous objects.
Set up the theodolite as near the point A as can be surmised.
In the figure this point is represented by E, but it is necessary to
observe that the distance from E to A is there much greater in pro-
portion to the other sides of the triangles than it should ever be
practised: it was impossible to render the figure clear and distinct
without making this so.
At E take the angles BEC and CE D, which being larger
than the original angles B A C and C A D, it is evident the point
is within the circumscribing circles of those triangles. Had our
angles been smaller than the original, the point would have been
without the circumscribing circles. Now, consider the angle A of
the triangle A B C to be altered to the value of the angle BEC,
and that the other angle diminished thereby is the angle C. With
B C as a base, and these angles compute the side B F of the trian-
gle BF C, subtract B F from A, produce B E, and make E G equal
to F A, and at G plant a picket. Again, consider the angle A as
of the value of B E C, and that the angle B is diminished in
consequence, find CH and H A, produce C E to I, making E I
equal to H A.
In similar manner treat the angles of the other triangle CDA,
and find AK and AM; produce C E to L; making EL equal
A K; produce D E to N, making E N equal A M. The intersec-
tion of the lines GI and L N, will be the lost station, provided all
the observations and calculations have been taken with sufficient
accuracy. To verify it the theodolite must now be placed on the
point supposed to be the point A, and the angles between B C and
CD retaken; if these read the same as the original the point is right,
but if not, it must be used as a second trial station, and the opera-
tion repeated. It is better, when possible, to let the operation
embrace three previous triangles, because if any mistake is made
in calculation, the three lines will not intersect each other at a
point, but will leave a small triangle between them, the centre of
which should be taken as the second trial station. On the other
hand, if they do intersect each other at the same point, it affords
strong proof of the accuracy of the whole work.
278
TRIGONOMETRICAL SURVEYING.
If the first trial station falls without the circumscribing circle of
the original triangle, the operation is precisely the same in every
particular, excepting that the differences of distance between the
sides found, and the original sides are set off from the trial station
E towards the points B C and D, instead of producing those lines,
as in the former case.
It often becomes desirable to fix the position of a station by
means of the angles taken at that station only. This may always
be done if three objects are visible, whose distances from each
other, forming three sides of a triangle, are known.
Let A B C, (fig. 164,) be three objects, whose several distances
from each other (A B, A C, and B C) are known.
Let D be the point whose position it is required to fix.
The angles ADC and C D B are taken.
Now, by inspection of the diagram, it is obvious that if about
the points A B D we circumscribe a circle, the angle E A B must
equal the angle EDB (being in the same segment of a circle,
Euclid B 3, Prop. 21), and the angle ABE equal the < ADE.
Therefore in the triangle A B E we have the base A B, and all the
angles to find the sides A E and B E.
In the triangle ABC, the angles are either known or can be
ascertained by calculation of the sides.
From the angle C A B subtract the < E AB, the remainder is
the < CA E, from which, and the two sides A C and A E find the
< ACE - ACD. Then with the base A C, and angles A CD
and AD C, find the sides AD and C D.
Again, from the angle A B C, deduct the < AB E, the remainder
is the < E BC, from which, and the two sides BE and B C, find
the angle BCE = BCD. Then with the base B C, and angles
BCD and BDC, find BD and CD. CD being common to
both calculations, proves the latter part of the work.
But the vertex C of the triangle A B C will sometimes be turned
towards the place of observation D, as in fig. 165.
Very little difference takes place in the arrangement of the cal-
culation. AB, A C and B C are known, and consequently their
contained angles. The angle AD C the < ADE = the
the <
ABE, and the < CDB = the < EDB = the angle EA B are
also known.
Therefore in the triangle ABE, the base AB and angles
ABE and BA E are given to find the sides AE and B E.
In the triangle ACE are given the sides A C and A E, and
the angle C AE = EAB plus B A C to find the angle A C E.
Now, the angle ACE is the external angle of the triangle
TRIGONOMETRICAL SURVEYING.
279
A CD, and (Euc. B 1, Prop. 32) equal to the two internal oppo-
posite angles CAD and CDA.
Hence, if from the angle ACE be taken the angle CDA, the re-
mainder is the <CAD, and in the triangle A CD we have the base
A C, and all the angles given to find the other sides C D and AD.
In like manner is found the < BCE in the triangle B CE; and
the < B C E being known, <° C D B and B C D are also known;
and the sides BD and CD are found from the base B C.
The three known objects A B and C may possibly fall in one
straight line, such as three stations of a base line.
Now, the < ADC = the <
And the < CDB the <
=
Fig. 166 represents this case.
ADE the < ABE is known.
EDB = the < EAB is also known.
Therefore, in the triangle A B E, the base A B, and all the angles
are known to find the sides A E and BE.
Next, the sides AC and A E and the contained < being known,
the < A CE is determined. And the < A CE being the external
< of the triangle A CD, the angles of that triangle, and the base
A C, are given to find the sides AD and CD.
And again, BC and BE, with the contained < being known,
the < BCE is obtainable; and the <B CE being the external <
of the triangle B CD, we have all the angles, and base B C of that
triangle given to find the sides CD and B D.
But the point of observation D will sometimes fall within the
triangle A B C.
Let fig. 167 illustrate this case.
Now, the < A D C is known, and the < ADE being the sup-
plement of < ADC is also known; and the < ABE standing
within the same segment, is equal to < B DE; < CD B is known;
and <E DB is the supplement of < CDB, and < BDE and
BAE being within the same segment, are equal.
Therefore, in the triangle A B E, the base A B and all the an-
gles are given, and the sides A E and B E can be thus obtained.
The angles within the known triangle ABC are also given or
obtainable.
Next, in the triangle C A E, the sides A C and A E are known
and the contained angle (equal the < C A B plus <BAE) to find
the < ACE=< ACD.
In the triangle A CD, the base A Cand all the angles are given
to find the sides AD and CD.
Again, in the triangle CBE, the sides B C and BE and the
contained angle (equal the < ABC+< ABE) are given to find
the < BCE = < B C D.
280
TRAVERSE SURVEYING.
Lastly, in the triangle B CD, the base BC and all the angles
are given to find the sides BD and CD.
It is sometimes desirable to fix the positions of two new stations
by means of observations, taken at those two stations with refe-
rence to two old stations, whose distances from each other are known.
Let A and B, (fig. 168,) represent the old stations, and C and D
the new; it is required to know the distances A C, BC, A D,
B D, and CD.
At C take the angles A CB and B CD, and at D take the <*
CD A and AD B.
To compute the triangles assume CD, equal any convenient.
distance G F.
Then with base G F and angles AGF = ACD, and A FG =
ADC, find A F and A G.
In like manner find E F and E G.
Then with the sides AG and the contained < A GE = <
AC B, find A E.
Again (as a proof) with the sides A F and E F, and < AFE
= <ADB, find A E.
Then, As AB: AE:: AG: A C.
BC.
As AB: AE:: EG: B C.
As AB: AE::AF: AD.
As AB: AE:: EF: BD.
As AB: AE::GF: CD.
Filling in.
The interior details of a Trigonometrical Survey can be “filled
in,” in the same manner as previously described for the filling in
of a parish or estate survey, or by a traverse. The distances from
one trigonometrical point to another can be chained, and between
these lines other lines can be laid out and measured, as often as
circumstances may require. Fig. 169 will illustrate this method.
SECT. III.-Traverse Surveying
Is a method of surveying by means of a chain and theodolite,
or other angular instrument (according to the degree of accuracy
required), which is frequently resorted to in filling in the roads
on a trigonometrical survey, where it is sometimes impossible to
adopt the more accurate, though less expeditious method of chain-
ing between every trigged station, and filling up the interior by
through lines. My survey of Guernsey is conducted in this way.
TRAVERSE SURVEYING.
281
The objects chosen to form the vertices of the principal triangles
(consisting of twelve windmills, seven church steeples, several
martello and other towers, batteries, signal masts, &c.) occupy for
the most part such inaccessible positions, and the country gene-
rally is so irregular and broken as to render any attempt to chain
some of the sides of the triangles ridiculously futile.
The "traverse system," while it possesses the advantage noticed
above, also possesses another advantage with reference to the
Guernsey Survey, inasmuch as it enables the survey of the nume-
rous roads with which the Island is covered to be proceeded with
during the fine weather of the summer months, which would have
been entirely prevented by the crops had the "right line" system
of filling in been exclusively adopted.
The little blocks between the roads are afterwards filled in by
a system of through lines from road to road, in the same manner
as though the roads bounded a right line triangle.
Fig. 170 represents the mode of carrying on a traverse survey.
A B C are the points of a triangle, whose positions have been
computed.
From A, line 1, proceeds by the nearest accessible route into
the road; lines 2, 3, 4, &c., continue along the road until the end
of line 9, which has arrived opposite the station B to which line 10
is directed. Lines 11, 12, 13, 14, 15, again proceed in the road;
and 16 starting from station C, and crossing the end of line 15,
continues the traverse along the road, and closes by line 20 falling
upon the end of line 1 and beginning of line 2. Line 21 com-
mences at a point on line 7, and proceeds to traverse the intersect-
ing road, which is completed by line 26 falling upon line 14.
The angles are now taken, and an opportunity is afforded, with-
out much (if any) loss of time, for rechaining the lines without the
offsets, as a proof of their accuracy.
The theodolite being placed at station A, is adjusted and set to
zero, and the telescope is directed to the magnetic meridian, or
in other words, the entire head of the instrument is turned round
until the marked end of the needle points to zero in the compass
box-the other or south end pointing to 180°.
The lower plate is then clamped, and the upper plate unclamped,
and the telescope is directed at station B: the bearing of which is
read off and entered; the upper plate is again unclamped, and the
bearing of line 1 is taken and entered.
The instrument is now taken to the beginning of line 2, and
there set up and adjusted. The telescope is turned upon line 1,
and since the upper plate has not been touched since the bearing
U
282
TRAVERSE SURVEYING.
of line 1 was taken, it still remains clamped at that bearing (but
this should always be verified by examination, as the operation of
carrying the instrument from one station to another will some-
times shake it a little out of place if the clamp screws are not very
securely fastened), and the screws may also be inadvertently
touched in the process of levelling the instrument.
It being obvious that the telescope and limb being now in a
position exactly parallel to the one they occupied at the station A,
excepting that they have been reversed 180°, the needle should,
when set free, settle down at the same bearing as above, saving
that the reading which was before at the marked or north end is
now at the south end, consequent upon the reversion of the in-
strument. Clamp the limb, or lower plate, and unclamp the
upper one; and as this is the point at which line 20 closes
the work, direct the telescope upon that line, before the bearing
of line 2 is taken, so that the last reading at the station may
be the bearing of the line from which the next line of the
series proceeds.
Here I should observe, that the compass or real bearing of the
line, when the instrument follows the work in the same direction
as the lines were measured, being always the bearing indicated by
the marked end of the needle (as taken at the beginning of any
line), it should always be written uppermost; the other or "op-
posite" bearing, which differs from the real bearing exactly 180°,
being placed below. Strict attention to this will serve to denote
at any
future time the direction of the lines; and as line 20 is now
taken at the end instead of the beginning, the bearing indicated
by the north end of the needle will be the "opposite" bearing of
the line when the instrument is placed in true position with re-
spect to it, and it must be so entered accordingly.
The bearing of line 2 being taken, the instrument is moved to
line 3, and in like manner the work proceeds regularly until it
arrives at line 10, when the instrument being placed on station B,
and directed at A, the bearing of A B should read the same (re-
versed) as it read at A; if it does, the angles have all been correctly
taken; if not, there is an error which must be detected before
greater mischief is done. Assuming the work to be correct the
bearing of A C is taken from B, and also the bearing of the
station forming the end of line 11, and the beginning of 12, to
which the instrument is next removed, and being adjusted and
levelled, and directed at the back bearing of A B, the bearing of
line 11 is taken, and then of line 12; and so we proceed until thẹ
end of line 14; from whence, if visible, after taking the bearing
PRISMATIC COMPASS.
283
of line 15, we take the bearing of A C, to which station we next
remove the instrument, and verify the bearing of B C. We then
take the bearing of C A, and after that of line 16, and proceed to
close our work with line 20, the bearing of which should prove
the same as at first taken from line 2.
The instrument is now taken to line 21. The nonius is ad-
justed to the bearing of line 7, to the most distant end of which
the telescope is directed, and from it is taken the bearing of line
21; and the work proceeds in the same manner until the end of
26, where the instrument being set up, and directed from the
bearing of line 26 to line 14, the bearing of this latter line should
prove the same, or very nearly, as when taken in the first series;
and this again proves the work.
It will not be possible at all times to set the theodolite over the
trigonometrical station; but it is generally practicable to place it
in line between two stations, so that the bearing thereof may be
taken, from which a bearing may be taken to some spot on the
first line from whence the bearing of the first line may be
taken.
No directions that can be written will render a person an ex-
pert surveyor: practice alone will effect that. Enough has been
said to convey a knowledge of the theory, the practice should be
acquired under the instructions of some able master.
SECT. IV.-Field Instruments.
THE PRISMATIC COMPASS.
With this instrument horizontal angles can be observed with
great rapidity, and, when used with a tripod stand, with a con-
siderable degree of accuracy. It is, consequently, a very valuable
instrument to the military surveyor, who can make his observa-
tions with it, while holding it in his hand, with all the accuracy
necessary for a military sketch. It is also a useful instrument for
filling in the detail of an extensive survey,* after the principal
points have been laid down by means of observations made with
* The prismatic compass was used for this purpose by the gentlemen engaged in
making the Ordnance Surveys.
284
PRISMATIC COMPASS.
the theodolite, hereafter to be described, and for any purpose in
short, in which the portability of the instrument and rapidity of
execution are of more importance than extreme accuracy.
C is a compass card divided
usually to every 20', or third
part of a degree, and having
attached to its under side a
magnetic needle, which turns
upon an agate centre, o, fixed
in the box B; n is a spring
which, being touched by the
finger, acts upon the card,
and checks its vibrations, so
as to bring it sooner to rest
when making an observation;
S is the sight-vane, having

P
C
B
n
a fine thread stretched along its opening, by which the
point to be observed with the instrument is to be bisected. The
sight-vane is mounted upon a hinge-joint, so that it can be turned
down flat in the box when not in use. P is the prism attached
to a plate sliding in a socket, and thus admitting of being raised
or lowered at pleasure, and also supplied with a hinge-joint, so
that it can be turned down into the box when not in use. In the
plate to which the prism is attached, and which projects beyond
the prism, is a narrow slit, forming the sight through which the
vision is directed when making an observation. On looking
through this slit, and raising or lowering the prism in its socket,
distinct vision of the divisions on the compass card immediately
under the sight-vane is soon obtained, and these divisions, seen
through the prism, all appear, as each is successively brought into
coincidence with the thread of the sight-vane by turning the in-
strument round, as continuations of the thread, which is seen
directly through the part of the slit that projects beyond the
prism.
The method of using the instrument is as follows:-The sight-
vane S, and the prism P, being turned up upon their hinge-joints,
as represented in our figure, hold the instrument as nearly in an
horizontal position as you can judge; or, if it be used with a tripod
stand, set it as nearly as you can in a horizontal position by
moving the legs of the stand, so that the card may play freely.
Raise the prism in its socket till the divisions upon the card are
seen distinctly through the prism, and, turning the instrument
round, until the object to be observed is seen through the portion
PRISMATIC COMPASS.
285
of the slit projecting beyond the prism in exact coincidence with
the thread of the sight-vane, bring the card to rest by touch-
ing the spring n; and then the reading at the division upon the
card, which appears in coincidence with the prolongation of the
thread, gives the magnetic azimuth of the object observed, or the
angle which a straight line, drawn from the eye to the object,
makes with the magnetic meridian.* The magnetic azimuth of a
second object being obtained in the same manner, the difference
between these two azimuths is the angle subtended by the objects
at the place of the eye, and, which is an important point, is inde-
pendent of any error in the azimuths, arising from the slit in the
prism not being diametrically opposite to the thread of the sight-
vane.
For the purpose of taking the bearings of objects much above
or below the level of the observer, a mirror, R, is supplied with
the instrument, which slides on and off the sight-vane S, with
sufficient friction to remain at any part of the vane that may be
desired. It can be put on with its face either upwards or down-
wards, so as to reflect the images of objects considerably either
above or below the horizontal plane to the eye of the observer ;
and, if the instrument be used for obtaining the magnetic azimuth
of the sun, it must be supplied with dark glasses, D, to be inter-
posed between the sun's image and the eye.
There is a stop in the side of the box, not shewn in our figure,
by touching which a little lever is raised, and the card thrown off
its centre, as it always should be when not in use, or the constant
playing of the needle would wear the fine agate point upon which
it is balanced, and the sensibility of the instrument would be
thereby impaired. The sight-vane and prism being turned down,
a cover fits on to the box, which is about three inches in diameter,
and one inch deep; and the whole, being packed in a leather case,
may be carried in the pocket without inconvenience.†
* The magnetic meridian now makes an angle of 24° with the true meridian at
London, the north point of the compass being 24° west of the true north point. This
angle is called the variation of the compass, and is different at different places, and
also at the same place at different times. Since this variation will affect equally, or
nearly so, all azimuths observed within a limited extent and during a limited time,
the angles subtended by any two of the objects observed, being the difference of their
azimuths, will not be affected by the variation, and hence the map, or plan, may be
constructed with all the objects in their proper relative positions; but the true meridian
must be laid down, if required, by observations made for the purpose.
† For much valuable information respecting the use of the prismatic compass, espe-
cially in military surveying and sketching, I can refer our readers to a Treatise on
Military Surveying, &c., by Lieutenant-Colonel Basil Jackson, in which the subject is
handled with great ability.
286
BOX SEXTANT.
THE BOX SEXTANT.
This instrument, which is equally portable with the prismatic
compass, forming, when shut up, a box of about three inches in
diameter, and an inch and a half deep, will measure the actual
angle between any two objects to a single minute. It requires no
support but the hand, is easily adjusted, and, when once adjusted,
but seldom requires re-adjusting.
When the sextant is to
be used, the lid, E, of the
box is taken off and screwed
on to the bottom, where it
makes a convenient handle
for holding the instrument.
The telescope, T, being
then drawn out, the instru-
ment appears as represented

B
a M
©
E
T
in our figure. A is an index arm, having at its extremity a
vernier, of which thirty divisions coincide with twenty-nine of the
divisions upon the graduated limb, 77; and the divided spaces
upon the limb denoting each thirty minutes, or half a degree, the
angles observed are read off by means of the vernier to a single
minute. The index is moved by turning the milled head, B, which
acts upon a rack and pinion within the box. To the index arm is
attached a mirror, called the index glass, which moves with the
index arm, and is firmly fixed upon it by the maker, so as to have
its plane accurately perpendicular to the plane in which the
motion of the index arm takes place, and which is called the plane
of the instrument. This plane is evidently the same as the plane
of the face of the instrument, or of the graduated limb, 77. In the
line of sight of the telescope is placed a second glass, called the
horizon glass, having only half its surface silvered, and which must
be so adjusted that its plane may be perpendicular to the plane of
the instrument, and parallel to the plane of the index glass when
the index is at zero. The instrument is provided with two dark
glasses, which can be raised or lowered by means of the little
levers seen at d, so as to be interposed, when necessary, between
the mirrors and any object too bright to be otherwise conveniently
observed, as the sun. The eye-end of the telescope is also fur-
nished with a dark glass, to be used when necessary.
The principle upon which the sextant is constructed is, that
the total deviation of a ray of light, after reflections succes-
sively at the index glass and horizon glass, is double the
inclination of the two glasses. Now the limb, 17, being di-
BOX SEXTANT.
287
vided into spaces, each of 15' extent, and these spaces being
figured as 30′ each, the reading of the limb gives double the
angle moved over by the index arm from the position in which
the reading is zero, or double the angle of inclination of the two mir-
rors, if these mirrors be parallel when the reading is zero. If, then,
the instrument be in perfect adjustment, and any object be viewed
by it after reflection at both the mirrors, the reading of the in-
strument gives the total deviation of the rays of light, by which
the vision is produced, or the angle between the bearing of the
object from the centre of the index mirror, and the bearing of the
reflected image from the place of the eye, that is, between lines
drawn respectively from the object to the centre of the index
glass, and from the reflected image in the horizon glass to the eye.
This angle is very nearly equal to the angle subtended by the
object and its image at the place of the eye, differing from it only
by the small angle subtended at the object by the place of the eye
and the centre of the index glass. This small angle is called the
parallax of the instrument, and is scarcely perceptible at the dis-
tance of a quarter of a mile, while for distances greater than that
it is so small that it may be considered to vanish. It also varies
with the amount of deviation, and vanishes altogether whenever
the centre of the index glass is in a direct line between the object
and the eye.*
To see if the instrument be in perfect adjustment, place the
dark glass before the eye-end of the telescope, and looking at the
sun, and moving the index backwards and forwards a little distance
on either side of zero, the sun's reflected image will be seen to
pass over the disc, as seen directly through the horizon glass; and
if, in its passage, the reflected image completely covers the direct
image, so that but one perfect orb is seen, the horizon glass is
perpendicular to the plane of the instrument; but, if not, the
screw at a must be turned by the key, k, till such is the case. The
key, k, fits the square heads of both the screws seen at a and b,
and fits into a spare part of the face of the instrument, so as to be
at hand when wanted. This adjustment being perfected, bring
the reflected image of the sun's lower limb in exact contact with
* We have seen a method given for what is called correcting the parallax, when an
observation is made at a short distance, by finding the deviation at this distance, when
the angle between the object and its image is equal to zero; this deviation being given
by the reading of the instrument, when the reflected image of the object observed
exactly coincides with the object itself, seen through the unsilvered part of the horizon
glass. This deviation, however, is not the parallax, even for a small angle between
the object and its image, and, if the angle be not very small, the error introduced by
the method will be greater than the parallax itself.
288
BOX SEXTANT.
the direct image of his upper limb, and note the reading of the
vernier; then move the index back, beyond the zero division of
the limb, till the reflected image of the sun's upper limb is in
exact contact with the direct image of his lower limb; and, if the
zero of the vernier be now exactly as far behind the zero of the
limb as it was at the former reading in front of it, so that the
reading now on the part of the limb called the arc of excess, be-
hind its zero division,* be the same as the former reading, the in-
strument is in perfect adjustment; but, if not, half the difference
of the two readings is the amount of the error, and is called the
index error, being a constant error, for all angles observed by the
instrument, of excess, if the first reading be the greatest, and of
defect, if the second reading on the arc of excess be the greatest.
In the former case, then, the true angle will be found by sub-
tracting the index error from, and in the latter by adding it to, the
reading of the instrument at every observation; but this error
should be removed by applying the key, k, to the screw at b, and
turning it gently till both readings are alike, each being made
equal to half the sum of the two readings first obtained. When
this adjustment is perfected, if the zeros of the vernier and limb
are made exactly to coincide, the reflected and direct image of the
sun will exactly coincide, so as to form but one perfect orb; and
the reflected and direct image of any line, sufficiently distant
not to be affected by parallax, as the distant horizon, or the top
or end of a wall more than half a mile off, will coincide so as to
form one unbroken line.
To obtain the angle subtended by two objects situated nearly
or quite in the same vertical plane, hold the instrument in the
right hand, and bring down the reflected image of the upper ob-
ject by turning the milled head B, till it exactly coincides with
the direct image of the lower object, and the reading of the in-
strument will give the angle between the two objects.
To obtain the angle subtended by two objects nearly in the
same horizontal plane, hold the sextant in the left hand, and bring
the reflected image of the right-hand object into coincidence with
the direct image of the left-hand object.
* In reading an angle upon the arc of excess, the division to read on the limb is
that next in front of the zero of the vernier, or between the zero of the vernier and the
zero of the limb, and the divisions of the vernier itself are to be read from the end
division, marked 30, and not, as usually, from the zero division: thus, if the zero
division of the vernier were a little further from the zero division of the limb, then the
first division on the arc of excess; and if the twenty-seventh division on the vernier,
or the third from the end division, marked thirty, coincided with a division upon the
limb, then the reading would be 33'.
BOX SEXTANT.
289
It will be seldom that the surveyor need pay any attention to
the small error arising from parallax; but, should great accuracy
be desirable, and one of the objects be distant while the other is
near, the parallax will be eliminated by observing the distant ob-
ject by reflection, and the near one by direct vision, holding the
instrument for this purpose with its face downwards if the distant
object be on the left hand. If both objects be near, the reflected
image of a distant object, in a direct line with one of the objects,
must be brought into coincidence with the direct image of the
other object, and the parallax will thus be eliminated.
For the purposes of surveying, the horizontal angles between
different objects are required, and the reduction of these angles
from the actual oblique angles subtended by the objects, would be
a troublesome and laborious process. If the angle subtended by
two objects be large, and one be not much higher than the other
the actual angle observed will be, however, a sufficient approxima-
tion to the horizontal angle required; and, if the angle between the
two objects be small, the horizontal angle will be obtained with
sufficient accuracy by taking the difference of the angles observed
between each of the objects, and a third object at a considerable
angular distance from them. With a little practice, the eye will be
able to select an object in the same direction as one of the objects,
and nearly on a level with the other object, and the angle between
this object and the object selected will be the horizontal angle
required.
S
At sea the altitude of an object may be determined by observing
the angle subtended by it and the verge of the horizon; but upon
land a contrivance, called an artificial horizon, becomes necessary
for correctly determining altitudes. The best kind of artificial
horizon consists of an oblong
trough, tt, filled with mercury,
and protected from the wind by
a roof, r r, having in either slope
a plate of glass with its two sur-
faces ground into perfectly pa-
rallel planes. The angle SES'

between the object and its re-
flected image seen in the mercury
is double the angle of elevation
SEH, and the angle SES' being
observed, its half will conse-
quently be the angle of elevation
required. If the angle of ele-
S
H
7
t
E
290
THEODOLITE.
A
vation be greater than 60°, the angle S ES' will be greater than
120°, and cannot be observed with the sextant we have been
describing.
The pocket sextant is a most convenient instrument for laying
off offsets or perpendicular distances from a station line; for by set-
ting the index at 90°, and walking along the station line, looking
through the horizon glass directly at the further station staff, or
any other remarkable object upon the station line, any object off
the station line will be seen by reflection when the observer arrives
at the point where the perpendicular from this object upon the sta-
tion line falls, and the distance from this point to the object being
measured, is its perpendicular distance from the station line.
For the mere purpose of measuring offsets, an instrument called
an optical square is now very generally employed, which consists of
the two glasses of the sextant fixed permanently at an angle of 45°,
so that any two objects seen in it, the one by direct vision, and the
other by reflection, subtend at the place of the observer an angle
of 90.
THE THEODOLITE.
The theodolite is the most important instrument used by sur-
veyors, and measures at the same time both the horizontal angles
subtended by each two of the points observed with it, and the
angles of elevation of these points from the point of observation.
This instrument may be considered as consisting of three parts;
the parallel plates with adjusting screws fitting on to the staff
head; the horizontal limb, for measuring the horizontal angles;
and the vertical limb, for measuring the vertical angles, or
angles of elevation.
The horizontal limb is composed of two circular plates, L and V,
which fit accurately one upon the other. The lower plate projects
beyond the other, and its projecting edge is sloped off, or cham-
fered, as it is called, and graduated at every half degree. The
upper plate is called the vernier plate, and has portions of its edge
chamfered off, so as to form with the chamfered edge of the lower
plate continued portions of the same conical surface. These cham-
fered portions of the upper plate are graduated to form the verniers,
by which the limb is subdivided to single minutes. The five-inch
theodolite represented in our figure has two such verniers, 180°
apart. The lower plate of the horizontal limb is attached to a
conical axis passing through the upper parallel plate, and termi-
nating in a ball fitting in a socket upon the lower parallel plate.
THEODOLITE.
291

N
(A)
B
P
N
B
a
A Five-inch Theodolite.
be
This axis is, however, hollowed to receive a similar conical axis
ground accurately to fit it, so that the axes of the two cones may
exactly coincident, or parallel.* To the internal axis the upper, or
vernier, plate of the horizontal limb is attached; and thus, while the
whole limb can be moved through any horizontal angle desired, the
upper plate only can also be moved through any desired angle, when
the lower plate is fixed by means of the clamping screw, C, which
tightens the collar, D: T is a slow-motion screw, which moves
the whole limb through a small space, to adjust it more perfectly,
after tightening the collar, D, by the clamping screw, C. There
is also a clamping screw, c, for fixing the upper, or vernier, plate
* Upon this depends, in a great measure, the perfection of the instrument, as far as
the horizontal measurements are concerned; and when we describe presently the ad-
justinents of the instrument, we shall explain the method of detecting an inaccuracy in
the grinding of the axes.
292
THEODOLITE.
to the lower plate, and a tangent screw, t, for giving the vernier
plate a slow motion upon the lower plate, when so clamped. Two
spirit levels, BB, are placed upon the horizontal limb, at right an-
gles to each other, and a compass, G, is also placed upon it in the
centre, between the supports, FF, for the vertical limb.
The vertical limb, N N is divided upon one side at every 30
minutes, each way, from 0° to 90°, and subdivided by the vernier,
which is fixed to the compass box, to single minutes. Upon the
other side are marked the number of links to be deducted from each
chain, for various angles of inclination, in order to reduce the dis-
tances, as measured along ground rising or falling at these angles,
to the corresponding horizontal distances. The axis, A, of this limb
must rest in a position truly parallel to the horizontal limb, upon
the supports, F F, so as to be horizontal when the horizontal limb
is set truly level, and the plane of the limb, N N, should be accu-
rately perpendicular to its axis. To the top of the vertical limb,
N N, is attached a bar which carries two Ys for supporting the
telescope, which is of the same construction as the Y spirit level, and
underneath the telescope is a spirit level, SS, attached to it at one
end by a joint, and at the other end by a capstan-headed screw as
in the Y level. The horizontal axis, A, can be fixed by a clamp-
ing screw, C, and the vertical limb can then be moved through a
small space by a slow-motion screw ¿.
Before commencing observations with this instrument, the fol-
lowing adjustments must be attended to:-
1. Adjustments of the telescope: viz.,
the adjustment for parallax.
for collimation.
2. Adjustment of the horizontal limb: viz.,
to set the levels on the horizontal limb to indicate the verticality of the
azimuthal axis.
3. Adjustment of the vertical limb: viz.,
to set the level beneath the telescope to indicate the horizontality of the
line of collimation.
1. Parallax and Collimation.-These adjustments are described
under the head of the Y level.
2. Adjustment of the Horizontal Limb.-Set the instrument up as
accurately as you can by the eye, by moving the legs of the stand.
Tighten the collar, D, by the clamping screw, C, and unclamping
the vernier plate, turn it round till the telescope is over two of the
parallel plate-screws. Bring the bubble, b, of the level, SS, be-
neath the telescope to the centre of its run by turning the tangent
THEODOLITE.
293
screw, i. Turn the vernier plate half round, bringing the telescope
again over the same pair of the parallel plate screws; and if the bub-
ble of the level be not still in the centre of its run, bring it back to
the centre half way, by turning the parallel plate screws over which
it is placed, and half way by turning the tangent screw, i. Repeat
this operation till the bubble remains accurately in the centre of
its run in both positions of the telescope; and then turning the
vernier plate round till the telescope is over the other pair of
parallel plate screws, bring the bubble again to the centre of its
run by turning these screws. The bubble will now retain its posi-
tion, while the vernier plate is turned completely round, shewing
that the internal azimuthal axis about which it turns is truly ver-
tical. The bubbles of the levels on the vernier plate being now,
therefore, brought to the centres of their tubes, will be adjusted to
shew the verticality of the internal azimuthal axis. Now, having
clamped the vernier plate, loosen the collar, D, by turning back
the screw, C, and move the whole instrument slowly round
upon the external azimuthal axis; and if the bubble of the level,
SS, beneath the telescope, maintains its position during a complete
revolution, the external azimuthal axis is truly parallel with the
internal, and both are vertical at the same time; but, if the bubble
does not maintain its position, it shews that the two parts of the
axis have been inaccurately ground, and the fault can only be
remedied by the instrument-maker.
3. Adjustment of the Vertical Limb.-The bubble of the level,
S S, being in the centre of its run, reverse the telescope end for
end in the Ys, and if the bubble does not remain in the same posi-
tion, correct for one-half the error by the capstan-headed adjusting
screw at one end of the level, and for the other half by the vertical
tangent screw, i. Repeat the operation till the result is perfectly
satisfactory. Next turn the telescope round a little both to the
right and to the left, and if the bubble does not still remain in the
centre of its run, the level, S S, must be adjusted laterally by means
of the screw at its other end. This adjustment will probably dis-
turb the first, and the whole operation must then be carefully re-
peated. By means of the small screw fastening the vernier of the
vertical limb to the vernier plate over the compass box, the zero of
this vernier may now be set to the zero of the limb, and the verti-
cal limb will be in perfect adjustment.
With an increase in the size of the theodolite, a second telescope
is placed beneath the horizontal limb, which serves to detect any
accidental derangement of the instrument during an observation,
by noting whether it is directed to the same point of a distant ob-
294
THEODOLITE.
ject at the end of the observation to which it has been set at the
commencement of the observation. Also the vertical limb, in the
larger theodolites, admits of an adjustment to make it move accu-
rately in a vertical plane, when the horizontal limb has been first
set in perfect adjustment. This adjustment is important, and should
be examined with great care; and in the small theodolites, when
the vertical limb is permanently fixed to the horizontal limb by the
maker, an instrument which will not bear the test of the examina-
tion which we proceed to describe must be condemned, till set in
better adjustment by the maker. The azimuthal axis having been
set truly vertical, direct the telescope to some well-defined angle of
a building, and making the intersection of the wires exactly coin-
cide with this angle near the ground, elevate the telescope by giving
motion to the vertical limb; and if the adjustment be perfect, the
intersection of the cross wires will move accurately along the angle
of the building, still continuing in coincidence with it. A still more
perfect test will be to make the intersection of the cross wires coin-
cide with the reflected image of a star in an artificial horizon, and
elevating the telescope, if the adjustment be perfect, the direct
image of the star itself will again be bisected by the cross wires.
THE USE OF THE THEODOLITE.
To take an angle, whether between the magnetic meridian and
a given line or object, whether between any two given lines, or at
one given point between any other given points.
Open the tripod stand, so that the centre is as nearly as possible
over the centre of the station, which can be ascertained by a plum-
met, [or what is better (inasmuch as it is always attainable when
wanted, and no encumbrance when done with, because it can be
thrown away), a stone tied to a string.] Level the instrument by
means of the parallel plate-screws, and the levels B B; then if the
angle required is one with the magnetic meridian, set the needle in
motion, unclamp the upper and lower plates of the limb, and bring
the zero division on the vernier to zero on the lower plate. Clamp
the plates approximately by the clamp screw, and accurately ad-
just them by the slow-motion screw. Unclamp the screw C, and
bring the letter N, in the compass-box, to the marked end of the
needle, by turning the whole body of the instrument. Clamp it
approximately by the screw C, and exactly adjust it by the slow-
motion screw D. The telescope and zero division of the scale is
now in the magnetic meridian. Unclamp the upper and lower
plates, and direct the telescope at the given object. Reclamp the
limb approximately with the clamp screw, and exactly bring the
THEODOLITE.
295
cross hairs of the telescope to intersect the object by means of the
slow-motion screw. The angle then indicated by the instrument,
is the measure of the angle required. If the measure of an angle
between two lines or between two objects is required, the process
is similar; excepting only, that part of it that relates to the mag-
netic needle, which is in this case not required; it is simply neces-
sary to place zero on the graduated arc with zero on the vernier,
and direct the telescope at the left-hand object instead of in the
magnetic meridian, as in the former case.
Most theodolites are furnished with two verniers on the upper
plate one corresponding with zero on the lower limb, and the oppo-
site one with the mark denoting 180°. In taking the bearings of
lines these verniers are very useful, as giving the true and apposite
bearing, but in the simple process of measuring angles, one only is
requisite.
To read an angle taken by the theodolite, it is necessary to un-
derstand the vernier scale-a very beautiful and ingenious con-
trivance, by means of which the half degrees on the lower plate are
accurately divided into single minutes.
The 30 minutes represented by the vernier, are equal in length
to 29 degrees on the graduated arc. Now, it is evident by the
fig. 171, the divisions on the vernier being 30, while those on the
graduated arc are 29, every division of the vernier must be one-
thirtieth of a division on the graduated arc, less than such division;
and, consequently, if the vernier is moved along until division 1
upon it is in contact with the first division or half degree on the
graduated arc, the zero of the vernier has moved one-thirtieth part
of such half degree or one minute; if 5 on the vernier is brought
in contact with the fifth division, or 24 degrees on the graduated
arc, then zero of the vernier must have moved five-thirtieths or
five minutes, so that by this contrivance the most minute subdi-
vision is accomplished.*
A vertical angle, or an angle of elevation or depression, is taken
with the theodolite by means of the vertical limb. Having levelled
the body of the instrument as before described, bring the bubble of
the telescope level into the centre of its run by means of the clamp
screw c, and slow-motion screw i; observe that zero on the vernier
and zero on the vertical arc are together, and then unclamp the
vertical limb; raise or depress the telescope until the cross hairs
intersect the object, and the angle denoted by the vernier on the
* A description of the vernier in this place will explain its use in every case to which
it can be applied. It often assumes various forms, but is so simple, that it must be
apparent to every mathematical mind.
296
LEVELLING.
vertical arc, will be the angle of elevation or depression, as the
case may be, which was required.
If the telescope be reversed in the Ys, and the angle taken with
the other end, the mean of the two readings, if they differ, will be
the nearest approach to accuracy, inasmuch as an error in the
adjustment of the vernier is thereby counteracted.
CHAPTER VIII.
LEVELLING
*
Is the art of tracing a line equidistant from the earth's centre,*
which shall cut the directions of gravity everywhere at right angles.
The earth being a globe, it is evident that the operation of
levelling does not consist in simply ascertaining the undulations of
the earth above or below any given horizontal line which may be as-
sumed to form its surface, as an extended plane, but in determining
the relative distances of different places from the earth's centre.
1
In other words, a level line is not, as is frequently supposed, a
true horizontal line, but the arc of a circle; so that if it were
possible to start from London, and level round the world, the
accurate level line would meet at precisely the same spot as that
from which it started.
I
It is therefore obvious that any instrument calculated to take
horizontal levels only, must, beyond a certain distance, become
appreciably in error, and require correction for curvature. The
horizontal line IH, in the
figure, is the line which
would be made by a levelling
instrument standing at the
point I, and for a certain
distance (the relative di-
ameter of the circle being
considered), there would be
no appreciable difference
between the apparent and

C
G
true level; but to shew my meaning, it must be palpably
obvious that the point H is considerably farther from the centre
* Supposing the earth a perfect sphere, which is not quite the case, but sufficiently
near for our purpose, the length of the equatorial diameter being 7,924 miles, while
the polar is only 7,898, the difference is only 26 miles or 3 part.
H
LEVELLING.
297
C than the point G is, and therefore it is not in the true level;
and if any level is taken at a greater distance than ten chains,
this error of curvature must be allowed for.
In addition to this error, on account of curvature, is another,
occasioned by refraction. It is well known that an object is never
seen by us in its true position, but in the direction of the ray of
light, which conveys the impression or image of the object to our
senses, the most curious of all, and as yet (at all events to me)
unexplained arrangement being, that the vertical position in which
every reflected image is left in the eye of the observer when in-
tercepted by the colouring matter that lines the back of the eye,
is the reverse of reality, notwithstanding the correction of this
anomaly, which takes place in the transference of the reflected
image to the mind.
The particles of light, in traversing the atmosphere, are always
bent towards the perpendicular, and consequently describe a
curved track, which to a certain extent modifies the effect of
curvature in levelling, and renders it only necessary, in correcting
for curvature, to do so to the extent to which the error is di-
minished by refraction.
Table 20, chap. I, shews the difference between the apparent and
true level, both in respect of curvature and refraction.
The practice of levelling requires greater care than any other
operation in surveying, owing to the numerous chances of error,
and the great difficulty of detecting it, without going over the
whole operation again; notwithstanding which, when skilfully
and circumspectly performed, the accuracy of the results may be
demonstrated to a degree, exceeding if possible the proofs of a
trigonometrical survey. For instance, suppose a series of levels
to be taken along the principal roads of a country, and afterwards
by circuitous routes, and a variety of methods, the levels of the
branch roads are taken, commencing at a given point on the main
line, and crossing it again and again, and finally terminating upon
some other point of the main line: if at these crossings, and at the
termination of the branch levelling, the reduced levels come out
within a few hundredth parts of a foot of the reduced levels of the
main line, there is little doubt that the levelling is correct.
The most satisfactory piece of levelling, within my practice, oc-
curred in the autumn of 1849. I was employed by the promoters
of a public company to take about thirty-five miles of parliamen-
tary levels,* commencing with a "Datum line one hundred feet
* Levels from which a section is to be made for deposit in Parliament, on the
30th of November, in compliance with the Standing Orders of the House.
V
298
LEVELLING.
below the stone sill of the south door to Wandsworth Old
Church, in the High Street, close to the middle of the door-post,
on the east side of the door." I subsequently discovered that the
promoters had, as a wise precaution against error, also employed
another gentleman to take the same levels.
When the levels were completed, myself and colleague met to
compare notes.
The following are a few of the results :-
MY OWN.
THOSE OF MY
FRIEND.
DIF.
B. M.* At Wandsworth Church
100
100
Fork of Roads near the
Printing Works
111.76
111.67
⚫09
Branch Roads near the Plough
Inn
111.65
111.63 •02
B. M. Mitcham Church
148.05
147.94 •11
A Junction near Mitcham
Common
159.33
159.30 ⚫03
B. M. On a Direction Post near Hack-
bridge
167.00
166.94
•06
B. M.
On the front of large House. 173.75
173.65
•10
Junction of Roads
164.95
164.94 •01
At Angle of Roads
130.11
129.98
•13
Centre of Bridge near the
Snuff Mills
141.58
141.47 •11
Junction of Branch
192.17
192·13 •04
Level of Water at Ford
191.28
191.27 ⚫01
At Waddon.
215.38
215.27 •11
The near side down Rail of
Epsom Railway.
224.62
224.56
•06
B. M. On Croydon Church, being the
close of work, on the stone
sill of the principal door under
the tower
228.11
228.10
•01
It will be seen that the greatest variation is 13, and that being
only at an undefined point on a road, it is quite possible that a
difference of a few hundredths might be made in holding the staff.
* B. M. is the short way of writing Bench Mark, which signifies a firm permanent
feature that can at any time be referred to. A mark on a brick or stone wall makes
a good Bench Mark; they are generally cut in the form represented in fig. 172.
The horizontal line A B being the level referred to.
LEVELLING.
299
The curious in such matters will observe, that my results are in
every instance the greater, and but that the levels of the Bench
Marks also vary on the same way, I should account for it by the
fact, that while my staff-holders used a tripod, those of my col-
league did not. The above is inserted to shew the great accuracy
with which levelling operations can be carried on.
It is usual in levelling to compute all the heights from one
common datum (imaginary) line, so that the relative level of any
two places may be readily ascertained by the simple subtraction
of one height from another. For instance, a place thirty feet
above datum is ten feet higher than another that is twenty feet
above datum. It is desirable that this datum line should be
chosen below the lowest point to be levelled, so that all the
heights may be positive quantities, which could not be the case
were some above and others below datum. It does not of course
follow, nor is it desirable that a datum line should coincide with
any one known point, it is sufficient that it refers to it; hence it
is customary to assume the datum to be 100 (or any other even
number) below some known permanent point, which can always
be referred to.
Levelling Instruments.
THE SPIRIT LEVEL.
The spirit level consists of a glass tube, differing from the
cylindrical form by having its diameter largest in the middle, and
decreasing slightly and with great regularity from the middle to
the ends. The tube is nearly but not quite filled with spirits of
wine, thus leaving in it a bubble of air, bb, which rises to the
highest part of the tube, so as to have its two ends equally distant
from the middle, when the instrument is in adjustment, as repre-
sented in the annexed figure. The tube is generally
fitted into another tube of metal, and attached to a frame
terminating in angular bearings, by which the level can
either be suspended from, or else be stood upon, cylindrical pivots.
When, however, the level forms a permanent part of any instru-
ment, the manner of attaching it is modified to suit the particular
form of the instrument to which it is attached. A small and
accurately-divided scale is attached to the best instruments, or
otherwise a scale is scratched upon the glass tube itself, as repre-
sented in the figure given ante.
300
LEVELLING.
The annexed figure is a repre-
sentation of such a level as is
used for levelling the axis of the
best astronomical instruments.
It is provided with a fixed scale,
seen in the figure, and is suspended by means of accurately con-
structed angular bearings.
The following criteria of a good level are extracted from Dr.
Pearson's valuable work on Practical Astronomy.

Firstly, the bubble must be long enough, compared with the whole tube, to
admit of quick displacement, and yet not too long to admit of its proper elonga-
tion by low temperature.
"Secondly, the curve must be such, that the sensibility and uniform run of
the bubble will indicate quantities sufficiently minute, while those quantities cor-
respond exactly to the changes of inclination, as read on the graduated limb of
the instrument of which it forms a part.
"Thirdly, the bubble must keep its station when the angles are moved a little
round the pivots of suspension.
66
"Fourthly, the opposite ends of the bubble must vary alike in all changes of
temperature, or, in other words, the ends of the bubble must elongate or con-
tract alike in opposite directions, so that the middle point may always be
stationary.
"Fifthly, the angles of the metallic end-pieces must be so nicely adjusted that
reversion on horizontal pivots that are equal will not alter the place of the
bubble.
"Sixthly, the distance between the two zeros of a fixed scale, when such a
graduated scale is used, should be equal to the length of the bubble at the
temperature of 60° of Fahrenheit's scale, and should be marked at equal dis-
tances from the visible ends of the glass tube. Then, as the bubble lengthens
by cold, or shortens by heat, its extreme ends may always be referred to these
fixed marks, 00, on the scale, and will fall either within, upon, or beyond them,
according to the existing temperature. The number of sub-divisions of the scale
that each end of the bubble is standing at, counted from the fixed zero marks, at
the instant of finishing an observation, must always be noted, that an allowance
may be made for the value of the deviation in seconds, or as the case may require.
"Seventhly, when the two ends of the bubble are not alike affected by a
change of temperature, the scale should be detached, and adjustable to the new
zero points, by an inversion of the level.
(( Eighthly, when the scale has only one zero at its centre, which is a mode of
dividing the least liable to misapprehension, the positions must be reversed at
each observation, and both ends of the bubble read in each position; for in this
case, if any change has taken place in the true position of this zero, the resulting
error will merge in the reduction of the observation. This mode of graduating
is generally practised on the continent."
LEVELLING.
301
I now proceed to the description of the most accurate instru-
ments for measuring the differences of level, or vertical distances,
between different stations.
Of spirit levels, for this purpose there are now three in use,
namely, the Y level, Troughton's improved level, and Gravatt's
level.
THE Y LEVEL.
The following figure represents this instrument. A is an achro-
matic telescope, resting upon two supporters, which in shape re-
semble the letter Y, and are consequently called the Ys.
lower ends of these supporters are let perpendicularly into a strong
The

Οι
EC
D
B
a
a
bar, which carries a compass box, C.
This compass box is con-
venient for taking bearings, and has a contrivance for throwing
the needle off its centre, when not in use. One of the Y sup-
porters is fitted into a socket, and can be raised or lowered by the
screw B.
Beneath the compass box, which is generally in one piece with
the bar, is a conical axis passing through the upper of two parallel
plates, and terminating in a ball supported in a socket. Imme-
diately above this upper parallel plate is a collar, which can be
made to embrace the conical axis tightly by turning the clamping
screw E, and a slow horizontal motion may then be given to the
instrument by means of the tangent screw D. The two parallel
plates are connected together by the ball and socket already men-
tioned, and are set firm by four milled-headed screws, which turn
in sockets fixed to the lower plate, while their heads press against
the under side of the upper plate, and thus serve the purpose of
setting the instrument up truly level.
302
LEVELLING.
Beneath the lower parallel plate is a female screw, adapted to
the staff-head, which is connected by brass joints with three ma-
hogany legs, so constructed as, when shut together, to form one
round staff, a very convenient form for portability, and, when
opened out, to make a very firm stand, be the ground ever so un-
even.
The spirit level 77 is fixed to the telescope by a joint at one end,
and a capstan-headed screw at the other, to raise or depress it for
adjustment.
In looking through a telescope a considerable field of view is
embraced; but the measurements indicated by any instrument, of
which the telescope may form a part, will only have reference to
one particular point in this field of view, which particular point is
considered as the centre of this field of view. We must therefore
place some fixed point in the field of view, and in the focus of the
eye-piece, and the point to which the measurement will have re-
ference will be that point of the object viewed, which appears to
be coincident with this fixed point, or which, as the technical
phrase is, is bisected by the fixed point.
The intersection of two fixed lines will furnish us with such a
fixed point, and consequently two lines of spider's web are fixed
at right angles to each other in the focus of the eye-piece. They
are attached by a little gum to a brass ring of smaller dimensions
than the tube of the telescope, and which is fixed to the tube by
four small screws, a, b, c, d. If the screw
d be eased, while at the same time c is
tightened, the ring will be moved to the
right; but if c be eased and d tightened, the
ring will be moved to the left; and in a like
manner it may be moved up or down by
means of the screws a and b.
When the instrument is in adjustment, the
B
Ա.
•

Da
Jo
axis of the tube of the telescope is set truly horizontal by means of
the level beneath it, and the line of observation ought consequently
to be parallel to this axis. Let A represent the proper position of
the intersection of the cross wires, and
OA the direction of the axis of a pencil
of light passing through the object-
glass and coming to its focus at A. Then, the axis of the tube of the
telescope being set truly horizontal, the line AO is also truly
horizontal, and every point bisected by the intersection of the
cross wires will be situated on the prolongation of the horizontal
line A O.

LEVELLING.
303
Suppose now the position of the diaphragm carrying the cross
wires to have become deranged, so that the point of intersection is
moved to B, then every point bisected by the intersection of the
cross wires will be on the prolongation of the line BO, and will
consequently be below the true level point on the line A O.
Let now the telescope be turned half round in the Ys, and let
the annexed figure represent it in its new position; then, in this
new position of the telescope, the pro-
longation of the line BO will rise.
above the prolongation of the level
line A O, and at the same distance from the telescope, the point
now bisected by the intersection of the cross wires will be as much
above the true level point on the line AO as the point before
bisected by them was below it. The true level point is therefore
midway between the two points observed in the two positions of
the telescope, and the diaphragm carrying the cross wires is to be
moved by means of the screws a, b, c, d, till their point of intersec-
tion coincides with that true level point. The telescope is then to
be again turned round upon the Ys, and if the same point be still
bisected by the intersection of the cross wires, they are in their
proper position; but if not, the same method of adjustment must
be repeated till the same point is bisected by the intersection of the
cross wires in every position of the telescope.
This error of derangement has a technical denomination. The
line O A, or O B, from O to the point of intersection of the cross
wires, is called the line of collimation, and the error arising from
their derangement, the method of detecting and correcting which,
I have shewn, is called the error of collimation.
When the image of the object viewed, formed by the object-
glass, either falls short of, or beyond the place of, the cross wires,
the error arising from this cause is called parallax. The existence
of parallax is determined by moving the eye about when looking
through the telescope, observing whether the cross wires change
their position, and are flittering and undefined.
To correct this error, first adjust the eye-piece by means of the
moveable eye-piece tube, till you can perceive the cross wire
clearly defined, and sharply marked against any white object.
Then by moving the milled-headed screw A, at the side of the
telescope, the internal tube a is thrust outwards or drawn inwards,
until you obtain the proper focus, according to the distance of the
object, and you are enabled at once to see clearly the object, and
the intersection of the wires, clearly and sharply defined, before it.
The existence of parallax is very inconvenient, and where disre-
304
LEVELLING.
garded, has frequently been productive of serious error. It will
not always be found sufficient to set the eye-glass first, and the
object-glass afterwards. The setting of the object-glass, by intro-
ducing more distant rays of light, will affect the focus of the eye-
glass, and produce parallax or indistinctness of the wires, when
there was none before; the eye-piece must, in this case, be adjusted
again.
Generally, when once set for the day, there is no occasion for
altering the eye-glass, but the object-glass will of course have to be
altered at every change of distance of the object.
In adjusting the instrument, the parallax should be first cor-
rected, and then the error of collimation. The line of collimation
being thus brought to coincide with the axis of the tube of the
telescope, two further adjustments are necessary: the first to ad-
just the bubble-tube, so that it may truly indicate when the axis
of the telescope is horizontal; and the second to set the axis of the
telescope perpendicular to the vertical axis round which the instru-
ment turns.
To adjust the Bubble-Tube.-Move the telescope till it lies in the
direction of two of the parallel plate screws, and by giving motion
to these screws bring the air bubble to the centre of its run. Now
reverse the telescope carefully in the Ys, that is, turn it end for
end; and should the bubble not settle at the same point of the tube
as before, it shews that the bubble-tube is out of adjustment, and
requires correcting. The end to which the bubble retires must
then be noticed, and the bubble made to return one-half the dis-
tance by turning the parallel plate screws, and the other half by
turning the capstan-headed screw at the end of the bubble-tube.
The telescope must now again be reversed, and the operation be
repeated, until the bubble settles at the same point of the tube, in
the centre of its run, in both positions of the instrument. The ad-
justment is then perfect, and the clips which serve to confine the
telescope in the Ys should be made fast.
Lastly, to set the Axis of the Telescope perpendicular to the Ver-
tical Axis round which the Instrument turns.—Place the telescope
over two of the parallel plate screws, and move them, unscrewing
one while screwing up the other, until the bubble of the level set-
tles in the centre of its run; then turn the instrument half round
upon the vertical axis, so that the contrary ends of the telescope
may be over the same two screws, and if the bubble does not again
settle at the same point as before, half the error must be corrected
by turning the screw B, and the other half by turning the two pa-
rallel plate screws over which the telescope is placed. Next turn
LEVELLING.
305
the telescope a quarter round, that it may lie over the other two
screws, and repeat the process to bring these two screws also into
adjustment; and when, after a few trials, the bubble maintains ex-
actly the same position in the centre of its run, while the telescope
is turned all round upon the axis, this axis will be truly vertical,
and the axis of the telescope. being horizontal by reason of the pre-
vious adjustment of the bubble-tube, will be perpendicular to that
vertical axis, and remain truly horizontal, while the telescope is
turned completely round upon the staves. The adjustment is
therefore perfect.
The object of the above adjustments is to make the line of colli-
mation move round in a horizontal plane, when the instrument is
turned round its vertical axis, and the methods above explained
suppose that the telescope itself is constructed with the utmost
'perfection, so that the axis of the tube carrying the object-glass is
always in the same straight line with the axis of the main tube,
which carries the diaphragm with the cross wires. If this perfec-
tion in the construction of the instrument does not exist, the line
of collimation will vary, as the tube carrying the object-glass is
thrust out, and drawn in, to adjust the focus for objects of different
distances. What is really required then is, that the cross wires be
so adjusted that the line of collimation may be in the same straight
line with the line in which the centre of the object-glass is moved,
and that the bubble of the level be at the centre of its run, when
this line of collimation is directed to view objects, at the same level,
or at the same distance from the centre of the earth.
We are indebted to Mr. Gravatt, of whose level I shall here-
after speak, for a method of collimating, which satisfies the above
requirements, and removes any error arising from imperfection in
the slide of the telescope, while at the same time the line of colli-
mation is set with the end at the object-glass, slightly depressed,
instead of exactly horizontal, so as to remove, or nearly so, the
errors arising from the curvature of the earth, and the horizontal
refraction.
To examine and correct the Collimation by Mr. Gravatt's Method.—“On a
tolerably level piece of ground drive in three stakes at intervals of about four or
five chains, calling the first stake a, the second b, and the third c.
"Place the instrument half way between the stakes a and b, and read the staff
A, placed on the stake a, and also the staff B, placed on the stake b ; call the two
readings A' and B'; then, although the instrument be out of adjustment,* yet the
*The axis of the instrument is to be set vertical by means of the parallel plate
screws, by placing the telescope over each pair alternately, and moving them until the
air bubble remains in the same position, when the instrument is turned half round
upon its axis.
306
LEVELLING.
points read off will be equidistant from the earth's centre, and consequently
level.
"Now remove the instrument to a point half way between b and c. Again,
read off the staff B, and read also a staff placed on the stake c, which call staff C
(the one before called A being removed into that situation.) Now, by adding the
difference of the readings on B (with its proper sign) to the reading on C, we get
three points, say A', B', and C', equidistant from the earth's centre, or in the same
true level.
"Place the instrument at any short distance, say half a chain beyond it, and
using the bubble merely to see that you do not disturb the instrument, read all
three staffs, or, to speak more correctly, get a reading from each of the stakes, a,
b, c; call these three readings A", B", C". Now, if the stake b be half way between
a and c,* then ought C"—C—(A"— A') to be equal to 2 [B" — B' —(A ' —
A')]; but if not, alter the screws which adjust the diaphragm, and consequently
the horizontal spider line or wire, until such be the case; and then the instru-
ment will be adjusted for collimation.
"To adjust the spirit bubble without removing the instrument, read the staff
A, say it reads A', then adding (A" — A') with its proper sign to B' we get a
value, say B'".
Adjust the instrument by means of the parallel plate screws †, to read B'"' on
the staff B.
"Now, by the screws attached to the bubble-tube, bring the bubble into the
centre of its run.
"The instrument will now be in complete practical adjustment for level, cur-
vature, and horizontal refraction, for any distance not exceeding ten chains, the
maximum error being onlyth of a foot.”
Before making observations with this instrument, the adjust-
ments should be carefully examined and rectified, after which the
screw B should never be touched; but at each station the parallel
plate screws alone should be used for setting the axis round which
the instrument turns truly vertical, when, in consequence of the
adjustments previously made, the line of collimation will be truly
level. For this purpose the telescope must be placed over each
pair of the parallel plate screws alternately, and they must be
moved till the air bubble settles in the middle of the level, and the
operation being repeated till the telescope can be turned quite
round upon the staff-head, without any change taking place in the
position of the bubble, the instrument will be ready to read off the
graduations upon the levelling staves, which we proceed to describe.
In all work where great accuracy is required, the Y level above
described, is preferable to either of the others; but both Trough-
* Whatever be the distances between the stakes a, b, and c, the following propor-
tions ought to hold, viz.:
The distance from ab: the distance a to c:: B" — B′ — (A″ —A'.) : C".
(A" — A'.)
C'
+ If this adjustment be made by the screw B, instead of the parallel plate screws,
the line of collimation will be brought into its proper position with respect to the
vertical axis.
LEVELLING.
307
ton's level and Gravatt's level are calculated, by their lightness,
and by their being less liable to derangement when once properly
adjusted, to get rapidly over the ground.
TROUGHTON'S LEVEL.

T
B
B
In this level the telescope T, rests close down upon the hori-
zontal bar, bb, the spirit level, 7 7, is permanently fixed to the top of
the telescope, and does not, therefore, admit of adjustment, and the
compass box, C, is supported over the level by four small pillars
attached to the horizontal bar. This construction makes the in-
strument very firm and compact. The staves, staff-head, and paral-
lel plates by which the instrument is supported, and the vertical
axis upon which it turns, are of exactly the same construction as
has been already described as used for supporting the Y level.
The diaphragm is furnished with three threads, two of them ver-
tical, between which the levelling staff may be seen, and the third,
horizontal, gives the reading of the staff by its coincidence with one
of the graduations marked upon it. Sometimes a pearl micrometer
scale is fixed on the diaphragm, instead of the wires. The central
division on the scale, then, indicates the collimating point, and by
its coincidence with a division of the levelling staff gives the re-
quired reading of this staff; and the scale serves the purpose of
measuring distances approximately, and of determining stations
nearly equidistant from the instrument, since at such equal dis-
tances the staff will subtend the same number of divisions upon the
micrometer-scale.
In selecting a level of Troughton's construction, and also in
testing and adjusting the collimation subsequently, Mr. Gravatt's
method, already described, is the best to be used; and when the
line of collimation is thus brought into adjustment, if the bubble
be far from the centre of its run, the fault can only be remedied by
the maker; but if the bubble settle very nearly in the centre of its
run, the instrument may be deemed a good one, and the divisions
on the glass tube which coincide with the ends of the bubble being
noted, the instrument must be set up for use with the bubble in
this position.
The line of collimation is set perpendicular to the vertical axis
308
LEVELLING.
in the same manner as in the Y level, by means of the capstan
screws B B, the bubble being made to maintain the requisite posi-
tion, as above determined, while the instrument is turned com-
pletely round on its axis.
MR. GRAVATT'S LEVEL.
This instrument is furnished with an object-glass of large aper-
ture and short focal length; and sufficient light being thus obtained

a
B
B
C
M
to admit of a higher magnifying power in the eye-piece, the advan-
tages of a much larger instrument are obtained, without the incon-
venience of its length. The diaphragm is carried by the internal
tube a a, which is nearly equal in length to the external tube. The
external tube TT is sprung at its aperture, and gives a steady and
even motion to the internal tube a a, which is thrust out, and drawn
in, to adjust the focus for objects at different distances by means of
the milled-headed screw A. The spirit level is placed above the
telescope, and attached to it by capstan-headed screws, one at either
end, by means of which the bubble can be brought to the centre of
its run, as in the case of the Y level, when the line of collimation
is brought to the proper level by Mr. Gravatt's method of adjust-
ment, already explained.
The telescope is attached to a horizontal bar, in a similar man-
ner to Troughton's level, but room is just left between the teles-
cope and the bar for the compass-box.
A cross level, k, is placed upon the telescope at right angles to
the principal level 77, by which we are enabled to set the instrument
up at once with the axis nearly vertical. A mirror, m, mounted
upon a hinge-joint, is placed at the end of the level, 77, so that the
observer, while reading the staff, can at the same time see that the
instrument retains its proper position-a precaution sometimes
desirable in windy weather, or on bad springy ground.
The telescope is attached to the horizontal bar by capstan-
headed screws, BB, as in Troughton's level, by which the line of
collimation is set perpendicular to the vertical axis ; and the instru-
ment is set up upon parallel plates, as before described, for the Y level.
LEVELLING.
309
The level I use, and which was specially constructed for me by
the Messrs. Elliott is without either the cross level, the compass-
box, or the mirror; the advantages obtained from the occasional
use of which, not being equal in my estimation, to the benefits
arising from the use of a light instrument, divested of every un-
necessary encumbrance.
Levelling Staves.
One kind of staff has superiority over another only in the degree
of its applicability to the purposes for which it is required—hence
a folding staff is more handy for travelling, but a staff in one
length is preferable for rough use, if it has not to be transported
from one place to another; but of whatever description of mecha-
nical arrangement the staff may partake, it is a great desideratum
that it present to the observer a clear, simple, graduated face,
upon which he can obtain for himself the reading of the quantities
by the aid of his telescope.
The old-fashioned vane staves are so far gone out of use that it
is not intended to notice them here.
Many levelling staves are figured by means of printed papers
pasted or rather stuck on; but these are objectionable, as in wet
weather the paper will, by constant use, rub off, and thus the uti-
lity of the staff is at once destroyed.
Levelling surveyors, who paint their own staves, have varied
fancies as to the method of doing it; all first divide the staff into
feet and tenths, but some subdivide those tenths into actual hun-
dredths. I have tried many ways, and will give the one my
experience has led me to prefer. Fig. 173 represents this
staff.
It will be observed, that the division of the feet is always rea-
dily distinguished by the top of the large figure which numbers
the feet, and the bottom of the large figure is always 85, conse-
quently, the division of the 90 always crosses the large figure at
3rd of its length, and the 80 is always a little below the foot of it.
•75 is marked by a red line, which differs from the 25 in this par-
ticular, that one crosses the staff in a plain white space, while the
other crosses through one of the black blocks. 70 is exactly at
the top of the block, immediately below the distinctive mark of •75,
and '60 is the mark intervening between 70 and 50, which latter
is represented by the top of the letter V; 40 is the bottom of the
V, and ⚫30 is next above the distinctive mark of 25, as 20 is next
below it. 10 is readily distinguished as next above the preceding
310
LEVELLING.
figure denoting the number of feet, and thus completes a very sim-
ple, and at the same time, a very bold and distinctly marked staff,
clearly legible in dull weather, and about the subdivision of which
to hundredths there is no difficulty whatever to a practised eye,
and no chance of error beyond a hundredth at most to an unprac-
tised one.
The absence of all other figures than those numbering
the feet render the mistake of one figure for another impossible,
and while there are doubtless many as good, it is confidently be-
lieved few are better.
The operation of levelling is performed in this simple way-a
staff is held up at the two places between which the difference of
level is required, and if the reading on one staff is more than that on
the other, the difference between them is the difference of level,
or the measure by which the distance of one from the earth's cen-
tre exceeds that of the other. We have already seen that within
a distance of 10 chains from the level there is no correction re-
quired for curvature and refraction, and, consequently, no level
should be taken beyond this distance from the instrument. It is
hardly necessary to mention this, for very few instruments, unless
too large and cumbersome for ordinary requirements, will read a
staff distinctly at a greater distance.
Let figure 173a represent a section of the surface between two
points A and G, the difference of level between which is required.
Set up the instrument at B, and read a staff at A; reverse the
telescope, and read a staff at C. Remove the instrument to D; get
another reading from the same staff at C, and from a fresh staff at
E; again remove the instrument to F, and get readings from E
and G. Now, it is evident from what has been said, that the sum
of the back readings, minus the sum of the fore readings, is the
difference of level required; and to avoid negative quantities, we
will assume the point A is 20 feet above an imaginary level plane,
which we call our Datum line. The calculation stands thus:-
Height of A above datum
Add reading of staff A
FEET.
20 ·
11.50
Deduct fore reading of staff C
•
31 · 50
11 · 90
Gives the height of C above datum
Add back reading of C as taken at D
19 · 60
12. 20
•
31 · 80
LEVELLING.
311
Deduct fore reading of E taken at D
Height of E above datum
Add back reading of E taken at F
Deduct fore reading of G taken at F
Height of G above datum
·
31 · 80
8.46
23 · 34
7.64
30.98
7.98
23·00
A being 20 above datum, and G being 23, G is obviously 3 feet
higher than A. It will however be seen, that the highest point is
E, which is 23.34 above datum, and consequently, 0.34 above G;
C is 19.60 feet above datum, or 0.40 feet below A.
In actual practice, the adding and subtracting the back and fore
readings is never (or at all events by very few surveyors) carried
out in detail, in the manner which, for the sake of explicitness, it
has been given above. It is obvious, that if the difference of level
between two staves be added when the fore reading is the lesser, or
subtracted when it is greater, it will produce the same result-for
example, the difference of level between A and C is 0.40 feet, and
the back sight being the lesser height if that is subtracted from the
datum at A, it will give the height of C, and so on throughout the
series.
There are several forms of levelling books in use among sur-
veyors, but they only differ as to the position and number of the
vertical columns; it will be only necessary for me to describe one
of these forms.
Taking our preceding example then, the annexed is a specimen
of the practical reduction of it in a Field Book.
Levels taken from A to G.

Distances.
Back Fore
Sights. Sights.
Rise. Fall.
Reduced
Levels.
REMARKS.
Links
20.
20.
800
11.50 11.90
20.
.40 19.60
Datum line 20 ft. below A
Station A.
C.
""
1500
12.20 8.46 3.74
23.34
E.
""
2000
7.64 7.98
.34 23.
G.
""
51.34 28.34|| 23.74
.74
28.34
23.
.74
23.
312
LEVELLING.
Very few remarks will serve to render this form of Field Book
intelligible. Distances have been inserted to shew the use of the
column headed distances; but in many cases distances are not taken
in levelling.
The datum line is first fully described in the column of remarks.
The height above datum is then placed in the column of reduced
levels, as the height of station A; and it is also repeated in the
columns headed "back sights," and "rise," for the purposes of the
proof of the casting, as will be hereafter seen. The back sight *
at A, and the fore sight at C, are now placed side by side in their
respective columns, and their difference placed in the proper column
of "rise or "fall," as the case may be. In like manner the back
sight at C, and the fore sight at E, are entered, and so on through-
out the series. The rises are now added to the preceding height
above datum, and the falls deducted and the results shew the re-
spective heights of each station.
""
The method of keeping a Field Book admits of two proofs.
First-If the sum of the fore sights is deducted from the sum of
the back sights, including the first height above datum, it will
give the relative height of the last station, and should conse-
quently correspond with the last item of reduced levels. In like
manner if the sum of the falls be deducted from the sum of the
rises, including the first height above datum, it will, if correct,
produce the same result.
Attention to a few trifling circumstances in levelling will secure
most important results. If the level is always placed perfectly
central between two stations, the results will always be correct
irrespective of any instrumental error. If it is sometimes neces-
sary to have a long back sight and a short fore sight, it is always
practicable to reverse the order within a station or two, so that
the back sights and fore sights are made to balance. Never get
a reading from a staff without first observing that the bubble of
the spirit tube is in the centre of its run; nor ever leave a staff
after the reading until it has been entered in the book, and has
been again examined. If accuracy is not of less importance than
expedition never use a staff as a rule, that is more than about ten
feet long; it is all very well to have an extra length for excep-
tional cases, but the best staff holder will not keep a long staff
perpendicular. It should be borne in mind, that errors of this
description are not, as is often the case in instrumental errors,
capable of balancing themselves by being sometimes of a positive,
* That is, the reading of the staff.
LEVELLING.
313
and at others, of a negative character, and thus standing a chance
of accidental adjustment. If a staff is not held perpendicular, the
error must always be that the reading observed is too much, the
perpendicular distance between any two points being always the
shortest distance possible.
Of course, if the same error exists in both back and fore read-
ing it is immaterial. But the use of these long staves is only
brought into action in descending or rising a hill, when one read-
ing is nearly zero, while the other is perhaps fifteen feet up the
staff. There is one chance of a balance with errors of this kind-
and it is in cases when the ascents and descents are equal; a cir-
cumstance against which the odds are very great. The staff
holders should always be provided with something to stand the
staff upon, to ensure the reversal of the staff between the readings
from the different stations of the instrument with mathematical
precision. A penny, or a small piece of tile or slate is better than
nothing, but far preferable to that, is what is called a "tripod."
This little instrument consists of a triangular piece of sheet iron
of about an eighth of an inch thick, shod at the corners to enter
the ground; and a semi-circular ball is rivetted on to the top, so
that whatever the position of tripod or staff, the latter is certain
to be placed on the same spot, notwithstanding any removal in the
interim between the first and last reading. A small chain, with
a ring or leather strap attached, enables the staff holder to lift it
from the ground, and carry it from station to station without in-
convenience.
If any intermediate readings occur, that is, points of which it
is competent to ascertain the level without moving the instrument
to do it; the most simple method is to treat the fore sight of the
intermediate as a fresh back sight, and re-enter it as such; but in
proving the castings these need not be cast in with the others, but
such as occur in both columns can of course be cancelled. I sub-
join one practical example.
Levels taken from Wandsworth to the Elephant and Castle.
314

Back
Fore
Distances.
Rise. Fall.
Sight.
Sight.
Reduced
Levels.
100.
100.
100.
REMARKS.
Datum line 100 feet below the
stone sill of the south door to
Wandsworth old Church, in
the High Street, close against
the middle of the door-post on
the east side of the door.
B. M. on stone sill of gate.
3.79
* 4.05
.26
99.74
000
* 4.05
4.96
.91
98.83
Centre of High Street.
600
4.28
2.09 2.19
101.02
1000
3.33 4.05
.72 100.30
1600
5.76
3.19
2.57
102.87
2100
7.44
*0.45
6.99
B. M. on stone at corner of
109.86 North Street.
* 0.45
0.23
•22
110.08
Junction of High Street and
North Street.
2300
7.84
1.52
6.32
116.40
2500
8.99 1.40
7.59
123.99
2700
9.18
1.33
7.85
131.84
3000
9.84
1.55
8.29
140.13
3600
9.93
1.84 8.09
148.22
3800
6.64
* 4.46
2.18
ham Roads.
150.40 Fork of Vauxhall and Clap-
4400
* 4.46
2.69
1.77
152.17
5.77
* 4.01
1.76
4650
* 4.01
6.27
2.26
5000
2.09 5.71
153.93
151.67
3.62 148.05
B. M. on top of hanging post
of gate into East Hill burying
ground, from the Vauxhall
Road.
6000
6.10
3.78 2.32
150.37
7000
5.32
5.84
7870
3.60 *1.00
2.60
1 mile
* 1.00
7.05
750
1.66
* 6.66
1000
* 6.66
12.20
.52 149.85
152.45
6.05 146.40
5.00 141.40
B. M. on top of coping of
bridge over S. W. Railway—
on the south side of bridge
immediately over the near side
down rail (about 27.25 above
rail).
5.54 135.86* *Road leads off to Tooting.
1400
1.17
12.53
11.36 124.50
1800
0.10
10.46
10.36 114.14
2100
1.86
* 7.34
5.48 108.66
2480
* 7.34
0.31 7.03
115.69
2720
9.04 0.56 8.48
124.17
2950
8.48
0.21
8.27
132.44
3300
9.24
1.58
7.66
140.10
9.24
* 6.76
2.48
142.58 | B. M. on the top of the guard
4300
* 6.76
1.46 5.30
147.88
5300
7.43 5.87 1.56
149.44
stone to western gate post at
entrance to a gentleman's
house, south of road.
6300
5.80 5.10
.70
150.14
7000
4.80 5.18
2 miles
4.59
4.37 .22
1000
4.67 5.54
1200
5.35
4.44 .91
1209
4.75
0.24
4.51
2000
3.10
6.02
2.92
3000
6.16 6.95
4000
5.61
2.26 3.35
.38 149.76
149.98
.87 149.11
150.02
154.53
151.61
.79 150.82
154.17
Clapham Common.
B. M. on the top of mile
stone marked by the Ord-
nance Officers.-Five Miles
from Standard, Cornhill.
Junction with Dorking Road.
5000
4.05 6.53
2.48 151.69
6000
2.54 9.28
6.74 144.95
299.54 154.59 211.21
66.26
154.59
66.26
144.95
144.95
Levels between Wandsworth and the Elephant and Castle.
315'

Distances
Back Fore
Sight. Sight.
Rise. Fall.
Reduced
Levels.
REMARKS.
144.95
144.95
6450
2.07 * 3.91
144.95
1.84 143.11
B. M on top of milestone,
marked 3 miles from West-
6500
* 3.91
8.98
5.07 138.04 minster Bridge.
7000
1.80
9.30
7.50 130.54
7500
.95
7.17
6.22 124.32
3 miles
6.09 3.22 2.87
127.19
300
7.37*3.74
3.63
130.82
1000
* 3.74
8.44
4.70 126.12
0.63
1.14
2000
1.14 12.58
3000
0.82
7.97
4.52
* 0.68
3.84
4000
* 0.68
7.81
5000
6.10
6.58
.48 103.25
.51 125.61 B. M. on top of water plug,
11.44 114.17 opposite St. John's Chapel and
7.15 107.02
the Elms.
110.86 B. M. on top of milestone,
marked three miles from
7.13 103.73 Blackfriars.
6000
5.13
6.95
1.82 101.43
6450
5.51
* 1.88
3.63
105.06 B. M. on top of milestone,
7000
* 1.88
5.66
3.78
101.28
marked two miles from West-
minster Bridge.
7400
4.57
2.14
2.43
4 miles
2.14
6.85
4.71
99.00
103.71 B. M. on top of milestone,
at corner of Albert Square.
1000
5.00
6.67
1.67
97.33
2000
6.31
5.39
.92
98.25
2500
7.90
* 5.35
2.55
3000
* 5.35
8.77
3.42
97.38
3830
4.16
* 2.65
1.51
100.80 Opposite the Griffin Inn.
B. M. on top of lower hook of
98.89 T. P. Gate, next Toll House,
4000
* 2.65
5.77
3.12
95.77 on Kennington Common.
5000
4.27
6.67
2.40
93.37
6000
5.10 5.50
•40
92.97
7000
5.94
6.21
.27
92.70
5 miles
4.09
4.23
.14
92.56
1000
4.21
2.82
1.39
93.95
1300
5.87
* 3.32
2.55
96.50
2000
*3.32
6.46
3.14
3000
3.67
66.6
2.99
90.37
3600
7.33
* 3.24
4.09
* 3.24
0.45 2.79
B. M. on top of Iron Water
Post, on North Side of Street
93.36 facing the Newington Registry
Office for Servants.
94.46 Centre of Roads at the Ele-
phant and Castle.
97.25 B. M. on the top of a mile-
stone facing the Shop of Con-
nelly, Stationer, &c.
257.64 160.39 177.15
79.90
160.39
79.90
97.25
97.2
NOTE.-It will be observed that the intermediate sets are cancelled
and omitted in the cast up of the pages.
316
PLOTTING.
CHAPTER IX.
PLOTTING.
THE first consideration in plotting is the choice of the paper upon
which to lay down the survey that has been made. In large sur-
veys it is often desirable to lay down the fundamental lines to a
very small scale (twenty or thirty chains to an inch), from which
to arrive at a tolerably correct notion of the size of the paper re-
quired, and the most eligible position thereon for the principal line.
The Officers of the Ordnance Survey have laid it down as a
standing rule always to keep the north of the map towards the
top of the paper; but I do not regard this as an essential feature,
especially in original maps. I would at any time sacrifice it to the
attainment of a more eligible position of the map upon the paper.
I do not mean to say I would reverse the order of things, and
place the south towards the top, but I certainly should not mind
so placing the east or west. As an instance of my meaning, the
survey of the parish of Horsell, hereinbefore referred to, required
paper about ten feet long by five wide, the length being in the
direction of east and west. To place such a map north upwards
would be to render what might be comparatively a handy roll of
five feet long, an unhandy one of ten feet, which few ordinary
tables in private houses would accommodate. Having selected
the position of the main line on the paper, the next thing is to lay
it down. This must be done with a straight edge proportioned to
its length, as it is a very difficult thing to produce a line by means
of several splicings-a "steel straight edge" will be found desirable
for this purpose. As soon as the line is down, the distances from
zero at every ten chains along its course should be marked off ac-
cording to the scale with which the work is to be plotted; this
should be done with the point of a needle, and the figures denoting
the number of chains should be very finely marked against the
several dots. The number of the line should then be placed on
the end at which the measurement of it commences, which answers
the double purpose of being an index to the line, and the direction
in which it ran. All future distances on the line laid down will
be laid off from the nearest dot, without reference to the zero of
the line, so that any inaccuracy arising from expansion or contrac-
tion of the paper will be obviated as much as possible.
It is generally less difficult to lay down the first line of a survey
than it is the second and third, inasmuch as the true position of the
PLOTTING.
317
latter as sides of a triangle have to be scrupulously attended to.
In large surveys it is often necessary to resort to a variety of mathe-
matical contrivances to get them down accurately; sometimes the
use of a thread or a slip of mounted drawing paper marked the re-
quired length from the main line will scribe an arc tolerably near,
but it is always safer and generally more correct to adopt the best
means at once, and do it mathematically. A simple process is to
compute the angles accurately, and then with any convenient
length as radius, say 100 chains, find the natural sine and cosine
by the Table. Let fig. 174 represent this method. Suppose the
triangle A D G to be a trigonometrical projection required to be
plotted, whose sides are beyond the limits of all drawing tables—
straight edges and scales at command. Lay off the cosine of angle
A from A to B, and of angle D from D to C. Erect perpendicu-
lars at B and C ; lay off the sine of angle A from B to F, and of angle
D from C to E; try that AF and DE are exactly equal to the
radius of 100 chains, and E and F may then be used as points
from which to raise G; FG and E G having now become in all
probability within manageable compass. The points E and F may
be sometimes better fixed by scribing the radius and sine—much de-
pends upon the angle. If a perpendicular is erected, it must be a
really accurate one; and if the work is very extensive, it will be as
well to calculate mathematically the length of EF. The point G
obtained, the straightness of the lines A F G and D E G must be
tested with the straight edge; but if the operation has been care-
fully performed, there is little probability but that they will prove
correct. As every line is plotted, the distances from zero should
be marked off at each ten chains, as on the main line, and the line
numbered as before directed. As many of the fundamental lines
as possible should be laid down at one time, so that in the event of
subsequent alteration of paper, which is almost certain to take
place, all the work may go together, and but the minimum of
inconvenience experienced.
In laying down the secondary lines of the survey, such as the
line R I, on the parish of Sunbury survey, having drawn the line
from point to point with the straight edge, previous to marking off
the furlongs, try the length on the paper, and compare it with the
book, for with the most careful chaining there is at all times a lia-
bility to disagreement, owing to the unevenness of the ground over,
and the hedges and other places through, which the chain has to
pass. This disagreement, for it is not error, should in no case ex-
ceed about a link in ten chains on an average of the whole length
of the line, and should be equally spread in plotting throughout
318
PLOTTING.
the whole length-that is, a line entered in the Field Book a
20005 may measure on the paper 20025, and yet be practically
correct; but it would be manifestly inaccurate to point off 200
chains 25 links from the end of the line. In such a case, 10 chains
must be plotted as 1001; 2000 as 2002; 3000 as 3003, &c. When
all the lines are down (and if expedient drawn in very finely with,
carmine or lake) the offsets can be plotted. Until tolerable skill
has been acquired by considerable practice, every point should be
carefully pricked off with a needle upon the chain line, and the
offset therefrom accurately marked off; but after a time it will be
sufficient to expedite the business by any contrivance that may
suggest itself, and in the absence of a better, let us suppose the
following:-Lay the edge of the plotting scale A B (fig. 175) pa-
rallel with the line CD, upon which the offsets are to be plotted,
at such a distance that the zero division of the offset scale E may
coincide with the line as it passes along it, and also that zero on
scale A B may be exactly opposite the zero end of the line; then,
by sliding the offset scale along the line any offset not exceeding a
chain in length (which, as has been already said in another place,
should be the maximum limit of the offset, and should also be the
maximum space between the chain line and scale) may be ac-
curately plotted on either side of the line.
To Plot the Notes of a Traverse Survey by the Table of Natural
Sines and Cosines.
The only difference between plotting the notes of a traverse and
any other survey consists in laying down the lines. In the case of
our previous example (fig. 170) we will assume that the trigono-
metrical points A B C are already plotted. With the aid of the
Table of Natural Sines and Cosines, lay off the angle between A B
and the magnetic meridian in the following manner:
A and B (fig. 176) are the two stations of the survey, whose
bearing is taken.
Take 1, 10, or 100 in the compasses, according to the extent of
the lines, and scribe the arc EF: produce A B, so that A D
shall be equal to the cosine, and DF the sine of the given angle:
join A F, and it will be the required meridian.
In like manner, line 1 is laid down by means of the angle con-
tained between it and the magnetic meridian, its length is then
marked off from A, and a line drawn through the end of it parallel
to the meridian from which line 2 is marked off; and so on through-
out the series.
PLOTTING.
319
The great objection to traverse surveying, as a means of filling
in, is the opportunity afforded for error in every line. It is ob-
vious, that a link too much or too little in laying down each line
will prevent the work from closing at the end; hence, the great
advantage of a system of right lines, which renders every one inde-
pendent of another.
As the method of laying down the lines of a traverse by means
of their sines and cosines may be considered troublesome in a sur-
vey of magnitude, a protractor, or circular instrument of brass,
may be employed to facilitate the laying off the angles.
THE CIRCULAR PROTRACTOR.
Our engraving represents one of the best kind of protractors.

20
360
e
09
40
U z z
340
320
300
α
α
140
120
И
B
с
270
Arny prz
w
240
C
091
081
002
It is a complete circle, A A, connected with its centre by four
radii, a a a a. The centre is left open, and surrounded by a
concentric ring or collar, b, which carries two radial bars, c c.
To the extremity of one bar is a pinion, d, working in a toothed
rack quite round the outer circumference of the protractor: to
the opposite extremity of the other bar, c, is fixed a vernier,
which subdivides the primary divisions on the protractor to single
minutes, and by estimation to 30 seconds. This vernier, as may
readily be understood from the engraving, is carried round the
protractor by turning the pinion d. Upon each radial bar, c c,
is placed a branch e e, carrying at their extremities a fine steel
pricker, whose points are kept above the surface of the paper
by springs placed under their supports, which give way when
the branches are pressed downwards, and allow the points to make
the necessary punctures in the paper. The branches e e are at-
tached to the bars cc, with a joint which admits of their being
folded backwards over the instrument when not in use, and for
320
PLOTTING.
packing in its case. The centre of the instrument is represented
by the intersection of two lines drawn at right angles to each
other on a piece of plate glass, which enables the person using it
to place it, so that the centre, or intersection of the cross lines,
may coincide with any given point on the plan. If the instrument
is in correct order, a line connecting the fine pricking points with
each other would pass through the centre of the instrument, as
denoted by the before-mentioned intersection of the cross lines
upon the glass, which, it may be observed, are drawn so nearly
level with the under surface of the instrument, as to do away with
any serious amount of parallax, when setting the instrument over
a point from which any angular lines are intended to be drawn.
In using this instrument, the vernier should first be set to zero (or
the division marked 360) on the divided limb, and then placed on
the paper, so that the two fine steel points may be on the given
line (from whence other and angular lines are to be drawn), and
the centre of the instrument coincides with the given angular point
on such line. This done, press the protractor gently down, which
will fix it in position by means of very fine points on the under
side. It is now ready to lay off the given angle, or any number of
angles that may be required, which is done by turning the pinion
d till the opposite vernier reads the required angle. Then press
downwards the branches e e, which will cause the points to make
punctures in the paper at opposite sides of the circle; which being
afterwards connected, the line will pass through the given angular
point, if the instrument was first correctly set. In this manner, at
one setting of the instrument, a great number of angles may be
laid off from the same point.
It is not essential that the centre be over the given point when
applied to the given line, provided the pricking points exactly fall
upon the line, for an imaginary line connecting the pricking
points in this instrument, correspond with the diameter. Some-
times, instead of a rack and pinion motion, a third radial arm
is attached to the centre at right angles to the other two, upon
which is fixed a clamp and tangent screw, by which the vernier
is not only fixed in position upon the circular limb of the instru-
ment, but by the tangent, or slow motion screw, it may be set to
the required angle with the utmost precision.
THE T SQUARE AND SEMI-CIRCULAR PROTRACTOR.
A convenient method by which a traverse can be most expe-
ditiously as well as accurately plotted, by the aid of a T square
PLOTTING.
321

B
A
E
B
B
and semi-circular protractor, is thus described by Mr. Howlett,
chief draughtsman, Royal Ordnance Office, in vol. i. of Papers on
Subjects connected with the Duties of the Royal Engineers:-
or,
"As, when away from home, it seldom happens that the surveyor can obtain a
good drawing board, or even a table with a good straight edge, I fix a flat ruler,
A, to the table BBB, by means of a pair of clamps, C D, and against this ruler
I work the pattern square E, one side of which has the stock flush with the blade;
if a straight-edged board be at hand, then the square may be turned over, and
used against that edge instead of the ruler A. Here, then, is the most perfect
kind of parallel ruler that art can produce, capable of carrying the protractor
over the whole of a sheet of plotting paper of any size, and may be used upon a
table of any form. It is convenient to suppose the north on the left hand, and the
upper edge of the blade to represent the meridian of the station.
"This protractor is held in the hand while the vernier is set, which is an
immense comfort to the sight; and it will be seen that, as both sides of the
arm are parallel with the zero and centre, the angle may be drawn on the
paper against either side, as the light or other circumstances may render
desirable."
From this description and a mere glance at the engraving, it is
clear that angles taken with the theodolite can be transferred to the
plot as accurately as the protractor can be set, namely, to a single
minute, and that, too, in a rapid and pleasant manner.
My own experience in plotting traverses as the "filling in" por-
tions of a survey is not favourable to the use of a metallic pro-
tractor, I prefer making a protractor in the following manner:-
With a radius of 10 inches describe a circle, and without altering
the compasses step round the circle pointing each step; this will
divide it into six parts, each being 60°. Now the chord of an arc
322
PLOTTING.
being equal to twice the sine of half that arc, if from the Table of
Natural Sines we take the sine of 5° and multiply it by 2, we get
the chord of 10°, which being laid off, subdivides each 60° into
six parts of 10° each. In like manner we continue to subdivide
the circle, until we have done so as minutely as required. Divi-
sions, each containing five minutes, will be found quite small
enough in practice, as lesser quantities are readily estimated by
the eye. The degrees should then be numbered, as in a theodo-
lite, and the protractor is fit for use.
The traverses of the Guernsey survey are plotted with a pro-
tractor of this kind, in the following manner:-Two trigonome-
trical stations that can be connected by a series of traverse lines
are selected. A sheet of tracing paper is laid over the protractor,
upon which the position of one of the points is marked. A straight
edge is then laid across the protractor to correspond with the bear-
ing of line 1, and by means of two wooden set squares or triangles
a parallel line is transferred to the point from which line 1 starts,
where the line is drawn to its proper length, and the station
marked for the commencement of line 2. The straight edge is
then laid across the paper to correspond with the bearing of line 2,
which is now marked off in its proper position parallel to the bearing.
In like manner all the lines are plotted until they close upon ano-
ther trigonometrical station. When the tracing paper is taken up,
the two trigonometrical stations thereon are laid over the corre-
sponding stations on the map, and the lines are transferred from
the tracing thereto.
On working maps, it is customary to distinguish the dwelling-
houses from other buildings, by tinting the former with carmine
or lake, and the latter with neutral tint. The rivers and waters
are also tinted blue, and the roads a light brown; any thing beyond
this in the way of colouring amounts to a decoration which is not
required. If the map is one of an estate or property, the names of
the owners of the adjoining lands should be written in their re-
spective positions; but if it is a parish map, the names of the ad-
joining parishes are substituted, as in plate 5. The names of all
gentlemen's seats, farms, hamlets, and remarkable places, should be
subscribed, and the whole should be invested with as much local
interest as possible.
Every field or parcel of property should be distinguished by a
separate reference number, by which it may be referred to from a
book containing all particulars relating thereto, as well as the
quantity of each field in statute measure.
The following are two specimens of reference books.
NUMERICAL REFERENCE.
323

Cultivation.
Quantity.
Remarks.
NUMERICAL REFERENCE.
Owner.
Occupier.
No. on
Plan.
Description.
A. R.
P.
Phipps, George
Ryde, Edward...
1
Barn Field
Arable.
9
2 6
Weale, John
Ryde, Edward...
2
Carthouse Field..
Arable.
6 1 30
Weale, John
Ryde, Edward...
Co
Garson Meadow
Grass.
13 1 6
Phipps, George
Donaldson, John
4
Doomsday
Grass
9 130
Weale, John
Ryde, Edward...
5
Garson Field.
Arable.
16 1 30
Weale, John
Ryde, Edward.
6
High Holborn Farm Homestead
1 1 10
Phipps, George
Donaldson, John .
7
The Retreat
House & Garden .
1 3 20
Total Content
58 1 12
324
COLLECTED REFERENCE.

Cultivation.
Quantity.
Remarks.
COLLECTED REFERENCE.
Owner.
Occupier.
No. on
Plan.
Description.
A. R. P.
Phipps, George
Ryde, Edward...
1
Barn Field
Arable
9
2 6
Phipps, George
Donaldson, John
•
4 Doomsday
Grass
9 1 30
7
The Retreat
House & Garden
1
3 20
11
1 10
Weale, John
Ryde, Edward..
2
Carthouse Field ..
Arable
6 1 30
3
Garson Meadow.
Grass.
13 1 6
5
Garson Field.
Arable
16 1 30
6
High Holborn Farm Homestead
1 1 10
37 1 36
COLLECTED REFERENCE.-SUMMARY.
325

COLLECTED REFERENCE.
SUMMARY.
Owner.
Occupier.
Description.
Quantity
in each
Holding.
Total
Quantity.
Remarks.
Phipps, George
Land.
·
""
99
Ryde, Edward...
Donaldson, John. House and Land.
House and Land. 11 1 10
9 2 6
20 3 16
Weale, John
Ryde, Edward.
High Holborn Farm 37 1 36
37 1 36
Total
Quantity
58 1 12
326
COMPUTATION OF AREAS.
PLOTTING SECTIONS.
Plotting the notes from a level book is a very simple process.
First draw the datum line an indefinite length near the bottom of
the paper, then mark off all the distances along the line at which
a level has been taken; at each one of which erect a perpendicular
line in pencil; mark off the vertical height above datum upon each
of these perpendicular lines; connect the points after the manner
of plotting a fence by offsets from a chain line, and the section is
complete. It is not usual to use the same scale vertically and hori-
zontally; the former requiring to be much larger than the latter.
Plate 11 represents a "Working Section" of a Railway.
CHAPTER X.
COMPUTATION OF AREAS.
THE method of computing the areas of fields by arithmetical
calculation, has been of late years superseded by the introduction
of two very ingenious little instruments called respectively the
"Pediometer," and the "Computing Scale."* These instruments
obviate calculation, economise time, and diminish the liability to
I will describe them both; but the "Computing Scale" is
the one used by civil surveyors.
error.
Description of the Pediometer.
The instrument consists of a square, and a graduated scale, con-
structed for three chains to the inch.
a-The milled head, by turning which, motion is given to the
brass slider B, and the two pointers R and W.
I-The index to be placed in coincidence with the ► division
upon the scale.
When the brass slider B is in contact with A, I coinciding with
‣ division, and R and W pointing to O upon their respective
scales, the instrument is in adjustment.
When deranged, restore it, by opening R and W to the proper
distance, and then moving A and I, the former into contact with
B, and the latter into coincidence with
Required the content of the trapezium E C F D.
1st.-Place the edge A upon the point E, and open B to the
point F.
* By some the "Tithe Computing Scale," simply because it was first introduced
for the "First Class Maps at the Tithe Office."
COMPUTATION OF AREAS.
327
THE PEDIOMETER.

0
W
R
E
F
Red
Scale
Scale
White
D
2nd.-Press the square firmly down with the right hand, and
with the left place the scale against the edge of it, as shewn in
the figure.
3rd. Now press the scale firmly, and slide the square up, until
the edge A B is upon the point C.
4th.-Press the square firmly, and slide the scale against its edge
until coincides with I.
Finally.-Press the scale and slide the square down until the
edge A B is upon the point D, and taking out the numbers to
which W and R point, subtract the latter from the former, and
the contents in acres and decimal parts of an acre will at once
be given.
The red pointer directs to the numbers that are to be taken
from the red scale, and the white one to those upon the white
scale.
When the pointers fall exactly upon the line engraved on the
ivory edge of the scale, the folding leaf is to be doubled down to
the left hand; but when the pointers fall between any two of the
lines on the ivory edge, the folding leaf must then be doubled over
to the right hand before the numbers are read off.
For instance, when the leaf is turned to the left and the red
328
THE COMPUTING SCALE.
pointer falls between the two lines which refer to 008 and 013,
turn the folding leaf to the right hand, and the pointer will
read 0.10.
It will be found most convenient and most accurate in practice
to take the shortest diagonal for the line E F.
THE COMPUTING SCALE.
This instrument answers the same purpose of giving mechani-
cally the contents of enclosures as the Pediometer, but is more
simple in its construction and principle of operation.
It consists of a scale divided for its whole length from the zero
point into divisions, each representing 2§ chains, and is used with
a sheet of transparent tracing paper, ruled with parallel lines at
equidistant intervals of one chain.

0
B
2
3
4
4
田
​The slider B, which moves along the scale, has a wire drawn
across its centre at right angles to its line of motion; and on each
side of this wire a distance equal to one of the primary divisions of
2 chains is laid off, and divided into 40 parts. It is evident, then,
that during the passage of the slider over one of the divisions of
21 chains, one rood has been measured between two of the parallel
lines on the tracing paper; and that one of the smaller divisions
would measure between the same parallels one perch. Four of the
larger divisions giving one acre; and the scale itself generally made
long enough to measure at once five acres, is thus used: Lay the
transparent paper over the enclosure the content of which is re-
quired, in such a position that two of the ruled lines shall touch
two of the exterior points of the boundaries, as at a and b.
Lay the scale, with the slider set to zero, over the tracing paper,
in a direction parallel to the lines, and so placed that the portions
c and d are estimated by the eye as equal to each other. Holding
the scale steady, move on the sliding frame until the equality of
the portions e and fare also estimated. With the slider kept at
this mark, move the scale bodily down the space of one of the ruled
lines (one chain), and commencing again at the left hand, estimate
the equal areas of g and h, sliding the frame on to k and l. When
the whole length of the scale, denoting 5 acres, is run out, com-
mence at the right-hand side, and work backwards to the left,
THE COMPUTING SCALE.
329
reading the lower divisions, by which the instrument is made to
measure up to 10 acres. By a continuation of this process, the
b
C
α

}
contents of any sized enclosures can be obtained without calcula-
tion, and with a degree of accuracy proportionate to the amount of
skill and care exercised on the equalization of the boundaries.
Where the wire of the slider coincides with any portion of the
boundary between two of the parallels no equalization is of course
necessary.
Explanation of the following Tables.
The use of the following Tables will be obvious at first sight.
If the area of a plan plotted to a scale of two chains to an inch be
computed with a three-chain computing scale, seek the result or the
the next smaller number thereto, in the column headed "Three
Chains," and immediately adjoining, viz., in that headed "Two
Chains," is the correct acreage. If the result by the three-chain
scale is more than 9 acres, it must be taken at twice, that being
the limit of the Tables.
•
The Tables have been so constructed as to exhibit the nearest
relative equivalent to the results given; for instance, 7 . 1
10 on
a three-chain scale is exactly equal to 3. 1. 0 on a two; but then
7.1.9 is also nearer thereto than to 3.0.39; and hence 7.1.9
is placed as the equivalent. Again, 9.0.0 (three-chain scale) is
exactly equivalent to 1.0.0 (one-chain scale); but as 8.3.36
is also nearer thereto than to O. 3. 39, that is stated as the three-
chain equivalent.
X
330
COMPUTING TABLES.

3-Chain 2-Chain 3-Chain
Scale.
Scale.
Scale.
2-Chain
Scale.
3-Chain 2-Chain 3-Chain
Scale. Scale. Scale.
2-Chain
Scale.
100
A.
B. P.
A.
0 0
2 0 0
A.
R. P.
10
R. P. A.
B. P.
2 12-0 1
A.
B. P.
A.
R.
P.
A. R. P.
A. R. P.
1 1
0 22-0 2
11
2 32
0
3
1
0
4=
4 0
0
2 0 2 14-0
1
21
0 24 0 2
2 1
2 34
0
3 2
0 0 -0 0
30
2 16=0
1
3 1
0 26
0
2
3 1
2 36 0
3 3
0 0 8 0
0
4 0
2 18-0
1
4
1
0 28
0
2
41
238 0 3 4
0
0 11 0
0
5 0
2 21—0
1
5
1
0 31
0
2
51
3
1-0
3 5
0
0 13 0 0
60
2 23=0
1
6
1
0 33
0
2
61
3 3 0
3 6
0
0 15 0
0
70
225=0
1
7 1
0 35 0
2
71 3
5
0
3 7
0
0 17
0
0
8 0
2 27 0
1
8 || 1
0 37
0
2
81
3 7
0
3
8
0
0 20 0
0
9 0
2 30 0
1
91
1 0
0
0
2
2 91
3 10
0
3 9
0
0 22
0
0 100
2 32=0
1 10 1
1
2 0
2 10 1
3 12 0
3 10
0
0 24
0
0 11 0
2 34-0
1 11 1
1
4
0
2 111
3 14
3 14:
0
3 11
0
0 26
0
0 12
0
2 36-0
1 12
121
1
6
0
2 12||1
3 16
0
3 12
0
0 29
0
0 13
0
2 39-0
1 13
1
1
9
0
2 13|1
3 19
0
3 13
0
0 31 0
0 14 0
3 1=0
1 14 1
1 11 0
2 14 1
3 21 0
3 14
0
0 33 0
0 150
3
3=0
1 15 1
1 13 0
2 151
3 23 0
3 15
0 0 35
0
0 16 0 3 5 0
1 16|| 1
1 150
2 16||1
3 25-0
3 16
0
0 38 0
0 1 0=0
=0
0 17 0
180
0 18 0 3 10-0
3 8 0
1 17 1
1 18 0
2 171
3 28-0
3 17
1 18 1
1 20 0
2 181
3 30-0 3 18
0 1 2 0
0 19 0 3 12—0
1 19 1
1 22 0
2 191
3 32-0
3 19
0 1 4 0
0 20 0
3 14 0
1 20 || 1
1 24-0 2 20||1
3 34 0
3 20
0 1 7
0
0 21 0
3 17—0
1 21 1
1 27-0
2 211 3 37
0
3 21
0 1 9 0
0 220
3 19=0 1 22 1
1 29-0
2 221 3 39
0
3 22
0 1 11 0
0 23||0
3 21=0 1 23
1
1 31 0
2 232 0
1-0
3 23
0 1 13
0
0 24 0
3 23-0
1 24
1
1 33
0
2 24||2
0
3 0
3 24
0
1 16 0
0 250
3 26-0
3 26 0
1 25
1
1 36
0
2 25|2
0
60
3 25
0
1 18
0
0 260 3 28=0
1 26
1 26 1
1 38
0
2 26 2
0
8 0 3 26
0 1 20 0
0 1 22
0 270 3 30-0
1 27 || 1
1
2 0
0
2 27|2
0
100
3 27
0
0 280 3 32 0
1 28 || 1
2
2
0
2 28||2
0 12 0
3 28
0 1 25 0
0 290 3 35
0
1 29|| 1
2
5
0
2 292
0 15 0
3 29
0 1 27-0
0 300 3 37
0
1 30 1 2 7 0
2 30 2
0 17
0
3 30
0 1 29 0
0 310
3 39=0
1 31 1
2 9 0
2 31 2
0 19
0
3 31
0
1 31 0
0 32 1
0 1=0
1=0
1 32
321
2 11 0
2 32||2
0 210
3 32
0
134 0
0 33|1
0 4 0
1 33 1
2 14 0
2 33 2
0 24
0
3 33
0
1 36 0
0 341
0 6=0
1 34 1
2 16 0
2 34 2
0 26
0
3 34
0
138 0
0 35 1
0 8=0
1 35 1
2 18-0
2 35 2 0 28
0
3 35
0 2 0 0
0 36 1
0 10 0
1 36 || 1
2 200
2 36||2 0 30
0
3 36
0 2 3 0
0 371
0 13-0
1 37 1
2 23-0
2 37||2
0 330
3 37
0 2 5 0
0 2 7 0
0 2 9 0
0 38 1
0 391
1 0 1
0 15-0
1 38 1
2 25 0
2 382
0 350
3 38
0 17 0
1 39 || 1
2 27-0
2 27=0
2 39 2
0 37 0
3 39
0 19 0
2
0 1
2 29 0
3 0 2
0 39—1
0 0
COMPUTING TABLES.
331

3-Chain 2-Chain 3-Chain
Scale.
Scale.
Scale.
2-Chain 3-Chain 2-Chain
Scale. Scale. Scale.
3-Chain 2-Chain
Scale.
Scale.
A.
R. P. A.
B.
2
1
2=1 0
P. A.
1 2
R. P.
A.
R. P.
A. R. P. A. R. P. A. R. P. A. R. P.
3 12-1
1 1
3
1 22-1
2
13
3 32-1
3
1
2
1
4=1
0 22
3 14-1
1 2
3
1 24=1
2
2 3 3 34-1
3 2
2 1
61 0
32
3 16-1
1 3
3
1 26
1
2
33 3 36-1
3
3 3
2
1
1
81 0
42
3 18-1
1
4
3
1 28 1
2
4 3 3 38-
3 4
2
1 111 0
5 2
52
3 21=1
1
53
3
1 31 1
2
54 0
1=1 3 5
2 1 13-1
0
62
3 23=1
1
63
1 33 1
2
64 0
3=1 3 6
2 1 15 1 0
72
3 25=1 1
7 3
1 35-1
2
74 0
5-1
3 7
2
1 17 1
17=1
0
82
3 27=1
3 27=1
1
83
1 37 1
2
8 4
0
7=1
3
8
2
120 1
0 9 2
3 30—1
3 30-1
1 9 3
2
0
0-1
2
9 4 0 101
94 9
3
2
1 22=1
0 10 2
0 10 2
3 32-1
3 32 1
1 10 3
2
2 1
2
10 4 0 12-1
3 10
2 1 24 1
0 11 2
3 34=1
1 11 3
2
4 1
2 11 4
0 14=1
3 11
2
1 26 1
0 12 2
3 36 1
1 12
3
2
6=
6-1
2 12 4
0 16 1
16=1
3 12
2
1 29-1
0 13 2
3 39-1
1 13
3
2
9
1
2 13 4
0 19-1
3 13
2
131=1
0 14 3
0 1=1
1 14
3
2 11
1
2 14 4
0 21 1
3 14
2
1 33
1
0 15 3
0
31
1 15
3
2 13
1
2 15 4
0 23=1
3 15
2 1 35 1
0 16 3
0
5 1
1 16
3
2 15
1
2 16 4
0 25=1
3 16
2 1 38-1
0 173
0 81
1 17
3
2 18
1
2 17 4
0 28=1
3 17
2 2 0 1
0 18 3
0 10-1
1 18
3
2 20
1
2 18 4
0 30-1
3 18
2 2 2 1
0 19 3
0 12 1
1 19
3
2 22
1
2 19 4
0 321
3 19
2 2 4
4 1
0 20|| 3
0 14
1
1 20
3
2 24
1
2 20 4
0 34 1
3 20
2 2
7-1
-1
0 21 3
0 17-1
1 21
3
2 27-1
2 21 4
0 37=1
3 21
2 2
9 1
9-1
0 22|| 3
0 19=1
1 22
3
2 29
1
2 22 4
0 39—1
3 22
2 2 11=1
0 23 3
0 21=1
1 23 3
2 31 1
2 234
1
1=1
323
2 2 13 1
0 24 3
0 23 1
1 24
1 24
3
2 331
2 24 4
1
1
3 1
3 24
2
2 16
1
0 25 3
0 26=1
1 25
3
2 36 1
36=1
2 254 1
6-1
3 25
2 2 18 1
0 26
3
0 28—1
1 26
3
2 38=1
2 38 1
2 264
1
8-1
3 26
2
2 20 1
0 27
3
0 30=1
1 27 3
3 0-1
2 27 4 1 10-1
3 27
2 2 22
1
0 28 3
0 32 1
1 28 || 3
3
2 1
2 28 4
1 12 1
3 28
2 225-1
2 2 27=1
2 2 29 1
2 231=1
2 31
2 2 34 1
0 29 3
0 35=1
0 30 3
0 31 3
0 39-1
1 29
0 37=1 1 30 3 3
1 31 3
3
3 3
5 1
2 29 4
1 15-1
3 29
7 1
2 304
1 17=1
3 30
9 19-1
1 2 31 4 1 19 1
3 31
1
0 32 || 3
1 1=1 1 32 3 3 11=1
2 32||4
1 21=1
3 32
0 33 3
1
2 2 36=1
0 343
1
4=1
6
1 33
1 34 |
2 2 38=1
0 353
1
2 3 0 1
0 36 3
8=1
1 10=1
1 35
1 36
að að að no
3 3 14 1
2 33 4
334
1 24 1
3 33
3 3 16 1
2 344
1 26=1
1 26 1
3 34
3 3 18
1
2 35 4
1 28-1
3 35
3 3 20
1
2 36 4
1 30=1
3 36
2 3
3-1
0 373 1 13-1
1 37 3 3 23
1
2 37 4
1 33-1
3 37
2 3 5 1
0 383
1 15 1
1 38 3
3 25 1
2 38 4
1 35 1
3 38
2 3
7-1
1
2 3
9-1
0 39 3 1 17=1
1 0 3
1 39 3
3 27 1
2 39 4
1 37=1
3 39
1 19 1
2 0 3
3 29—1
3
0 4
1 39 2
0 0
332
COMPUTING TABLES.

3-Chain 2-Chain 3-Chain
Scale.
Scale.
Scale.
2-Chain
Scale.
Scale.
3-Chain 2- Chain
Scale.
3-Chain
2-Chain
Scale.
Scale.
A.
R. P.
A. R. P. A.
R. P. A.
B. P.
A. R. P.
A. R. P.
A.
R. P. A. R. P.
4 2 2
2
0
0
15
0 12 2
1
1
5
2 22
2
2
1 6
0 32—2 3 1
4 2 4
2
0
2||5
0 14-2
1
2
5
2 24 2
2
26
0 342 3 2
4 2 6:
-2
35
016-2
0
0 16 2
1
3
5
2 26-2 2
36
0 362 3 3
4 2 8 2
0
45
4 5
0 18-2
1
4
5
228-2
2
4 6 0 38 2 3 4
4 2 11 2
0
5 5
0 21=2
1 5
5
2 31-2
2
56
1 1
2
3
5
4 2 13 2 0
65
023=2
1 6
5
2 33=2 2
6 6 1
3
2
3 6
4 2 15-20
75
0 25-2
1
7
5
2 35-2 2
7 6
1
5 2
3
3
7
4 2 17 2 0
85
0 27 2
1
8
5
2 37-2
2
8 6
1
7=
7-2
3 8
4 2 20 2 0
95
0 30
0 30=2
2
1
9
5
3
2
2
96
1 10 2
3 9
4 2 22 2
0 10 5
0 32 2
1 10
5 3
2 2
2 2 10 6
2 10|6
1 12-2
3 10
4 2 24-2
0 11
5
0 34
2
1 11
5 3
42
2 116
1 14 2
3 11
4 226-2
0 12 5
0 36
2
1 12
5
3
6-2
2 12 6
1 162
3 12
4 2 29 2
0 13 5
0 39-2
1 13
5
3 9
2
2 13 6
1 19 2
3 13
4 2 31-2
0 14 5
1
1 1=2
1 14
5
3 11
2
2
2 14 6
2 14 6
1 212
3 14
4 2 33 2
0 15 5 1
3-2
1 15
5
3 13
2
2 15 6
1 23-2
3 15
4 2 35—2
0 16 5
1
5 2
1 16
5
3 15
2
2 166
125—2
3 16
4 2 38-2
0 17 5
1
8 2
1 17
5
3 18—2
2 17||6
1 28-2
3 17
4 3 0 2
0 185
1 10-2
1 18
5
3 20 2 2 18 6
1 30 2
3 18
4 3 2-2
0 19 5
1 12-2
1 19
5
3 22 2
2 196
1 322
3 19
4 3 4 2
0 205
1 14 2
1 20
5
3 24-2
2 206
1 342
3 20
4 3 7
2
0 21 5
1 17 2
1 21
5
3 27
2
2 21 6
1 37—2
3 21
4 3 9
2
0 225
1 19-2
1 22
5
3 29
2
2 22 6
1 39—2
3 22
4 3 11 2
0 23 5
1 21 2
1 23 5
3 31
2
2 23 6
2 1 2
3 23
4 3 13
2
0 24 5
1 23-2
1 24 5
3 33
2
2 24 6
2
3
2
3 24
4 3 16
4 3 18 2
2
0 255
1 26-2
1 25|| 5
5
3 36-2
3 36 2 2 256
2
6—2
3 25
0 265
1 28-2
1 26 5
3 38-2
2 26 6 2 8
2
3 26
4 3 20 2
0 27 5
1 30 2
1 30—2
1 27 6 0
0-2
2 27 6
2 10
2
3 27
4 3 22-2
0 285
1 322
1 28
6 0
2 2
2 28 6
2 12
2
3 28
4 3 25-2
0 295
1 35—2
1 29
6 0
5
2
2 296 2 15
2
3 29
4 3 27 2
0 30 5
1 37-2
1 30
60
7
2
2 306 2 17
2
3 30
4 3 29-2
0 31 5
1 39 2
1 31
6 0 9 2
2 316 2 19-2
3 31
4 3 31 2
0 32 5 2 1
2
1 32
6
6
0 11 2
2 32||6 2 21=
332
4 3 34 2
0 33||5
0 335 2
2
4 3 36-2
0 34 5 2
4=
4 2
6-2
1 33
6
6
0 14-2
0 14 2
2 336
2 24 2
3 33
1 34 || 6
0 16 2
2 346
2 262
3 34
4 3 38-2
5 0 0 2
0 35 5 2 8=2
0 36 5 2 10-2
1 35 6
0 18 2
2 356
2 28-2
3 35
1 36
6
0 20
2
2 36 6
2 30- -2 3 36
0 3 2
5 37||5
0 37 5 2 13-2
1 37
6
0 23-2
2 37 6
5 0 5 2
0 38 5 2 15
2
1 38
6
0 25 2
2 38||6
5
07-2
0 39 5 2 17
2
1 39
6
0 27 2
2 396
2 33 2 3 37
235=2_3 38
2 37 2 3 39
5 0 9 2
1 05 2 19-2
2 0
6
6
0 29
0 29-2
2
3 06
2 39 3 0 0
COMPUTING TABLES.
333

3-Chain 2-Chain
Scale.
Scale.
3-Chain
Scale.
2-Chain 3-Chain 2-Chain 3-Chain
Scale. Scale. Scale. Scale.
2- Chain
Scale.
A.
B. P.
A
R. P. A. R. P. A.
R.
P.
A.
R. P. A. R. P. ለ.
R. P.
A.
R. P
6
3 2
3
0
17
1 12=3 1
1
1
7
3 22-3
2
18
1 32-3
3 1
6 3 4
3
0
27
1 143
1 2
7
3 24 3
2
28
1 34 3 3
2
6
3
6 3
0
37
1 16-3
1
3
37
7
3 26=3
2
38
1 36-3
3
3
6 3
8=3 0
4|7
1 18-3
1
4 7
3 28=3
2
4 8 1 38-3 3 4
6 3 11 3 0
57
1 21=3
1
5
7
3 31-3
2
2
5
5 8
2
1 3
1-3
3
5
6
3 13-3
0
6|7
123=3 1
6
7
3 33 3
2
2
6
68 2
3 3
3
6
6 3 15 3
0
77 7
1 25-3 1 7
7
3 35-3
2
78 2
2
5-3
5 3
3
7
6
3 17 3
0
8 7
1 27=3 1
8
7
3 37=3
2
8
2
7-3
7 3
3
8
6 20-3
3 20 3
0
97
1 30-3
1 9
6
3 22-3
0
10 7
1 32-3
1 10
6 3 24 3
0 11 7 1 34 3
1 11
6 3 26-3
0 12 7
1 36=3
1 12
∞ ∞ ∞ ∞
8
0
0
3
2
2
98
98
2 10–3
2 10 3
3 9
8 0
2 3
2 10 8
2 12-3
2 12 3 3 10
8
0
4 3
4-3
2
2 11 8
118
2 14 3
14=3
3 11
8
0
6 3
2 128
2 16 3
3 12
6
3 29 3
0 13 7
1 39=3
1 13
8
0 9=
2 13 8
2 19–3
3 13
6
3 31=3
0 14 7
2
13
1 14
8
011
0 11-3
2 14
3
2 14 8
2 21-3
3 14
6
3 33 3
0 15 7
2
3-3
1 15
8
0 13
3
2 15 8
2 23-3
2 23 3
3 15
6
3 35
3
0 16 7
2
5 3
1 16
8
0 15
3
2 16||8
2 16 8
2 25-3
2 25 3
3 16
6 3 38=3
0 177
2 8=3
1 17
8
0 18=3
2 178
2 28-3
7 0
0-3
0 18 7
18|7
2 103
1 18
1 18 8
0 20=3
2 188
2 18 8
7 0
2 3
0 19 7
2 12=3
1 198
0 22 3
2 19 8
7 0 4 3
0 207
2 14 3
1 20
8
0 24 3
2 208
2 208
28=3 3 17
2 30-3
2 30-3 3 18
2 323 3 19
2 34-3 3 20
NNNN
7 0
7-3 0 217
2 173 1 21
8
0 27 3
27=3
2 21 8
21||8
2 37=3
2 373
3 21
7 0 9-3 0 22 7
2 19-3 1 22
8
0 29 3
2 228
2 39-3 3 22
7 0 11=3
0 237
2 21=3 1 23
8
0 31=3
2 23
238 3 1-3
3 23
7 0 13 3
0 24 7
2 23-3 1 24
8
0 33-3
2 24||8 3
3 3
3 24
7 0 16 3
7 18-3
0 25 7
2 26-3 1 25|| 8
0 36=3
2 258
3
3
6-3
6-3
3 25
0 18 3
0 26||7
0 267
2 28-3 1 26 8
0 38 3
2 268
3
8 3
8=3
3 26
7
0 20 3
0 277 2 30—3 1 27
8 1
0-3
2 27 8
278
3 10-3
3 27
7 0 22-3
0 287 2 32-3 1 28
8
1
2 3
3
2 28||8
2 288
3 12-3
3 12 3
3 28
7 0 25-3
0 29 7
2 35-3 1 29
8 1
5 3
53
2 298
3 15 3
15=3
3 29
7
0 27 3
0 307
2 37-3 1 30
8 1
7=3
2 308
3 17=3
3 30
7 0 29 3
0 31|7 2 39—3 1 31
8
1 9 3
2 318
3 19-3
3 31
7 0 31
3
0 327 3 1=3 1 32
8
1 11 3
2 328
3 21=3
3 32
7 0 34=3
7 0 36=3
7 0 38 3
0 33 7 3 43
0 347 3 6-3
0 357 3 8 3
1 33 || 8
1 14 3
2 33||8
3 24
3
3 33
1 34 || 8
1 16—3
1 16 3
2 348
3 26 3
3 34
1 358
1 18=3
2 35
3 28 3
3 35
7
1 0
3
0 367 3 10 3
1 36 8
120 3
2 368
3 303
3 36
7
1 3 3
0 377 3 133
1 37
8
1 23
3
2 37 8
3 33=3
3 37
7
1 5 3
0 387 3 15
3
1 38
8
1 25
3
2 38 8
3 35 3
3 38
7 1
7=3
0 397 3 17
3
1 39
8
1 27 3
2 398
3 37 3
37=3
3 39
7
1
9 3
1 07 3 19
3
2 0
8
1 293
3 09
0
0 0 4 0 0
334
COMPUTING TABLES.

3-Chain 1-Chain
Scale.
Scale.
3-Chain 1-Chain 3-Chain
Scale. Scale. Scale.
1-Chain
Scale.
3-Chain 1-Chain
Scale. Scale.
A.
R. P.
A.
R.
P. A.
R. P. A.
R. P.
A.
R. P.
A.
R. P.
A.
R. P.
A.
R. P.
0
0 5 0 0
12
12
1
1 5=0
1
1
4 2 5
0
2
1 6
3 5 0 3
1
0
0 14-0
0
22
1 14-0
1
2
4
2 14
0
2
2 6
3 14-0
3
3
2
0
0 23 0
0
0
32
1 23 0
23-0
1 3
4
2 23
0
2
3 6
3 23-0
3
3
0
0 32=0
0
4 2
1 32—0
1
1 4
4
232 0
2
4 6
3 32 0
3
4
0 1
1=0
0
5 2
2 10
1
5
4 3 1-0
2
57
0 10
3
5
0
1 10 0
0
62 2 100
1
6
4
3 10 0
2
6 7
0 10 0
3 6
0
1 19 0
0
72
2 19
0
1
7
4
3 190
2
77
7
0 190
3
7
0
1 28 0
0
8 2
2 28
0
1
8
4
3 28 0
2
8 7
0 28 0
3
8
0
1 37-0
0
9 2
2 370
1
9
4
3 370
2 97
0 370
3 9
0 2 6 0
0 10 2
3
6 0
1 10
5
0 6
0
2 10||7
1 6 0 3 10
0
2 15 0
0 112
3 15-0
1 11
5
0 15 0
2 117
1 15-0
115 0
3 11
0
2 24
0
0 12 2
3 24 0
1 12
5
0 240
2 12 7
1 24 0
3 12
0
2 33
0
0 13 2
3 330
1 13
5
0 33 0
2 137
1 33 0
3 13
0
3 2
0
0 143
0
2 0
1 14 5
1 20
2 14 7
2 2 0
3 14
0
3 11
0
0 15 3
0 11
0 11:0
1 15
5
1 11 0
2 15 7
2 11=0
3. 15
0
3 20
0
0 16 3
0 20 0
1 16
5
1 20
0
2 16 7
2 20 0
3 16
0
3 29 0
0 17 3
0 290
1 17
5
1 29-0
2 17 7
2 29
0
3 17
0
3 38-0
0 183
0 38=0
1 18 5
138 0
2 18 7
2 38
0
3 18
1
0 7 0
0 193
1 7 0
1 19 5
2 7
0
2 19 7
3 7
0
3 19
1
0 16 0
0 20 3
1 16-0
1 20 || 5
2 16
0
2 207
3 16
0
3 20
1
0 25 0
0 21 3
1 250
1 21 5 2 25-0
2 21 7
3 250
3 21
1
0 34 0
0 22|3
1 34 0
1 22
2 34 0
2 227
3 340
3 22
1
1 3
0
0 23 3
2 3
0
1 23 5
3 3 0
2
2 238 0 0 3 0
3 23
1
1 12 0
0 24 3
2 12
0
1 24 || 5
3 120
2 248
0 12 0
3 24
1 1 21 0
0 25 3
2 21-0
1 25 || 5
5
3 21-0
3 21 0
2 25 8
2 258
0 21 0
3 25
1
1 30-0
0 26 3
2 30-0
1 26 5
3 30 0
2 268
0 30 0
3 26
1
1 39 0
0 273
2 39-0
1 27 5
3 39 0
2 27 8
2 27 8
0 390
3 27
12 8
0
0 28 3
3 8 0
1 28 || 6
0 80
2 288
1 8 0
3 28
1
2 17 0
0 29 3
3 17
0
1 29
6
0 17 0
2 29 8
1 17 0
3 29
1 2 26 0
0 30 3
3 26
0
1 30
6
0 260
2 308
1 26 0
3 30
1
2 35 0
0 31 3
3 35
0
1 31
6
0 35 0
2 318 1 350
3 31
1 3 4
0
0 324
0 4
0
1 32
6
1 4-0
2 328 2 4 0
3 32
ATH Q
1
3 13 0
0 334
0 13-0
1 33
6
1 13 0
2 33 8 2 13 0
3 33
1
3 22 0
0 344
0 34 4
0 22 0
1 34 6
1 22 0
22-0
2 34 8
2 22=0
3 34
1
3 31-0
0 35 4
0 31-0
1 35 6
1 31-0
2
0 0 0
0 364
1 0 0
1 36 6
2 0 0
2 35 8
358
2 36
368
2 310
3 35
3 0 0
3 36
2 0 9 0
0 37 4
1 9–0
1 37 6 2 9 0
2 37||8
3 9 0
3 37
2
2 0 18 0
0 27 0
2 0 36 0
0 384
0 38 4
0 39 4
1 0 4
1 18 0
1 38 6
2 18
0
2 38 8
3 18 0
3 38
394
1 270
1 27
0
1 39 6
2 27
0
2 39 8
3 27 0
3 39
1 36 0
2 0
6
2 36
0
3 08
08
3 36=1
3 36=1
0 0
COPYING MAPS.
335
CHAPTER XI.
COPYING MAPS.
VARIOUS methods, according to circumstances, are resorted to for
multiplying Copies of Maps; two only, which are the most usual,
will be mentioned here. To copy a map by "pricking it off," lay
the original over the paper intended for the copy, and with a very
fine needle prick through every point at which a change takes
place in the relative position of the lines of the plan; connect all
these points by lines similar to those of the original, and a fair du-
plicate plan will be obtained. Plans copied in this manner gene-
rally answer to scale better, that is, are more nearly accurate in
general features than any other duplicate maps; but the details are
apt to get distorted in minute peculiarities, notwithstanding the
greatest amount of care and attention. One very great disadvantage
also is, the impossibility of placing the original again over the copy
in the same position after it has been once removed, so as to enable
any omission to be supplied.
In pricking off maps there are a few things to be attended to, to
secure success. The needle should always be held perfectly erect,
so that the impression may be directly under the point on the ori-
ginal. In narrow parallel lines, such as a river, brook, or road, a
dot should not be pricked on one side without pricking one imme-
diately opposite it in the line forming the other side, by which
means confusion of the dots in drawing the lines of the copy is
avoided. All straight lines should have a dot in the centre, as well
as at either end, both as an additional precaution to ensure accu-
racy, and also to afford a means of identifying the dots with the
lines. Many other things will suggest themselves with practice
that would occupy more space than can be appropriated here.
To Copy a Map by means of" Transferring Paper."-Get a
sheet of thin paper, and rub over it some powdered black lead-
the palm of the hand is the best thing to rub this black lead on
with; and when it has been well rubbed in, a rough cloth should
be passed over it to get off as much of the superfluous lead as pos-
sible, so that it may not wipe off upon the map. Place the black
side towards the paper that is to receive the copy of the plan, and
put the original upon the whole; then with a blunt steel point or
336
THE PENTAGRAPH.
tracer go over all the lines of the original, and the pressure of the
tracer will cause the black lead to come off upon the under paper,
and thus delineate a fac-simile of the original. We may as well
consider at once, that a tracing will first have to be taken from
the original, as the paper upon which plans are plotted is in
the generality of cases in practice, much too thick to admit
of a transfer being made direct from it with any accuracy, or
at all events without spoiling the original, which is at all times a
thing worth any trouble in the avoiding.
Plans may also be copied by the Pentagraph, an instrument
which next claims our attention.
THE PENTAGRAPH.
This is an instrument but very imperfectly understood, even by
those who are most frequently using it. It requires to be very ac-
curately constructed and skilfully handled, and then very beautiful
work will be the result. Its chief use is to reduce or enlarge plans,
but it will also copy the same size. In describing the use of the
Pentagraph, we may as well confine our attention to the reduction
of maps, as work cannot be enlarged with any degree of satisfac-
tion; small unappreciable errors are magnified into important ones,
and the whole features become distorted. With reduction on the
contrary, errors of all kinds are reduced in magnitude, and many
entirely disappear.
This instrument is represented in the annexed engraving, where
it is shewn as in the act of copying a plan H, upon a reduced scale
h. The Pentagraph consists of four rulers, A, B, C, and D, made
of stout brass. The two longer rulers, A and B, are connected
together by, and have a motion round a centre, shewn at the upper
part of the engraving. The two shorter rulers are, in like manner,
connected with each other, and with the longer rulers, as may be
clearly understood from an inspection of the engraving. The whole
instrument is supported by small pillars resting upon ivory rollers,
a a a, &c., which have a motion in all directions exactly like the
brass castors fixed to ordinary tables. The rulers A and C have
each an equal number of similar divisions, marked †,†, &c.; and
likewise a sliding index, E and F, which can be fixed to any divi-
sions on the ruler by a milled-headed clamp screw shewn in the
engraving. The sliding indeces, E and F, have each of them a
tube adapted to slide on a pin, rising from a heavy circular weight
called the fulcrum, which acts as a centre for the whole instrument
to turn upon when in use, or to receive a sliding holder with a
pencil, or a tracing point, as may be required.
4
THE PENTAGRAPH.
337

a
E
h
A
B
F
O
D
H
Our fig. represents the instrument. The principle will at once
become apparent. The bars B and C must always remain parallel
to each other under every position of the instrument, as well as A
and D. EFG are all in one straight line. Hence, two similar
triangles are formed, whose sides are to each other as E F is to
E G. By securing the point E in one spot, and by moving a tracer
at G over the lines of the original, a pencil at F, left to follow the
course of the instrument, will describe an exactly similar line,
bearing the same proportion to the original as E F does to E G.
The Pentagraph is usually constructed in brass, with steel cen-
tres, and travels parallel to the paper, supported by the six ivory-
mounted wheels. The pencil, in the best made instruments, is
fixed in a case, something like the point of an ever-pointed Mordan
pencil, by which contrivance the point is always in the centre. A
small silken thread passes round the instrument from the pencil to
the tracer, by means of which the pencil is caught up when it is re-
338
RAILWAY SURVEYING.
quired to move the instrument across the plan in a direction that
is not required to be delineated. The bars A and C are generally
divided, but it is not at all necessary they should be so, as the ipse
dixit of the maker should never be taken for granted, and the in-
strument is easily set. Say, as the length in inches and decimals
of any line upon the large map required to be reduced, is to the
length of the bar B; so is the length to which the same line is re-
quired to be reduced to the proper length on the bar C. Again,
as the difference in length of the line upon the large and small scale
is to the length of that part of the bar A, between the bars C and
B, so is the length of the line on the large map to the whole length
of the bar A; or on the small map to that part of the bar A, be-
tween the bar C and the fulcrum. See that E F and G are in the
same straight line and the instrument is set for use.
While the scale of the reduced map is required to be as small as,
or smaller than, one-half of the original, the position of the fulcrum
will be somewhere on the bar A; but when the proportion of the
small map to the original becomes such as 3 to 5, 6 to 9, 10 to 12,
&c., then the fulcrum and pencil must exchange places, and the
proportion is calculated as EF to F G.
An inspection of the instrument, and a very little practice, will
suggest all other explanation.
CHAPTER XII.
RAILWAY SURVEYING.
SECT. I.—Exploration and Trial Levels.
THE services of an engineer or surveyor, in connection with a pro-
jected line of railway, commence with what is technically termed
an "exploration of the country," through which it is desirable or
intended that it should pass. This exploration is a general exami-
nation of the district by the engineer for the purpose of making
himself thoroughly acquainted with its geographical contour, and
geological features. He then, by the aid of an Ordnance Map, if
the line is situated in the south of England, or in Ireland, where
such a map is obtainable, sketches out a line, over which he causes
what are called " Trial Levels" to be taken. These Trial Levels
are frequently but very rough affairs, but care should be always
observed that the right point is taken at the crossing of all public
RAILWAY SURVEYING.
339
roads, and B M should be frequently noted, as a check upon the
levels of any future process.
In taking Trial Levels, it is generally the custom, in critical
localities, to level one or two alternative lines, but I would sug-
gest, that one line with a number of cross sections at frequent
intervals is more convenient, and affords a greater amount of
useful information. The use of the "Exploration" is palpable;
and the utility of the Trial Levels and Section must be obvious
upon a very little consideration. By their aid the most favour-
able gradients can be selected, and even the absolute practicability
of the railway in the proposed direction can be determined. It
not unfrequently happens, in selecting the route for a line of
railway, that a slight detour from the most direct course will save
a long heavy embankment, or a deep cutting, and will moreover
improve the gradients to a very great extent. Practice and ex-
perience will, as in most other things connected with the profes-
sion of an engineer or surveyor,. be the only sure guides to
success, in selecting the gradients and determining the mode of
overcoming the difficulties presented by the face of the section.
As a general rule, however, the cuttings should balance the em-
bankments, so that the stuff taken out of the one may serve to
create the other; but if it is necessary that one should predomi-
nate, I would in most cases give a preference to the latter, it
being generally more easy to obtain a piece of side cutting than
to carry to spoil* a large amount of superabundant earth.
When railways were more in their infancy easy gradients were
insisted upon, and an inclination of 1 in 100 was thought as a rule
sufficiently steep; but now that locomotive science and the
whole subject are becoming more practically known, inclines of
1 in 80, 1 in 70, and 1 in 60, are to be frequently found on the
sections of new and branch lines. All of which is of course but a
question of expediency, between present economy of construction
and the future expense of working the line.
The following is a brief extract of some of the requirements of
the Standing Orders of the two Houses of Parliament, so far as
they relate to the preliminary, or, as it is technically termed,
"Parliamentary Survey" for an intended railwayf.
* Banks formed of surplus excavated earths are called "Spoil Banks," and the
earths so treated are said to be "carried to spoil."
† It is not intended to render service to the professional student, as he will find it
expedient to procure a copy of the Standing Orders every successive session, in order
that he may be fully acquainted with all amendments which from time to time may
take place in them; but to the non-engineering enquirer this brief summary may con-
tain all the information he is in search of.
RAILWAY SURVEYING.
340
Plan and Sections.
That a plan shall be drawn on a Scale of NOT LESS than four
inches to a mile, and shall describe the line or situation of the
whole work, and the lands in, or through which it is to be made,
maintained, varied, extended, or enlarged, or through which every
communication to or from the work shall be made.
When powers to make any lateral deviation from the line of
the proposed work is intended to be applied for, the limits of such
deviation shall be defined upon the plan, and all lands included
within such limits to be marked thereon, and in all cases, except-
ing where the whole of such plan is upon a scale of not less than
a quarter of an inch to every 100 feet, an additional plan of
every building, yard, court-yard, or land within the curtilage of
any building; or of any ground cultivated as a garden, either on
the original line, or within the limits of the deviation, to be laid
down on the plan, or on an additional plan to be deposited there-
with, upon a scale of not less than a quarter of an inch to every
100 feet.
A section shall be drawn to the same horizontal scale as the
plan, and to a vertical scale of not less than one inch to every 100
feet, which shall shew the surface of the ground marked on the
plan, the intended level of the proposed work, and a datum hori-
zontal line, which is to be the same throughout the whole length
of the work, or any branch thereof respectively, and to be referred
to some fixed point stated in writing on the section, near either of
the termini.
The plan to exhibit thereon the distances in miles and furlongs
from one of the termini, and a memorandum of the radius of every
curve, not exceeding one mile in length, to be noted on the plan
in furlongs and chains.
The line of railway marked upon the section to correspond with
the upper surface of the rails.
The distances on the datum line to be marked in miles and
furlongs to correspond with those on the plan, and a vertical
measure from the datum line to the line of the railway to be
marked in feet and inches at each change of the gradient or in-
clination, and the proportion or rate of inclination between each
such change must also be marked.
The height of the railway over or under the surface of every
turnpike road, public carriage road, navigable river, canal or
RAILWAY SURVEYING.
341
railway, or junction with a railway, and the height and span of
every arch of all bridges and viaducts to be marked in figures at
every crossing thereof, and the extreme height over or under the
surface of the ground must be marked for every embankment and
cutting; and if any alteration in the present level or rate of in-
clination of any turnpike road, carriage road, or railway, be in-
tended, then the same to be stated on the section, and each
numbered; also cross sections in reference to the same numbers
on a horizontal scale of one inch to every 330 feet, and on a
vertical scale of one inch to every 40 feet, to be added, to explain
the nature of such alterations more clearly.
Where tunnelling as a substitute for open cutting, or a viaduct
as a substitute for solid embankment, be intended, the tunnelling
to be marked by a dotted line on the plan, and also to be marked
on the section, and the viaduct to be marked on the section.
Deposit with the Clerk of the Peace.
Duplicate plans and sections, with a book of reference, to be
deposited for public inspection at the Office of the Clerk of the
Peace, for every county, riding, or division in England or Ireland,
or in the Office of the principal Sheriff Clerk of every county in
Scotland, in or through which the work is proposed to be made,
maintained, varied, extended, or enlarged, on or before the 30th
day of November, immediately preceding the session, in which
application for the bill is to be made.
The Clerks of the Peace, or Sheriff Clerks, or their respective
deputies, to mark in writing upon the plans, sections, and books
of reference deposited with them, denoting the time at which the
same are lodged in their respective offices, and at all seasonable
hours of the day permit any person to view and examine one of
the same, and to make copies or extracts therefrom; and one of
the two plans deposited to be sealed up and retained in the pos-
session of the Clerk of the Peace, or Sheriff Clerk, until called for,
by order of one of the two Houses of Parliament.
Deposit at Board of Trade.
A copy of the Plans, Sections, and Books of Reference, to be
deposited in the Office of the Railway Department of the Board
of Trade, on or before the 30th of November, immediately pre-
ceding the Session of Parliament, in which application is to be
made; together with a published map, to a scale of not less than
342
RAILWAY SURVEYING.
half an inch to a mile, with the line of railway delineated thereon,
so as to shew its general course and direction.
Deposit with the Railway Commissioners.
That in the case of Railway Bills a copy of all Plans, Sections,
and Books of Reference, required by the orders of the House to
be deposited in the office of any Clerk of the Peace, or any Sheriff
Clerk, on or before the 30th day of November preceding the
application for the bill, together with a published map to a scale
of not less than half an inch to a mile, with the line of railway
delineated thereon, so as to shew its general course and direction,
shall, on or before the same day, be deposited in the Office of the
Commissioners of Railways.
Deposits at the Private Bill Office.
That on or before the 30th of November, a copy of the said
Plan, Sections, and Books of Reference; and in the case of Rail-
way Bills, also a copy of the said published map, with the line of
railway delineated thereon, be deposited in the Private Bill Office
of the House of Commons.
Deposit with Parish Clerks, &c.
A copy of so much of the plans and sections as relates to each
parish in or through which the work is intended to be made,
maintained, varied, extended, or enlarged, with a Book of Refe-
rence thereto, to be deposited on or before the 30th of November
with the parish clerk of each such parish in England; the school-
master of each such parish in Scotland (or in the Royal Boroughs,
with the Town Clerk), and the Clerk of the Union, within which
such parish is included in Ireland.
When any lands or houses are intended to be taken, or an ex-
tension of the time granted by any former Act for that purpose,
is sought, application in writing, in the form hereinafter set forth
to be made to the owners, lessees, and occupiers, on or before the
15th day of December, which application must be delivered per-
sonally, or left at their usual place of abode; or in the event of
their being absent from the United Kingdom, be left with their
respective agents; and separate lists to be made of the names of
such owners, lessees, or occupiers, distinguishing which of them
have assented, dissented, or are neuter in respect thereto.
RAILWAY SURVEYING.
343
Lists of owners, lessees, and occupiers, to be lodged in the
Private Bill Office, and the receipt thereof acknowledged on the
petition before it is presented.
Notice in writing of a bill, whereby any part of a work autho-
rised by any former Act is intended to be relinquished, to be given
to the owners and occupiers of lands in which the part of the
work intended to be thereby relinguished is situate.
Form of Notice to Owners, Lessees, and Occupiers.
SIR,-We beg to inform you that application is intended to be
made to Parliament in the ensuing session for "An Act," [Here
insert the title of the Act.] and that the property mentioned in
the annexed schedule, or some part thereof, in which we under-
stand you are interested, as therein stated, will be required for
the purposes of the said undertaking, according to the line thereof
as at present laid out, or may be required to be taken under the
powers of deviation, which will be applied for in the said Act, and
will be passed through in the manner mentioned in such Schedule.
,
We also beg to inform you, that on or before the 30th day of
November last a plan and section of the proposed undertaking,
and also a duplicate of such Plan and Section, together with a
Book of Reference thereto, and also a copy of the notice pub-
lished in the London Gazette, were deposited with the Clerk of
the Peace for the county of
at his office in
in the said county; and that on or before the said 30th day
of November last a copy of so much of the said plan and sec-
tion as relates to the parish or parishes in which your property
is situate, together with a Book of Reference to such plan, and also
a copy of the notice published in the London Gazette, was also
deposited with the parish clerk of each such parish, at his place of
abode, on which plans your property is designated by the numbers
set forth in the annexed Schedule.
As we are required to report to Parliament whether you assent
to, or dissent from, the proposed undertaking, or whether you are
neuter in respect thereto, you will oblige us by writing your an-
swer of assent, dissent, or neutrality in the form left herewith, and
returning the same to us, with your signature, on or before the
day of December instant; and if there should be any error or
misdescription in the annexed Schedule, we shall feel obliged by
your informing us thereof at your earliest convenience, that we
may correct the same without delay.
We are, sir,
Your most obedient servants,
344
RAILWAY SURVEYING.

Property within the
for.
applied
Limits of Deviation intended of the proposed
to be
at
Property in the line
present laid
work as
out
Parish,
Township, or
No.
on
Descrip-
tion.
Owner.
194 {
Arable
Arable }
Land
ship, Extra
Parochial, or
other place.
on
Plan.
No. Descrip-
tion.
Schedule referred to in the foregoing Notice, describing the Property therein alluded to, and the manner in
which the line of the proposed work, as delineated upon the plan and section, will affect the same.
extra paro- Plan.
chial place.
Bigwood
Smallcopse 391
391
Parish, Town-
{Meadow} The same.
Land
Description of the Section of
the Line deposited, and of
Occupier. the greatest height of Em-
bankment & depth of Cutting.
Cutting.
Inches.
Lessee.
Embankment.
Feet. Inches.
Feet.
The Rt. Hon. John Smith
Wm. Eager. Brown, Esq.
The same. Felix Gregory
David Wilson 6
6 2
9 8
Owner.
Lessee.
Occupier.
Bigwood
195 Arable} The Rt. Hon.
Land Wm. Eager.
Bigwood
196
Wood
Land S
The same
John Smith
Brown, Esq.
The same
David Wilson
The same
Pasture
Smallcopse
392
Land S
The same
The same. Felix Gregory
The Moors
RAILWAY SURVEYING.
345
Preparation of Parliamentary Plans and Sections.
The Plans and Sections required by the Standing Orders of the
Houses of Parliament, to be deposited at the Private Bill Office,
and other places, on or before the 30th November, preceding the
Session of Parliament, in which application is intended to be made
for any powers in respect of works connected with such plans and
sections, are generally very simple in construction to any one ac-
quainted with surveying.
To describe a system which shall be best to adopt under all
circumstances, would only serve to mislead, without being prac-
ticable. If the country to be surveyed is tolerably open, and
the landowners and occupiers favourably disposed, it may be
best to range a base line in the direction of the proposed rail-
way, and thereon to build such other lines as may be necessary
to take up the features of the country to a sufficient width on
either side, care being taken in every change of base to cross the
old and new bases a sufficient length beyond the junction, to admit
the admeasurement of a tie line on either side. (See fig. 177.) And
in plotting the distances A B, B C, C D, D B, B E, and A E, they
should be tripled or quadrupled, as circumstances may admit, to
enable their more accurate delineation on the map.
If the country is thick, and the landowners and occupiers not
very friendly disposed, a traverse of the roads first made will much
facilitate the work, as a base line cannot be ranged without cutting
hedges, and nothing more exasperates a hostile farmer. A traverse
of the nearest roads completed, the filling in, is a business that
may be entrusted to a less experienced surveyor.
In the extract of the Standing Orders given herein, it will be
observed, that the scale of the plans is required to be NOT LESS
than four inches to a mile, which is twenty chains to an inch; but
all buildings, gardens, &c., must be drawn to a scale NOT LESS than
a quarter of an inch to every hundred feet, which is six chains and
about six links to an inch.
Were not this latter condition necessary to a compliance with
Standing Orders, most engineers would deposit plans to the
smaller scale; not only because they would require less time in
drawing, but also, and principally, because it would be far more
difficult to detect any omission or error in them, upon which an
alleged non-compliance might be founded. But the trouble of sup-
plying all the requisite enlargements, and the danger of omitting
some, has led to the almost universal adoption of a scale not
less than six chains to an inch. Some engineers use a five-chain
Y
346
RAILWAY SURVEYING.
scale for their plans, principally, because curves of any given
number of furlongs, or half furlongs radius, can be drawn by
curve rulers of some number of inches or half inches radius;
independent of which, a five-chain scale is a very pretty one;
but, as I have previously observed, the larger the scale, the greater
is the facility for detecting an error; and, therefore, as these plans
have generally to be prepared in a very great hurry, in the bad
weather and short days of the month of November, circumstances
favouring as much as possible the chances of error, the scale is
generally kept as small as the regulations permit, obviating the
enlargements.
When the plan is prepared, the course of the intended line is
delineated thereon, and this is an operation requiring great care
and circumspection. The trial section must be constantly con-
sulted, in order that the cuttings and embankments may balance
each other. Attention should also be given to the crossings of
roads. If two roads fork in the vicinity of the line, so that they
will each require to be crossed, an attempt should first be made to
cross them at the fork, so that one bridge may serve the two; or,
in the event of that being impracticable, a trial should be made to
divert each road a little, so as by that means to effect the object of
making one bridge serve the purpose.
A crooked river will very frequently traverse the same valley as
an intended railway; and there, again, a little scheming in laying
down the line on the map, may save the future expenditure of
large sums of money in building bridges, which might be required
were the line recklessly drawn.
Property possessing considerable local value, whether houses or
land, should be avoided, if a slight curve will do so, without run-
ning into worse ground for the section; but if this latter contin-
gency presents itself in opposition to the property, it will be found
more economical, as a general rule, to pay for land than works.
When the line is drawn on the plan, the limits of deviation fol-
low, either parallel thereto, or otherwise, as deemed expedient ;
then the line must be miled consecutively from one end to the
other. A memorandum must be entered under each curve of its
radius in furlongs and chains. The tunnels, if any, must be dis-
tinguished by a dotted line instead of a hard line; any diversion of
roads or rivers must be drawn, the necessary writing and reference
figures inserted, and then the plans are ready for deposit.
The plans completed, a section of the line will be carefully made,
in manner explained under the head of Levelling; after which
the Gradients must be determined.
Much diversity of opinion exists among engineers as to the ex-
RAILWAY SURVEYING.
347
pediency of making the attainment of easy gradients subservient
to economical considerations; but without discussing that subject
in this place, it may be observed, that our most eminent engineers
of the present day are constantly laying out severe gradients, as
well as curving lines, to save heavy cuttings and embankments-
1 in 80 being a very common inclination, while in one case which
has come under my notice in the present Session (1852-3,) 1 in 60
is laid out for a distance of upwards of six miles, with very little
intermission.
It has been previously remarked, that cuttings and embankments
should balance each other as nearly as may be, and that if a pre-
ponderancy exists, it should be of the latter rather than the former,
by reason of the facility with which side cuttings can in most in-
stances be resorted to. But other considerations present themselves.
It is at all times desirable to affect as little as possible the ex-
isting levels of public roads; an attempt should therefore be made
either to cross them on a level*, or to pass 20 feet above or below
them. It is decidedly advisable, if practicable, to lay out an as-
cending gradient from either way of the line towards a terminus,
station, or junction point. Such a gradient not only serves to
check the speed of a train when approaching such a point, but it
also assists it on its way when leaving. The nearer we can fulfil
these conditions in practice the better.
Where public roads are altered in level, a cross section is re-
quired to be deposited, shewing the nature of the alteration. The
level of any turnpike road must not be altered to a steeper rate of
inclination than 1 in 30, or of any other public road to 1 in 20.
The height of the railway over or depth under the surface of any
turnpike or public carriage road, navigable river, canal, or existing
railway, must be marked in figures at each crossing thereof, as well
as a memorandum made of the height and span of the bridge or
arches by which the crossing is proposed to be effected.
If the railway passes any turnpike, or public carriage road, or
railway, upon the same level, a memorandum to that effect must
be made upon the section. The section must be miled to corres-
pond with the plan, and a very full and explicit description of the
datum line must be noted thereon. All tunnels and viaducts must
be drawn upon the section, and the extreme height of every em-
bankment, or depth of cutting, when the same exceeds 5 feet, must
be marked. With the addition of the horizontal and vertical scale,
the section is complete. Plates 8 and 9 represent a map and
* Generally speaking a practice fraught with great danger to the public, saving
present outlay, at the cost of annual expenditure.
348
RAILWAY SURVEYING.
section, in accordance with the requirements of Standing Orders.
The Parliamentary deposits involving several copies, lithography
This is
is usually resorted to for the purpose of supplying them.
a very sore point with most engineers and surveyors; few there
are who cannot call to mind some case, many there are who have
experienced several, nay, are yearly experiencing them, in which
very excellent drawings have been entirely botched and placed
below par in their passage, through the office of the lithographer
in the last days of November. Some of the most anxious hours
of my professional life have been spent in these offices, alternating
between hope and fear, and speculating upon the probable chances
of the work being completed in time for deposit. Lithographers
rarely refuse works of this description, however many of them
they may have in hand; so well are they acquainted with the
absolute necessity of their completion by a certain time and the
safe pretext it affords for making a very heavy charge. I dare
say this is fair enough as a stroke of business policy, but I think
they should say when they have as much in hand as they can
creditably accomplish.
I do not assert that lithography and zincography are not admi-
rably adapted for this very purpose of multiplying copies of plans
and sections, if used as an art should be, and not abused; but speak-
ing from ample experience in both methods, I advisedly say, that if
time is short, and a sufficient number of assistants capable of making
tracings can be secured, with a man to mount them, the deposit of
mounted tracings will be found both economical and preferable.
It is easy to calculate the number of tracings of any one or more
sheets of drawing a clerk will make, in a given time, and it can
be done under the surveyor's own superintendence; but he cannot
know how long zincography will take to execute unless he knows
how many other works of a similar nature the lithographer has in
hand at the same time. The objection that in the case of tracings
they may not be all alike, does not well apply if they are carefully
made, and if they are mounted upon a preparation of white paper
mounted on holland, and are neatly drawn, they look very nicely.
The deposits duly made, the engineer has a rest on the 1st
December sweeter than can be realised by the non-experienced
reader. The work of serving the notices devolves upon the solicitors
and their local agents; but the engineer must furnish the information
for the notices, as to what properties are situated on the line as
laid out, and what are only within the limit of deviation; with
the nature of the works proposed to be constructed on such
properties.
The plans, sections, and book of reference being once deposited
RAILWAY SURVEYING.
349
become public documents to which any one may have access at
the Private Bill Office on payment of five shillings for an inspection
or one pound for the privilege of copying them. At the office of
the Clerk of the Peace of the County, the Documents may be
inspected for one shilling, or copied at a charge of one shilling an
hour for every hour during which a person is so engaged. This
publicity of the Deposited Documents, is further coupled with the
privilege to every person who may be specially affected by the
non-compliance with any standing order to appear, and to be heard
by themselves, their agents, and witnesses upon a memorial ad-
dressed to the examiner complaining of such non-compliance, pro-
vided the matter complained of be specifically stated in such
memorial, and the party so specially affected has signed the same
and shall not have withdrawn his signature thereto, and such
memorial has been duly deposited in the Private Bill Office. The
memorial complaining of the non-compliance with the standing
orders, if the same relate to the petition for a Bill numbered in
the General List of Petitions :--
From
1 to 100
101 to 200
وو
201 upwards
must be deposited
on or before
January 17
24
وو
31
before six o'clock in the evening of any day in which the house
shall sit, and before two o'clock on any day on which the house
shall not sit; and two copies of such memorial for the use of the
examiners must be deposited before twelve o'clock on the follow-
ing day.
The object of the Legislature in framing the standing orders,
and in granting these privileges was manifestly a very sound and
just one; affording, as they were evidently intended to do, the
means by which every landowner and occupier could ascertain the
exact extent and manner by which his particular interests would be
affected; at the same time giving him the legitimate means of
opposing the passage of the Bill through the House if he should
be hostile to its preamble, or dissatisfied with its provisions or
clauses.
The examination of the petitions for private Bills which have
been duly deposited in the Private Bill Office, commences on the
25th day of January, in such order, and in accordance with such
regulations as shall be made by the Speaker.
Seven days' notice is given by the Examiner in the Private Bill
Office, of the day appointed for the examination of each petition
and in case the promoters do not appear at the time appointed, the
examiner strikes the petition out of the list, and has no power to
re-insert it without the order of the House.
350
RAILWAY SURVEYING.
The examiner endorses upon the petition, a certificate of com-
pliance or non-compliance with the standing orders, and in the
event of the latter, he reports to the House the facts upon which
his decision is founded.
A description of the several stages by which a Railway Bill
passes through Parliament, is hardly in accordance with the in-
tentions of this paper; those who wish to acquaint themselves
fully upon the subject, can do so by reference to a "Treatise upon
Parliamentary Proceedings," lately published by Mr. May, one
of the Examiners.
Sec. 2.-Proceedings subsequent to the passing of the act.
The first operation after the passing of an Act of Parliament
authorising the formation of a railway is the carrying out a very
careful and particular survey and the preparation of an exceed-
ingly accurate map, plotted to a scale of two chains to an
inch, or some other large scale exhibiting faithfully every possible
detail. Upon this plan all the future works can be correctly laid
down, and the contents of the several lands required can be ac-
curately computed. When these plans are completed the line of
railway is carefully laid down thereon, either in the same course
as drawn on the deposited plans, or in such an altered direction
within the limits of deviation, as subsequent enquiries and a
less hurried examination may have suggested.
Now comes the important business of setting out the centre line.
To do this with accuracy is frequently a troublesome operation, de-
pending upon the nature of the ground. For, with the most accu-
rate plan, it is not always possible at the first attempt in a hilly or
a wooded country to range the long straight pieces of the line; if a
piece of rising ground can be found intermediate, from which both
ends can be seen, or any other two well defined points upon the plan
which can be exactly identified upon the land, the best course to
adopt will be to plant a theodolite or transit instrument upon
the high ground with which the line can be ranged towards either
end. Practice and experience are required to set out these straight
lines with accuracy. A person accustomed to the conduct of large
surveys will do this work much more readily than the constructive
engineer. It is always advisable, however long the staight lines
may be, to commence the ranging in the centre, and for this rea-
son; a very small deviation at the commencement, although too
minute to be detected on the Plan, would become clearly discern-
ible, and require correction if carried on and increased throughout
RAILWAY SURVEYING.
351
the whole line; but if the work commences in the centre this error
can at any rate only arrive at half the magnitude, and may possibly
to that extent be unimportant.
It is desirable, if possible, that the straight lines forming tan-
gents to curves, should be produced until they intersect each other,
where a flag staff should be erected as a permanent mark of refer-
ence throughout the construction of the works. This cannot often
be done, but the tangents should at all times be produced to some
spot beyond the works, whereon the pole may be erected, so that
its continuance may not interfere with or be likely to be disturbed
by the convenience of the landowners and occupiers.
The methods of setting out curves, to which I purpose to direct
attention here, are five in number. The three first are given by
Mr. Law, in Simms' Treatise on Levelling, the fourth is described
by Mr. Rankin, in a communication to the Institution of Civil
Engineers, and the fifth is a method suggested by myself, in a
Book of Tables, (published about five years since,) for setting out
slopes and curves. Mr. Law's first method is that which has in
practice, perhaps, been most extensively used, although it possesses
some objections which I shall point out in the sequel.
Let A B and C D, (fig. 1, plate 6) be the two straight portions of
the line, which it is desired to connect by a curve; B and C being
the two points at which the curve falls into the straight lines; and
let B b₁, b₁ b₂, b₂ b3, &c., be the distance which it is desired that the
points to be found in the curve shall be apart. Then measure
upon the straight line A B produced, the distance B a₁, equal è̟, in
formula IV below, and from the point a₁, set off, perpendicular to
the same line, the distance a, b, equal to o₁, in formula III,
which will give the first point required in the curve; then range
a straight line through the points B, b₁, and upon this line lay off
the distance b₁, a2, equal to d2, in formula VI, and from the point
a set off perpendicular to the line B a₂, the distance a2, b2, equal to
02 in formula V, and the point b₂ will be the second point in the
curve; then in a similar manner range another line through the
points b₁ b₂, upon which measure the distance b₂ as equal to the
distance 2 or b₁ a2, and from a, set off as before, perpendicular to
the line b₁ as, the distance a, b, equal to 02, which will determine the
third point in the curve; and thus proceed until the whole extent
of the curve has been set out.
3
2
In order to obtain the values of 81, 82, 01 and 02, let r equal the
radius and d equal the distance B b₁, or b₁ b₂, &c., which it is de-
sired that the points found in the curve shall be apart, (both
expressed in feet); then
352
RAILWAY SURVEYING.
d²
III.
IV.
V.
VI.
= 01
01 ·
2 r
√ d²-0²
d 81
=02
d (r ·
01)
= 8
82.
ጥ
As an example of the application of this method, let the radius
of the curve (r) be 15 chains or 990 feet, and the distance B b₁ (d)
one chain or 66 feet; then from formula III
662
2 x 990
=
2.2 feet = 01
will be the first offset at a₁; and
2.2265·963 feet = di
√ 66² — 2.22
will be the distance Ba₁, to be laid off upon the line A B produced
to give the place for this offset.
66 × 65.963
990
Again,
=4.397 feet = 02
will be the offset at a₂, a,, a₁, &c.; and
66 × (990-2.2)
990
= 65.85 feet 82
will be the distance b₁, a2, b₂ as, &c., to be measured from the
points b₁, b₂, &c., in order to give the points a₂, ɑ3, ɑ4, &c., from
which the offsets o, are to be taken.
To this method there are, as has been already stated, some prac-
tical objections, inasmuch as any error which may be committed
in setting out only one of the points in the curve, will occasion a
corresponding error in every succeeding one; and a very trifling
inaccuracy in calculating either the distance 82, or the length of the
offset 02, from its being frequently repeated, may ultimately cause
a very considerable deviation from the true curve. Both these
objections, however, may be in a great measure removed by the
adoption of the following method of checking the position of about
every fifth point; or which would be better, first determining the
position of these points, and then filling in the intermediate ones;
and as I consider this modification does away almost entirely with
the above mentioned sources of error, I shall give an example of
its application.
2
Suppose r and d, or the radius, and the distance the points
B, b₁, b₂ &c., are apart (see fig. 2, plate 6) to be the same as in the
last example, viz., 990 feet and 66 feet respectively, and let it be
determined to check the position of every fourth point: then the
RAILWAY SURVEYING.
353
19
values of 81, 82, 01 and 02, will be the same as before; but previous
to setting out points b₁, b₂, bg, &c., we must calculate the distance
BB₁, to be measured along the line A B produced, and the distance
B₁, b₁, to be set off from the point B₁ to give the position of the
fourth point (64) in the curve: which may be done as follows: Let
the distance B B, equal A and B, b, equal 0,; and let D, be the
length of the chord line connecting the two points B and b₁, and ß
be the angle a, B b₁; then
1
4
1
1
and
01 rad
d
sin 6,
2r sin 4 ß- D₁.
rad
2
2
Then, by substituting D₁, O1, and A, for d, 0, and 8, in the for-
δι 1
mulæ III, IV, V, and VI, we shall obtain the values of O₁, ▷19
O2 and 2, where ▷ is the distance b₁ B₂ to be measured upon the
chord line B₁ b4 produced, and O2 is the distance B₂ b, to be set off
from B, in order to give the eighth point (bs) in the curve; for the
values of r and d given above we shall obtain
Log of o
Log rad
0.342423 = 2.2
= 10·000000
Log of d
Log sin of ẞ
and ẞ = 1° 54′ 37″; then
Log of 2 r
Log sin of 4 ß
||
10.342423
1·819544 = 66
8.522879
3.296665
=
1980
7° 38′ 28″
9.123745
12.420410
Log rad
= 10.000000
2·420410 = 263·27.
Log of D₁
Then from formula III,
263.272
= 35 feet = O₁;
2 × 990
from formula IV,
√ 263·27² — 352
= 260·92 feet = ▷ 1;
from formula V,
263·27 × 260·92
990
69.4 =
O2;
and from formula VI,
263.27 × (990 - 35)
= 253·96 =▷ 2.
990
354
RAILWAY SURVEYING.
These being obtained, the position of every fourth point, b₁, bɛ, b,
&c., should be first determined by the dimensions 41, O₁, 42, and
O2; and then the intermediate points, b₁, b₂, bз, bы, bε, &c., by d1, 01,
2, and 02, as first described.
The second method which I shall describe may be advan-
tageously employed when the radius of curvature is large and the
centre can be seen from every part of the curve.
Let the lines (fig. 3, plate 6) A B and C D, as before, repre-
sent the two straight portions of the line required to be connected
by a curve having a radius of 80 chains or 1 mile. First, set up a
theodolite at B and another at C (the two terminations of the
straight portions of the line) and from each point range a line at
right angles to the lines A B and C D respectively, and at the in-
tersection of these lines (E) which will be the centre of the curve,
put up a signal sufficiently conspicuous to be seen from any point
between B and C: then produce the straight lines A B and CD
until they intersect in the point F, and on these lines drive in
stakes at equal distances, a1, a2, as, &c., commencing from the points
B and C. If r equal the radius, and ♪ equal the distance between
the points a, a, a,, &c., both in feet, then
✓ p² + №²
r = 019
will be the distance which must be set off from the first point a1,
not perpendicular to the line B F, but in the direction a, E; in
like manner
√ p² + 2 ô² — r
r = 029
1
will be the distance to be set off from the point a, in the direction
a, E; and generally
√ p² + n s ² — r — On,
will be the distance to be set off at the nth points from
B and C.
For example, let r be 5280 feet and ♪ equal 100 feet; then
528094 feet = 01
✔ 5280² + 1002
will be the distance a₁ b₁, which must be set off from a₁ in the direc-
tion a₁ E to obtain the first point b₁ in the curve, and proceeding
in a similar manner with the others, the following table will exhibit
the distances to be set off at the respective points a1, a2, as, &c.
At a or 100 feet from B, the offset will be
•94 feet
3.79
02
аз
200
300
""
8.52
وو
وو
15.13
400
""
""
23.62
α5
500
""
وو
33.98
α6
600
""
>>
RAILWAY SURVEYING.
355
At a or 700 feet from B, the offset will be 46.19
Ag
800
ag
900
"
α10
1000
وو
1100
a12
1200
a13
1300
α14
1400
α15
1500
وو
وو
60.26
76.16
"
93.86
113.36
""
134.65
157.68
182.45
وو
208.93
وو
وو
وو
وو
وو
وو
If the extent of the curve is such that the length of the offsets
before reaching the point F where the two tangent lines intersect
become inconveniently long, so as to occasion a loss of time in
setting them off, it will be advisable to make use of another tan-
gent line as shewn at G I, fig. 4, plate 7; for determining the
position of which line the following method may be made use of.
Let r, as before, be the radius, & the number of degrees contained
by the angle BEC, and n the number of tangent lines (as B G,
G H, HI, IC) intended to be employed; then
ε
&
r sin
n
COS
ε
n
will equal the length of any one of these tangent lines. As an
example, let r equal 5280 feet, & equal 60°, and n equal 4; then
Log of r
Log sin
ε
N
ε
Log cos
2
= 3·722634 = 5280
= 9.412996 = 15°
13.135630
= 9.984944
3.150686 = 1414.8 feet
will be the length of the lines B G, GH, &c.
Now having ascertained this length, nothing more remains than
to set it off from B, and C towards F, and then to range a line GI
from the two points thus obtained, which will be the required tan-
gent line: this line must then be bisected in the point H, which
may readily be done by ranging a line from F to E, which having
been done, proceed as already described to set off the equal dis-
tances α₁, ɑ2, ɑs, &c. from B and H towards G, and from H and C
towards I; and then by setting off the distances a₁ b₁, a₂ b₂, &c.
contained in the Table already given, from the several points
356
RAILWAY SURVEYING.
a1, a2, &c., in directions radiating to the centre E, the course of the
curve will be marked by the points b₁, b₂, b, &c. thus obtained.
One advantage possessed by the above method is, that knowing
exactly the direction in which to lay off the offsets, (and that by
the range of a comparatively distant object,) the errors which have
frequently arisen from their not having been set off perpen-
dicularly, where the eye has been the only criterion, are entirely
obviated; and this method is also entirely free from the objections
made to the former method.
When the centre point E cannot be seen from every part of the
curve, so as to allow of the offsets been laid off radially, the more
usual method may be adopted of laying off the offsets perpen-
dicularly to the tangent B F, but in this case a cross staff should
always be employed to insure accuracy, and the distances to be set
off from the points a₁, a₂, as, &c. will be greater than those em-
ployed in the previous method, and must be calculated from the
formula
2
✔ p²
d2
01
instead of that given at page 355.
The third method is most applicable where the radius of the curve
is small as compared with its extent, and is deduced from the
well known theorem, that all angles contained in the same seg-
ment of a circle are equal to one another.* The method is as
follows:-place a theodolite at B and another at C, (fig. 5,
plate 7) the two terminations of the straight portions of the line,
setting the telescope of the instrument at B on C, and that at C
on F, the point of intersection of the lines A B and CD pro-
duced; then if the former be moved through an arc of any
number of degrees, towards F, and the latter the same number of
degrees towards B, the point a₁, where the lines of collimation of
the two telescopes intersect, will be a point in the curve; now let
both theodolites be again moved the same number of degrees and
in the same directions as before, and their axes produced, or lines
of collimation, will again intersect at a2, another point in the curve;
and in fact, to whatever extent the theodolites are moved, so long
as the arc described is equal in both, the point of their intersection
will always be in the required curve. Or more generally, suppose
the two theodolites to be placed as first described, and then
simultaneously to commence to revolve with the same uniform
angular velocity, the point of intersection of their lines of col-
limation will describe the circular arc C, ɑ1, ɑ2, ɑз,
B; and
in equal intervals of time, equal portions of the arc will be de-
scribed, which will be half as great as the arc, which would have
* Euclid, Book III. prop. 21.
RAILWAY SURVEYING.
357
been described in the same time, by the same angular velocity, at
the centre of the circle (E); from which last mentioned circum-
stance, we may readily calculate the magnitude of the angle
through which the theodolites at B and C must be successively
moved, in order that the points a1, a2, a,, &c., at which their axes
intersect, may be at the distance apart which it is desired that
they should be. If r equal the radius of the curve, d the required
distance, and ẞ the angle a, B C; then
d rad
2 r
sin ß
VII.
As an example of the application of this method, let r equal 20
chains, or 1320 feet, and let it be required to determine points in
the curve at distances of about 100 feet; now from the above
formula we shall obtain
Log d
Log rad
Log 2 r
Log sin &
2.000000
100
10.000000
12.000000
=
3.421604
2640
8.578396
2° 10' 15"
As it would be inconvenient, however, in practice, to lay off so
frequently as would be required an angle, with odd minutes and
seconds, we may instead of the above take an angle of 2 degrees,
which will make the distance d equal 92.13 feet. Having thus
determined the angle, and placed the theodolites as previously de-
scribed, viz., that at B in the direction of B C, and that at C in the
direction CF; the former must be moved 2° towards F, and the
latter 2° towards B, and a stake driven down at their point of
intersection a₁, the former must then be removed 2º more towards
F, and the latter 2° towards B, and another stake put down at
their point of intersection a,, and so on until the theodolite at B,
is brought to the direction B F, and that at C to the direction C B,
when the whole of the curve will have been staked out as required
the stakes being 92.13 feet apart. This method, the same as the
last is not liable to the objections that the first method was, and
in addition possesses the very important practical advantage, that
its accuracy is entirely independent of any undulation or change of
level in the surface of the ground, an advantage which is not pos-
sessed by any of the other methods which I have described, the
whole of which would require to have the distances and offsets cor-
rected in proportion to the slope of the surface of the ground. In
a hilly country-and it is in such districts that curves most fre-
quently occur-this circumstance will render the last described
method far superior to either of those which precede it.
358
RAILWAY SURVEYING.
The next method which I shall give, is that described by Mr.
Rankin, in a communication to the Institution of Civil Engineers,
and depends on the theorem* that the angle, subtended by any arc
of a circle at the centre of the circle, is double the angle subtended
by the same arc at any point in the circumference of the circle.
The method of proceeding is as follows:-first place a theodolite at
B (fig. 6, plate 7) the point where the curve commences; and
then lay off from the line B F, the angle B, calculated from for-
mula VII, (supposing, as before, r to represent the radius of the
curve, and d the distance required between the points in the curve,)
and in the direction of the axis of the instrument set off the dis-
tance d, which will give the first point a, in the curve; in the same
manner lay off from B F the angle 26, and from a₁ set off the same
distance d, and the point where it cuts the axis of the instrument
produced will be the second point a2; and generally by laying off
the angle n ẞ, and setting off from the proceeding point am, the
distance d, the point a will be given.
As an example of the application of this method, let r equal 19
chains, or 1254 feet, and d equal 100 feet; then from formula VII
we obtain
Log d
Log rad.
Log 2 r
Log sin ß
|| ||
2.000000
100
=
10.000000
12.000000
3.399328
2508
2° 17' 6"
||
8.600672
then having placed the theodolite at the point B, lay off this angle
2° 17' 6" from the line B F, and upon the line B a, thus obtained
set off 100 feet, which will give the first point in the curve a₁; then
with an angle of 4° 34′ 12″ or 2 ẞ set off another 100 feet from a₁,
which will give the second point a2, and thus proceed, until the
whole extent of the curve has been set out.
The last method I extract from my own Work upon the subject.
"Suppose we have arrived, by a piece of straight work, at the
commencement of a curve, of 80 chains radius, which for demon-
stration we will call point A, (fig. 173f); the first proceeding is to
produce the straight line or tangent, one chain to C; then turning
to the tables (as hereafter explained) we find the single offset
CD = 4.9 inches; this must be very exactly set off at right angles
(in the first case only) with the tangent AC to D, which becomes
a point in the curve. We now produce AD, one chain to E.
Then turning again to the tables, we ascertain the double offset,
* Euclid, book III, prop. 20.
RAILWAY SURVEYING.
359
(as the single offset serves only to connect the tangent with the
curve,) to be 9.9 inches; so with one handle of the chain held
firmly at D, and one end of a tape held at E, we proceed to make
DF = one chain; and E F = 9.9 inches; and F is another point
in the curve. We then produce DF in the same manner as A D,
and so on throughout to the end of the curve;-always bearing
in mind that the tangent leaves the curve as it came on, with the
single or half offset, as shewn at I.
The above method requires some further test to ensure complete
accuracy, as explained with reference to the first method.
We will again suppose ourselves at the commencement of the
curve, which we will now consider point A, fig. 173g; produce the
straight line ten chains to C; there erect a perpendicular,* which,
on reference to the tables, we find to be 62.7 links, and being
accurately set off, we obtain D, a point in the curve.
In measuring the ten chains A C, reference is required to the
tables to ascertain the point B at which the next tangent inter-
sects, and which is found to be 502 links from A, at which point
a mark should be set up.
If we produce a line formed by the points B and D, ten chains
from D to F, we have a new tangent DF with which to proceed
in the same manner as with A C: and so on throughout the con-
tinuance of the curve.
The dimensions A C and C D, D F and F G, &c., corresponding
respectively with the sine and versed sine of the curve, and being
of sufficient length to bear a comparison with the radius, must
obviously subtend to great accuracy.
The tables afford one other test, by giving the angles CBD,
FEG, &c., between the intersecting tangents, in our illustra-
tion, 7° 10′ 50″
Example.
It is required to set out a curve of 20 chains radius:
Seek in the column headed "radius" in the tables, 20 chains, then
opposite the radius in
1-ft. 7.8 inches.
Column 2, is the single offset CD, fig. 173ƒ,
Column 3, is the double offset E F, fig. 173f, = 3-ft. 3.6 inches.
Column 4, is the perpendicular CD, fig. 173g, at 10 chains on the
tangent A C=267.9 links.
Column 5, is the distance A B on the old tangent A C, at which
the new tangent B F intersects 536 links; and in
Column 6, is the angle C B D, fig. 173g, formed by the intersec-
tion of the old and new tangents = 30 deg.
* This perpendicular being of some length is calculated in the tables to links, as
more easily measured with a chain than a tape.
360
RAILWAY SURVEYING.

TABLES FOR SETTING OUT CURVES.
RADIUS.
SINGLE OFFSET
AT 1 CHAIN ON
TANGENT.
DOUBLE OFFSET
AT 1 CHAIN ON
TANGENT.
PERPENDICULAR
OFFSET AT 10
CHAINS ON TAN-
GENT; OR COR-
RESPONDING
VERSED SINE.
DISTANCE ON
THE OLD TAN-
GENT AT
WHICH THE
NEW ONE
INTERSECTS.
ANGLE FORMED
BY THE INTER-
SECTION OF THE
OLD AND NEW
TANGENTS.
Chains. Feet. Inches. Feet. Inches.
Links.
Links. Deg.Min. Sec.
10
3 3.6
6 7.2
1000.
1000
90 0 0
11
3 0.
6 0.
641.7
706
65 22 34
12
2 9.
5 6.
536.6
644
56 26 33
13
2 6.4
5 0.9
469.3
610
50 17
5
14
2
4.2
4 8.5
420.2
588
45 35 4
15
2 2.4
4 4.8
381.9
573
41 48 37
16
2 0.7
4 1.5
351.
562
38 40 55
17
1 11.3
3 10.6
325.2
553
36 1 54
18
1 10.
3 8.
303.3
546
33 44 56
19
1
8.8
3 5.6
284.4
540
31
45 24
20
1 7.8
3 3.6
267.9
536
30
0 0
25
1 3.8
2 7.6
208.7
522
23 34 41
30
1 1.2
2 2.4
171.5
515
19 28 16
35
0 11.3
1 10.6
145.9
511
16 36 5
40
0 9.9
1
7.8
127.
508
14 28 39
45
0 8.8
1 5.6
112.5
506
12 50 22
50
0 7.9
1 3.8
101.
505
11 32 13
55
0 7.2
1 2.4
91.6
504
10 28 32
60
0 6.6
1 1.2
83.9
503
9 35 38
65
0 6.
1 0.1
77.3
503
8
50 58
70
0 5.6
0 11.3
71.8
502
8
12 47
75
0 5.2
0 10.5
66.9
502
7 39 44
80
0 4.9
0 9.9
62.7
502
7 10 50
Miles. Fur.
1 1
0 4.4
0 8.8
55.7
502
6 22 45
1
2
0 3.9
0 7.9
50.1
501
5 44 21
1 3
0 3.6
0 7.2
45.5
501
5 12 57
1 4
0 3.3
0 6.6
41.7
501
4 46 48
1
5
0 3.
0 6.
38.8
500
4 24 42
1 6
0 2.8
0 5.6
35.7
500
4 5 45
1 7
0 2.6
0 5.2
33.3
500
3 49 21
2 0
0 2.4
0 4.9
31.2
500
3 35
35 0
2 2
0 2.2
0 4.4
27.8
500
3 11 5
2 4
0 1.9
0 3.9
25.
500
2 51
51 57
2 6
0
1.8
0 3.6
22.7
499
2 36 18
3 0
0 1.6
0 3.3
20.8
499
2 23 16
RAILWAY SURVEYING.
361
Having now given several methods by one or other of which
all curves may be correctly set out, the object of my paper has been
satisfied. I might have gone at some length into the absolute ne-
cessity for all curves to be truly tangential to the straight work, as
well as to each other; the practical tests that are required when
working from an incorrect map (although as a surveyor I am bound
to say the map should, in all cases, and for many reasons, be a very
good one,) but I have felt that I could not do so without going still
further, and perfecting, what is not at all intended, a complete trea-
tise on the subject. I venture to suggest that much future eco-
nomy always depends upon the manner in which the curves of a
railway are originally laid out; to say nothing of the jerks and un-
pleasant oscillations to which the passengers are subjected if they
are untrue, or the danger by that means incurred.
As soon as the line is set out, a square peg, about two and a half
inches in section, and two feet long, should be driven into the
ground about twenty inches, at intervals of a chain, very carefully
and correctly measured from one of the termini, and between each
of these pegs a triangular sod, about ten inches wide, should be cut
out, and this is what is called "nicking out."
I should observe, that at the tangent points of the curves a peg
should be driven in, although they may not fall at an equal chain's
length; and to secure the certainty of finding the exact point at a
future occasion, a peg should be driven into some place where it
may remain undisturbed, on either side of the line, directly at right
angles with the tangent.
When the line is stumped and nicked out, we prepare for making
the "Working Section," by driving into the ground by the side of
each of the chain stumps a peg for the levelling staff to stand upon.
These pegs should be about fifteen inches long and two and a half
inches square, and should be driven into the ground level with the
surface.
The levels are then minutely taken at each chain, or oftener if
any variation in the ground between the chain pegs require it, and
for the purposes of the method I am about to describe for setting
out the slopes, a reading should be also obtained from the staff,
held at fifty links from the centre peg on either side of the line.
This extra reading furnishes the rate of inclination per chain of the
cross section. What are called permanent posts, for B. Ms. of refe-
rence during the execution of the works, should be fixed at înter-
vals, as the levelling proceeds in situations not likely to be dis-
turbed. They may be about four feet in length, should be hooped
at top to prevent them from splitting, and should have an iron plate
Z
362
RAILWAY SURVEYING.
on the top of them for the staff to stand upon. To these B. Ms.
the levels must be very accurately proved. Plate 11 is a specimen
of a working section.
When the working section is completed, the gradients may be
carefully laid on. Two lines will be required to be drawn upon the
section: the upper one representing the top surface of rails when
laid, and the lower one exactly two feet below the other one,
the line which is called the "Formation Level," that is the line to
which the cuttings and embankments have to be constructed.
Engineers generally insert upon their working sections two sets
of figures—some shewing the height of the formation level at every
chain above the datum line, and the depth of cutting or height of
embankment; others shewing the heights of the level pegs above the
datum line at the surface of the ground, and the depths of cuttings
or height of embankments. In my opinion, the section should ex-
hibit all three, viz., first, the height of the surface peg above the
datum line; secondly, the height of the formation level above
datum at every chain, arrived at by calculation; and, thirdly, the
depth of cutting or height of embankment, arrived at by the sub-
traction of the first and second row of figures, the one from the
other.
On Setting out the Widths of Ground required for the Works of a
Railway or Canal, &c., &c.
I shall give two methods of setting out slopes. The first will
be the same as given in Simms' Levelling. The second is extracted
from Tables published by myself, under the title of the Civil
Engineers' and Surveyors' Assistant, in setting out Slopes, Curves,
Cuttings, and Embankments.
MR. SIMMS' METHOD.
When the natural surface of the ground, both longitudinally and
transversely, is upon the same level as that of the intended works,
the process of setting and staking out the widths is very simple.
Let us take, for example, the case of a railway, the base or bottom
width of which, when prepared for the reception of the ballasting
and permanent way, is to be 36 feet; the ratio of the inclination,
or batter, of the slopes to the heights, both in the cuttings and the
embankments, to be 2 to 1; beyond which, or at the outward edge,
a slip of land 12 feet wide is to be taken on each side of the rail-
way for the fences, &c. First, the centre line must be staked out
RAILWAY SURVEYING.
363
and carefully levelled: it is customary to drive a stake about 2 feet
long, and about 1½ inches square, into the ground at each chain's
length, their tops to be upon the fair level of the natural surface,
thus affording good stations for the levelling staves to be held
upon; the relative level of each stake being then very accurately
determined with respect to some given datum, they become so
many zero points for reference in the subsequent operations. From
each of the centre stakes a line must be set out on both sides, and
at right angles to the centre line, or at right angles to a tangent to
the centre line at that point, if the centre line be curved; upon
these transverse lines the required widths of land must be set out.
Now, if the ground at any of the centre stakes is upon the same
level as the intended base of the railway, nothing more will be re-
quired than to measure on each transverse line, and in both direc-
tions from the centre stake, one-half the required width, which, in
our supposed case, is 18 feet for the half width of the railway, and
12 feet for the fences, in all 30 feet on each side of the centre.
But when, as it mostly happens, the ground is not on the proposed
level of the railway, the operation is not quite so simple; and if,
in addition thereto, the ground slopes sidewise or at right angles to
the general direction of the line, the business is still more compli-
cated, and requires some skill and care to do the work correctly.
The method of doing this is our business to explain.
The next most simple case to the above is when the cross sec-
tion of the ground is horizontal, be the depth of cutting or height
of embankment what it may.
This is shewn in fig. 173h, which represents a cross section
of a 20 feet cutting with slopes of two horizontal to one per-
pendicular. The horizontal line at AB right angles to the
centre line represents the natural surface of the ground. Under
these circumstances it will readily be seen that the half width of
the cutting, or the distance from the centre to the edge of the
slopes C and D, equals the half width of the base (18) added to the
batter of the sloping sides (40), and including the 12 feet for the
fences, the total half width of land required for the purposes of
such railway would be 18+ 40+12= 70 feet, and consequently
the whole required width to be so appropriated and fenced in for
a 20 feet cutting or embankment, when the ground does not slope
sidewise, would be 140 feet.
The next and more complicated, and also the most frequently
occurring case, is, when the cross section of the natural surface
is not horizontal, as shewn in the annexed diagram, which also
represents a cutting of 20 feet.
364
RAILWAY SURVEYING.
Let the line AB represent a horizontal line, passing through
the centre line C of the railway, which, if it
coincided with the surface of the ground
would give AC and CB (each half width)
70 feet, as in the former example, the depth
of cutting and the slopes being assumed the

same.
Let the line E H represent the natural
surface of the ground upon this transverse
section; it will readily be perceived that the
real half width CE (on the left of the diagram)
is much shorter than the horizontal or com-
puted half width A C, because the ground-
line is depressed on that side of the centre;
likewise the half width C H on the other side
of the centre is greater than the said horizon-
tal or computed half width, because the
ground is there elevated above the horizontal
line A B passing through the centre. To de-
termine exactly the distances CE and CH
in actual operations in the field, would be
attended with some difficulty, and consume
much time; but the following method, which
at the same time that it gives a sufficiently
correct approximation in practice, is also a
very expeditious one.
H
to 1
B
Centre 008
ૐ
A
F
E 2 to 1
Let us suppose that the point E or dis-
tance CE be known, and that with a spirit
level we determine the difference of level
between the points C and E, this difference
is represented by the line E F, which sup-
pose to be one foot; now we have a small right angled triangle
A EF, of which E F is determined, being the difference of level
(one foot), and the slope or ratio of AF to E F also given, (2 to
1,) therefore the side A F is known (2 feet,) which subtracted from
the computed half width A C, leaves FC approximately equal to
EC, the required half width, sufficiently exact for all practical
purposes, where the cross section of the ground does not differ
materially from a horizontal line.
We have been supposing that the point E is known, whereas
that point is the object of our search; in practice, therefore, we
proceed thus:—take the computed half width, and if the ground is
depressed, let a levelling staff be held somewhat nearer the point C
36
>
RAILWAY SURVEYING.
365
than the said computed half width, for a first approximation to the
point E; then determine the difference of level between this as-
sumed point and the centre point C, multiply this difference of level by
the ratio of the slopes, (which doubles it when the slope is 2 to 1,) and
subtract the result from the computed half width, which gives a
more correct approximation to the point E; now hold the staff at
this new point and find the difference of level as before; again mul-
tiply by the ratio of the slopes, and deduct the result from the
computed half width, which second result will in most cases be
sufficiently near the real half width for a depressed line for all prac-
tical purposes.
Example.-Central height (or depth of cutting), 20 feet, slopes
2 to 1, base 36 feet, the computed half width was therefore 58 feet ;
the ground being depressed, we estimated that the point E might
fall short of the computed half width 2 feet; we therefore directed
a levelling staff to be held at 56 feet from the centre line (or stake)
C, at which point another staff was held, and by means of a spirit
level set up at a convenient distance, we found the difference of
level between these points to be 0.87 feet, which multiplied by the
ratio of the slopes 2 to 1, gave 1.74 feet to be subtracted from the
computed half width 58 feet, leaving 56.26 feet for a first approxi-
mation to the half width CE (see last diagram.) Now, upon re-
moving the staff to this new point, the difference of level was again
taken, (or rather we should say that the staff was again read off as
the level had not been disturbed,) and found to be 0.91 feet, which
also multiplied by the ratio of the slopes (2 to 1), gave 1.82 feet to
be subtracted from 58 feet, leaving 56.18 for the second approxi-
mation, and which was adopted as the correct half width for the
depressed side of the centre; indeed, in such a case as is above
given, where the ground is so nearly horizontal, the first approxi-
mation (taken by a person after a little practice) may be assumed
as the correct result, for in the above example it differed but 08
from the second determination, and if it had been taken a third
time, it could not have been more accurate as far as practice is con-
cerned: this, however, is not the case where the inclination or slope
of the ground is considerable, for then (if this method be followed)
several approximations will be necessary to bring the result within
admissible limits.
When the ground is elevated above the horizontal line, as shewn
on the right hand of the diagram, the mode of procedure will some-
what differ: thus, instead of holding the staff and finding the dif-
ference of level at a less distance than the computed half width, it
must be held at a greater distance to obtain the point H by approxi-
366
RAILWAY SURVEYING.
mation, the difference of level between that point and the centre
point C being equal to H I, and multiplied by the ratio of the
slopes will give the distance BI to be added to the computed half
width CB, to obtain the half width C H; this may likewise be re-
peated to obtain a more correct result as described for the other,
or depressed side of the centre C. It will also here be obvious to
a person possessing but the smallest share of mathematical know-
ledge, that this result is not strictly correct, inasmuch as the line
C H can never be equal to CI, but for practical purposes it is, as
before observed, sufficiently correct. It may not be altogether un-
necessary to observe, in this place, that the corrections B I, &c.,
as shewn in the foregoing diagrams, are much exaggerated, being
far greater in proportion to the computed half width CB, than
ever occurs in ordinary practice, but this has
been done to make our explanations more
distinct than otherwise.
The above particulars have been confined
to the case of excavations; we must now
shew in what the process differs when the
ground is to be covered with an embank-
ment.
By reversing fig. 173h, it then represents
an embankment. The rule for finding the
half width for an embankment where the
transverse section of the ground is horizontal,
remains the same as for the cuttings under
like circumstances, as may be seen by an
inspection of the inverted figure, but upon
inverting the second diagram, it will at once
be seen that some variation in the process is
required. Thus :—
The horizontal line is represented by that
marked AB; C D and CF the computed
half widths; CE the required half width on
the depressed side, and CH the required
half width on the elevated side, the line KL
representing the natural surface of the
ground. In the case of an excavation, we
have shewn that the real half width is greater
on the elevated side than the computed half
width, and less on the depressed side; but it
will be seen by the diagram that for an
embankment the real half widths are less on the

E
2 to 1
< 18
2 K-20 v
B
F
**
H
RAILWAY SURVEYING.
367
elevated side, and greater on the depressed side than the said com-
puted half widths; therefore, in determining the approximate
place of the point E on the depressed side for an embankment,
the staff must be held further from the centre than the computed
half width; and for the point H or the elevated side, it must
be held nearer to the centre than the computed half width; and
finally, for computing the real half widths from the differences of
level between the points E and the centre, and H and the centre,
on the depressed side the difference of level multiplied by the ratio
of the slopes is to be added to the computed half widths to obtain
the point E, and to be subtracted from the computed half widths to
obtain the point H.
The process above described may appear to the reader a very
tedious one; it perhaps is so to read, but a little practice will
convince him that it is a very expeditious method, for in most
cases one setting up of the level will answer for several stations,
and the multiplications by the ratio of the slopes upon such
small numbers as mostly occur is easily performed, especially
if it be an even number as 2 to 1. The columns of the Field
Book may be arranged as in the following example for making
the calculations in the field, or may be abridged to suit a more
convenient-sized book for the pocket, at the pleasure of the
surveyor; indeed, all that can be accomplished now of this kind is
to give general rules which can be altered and arranged to suit
the convenience of the surveyor, as experience may point out a
more suitable mode of proceeding. The example is taken from an
extensive field operation by the writer, and shews the work both
for a cutting and an embankment; the change from one to the
other, or the tailing out of the cutting, as it is called, being in-
cluded therein. The slope of the cutting is calculated at 1½ to 1,
and that of the embankment at 2 to 1. The width of the railway
was 36 feet, consequently half the said width was 18 feet.
368
RAILWAY SURVEYING.

No. of Stake.
Depth of Cutting
or Embankment.
Computed half
width.
Section or Level Readings at
right angles to Line.
EXAMPLE.
Difference of Level.
+
South. Centre.
North.
South.
North.
South.
North.
South.
North.
Difference of Level,
ratio of Slope.
X
+
EMBANKMENT.
Feet. Feet.
285 16.97 51.94 10.90
Feet.
Feet.
Feet.
Feet.
7.50
3.96
+ 3·40
286 1.43 20.86
7.06
4.74
3.24
+ 2.32
Feet.
3.54
0.07}
Feet.
Feet.
Feet.
Feet.
+ 6·80
- 7.08
58.74
44.86
287 2.77 23.54
8.00
5.80
4.26
+ 2.20
+0.077
1.50
1.54
+ 4·64
+ 0.11
25.50 | 20.97
+ 4·40
3.08
27.94 20.46
288
3.0624.12
8.82
6.42
5.12
+ 2·40
289
2.0122.02
7.02 5.13 3.74
+1.89
- 1.30
1.39
+ 4.80
- 2.60
28.92
21.52
+ 3.78
2.78
25.80
19.24
290
1.22 20.44
291 1.91 21.82
6.00 4.10 2.76
7.52 6.95 5.20
+1.90
+ 0.57
{+0.12}}
1.34 S
1.75
+ 3·80
+ 0·18
24.24 20.62
+ 1·14
I
CUTTING.
292 1.39 20-7812-20 11.35 10.52
-0.85
+ 0.83
- 1.27
293 4.51 27.02
9.56 7.98 6.22
- 1.58
+1.76
- 2.37
+ 2·64
3.50 22.96 18.32
+1.24 || 19.51 | 22-02
24.65
29.66
294 5.72 29.44
8.40 6.52
4.27
-1.88
+2.25
- 2.82
295 6.85 31.70
7.06
5.10
3.02
· 1.96
+ 2·08
- 2.94
296 8.61 35.22
7.53
5.28
2.76
- 2.25
+ 2.52
3.37
+++
+ 3·37
26.62 |
32.81
+ 3.12
28.76 | 34.82
+ 3.78
31.85
39.00
Required half
width for edge of
Cutting or foot of
Embankment.
The first column contains the number of the
central stakes
The second column contains the depth of cutting or the height
of embankment, as the case may be, at that point on the centre
line.
The third column, the computed half width from the centre line
to the edge of the cutting, or foot of embankment, upon the sup-
position that the ground is horizontal at right angles to the centre
reckoned from the commencement of the work, which are conve-
nient for reference.
RAILWAY SURVEYING.
369
line, this half width, as before explained, is found by multiplying
the central height by the ratio of the slopes, and adding to the
product half the width at the base of the railway.
The fourth, fifth, and sixth columns contain the readings from
the levelling staves at the centre stake, and at the approximate
points E and H, (see last diagram.)
The seventh and eighth columns contain the differences of level
between the centre stake and the above approximate points. These
numbers are simply the differences of the quantities in the three
preceding columns, (except at stakes 286 and 290, which we shall
presently explain,) and the signs + or - denote whether they are
positive or negative quantities as respects the centre, and the
approximate points E and H.
The ninth and tenth columns contain the differences of level
(contained in columns 7 and 8) multiplied by the ratio of the
slopes, and must have the same signs or as the corresponding
numbers in the preceding columns.
+
The last two columns contain the final half widths, obtained by
adding or subtracting, according to the prefixed signs + or, the
numbers in the two preceding columns to the computed half width
contained in column 3.
After the explanations already given, the reader can find no
difficulty in tracing the steps of the example, except perhaps with
the stakes 286 and 290, where the difference of level on the north
side is represented by two numbers bracketed tegether, one having
the sign + and the other : for the stake 286 the real difference
of level on the north side the centre is a rise of 150, that is, the
approximate point H is 1.50 feet above the centre stake: but it
happens that the height of the embankment itself at that point is to
be but 1.43 feet (column 2); therefore the approximate point H is
above the intended top of the embankment, and consequently will
not represent the foot of an embankment, but the edge of a cutting,
and therefore the calculation for the half width on the north side,
must be treated as for a cutting whose depth is equal to the height
of the approximate point H above the intended top of the embankment
or in other words, the excess of the difference of level between the
centre stake and the approximate point H, above the intended
height of the embankment, is the quantity to be entered in the
column (7 or 8) "difference of level," and to be computed as for a
cutting instead of embankment. In the case of stake 286 this ex-
cess is 0.07, to which is prefixed the sign plus; this sum multiplied
by the ratio of the slope being additive (for a cutting) on the ele-
vated side of the centre, as before explained.
370
RAILWAY SURVEYING.
—
=
For the stake 290, the north side of the line (column 6) is 1.34
higher than the centre stake, and it being embankment, would
have the sign - prefixed (as shewn by the lower number, column
8): but the central height of the embankment at that point is but
1-22 (column 2); therefore, 1.34 1.22 0.12, which is the depth
of cutting on the elevated side, and when multiplied by the ratio of
the slopes, is to be added to the computed half width to obtain the
correct result. When the surface of the ground is much inclined
at right angles to the centre line, the numbers to be operated upon
become proportionally large.
As it is a case of frequent occurrence that
one side will be a cutting when the other is
an embankment, we wish it to be well
understood, and therefore annex the follow-
ing diagram to illustrate it.
The line F G represents the natural sur-
face of the ground, A B the horizontal line
at the centre stake, CD the intended height
of the embankment, KL the width or base
of the railway, 36 feet, part of which is an
embankment and part in cutting; the point E,
or foot of the embankment will be determined
in the usual way, as explained at page 368;
but the point H, which is to be the edge of
the cutting, must be found by subtracting
DC (the height of embankment) from HI
(the difference of level,) the remainder H M,
(which is the excess of the difference of level
between the centre stake and the approximate
point H above the intended height of embank-
ment,) multiplied into the ratio of the slope,
must be added to the computed half width,
or in other words, treated as for a cutting, to
obtain the said point H as before stated. By
reversing the diagram, the corresponding
case will become evident, namely, when the
centre line is in cutting, and one side on em-
bankment, while the other is in excavation,
and the mode of proceeding will at once
strike the reader after perusing what we
have above written.

H
Κ
Base of Railway,
36 feet.
D
Y...---
JAI!
L
B
I
E
F
RAILWAY SURVEYING.
371
MR. RYDE'S METHOD.
It will be observed, that the preceding method is somewhat com-
plex and tedious, unless to the practised surveyor. In consequence
of this, some few years ago, I turned my attention to the compu-
tation of a series of Tables which should obviate this and combine
other advantages.
The first information required under my system is, the rate of
inclination per chain of the cross section. This has already been
directed to be taken while levelling for the working section, when
it will be found to occupy but very little time. The whole work
is then done in the office, with the exception only of measuring out
the widths, which can be done by a surveyor of very limited
experience.
I append Examples of the Tables, and of their use in Setting
out Slopes, as well as a Specimen of the Field Book suited to
them. It is hardly necessary to say that columns one, two, three,
four, five, and six, are taken from the working section; that seven
is computed; and that eight and nine are the tabulated results.
And as these tabulated widths are given in links, they are more
readily set out on the ground with a chain; they are easily set off
on the plan by the scale with which the plan has been plotted; and
the quantity of land required for the railway is simply and cor-
rectly computed. On the contrary, the system in general use
gives the width of the railway only on the ground, from which it
has to be measured before it can be laid off on the plan.
Explanation of the Tables for Setting out Slopes.
Note.—In these Tables fractional parts of feet are not given in
treating of the depth of cuttings or height of embankments; it is
considered sufficiently accurate in practice, when those decimals do
not amount to half, to reject them altogether; when they do, to
add one to the integer.
The columns of widths in links have been prepared by the same
rule; and it may be well to observe, that these distances refer to
horizontal measure.
If any case should occur exceeding the greatest depth of cutting
or height of embankment given in the Tables, it is easily obviated
by taking the half, and doubling the result.
The Tables have all been calculated by the application of loga-
rithms to trigonometry, and are consequently of the most accurate
solutions.
372
RAILWAY SURVEYING.
Examples.
Case 1.-When the surface of the land across the railway is level,
and the work is a cutting or embankment.
Let fig. 173b represent the cross section of a railway in a cutting;
the depth A B at the centre peg A being 40 feet, the width of
the permanent way DG 30 feet, and the ratio of the base to the
slope 1 to 1; required the widths AE and A F on either side
the centre peg A?
First, find the distance B C by comparing the ratio of the slope
with the half width of the permanent way B G or B D.
As 1:1 BG 15 ft. BC= 10 ft.
and B C being added to A B, we have a total depth of 50 feet to
the point at which the slopes would intersect themselves and the
vertical line A C, and form the triangles ACE and AC F.
AC = 50 feet depth of cutting becomes the reference to the
Tables, under which, and the slope of 1 to 1, and opposite level,
we have 114 links on either side-the widths required.
Case 2.--When the surface of the ground across the railway is
not level, and the work a cutting or embankment :
Let fig. 173c represent the cross section of a railway in a cutting;
the depth A B being 40 feet, the width of way D G 28 feet, the
ratio of the base to the slope 2 to 1, and the rise per chain in the
cross section EAF 4.5 feet; required the widths AE and A F
on either side the centre peg A?
Proceed as in the last case to find B C
As 2: 1 :: BG 14 ft.: BC= 7 ft.
AB = 40+ BC=7= A C 47 feet.
In the page of the Tables headed Depth of Cutting 47 feet,
under slope 2 to 1, and opposite the rise of 4.5 feet per chain,
stands the required widths, 165 and 125 links respectively.
Case 3.-When the surface of the land across the railway is not
level, but when the centre of the railway is neither cutting nor
embankment:
Let fig. 173d represent the cross section of a railway in which the
width of way D G is 30 feet; the ratio of the slope 1 to 1; and the
rise per chain in the cross section EAF 5 feet; required the widths
A E and A F on either side the centre peg A?
RAILWAY SURVEYING.
373
Find A CAB as before.
As 1:1:: AD or AG = 15 feet: A C or AB = 15 feet.
In the page of the Tables headed Depth of Cutting or Height
of Embankment 15 feet, under slope 1 to 1, and opposite rise per
chain 5 feet, is 24 links; the greater width, which is here required
on both sides, being the lower side of an embankment, and the
higher of a cutting.
Case 4.-When the surface across the railway is not of one uni-
form inclination on either side the centre peg:
Let fig. 173e represent the cross section of a railway embankment,
the height A B being 20 feet; D G 30 feet; ratio of the base to
the slope 1 to 1; and the rise per chain in the cross section E A
4. 5 feet; and AF 7 feet; required the widths AE and A F on
either side the centre peg A?
Find B C as before,
As 11:: B G 15 feet: B C 10 feet.
AB 20 plus B C 10 AC 30 feet.
In the page of the Tables representing Height of Embankment
30 feet, under slope, 1½ to 1, and opposite a rise of 4. 5 per chain,
we have the lesser width A E 62 links, and farther down, opposite
a rise of 7 feet per chain, we have the greater side A F 81 links.
374
SETTING OUT SLOPES.
174

SPECIMEN OF FIELD BOOK FOR SETTING OUT SLOPES.
DEPTH OF
DISTANCE
NATURE
WIDTH
RATIO
RISE PER
ON
OF
CUTTING
OR
HEIGHT
OF
|COMPUTED
DEPTH
OR
WIDTHS
CHAIN
OF
OF
HEIGHT
FOR
TAKEN
REMARKS.
IN CROSS
RAILWAY.
WORKS.
EMBANK-
MENT.
WAY.
SLOPES.
REFER-
ENCE TO
FROM THE
SECTION.
TABLES.
TABLES.
Miles. Fur. Ch.
Feet.
Feet.
Feet.
Feet.
Links.
Links.
11
2 5 Cutting
40
30
1½ to 1
Level
50
114
114
See case 1.
15 1 8 Cutting
40
28
2 to 1
4.5
47
165
125
See case 2.
19 0 6 Level
0
30
1 to 1
5.
15
24
24
See case 3.
North
4.5
19 7 4 Embankment
20
30
1 to 1
South
7.
}
62
30
See case 4.
81
SETTING OUT SLOPES.
375

SPECIMEN OF
TABLES FOR SETTING OUT SLOPES.
DEPTH OF CUTTING OR HEIGHT OF EMBANKMENT.
15 Feet.
SLOPE 1 TO 1.
SLOPE 1 TO 1.
SLOPE 2 TO 1.
RISE
Required
RISE
Required RISE
Required
per
Widths,
per
Widths,
per
Widths,
Chain
in
Chain
in
Chain
in
in Feet.
Links.
in Feet.
Links.
in Feet.
Links.
Level
23
23
Level
34
34
Level.
45
45
.5
23
22
.5
34
34
.5
46
45
1.
23
22
1.
35
33
1.
47
44
1.5
23
22
1.5
35
33
1.5
47
43
2.
23
22
2.
35
32
2.
48
43
2.5
3.
3.5
4.
4.5
5.
33 FFFFF
23
22
24
24
21
24
21
24
21
24
21
5.5
25
21
6.
25
21
6.5
25
7.
25
7.5
26
8.5
8.5
20 20
26
26
9.
26
9.5
26
10.
27
10.5
27
12 22222 22222 22222 9
2.5
36
32
2.5
3.
36
32
3.5
37
31
4.
37
31
4.
4.5
38
31
5.
38
88889
30
að að + Hi Lő
3.
50
3.5
4.5
5.
5.5 39
30
5.5
6.
39
30
6.
20
6.5 40
29
6.5
20
7.
40
29
7.
20
7.5
41
29
7.5
20
8.
41
29 8.
20
20
∞ oi
8.5
42
28
ထံထံ
8.5
9.
42
28
9.
20
9.5
43
28
9.5
20
10.
44
28
10.
19
10.5
44
27
10.5
11.
27
19
11.
45
27
11.
11.5
27
19
11.5
46
27 11.5
12.
28
19
12.
47
27
12.
12.5
28
19
12.5
47
26 12.5 73
13.
28
19
13.
48
26
13.
13.5
28
19
13.5
49
26
13.5
14.
29
19
14.
50
26
14.
14.5
29
19
14.5
51
25
14.5 81
15.
29
18
15.
51
25
15.
8PIIN ZEN88 AR*2* ***** ***** *
42
42
41
40
40
39
39
55
38
38
37
37
36
36
62
35
64
35
65
35
34
68
34
70
34
33
33
75
32
32
79
32
31
83
31
376
SETTING OUT SLOPES.

SPECIMEN OF
TABLES FOR SETTING OUT SLOPES.
DEPTH OF CUTTING OR HEIGHT OF EMBANKMENT.
30 Feet.
SLOPE 1 TO 1.
SLOPE 1 TO 1.
SLOPE 2 TO 1.
RISE
Required
RISE
Required
RISE
Required
per
Widths,
per
Widths,
per
Widths,
Chain
in
Chain,
in
Chain
in
in Feet.
Links.
in Feet.
Links.
in Feet.
Links.
Level
45 45
Level
68
68
Level
91
91
.5
46
45
1.
46
45
292
.5
69
1.
1.5
46
44
1.5
2.
47
44
2.5 47
44
ai ci
2.
2.5 72
3.
47
43
3.5 48
43
4.
48
43
4.
4.5 49
42
5.
49
42
að að ti ti zö
3.
73
3.5
4.5
5.
5.5
49
42
5.5
6.
50
42
6.
6.5 50
41
6.5
7.
51
41
7.
81
7.5
51
41
7.5
8.
52
40
8.
88REN CERCE ERI* *
67
.5
92
89
69
66
1.
94
88
70
66
1.5
95
87
71
65
2.
97
85
64
2.5
98
84
64
3.
100
83
74
63
3.5 102
82
75
62
4.
103
81
76
62
4.5
105
77
61
5.
107
77
60
79
60
as or
5.5
109
6.
111
80
59
6.5
113
59
7.
115
ཟླུ། ཟུ་ྲཆ
80
79
77
76
75
82
58
7.5
117
74
83
57
8.
120
73
8.5 52
40
∞
8.5
84
57
8.5
122
72
9.
52
40
9.
85
56
9.
125
71
9.5 53
40
9.5
87
56
9.5
127
70
10.
53
39
10.
88
55
10.
130
70
|
10.5
54
39
10.5 89
11.
54
39
11.
90
11.5
55
39
11.5
92
12.
55
38
12.
93
12.5
56
38
12.5
95
388
55 10.5
133
69
54 11.
136
68
54
11.5
139
67
53 12.
143
67
53
12.5
146
66
13.
56
888
38
13.
96
52
13.
150
65
13.5 57
38
13.5
98
52
13.5
154
64
14.
57
37
14.
99
52
14.
158
64
14.5
58
37
14.5
101
51
14.5
162
63
15.
59
37
15.
103
51
15.
166
62
SETTING OUT 8LOPES.
377

SPECIMEN OF
TABLES FOR SETTING OUT SLOPES.
DEPTH OF CUTTING OR HEIGHT OF EMBANKMENT.
47 Feet.
SLOPE 1 TO 1.
SLOPE 11 TO 1.
SLOPE 2 TO 1.
RISE
Required
RISE
Required
RISE
per
Widths,
per
Widths,
per
Required
Widths,
Chain
in
Chain,
in
in Feet.
Links.
in Feet.
Links.
Chain,
in Feet.
in
Links.
Level
71 71
Level
107 107
Level
142 142
.5
72
70
.5
108 105
.5
145
140
1.
72
70
1.5
73
69
2.
73
69
2.5
74 68
Fricici
1.
109
104
1.
147
138
1.5
110 103
1.5 149
136
2.
111
102
2.
151
134
2.5
113
101
2.5
154
132
3.
74
68
3.5 75 67
4.
76
67
+
4.5
76
66
5.
77
66
að að ti ti zồ
3.
114
100
3.5
116
99
4.
117
98
4.5
119
97
5.
120
96
að að tí ti zô
3.
157
130
3.5
159
129
4.
162
127
4.5
165
125
5.
168
124
6.
7.
20 CÓ CÒN
5.5
77
66
5.5
122
95
5.5
171
122
78
65
6.
123
94
6.
174
120
6.5 79 65
6.5
125
93
6.5
177
119
7.5 80
888
79
64
7.
127
92
7.
180
117
64
7.5
128
91
7.5
184
116
8.
81 63
8.
130
90
8.
188
114
8.5
82
63
8.5
132
89
∞
8.5
192
113
9.
82
62
9.
134
88
9.
196
112
9.5
83
62
9.5
136
87
9.5 200
110
10.
84 62
10.
138
87
10.
204
109
10.5 84
61
10.5
140
86
10.5
209
108
11.
85 61
11.
142
85
11.
213 107
11.5 86 61
11.5
144
84
11.5
218
105
12.
87 60
12.
146
84
12.
223
104
12.5 88
60
12.5
149
83
12.5
229
103
13.
89 59
13.
151
82
13.
235
102
13.5 89 59
13.5
153
81
13.5
241
101
14.
90 59
14.
156
81
14.
247
100
14.5
91
58
14.5 159
80
14.5
254
99
ཟ
15.
92
58
15.
161
79
15.
261
98
2 A
378
SETTING OUT SLOPES.

SPECIMEN OF
TABLES FOR SETTING OUT SLOPES.
DEPTH OF CUTTING OR HEIGHT OF EMBANKMENT.
50 Feet.
SLOPE 1 TO 1.
SLOPE 1 TO 1.
SLOPE 2 TO 1.
RISE
Required
RISE
Required
RISE
Required
per
Widths,
Chain,
in
per
Chain,
Widths,
per
Widths,
in Feet.
Links.
in Feet.
in
Links.
Chain,
in
in Feet.
Links.
Level
76
76
Level
114 114
Level
151 151
.5
1.
1.5
ai ai
2.
2.5
að að Hi Hi Lå
zo
3.
3.5 80
4.
4.5
5.
CEE02 2
77
78
73
71
82
5.5 82
6.
83
6.5
84
7.
85
7.5 85
8.
∞ ∞ó oi
86
8.5
87
9.
87
*** ***88 SEENN JJ7N22
75
5.
115
112
.5 154 149
74
1.
116
111
1.
156
147
74
1.5
117
109
1.5
159
145
2.
119
108
2.
161
143
2.5
120
107
2.5
164
141
72
72
70
að að ti ti 23
121
106
3.5 123 105
4. 124
104
4.
4.5
126
103
5.
128
102
70
5.5
129
101
69
6.
131
100
að að tí ti zö
20 có
3.
167
139
3.5
169
137
172
135
4.5
175
133
5.
178
131
5.5
182
130
6.
185
128
69
6.5 133
99
6.5
189
126
68
7.
135
98
7.
192
125
68
7.5
136
97
7.5
196
123
67
8.
138
96
8.
67
8.5
140
95
ထံထံ
200
122
8.5
204
120
67
9.
142
94
9. 208
119
9.5 88
66
9.5
144
93
9.5 212
117
10.
89
66
10.
146
92
10.
217
116
10.5
90
65
11.
91
65
11.5
92
12.
92
12.5 94
13.
94
13.5 95
14.
96
14.5
97
15.
98
PUTIH CINNN
10.5
149
91
10.5
222
115
11.
151
91
11. 227 114
64
11.5 153
90 11.5 232 112
64
12. 155
89
12. 238
111
64 12.5 158
88888
12.5 244
110
63
3.
161
87
13.
250
109
63 13.5 163
87
13.5
256 107
62
14.
166
86
14.
263 106
62
14.5
169
85
14.5
270 105
62
15.
172
84
15.
277 104
RELATIVE GRADIENTS, &c.
379

TABLES OF RELATIVE GRADIENTS
AND
CORRESPONDING ANGLE.
1
75
50
25
ANGLE.
CHAIN.
LINKS.
LINKS.
LINKS.
Feet.
Feet.
Feet.
Feet.
Deg. Min.
.5
.37
.25
.12
0 25
1.
.75
.5
.25
0 51
1.5
1.12
.75
.37
1
16
2.
1.5
1.
.5
1 42
2.5
1.87
1.25
.62
2 8
3.
að að ti ti zồ
2.25
1.5
.75
2 33
3.5
4.
4.5
5.
2.62
1.75
.87
2 59
3.
2.
1.
3 24
3.37
2.25
1.12
3 50
3.75
2.5
1.25
4 16
5.5
4.12
2.75
1.37
4 41
6.
4.5
3.
1.5
5 7
6.5
4.87
3.25
1.62
5 32
7.
5.25
3.5
1.75
5 58
7.5
5.62
3.75
1.87
6 24
8.
6.
4.
∞
8.5
6.37
4.25
ai ai
2.
6
49
2.12
7 15
9.
6.75
4.5
2.25
7 40
9.5
7.12
4.75
2.37
8 6
10.
7.5
5.
2.5
8 32
10.5
7.87
5.25
2.62
9 17
11.
8.25
5.5
2.75
9 23
11.5
8.62
5.75
2.87
9 48
12.
9.
6.
3.
10 14
12.5
9.37
6.25
3.12
10 40
13.
9.75
6.5
3.25
11
5
13.5
10.12
6.75
3.37
11 31
14.
10.5
7.
3.5
11 56
14.5
10.87
7.25
3.62
12 22
15.
11.25
7.5
3.75
12 48
380
RAILWAY SURVEYING.
•
The Table of relative Gradients is inserted for use in cases
wherein the cross section rises too severely, although regularly to
be taken at one operation with the level. It affords an opportu-
nity of determining the inclination per chain by means of an incli-
nation taken at a less distance and renders results so taken at
once applicable to the general Tables. The corresponding angle
affords an opportunity of determining the inclination of the cross
section by means of an angular instrument, if such a method pleases
the surveyor.
We have now arrived at the stage for the preparation of the
Land Plans. The several widths required for the formation of the
railway, with a sufficient addition for the bank and ditch, are laid
off on the large scale plan, and the several quantities of land required
out of each field are computed. These quantities admit of checking
by a very simple mode at any given length of line, when the widths
have been calculated by my Tables, it being only necessary to mul-
tiply the average width by the length. And again, my Tables of
Land Measure will obviate this multiplication.
Plate 10 is a Specimen Land Plan.
The contents of railway cuttings and embankments are, in most
cases, found by tables, calculated for the purpose. Mr. Baker has
recently gone fully into the subject, and as the author of some
Tables thereon, I extract his own statement in full.
He says, numerous Tables exist for this purpose, some of which
are voluminous; those by M'Neill, Bidder, Huntington, Hughes,
Bashforth, Sibley and Rutherford, Law and Lowe, are well adapt-
ed for the purpose, assuming the surface line of the cross sections to
be level, or to be reduced to that position; but none of these
tables will properly apply to sectional areas, which is the most
important part of their use, excepting Bashforth's; but his method
of using them is erroneous, the error approximating to 50 per cent as
a maximum. I would therefore recommend for this purpose, the
General Earthwork Table,* in conjunction with Two Auxiliary
Tables, on the same sheet, in Baker's Engineering, as being applic-
able to all varieties of ratio of slopes and widths of formation level
in common use; and with the help of Barlow's Tables of Square
Roots, these tables will apply to sectional areas, with all the
mathematical accuracy that can be attained, with very little more
calculation than adding the contents between every two cross
sections, as given by the General Table.-The contents in the
* The numbers for the side slopes, forming the alternate lines in Bidder's Table,
will supply the place of the General Table.
RAILWAY SURVEYING.
381
General Table are calculated to the nearest unit, as are also those
in the Auxiliary Table, No. 2, which is for the decimals of feet in
the depths. The Auxiliary Table, No. 1, shows the depths of the
meeting of the side slopes below the formation level, with the
number of cubic yards to be subtracted from the contents of the
General Table for each chain in length, for eight of the most
common varieties of ratio of slope.
Note 1.-These Tables, with very little additional calculation,
may be extended to every variety of formation level and ratio of
slopes that can occur, and even to cases where that ratio differs in
the two sides of the same cutting, as shall be shown in the fol-
lowing Problems.
Note 2.-The investigations of the method of forming these
tables and using them are given in Baker's Railway Engineering,
also further investigations are given, at the end of the following
Problems, respecting Mr. Bashforth's Erroneous Methods of Cal-
culating Earthwork.
The following explanations will further illustrate the method of
taking the dimensions of railway cuttings, preparatory to using
the above named tables.
Let ABDC cabd, fig. 173i, be a railway cutting, of which
ABDC, abde are the cross sections, AB = ab = width of for-
mation level, MM', mm' the middle depths of the two cross-
sections; the side-slopes A C, B D, a c, bd, when prolonged two
and two, will intersect at N and n, at which points the prolonga-
tions of M M', m m' will also meet, thus constituting a prism
ABN nab, the content of which is to be deducted from the
whole content, given by the General Table, by means of the
Table, No. 1; in which the depth M'N = m'n is also given, as
already stated, to several varieties of slope and bottom width.
To place this subject in a more practical point of view, let
figure 173k represent a longitudinal and vertical section of a
cutting, passing through the middle A E of the formation level.
HI, the line of the rails, and a h, the line in which the slopes, if
prolonged, would meet. It will be seen that the cutting AbcdE
commences and runs out on the formation level A E, and that
the depth A a= Be=Cf= &c. is to be added to the several
depths Bb, Cc, Dd of the cutting, the first and last depth
at A and E being each = 0; or, what amounts to the same
thing, the several depths must be measured from the line ah:
thus, A a, be, cg, &c. are the depths to be used. And since
the depth A a is given in Table, No. 1, for all the most com-
mon cases, or it may be readily found by calculation for all cases,
382
RAILWAY SURVEYING.
as shall hereafter be shown, the line corresponding to ah must,
therefore, be ruled on the railway section, at the proper distance
below A E, from which the several depths must be measured; or
the vertical scale may be marked with Indian ink (which may be
readily rubbed off) at the same distance, and this mark may then
be applied to the formation level A E, for the purpose of measur-
ing the several depths.-In the case of an embankment, the line
for the several depths must be placed at a like distance above the
formation-level.
PROB. I.—The several depths of a railway cutting to the meeting
of the side slopes, its width of formation level, and the ratio of the
slopes being given, to find the content of the cutting in cubic yards,
from the Tables referred to, the distances of the depths being one
chain each.
Rule.-Take the several quantities, corresponding to every two
succeeding depths of a cutting or embankment, measured to the
meeting of the side slopes, at the distance of one chain each, from
the General Table in Baker's Railway Engineering and multiply
their sum by the ratio of the slopes; from the product subtract
the cubic yards, corresponding to the given bottom width and
ratio of slopes from Table, No. 1, multiplied by the whole length of
the cutting, and the remainder will be the content of the cutting
in cubic yards.
But when the distances of the depths are greater or less than one
chain, the quantities of the General Table must be multiplied by
their respective distances.-And, when the distances are given in
feet, the quantities must be multiplied by those distances, and the
final result divided by 66 for the content in cubic yards, as in the
following examples.
Examples.

1. Let the depth of the railway cutting
or embankment to the meeting of the side
slopes, at the end of every chain, be as in
the following table, the bottom width 30
feet, and the ratio of the slopes as 2 to 1;
required the content in cubic yards.
Dist. in
chains.
Depths Qnts. per
in feet. G. Table.
0
10
1.00
33
1238
2.00
39
3175
3.00
35
3350
4.00
10
1365
Note.-In the annexed table the quantity For slope 1 to 1. 9128
1238, corresponds to the depths 10 and 33
feet in the General Table; the quantity
3175 to the depths 33 and 39, and so on for Subtract
the succeeding depths. By the Auxiliary
Table, No. 1, it will be seen, that the depth
to be added below the formation level, for
275 X 4
Content in
cubic yds.
2
2 to 1. 18256
}
1100
17156
RAILWAY SURVEYING.
383
the given width and ratio of slopes, is 7·50 = 73 feet, therefore,
the cutting begins and ends with a depth of 10 — 71
7금 ​2 feet.
The corresponding number of cubic yards, to be deducted for each
chain in length, is multiplied by 4 chains, the whole length of the
cutting, thus giving the whole quantity to be deducted, the re-
mainder being the true content in cubic yards of the cutting.

2. The several depths of a
railway cutting to the meet-
ing of the side slopes are as
in the annexed table, the
bottom width being 30 feet,
and the ratio of the slopes 1
to 1; required the content of
the cutting.
Note. When any of the
distances between two suc-
ceeding depths is greater or
less than 1 chain, the corres-
ponding quantity from the
General Table must be mul-
tiplied by that particular dis-
tance; as the distances be-
Dist. in
chains.
1.00
Depths
Products for Dist.
Total
in feet. greater than 1 chain. quantities.
10
0
10
16
420
2.00
20
795
4.00
25
1243 x 2
2486
5.00
32
1996
7.00
39
3091 x 2
X
6182
8.00
45
4319
10.00
50
5520 × 2
11040
12.00
40
4971 × 2
9942
13.00
30
3015
14.46
10
1059 × 1.46
1546
For side slopes
1 to 1
41741
to 1
20870
1 to 1
62611
366.67 x 14.46
5302
Content in cubic yards 57309
tween the depths 20 and 25, and between 32 and 39, &c. the dis-
tances being 2 chains. The last distance, viz., that between 30
and 10, is 1·46; in this case 2 figures must be cut off for decimals,
after multiplying.

3. Let the depths of a rail-
feet.
by length.
way cutting to the meeting of Dist. in Depths Quantities multiplied
the side slopes, and their dis-
tances in feet be as in the an-
nexed table, the bottom width
30 feet, and the ratio of the
slopes 1 to 1; required the
content in cubic yards.
Note.-When the distances
are in feet, the quantities from
General Table must be respec-
tively multiplied by their dis-
tances, the quantity from
Total
quantities.
0
37
90
50
4660 × 90
419400
178
61
7554 88
X
664752
278
39
6210 × 100
621000
For slopes 1 to 1
1705152
•
to 1
852576
14 to 1
2557728
366-67 × 278
101933
66) 2455795
Content in cubic yards 37209
Table, No. 1, by the whole distance, and the result divided by 66,
the feet in 1 chain, for the content in cubic yards, as in the an-
nexed operation.
384
RAILWAY SURVEYING.
PROB. II. CASE I.—The areas of two cross sections of a railway
cutting to the intersection of the side slopes, its length in chains, bottom
width, and ratio of the slopes are given; required the content of the
cutting in cubic yards.
Rule.—With
Rule. With the square roots of the given areas, as depths, find
the content from the General Table, as in the last Problem, from
which subtract the quantity answering to the given width, and the
ratio of sides slopes from Table, No. 1, and the remainder, being
multiplied by the length, will be the content required.
Note.-If the length be given in feet, proceed as in Example 3,
last Problem.
Example.
1. Let the two sectional areas of a cutting be 4761 and 1296
square feet, the bottom width 36 feet, the length 3.25 chains, and the
ratio of the side slopes 2 to 1: required the content in cubic yards.
√ 4761 = 69
content per General Table . . 6959
For bottom with 36 and slopes 2 to 1 per
✓ 1296 = 36
}
Table, No. 1
Content for 1 chain in length
396
6563
31
19689
1641
Content for 3.25 chains
21330 cubic yards.
CASE II. To find the content when the depths are given in feet
and decimals of feet.
α
Rule.-Let a and b be the feet in any two succeeding depths,
and and their respective decimal parts; find the quantity an-
В
swering to a and b from General Table, as in the former cases: then,
2 a + ẞ, rejecting the last figure, and a will shew the number
to be added in Auxiliary Table, No. 2, and
26+a, rejecting the last figure, and 6 will shew the number
to be added in the same Table.
After which deduct for the quantity below the formation level, as
before.
Example.
Let the sectional areas be 1406 and 2560 square feet, the
bottom width 36 feet, length 4 chains, and ratio of slopes 1 to 1;
required the content in cubic yards.
RAILWAY SURVEYING.
385
Here ✔ 1406 = 37·5 and ✓ 2540
50.4. Put 37 = a,
50 = b ·5 = a•4
•5 = ß; then the depths a and b, per General
Table, give
2 a + b =
124, or 12, (by rejecting last figure)
and ß = ·4, per Table, No. 2 give
2 b+ a = 137, or 14 nearly, (by rejecting last
figure) and a 5 give
For bottom width 36 and ratio of slopes 1 to
1 deduct
Content for 1 chain in length
4660
39
57
4746
528
4218
4
16872 cubic yds.
Content for 4 chains in length .
0
CASE III.-In measuring contract work where great accuracy
is required, the ths, of a foot, or second decimals, must be used in
the calculation, by taking for them th of their respective quantities
in Table, No. 2.
Example
The areas of seven cross sections of a railway
cutting to the meeting of the side slopes, and their
distances are as in the annexed table; the bottom
width is 30 feet, and the ratio of the slopes 11
to 1; required the cubic yards in the cutting.

Dist. in
Chains.
Areas in
8q. feet.
0
2727
2.00
3136
6.00
4221
9.60
4100
14.00
5141
3759
2161
16.00
18.00
Ans. The content, per General Table, and
Table, No. 2, is 172318 cubic yards from which
the quantity corresponding to the given bottom
width and ratio of slopes × by the whole length,
viz. 275 x 18 = 4950 cubic yards, must be deducted, which leaves
167568 cubic yards, the content required.
Note 1.-When the distances of the sectional areas are given in
feet, the quantities of the General Table must be multiplied by
their respective distances, and the final result divided by 66, as in
Example 3. Prob. I.
Note 2.-When the surface lines of the sectional areas are either
level or are readily reducible to that position, the decimals, if any,
in depths must be taken into the calculation, as in Cases II
and III.
PROB. III. To adapt the General Table to such widths of the
formation level and ratios of slope as are not found in Table, No. 1.
Put width of formation level, and r: 1 the ratio of slope.
Then =feet to be added to the depth of cutting below
ω
r
formation level.
386
RAILWAY SURVEYING.
22 w2
= cubic yards to be subtracted for each chain in
And
9 r
length.
Example.
= 10·4 ft. = distance
Let the width of formation level be 26 feet, and the ratio of
slopes 1 to 1; then r = 13 ÷ 14
w
below formation level to meeting of slopes.
And 22 × 13º ÷ 9 × 14 = 330.5 cubic yards to be deducted
for each chain in length from the contents of the General Table.
PROB. IV. To find the content of a cutting when each of the sides
have two different ratios of slope.
Rule.-When the cutting A B C D (fig. 1737) has two different
slopes, as A a or B b and a C or b D; it must be divided into two
parts by the line a b, and the quantities of the parts A B b a,
a b D C of the cutting must be found separately by Prob. I. If
the surface line C D be sloping or curved, Prob. II. will also be
required; and, if the depths m'n' m N and their corresponding
quantities of cubic yards are not found in Table, No. 1, they must
be found by Prob. III, the sum of the contents of the two parts
being the required content of the cutting.
Note.-Cuttings of this kind are often advantageously adopted,
where their upper parts are of loose or springy earth, and their
lower parts strong clay or rocky.
PROB. V. To find the content of a cutting when the ratio of the
slopes of the two sides are different.
CASE I.—When the surface is level.
RULE.-Find the central depths to the meeting of each of the
side slopes, and take their corresponding contents by Problem I
for the whole length of the cutting, in the same manner as if it
were for two cuttings, and, from the sum subtract the sum of the
cubic yards corresponding to the given bottom width and ratios of
slope multiplied by the whole length of the cutting, and half the
difference will be the content required.
CASE II.-When sectional areas are given.
RULE.-Find the contents corresponding to the sectional areas
to the meeting of the side slopes by Prob. II, and from their sum
RAILWAY SURVEYING.
387
deduct
W
=
44 w² 7
W
g(r+r')
cubic yards for the content. In this formula
bottom width, 7 = whole length of cutting, and r and r' the
first terms of the ratios of the side slopes.
Note.-Cuttings with slopes of this kind are frequently adopted
in practice, where the ground is springy on one side of them, the
greater ratio of slope being on the springy side.
PROB. VI.-To find the quantity of the cutting of a tunnel.
RULE.-Multiply continually together the width, mean height
and length; divide the product by 9, if the length be given in
yards, but if the length be given in chains, multiply the product
by 22 and divide by 9, the width and height, in both cases, being
given in feet.
Note.-Examples are not given in the three last Problems, the
methods of solving which being sufficiently obvious from the Rules
and the first three Problems.
THE FOLLOWING EXAMPLES SHOW THE ERRORS OF METHODS
PUT FORTH BY MR. BASHFORTH AND OTHERS, TO FIND THE
CONTENT OF CUTTINGS.
Examples.
1. The areas of two cross sections of a cutting to the meeting
of the intersection of the side slopes, are 1296 and 361 square feet,
their distance one chain, the bottom width 36 feet, and the ratio of
the slopes 1 to 1; required the content of the cutting by the true
and the erroneous methods practically used.
(1.) By the true method:-
✓ 1296 = 36
361
19
content by General Table 1907
Deduction from Table, No. 1.
True content for 1 chain in length
(2.) By Mr. Bashforth's method :—
792
1115 cubic yards.
By Table, No. 1, the depth of the meeting of the side slopes
below formation level is 18 feet; hence the area of the triangle
below it is 36 × 9 = 324 square feet, which, being taken from the
given sectional areas, will give 972 and 37 square feet for the areas
used by Mr. Bashforth; whence,
388
RAILWAY SURVEYING.
✓ 976 = 31·18
✓ 37
37 = 6.08)
}
content by General Table, &c., 975 cubic yards.
This content taken from the true content, given above, leaves
140 error in defect.
Whence 975: 140:: 100: 14:36, or above 141 per cent, the error
in defect by Mr. Bashforth's method.
2. Let the areas of the two cross sections to the intersection of
the slopes be 324 and 2916, and the other things as in the last ex-
ample, required the content of the cutting by the correct and er
roneous methods.
(1.) By the true method.
√ 219654 content by General Table .
✓ 324 = 18
Deduction from Table, No. 1.
True content for 1 chain in length
3432
792
2640 cubic yds.
(2.) By Mr. Bashforth's method :—
Here the sectional arcs used are 2592 and 0, whence
2592 =
0
50.91
0
content by General Table 2112 nearly, which
taken from the true content leaves 528 error in defect.
Whence 2112: 528 :: 100: 25 per cent., the error in defect in this
case.
By taking a mean of the areas in Example 1.
22
(972 + 37) × 9 = 12233 cubic yards, which exceeds the true
content 1183 cubic yards, being about 93 per cent. in excess.
By taking a mean of the areas in example 2.
22
9
1 (2592 + 0) × = 3168 cubic
content by 528 cubic yards, being 16
yards, which exceeds the true
per cent. in excess.
Note.-By taking a mean depth the error in defect is just half
the preceding one, or 83 per cent. These methods only give a
near approximation to the true content, when the sectional areas
of a cutting are nearly equal. See the results of the following for-
mula and remarks.
The above examples show with sufficient clearness the inaccur-
acy of Mr. Bashforth's method; but since it has been defended,
as sufficiently correct for practical purposes, the following formula
RAILWAY SURVEYING.
389
will more rigidly prove its failure. Let A' and B' be the sectional
areas of a cutting, as used by Mr. Bashforth, and a the area be-
tween the formation level and the meeting of the slopes; then by
Baker's Railway Engineering, page 55, §1 (√ A' + a × B' + a
✓ A' B'
A′ × B′ — a) = his error in defect, the content by his method
being (A' + B' × √ A′ + B′), the length being unity; whence
81
100 (√ A' + a × B' + a−√ A′ × B′
A' + B' +√ A' × B'
Mr. Bashforth's method.
81
a)
= error per cent. by
Examples.
1. When A' = a and B' = 9 a, the above formula gives
100 (✓ 3º × 10 −√ 3 × 9
1, a
(3 × 9 + √ ‡ × 9,) a
10
1-2
1200
10/1/
91
131 per cent. error in defect.
2. When A' = 0 and B' = 3 a, the above formula gives,
100 (2 — 0 — 1)
3
= 333 per cent. the error in defect.
3. When A' = 0 and B = a, the error in defect is 41 per cent.
Errors of this kind will repeatedly occur in practice, where cut-
tings and embankments are made, as in the following figure;
wherein A B is the formation level, and the corresponding curved
line is a section of the earth's surface; the small figures below being
cross sections taken to the intersection of the slopes, in which M N,
m n, represent the formation level, the sectional areas, used by Mr.
Bashforth, being those above the lines M N, m n, the cross section
cdmn may either be very small, as in Example 1, or 0, as in
Examples 2 and 3; in which latter cases the surface c' d' of the
section cuts m n.

C
N
m
B
From the above figure it will at once be seen that more than one-
390
RAILWAY SURVEYING.
half of the sectional parts of the cuttings and embankments will be
affected by errors in defect of an average of the above-named per-
centages, which are most decidedly prominent; and sufficient, in
many cases that occur in practice, to take away more than the whole
of a contractor's profits.-The error of Mr. Bashforth's method at-
tains its maximum, which is 50 per cent., when both the sectional
areas A' B' vanish, which, however, is a case that can never occur
in practice.
I have given Mr. Baker's comparisons at length, because he
complains in his Rudimentary Treatise on Land and Engineering
Surveying, that notwithstanding the errors he has proved to exist
in the method given by Mr. Bashforth, for finding the contents
of cuttings, that gentleman accuses him of copying. Now, had
this been the case, Mr. Baker observes, he must also have copied
the errors, that is, he ought to have adopted Mr. Bashforth's me-
thod of finding the contents of cuttings, from sectional areas,
where the surface of the ground is laterally sloping or curved, in
which method the prism below the formation level is left out of
the question, whereas Mr. Baker has included it in his calculations.
Moreover, Mr. Baker asserts that his method was communicated
to several gentlemen long before the publication of Mr. Bashforth's
method, among whom was Professor Tate, of the Training Insti-
tution, near Twickenham, who is a competent judge of such mat-
ters, and who has himself published on the same subject in his
Geometry. As for the General Table, Mr. Baker defends it by
saying it is calculated from one of the same formulæ, used by
Sir John McNiell, Mr. Bidder, and others, as the basis of their
Tables, and must, therefore, be common property.
Tunnelling is generally adopted on a railway when the cutting
would require to be more than about 60 feet. It is desirable that
the gradient in a tunnel should have a fall in one direction, for the
purpose of allowing the water generated therein to be discharged
by the natural force of gravitation. If the tunnel is very long, a
fall
may be given to the gradient from the centre towards either
end. A tunnel on a curve requires to be very accurately set out,
as well as levelled, or very great embarrassments may arise in its
construction.
The mining operations in a tunnel are directed by a miner's
compass. The direct bearing of the line, if straight, or of the tan-
gent of the curve, if in a curve, being taken at the top of a shaft,
and laid out in the same direction at the bottom. Experience in
the use of instruments is required in these operations, to detect
any concealed attraction of the needle, or other instrumental errors
that may so easily occur. It must be borne in mind, that the forma-
RAILWAY SURVEYING.
391
tion line in a tunnel is much below an ordinary cutting, inas-
much as there is generally an inverted arch to be turned beneath
the ballasting, except indeed in those strata that are of themselves
sufficient to maintain the shape of the tunnel.
The following notes on the construction of tunnels, are extracted
from Dempsey's Practical Railway Engineering.
NOTE 1. Like mining and all other subterranean operations, the construction
of a tunnel can be but little aided by mechanical appliances; it chiefly requires
hard manual labour, exercised under circumstances which do not admit of that
thorough superintendance which promotes economy, and, moreover, liable to un-
foreseen interruptions, of surmounting which neither the manner nor the expense
can be predetermined. Thus the Kilsby tunnel, on the North Western Railway,
was estimated to cost £40 per yard lineal; whereas the actual cost was £130 per
yard, owing to its intersecting a quicksand that had escaped the trial borings.
Thus a vast expense was incurred in setting up and working pumping machinery to
dry the sand. The Box tunnel on the Great Western Railway, excavated through
oolite rock, and lined with masonry only through a portion of its length, cost up-
wards of £100 per lineal yard. The length of this tunnel is 3123 yards, or upwards
of 1 miles; it has eleven principal shafts, and four intermediate ones. The Blet-
chingley and Saltwood tunnels, on the South Eastern Railway, cost respectively
£72 and £118 per lineal yard, the greater cost of the latter work arising from the
great body of water in the sand which it intersects.-The method of proceeding
with tunnelling depends mainly upon the kind of material to be excavated. This
having been generally ascertained by boring and trial shafts, which must be suffi-
ciently capacious to admit readily of lowering men and materials, raising materials
excavated, fixing pumps, and also for starting the head way of the intended tunnel
when the required depth is reached.
NOTE 2. The working shafts are made from 8 to 10 feet internal diameter. They
are of brick work, usually 9 inches thick, and carried up 8 or 10 feet above the sur-
face of the ground. These, and all other shafts, rest upon curbs of cast iron, fitted
into the crown of the tunnel, and forming a level base for the shaft. The air shafts
are of a smaller thickness and diameter, the latter of which is usually about 3 feet.
-The number of working shafts will depend chiefly on the rate of speed with which
the work is required to be accomplished. With plenty of men, horses, material,
and plant, the work is much facilitated by sinking extra shafts, which will usually
well repay their cost.
NOTE 3. The Watford tunnel, 75 chains in length, on the North Western
Railway, was worked with six shafts, about 8 feet internal diameter; the brick
work was moulded to fit the circumference of the shafts, and laid in two half-brick
rings. Air shafts were sunk at about 2 chains distance on each side of each
working shaft. The arch and side of the tunnel were chiefly made two bricks
thick, and the invert, one and a half brick, except where the stratum passed
through seemed to suggest an increased or diminished thickness. The form of
the top of the tunnel is nearly semi-circular, supported by curved side walls stand-
ing on side footings, or skew backs, which rest on the invert.
392
RAILWAY SPECIFICATION.
SPECIFICATION.
SPECIFICATION to be observed by the Contractor for the
works to be executed upon the railway, com-
mencing at a peg numbered 1901 on the plans of
the said railway, and terminating at a point where
the said new railway forms a junction with the
main line in the parish of being a distance
of three miles and sixteen chains, or thereabouts.
It includes the formation of the railway, with
all the excavations and embankments complete;
the drains, fences, gates, and other works connected
therewith; and the erection of the following bridges,
[here set forth fully a description of the bridges,]
together with the formation and completion of the
several approaches thereto, and roads over them.
The building of the culverts, in the position
shown in the plan and section, and of the dimensions
there given, together with all the necessary diver-
sions of the streams and drains to lead the water
into and from the culverts; the laying and ballast-
ing of the permanent way; the providing of all
timber, bricks, lime, stone, or other materials ne-
cessary for the completion of the works in a sound,
substantial and workmanlike manner; the excava-
tions of the occupation bridges, occupation roads,
and diversions, marked upon the plan and section,
and of all other works mentioned and described in
the accompanying drawings and specifications, and
the keeping of the whole of the works in a perfect
state of repair for twelve months after completion.
[Here must follow a full and minute description of
all the drawings.] The preceding enumerated works,
and the mode of execution are described at length
in the specification of each particular work, and
their forms and dimensions described in the ac-
companying drawings, which are referred to in
RAILWAY SPECIFICATION.
393
Written di-
mensions to
be taken.
All minor
parts to be
inclnded,
though not
described.
Contractor
to nick out
cavations and
ments.
-
each specification; but should any discrepancies
exist between the measurement by the scale
attached, and the written dimensions, the latter
are to be taken as correct, any thing contained in
the drawings or specification shall be considered as
contained in both.
The written dimensions are those by which it is in-
tended the contractor shall make his estimate.
And wherever neither the drawings nor the specifica-
tion contain any notice of minor parts, the intention to
include which is nevertheless clearly to be inferred, and
which parts are obviously necessary for the completion and
stability of the work, all such additional parts are to be
provided by the contractor, and are supposed to be included
in the sum at which he contracts for the works, and
wherever any thing is directed to be done, or to be pro-
vided, if required, or words of similar import, it must be
understood that every thing so referred to will be consi
dered as included in the contractor's tender.
The centre line of railway is staked out on the ground,
slopes of ex but the contractor must at his own expense nick out the
embank- slopes of the excavations and embankments, as also the
exterior of the ditches previously to the commencement
of any of the works, and provide the engineer with all
necessary assistance in setting out and measuring off work
during the continuance of this contract.
Contractor to
adhere to
liament.
The contractor will in all cases be required to strictly
provisions of adhere to the provisions contained in the Act of Parlia-
Act of Par-ment, for making this railway, as he will be held respon-
sible for all claims which may be brought against the
Company in consequence of any infringement of the stipu-
lations therein contained.
Trees that
are felled on
line to be
barked.
Fencing of
two kinds.
All trees that are in the line of the railway, and which
require to be felled, must, if the season permit, be carefully
barked, and the bark properly stacked.
FENCING AND DITCHING.
The fencing and ditching described in the following
specification is of two kinds, the first, temporary, for the
protection of lands adjoining the railway, during the pro-
gress and until the completion of the works; the second the
permanent for the enclosure of the railway when finished.
2 B
394
RAILWAY SPECIFICATION.
Temporary
Fencing.
Slip Rails to
afford con-
venient ac-
cess to lands.
TEMPORARY FENCING.
Immediately after the delivery of any portion of the
site of the intended railway into the possession of the
contractor, and previous to the commencement of the other
works, the temporary fencing shall be completed, and
shall include the whole area of land belonging to the
company, as also all land occupied by any of the works
Gates and contained in this contract; and gates and slip rails shall
be placed to be so placed as to afford a convenient occupation of the
adjacent lands, for the convenience of cartage of mate-
rials, and a general passage along the line; openings shall
be made in the cross fences and gates or slip rails erected
for more effectual prevention of trespass, and the con-
tractor shall be held liable for all damage done to the
adjoining lands by cartage of materials, or by the stray-
ing of horses, cattle, or other beasts that may happen by
his neglect, or by that of his agents or workmen, in not
maintaining the fences or gates, or otherwise; and the
contractor shall, without delay, when required, make
good any fence, or gate, or railway, that may have been
destroyed or injured, from whatever cause, and shall pre-
serve the most effectual security to the cattle grazing in
the land adjoining, in neglect of which the engineer shall
have full power to pay all claims for trespass to the pro-
per parties, and to deduct the same from the account due
to the contractor at the next or any subsequent payment.
Temporary
fencing de-
scribed.
Permanent
fencing.
Ditch.
The temporary fencing shall consist of split oak posts
placed nine feet apart, and three and a half feet high
above the ground, morticed for the reception of three
horizontal oak or larch rails, which are to be supported
by an intermediate stay or prick post, firmly nailed to
each of the rails.
PERMANENT FENCING.
Drawing, No. 16.
The permanent fencing will consist of post and rail
fencing, ditches and quicksets, and must be placed within
the limits of the slip of land allowed for this purpose,
beyond the termination of the slopes.
A ditch of three feet wide at the top and one foot
wide at the bottom, and twelve inches deep, shall be made
RAILWAY SPECIFICATION.
395
Company's
property.
Drains.
Mound or
Cop.
Quicks,
Posts.
upon the higher side of the ground occupied by the rail-
way, and a ditch three feet wide at the top, one foot
wide at the bottom, and one foot six inches deep on the
lower side of the ground.
These dimensions shall be increased or diminished, as
in the opinion of the engineer the circumstances may
require, so as to produce an effectual drainage and keep
the water out of the excavations, and carry it away from
the foot of the embankments, and where necessary, the
existing drains and ditches must be deepened to obtain
a sufficient fall.
The outer slopes of the ditch must, in all cases, cor-
respond with the boundary of the company's property.
All drains, or alterations, or deviations in existing
drains, or water courses necessary for the exclusion of
the water from the cuttings, or for the prevention of
drainage to the adjoining property, or any other property
whatsoever, shall be made by the contractor at his own
expense.
The material excavated from the ditch shall be used to
form a mound on the space between the edge of the
ditch and the railway slope, and the side adjoining the
ditch shall be neatly ramparted with turf sods, which
shall not exceed four inches in thickness, to be ten
inches wide, and eighteen inches long.
When the material excavated from the ditch shall be
more in quantity than sufficient to form the mound, the
surplus must be conveyed to the nearest embankment.
The best portion of the vegetable soil excavated from
the ditch shall be placed in the middle of the mound, on
which a row of three years old good quicksets shall be
planted, and not less than nine quicksets shall be con-
tained in one lineal yard; on the inner edge of the ditch,
oak posts and rails must be set to protect the quicksets.
The posts are to be of split oak or good larch, six feet
six inches in length, and equal to at least five inches by
three and a half in sectional area; they are to be placed
at a distance of nine feet, from centre to centre, and to
stand four feet above the surface of the land.
Each post is to have three mortices for the reception
of the ends of the rails, which are to be made of split oak
or larch, and to be as straight and nearly of an uniform
size as possible.
396
RAILWAY SPECIFICATION.
Rails.
Prick Posts.
Hoops.
Fencing
to
be made with
ings as pos-
sible.
The horizontal rails, three in number, between each
pair of posts, are to be of oak or larch, not less than four
inches in sectional area at the small end, and ten feet in
length, and the ends are to be scarfed so as to fill the
mortices of the posts.
Midway between the posts an oak or larch stay five feet
six inches long, and two and a half inches square, being
driven into the ground, at least eighteen inches is to be
firmly nailed to each of the three horizontal rails with
good tenpenny nails.
The posts must be firmly fixed, by being set in the
ground without being sharpened, the ends of the rails
properly fitted into the mortices of the posts, and a piece
of new iron hoop one inch and a quarter wide, and one
sixteenth of an inch in thickness, shall be nailed round
the top of every post to prevent its splitting.
The fencing shall be made with as few bendings as the
as few bend- nature of the ground will permit of, and the ditch along-
side the mound shall descend as uniformly as possible to
the nearest main drain, or watercourse, by which the
draining of the adjacent land is at present effected.
Draining
tiles through
mound.
Fencing to
be kept in
order.
Quicks to be
cleaned, and
The permanent fencing shall proceed as rapidly as the
progress of the works and the nature of the season will
admit of.
At the bottom of the embankments small draining tiles
shall be laid through the quick mounds at intervals of not
more than ten yards, to convey the water draining from
the slopes into the fence ditches.
Such parts of the permanent fencing as shall have been
completed, before the finishing of the other parts of the
work, shall be kept in complete order by the contractor.
The quicksets shall be cleaned or weeded twice at least
broken rails in a year, and any broken rails, or posts, or stays replaced
by new ones, equal in quality to those originally used.
replaced.
Dead quicks
to be pulled
up.
Cross fences
to be joined
up.
All quicksets which may not take root and grow must
be pulled up, and three years old living quicksets planted
in their stead.
The railway fencing must be effectually joined to the
cross fences by posts, rails, and quicks, and the mound
for the cross fence must be carried over the ditch of the
railway by means of a short culvert, of a sufficient size to
preserve a free and uninterrupted water-way along the
railway ditch.
RAILWAY SPECIFICATION.
397
Fencing to be
substantial.
Temporary
fences dis-
in particular
cases.
The whole of the fencing, both temporary and perma-
nent, must be firmly and substantially fixed, so as to
exclude sheep, pigs, and all other cattle from the excava-
tions and other works, and effectually prevent the adjoin-
ing lands from trespass during the progress of the
works.
Should the contractor be prepared to erect the per-
pensed with manent fencing on any part of his contract, previous to
any interference with the existing fences of the fields, he
will be permitted to do so, in which case the temporary
fencing may be dispensed with altogether, on that parti-
cular part of his contract.
Temporary
fencing may
be used in
Such part of the temporary fencing as can be made
available shall be permitted to be used in the permanent
nent fencing. fencing, provided the material be of the requisite strength
and quality, and uninjured in other respects by its previ-
the perma-
Fence wall-
ing described.
Gate Posts,
&c.
ous use.
When stone walls are made use. of for permanent
fencing they are to be built of good sound red sandstone
rock, in block, and course work set in lime of the form
and dimensions shown in Drawing, No. The stones
to be firmly bedded and break joint properly.
The
The gates and posts, &c., are represented in Drawing
No. The heads and heels are to be made of sound
oak or ash morticed to receive the horizontal bars,
which together with the diagonal stays and uprights may
be of memel timber, sawn or dressed, or of oak, ash, or
larch; the hanging and clapping posts must be of oak or
stone, if of oak the lower ends are to be charred.
iron work to be of the best quality, neatly fitted up and
riveted to the woodwork; the diagonal and upright pieces
are likewise to be riveted to the horizontal bars. The
whole of the wood to be well seasoned and of sound
quality, and to be put together and fixed in a workman-
like manner, and to receive two coats of good oil paint.
The contract includes gates, with their posts, covered
drains, &c., complete, and comprises about
lineal
yards of single post, rails, and quickset fencing.
If stone gate posts are used the dimensions must not be
less than nine feet in length, with a sectional area of 1½
square feet or fifteen inches square.
398
RAILWAY SPECIFICATION.
Width of
slopes.
Slopes to be
dressed
sown.
and
Slopes to be
altered if
engineer.
EXCAVATIONS AND EMBANKMENTS.
The excavations and embankments throughout this con-
tract shall be thirty feet wide at the level of the red line,
on the section, neither more nor less, and shall extend at
that level to an equal distance on each side of the outside
rails when they are finished and laid in their proper line
as hereinafter described under the head of permanent
way.
The excavations are to be made with the slopes marked
upon the section, where it is stated" 13 to 1," it is under-
stood that where the base of the slope is one foot and a
half, the height shall be one foot only, and when "2 to 1,”
that for the base of the slope two feet, the height shall be
one foot only.
As the cuttings and embankments advance and the
latter become consolidated, the slopes shall be carefully
dressed or trimmed to the specified inclinations, and as
near to the face of the work as possible, and covered with
turf or soil, which shall be carefully obtained from the
surface of the ground to be occupied by the railway.
The soil must be uniformly laid on of the thickness of
six inches, and sown with rye grass and clover seeds, as
soon as the proper season will admit of its being done;
and not less than one pound and a half of rye grass and
one pound and a half of clover seed to be sown on each acre.
When the engineer shall require it, the slopes must be
neatly faced with the turf, not less than eight inches in
thickness, and laid with the green sward outwards.
In the formation of the excavations and embankments,
in this contract, the contractor shall not remove the turf
or soil from the ground for a greater distance than half a
statute chain in advance of the face of the excavation or
embankment, and that which has been cut must be re-
moved back to a point where the slope is ready for receiv-
ing it, and laid down as directed with as little delay as
possible.
Should the contractor be required by the engineer to
required by alter the rate of the inclination of the slopes, he shall do
so, and a proportionate addition or reduction (as the case
may be) shall be made to or from the contract sum, at the
average price per cubic yard stated in the schedule.
Borings.
Shafts have been sunk and borings made on the line in
RAILWAY SPECIFICATION.
399
Contractor to
find all mate-
gons, bar-
rows, &c.
various situations with the view of ascertaining the nature
of the material.
The contractor may see the account, but must satisfy
himself of its accuracy, as no allowance will be made
should the material differ from that account.
Their situations are marked in the general section.
In the formation of the excavations and embankments,
rials, as wag- the contractor must provide all necessary rails, chairs, keys,
pins, blocks, and sleepers, as well as waggons, barrows,
planks, and other machinery, materials or utensils, which
stipulation is however modified to a certain extent by the
following conditions.
Delivery of
permanent
It is not intended to deliver to the contractor any of the
rails, &c. &c. permanent rails, chairs, keys, or pins, until, at least, one
continuous mile of railway, together with three hundred
yards in continuation of each extremity of such mile, shall
have been completed and certified by the engineer as being
ready for the reception of the permanent ballasting, as in
this contract is hereinafter mentioned: on which certifi-
cate, a sufficient number of rails, chairs, keys and pins,
shall be delivered to the contractor by the company, and
he shall be permitted to use them in such manner only as
is hereinafter described in the specification of the laying
and ballasting of the permanent way. Provided, however,
that such permanent rails shall, in no case whatever, be
laid down and employed within three hundred yards of the
face of any excavation, or at the end of any embankment
then in progress.
Surplus ma-
terial to be
Spoil Banks.
The surplus material beyond that required for the for-
deposited in mation of embankments, approach roads, and other em-
banking, is to be deposited in spoil banks, in such places
immediately contiguous to the line of railway as the en-
gineer may direct, the company giving the contractor
temporary possession of the land; the foot of the slopes
of the spoil bank in no case being placed nearer than five
yards to the top of the slope of the railway excavation ;
the height of the spoil bank shall in no place exceed fifteen
feet above the natural surface of the ground. The sides
of the spoil banks are to be sloped at the rate of six hori-
zontal to one perpendicular.
Previous to laying out any spoil bank, the contractor
shall give to the engineer notice in writing, together with
400
RAILWAY SPECIFICATION.
Soil to be re-
moved and
laid upon
Spoil Banks,
and the
slopes of cut-
bankments.
a plan, describing the quantity and situation of the land
he requires for that purpose.
If so directed by the engineer, the contractor must con-
vey the material to any greater or less distance, according
to which, if the cost be thereby increased, he is to receive
a greater or less price as specified in the schedule.
The whole of the soil upon the surface of the ground
through which any excavation extends, or over which
there is any embankment or spoil bank, is to be removed,
tings and em- and afterwards laid upon the slopes of the cuttings and em-
bankments and the surface of the spoil banks, so as to leave
the spoil banks in a state fit for agricultural purposes, and
the slopes of the cuttings and embankments in a state fit for
the growth of grass, or shrubs, either on the line of rail-
way, or on the side of diverted roads or bridge approaches,
or in any situation. The thickness of soil and sodding
over the whole surface and slopes of the spoil banks must
be not less than twelve inches, nor less than eight inches
on the slopes of the embankments, and the contractor is
to sow the slopes of the embankments and the spoil banks
with grass or any other seed which the engineer may
direct. The period at which the soil is laid on and the seed
sown is to be determined by the engineer.
Slips in Ex-
cavations.
All slips which may take place in the excavations, and
which are not attributable to the improper mode in which
the contractor may have conducted the work, are to be
removed by him at the price stated in his schedule: such
as are attributable, in the opinion of the engineer, to any
improper mode of conducting the work, are to be removed
at his own expense, and will be considered as included in
the tender.
Embank
ments.
EMBANKMENTS.
The embankments are to be made with the slopes
stated upon the section, to which the foregoing explana-
tions under the head of excavations will apply.
The embankments are to be formed of the materials
obtained from the excavations, and when finished and con-
solidated they are to be of the height represented by the
red line on the longitudinal section, and of the width
Width and shown on the cross section, viz., thirty feet, being made of
such extra height and width in the first instance, as to
Height.
RAILWAY SPECIFICATION.
401
Embank-
ments to be
kept dry.
Deficiency of
material to
allow for the subsidence of the embankment and they are
to be made at the full height and width at once in a single
battery. The surface of the embankment at the height
of the red line is to be made slightly convex.
Every part of the embankment must be kept dry, and
no water must be allowed to remain either at the base or
upon the surface.
Should there be a deficiency of materials in the adjoin-
be supplied. ing cutting to make up any of the embankments, the con-
tractor must make up the deficiency, either by side cutting
near the spot, or by increasing the width or slopes of the
adjoining cuttings, uniformly, throughout their entire
length, as the engineer may determine. The company
will provide the contractor with land for this purpose,
in such a situation as the engineer may approve, the
contractor bringing the surface of the ground to an uni-
form slope of 6 to 1, and covering it with a layer of sods
and soil not less than twelve inches in thickness.
Pitching
sides.
Slips in Em-
bankments,
Earth to be
trimmed to
slopes and
widths at
In the schedule a price must be named for paving or
pitching the sides of the embankment with red sandstone,
nine inches thick, the price per cubic yard for the em-
bankments remaining the same.
In case of slips taking place in the embankments, the
contractor will be required to make them up at his own
cost.
Whenever the material teemed over the end of the em-
bankment shall not form the proper slope, it shall be care-
once, and no fully trimmed to its required slope, and this operation
made after- must proceed at the same time with the end of the em-
bankment, so as to obviate the necessity of any further
addition of material to the sides of the embankments.
additions
wards.
Large lumps
to be broken.
When the material brought to the embankment consists
of large lumps, they shall be broken into pieces of not
more than six inches in diameter, unless they consist of
rock.
A cross section of an embankment is shown in Drawing,
No.
DISPOSAL OF MATERIAL.
Throughout the whole of this contract, the material
from the excavations is to form the next adjoining em-
bankment as well as the approaches to the bridges, and
402
RAILWAY SPECIFICATION.
Bricks.
No broken
bricks al-
lowed.
Grouting.
Brick on
edge.
Stone to be
of hard sound
quality.
paved crossings of every description, and whenever and
wherever any excavation shall not be sufficient in quan-
tity to complete the next adjoining embankment and
approaches to bridges, or sloped roads, the quantity so
deficient must be brought from the nearest excavation
which shall have a surplus or otherwise obtained by side
cutting at the contractor's own cost, and according to
the conditions contained under the head of general stipu-
lations hereinafter given.
BRIDGES, CULVERTS, &C.
General Stipulations
Which are to apply to the whole of the bridges, cul-
verts, and other works, wherein the workmanship or ma-
terials here described may be used excepting to such work
as may be directed otherwise.
BRICKWORK.
The Bricks made use of thoughout the work shall be
hard, sound, well shapen, thoroughly burnt and of uni-
form size and those used in the face of the work shall be
of uniform colour and unless made a year before they
are used, every brick shall be well saturated with water
before being set.
No broken bricks will be permitted to be used either
externally or internally unless absolutely necessary as
closers, except in case of backing when no course shall
contain a greater number of bats than whole bricks.
No difference of workmanship will be allowed in the
inside and outside work, every course shall be well
grouted, the whole of the joints shall be flushed up solid
with mortar, and the outside joints to be neatly pointed
and drawn. No joint of mortar shall exceed one quarter
of an inch in thickness, and the work shall be laid in
English or Flemish bond, as the engineer may direct.
In all cases where brick on edge is used as coping,
the bricks are to be laid as headers in Roman cement.
STONE.
All the stone used for bridges, culverts, or other masonry
throughout the contract, shall be of a sound and hard
quality, and approved by the engineer and free from
spots and flaws of every description.
RAILWAY SPECIFICATION.
403
Beds to be
dressed.
Cramps to be
used if di-
rected.
Block in
course work.
ASHLAR WORK.
The Ashlar work shall be laid in courses at least nine
inches in thickness, all the beds and joints being chisel
dressed throughout. The whole to be square jointed and
made to fit close. The courses to be laid in such propor-
tion that there shall be at least one header to every
stretcher. No stone shall be less in area of bed than
five feet, nor shall the width of any stone be less than
one and a half times its thickness, and all the joints to
overlap at the least twelve inches.
The greatest care will be required to have all the beds
dressed to accurate planes, and no pinning of any kind
will be permitted in any part of the work, the faces shall
be fair tooled or left rough with rustic champhered joints
as may be directed in the description of each particular
work. The beds of the stones in all arches consisting of
ashlar shall be carefully dressed to fit the summering of
the arch. The whole to be laid in mortar and grouted
at every course.
When the engineer shall deem it necessary the work
shall be cramped together with iron cramps run with lead;
but in this case, the contractor shall be paid extra for
the iron work according to the schedule of prices.
BLOCK IN COURSE WORK.
The block in course shall consist of stones in courses
at least six inches in the thickness and as nearly of an
uniform thickness as practicable. No stone shall be less
on the bed than ten inches by fourteen inches, and where
rubble or brickwork backing is employed there shall be a
through at every six feet in each course so as to bond the
whole effectually together. The face beds and ends of
each stone shall be carefully hammer dressed to accurate
planes, and no pinning of any kind will be allowed.
In all cases where block in course work with rubble
backing is employed, the area in any cross section of
the work shall contain as much block in course as
rubble.
The whole of the block in course work shall be neatly
pointed.
404
RAILWAY SPECIFICATION.
Rubble
Stones not
of a foot.
RUBBLE.
The rubble shall be constructed of stones, each con-
less than 1-6 taining not less than one-sixth of a cubic foot, to be care-
fully laid so as to make the closest possible work; when
employed as backing, each stone to be bedded in mortar
when laid, and the upper surface of the work brought to
an uniform level at the height of every course of the face
work, and the whole to be well grouted at this level.
Squared up
at 18 inches.
A good bond
with Ashlar
When the rubble is not used for backing to the block
in course work, the whole may be brought to a level at
every eighteen inches in height and then grouted.
In all cases great care must be taken to make close work
and effect a good bond with the face, whether it be block
Brickwork. in course work, ashlar, or brickwork.
and
Mortar of
Welsh Lime
and Sand.
dry state.
MORTAR.
The mortar shall consist of fresh burnt Welsh lime, or
other lime approved of by the engineer, and clean sharp
sand in the proportion of two measures of sand to one of
unslacked lime.
Mixed in a They shall be intimately mixed in a dry state, and well
tempered with a proper quantity of water, and only mixed
as required for use; the mortar that has previously set or
become hard upon the ground shall not be permitted to be
used in any part of the work.
Water Lime.
Roman
Cement.
Gravel to 1
of Lime.
If in any situation water lime is ordered to be used, the
contractor shall do so without any extra charge; and where
the engineer shall deem it necessary, the mortar shall be
tempered in a pug mill.
ROMAN CEMENT.
The Roman cement is to be of the best quality, and
shall be mixed with an equal quantity of clean sharp sand.
None shall be used which has set or become hard.
CONCRETE.
Concrete 6 of All concrete must be composed of gravel perfectly clean
and mixed with fresh well burnt quick lime, in the pro-
portion of six parts of gravel to one of lime.
The proportions are to be accurately guaged and mixed
in the dry state, it is then to be moistened and well beaten
RAILWAY SPECIFICATION.
405
To be
Levelled at
every 18
inches
Arches to be
laid with
Mallet.
Ashlar
Quoins.
Any imper-
removed.
until a thorough admixture of all the parts is effected and
brought to a tough consistency, when it is immediately to
be filled into barrows and teemed from a height never less
than eight feet, as near as may be to the place required, so
as to need as little levelling as possible, the runs being
shifted for that purpose.
It is to be brought up in layers not exceeding eighteen
inches in thickness, each layer to be completed and brought
to a level surface before another layer is commenced; the
lime to be fresh burnt, well mixed, and carefully preserved
from moisture until actually used.
ARCHES AND COUNTERFORTS.
The arches, when of brick, shall be laid carefully with a
mallet, and built either in concentric half-brick rings, or
in such other manner as the engineer may direct; and
where counterforts are built upon any part of the arch,
they shall be worked into the body of the arch, and their
courses shall run in the direction of the radii of the said
arch.
In all cases where ashlar stone quoins are used in the
face of the arch, the greatest care will be required to pre-
vent an unequal settlement.
Great care must be taken in the proper summering of
fections to be the bricks or stones in each course, and any irregularity
of form created by imperfections in the laggings, work-
manship, centring, or any other cause, shall be removed
and amended by the contractor.
Askew
Bridges,
laid in spiral
When the arches are askew, the contractor shall lay the
courses to be courses in spiral lines, at right angles to the face, when-
lines. ever he shall be so directed by the engineer; and the beds
of the stones forming the arches shall be carefully dressed
to the proper twist; also, in all elliptical brick arches,
six feet in width measured on each side of the crown shall
be laid in Roman cement.
Soffits
Pointed.
The soffits of all the brick arches shall be well and neatly
pointed.
BACKING TO ARCHES.
The Backing shall consist of rubble work, laid in
mortar, as before described.
406
RAILWAY SPECIFICATION.
Abutments
of Brick or
Stone as
drawings de-
scribe.
Bricks in
Spandrills to
be dressed.
Openings to
be left in
wings.
Parapet.
Imposts.
Skewbacks.
String
Courses and
Coping.
ABUTMENTS, WINGS, AND SPANDRILS.
The abutments, wings, and spandrils will consist either
of brickwork or stonework laid in mortar, as before de-
scribed, and they will be built battering or plumb, as shown
on the drawings.
The bricks in the spandrils must be neatly cut, or the
stone work neatly dressed, so as to fit the extrados of the
arch; where the work is battering on the face, the courses
shall be laid at right angles to the batter.
Small openings shall be left in the lower parts of the
abutments and wing walls for the effective drainage of
water which might otherwise lodge behind them.
PARAPET WALLS.
The parapets to be built plumb on each of the sides,
the straight part to be perfectly true, and the curvature
of that portion upon the wing walls uniform and regular.
The courses to be made parallel to the string course
and coping.
STONE IMPOSTS.
Where stone impost or springing courses are used, the
stone shall always be equal to the full thickness of the
arch, and no stone shall be less than two feet six inches
in length, and when required they shall be dowelled and
cramped together.
In cases of skew arches, the skewbacks must be worked
so as to suit the oblique directions of the springing of the
courses, and in every course the stones shall be fair tooled
all over, excepting at the back which may be left rough.
STRING COURSES AND COPING.
These must be of the form and dimensions shown upon
the drawings. No stone must be less than two feet
six inches in length, and the whole to be throated under-
neath.
Each stone in the coping must be dowelled and leaded
to the adjoining one.
All the surface must be fair tooled or chisel dressed,
and the joints made square and to fit close.
RAILWAY SPECIFICATION.
407
Cast Iron
from Cupola.
IRONWORK.
Wherever cast iron is required to be used, it shall be
cast from the cupola, and be of the toughest grey iron,
free from air bubbles or pin holes, or any other defect.
All the abutting faces must be filed and accurately fitted.
All wrought iron work to be of the best hammered
scrap iron.
Iron Work to All iron work to be subjected to whatever test the engi-
be tested.
neer may think it expedient to prescribe, and any defect
which may be detected, is to be rectified at the expense
of the contractor, and likewise the cost of testing defrayed
by him; but the contractor is not exempted by the above
provision from the obligation to uphold the work when
erected.
Wood to be
Kyanized.
Drains under
Bridges.
Wall 9 inches
WOODWORK.
All woodwork in gates, sleepers, &c., and all other wood-
work to be subjected to Kyan's patent process, to be of
sound memel timber or American pitch pine, free from
knots and other imperfections, and to be well seasoned
before subjected to Kyan's process, to receive three coats
of good oil paint.
All bolt holes to be well charged with thick white paint.
All arrisses to be champhered.
DRAINS UNDER Bridges.
Drains must be constructed under all the bridges which
are in the excavations on each side of the railway, fifteen
inches wide at the top, and twelve inches at the bottom,
to be sunk as low as the drain at the outside of the bal-
lasting.
They will be formed by a wall of brick or of block in
course stone work to support the ballasting, nine inches
deep and three feet deep parallel with the abutments, and
the length will be equal to the width of the bridge, and
as much more as shall be necessary to conduct the water
easily in the common side drains.
The whole to be laid in mortar in the same manner as
described for the bridges.
408
RAILWAY SPECIFICATION.
Contractor
to excavate
EXCAVATONS OF FOUNDATION, PROVIDING CENTRING,
FILLING IN OVER BRIDGES, AND OTHER GENERAL
REGULATIONS.
The contractor is to excavate for the foundations of all
foundation of bridges, culverts, and all other works, to keep out the
Bridges. water by coffer dams, if necessary; form drains, do all
necessary pumping, and provide all centring, planks, and
tools of every description necessary to the perfect execu-
tion of the works at his own expense, and they are to be
included in the amount of this tender.
If founda-
tions carried
price as per
Schedule.
In case the foundation of any of the works require in
lower, extra the opinion of the engineer to be carried lower than is
shown upon the drawing, the contractor is to make such
extra excavations, provide extra coffer dams, and to do all
extra pumping or other contingent works incident thereto,
being paid only for the increased quantity of brickwork
or masonry, concrete, or other material according to the
prices set forth in the schedule for such description of
work.
Foundations.
puddled
over.
The foundations must be cut out as nearly to the size
of the brickwork or masonry as possible, and the vacant
spaces must be carefully punned up to the surface of the
ground.
Arches to be The arches of all bridges are to be carefully puddled
over their entire surface with a layer of puddle not less
than nine inches in thickness; and the space between the
wing walls of all the bridges shall be filled in with hard dry
material well rammed down where it can be obtained, but
when it is necessary to use clay for that purpose, it shall
be firmly punned in layers of not more than nine inches
in thickness.
Bridges to be
balanced.
Stays if ne-
cessary to be
used.
In bringing an embankment up to a bridge the con-
tractor shall load the bridge equally on both sides, by wheel-
ing the material from the embankment or elsewhere, or
by teeming from off the bridge so as to allow of its laying
against the abutment, with a slope outward from it, and
punning it as previously described, so as to ensure its per-
fect form and safety.
He shall also take such additional precaution as the en-
gineer may consider necessary, by setting up temporary
or permanent stays or shores without making any extra
charge.
RAILWAY SPECIFICATION.
409
Water from
Bridges to be
through
In all bridges where there is more than one arch, the
carried spandrills shall be completely drained by means of iron
Abutments. pipes, or the openings cased with brick, in cement, through
the centre of the piers and abutments.
Piers and
String course
and parapet
on till di.
The string course, parapet walls, and coping shall not
not to be put be put on until after the centres are withdrawn; and in
no case shall the centring be struck before permission of
the engineer is obtained.
rected.
Centring.
Rails to be
laid equi-dis-
tant from
side walls.
Embanked
Approaches.
Surplus ma-
terial to be
approaches to
All the centring shall be such as shall be approved of
by the engineer.
Great care must be taken that each bridge is so placed
that the outside rails, when laid in their uniform and
pro-
per line, are equidistant from, and parallel with, the
faces of the abutments or parapet walls, according as the
bridge is over or under the railway.
It is to be understood, that whenever in the drawings,
or in
any part of the particular specification, the dimen-
sion of parts, or the nature of materials, may be directed
differently from the above general stipulations, the parti-
cular directions are to be complied with.
APPROACHES TO BRIDGES AND PAVED Crossings.
Drawings, No.-.
These excavations and embankments are to be made in
the same manner as before described for the main line of
railway, and with such slopes as may be directed by the
engineer.
The contents of the excavation shall be conveyed to
the nearest embankment or spoil bank.
The embankments are to be made from the surplus ma-
terial in the excavation.
When no surplus exists, then the material shall be pro-
cured from side cutting in the nearest excavation, and the
contractor to be paid for it at the rate specified in the sche-
dule of prices attached to his tender.
But wherever there is a surplus material, the contractor
used to form shall employ it to form approaches to bridges or sloped
Bridges, &c. roads, and the cost of so employing it shall be considered
a part of his contract, to which the stipulations and prices
for extra work do not apply.
Excavated
approaches.
The same regulations shall be applicable (where side
cutting is required) to the excavation of these approaches.
2 C
410
RAILWAY SPECIFICATION.
Approaches
to be of height
All the approaches shall be made of the height, depth,
in the Draw- and inclination shewn upon the section of the approaches
to each bridge.
ings.
Metalling.
Length.
The metalling shall in all cases be the width of the
bridge between the abutments and parapet walls, as the
case may be, and the width of the cutting or embank-
ment shall be five feet more than this at the level of the
top of the metalling.
The length shall be equal to the whole distance of the
altered surface as shown in the section of approaches.
Slopes 11 to 1 All the slopes of both excavation and embankment of
bridge approaches being made at the rate of 18 inches
horizontal to 1 foot in height.
Embank-
ment to be
beaten.
2 Coatings of
Broken
Stones.
Ruts to be
filled up.
To be fenced.
Rails to be
painted.
Two Lines of
Posts and
Rails.
The surface of the embankment when formed, shall be
made regular and even, and well beaten with heavy
beaters.
First, a cover of brushwood or heath, and then a coating
of good gravel or broken stone must be laid over the whole
surface eight inches in thickness, and as soon as it shall
have become hard by the carriages passing over it, another
covering of material, of equal quality with that upon the
road at present, shall be laid on seven inches thick in the
middle, and four inches thick on each side.
The ruts must be filled up from time to time, and the
surface kept smooth and even.
The whole of the approaches which are embanked from
either termination of the earthwork to the parapet walls
of the bridges must be protected on both sides by wood
posts and rails, as shown in Drawing, No. -.
The wood railing must be made of good oak, free from
sap, and straight grained.
The rails, and so much of the posts as are shown above
the ground, shall be sawn out square, neatly planed, and
painted with two coats of stone-coloured paint; all the
joints must be made with white lead, and all the wood
beneath the surface of the ground well charred.
Those approaches where the line of road and not the
level is altered, and also those that are formed by exca-
vating, must be protected on each side and throughout
the whole of the extent of the alteration by quickset
fencing and ditching, similar to that described for the
railway, but having an additional line of posts and rails,
namely, one on each side of the quicksets.
RAILWAY SPECIFICATION.
411
Temporary
Roads to be
fenced
during
alterations
to public
Roads.
Previous to the works connected with any bridges,
provided and approaches to bridges, approaches to paved crossings, or
diversions of roads, which may in any way affect existing
roads, being commenced, a good and well-made tempo-
rary road shall be provided and maintained for the free
and uninterrupted passage of carriages of every descrip-
tion. Every precaution shall be taken by the contractor
during the alteration of any road to erect proper fencing,
and fix and maintain lights for the protection of travellers,
as the company will not be held responsible for any injury
which may arise from the neglect of these precautions.
The whole of these observations shall be considered to
apply, unless in any particular case they may be directed
otherwise.
Paving
Stones.
Rails to be
protected by
Iron Bars.
PAVED CROSSINGS.
Drawing, No. —.
All the roads crossing the railway without bridges, are
to be paved at the intersection with the railway, in the
same manner as shown in Drawing, No.
with good
six-inch paving stones of Penmaen Mawr, Dublin, or other
granite equally good.
The paving must be laid on a bed of fine clean gravel
of six inches in thickness, in a solid and substantial
manner.
The paving stones must be cubes as near as possible.
Each rail must be protected by two iron bars, as shewn
in Drawing, No.-; they will be considered part of the
rails, and provided by the company. The present con-
tract is to comprise six of these, and any additional number
that may be required shall be executed at a price to be
named in the schedule.
Culverts.
CULVERTS.
Drawing, No.
The culverts throughout this contract are to be built in
the situations marked upon the general section, of the
form and dimensions shown in Drawing, No.-. The size
being selected to suit the particular situation.
412
RAILWAY SPECIFICATION.
Directions of
Drain to be
altered.
Soft Ground
to be taken
out.
Cover of dry
material to
Culverts.
Wherever the direction or position of the culvert does
not correspond with that of the stream, either in line or
level, the stream shall be altered so that the water may
be conducted to or from each end of the culverts in the
manner best fitted for facilitating the drainage.
Where the foundations are insecure, the soft ground is
to be taken out, and the space filled in with solid dry
material, such as the engineer shall approve of, without
any extra charge.
All culverts exceeding three feet diameter, shall be
be laid over covered with dry or hard material two feet above the top,
and ten feet on each side; and the part adjoining the cul-
vert, extending to a distance of four feet from the brick-
work or masonry, to be well punned in layers of one foot
in thickness, before the embankment shall be allowed to
come upon it.
Culverts to
extend under
Fences.
Alterations
in Roads.
Soil to be
taken off.
Metalling.
Where no
Fencing or
quired.
Culverts, under three feet in diameter, are to extend in
length under the fence of the railway; each culvert must
be built in a direction which may, in the opinion of the
engineer, afford a free and uninterrupted passage for the
water.
The general stipulations for masonry and brickwork,
hereinbefore given, are applicable to these culverts.
DIVERSION OF ROADS.
The alteration necessary to be made in the direction of
the existing roads for this contract, exclusive of those
which are required in approaching bridges, are shown upon
the general plan (Drawing, No. —).
Where the level of the new roadway is near the sur-
face, the top soil must be removed from the space to be
occupied by the road, and the surface made uniform and
regular for receiving the metalling.
The material and manner of laying it on to be the same
as described for the approaches to bridges, the thickness
being twelve inches when a public road, and eight inches
when an occupation road.
In cases where, in the opinion of the engineer, no me-
Metalling re-talling or fencing is required, a deduction will be made of
the cost of such metalling or fencing, according to the
schedule of prices.
Excavations
or Embank-
ments.
Any excavation or embankment that may be necessary,
RAILWAY SPECIFICATION.
413
Fencing.
Planes.
Curves.
Laying and
Ballasting.
shall be done by the contractor in the same manner as
directed for similar works upon the line of the railway.
The fencing shall be similar to that described for the
railway, but having an additional line of posts and railing,
viz., one on each side of the quicksets.
BALLASTING AND LAYING THE PERMAnent Way.
The railway is intended to form a double way, composed
of four single lines of rails.
The several level and inclined planes are shown by the
blue line on the Section Drawing, No. —, which repre-
sents the surface of the rails, and the directions on the
general plan, (Drawing, No. —).
The greatest care will be required that the portions
shown upon the plan as straight be made strictly so upon
the ground, and that the curves are all uniform and neatly
brought into the straight lines.
The laying and ballasting the permanent way is in-
tended to be completed in such portions and at such
times as will suit the convenience of the contractor in
executing the works.
Previous to the delivery of the materials of the perma-
nent way to the contractor, the surface of the embank-
ments and bottoms of the excavations shall have been
made of the proper line, height, and depth, and uniform
Embank- in width, level, and inclination. They shall be completely
Excavations drained from all water, and certified by the engineer as
&c. being in a fit state to receive the permanent ballasting.
Materials. The materials to be delivered to the contractor will con-
ments and
to be drained,
Delivery of
Materials.
Lengths.
sist of sleepers or blocks, rails, chairs, and fastenings;
and he will be held responsible for the replacement in case
of loss or injury to the materials thus delivered to him
from the time of their delivery till the expiration of this
contract.
They will be delivered by the company at some conve-
nient wharf, whence they must be conveyed by the con-
tractor to the works at his own expense.
The company
will provide the necessary sleepers, a particular description
of which is hereinafter given.
The rails will be in lengths from 12 to 18 feet; they will
be supported at every yard by a cast-iron chair or pedestal,
which will be accompanied by wrought-iron keys for fixing
414
RAILWAY SPECIFICATION.
Broken
Stone Bal-
last.
Inches thick.
Top Layer of
Broken
Stone.
Ballast to be
beaten.
Bed of Sleep-
ers to be
beaten,
If too low to
be raised.
Rails to be
laid level.
the rails on the chair, and with two pins or spikes for
fixing the chair on the sleeper.
The dimensions of each part, and the construction of the
whole, are shown on Drawing, No.-.
The material for ballasting shall be composed of broken
stone, cinders, or clean gravel, entirely free from any ad-
mixture of clay or material retentive of moisture; if broken
stone be used, none shall be larger than will pass through
a ring two inches in diameter.
The ballasting shall be spread over the whole surface of
the tops of the embankments or bottoms of the excavations
between the drains, of an uniform thickness of twelve
inches.
And as soon as the sleepers have been carefully laid, the
intervals between them, and between the outer ends and
the edge of the embankment, or the drain at the bottom of
the cuttings, are to be filled in to the level of the top of the
sleeper with broken stones, equal in quality to those in the
bottom bed, and to a height of two and a half inches below
the surface of the rail, and the interstices to be filled in
with smaller stones, they being beaten down to render the
entire width a consolidated mass.
This stratum of ballast shall be beaten into a firm and
solid mass by heavy beaters, worked by at least two men;
and the thickness before mentioned shall be considered to ap-
ply only after this operation has been effectually performed.
Upon this surface the sleepers are to be laid in their
proper situations for receiving the rails.
The ballasting intended for the bed of the sleepers shall
be beaten by heavy beaters, and each sleeper also forcibly
beaten when it has been placed in its position until it has
become firmly and uniformly bedded throughout its whole
length and reached its proper level.
If it should be found lower than required, it shall be re-
moved, and additional material to be placed in its bed; the
same process as before must then be renewed until it has
reached its proper level.
The rails must be laid at the proper level and inclina-
tion, and at the proper bevil to fit the cone of the wheels,
to be perfectly parallel, and at the same height at any one
point; the joints must be made perfectly even, whether
square, half-lapped, or scarfed, and be firmly secured in
the chairs.
RAILWAY SPECIFICATION.
415
feet apart.
Lines to be 6 The two lines of way are to be six feet apart, and the
width between the insides of the rails of each way four feet
eight inches and a half.
Sleepers to
be chaired,
Rails to be
straightened.
Contractor
may use
Excavations,
casion defi-
The wood sleepers must be cut on the upper surface to
the proper level for the reception of the chair, which must
be firmly fixed on the exact guage, to be furnished by the
engineer. The pins shall not on any account be driven
into the sleepers without the hole having been previously
bored with a proper sized auger.
The rails must be securely fixed in each chair by keys;
the chair shall be firmly fixed on the sleeper.
Any of the rails which may be twisted or bent in the
least degree, to be made perfectly straight with proper
hammers and anvils, previous to their being laid down.
The contractor may use any rock, gravel, or other
Gravel out of suitable material for ballasting which may occur in any of
but not oc- the excavations included in this contract; but if in so doing
ciency. he shall cause any deficiency in the material for the for-
mation of the embankments, he shall make up the deficiency
by a side cutting in such of the excavations as the engineer
may point out, and at his own expense.
Stone taken
from Cut-
tings not to
occasion de-
ficiency.
No material
to be taken
from Em.
bankments.
Tile drains.
To be laid
without mor-
tar part in
water lime.
The contractor is also at liberty to obtain stone for
bridges, culverts, drains, or other masonry, provided it is
of a quality approved by the engineer; but if in so doing
he shall cause any deficiency in the material for the forma-
tion of the embankments, he shall make up the deficiency
by a side cutting, at his own expense, in such of the exca-
vations as the engineer may point out; and if such side
cutting shall require an additional quantity of land, the
contractor shall indemnify the company for the purchase
of the same.
The contractor shall in no case remove any material
from the intended sites of any of the embankments unless
permitted by the engineer.
Tile drains, throughout all the excavations, are to be
laid in the ballasting, as shown in Drawing, No.-; one
shall be laid in the centre of the ballasting throughout the
whole extent of the excavation, and shall have cross drains
at intervals of every five yards, communicating with the
drains on either side alternately; they must be properly
and securely laid, without mortar, excepting 18 inches in
length at the open ends, which shall be laid with water
lime.
416
RAILWAY SPECIFICATION.
Receipt for
Rails.
Contractor
may make
Sidings.
Limit to
weight car-
porary wag-
gons.
The contractor shall give the assistant engineer a receipt
stating the number of rails or other materials in each par-
cel delivered to him and placed in his possession; he shall
be accountable for the loss of any part of them; he shall
also replace any rails, chairs, pins, blocks, trenails, or
sleepers which may have been broken, or otherwise ren-
dered unfit for use while in his possession, or during the
progress of the works.
The contractor shall be at liberty to make sidings or
crossings from one line of the permanent road to the other,
for his own convenience during the progress of the work,
provided he does not injure the rails in so doing, and re-
moves them when the works are complete.
No waggons, carriages, or engines employed by the con-
ried on tem- tractor on the permanent road, shall have a greater weight
placed on any one axle than three tons, unless the engine
or carriages are placed on good and sufficient springs; and
when they are so mounted, the weight on any one axle
shall not exceed four tons.
Permanent
way to be
Such portions of the permanent road as are used by the
maintained. contractor in conveyance of material from the excavations
(according to the stipulations already described under that
head,) or for any other purpose, shall be carefully attended
to, and kept well drained, and in good repair, and ad-
justment.
No Sleeper
to be used if
injured.
Sleeper to be
No sleeper which has been used in any temporary road
during the progress of the work shall be made use of in the
permanent road, unless such shall have been inspected and
pronounced sufficient by the engineer.
WOODEN SLEEPERS.
The sleepers to be of larch, oak, pitchpine, or teak.
Larch sleepers to be cut from sound trees, slowly grown;
9 feet long. each sleeper to be nine feet long by 10 inches wide and
five inches thick, at the centre of the smaller end, being a
pole of larch ten inches in diameter (exclusive of bark,) at
the smaller end, and nine feet long, sawn up the middle.
Oak, Larch,
or Teak.
When sleepers are cut from oak trees not larger than
those above specified for larch, they shall be sound, and of
the same dimensions and thickness, but these dimensions
are only to include half an inch of sap.
When the sleepers are made from large timber, whether
RAILWAY SPECIFICATION.
417
To be
Kyanized.
Sidings to be
as drawn and
directed.
Rails to be
Cut.
Contractor
to find Bal-
last.
Time of
Completion.
Measure-
ments.
Contractor
to be
present on
works.
Contractor
oak, pitchpine, or teak, they shall be sound, free from sap
or decay, and not shaken, to be squared up to the dimen-
sions of nine inches by four and a half inches at the smallest
part and nine feet long. All the wooden sleepers above
described are to be subjected to Kyan's Patent Process.
LAYING AND BALLASTING THE PERMANENT SIDINGS.
The sidings are to be laid in such positions and in such
lengths as may be directed by the engineer; they must be
laid in the manner and form shown in the Drawing.
The contractor will be required to take up any part of
the rails already laid down that may be found necessary to
cut them into their proper lengths for the reception of the
other iron work, to relay them, and fix all the necessary
crossing plates, check rails, moveable points, or sliding
rails, with the requisite machinery for moving them.
The whole must be made equally as firm and substantial
as the other parts of the permanent way. The specifica-
tion of the permanent ballasting, already described, must
be considered applicable in all respects to the construction
and ballasting of the sidings. The iron rails, chairs, keys,
pins, points, crossings, switches, check rails, moveable
points, or siding rails, and sleepers, being found by the
company.
TIME OF COMPLETION, MEASUREMENTS, PAYMENTS, &c.
The contractor shall, on or before the
complete the whole of the works herein specified, and
such additional works as the engineer may direct to be
executed, so as to render the line of railway along the
whole distance in every respect fit for the safe and conve-
nient transit of locomotive engines and other carriages.
All measurements of works shall be according to the
actual dimensions, notwithstanding any general or local
custom to the contrary.
The contractor shall at all times be present on the works,
or in his absence he shall provide a competent representa-
tive, fully authorized to act in his behalf in all matters re-
lating to this contract.
The contractor shall at all times, by day and by night,
418
RAILWAY SPECIFICATION.
and materials
and to
proceed as
Engineer
directs.
to find labour provide and use, at his own cost, all overlookers, labour,
and materials of every description whatever that may be
required for proceeding with and completing the works in
a workmanlike manner, and shall proceed therein at the
rate of progress that may be from time to time required
by the engineer.
Descriptions
and stipu-
lations,
It is to be understood, that though certain descriptions
and stipulations are not repeated or implied in different
repeated, to parts of this specification, and in the contract to be entered
though not
be under-
stood.
Contractor
to furnish
every two
months.
be made.
into for the fulfilment of the same, it shall not be thence
inferred that the remaining directions, descriptions, and
stipulations, of which there shall be no repetition or ampli-
fication, are in anywise invalidated.
The contractor shall at intervals of every two months
statements furnish to the engineer a statement of all contract work
done by him during that period; the value of which work
shall be estimated according to the schedule of prices at-
tached to the contract, and the amount of such account,
Payments to after being certified by the engineer, shall be paid to the
contractor after deducting 10 per cent. off the amount;
one half of such deducted sum for the preceding six months
shall, at the discretion of the company, be paid over to
the contractor at the termination of every interval of six
months, if the contractor is proceeding with the works to
the satisfaction of the engineer, and he shall certify to that
effect, and the remaining half shall remain in the hands of
the company during the progress and till the completion
of the works, and for twelve months after their completion,
when the amount, together with interest at the rate of 4
per cent., calculated from the period of completing the
work, shall be paid to the contractor upon the certifi-
cate of the engineer of the whole of the work being in a
satisfactory and proper state.
Advances to
the Con-
tractor.
Contractor
to furnish
previous to
advances
In intervals between the periods of payments above-
named, viz., every two months, the company will, if re-
quired, advance to the contractor payments on account of
work and materials; the amount of such payments being
dependent upon the certificate of the engineer.
The contractor shall furnish to the engineer a statement
statements of work done, and in respect of which he requires inter-
mediate advances; but the certificate of the engineer shall
only be for such amount as he may think proper to certify.
And should the engineer be at any time dissatisfied with
being made.
RAILWAY SPECIFICATION.
419
do not
proceed
satisfactorily,
If the works the nature or mode of proceeding in or at the rate of pro-
gress of the work, or any part thereof, he shall have full
Engineer has power to procure and make use of all labour and materials
procure any which he may deem necessary, deducting the cost of such
assistance he labour and materials from the money that may be due or
power to
labour or
may deem
necessary,
and charge
cost to
Contractor.
Alterations
in additions
tions from,
any of the
works.
become due to the contractor. But it is hereby expressly
declared, that the possession of this power by the engineer
shall not in any degree relieve the contractor of his obli-
gation to proceed in the execution of, and to complete the
works with the required expedition. Should the con-
tractor fail to proceed with the works in the manner and
at the rate of progress required by the engineer, this con-
tract shall be (at the option of the company but not other-
wise) considered void, so far as relates to the work remain-
ing to be done; and all sums of money that may be due to
the contractor, together with the materials and implements
in his possession, and all sums of money named as penalties
for the non-fulfilment of the contract, shall be forfeited to
the company, and the amount shall be considered as ascer-
tained damages for breach of contract.
It is to be distinctly understood that the engineer may
to, or deduc- at all times direct that there shall be made any alterations
in, additions to, or deductions from, any of the works
hereinbefore described or referred to; and which alter-
ations in, additions to, or deductions from, the amount of
work contracted for, shall be valued or estimated according
to the schedule of prices, filled up by the contractor, and at-
tached to his tender, and that the prices inserted in the
schedule shall be considered including all labourage, mate-
rials, and all contingent expenses connected with the work
to which such prices apply, and the contractor is required
to fill up the whole of the schedule, whether the same
appears applicable to the present contract or not.
420
RAILWAY TENDER.
of
I
FORM OF TENDER.
do hereby propose
to make and complete the railway, with all the excavations, em-
bankments, bridges, culverts, drains, fences, and other works con-
nected therewith, including the laying and ballasting the permanent
way throughout the entire length, from
to
being a
and to keep the same
distance of
in repair for one year after completion, and to find and provide all
the requisite materials (except the iron rails, sleepers, chairs, and
fastenings) according to the plans and specifications, and within
the periods, and upon the terms and conditions mentioned and
contained in the draft contract, exhibited to me, for the sum
of
And I have in the SCHEDULE hereto annexed, set forth the
price of the different descriptions of work at which the aggregate
amount of this tender is computed, and according to which the
value of all additions to, or deductions from, the work specified, is
to be estimated; and hereby undertake to execute a contract accord-
ing to the draft before referred to within a fortnight from this date.
And I propose
and
of
of
as sureties
day of
for the due performance of such contract.
WITNESS my hand this
SCHEDULE referred to, containing a list of the prices at which the
foregoing tender of
is computed, and according
to which the value of all additions to, or deductions from,
the work specified, is to be estimated.
Average price of earthwork deposited in embank-
ments, per cubic yard
Earthwork deposited in embankments when the
length of lead does not exceed one quarter of a
mile, at per cubic yard
Not exceeding half a mile
£ s. d.
at per cubic yard
Not exceeding three-quarters of a mile
do.
Not exceeding one mile.
do.
Not exceeding one mile and a quarter
do.
Not exceeding one mile and a half
do.
Not exceeding one mile and three-quarters do.
Not exceeding two miles
do.
For every additional quarter of a mile
do.
RAILWAY TENDER.
421
Average price of earthwork in spoil banks per cub. yd.
Earthwork in spoil bank excavated to the depth of
10 ft. below the surface of the ground, at per cubic
yard
Earthwork for every succeeding 10 ft. in depth, at
per cubic yard
Earthwork barrowed a distance not exceeding 25
yards, at per cubic yard
Ditto for every additional 25 yards, ditto
Soiling and sodding embankments, &c., including
sowing with hay seeds, per sup. yard
Soiling and sodding cuttings, per do.
Dry pitching with sand stone, 9 in. thick, per do
Ashlar stone in foundations and in bond courses,
pick dressed, and set in mortar, at per cubic yard
Ashlar stone in walls from quarry, per cub. foot
£ s. d.
Tool dressed and set
Hammer dressed and laid
in mortar.
in mortar.
Do.
Do.
Do.
Do.
Do.
وو
وو
وو
وو
do.
do.
do.
do.
do.
Block in course stone work from quarry, per
cub. yard
Do.
Do.
Do.
Do.
Do.
Do.
وو
from
وو
وو
دو
وو
do.
do.
do.
do.
do.
do.
Coursed rubble backing with mortar, per cubic yard
Random rubble backing
Do.
do.
do.
laid dry
Well-burnt hard bricks, per thousand
do.
do.
Brickwork of do. set in mortar, at per cubic yard
Brickwork of blue Staffordshire or Bulkley mountain
bricks, at per cubic yard
Extra price of masonry in askew arches, at do.
Extra price of setting masonry or brickwork in Ro-
man cement, at do.
Do. of setting masonry or brickwork in water lime,
at do.
Concrete (6 of gravel to 1 of lime) with common
lime, at do.
422
RAILWAY TENDER.
Concrete with water lime, at per cubic yard
Puddle of clay, well tempered, at do.
•
Do. laid in 9 in. courses, and well punned, at do.
Common rubble walls for feuces, including coping
set in mortar, per Drawing, No.-, at per sup.
yard
•
Larch sleepers, Kyanized, at per sleeper
Do. do. chaired and laid, at do.
Oak sleepers do., at do.
Do. do. chaired and laid, at do.
Common draining tiles laid in drains, at per thousand
Bulkley mountain drain tiles, at do.
Post and rail fencing, including ditch and quicksets,
at per lineal yard
A field gate, with posts, &c., complete
Larch posts for fencing, 6 ft. 6 in. long, at per post
Oak posts
Larch rails
do.
do.
do.
do.
10 ft. 6 in. long, at per rail
Post and rail fence for approaches to bridges, as per
Drawing, per lineal yard, single fence
Laying and ballasting permanent way, including tile
or brick drain, per lineal yard
Laying permanent way, exclusive of ballast and
drains, per lineal yard
Ballasting only, per cubic yard
Furnace slags, broken or spread, per ton
Common cinders,
do.
do.
A paved crossing, complete, (see Fig.—, Drawing,
No.—).
Leading rails, and other materials, including loading
and unloading, at per ton per mile
Pitch pine timber in balks, or large scantlings, de-
livered, at per cubic foot
American red pine, do.
Do. yellow pine, do.
Baltic or Memel do.
Subjecting timber to Kyan's patent process, do.
Cast-iron in girders or heavy work, fit and fixed, at
per ton
Do. in columns or piles,
Do. small and ornamental,
do.
do.
do.
do.
Wrought-iron, upwards of 7lbs. in a piece, such as
plates, bolts, &c., fit and fixed, at per cwt.
£ 8. d.
RAILWAY TENDER.
423
Wrought-iron, less than 7 lbs., and more highly
finished, fit and fixed, at per cwt.
Paving roads or streets with Welsh boulders, 6 inches
thick, per sup. yard
Ditto square sets,
do.
do.
Metalling roads with hard stone, broken and spread,
at per cubic yard
An occupation bridge over the railway
Do.
do.
Culverts of 6 ft. diam. without fronts, per cub. yd.
£ s. d.
According to general
Drawing.
under
Do.
5
do.
do.
do.
Do.
4
do.
do.
do.
Do.
3
do.
do.
do.
Do.
2 do.
do.
do.
Do. 1-6 do.
do.
do.
Culvert fronts
do.
The price of sheet piling of Dantzic or Memel tim-
ber from 4 to 8 inches in thickness, shod with iron,
hooped, and driven to any depth not exceeding 15
feet, and the tops cut off level and bolted to the
walling, at per cubic foot
Do. driven to a greater depth than 15 feet, but not
exceeding 20 feet, at per cubic foot
Do.
25 feet,
at per do.
The price of memel or beech sleepers (" Waling tim-
ber") bolted to the pile heads, complete, at do.
The price of larch, beech, or memel bearing piles,
from 10 to 16 inches diameter, hooped, shod, and
driven, with their tops cut off and levelled, ready
to receive the planking-
For any length not exceeding 15 ft., at per cubic foot
Do.
Do.
20 ft.,
25 ft.,
do.
do.
The price of memel or beech planking, 2 to 4 inches
thick, spiked to the pile heads, and prepared for
the masonry, at per cubic foot
The price of maintaining or keeping in good order
the double line of permanent way and fences for
the period of one year after the completion of the
whole works, at per mile
N.B. It is to be understood that only the exact quantity or net
measurement of any material or work is to be taken in all cases,
notwithstanding any custom to the contrary.
424
COLONIAL SURVEYING.
CHAPTER XIII.
COLONIAL SURVEYING.
THE first operations required in a perfectly new settlement, are,
the division of the land upon which settlers are to be located into
sections of such size as may be considered best adapted to their
wants,—and the marking out the plan of the first town or towns,
the sizes and positions of which will of course be regulated by local
circumstances and advantages; whilst the first rural sections will
naturally be required either in their immediate vicinity, or conti-
guous to the main lines of communication leading to the different
portions of the province, whose local importance is the earliest
developed.
In the case of a small settlement established upon the coast of
any country for the immediate reception of settlers who require to
be put in possession, directly upon their arrival, of a certain stipu-
lated amount of land for agricultural or other purposes, the
simplest form of survey must necessarily be adopted; that de-
scribed in Capt. Dawson's Report upon the Survey of New
Zealand for instance,-which consists simply in marking methodi-
cally upon the ground the angles of a continued series of square
or rectangular figures, leaving even the roads which are intended
to surround each block of sections, to be laid off at some future
period,―would answer the purpose of putting impatient emigrants
in possession of a homestead containing about the number of acres
to which they might be entitled. But this system could not be
carried out extensively with any degree of accuracy, even in a
comparatively level country, and not at all in a mountainous or
irregular one. In fact, it is not a survey; and though perhaps it
may sometimes be necessary to adopt what Mr. F. Wakefield, in
his recently-published pamphlet upon Colonial Surveying, terms
this "make-shift process," the sooner a regular survey takes its
place the better for the colony, even on the score of the ultimate
saving that would be effected by getting rid of the necessity of
incessant alterations and corrections; to say. nothing of the amount
* For an explanation of the details of this species of surveying, see Mr. Kingston's
Statements, page 33, Third Report of the South Australian Commissioners, 1838; and
Captain Dawson's Report on the Survey of New Zealand, 1840.
COLONIAL SURVEYING.
425
of litigation laid up in store by persevering in a system necessarily
entailing an incorrect division of property, upon which there is no
check during the progress of the survey, and for which there is no
remedy afterwards.
Excepting in some isolated instances such as described above,
where every thing is required to give way to the imperative
necessity of at once locating the first settlers upon land for which
payment has been received, (for, by the present system of colo-
nization, no land is alienated from the Crown otherwise than by
purchase, the greater portion of the proceeds of the sale being
devoted to the purpose of further emigration,) the first step to be
undertaken at the commencement of the survey of a new country,
is a careful and laborious exploration within the limits over which
its operations are to extend; during which would be collected for
subsequent use a vast amount of practical information as to the
number and physical condition of the aboriginal natives (if any);
the geological character of the soil; its resources of all kinds;
sources and directions of rivers; inland lakes and springs; the pro-
bable sites of secondary towns; the most apparent, practicable, and
necessary main lines of communication; prominent sites for trigo-
nometrical stations, &c., &c. A sketch of the country examined,
rough and inaccurate doubtless, but still sufficient for future
guidance, is at the same time obtained; the positions of many of
the most important points for reference being determined by astro-
nomical observation, and the altitudes of some of them by the
mountain-barometer or aneroid.
The next step should be, if this question has not been already
determined by strongly-marked local advantages, or previous
settlement, the position of the site of the first principal township;
a nucleus being immediately required where fresh arrivals may be
concentrated, prior to their dispersion over the country. The size*
and figure of the town will of course vary according to circum-
stances; and the principal general requirements that should suggest
themselves to any one charged with a decision of this nature, are,—
facilities of drainage; plentiful supply of good water; easy access
both to the interior of the country, and, if not situated on the coast,
to the adjacent port; the apparent salubrity of the site; facility of
procuring timber and other building materials, such as sand, lime,
* The size of the lots into which the township is to be divided may vary from a
quarter of an acre to one acre; half an acre would be found generally sufficient. It is
customary to give to the first purchasers of rural sections one town lot in addition for
every such section, the remaining lots to be sold either by auction, or at some fixed
price.
2 D
426
COLONIAL SURVEYING.
brick-earth, stone, &c.; security from predatory attacks, and vici-
nity to sufficient tracts of land suited to agricultural and pastoral
purposes.
The site of the town, with its figure and extent, being decided
upon after a careful investigation of the above and a variety of
other minor considerations, the best main lines of road diverging
from it in all the palpably-required directions should be marked
out; and upon these main lines should abut the sections to be first
laid out for selection. Errors of judgment will doubtless be sub-
sequently found to have been made in the directions of some of
these roads; but this is certainly productive of less injury to the
colony than the plan of systematically marking out the land
without providing for any main lines of communication at all, leaving
them to be afterwards forced through private property under the
authority of separate acts of the colonial legislature; a system
entailing discontent, litigation, delay, and expense. The marked
natural features of the ground, such as the lines of the coast, or the
banks of lakes or rivers of sufficient importance to constitute the
division of property, and the main lines of roads alluded to, will,
where practicable, guide the disposition of the lines forming the
boundaries of the sections to be now marked out. Where no such
natural or artificial frontages exist, the best directions in which
these rectangular figures can be laid out are perhaps those of the
cardinal lines, excepting in cases where the nature, inclination, and
general form of the ground evidently point out the advantage of a
deviation from this rule.
The size of these sections is a question to be determined by that
of the minimum average number of acres which it is supposed is
best adapted to the means and wants of the settler; the latter being
in a great measure regulated by the apparent capabilities of the
soil. Land divided into very large farms is placed beyond the
reach of settlers of moderate capital; and if subdivided into very
small portions, the expense of the survey is enormously increased,
and labourers are tempted to become at once proprietors of land,
very much to their own real disadvantage, as well as that of the
colony. In South Australia, 80 acres has been adopted as the
average content. In parts of New Zealand and elsewhere, 100
acres. In Canada†, generally more than double that quantity.
* In the Canterbury Settlement, on the Middle Island, New Zealand, 50 acres has
been fixed as the minimum size; the maximum is unlimited. As in South Australia,
no reservation is made of coal and other minerals, the purchaser being put in possession
of all that is on and under the surface.
†The rude and inaccurate mode in which land has been marked out in Canada by
COLONIAL SURVEYING.
427
Whatever size may be determined upon, it is advisable to adhere to
it as nearly as possible, in all general cases; though, where special
application is made for rather larger blocks, there has been found
no mischief in departing from the average size, provided this devia-
tion is not so extreme as to prevent fair competition for any pecu-
liarly valuable locality. In such cases, it is however always
necessary to guard particularly against the monopoly of surface
water within the area of the section, or of any extended valuable
frontage; as well as against any impediment that might be placed
in the way of forming roads through the property. Where the
main lines of communication have not been previously laid out, it
is requisite, especially in large blocks of land, to reserve to the
government, at all events for a limited number of years, a right of
forming such roads as are evidently for the public benefit, making
of course compensation for any damage that may be thereby done,
though this can generally be met by a previous allowance of a cer-
tain number of acres in excess of the proper content of the block*.
Indeed, if proper precautions could be taken to prevent its being
abused, it would be advisable to reserve this power of making such
general roads as are clearly advantageous to the community, through
all sections of land of whatever size; with the right of taking stone
and timber for making and repairing these roads and the bridges
erected along their line; though all such interference with private
rights should as much as possible be obviated by previous careful
examination of the country.
The rapid settlement of a newly-formed colony being an object
always to be fostered, the sections marked out for sale should be so
arranged as to conduce as much as possible to this desideratum; to
attain which end, the surveys should, at all events at first, be kept
well in advance of the demand for land, for the purpose of giving
the most ample choice of selection to intended purchasers. By the
opposite system of selling land in advance of the survey, an unfor-
tunate emigrant not unfrequently finds the greater part of his sec-
tion occupied by the bed of a salt lagoon or swamp, and experiences
no slight dismay in discovering that he is not even in possession of
the number of acres for which he has paid, and to which perhaps
he has no access with any sort of wheeled vehicle, in consequence
of the occupation roads being marked down upon the ground
the chain and compass, and the little value that has been set upon waste land which
used to be alienated from the Crown in grants of extensive size, render the survey of
that country not a fair point of comparison with that of more modern colonies.
* Two or three per cent. upon the average, is proved amply sufficient in small or
moderate-sized sections. In very large blocks, one per cent. would perhaps be as much
as could be required.
428
COLONIAL SURVEYING.
to correspond with straight lines previously drawn upon paper;
so that they lead, without any controlling power in the surveyor
to alter their course, up and down almost inaccessible ravines, or
probably for several hundred yards at a stretch along the bed of a
stream.
In marking out these sections, the following remarks* will
direct attention to the different local peculiarities which require a
deviation from established rules, and to the general system of con-
ducting the work in the field; the mechanical practice of surveying
being of course supposed to be already known.
Sections laid out with frontages upon main lines of road,—
rivers, or wherever increased value is thereby conferred upon the
land, should have their frontage reduced to one-half, or even one-
third of the depth of the section, so as to distribute this advantage
among as many as can participate in it, without rendering the dif-
ferent sections too elongated in figure to be advantageously cul-
tivated as a farm.
In addition to this contraction of frontage, easy access by roads
must be provided from the country in the rear leading to this
water, or main road; without which precaution the owners of the
front lots would, by blocking up the land behind them, virtually
obtain possession of it, for at least pastoral purposes, without pay-
ment. These roads should occur at intervals proportioned to their
requirement, generally between every third or fourth section.
Every section should have an available road on one of the four
sides forming its boundaries, by which the proprietor has access to
the main lines of communication; its breadth may vary from half
a chain to one chain, according to circumstances. In square or
rectangular sections of 80 or 100 acres each, roads surrounding
each block of six or eight sections have been found amply sufficient;
but in a country at all broken or irregular, some of the roads so
laid out would often be found quite impracticable; in such cases,
it is necessary either to trace and mark on the ground along the
ridges of the secondary features, or wherever the ground may offer
fewest impediments, cross roads leading into the main lines, and to
lay off the sections fronting upon them; or to make these by-roads
run through the sections; which is to be avoided as much as pos-
sible on account of their cutting up small properties, and entailing
a very considerable expense in the increased quantity of fencing
required.
In parts of the country where water is scarce, the greatest care
should be taken to prevent its monopoly by individuals. Springs
* Partly extracted from the instructions issued to surveyors employed in South
Australia.
COLONIAL SURVEYING.
429
and permanent water-holes should in such localities be enclosed
within a small block of land (one or two acres), and reserved for
the use of the neighbouring flock-owners and the public generally;
and practicable roads must be arranged leading to these reserves,
without which, excellent and extensive tracts of land would often
be comparatively valueless.
As it would evidently very much increase the cost of laying out
sections having broken and irregular frontages, if they were re-
quired each to contain exactly the same number of acres; the
nearest approximation that can be made to the established size by
the judgment of the surveyor should be adopted, and the section
afterwards sold according to the quantity of land it is found to
measure.
For the purpose of giving to settlers seeking for land upon which
to locate, every facility for acquiring information respecting its
capabilities, and the positions of the different surveyed portions,
the freest access to the statistical reports of the surveyors, and to
the plans of the different districts deposited in the Survey Office,
should be given. In addition to which, the sections themselves
should be marked so distinctly upon the ground by short pickets,
driven at intervals, regulated by the comparatively open and level
character of the country, as to enable any person to follow up their
boundary lines without difficulty. The angular pickets should be
much larger, and squared at the head, on which the number of the
section, and of all the contiguous sections, should be marked. Ad-
jacent roads should also be designated by the letter R. Inde-
pendent of the corners of sections being pointed out by these
pickets, they should be deeply trenched with a small spade or pick,
showing not only the angle formed by contiguous sections, but also
the directions of their boundary lines.
Road. Such marks remain easily recognised for years, and are
not injured either by bush fires or by the constant pas-
of herds of cattle, by both of which means many
sage
the wooden pickets are soon destroyed.
120 121
of
It has been generally considered expedient, that roads
should be reserved, if not actually marked on the ground, (excepting
in cases where they would interfere with the erection of wharves,
mills, &c.,) along the banks of all navigable rivers, the borders of
lakes, and along the lines of a coast. This regulation, if stringently
applied, without reference to peculiar circumstances in different
localities, would often be found oppressive and mischievous. Very
frequently, roads laid out with judgment to the various points on
the margins of these waters which are best adapted for the pur-
poses of fisheries, watering flocks, establishment of ferries, building
430
COLONIAL SURVEYING.
or launching boats, &c., with a sufficient space reserved for the
use of the public at these spots, would prove of more general
utility.
As a general rule, as many sections as possible should be laid
out in the same locality, if the land is of a nature to be soon
brought into cultivation. Whilst greater choice of selection is
thus given, the comparative cost per acre of the survey is
diminished; of course, this remark applies only to situations the
rapid settlement of which is anticipated.
In marking the boundaries of sections on the ground, all natural
features crossed by the chain should be invariably noted in the
Field Book, on the outlines plotted from which are drawn the
general character of the contours of the hills, the different lines
proposed for roads, directions of native paths, wells, springs, and
every other object tending to mark the nature and resources of
the country. Copies of these plans* should always be transmitted
to the principal Survey Office, accompanied by a rough diagram,
showing for future reference, the construction lines of the work,
and the contents and length of the sides of all sections, also the
measure of the angles, when not right angles; and by an expla-
natory report, describing the nature of the soil, description of
timber, &c., upon each section, and the facilities for making and
repairing roads and bridges, and peculiar geological formations of
the different districts. A collection of botanical and mineralogical
specimens from all parts of the province will also contribute mate-
rially to the early development of its natural resources; and sur-
veyors should not be deterred from giving their attention to this
subject by ignorance of these sciences, as the specimens can be
afterwards weeded and arranged, and afford invaluable statistical
information.
At the head Survey Office, a meteorological register is of course
supposed to be kept. It is also very desirable that each of the
surveyors employed in any large district should be furnished with
a good thermometer, rain-guage, and a mountain-barometer, or
aneroid, for the purpose of registering daily observations to be
forwarded periodically to the general office for comparison with
those obtained from different parts of the province, between which
the difference of peculiarities of climate will be thus arrived at.
Surveyors working on a line of coast should be particular in
noting all phenomena connected with the rise and fall of the tides;
and obtain soundings, laid down with reference to established and
easily-recognised marks on shore, of all creeks and harbours, when-
*Two inches to one mile is found a very convenient scale for plans of these sec-
tions, intended for the information of the public.
COLONIAL SURVEYING.
431
ever this may be in their power. The depths and velocities of all
rivers should also be noted at different points in their course, as
well as the periods of floods, and their observed influence upon the
volume of water in the river.
In laying out sections up narrow rocky ravines, or in situations
where creeks or any other natural features present obstacles to the
continuance of the methodical rectangular form adopted as the
standard figure, a deviation from this form becomes of course neces-
sary, and the contents of some of the sections thus often unavoidably
differ from the established average. Care should however be taken
in such cases, to make the outline of these irregular figures as
simple as the ground will admit of, both on account of the addi-
tional trouble and time lost in their survey, and the increased cost
of subsequent fencing by the purchaser.
Attention has already been drawn in page 428 to the necessity of
guarding against the monopoly of road or water frontage. The
same sort of precaution is also required in marking out land in
rich narrow valleys, or in spots valuable on account of minerals.
As a general rule, from which no deviation whatever should be
allowed, it may be laid down that no section should ever be per-
mitted to enclose an undue proportion of land, unusually valuable
from whatever cause, by extending its length in the direction in
which that valuable portion of land runs; whether it be a rich
agricultural valley, a mineral lode, a stream, or water-course.
As regards the actual marking out of the sections upon the
ground, when the figure is of a square or rectangular form, the pro-
cess is a very simple one; whether the true meridian, or the direct
line of some main road, or a line forming any angle with the meri-
dian that may be found better adapted to the local peculiarities of
the district, be adopted as the guiding line of direction.
A spot being fixed upon for the starting
point, represented by A in the accompany-
ing figure*, the normal line AB is carefully
marked out by a good theodolite in the re-
quired direction; if intended to correspond,
or to form any fixed angle, with the meri-
dian, this must be previously determined
by one of the methods usually practised.
The right angle B A C is then set off, which
angle should be observed on both sides of
A B (produced on purpose to D), and the
chain measurement along these lines A B

IB
A
D
C
* This figure represents rectangular sections of 80 acres, as laid out in South Australia,
432
COLONIAL SURVEYING.
and A C, and afterwards along the parallels to A C, may, if two
parties are employed together, which can generally be managed
under the charge of one efficient surveyor with an intelligent
assistant, be carried on simultaneously, the points of junction at
the angles of the blocks forming in some measure checks upon the
accuracy of the work as it proceeds. The size of these sections,
and the intervals between the parallel sectional roads, will depend
of course upon local regulations. The operation would evidently
be simplified by running all the measured lines in the middle of
these roads, leaving half their breadth to be afterwards set off on
each side by the proprietors of the land, but the palpable objections
to this are too serious to be compensated by the trifling saving
thereby effected. In fact, the real boundaries of no one section
are by this plan marked on the ground by the surveyor; and con-
stant disputes and encroachments would be the consequence of
adopting it.
It must be obvious to every practical surveyor, that it would be
impossible for him to continue this mechanical system of marking
a series of rectangular figures on the ground to any great extent,
without being liable to constantly-increasing errors, which could
not be guarded against by any degree of care in the operation, and
of the amount of which he could never be aware, without estab-
lishing some check altogether independent of the chain measure-
ment of the sections themselves: this is only to be accomplished by
combining with it a triangulation of the country, more or less ac-
curate, according to the nature of the survey. Whilst, then, this
methodical division of the land is in progress, it is advisable, if
any thing like accuracy is required, and if the detached portions of
settled country are to be laid down upon a general map, that the
sites of the trigonometrical stations should be decided upon, and
the stations themselves (however roughly they may be constructed)
erected, in order that they may throughout be made use of as
guides and checks upon the measurements. The triangulation
indeed would be found of the greatest service, if carried on rather
in advance of the detail, as in the survey of old countries. Any
great accumulation of error could be then easily guarded against,
by the angles observed at different parts of the chain survey, sub-
tended by three or more of the trigonometrical stations; and in
very many instances these stations could be actually measured up
to, which should be done wherever practicable; by which means
the length of which bore to their breadth the proportion of 2 to 1-occupation roads
one mile apart, enclosing eight sections. They were, however, frequently laid out
square, according to the nature of the ground.
COLONIAL SURVEYING.
433
the marking out of the sections answers the same purpose that is
obtained in ordinary surveys by the measurement of check lines,
and traversing along the roads, by which the interior detail is
mostly filled in. Angles of depression and elevation should also be
taken to these trigonometrical points (whose altitudes are all ob-
tained by the triangulation), from various parts of the chain survey,
the heights of which positions, above the level of the sea, are thus
obtained with tolerable accuracy.
As to the mode of conducting this triangulation, all necessary
instructions have already been previously given. The degree of
accuracy with which the base is measured, and the angles observed,
will depend evidently upon various contingencies; for instance-
the extent over which the triangulation is to be carried; the time
and expense that can be bestowed upon it; the degree of minutiæ
required in the maps, &c., &c. On the survey of South Australia
the base was measured upon a nearly level plain very little ele-
vated above the sea, with a standard chain, the operation being
repeated several times, to obtain a more correct mean value: the
angles were observed with a very excellent 7-inch theodolite; and
the result was found sufficiently accurate for the purpose of con-
necting all the detached blocks of surveyed land, and laying down
the work to the scale of 2 inches to 1 mile.
In addition to the above use of the triangulation, it is found, in
the survey of a wild country, peculiarly serviceable in enabling
the Government to define, with the aid of marked natural features,
the boundaries of the extensive tracts of land leased to different
individuals for pasturage, until, with the increase of population and
civilization, more convenient and better-defined demarcations are
substituted. Some of the principal natural landmarks of a country
also, such as chains of mountains and rivers, traverse the wildest
parts of the land, where chain surveying would never penetrate.
Many of these landmarks are made the boundaries of counties,
and other internal territorial divisions; and their positions in differ-
ent parts of their course are often only to be determined by refer-
ence to the trigonometrical stations, which likewise serve as
guides for ascertaining and laying down upon paper the direc-
tions of roads through extensive, barren, and uninhabited tracts of
country.
Most of the foregoing remarks have been made under the sup-
position that a number of detached surveying parties are distri-
buted over different parts of the country, all working under the
directions of, and reporting to, a central Survey Establishment.
As the population becomes distributed over a wider extent, and
434
COLONIAL SURVEYING.
applications are constantly made for the survey of small, irregular
blocks of land to complete and consolidate properties, some altera-
tions will be required in the method of carrying on the measure-
ment of land, to meet these new demands*. It could evidently
be only by an increased expenditure of time and money that sur-
veying parties could be kept constantly moving from one distant
spot to another, to lay out perhaps, only a very limited number of
acres at each; and the division of the country into Districts, for
the purposes of the survey, becomes almost imperative. Copies of
the plans of sections open for selection, and other information of
a similar character, would be thus placed more within reach of dis-
tant settlers, and their wants could more readily and rapidly be met
without augmented expense.
Portions of the work might also at this advanced stage of pro-
gress be filled in by contract, subject to careful and rigid examina-
tion; the triangulation, and the previous chain measurement con-
nected with it, affording sufficient checks for this purpose; without
which, surveying by contract should be most carefully avoided,
especially in new communities where but little competition can be
expected, and where it would be unreasonable to expect to find
competent surveyors distributed over the remote parts of the
colony.
The rate of progress and cost per acre of a sectional survey, such
as has been described, must vary considerably, according to the
nature of the country, the prices of labour and provisions, and the
minuteness of the divisions. If the size of the sections is small,
80 or 100 acres for instance, the number of lineal miles to be mea-
sured is of course very much greater in proportion than would be
the case with blocks of a larger area, and the progress must bear
an inverse ratio to the increased expense. The facility of trans-
port is another item that materially influences both these questions,
as also the system of marking out patches of land in whatever loca-
lity they may be applied for, instead of carrying the survey regu-
larly forward, embracing all the available land in its progress.
The expense of the surveys in all new colonies is now defrayed
out of the proceeds of the sales of land; and proof of the recogni-
tion of the advantages of the accurate delineation of the boundaries
* These subsequent wants and demands do not affect the first stage of the survey
in a new country; it is only as it becomes gradually settled that they are felt. The
first survey evidently cannot be a complete one, unless it could embrace every acre of
land that might by possibility be required; it is constantly demanding extension in
every direction, therefore the more imperatively necessary it is, that the first land sur-
veyed and laid down on the maps should be based upon a triangulation sufficiently
accurate to allow of this extension, without the certainty of accumulating error.
COLONIAL SURVEYING.
435
of property, features of the ground, and main lines of roads, &c., is
given by the system adopted by the New Zealand Association, in
the establishment of the "Canterbury Settlement," of charging for
all land the uniform price of £3 per acre*, (instead of the £1 fixed
as the lowest upset price in the other Australian colonies, where
the plan of selling land by auction is in force), to provide funds for
a superior nature of survey, and a variety of works of a public
character; the proportions being 10s. per acre as the price of waste
land; 10s. per acre for the cost of the surveys, formation of roads,
and other miscellaneous expenditure; 20s. per acre to be devoted
to the purposes of emigration; and another 20s. per acre to eccle-
siastical and educational purposes.
The boundaries of what in the Australian colonies are termed
Runs," for depasturing sheep and cattle, are not generally
marked out during the survey, but are described by reference to
the trigonometrical stations, and other known fixed points; the
approximate distances and bearings of the lines being stated. As
portions of this land are at all times liable to be purchased by in-
dividuals after a due stipulated notice to the occupier of the run, who
pays yearly a trifling sum for his licence, it would of course be a
waste of labour to mark out such temporary divisions; but the
settlers themselves very frequently define their respective limits,
either by blazing the trees in a wooded country, or by running a
plough line across it in an open one.
As regards the interior division of a colony into counties, &c.,
the following general regulations, established many years since,
are still in use:-
Counties are to contain, as nearly as may be, 40 miles square;
hundreds, 100 square miles; and parishes, 25 square miles.
Natural divisions, such as rivers, streams, highlands, &c., to con-
stitute as much as possible these boundaries; and, for the purpose
of obtaining a well-defined natural boundary, a smaller or greater
quantity than the above averages is permitted; but not to exceed
or fall short of such established areas by more than one-third
of each.
Reserves are allowed to be made for all necessary public roads
and other internal communications, either by land or water; also
* Formerly land used to be sold in South Australia at the uniform fixed price of
17. per acre. The system of selling by auction was introduced by the Australian
Waste Land's Act in the year 1843. There are various opinions as to the comparative
merits of these opposite systems, the first of which was introduced by Mr. E. G.
Wakefield; and its advantages are strongly set forth in the pamphlet upon Colonial
Surveying, recently published by his brother, Mr. F. Wakefield.
436
COLONIAL SURVEYING.
for the sites of towns, villages, school-houses, churches, and other
purposes of public utility and convenience.
When the division between Provinces or Counties, or other lines
of territorial demarcation, is represented, either altogether or in
part, by a meridian line; or a line having any fixed angle with the
meridian; or by a portion of the arc of a parallel (as is the case in
many of the Australian provinces), it is of course necessary to be
able to determine and mark upon the ground with accuracy such
meridian or parallel. Most useful practical information upon this
subject will be found in the narrative of the survey and marking
of the boundary between the British possessions in North America
and the United States of America, in 1842, published by Major
Robinson, Royal Engineers, in the second and third volumes of
the "Corps Papers."
Operations of this nature, if conducted with the very great care
and precision that were bestowed upon the boundary alluded to,
involve the perfect knowledge of the manner of using and adjusting
the transit, and altitude and azimuth instruments; and also the
management of chronometers. The boundary line between South
Australia and what now constitutes the province of Victoria,
(the 141st degree of east longitude) was however determined (and
since marked on the ground for a considerable distance,) under
the New South Wales Government, by one of their surveyors*,
with only a sextant, a pocket chronometer, and a small 3-inch
theodolite; but though the work was performed with the greatest
care and attention, and with probably as great a degree of accuracy
as could be obtained with these imperfect instruments, the result
can of course only be looked upon as an approximation far too
vague for the determination of a division of importance. The
North American boundary, on the other hand, may perhaps have
been defined with more precision than was absolutely necessary in
a line of demarcation running for its whole length through a wild
uncleared country.
Having now gone through the method of dividing the land into
minute sections for occupation, and its further division for terri-
torial purposes; we will conclude with a short reference to the
objects to be held in view in conducting exploring expeditions be-
yond the bounds of the settled districts, for the purpose of adding
to the geographical knowledge of the country and developing its
resources; which objects are very similar in character to those
already alluded to, when treating of the preliminary operations of
a survey in a newly-formed colony.
* Mr. Tyers.
COLONIAL SURVEYING.
437
The nature of the country to be traversed will, as far as this is
known, indicate the method of travelling that must of necessity be
adopted. Extensive inland water communication, as in the Cana-
das, points to the canoe as the readiest mode of transport; com-
paratively open and generally grassy land, as in Australia and
Southern Africa, requires the use of horses and oxen; whilst in
many other countries the thick underwood can, in parts, be tra-
versed only on foot, and barren deserts by the aid of camels. These
different modes of locomotion evidently all require different pre-
liminary arrangements. The objects in view, however, are much
the same in all cases*; viz., a knowledge of the climate, soil, native
population, geological formation, botanical character, of the
country, and its resources of all kinds; as well as the delineation
(as perfect as the time and means that are available will admit) of
the natural features of the ground.
All points known as portions of the settled country being soon
left behind, the explorer has to trust to his own judgment as to
the best directions in which to conduct his party; to his own energy
in overcoming the natural obstacles that he will be certain to en-
counter; and his own practical skill in fixing at proper intervals.
his different positions by means of astronomical observations, and
mastering rapidly the general massive features of the ground for
the purpose of making a rough sketch of the country passed over,
showing more particularly the directions of the principal ranges of
hills, and of rivers, and water-courses.
In a large party these labours may often be subdivided advan-
tageously; but the leader must remember that the entire respon-
sibility still rests with him; and if he does not actually participate
in every portion of the work, he must nevertheless exert a general
influence over the whole.
As regards the fixing, with as much accuracy as may be attain-
able, the various positions of encampments, the directions and
sources of rivers, and all marked prominent features; much assist-
ance is to be obtained by carrying on, as far as it can be done, a
species of rough triangulation (with a sextant or other portable
instrument), from the extreme trigonometrical stations, or any
prominent landmarks the positions of which are known and repre-
sented on the plans. This may however very soon become imprac-
ticable from the nature of the country or other causes, and the
traveller then finds himself much in the same predicament as at
sea, having little beyond his dead-reckoning to trust to for the de-
* Expeditions for one single definite object, such as tracing the sources of a river,
&c., are not intended to be here referred to.
438
COLONIAL SURVEYING.
lineation on paper of his day's work. In this position he must
look to the heavens for his guide: and hence the necessity for his
becoming himself, or having with him, a good and rapid observer.
At sea, the latitude is always obtained at noon by a meridian
altitude of the sun (when visible); "sights," as they term obser-
vations of single altitude for time, having been taken three or four
hours before. The latitude obtained at noon is then reduced
by dead-reckoning to what it would have been at the time and
place of the morning observation, (using the traverse table ;) and
with this deduced latitude the hour angle is computed, and the
equation of time, plus or minus, applied for the mean local time,
which, when compared with the Greenwich time, shown by the
chronometer, (allowing for its rate and error), gives the longitude
east or west of Greenwich at the time of the morning observation.
By applying, by dead-reckoning, the change in longitude between
that time and noon, the longitude of the ship at noon is obtained,—
the latitude has already been found by direct observation,-and the
two determinations afford the means of recording upon the chart
the position of the ship at noon on that day.
Somewhat similar to the above proceeding, must be that of the
explorer in a wild unknown tract of country. He would not
probably find it convenient always to obtain his latitude at noon;
but he can generally do so, and more correctly, at night, by the
meridian altitude of one or more of the stars of the first or second
magnitude, whose right ascension and declination are given in the
Nautical Almanac. His local time can, immediately before or
after, be ascertained by a single altitude of any other star out of
the meridian (the nearer to the prime vertical the better); and if
he carries a pocket chronometer upon which any dependance can
be placed, he has thus the means, by comparison with his local
time, of obtaining his approximate longitude, and of laying down
his position upon paper.
In travelling, the rate of the chronometer will probably be found
to vary; but as frequent halts of two or three days are likely to
occur, these opportunities should never be lost of ascertaining its
change of rate.. The longitude should also be obtained occasionally
by lunar observations on both sides of the meridian; or by some
of the other methods given in the works on Practical Astro-
nomy.
The results deduced from such observations must not be relied
upon within ten or twelve miles, but a careful observer should
rarely exceed these limits; and his latitude ought always to be
within half a mile, or under the most unfavourable circumstances,
one mile, of the truth.
COLONIAL SURVEYING.
439
With these all-important data, enabling him to fix with approxi-
mate accuracy point after point* in his onward course, the explorer
can have no difficulty in interpolating by angles, taken with a
sextant or with an azimuth compass, all strongly-marked promi-
nent features, or in laying down his route upon paper correctly
enough for the purposes of identifying particular spots, and giving
a faithful general representation of the features of the ground he
has travelled over. The value of this sketch will be much enhanced
by its having recorded on it, as nearly as they can be ascertained
by the mountain barometer or aneroid, or by the temperature at
which water is found to boil, the altitudes of the most important
positions, as the summits of hills, the levels of plains, and sources
of springs and rivers.
Daily meteorological observations, even of the most simple cha-
racter; such as merely recording the readings of the thermometer
and barometer at stated times, will also prove of essential service
as illustrative of the climate; and these will be of additional value
if accompanied by a record of the quantity of rain fallen on
different days, should any portion of the party be stationary for
sufficient length of time at any one spot, to make these observa-
tions. If not provided with a rain guage of a better description, a
tin pipe with a large funnel, the area of the top of which bears a
certain proportion to that of the tube, will answer perfectly to
measure the quantity of water fallen. A light graduated
wooden rod is fixed in a cork float, and indicates, above the
level of the top of the funnel, the number of inches; the
graduations of the rod of course being proportioned to
the ratio between the areas of the surface of the funnel and
that of the tube. Thus, if the proportion is 10 to 1, the
measuring rod will be lifted 10 inches for every inch of
rain.
* The distance between positions, the latitudes and longitudes of which have been
determined, can be easily obtained by calculation; by which means they can be laid
down with more accuracy, provided the extent of ground travelled over is not very
great.
440
HYDRAULICS.
CHAPTER XIV.
HYDRAULICS,
IN CONNECTION WITH DRAINAGE, SEWERAGE, AND WATER
SUPPLY.
THE first principle to be understood and to be ever borne in mind
in hydraulic or hydrostatical calculations is that, unlike "solids,"
whose pressure is always downwards in the direction of gravity,
"fluids" press equally in every possible direction, even upwards;
consequently, if any portion of the upper part of a fluid be replaced
by a part of the vessel containing it, the pressure against this from
below will be the same which before supported the weight of the
fluid removed, and every part remaining in equilibrium, the pressure
on the bottom of the vessel will be the same as it would be if the
vessel were a cylinder or a prism.
It is usual to calculate the pressure of fluids with reference to
a square inch of the surface of the vessels containing them, or in
contact with them; but, whatever may be the modicum of surface
assumed, the pressure is equal to the weight of a column of the
fluid whose base is equal to that modicum, and whose height is
equal to its depth below the apex or top surface of the fluid.
Hence what is called "head," or the height of a fluid, is of the
utmost possible importance, for, if there is but a sufficiency of head,
a column of fluid of the smallest possible diameter, may be made
to balance another quantity, or any weight as large as you please.
This principle has been denominated the Hydrostatic Paradox, but
as I believe, inappropriately, for I do not think there is anything
paradoxical about it.

I
H
C
The figure represents a machine called the
hydrostatic bellows, which is sometimes used
to illustrate this principle. The bellows con-
sists of two thick boards CD and E F, con-
nected with leather, or other expansive material; &
a pipe of very small diameter, but of considerable
length, communicates with the bellows a little
above the point F. Now if water be allowed to run into the pipe
at the point A—either by connecting it with a cistern, or, if the
experiment be made in a room, with an ordinary water-can
B
F
E
HYDRAULICS.
441
suspended from the ceiling, it will fall down the pipe into the
bellows, and will gradually separate the bellows boards raising
and sustaining a weight that may be placed thereon, bearing the
same proportion to the weight of water in the pipe above the level
of D C as the area of the bellows board bears to the sectional area
of the pipe, and this is evident from what has been said as to the
equilibrium of the pressure of fluids; since whatever may be the
downward pressure of water in the pipe, there is an upward
pressure in the bellows upon every fractional part of its surface
that corresponds with the sectional area of the pipe, equal to the
weight of a column of water, whose diameter is the diameter of
the pipe, and whose height is the height of the pipe diminished by
the height of the water in the bellows.
It is a well known principle of hydraulic science that “water
will always find its level," hence water poured into a bent tube at
one end will rise to the same level at the other end before it
becomes quiescent: thus are we able to supply water to the
inhabitants of a town from a reservoir on a hill, to any height
in their dwellings that shall not exceed the level of the water in
the reservoir, notwithstanding the pipes conveying the water may
in their passage from the reservoir to the town, have passed through
valleys and hollows of great depth.
Fluids of different specific gravities that do not mix will
counterbalance each other in a bent tube when their heights
above the surface of junction, are inversely as their specific
gravities.
In common-place matters of business, the most useful, although
perhaps, the most difficult, and until lately the least advanced branch
of hydraulic science, is that which relates to the motion of fluids,
and the part which friction plays upon them in their passage
through confined channels and (especially at the present day)
conduit pipes.
There is little doubt that some simple fixed mathematical law,
prevails throughout all nature's works, and that such is the
case with regard to fluids in motion has been demonstrated by
frequent experiments. Perhaps the most able exposition of
this law in hydraulics, is to be found in a work called "Prac-
tical and Experimental Researches in Hydraulics," by R. A.
Peacocke, C.E. extracted from Weale's Quarterly Papers on
Engineering.
I have already explained that the pressure of fluids is alike
in all directions, consequently in considering the question of
2 E
442
HYDRAULICS.
discharge of water through pipes, we must make no difference
between a pipe laid level but having a constant head behind it, and
another pipe whose gradual fall amounts in the aggregate to that
constant head. As an illustration, let B C, fig. 179, be a constant
head of water, and A B a horizontal pipe; then the same quantity of
water will be discharged at the point A, in the same time, by the
horizontal pipe, as would be discharged by a pipe laid hypothe-
nusally, as in fig. 180, provided that the top surface of the
water be kept at the same height at C, above the point A in
each case, and that the point A, is at the same horizontal distance
from C.
If any be inclined to doubt the correctness of this principle,
they may find a strong confirmation of it, in the results of some
very valuable experiments communicated to the Institution of
Civil Engineers by Mr. W. A. Provis, M.I.C.E., and contained
in the "Account of the Transactions of that Society," vol. ii,
p. 201.
But for the existence of friction, water would fall a given
height in the same space of time whether the points of supply
and discharge were situated vertically above each other or
whether a considerable horizontal space intervened, but inas-
much as the discharge of water must be vertical unless con-
ducted otherwise by some artificial medium, the resistance offered
by friction is greater or less according to the rate of inclination
at which the conducting medium is brought in contact with the
water.
At a time then when sanitary questions are occupying a very
great share of public attention, and every town in the kingdom is
establishing its waterworks and carrying out works of drainage,
it becomes more than ever important that the quantity of water
discharged from pipes under all the varied circumstances of
greater or less diameter, head and pressure, should be distinctly
understood.
Among the several rules for calculating the discharge of water
through pipes, may be mentioned that of the Chevalier Dubuat,
in his Principes d'Hydraulique, an abridged account of which is
given by Professor Robison in his article on rivers and water
works in the Encyclopædia Britannica; the formula of M.
Eytelwein, a German mathematician, who devoted much time to
enquiries of this nature, and published at Berlin in 1801 a
valuable compendium of hydraulics, entitled Handbuch der
Mechanik und der Hydraulik. The formula and table of Mr.
HYDRAULICS.
443
Smeaton; the formula of M. Prony; Dr. Young's deductions
from experiments and comparisons; the conclusions of M. Genieys
contained in a quarto work, published in Paris in 1829, entitled
Essai sur les Moyens de conduire, d'élever et de distribuer les Eaux,
par M. Genieys, Ingénieur au Corps Royal des Ponts et Chaussées,
attaché au service de la Distribution des Eaux dans Paris; the
experiments of the Abbé Bossuts; and the experiments of
M. Couplet; the results of the very valuable experiments by
Mr. Provis, M.I.C.E.; the researches of Mr. Peacocke, C.E.;
and the formula of Mr. Hawkesley.
The rules and formula of most of the early authors are
expressed in such different terms, and produce such conflicting
results, that they are of little value for the practical requirements
of the present day.
Two or three years ago, I turned my attention to this
subject; collected and investigated the several formula, in
connection with the recorded experiments, and tabulated the
results. A second and very extended edition* of these Tables
has been for several months in progress, and will probably be
ready for the press by the time this work leaves the hands of the
printer.
* Synopsis of the Second Edition of "RYDE's Hydraulic Tables.”
Table 1. Relative inclinations, especially applicable to Table 8.
""
2. Relative inclinations, especially applicable to Table 10.
""
3. Relative values of the properties of a circle, (very complete).
""
4. Square roots of numbers, from 1 to 1000.
""
5. Cube roots of numbers, from 1 to 1000.
""
6. Logarithms of numbers.
7. Hyperbolic logarithms.
""
""
وو
""
""
""
""
""
">
8. Discharge and velocity of water and sewage passing through pipes.
9. Loss of head, occasioned by the friction of bends and angles, whether
in pipes, rivers, canals, or other arterial cuts.
10. The mean velocity of water flowing through rivers, canals, drains, or
other arterial cuts, according to depth and fall.
11. Surface, mean and bottom velocities of rivers.
12. Approximate swell occasioned by the piers of a bridge or other con-
traction of the water way.
13. Weight and thickness of cast iron pipes, required to sustain the pressure
of different heads.
14. Velocity of water discharged from reservoirs, sluices, bridges, and ver-
tical pipes.
15. Discharge of weirs and overfalls.
16. Quantity of water in cubic feet due to rain-fall, on any number of acres.
17. Relative quantities of rain-fall for different measures of time.
444
SPECIMEN OF HYDRAULIC TABLES.

DIAMETER
OF
PIPE.
INCLINATION 1 IN 15.
DISCHARGE
PER
MINUTE.
Inches.
Gallons.
VELOCITY
PER
MINUTE.
Feet.
Feet.
1
8.
1.2
228.
1/1/10
21.
3.4
278.5
2
43.
6.9
318.
2/1/18
76.
12.2
358.
3
120.
19.2
392.5
4
245.
39.3
451.5
5
429.
68.9
505.5
6
677.
108.7
554.
7
996.
159.8
598.
8
1390.
223.2
639.5
9
1867.
299.6
678.5
10
2429.
389.9
715.
11
3082.
494.8
750.
12
3832.
615.1
783.
13
4678.
750.8
814.5
14
5626.
903.
845.
15
6694.
1075.
875.5
16
7862.
1262.
904.
17
9143.
1468.
931.
18
10560.
1695.
959.
HYDRAULICS.
445
The Tables (of which a specimen is given on page 444) show
the discharge and velocity of water and sewage flowing through
pipes of any diameter from 1 inch to 18 inches, and at any rate of
inclination from 1 in 10 to 1 in 1000. They are equally applicable
to the passage of sewage through drains, or pure water through
water pipes; because in the case of the former, every additional
junction throughout the entire course of the drain increases the
pressure, and consequently the velocity; while in the case of the
latter, the effect produced by each branch of a water service, in-
creases the friction, and therefore diminishes the flow.
The arrangement of the Tables is so simple as to need but little
explanation. If it be required to ascertain the size of pipe that
will discharge a certain amount of sewage, or supply a given
amount of water at a known fall, it is simply to turn to the page
headed with the given rate of inclination, and take out the dia-
meter, which stands opposite the number most nearly representing
the given discharge.
It is not at all times understood why a small pipe drain shall
effectually perform the functions for which it is intended, when a
larger pipe has been previously deputed to the same task and failed.
In a large drain the run of water is spread over a broad surface in
a thin sheet, by which means the friction is considerably increased,
indeed exerted to the utmost-the flow is greatly retarded thereby,
and the heavier matters at first held in suspension are by the
natural law of gravity eventually deposited. In the small pipe on
the contrary the water is concentrated, friction is reduced-the
flow is greatly accelerated in consequence and all matters are held
in suspension and carried away. Thus if anything not intended
to be received by the drain, should accidentally find its way
thither, the shallow stream with little velocity or power to float a
heavy body, and having moreover plenty of room to pass it by,
adopts the opportunity afforded by the unnecessary size of the
large drain, and leaves the foreign substance where it found it;
there to accumulate other matters and become the nucleus to
what may eventually choke the drain. In the small drain on the
contrary, if a foreign substance enter, or an impediment of any
kind is presented to the ready flow of the water--the hydraulic
pressure is immediately increased and brought to bear upon the
resisting medium, which cannot long resist, and it is carried head-
long down the channel by means of the superior force itself has
created, and never stops again until it is precipitated at the outlet
of the sewer.
Fig. 181 represents a 15-inch drain in which
the height of water is supposed to be as there shown-and
446
HYDRAULICS.
the impeding substance is also drawn. But if this were a 4-inch
pipe as shown in fig. 182, the same quantity of water would have
assumed a very different relation towards the impediment, and its
power to remove it will be readily comprehended on examination
of the sketch.
Having referred to my tables as simple expositors of the
capacities of pipes for the purposes of drainage, sewerage, and
water supply, according to the inclination at which they are laid,
I now propose to treat briefly the practical operation of draining a
town and supplying it with pure water.
Undoubtedly the first desideratum in considering the question,
is to secure the best possible outfall for the drainage, sufficiently
removed from the town to prevent inconvenience or nuisance from
noxious effluvia, and yet in a position if possible to enable the
sewage to be intercepted and used as an agricultural manure,
if the agriculturists in the neighbourhood are willing and can make
it answer their purpose to co-operate with the town's people for
its purchase.
Upon this question of application of sewage to agricultural
purposes, much diversity of opinion exists; personally I am
inclined to believe, that if the landowners and farmers in the
vicinity of every town in which proper works of drainage have
been executed be invited to make propositions for the right of
using the sewage, it will be found that in most cases, after a
sufficient trial has been allowed to enable them to discover the
proper mode of using it, and most economical manner of applying
it, that a revenue of 5s. per annum for each inhabitant, at the very
minimum, may be realised from that which is at present not only
thrown away, but what is far worse, is suffered to injure to a large
and unknown extent the health and physical condition of our
town populations.
Having determined upon the outfall, the next question is to lay
out judiciously the main sewers, so that each street may have at
least one drain, laid at such a depth as shall drain the foundations
of the houses; into which surface grates, at properly regulated
intervals, will open by means of trapped side drains, as well as the
secondary drains from houses, courts, &c.
There are few towns, excepting only the very largest, that may
not be efficiently drained by means of glazed stone ware pipes,
without resorting to more expensive, and less serviceable sewers.
The main drains should be laid out, so as to reach by as direct
a course as possible the point of outfall, for to decrease the length
of a drain is the same as to increase the fall; they should also be
}
HYDRAULICS.
447
as free as possible of sharp angles and bends, and should maintain
throughout, as nearly as can be accomplished, a regular rate of
inclination.
The greatest internal diameter of drain pipe recommended to be
used, is 15 inches; beyond this size they are rarely true in form,
and are very difficult to lay down properly. I have had laid down
under my supervision pipes 18 inches in diameter, but the work
is not nearly so satisfactory as the smaller sizes, although it has
now worked very efficiently for more than four years. In all future
operations, I shall consider the propriety of making two drains in
all cases in which a 15-inch pipe will not meet the requirements.
In digressing a little from my subject to describe the kind of
map upon which the drains must be marked out, I feel I cannot do
better than refer to the valuable suggestions of the General Board
of Health on this particular question, bearing as they do the high
stamp of official authority, and being exempt, as they neces-
sarily must be, from every imputation of interested motives, which
generally attaches to a professional man, when suggesting works
tending to benefit himself or his order.
Having issued to engineers and surveyors specimen plans on a
prescribed scale showing every possible detail relating to sewerage,
drainage, and water supply, the General Board in their Minutes
of the 26th July 1850, remark:—
“There appears to be generally an imperfect acquaintance with the actual
necessity and value of proper surveys upon which required works of improvement
have to be founded. It seems to be very frequently supposed that if any sort of
plan exists of a town or neighbourhood it will answer the purpose and that
further expenditure upon the survey of a district would be both unnecessary and
wasteful. It may be safely asserted however that so far from these surveys being
either valueless or costly, that works of sanitary improvement cannot be satis-
factorily or economically carried out without trustworthy plans prepared from
these surveys.
"In respect to the principal works of improvement, namely, drainage works,
one chief source of waste from inefficiency, arising from the want of a complete
system of levels, has been the laying down of lines of sewers at insufficient or
wrong inclinations, which combined with errors as to forms and modes of con-
struction have made drains and sewers, instead of serving for the rapid discharge
of all matters intended to be conveyed away, mere reservoirs of deposit, increasing
the amount of noxious evaporating surface beneath the site of the town.
"It has been moreover the usual custom hitherto to lay out the lines of
drainage upon street plans merely, without regard to the disposition of properties,
or other facilities for the work which would present themselves upon good and
complete plans. Thus a line of sewer is necessarily marked down every street
into which the drainage of each house has to be separately led.
"It has appeared also upon recent investigations, that there has been great
extravagance, not only from this want of complete general surveys as the founda-
448
HYDRAULICS.
tion of drainage works, but from the insufficiency of any district surveys for the
laying out of the main works, those of house drainage.
"Various comparisons have been recently made of different districts of the
metropolis, with the view of exhibiting the immense economy of the proposed
detailed plans on a large scale as affording the opportunity of laying out lines
of drainage in the most judicious directions; and looking at the question as
one of mere economy, without reference to the advantages of better drainage
by greater falls and quicker flows, it has invariably been found that the saving
of public sewer alone rendered practicable by the detailed survey, amounted to
many times the actual cost of the survey, and that one half of the cost of private
house drains might be economised by aid of the same guide.”
With reference to the new survey of the metropolis undertaken
by the Ordnance Survey Department at the recommendation of
the Metropolitan Sanitary Commission, and now in course of com-
pletion, the General Board of Health remark in their report on
the water supply:-
in
"By the aid of this survey, combined works may now be executed with
certainty. Under the present method, according to which water works are laid
down piecemeal, and in disorganised portions, the mains are separated from the
other and most important part, the apparatus for the delivery of water into
houses, and under this system an accurate system of levels is not apparent. But
by means of the accurate levels set forth on the survey, the inclines and directions
of the branches may be determined, with the effect of saving considerable lengths,
and of securing the greatest amount of flow and the readiest supply of water at the
least cost. By the system of levels, the relation of every minute portion of the work
to the whole system, the degree of pressure and strength of the apparatus required
any room, the height and force of the jets; and the quantity of water delivered
for
any purpose on any spot and the average pressure of the water supply in any
district; may be known and regulated at any period; whilst, every workman
engaged in the execution of combined works in the dark and densely crowded
districts, may be guided by the survey in laying down house and branch drains for
the discharge of soil water at the proper inclinations, and in directions having
correct relation to works often at several miles distant. By the levels taken for
this survey, the waste in laying out extensive lines of sewers with no fall, or with
falls the wrong way, waste such as that of laying out a table of drainage, in-
cluding an entire district in such imperfect relation to other districts as would
involve in the opinion of the chief surveyor, an expense of upwards of £250,000,
to set the levels right, may be prevented; and the whole of the public works of
the metropolis, including roads may now be placed in correct relation to other
works.
A
"The General Board desire to lay stress, at the present time, upon the im-
portance of this view of the subject alone; but, surveys sufficient for sanitary
purposes, will be permanently available for all others, and will prove of great
value for the complete map delineation of many classes of information. In the
general consideration of the necessity of such plans for the purposes of the Public
Health Act, the General Board have not overlooked these several other uses to
which they may be applied, tending in various ways to much ultimate improve-
ment and advantage.
"Besides the more immediate uses of plans, therefore, for the complete delinea-
HYDRAULICS.
449
1
tion of main and house drainage, water works, gas works, and pavements, specimen
plans have been prepared, exhibiting among other things, the value of such
surveys in the registration of property, in street and building improvements, in
valuations and assessments, in rate collections, and in the records of public officers,
the District Surveyor, the Officer of Health, the Registrar, the Relieving Officer,
and the Police. Plans adapted to these additional uses might be made to present
in time a complete historical record of the progressive improvement of town
populations of greater national value than any registration in books.
In order to lay out with completeness and efficiency works of improvement
under the Public Health Act, two plans will be required to be prepared from the
survey, one a general plan to a small scale, affording a complete view of the entire
district, and the other a detailed plan of the town portion of the area.
"The scales proposed by the General Board of Health are for the general plan
two feet to the mile, and for the detail plan 10 feet to the mile.
“In fixing the scale of the general plan it appeared to be desirable that it should
be so small as to afford a complete view at once of the entire district under con-
sideration but at the same time large enough to admit of the accurate measurement
of areas of land and other general uses. For the first consideration a smaller scale
than that proposed would have been equally serviceable, but the experience of the
Tithe Office has found that areas cannot be determined with the required accuracy
upon a less scale than three chains to an inch. A scale of two feet to the mile has
been adopted as the nearest approach to the tithe scale that would form an aliquot
division of the scale of the detailed plan.
"A complete system of levels should form one most essential feature of the
general plan. In the practical carrying out of proposed works the general board
have every reason to believe that a great number of fixed points of level, which
can at any time be found and referred to on the ground, will be of infinitely
greater service than any system of contour lines, which, after they have been
levelled, have no existence but on the plans. The comparatively small value of a
system of contour lines does not appear to warrant the very large expense of their
execution, more particularly as with an extensive system of fixed points of level
for guidance, the general configuration of the ground may be lined out by the
surveyor on a small scale plan with sufficient accuracy for all the purposes for
which contour lines are generally serviceable.
"The scale of the detailed plan has been determined mainly by the experience
of what is required for the complete exhibition of all the particulars of main and
house drainage; for it has been found that any scale large enough for this
purpose would be sufficient also for any other service for which a complete and
detailed map would be required.
"Prior to any decision on this important point, considerable trial was made of
various scales, and all available experience sought upon the subject. The scale
adopted is an inch to 44 feet, or 10 feet to the mile.
"The Ordnance Town Scale is only one half of this, or five feet to the mile,
but in some towns in which recent surveys have been made, considerably larger
scales than now proposed have been adopted.
The Town Council of Liverpool have had a plan executed to a scale of 22
feet to the mile, notwithstanding that the ordnance had already made a survey
of that town to the scale of 5 feet to the mile; but the trials which have been
made by the General Board, and the experience on the subject obtained in the
metropolis, have clearly shown that while, on the one hand, so large a scale is
inconvenient and unnecessary, the Ordnance Scale for Town Surveys first
450
HYDRAULICS.
adopted in Ireland is, on the other, quite inadequate to the puposes for which the
plans are now required.
"Provided that the scale is sufficiently large for the proper exhibition of the
most crowded subject matter of information-the house drainage, it appears to be
far more desirable, for the clear exhibition of the various particulars required, that
the separate classes of work should be shown on separate copies or tracings of
the plan, than that the scale should be enlarged for the purpose, for no practicable
enlargement avoids the confusion which arises from crowding these different
classes of work, however imperfectly, upon the same plan.
"There is one essential feature in the specimen plan, which has not hitherto re-
ceived attention, and without which no attempt should be made to lay out works
of drainage, that is, the level of the basement or lowest floor of every house. In
the absence of this information, it continually occurs that sewers are laid down
some feet higher than the places they are intended to drain, and the sewers drain
into them instead. The great object of the deep drainage of towns is effectually
to carry off the refuse from habitations, and yet works are constantly executed
without any certainty of accomplishing this special object. The General Board
have already had presented to them, under the Public Health Act, plans for ap-
proval, in which no information whatever has been obtained on this point, and in
which there was not the least security that the sewers would not be laid above the
level of the basement."
It
To resume my subject, the main drains having been marked
out on the map, the next consideration is, the size they will require
to be constructed, to fulfil all the uses for which they are in-
tended; at the same time it should be forcibly borne in mind that
the less the diameter of the sewer is in excess of its actual require-
ments, the easier it is to be constructed, the cheaper will be the
present cost and future repairs, and the easier and more effectively
will it cleanse itself with the aid of the ordinary sewer water.
is a very common error to assume that a sewer to a reasonable size
cannot be too large; and it is the most certain course for the inha-
bitants of a town to take, upon the first mention of improvements
of this nature, to set about framing extravagant estimates of the
cost of a sewer large enough to drain five times the amount of
their population, as though there were no medium between the
absence of drains in their town, and the existence of sewers
that would require the full force of a large river to keep
them clean.
It has been found in many instances, upon opening large sewers
that have become stopped up from a supposed inability to carry
off all the water they have been required to do, that the sole rea-
son has been the deposit of cesspool matter, accumulated beyond
the
power of water to remove it, and leaving but a mere fractional
part of the sectional area of the sewer for the passage of the
water.
HYDRAULICS.
451
Fig. 183 represents a large sewer in the metropolis, and the
condition in which it was found by the officers of the Sewers
Commission. The space occupied by the ordinary run of the
sewage in the form to which it had worn itself, is shown near the
crown of the arch.
Figs. 184 and 185 represent two instances in large sewers in which
the actual requirements of the run of the sewage is depicted in a
smaller amount of deposit. It will be seen by these examples that
a pipe sewer would have carried off all the ordinary sewage water,
and, as has been previously advanced, would, in its passage, have
carried off all the matters which formed the deposit in the larger
one.
The notion that large sewers must be used to carry away an oc-
casional excess of storm water is at once refuted by these examples,
for since accumulations of this kind will continually take place
under ordinary circumstances, these extraordinary occasions find
no greater accommodation in the larger sewer than in the
smaller one.
The proper functions of sewers are obviously to convey away
from a town the whole of the sewage refuse of every house in the
district, the accumulations of foul matter in courts, lanes, and
alleys; and so much of the rain-fall of the district as may fall upon
the surface of the roads, streets, courts, &c., the roofs of buildings,
and of yards, or other spaces attached to them; but to attempt
to provide for the subsoil drainage of the site of the town by
any other than the natural means, or an independent system,
totally separated and distinct from the sewers, is expensive and
futile.
If the whole of the rain or storm waters falling upon the streets
and buildings of the town is conducted away in the sewers within
a reasonable space of time after it falls, and the whole of the house
drainage is provided for in the same way, what can be the amount
of dampness or moisture from below that it may be necessary to be
careful for?
In determining the capacity of sewers, we therefore have to as-
certain, the amount of house drainage to be provided for, by
estimating the number of houses we intend to drain into the
sewers, and by assuming that each house will, in a given time,
discharge a certain quantity of sewage. This calculation is of ne-
cessity only an approximation, but it will be found to be a
useful one.
an
For its basis, we may consider that each house contains on
average five individuals, and that for every individual
452
HYDRAULICS.
twenty gallons of sewage matter, including waste water from
all household sources, will pass into the drain in the course of
the day.
The maximum rain-fall may be taken as two inches in any one
day, and may be computed on the total area of site occupied by
streets, houses, buildings, yards, and gardens, according to circum-
stances, and the probability of the whole or chief part of the bulk
being discharged without evaporation into the sewer.
We have taken the house drainage and rain-fall of one entire
day of twenty-four hours; but inasmuch as the drainage is exceed-
ingly irregular and uncertain, and not at all likely to be spread
equally throughout the whole time, and a July storm may cause a
large accumulation of surface water in a very little while, it has
been deemed advisable by very able and experienced practitioners
to allow for the possibility of the combined quantity being dis-
charged in two hours.
It frequently happens that a few straggling houses stand in
grounds of considerable extent, but it must not be understood that
the calculation for rain-fall is to be computed on such sites; it has
already been explained that for the drainage of such properties the
natural drainage out-fall of the district must be resorted to, as it
would hardly be sanctioned by the loudest economists to build a
sewer sufficiently large to provide against inconvenience such as
this, which may not arise twice in the year.
Having arrived at the approximate quantity of sewage matter
to be conveyed away by the sewers in two hours, and having al-
lowed some additional quantity for the probable increase of the
neighbourhood, if we divide the sum in the aggregate, reduced into
cubic feet by 120, we get the quantity per minute, which at once
identifies us with our Tables. But the quantity we have now ob-
tained is the total quantity at the outfall, and the sewer will not be
required to accommodate so large a supply throughout the entire
length of its course; it will be expedient, therefore, in the first
place, to consider such a length of it only, commencing from the
outfall, as partakes of no very great diminution, and by taking the
rate of inclination from the section, ascertain from the Tables the
size of pipe that will be necessary to fulfil the requirements. Other
portions may then be taken, and the sewer may be gradually dimi-
nished in size, as the purposes for which it is intended may become
lessened in extent. It may, however, be well to limit the minimum
size of a main or principal sewer to nine inches of clear internal
diameter, thence increasing to twelve, and reaching its maximum
at fifteen.
HYDRAULICS.
453
If it becomes necessary to exceed the diameter of fifteen inches,
it will be desirable to resort to the old description of brick sewers;
consequently, a few words with reference to the most approved
form of such drains, will be in consonance with the object of the
present work.
The form of a sewer should be conducive to strength, at a mini-
mum cost; hence the adoption of the circle, as a form offering to
all the exterior parts of the surface a uniform resistance to pressure
from without. But the top, sides, and bottom of a sewer are not
required to sustain a uniform pressure, being acted upon in very
different directions, the greatest amount of pressure being verti-
cally, and consequently the greatest ability to resist pressure should
be above and below, the sides being more or less tried, according
to the nature of the surrounding soil, and its ability to support
itself by its own tenacity.
As fluids flow with greater velocity the less they are exposed to
friction, the best description of sewer must be that which offers
under all circumstances of more or less supply, the least amount of
surface in contact with the fluid.
It will, therefore, be seen, that what is called the "Egg-shaped
Sewer," which is illustrated in fig. 186, affords in the greatest de-
gree the two considerations we have been discussing, viz., "strength
vertically," with the advantage of a confined channel, and a "mini-
mum amount of surface exposed to friction," under all circum-
stances, of much or little matter in the sewer.
This form of sewer is simply constructed by observing the fol-
lowing proportions:-Let the diameter of the lower arc be 1; the
diameter of the upper arc 2; the height of the sewer 3; and the
radius of the side arcs 3.
In computing the capacities of brick sewers, the values given in
the Tables must not be depended upon, as they are based upon
the discharges of pipes having a glazed internal surface, through
which the sewage matter passes more freely than the surface of the
brick sewers will allow it to do. The discharge will, therefore, be
considerably less, more or less varied, according to circumstances,
but probably 30 or 40 per cent; the pipes being altogether better
suited to the purpose.
It is interesting to investigate the varied powers possessed by
water in motion under different circumstances. A stream of water
4 feet wide and an inch deep, with a fall of 1 in 150 is sluggish,
while the same water running through a 12-inch drain pipe, laid
at the same rate of inclination, flows at a considerable velocity.
454
HYDRAULICS.
The former would deposit silt or sand, the latter would certainly
remove it.
One very great objection to large drains is the necessity of
cleansing them by manual labour.
The legislature has very properly prohibited the sweeping of
chimnies by boys as an occupation degrading to human nature,
eminently cruel, and belonging to a low state of art; but that oc-
cupation was a princely one as compared with the employment of
cleansing sewers by hand. Instances have occurred of the death
of men who have been sent to crawl up sewers charged with foul
gases, while many have had their health irreparably injured in this
disgusting labour for their daily bread.
The following are extracts from some of the reports of the sur-
veyors employed upon the subterranean survey of the metropolis,
recently conducted for the Metropolitan Sewers Commission:-
66
'69 miles of sewers have been surveyed in the Surrey and Kent district.
The surveyors find great difficulty in levelling the sewers of this district; for,
in the first place, the deposit is usually about 2 feet in depth, and in some
cases it amounts to nearly 5 feet of putrid matter. The smell is usually of the
most horrible description, the air being so foul that explosion and choke damp
are very frequent. On the 12th January, 1849, the surveyors were very nearly
losing a whole party by choke damp, the last man being dragged out on his back
(through 2 feet of black fœtid deposit) in a state of insensibility. Another ex-
plosion took place on the 12th February, in the Peckham and Camberwell Road
sewer, and one on the 21st February, in the Kennington Road sewer; in both
cases the surveyors had the skin peeled off their faces, and their hair singed. Two
men of one party had also a narrow escape from drowning in the Alscot Road
sewer, Rotherhithe, on the 24th instant; but fortunately none of the foregoing
cases were attended with serious damage.
"The sewers on the Surrey side are very irregular; even where they are in-
verted they frequently have a number of steps and inclinations the reverse way,
causing the deposit to accumulate in elongated cesspools. It must be considered
fortunate that the subterranean parties did not first commence on the Surrey side,
for if such had been the case, they would most undoubtedly have broken down."
These surveyors report that in the modern district of Belgrave
and Eaton Squares, although the brickwork of the sewers is gene-
rally sound and good, they contain several faulty places, and
abound with noxious matter, in many cases stopping up the house
drains, and smelling horribly. In the neighbourhood of Hyde-park
Gardens, and the costly squares and streets adjacent, the sewers
abound with the foulest deposit, from which the most disgusting
effluvia arises.
It has been estimated by professional men that the whole eva-
porating surface of stagnant and pestilential matter beneath the
HYDRAULICS.
455
houses and streets of the metropolis is equal to a canal 50 feet wide,
10 miles long, and 6 feet deep, and that it would form a putrid
swamp nearly 800 acres in extent, or nearly tiree times as large a
surface as the whole population could lie down upon.
Without any reference to the injury to heath that must inevi-
tably result, even to the strongest constitutions exposed to such
emanations, or how insensibly yet fatally they prove when concen-
trated upon the weakly, and without any reference also to the very
great cost of such large sewers, I submit, tha: on the question of
efficiency alone, I have shown ample reason for their abandonment,
excepting under the most urgent contingencies.
The main sewers having been laid out and their sizes determined,
the arrangement of the house drainage next denands our attention.
Perhaps no branch of the constructive art has received greater
improvements from science, than the formatim of house drains.
Prior to the year 1846, it was the custom in the metropolis to
construct house drains, either square or circuar, 12 or 9 inches in
width or diameter, the latter being the minimum size permitted by
the regulations. These drains were constructed either of brick
or stone, emptying into large brick sewers 5 feet to 5 feet 6
inches in height, 2 feet 6 to 3 feet in width, vith curved top and
bottom and straight sides. The expense of this method amounted
to about ten guineas per house.
In 1846 this system was modified, under the direction of the
Westminster District Sewer Commission, a sx inch pipe was sub-
stituted for the former house drains, dischargig into an egg shaped
sewer 3 feet 3 inches by 1 foot 9 inches in courts from 300 to 400
feet in length, 2 feet 9 inches by 1 foot 6 incies, in places varying
from 150 to 300 feet in length, and 2 feet 3 inches by 1 foot 3
inches, in places less than 150 feet in length.
The expense of this improved system averaged about five guineas
per house.
About the year 1849 a system of back drinage was introduced
into London by the surveyors of the Metropolitan Commission of
Sewers, which, for economy and efficiency, surpassed every thing
of the kind that had preceded it to an astonising degree. A great
number of house drains were laid down, conposed of glazed stone
ware impermeable pipes four inches in diameter, and instead of the
previous system of leading the drainage (the most deleterious por-
tions of which are generated chiefly in the back premises) through
the house, into the main sewer in the midde of the street, favor-
ing to the utmost the emission of effluvia n the passage through
the house, and having, moreover, to pass over a considerable space,
456
HYDRAULICS.
with the least possible declivity and proportionate velocity, the
new system concentrated the sewage in smaller drains at the
farthest possible disance from the houses, and conveyed it away
from them with far greater velocity produced by the increased
inclination consequent upon the shortened length of drain. The
junctions too were formed so as to interfere, as little as possible,
with the flow of the sewage being made curvilinear, instead of the
right angled construction of the old system. In addition to all
which advantages, he expense of construction is reduced to its
minimum.
Plates 13 and 14 are two plans of the same block of 40 houses,
and will illustrate tle old and defective system, as well as the im-
proved one now recommended.
In this block, the total length of drains by the old separate
system is 2,956 fed, by the improved system of back drainage
1,300 feet; while the cost is considerably less by the latter than
by the former arrangement.
The sizes of house drains will, of course, become the subject of
calculation, in the same manner as the larger drains. Three inch
pipes are recommended to be the minimum, and six inches will
be found sufficiently large for the maximum.
Besides the advanages of diminished friction, economy in con-
struction and improvement in form, obtained by the use of pipes
for house drains, a positive gain in fall is obtained, without alter-
ing the relative position of the drain. The height of a nine inch
barrel drain with a 4 inch rim is 13 inches above the level of the
outfall, while the heght of a 4 inch pipe is but about 5 inches.
So that, if a drain feet long would require, if constructed in
brickwork to be laid level, the pipe might have a fall of more than
8 inches, equal to an inclination of 1 in 90, and this gain would be
considerably more important and apparent, if the length of drain
were shorter, such, for instance, as the case of a drain in a court
yard 10 feet long, towhich the gain of 8 inches in the fall would
impart an inclinationof 1 in 15, and a capacity to discharge 245
gallons of water per ninute, while the old brick drain would not
discharge 30 gallons in the same time.
I will now add a few words relative to the new theory of back
drainage, in addition to what has been previously advanced. Be-
sides diminishing the ength of the drains in the aggregate, and
so increasing the velocity and reducing the expense, great improve-
ment is effected in eachseparate drain. Water is chiefly used in and
about the back offices of houses; closets are generally situated
there, and thence the lischarge of waste water will principally be.
HYDRAULICS.
457
I have already noticed the common practice of placing sewers
for the reception of house drains, so as to compel the necessity of
passing the drain across the court yard, underneath the basement
rooms of the house, under the foot paving and into the middle of
the carriage way; while by the new system, the drain is not re-
quired to be nearly so long, and hence the rate of inclination is
considerably greater.
Figs. 189 and 191 are plans, and figs. 188 and 190 are sections
of a house, which will illustrate this more fully. The plan, Fig.
191, shows the old system: C is the sewer in the centre of the
street: A is the closet in the yard and B in the house. The plan
from A and B to C displays the proportion of noxious evaporating
surface formed by the house drains.
The lines from A and B to C, in the section, fig. 190, show
the proportion of the capacity of the drains and so much of
the sewer as are unoccupied by deposit, to act as reservoirs of
foul
gases.
The plan, fig. 189, is illustrative of the improved system. The
diminished extent of evaporating surface obtained by the pipes,
supposing them to be proportionately occupied by ordure, will be
apparent, but when the pipes are properly laid, they will keep them-
selves perfectly clear of all deposit.
The section, fig. 188, of these improved drains exhibits a rapid
fall, in place of the slight inclination under the old system.
One other great desideratum of improvement possessed by the
new system over the old, must not be omitted a notice. When a
stoppage takes place in one of the old description of drains, it fre-
quently can only be rectified by taking up, first the carriage way,
next the foot paving, then the flooring of the front and back room,
and, finally, perhaps the paving of the yard. Under the new sys-
tem, this latter operation is all that can possibly be required.
The rats, too, had the means of conducting the noxious effluvia
from the old defective brick drains into the house; but the glazed
stone ware pipes prevent them the exercise of this mischievous
pastime.
Before I take leave of this part of my subject, I must state, that
all the improvements I have suggested and explained will be en-
tirely futile, unless works are skilfully and properly executed;
and I am firmly of opinion, that so far from the professional
man's fee being thrown away for advice in matters of this nature, it
will very frequently save double its amount in present outlay, besides
rendering the expenditure serviceable to the purposes for which it
is intended. I never yet knew a case of failure of pipe drainage
2 F
458
HYDRAULICS.
that did not result from some accountable cause that should have
been avoided at the commencement; and so rapid is the flow of the
sewage in some of the well-constructed pipe drains, at good in-
clinations, that pieces of paper in a perfect state have been observed
to pass the outlet of the sewer.
A word on the subject of junctions for house drains will but oc-
cupy an appropriate place in a paper of this kind. The general
custom with engineers and surveyors was to make the junctions of
house drains at right angles. Experiments have proved that while
a given quantity of water running direct in a drain was discharged
in 90 seconds, it required 140 seconds to discharge the same
amount of water from a drain of equal size and fall which turned
at a right angle, but 100 seconds only was required with a drain
laid in a true curve. A house drain at right angles, whether hori-
zontal or vertical, is vicious in principle; the sewage will never flow
so freely as in one properly constructed, and accumulations will
constantly take place. The right-angled junction for horizontal
drains is pretty generally abandoned at the present time, but it
is still erroneously continued by some for vertical drops.
Exactness of workmanship, both in the make of the pipes, and
in the method of laying them is equally as essential as the skilful
arrangement of the drains throughout the house; for, from what
has been said, it must be evident, that in a proper system of drain-
age, water is not required to clear away accumulations, but to pre-
vent their ever forming.
Cases will frequently occur in which a junction of a four-inch
branch with a four-inch main will require no additional capacity
in the main to receive the sewage of the branch, the additional
hydraulic pressure counteracting the effect of the additional quan-
tity; and the same may be said of other sized branches and mains;
but in all cases when such is not the fact, the main should be in-
creased by a tapering pipe.
When drains are left to the management of bricklayers without
professional supervision, it is not at all an uncommon circumstance,
indeed, I dare say, I may call it a "common one," to increase or
diminish the size of a drain by pushing the end of the smaller pipe
into the larger one. I have also seen a man very busily engaged
cutting a hole in a pipe into which to insert another, and thus form
a rude junction; the result of these practices is a speedy failure of
the drain, a wholesale condemnation of the system, and an increased
additional expenditure on some more favoured but far less scientific
substitute.
In passing in review the works of house drainage, as recom-
HYDRAULICS.
459
mended under the new system of back drains, we find that we
must provide to every closet, sink, court yard stone, and roof or
stack pipe, a 3 or 4 inch drain, communicating by proper curvi-
linear junctions with the main sewers, and these must be properly
trapped.
With reference to the mode of trapping house drains and of pre-
venting the egress of foul gases into habitations, the best form,
because the most economical, simple, and least liable to derange-
ment, is the common syphon trap, which being made of the same
material, and of the same guage and length as the drain pipes, is
readily adapted to its purpose, and may be inserted at any interval
or in any position along the drain. It is a very popular error, that
the new system of drainage requires better traps than the old.
Nothing is more common than for an engineer to be told-"Ah!
now that we have these new drains, we must take care that they
are well trapped, or we shall be in a fine state." Why the best
protection we can have against inconvenience of this nature is, the
removal of all masses of decomposing matter from beneath or near
habitations before decomposition can have advanced, and before
any part of it can get into those ultimate stages of decay which in
the present, or perhaps I ought to say, old methods of town drain-
age, it usually reaches before removal. It has been found by an
experience of three years, that house sewage, drained through im-
permeable pipes into a water-tight tank, may be stored even for
four or five days without becoming offensive.
It should be borne in mind that such sewage, so stored in an im-
permeable receiver, differs very strangely indeed in its degree of
fluidity and other qualities from the noxious contents of an ordinary
cesspool, from which the more fluid portions are constantly oozing.
I might, perhaps, advance a few observations on the construc-
tion of the chief apparatus for the decent and efficient sanitary ar-
rangement of every house-I mean the water-closet. It is a room
to which but very slight attention is paid by too many of our popu-
lation, with the machinery of which too many are wholly unac-
quainted, and of the importance of attention to the perfectness of all
its parts, more especially the apparatus for preventing the effluvia
from returning into the house, so few are sufficiently alive. But
my chapter has already extended far beyond the limits within
which I originally intended to confine it. I will, therefore, simply
suggest, that the chief points to be sought in the construction of
the apparatus appear to be:-
1. A sufficient spread of the water to effect a complete scour for
the removal of the soil;
460
HYDRAULICS.
2. Economy of water to effect the scour and replenish the trap;
3. The best trap to prevent the ingress of the effluvia from the
general system of drainage, with which the apparatus must be in
connection, and also to prevent the return of any effluvia from the
soil of the closet itself;
4. Freedom from stoppages;
5. Non-liability to derangement;
6. Facility for repair; and
7. Economy in price.
The effectual removal of rain and storm water from the surface
of the public highways, will require a grating at properly
regulated intervals, on either side of the street, according to
the nature of the road and the rate of inclination. These grat-
ings must be made to communicate with the main sewer through a
properly constructed trap and pipe drain. If the road be a Mac
Adamized one, some contrivance will be necessary to intercept the
detritus that will pass the grating from entering the sewer, to
which it is very injurious by reason of the short time in which it
concretes, and forms an impediment to the flow of the sewage.
Fig. 192 is the plan, and fig. 193 the section, of a trap and cesspit,
which has been advantageously used in many cases, and of which
favourable reports have been made. Fig. 194 is a plan, and fig.
195 a section, of an extension of the same principle by means of a
double cesspit; but in either case, periodical cleansing with water
is required. The surveyor to the Preston Local Board of Health
has adopted an extra grating placed within the cesspool in a vertical
position over the mouth of the shoot, the advantage of which is,
that the street grating may be made of such a width as not to be
liable to become choked.
A perforated plate would be preferable to long bars, through
which substances of considerable length although narrow can easily
pass.
The manufacture of earthenware pipes for drainage purposes
dates only since the year 1842, when the sanitary enquiry gave
rise to their adoption, and since that time the demand has been so
great, that manufacturers have given very little attention to im-
provements which, under a less extensive demand, and with greater
competition, must have been inevitable.
As much as 35 per cent. upon the prices advertized was offered
to me by a manufacturer if I could procure him the order for about
£1000 worth of pipes required in the drainage of a provincial town
to which I was acting as engineer. Such an offer is quite sufficient
to convey an idea of the large profits which have arisen in the
HYDRAULICS.
461
trade; and I only notice it here, to justify any person purchasing
drain pipes, in insisting upon perfect symmetry and workmanship
in the articles that are supplied him.
The first joint that was suggested to these stoneware drain pipes
was, the “butt joint," which simply consisted in pushing one pipe
against another, and joining them as well as might be practicable.
This was soon improved by the introduction of the socket joints
The objection to these pipes principally consists in the difficulty of
opening the drain in case of necessity, as it will be evident that if
the flanges or sockets are sufficiently long, a pipe must be broken
to accomplish an entrance to the drain. To obviate this, pipes
with half sockets have been used, the socket extending only on the
under side of the pipe; and it has been suggested, that one moiety
of the pipes to be used should have one of these half sockets on
either end, while the other moiety should be without sockets, so
that every alternate pipe, as it were, drops into its place upon the
half sockets of the pipes before and after it, and could of course be
removed with equal facility.
Another suggestion gave rise to the adoption of a pipe to be laid
at intervals along the drain, the upper half of which could be
removed, and thus afford the means of more readily ascertaining
the point at which a drain might have become choked, or for the
insertion of a junction. This pipe, however, will not efficiently
answer the purpose of such pipes, it cannot be impermeable, and
consequently should not be used.
An objection to any socket at all on the pipes arises from the
fact of its interfering with the proper laying of the pipe, which
generally acquires a bearing upon the flange without being bedded
in the centre, and consequently its liability to be broken is much
increased. As an improvement upon this, the rabbeted cone junc-
tion pipes have been introduced. The drainage of Croydon has
been (I believe) entirely carried out by pipes of this make.
Upon the question of laying the drain pipes, making the exca-
vations, joints, junctions, traps, and such like, I omit a description
here, as full particulars will be found contained in one or other of
the specifications appended to this chapter.
WATER SUPPLY.
We next come to the question of Water Supply, and unlike the
drainage question, in which our first concern was to look out for a
place of deposit, we now have to do exactly the reverse, and to find
the purest and best source from whence we may obtain a supply.
According to the highest authorities, the qualities for the water
462
HYDRAULICS.
supply of a town population range themselves in the following
order :-
1. Freedom from all animal and vegetable matter especially
matter in a state of decomposition.
2.
3.
4.
Pure aeration.
Softness.
Freedom from earthy or mineral, or other foreign matters.
5. Coolness in delivery, at a medium temperature, neither
warm in summer, nor excessively cold in winter.
6. Limpidity or clearness.
If the slightest taste or smell is perceptible in water, some
foreign matter is present which should be expelled if possible, the
smell either denoting organic matter in a state of decomposition,
or some insalubrious mineral property. If water is tinged with
colour, it is caused by earthy or vegetable matters which require
to be removed by filtration.
In seeking a supply of water for all the uses of a town popu-
lation, it is doubtless desirable, if possible, to avoid the adoption of
a river source in which the water may possess many degrees of
hardness; but if the natural physical features and the geological
stratum of the surrounding country, do not present that facility
for obtaining a supply of soft water from gathering grounds, it
certainly becomes a question of expediency whether the waters of
the river source cannot be so far purified from animal and
vegetable matter as to render them eligible for the purposes
required.
Those towns that are without the presence of a neighbouring
river are generally well situated for obtaining an abundant supply
from gathering grounds and storage reservoirs. Water obtained
from such a source will undoubtedly be more or less superior in
quality according to the soil and subsoil of the lands upon which
it is collected. The less the interval during which rain water
remains upon the surface, the smaller must necessarily be the im-
purities it will take up during that time. And again, the smaller
the surface over which it is driven before it can percolate into the
land, the smaller will be the amount of organic matter with which
it will become impregnated.
If the town to be supplied has in its vicinity a sufficient area of
hill lands at an elevation to enable the collection of the required
quantity of water, and its storage in a reservoir situated above
the level of the top floors of the highest houses in the town, that
is of all others the most desirable site for gathering ground be-
cause all lifting of the water by pumping will be entirely obviated,
HYDRAULICS.
463
and every house, indeed every room in the town, may be supplied
by the natural power of gravitation.
The method of catching the rain fall of an elevated area must
be varied according to circumstances. For manufacturing pur-
poses in the North of England the practice has been to cut a cer-
tain number of catch water ditches around the apex of the hill,
in the form of contour lines, varied of course according to the
extent of the gathering ground and other physical features; and
below these catch water contrivances, to construct a reservoir,
regard being had to the relative elevation of the reservoir and the
place at which the water is required for use.
Large pasture lands on a sharp sandy or gravelly porous soil
incumbent in a clay subsoil, offer the most geological advantages
for gathering grounds; and the modern method of land drainage
by permeable pipes is probably the best mode of collecting the
water. The impurities held in suspension by the water are dis-
turbed in its passage through the sand, and the organic and other
matters held in solution are seized upon by the growing herbage, so
that water so collected will flow from the pipes in a state superior,
generally speaking, to water from all other sources. If no gather-
ing grounds can be found of sufficient altitude to supply the town
by natural gravitation, the water must be lifted to a reservoir on a
site that is high enough for that purpose. It will be found far
more convenient to lift the water previous to storage than after-
wards, because if the water is supplied to the inhabitants by gra-
vitation, the pipes will always keep themselves full and a constant
service may result. The pumps will then only be required to
work as water from the collecting pipes requires to be lifted to the
reservoir. Water from deep wells may be sometimes found free
from animal, vegetable, and mineral impurities, and in such cases
it only becomes a question of pecuniary expediency as to its use.
In estimating the quantity of water that may be collected by
means of gathering grounds, the first information must be, the
average rain fall of the district, and in estimating the proportion
of that fall which may be reasonably expected to be collected and
stored, considerable attention must be given to the absorptive pro-
perties of the surface soil, and also to the nature of the subsoil.
The first should allow the water to soak into the land as fast as it
falls, and the latter, if impervious, will allow little to pass the pipes
and be lost.
If water can be collected by means of land drainage, such as
we have hinted at above, and from a bed of vegetation, such as
pasture grasses, on sandy or gravelly soils, it will require no filtration
464
HYDRAULICS.
if properly stored in a well constructed reservoir, a better filter
than this natural one being beyond the power of science to
suggest.
It will take about an inch and a half of rain-fall on an acre to sup-
ply a house with the quantity of water we have herein assumed
to be the proper supply, viz., 100 gallons per day, (always bearing
in mind we are speaking of an average; a house with six inhabi-
tants having 120 gallons, while one with four inhabitants has but
80 gallons), so that if we can save nine inches of the annual depth
of fall, every acre of gathering ground will supply six houses;
and for a town of 6000 inhabitants, or (at our average) 1200
houses, 200 acres of gathering ground will be sufficient.
In computing the expense of this mode of collection, much will
again depend upon circumstances, the price of pipes, and skilled
labour in the neighbourhood, but £6 per acre may be pretty
safely taken as the maximum, against which a considerable set-off
may be generally calculated on from the owner of the soil, whose
land would be benefited by the execution of the works. But if
we take the full cost as a first outlay it amounts to £1200, or £1 per
house on the houses benefited, which may be said to be placed in
the same position as they would be by the sinking of a well on
every premises, with this advantage, that the water in the former
case is ample in quantity and pure in quality; while in the latter
it is often scarce, or else so hard as to be unfit for many domestic
purposes, and so contaminated with the percolation of the neigh-
bouring cesspools as to be injurious to health and unpleasant to
taste.
It may be useful to bear in mind that the quantity of water here
allotted to each individual, is a very bountiful allowance. Some
engineers, I am aware, estimate one inch of rain-fall per acre
as sufficient to supply each house, the allowance being about 62
gallons per day, or assuming the average of five occupants, 12
gallons to each person. It is no doubt as essential to have quan-
tity as quality, but still, if instead of finding that a town of 1200
houses possesses an eligible gathering ground of 200 acres, we
find only 130 or 140 acres; we may nevertheless consider that
with an occasional auxiliary supply for those purposes in which
quality is not a consideration, such a town to be well supplied.
The next question that will demand attention, whether we adopt
the gathering ground as a source of supply, or whether we
obtain our water from a river or a well, is the storage reservoir.
In elevation we have already said this should be sufficient to serve
the highest houses in the district, in their upper floors, by the simple
HYDRAULICS.
465
power of gravitation. In size it will be guided by the source of
supply; if this is from a river or a well, a capacity to contain enough
for six days' use will be ample, because the pumps may be worked
at any time, the six days' being only provided as a provision in
case of accident; but if the supply is from gathering grounds,
calculated upon a basis which assumes that none of the water
falling thereon shall be wasted, our reservoir must be sufficient to
hold the excess of the supply above the demand in wet seasons,
to provide for the deficiency of supply in seasons of long draught.
If we assume that a reservoir should contain a four months' supply,
we shall appear to make ample provision for this irregularity. If
our reservoir is within reasonable dimensions, it should be certainly
covered over, and the light should be excluded. A reservoir in-
tended to contain the four months' supply just spoken of could
hardly be so treated. In all cases, the reservoir should be con-
structed as deep as possible; but this is of less importance in a
covered reservoir than in an open one, the great desideratum being
to prevent as much as possible the rays of light from exercising
any objectionable influence upon the purity of the water.
Having determined the site of the reservoir and the size, we
come next to the consideration of the course and direction of the
service mains. The same desiderata should now occupy attention
as influenced the laying out of the main sewers. Friction should
be avoided as much as possible, and a regular inclination will in-
sure a more steady pressure upon the pipes. In calculating the
sizes of the mains, a distinction will become apparent between a
constant and an intermittent system. In the former we may with
tolerable security assume that the whole of one day's supply will
not be required in a less space of time than four hours; while in
the latter, the cisterns of the inhabitants will be filled in a time,
limited only by the capacity of the machinery adopted for the
purpose.
A few words on the comparative merits of the two sources of
supply may not be out of place.
The expense of erecting cisterns, and the necessary apparatus
for the intermittent system in new houses of the first class in the
fashionable districts of the metropolis, rarely comes under £100
per house; and in one block of building, the details of which have
come under my observation, the expense of cisterns, ball-cocks,
and extra pipes amounted to £900, of which £500 was for the
cisterns alone; whereas £200, or, at the most extravagant estimate,
£300 would have furnished the means of a better supply by the
constant system. In all towns that are supplied with water under
466
HYDRAULICS.
the constant system, the advantages are apparent in the immense
saving of water, and the general comfort and cleanliness of the
inhabitants, without reference to the pecuniary advantage above
alluded to. Independent of other advantages, the quality of
water suffers less deterioration under the constant than the inter-
mittent system; and beyond doubt, the strain upon the mains and
submains is not so severe, inasmuch as all hydraulic shocks common
to the intermittent system have not to be resisted under a constant
supply.
It is in accordance with common sense, that water exposed in a
cistern out of doors, in a smoky neighbourhood, must soon become
impregnated with the impurities that are floating about in the at-
mosphere in every possible direction; and if the cistern is within
doors, the water soon loses its freshness, and acquires a slimy cha-
racter. Under the constant system of supply, if all the pipes are
made to communicate, a free circulation is kept up by the constant
drawing from one pipe or another, and as nearly as may be the
same quality of water is maintained throughout the town; the water
always flowing towards the point of draught.
From what has been stated, it is evident that no town can be
said to have a proper supply of water that does not give to every
house a tap, from which an unlimited draught can be taken at any
hour of the day and night.
That the establishment of apparatus to carry out the constant
supply is less expensive, and that the water so supplied is better in
quality than by any other method of distribution.
The basis of a calculation for the sizes of the mains being a given
quantity of water required to be conveyed a certain distance in a
certain time with a known head, the Hydraulic Tables will speedily
determine the requisite diameters. It should be added, that in all
cases where practicable, the water pipe and the drain pipe should
be laid in the same trench, by which means a great saving
is effected in the excavation and replacement of the ground in
laying down the pipes. But in every case, the water main should
be above the drain, so that all chance is avoided of any escape from
the drain polluting the water service.
The sub mains and house services, stand pipes for street watering,
fire plugs, stop-cocks, and other minutiae of detail, will be laid out
at the discretion of the engineer.
The method of carrying out the works on the ground we will
endeavour to illustrate in the specifications annexed.
As much misconception exists with reference to artesian wells
and springs, a word or two thereon may be appropriately advanced
HYDRAULICS.
467
under this branch of our subject. Some assert that an artesian well
ceases to become so directly it ceases to throw up water, but such
an argument is not tenable for a minute. An artesian well, so
called from the province of Artois, in France, (at which place the
practice of boring used in the construction of an artesian well was
chiefly carried on,) is nothing more than an illustration of the old
and well known hydraulic fact, that "water will always find its
level." The theory of these artesian wells is very simple. Let
the points A A, fig. represent the exposed surface of a porous
strata, perfectly absorptive of water, and on the contrary, let the
points B B be the surface of a strata of tenacious clay, wholly im-
permeable; now if it be desired to create an artesian well at the
point C, we shall have to bore through the impermeable clay, and
while so doing, no discharge of water will take place; but as soon
as we tap the porous strata at D, the water therein will rise to the
surface C, and (if confined by a stand pipe) to such a height above
C as shall correspond with the level of the water in the porous
strata.
Inasmuch as it is possible to exhaust the supply, so will the
working capacity of this well depend upon the extent of surface
area of the collecting porous strata, as it must be evident that in a
dry season the longer the well is worked the lower must the alti-
tude of the water in the strata become, and the less efficient will
be the discharge, and if rain does not replenish before the water in
the earth is drawn to the level line E, the well can no longer dis-
charge water above the surface, the hydrostatic pressure being all
removed from it. But this by no means deprives the well of its
character or right to its name, since no sooner is the water in the
porous strata replenished by a fall of rain on the surface, than the
well resumes its operations with a vigour proportionate to the fall
of rain. Some porous strata stretch out so wide and offer so vast
an area of exposed surface, that the water contained in them can
hardly ever become exhausted.
What has been said with reference to artesian wells, will also
serve to explain the properties of springs, which are only so many
additional examples of hydrostatic pressure acting upon water con-
tained in porous strata, which freely finds vent at the first place at
which such strata becomes exposed to the surface of the earth at a
low level. In Mr. Weale's Rudimentary Treatises will be found
a little work, entitled, Well Digging, Boring, and Pump Work,
by John Geo. Swindell, R.I.B.A., which will be found to be a most
able though brief elementary description of this question.
Before finally closing this subject, I will observe, that the re-
468
SPECIFICATION.
gulations of good drainage can hardly tolerate the existence of old
cesspools, and positively prohibits the creation of new ones within
the vicinity of, or in proximity to, any collection of dwellings, of
whatever description, as well as an untrapped connection with any
drain or sewer.
Interpreta-
tion.
Extent of
Contract.
Quality of
Iron.
Casting of
Pipes.
SPECIFICATIONS, &c.
BIRCH END LOCAL BOARD OF HEALTH.
1853.
Contract, No. I.
IRON PIPES AND CASTINGS.
Specification to be observed by the contractor for making
and delivering at the railway station at Birch End,
certain iron socket pipes and castings, required for
purposes of water supply by the Local Board of
Health, Birch End.
In this specification the words " Local Board of Health,"
shall be understood to mean the Local Board of Health,
for the time being, duly elected and acting in and for, the
district of Birch End. The word "Engineer" shall
mean, Edward Ryde of 14 Upper Belgrave Place, Eaton
Square, London, Civil Engineer and Surveyor, or other,
the duly appointed Engineer, or Surveyor, to the said
Local Board of Health for the time being; and the word
Contractor shall mean one or more Contractor or Con-
tractors, and shall include his or their heirs, executors, and
administrators.
This contract includes the manufacture and supply of
all the pipes, cocks, and special castings that are required,
to construct and completely finish the water works about
to be carried out by the Local Board of Health.
The iron shall be remelted in the cupola or air furnace;
and shall be of the best description without admixture
of cinder, or other matter, to render it inferior in quality.
It shall be strong, close grained, and tough, and shall be as
hard as can be conveniently drilled and clipped.
All the pipes shall be cast vertically in dry sand, and
shall be of the kind, or description, usually denominated
"socket pipes:" they shall be of the forms, thicknesses and
dimensions shown in the drawings, and in case of any
Pipes must
be sound and
free from
Defects.
Pipes shall
be proved.
Engineer
may attend
dry.
IRON PIPES AND CASTINGS.
469
discrepancy between the scaling and figured dimensions,
the latter are in all cases to be observed.
The pipes are to be cast perfectly sound, free from cold
shuts, honey comb holes, or other defects, and shall be
truly cylindrical in the bore, straight in the axis, and
internally of the full specified diameter. They shall be
thoroughly cleaned, internally and externally, and great
care shall be taken in cutting off the runners to preserve
a square angle on the inner edge of the socket against
which the lead joint is made. At the junction of the
branch pipes the inside diameter of the outlet pipe is to be
made half an inch larger than the other portions; and the
thickness of the sockets shall be in all cases a quarter of
an inch more than the body of the pipe. To insure that
in all cases the beads will enter the sockets, a circular iron
template shall be passed to the bottom of every socket, and
a circular iron ring shall be passed over every bead. The
socket shall not be larger than is absolutely required, and
stated in the drawings, otherwise the expense of jointing
will be unnecessarily augmented.
The pipes are to be each proved before leaving the
foundry under a pressure equal to a column of water 600
feet in height, and such pressure shall be maintained for at
least three minutes, whilst the pipe is being sufficiently
and repeatedly struck in every part with a hammer of
weight suitable to the size of the pipe.
The engineer is to be at liberty to attend at the foundry
at the Foun- during the casting of the pipes or any of the special cast-
ings referred to in this specification, or he may depute a
competent person to attend on his behalf, for the purpose
of ascertaining that his instructions and the provisions of
this specification are complied with; and the contractor
shall at all times afford him every facility he may require,
and pay immediate attention to any directions he may
give.
Length of
Pipes.
Pipes.
The two-inch pipes shall be cast in lengths of six feet;
the larger sizes in lengths of nine feet; exclusive of the
socket in either case, and shall be of the weights contained
in the schedule hereto annexed.
Quantities of The probable quantities of the various pipes and castings
required are set forth in the schedule hereto annexed; but it
is to be distinctly understood that the engineer shall have
the power at any time to make alterations in, additions
470
SPECIFICATION.
Pipes, &c., to
be coated
with Dr.
Smith's pre-
paration.
Contractor
responsible
in pipes.
to, or deductions from, any part of this contract, which
alterations in, additions to, or deductions from, shall not
annul the contract, but an equivalent shall be given or
taken as the case shall require.
The whole of the pipes and pieces, as soon as they are
cast and cleaned, and before any rust shall have been
produced upon them, are to be submitted to Dr. Angus
Smith's patent process, in such a manner as to receive,
while at the proper temperature, a complete and thorough
coating of the preparation over the whole of the internal
and external surface.
Should the iron be of inferior quality, or the pipes too
for all flaws light, or any flaw or other defect appear in any of them
after they have been delivered, the contractor is to be
responsible for that defect, and is to replace the defective
pipes with good ones to the satisfaction of the engineer.
Delivery of
pipes.
Contractor
responsible
within
twelve
months.
Cocks.
Engineer to
have same
The pipes and pieces are to be delivered by the con-
tractor, at the railway station, Birch End, in such
quantities and at such times, as the engineer may from
time to time direct, the whole quantity to be sent in on
or before the 31st December next.
In the event of the failure of any of the pipes within
twelve months of their delivery, and the failure should
arise from any defect in their construction, of which the
engineer shall be sole judge, the contractor shall be held
responsible for the damage, and shall on demand, refund
to the Local Board of Health, any expense to which they
may have been subjected by reason of such failure.
The cocks required are of the description commonly
called,
"double faced screw cocks." The shell of each
cock is to be cast in one piece, and to be a sound clean
casting, made from the best description of iron, and fitted
up with bored and turned stuffing boxes, faced joints, and
all the necessary bolts and nuts for the same.
The spin-
dles are to be of gun metal, with square thread, and
each to be provided with a wrought iron box key head,
cottered in. The valves of the cocks from two inches, to
four inches in diameter, are to be of gun metal; above
that diameter iron castings will be allowed, but with gun
metal facings. Each cock must be perfectly tight, and of
the best workmanship.
All the powers conferred upon the engineer with
power, and reference to the pipes, in this specification, and all the re-
IRON PIPES AND CASTINGS.
471
ity with
cocks as
same liabil- sponsibility of the contractor shall equally relate to the
cocks and other special castings, so long as the same is not
repugnant to, or inconsistent with, any acknowledged
engineering practice.
pipes.
Special
castings to
be made as
soon as possi-
ble after
ordered.
Sureties.
Payment.
All branches, bends, taper pipes, fire plug pipes, and
special castings of every description shall be made and
delivered as soon as possible after the receipt of the orders
by the contractor.
The contractor shall, if so required, find two good and
sufficient sureties, in a penal sum as nearly as may be
equal to one quarter of the amount of the accepted tender,
for the due performance of his contract.
And the said contractor shall be entitled to payment
for his work, in manner following, that is to say, 50 per
cent. of the value of pipes and castings from time to time
made and delivered, within one month of such delivery;
forty per cent of the value of the whole of the pipes and
castings delivered, within two months of the final comple-
tion and delivery of the whole contract; and the remaining
10 per cent. at the expiration of six months from the final
delivery of the pipes, provided the said pipes have proved
sound, or the balance of such 10 per cent., if any, as may
remain due to the Contractor, after deducting any costs
and expenses the Local Board may have been obliged to
incur, by reason of any unsoundness, or failure of the
pipes. Always premising that the certificate of the En-
gineer will be required, in all cases, before any payment
will be made by the Local Board.
Inside
Diameter of
Pipe in Inches.
Schedule hereinbefore referred to.

Length of
each Pipe
in Feet.
Weight of each
Pipe.
Probable number
of each kind
required.
Cwt. Qrs. lbs.
2
∞∞29 C I WON
6
0
1 20
3
9
4
9
5
9
6
9
7
9
8
9
9
10
9
11
9
12
9
12230 + + 20 co
0 3 20
1 1 7
1 3
0
1 U
3
0
3
1 20
4
0
0
4
2
0 12
6 1
14
15
472
TENDER.
Contract, No. I.
TENDER FOR PIPES AND CASTINGS.
We the undersigned Contractors will undertake to make
and deliver, according to the specification annexed, the
several probable quantities of pipes and special castings
therein referred to at the prices stated below.
Straight pipes not exceeding 2 inches in diameter, at
per Cwt.
£ s. d.
Curved pipes
Taper pieces
Branch pieces
Straight pipes, exceeding 2 and not exceeding 4
inches in diameter
Curved pipes
Taper pieces
Branch pieces
Straight pipes, exceeding 4 and not exceeding 6
Curved pipes
Taper pieces
Branch pipes
inches in diameter
Straight pipes exceeding 6 and not exceeding 9
Curved pipes
Taper pieces
Branch pipes
inches in diameter
Straight pipes exceeding 9 and not exceeding 12
Curved pipes
inches in diameter
Taper pieces
Branch pipes
Cock and plug castings and other hollow castings
not exceeding 3 inches in diameter
Exceeding 3 inches and not exceeding 6 inches
Exceeding 6 inches and not exceeding 9 inches
Exceeding 9 inches and not exceeding 12 inches
And we will undertake to execute an agreement (to be
prepared by, and at the expense of, the Local Board) for the
due and complete fulfilment of all the conditions expressed,
and implied in and by, the specification hereto annexed.
Gentlemen,
Your most obedient servants,
CONTRACTORS.
SPECIFICATION.
473
Interpreta-
tion.
Extent of
Contract.
Quality and
description
of pipes.
BIRCH END LOCAL BOARD OF HEALTH.
1853.
Contract, No. II.
STONE WARE DRAIN PIPES.
Specification to be observed by the Contractor for making
and delivering at the Railway Station, at Birch
End, certain glazed stone ware tubular socket pipes,
half socket pipes, bends, curves, junctions, traps,
soil pans, &c., required by the local Board of Health,
Birch End, for the purposes of drainage.
In this specification, the words, "Local Board of Health,"
shall be understood to mean the Local Board of Health
for the time being, duly elected and acting in and for the
district of Birch End. The word "Engineer," shall mean
Edward Ryde, of No. 14, Upper Belgrave Place, Eaton
Square, London, Civil Engineer and Surveyor, or other
the duly appointed Engineer or Surveyor to the said Local
Board of Health, for the time being; and the word Con-
tractor shall mean one or more Contractors, and shall
include his or their heirs, executors, and administrators.
This contract includes the manufacture and supply of
all the straight and curved drain pipes, curve, bend, taper,
and junction pieces, traps, soil pans, &c., required to con-
struct and entirely complete the drainage of the town of
Birch End, as the same are particularly delineated, and
described upon the plans and drawings deposited in the
offices of the Engineer, in London, and of the Clerk to
the said Local Board of Health, at Birch End, and accord-
ing to this specification.
The ordinary pipes and pieces shall be of the descrip-
tion usually denominated "socket pipes," sound, well burnt,
glazed stone ware, free from cracks, flaws, and all other
imperfections, perfectly impermeable, truly cylindrical in
the bore, straight in the axis, internally of their full
specified diameter, with their inner and outer surfaces as
nearly as possible concentric, and especial care must be
taken that the sockets, which in the larger sizes of pipes
exceeding nine inches internal diameter, shall be at least
three inches in depth, will receive the smaller ends of the
pipes.
The engineer shall be at liberty so often, and for so
2 G
474
SPECIFICATION.
power
attend at
Manufactory
&c.
Engineer has long as he may think fit to attend at the manufactory,
either by himself or his duly authorised clerk, for the pur-
to inspect, pose of inspecting the processes of the manufacture, and of
ascertaining if his own instructions and this specification
are properly attended to; and the contractor shall pay im-
mediate attention to any directions he may think proper
Length and
dimensions
to make.
All pipes not exceeding six inches in diameter shall be
of pipes, &c. made in lengths of two feet exclusive of the socket;
Soil Pans.
Times of
delivery.
Engineer has
power to
tests, and to
fect pipes.
beyond that diameter the length shall be three feet. The
dimensions of the several pieces of bend pipe, curves,
junctions, traps, and soil pans, are mentioned and described
in the drawings, and should any discrepancy exist between
the figured or written dimensions and the admeasurements
by scale, the former are in all cases to be taken as the
correct dimensions.
The soil pans must be of the shape delineated in the
drawings, and the spreaders must be so adjusted as to keep
the pans entirely clear of soil.
The whole of the pipes, bends, junctions, curves, traps,
and soil pans, must be delivered at the railway station,
Birch End, in such quantities and at such times as the
engineer may from time to time direct; the whole of the
contract to be finally completed and delivered on or before
the 31st December next.
The engineer shall be fully at liberty to make a further
make further test of the pipes after their delivery, either as to their
reject imper- impermeability or strength or any other quality he may
think fit, and if from any cause whatever he shall consider
the pipes or other contrivances and things contained in
this specification are not in his judgment of the best
quality both in material and workmanship, according to
the true intent and meaning of this specification, he shall
be at liberty to reject the whole, or any part thereof, and
the contractor shall immediately remove, at his own cost
and charges, the pipes or pieces so rejected.
Samples of
pipes, &c.
Contractor
to find
sureties.
The contractor shall submit with his tender, samples of
each description of pipes and pieces he intends to supply.
The contractor shall, if required, find two good and
competent sureties, who are willing to become bound in a
penal sum equal in amount to one-fourth of the tender,
for the due and complete performance of the contract.
The quantities of the several descriptions of pipes and
TENDER.
475
pipes, etc.,
required.
Quantities of pieces, so far as it is possible to ascertain, are stated in the
schedule hereto annexed, and they are believed to be close
approximations, but it is to be distinctly understood, that
the engineer shall at all times have power to make any
alterations in, additions to, or deductions from, the quan-
tities so stated, which alterations in, additions to, or de-
ductions from, shall not annul the contract, but an allow-
ance shall be given or taken as the case may require; for
the calculations of which allowance the schedule of prices.
shall be the basis.
Engineer
shall deter-
In the event of any doubt arising after the execution
mine doubts. of the contract, as to the true intent or meaning of this
specification, the said drawings therein referred to, or the
said contract, the same shall be referred to the engineer,
and his decision shall be conclusive and binding; any
order or rule of court of law or equity to the contrary
notwithstanding.
Times of
payment.
And the said contractor shall be entitled to payment
for his work, in manner following, viz., i.e., 50 per cent.
of the value of the pipes and pieces delivered from time
to time, within one month of such delivery, and the re-
mainder within two months of the final completion of
the contract; the certificate of the engineer to the effect
that the contractor is entitled to payment, being required
in either case, before any money will be paid by the local
board.
Tender for impermeable glazed stoneware, tubular socket,
sewerage, and drain pipes, soil pans, &c.
1853.
To the Birch End Local Board of Health.
agree
We, the undersigned contractors, hereby offer and
to make and deliver at the railway station, at Birch End,
impermeable glazed stoneware tubular socket pipes, half
socket pipes, bends, curves, junctions, traps, soil pans, &c.,
in accordance with the terms and conditions of the an-
nexed specification, and of the following schedule.
476
TENDER.
Description.
Straight Pipes
SCHEDULE.

Internal
Diameter
Probable
of each
Pipe and
Piece.
quantities
required.
Length of
each Pipe
exclusive
of Socket.
Price per Foot.
(Whole Sockets.))
00 + 20 Co
3
500
4
650
1000
6
1150
9
2300
12
3800
15
1261
NNNN ∞ ∞ ∞ɔ
2
2
2
2
3
3
Curved Pieces
and Bends .
OOH LO
3
12
2
4
16
2
5
23
2
6
25
2
9
40
3
12
60
3
15
10
3
Straight Pipes
(Half Sockets.)
6
22
2
9
46
3
12
76
3
15
30
3
Taper Pieces..
4
:당
​3 to 4
10
5
20
5
6
30
""
6
9
30
9,, 12
30
12.15
15
NAN∞ ∞ að
2
2
2
3
3
Single Junction
Pieces
}
""
Diameter
of straight
Piece.
3
20
5
4
10
5
20
6
20
9
30
12
30
15
30
NNNN ∞ ∞ ∞
2
2
2
2
3
3
3
Double Junction
Pieces
3
4
10
6
10
9
10
12
10
15
10
4-99999
5
7
CO CO CO NNNN
2
3
3
3
SPECIFICATION.
477

Description.
Bore.
Number
required.
Length.
Price each.
Inches.
ននននន នននន
50
50
NNNN M
2
2
Patent Syphon Traps
6
23 + CO
4
50
50
9
50
Patent Yard Syphons,
4
with detached Grating, by
which means they can be
easily cleansed.
6
9

12
50
Common Syphon Pans.
50
Patent Syphon Pans.
50
Hopper Pans and
Syphon Traps.. S
50
Gully Sinks,
12
with Traps for Street Gratings
15
22
18
នន
50
50
50
And we will undertake to execute an agreement (to be
prepared by and at the expense of the local board) for
the due and complete fulfilment of all the conditions ex-
pressed and implied in and by the specification hereto
annexed.
We are, Gentlemen,
Your obedient servants,
CONTRACTORS.
Interpreta-
tion.
BIRCH END LOCAL BOARD OF HEALTH.
1853.
Contract, No. III.
PIPE LAYING.
Specification to be observed by the Contractor for laying and.
jointing water and drain pipes, for the Local Board
of Health, Birch End, according to the instructions of
Mr. Edward Ryde, the Engineer to the Local Board.
In this Specification the words "Local Board of Health"
shall be understood to mean, the Local Board of Health
duly elected, and acting in and for the district of Birch
47.8
SPECIFICATION.
Extent of
Contract.
End, and shall include themselves and their successors.
The word "Engineer" shall mean Edward Ryde, of No. 14,
Upper Belgrave Place, Eaton Square, London, Civil Engi-
neer and Surveyor, or other, the duly appointed Engineer
or Surveyor to the said Local Board of Health for the time
being. The word "Contractor" shall mean one or more Con-
tractors, and shall include his or their heirs, executors, or
administrators.
This contract includes the excavating for, and the laying
and jointing of, all the water and drain pipes and other
contrivances connected therewith, required to construct
and completely finish the several sewers, drains, water
mains, sub mains, &c., described and delineated upon the
drawings prepared by the engineer; the taking up and sub-
sequent replacement of the pavement, roadway, or surface
soil, of whatever description; filling in and punning up
the trenches; carting away the surplus earth; carting the
pipes and pieces from the railway station at Birch End to
the situations in which they will be required; lead and
gasket for joints of water pipes, and clay or cement for
joints of drain pipes; watching day and night to guard the
public from accidents; the finding and providing of all and
all manner of labour, and tools and materials (excepting
only the pipes and pieces which will be delivered at the
railway station by other contractors), necessary to the com-
pletion of the works to the entire satisfaction of the engineer.
Directions of The directions of the several sewers, drains, water mains,
and sub mains, are respectively marked and delineated upon
the plan, and the depths of cutting, and rates of inclination,
are severally drawn upon the section, and marked in figures
thereon. No deviation whatever from these drawings will
be allowed, except by the express direction of the engineer,
and should any descrepancies exist between the figured di-
mensions and the admeasurement by scale, the former are,
in all cases, to be taken as the correct dimensions. The
engineer will, at all times, set out and mark the several
works upon the ground, and the contractor shall provide
proper assistants, implements, and materials for that pur-
pose, when called upon, from time to time, to do so.
Works and
depths of
cuttings.
Contractor
to give notice
of Highways
Before commencing to break up any public road, footway,
to Surveyors or street, for the purposes of this contract, the contractor
before break shall give all necessary notices to the surveyors of high
ways, or other proper authorities, and shall pay any
ing up roads.
PIPE LAYING.
479
Excavations.
Laying the
fees that may be legally payable in respect of the
same.
The excavations of the specified depths shall be made in
such lengths as the engineer may direct, and of sufficient
widths, as shall, in the judgment of the engineer, enable
the pipes to be properly laid and backed up. The bottom
of the trench, for the larger sizes of drain pipes, shall be
moulded to the shape of the pipe, and a notch shall be cut
for the socket, so that the pipes may take a firm bearing
and be securely bedded upon the foundation. The trench is,
in all cases, to be an open cutting, as no tunnelling or bench-
ing will be allowed, excepting in cases of special emer-
gency by express permission of the engineer. The sides
of the cuttings are to be securely shored up where requisite,
to prevent the adjacent earth from slipping or colting in, to
protect the adjacent buildings, or to ensure the proper con-
struction of the sewer. Where the foundations shall be
unfit for the bedding of the pipes, the soft ground is to be
taken out, and a proper and sound bedding, or foundation,
substituted. If clay is met with in the excavations, so
much of it is to be preserved as will be sufficient to make
a layer of nine inches, at least, in thickness round all the
sewers, so as to form an impermeable clay collar or casing
to the same. The excavations are to be kept perfectly free
from water during the progress of the work, the contractor
providing all necessary apparatus for that purpose. The
excavated earth is not to be thrown about in any direction
most convenient to the navvies, but it is to be so
placed as to cause as little interruption as possible
with the free passage of the public, or annoyance to
the adjacent inhabitants. When the line of sewer
crosses through private property, none but unavoidable
injury shall be done to the same, or the contractor shall
be responsible.
The pipes shall be carted from the railway station, at
drain pipes. the cost and expense of the contractor, and shall be stacked
as conveniently as possible for use, without unnecessarily
impeding the public highway.
The trench being opened to the satisfaction of the engi-
gineer or his clerk of works, the pipes are to be properly
and carefully fitted and matched, before they are taken
into the trench. The pipe layer shall then be furnished
with a bag stuffed with shavings or hay, of a size to fit the
480
SPECIFICATION.
Filling in.
Water pipes.
Pipe laying.
Hydrants
and Screw
Cocks.
pipe rather tightly, with a rope about ten yards in length,
fastened at one end to the mouth of the bag.
The bag must be placed in the first pipe at the outfall,
and the rope passed through each pipe as it is laid down,
until the rope is served out; the joints are then to be
made with clay of approved quality, and properly tem-
pered, and left perfectly water tight. The bag is then to
be drawn forward through all the pipes into the last pipe
laid down, when other pipes are laid down until the rope
from the bag has been again served out, when the joints
are made as before. Curved, half socket, junction, and
taper pieces are to be laid where directed. Neither the
pipe layer, nor any other person, shall be allowed to walk
over the pipes until they are covered over to an extent of
at least nine inches.
The pipes being laid, and the joints made to the satis-
faction of the engineer, a layer of clay of nine inches thick
is to be well punned in around the pipes, so as to form
an impermeable casing of clay. The trench may be then
filled in with the excavated earth up to the level of the
bed for the water pipes, two men being constantly kept in
the trench ramming to every man filling in.
The contractor to cart, at his own expense and cost, all
the iron pipes and castings delivered at the railway station
by another contractor to the respective positions in which
they will be required, there to be stacked in places that
may be least objectionable to the general public.
Before the pipes are lowered into the trench, they are
to be thoroughly cleaned out, so that no earth or rubbish
may be contained in them. The joints are to be made
sound, of lead and gaskett of approved quality; the depth
of lead in the sockets to average two inches. No split or
defective pipes or castings are on any account to be laid
down, nor any screw cocks or hydrants to be fixed which
leak or allow the water to pass by them; and should it be
found that any such have been laid down or fixed, the con-
tractor will have to take them out and substitute others at
his own expense.
The contractor is to fix screw cocks and hydrants where
indicated by the drawings or directed by the engineer; the
hydrants to be connected with the main by two inch pipes.
All branch pipes and dead ends are to be properly capped
and left secure.
PIPE LAYING.
481
Gully Gra-
tings, &c.
Remaining
earth to be
filled in.
Pavements,
Roads, etc.
good.
The contractor shall securely fix in brickwork set in
hydraulic mortar, such gully gratings, sinks, fire plugs, and
other contrivances as may be marked on the drawings, or
directed by the engineer.
The engineer being satisfied with the works that have
been constructed, the remaining excavated earth, or so
much thereof as may be required, shall be filled in in re-
gular layers, not exceeding six inches in thickness, two
men being kept ramming to every man filling in. If in the
opinion of the engineer, the shoring and strutting timber
cannot be removed from the deeper trenches with safety to
the adjoining buildings, the same shall be left in the
ground, and the contractor shall not be entitled to any
extra payment on that account. Care is to be taken that
all materials for re-forming the road are to be retained until
the last, or until it becomes necessary to use them.
The pavement, roadway, or surface soil is to be made
to be made good, and left in as perfect a state as it was found to be
previous to the commencement of the works, or as near
thereto as may be, to the satisfaction of the engineer, his
clerks, and assistants, and the surveyor of the highways, or
other proper authorities.
Surplus
earth.
Commence-
ment and
of works.
The contractor is to cart away all surplus earth at his
own expense, the same to be emptied into such open
ditches or other places as the engineer may direct.
GENERAL CONDITIONS.
The contractor is to commence the several portions of
completion the work immediately on an order being given by the en-
gineer to that effect, and shall, on or before the 31st
December next, complete the whole of the works herein
specified, and such additional works as the engineer may
direct to be executed.
Contractor to
works.
The contractor shall at all times be present on the works,
be present on or in his absence he shall provide a competent representa-
tive, fully authorized to act in his behalf in all matters
relating to this contract.
provide la-
terials, and to
Contractor to The contractor shall at all times, by day and by night,
bour and ma- provide and use at his own cost all overlookers, labour, and
prevent acci- materials of every description whatever, that may be re-
quired for proceeding with and completing the works con-
tained in this contract in a workmanlike manner, or for
preventing accidents, or affording accommodation to the
dents.
482
SPECIFICATION.
Minor parts
included in
contract.
Descriptions
not repeated
validated.
public during the progress of the said works, and shall in
all cases immediately attend to the reasonable requirements
of the engineer.
Wherever neither the drawings nor specification contain
any special notice of minor parts, the intention to include
which is nevertheless to be inferred, and which parts are
necessary for the completion and stability of the said works,
all such additional parts are to be provided and performed
by the contractor, and are supposed to be included in the
sum at which he contracts for the works; and where any
thing is directed to be done, or to "be provided if required,"
or words of similar import, it must be understood that every
thing so referred to will be considered as included in the
contractor's tender.
It is to be distinctly understood, that though certain de-
are not in- scriptions and stipulations are not repeated or implied in
different parts of this specification, and in the contract to
be entered into for the fulfilment of the same, it shall not
be thence inferred that the remaining directions, descrip-
tions, and stipulations, of which there shall be no repetition
or amplification, are in anywise invalidated.
Contractor to
proceed with
works to
satisfaction
The contractor shall at all times proceed with the works
at the rate of progress required by the engineer; and should
of engineer. the engineer be at any time dissatisfied with the nature or
mode of proceeding in, or at the rate of progress of the
work, or any part thereof, he shall have full power to pro-
cure and make use of all labour and materials which he
may deem necessary, deducting the cost of such labour and
materials from the money that may be due or become due
to the contractor. But it is hereby expressly specified and
declared, that the possession of this power by the engineer
shall not in any degree relieve the contractor of his obli-
gation to proceed in the execution of, and to complete the
works with the required expedition.
Contract to
be void if con-
to proceed
Should the contractor fail to proceed with the works in
tractor fails the manner and at the rate of progress required by the su-
with works perintending engineer, this contract shall be (at the option
of engineer. of the Local Board of Health, not otherwise) considered
to satisfaction
void, so far as relates to the work remaining to be done;
and all sums of money that may be due to the contractor,
together with the materials and implements in his pos-
session, and all sums of money named as penalties for the
non-fulfilment of the contract, shall be forfeited to the
PIPE LAYING.
483.
Engineer
may direct
Local Board, and the amount shall be considered as ascer-
tained damages for breach of contract.
It is to be distinctly understood, that the engineer may
alterations. at all times direct that there shall be made any alterations
in, additions to, or deductions from, any of the works here-
inbefore described or referred to; and which alterations
in, additions to, or deductions from, shall not annul the
contract, but the same shall be valued according to the
schedule of prices, filled up by the contractor, and attached
to his tender, and that the prices inserted in the schedule
shall be considered as inclusive of all labourage, materials,
and expenses connected with the work to which such prices
apply.
Sureties.
Payments.
Contractor
responsible
The contractor shall (if so required) find two good and
sufficient sureties in a penal sum, as nearly as may be equal
to one-fourth the amount of the accepted tender, for the
due performance of his contract.
Payments to the extent of two-thirds of the value of the
work executed will be made to the contractor upon the
certificate of the engineer that the works have been exe-
cuted in accordance with this specification, and to his satis-
faction; one moiety of the remaining one-third will be paid
to the contractor on the completion of the whole of the
works contained in his contract, and the balance upon the
expiration of six months, upon the certificate of the engi-
neer that the whole of the work is in a satisfactory and
proper state, and that no penalty under this specification
has been incurred.
The contractor shall guarantee and hold harmless the
for damage. Local Board of Health from any damage that may arise by
reason of the negligence of his workpeople, or from any
other cause, during the execution of this contract. And
Engineer to should there be any doubt as to the meaning of any portion
determine
doubts.
of this specification, the contractor tendering is requested
to set forth the particulars of such doubt or obscurity in
writing, and submit the same with his tender before the
contract is signed; the question shall be discussed by the
engineer and contractor, and if necessary, shall be formally
settled in writing. After the execution of the contract,
the decision of the engineer shall be conclusive and binding.
The Local Board do not bind themselves to accept the
lowest or any tender.
484
TENDER.
BIRCH END LOCAL BOARD OF HEALTH.
Contract, No. III.
TENDER FOR PIPE LAYING.
1853.
To the Local Board of Health, Birch End.
Gentlemen,
I hereby propose, undertake, and agree to exe-
cute, perform, and do, the several works described in the
foregoing specification, and in the drawings, according to
the true, intent, and meaning thereof for the sum of
pounds; and I also agree that the prices
mentioned in the following schedule shall form the basis
of a calculation for ascertaining the equivalent to be given
or taken, in respect of any alterations in, additions to, or
deductions from, the said works, that may be made from
time to time, by order of the engineer.
I am, Gentlemen,
Your obedient servant,
CONTRACTOR.
Schedule of Prices before referred to.
For laying stoneware drain pipes and pieces,
including excavating, laying, jointing and filling
in, punning ground, making good surface, cart-
ing away surplus earth, and every other expense
in conformity with the specification.
3 inches to 6 inches diameter 2 feet deep
Price per foot
lineal.
£ 3. d.
4
""
6
8
وو
10
9 inches to 15 inches diameter 2
وو
4
وو
6
وو
8
وو
10
"
12
""
For fixing gully shoots and traps
sink and yard gratings
59
each
وو
SPECIFICATION.
485
For laying water pipes and pieces, including
excavating, laying, jointing, filling in, and pun-
ning ground, and every other expense in confor-
mity with the specification.
3 inches diameter per lineal yard
£ s.
4
""
5
وو
99
6
"9
""
7
وو
8
وو
9
""
39
10
وو
11
12
99
وو
وو
""
For fixing stop cocks, including fixing and
jointing, providing and fixing elm box over cock,
and making good paving up to box.
4 inches diameter each
5
95
6
دو
7
""
8
رو
9
دو
10
11
12
وو
وو
For fixing hydrants, including excavating,
laying connecting pipes, and uniting the same
to the mains, jointing, filling in and punning
ground, and making good paving
each
d.
BIRCH END LOCAL BOARD OF HEALTH.
Contract, No. IV.
RESERVOIR.
Specification to be observed by the Contractor for the works
set forth therein, required to be executed by con-
tract, for the Local Board of Health, Birch End,
according to the designs, drawings, and instructions
of Mr. Edward Ryde, Civil Engineer and Surveyor.
486
SPECIFICATION.
Excavator.
Embanking
top of reser-
voir.
1 to 1.
Extent of Contract.—The works comprised in this con-
tract, include the excavating for, and embanking and con-
structing a covered reservoir; the finding of all and
all manner of materials, labour, tools, carriage, tra-
velling expenses, and all other things of whatsoever
description that may be required to carry on, erect, con-
struct and completely finish such reservoir, as the same is
particularly delineated and described in the several draw-
ings, and in this specification.
Plate
DRAWINGS.
Plan and Section of Reservoir.
To excavate for the proposed reservoir to such depths
as shown in the drawings, care being taken that the whole
of the top soil or turf is to be removed and placed in a
heap by itself, and to be used again in covering over the
embankment and slopes of the said reservoir, when the
same is constructed, and also that those soils which may
be most retentive of water, may be placed as much as pos-
sible by themselves, to be used again on the embankment
of the reservoir.
To embank the reservoir when constructed, with such
of the excavated earths as the engineer may direct to be
used for that purpose; the same to be executed in regular
layers not exceeding six inches in thickness, and well
punned, the proportion of punners, being such as the engi-
neer may from time to time approve, but never less than
three to one barrow load.
Capping the To cap the top of the reservoir with the remaining excavated
earths, regularly laid on in thin layers, well and solidly
rammed over the arches before the removal of the cen-
tering. It is proposed to slope the embankments at an incli-
Slopes to be nation of 1 to 1, that is the base, being one foot and a
half to every foot of height. But if, during the execu-
tion of the work, the contractor should have reason to
suppose that such rate of inclination will not ensure the
stability of the embankment, the engineer is to be imme-
diately apprised of his misgivings, and the contractor will
be held responsible for all damage arising from slipping or
any other cause.
Slopes to be
trimmed and
As the embankments advance and become consolidated,
covered with the slopes shall be carefully dressed or trimmed to the
turf. specified inclinations, and covered with the turf that was
RESERVOIR.
487
Lining of
puddle.
Puddle:
Foundation
of concrete.
removed from the site of the reservoir. This shall be
done in the manner pasture lands are sometimes grafted;
that is, the turf shall be laid on in slips, with an interval
of uncovered ground between each slip, so that the turf
taken off the horizontal surface, before the excavation for
the reservoir, may by this means be made sufficient to
cover with sward the increased surface of the reservoir
and slopes, which shall then be sown with good and proper
grass seeds.
To line with a coating of puddle at least nine inches in
thickness the bottom of the reservoir; to line with a similar
coating of puddle the space between the sides of the ex-
cavation and the brickwork, from the foundation upward,
to about 1 foot 6 inches above the top water line, so that such
lining may be about 9 inches thick at the top, 12 inches
thick at the springing of the arches, and gradually in-
creasing in width to the foundations, as shown on the draw-
ings; to line thoroughly, with a similar coating of puddle,
the whole of the excavations for the main and other pipes
passing into and out of the reservoir, and extend the same
a sufficient distance beyond the outside of the brickwork,
the object being to seat the reservoir in an impermeable
puddle basin.
The puddle is to be made of pounded clay, of approved
quality, well worked with water, cut, and rammed solid,
and free from stones and rubbish. Great care is to be
taken after it is placed, to preserve it from the effects of
sun, air, wind cracks, or other flaws; and the contractor
shall repair, at his own cost, all damage resulting from
such causes.
To form a foundation for the brickwork of the reser-
voir by spreading a layer of concrete, three inches in thick-
ness on the top of the puddle, all over the bottom
of the excavations forming the site of the intended
reservoir.
Fill in span - To fill in the spandrel of the arches to a height of 18
drel of arches inches above the top water line, with concrete, before the
centering is removed from the arches.
Clay.
Concrete.
If sufficient clay for the puddle, should not be found in
the excavations, concrete must be substituted in lieu of
the puddle.
The concrete must be compounded of gravel, perfectly
clean and mixed with fresh well-burnt hydraulic lime of
488
SPECIFICATION.
Gravel,
Proportions
of lime,
sand in con-
crete.
approved quality, in the proportion of six parts of gravel
to one of lime.
The gravel to be perfectly clean and free from marl or
loam, being a nice admixture of about two parts gravel to
one part coarse sand. All stones in the gravel larger
than about an inch and a half in diameter are to be
broken.
The proportions of lime, gravel, and sand are to be
gravel, and accurately gauged. The lime is to be brought upon the
ground fresh from the kiln, laid on a bed of gravel and
sand not less than twelve inches thick, and spread over
this to a depth of about 18 inches; and, while spreading,
is to be slowly but continually sprinkled with clean water,
from a rose headed watering pot, until the steaming has
commenced, when the lime is to be covered up with
gravel and sand so that no steam can escape, and to be left
in that state until it is completely slaked and turns out
an impalpable powder; the gravel and lime are then to be
mixed in a dry state, to ensure their thorough incor-
poration, after which on a clean platform a proper pro-
portion of clean water is to be added, the whole is to be
turned over and well beaten, until a thorough admixture
of all the parts is effected and brought to a tough
consistency, when it is to be immediately filled into
barrows, and teemed from a height of at least ten feet
on to the place required, when it must be levelled at once
to its proper thickness before it has time to set.
Barrow road.
Bricks.
Bats.
Workman-
ship.
Mortar.
The contractor shall erect a proper barrow road or
scaffold, from which the concrete can in all cases be teemed
on to the place at which it is required.
BRICKLAYER.
The bricks made use of throughout the work shall be
hard, sound, well shapen, thoroughly burnt, and of uniform
size, and shall be well saturated with water before being
set.
No broken bats will be allowed to be used either
externally or internally, unless absolutely necessary as
closers.
The workmanship shall be of the best description. No
joint of mortar shall exceed one quarter of an inch in
thickness, and the work shall be laid in English bond.
The mortar shall consist of fresh burnt lias lime of
RESERVOIR.
489
Lime.
Concrete
foundations.
Brickwork.
Skewbacks.
Arches over
Reservoir.
Soffits of
Arches.
Groined
Arch.
Centring.
approved quality and clean sharp sand, in the proportion
of two parts sand, to one of unslacked Lime. They shall
be intimately mixed in a dry state and well tempered with
a proper quantity of water, and only mixed as required
for use, the mortar that has previously set or become hard
upon the ground shall not be permitted to be used in any
part of the work.
When the lime is required to be slacked it shall be done
with clean water, and covered up with sand so that no air
slacked lime shall be used for any purpose whatever. No
brickwork is to be commenced on the concrete foundations
until they have become hard and solid.
To build the pier, side, and end walls of reservoir in
English bond, the whole of the joints to be flushed up
solid with mortar, and in all walls of 18 inches thick and
upwards, every third course shall be well grouted; the
internal bricks of that course being properly floated in,
and driven up one against another in the grouting so as to
fill up all the interstices, and render the whole of the work
a compact solid mass. The longitudinal pier and cross
walls are to be well and properly bonded together, and the
side and end walls must be battered and have piers, offsets,
and step buttresses as shown in the drawings.
The skewbacks of walls to be correctly worked to tem-
plates, and to be built with feather edge bricks made to
shape, as no filling in with bits or pieces will be allowed.
The arches over the reservoir are to be composed of two
four and a half inch rings; the whole of them are to be
proceeded with at one time, and carried on as regularly as
possible. The side and end arches must spring from the
brickwork on a line forming a right angle with the batter
face of the centre of the arch.
To set close, and well flush up with mortar, the soffits
of all the arches; and after the centring has been drawn,
point the under side.
To turn a groined arch in side wall for entrance into
reservoir.
All centring, as may be requisite to turn all the arches
of the reservoir, as well as all struts, close planking, and
ribs necessary for carrying on the whole of the arches
together in one breast, shall be found by the contractor.
And no centring shall be removed until the whole of that
set of arches has been properly keyed and backed with
2 H
490
SPECIFICATION.
Other
Brickwork.
Masonry.
Carpenter's
Work.
Painter's
Work.
Smith's
Work.
Commence-
ment and
of Works.
Contractor to
find materi-
the concrete spandrels, and the capping brought up as
close as the work will permit.
To do all other brick work that may be required to
complete the construction of the reservoir, according to
the directions expressed or implied in the specification and
drawings and to the satisfaction of the engineer.
Cover the entrance to reservoir with three inch York
flagging, and provide and fix tooled and rounded York
stone treads and brick risers.
Perform any other masonry, necessary and requisite,
for the completion of the work.
Fit up the doorway at entrance with 13 inch four
paneled door; hang the same with a pair of 4 inch butts
to 4 by 3 inch rebated frame; and provide and fix a
suitable lock and key.
Perform any other carpentry necessary to complete the
works.
Knot, stop, pumice, paint in four oils, grain oak and
varnish the door, and door frame.
Provide and fix a wrought iron step ladder as shown in
drawing, and a wrought iron grating in York flagging over
entrance.
TIME OF COMMENCEMENT AND COMPLETION.
The works are to be commenced immediately on an
order being given by the engineer and to be proceeded
with at a rate of progress satisfactory to him-and to be
finally completed within four months of the date of such
order to commence, or the contractor shall forfeit £10 for
every day that the work is delayed beyond the time
specified, unless the engineer shall certify that the delay
arises from any unavoidable or excusable cause.
The contractor is to provide all materials of every
als to be re- description and labour of every kind, that may be neces-
sponsible for
damage; and
six months.
to keep work sary to construct, and properly complete the work. He
in repair for is to be responsible for all damage and accidents of every
kind that may occur during the execution of the work and
he is to keep the works in repair for six months, from the
date of their completion.
Minor parts
to be in-
cluded, al-
though not
And wherever neither the drawings nor this specifica-
tion contain any special notice of minor parts, the intention
noticed in to include which is, nevertheless, to be inferred, and which
parts are necessary for the completion and stability of the
Specification.
TIMBER MEASURING.
491
Works to be
executed to
of Engineer.
works, all such additional parts are to be provided and
performed by the contractor, and are supposed to be in-
cluded in the sum at which he contracts for the works,
and wherever any thing is directed to be done, or to be
provided, if required, "or words of similar import,” it must
be understood that every thing so referred to will be
considered as included in the contractor's tender.
The whole of the works herein described, both as regards
satisfaction quality of materials and workmanship, shall be executed to
the entire satisfaction of the engineer according to the
true intent and meaning of the specification of which the
engineer shall be the sole judge.
Engineer
may direct
alterations.
Payments.
It is to be distinctly understood that the engineer may
at all times direct, that there shall be made alterations in,
additions to, or deductions from the works herein described
or referred to; which said alterations in, additions to, or
deductions from, shall not annul the contract, but an
equivalent based upon the schedule of prices annexed to
the contractor's tender shall be given or taken as the case
may require.
Payments to the extent of ninety per cent will be made
monthly upon the value of the work executed provided
the engineer shall certify that the work is proceeding to
his satisfaction.
In one or other of the preceding specifications will be found the
general stipulations usually contained in such documents.
CHAPTER XV.
TIMBER MEASURING.
TIMBER is computed at its solid contents, whether standing,
rough, or hewn. Boards and planks are measured superficially.
40 feet of rough timber or 50 feet of hewn properly make a load,
but in practice it is usual to consider 50 feet of timber, of any
description, as a load. The reason assigned for the establishment
of the different sizes of the load of rough and hewn timber is, that
the former being measured in a round state (as will be presently
shown) by taking one-fourth of the circumference as the side of
equal square produces a result one-fifth short of the actual solid
492
TIMBER MEASURING.
content, while squared or hewn timber is measured upon more
accurate mathematical principles.
In treating the subject of measuring solid timber, it is necessary
to premise that the rules about to be given are such as have be-
come customary in practice, and not those which a mathematician
would apply to the operation. The true mathematical solid con-
tent of any piece of timber may be found by the application of one
or more of the rules contained in the mensuration of solids in a
former part of this work, but such a content would not be in ac-
cordance with customary usages, and consequently but of little
value to the practical man, while the mode of its attainment would
also be tedious and complex.
In measuring standing timber, the first thing to be estimated
approximately is the height of the tree. This is done by holding
a 20-feet rod as high up the tree as a man can reach, and by guess-
ing the remainder, which may generally be very nicely done; for
supposing the bottom of the rod to be held 6 feet from the ground,
26 feet up the tree is actually measured, and the proportion which
the unmeasured height bears to the measured will become tolerably
apparent to the eye. I have heard of a ladder being carried about
with which to measure the heights of the trees, but never saw it
done. What is called the lop and top of the tree is measured or
estimated separately, as it generally carries a less price. Up to 24
inches circumference or 6 inches quarter girt is generally taken as
timber, and all below that size goes as "lop and top;" but the ex-
act minimum of the timber and maximum of "lop and top " is made
the subject of agreement between the "surveyors for buyer and
seller" before they commence their work.
CC
The method of taking the "girt" of a tree and allowing for
bark is also (in many cases) the subject of agreement between the
surveyors." It is in some localities (but we will hope very few)
customary for the purchaser's surveyor to insist that the girting
line be first divided into three parts, and that one-third of the cir-
cumference be entirely thrown out as an allowance for bark, the re-
maining two-thirds only to be divided into four for the "quarter girt."
Another custom allows the "purchasing surveyor" to girt the
tree where he pleases between the middle and bottom part.
A third insists that, let the tree taper however irregularly, the
girt shall be taken exactly half-way up the tree.
But these and all similar customs are so obviously uncertain in
the results they produce, that no surveyor of common ability or in-
tegrity will agree to adopt them. The simple business-like way
is to ascertain as nearly as possible the fair average quarter girt,
TIMBER MEASURING.
493
or one-fourth part of the circumference, and to make therein such
an allowance as may be fairly estimated to reduce it to what it
would have been had the tree been without bark. This allowance
in the quarter girt for bark may be very fairly reduced to an
agreed standard. Up to a given figure in quarter girt, the allow-
ance to be one inch; beyond that, and up to some other size, an
inch and a half; and so on. The description of tree will of course
have great weight in arranging this standard. Oak trees, in which
the quarter girt is 12 inches, may require 1 inch allowance there-
out for bark, while in the case of ash, elm, and beech, half an inch
may in some cases be sufficient.
A mathematically educated surveyor will of course readily as-
certain the correct allowance to be made for bark by guaging its
approximate thickness, and deducting twice that thickness from
the calculated diameter of the tree, including bark, and he will
then have the actual diameter without the bark. This being re-
duced to circumference and divided by 4, the actual quarter girt
of the timber may be placed in comparison with the quarter girt of
the tree, and the true allowance for bark will be their difference.
A calculation of this kind applied to about three sizes of trees will
form the basis of an arrangement which may be fairly adopted in
the manner I have previously suggested.
The average quarter girt of a standing tree that tapers with
tolerable regularity may be ascertained by girting it at the bot-
tom, and taking the mean between the quarter girt there and the
six inches, or whatever may be agreed on as the minimum quarter
girt at which the timber of the first quality is to cease, and the
"lop and top” to commence. The point at which the tree will
girt 24 inches in circumference is of no importance in taking the
quarter girts, but it requires the exercise of the surveyor's judg-
ment in ascertaining the heights. It is well for the sake of accuracy
that it is not so, as an error in the girt would enter into the whole
calculation of the tree, while an error in length is confined to the
extent of the error itself.
Where the tree does not taper regularly, various expediences
must be adopted to ascertain the average girt. It is impossible to
lay down rules that may produce approximate results in every case;
the exercise of a very little ingenuity will overcome most of them.
When a tree continues up to a certain height, nearly the same size,
and then tapers, it will be best to measure the two parts separately.
The girt of these two parts may be very often obtained in this way,
suppose the lower part to be 14 feet high, take the quarter girt
at 7 feet, which suppose to be 30 inches, this will be the mean of
494
TIMBER MEASURING.
the lower part; take the quarter girt at the bottom of the tree,
which suppose 35 inches, which being 5 inches greater than the
quarter girt at 7 feet high, we may consider the quarter girt at that
point is 5 inches greater than at 14 feet high; hence we have 25
inches, to average with 6 inches, for the mean quarter girt of the
upper part of the tree.
To
In measuring round timber that has been felled, the length can
be accurately taken, and the girt as often as required to obtain
a correct average, bearing in mind, that when the girt is taken
several times, it should always be at equidistant points.
illustrate this, let fig. 196 be the section of a piece of timber 25
feet long, and of the respective quarter girts as figured. Incom-
petent measurers would take the girt at about three places, namely
at B which they would suppose to represent the girt of the length
A B C; at D, and at F, and would average them in this way:
Quarter girt at
B
20
at D
14
وو
وو
وو
at F
10
3) 44
141
Mean quarter girt
Now let us see the correct result of averaging the quarter girts,
taken at equidistant points.
Quarter girt at A
220
at B
""
99
""
""
at C
20
at D
14
وو
وو
at E
15
""
at F
10
6) 99
16
36 ft. 6 in.
Correct average quarter girt
The content of a piece of timber 25 feet long
by 14 inches quarter girt is.
The same length, but 16 inches quarter, girt is.
Loss by the incorrect method of taking the dimensions
47 3
وو
وو
10 ft. 9 in.
Practical timber surveyors generally have a tape or strap for
taking the girt of trees, marked to inches, but numbered only at
every fourth division; that is, at 4 inches it is numbered 1; at 8,
2; at 12, 3, and so on; by which simple arrangement, the quarter
girt in inches and quarters is shown at once.
Squared timber is measured by taking the length, breadth, and
TIMBER MEASURING.
495
thickness. The length and breadth are reduced to the side of equal
square, which is then treated as the quarter girt. It is very cus-
tomary to add the breadth to the thickness, and take half for the
side of equal square, but such a custom is very erroneous, and a
Table has been added to obviate it.
The superficial content of planks is found, by multiplying the
length, in feet and inches, by the widths; attention is required in
taking the widths of irregular planks, to do so at equidistant points,
as explained in the girting of irregular timber.
EXPLANATION OF TABLE No. 1.
Table of solid measure.
Each page of this table is divided into two parts, and each part into
five columns. At the head of each part, is set forth the length in
feet; and in the first column of each part is the quarter girt or side
of equal square in inches. In the second column of each part is the
solid content in feet and inches, of the piece of timber (or any cube)
whose length is equal to the length set forth at the head of the table;
and whose quarter girt, or side of square, is equal to the one
expressed in column 1, opposite to the cubic content in column 2.
In columns 3, 4, and 5, are contained the contents of solids,
corresponding to the same length; but whose respective quarter
girts are increased by the fractional parts of an inch, which are
severally denoted at the heads of such columns.
Ex. 1.-What is the content of the standing tree (according to
the customary method of treating one-fourth of the circumference,
or quarter girt, as the side of equal square), whose height is 39
feet, and average quarter girt 40 inches.
In the section of the table headed 39 feet, and in column 2,
opposite 40 inches in column 1, stands 433 ft. 4 in., the required
content of the tree.
Ex. 2-Required the content of the piece of timber whose length
is 20 feet and quarter girt 164 inches.
In the section of the table headed 20 feet long, opposite 16
inches quarter girt, and in the column headed inch, stands 36
feet 8 inches, the required content.
Ex. 3.-Required the content of the tree, 15 feet long and 201
inches quarter girt.
In the table headed 15 feet long, opposite 20 inches quarter girt,
and in the column headed inch, stands 43 feet 9 inches, cubic
content.
496
TIMBER TABLES.-No. 1.

Quarter
Girt.
inches
ft. in.
1 foot long.
Quarter
Girt.
2 feet long.
14
11
11/8
3
4
ft. in,
ft. in.
ft. in.
inches
ft in.
ft. in.
11
34
ના
ft. in. ft. in.
1 Q3
0
0
0
1
0
0
0
0
2
0
0
1
1
1
1
1
1
1
1
3
1
2
1
1
2
2
3
3
4
5
2
2
3
4
5
5
6
3
3
3
4
6
6
4
4
5
5
8
9
10
8
6
6
6
8
11
11
1
0
1 1
9
10
78
7
7
8
9
1
1
1 2
1 3
1 4
9
9
10 10
11
10
10
11
11
12
1 0
1
0
1
1
1
1
13
1 2
1
3
1
3
1
4 13
IEEE 8
1
5
1 5
1 6
1
7
1 8
1
9
1 10
1 11
12
20
2 1
2 2
2 3
4
2 5
2 6
2 7
14
1
4
1
5
1 5
1
6 14
2 9
2 10
2 11
3 0
15
1 7
1 7
1 8
1 9 15
3 1
3 3
34
3 5
16
1 9
1 10
1 11
1 11 16
3
3 8
3 9 3 11
17
2 0
2 1
2 1
18
2
3
2 4
2
4
19
2 6
2 77
28
20
2
9
2 10
2 11
2223
2 17
4 0
4 2
4 3
4 4
5 18
4
6
4
4 9
4 10
8 19
5 2
5 3
5 5
0 20
5 7
5 8
5 10
60
22*******. 7******88*
3 1
3 2
3 2
3 4
3 5
3 6
3 8
3
9
3 10
co co co
3 3 21
6
1
63
3
7 22
6 9
6 10
3 11
23
7
7 6
677
6 5
6 7
0
7 2
8
7 10
24
0
4 1
4 2
4 3 24
8 0
8 2
8 4
86
25
4 4
4 5
4 6
4 7 25
88
8 10
90
9 2
26
27
4 8
4 10
0 26
9 5
9 7
9 9
9 11
5 1
5 2
5 3
5
4 27
10 1
10 4
10 6
10 8
5 5
5 6
5 8
9 28
10 11
11 1
11 3
11 6
5 10
5 11
60
6
2 29
11 8
11 11
12 1
12 3
30
6 3
6 4
6 5
6
7 30
12 6
12 8
12 11
13
13 2
86
32
33
34
35
6 8 69
0
677∞ ∞
817
67780
6 11
3
7 4
7 9
8 3
7777
0 31
13 4
13 7
13 9
14 O
0
51 32
14 3
14 5
14 8
14 11
7 11 33
15 1
15 4
15 7
15 10
8 4 34
16 1
16 3
16 6
16 9
8
8 9
8 10 35
17 0
17
3
17 6
17 6
17 9
36
9 0 9 1
9 3
9 4 36
18 0
18 3
18 6
18
18 9
9 6 9 8
9 9
9 11 37
19
0
19
3
19 6
19 9
10 0 10 2
10 3
10 5 38
20
1
20 4
20 7
20 10
39
10 7
10 8
10 10
11 0 39
21
121 5
21 8
21 11
40
11 1
11 3
11 3
11 5 11 6
40
22 3 22
6
22 9
23
23 1
41 11 8
11 10
11 11
12
42 12 3
12 5
12 6 12
1 41
842
23 4 23
8
23 11
24 2
24 6 24 9
25 1
25 5
43 12 10 13 0
44 13 5 13 7
13 2
13 3 43
25 8 8 26 0
26 3
26 7
13 9
13 11 44
26 11 27 2
27 6
27 10
45
14 1
14 3
14 3
14
14 4
14 6 6 45
28 1 28 5
28 9
29 1
46 14 8
14 10
15 0
15 2 46
29 5 29 8
30 0
30 4
47 15 4
48 16 0 16 2
15 6
15
15 8
15 10 47
30 8
31 0
31
31
4
31
164
16
16 6 48
32 0
32
32
4
4
32 8
33
50
49 16 8
17 4
16 10
17 0
17
17 2 2 49
33 4 33 8
34
0 34 4
4 17 6
17
8
17 11 50
34 9 35
35 1
35 5
35
35 9
SOLID MEASURE.
497

Quarter
Girt.
inches
3 feet long.
Quarter
Girt.
4 feet long.
1
4
1
143
3
ft. in.
ft. in.
ft. in.
ft. in. inches
ft. in.
ft. in.
ft. in.
3
14/0
ft. in.
2
3
12
1
1
2
3
3
3
4
4
5
6
QB4
1
2
3
3
3
4
6
77
267
5
6
7
8
5
9
10
6
10
10
11
6
7
1 0
1 1
1
2
1 3
8
1 4
1 5
1 6
1 7
9
1 8
1
9
1 10
20
9
10
2 1
2 2
23
2 5
10
HIIQQ
1
0
1
1
1
1
4
1 5
27
1 7 1
1
9
1 11
2 0
3
2 4
2
6 2
9
2 11
3
1
TIQQM
11
1 3
8
2
3 2
∞ ∞ 1∞ Q
11
26
2 8
2 9
2 10
11
3
4
3 6
3
8
3 10
12
3 0
3
1
3 3
3 5
12
13
3 6
38
3
9
3 11
13
++
4
0
4 2
4 4
4 6
8
4 10
0
5
3
14
4 1
4 3
4 4
4 6
14
5 5
58
5 10
6 0
15
4 8
4 10
5
0
5 2
15
63
6 5
68
6 10
16
5 4
5 6
5 8
5 10
16
1
7 4
7 7
77 9
17
6 0
6 2
6 4
6 7
17
8 0
8 3
8
6
8 9
18 6 9
6 11
7 1
7 4
18
9 0
9 3
9 6
9 9
21
222 223*
19
7 6
7 9
7 11
8 1
19
10 0
10 3
10 7
10 10
20
84
86
8 9
9 0
20
11
111
1 11 5
11
8
11 11
9 2
9
5
9 8
9 10
21
12 3 12 6
12 10
13 2
10 1
10 4
4
10
10
6
10 9
22
13 5
13 9
14 1
14 4
11 0
11
3
11
6
11 9
23
14 8
15 0
15 4 15 8
24
12 0
12 3
12
6
12 9
24
16 0
16 4
16
17 0
25
13 0 0 13
3
13
13
6
13 10
25
17 4
4
17
17 8 18
1
18 5
26 14 1 14
4
14 7
14 11
26
18 9
19 2
2
19
6
19 10
27 15 2 215
6
15
6
15 9
16 0
27
20 3
20 7 7 21
0
21 5
33
322 788
28 16 4 16 7
16 11
17 3
28
21 9
22
22 222
22
7
7 22 11
29
17 6 17 10
18 1
18 5
29
23 4
23 9 24 2 24
30
18 9 19 1
19
19 4
19 8 30
25
0
0 25
25 5
25 10
26 3
20 0 20 4
20
8
21 0 31
32
22 8
21 4 21 8 22 0
23 0 0 23 4
22 4 32
23 9
34
24 1
24 5 24 9
25 2 34
35 25 6
25 11
26
26 3
26 7 35
36
27 0
27 4
27 4
27
27 9
28 2 36
288*88
26 8
27 1
27 7 28 0
28 5
28 11
29 4 29 9
33
30 3
30 8
312 31
231 8
32 1 32 7
33 1 33 6
34 0
0
34
34 6
35
0
35 6
36 0
36 6 6
37
0
37
37 6
37 28 6
28 11
29 3
29 8
37
38 0
38 6 39
1
39 7
38
30 1
30 6
6
30 10
31 3
38
40 1
40
7 7
41
2
2
41
41 8
39 31 8
32 1
32 6
32 11
39
42 3
42 9 9
43
43
4
43 11
40
33 4
4
33 9 34
34 2
34 7
40
44 5
45
0
45
7
46 1
41
35 0
35 5 5
35 10 36 4
41
46 8 47
3
47 10 48 5
42
36 9
37
237
37 7 38 1
42
49 O
49 7
50 2 50 9
43
38 6
6
38 11 39 5 39 10
43
51 4
51 11
52 7 53 2
44
40 4
45
40 9
42 2 2 42 8 43
41
3 41 9
44
53 9
43 143 7
45
56 3
56 10
46 44
44 7
45
0 45 6
46
58 9
59 5
5
54
54 5
55 0 55 7
57 6 58 2
60
60 1 1 60 8
47 46 0 46 6
47
47
0 47 6
47
61 4
62 0
62 8 63 4
48
48 0 48
6 49 0 49 6 48
64 0
64 8
65 466
4 66 6
49
50 0 0
50
6 51 0 51 7 49
66 8
67 4
68 068 9
50
52 1 52
7
53
53 1 53 8
50
69 5
70
5
70 2
70 10 71 6
498
TIMBER TABLES.—No. 1.

Quarter
Girt.
inches
ft. in.
5 feet long.
1
111
ft. in.
914
~~3/+
Quarter
Girt.
6 feet long.
1
1/3/1/18
3
4
ft. in.
ft. In.
ft. in. ft. in. inches ft. in. ft. in.
Q34
2
247
2
3
3
4
5
6
7
9
233
240
10
11
1 1
1 2
1 0
1 2
6
1 3
1 4
1 6
1 7
1 6
1 7
4867 6
2
3
4
6
7
9
0
11
1 3
1 4
9
1 11
1
8
1 10
1 11
2 1
0
2 2
2
4
2 6
2 3
2 4
2 6
2
8
8
28
2 10
3 0
3 2
9
2.10
3
0
3 2
3 4
9
4
3 7
3
9
3 11
10
36
3 8
3 10
4 0
10
4 2
4 4
4 7
4 10
11
4 2
4 5
4 7
4 9
11
5 0
5 3
5
6
59
12
5 0
5
2
5 5
58
12
0
6
3
6 6
69
13
5 10
6
1
6 4
6 7 13
7 0
7 4
77
7
7 10
14
6 10
7 0
7 3
7 6 14
8 2
8 5
8 9
9 1
15
7 10
8 1
8 4
8 77 715
9 4
9 8
10
0
10
4
16
8 11
9 2
9 5
9 9 16
10 8
11 0
11 4
11 8
17
10 0
10 4
10 8
10 11
17
12 0
12 5
12 9
13 1
18
20
122 72***ANA..
11
3
11 77
11 11
12 2
18
13 6
13 10
14 3
14 8
12 6 6
12 10
13 2
13 6
19
15 0
15 5
15 10
16 3
13 11 14 3
14 7
14 11
20
16 8
17 1
17 6
17 11
21 15 4
15 8
16
1
16 5
21
18 4
18 10 19 3
19 8
22
16 10 17 2
17 7
18 O
0
22
20 2
20 7 21 1
21 7
18 4
18 9
19 2
19 7
23
22 0
22 6 23 0 23 6
24
20 0
20 5
20 10
21 3 24
24 0
24 61 25
0
25
21 8
22 2
22 7
23 0 0
25
26 0
26 7 27
25 6
127 by
7
23 6
23 11
24 5
24 10
26
28 2
28 8 29 3 29 10
25
4
25
25 9
26 3
26 9
27
30 4
30 11
31 6 32 1
27 3
27 8
28 2
28 8
28
32 8
33
3
33 10 34 5
33 10
29 2
29 8
30 3
30 9
29
35 0
35
8
36 3 36 10
30
31 3
31 9
32 4
32 10
30
37 6
38 1
38 9
39 5
31
33 4
33 10
34 5
35 0
31
40 0
40 8
41
4
42 0
32
35 7 7
36
36 1
36 8
37 3
32
42 8
43 4
44 0
44 8
33
37 10 38 5 39 0
39 7
33
45 4
46 1
46 9
47 5
34
40 2 40
9
41 4
41 11
34
48 2
48 10
49 7
50 4
35
42 6 43 2
43 9
44 4
4
35
51 0
51 9
52
6 53 3
36 45 0 45 7
46 3
46 10
36
54 0
54 9
55 6 56 3
37
47 6 648
48
2
48 10
49 6
37
57 0
57 10
58 7 59 4
38
50 2 50 10
51 5
52 2
38
60 2
60 11 61 9
9
62 7
39
52 10 53 6
54 2
54 10
39
63 4
64 2 65 0
65 10
40
55 7 56 3
56 11
57 8
40
66 8
67 6 68 4
69 2
41
58 4
59 1
59 10 60
6
41
70
0
42 61 3
61 11
62
62 9
63 5
42
73 6
45
43 64 2
44 67 3
70 4
46 73 6
64 11 65 8
68 0 68 9
66 5
43
77 0
69 6
44
80 8
71 1 71 11
72 8
8
45
84 4
85
74 3 75 1
75 11
46
47 76 8 77 678 4
48 80 0 0 80 10 81 8
49 83 4 84 3 85 1
79 2
47
92 0 93
82 6
48
96 0 97
70 11
74 4 75 3 76 2
71 9 72 7
77 11 78 10 79 9
81 7 82 6
82 6 83 5
4 86 3 87 2
88 2 89 1 90 1 91 0
094 095
98 0 99 0
0
85 11
49
100 0 101
1102 1103 1
50
86 10 87 8 88
7
89 5
50
50
104 2105
2106 3 107 4
SOLID MEASURE.
499

Quarter
Girt.
inches
ft. in.
7 feet long.
1
114
1 음
​3
4
ft. in.
ft. in.
Quarter
Girt.
ft. in.inches
8 feet long.
1
1247
catat
44
ft. in.
ft. in.
ft. in.
ft. in.
234567∞ a
2
3
4
4
2
6
7
8
9
10
1
0
1
1
1 3
1 4
1
6
1 7
1 9
1 11
2 1
2 2
2 5
2 7
29
2 11
8
3 1
3
4
3 6
3 9
9
3 11
2
4 7
Q345 6 7 ∞ ∞
3
3
4
5
6
7
8
9
11
1 0
1 1
1 5
1 6
18
2 0
2 2
2 4 2 6
2
9
2 11
3 1
3
7
3 9
4 0
4 6
4 9
5
0
10
4 10
5 1
4
5 7 10
5 7
5 10
6 1
1HQ CO HILO co
3
1 10
3
4
4 3
5 3
6 5
11
5 10
12
7 0
67
6 2
6
5
6 8 11
6 9
7 0
7
3
7 7
7 11
12
0
8
4
4∞
7 8
8 8 9 0
13
8 3
8 6
810
9 2
13
9 5
9 9
10 1 10 6
14
9 6
9 10
10 2
10 7
14
10 11
11 3
11 8 12 1
15
10 11
11 4
11
8
12 1
15
12 6
12 11
13
4 13
9
16
12 5
12 10
12 10
13
3
13 8
16
14 2
14 8
15
1
15 7
17
14 1
14 5
14 11
15 4
17
16 1
16
6 17
0 17 6
18
15 9
16 2
16 8
17 1 18
18 O
18
6 19
619 0
19 6
19
17 7
18 0
18
6
18 11
20
19 5
19 11
19 11
20
5
20 11 20
21
21 5
21 11 22
5
23 0
22
23 6
6
24
24 1
24 7
25 2
23
25 9 9
26 3
26 10
27 5 23
22 72*
20 1
20
7 21 1 21 8
22 3
22
9
23 4
23 11
24 6
25
1
25
8
26 5
22
26 11
27
6
28 1
28 9
29 5
30
30 0
30 8 31 4
24 28 0
28 7
29 2
29 9
24
32 0
32 8 33 4
34 0
25
30 5
31
31 0
0
31
7
32 3 25
34 9
35
5
5
36 1
36 10
26
32 10 33 6
34
6
34
2
34 9
34 9 26
37 7
38 3
39 0
39 9
27
35 5 5
36
36
1
36
36 9
37 5 27
40 6
41
3
42 0
42 9
28
38 1
38
9
39
6
40 2
28
43 7
44 4
4
45 1
45 11
29
40 11 41
7
42 4
43 0
29
46 9
47 6 48 4 49 2
30
43 9
44
6
45
3
45 11
30
50 0
50 10
51 8
52
6
31
46 9
9
47
47 6
48
3
49 0 0 31
53 5
54 3
55 2
56 0
32
49 9 9
50 7
51 4
52 2
32
56 11
57 9
58 9
59
59 7
33
52 11 53 9
54 7
55
55 4
33
60 6
61 5
62 4
63 3
34
56 2 57 0
57 10
58
58 8
34
64 3
65 2
66 1 67
35
59 7
7
60 5
61 3
62 1 35
68 1
69
0 0 70 0 71 0
36
63 0 63 10
64 9
64 9
65
65 8
36
72 0
37
66 7 7
67
67 5
5
68 4
69 3
37
76 1
73 0 74 0 75
77 1
78 1 79 2
38
70 2
71 1
72 0
73 0 38
80 2
39
73 11 74 10
75 10
76 10
39
40
куку
9
9 78 9
79 9
80 9
40
81 3
84 6 85
88 10 90
82 4 83 5
7 86 8 87
0 91 192 3
7310025a m
9
41
81 9
9
82
9
83 9
42
85 9 9
86 9
9
87 10
43
89 11 90 11 92 0
44 94 1
95 2
2
96
96
84 9 41
88 10 42
93
93 0 43
3 97 4 44
9 103 11105
93 5 94 6
695 8 96 10
98 0 99 1100 4 101 6
102
1106 4
107
7 108 9110
0111 3
45 98 5
5
99
6 100
8 101 9 45
112
6 113
9 115
0116 3
46
102 10 104
0105
1106 3 46
117
7118 10120
1121
5
47 107 5 108
6109
8 110 10 47
122
9 124
9 124
0 125
4126
8
48 112 0113 2114
49 116 9 117 11119
4115 6 48
128
0129
4 130
8 132
0
1120 4 49
133
5134
9136
9136
1137
6
50
121 6 122 9 124
0 125 2 50
138 11 140
3 141
8 143 1
500
TIMBER TABLES.-No. 1.
Quarter
Girt.
inches
ft. in.
9 feet long.
12
तम
1
ft. in. ft. in.
Go44
ft.
Quarter
Girt.
in. inches ft. in.
10 feet long.
14
1/1/143
3
4
ft. in.
ft in. ft. in.
QB +
2
3
3
7
48
5
6 2
3
4
5
6
9
10
3
7
9
10
1 0
1
0
1
1
1 2
1 5
4
5
1 7
1
9
1 11
2 1
5
6
2 3
2 5
28
2 10
6
3
1
3 3
3 6
3 9
7
8
4
0
4
3
4 6
4 9
5
1
5 4
5 8
5 11
9
10
6 3
6 7
6 11
7 3
10
1AQ∞ CO
1
1 3
1 5
1 7
19
1 11
2 1
2 3
2 6
28
2 11
3 2
3
5
3 8
3 11
4 2
4 5
4 9
5 0
5
5 7
5 11
6 3
6
6 11
7 3
7 8
8 0
11
7
7
7 11
8 3
8 7
11
8 5
8 9
9 2
9
7
12 9 0
9 4
9 9
10 2
12
10 0
10
5
10 10
11
3
13
10 7
11 0
11 5
11 10
13
11 9 12 2
12 8
13 1
14 12 3
12
8
13 2
13
7
14
13
7 14 1
14 7
15 1
15
14 1
14
6
6
15 0
15 0
15
6
15
15 7
16 2
16 8
16 8 17 3
16 16 O
16 6
17 0
17
6
16
17
9
18
4
18 11 19 6
17 18 1
18 7 19 2
19 8
17
20
1
20 8
21 321 10
18
20 3
20 10
21 5
22 0
18
22 6
23
1
23 9 24 5
19 22 7
23 2
23 9
24 4
19
25 1
25 9
26
5 27 1
20
25 0
25 7
26 3
26 11
20
27
9
28 6
29 2
29 11
228
21 27 7
28 3
28 11
29 7
21
30
7
31
4
32 1
32 10
30 3
30 11 31 8 32 4
22
33
7 34 4
35
2
35 11
23
33 1
33 934 6
35 3
23
36 9
37 6
38 4
39 2
24
36 0
36 9 37 6
38
3
24
40 0
40 10 41 8 42 6
25 39 1
39 10
40 8
41
5
25
43 5
44 3
45 2 46 0
26 42 3
43 1
43 11
44
9
26
46 11
47 10
47 10
48 9
48 9 49 8
27 45 7
46 5
47 3
48
1
27
50 7
51 7
52 6
53 6
28 49 0
49 10
49 10 50 9
51
8
28
54 5
55 5
56 5 57 5
29 52 7
53 6 54 5 55
4
29
58 5 59
5
5
60 5 61 5
30
56 3
57 258 259
1
30
62
6
63
6
64 7 65 8
31
60 1 61
0 62 0 63
0
31
66 9 67 10
68 11 70 0
32
64 0 65
066 0 67 0
32 71
33
68 1 69 1 70 271 2
33
75
34 72
373
73 4
74 5 75 6
34
1 72 3
776 9
80 3 81 5
73 474 6
77 11 79 1
82 8
83 10
35
76 777 8
8
78 9
78 9 79 10
35
85 186
1 86 3
87 6
88 9
39 95 1 96 3
40 100 0 101 3 102 6 103
36 81 0 82 1
37 85 7 86 9 87 11
38 90 3 91 5
97 6 98 9
83 3 84 5
36
90
0
0 91 3 92 6
93 9
89 1
37
95
1 96 4
97 8 98 11
92 8
93 10
38
100
39
9
105
40 111
41
105
42 110
1 106 4 107 8 108 11
3111 6 112 11 114 3
41
116 9 118 2119
3 101 7 102 11 104 3
7 106 11 108 4 109 9
1112 6 113 11 115 4
7 121 0
42
122 6 123 11 125
5 126 11
46 132 3 133
47
138
1139
48 144
0145
43 115 7 116 11 118 3119
44 121 0122 4 123 9 125 2
45126 7 128 0 129 5 130 10
8135 2136
6 141 0142 6
6 147 0148 6
49 150 1 151 7153 2 154 8
50 156 3 157 10 159 5 161 0
7
43
128 5 129 11 131
5 132 11
44
134 5 136 0137
45
140 7 142
2 143
7
46
146 11 148
6 150
47
153 5 155
0156
48 160 0161
8 163
49 166
9 168 5 170
6139 1
9 145 4
2 151 9
8 158
4
4165 0
2171 10
50
173 7 175 4 177
1 178 10
鲁
​
SOLID MEASURE.
501

Quarter
Girt.
11 feet long.
1
inches
in.
ft.
ft. in.
Quarter
Girt.
12 feet long.
914
114
11/1
31
4
ft.
in. ft. in. inches
ft. in.
ft.
in.
ft.
in.
ft.
in.
23 45O
1
488
5
6
7
10
11
1
1
3
1
4
1 6
9
234+
4
5
6
7
9
10
1 0
1
2
1 4
1 6
1 8
1 10
1 11
2
1
2 4
6
5
2 1
23
2 6
2 9
6
2 9
3 0
3 3
3
6
6
3
0
3 3
36
3 9
7
3 9
4 0
4 3
4 7
7
1
4
4 8
5 0
4 11
5 2
5 6
5 10
8
5
4
8
6
0
6 4
50
9
6 2
66
6 11
7 3
9
6
9
7
1
7 6
7 11
10
17 8
8 0
8 5
8 10
10
8 4
8 9
9 2
9 7
11 9 3
98
10 1
10 6
11
10
1
10
6
11 0
11 6
12
11 0
11 5
11 11
12 5
12
12 0
12
6
13 O
13 6
13
12 11
13 5
13 11
14
5
13
14 1
14 7
15
2
15 9
14
15 0
15 6
16 1
16 7
14
16 4
16 11
17 6
18
18 1
15
17 2
17 9
18 4
18 4
18 11
15
18 9
19 4
20 0
20 8
16
19 7
20 2
20 9
21 5
16
21
4 22 0
22 8
23 4
17
22 1
22 9
23 5
24 1
17
24
1
24 9
25
6
26 3
18
24 9
25 5
26 2
26 10
18
27
0
0
27
27 9
28 6
29 3
19 27 7 28 4
29
29 0
29 9 19
20
30 7 31 4
32 1
32 1
32 11 20
888333
30 1
30 10
30 10
31 8
32
32 6
33 4
34 2
35 0
35 10
21 33 8 34 6
35 4
36 21 21
36 9
9
37
37 7
38 6
39 5
22 37 0 37 10
23 40 5
38 8
39
39 6 22
40 4
41 3
42 2
43 1
41 3
42 2
43 11 23
44 1
45 0
46 0 47 0
24
44 O 0
44 11
45 10 46
9|24
48
0 49
O
25
47 9 48 8
49 8
49 8
50 8 25
52
153
50 051 0
154 2 55 3
26 51 8 52
8
53 8
54
54 8
26
56
4
57
57
5
58 6 6
59 7
27
55 8 8
56 9
57 9
58 10
27
60 9
61 10 63 0
64 2
28
59 11
60 11
62 0 063
2 28
65 4
66 667
67 8
68 10
29
64 3
65 4
66 6 67
7 7 29
70 1
71 3 72 6
73 9
30
68 9
69 11
71 1
71 172 3
30
75 0
76
3
77 6
78 9
31 73 5 74 7
75 9 77 0
31
80 1 81 4
82 8
84 0
32
78 3 79 5
80 8 81 11
32
85 4 86
8
88 O
89 4
33
83 2 84 5
85 9 87 0
33
34
88 4 89 7
90 11 92 3
34
90 9 92 1
96 4 97
97
93
6
94 11
9 99
2100 7
35
36
93 7 94 11 96
99 0 100 4101
37
104 7 106
0107
38
110 4 111
9113
39 116
2117
2117
8119
40 122 3 123
9 125
5 108 10 37
3114 838
2120 8 39
3 126 10 40
41 128
5 130
0131
42 134 9 136 3 138
43 141 3 142 11 144
44 147 11 149 7 151
45 154 8 156 5 158
46 161 8163 5165
47 168 9170 6172
48 176 0177 10179
49 183 5 185 3187 2189 1 49
50191 0 192 11 194 10 196 9 50
7133 2 41
0139 7 42
140
3 97 7 35102 1 103 6 105
9103 236
0 106 6
112 6
2118 9
6 125 1
8
0131
8 138 4
6 145 3
108 0 109 6 111
114 1115 7117
120 4 121 11 123
126 9 128
133 4 135
4130
0 136
1 141
9143
147
0 148
8 150
6 152 3
6 146 2 43
154
1155 10 157
8159 6
3153 0 44
161
4163 2165
0166 10
2 159 11 45
168
9 170
7 172
6 174 5
2166 11
46
176
4 178
4 178
3 180
2182 1
4 174 2
47
184
1186
0188
0190 0
8181 6 48
192
0194
200
1202
208
4 210
0196
1 204 2 206 3
5 212 6 214 7
0198 0
502
-No. 1.
TIMBER TABLES.

Quarter
Girt.
inches
ft.
121414
13 feet long.
1
Ha
2
من احد
3
4
Quarter
Girt.
14 feet long.
1
1242
용
​3
4
in.
ft.
in.
ft. in.
fit.
in. inches ft. in.
ft. in.
ft. in.
ft. in.
2345 C
4
5
7
8
10
11
1 1
1 3
1 5
1 7
1 10
20
G1 M →
2
5
6
7
9
3
10
1 0
1 2
1 4
4
1 7
1 9
2 0
2
23
2
6
29
3 0
5
2 5
2 8
2 11
3
2
3 3
3
6
3 10
4 1
36
3 9
4 1
4 5
4
5 1
5 5
4 9
5 1
5
5
5 10
8
5 9
6 2
6 6
6 11
8
6 3
6
7
7
0
7 5
9
7
4
77
8 2
8 7
9
7 10
8 4
8
9
9 3
10
90
9 6
9 11
10 5
10
9 9
10
2
10 9
11
3
11
10 11 11
5
11 11
12 5 11
11 9
12
12
4
4
12 10
13 5
12
13 0
13 6
14 1
14 8 12
14 O
14 7
15 2
15 10
13
15 3
15 10
16 5
17 1 13
16 5
17 1
17
9
18 4
14
17 8
18 4
19 0
19 8 14
19 1
19
9
20
5
5
21 2
15
20 4
21 0
21
8
22 5 15
21 10
22 7
23
4
24 1
16
23 1
23 10 24 7
25 4 16
24 11
25 8
26
6
27 3
17
26 1
26 10 27 8
28 5 17
28 1
28 11 29
9
30 7
18
29 3
30 1
30 11
31 9 18
31 6
32 4 33
3
34 2
20
22 7******888
19
32 7
33
33 5
34 3
35 2 19
35 1
36 0
37 0
37 11
36 1
37 0
37 11
38 10 20
38 11
39 10
40 10
41 10
39 10 40 9
41 9
42 8
21
42 10
43 11
44 11
46 0
22 43 8
44 8
45 8
46 9
22
47 1
48 1
49 3
50 3
23
47 9
48 10
49 10
50 11
23
51 5
52 7
53
8
54 10
52 0
53 1
54 2
55 4 24
56 0
57 2
58 4
59 7
25
56 5
57
7
58 8
59 10 25
60 9
62 0
63
3
64 5
26
61 0 62
2
63 5
64 7 26
65 9
67 0
68 3
69 7
65 10 67 0
68 3
69 6 27
70 10
72 2
73
73
6
74 10
70 9 72
0
73 4
74 7
28
76 3
77 7
79
0
80 4
75 11 77
3 3
78 7
79 11 29
81 9
83 2
84 7
86 0
30
81 3 82
7
84 0
85 4 30
87 6
88 11
90
5
91 11
31
86 9
88 2
89 7
91 0 31
93 5
94 11 96
5
98 0
32
92 5
33
35
110 7 112
93 11 95 4 96 101 32
98 4 99 9101 4102 10 33
34 104 4 105 11 107 5 109 0 34
2113 9 115 4 35
99 7 101 1102
105 10 107 6 109
8104 3
1110 9
112 5 114 0115
9117 5
119
1120 10 122
6 124 3
36
117 0118
7 120 3 121 11 36
126
0127 9 129
6131 4
37
123 7 125
3 126 11 128 8
37
133
1134 10 136
8138 6
38
130 4 132
1133 10 135 7
38
140 5 142 3 144
1145 11
39 137 4 139
40 144 5 146
1140 10 142 8
3 148 1 149 11
39
40
147 10 149 9 151
155 7 157
8153 7
6 159
6 161 5
41 151 9153
6157 4 41
42 159 3 161
1 163 1165 0 42
43 166 11 168 10 170 10 172 9 43
44 174 9 176 9 178 9180 9 44
45 182 10 184 10 186 11 188 11 45
46 191 0 193 1 195 2 197 4
7155
46
48 208
49 216
47 199 5 201 7 203 8 205 10
0210 2 212 4 214
9218 11 221 2223
50 225 8 227 11 230 3 232
47
163 5165 2167 5169 5
171 6173 5 175 7 177 8
179 9 181 10 183 11 186 1
188 3 190 4192 6194 8
196 10 199 1201 3 203 6
205 9 207 11 210
214 9 217 1219
3 212 6
4 221 8
7
48
224 0 226 4 228
8 231 0
5
49
6 50
233 5 235 10 238 3 240 7
243 1 245 6 247 11 250 5
SOLID MEASURE.
503

Quarter
Girt.
inches
15 feet long.
Quarter
Girt.
16 feet long,
144
1-140
goo
1
1-24
مداح
ft. in.
ft.
in.
ft.
in.
ft.
in. inches
ft. in.
ft.
in. ft.
in. ft. in.
Q34567
2
เล
5
6
9
2
5
7
8
10
11
1 1
1
3
1 5
3
1
0
1
2
1
4
1 7
1 8
1 10
2 1
2 4
4
1 9
2 0
2
3
2 6
27
2 10
3 2
3 5
5
29
3
1
3 4
38
3 9
4 1
4 5
4 9
6
4 0
4 4
4
5 1
1
5
6
5 10
6 3
8
68
1
7 6
8 0
9
8 5
8 11 9
5
9 11 9
684
5 5
5 10
6
6 8
7 1
7 7
8
0
8 6
9 0
9 6
10 0
10 7
10
10 5
10 11
11
11
6
6
12 0
10
11 1
11
8
12
3
12 10
11
12 7 13
12
15 0 15
13
17 7 18
273
13
9
14 4
11
13 5
14
1
14
8
15 4
16 3
16 11
12
16 0
16
8 17
4
18 1
19 O
19 8
13
18 9
19 6
20
3 21 0
14
20 5 21
2
21 11
22 8
14
21 9
22 7
23
4 24 2
15
23 5
24
3
25
0
25 10
15
25 0
25 10
26
8
27 7
16
26 8 27
6
28 4
29 3
16
28 5 29 4
30
3
31 2
17
30 1
31
0
31 11
32 10
17
32 133 1
34
0
35
35 0
18
33 9
34
8
35 8
36 7 18
19
37 7 38
7
39 7
40 7
2 22***ANKA.
20
41 8 42
8
43 9
44 10 20
21
45 11 47
0 48 2
49 3 21
50 5
51
7 52 9
53 11
222 22
36 0 37
0 38
0
39 1
40 1
41 2
42
3
43
43 4
44 5
45
7
46
8
47 10
49 0
50 2
51
4
52 7
22
53 9
55 0 56
3 57 6
23
55 1
56
4 57
6
58 9 23
58 9
60 1 61
4 62 8
24
60 0 61
3 62 6
63 10 24
64 0
65 4
66
8 68 1
25
65 1 66
5
67 9
69 0 25
69 5
70 9
72
373 8
26 70 5
71
9
73 2
74 6
26
75 1
76 7
78
78
0 79
079 6
27
75 11 77
4
78 9
80 2
27
81 0
82 6
84
0 85 7
28 81 8
83
1 84 7
86
1 28
87 1
88 8
90
3 91 10
29 87 7 89 1
90 8
92 2
29
93 5 95 1 96
8 98
98 4
30
93 9 95
4
96 11
98
6
30
100
0 101 8 103
4 105 1
100 1101
88
31
32 106 8 108
33 113 5 115
34 120
35 127
36 135
37 142
38 150
5122
7 129
0136 10138
7 144
5152
9103
4 105
0 31
106
9 108 6 110
4 110 0111
9 32
113
9 115 7 117
2116 11 118
2124
5 131
8 33
121
0122 10124
0125
3133 1 35
9
34
128
5 130 4 132
136 1 138
1140
3112 0
4 119 2
8126 7
3 134 2
0142 0
9 140 8
36
144
0146
0148
0 150 1
6 146
6148 5
37
152
1154 2 156
3158 4
5154
5 156
5
38
160
5162 6 164
8166 10
39 158 5 160
5 162
6164 7
39
169
0171
2 173
4 175 7
40 166 8 168
9 170 10 173 0
40
177
9 180
0182 3 184 6
41
175 1 177 3179
42
183 9 185 10 188
43 192 7 194 10197
44 201 8 203 11 206
45 210 11 213 3 215
46 220 5 222 10 225
47 230 1 232 7 235
48 240 0 242 6|245
49 250 0 252 8 255
8 255
50 260 5 263 0 265
5 181 7
41
186
9189
1191 4 193
2 190 4
42
196 0 198 3 200
8203
1
1199
4 4
43
3 208 7 44
7 218
2 227 8
0 237 6
0 247 6
2257 10 49
8 268 3 50
0
45
46
47
48
205 5 207 10 210
215 1 217 7 220
225 0 227 6 230
235 1 237
245 5 248
256 0 258
3212
0222 6
0 232 7
∞ ∞ ∞
8
8
8 240
3 242 10
1 250
8 253 4
8 261
4 264 0
266 9 269
6 272
3 275 0
277 9 280
7 283
4 286 2
504
TIMBER TABLES.No. 1.

Quarter
Girt.
inches
ft. in.
17 feet long.
11/14
ft. in.
1-2/4
ft. in. ft.
09/+
Quarter
Girt.
in. inches ft. in.
18 feet long.
1
11/
3
4
ft. in.
ft.
in.
ft. in.
23 4
6
7
11
2
6
1
1
1
3
1
5
1
8
1 1
1 11
2 2
2 5
28
4
2 0
2 11
3 3
3 *7
3 11
3 1
3
∞ 4 M LO
123
8
9
11
1 6
1 9
3 2 6
2 10
5
3 9
4 2
6
4 3
7
5 0
5
4
4 6
4 11
5 3
5 8
5
9
6 2
68
7 1
6
1
6 7
7
0
7 6
8
7
8
0
8 6
9 0
8
8
0
8 6
9 0
9 7
9
9
10
7
1
10 8
11 3
9
10 1
10
8
11
3
11 11
10
11 10
12 5
13
0
13
8 10
12 6
13
2
13
9
14 5
11
14 3
14 11
15 7
16
4
11
15
1
15 10
16 6
17 3
12
17 0
17 9
18 5
19
2 12
18
0
18 9
19 6
20 4
13
19 11
20 9
21 6
22
4
4
13
21
1
21 11
22 9
23 8
14
23 2
24
24 O
24 10
25
8 14
24 6
25 5
26
3
27 2
15
26
27 5 28 4
29
3 15
28 1 29
1
30
031 0
16
30 3
31
232 2
33 1
16
32 0 33
0
34
0
35 1
17
34 1
35 1 36 237
37
2
17
36
1 1
37
2
38 3
39 5
18
38
3
39 4
40
5 41 6
18
40
6 41
8
42 9
43 11
19
42 7
43 9
44 11
46 1
19
45 1 46
4
47 6
48 9
20
47 3
48
5
49 7
50 10
20
50 0
51
3
52 6
53 10
21
52
53 4 54 7
55 10
21
55 1
56 5
57 9
59 2
22
57 2 58 5
59 9
61 1
22
60 6
61 11
63 3
64 8
23
62
63 10
65 2
66
7
7 23
66 1
67 7
69 0
70 6
24
68
69 5
70 10
72
41 24
72 0
73
6
75 0
76 7
25
73 9
75 3
76 9
78
3 25
78 1 79
8
81 3
82 11
26
79 10
81
4
82 11
84 6
26
84 6 86 2
87
9
89
89 5
27
86 1
87
8
89 3
90 11
27
91
1
92 10 94
6
96 3
28
92 7
94
3 95 11
97 7
28
98
0 99 9101
6103 4
40
28 78********
29
99 3 101
0102 9104
6
6
29
105
1106 11108
9110 8
30106
3 108
0 109 10 111
7
30112
6 114
5 116
3 118 2
113 5115
3117
2119
0
31
120
1 122
32
120 11 122
9 124
8126
7 32
128
0 130
1124
0132
0126 0
0134 1
33
34
128 7130
6132
6134
6 33
136
1138
2140
3 142 5
136 6 138
6140
6142
7 34
144
6 146
8 148
9150 11
35144
144 7 146
8 148
9 150 11 35
35
153
1 155
4 157
36
153 0155 2157
3159 5
36
162
0164
3166
161
7163 10 166
0168 0 37
171
1173
5 175
38 170 6 172 9 175
39 179 7181 10184
0177
0177 3 38
2186 6 39 190
180
6182 11185
188 11 191 3 193
8 196
0
40200
1192 7 195
0202 6 205
6 159 9
6 168 10
9178 2
3 187 8
0197 6
0207 7y
41
42
43
198 5 200 10 203
208 3 210 71213 3 215
218 3 220 10 223 5 226
4 205
9
9
44 228 7 231
210
1 212 8 215
42 220 6 223 0 225
231
0 43
1 233 10 236
7 231 2 233 9 236 5 44 242 0 244 9 247
41
3 217 11
9228 5
6 239 3
6 250 4
45 239
46
239 1 241 9244 5 247
249 10 252 6 253 3 258 0 46
1
1
45
45
253
1 255 11 258
9 261 8
264
6 267
5 270
47
48
260
272 0 274 10 277 8 280 7
9 263 7 266 4 269
2 47
276
1 279
1282
48
288
0 291
49
283 5 286 4 289 3 292
2
50 295
295 2 298 1 301 1304
2 49 300
7 50 312
1303
6 315
0 294
2
0285 0
0 297 1
2 306 3 309 5
8 318 9 321 11
3 273
SOLID MEASURE.
505

Quarter
Girt.
inches
ft. in.
19 feet long.
1-44
ft. in.
ft. in.
3318
4
Quarter
Girt.
ft. in, inches ft. in.
20 feet long.
1
142
3
4
ft. in. ft. in.
ft. in.
2 3 4 5
6
8
10
1
0
1
2
1 5
1 7
1
10
23
7
8
10
1 1
1 3
1
6
1 8
1 11
2 1
2 5
28
3 0 4
2 3
2 6
2 10
3 2
3 4
38
4 0
4
4
5
36
3 10
4 2
4 7
6
4 9
5 2
5 7
6 0
5 0
5 5
5 10
6 4
7
6 6
6 11
7
5
7 11
6 10
7 4
7 10
8 4
8 5
9 0
9 6
10 1
8 11
9 5
10 0
10 8
9
10 8
11 3
11 11
12 6
9
11 3
11 11 12 6
13 2
10
13 2
13 10
14 6
15 3
10
13 11
14 7
7
15 4
15 4 16 1
11
16 0
16 8
17. 5
18
3
11
16 10
10
17 7
18 4 19 2
12
19 0
19 10
20 7
21 5
12
20 0
20 10
21
8
22 7
13
22 4
23
2
24 0
24 0
24 11
13
23 6
24 5
25
4
26 3
14
25 10 26 9
27 9
28 8
14
27 3
28 2 29
2 2
30 3
15
29 8
30 8
30 8
31
31 8
32
9
9
15
31 3
32 4
33
4
34 5
16 33 9
34 10
35 11
37
0 16
35 7
36
8
37
9
39 0
17
38 2
39 3
40 5 41
7 17
40 2
41
4
42 6
43 9
18
42 9
43 11
45 246 5 18
45
0
46 3
47
47 6
48 10
19
47 8
48 11
50 2 51 6
19
50 2
51 6
52 10
54 2
20
52 9 54 1
55
5
56 10
20
55 7
56 11
58 4
59 10
2283
21 58 259
59 7
61
062
62 5
21
61 3
62 9
64 2
65 8
63 10 65 4
66 9
68 3
22
67 3
68
9
70
70 4
71 11
23
69 9 71 4
72 10
74 5
23
73 6
75
1
76 8
78 4
24 76 0 77 7
79 2
80 10
24
80 0
81
8
83
4
85 1
25
82 6 84 1
85 9
87 6
25
86 10 88
7 90
4 92 1
26
89 2 90 11
92
8 94
94 5
26
93 11 95 8 97
6 6 99 5
2828
27
96 2 98 0 99 9101 17
27
101 3103 2105
0106 11
103
29
5105 4 107 2109 1
111 0 112 11114 10 116 9
30118 9 120 9 122 9 124
28
108 11 110 10 112 10 114 10
29
9
30
125
0 127
31
126 10 128 10 130 11 133
32 135 1137 3 139 4 141 6
33 143 8 145 10 148
34 152 6 154 9 157
0
31
133
116 10 118 10 120 10 122 11
0 127 1 129 2131 4
6135
8137 10140 0
32
142
3 144
5 146 8149 0
1150 3
33
151
3153
7 155 10158 2
0159 4
34
160
7 162 11 165
39 200 8 203
35 161 8 163 11 166
36 171 0173 5 175
37 180 8 183 1185 6188 0 37
38 190 6 193 0195 7198 1
3 205 10 208 6
3 168 8
35
170
2 172
7 175
4167 9
0177 6
9178 2 36
180
0182
6 185
190 2 192
38
39
211
40 211 1 213
9 216 5 219
1
40
222
200 7 203
3 214
3 225
0187 7
9195 4 197 11
2 205 10 208 7
0216 8 219 5
0 227 10 230 8
41
221 10 224 6 227 3 230
42 232 9 235 5 238 4 241 2
0
41
42
43 244 0 246 10 249 8 252
7
43
44 255 5 258 4 261 3 264
45 267 2 270 2 273 2 276
3
44
233 6 236 4 239 2 242 1
245 0 247 9 250 10 253 10
256 10 259 10 262 10 265 10
268 11 271 11 275 0 278 2
2
45
281 3 284 5 287
6 290 8
46
279 2 282 3 285
3 288 4
46
293 11 297
1300
4303 7
47
291 6 294 7 297 8 300 10
47
306 10 310
1313
4 316 8
48 304 0 307
2310 4 313 7
48
320 0 323
4 326
8330
1
49
316 10 320 0 323
50329 10 333 2 336
3 326 7
49
333 6336 11 340
4343
9
6 339 10
50
347
3 350 8 354
2 357 9
2 I
506
-No. 1.
TIMBER TABLES.

Quarter
Girt.
inches
ft.
21 feet long.
1
1--14
من الحر
3
Quarter
Girt.
22 feet long.
1
4
11/18
3
in.
ft. in.
ft. in.
ft. in.inches
ft. in.
ft. in.
ft. in.
ft. in.
23 4
9
11
1
1
1
4
1 6
1 9
2 1
2 4
2
8
2 11
3 3
5
38
4
0
4 5
4 10
Q MTH LO
7
9
11
1
3
1 4
4
2 5
5
3 10
124
7
1 10
2 2
૭૭
2 9
3 1
3 5
4 77
5 1
6
5 3
5
8
6 2
6 8
5 6
6
6 5
6 11
7
7 2
7 8
8 2
8 9
7 6
8 0
8
7
9 2
8
9 4
9 11
10
6
11 2
9 9 10
5
11
0
0
11
11 8
9
11 10
12
6
13 2
13 10
12 4 13 1
13 9
14 6
10
14 7 15
4
16
1
16 10 10
15 3 16
1
16 10
17 8
11
17
8
18 5
19
3
20 2
11
18 6 19
4
20 2
21 1
12
21 0
22 11 22 9
23 8
12
22 0
22 11
23 10
24 10
13
24 8
25 7
7
26
7
27
7
13
25 10
26 10
27 10
28 11
14
28 7
29 7
30 8
31
9
14
29 11 31 0
32 1
33 3
15
32 10
33 11
35 0
36 2 15
34 4 35
6
36
8
37 11
16
37 4
4
38
38 6
39
39 8
40 11
16
39 1 40 4
41
41 7
42 10
17
42 2
43 5
44 8
45 11
17
44 2
45
5
46 9
48
48 2
18
47 3
48 7
49 11
51 3
18
49 6
50 11
52 3
53 8
19
52 8
54 0
55 5
56 11
19
55 2
56
56 7
58
1
59 7
20
58 4 59 10
61 3
62 9 20
61 1
62
8
64
2
65 9
21
64 4
65 10
67 5
69 0
21
22
70 7
72 2
73 10
75 6
283
67 4
69
0
70 7
72 3
22
73 11
75 8
77
4
79 1
23
77 2
78 10 80 6
82 3
23
80 10
82 7
84
4
86
86 2
24
84 0
85
85
987
9 87 6
89 4
24
88 0
89 10 91
8
93 7
25
91 2 93
0 94 10
96
8
25
95 6 97 5 99
4 101 4
26 98
7100 6 102 5 104
26
103
3105 3107
3 109 4
27
106 4 108
4 108 3 110 3 112
4 4
27
111
4113 5 115
6117
8
4116
28 114
29 122 8 124 9 126 11 129 1
30 131 3 133
4 116 5 118 5 120
6
28
119 9 121 11 124 1126
3
29
5 135 8 137 11 30
128 6 130 8 132 11 135 3
137 6 139 10 142
1 144 5
31 140 2 142
32 149 4151
33 158 9 161
34 168 7171
35 178 8 181
36 189 0191
37 199 8 202
38 210 7 213
39 221 10 224 8 227
40 233 4 236 3 239
5 144 8 147 0
8 154 0156 5
3 163 8 166 1
1173 7 176 1
2 183 9 186 5
31
32
33
34
35
8 194 3 196 11
36
4 205
1 207 10
37
146 10 149 2151
156 5 158 11 161 4 163 10
166 4168 11 171 5 174 0
176 7 179 3 181 10 184 6
187 2 189 10 192 6 195 3
198 0 200 9 203 6 206 4
209 2 212 0 214 10 217 9
7154 0
4 216
2 219
0
38
220 7 223
6 230
5
39
232 4235
6 226 5 229 5
4 238
4241 5
2 242
2
40
244 5 247
6 250
7 253 8
43
41 245 2 248 2 251
42 257 3 260
3 260
269 8 272 9 275 11 279
2 254
2
41
256 10 259 11 263
1266 4
2 263 5 266
6
42
269 6 272 7 275 11 279 2
2
43
44 282 4 285 7 288 9 292 0
44
45295
45 295 4 298 7 301 11 305
3
45
282 6 285
295 9 299 2 302
309 4 312 10 316
9 289 1 292 5
6 305 11
3 319 9
47
48
322 2 325
336 0339
49 350 2 353
46 308 7 311 11 315 4 318 9 46
7 329
323 3 326 10 330
4333 11
0 332 6 47
337
6 343
0346 7 48
9 357
9 357 4 360 11 49
352
6341
0355
1344
8 359
8 348 4
4363
1
366 10 370
7374
4378
2
50 364 7 368
3 371 11 375 7 50
381 11 385
9389
7 393
6
SOLID MEASURE.
507

Quarter
Girt.
23 feet long.
11414
1
2
4
2010
Quarter
Girt.
inches
ft.
in.
ft. in.
ft.
in.
ft.
in. inches
24 feet long.
1
1-1-18
ft. in. ft. in. ft. in.
3
/
4
ft.
in.
2 3 4 5 CO
8
10
1 0
1
2
2
10
1 0
1 3
1
5
1 8
1 11
2 3
3
1 6
2 7
2 11
3 3
3 7
4
2 8
13
9
2
0
2 4
0
3 4
3 9
4 0
4 5
4 10
5 3
4 2 4
5 0
5 6
5 9
6 3
69
7 3
6 0
6
6
7
0
7 7
7 10
8 5
9 0
9
7
8
2
8
9
9 4
10 0
8
10 3
10 10
11
6
12
3
8
10 8
11 4
12 0
12 9
9
12 11
13
8
14
5
15 2
9
13
6
14
3
15
0
15 10
10
16 0 16
9
17 7
18 5
10
16
8
17
6
18
4
19 3
11
19
4
20
2
21 1
22 1
11
20 2 2 21
1 22
0
23 0
12
23 0
24
0
24 11
25 11
12
24 0 25 0
26 0
27 1
13
27 0
28 0
0
29 1
30 2
13
28 2
29 3
30 4
31 6
14 31 4
32
5
33 7
34 9
14
32 8
33 10 35 0
36 3
15
35 11 37
2
38 4
39 7
15
37 6
38
9 40
9 40 0 41 4
16 40 11 42 2
43 6
44 10
16
42 8 44
0 45 4 46 9
17 46 2
47
6
48 11
50 4
17
48 2
49 7 51 0
52 6
18 51 9
53 2
54 8
56 2
18
54 0
0
55
6
57 0
58
19 57 8
59
2
60 9
62 4
19
60 2 61 9
63 4
65 0
20
63 11
65
6
67
67 1
1
68
9
20
66 8 68 4
70
0
71 9
2223
21
70 5
72
1
73 10
75 7
21
73 6
75
3
77
0
78 10
77 4
79
1
80 10
82
8
22
80 8 82
6
84
4
86 3
23
84 6
86 4
88 2
90 1
23
88 2 90
1 92
0 94 O
24 92 0 93 11 95 10
97 10
$135
24
96 0 98
0100
0102 1
25
99 10 101 10 103 10 105 11
26 108 0 110 1112 2114 3
27 116 5118
25
104 2 106
3 108
4 110 6
26
112
8 114 10 117
0 119 3
7 120 9 123 0
27
121
28 125 3 127 6 129
9 132
0
28
130 8 133
0135
29 134
4136
8139
0141 4 29
140 2 142
7 145
30 143 9 146
2 148
7 151 0
30
150
0 152
6 155
31 153 6156
0158
6161 0
31
160
2162
2162
9165
32 163 7166
1168
8 171 4
32
170
8 173
4 176
33
173 11 176
7179
3181 11
33
181
6 184
3 187
6 123 9 126
0 128
4 137
4
9
0147 6
0 157 7
4168 0
0 178 9
0189 10
36
37
38
34
35 195 8 198 5 201
207 0 209 11 212
218 8 221 7 224
230 8 233
8 233
39 242 11 246
40 255 7 258
184 8 187 4 191
1192 10
34
192
8195
8195
6 198
4 201 3
3 204 1
35
204
2 207
1 210
0 213 0
9 215 8 36
216
0219
0 222
0 225 1
7 227 7
8 236 9 239 10
37
228
2 231 3 234
4 237 6
38
240
8 243 10 247
0 250 3
0 249
0 249 2 252 4
39
253
6 256
6 256 9 260
0 263 4
9 262 0 265 3
40
266
8 270
0 273
4 276 9
41 268 6 271 9 275
42 281 9 284 11 288
43 295 4 298 9 302
44 309 3312
1 278 5
41
280
2 283
7 287
0 290 6
6 291 11
42
294 0 297
4 301
0 304 7
3 305 9
43
308
2311
9 315
4 319 0
9 316 3 319 10
44
322 8 326
4 330
0 333 9
45 323 5 327
0 330 8 334 4
45
337 6 341
3 345
0 348 10
46 338 0341
8 345 4 349 1
46
352 8 356
6 360
4 364 3
47
48
352 10 356 7 360 4 364
368 0 371 10 375 8 379
49 383 6 387 5 391
50 399 4 403 4 407
2 47
368 2 372
1376
0 380 0
7
48
384
0 388
0 392
0 396 1
4 395 4
4 411 4 50
49
400
2404 3408
4 412 6
416
8 420 10 425
0 429 3
508
TIMBER TABLES.-No. 1.

Quarter
Girt.
inches
ft.
25 feet long.
Quarter
Girt.
26 feet long.
1
1
18
2
3334
1/4
1-1/48
3
4
in.
ft.
ft.
in.
in.
ft. in. inches
ft.
in.
ft.
in.
ft.
in.
ft.
in.
2 3 4
1
2 9
878
10
1 10
12
1
1 4
2 1
2 5
3 2
36
3 11
234
9
11
1 1
1
4
1 7
1 11
2 2
2 6
2 11
3 3
3
8
1
5
4 4
4 9
5 3
59
5
4 6
5 0
5
5
60
6
6 3
69
7 4
7 11
66
8 3
7
8 6
9 1
9 9
10 5
8 10 9
6
10 2
10 10
8
11 1
11 10
12 6
13 3
8
11 7 12
3
13
0
13 10
857EIGASSE 5.
14
1
14 10
15 8
16 6
9
14 7
15
5
16 3
17 2
10
17 4
18 3
19 1
20
1
10
18 1
19
0
19 11
20 10
21 0
22
0
22 11
24 0
11
21 10 22 10
23 10
24 11
12
25 0
26
1
27 1
28 3
12
26 0
27
1
28 2
29 4
29
4
30 6
31 8
32 10
13
30 6
31
8
32 10
34 2
14
34 0
35 3
36 6
36 6
37 10
14
35 5
36
8
37 11
39 3
15
39
1
40 4
41 8
43 1
15
40 7 42
0
43 4
44 9
44
5
45 10
47 3
48
8 16
46 3
47
8
49 2
50 8
50 2
51
51 8
53 2
54 8
17
52 2
53
9
55 3
56 11
56
3
57 10
59 5
61 0
18
58 6
60
2 2
61 9
63 6
62 8
64 4
66 0
67 9 19
65 2
66
11
68 8
70 5
20 69 5
71 2
72 11
74
9
20
72 3
74
0
75 10
77y
223
21
76 7
7
78
78 5
80 3
82 1
21
79 8
81
6
83 5
10
85 5
22
84 0
85 11
87 11
89 10
22
87 5
89
5
91
5 93 5
23
91 10 93 10
95 10
95 10
97 11 23
95 6 97
7
99
8101 10
24
100 0 102
0 102
1104 2106
41 24 104 0106
2 108
2 108
4 110 7
25108
6 110 8 112 11 115
1
25
25112
112 10 115
1 117 5 119 9
26
117 4 119 7 121 11|124
3
26 122 1124
5 126
9 129 2
27 126 7 128 11 131
3 133
8 27
131 7134
1136
6139 0
888888
28 136 1 138 7 141
29
146 0148 6151
30156 3 158 10 161
0143
6 28
141
7144
1146
8149 3
1153
8 29
151 10154 10 157
1159 10
6 164
2 30
162 6 165
3 167 11 170 9
31 166 10 169 6 172
3 175
0 31
2 32
32 177 9180 7 183 4186
33 189 0 191 11 194 10 197 9
9 33
34 200 8 203 8 206 8 209 8 34
35 212 8 215 8 218 9 221 11 35
36 225 0 228 2 231 3 234 6 36
237 8 240 11 244 2 247 5 37
173 6 176
184 11 187
196 7 199
208 9 211
2 224
221
234
0237
37
247
2 250
38
250 8 254 0 257 4 260 8
38
260 9 264
39 264 0 267
0 267 5 270 10 274
40 277 9 281 3 284 9 289
4
39
3
274 7 278
40288 11 292
41
0302
741
291 10 295 5 299
42
306 3 309 9 313 7 317 3 42
43 321 0 324 9 328 6 332 4 43
44
336
1 339 11 343 9 347 8 44
45 351 7 355 6 359 5 363 4 45
46 367 4 371 4 375 5 379 5 46
47 383 6 387 7 391 8 395 10 47
48 400 0 404 2408 4 412 7 48
49 416 10 421 1 425 5 429 8 49
50 434 0 438 4 442 9 447 2 50
4 179 2 182 0
9190 8 193 8
7 202 7 205 8
10 214 11 218 0
4 227 6 230 9
3 240 6 243 10
6 253 11 257 4
2 267 7 271 1
2 281 8 285 3
6 296 2 299 10
303 6 307
318 6 322
333 10 337
349 7353
365 7 369
382 1386 3 390 5 394 7
398 101403 1 407 4 411 8
416 0 420 4 424 8 429 1
433 6 437 11 442 5 446 11
451 5 455 11 460 5 465 0
3 310 11 314 9
1 326 1330 0
9 341 8 345 7
6 357 6 361 7
8 373 9 377 11
SOLID MEASURE.
509

27 feet long.
Quarter
Girt.
28 feet long.
11
101
34
Quarter
Girt.
4
1
ㅎ
​3
2
3
4
inches ft.
in.
ft. in.
ft. in.
ft.
in. inches ft.
in. ft.
in.
ft. in.
ft. in.
6
QM TO CO
2
3
9
1 8
11
3
2 0
3
4
8
5 2
5
Q 3 -
1Q35O
2
2 3
9
124
∞ ∞ cr
5
8
6 2
2345
9
1 9
3 1
4 10
6
9
7 4
8 0
8 6
7 0
1 2 3 N
1 0 1 3
1. 6
1
2 5
2 9
6
3 11
4 5
5 4
5 10
6 5
7 7
8 3
8 10
7
9 2
9 10
10
6
11 3
9 6 10
10 3
10 11
11 8
8
12 0
12 9
13 6
14 4
12 5
13 3
14 1
14 11
9
15 2
16
16 0
16 11
17 10 9
15 9
16
8
17 7
18 6
10
18 9
19
19 8
20 8
21 8
10
19
5
20
5 21
5
22 6
11
22 8
23
23 9
24
9
25 11 11
23 6
24
7
25
9
26 10
12
27 0
28 2
29 3
30 61 12
28 0
29
0
29 2
30 5
31 7
13
31
8
32 11 34 2
35 2 13
32 10 34 2
35
35 5
36 9
14
36 9
38 1
39 5
40 9
14
38 1 39
6
40 11
42 4
15
42 2
43
43 7
7
45
45
0
46
6 15
43 9 45
3
46 9
48 3
16 48 0
49 6
51 0
52
52 7
16
49 9 51
4
52 11
54 7
17
54 2
55
55 9
9
57
57 5
59 1 17
56 2 57 10
59
59 7
61 3
18
60 9
62
64 2
65 11
18
63 064 9
9
66 7
68 4
19
67 8 8
69 6
71 3
73 2
19
20
75 0
76 11
76 11-
78
78 9
80 9 20
70 2 72
777 9 79 9 81
73 11
75 10
9
83 9
21
82 8
84 8
27
24 108
25 117 2119
26 126 9 129
9129
136 8 139
86 8 88 8 21
22 90 9 92 10 94 11 97 0 22
23 99 2101 4 103 6 105 9 23
0110 3 112 6114 10 24
85 9 87 10
94 1 96 3
89 11
91 11
102 10 105
112 0114
6 121 11
6 121 11 124 4 25
2131 8 134 2 26
121 6 124
0126
131
5 134
3 141
9144 5
27
141
9 144
28 147 0 149
8 152
3 154 11 28
152
5 155
98
1107
4 116
9 119 1
0 126 5 128 11
0136
9 144 5 147 1149
5 155 2 157 11 160 9
5100
8
5109 8
7 139 2
9
29
8160
5163
5163
2 165 11 29
7 174
5 177 3
0189 0 31
0 201 1 32
5 213 7 33
2226 5
3 239
9 253
8
3
6
157
30168 9 171
31 180 2183 1186
32 192 0195 0198
33 204 2 207 3 210
34 216 9 219 11 223
35 229 8 232 11 236
36 243 0 246 5 249
37 256 8 260 2 263 8 267
38 270 9 274 4 277 11 281
39 285 2 288 10 292 6 296
40 300 0 303 9 307 6 311
祐​市
​41
315
42
43
2 319 0322 11 326 10 41
$30 9 334 6 338 8 342 8 42
346 8 350 8 354 9 358 1 43
44 363 0367 2371 3 375 6 44
45 379 8 383 11 388 2 392
46 396 5 401 1405
47 414
2418 7423
10 273
6 288
7 303
7 303 5 307 3
0 318 11 322 11
3 292 0
326 10 330 10 334 11 338 11
343 0 346 11 351 3 355 4
359 6 363 9 367 11 372 11
376 5 380
5 380 9 385 1389 5
393 9 398 2 402 7 407 0
411 5 415 11 420
429 6 434 1 438
448 0 452 8457
8 476
5
45
45
5 409 9 46
0427 6 47
48 432 0 436 6 441 0445 7 48
49 450 2 454 9 459 5 464 1 49
50 468 9 473 5 478 2 482 11 50
50
466 10 471
486 1 491
5 425 0
9443 4
5 462 1
5481 3
0 495 11500 10
163
6 166 4 169 3 172 1
338
175
0 177 11 180 11 183 10
186 10 189 11 192 11 196 0
199 1 202
211 9 215
34
224
9 228
1 231
35
35
238
2 241
7 245
36
252
0 255 6 259
2 205 5 208 7
0 218
0 218 3 221 6
5 234 10
1 248 6
1262 7
2 37
266 2 269
5 277 1
6 38
3
280 9 284
3 39
4 40
295 9 299
311 1 315
510
TIMBER TABLES.-No. 1.

Quarter
Girt.
29 feet long.
1
4
-~
Quarter
Girt.
}
3
4
inches ft. in.
ft. in.
ft. in.
ft
in. inches ft. in.
30 feet long.
14
3
cokk
ft. in. ft. in. ft. in.
2
3
M
10
1 10
1Q
0
1 3
1 6
2 1
2
6
2.10
3 3
3 8
4 1
4 6
234
10
1
1
1 4
1 7
1 10
2 2
2
7
2 11
3 4
3 9
4
3
4 8
5 0
5 7
6 1
6
8
5
5 2
5 9
6 4
6 11
7 3
710
8 6
9 2
6
7
6
8 2
8 10
9 6
7
9 10 10 7
11
4
12
1
10
3
10 11
11 9
12 6
8
12 11
13 8 14
7
15 5
16 4
17 3
18
2
19 2
∞ a
8
13 4
14 2
15 1
15 11
16 10
17 10
18 10
19 10
10
20 2
21
21
2
2
22
2
23 3
3 10
20 10
21 11
23 0
24 1
11
24 4
25
6
26
8
27 10 11
25 2
26 4
27
7
28 9
12 29 0
30 3
31
6
32
32 8
12
30 0
31
3
32 7
33 10
13
34 0
35 4
36 8
38
1
13
35 2
36 7
36 7 38
38 0
39 5
14
39 6
40 11 42 4
43 10
14
40 10
42 4
43 10 45 4
15
45 4
46 10
48 5
49 11
15
46 10
48
5
50 1
51 8
16 51 77
53 2
54 10
56 6
16
53 4
55
0
56 9
58
58 5
17
58
2
59 11
61 8
63 5
17
60 2
62
0
63 10
65 8
18
65
3
67 1
68 11
70 10
18
67 6
69
5
71
71 4
73 3
19 72 8
20
8888
74 7
76 7
78 7
19
75 2
77 2
79
79 3
81 3
80 7
82 7
84
8
86 8
20
83 4
85
5
87
7 89 8
21
88 10 90 11
93
1
95
3
21
91 10 94 10 96
4 98 7
22 97 6 99 8 101 11 104
23 106 6 108 10 111 3113
24 116 0118 5 120 11123
25 125 10 128
26 136 2138
27 146 10 149
28 157 11 160
29 169 4 172
30 181 3 184
6196
3
22
100 10 103
10103
2105
6 107 10
7
23
110 2112
7115
1117 6
4 24
120 0122 6 125
1127 7
5 130 11 133
6
25
130
2 132 10 135
6 138
2
9 141 5 144
1
26
140 10 143 7 146
4 149
1
7 152
4155
1 27
9163
4 175
7166 5
3 178 3
3 187 4 190
5
206 3 209
31 193
32
33 219 4 222
34 232 10 236 3 239 8 243
35 246 8 250 3 253 1 257 5
36 261 0 264 8 268
37 275 8 279 5 283
38 290 10 294 8 298 6 302
39 306 4 310 3 314 3 318
40 322 3 326 3 330 4 334
8 199 10 203
0
31
200 2 203
5 212 9 216
0
32
213 4 216
8 226 0 229 5
33
226 10 230
2
34
240 10 244
151 10 154 8 157
28 163 4166
29 175 2 178
30187 6 190
3 172
4184 5
8 193 10 197 0
5 206 9 210 0
8 220 1223 5
4 233 10 237 4
5 248 0 251 7
7 160 5
3 169
3 181
2
5
35
255 2 258
10 262
7 266 3
4 272 0
36
270 0 273
9 277
9 277
7 281
7 281 4
2 287 0
37
285 2 289
1 293
0 296 11
5
38
300 10 304 10 308
10 312 10
2
39
5
40
40
333 4 337 6 341
316 10 320 11 325
9 345 11
1329 2
43
44
41 338 6 342 8 346 10 351
42 355 3 359 3 363 9 368
372 4 376 8 381 1385
389 11 394 4 398 10403
0
41
350
1
42
6
43
3 44
2354 6 358
367 6 371 8 376 4 380
385 2 389 8 394
403 4 407 11 412
10 363 2
3 398 9
7 417 2
45 407 10 412
4 416 11 421 6
6
45
421 10 426
7 431
4 436 1
46
426 2 430 9 435 5 440
2
46
440 10 445
8 450
6 455 4
47
444 10 449 7 454 5 459
2
47
460 2 465
1470
1475 0
48 464 0 468 10 473 8 478
49 483 6 488 6 493
7
48 480 0 485
0 490
1495 1
5 498
5
49 500 2505
4510
6 515 8
50 503 6 508 6 513 7 518
8
8
50
50520 10 526
1 531
4 536 7
SOLID MEASURE.
511

Quarter
Girt.
inches
ft. in.
31 feet long.
1
1/2
Quarter
Girt.
32 feet long.
*400
3
114
1124
3
4
ft. in.
ft.
in.
ft.
in. inches ft. in.
ft.
in.
ft.
in. ft.
in.
2 3 4
10
1 1
1
4
1 11
2 3
2
8
180
7
2
11
1
2
1 5
10
1 8
3 0
3
2 0
2
4
2 9 3 2
3 5
3 11
4 4
4 10
3
7
4 0
4 6
5
5
5
5 11
6
6
7 1
5
7
62
69
7 4
6
9
8 5
9
1
9 10
6
0
8 8
9 5
10 2
10 7
11 4
12
1
12 11
7
11 11
11
8
12 6
13
8
13 9
14 8
15
7
10 6
8
14 3
15
2
16 1 17
9
17 5
18 5
19
5
20
20 6
9
18 0
19 0
20 1 21
10
21 6
22
22
7
7
23
23
9
24 11
10
22 3
23 4
24 6 25 8
4028
11
26 1
25 3 28
6
29 9
11
26 11
28
2
29 5
30 8
12
31 0
32 4 33
8
35 0
12
32 0
33 4
34 9
36
2
13
36 5
37 10 39
3
40 8
13
37 7
39 0
40 6
42
0
14
42 2
43 9 45
3
46 10
14
43 5
45 2
46 9
48
4
15
48 5
50 151
50 1 51
9
53 5
15
50 0
51
51
8
8
55
55 5
55 2
16 55 1
56 10 58 7
60 5
16
56 11
58 8
60 6
62 4
17 62 3
64 1
65 11
67 10
17
64 3
66 2
68 1
70 0
18
69 9
71 8
73 8
75 8
18
72 0
74 O
76 1
78 2
19 77 9
79 9
81 10
84 0
19
80 3
82 4
84 6
86 9
20
86 1
88 3
90
6
92
92 8
20
88 11 91
2
93 5 95 8
21
94 11 97 2 99
6101 10 21
98 0 100
4102 9 105
2
22 104 2 106 7 109
23 113 11 116 4 118
24 124 0126
25 134 7 137
0 111 5
22
107 7 110
0112
6 115 0
11 121 5
23
117 7 120
2129
9 125 4
7 129
3131 10
24
128 0130
8133
3 140
0 142 9
25
138 11 141
9 144
26 145 6148
6 148
4151 2154
0
26
150 3153
1156
156 11 159 10 162 10 165
27
28 168 9171 10 174 10 177 11
29 181 1184 2 187 4190 6
30 193 9 197 0 200 3 203 7 30
9
27
162 0165
0168
28
174 3 177
4 180
5136 2
6 147 4
1158 11
1171 2
6183 8
29
186 11 192
2 193
5 196
200 0 203
4 206
9 210 2
31 206 11 210 3 213
32 220 5 223 11 227
33 234 5 238 0 241
34 249 10 252 6 256
35 263 9 267 6 271 4 275
36 279 0 282 11 289 10 290
37 294 9 298 9 302
38 310 10 315 0 319
7 217 0
0
31
213
7 217
0 220
6 224
0
5 230 11
32
227
7 231
2 234
9 238
4
7 245 3
33
242 0 245
8
249
5 253
2
3 260 0 34
256 11 260
8 264 6 268
4
2
35
35
272
3 276
2 280
1284 0
9
36
288
0 292
0 292
0 296
0 296
1 300 2
9 306
9 37
304 3 308
4 312 6 316 8
1323
3 38
39
327 5 331 8 335 11340
40 344 5 348 9 353 1 357
2 39
6
40
355
320 11 325 2 329
338 0 342 4 346
7360
5 333
9 351 2
0 364
6 369 0
1402
1402
41 361 11 366 4 370 9 375
42 379 9 384 1 388 10 393 5
43 398
8407 4 412 1 43
44 416 9 421
45 435 11 440
46 455 6460
6 460
47 475 7 480
3
41
373
7 378
7 378
2 382
9 387 4
42
392
0 396 6 401
5 406 2
6 426
4 431 1 44
410 11 415 8 420
430 3 435
6 425 4
2 440
9 445
8 450
7
45
450 0 455
0 460
6465
6 470 6
46
470 3 475
4 480
•
1445
0
1 465 2
6 485
6485 8
7485
48 496 0 501
49 516 11 522
50 538 2 543
2 506
2527
9490 10 47
5 511 7
6 532 10 49
48
7 549
0 554 6
50
50
490 11 496
512 0 517 4 522
533 7 539 0 544
555 7561 2 566
2 501
5 506 8
9 528 1
0 550 0
9 572
4
512
TIMBER TABLES.-No. 1.

Quarter
Girt.
inches
ft. in.
33 feet long.
118
Ho
Alw
Quarter
Girt.
34 feet long.
1
114
3
12/0
ft. in.
ft. in.
ft. in. inches
ft. in.
ft. in.
ft.
in.
ft. in.
2
Q345 CO
11
1
2
1 5
19
2
1
2 5
2 10
3 3
23
11
1
2
1 6
1
9
2 2
2
6
2 11
3 4
3
8
4 2
4 8
5 2
3 9
4
3
4 9
5 4
5 9
6 4
6 11
7 7
5 11
6 6
7 2
7 10
8 3
8 11
98
10 5
6
6
9 3
10
0
10 9
7
11
3
12 1
12 11
13
9
7
11
7
12 5
13
3 14 2
8
14 8
15 7
16 7
17 7
8
15 1
16 1
17
1.18
1
9
18 7
19
19 7
20
8
21
9
9
19 2
20 2
21
21
4 4 22 5
10
22 11
24 1
25 3
26 6
10
23 7
24 10
26
0 27 3
11
27 9
29
29
0
0
30 4
31 8
11
28 7
29 11
31 3
32 7
12
33 0
34
5
35 10
37 4
12
34 0
35 5
36 11
38 5
13
38 9
40
3
41
41
9
43 4
13
39 11
41
5
43 0
44 8
14
44 11 46
6
48 2
49 10
14
46 3
47 11
49
8
51 4
15
51 7
53
4 55 1
56 10
15
53 2
54 11
56
9
58 7
16 58 8
60
6
62 5
64 4
16
60 5
62 4
64 3
66 3
17
66 3
68 2
70
2
72 2 17
68 3
70 3
72 4 74 5
18
74 3
76 4
78
5
80
7
19
82 9
84 11 87 2
89 4
20
91 8
94 0 96 4
98 8 20
252
18
76 6
78 8
80 10
80 10
83
0
19
85 3
87 6
89 9 92 2
94
5 96 10
99
3 101
8
21 101 1103 6 105 11 108 5 21
104
2106 7109 2111 8
22
110 11113 5 116
0118
71 22
114 3 116 11119
6122 2
23
121
3123 11 126 7 129
3 23
124 11 127 8 130
5 133 2
24 132
0134 9 137 7 140 5
24
136 0138 10 141
25
143 3 146 1 149 0 151 11
25
147
7 150
6 153
9144 8
6 156 7
26
154 11 157 11 160 11 163 11 26
159
7162
8165
10 168 10
27 167 1 170 2 173
4 176 6
27
172
2175
4 178
7 181 10
28 179 8 182 11 186
29 192 9 196 1 199
30 206 3 209 8 213
2189 5
28
185
1188
5191
9 195 2
5 202 10 29
2216 8 30
198 7 202
0205
6 209 0
212 6 216
1 219
8 223 3
40
31 220 3 223 10 227
32 234 8 238 4 242 1 245 10 32
33 249 7 253 4 257 2 261 0 33
0
34 264 11 268 10 272 9 276 9
35 280 9 284 9 288 10 292 11
36 297 0 301 2 305 4 309 6
37 313 9 318
38 330 11 335
8344 1 38
39 348 7 353 1 357 7 362 1 39
366 8 371 3 375 11 380 40
5 231 0 31
226 11 230
241 9 245
257 2 261
34
272 11 277
7234 3 238 0
7 249
7 249 5 253 3
0 265 0 268 11
0281
0 285 1
35
289 3 293
289 3 293
5 297
7 301 9
36
306
0 310
3 314
7 318 11
0 322 3 326 7
3 339
37
323 3 327
7 332
0 336 6
340 11 345
5 350
0 354 6
359 2 363
9 368
5 373
1
7
40
377 9 382
6 387
3 392 1
41
385 3 389 11 394 8 399 5
41
396 11401
9 406
8 411
7
42
404
3408 10 413 11 418 10
43 423 9 428
42
416
6421
6421
8 433 8 438 8
43
436 7 441
44
443
45 464 1 469
46 484 11 490
47 506 3 511
48 528 0 533
8448
9 453 10458 11
3 474 5 479
8
2495 6 500 10
8 517 1522
6
44 457 1 462
45 478 2 483
46 499 7 505
47
3 426 6 431 6
8446 9 451 11
4 467 7 472 10
5 488 10 494 2
1510
6 516 0
49
50
6 539 1 544
550 3 555 10 561 6 567 2 49
572 11 578 8 584 5 590 3 50
8
521 7 527
48 544 01549
2 532
9 538
4
8 555
5 561
2
566 11 572
8 578
578 6 584 5
590 3 596
2 602 2 608 1
SOLID MEASURE.
513

Quarter
Girt.
inches
35 feet long.
1
14
937
Quarter
Girt.
36 feet long.
114
13/13
4
00/+
3
ft.
in.
ft.
in.
ft.
in.
ft.
in.inches ft. in.
ft. in.
ft.
in. ft. in.
QEHLO CO
2
1
0
1
3
1
6
1 10
2
3
2 2
2
7
3 0
3 5
3 11
4
5
4 11
5 6
6 1
6
8
7 4
8 0
6
8 9
9
6
10 3
11
1
7
11 11
12 9
13
8
14
77
8
15 7
16 7
17 7
18
7
9
19 8
20 10
21 11
23
1
10
24 4
25 6
26 10 28
1
10
11
29 5
30
9
32
233
7
11
12
35 0
36 6
38
0 39 6
12
13
41 1
42 8
44
4
45 11
13
Q 34E CO
** R*
1
0
1 3
1 7
1 11
2 3
28
3
1
3 6
4
0
4 6
5 1
5 8
63
6 11
ry my
8 3
6
0
9 9
10
7
11 5
12
3 13 2
14 1
15 O
16
0 17 0
18 1
19 2
20
321
21 5
22 7
23 9
25
0 26 3
27 7
28 11
30
3 31 8
33
33 1
34 6
36
0
37 6
39 1
40 8
42 3
43 11
45 7
47 3
14
47 8
49 4
51
1
52 11
14
49 0
50
50 9
52 7
54 5
15
54 8
56
6
58
5
60 4
15
56 3
58 2
60 1
62
62 0
16
61 3
64 2
66
2
68 2 16
64 0
66 0
68
1
70 2
17
70 3
72 4
74
5
76
1
17
72
3 74 5
76 7
78 9
18
78 9
80 11
83
2
85 5
18
81
083 3
85
7 87 11
19
87 9
90 0 92
5
94 10 19
90
3 92
8
95
1
1 97 6
20
97 3
99 8 102
2104 8
20
20
100
0 102
6 105
1107 8
21
107 2109
9 112
4 115 0
21
110
3 112
22
117 8120
4123
1125 10
22
121
0123
23 128
24
7131
140 0142 11 145
5134
3137 1 23
132
3135
11148 11 24
144
0147
11115
9 126
2138
0 150
7 118 3
7 129 5
1141 0
1153 2
25
151 11 155 0 158
26 164 4 167 6 170 8 173 10 26
1161
2 25
25
156
159
5 162
7 165 9
169
0172
3175 7 178 11
27 177 2180 5 183 10 187
10187 2
28 190
27
182
3 185
8189
1192 6
7194 0197 5 200 11 28
29 204 5 207 11 211
30 218 9 222 5 226
196
0199
6 203
1206 8
6 215 1
29
210
3 213 11 217
7 221 3
1 229 10
30
30
225
0 228 9 232
7 236
5
31 233 7 237 4 241
32 248 11 252 10 256
33 264 9 268 9 272
34 281 0 285
35 297 9 302
2 245
0
31
240
3 244
2 248
1|252 0
9 260
8
32
256
0 260
0 264
1268 2
9 276 10
33
272
3276
5 280
7284 9
1 289 4 293 6
34
289
0 293
3 297
7 301 11
0306 4 310
8
35
35
306
3 310
8 315
1 319 6
36 315
37 332
0319
9 337
5 323 10 328
3
36
324
3341 10 346
4
37
342
0 328 6 333
3 346 11 351
1337 8
7 356
3
38
351
0355
7360
0
39 369 8 374
8 374
5379
5 379
40388 11 393
9398
3365
3384 1 39 380
8403 7 40
40400 0 405
38 361
0 365 9 370
7 375 5
3 385 2 390
1 395 0
0 410
1415 2
41 408 7 413 7 418
42 428 9 433 8 439
43 449 5 454 8459
44 470 7475 11481
45 492 2 497 8 503
46 514 4 519 11 525
47 536 11 542 8 548
7423 8 41 420
0444 2 42 441
3 425
5 430
7 435 9
0 446
0451
7 456 11
11 465
2
43
462
3 467 8 473
4 486
9 9
44
484
0 489 6 495
2 508
9 45
506
3 511 11 517
1478
1500
6
8
7 523 3
7 531
3
46
529
0 534 9 540
7 546 5
5 554
2
47
552
3 558
1564
1570 0
48 560 0 565 10 571
49 583 7 589 7595 7 601 7
9 577
8
48
576
0 582
0588
1594 2
49
600 3 606
5 612
7618 9
50
607 8 613 9 619 10 626
0
50
50
625 0 631
3 637
7 643 11
514
TIMBER TABLES.-No. 1.

Quarter
Girt.
inches
37 feet long.
11-4
ft.
in.
ft.
12
19/20
Quarter
Girt.
in. ft. in. ft. in. inches ft.
38 feet long.
114
1-2/14
03/1
4
in.
ft. in.
ft. in. ft. in.
234
1 0
1
4
2 4
2
9
4 1
4
8
5
6 5
7 1
1357
79
7229
1 11
3 7
Q2 00
1 1
1
4
1
8
1 11
3
2 5
2
9
3 3
3 9
5 10
4
4
3
4 9
5
4
5 11
86
6 7
7 3
8 0
8 9
6
9 3
10
0
10 10
11 8
6
9 6
10 4
11 2
12 0
12 7
13 6
14 5
15 5
12 11
13 10
14 10
15 10
8
16 5
17 6 18
7
19 8
16 11
18 O
0
19 1
20 2
9
20 10
22 0
23
2
24 5
9
21 5
22 7
23 10
25 1
10
25 8
27
0
28
4
29 8
10
26 5
27
9
29 1
30
6
11
31 1
32
6
34
0
35 6
11
31 11
33 5
34 11
36 5
12
37 0
38
7
40
2
41 9
12
38 0
39 7
41 3
3
42 11
13
43 5
45 1
47
0
48 7
13
44 7
46 4
48
1
49 11
14
50 4
52 2 54
0
55 11
14
51 9
53
7
55
6
57 5
15
57 10
59 9 61
59 9 61 9
63 9
15
59 5
61
4
63
5
65 6
16
65 9
67 10 69 11
72 1
16
67 7
69 8
8
71 10
74
74 O
17
74 3
76 5 78 8
80 11
17
76 3
78
6 6
80 10 83 2
18
83 3
85 7
87 11
90 4
18
85 6
87
11 90 3 92 9
19
92 9
95
3
97
3 97
8 100 2
19
95 3 97
9 100 4 102 11
20
102 9 105
4 108
0 110
0 110 8
8
20
20
105 7 108
105 7 108 3 110 11 113 7
21 113 4 116
30
0 118
22 124 4 127 2 130
2130 1133 0 22
23 135 11138 11 141 11 144 11 23
24 148 0151 1154 3157 5 24
25 160 7 163 10 167 1 170 4 25
26 173 8 177 1180 5183 10
27 187 4 190 10 194 4|197 10
28 201 5 205 0 208
0 208 8 212 5
29 216 1 219 10 223 0227 5
231 3 235 1 239
0 118 9121 7 21
116 5119 2 122
0 124 10
9130 8 133
26
27
28
127
139 7142 8145
152 0155
0 155 2 158
164 11 168
164 11 168 3 171
178 5 181 10 185
192 5 195 11 199
206 11 210 7 214
5161 8
7 175 0
7 136 7
9 148 10
4 188 10
7 203 3
4 218 1
29
221 11 225 9 229
0 242 11
30
237 6 241
237 6 241
6 245
8233
6 249
7
6
31
246 11 250 11 254 11 259 0
32 263 1 267 3 271 5 275 7
31
253 7 257
8 261
10 266
0
32
270
33
279 10 284 1 288 4 292 8
33
287 5 291
34
297 0 301
5 305 10 310 3
34
3 274 6 278
5 291 9 296
305 1309 7314
9 283 0
2 300 7
35
314 9 319 3 323 10 328
5
35
323 3 327 11 332
1318 8
7 337
3
36 333 0 337 8 342 4 347 0
0
36
342 0 346 9 351
7 356 5
37
351 9 356 6 361 4 366 2 37
361
3 366
2 371
38 371 0 375 11 380 10 385 10
39 390 10 395 10 400 11 405 12
40 411 1 416 3 421 5 426 8
38
381
1386
39
401
5 406
1 391
6 411
6411
1376 1
2 396 3
9 417 0
40
422
3 427
6 432 10 438 2
41 431 11 437
42 453 3458
2 442 6 445 10
41
443 7 449
0 454
6 460 0
5 464 1 469 7
42
465 6 470 10 476
8 482 3
43
44
475 1480
497 5 503
8 486 2 491 10
43
487 11 493 7499
4 501 1
45 520 4 526
46 543 8 549
1 508 10514 7
1 531 11 537 10
537 10
7 555 7 561 7
44
510 11 516 9 522
7 528 5
45
45
534 5 540
534 5 540 4 546
4 552 4
46
558 5 564 6 570
7 576 9
47 567 7573
48 592 0 598
8 579 9 585 10
47
582 11 589
2 595
5 601 8
2 604
2 604
5610 8
48
608 0 614
4 620
9 627 2
49
3 629 7 635 11 49
50
616 11 623 3 629
642 4 648 10 655 3 661 9 50 659 9 666
633 7 640
1646
7 653
659 9 666
4 673
0 679 8
SOLID MEASURE.
515

Quarter
Girt.
inches ft. in.
39 feet long.
1
3
Quarter
Girt.
40 feet long.
4
14
11.
324
ft. in.
ft.
in.
ft. in. inches
ft. in.
ft.
in.
ft. in.
ft. in.
2
3
2
15
1Q
1
4
1
8
2 1
2
1
1
1
5
1
9
2 1
2 10
3
4
3 10
3
2 6
2 11
3
5
3 11
4
4
4 11
5 6
6 1
4 5
5 0
5 7
6 3
5
69
76
8 2
8 11
5
6 11
7 8
8
5
9 2
6
9 9
10 7
11 5
12 4
10 0
10 10
11
9
12 8
7
13
3
14 3
15 3
16 3
13 7
14 7
15
7
16 8
8
17 4
18 5
19 7
20
9 8
17 9
18 11
20
1
21 3
21 11
23 2
24 5
25 9
22 6
23 9
25
1
26 5
10
27 1
28 5
29 10
31
4 10
27 9
29
29
2
2
30
7
32 1
11
12
13
FREE
32 9
34 3
35 10
37
5
11
33 7
35
2
36 9
38 4
39 0
40 8
42 4
44
0
12
40 0
41
8
43 5
45 2
45 9
47 7
49 4
51
2
13
46 11
48
9
50 7
52 6
14
53 1
55 0
57 0
58
11
14
54 5
56
5
58 5
60 5
15
60 11
63 0
65
1
67
2
15
62 6
64
7
66
9
68 11
16
69 4
71
6
73 9
76
0
16
71 1 73
4
75
7
77 11
17
78 3 80
7
82 11
85
4
17
80
382 8 85
1
87 6
18
87 9 90 2
90
2
92 8 95
3
18
90
0 92 6 95
1
97 8
19 97 9100
20 108 4 111
21 119
4103 0105
8
19
100
3102 11105
7108 4
1113 10 116
7 20 111
22 131
5 122
1134
23 143
24 156
3 146
0159
3 162
25 169 3 172
8 176
26 183 1 186
27 197 5 201
7190
4 125 2128 1 21
1137 1140 2 22
5 149 7 152 9 91 23
7 165 11 24
1 179 7 25
2193 10 26
122
134 5137
146 11 150
160 0163
173
7 177
1 180
187
9191
1204 10 208 7
27
202
6 206
28 212 4 216
29
2 220 0 223 10
227 9 231 9 235 8 239 8 29
30 243 9 247 10 251 11 256 1 30
28
217 9 221
8 225
1113 11 116
6 125 5 128
6140
2153
4 166
5 195
3210
9 119 7
5 131 5
7143
9
5 156 8
9170 2
7 184 2
1 198 9
1213 11
7 229 7
233 7 237
250
8 241
9 245 10
0 254
2 258
5 262 8
283
31
33
260 3 264 6 268 9 273 0 31
32 277 4 281 8 286 1 290 61 32
294 11 299 5 303 11 308 6 33
34 313 1317 8 322 4 327 0 34
35 331 9 336 6 341 4 346 2 35
36 351 0 355 11 360 10 365 9
37 370 9 375 10 380 10 385 11
266 11 271
3 275
7280 0
284
302
5288 11 293
6307 1 311
5 297 11
9 316 5
321
1325 10 330
340
3 345
36
360
0 365
2 350
0370
7335 5
1 355 0
1375 2
37
380
3 385
5 390
7395 10
38 391 1 396 3401 406 8
38
401
1 406
5 411
9 417 1
39
40
411 11 417 3 422 7 427 11
433 4 438 9 444 3 449
39
9
422
40444
6427
11 433
5 438 11
5 450
0 455
7 461 3
44
45
0 630 6 637
3 656 11 663
677 1 683 10 690
41 455 3 460 10 466 5 472 1 41
42 477 9 483 2 489 2 495 0142
43 500 9 506 7 512 6 518 5 43
524 4 530 4 536 4 542 4 44
548 5 554 6 560 8 566 10 45
46 573 1 579 4 585
47 598 3 604 8 611
48 624
49 650
50
466 11 472
8 478
490 0 495
7 501
5484
9 507 8
2
513 7 519 7 525
7 531 8
537 9 543 11 550
1556 3
562
6 568
9 575
1 581 5
7 591 11 46
587
9 594
9 594
2 600
2 600
7607 1
1617 6 47
613
7 620
2 626 9 633 4
1 643 81 48
640
0 646
0 646 8 653 5 660 2
7 670 4 49
8 697 6 50
694 5 701
666 11 673 9 680 7 687 6
5 708 5 715 5
516
TIMBER TABLES.-No. 2.
TIMBER TABLES, No. II.
Tables of unequal sided Timber, and side of equal square.
Each page of these Tables contains twelve columns. In the
outer column on either side is set down the greater side in inches,
and in the remaining columns are contained the side of equal
square corresponding to the unequal sides.
USE OF THE TABLE.
Ex. 1.-A piece of timber 27 inches broad, and 40 inches
deep, what is the side of equal square?
In the column headed 27 inches lesser side, and opposite
40 inches greater side, stands 334 inches side of equal square.
Ex. 2.-A piece of timber 25 feet long, 23 inches broad, and
37 inches thick, what is its solid content?
In Table, No. 2, under 23 inches lesser side, and opposite
37½ inches greater side, is 292 inches side of equal square.
In Table, No 1, in the portion headed 25 feet long, opposite 29
inches quarter girt, and in the column headed inches, is 153 ft.
8 in. solid content.
It is not unfrequent in practice for measurers to add together the
unequal sides and consider half their sum as the side of equal
square. When there is not much difference in the dimensions of
the two sides, this is not productive of great error; but the two
preceding examples will show, that when the sides are very dis-
proportioned the error is considerable.
In Ex. 1,
27
401
2) 68
sum of two sides
34
mean
334 True side of equal square.
3 difference.
UNEQUAL SIDED TIMBER.
517
In Ex. 2,
2) 61
30
mean
29
231/
37/1/2
sum of two sides
True side of equal square
error.
ft. in.
Content of a tree 25 feet long, 30
inches quarter girt,
161, 6
Content of a tree 25 feet long, 29
inches quarter girt,
153, 8
Error due to the incorrect method of determining
the side of equal square
7, 10
518
—No. 2.
TIMBER TABLESTABLES..

Lesser
side, Lesser
Greater
2
side,
Lesser
side.
in.
21
side,
in.
3
Lesser
side,
in.
3/1/20
in.
Side of
Lesser
equal
Side of
side,
square.
equal
square.
Side of
4
Lesser
side,
Lesser
equal Side of
in.
4/1/1
side,
Lesser
square.
inches. inches.
equal
in.
5
side,
square.
inches.
in.
51
inches
Side of
in.
Lesser
inches.
equal Side of
side,
2334
NNNN
HE -2 Mj mle
238
23
or cr h
41
3
İQ
co na ma m
Bid Bid
6778
3/3/20
6
6/1/1 8
3/2/20
7/12/20
4
08/12/20 4 4/1/20
9
9/1/20
10
10/1/ 4/12/2
11
111
12
121/ 5
4329290
4 20
5/1/
51 500
44
Old Col Col
41
2/1/12 21
3/12/20
2112
29
2 OFF
31/12
31/
31
31 3 39 0
3/1/2
33 110
39 90
3 OFF
39 0
4
41
41
49 F
5
51
3
4
41
411
4292909
41
4/1/20
51 5/1/
51
5/1/
444
14 12 BE BE
HAHN
LO LO LO CO
LO LO LO LO
HT HE HA
- M< <
4445
CO
10 10
HK 4
LO LO LO LO
HE HE HA
F BE B
4445
5
51
51
IN BEBE
5/1/
5
5
6
6
6
61
61
6 61
61
520
6
61
64/12
61 6/1/1
61 69210
7N77
HITHE HO∞ld
69/
7211
71
K
6777
IQ BT Bl<
6/1/10
CO CO
63210
HE HE HQ ME
81
8/1/
∞ ∞ ∞ ∞
FRE
7788
71
7
7 NN7
HATA MIE
67727
Hea old co}<
<
6/
69/1/
7 7
61 630 7/1
77
13
13
51
5 20
61
14
51 6
730
8777
IN BİQ BİER
square.
equal
square.
Side of
equal
6
Lesser
side,
inches.
square.
Side of
equal
in.
6/1/
in.
square.
inches.
inches.
Side of
inches.
equal
Side of
4&
H HQ +
cold
44
HAHN
square.
equal
square.
Greater
5
51
51
5/1/2
HAHA
inches.
side.
5
inches.
5
5/1
H2 HQ B
LO LO LO CO
10
HA HA H
5/1/
5/1/
5320
6
61
6
61
61
6
7
6
61
<<
778
7/11
7931
I BE BE
730
8
81
8/1/20
8/3/10
∞ ∞ ∞ ∞
H4 Hle ole osle
9
9/1/20
10
101/20
11
11/1/0
12
8 1/1/0
∞ ∞ ∞ ∞
81
81
∞ ∞ ∞ ∞
8/1/10
8 20
9
12
989 1990
941
13
921
13/1/20
91
9/14
HIQ BE B{E
7778
HE HE HA
7
7፤
7፤
141
15
15/1/
51
16 5元
​10 10 10 LO
HAHA HAI Old
cold cal
LO LO COCO
16/1/20 52
17
17
18
5 /
6
6
61
61
61
6
6/1/ 7
6
71
7/1
HD HQ H<
HOME BIE
71
~~
73
∞ ∞ ∞
6 6
HOME MICH
9
91/1
9/14/20
9
91/
10
15
941
992
10
15/1/1/0
קט
9 9/12
99
10
16
91
91
9/11
9/21/20
HD HD HQ HIN
91/20 10
101 161/20
921
10
101 17
99
101/ 10
10 10/10 10
17
18
8/1/12
81/1
HH HH HO
8
∞ ∞ ∞ ∞
1/2 + 01+
∞ ∞ ∞❤
83 9
UNEQUAL SIDED TIMBER.
519

Lesser
Lesser
side,
Greater 7 side.
side.
in.
7/1/20
Lesser
side,
in.
8
Lesser
side,
in.
8/1/
Side of
equal
square.
in.
Lesser
Side of
side,
Lesser
equal
inches. inches.
square.
inches.
inches.
inches.
Side of
equal
square.
9
side,
Side of
in.
9/1/
Lesser
side.
equal
square.
in.
10
Lesser
side,
in.
10/1/
Side of
in.
Lesser
equal Side of
side,
Lesser
9/1/20
10
10/1/
8/1
8/1
8/1/20
11 89100
111 9
HA HOME
12
7778
7∞∞
HA
∞ ∞ ∞ ∞
HI HA HA MK
square.
788
732
equal
square. equal
Side of
11
side,
Side of
in.
11/
8/1/
∞ ∞
8/1
8/1/10
1412
square.
inches.
∞
08900
equal
square.
in.
inches.
inches.
inches.
СО СО СО 00
8
cold
9
9/11
Side of
equal
square.
Side of
equal
9/1/12
9/1/20
92910
square.
Greater
9/1/1
9/2
10
101
inches.
side.
9/1/20
993/9 10
10
10 10
inches.
CO
9/21/2
9/1/20 10 101
10/1/20
12
9/1/20 91
929/200
10
10/1/20 1032
HQ ME
102/2 11
11 111
12/1/ 91
10
10/1/
10/1/10 11
111
11/1/
13
9/1/10 9300
101 101
10
11 11
112
Ha col
111
11/1/20
1121
12
122
HHA BH
112
223
12/1/
13/
93/1 10 10/1/
14
10 1011
10/1/20
141 10 10/1 103/
12 12 BH
102 11 114
11
111
11 1/2/
11
11
119/2
HAHAB
111
129
12
124
12
11/2/20 12 12/
12/1/20
15
101 101 11
111
12 121 123/
111 12 121 121 12
123/
PH HIS CO
13
131
14
14/1/
13
15
15
ט
10/1/2
16
10/1/
16 1/1/20
10%/
HI HIQ B}<
102 11 11
114
11 111 112 12
11/3/20 121
121
11
17
11
11
112 112/20
11 12
121 12/1/
121 122
HHHHHIN COE
12/
123/
13
131
15
123/ 13 131
13/31/20
16
123
13
131
13 13
131/1
132 16/
14 17
17/ 11 11/1/ 11
18 111 111/ 12 121
121
19
18/1/ 111
11A
112 12 12
12 124 12
12/1/20 13 131
123/20 13 13/
13 131 131
13 131/ 13/9/1
HHN HINI ME
13
1321
1234
133
141 17
14
14/1/0
18
14
19
14 141 14 18
141 1423/20
13/1/20 14 141 14/3/20 15 191
139/
14
141 14/ 143/2 15 20
141 143 15 15
14 14 14 151 15
HK HK HK¥ OD/F#
1431 15
20
21
151 15
21
14 15 15 16 22
15
151
151 152 16 22
161 23
151 15 16
21
12 12/1/20
191
131
11/9/ 12 12 12
20 119 121 1280 13 13
20/1/1 12 12/ 122 131
HE HN HN Col
13/
13 131 13
HN
21
22
12/1/
22/1/10
123
23
12
૭ ૭ ૭
121
H HIS Hoa coleg
1291 13 131 14
141
1231 131 13
14
14
13
131 132 141
14
13
13 14 14 14
520
TIMBER TABLES.—No. 2.

Greater Lesser
side. side,
Lesser
16
153
161 16
16/1/
16
4
161
20
163/ 162
16/ 16 17
in.
12 side,
Lesser
121 side,
Lesser
in.
13
side,
in.
131
Side of
equal
in.
Lesser
Side of
side,
Lesser
square.
equal
Side of
14
side,
square. equal
Lesser
Side of
in.
141
side,
inches. inches.
square. equal
Lesser
in.
15
side,
inches.
square.
in.
15
inches.
Side of
in.
Lesser
inches.
equal Side of
side,
13/
14
HTHA BH
223
HE HC BD ca
121
13
121
12/1/20
123
13
14/1/
15
131
13/12/
15/1/20 139
16
161/1 14
17
141
171
141
18
142
#IWDT PL
1234
18
15 15 15/0
19
15 151
15/1/
19/ 151 15/1/20 153/
151 152 16
HQ HQ M}<
square
mky col
129/00
13 13
131 132
131/
1323/
14
139/
139/10 14
14 14/
141 141
132 141 14 14/12
141
14/1/1
143
15
equal
square.
Side of
16
Lesser
side,
equal
Side of
in.
161
square.
inches.
equal
in.
square.
inches.
inches.
Side of
inches.
44
HIT HIN COCH
Hit Hky cl➡
square
1432
equal Side of
equal
square.
15 151
151 15 15
inches.
Greater
inches. side.
141
14/1/
14312
143 15
151
10 10
151
15/1/
15/
1521
HE MIGH
14232
15
151
152/2
16
15
151
15 16 161 16 16
152
16
161
16
161
161
16/1/20
HAHA +
16/1/0 163/ 17
1632 17 171/
17
17
18
4
-ka Hla colet
163
17
17
171
17
17/
171 17
HTHIN HIN
171
17/1/20
17
18
17 3/4
19
1732
18
19/1
18
18 20
20/1/
159/ 16
161 162
21
152
161
16/
163/1
Colt Calst
17
171
17/1
223
21/
16 16/1/20
162 17
171
16
161 17 171
171
HAHA IN
17/
173
17
HAHAHH
17/
173
18 18/201
173
18 181 181
21
18 181
181
18 21/
181 181 18 19
22
2***
221/1
161
999
HOME MEH
169/1 17 17
17
17
23 163
23/1/20 16232
24 17
24/1/1 171
25 171
251
26
HAHAHN ©}<
17/1/20
17
171 172 18
17/
17/
181
18
171
17
17/1/10
173
Hka Hika cakH
172/
181 18/1/20
18/ 18/3/2
183 19 19/
18 18 19 191 19
26/1/1
17939
27
17 18 181
18 181 181 19 1911 19/1/20 193/20
18/1/20 189/9 19 19/1/ 19 20
181 183
1234
19
19 1914 19/1/20 20 201 201 202 26
19 193 201201 202/1 21 27
19 20 201 202 21 21 27
19 20 201 202
20 211 21 28
18 181 183/2
27/ 181 18/1/ 19 191
28
181 18 19 19
HK HA
18
181
18
181
183 19 19
191 19
22
23
19 23
19 20
24
∞ ∞
18/ 18/3/
183
19 191
191
19/1/20
4
198
HION COLCH COLCH
20
19232 20
24/1/
201 25
201
20
HK HA
20 25
20
26
UNEQUAL SIDED TIMBER.
521

Greater 17
Lesser
side, Lesser
side.
Lesser
side.
in.
17
side,
Lesser
in.
18
side,
in.
18/1/1
in.
Side of
equal
Lesser
Side of
side,
Lesser
square.
equal
Side of
19
side,
Lesser
square. equal Side of
in.
19
side.
Lesser
inches. inches.
square.
equal
square.
in. 20
side,
inches.
in.
20/
inches.
in.
17/1/
17/1
18
17/
173/
Side of
inches. equal
equal
square.
square. equal
Lesser
Side of
side,
Lesser
equal Side of
21
side,
Side of
in.
21/1
19
18
18/1/ 17/3/1 18 181
181 1811
square.
inches.
equal
in.
18%
square.
inches.
inches.
Side of
inches. equal
Side of
square.
19/1/
181
20
18 1/1
20/1/
183
FEHN COLEH
18/1/20 18/3/20
19
191
equal
square.
183/ 19
191
19 191 19/1/20
21
19
191
19
193
19/1/20 193
·193 20 20/41/
20 2014 201
inches.
Greater
side.
20/21
inches.
211/2 19
22 191
191
192 20
1932
2220
20/1
20/1/1
22/1/1
23
19/1
193/
24
201
241/
201/20
25
201/2
201 20/0 203/
199 20 201 202/1 21
23/12/20
20
Ha Ha H
201
2011
2223
20/1/
220
IN MA
20-3/1
20/31/ 211
211
21
aaa
HOME HV COE
211
2013/ 21 214
21 211 21 21
251/ 203/10 21
212
22
211
HN HOME
21/
2272
Ale mlb cakes
2272
20/1/1
21
203/2
20/31/ 21
21
214
aaa
211
211
21
21/
21
211 212 213
21/
HQ ME M<
21/3/1
21/1/1
22
219319
221
2222
- Ha Bl<
22/1/2
2222
23
23
221
26
21
21/1/
22
221
221
26/1/
214
27
211/
14-2
212
21
221
221 223/1
- Ha cslett
221/1
223/1
231
23/1/20
223/10
23
231
233
23
231
23/1/20
23
21
221 22
23
231
23 233
24
27
27/1/0
28 21
21
~~~~
223
221 22
223
231
23/1/20
221
22 223
23
2341
233/14
28/1/20
22
221
22 23
231
231
233/1
- clodH
233/20
24
24 27
24
241
24/1/20
28
241
24
243/28/
29
221
22
221
231
333
233
24
241 24
25
29
291/10 22/ 223 23 231/1 233/
4
30
221/
231
301/ 22$ 23 231/
31 23 231 23
23
23/1/20
233/1
311 231
32
23/
23/31/
241
24
231
23-3/1
24
241
243
32 1/1/0 231
233 241 24 243
DKO PEORGH
22
24
24/1/10
22
241
241/
2391 24 24/1/1
24 241 24 25
IT IN MI
243
24時
​1234
25
25
243/2
25
25291
25/1/
30
251
25 30
2223
2228
IKH HON ME
222
213/1
22
22/1/10
22 23
221231
24
223/
24/1/20
231 25
Hi coles coleti
25/1/
26
26/1/
25 25 25 31
22
242
25
25/1/
25
251
251 25/
25/1/
HA HOM
25
25
35
253
26
31 /1/20
~~
26 261
32
26
261/2
321/10
26 26 33
33 233
24 24 24 25
2 K
522
TIMBER TABLES.-No. 2.

Greater Lesser
side. side, Lesser
22 side,
Lesser
in.
22/1/2 side,
in. 23
Lesser
side,
in.
23
Side of
equal
square.
in.
Lesser
Side of
side,
Lesser
equal
square.
Side of
24
side,
Lesser
equal Side of
in.
24/1/
side,
square.
Lesser
inches. inches.
equal
in.
25
side,
square.
inches.
in.
25/1/
inches.
Side of
in.
Lesser
inches. equal Side of
side,
2***
22/1/1
221
23
22/1/
23/1/10
24 23
223/1
P/CO 29/- *-
square.
Lesser
equal
Side of
26
side,
22/3/
square.
equal
Side of
in.
26
23
231/1
inches.
square.
equal
in.
231
231 23
square.
inches.
inches.
Side of
inches. equal Side of
241
25
راحة
231
23/1/
233/1 24
241
23/1/
233140
наколя
24 24/1/1
241/
25/1/
233 24
241 241 242
24¥
141234
26
24 241 24 24 25
26
24
27
244
22
24/1/
242 25
243210
25 251
10 10
24210
equal
square.
25
251
inches.
Greater
side.
25 25 25%
inches.
251 25
25/12/ 25/
25310
26
26
261
2641 261
HIT HA MI<
261
26/1 26/3/20 27
26-3/10 27 27/
square.
27/ 24
243 251 251 259 26
28 249190 25 251 252 26 261 261 26
28/1/20
25
2511
29
251
25
8228
HD kame
29/1/
25/ 2531
30 25 26
25910
25 25 261
26 261
261/1
26/
26 261 26/1/0 27
mica coleti
26/1 27
27
27
28
27/ 27 28
27 271 27/ 273/ 29
271 27! 27/3/20 28 29/1/20
261 262 26 27 271 27 28 28 30
2223
30/1/1 26 261
261 262 27
271
31 26 26/1/0 26/3/ 27
27
31
261 261/
27 271
27/1/20
HAFIQ B
27
27
22888
POOL PL
27/
27/
28
HQ H
70
32/1/20
262
27
33 27 27/1/
331/1 271
34
27
271 27
HAHN BA
22
288
26 26 271 271 2792108
271
27/1/0
27
28/1/0
888888
27/
28
281 28/1/20
28/1/20
30/1/
283 31
28/1/
28/1/20
282 31
1/
H4 HQ H
27/1 28 281
28/1/20
283/
ко
273/
281/1
28 1/1/0 28/31/0
28 28/14/ 289/90
281 28
28%
291
29
29 291 29/1/
291 292
28 28 29 32
29 291 321
291/1 29/1/ 33
29 33
30
34
341
35
27/
27 281/
28/1/20 283/1
29
35 28
36
888888
281 28
888888
273/ 28 28/1/1 28/9/10 29
281
29
28/1/20
291
291 2921 30 30/1/20 341/
29/1/0 293/ 301 30/1/20 35
88888
28 29
2833
291
29/1/
293/ 30 30
303/
35/1/20
29 29
30 30 30
31
36
37
361/1 281/1/
2891
28/1/20 283/
29
3888888
37/
28/9/1 29
2222
29/1/1 29/1/2 30
291
3041 30 30 31 361/1
29/1/20 293 30 301
303/1 31
2941
293/ 30
301/1 301 31 311
29 29 29 29 30 30 30 31 311
311
31 1/1/0
HEIN BE
37
37/
31 38
UNEQUAL SIDED TIMBER.
523

Greater Lesser
side. side, Lesser
27}
271
28
27/1/1
28/12
273
29
28
27
side,
Lesser
in.
27
in.
28
side,
Lesser
side,
in.
28/1/2
Side of
in.
Lesser
equal
Side of
side,
square.
Lesser
equal
Side of
29
square.
side, Lesser
equal
Side of
in.
29/1/
side,
square.
Lesser
inches. inches
equal
in.
30
side,
inches.
square.
in.
30/1
inches.
Side of
in.
Lesser
inches.
2282
TH-IN CO
equal
square.
Side of
equal
Side of
side,
31
2888888
square. equal
Side of
in.
281
281 282
inches.
square.
equal
square.
inches.
inches.
inches.
Lesser
side,
31
in.
29/1/
281 28
30
28/ 283/20
28/21 29
29 29-
301/20 289190 29 291
31
29 29/1/1
2223
29/1/20
29/1/20
29/
293/
HE HQ ME
29 29 30
293
30 301
inches.
Greater
30
30 30%
4
inches. side.
Side of
equal
square.
square
Side of
equal
311
32
291 29/1
29/1 293
29/9/ 30 30/1/20
30 301
33
32/1/2 29/
29 30
293
301
30/1/20
30 30%
HEIN BE
301
30/2
303
HE HABEH
30/1/20 303/20
302
31
4
31
34
311
31
314
31/1/1
1412
313
HEIN M
31
311
31/1/2
HE HIN Mer
331/
34
34/1/20
30
30/1
3034
31
311
301 301 303/1 311 31/1/20
30/1/
303/1
31
314
31 3/4
35 30 31
31 31
31
HITHIN MICH COLCH
31
313
312
32
3211
4
311
31 1/1/0
313/
32
32 321
32
32
4
32
32/1/20 323
32
33
33/1/20
34
313/ 32
:
32
321
32
32
14 12
321/10
323/10 33
34/
32
33
33 35
351
36
361/1
37
مرات
12
HE HADO
8888888
Ha
37
38
31
314
311
31
313/
32 321 32/1/20
38 321
323
321/20
39 325 32 33
331/
391/10 323 33 331
40 3230 331
401 33 331
311
31/1/20
313
ww
31/
313 32
3123 32 321/1 321/ 32314 331 33/1
32 3211 32/ 323/ 33 331
321 323100
33 331
33/1/20
33 31/0
35/1/0
36
333/20
34
361/
32
32
32
323 33 33 33
333
الايم
341 37
32
321/10
12 12 3ojen
323/1
33
33
331
3311 33/
33 1/1/0 331/20
333/
34
34 37
34
341
34/
38
33
33
33/3/2 34 341
34
343 38
3311 33
34
34/1/1
34 341
35 39
33320
41
331 331/10 34
- FİQ Odje
33
34
333
34 341 345/ 343
341 34 343 35
411/20 331/1 33330 34 34 343/2 35
42 33
34
421
33 3/10
341
43
34 34
لمواتير سرت
344/ 34
35 351
343 342 35 351/1
343
35
1 -2 -2
351/ 351 353 36 411
36 361 42
ACP p | pat
35/
353/1
353
36
361 36/1 421/1
36/1/0 36 43
35 35 36 361
33 34 341/20
341 343210
218885
HQ MİTH ME
343
35
35 39
35
351
35/1/20
40
35
3512
35% 40
352
36
41
524
TIMBER TABLES.No. 2.

Lesser
side,
Greater 32
Lesser
side,
side
Lesser
in,
321 side, Lesser
in.
33
side,
in.
331/
Side of
in.
Lesser
equal Side of
side,
square
Lesser
equal Side of
34
square. equal
Side of
side,
in. 341/1
Lesser
side,
inches. inches.
square. equal
Lesser
in.
35
side.
inches.
square.
in.
35/1/
inches.
Side of
in.
inches.
Lesser
equal Side of
side.
3232
square. equal
Lesser
Side of
36
side,
33
321/1
331/1
323/20
HBE
323/1
square. equal Side of
in.
36
33 331
inches.
34
33
331 332 33
inches.
inches.
34
33 33/1/
33 3/1
colet
34 341
square. equal
square.
Side of
inches. equal Side of
square. equal
in.
35 331/1
332/2
34
341
34 3432
square.
35 333/1
34 341
342
343 35
36
34
341
342
34
35
351
335
351
inches.
Greater
size.
35
H
352/1
inches.
36
341
37
37
ཚཚ
34/
ကက
34
343/20
35 351
351
35232 36 361
34232
35
35 35
353
36 361 36
36
37
342
35
351
352
35
36 361
361 362
37
38
343
35
35
35 35
35
35
35
4
36 36
36 37
37
55888
371/
38
38
35
351
352/
36
36
361
39 351
35
35 36
361 362
1234
39
35
352/ 36 36
36 37
40
35
36
36 36
36
36
371
co co
37 371
371
37
37 37
HHH CH
38
40/ 36
361 361 362
37
37/1/1/0
37/3/1
38
363/1 37 37 37 38
371/ 3732/4 39
373/
38 391/1
38 40
3840
381
41
361 361/ 36212
37
371
37/1/0
38 381
41
N
42
36
36/ 363 37 371
37 37 37
H
37
37
38 381
37
8888
421 37
43
37
43/1/
371/
www
371
37/
37/
373
373 38
44 37 37 38
Ika ole
88
777
HI HA HAa colet
3723/1
38 381 38
38 381 381/1 382/20 39
38 38 38/ 38/3/20 39
HAHAHA
38/1/ 383
383/1
41
39 411
39
39 42
391/
3942
391
381
381 3893/42 39 391 391/
38 38 39 39 39
4
39
PWNH PH
391/
421/
43
393/
43/1/
40
44
44 373
38
381
381/ 383
391
45 38 381
45 38 381 381
46 3811 38 38 39
38
383/20
39
391/
39
4
391
39 39
39
HK HK HKI CH
391/
3932
40 401 441
3931
40 401 40 45
40
401 402
403 45½
40
401 402
41 46
46
381 382
47 3832 39
471 39 391
48 39 39 39
4
8888
39
392 393
40
401
40/1/
41
391
39232 40 401
39/
40
40
40/1/
4
cole
40
401
40
HHQ Bler
40/1/ 43/3/20
411
402/20 41 411
41
411
41
واطر ماهر و
41 46
41/1/20
47
412 47
412 48
UNEQUAL SIDED TIMBER.
525

Lesser
side, Lesser
Greater 37 side,
size.
Lesser
in. 37/1/20 side,
Side of
equal
in. 38
Lesser
side,
in.
381/
in.
Lesser
Side of
side,
square.
Lesser
equal
square.
Side of
39
side,
Lesser
inches. inches.
equal
square.
Side of
in.
391/1 side,
equal
in.
40
Lesser
side,
inches.
square.
in.
40/1/
inches.
Side of
in.
Lesser
inches. equal Side of
side.
Lesser
37/1/ 371
square.
equal
Side of
41
side,
38 37
373/
square.
equal Side of
in.
411/
38/1/ 37
38 381/1
inches.
square equal
in.
39
38
381
38 38
square.
inches.
inches.
Side of
inches.
391
سراحه
40
381
381/20
40/1/
38
HI HA MCH
381/ 3831 39
391
equal
square.
Side of
equal
383/
39 391
39 391 39/
41
39
39
39 39
HHH MICH
391/
393/1
PAGIP
393/1
square.
40
401
inches.
Greater
side.
40
401 402 40
inches.
41
391 391/
3932 40
401 402 403 41
411
40
42 391/1 393/
42 393 40 401
43 40 40 401 402 41 411 41/
401
40/1/
40/1/
402/2 41 411
411/
402
41 41
4
411
41
IPKO KOI MP
HE HOME
413/2
42
413 42 423
42
424
43
44
45
431/1
40
401
442/
401/1
40
090
401
Het mica col-H
PPPON-
451
41
46
411
461/
41/
47
419
47
42
421
421
48
48/1/ 421
49 42
49/1/2 423/1 43
50 43 431
HHHHK
42/
423/
423
HH HCG CG evaluati
PW NH HP
HIGH HOT COK
42
403-
402
41 411 41
411
41
412
412
42
411 412 42
413/2 42 424
42
421 421/
421 42 421
402/2 41 411
41
41
41
41
411
HAHAHAI
HH Hea Col
41 412
413/2 42
42 421
421 42
42
421
421
42
42
423
HAHN CH
42
43
422 432
42210 44
43 442
431 45
HH HON COK
422 423 43
4231 43 431
431 43 45
431 432 46
423 431 431/
432 44 46
43
431 431
44 44 47
421 422
43
50/1/ 431
432
51
431/10
43
51
43/3/20
52
4321
COLER COLEH
52/1/1
44
53 441
مراه مراح تتهم
421/1 43
431 43/1/20 4332
431 431 432 44
43/ 432/2 44 441
423 431
43 43 43
431 432 44
431 432 441
433 44 444
44 441 44
ور سرحد ساوه
44 441 44 442/2
441 44/
441 4432/2
44
44
mika coleri ester
44 441
441
441 443
44
48
44 48
44 45 49
441 44 443/4 45
4549
441 442
45
451 45 50
443/
45
451
45/ 45 50
45
451
45
45 46 51
45
452 46
46 51
45
453
46
46
46 52
46
461 46
47
53
45
44232 45 451
45
451
45/2
45
45/1/ 45
H
mdagi mica coleg
46 46 46 52
441 | 44 | 47½
526
TIMBER TABLES. NO. 2.

Greater Lesser
side. side, Lesser
42
side, Lesser
in.
421/
side,
in.
43
Lesser
side,
in.
431/1
Side of
in.
Lesser
equal
Side of
side,
Lesser
square.
equal
Side of
44
side,
Lesser
square.
equal
Side of
in.
44/1/
side,
inches. inches.
square. equal
Lesser
in.
45
side,
inches.
square.
in.
451
inches.
Side of
in.
Lesser
inches. equal
Side of
side,
42/1/20 421
square.
Lesser
equal
Side of
46
side,
43
42 422/1
square.
equal
Side of
in.
461/
431/ 423/1 43
44
43
431
434 43 43
inches.
square.
inches.
equal
square.
in.
inches.
Side of
inches. equal | Side of
44/1/
431
431/1 433
44
441
45
431/ 433 44 441
44/2
46
451 432/2 44 44 44
44 441 442 44
443/2
HE HA MJEH
square.
44232
equal
square.
45
Greater
451
inches.
side.
45
45 45 45
inches.
46/1/
441
47
442
47/1/ 44/9/20
HAHABE
441/ 442/2 45
443 45 451
48
45
45 45
45 451 45 45
HAHA MH
9999
HE HOCH
451
451/
45
46 461
451
453/20
452 46
461
462
4632 47
46
461
461/
463/2
47 47/
46
46
46
46
47
471
48
48/1/1 451 45/1/2 453 46
49 451 451 46
49/1/2
45/1/ 452/2 461
50 45
46 46 46 47 471 471
9999
461
461/1
463
47
471 471/
48/1/20
461
461 461/
46232
463
47 471
47
473/1
49
47 471 473
47
48
491/
47
48
48
50
4
47/2
473/
47&
HQ MEHME
473/4
48
481
48
481 482
48 48
கக
4814
48/1/
483/2
سرار مروة تتهم
489/90
49
48
50
483 51
49
511
4914
52
483/1
49
HS Hica col
48
483/2
49
4952
子
​483/1
49
491
493 53
4
49
491 491/
49 53
491 49 49
50
54
50/1/ 46
46/14/
461 462 471
51
461
51
461/
52
46
461/ 469/ 47
462/2 47 471
47 471 47/ 47
47
47
HA HA HQ ME
52
47
471
53
471
53
47
54
471
HAININ
47/1
473/
THE MI<
2 BH
48
47/1/
472/
48
481 481
4732/ 48
48
481
489
HD HQ Col<
481
481 48
48/1/20
UNEQUAL SIDED TIMBER.
527

Greater Lesser
side. side, Lesser
47
side,
Lesser
in.
471/10
side,
Lesser
in. 48
side,
in.
48/1/1
Side of
in.
Lesser
equal
Side of
side,
Lesser
square.
equal
square.
Side of
49
side.
Lesser
equal
equal
Side of
in.
491/
side,
Lesser
inches. inches.
square.
equal
in.
50
side,
square.
inches.
in.
50
inches.
Side of
in.
inches.
equal Side of
Lesser
471/ 471
square. equal
side,
Lesser
48
481/1 473/ 48
47 473/20
Side of
51
side,
square.
equal Side of
in.
511
481
inches.
square.
equal
in.
49
48
481
48
483
inches.
square.
inches.
Side of
inches.
491
481
481
482
49
491
equal Side of
square. equal
50
50/ 483/2 49 491
481 483/ 49
491
49 4932
square.
491
493/20
50
501
inches.
Greater
side.
51
49
491
49
49
50
50
50 50
inches.
51
491
49/1/ 4932
50
501
4
50/
52
49/1/20 4932
50
50
50
5032
Flea colet
521
493 50 501
50
50% 51
502 51
51 514
511 51
511
53
50 50 50
50 | 51
51
51
51
HEINWE
531/1
501 50 503
54
50 50 51
51 511
51 51
511
512/
34
51 52
521/
53
52
521
521
531
521
52
52
54
51 5132 52
51 52
52 52
Greater Lesser
side.
side,
Lesser
52 side,
Lesser
in.
521 side,
Lesser Lesser
in.
53
side, side,
in.
531
54
Side of
in.
in.
equal
Side of
square.
equal
Side of
square.
equal
Side of Side of
inches. inches.
square.
equal equal
inches.
square. square.
inches.
inches. inches.
5252
53
53
بياسر
54
53
521 5232
522 53 531
53 53 53 54
528
TIMBER TABLES.-No. 3.
1
TIMBER TABLES, No. III.
Tables of Superficial or Flat Measure.
These Tables commence with 1 inch in width, and extend by
the progressive addition of an inch up to 2 feet, and from thence
by the addition of 2 inches up to 10 feet.
The first and fifth columns contain the lengths from 1 inch to 30
feet. The remaining columns contain the superficial contents due
to any given length and width, the columns of which intersect
each other in the positions in which such quantities severally
stand.
The use of the Tables is too obvious to require comment.
Ex. 1.-Required the superficial content of a board 19 feet long
and 16 inches broad.
In page 531, opposite 19 feet long, and under 1 foot 4 inches
broad, stands 25 feet 4 inches, the content required.
Ex. 2. The side of a room 9 feet 10 inches high, is 26 feet 7
inches, what is its superficial content?
In page 540, under 9 ft. 10 in.
broad and opposite
Ft. In. Ft. In.
26
0 is 255 8
0
7 is
5 8
26 7 261
261 4 Required
content.
SUPERFICIAL MEASURE.
529

Lengths.
1 inch
wide.
2 inches 3 inches
wide. wide.
Lengths.
ft. in.
ft. in.
ft. in. ft. in.
ft. in.
4 inches 5 inches 6 inches
wide. wide. wide.
ft. in. ft. in. ft. in.
0 1
0
0 2
0
00
0
0
0 3
0
0 4
0 5
0 6
بار بار مراه براد
-H HK 2/5 yj
0
0 7
08
09
0
0 10
0 11
HAHN ocker celer
0
0
- Ha colt AIA
0
0
2
0 3
1
0
4
1
0 1
1
0
5
0 1
0
1
0
6
0 2
0 2
HDF 22
0 2
0
0 3
ANTIQ QI OD
2
1
0 1
0
1
0 2
0
0
0 1
0 2
0
1
0
IQQQN
0 7
0 2
0 2
0 3
08
0 2
0
3
0 4
2
09
0 3
0 3
4
0 10
0 3
0
4
0
2
0 11
0 3
04
0 5
1 0
0 1
0 2
03
1 0
0 4
0 5
0
6
2 0
2
0 4
0 6
2 0
08
0 10
1 0
3 0
3
0
09
3 0
1 0
1 3
1
6
4
04
0
1
0
4 0
4
1
8
2 0
5 0
0 5
0 10
1 3
5 0
2 8
2 1
2 6
60
0 6
1 0
1 6
6 0
2 0
26
3 0
7 0
0 7
1
2
I
9
7 0
2 4
2 11
3 6
8 0
08
1 4
2 0
2 8
3 4
4 0
9
0
0 9
1
6
2 3
9
3 0
3 9
4 6
10
0
0 10
1.8
2
6
10 0
3 4
4 2
5 0
11 O
0 11
1 10
2 9
11 0
38
4 7
5 6
12 0
1 0
2 0
3 0
12 0
4 0
5 0
6 0
13 0
1 1
2 2
3 3
13 0
4 4
5 5
66
14 O
1 2
2 4
3 6
14 0
4 8
5 10
7
0
15 0
1 3
2 6
3
9
15 0
50
6 3
7 6
16 O
]
17 O 0
1 5
18 O
1
19 0
20 0 1 8
1
45678
O Q M M ca
2
8
4 0
16
O
5 4
68
8 0
2 10
4 3
17
0
5 8
7
1
8
6
3
0
4 6
18
O 0
6 0
7 6
9 0
3
2
4 9 19 0
6
4
7 11
9 6
3 4 5 0
21 0
1 9
3
6
22 0
1 10
3
8
10 10
5
3
23 0
1 11
3 10
5 9
24 0
2 0
4 0
5 6 22 0
23 0
6 0 24 0
2 288*
20 0
68
8 4
10 0
21 0
25 0
2 1 4 2
6 3 25 0
777 ∞ ∞
7 0
8 9
10 6
4
9 2
11
0
8
9 7
11 6
8
0
10 0
12 0
8 4
10 5
12 6
26 0
27 0
28
0
29
30 0
20 10 10 10 10
4
4
6 6
26 0
10 10
13 0
4 6
6 9
27 0
9 0
11 3
13 6
4 8
7 0
28 0
9
11 8
14 O
5
4.10
7 3
29 0
9 8
12 1
14 6
2 6
5 0
77 6
30 0
10 0
12 6
15 0
530
TIMBER TABLES. -No. 3.

Lengths.
wide.
7 inches 8 inches 9 inches
wide.
wide.
Lengths.
ft. in.
ft.
in. ft. in.
ft.
in. ft.
in.
10 inches 11 inches 12 inches
wide. wide. wide.
ft. in. ft. in. ft. in.
0
1
0
0
2
0
0
3
0
1
0 2
0
0 4
0
2
0 2
0
0
5
0
0 3
0
0
6
0 3
04
0
* Q * CO ◄
3
0 1
0
0
0 2
2
0 3
0 2
0
3
0
4
0
0
3
0
0
4
0 4
4
0 6
0 5
0 5
* Q * 45
0 1
1
0 2
2
0 3
0 4
0 5
0 6
0 7
0 4
04
0
5
0
7
0 5
0 8
0 4
0 5
0 6
0 8
0
0 9
0 5
0 6
0 6
0 9
0
0 10
0 5
0 6
0
7
0 10
0 8
0 11
0 6
07
08
0 11
09
667∞ ∞
06
0 7
077
08
08
0 9
09
0 10
0 10
0 11
1 0
2
0 7
1
3
1 9
2
729+
08
1
4
2 0
4
2 8
5
2 11
3 4
☺ present Q? ∞ ∞
0 9
1 6
2
3
3
0
1234
0
0 10
0 11
1 0
0
1 8
1 10
20
0
2
6
2 9
3 0
4 0
3 4
3 8
4 0
39
5
0
4 2
4 7
5 0
6
0
3 6
4 0
4 6
6 0
5 0
5 6.
60
7
0
4 1
4 8
5 3
7
0
5 10
6 5
7 0
8 0
4 8
5 4
6 0
8 0
6 8
7 4
8
0
9 0
5 3
6 0
6
9
9 0
7 6
8 3
9 0
10
0
5 10
6 8
7 6
10 0
8 4
9 2
10 0
11 0
6 5
7 4
8 3
11
0
9 2
10 1
11 O
12
O
7 0
8 0
9
0
12 0
10 0
11 0
12 0
13 0
7 7
8
9 9
13 0
10 10
11 11
13 0
14 0
8 2
9 4
10 6
14 0
11
8
12 10
14 O
15 0
8 9
10 0
11 3
15 O
12 6
13 9
15 0
16 0
9 4
10 8
12 0
16 0
13 4
14 8
16 0
17 0
9 11
11 4
12 9
17 0
14 2
15 7
17 0
18
20
228 78*** 2**28
0
10 6
12 0
13 6
18 0
15 O
0
16 6
18 0
19 0
11 1
12 8
14 3
19 0
15 10
17 5
19 0
0
11 8
13 4
15 0
20 0
16 8
18 4
20 0
21 0
12 3
14 O
15 9
21 O
17 6
19 3
21 0
22
0
12 10
14 8
16 6
22 0
18
4
20 2
22 0
23
0
13 5
15 4
17 3
23 0
19 2
21 1
23 0
24
14 0
16 0
18 0
24 0
20 0
22 0
24 0
25 0
14 7
16 8
18
9
25 0
20 10
22 11
25 0
26 0
15 2
17 4
19 6
26
0
21 8
23 10
26 0
27
0
15 9
18 O
20
3
27 0
22 6
24 9
27 0
0 16 4
18 8
21 0
28 0
23 4
25 8
28 0
29
0
16 11
19 4
21 9
29
24 2
26 7
29 0
30
0
17 6
20 0
22 6
30 0
25 0
27 6
30 0
SUPERFICIAL MEASURE.
531

Lengths.
wide.
1ft. lin. 1ft. 2in. 1ft. 3in.
wide.
wide.
Lengths.
1ft. 4in. 1ft. 5in. 1ft. 6in.
wide. wide.
wide.
ft.
in.
ft. in.
ft. in.
ft. in.
ft.
in.
ft. in.
ft. in.
ft. in.
0
1
1
0
1
0
1
0
0
0
2
0
2
0 2
0
0 3
0
3
0 3
03
0
0
4
0 4
0 4
0
4
0
0 5
0
5
0
0 5
0
0 6
06
07
0 7
0 6
1 2 3 4 5 6
1
0 1
0 1
0 1
2
0 2
0
2
0 3
0 4
0
4
0 4
0 5
0
5
0 6
0
6
0
7
0
08
08
0 9
pand CO79
0
་
0 7
0
8
08
0 7
09
09
0 10
08
08
0 9
0 9
08
0 10
0 11
1 0
0 9
09
0 10
0 11
0 9
1 0
1 0
1 1
0 10
0 10
0 11
1 0
0 10
1
1
1
2
1 3
0 11
0 11
1 0
1
1
0 11
1 2
1 3
1 4
1 0
1
2 0
2 2
3 0
3
4 0
4
070-0
5 0 5 5
6 0
1 2 3 4 5
1
2
1
3
1 0
1
4
2
4
2
6
20
28
3 6
3 9
3 0
4 0
4 8
5 0
4 0
5
5 10
6 3
5 0
6 8
12 457
20
5
210
13
6
3 0
4 3
4 6
6 0
1
7
6
66
~
ཌ 0
7
6
60
8
0
8 6
9 0
0
7 7
8 2
8 9
7
0
9 4
9 11
10 6
8 0
8 8
9
4
10 O
10
8
11
4
12 0
9 0
9 9
10 6
11
3
9 0
12 0
12 9
13 6
10 0
10 10
11 8
12 6
10 0
13 4
14 2
15 0
11 0
11 11
12 10
13 9
11 0
14 8
15
7
16 6
12 0
13 0
14 O
15 0
12 0
16 0
17 0
18 0
13 0
14 1
15 2
16 3
13 0
17 4
18 5
19 6
14 0
15 2
16 4
17 6
14 O
18 8
19 10
21
15 0
16 3
17 6
18 9
15 0
20 0
21 3
2233
0
6
16 0
17 4
18 8
20 0
16
O
0
21
4
22 8
24
0
17 O
18 5
19 10
21 3
17 O
0
22 8
24 1
25
6
18 O
19 6
21 0
22 6
18 0
24 0
25 6
27 0
19 O
20 7
22 2
23 9
19 O
25 4
26 11
28 6
20 0
21 8
23 4
25 0
20 0
26 8
28 4
30 0
21 0
22 9
24 6
26 3
21 0
28 0
29 9
31 6
22 0
23 10
25 8
27 6
22 0
29 4
31 2
33 0
23 0
24 11
26 10
28 9
23 0
30 8
32 7
34 6
24 0
26 0
28 0
30 0
24 0
32 0
34 0
36 0
25 0
27 1
29 2
31 3
25 0
33 4
35 5
37 6
26 0
28 2
30 4
32 6
26 0
34 8
36 10
39 0
27 0
29 3
31 6
33 9
27 0
36 O
38 3
40 6
28 0
30 4
32 8
35 0
28 0
37 4
39 8
42 0
29 0
31 5
33 10
36 3
29 0
38 8
41
1
43 6
30 0
32 6
35 0
37 6
30 0
40 0
42 6
45 0
532
TIMBER TABLES.-No. 3.

Lengths.
wide.
1ft. 7in. 1ft. 8in. 1ft. 9in.
wide.
wide.
Lengths.
1ft. 10in. 1ft. 11in. 2ft. Oin.
wide. wide. wide.
ft. in.
ft. in. ft. in. ft. in. ft. in.
ft. in.
ft.
in. ft. in.
0
0
0
123
0 1
0 1
0
1
0
1
0
1
0
1
0 2
0
3
0 3
0 3
0 2
0
3
0
3
0 4
0 4
0 5
0 5
0
3
0
0 6
0
4
0 6
0
6
0 7
0
0
77
0
77
08
0 5
06
7
08
0 8
0
5
0 9
0 9
0 10
09
0 10
0 10
0
6
0 11
0 11
1 0
0 7
0 11
0 11
1
0 8
1 0
1 1
1
0 9
1
2
1 3
1
0 10
1 3
1 4
1 5
0 11
1 5
1 6
1 7
O QIM L7
0
0 7
1 0
1
2
0 8
1
2
1
3
9 9
1
4
1
0 10
1 6
1
0 11
1 8
19
13579
1 2
1 4
1 6
1 8
1 10
12345
0
I S
1 7
1 8
1
9
3
2
3 4
3 6
4 9
5 0
5 3
4 0
6 4
68
7 0
5 0
7 11
8 4
8 9
1∞∞ + LOO
0
1 10
1 11
20
2
0
3 8
3 10
4 0
3
0
5 6
5 9
4 0
7
4
77
8
8 0
50
9 2
9 7
10 0
6 0
9 6
10 0
10 6
7
11 1
11 8
12 3
8 0
12 8
13 4
14 0
9
0
14 3
15 0
15 9
6789
6 0
11 0
11
6
12 0
0 12 10
13
5
14 O
0
14 8
15
4
16 0
0
16 6
17 3
18 0
10 0
15 10
16 8
17 6
10 0
18 4
19 2
20 0
11 0
17 5
18 4
19 3
11 0
20
2
21 1
22 0
12 0
19 0
20 0
21 0
12 0
22 0
23 0
24 O
13 0
20 7
21 8
22 9
13 0
23 10
24 11
26 0
14
0
22 2
23 4
24 6
14
0
25 8
26 10
28 0
15 0
23 9
25 0
26 3
15
0
27 6
28 9
30 0
16 O
25 4
26 8
28
0
16
0
29 4
30 8
32 0
17 0
26 11
28 4
29 9 17 0
31 2
32 7
34 0
18
0
28 6
30 0
31 6 18 0
33 0
34 6
36 0
19 0
30 1
31 8
33 3
20 0
31 8
33 4
35 0
21 0
33 3
35 0
36 9 21 0
22 0
34 10
36 8
38 6 22
23 0
36 5
38 4
40 3
24 0
38 0
40 0
42 0
25 0
39 7
41 8
26 0
41 2
43 4
45 6
27 0
42 9
45 0
47 3
28
0
44 4
46 8
49 0
3280
29 0
45 11
48 4
50 9
30 0
47 6
50 0
52 6 30 0
23 78324 27828
19
34 10
36 5
38 0
20 0
36 8
38 4
40 0
38
6
40 3
42 0
0
40
42
0
44
43 9 25 0 45 10
+200
33
4
42 2
44 0
44 1
46 0
46 0
48 0
47 11
50 0
26 0
47 8
49 10
52 0
27 0
49 6
51 9
54 0
28 0
51 4
53
8
56 0
29
53
0
55 0
2
55 7
58 0
57 6
60 0
SUPERFICIAL MEASURE.
533

Lengths
2ft. 2in. 2ft. 4in. 2ft. 6in.
wide.
wide.
wide.
Lengths.
2ft. 8in. 2ft. 10in. 3ft. Oin.
wide. wide.
wide.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
0 1
02
2
0 2
0
1
0 2
02
0 3
02
0 4
0
0 5
0 2
0
5
0 5
06
0
3
0 6
0 7
0 7
0
3
0
08
09
0 4
08
0 9
0 10
0 4
0 10
0 11
1 0
0
5
0 10
0 11
1 0
0
5
1
1
1 2
1 3
0 6
1 1
1 2
1 3
0 6
1 4
1
5
1 6
0 7
1 3
1
4
1 5
0
7
1 6
1 7
1 9
08
1 5
1
6
1 8
08
9
1 10
2 0
09
1 7
1 9
1 10
09
2
0
2 1
2 3
0 10
1 9
1 11
2 1
0 10
2
2
2 4
2 6
0 11
1 11
2
1
23
0 11
2 5
2 7
2 9
1 0
2 2
2 4
2
0
4 4
4 8
3 0
66
7
0
257
2 6
0
6
4
0
88
9 4
10 0
5
0
10 10
11
8
12
6
12345
0
2
8
2.10
3 0
2 0
5
4
58
6 0
0
8 0
86
9 0
0
10
8
11 4
12 0
5 0
13 4
14 2
15 0
60
13 0
14 0
15 0
6 0
16 O
17 0
18 0
7
0
15 2
16 4
17 6
7
0
18
8
19 10
21 0
8 0
17 4
18 8
20 0
8 0
21 4
22 8
24 0
9 0
19 6
21 0
22 6
9 0
24 0
25 6
27 0
10 0
21 8
23 4
25 0
10
0
26 8
28 4
30 0
11 0
23 10
25 8
27 6
11 O
29 4
31 2
33 0
12 0
26 0
23 0
30 0
12 0
32 0
34 0
36 0
13 0
28 2
30 4
32 6
13 0
34 8
36 10
39 0
14
0
30 4
32 8
35 0
14 0
37 4
39 8
42 0
15 0
32 6
35 0
37
6
15 0
40 0
42 6
45 0
16 0
34 8
37 4
40 0
16 0
42 8
45 4
48 0
17 0
36 10
39 8
42
6
17 0
45 4
48 2
51 0
18 0
39 0
42 0
45 0
18
48 0
51 0
54 0
19 O
41 2
44 4
47 6
19 0
50 8
53 10
57 0
20 0
43 4
46 8
50 0 20 0
53 4
56 8
60 0
21 0
45 6
49 0
52 6
21 0
56 0
59 6
63 0
22 0
47 8
51 4
55 0
22 0
58
8
62 4
66 0
23 0
49 10 53 8
57 6
23 0
61
4
65 2
69 0
24 0
52 0 56 0
0
60 0
24 0
64 0
68 0
72 0
25 0
54 2
58 4
62
6
25 0
66 8
70 10
75 0
26 0
56 4
60 8
65 0 26 0
69 4
73 8
78 0
27 0
58 6
63 0
67 6
27 0
72 0
76 6
81 0
28 0
60 8
65 4
70 0
28 0
74 8
79 4
84 0
29 0
62 10
67 8
72 6
29 0
77 4
82 2
87 0
30 0
65 0
70 0
75 0
30 0
80 0
85 0
90 0
534
TIMBER TABLES.-No. 3.

Lengths.
3ft. 2in. 3ft. 4in. 3ft. 6in.
wide.
wide.
wide.
Lengths.
3ft. 8in. 3ft. 10in. 4ft. Oin.
wide. wide. wide.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
0 1
0 3
03
0 3
0
1
0 3
03
0 4
0
2
0 6
0 6
0 7
0 2
0 7
0 7
0 8
0 3
0
9
0 10
0 10
0
3
0 11
0 11
1 0
0
4
1
0
1 1
1 2
0
4
1 2
1 3
1 4
0
5
1 3
1 4
1 5
0
1 6
1 7
1 8
06
1 7
1 8
1 9
0 6
1 10
1 11
20
0 7
1 10
1 11
2
0
0 7
2 1
2 2
2 4
08
2 1
2 2
2 4
0 8
2 5
2
6
2
8
0
9
2 4
2 6
2
7
0 9
29
2.10
3 0
0 10
2 7
2 9
2 11
0 10
3 0
3 2
3 4
0 11
2 10
30
3 2
0 11
3 4
3 6
38
1
0
3 2
3 4
20
6 4
6 8
37
3 6
0
3
0
9 6
10 0
10 6
4 0
12 8
13 4
14 0
5
0
15 10
16 8
17 6
12345
0
3
8
3 10
4 0
0
7
4
7 8
8 0
0
11
0
11 6
12 0
0
14
8
15 4
16 O
5 0
18
4
19 2
20 0
60
19 O
20 0
21 0
6 0
22
0
23 0
24 0
7 0
22 2
23 4
24 6
7 0
25 8
26 10
28 0
8 0
25 4
26 8
28 0
29 4
30 8
32 0
9
0
28 6
30 0
31 6 9 0
33
0
34 6
36 0
10 0
31 8
33 4
35 0
0
10 0
36 8
38 4
40 0
11 0
34 10
36 8
38 6
11 0
40 4
42 2
44 0
12 0
38 0
40 0
42 0 12
44 0
46 0
48 0
13 0
41 2
43 4
45 6
13 0
47 8
49 10
52 0
14 0
44 4
46 8
49 0 14 0
51 4
53 8
56 0
15 O
0
47 6
50 0
52 6
15 0
55 0
57 6
60 0
16 0
50 8
53 4
56 0 16
58
61 4
64 0
17 0
53 10
56 8
59
6 17 0
62 4
65 2
68 0
0
57 0
60 0
63 0
18 0
66 0
69 0
72 0
21
22 72*** ***88
0
60 2
63 4
66 6 19
0
69 8
72 10
76 0
20 0
63 4
66 8
70
0 20 0
73 4
76 8
80 0
0
66 6
70 0
73 6 21 0
77 0
80 6
84 0
22
0
69 8
73 4
77 0 22 0
80 8
84 4
88 0
23 0
72 10
76 8
80 6 23 0
84 4
88 2
92 0
24 0
76 0
80 0
84 0 24 0
88 0
92 0
96 0
25
0
79 2
83 4
87 6 25 0
91 8
95 10
100 0
0
82 4
86 8
91 0
26 0
95 4
99 8
104 O
0
85 6
90 0
94 6 27 0
99 0
103 6
108 O
28 0
88 8
93 4
98 0 28 0
102 8
107 4
112 0
0
91 10
96 8
101 6 29 0
106 4
111 2
116 O
30 0
95 0
100 0
105
0 30 0
110 O
115 0
120 0
SUPERFICIAL MEASURE.
535

Lengths.
4ft. 2in. 4ft. 4in. 4ft. 6in.
wide.
wide.
wide.
Lengths.
4ft. 8in. 4ft. 10in. 5ft. Oin.
wide.
wide.
wide.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
0 1
0 4
0 4
0 4
0
1
0 4
0 4
0 5
0 2
08
08
0
9
0
2
09
09
0 10
0 3
1 0
1
1
1
1
0 3
1 2
1 2
1 3
0
4
1 4
1
5
1 6
0 4
1 6
0
5
1 8
06
2
1
12
1
9
1 10
0 5
1 11
2
2 3
06
2 4
705
122
8
2 1
2 5
2 6
0
7
2 5
2 6
2 7
07
2 8
2
9
2 11
0
8
2 9
2 10
3 0
0 8
3
1
3
2
3 4
09
3 1
3 3
3 4
0 9
36
3
7
3
9
0 10
3
3 7
3 9
0 10
3 10
4
0
4 2
0 11
3 9
3 11
4 1
0 11
4 3
4 5
4 by
12345
0
4 2
4 4
4
6
1 0
4
8
4 10
5 0
20
8 4
8 8
9 0
2 0
9 4
9 8
10 0
0
12 6
13
O
0
13 6
3 0
14
0
14 6
15 0
0
16 8
17 4
18 0
4 0
18 8
19 4
5 0
20 10
21
8
22 6
5 0
23 4
24 2
223
20
0
25 0
6 0
25 0
26 O
27 0
85ZEL CERSE 50.0 A
0
29 2
30 4
31 6
67
60
28 0
29 0
30 0
32 8
33 10
35 0
0
33 4
34 8
36 0
8 0
37 4
38 8
40 0
0
37 6
39 0
40 6
9 0
42 0
43
6
45 0
10 0
41 8
43 4
45 0
10 0
46 8
48
4
50 0
0
45 10
47 8
49 6
11 0
51 4
53 2
55 0
0
50 0
52 0
54 0
12 0
56 0
58 0
60 0
0
54 2
56 4
58 6
13 0
60 8
62 10
65 0
14 0
58 4
60 8
63 0
14 0
65 4
67 8
70 0
15 0
62 6
65 0
67 6
15 0
70 0
72 6
75 0
0
66 8
69 4
72 0
16 O
74 8
77
4
80 0
70 10
73 8
76 6
17 0
79 4
82 2
85 0
0
75 0
78 0
81 O
18 0
84 0
87 0
90 0
19 0
79 2
82 4
85 6
19 0
88 8
91 10
95 0
20 0
83 4
86 8
CO 0
O
200
93 4
96 8 100 0
21 0
87 6
91 0
94 6
21 0
98 0
101 6 105 0
22 0
91 8
95 4
99 0
22 0
102 8
106 4
110 0
23
95 10 99 8
103 6
23 0
107 4
111 2 115
24 0
100 O
0
104 O
108 0
24 0
112 0
116 0
120
25 0
104 2
108 4
112 6
25 0
116 8
120 10
125 0
28 0
29 0
30 0
26 0
27 0 112 6 117 0
116 8 121 4
120 10 125 8
125 0 130 0
130 0
108 4
112 8
117
121 6 27 0
126 0 28 0
130 6 29 0
135 0 30 0
0 26 0
121 4
125 8
126 0
130 6
130 0
135
0
130 8
135 4
140 0
135 4
140 2 145 0
140 0 145 0 150 0
536
TIMBER TABLES.-No. 3.

Lengths.
5ft. 2in. 5ft. 4in. 5ft. 6 in.
wide.
wide.
wide.
Lengths.
5ft. 8in. 5ft. 10in. 6ft. Oin.
wide. wide.
wide.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
0 1
0 5
0 5
0 5
0 1
0 5
0 5
0 6
0 2
0 10
0 10
0 11
02
0 11
0 11
1 0
3
1 3
1 4
1 4
0 3
1 5
1 5
1
6
0
4
1 8
1 9
1 10
0
4
1 10
1 11
2
0
0
5
2
1
2. 2
2 3
0 5
2 4
2 5
2 6
0
6
2 7
28
29
0 6
2 10
2 11
3
0
0
7
3
0
3 1
3 2
0 7
3 3
3 4
3 6
08
3 5
3 6
38
08
3 9
3 10
4 0
0
9
3 10
4 0
4 1
0
9
4 3
4 4
4
6
0 10
4 3
4 5
4 7
0 10
4
8
4 10
5
0 11
4 8
4 10
5
0
0 11
5 2
5 4
5 6
1 0
5
2
5 4
5 6
1 0
5 8
5 10
6 0
2 0
10
4
10
8
11
0
2
0
11
4
11 8
12 O
3 0
15
6
16 O
16 6
3 0
17 O
17 6
18 0
4 0
20 8
21 4
22 0
4 0
22
8
23 4
24 0
5 0
25 10
26 8
27 6
5 0
28 4
29 2
30 0
60
31 0
32
33 0
6 0
34 0
35 0
36 0
36 2
37 4
38
6
7 0
39
8
40 10
42 0
8 0
41 4
42 8
44 0
8 0
45 4
46 8
48 0
9 0
46 6
48 0
49 6 9 0
51 0
52 6
54 0
10 0
51
8
53 4
55 0
0
10 0
56 8
58 4
60 0
11 0
56 10
58 8
60 6
11 0
62 4
64 2
66 0
12
0
62 0
64 0
66 0
12 0
68 0
70 0
72 0
13
0
67 2
69 4
71 6
13 0
73 8
75 10
78 0
14 0
72 4
74 8
77 0
14 O
79 4
81 8
84 0
15
0
77 6
80 0
82 6
15 0
85 0
87 6
90 0
16 0
82 8
85 4
88 0
16 O
90 8
93 4
96 0
17
0
87 10
90 8
93 6
17 0
96 4
99 2
102
0
18 0
93 0
96 0
99 0
18 O
102 0
105 0
108 0
19 0
98 2
101 4
104 6 19 0
107 8
110 10
114 0
20 0
103 4
106 8
110
0
0
20 0
113 4
116 8
120
120 0
21 0
108 6
112 0 115
6
21 0
119 0
122 6
126
22 0
113 8
117 4
121 0
22 0
124 8
128 4
132 0
23 0
118 10
122 8
126 6
23 0
130 4
134 2
138 0
24 0
124 0
128 0
132 0
24 0
136 0
140 0 144
25 0
129 2
133
4
137
6
25 0
141 8
145 10
150 0
26 0
134 4 138 8
27 0
139 6
28 0
144 8
29
0
149 10
143 0
144 0 148 6
149 4 154 0
154 8 159
26 0
147
4
151 8
156 0
27 0
153 0
157 6
162 0
28 0
158
8
163 4
168 0
6 29 0
164 4
169 2
174 O
30 0
155 0
160 0 165
0
030 0
170 0
175 0
180 0
SUPERFICIAL MEASURE.
537

Lengths.
wide.
6ft. 2in. 6ft. 4in. 6ft. 6in.
wide.
Lengths.
wide.
6ft. 8in. 6ft. 10in. 7ft. Oin.
wide. wide.
wide.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
0 1
06
0 6
0 6
0
1
0 6
06
0 7
2
1 0
1
0
1
1
0 2
1 1
1 1
1 2
0
3
1 6
1 7
1 7
0 3
1 8
1
8
1
9
0
4
2 0
2 1
2
2
0 4
2
2
2 3
2 4
0 5
26
2 7
2 8
0 5
2 9
2 10
2 11
0
6
3 1
32
3 3
0 6
3 4
3 5
36
0 7
3 7
3
8
3 9
0 7
3 10
3 11
4
1
08
4 1
4 2
4 4
0 8
4 5
4 6
4 8
0
9
4 7
4 9
4 10
0 9
5 0
5 1
5 3
0 10
5 1
5 3
5 5
0 10
5
6
5 8
5 10
0 11
5 7
5 9
5 11
0 11
6
1
63
6 5
1 0
62
6 4
6 6
1 0
68
6 10
7 0
2 0
12 4
12 8
13
0
2 0
13 4
13 8
14
0
3 0
18 6
19 0
19
6
3
0
20 0
20 6
21
0
4 0
24 8
25 4
26 0
4 0
26 8
27 4
28 0
5 0
•
30 10
31
8
32 6
5 0
33 4
34 2
35 0
6
0
37 0
38 0
39 0
60
40 0
41 0
42 0
7 0
43 2
44 4
45 6
7
0
46 8
47 10
49 0
8
0
49 4
50 8
52 0
8 0
53 4
54 8
56 0
9
0
55 6
57 0
58 6
9 0
60 0
61 6
63 0
10 0
61 8
63 4
65 0
0
10 0
66 8
68 4
70 0
11
0
67 10
69 8
71 6
11 O
73 4
75 2
77 0
12 0
74 0
76 0
78 0
12 0
80 0
82 0
84 0
13 0
80 2
82 4
84 6
13 O
86 8
88 10
91 0
14 0
86 4
88 8
91 0
14 O
93 4
95 8
98 0
15
0
92 6
95 0
97
6
6
15 0
100 0
102 6
105 0
16 0
98 8
101 4
104
0
16 O
106 8
109 4
112 0
17 0
104 10
107 8
110 6
17 O
113 4
116 2
119 0
18 0
111 0
114 0
117 O
18 0
120 0
123 0
126 0
19
0
117 2
120 4
123 6
19 O
126 8
129 10 133 0
20 0
123 4
126
8
130 0
20 0
133 4
136 8
140 0
21 0
129 6
133 0
136 6
21 0
140 0
143 6
147 0
22
0
135 8
139 4
143 0
22 0
146 8
150 4
154 0
23 0
141 10
145
145 8
149 6
23 0
153 4
157 2 161 0
24 0
148 0
152 0
156 O
24 0
160 0
164 0 168 0
25 0
154 2
158 4
162 6
25 0
166 8
170 10
175 0
26 0
160 4 164 8
169 0
26 0
173 4
177 8
182 0
27 0
166 6 171 0
175 6
27 0
180 0
184 6
189 0
28
172 8
177 4
182 0
28 0
186 8
191 4
196 0
29 0
178 10 183 8 188 6
29 0
193 4
198 2
203 0
30 0
185 0 190 0 195 0
30 0
200 0
205 0
210 0
2 L
538
TIMBER TABLES.-No. 3.

Lengths
wide.
7ft. 2in. 7ft. 4in. 7ft. 6in.
wide.
wide.
Lengths.
7ft. 8in. 7ft. 10in. 8ft. Oin.
wide. wide. wide.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in. ft. in.
ft. in.
0 1
0 7
0 7
0 7
0
1
0 7
07
08
0 2
1 2
1 2
1 3
0 2
1 3
1 3
1
4
0 3
1 9
1 10
1 10
0
3
1 11
1 11
2 0
0 4
2 4
2 5
2 6
0 4
2 6
2 7
2
8
0 5
2 11
3 0
3 1
0
5
3 2
3 3
3
0
6
3 7
38
3 9
06
3 10
3 11
4 0
0 7
4 2
4 3
4 4
0
7
4 5
4 6
4 8
08
4 9
4 10
5 0
0 8
5 1
5 2
5 4
0
9
5 4
5 6
5 7
0 9
59
5 10
6 0
0 10
5 11
6 1
63
0 10
6 4
6 6
6 8
0 11
66
68
6 10
0 11
7 0
7 2
77 4
1 0
7
2
7 4
7 6
1 0
7 8
7 10
8 0
2 0
14 4
14 8
15 0
2 0
15
4
15 8
16 0
3 0
21 6
22 0
22 6
3 0
23 0
23 6
24 0
4 0
28 8
29 4
30 0
4 0
30 8
31 4
32 0
5 0
35 10
36 8
37 6
5 0
38 4
39 2
40 0
6
0
43 0
44 0
45 0
6
0
46
0
47 0
48 0
7 0
50 2
51 4
52 6
17
0
53 8
54 10
56 0
8
0
57 4
58 8
60 0
8 0
61 4
62 8
64 0
9 0
64 6
66 0
67 6
9 0
69 0
70 6
72 0
10
0
71 8
73 4
75 0
10 0
76 8
78 4
80 0
11 0
78 10
80 8
82 6
11 0
84 4
86 2
88 0
12 0
86 0
88 0
90 0
12 0
92 0
94 0
96 0
13 0
93 2
95 4
97 6
13 0
99 8
101 10
104 O
14 0
100 4
102 8
105 0
14
107 4
109 8
112 0
15 0
107 6
6
110 0
112 6
15 0
115 0
117 6
120
120 0
16 0
114 8
117 4
120 0
16 O
122 8
125
4
128 0
17 O
121 10
124 8
127 6
17 0
130 4
133
2
136 0
18 0
129 0
132 0
135 0
18 0
138 0
141 0
144 0
19 0
136 2
139 4
142 6
19 0
145 8
148 10
152 0
20 0
143 4
146 8
150 0 20 0
153 4
156 8
160
160 0
21 0
150 6
154 0
22 0
157 8
157
161 4 165
621 0
161 0 164 6
168 0
0
22 0
168 8 172 4
176 0
23 0
164 10
168 8 172 6
23 0
176 4
180 2
184 0
24 0
172 0
176 O
180 0
24 0
184 0
188 0
192 0
25 0
179 2
183 4
187 6
25
0
191 8
195 10
200
200 0
26 0
186 4
190 8 195 0
26 0
199 4 203 8
208 0
27 0
193 6
198 O
202 6
27 0
207 0 211 6
216 0
28 0
200 8
205 4
210 O
28 0
214 8
219 4
224 0
29 0
207 10
212 8
217 6
29 0
222 4
227 2
232 0
30 0
215 0
220 0
225 0
30 0
230 0
235 0
240
240 0
SUPERFICIAL MEASURE.
539

8ft. 2in. 8ft. 4in. 8 ft. 6in.
Lengths.
wide.
wide.
wide. Lengths.
8ft. 8in. 8ft. 10in. 9ft. Oin.
wide. wide.
wide.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
0 1
08
08
0 8
0 1
08
08
0 9
0 2
1 4
1
4
1 5
0 2
1
5
5
1 6
0
3
2
0
2 1
2 1
0 3
2 2
2 2
2 3
0
4
2
8
2
9
2 10
0 4
2 10
2 11
3 0
0
5
3 4
3 5
3 6
0 5
3 7
38
3 9
0
6
4
1
4 2
4 3
06
4 4
4 5
4 6
0 7
4
9
4 10
4 11
0 7
5 0
5 1
5
3
08
5
5
5 6
5 8
08
5 9
5 10
6 0
0 9
1
6 3
6
4
09
6 6
6 7
6 9
0 10
6
9
6 11
7 1
0 10
7 2
7 4
7 6
0 11
7 5
7 7
7
9
0 11
7 11
8
1
8 3
1
0
8 2
8 4
8 6
1 0
88
8 10
9 0
2 0
16 4
16
8
17 0
20
17 4
17 8
18 O
3 0
24 6
25 0
25 6
3 0
26 0
26 6
27 0
4
32 8
33 4
34 0
4 0
34 8
35 4
36 0
5 0
40 10
41 8
42 6
5 0
43 4
44 2
45 0
60
49 0
50 0
51 0
60
52 0
53 0
54 0
7
0
57 2
58 4
59 6
7 0
60 8
61 10
63 0
8 0
65 4
66 8
68 0
8 0
69 4
70 8
72 0
9 0
73
6
75
76 6
9 0
78 0
79 6
81 0
10
0
81 8
83 4
85 0
10 0
86 8
88 4
90 0
11 0
89 10
91 8
93 6
11 O
95 4
97 2
99 0
12 0
98 0
0
100 0
102 0
12 0
104 0
106 0
108 0
13 0
106 2
108
4
110
110 6
13 0
112 8
114 10
117 0
14 O
114 4
116 8
119 O
14 O
121 4
123 8
126 0
15 0
122 6
125 0
127 6
15 0
130 0
132 6
135 0
16 O
130 8
133 4
136 0
16 0
138 8
141 4
144 0
17 0
138 10 141 8 144 6
17 0
147 4
150 2
153
153 0
18 0
147 0 150 0
153 0
18 0
156 0
159 0
162 0
19 0
155 2 158 4
161 6
19 0
164 8
167 10
171 0
20 0
163 4
166 8
170 0
20 0
173 4
176 8
180 0
21 O
171 6
175 0
178 6
21 0
182 0
185 6 189 0
22 0
179 8
183 4
187 0
22 0
190 8
194 4 198 0
23 0
187 10 191 8
195 6
23 0
199 4
203 2207 0
24 0
196 0 200 0
204 0
24 0
208 0
25 0
204 2
208 4
212 6
25 0
216 8
212 0 216 0
220 10 225 0
26 0
212 4
216 8 221 0
26 0
225 4
27 0
220 6
6
225 0 229 6
27 0
234 0
229 8
238
234 0
6
243 0
28 0
228 8 233 4 238
0
28 0
242 8
247 4
252 0
29 0
236 10 241 8 246 6
29 0
251 4
256 2 2
261
30 0
245 0 250 0 255 0
30 0
260 0
265 0 270 0
540
TIMBER TABLES.—No. 3.

Lengths.
9ft. 2in. 9ft. 4in. 9ft. 6in. Lengths. 9ft. 8in. 9ft. 10in. 10ft. Oin.
wide.
wide.
wide.
wide.
wide.
wide.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
ft. in.
0 1
09
0 9
09
0 1
09
09
0 10
0 2
1
6
1 6
1 7
0 2
1
7
1 7
1 8
0 3
2 3
2 4
2 4
0
3
2
5
2 5
2
6
0
3 0
3 1
3 2
0
4
3
2
3 3
3 4
3 9
3 10
3 11
0 5
4 0
4 1
4
2
0 6
4 7
4 8
4 9
0
6
4 10
4 11
5 0
0
7
5 4
5 5
5 6
0 7
5
7
5 8
5 10
0 8
6 1
62
6 4
0
8
6
5
6 6
68
0 9
6 10
7 0
7 1
0 9
7
3
7 4
7 6
0 10
7 7
7 9
7 11
0 10
8
0
8
2
8 4
0 11
8 4
86
88
0 11
8 10
90
9 2
1 0
9
2
9 4
96
1 0
9
8
9 10
10 0
2 0
18
4
18 8
19 0
2 0
19 4
19 8
20 0
3 0
27 6
28 0
28 6
3
0
29
29 6
30 0
4 0
36 8
37 4
38 0
4 0
38 8
39 4
40 O
5
0
45 10
46 8
47 6
5 0
48 4
49 2
50 0
6 0
55 0
56 0
57 0
6 0
58
0
59 0
60 0
7
64 2
65 4
66 6
77
0
67
8
68 10
70 0
8 0
73 4
74 8
76 0
8
0
77 4
78 8
80 0
9
0
82 6
84 0
85 6
9 0
87 0
88 6
90 0
10 0
91 8
93 4
95 0 10 0
96 8
98 4
100 0
13
HRRAD
11 0
100 10
102 8
104 6 11 0
106 4
108 2
110 0
12
0
110 0
112 O
114 0
12 0
116 0
118 O
120 0
0
119 2
121 4
123 6
13 0
125 8
127 10
130 0
14
0
128 4
130 8
133 0
14 0
135 4
137 8
140 O
15 0
137 6
140 0
142 6
15 0
145 0
147 6
150 0
16 O
146 8
149 4
152 0
16 O
154 8
157 4
160 0
17 0
155 10 158 8
161 6
17 0
164 4
167 2
170 0
18 0
165 0
168 O
171 0
18 0
174 0
177 O
180 0
19 0
174 2
177 4
180 6
19 0
183 8
186 10
190 0
20 0
183 4
186 8
190 0
20 0
193 4
196 8
200 0
21 0
192 6
196 O
199 6
21
21
0
203 0
206 6
210 O
22 0
201 8
205 4
209 0
22 0
212
8
216 4
220 0
23 0
210 10
214 8
218 6
23 0
222 4
226 2
230 0
24 0
220 0
224 0 228
0
24 0
232 0
236 0
240 0
25 0
229 2
233 4
237
6
25
25 0
241 8
245 10
250 0
26 0
238 4
242 8
247 0
26 0
251 4 255 8
260 0
27
247 6
252 0
256 6
27 0
261 0 | 265
6
270 0
28 0
256 8
261 4
266 0
28 0
270 8
275
4
280 0
29 0
265 10
270 8
275 6
29 0
280 4
285
285
2
290 0
30 0
275 0
280 0
285 0
30 0
290 0
295 0
300 0
ARTIFICERS' WORK.
541
CHAPTER XVI.
ARTIFICERS' WORK.
SECT. I.-Bricklayer and Excavator's Work.
THE standard measure for Brickwork in London is the rod of
16 ft. 6 in. square, which dimension being multiplied into itself
produces 272 ft. 3 in., but the odd 3 inches are never taken into
account. It is therefore always considered as 272 superficial feet,
at 1 brick, or 13 inches thick, or 306 feet cube, viz., 272 ft. by
1 ft. 1 in. All the other thicknesses are reduced to this standard,
as shown hereafter in the manner of taking the dimensions and ab-
stracting the work.
In measuring bricklayers' work, it is usual to begin by taking
the excavations; first, for the basement story, if any, which is
stated as digging and throwing out or wheeling away; the ground
for sunk stories, according to circumstances; next the excavations
for footings to walls.
It is customary in taking the digging to footings of walls, to
allow about six inches on each side, over and above the thickness
of the walls, for room to work them; but if they are deep, and the
ground bad and loose, allow nine inches on each side on account of
its falling in. But in sunk stories only allow to the extent of the
footings, except in very loose ground.
In taking the dimensions, the length, depth, and width must be
measured as before described, and reduced to the yard cube of 27
feet, viz., 3 ft. by 3 ft. by 3 ft.
Claying of Vaults, by the yard square of 9 feet, describing the
thickness, 3 ft. by 3 ft.
In measuring digging in sideling ground, where the areas of the
two ends of the excavation are unequal, the cubic content must be
found by the following rule:-
Multiply the sum of the extreme areas, plus four times the mid-
dle area, by one-sixth of the length, and the product will be the
answer required.
Ex.-To find the cubic content of the excavation A B C D E F
542
ARTIFICERS' WORK.
for the sunk stories of a house, to be built on the side of a
hill:-

6.0
84.0
8.0
120.0
112.0
B
140 x 10
2
700
84 × 6
2
252
112 x 8
2
140.0
G
H
952 sum of extreme areas
= 1792 four times middle area
2744
120 length
54880
2744
6)329280
27) 54880 ( 2032 yards 16 feet
54
88
81
70
54
|
16
As an illustration of the correctness of the rule, let us take the
same example on a different principle of measurement. The solid
BRICKLAYER.
543
ABCDEF may be divided into the two prisms GHIBED,
and EFCIHD and the pyramid DA HG. Taking each of
these separately, we have—
Prism G H IBED=
84 x 4 x 120
20160
2
Prism EF CIHD
120 × 6 × 84
2
= 30240
56 × 4 120
Pyramid DA HG =
X
4480
2
3
or 2032 yards 16 feet, as before.
Total. 54880 cubic ft.
In measuring brickwork, always begin with the foundations, then
proceed with measuring each story separately (or as high as the
wall continues of the same thickness), as solid work, according to
its respective thickness; then add for all projections, as breasts of
chimneys, &c., deducting the openings, but not the flues, as the
extra trouble and the pargetting is deemed equivalent to the defi-
ciency of materials; but deduct the openings of doors, windows, &c.
If the house or building be rectangular, measure two walls the
whole length of the external face, and the other two internally, so
as to get the true cubical contents.
But in measuring for labour only, the external face of the work
is girt, and multiplied into the height and thickness, to pay for the
extra labour of plumbing the angles, andworking the returns fair.
In measuring walls that are faced with superior bricks, the walls
are first measured as common work, and then the superficial quan-
tity of facing is taken, as hereafter shown, and is valued by con-
sidering the facing as two-thirds of a brick thick, and deducting
the common brickwork from the price thereof, the same thickness,
viz., two-thirds of a brick; by which the value per foot superfi-
cial is ascertained.
In measuring circles, or semicircles, they are marked accordingly
in the measuring-book, thus:
with the diameters figured.
3.4
or 3.4
To measure angle chimneys, draw lines on the floor, parallel to
the two sides of the room, cutting the parts intersected by the chim-
ney; take either side by the height of the floor, and half the other
(the work forming a triangle) for the thickness, either as the
number of bricks, or as cube work, which, by the directions before
544
ARTIFICERS' WORK.
given, prove it to be exactly the same: consequently, if the pro-
jection should not amount to any certain number of half-bricks,
it would be best to take it as a cube dimension. In all cases it is
supposed that the walls are measured before the projecting chim-
neys are taken, which is the usual custom.
In taking the dimensions of vaults, measure the abutments, or
side walls, to the springing of the arch, then bend your rods round
the soffit of the arch; and add once and a half the thickness there-
of, by which you obtain the average girt of the arch; then take the
length clear of the walls; but if the arch is turned over one or both
walls, add the thickness thereof to the length of the arch. But in
taking the height of the walls, measure to the crown of the arch,
without making any deduction for the declivity of the arches, on
account of the additional trouble and waste of bricks, in cutting
and fitting them to the curved soffit of the arch. Likewise, in
deducting openings with circular heads, the dimensions should
only be taken to the springing of the arches, on account of the
trouble and waste of bricks in fitting them to the arches.
Drains to be taken and reduced as common brickwork if built
with mortar.
Shafts of chimneys are measured as solid work.
*
Ovens and coppers are measured as solid cube brickwork, de-
ducting the ash-holes only. Tiles, Welsh lumps, and fire bricks
are to be allowed as extras.
In these, or any other brickwork that it is considered best or
most convenient to measure by the cubic foot, multiply the solidity
by 8, the number of 1 inches in a foot, and divide it by 9, the
number of 1½ inches in 13 inches, which will reduce it to the
standard of 1½ brick or 13 inches in thickness.
In measuring brickwork no allowance is to be made in quantity
for small or difficult works. Timbers inserted in the walls are not
to be deducted. When plates are bedded in the walls, two inches
to be allowed for ditto where no brickwork is over them. All sills
and stone strings are measured in.
All cuttings to be measured superficial; as outside splays, cut
and rubbed to show fair, or inside ditto rough cut for battens, &c.
Birds' mouths at per foot run, being notched to fit.
Facings of all descriptions to be measured extra by the foot
superficial; in which case the reveals are also measured, except
where intended to be stuccoed.
* This method is in common use amongst surveyors; but it would be far more con-
sistent to measure the actual quantity of brickwork, allowing for the extra labour in
price.
BRICKLAYER.
545
Gauged arches to doors, windows, &c., are also measured by the
foot superficial.
Groins are measured as common work, only taking the run of
cut groins at per foot.
Bricknogging, by the yard square of nine feet, including the
timbers.
Brick paving, ditto, ditto.
Facias, beads, and quirks, dentil or plain cornices, &c., measured
and valued by the foot run.
TILING.
Plane and pan tiling are measured by the square of 100 feet.
In measuring plane tiling—
Allow for the eaves 4 inches extra.
Ditto for dripping do. 6 inches extra.
Ditto for all cuttings, hips, &c., 3 inches extra.
Ditto for valleys, 12 inches extra.
In measuring pan tiling―
Allow for the barge per foot run.
Ditto for heading to barge per foot run.
Ditto for cutting to hips and splays per foot run.
Ditto for hips and ridges per foot run.
Number the hip hooks, which should be painted three times
in oil.
Ditto T nails, ditto.
Deduct for chimneys, and deduct and add for dormers.
If the roofs are hipped, take the length at the bottom of the
sides, and not measure the end; the two side triangles being equal
to the hipped end one.
VALUATION OF BRICKLAYERS' WORK.
CALCULATION OF MATERIALS.
Digger.—27 cubic feet, or one cubic yard, is called a single
load, and contains 21 striked bushels. Two cubic yards = one
double load.
In estimating the cubic content of excavation required to form
a given amount of embankment, due regard must be paid to the
nature of the soil of which the embankment is to be formed.
The following may be safely taken as average rates of the alter-
ation in bulk of various soils when excavated and carried into
embankment.
546
ARTIFICERS' WORK.
Clays.—Compression about one-tenth of the original bulk in
excavation.
Gravels.-Compression about one-twelfth of the original bulk in
excavation.
Sand occupies the same space in bank as in excavation.
Chalk.-Slight increase of the original bulk in excavation, pro-
portionate to the size and hardness of the fragments.
Rock.-Increase about one-half of the original bulk in excava-
tion, according to the size of the fragments.
234 cubic feet of sand weigh one ton.
213
do.
gravel
do.
17
do.
clay
do.
13
do.
chalk
do.
18
do.
night-soil do.
Concrete is made of ground stone lime and sharp gravel, with a
proper proportion of sand, mixed in the proportion of five or six
parts of gravel to one of lime, according to the nature of the lime
and the proportion of sand mixed with the gravel. Its quality is
much improved by the addition of smith's ashes, or any material
containing iron; and for this reason ferruginous gravel is to be
preferred whenever it can be obtained.
A cubic yard of concrete, containing 27 cubic feet when mixed,
requires 34 cubic feet of gravel, sand, and lime. Therefore, at the
proportion of six of gravel to one of lime, a cubic yard of concrete
will require 1.1 cubic yard of gravel and sand and three bushels
of lime.
Concrete expands slightly in slaking; but this expansion is too
trifling to be taken into account in framing an estimate.
Size and Weight of various Articles.


Length.
Breadth. Thickness. Weight.
ft.
in.
ft. in.
10-inch
Stock bricks
Paving do.
Dutch Clinkers
12-inch paving tiles
Pan tiles
Plain tiles
do.
Pan tile laths, per 10 ft. bundle
Ditto, per 12 ft. bundle
•
each
do.
0
•
832343 0
41
ft. in.
0 21
lbs.
OZ.
5 0
0
9
0
4
0
12
4 0
•
do.
0 61
0 3
0 13
1 8
do.
•
do.
•
do.
do.
흡흡​흡흡
​0 112
0 112
0
13
0
0 93
0
0
1
8
9
1 14 0
0
0 101
0
ager*-
5
4
2
5
120
0
1
0
1
4
6
144 0
0
1
5 0
A bundle contains 12 laths.
Plain tile laths, per bundle
500
0
0 1
0
01
3 0
Thirty bundles of laths make a load
BRICKLAYER.
547
A bricklayer's hod measures 1 ft. 4 in. x 9 in x 9 in., and will
hold 20 bricks.
A single load of sand is 27 cubic feet, or one cubic yard.
A double load of sand is 54 cubic feet, or two cubic yards.
A measure of lime is 27 cubic feet, or one cubic yard, and con-
tains from 16 to 18 bushels.
QUANTITIES, ETC.
A rod of brickwork measures 16 ft. 6 in. x 16 ft. 6 in., or 272
ft. 3 in. superf., 1 brick or 13 inches thick, called the standard
thickness, or 306 cubic feet, or 11 cubic yards.
A rod of brickwork laid to a 12-inch gauge, i.e., four courses to
measure one foot in height requires 4353 stock bricks.
Ditto, laid to 11-inch gauge, requires 4533 stock bricks.
A foot of reduced brickwork requires 16 bricks.
These calculations are made without allowance for waste; and
indeed there is very little, as nearly every part is worked in, and
much space is occupied by timbers, flues, &c., for which no deduc-
tion is made in measurement; and therefore in the erection of
dwelling-houses containing flues and bond timbers, 4300 stocks is
quite sufficient, and this is the usual number allowed for a rod of
brickwork.
5370 stocks to the rod, if laid dry.
4900 do. in wells and circular cesspools.
A rod of brickwork, laid four courses to gauge 12 inches, con-
tains 235 ft. cube of bricks, and 71 ft. cube of mortar; and the
average weight is about 15 tons.
A rod of brickwork requires 1 cubic yard of chalk lime and
three loads of sand; or one cubic yard of stone lime, and 3 loads
of sand; or 36 bushels of cement, and 36 bushels of sharp sand.
A cubic yard or load of mortar requires nine bushels of lime and
one load of sand.
The proportion of mortar or cement, when made up, to the ma-
terials in their mixed state, is as two to three.
Facing requires 7 bricks per foot superficial.
Gauged arches 10 do.
do.
Bricknogging per yard superficial, requires 30 bricks on edge, or
45 laid flat.
Description.
Stock bricks, laid flat
Do.
PAVING.
Number required.
per yard
36
on edge.
52
وو
548
ARTIFICERS' WORK.
Description.
Paving bricks, laid flat
Do.
Dutch clinkers
12-inch paving tiles .
10-inch do.
on edge
•
وو
TILING.
Number required.
per yard
36
82
99
140
وو
وو
وو
9
13
•
Number
Gauge.
required.
inches.
Pan tiles, per square
12
150
Ditto
ditto
11
164
Ditto
ditto
10
180
A square of pan tiling requires one
bundle of laths and 14 hundred of 6d.
nails.
Plain tiles, per square
1
4
600
Ditto
ditto
3 3/1/20
700
Ditto
ditto
3
800
Ditto
ditto
laid flat
210
A square of plain tiling requires one
bundle of laths and nails, one peck of tile
pins, and three hods of mortar.
CALCULATION OF LABOUR.
Digger. The amount of digging which a man can perform in a
day depends so much on the nature of the soil on which he has to
operate, that it is almost impossible to fix a constant for this de-
scription of labour: the following data may, however, serve as a
slight guide.
In loose ground a man will throw up about ten cubic yards per
day; but in hard or gravelly soils, where hacking is necessary, from
three to five cubic yards, according to the hardness of the ground,
will be a fair day's work.
Wheeling is estimated by the run of 20 yards. A gang of three
men, two for filling and one for wheeling, will remove about 30
yards per day to this distance; and the labour of removing earth
may be calculated according to distance, allowing three men to the
first run, and an additional man for every twenty yards of distance.
The following table, although far from complete, contains con-
stants for all the principal descriptions of bricklayer's work.
SLATER.
549
Concrete.-Labour in mixing, wheeling, throwing
in from a stage, and puddling (where required to
be done), including erection of scaffolding, per
yard cube
Brickwork, per rod
Extra labour to malm facings
Paving.
Brick paving laid flat in sand .
Do. laid on edge in sand
Do. laid flat in mortar
Do. laid on edge in mortar
per yard
وو
وو
وو
Constant.
To be multiplied by
the rate of wages for
a labourer per day.
.335
To be multiplied by
the rate of wages for
a bricklayer and la-
bourer per day.
4.941
To be multiplied by
the rate of wages for
a bricklayer per day.
.014
To be multiplied by
the rate of wages for
a bricklayer and la-
bourer per day.
.046
.075
.056
•
.084
Paving-brick paving laid flat in sand.
.046
29
Paving-brick paving laid on edge in sand, per yard
.106
Do. laid flat in mortar
.075
""
Do. on edge in mortar
.121
Clinker paving on edge in sand
10 or 12 inch tile paving
وو
وو
وو
.132
.010
Tiling.
Pan tiling laid dry
per square
.422
Do. pointed outside
.685
وو
Do. pointed inside and outside
.790
وو
Plain tiling laid to a 4-inch gauge
.739
Do.
Do.
to a 34-inch gauge
to a 3-inch gauge
.764
وو
.790
SECT. II.-Slater's Work.
Slating is measured superficially, and charged per square of 100
feet.
In measuring, allow for the eaves whatever the bottom course
measures, and for the hips and valleys measure their length by 12
inches, viz., six inches on each side; also the length of all irregular
angles, as chimneys, dormers, &c., by six inches wide, as a
fair allowance for cutting and waste.
For circular slating allow one-third extra.
550
ARTIFICERS' WORK.

VALUATION OF SLATER'S WORK.
Table of Materials and Labour.
Average
1200 will
Average sizes of Slates.
gauge
when laid.
cover
squares.
Weight per
thousand of
1200 in tons.
Number
required to
cover one
square.
Nails required to a square.
Iron, cast
or wrought,
at per
hundred.
Constant.
To be multi-
plied by the
Copper, at
per lb.
rate of wages
for a slater
per diem.
ft. in. ft. in.
in.
lbs.
Doubles
1
1 by 0 6
5/1/2
21
480
480
5
Ladies
1
3 08
7
""
Countesses
1
8 0 10
""
10
7호
​Duchesses
2 0 1 0
11
10
122
11
280
280
160
320
33
""
3
127
254
22
коко
Tavistock
31/2
A ton will
cover.
Imperials
2
6
2 0
""
Rags and Queens
3
0 2 0
""
Westmorelands, various
21 to 21
21
.173
.155
.137
.119
CARPENTER AND JOINER.
551
Example.-To find the value of a square of duchess slating
copper nailed.
No. 127. Duchesses, at per thousand.
2 lbs. of copper nails, at per lb.
£ s. d.

per cent. profit
Labour on above, at per day.
Value per square
£
SECT. III.—On Carpenters' and Joiners' Work.
MEASURING.
There are two methods of measuring carpenters' work: one
by taking the superficial contents of roofs, floors, partitions, &c.,
at per square of 100 feet for the labour and nails, and then the
cube contents of the timber without labour; the other, by mea-
suring the cube contents of the timber as cube fir and labour,
framed, &c. &c.
If the scantlings of the timber are small or light, it will pay the
carpenter best to measure the roofs, floors, &c. as labour and nails,
and the timber as no labour; but if the scantlings of the timber
are large and heavy, then it will be more to his advantage to
measure the work as timber, with the particular labour thereon, as
follows:-
If the work is measured as timber and labour, the scantling of
each piece is taken as cube fir or oak and labour, and entered
accordingly; as
Cube fir, or oak, in ground joists, bonds, lintels, plates, &c., labour
and nails, included.
Do. framed in roofs, partitions, naked floors, &c., labour and nails
included.
Do.
do.
Do. wrought and framed
Do. wrought, framed, and rebated
truss framed
do.
do.
do.
Do. wrought, framed, rebated, and beaded, labour and nails
included.
Do. in door-cases.
Oak trusses put into girders, per foot run, stating their size, as 4
inch square, &c.
In measuring for labour and nails to roofs, naked framed floors,
ceiling floors, quarter partitions, or any other rough framed work,
552
ARTIFICERS' WORK.
the dimensions should be taken from the exteme ends of the timber
each way, to ascertain the superficial contents thereof, as labour
and nails at per square of 100 superficial feet. The openings to
chimneys, staircases, &c. are not to be deducted, as the trouble
of framing the trimmers and the joists into those openings
is fully equivalent to running the joists through them. The
same rule must be observed in taking the labour and nails in
quarter partitions, as doors, &c., which must be entered in the
measuring-book and valued according to the description of the
work, as follows :—
For Roofs.
Labour and nails to common shed roofing.
Do.
do.
with purlins.
Do.
do.
with purlins and struts.
Do.
do.
rafters.
Do.
do.
common span or valley with purlins and
span with collars, dovetailed into sides of
rafters notched to receive purlins, filled in with common rafters.
do. framed with principals, king posts, two struts
Do.
and purlins, filled in with common rafters.
Do.
Do.
do. do. with king and queen posts.
do.
For Floors.
common kerb roof.
Labour and nails to fir ground joists, bedded and not framed.
Do.
do.
Do.
do.
stairs.
Do.
do.
Do.
do.
and ceiling joists.
Do.
do.
and ceiling joists.
pinned down on plates and framed to chimneys.
single framed floors, trimmed to chimneys and
with girders and cased bays.
framed floors, with girders, binding, bridging,
to common framed ceiling floors, with binding
Quarter Partitions.
Labour and nails to common 4 in. quarter partitions.
Do.
do.
Do.
do.
5 in.
6 in.
do.
do.
Do.
do.
truss framed with king posts.
Do.
do.
do.
with king and queen posts.
If oak is used, describe it.
Having taken the labour and nails, you must then proceed to
take the timber therein, which must be entered as cube fir, or oak
without labour.
CARPENTER AND JOINER.
553
In roofs, it is customary to take the highest timbers first, as the
ridge piece, hips, &c., next the rafters, and so proceed downwards
to the ceiling floor.
In partitions, floors, &c., begin with the timbers of the largest
scantlings. Wherever a tenon is made, the length must be taken
from the ends of the tenon, and not from the shoulders. Likewise
the length of joists, including the part in the wall.
In measuring king and queen posts, take the whole length by
the scantling of the shoulders. The parallel pieces sawed out for
the abutment of the principal rafters must be deducted, should
they exceed 2 feet in length and 2 inches in thickness; but
taken 5 or 6 inches short of the length between the shoulders,
as the saw cannot enter with much less waste. But if the pieces
are less than 2 inches thick, no deduction must be made, they
not being worth more than the labour of cutting them out.
ROOFS.
Hips and valley to be taken at per foot run, for cutting and
waste.
All plates, lintels, discharging pieces, to be taken as bond
timber.
Gutter plates, diagonal ties, dragging pieces or braces, struts,
and tie-beams, as fir framed.
Deduct half the length of bond timbers running through
openings.
Allow the length of dovetails or scarf in bond timber, but only
taken as bond timber.
Fixing iron straps, screw bolts, hanging ditto, and all iron-work,
to be taken and allowed extra.
FLOORS.
Oak trusses, let into breastsummers, to be taken at per
foot run.
at
Oak king or queen posts, let into brestsummers, each
Girders sawed down, reversed and bolted, per foot run
extra.
Letting in screw-bolts, plates, &c., each extra.
Common or herring-bone strutting between the joists, per foot
run extra.
Furrings to ceilings, quarter partitions, battenings to walls, &c.,
are measured by the square, including labour and nails, and valued
according to the thickness of the deals, used from 2 to 3 inches
2 M
554
ARTIFICERS' WORK.
thick. Describe the battening either as framed or nailed only, or
if plugged, or if with horizontal backings.
All wall-hooks and holdfasts to be allowed extra.
Centring to groins, vaults, recesses, &c.-Take the depth by
the circumference for the superficial dimensions, which is valued
at per square for use and waste, materials and time. If taken in
this way, the whole of the vaults or recesses must be taken,
although the same centring might have been used. But where
there are a number of vaults or recesses of the same size, the
fairest way is to allow the whole of the materials and time, or if
any trifling alteration only is wanted, to allow the time expended
in doing it.
Bracketing to cornices, to be measured at per foot
superf., according to the girt, viz., 24 inches by the
length, as whole or 1½ inch deal, according to the thick-
ness of deals used. Some allow the bracketing the
same girt as the cornice.
inches.
6
11/1
9
64
11/1
244
Cradling for entablatures, measured and charged per foot superf.,
according to their thickness.
All circular bracketing, cradlings, &c., to be charged double
those of straight work.
Ashlering at per foot superf., according to the thickness of the
deals used.
Gutters and bearers.-Measure the length, then the breadth
of the bottom and half the eaves-board.
Gutters between the roofs having two eaves-boards, one on each
side, take for the width of gutter one of them.
Arris or fillet gutters per foot superf.
Water trunks per foot run; describe size, and allow for laps and
half the length of shoe.
Sound boarding.-Measure the dimensions between the joists at
per foot superf.; observe if single or double fillets.
Chimney grounds, per foot superf.
If the side grounds are very narrow, framed only for small
mouldings, take them by the foot run, and enter them as narrow
framed grounds.
Hinges to be numbered and described.
Skirtings, either plain or raking, taken at per foot superf.
If on narrow grounds, take them per foot run.
If plugged to the walls, allow extra for plugging.
Moulded plinths.-Measure the square part by the length and
width, and enter it. Whole deal, wrought one side, rebated and
backed plinth. Girt the moulding, and allow half an inch behind
the plinth.
CARPENTER AND JOINER.
555
Flooring.—In measuring boarded flooring, the dimensions must
be taken, allowing the thickness of the skirting, and valued at per
square.
Enter them according to their thickness, and if yellow or white
deal, if common or second best or clean deal, if laid folding,
straight joint or dowelled.
The slabs are not generally deducted if they have mitred bor-
ders; if they have not mitred borders, deduct the opening or slab
from the flooring. If the deduction is made when there are bor-
ders, the borders must be taken at per foot run, which will amount
to as much as the deduction made on the floor.
Moulding, such as architraves, round doors, windows, &c., base,
surbase, &c., &c., are to be measured round the mitres and girt
with a fine tape, and entered as moulded architrave, base, &c., as
the case may be. But in the abstract, they must be all classed
under the same head as mouldings.
Single mouldings, as Q O G and bead, or Q* ovolo and bead,
&c., may be taken at per foot run, but their girt must be described,
as they will be valued accordingly.
Doorcases, linings, &c., &c.-Doors are measured and valued at
per foot superficial, according to their description. Solid doorcases
are taken at per foot cube.
Door linings, grounds, &c, at per foot superficial.
If there is a sill, take it the same as the head, viz., by making
an allowance for its passing under and beyond the jambs, as may
be; and also allow the additional length of jambs for framing into
ditto. If a stone sill, iron shoes should be secured to the bottom
of jambs, which must be numbered.
Sashes and frames, shutters, and fitting up to windows. Take
the dimensions from the beads of sashes on the inside, and allow
seven inches additional height for head and sill, and eight inches
in width for frames in common sashes; but nine inches for large
sashes.
French sashes, hung on hinges, or sashes hung on centres in
solid frames.-Take the sashes separate, and the frames as directed
for doorcases. If Venetian frames, describe them as such.
If mouldings up munten, take them per foot run.
If circular heads, take the sash by itself, and the frames as run
of circular frames, as per description, viz., with beads, parting
slips, &c., &c., as may be.
Window shutters are taken per foot superficial, allowing for the
rebates.
Number the sash fastenings, locking bars, spring latches, hinges,
&c., &c.
556
ARTIFICERS' WORK.
The framed grounds, rebated and beaded boxings, linings,
moulded architraves, &c., are taken per foot superficial, similar to
the doors.
Staircases are taken per foot superficial, by girting the riser and
tread by the length of the step, allowing extra for the thickness
of the skirting, which is entered in the measuring book, according
to their thickness and description, viz., inch deal common steps,
risers, and carriage.
14 inch deal second best, steps, risers, and carriage, with moulded
nosings, close or cut string; or,
14 inch deal second best, S R & C M nosings, mitred to receive
brackets or string boards and return nosings, and dovetailed to re-
ceive balusters.
14 inch clean deal, do. do.
14 inch clean deal, S R & C, to geometrical stairs on a circular
plan, the risers mitred to the string board.
VALUATION OF CARPENTERS' AND JOINERS' WORK.
Memoranda.
50 cubic feet of timber equal one load.
100 feet superficial equal one square.
120 deals are called one hundred.
A reduced deal is 1 inch thick, 11 inches wide, and 12 feet long.
120 12 ft. 3 in. deals equal 5% loads of timber.
400 feet superficial of 1½ inch plank or deals equal one load.
Planks are 11 inches wide, deals 9 inches, and battens 7 inches.
A square of flooring requires-
Laid rough
Do edges shot
Wrought and laid folding
Do.
straight joint
Do.
do. and ploughed and tongued
•
One square of wrought folding floor requires
Do. straight joint
Number of
12 ft. boards.
121
121
13
131
14
Number of
12 ft. battens.
17
18
WEIGHT OF TIMBER.
39 cubic feet of oak
equal
1 ton.
65
fir
do.
وو
وو
66
39
deals.
do.
وو
CARPENTER AND JOINER.
557
60 cubic feet of elm
51
beech
وو
45
ash
دو
34
وو
mahogany.
equal to
1 ton
do.
وو
do.
وو
وو
do.
CALCULATION, showing the method of ascertaining the VALUE of
a CUBE FOOT of FIR or other timber from the prime cost
prices:-
Fir timber at per load, say
Carriage (according to distance)
Sawing on an average
Waste in converting, fo
20 per cent profit
£ s. d.
5 0 0
050
0 10 0
5 15 0
. 0 11 6
6 6 6
1 5 3/1/2
£ s. d.
7 11 91
7
11 9/1/2
= 3s. 04d. per foot cube.
50
The constants in the following tables are to be multiplied by the
rate of wages for a carpenter per day.
LABOUR AND NAILS TO ROOFS.
At per square of 100 superficial feet.
If two stories, add
Labour.
Nails.
Days.
8. d.
To common shed roofs, one story high
Do. do. with purlins
.650
2
0
.800
2
0
. .084
.169
. 1.000
.084
20
If three do. add
Common span or valley, with purlins and
rafters two stories high.
If three stories, add.
Framed roofs, with collars dovetailed into
sides of rafters, notched to receive pur-
lins, and filled in with common rafters
Roofs framed with principals, king posts,
purlins, braces, and common rafters
Do. do. with king and queen posts,
Common kerb roofs on one side
If two sides, add
If three sides, add
If above two stories, add
. 1.906
2.940
. 3.170
3 6
4
0
4 0
1.125
2 0
.084
.169
.100
558
ARTIFICERS' WORK.
LABOUR AND NAILS TO NAKED FLOORS.
At per square of 100 superficial feet.
Labour
Nails.
days.
8. d.
Ceiling floors, joists only
Do. framed with tie-beams
Do. with binding and ceiling joists
.584
1
6
.834
1
9
. 1.000
1
11
Ground joists, bedded but not framed
Do. pinned down on plates and framed to chimneys .836
Single framed floors trimmed to chimneys and
stairs
If above 9 in. deep, add
•
.500
1
6
1
6
1.050
1 9
•
.169
Framed with girders and cased bays
. 1.700
3 0
Framed with girders, binding, bridging,
and ceiling joists
. 2.500
4 0
LABOUR AND NAILS TO QUARTER PARTITIONS.
At per square of 100 superficial feet.
Common 4 in. partitions
.900
1
3
Do.
5 in.
do.
1.050
1
6
•
Do.
6 in.
do.
. 1.100
1
6
Truss framed with king posts
Do. with king and queen posts
. 1.736
2.000
1 6
If oak, extra one-third.
LABOUR ON FIR TIMBER.
At per foot cube.
Cube fir bond
Do. framed
Do. truss framed
Do. framed and chamfered
Do. wrought and framed
Do. do. and rebated
Do. W, F, R, and beaded
Do W, F, R, and D beaded.
Do. proper doorcases
Planing fir per foot superf.
Days.
.063
.126
.168
.168
.210
.252
.294
.336
.378
.014
Bond timbers, wall plates, wood bricks, pole and kerb, &c., are
all to be under the head of bond.
CARPENTER AND JOINER.
559
CALCULATION, showing the method of finding the VALUE of
DEALS or BATTENS from the prime cost prices.
Prime cost per hundred of 12 ft. 3 in. deals, say
Carriage according to distance
20 per cent profit
£
s. d.
*
42 12 0 = 7s. 1d. to be allowed in day-bills
120
for each 3 in. deal
In measured work, allow for waste, o
£
8. d.
35 0 0
0 10 0
35 10 0
7 2 0
£ 42 12 0
07 1
008/1/2
0793
In calculating the value of deals in thicknesses, add the value of
the sawing, according to the number of cuts.
Every rise and fall of 97. per hundred, will increase or diminish
the price of deals as near as possible, per foot superficial, 1d. per
inch in thickness. This rule will be found sufficiently correct for
practice where the quantities are not large; where they are, the
exact calculation should be made.
LABOUR ON DEALS, AT PER FOOT SUPERFICIAL.
In order to facilitate the fixing of proper prices for the labour
on deals, at per foot superficial, the different descriptions of work
which have always been considered of equal value, are classed to-
gether, by which the system adopted for valuing the various sorts
of labour on deals, will be rendered more simple and easy; over
the column in which is inserted each kind of work of equal value,
is placed the decimal which, multiplied by the rate per day allowed
for a carpenter at the time and place where the work is performed,
will show the fair and equitable price to be allowed.
560
ARTIFICERS' WORK.

No. 1.
No. 2.
No. 3.
No. 4.
For deals from to 1
.009
.019
.027
⚫037
ín. thick
•
For deals from 2 to 3)
in, thick
.013
.027
.037
.049
Edges shot.
Labour and
Cut circular. Cut standards
Plugged.
nails.
Sunk Shelves.
Jacked,
Planing on
Scolloped.
Rounded.
each side.
Ledged.
Dovetailed.
Grooved.
Rebated.
Ploughed &
tongued.
Framed.
Battened.
Mitred.
Scribed.
Backed.
Throated.
Clamped.
Beaded.
BATTENING, PER SQUARE.
Labour. Nails.
Days. 8. d.
₫ in. to 14 in. 12 in. from centre to centre
If plugged to walls, add
.590
2 0
.170
1 0
Extra for wall hooks.
WEATHER BOARDING, PER SQUARE.
Rough
.420
2 6
Ditto splayed edges
.680 3 0
Wrought
1.000 3 3
Ditto and beaded
1.255
3 6
ROUGH BOARDING, PER SQUARE.
2 in. deal, rough
.500 2 6
Do.
edges shot
.667
3 0
Do.
ploughed and tongued
.750 3 0
Inch deal, rough
.542
2 9
Do.
edges shot
.709
3 0
Do.
ploughed and tongued
.918 4 0
Whole deal, rough
.584 3 0
Do.
edges shot
.750
3 6
Do.
ploughed and tongued
1.042
4 0
1 in deal, rough
.667
3 0
Do.
edges shot
.862
3 6
Do.
ploughed and tongued
1.167
4 0
DEAL FLOORS, PER SQUARE.
Inch, rough edges shot
.765
2 6
A
CARPENTER AND JOINER.
561
Labour.
Days.
Nails.
8. d.
Do. wrought folding
1.180
2
6
Inch, wrought folding straight joint
1.500
3 6
Whole deal, rough edges shot
.840
3 0
Do.
wrought folding
1.255
4 0
Whole deal, wrought straight joint, splayed
headings
1.760
4 6
Do.
do. dowelled
€ 3.170
8 0
1½ in. deal, rough edges shot
.920
3 0
Do.
wrought folding
1.340
4 0
Do.
do. straight joint, splayed heading 2.000
4 6
If ploughed and tongued headings, add
.295
If ploughed and tongued edges, add
.510
For tongues to edges of boards, add
.840
BATTEN FLOORS, PER SQUARE.
Inch, wrought folding
1.500
4 6
Do. straight joint, splayed headings
. 1.792
4 9
14 in. wrought folding
1.667
6 0
dowelled
Do. straight joint, splayed headings
Do.
2.167
6 3
4.167
10 O
If ploughed and tongued headings, add
If ploughed and tongued edges, add
.431
.750
For tongues to edges of boards, add
If battens less than 5 in., add
1.250
.334
FRAMED GROUNDS, PER FOOT SUPERFICIAL.
Common framed grounds
1 in. do. ploughed for plastering
1 in. do.
do.
do.
1 in. do.
do.
do.
SKIRTINGS, PER FOOT SUPERFICIAL.
Labour
and Nails.
.063
.070
.076
.083
Plain skirting
.037
Do. raking cut to steps
.070
Torus skirting
.065
Do. raking cut to steps
.085
GUTTERS AND BEARERS, PER FOOT SUPERFICIAL.
Inch or whole deal
.076
562
ARTIFICERS' WORK.
DOOR LININGS, PER FOOT SUPERFICIAL.
Labour
and Nails.
Plain single rebated
.056
Do. and beaded
.063
Do. double rebated
.070
Do. do.
do. and double beaded
.077
Square framed jambs, each in 2 panels and soffit in 1 panel .105
If bead butt, or moulded, add
.013
Bead flush, or quirk moulded
.027
Raised panel and moulded
.042
For every extra panel if square
.021
Do. flush or moulded
.027
If double rebated
.021
If double beaded
.013
LEDGED DOORS, PER FOOT SUPERFICIAL.
14 in. rough edges shot
.065
Add,
If ploughed and tongued
.013
If ploughed and beaded
.021
If wrought each side
.013
If braced
.027
If hung folding
.021.
If 1 in. thick
.013
FRAMED PARTITIONS, PER FOOT SUPERFICIAL.
1½ in. square framed
.065
2 in. do.
.076
Add,
If BB or moulded
.027
If BF or quirk moulded
.042
DEAL MOULDINGS, FIXED COMPLETE.
Common mouldings
.128
.028
Add, if quirked
The materials for mouldings in deal will be found as near as
possible of the same value as the labour. Small mouldings may
be measured at per foot run, and valued according to the girt
and form.
DOORS HUNG COMPLETE, PER FOOT SUPERFICIAL.
Two panel square framed
.070
Add, for every additional two panels ;
CARPENTER AND JOINER.
563
If framed square,
For 1½ in. deal
2 in. do.
21 in. do.
If framed BB and square,
For 14 in. deal
2 in. do.
21 in. do.
If framed BF and square,
For 1 in deal
2 in. do.
2 in. do.
If framed Q. O G and Bd. and square, or Q O. and Bª.
and square,
For 1 in. deals
2 in. do.
23 in. do.
If double margins 4 in. wide
Do.
Hung folding
5 or 6 in. do.
WINDOW LININGS, PER FOOT SUPERFICIAL.
Inch deal two panel square framed back linings
If B B or moulded, add
BF or quirk moulded, add
For each panel above two, if square
Do.
do.
If splayed
if moulded
Labour
and Nails.
.019
.021
.027
.021
.024
.027
.027
.037
.042
.021
.024
.027
.021
.042
.013
.101
.013
.021
.021
.027
.007
WINDOW BACKS, ELBOWS, AND SOFFITS, PER FOOT SUPERFICIAL.
Inch deal, plain keyed or two panel square backs
Do. two panel square backs, elbows and soffits
Add for each panel above three,
If splayed
If bead butt or moulded
BF or quirk moulded
BOXINGS TO WINDOWS, PER FOOT SUPERFICIAL.
Framed, rebated, and beaded boxings
Splayed FR and beaded boxings
.085
.098
.010
.013
.021
.101
.120
564
ARTIFICERS' WORK.
INSIDE WINDOW SHUTTERS, PER FOOT SUPERFICIAL.
Labour
and Nails.
in. deal clamped flaps in one height
.120
Inch do. two panel square in one height
.125
For every panel above two add,
If framed square
If B B or moulded
.022
.022
BF or Q. moulded
QOG & b, or QO & b & square
For every extra height add
.026
.026
.013
SASHES AND FRAMES HUNG COMPLETE, PER FOOT SUPERFICIAL.
Sashes-
1 in. deal ovolo sashes
Do. wainscot or mahogany
If 2 in. or 2 in. sashes deal, add
If do. wainscot or mahogany, add
.049
.070
. .021
.
.028
If astragal and hollow in deal, add
.013
If do. in wainscot or mahogany, add
.021
Frames-
Deal cased frames O S sills, DPPB & PS, S hung
.070
If prepared for 2 or 2țin. sashes, add.
.013
If prepared with wainscot or mahogany PP Bds. & P slips
add
.085
If for 2 or 2 in. sashes add
1 .019
If double hung, add
.013
To find the value of sashes and frames, add to the above for
labour and nails only, the amount of materials expended.
STAIRCASES, PER FOOT SUPERFICIAL.
Common steps and risers and two fir carriages
Do. moulded nosings and close strings
.070
.098
Do. do. mitred to cut string-boards and dove-tailed to balusters .127
Add,
If winders circular one end
.042
Do. circular two ends
.085
Do. geometrical with wrought and blocked carriages
.056
Riser tongued to step bottom edge
.021
Do. do. both edges
.042
Feather tongue joints
Add for each-
.021
Quarter curtail glued upright
.667
CARPENTER AND JOINER.
565
Do. blocked and veneered
Proper curtail step and riser
Returned moulded nosing
Do. circular
Plain cut bracket
Do. circular
Housing to step and riser
Do. to winders
Do. to moulded nosings
Do. to do. circular ends
Labour
and Nails.
OUTSIDE STRINGS TO STAIRS, PER FOOT SUPERFICIAL.
Whole deal, plain
Do. sunk
Do. sunk and moulded
Do. do. cut
Do. do. mitred to risers
If wreathed,-four times the above.
If ramped,—once and half do.
WALL STRINGS, PER FOOT SUPERFICIAL.
Plain and plugging
If moulded, add
If rebated for plastering, add
DADOS, PER FOOT SUPERFICIAL.
Proper dado, with dovetailed keys, joints secured with
slips, and dovetails hung to grounds by keys grooved into
do. and dado
Add,
If raking scribed to steps
Do. to moulded nosings
If base grooved into floor
For each external mitre beyond two in the room
If circular on the plan,-double the above.
If wreathed do, treble do.
1.167
3.334
.250
.417
.250
.417
.098
.125
.167
.459
.084
. .098
.112
.127
.140
.080
.021
.028
.070
.019
.021
.009
.228
566
ARTIFICERS' WORK.
COLUMNS AND PILASTERS PER FOOT SUPERFICIAL.:
Labour
and Nails.
14 in. deal plain pilasters, properly glued and blocked
Do. do. diminished
14 in. deal diminished columns, properly glued and blocked,
. .112
.153
under 14 inches diameter
.420
Do. do. above do.
.350
Add for
Arris or deep fluting to pilasters, one inch wide
.021
Do. two inches wide
.028
Do. three inches wide
.042
Arris or deep fluting to columns, one inch wide
.027
Do. two inches wide
.042
Do. three inches wide
.056
Straight grooves to columns
.021
Headings to flutes to do..
.070
.013
.042
Straight grooves to pilasters
Headings to flutes to do.
SECTION IV.-Sawyers' Work.
The charges for sawyers' work are often very inconsistent, and
differ widely in various parts of the country.
The proper mode of valuing the labour on sawing fir or any
other kind of timber is by the square of 100 superficial feet, the
price depending on the usual rate of wages and the hardness of the
timber:
Sawing to old timber is usually charged double, on account of
the extra labour occasioned by nails, &c:
Small scantlings may be charged by the foot run.
Planks, deals, battens, and flat cuts, according to their length,
at per dozen cuts.
And all other descriptions of sawyers' work may be valued in a
similar manner, according to the circumstances of the case.
SECTION V.-Stone-Masons' Work.
There is a variety of opinions respecting the manner of mea-
suring stone-masons' work, both in taking the dimensions for the
stone, and also for the labour. It certainly requires more practi-
cal knowledge of the operative or working part of the business
STONE MASON.
567
than any other trade, to determine correctly between these con-
flicting opinions. The following rules may be considered suffi-
ciently explanatory of the principle on which the practice is
governed or founded.
In measuring cube Portland or other stone; all stones that are
worked square should be taken accurately as they come from the
saw to the banker, of course including the parts laid on or pinned
into the walls. But as bevelled or irregularly formed stones can-
not be converted without more waste than square ones, the dimen-
sions should be taken so as to make a fair allowance for such
additional waste, particularly as the solid contents of all the dif-
ferent descriptions of Portland stone, whatever shape the stones
may be worked to, are abstracted under the same head, (viz., cube
Portland,) and therefore should be of the same value; but which
cannot be the case, unless the extra waste in the bevelled stone,
&c., is allowed for in taking the dimensions. When this is done,
it is only requisite, in estimating the prime cost, to calculate for
the waste as if all the stones in the building were cut and worked
square. If this method were not adopted, it would be requisite,
in ascertaining its real value, to make so many different heads in
the abstract for cube Portland, as there are different shaped or
bevelled stones, accurately describing each; when the calculations
for waste, and of course the price, must vary according to each
particular form, the trouble of which would be endless, and without
any advantage; indeed, it would come to the same thing, viz.,
making the necessary allowances for waste, according to the form
of the stone. Bevelled or arch stones should be taken about one-
sixth above the mean dimension to allow for waste.
In measuring the cubic contents of spandrel steps, some diffe-
rence of opinion exists as to the best method of taking the re-
quisite dimensions. The following three methods are in common
use, viz.:-
1st. Take the length of the step by its extreme width, and
by the whole height of the riser measured from tread to
tread.
2nd. Take the length of the step by the extreme width from the
nosing of the tread to the acute angle, and by half the height of
the riser taken from the top of the tread to the acute angle
downwards.
3rd. Take the length of the step by its extreme width, and by
three-fifths of the depth of the riser taken from the top of the tread
to the acute angle downward.
A better way than either of the above methods is to take the
568
ARTIFICERS' WORK.
length of the step by a dimension found as follows, allowing half
an inch on each step for waste.
18
116
1
3 width of step.
6
2 base of rectangle.
1.3
4 half do. of triangle.
6

12//
This gives
5
0
1 3
6
3 1 6 as before.
In measuring winders, the content may be found in the same
way, taking the extreme length of the step by the mean sectional
area, making due allowance for waste.
The labour on the under side to be taken as circular sunk
work.
All stones exceeding three inches thick should be taken as cube
measure, with the labour, &c., on do.
All stone, three inches thick and under, should be taken as slab,
at per foot superficial.
The usual custom has been to measure in such edges as are
worked and show fair. Objections have been made to this prac-
tice, and with some degree of justice; but it will make very little
difference, if the edges of thin slabs are measured separate, and a
fair price allowed for the labour; and for cutting into narrow pieces
for mantles, jambs, &c., it would be nearly equal to the value of
the stone; but in thick slabs the same argument will not hold good;
and, therefore, as the object in measuring work should be to ascer-
tain its real value, and allow only a fair remunerating price, it
appears more correct to measure the labour on the edges at per
foot run, offering a fair price, according to their thickness, instead
of entering it as stone. An extra price should be allowed for very
large scantlings, also for hoisting stones on exceedingly high build-
ings, according to circumstances.
MASON.
569
LABOUR ON PORTLAND OR OTHER STONE.
In measuring the labour of working Portland stone, the principal
difference of opinion arises in determining what faces or beds.
should be taken as plain work. In superior work, a plain face must
be taken previous to measuring the sunk, moulded, or other work,
when the mould could not be applied without first making that
plain face. There cannot be much difference of opinion in taking
the other labour, such as sunk work, moulded work, circular-sunk
or circular-moulded work, &c., which must be girt as it appears
when the work is finished, but which is not always the case with
the plain work; and therefore it is requisite to know the manner
in which the work is executed, to form an accurate conclusion, and
to do justice to the workman in its measurement.
WEIGHT OF STONE.
14 cubic feet weigh one ton.
Purbeck stone
Portland
Bath
Yorkshire
Granite
Marble
16
17
99
15
99
131
13
وو
وو
وو
وو
Purbeck paving
50 feet superf.
Do. step 13 by 61
25 feet run
do.
99
do.
وو
do.
do.
do.
do.
do.
VALUATION OF LABOUR.
Table of Constants for the different descriptions of Mason's, Work.
N.B.-The factor to be applied is the rate of wages for a mason per day.
Days.
Labour, squaring and laying new York or Purbeck paving
per foot superficial
.021
If in courses, add
.010
Labour on Portland or similar stone per foot superficial.
Sawing to be taken as half plain work.
Plain work to bond stones
per foot superf.
.140
Do.
to beds and joints
do.
.181
Do.
rubbed face
do.
.209
Do.
do. circular
do.
.291
Sunk work rubbed
do.
.250
Do.
do. circular
do.
.313
Moulded work rubbed
do.
.292
Do.
do. circular
do.
.417
2 N
570
ARTIFICERS' WORK.
Days.
Circular work to shafts of columns
having the neck moulding or part of
the base worked in the same stone
per foot superf.
.334
Circular circular or spherical work to
domes or balls
do.
.500
If rubbed, add extra
do.
.049
Taking up, squaring, and relaying old
paving
do.
.042
Add, if in courses
do.
.015
LABOUR ON STATUARY OR VEIN MARBLE,
Including Sawing, Working, and Polishing.
Plain work
per foot superf.
. .875
Circular work
do.
1.250
•
Sunk work
do.
1.667
•
Moulded work
do.
. 2.334
Circular sunk work
do.
2.334
Circular moulded work
do.
3.000
ON OLD WORK.
Old vein marble chimney reset
Do. do. squared and reset
per foot superf.
do.
.125
.167
Do. do. sanded, grounded, and squared do.
.209
Do. do. and reset
do.
.250
Do. do. cleaned and reset
do.
.250
Do. do. sanded, polished, and reset
do.
.375
Do. do. sawed, sanded, polished, squared,
and reset
do.
.626
In the west of England, and all the counties in which stone is
abundant, it is usual and customary to build with the rough stone
of the country, and the practice generally is to measure the walls
by the perch of 18 superficial feet, supposing them 24 inches thick;
to which thickness all the walls, whether more or less, are reduced
by multiplying the superficial contents by the thickness in inches,
and dividing them by 24; or they may be reduced to the cube
perch of 36 feet: but some regulate the prices per perch, according
to the thickness of the walls.
In measuring the work, some contend to girt the quoins and all
projections, as they say, to pay them for the extra trouble in work-
ing and setting the stones; but this should not be allowed, except
for labour only; and even then it is much fairer to measure the
quantity of walling as it is, and make a proper allowance for the
extra labour, either in quoins, chimney breasts, flues, reveals, &c.
PLASTERER.
571
SECT. VI.-On Measuring Plasterers' Work.
Plasterers' work is taken superficially, and valued by the square
yard of 9 feet.
If cornices are round the room, take the ceiling only to half the
projection of the cornice, or one projection in and one out; or mea-
sure the ceilings clear of the cornices, and take the whole of their
projection as lathing and pricking up.
If the cornices are bracketed, measure the ceilings clear of the
cornice.
The sides of the room should be taken from the ground, through
the bed-mould, or half the height of the cornice.
1
If on brick, or bracketed, take them only to the bottom of
cornice.
In taking the length of cornices, measure the size of the room,
taking one projection in and one out, and girt them from the mould,
or from the ceiling to the wall line.
Number all the angles in the room above four, as extra.*
In taking cornices where there are coves, take the coves as su-
perficial of cove to cornices, and allow 1 inch extra on the girt of
the cornice for the return of the mould on the cove.
All enrichments to be taken separately.
Friezes, under the cornice, must be taken as superficial of plain
floated frieze. A floated ground must be taken under all enriched
friezes.
If cornices are run to old ceilings, a screed must be allowed.
Enriched friezes, ceilings, or soffits must be measured first as
plain work, and then the enrichments taken separately at per foot
run, and a price fixed, according to their description and value.
All circular mouldings and enrichments to be taken one face in
and one out.
Take first the ceiling through the reeds.
Second, length of cove above the cornice by 2 ft.
Third, do. of moulded cornice by 1 ft. 2 in., being 1 in. extra
for top on cove.
Fourth, do. of plain floated frieze by 6 in.
Fifth, do. of moulded architrave by 8 in.
* The present practice, however, of making four additional mitres to carry the
cornice round a projecting chimney, is as absurd a deformity as it is an extravagant
waste. Even the architects of the last generation had the wit to keep their ceiling a
simple rectangle, by arching in brick the recesses on each side of the chimney.
572
ARTIFICERS' WORK.
Sixth, length of moulded reeds by 9 in.
Reveals to windows taken at per foot run, price according to
width.
VALUATION OF PLASTERERS' WORK.
Calculation of Materials.
1 hundred of lime = 25 strike bushels (old measure).
Materials.
100 yards of render ( 14 hd. of lime.
set require
130 yards of lath,
plaster, and set
require
1 double load of sand.
4 bushels of hair.
1 load of laths.
10,000 nails.
23 hd. of lime.
1 dble. Ids. of sand.
7 bushels of hair.
LATHING.
Labour.
Plasterer, labourer
and boy, three days
each.
Plasterer, labourer
and boy, six days
each.
1 bundle of laths and 384 nails will cover 5 yards.
RENDER ONLY.
1 hd. of lime.
1874 yards require
2 double loads of sand.
5 bushels of hair.
Floating requires more labour, but not more than half the
quantity of stuff as rendering.
SETTING ONLY.
11 hd. of lime.
375 yards require
5 bushels of hair.
20 per cent. is always allowed on the prime cost of the materials.
Calculation of Labour.
The decimal is to be multiplied by the rate of wages for plas-
terer, labourer, and boy, per day.
Days.
Rough render
.019
Floating do.
.021
Setting
.016
Lathing
.019
If circular work, add on the lathing and also on each coat
of plastering
.008
If to groins, add as above
.010
L
IRONMONGER.
573
SECT. VII.-Ironmongery.
Nails are sold by weight, and charged by the hundred. Screws
at per dozen. Iron bolts and screws at so much each. Brass flush
bolts at per inch. Pulleys each, according to diameter.
and screws at per pair. Locks at so much each.
Hinges
Twenty per cent. profit is allowed on the prime cost of all
ironmongery.
MEASUREMENT OF IRON-WORK.
Cast iron in girders, story-posts, columns, &c., is charged by the
ton or the cwt.
Moulds are generally charged extra, if out of the common run.
Articles in common demand, as cast-iron water pipes, gutters,
&c., are sold by the yard, according to diameter.
Cast-iron in railings, gratings, casements, brackets, &c., is
charged by the pound, according to the nature of the work.
Wrought-iron in chimney-bars, railings, hand-rails, shoes to
piles, &c., is charged by the pound.
SECT. VIII.—Painter's Work.
In measuring painters' work, all work not cut in on both edges,
must be taken, including edges and projections, at per yard square
of 9 feet.
Work cut in on both edges, as skirtings, cornices, shelves, &c.,
are measured at per foot run.
Ornamental work first taken as common, and then superf. of
labour to ornaments at per foot superf. or run.
Sash frames, window lights, casements, bars, dormers, frontis-
pieces, chimney-pieces, &c., numbered and valued at each. Sash
squares at per doz.
Iron or wood railings, balusters to stairs, &c., are measured on
both sides as solid work, to allow for the extra trouble of painting
round the bars, rails, &c., at per yard.
If ornamented, add extra one face in the width of such
ornamental parts.
If ornamented turned balusters, also add one extra face as far
as the turned work goes.
Handrails, &c., grained mahogany, first measure them in with
the balusters, and then per foot run for graining.
Soffits to windows per foot run.
Letters or figures numbered and valued at per inch in height.
574
ARTIFICERS' WORK.
Windows and doors are measured thus:-
WINDOWS.

ft. in. ft. in.}
11 O
Window front.
5 5
ft. in.
ft. in.
7 6
4
6
0 4 edges.
1 6 boxings and edges.
7 10
Shutters
6 0
710
6 0
7
6 If the backs
10 61
ft. in.
viz.26 3
7
6 are cut away
10 65
linings
1 2
0
9
the linings
4 6 soffit
20
3
Linings
must be
4
6
0 9 elbows
1 2
measured
to the floor
20 3 thus:
26 3
7 6
39
22 6
Beads varnished, supposing
them to be mahogany or
11 3
wainscoat sashes and beads
11 3
22 6
12 squares varnished.
1 locking bar.
Some only allow the shutters
to be taken thus:
•
The outside of window
would be taken as .
1 6 boxings.
0 6 edges.
20
3 9 shutters.
5 9 instead of 6 feet.
N 1 frames.
1 dozen of squares.
1 sill, if the stone still
is painted.
Doors.

2)7 0
4 4
Door fronts for both sides
40 projection of archi-
0 4 f traves.
4 4
6 6
6 6
16 0
08
Linings
3 0
0 6 f edges of door and
0 21 rebates.
08
16 O
PAINTER.
575
VALUATION OF PAINTER'S WORK.
Calculation of Materials.
45 yards of work, 1st coat, including
knotting, stopping, and every pre-
paration requisite for the second
coat, will require
Second and following coats
5 lbs. of white lead.
5 lbs. of putty, litharge,
&c.
1 quart of oil.
5 lbs. of white lead.
1 quart of oil.
20 per cent. profit is always allowed on the prime cost of the
materials.
Calculation of Labour.
The decimal to be multiplied by the rate of wages for a painter
per day:
First coat, including stopping, &c.
Second and following coats
.027
.019
The above data will suffice for the valuation of common work,
for which alone it is possible to lay down any rules, as the value of
decorative work, as graining, imitations, &c., depends upon the
ability of the artist, and the manner in which the work is executed.
SECT. IX.-Glaziers' Work.
In measuring glaziers' work, the dimensions must be taken
between the rebates, and all irregular panes the extreme size
each way.
The price per foot must be calculated from the prime cost per
crate, allowing for carriage and 20 per cent. profit. The larger
the panes are, the more difficulty, risk, and waste; consequently
the price should increase in the following proportions :—
Panes whose superficial con-
tents are
Do. do. do.
ft. in. ft. in.
under
2
0 at per foot.
from 2 0 to 2
6 add 2d.
Do.
do.
do.
do 2 6 to 3
0 add 4d.
Above the
squares whose
Do.
do.
do.
do 3
0 to 3
6 add 6d.
contents
under 2 feet.
are
A CRATE OF CROWN GLASS
Contains 12 tables of the best, at per crate
وو
وو
وو
15
18
18
وو
وو
seconds
thirds
fourths
33
وو
Each table is from 4 ft. to 4 ft. 6 in. diameter: some tables
576
ARTIFICERS' WORK.
may be cut to within 2 in. of the centre, others not nearer than
4 inches.
Supposing a crate to be 4 ft. 6 in. diameter, and that it
may be cut to 2 in. from the centre, the quantity of
glass that may be cut from it, including the triangular
pieces, will be
ft. in.
14 2
If only 4 ft. diameter, and cannot be cut nearer that 4
in. of the centre
10 10
25 0
And deducting the triangular pieces, which are of very
little value
2 6
We have as the available contents of the two tables
The average contents per table
22 6
11 3
Taking the sizes of squares that will cut to the most advantage:
but as squares of all sizes must be cut from the tables as they are
wanted, the average produce per table is not more than 10 ft.
superficial.
Labour and putty per foot may be found by multiplying the
rate of wages for a glazier per day by the decimal .110.
Ex.-To find the value per foot of glazing, with best Newcastle
crown glass, or any other kind of glass:-
Prime cost of crate (12 tables)
Carriage, &c.
20 per cent. profit
£ S. d.
0 0 0
0 0 0
0 0 0
0 0 0
120)
0
0 0
Divide by No. of feet the crate will pro-
duce, for best glass
0 0 0 per foot:
Labour and putty
0 0 0
Total per foot
£0 0 0
SECT. X.-Paper-Hanger.
A piece of paper is 12 yards long, and when hung, 20 inches
wide. Twelve yards running measure is equal to 6 square
yards, or 60 feet superficial; therefore divide the superficial feet
by 5, which will give the number of yards, and these divided by
12 will give the number of pieces of paper.
It is usual to allow one piece in seven for waste.
VALUATION OF ESTATES.
577
CONSTANTS OF LABOUR.
These constants represent the time requisite to perform a given
quantity of work, of the kind specified, in days and decimal parts
of a day; the factor to be applied, being the rate of wages per
diem for one or more men, according to the nature of the work.
These decimals are calculated, in all the trades, for the price
per day allowed the master in his day bills, consequently, with his
profit thereon, being the only rate that can be ascertained, the
master, of course, paying each man per week, according to his
abilities and industry; therefore the full value of the labour,
including the master's profit, will be found by multiplying the
decimal by the rate of wages, as shown in their respective tables.
Likewise, in all cases it must be understood that the prices stated
in the tables for labour and nails include fixing; and when added
to the price of deals, will give the value of the work fixed
complete, including labour, nails, and materials, according to the
prime cost of materials and rate of wages allowed.
CHAPTER XVII.
THE VALUATION OF ESTATES.
UNLIKE all the other subjects that have been treated of in this book,
this one cannot be demonstrated. The theory may indeed be enun-
ciated, but in the event of a difference of opinion arising, there is no
mode of reconciling the variance in a manner that shall place it be-
yond doubt. The profession of a land valuer is very often confounded
with, and designated by, the title of that of the land surveyor. I do
not mean to say a land valuer cannot by possibility be also a land sur-
veyor; on the contrary, I am personally acquainted with several bril-
liant examples of the practice-the successful practice-of both pro-
fessions; but, as a general rule, the land valuer, most efficient in
his calling, is a man who has spent the greater portion of his early
life upon land, in the study and practice of agriculture; who has by
experience gained such a knowledge of the several treatments
which may be most successfully applied to those particular soils
that chiefly abound in the vicinity of his agricultural operations,
or in the adjoining counties; who is thoroughly acquainted with
578
VALUATION OF ESTATES.
No
the cost of labour and tillages upon these lands, and of the seasons
and periods of which advantage must be taken in due course.
one can doubt for a moment that such a man, particularly if he be
more intelligent than the generality of his order, is the most fitting
person to exercise a profession requiring a practical knowledge of
all these things as its chief ground work. But then to call such a
man a land surveyor is a libel upon a very different profession-a
profession moreover which requires quite as long practice as the
other to make its possessor thoroughly efficient; and, therefore, the
two are not likely to be perfectly acquired by the same person in
very early life. I said I knew of one or two brilliant examples of
the exercise successfully of the two professions by the same persons.
These gentlemen, whom I have in my mind, are men of excellent
abilities; were originally educated as land surveyors, at which, as
it is their great pride to boast, they for several years earned a
maintenance. During that time each kept his attention steadily
riveted on the different kinds of agriculture practised in the varied
localities and counties over which his legitimate profession called
him; observed with interest every variation of treatment to which
land, apparently of the same nature, but in different counties, was
treated by different farmers; investigated the reasons of such ap-
parent anomalies by all possible references to climate, soil, and
pecuniary consideration, until, I have no hesitation in saying, he
gradually and contemporaneously with the exercise—the profitable
exercise—of the profession of land surveying for a sufficient number
years to be thoroughly experienced and grounded therein, en-
tirely qualified himself to conduct the profession of land valuing.
of
Such is the prospect and such the possibility of a land surveyor
acquiring in time a competent knowledge to act as a land valuer.
Another way of effecting this object has been adopted, though not,
as I believe, successfully, nor without considerable pecuniary sacri-
fice. The land surveyor has taken a farm whereon he of course
has gained knowledge by experience, but then the knowledge thus
acquired has been of necessity limited, and too often the harass
and worry of the farm must have distracted his attention from the
proper exercise of land surveying, or the duties of the latter call-
ing must have been located in a quarter many miles from home, at
the same time that the business of the farm required the presence
of the master.
Now let us take a view of our experience among the several in-
stances of persons who are legitimately land valuers, but who also
practice as land surveyors. I do not hesitate for myself to state,
that I am unacquainted with any single instance in which a land
VALUATION OF ESTATES.
579
valuer, qualified either by his experience as a farmer, or by early
education as a valuer, has subsequently adopted land surveying
with any pretensions to the title of a land surveyor, or with the
smallest atom of success. He may, as I am aware by an example I
have in my mind, acquire a rudimental knowledge that may enable
him to map a field, a farm, or a small estate. But while as a valuer
he would, the moment he entered a field, detect a gravelly brow
subject to burn, or slovenly farming, and the presence of couch, a
glaring error in a plan, that would at once rivet the attention of
the experienced surveyor, would entirely escape his notice. Thus
he might be able to define within a shilling an acre the value of the
land, but by attempting the exercise of both professions, the emi-
nent knowledge in the one would be entirely nullified by some
error of two or three acres in the quantity, which an acquaintance
with the other would have corrected.
I knew an instance of a man who was brought up as a tradesman
in London, and who, much to his credit, so industriously pursued
an honest calling, that at the age of 40 he had saved a sufficient
sum of money to retire from his business into the country, where
he took a farm. Being somewhat intelligent, he announced him-
self as a land valuer, and very shortly afterwards a land surveyor.
Some ten years after, a gentleman, who knew nothing of the qua-
lifications of a land surveyor, had occasion to employ a number of
surveyors as witnesses in a law suit; among them came this one.
Of course the opposing counsel was duly instructed as to the qua-
lifications of the witnesses, and in cross-examination endeavoured
to furnish the jury with the information he himself possessed. In
vain our witness appealed to his age, and his ten years' residence
on his farm. The counsel was perfectly willing to accord to him
the benefit of his experience in his London calling, and on his
farm; but unless said he, he were a heaven-born surveyor, or could
point to some work which he had performed, he could not allow a
jury to attach importance to his evidence as a surveyor. The very
age upon which he relied but aggravated his insufficiency; since
three years spent in the acquirement of correct first principles in
any science are better than ten years bungling in erroneous ones.
Notwithstanding this little check our friend continued his career,
his greatest ignorance being apparent in his want of information
that his own works were at all below par.
The tendency of my remarks has been to show that land survey-
ing can only be learned in youth, and thorougly acquired by con-
siderable subsequent experience. That a land valuer cannot take
it up at pleasure and exercise it any more than a lawyer can prac-
580
VALUATION OF ESTATES.
tise medicine, or the surgeon carry on the law. But that a clever
land surveyor may by a long course of industry become a qualified
land valuer. And the object I have had in view in making these
observations has been to promulgate correct ideas upon the subject,
affording employers the means of forming an opinion of the quali-
fications of men to whom they entrust their interest, and furnishing
a hint to those who may select these professions for their sons, as
to the proper course to pursue to conduce to future advantage.
The greatest amount of success is attained in matters of valua-
tion by the joint co-operation of two professional men; the one
being a competent valuer, the other a qualified surveyor; the
practical knowledge of the one is considerably assisted by the
science of the other, and appreciable advantages ensue. It is much
to be pitied that so much jealousy exists between the two profes-
sions, which militates to the injury of both.
The practice adopted by most valuers is to assume that they are
aware on inspection, without any enquiry, of the worth of an acre
of land per annum. Now this is in many instances an erroneous and
in all cases a vicious theory. I will endeavour to illustrate my
meaning by an example: Assume a valuer to have a farm
for which he pays, he believes, from experience, of its pro-
ductiveness, and we will consider equitably 20s. an acre as
rent; therefore, directly he comes to similar land in making a
valuation, he says, this is worth 20s. an acre. But now just as-
sume his own land to be situated in a parish where the local bur-
dens amount, on an average, to 3s. in the pound, while the land he
is valuing is situated in a parish where those burdens are 6s. in the
pound. The calculation then stands thus, his own land which he
has taken as his standard of value is worth in the aggregate of rent
and rates 23s. per acre, which, when reduced by the amount of
rates, exhibits 20s. as its net value. Now reduce the aggregate
value of the land he is valuing by the amount of the rates, and we
shall get but 17s. as the net value. The two lands being similar in
every respect as to quality, tenacity, and eligibility of situation,
but the one being subject to 3s. excess of taxation over the other,
is to that extent depreciated in value for rental. The difference is
doubly apparent if we assume the standard to be worth 46s. per
acre, rent and rates, or reduced by the amount of the latter at 3s.
in the pound to 40s. Our compared acre of equal fertility upon
which the rates are 6s. in the pound, would be reduced in value to
34s., so that land otherwise equal in value, but affected by a cause
which the generality of valuers entirely disregard, is, when properly
adjusted, equitably worth in one parish 40s., in the other only 34s.
VALUATION OF ESTATES.
581
This comparison is sufficiently accurate for practice, but in reality
it is not the actual equity of the case. For the rates of 3s. and 6s.
in the pound are levied on the rental, and therefore the calculation
stands as under:—
£ s. d.
•
Rent at 40s. per acre
Rates at 3s. in the pound
2 0 0
06 0
26 0
Rent at 34s. per acre
Rates at 6s. in the pound
1 14 0
•
0 10 41
2 4 4/1/
The correct adjustment of the latter example would be—
Rent at 35s. 4d. per acre
Rate at 6s. in the pound
£ s.
d.
1 15 4
0 10 8
2 6 0
In some counties (Surrey to wit,) the acts of husbandry per-
formed on the fallows of the last year are paid for at valuation by
the incoming tenant. This is a matter which again affects the
rental of land. These valuations of tillages, and what is called
tenant right, will be treated of bye and bye; my present purpose is
to show how they influence the rent.
I have mentioned Surrey-in that county the valuation of fallows
frequently amounts to four pounds per acre, and the dressings to
other four pounds. Now, if we take the fallow lands to be one-
fourth of the whole farm, we have a sum amounting to 27. per acre
all round, to be paid down by the tenant on entering, and there
locked up for the whole term, without any advantage or benefit to
him, except indeed it is taken into consideration in fixing the rent.
Even if it is so, the capital thus expended would be far more useful
and remunerative to the tenant than such a reduction of rent.
Therefore we must once more suppose that the land which we
assumed to be worth 40s. an acre in one parish is not subject to this
valuation, but that of equal quality which the excess of local bur-
dens reduced to 35s. in the other parish is. And we shall again
see how this charge tends to a still farther reduction.
I think no man would take a farm and risk capital in it if he did
not expect to get 10 per cent. for the use of his money, so that we
582
VALUATION OF ESTATES.
have 4s. to deduct from the already reduced estimate of 35s. 4d.
per acre to arrive at the fair rental. Thus
Original value
£ s. d.
200
Reduced by excess of local burdens to 1 15 4
Further reduced by interest on money
paid for valuation to
1 11 4
The cost of production materially influences the value of land.
Lands of equal fertility but of different tenacity are of very dif-
ferent values. Indeed if we seek an example among the poorer
soils, we shall find that in some cases the cost of labour entirely
consumes the value of the produce, leaving nothing for rent, while
on a lighter soil, less expensive to cultivate, but of the same fer-
tility, a small rent is deducible.
I think I have said enough to show that the system of valuing
lands by "experience only," as it is called, is erroneous; it is indeed
comparing the net rent of land and not the gross, for after all, taxes
and outgoings of a similar nature are but rent, expressed by ano-
ther word.
And this leads me to the consideration of what is rent? It is
undoubtedly the surplus that remains for the landlord after all the
expenses of cultivation, tithe, taxes, outgoings of every description,
tenant's profit, interest for his capital, and provision for wear and
tear, and for renewals, have been satisfied out of the value of the
produce; and land which leaves no such surplus, is worth no rent
for the purposes of agriculture.
The first thing, therefore, which has to be done in entering
fairly on the valuation of an estate is to estimate the yearly value
of the produce it is capable of yielding under skilful management,
and with a liberal but judicious expenditure of capital.
Next to appraise the cost of the labour and other outlays neces-
sary to ensure in the ordinary chances of the seasons the estimated
amount of produce. Then the amount of tithe rent charge, and
tenant's rates and taxes are matters to be ascertained by enquiry.
The tenant's profit should be such an amount of remuneration as a
person should receive at the current rate of skilled labour for such
an amount of supervision and attention as the farm may require,
without any reference to the style in which he lives, whether he
dines at one o'clock or five, keeps hunters, or walks to market.
The tastes and habits of a tenantry on a large estate may vary im-
mensely, but their rights are identical and equal.
VALUATION OF ESTATES.
583
Allowance for wear and tear of live and dead farming stock
must also be made. This involves an estimate of the value of the
whole stock, and when this is arrived at, a calculation must be made
of the probable average length of time within which the whole will
be required to be renewed, and the proper proportion thereof for
the one year must be placed among the deductions from the value
of the produce. The interest on capital must be a fair liberal al-
lowance, according to the current rate of money, subject to risks
and casualties; and when all these deductions have been made, the
landlord has for the first time an interest in the residue (if any,)
as rent.
Our theory, when illustrated, stands thus-
Assume the value of produce
the cost of cultivation
100
53
Tithe
10
Tenant's rates and taxes
Tenant's profit
7
Interest on capital
5
Wear and tear
5
Residue rent
20
100
دو
وو
وو
وو
وو
It was formerly the custom to say that the produce of a farmı
should carry three rents-one of which was to be apportioned to
the landlord, a second to the tenant, and the third to pay expenses.
It is hardly necessary to observe that such an apportionment must
be very impracticable and ridiculous. Take for example the case of
our illustration, where the landlord gets one-fifth only; the tenant
rather less than that; and more than three-fifths are absorbed for
expenses. I may also observe, that in framing that illustration,
the farm I had in my mind was a light land farm; had it been a
tenacious clay, the expenses might have been so swollen as to in-
trench considerably on the surplus rent.
The method of including farm homesteads (by which I mean both
farm houses and buildings,) in the valuation, has been a much
vexed question among valuators. Some omit to consider the
homestead at all, alleging that a discretion is exercised in
fixing the value of the land: others add so much to their valua-
tion for every 50 acres of land possessing a homestead, omitting to
make the addition where no buildings exist. Others, and this is I
believe the more common way, profess to value the house and each
separate building at its intrinsic value, and add the amount to their
valuation of the land.
584
VALUATION OF ESTATES.
In my opinion none of these are worthy of imitation. To con-
vert the produce of land a certain number of buildings are requi-
site, as well as a house for the farmer, and lodging for his cattle.
Without these accommodations the farm would not be tenantable,
and the value of it would be entirely problematical, as it might be
difficult to hire suitable buildings elsewhere; or if they were to be
had, the rent might be so excessive as to consume a large portion
of the value of the produce. Therefore it appears to me that the
only correct way to adopt in practice, is to assume when valuing
land, that all requisite building accommodation exists in a conve-
nient position upon the farm, the value of which is included in the
estimate of the land. If upon examination the buildings are too
small or are inconvenient, a proportionate reduction must be made
from the valuation: but if, on the other hand, a surplus number of
buildings are situate on the estate, no addition should be made, as
the farmer is not benefited thereby; on the contrary, all beyond his
actual requirements are so many additional expenses to him in
keeping them in repair; unless indeed he can rent some land ad-
joining the farm that is without a homestead, in which case it
would be only fair to charge him with the excess. If lands that have
been so valued are found to be without a homestead, then the
damage occasioned thereby must be deducted.
When I first promulgated this system of valuing farm buildings
among my professional friends, I recommended that the farm
houses should be subject to the same arrangement, but a practical
difficulty arose with respect to them. The requirements of a farm-
stead with reference to farm buildings may be defined, and as I
have shown, any excess is valueless to the tenant, except under an
unlikely or a rare contingency. But it is not so with the house.
If a farm has a good house upon it, pleasantly situated, that farm
will more readily let than one affording merely accommodation to
the farmer; and excess of room in a farm house may be very fre-
quently profitably let. Moreover, a farmer has no right to expect
that the profits of his business are to be estimated differently to
those of other people, who pay the rent of their houses out of their
profits: so that it appears reasonable that while all other build-
ings are included in the arrangement, and treated as I have sug-
gested, the house should be made the subject of separate and
additional valuation.
I have described the mode of valuing adopted in general
practice, which assumes the valuator to be possessed of the
capability of at once determining the value of a piece of land while
he is upon the field without reference to particular circumstances
VALUATION OF ESTATES.
585
that may specially affect it. To that practice I take an exception,
and say that it is not a correct one. I am fully aware of all the
imputations to which I shall be subjected for promulgating ideas
contrary to generally accepted customs. I shall be dignified with
the title of "Theorist," and many similar appellations. But
"theory with practice " has ever been a favorite motto with me,
and I have sufficiently considered the matter to know that a sound
theory is as requisite in land valuing as in any other art or science.
The only thing that requires to be estimated on the ground is
the produce the land is capable of yielding, which may be expressed
in bushels of wheat or barley, according to the nature of the soil,
which should be noted.
I would then advise every valuer to reduce to the same mea-
sure (bushels of wheat or barley,) all other items that enter into the
computation of the cost of production, out-goings, &c., and to tabu-
late the results according to his notions of expense and profit, and
he will find the arrangement conducing to convenience and
advantage.
To illustrate what I mean and what the Tables should be, take
the figures in my previous example to represent the produce in
bushels of wheat on three acres of land.
We will discuss four cases and tabulate the results. The first
shall be in every respect as it stands originally, and shall be sup-
posed to be on light land: the second is supposed to be land of
the same density and fertility, but subject to 5 bushels of taxation
instead of 10. The third case is heavy land, and the cost of culti-
vation becomes 70 instead of 53; other charges remaining the same.
The fourth and last case is on heavy land, with the same charge of
70 bushels for cost of cultivation, but taxes reduced to 5.
The Table would be thus-

PRODUCE 100 BUSHELS.
LIGHT ARABLE LAND.
HEAVY ARABLE Land.
Local Burthens, in-
Rent in
cluding Tithe Rent
Bushels of
Charge, Rates, and
Tenant's Taxes.
Wheat.
Local Burthens, in-
cluding Tithe Rent
Charge, Rates, and
Tenant's Taxes.
Rent in
Bushels
of Wheat.
When amounting
to 10 Bushels p. acre
20
When amounting
to 10 Bushels p. acre
5
25
5
∞ 00
3
8
""
20
586
VALUATION OF ESTATES.
It will be obvious that a system of Tables of this nature ex-
tended to every variety of soil that differs in its cost of cultiva-
tion and in fertility, and to all the variations of taxation, would be
the most equitable mode of valuing land that could be well devised.
The Tables once made would be permanent, as the results
show the rent in bushels of wheat, and whether that grain were
worth in the market 5, 6, or 7s. per bushel, would be equally
applicable.
When time permits, it is my intention to calculate, for publication,
a series of tables of this nature.
Cottages on a farm should form the subject of an additional
item in the valuation, affording as they do the convenience of
locating the permanent labourers in desirable proximity to their
several occupations. Cottages, therefore, if judiciously situated
quite enhance the value of a farm, to the extent of their fair annual
value.
It is not intended in this paper to treat of the geological
knowledge necessary to the proper practice of land valuing, but
simply to elucidate correct principles therein. Consequently we
now approach the consideration of those special circumstances
which affect the value of land in particular localities, and raise it
above its ordinary value to an extent only limited by the nature
of the particular causes which operate upon it. This is what is
properly called accommodation land. Land in the neighbourhood
of a large town, desirable in small quantities to the inhabitants,
for the acquirement of which great competition usually exists,
partakes of this character; as does also land adjoining, but not
belonging to a gentleman's residence, the renting of which will
afford him pleasureable amusement, or the means of removing or
preventing a nuisance; and many other cases, too numerous to
mention, but which will at once suggest themselves to every man
of business.
It will be obvious that the value of this description of land,
depends upon circumstances wholly beyond the rules which
regulate the worth of ordinary estates. And it will be equally
manifest that no defined directions can be given for estimating this
extra value, which can be alone arrived at by a full consideration
of all the attendant circumstances.
Wood Lands occasionally perplex the valuation of an estate. If
the tenant has the liberty of using the lands in his occupation as
may be most conducive to his own interest, the value of mere
coppice lands, by which I mean lands growing underwood, is
manifestly in accordance with the agricultural character of the soil
VALUATION OF ESTATES.
587
and subsoil; and for this reason-a valuation should always re-
present the worth of an estate at the time it is made according to
its natural capabilities under liberal and judicious treatment; there-
fore, it should be assumed, that whatever the mode of cultivation
might be, it is such as has been found by experience to conduce
most largely in conjunction with local circumstances to the
advantage of the occupier.
On the other hand, if a valuer is exercising his profession for the
purpose of estimating the rent of a farm upon which the tenant is
bound to maintain all existing coppices and underwoods, either as
preserves for game, or for other purposes over which he has no
control, then, although the intrinsic value of the land remains the
same, and should be so reported, still a greater rent cannot be
charged the tenant than he can be enabled to pay out of the pro-
ceeds of the sale of the underwood, after defraying the whole of the
expenses attending its cultivation and conversion, a proper interest
for the use of his capital, and a fair remuneration to himself for his
superintendence; and if the worth of the underwood when con-
verted is not sufficient to meet these demands, then a sufficient sum
must be deducted from the rent of the remaining lands to make up
the deficiency, as it is manifestly in strict accordance with justice
and equity that the landlord should alone suffer from a cause which
he only is instrumental in perpetuating.
Wood lands, properly speaking, that is to say, lands growing
timber trees, can only be estimated by the value of the timber
they are capable of producing after a certain number of years'
growth. A very small annual value sometimes attaches to wood
lands offering pasture to cattle, but no general rule can be laid
down for its computation.
Before I conclude this portion of my subject, it will be proper to
observe, with reference to the cost of labour upon a farm, that the
interest of an agricultural peasant in the land he cultivates must al-
ways be such as will afford him a maintenance, to whatever fluctua-
tions the landlord's and tenant's interests therein may be nevertheless
subjected. Both the proprietor and the occupier may be possessed
of means that will enable them to speculate upon the future pros-
pects of their respective positions, and to agree upon some arrange-
ment that may exist between them throughout the continuance of
a long lease; but the labourer of necessity can become no party to
such a contract. The daily wants of himself and family are the
same continually, partaking only of a pecuniary character, inas-
much as his requirements consist of a sufficiency of the necessities
of life to enable him to conduct and carry on his humble avoca-
588
VALUATION OF ESTATES.
tions with comfort to himself and satisfaction to those for whose
advantage he is toiling, and who are in consequence equally in-
terested in his prosperity.
Therefore, in considering the cost of labour, the rate of wages is
a primary consideration, and no method seems better calculated to
ensure the proper fulfilment of this desideratum, than the method
of valuing I have endeavoured to explain, that takes for its basis
an estimate of all the items in bushels of wheat, inasmuch as it
affords to the labourer a uniform amount of bread-stuff for the sus-
tenance of his family irrespective of fluctuations in price.
THE PURCHASE VALUE OF ESTATES.
Having arrived at the annual rent which land is fairly worth to
a tenant, if we deduct the amount of landlord's out-goings and bur-
thens to which it is subject, we obtain a clear income or net an-
nuity in perpetuity to the possessor, the value of which in fee
simple it is very easy to determine. It is customary to assume
that freehold land is worth 30 years' purchase, but its exact value
must of course depend upon the worth of other good securities at
the same time. The following Tables will be found to contain all
the information and assistance that can be required in reducing
the net annual rental of an estate to its purchase value, whether it
be freehold (equal to an annuity in perpetuity,) or leasehold of
any denomination.
VALUATION OF ESTATES.
589
A
Table 1. Showing the NUMBER OF YEARS' PURCHASE upon
the Net Rental required to return a given Rate of Interest.

Rate of Interest
per Centum per
Annum.
Number of Years'
Purchase on the net
Rental.
2
50
44.4
40
23030
36.3
3
33.3
31
30.7
31/1
28.5
26.6
4
25
44
23.25
22.2
21
5
6
LO LO LO LO CO CÓ CONT778
20
19
51
18.1
52
17.4
6
16.6
16
15.4
14.8
14.2
71
13.7
13.3
12.9
12.5
EXAMPLE. 1. An Estate required to pay 4 per cent. interest must be purchased
at 22.2 years.
EXAMPLE 2. An Estate purchased at 30.7 years' purchase pays 31 per cent
interest.
590
VALUATION OF ESTATES.
Table 2. Showing the PRESENT WORTH of an ESTATE, LEASE,
or ANNUITY, for any number of years certain and in perpetuity, a t
the several rates of Interest which a purchaser may thereby make o f
his money.
Note.-The rate of Interest shown in this Table is that which a purchaser may
make of his money, and get back his Capital, provided he can re-invest his money at
the same rate of Interest.

Years Purchase at
Years Purchase at
3
4
5
Term of
6
Years.
per cent. per cent. per cent. per cent.
8
9
↑
10
per cent. per cent. per cent. per cent.
.5
.5
.5
.5
1.
1.
1.
.9
1
.9
is ir
.5
.5
.5
.5
.9
.9
.9
1.4
1.4
1.4
1.4
11
1.4
1.4
1.3
1.3
1.9
1.9
$1.9
1.8
1.8
1.8
1.8
1.7
2.4
2.3
2.3
2.3
23/
2.2
2.2
2.2
2.1
2.8
2.8
2.7
2.7
2.6
3.3 3.2
3.1
3.1
3호
​3.
ai ai
2.6
2.5
2.5
3.
2.9
2.8
3.7 3.6
3.5
3.5
4
3.4
3.3
3.2
3.2
4.2 4.
3.9
3.8
3.7
3.7
3.6
3.5
4.6
4.5
4.3
4.2
cr
4.1
4.
3.9
3.8
5.
4.9
4.7
4.6
5-1/2
4.4
4.3
4.2
4.1
5.4
5.2
5.1
5.
6
CO
4.8
4.6
4.5
4.4
5.8 5.6
5.4
5.3
61/1
5.1
4.9
4.8
4.6
6.2
6.
5.8
5.6
6.6
6.4
6.1
5.9
7.
6.7
6.5 6.2
778
5.4
5.2
5.
4.9
7호
​5.7
5.5
5.3
5.1
6.
5.7
5.5
5.3
7.4
7.1
6.8
6.5
8호
​6.2
6.
5.8
5.6
7.8 7.4
7.1
6.8
9
6.5
6.2
6.
5.8
8.2 7.8
7.4
7.1
91
6.8
6.5
6.2
6.
8.5 8.1 7.7
7.4
10
7.
6.7
6.4
6.1
8.9 8.4
8.
7.6
101
7.3
6.9
6.6
6.3
9.2 8.8
8.3
7.9
11
7.5
7.1
6.8
6.5
9.6
9.1
8.6
8.1
111
7.7
7.3
7.
6.7
9.9
9.4
8.9
8.4
12
7.9
7.5
7.2
6.8
10.3 9.7
9.1
8.6
121
8.2
7.7
7.3
7.
10.6 10.
9.4 8.9
13
8.4
7.9
7.5
7.1
11.
10.3
9.6
9.1
131/1
8.6
8.1 7.6
7.2
11.3 10.6 9.9 9.3
14
8.7
8.2
7.8
7.4
11.6 10.8
10.1
9.5
14
8.9
8.4
7.9
7.5
11.9 11.1
10.4 9.7
15
9.1
8.6
8.1
7.6
12.2 11.4 10.6
9.9
151
9.3
8.7
8.2
7.7
12.6 11.7
10.8 10.1
16
9.4
8.9
8.3
7.8
12.9 11.9 11.1 10.3
13.2 12.2 11.3 10.5
13.5 12.4 11.5 10.7
13.7 12.7 11.7 10.8
161
9.6
9.
8.4
7.9
17
9.8
9.1
8.5
8.
171
9.9
9.2 8.7
8.1
18
10.1
9.4 8.8
8.2
EXAMPLE. A Lease for seven years to make 5 per cent. is worth in present money
5.8 years' purchase.
If it is required to make 6 per cent. it will only be worth 5.6 years' purchase.
Again, a Lease for fourteen years that can be purchased for 8.2 years' purchase
will pay 8 per cent. and get back the principal.
VALUATION OF ESTATES.
591
Table 2. Showing the PRESENT WORTH of an ESTATE, LEASE,
or ANNUITY, for any number of years certain and in perpetuity,
at the several rates of Interest which a purchaser may thereby make
of his money.
Note. The rate of Interest shown in this Table is that which a purchaser may
make of his money, and get back his Capital, provided he can re-invest his money at
the same rate of Interest.

3
Years Purchase at
4 5
per cent. per cent. per cent. per cent.
Years Purchase at
Term of
6
7
Years.
8 9
per cent. per cent. per cent. per cent.
10
14. 12.9 11.9
14.3 13.1 12.1
11.
18/1/
10.2 9.5
8.9
8.3
11.2
19
10.3
9.6
8.9
8.4
14.6
13.4 12.3
11.3
193
10.5
9.7
9.
8.4
14.9
13.6 12.5
11.5
20
10.6
9.8
9.1
8.5
15.1 13.8 12.6
11.6
201
10.7
9.9
9.2
8.6
15.4 14. 12.8
11.8
21
10.8
10.
9.3
8.6
15.7 14.2
13.
11.9
211
10.9
10.1
9.4
8.7
15.9 14.5
13.2
12.
22
11.1
10.2
9.4
8.8
16.2 14.7
13.3
12.2
221/
11.2
10.3
9.5
8.8
16.4
14.9
13.5
12.3
23
11.3
10.4
9.6
8.9
16.7 15.1
13.6
12.4
231
11.4
10.5
9.6
8.9
16.9 15.2
13.8 12.5
24
11.5 10.5
9.7
9.
17.2 15.4
13.9
12.7
243
11.6 10.6
9.8
9.
17.4 15.6
14.1 12.8
25
11.7
10.7
9.8
9.1
17.6 15.8
14.2 12.9
253
11.7
10.7
9.9
9.1
17.9 16. 14.4 13.
26
11.8
10.8
9.9
9.2
18.1 16.2 14.5
13.1
261
11.9
10.9 10.
9.2
18.3 16.3 14.6 13.2
27
12.
10.9
10.
9.2
18.5 16.5 14.8 13.3
271
12.1
11.
10.1
9.3
18.8
19. 16.8 15.
19.2 17. 15.1 13.6
19.4 17.1 15.3
19.6
19.8 17.4 15.5
16.7 14.9 13.4
28
12.1 11.1
10.1 9.3
13.5
281
12.2 11.1
10.2 9.3
29
12.3 11.2
10.2
9.4
13.7
291
12.3 11.2
10.2
9.4
17.3 15.4
13.8
30
12.4 11.3
10.3 9.4
13.8
30
12.5 11.3
10.3 9.5
20. 17.6 15.6 13.9
31
12.5 11.3
10.3 9.5
20.2 17.7 15.7 14.
311
12.6 11.4
10.4 9.5
20.4 17.9 15.8
14.1
32
12.6 11.4
10.4
9.5
20.6 18. 15.9
14.2
321
12.7 11.5
20.8 18.1 16. 14.2
33
12.8
20.9 18.3 16.1 14.3
331
10.4 9.5
11.5 10.5 9.6
12.8 11.6 10.5 9.6
21.1 18.4 16.2
14.4
34
12.9
11.6 10.5
9.6
21.3 18.5 16.3
14.4
341
12.9
11.6 10.5
9.6
21.5 18.7 16.4 14.5
35
12.9
11.7 10.6
9.6
21.7 18.8 16.5 14.6
21.8 18.9 16.5 14.6
351
13. 11.7 10.6
9.7
36
13.
11.7 10.6
9.7
EXAMPLE.—A Lease for 21 years to pay 4 per cent and get back the principal is
worth in present money 14 years' purchase.
To pay 5 per cent. the same Lease is worth 12.8 years' purchase.
To pay 7 per cent. 10.8 years' purchase, &c.
592
VALUATION OF ESTATES.
Table 2. Showing the PRESENT WORTH of an ESTATE, LEASE,
or ANNUITY, for any number of years certain and in perpetuity, at
the several rates of Interest which a purchaser may thereby make of
his money.
Note.-The rate of Interest shown in this Table is that which a purchaser may
make of his money, and get back his Capital, provided he can re-invest at the
same rate.

Years Purchase at
Years Purchase at
3
4
5
6
Term of
Years.
7
8
9
10
per cent. per cent. per cent. per cent.
cent.per
per cent. per cent. per cent. per cent.
22.2 19.1 16.7
14.7
37
13.1
11.8 10.7 9.7
22.5 19.4 16.9
22.8 19.6
23.1 19.8
14.8
38
13.2
11.8 10.7
9.7
17.
14.9
39
13.3
11.9
10.7
9.8
17.2
15.
40
13.3
11.9
10.8
9.8
23.4 20. 17.3
15.1
41
13.4
12.
10.8
9.8
23.7 20.2
17.4
15.2
42
13.5
12.
10.8
9.8
24.
20.4 17.5
15.3
43
13.5
12.
10.8
9.8
24.3 20.5
17.7
15.4
44
13.6 12.1
10.9
9.8
24.5 20.7 17.8
15.5
45
13.6
12.1
10.9
9.9
24.8
20.9
17.9
15.5
46
13.6
12.1 10.9
9.9
25.
21.
18.
15.6
47
13.7 12.2
10.9
9.9
25.3 21.2 18.1
15.6
48
13.7 12.2
10.9
9.9
25.5 21.3 18.2
15.7
49
13.8
12.2
10.9
9.9
25.7
26. 21.6 18.3
21.5 18.3 15.8
50
13.8 12.2 11.
9.9
15.8
51
13.8
12.3
11.
9.9
26.2 21.7 18.4 15.9
52
13.9
12.3
11.
9.9
26.4 21.9 18.5 15.9
53
13.9
12.3
11.
9.9
26.6 22. 18.6 15.9
54
13.9
12.3
11.
9.9
26.8 22.1
18.6 16.
55
13.9
12.3
11.
9.9
27. 22.2
18.7 16.
56
14.
12.3 11.
10.
27.2 22.3
18.8 16.
57
14.
12.3 11.
10.
27.3 22.4 18.8 16.1
58
14.
12.4 11.
10.
27.5 22.5 18.9
16.1
59
14.
12.4
11.
10.
27.7 22.6 18.9
16.1
60
14.
12.4
11.
10.
27.8 22.7 19.1 16.2
61
14.
12.4 11.
10.
28. 22.8
19. 16.2
62
14.1
12.4 11.1 10.
28.1 22.9
19.1
16.2
63
14.1
12.4 11.1 10.
28.3 23.
19.1 16.3
64
28.5 23. 19.2 16.3
65
14.1 12.4 11.1 10.
14.1 12.4 11.1 10.
28.6
28.7
23.1 19.2
23.2
16.3
66
14.1 12.4 11.1 10.
19.2 16.3
67
28.9 23.3 19.3 16.3
68
14.1 12.4 11.1 10.
14.1 12.4 11.1 10.
29. 23.3 19.3
16.4
69
14.1
29.1 23.4 19.3 16.4
70
12.4 11.1 10
14.2 12.4
11.1 10
29.2 23.4 19.4 16.4
29.3 23.5 19.4 16.4
2223
71
14.2 12.4 11.1 10
72
14.2 12.4 11.1 10.
EXAMPLE.—An Estate held for sixty years to get back principal and interest is.
worth in present money:
If 3 per Cent. Interest is required
•
27.7 years' purchase
4
22.€
"
10
5
18.9
""
35
16.1
VALUATION OF ESTATES.
593
Table 2. Showing the PRESENT WORTH of an ESTATE, LEASE,
or ANNUITY, for any number of years certain and in perpetuity, at
the several rates of Interest which a purchaser may thereby make of
his money.
Note.-The rate of Interest shown in this Table is that which a purchaser may
make of his money, and get back his Capital, provided he can re-invest at the
same rate.

3
Years Purchase at
4
5
6
Term of
Years.
Years Purchase at
8
9
10
per cent. per cent. per cent. per cent.
29.5 23.6 19.4 16.4
29.6 23.6
19.5 16.4
29.7 23.7
19.5
16.4
29.8 23.7
19.5 16.5
29.9 23.8
19.5 16.5
30.
30.1 23.9
23.8
19.5 16.5
19.6 16.5
30.2 23.9 19.6
16.5
8IILIAFI
per cent. per cent. per cent. per cent.
14.2 12.4 11.1 10.
14.2 12.5 11.1 10.
75
14.2
76
14.2
12.5
12.5 11.1 10.
10.
11.1
77
14.2
12.5
11.1 10.
14.2
12.5
11.1
10.
14.2
12.5 11.1
10.
80
14.2
12.5
11.1
10.
30.3 24. 19.6
16.5
81
14.2
12.5
11.1
10.
30.4 24.
19.6
16.5
82
14.2
12.5
11.1
10.
30.5 24.
19.6
16.5
83
14.2
12.5 11.1
10.
30.6 24.1
19.7 16.5
84
14.2
12.5 11.1 10.
30.6 24.1 19.7
16.5
85
14.2
12.5 11.1 10.
30.7 24.1 19.7
16.5
86
14.2
12.5 11.1 10.
30.8 24.2 19.7 16.6
87
14.2 12.5 11.1
10.
30.9 24.2 19.7
16.6
88
14.2
12.5 11.1 10.
30.9 24.2
19.7 16.6
89
14.2
12.5 11.1 10.
31. 24.3
19.7 16.6
90
14.2
12.5 11.1 10.
31.1 24.3
19.8 16.6
91
14.2
12.5 11.1 10.
31.1 24.3
19.8 16.6
92
14.3
12.5 11.1 10.
31.2 24.3 19.8
16.6
93
14.3
12.5 11.1 10.
31.3 24.4
19.8 16.6
94
14.3
12.5 11.1 10.
31.3 24.4 19.8
16.6
95
14.3
12.5 11.1 10.
31.4 24.4 19.8
16.6
96
14.3
12.5 11.1 10.
31.4 24.4 19.8
16.6
97
14.3 12.5
11.1 10.
31.5 24.5 19.8
16.6
98
14.3
12.5
11.1 10.
31.5 24.5 19.8 16.6
31.6 24.5 19.8 16.6
99
14.3
12.5
11.1 10.
100
14.3 12.5
11.1 10.
33.3 25. 20.
16.7 Perpetuity 14.3
12.5 11.1 10.
EXAMPLE.—A Lease for ninety-nine years to pay 7 per cent., and get back the
principal, is worth 14.3 years' purchase.
The Fee Simple of a Freehold Estate to pay 5 per cent. is worth 20 years' pur-
chase or to pay 3 per cent., 33.3 years' purchase.
594
VALUATION OF ESTATES.
Table 3. PRESENT WORTH of Property held on a single life, as
of a person in possession of a LIVING or BENEFICE, or the
holder of a LEÃSE, ESTATE, or ANNUITY, according to the
Northampton Table of Mortality.
*
Note. The rate of Interest shown in this Table is that which a purchaser can
make of his money, and get back his Capital, provided he can re-invest at the
same rate.

Years Purchase at
Years Purchase at
Age of
3
4
5
6
7
8
the Life.
per cent.
per cent.
per cent.
per cent.
per cent.
per cent.
16.
13.5
11.6
1
10.1
9.
8.
18.6
15.6
13.4
2
11.7
10.4
9.3
19.6
16.5
14.1
3
12.3
10.9
9.8
20.2
17.0
14.6
4
12.8
11.3
10.1
20.5
17.2
14.8
5
13.
11.5
10.3
20.7
17.5
15.
6
13.2
11.7
10.5
20.9
17.6
15.2
7
13.3
11.8
10.6
20.9
17.7
15.2
8
13.3
11.8
10.6
20.8
17.6
15.2
9
13.3
11.8
10.6
20.7
17.5
15.1
10
13.3
11.8
10.6
20.5
17.4
15.
11
13.2
11.8
10.6
20.3
17.3
14.9
12
13.1
11.7
10.5
20.1
17.1
14.8
13
13.
11.6
10.5
19.9
16.9
14.7
14
13.
11.5
10.4
19.7
16.8
14.6
15
12.9
11.5
10.3
19.4
16.6
14.5
16
12.8
11.4
10.3
19.2
16.5
14.3
17
12.7
11.3
10.2
19.
16.3
14.2
18
12.6
11.2
10.1
18.8
16.2
14.1
19
12.5
11.2
10.1
18.6
16.
14.
20
12.4
11.1
10.
18.5
15.9
13.9
21
12.3
11.
10.
18.3
15.8
13.8
22
12.3
11.
9.9
18.1
15.7
13.7
23
12.2
10.9
9.9
18.
15.6
13.7
24
12.1
10.9
9.9
17.8
15.4
13.6
25
12.1
10.8
9.8
17.6
15.3
13.5
26
12.
10.8
9.8
17.5
15.2
13.4
27
11.9
10.7
9.7
17.3
15.1
13.3
28
11.8
10.7
9.7
17.1
14.9
13.2
29
11.8
10.6
9.6
16.9
14.8
13.1
30
11.7
10.5
9.6
16.7
14.6
13.
31
11.6
10.5
9.5
16.5
14.5
12.9
32
11.5
10.4
9.5
16.3
14.3
12.7
33
11.4
10.3
9.4
16.1
14.2
12.6
34
11.3
10.3
9.4
15.9
14.
12.5
35
11.2
10.2
9.3
15.7
13.9
12.4
36
11.1
10.1
9.2
EXAMPLE. An Estate, Annuity, or a Lease, held on a single life aged 29, to make
4 per cent, and to get back the Principal, is worth 14.9 years purchase.
To make 5 per cent. it would be 13.2 years' Purchase
The Carlisle Tables of Mortality are the most favorable to the seller of
Lifehold Estates, and the London the most favorable to the purchaser. The
Northampton Tables as the mean may perhaps be considered the most equitable.
VALUATION OF ESTATES.
595
Table 3 continued. PRESENT WORTH of PROPERTY held on a
single life, as of a person in possession of a LIVING or BENEFICE,
or the holder of a LEASE, ESTATE, or ANNUITY, according to
the Northampton Table of Mortality.
Note.-The rate of Interest shown in this Table is that which a purchaser may
make of his money, and get back the Principal, provided he can re-invest at the
same rate.

Years Purchase at
Years Purchase at
Age of
3
4
5
6
17
8
the Life.
per cent.
per cent.
per cent.
per cent.
per cent.
per cent.
15.5
13.7
12.2
37
11.
10.
9.2
15.3
13.5
12.1
38
10.9
9.9
9.1
15.1
13.4
12.
39
10.8
9.8
9.
14.8
13.2
11.8
40
10.7
9.8
8.9
14.6
13.
11.7
41
10.6
9.7
8.9
14.4
12.8
11.6
42
10.5
9.6
8.8
14.2
12.7
11.4
43
10.4
9.5
8.7
13.9
12.5
11.3
44
10.2
9.4
8.6
13.7
12.3
11.1
45
10.1
9.3
8.5
13.4
12.1
10.9
46
10.
9.2
8.4
13.2
11.9
10.8
47
9.8
9.
8.3
13.
11.7
10.6
48
9.7
8.9
8.2
12.7
11.5
10.4
49
9.6
8.8
8.1
12.4
11.3
10.3
50
9.4
8.7
8.
12.2
11.1
10.1
51
9.3
8.6
7.9
11.9
10.8
9.9
52
9.1
8.4
7.8
11.7
10.6
9.7
53
9.
8.3
7.7
11.4
10.4
9.6
54
8.8
8.2
7.6
10.9
10.
9.2
56
8.5
7.9
7.4
10.3
9.5
8.8
58
8.2
7.6
7.1
9.8
9.
8.4
60
7.8
7.3
6.9
9.2
8.5
8.
62
7.4
7.
6.6
8.6
8.
7.5
64
7.1
6.6
6.3
8.
77.5
7.4
6.9
6.7
6.4
6.1
5.8
5.5
5.2
4.9
4.7
4.4
4.2
3.8
3.6
3.2
3.1
2.8
2.7
ZÓW ti ti að aɔ ci
7.
66
6.6
6.3
5.9
6.5
68
6.2
5.9
5.6
6.
70
5.7
5.4
5.2
5.5
72
5.2
5.
4.8
5.
74
4.8
4.6
4.4
4.5
76
4.3
4.2
4.0
4.
78
3.9
3.7
3.6
3.5
80
3.4
3.3
3.2
3.
82
2.9
2.8
2.8
2.6
84
2.6
2.5
2.4
2.5
2.4
2.3
86
2.3
2.2
2.2
2.2
2.1
2.1
88
2.
2.
1.9
1.8
1.8
1.7
90
1.7
1.7
1.6
EXAMPLE. An Estate, Annuity, or a Lease, held on a single life aged 50, to
make 3 per cent. and to get back the Principal, is worth 12.4, years' purchase.
To make 4 per cent. it would be 11.3 years' purchase.
The next presentation to a living being vacant is to be considered as a Lifehold
at 5 per cent. All annual charges, of whatever kind (including that of a Curate,)
must be deducted from the gross income to find the net annual income.
596
VALUATION OF ESTATES.
Table 4. PRESENT WORTH of Property held on a single life, as of
a person in possession of a LIVING or BENEFICE, or the holder
of a LEASE, ESTATE, or ANNUITY, according to the Carlisle
Table of Mortality.
Note.-The rate of Interest shown in this Table is that which a Purchaser may
make of his money, and get back his Principal, provided he can re-invest at the
same rate.

Years Purchase at
Years Purchase at
3
4
5
Age of
the Life.
6
7
8
per cent.
per cent.
per cent.
per cent. per cent.
per cent.
20.1
16.6
14.
21.5
17.7
15.
22.7
18.7
15.8
23.3
19.2
16.3
23.7
19.6
16.6
23.8
19.7
16.7
23.9
19.8
16.8
123 LO CON
12.1
10.6
9.4
12.9
11.3
10.1
13.7
12.
10.7
4
14.
12.3
11.
5
14.3
12.6
11.2
6
14.5
12.7
11.3
7
14.5
12.8
11.4
23.8
19.8
16.8
8
14.5
12.8
11.4
23.7
19.7
16.7
9
14.5
12.8
11.4
23.5
19.6
16.7
10
14.4
12.7
11.3
23.3
19.5
16.6
11
14.4
12.7
11.3
23.1
19.3
16.5
12
14.3
12.6
11.3
23.
19.2
16.4
13
14.3
12.6
11.2
22.8
19.1
16.3
14
14.2
12.5
11.2
22.6
19.
16.2
15
14.1
12.5
11.1
22.4
18.8
16.1
16
14.1
12.4
11.1
22.2
18.7
16.1
17
14.
12.4
11.1
22.1
18.6
16.
18
14.
12.3
11.1
21.9
18.5
15.9
19
13.9
12.3
11.
21.7
18.4
15.8
20
13.8
12.3
11.
21.5
18.2
15.7
21
13.8
12.2
10.9
21.3
18.1
15.6
22
13.7
12.2
10.9
21.1
18.
15.5
23
13.6
12.1
10.9
20.9
17.8
15.4
24
13.5
12.
10.8
20.7
17.6
15.3
25
13.5
12.
10.8
20.4
17.5
15.2
26
13.4
11.9
10.7
20.2
17.3
15.1
27
13.3
11.8
10.7
20.
17.2
14.9
28
13.2
11.8
10.6
19.8
17.
14.8
29
13.1
11.7
10.5
19.6
16.9
14.7
30
13.
11.6
10.5
19.3
16.7
14.6
19.1
16.6
14.5
32
18.9
16.4
14.4
33
18.7
16.2
14.3
18.4
16.
14.1
18.2
15.9
14.
22828
12.9
11.6
10.5
12.9
11.5
10.4
12.8
11.4
10.4
34
12.7
11.4
10.3
35
12.6
11.3
10.2
36
12.5
11.2
10.2
EXAMPLE. An Estate, Annuity, or a Lease held on a single life aged 29, to
make 4 per cent. and get back the Principal, is worth 17 years' purchase.
To make 5 per cent., 14.8 years' purchase.
VALUATION OF ESTATES.
597
Table 4 continued. PRESENT WORTH of Property held on a single
life, as of a person in possession of a LIVING or BENEFICE, or
the holder of a LEASE, ESTATE, or ANNUITY, according to the
Carlisle Table of Mortality.
Note.-The rate of Interest shown in this Table is that which a Purchaser can
make of his money, and get back his Capital, provided he can re-invest at the
same rate.

Years Purchase at
Years Purchase at
3
4
5
Age of
the Life.
6
17
8
per cent.
per cent.
per cent.
per cent.
per cent.
per cent.
17.9
15.7
13.8
37
12.4
11.1
10.1
17.7
15.5
13.7
38
12.2
11.
10.
17.4
15.3
13.5
39
12.1
10.9
9.9
17.1
15.1
13.4
40
12.
10.8
9.9
16.9
14.9
13.2
41
11.9
10.8
9.8
16.6
14.7
13.1
42
11.8
10.7
9.7
16.4
14.5
13.
43
11.7
10.6
9.7
16.1
14.3
12.8
44
11.6
10.5
9.6
15.9
14.1
12.6
45
11.4
10.4
9.5
15.6
13.9
12.5
46
11.3
10.3
9.4
15.3
13.7
12.3
47
11.2
10.2
9.3
15.
13.4
12.1
48
11.
10.1
9.2
14.7
13.2
11.9
49
10.8
9.9
9.1
14.3
12.9
11.7
50
10.6
9.7
9.
13.9
12.6
11.4
51
10.4
9.6
8.8
13.6
12.3
11.2
52
10.2
9.4
13.2
11.9
10.9
53
10.
9.2
12.8
11.6
10.6
54
9.8
9.
12.
11.
10.1
56
9.3
8.6
∞ ∞ ∞ ∞Ó
8.7
8.5
8.4
75+
8.
11.2
10.3
9.5
58
8.8
8.2
7.6
10.5
9.7
8.9
60
8.3
7.7
7.2
9.9
9.1
8.5
62
7.9
7.4
6.9
9.2
8.6
8.
64
7.5
7.
6.6
8.6
8.
7.5
66
7.
6.6
6.3
7.9
7.4
6.9
68
6.5
6.2
5.9
7.1
6.7
6.3
70
6.
5.7
5.4
6.4
6.
5.7
72
5.4
5.2
4.9
5.8
5.5
5.2
74
4.9
4.7
4.5
5.3
5.
4.8
76
4.6
4.4
4.2
4.8
4.6
4.4
78
4.2
4.1
3.9
4.4
4.2
4.
80
3.9
3.7
3.6
3.9
3.7
3.6
82
3.5
3.3
3.2
84
mai ai
3.
2.9
2.8
86
2.8
2.5
- ∞
2.7
2.6
88
2.4
2.3
90
∞ ∞ ai ci ai
3.5
3.4
3.2
3.1
3.
2.9
2.7
2.7
2.6
2.5
2.4
2.4
2.3
2.2
2.1
EXAMPLE. An Estate, Annuity, or a Lease held on a single life aged 50, to
make 3 per cent. and get back the Principal, is worth 14.3 years' purchase.
To make 4 per cent., 12.9 years' purchase.
Note.-It will be observed that the Carlisle Table of Mortality is more favor-
able than the Northampton, and may be used accordingly on healthy lives.
598
VALUATION OF ESTATES.
Table 5. PRESENT WORTH of an ESTATE, ANNUITY, or a
LEASE held on Two Joint Lives, according to the Northampton
Table of Mortality.
Note.-The Rate of Interest shown in this Table is that which a purchaser may
make of his money, and get back his Principal, provided he can re-invest at the
same rate.

Years Purchase at
Years Purchase at
3
4
Ages.
5
6
per cent.
per cent.
per cent.
per cent.
16.34
14.28
10
10
12.66
11.34
15.15
13.36
10
20
11.91
10.72
14.15
12.59
10
30
11.30
10.24
12.79
11.51
10
40
10.44
9.54
11.04
10.08
10
50
9.26
8.55
8.95
8.31
10
60
7.75
7.25
6.35
6.01
10
70
5.70
5.42
3.65
3.52
10
80
3.39
3.28
14.13
12.53
20
20
11.23
10.16
13.29
11.87
20
30
10.71
9.73
12.10
10.92
20
40
9.94
9.10
20.52
9.63
20
50
8.86
8.19
8.60
8.00
20
60
7.46
6.99
6.15
5.83
20
70
5.53
5.26
3.57
3.44
20
80
3.32
3.21
12.59
11.31
30
30
10.25
9.36
11.57
10.49
30
40
9.58
8.79
10.16
9.32
30
50
8.60
7.97
8.38
7.80
30
60
7.29
6.84
6.04
5.73
30
70
5.44
5.18
3.53
3.41
30
80
3.29
3.18
10.76
9.82
40
40
9.02
8.32
9.59
8.83
40
50
8.18
7.60
8.02
7.49
40
60
7.01
6.59
5.87
5.57
40
3.47
3.35
40
8.71
8.08
50
7.46
6.99
50
5.58
5.30
50
3.36
3.25
50
6.61
6.23
60
5.14
4.90
60
3.20
3.09
60
4.26
4.09
70
| | | | | | | | | |
70
5.30
5.05
80
3.24
3.13
50
7.52
7.03
60
6.57
6.19
70
5.05
4.82
80
3.14
3.04
8282
60
5.89
5.58
70
4.68
4.48
80
2.99
2.90
70
3.93
3.78
EXAMPLE.-An Estate, Annuity, or a Lease held on Two Joint Lives, aged 40
and 50 years, which is to be determined on the death of either, to make 3 per
cent. and get back the Principal, is worth 9.59 years' purchase. To make 4 per
cent. it is worth 8.83 years' purchase.
Ages of
the Lives.
5
5
10
5 5 25.3 20.9
5 15 24.7 20.6
5 25 24.0 20.0
5 35 23.3 19.6|
45|| 22.6 19.0
5 55 21.9 18.5
65|| 21.3 18.0
-75 20.9 17.7
10 25.0 20.8
10 20 24.1 20.2|
10 30 23.4 19.7
10 40 22.7 19.2
10 50 22.1 18.7|
10 60 21.5 18.2
10 70 21.0 17.9 15.5
10 80 20.8 17.6| 15.3| 13.4|40
VALUATION OF ESTATES.
599
Table 6. Showing the PRESENT VALUE of an ESTATE, AN-
NUITY, or a LEASE, held on the longest of Two Lives, calculated
according to the Northampton Table of Mortality.
Note. The rate of interest shewn in this Table is that which a purchaser may
make of his money, and get back his Capital, provided he can re-invest at the
same rate.

10 40
or er er
Years Purchase at
5
3 4
6
p. cent. p. cent. p. cent. p. cent.
Ages of
the Lives.
Years Purchase at
4
5
6
3
p. cent. p. cent. p. cent. p. cent.
15.3
13.6
13.1
12.7
17.7 15.3 25 65|| 18.7 16.3| 14.3| 12.7
17.5 15.1 25 — 75|| 18.2 15.8
75 18.2 15.8 13.9 | 12.4
17.1| 14.9|30-30|| 20.3| 18.2
30 20.3 18.2 15.9 14.0
16.8| 14.6|30-40|| 20.2 | 17.5
40 20.2 17.5
16.4| 14.3 30 50 19.2 16.7 14.7
16.0 13.9 30. 60 18.3 16.0 14.2
15.6| 13.6|30 70 17.6 15.4 13.7 12.2
15.2 13.3 30
17.6| 15-2| 35
80
17.2 15.0| 13.3| 11.9
35
20.1 17.5 15.3 13.6
17.2| 15.0 | 35
45
19.0 16.6 14.7 13.1
16.9
14.7 35
55
18.0 15.8 14.0 12.5
16.5
14.5 35
65
17.1
17.1 15.0 13.4 12.0
16.1| 14.2 | 35
75
16.4 14.5 12.9 11.6
15.8
13.9 40
40
18.9 16.6 14.7 13.1
13.4 40
J
50 17.7 15.6 13.9 12.5
15.3
13.4 40
15
15| 24.0 20.2| 17.2
14.9 40
60 16.6 14.7 13.2
70 15.7 14.0 12.6 11.4
11.9
15
25|| 23.2 19.6 16.8
14.7 | 40
· 80 15.2 13.5 12.1
11.0
15
35|| 22.4| 19.0
16.4
14.4|45
45
17.6
15.6 13.9 12.5
15 45 21.7 18.5 16.0
15 55 21.0 17.9 15.6
15 65 20.4 17.4 15.2 13.3 45
15 75 19.9 17.1 14.8 13.1 50
20 20 23.1 19.5 16.8 14.6 50
20 30 22.3 18.9 16.4 14.3 50
20 40 21.4 18.3| 15.9 | 14.0|50
20 50 20.6 17.7 15.4 13.6 55
20 60 19.8 17.1 14.9 13.2 55
20 70|| 19.2 16.6| 14.5| 12.91 55
20 80 18.8 16.2 14.2 12.6 60
25 25 22.2 18.9 16.4 14.4 60
25 35 21.3 18.3 15.9 14.0 60
25 45 20.3 17.6| 15.4 13.6 65
25 55 19.5 16.9 14.8 13.170
14.0 45
55
16.3
16.3
14.5 13.1 11.8
13.7 45
65
15.1 13.6 12.3 11.3
75
14.3 12.9 11.6 10.6
55
50 16.2 14.4 13.0 11.8
60 14.8 13.3 12.1 11.0
70 13.6 12.3 11.2 10.3
80 12.9 11.7 10.6 9.8
14.6 13.2 12.0 11.0
65 13.1 12.0 11.0 10.1
75 12.0 11.0 10.1 9.3
710
- 60 12.9 11.9 10.9 10.1
70 11.4 10.5 9.7 9.1
80 10.4 9.6 8.9 8.3
75 9.5 8.9
9.2 8.6
8.4
8.1 7.6
7.8
EXAMPLE. An Estate, Annuity, or a Lease, to be determined at the death of
the longest of Two Lives, whose ages are 25 and 35 years; to make 3 per cent. and
get back the Principal, is worth 21.3 years' purchase; to make 4 per cent. it is
worth 18.3 years' purchase.
600
VALUATION OF ESTATES.
Table 77. PRESENT WORTH of an ESTATE, ANNUITY, or a
LEASE, held on the longest of Three Lives, according to the
Northampton Table of Mortality.
Note.-The rate of Interest shewn in this Table is that which a purchaser may
make of his money, and get back the Principal, provided he can re-invest at the
same rate.

Years Purchase at
Years Purchase at
Ages of the
Lives.
3
4 5
6
Ages of the
Lives.
3 4 5
6
p. cent.p.cent.p.cent.p.cent.
p.cent.p.cent. p. cent. p. cent.
10 10 10 26.6
||
10 10 20 || 26.2|
21.9 18.3
15.7
10 40 40
23.7 19.9 17.1 14.9
21.7| 18.3
15.7
10 40 50
23.1
19.6 16.8 14.7
10 10 30 25.8
10 10 40|| 25.4
21.4 18.0
15.6
10 40 60
22.9
19.4 16.7
14.6
21.1 17.9
15.5
10 40 70
22.7
19.1
19.1 16.5 14.4
10 10 50 25.3
20.8 17.7
15.3
10 45 45||
23.3
19.5 16.8 14.7
10 10 60
10 10 70
25.0
20.8 17.6|
15.2
10 45 55
22.6
19.2
16.6 14.6
25.0
25.0 20.8 17.6
20.8 17.6
15.2
15.2 10 45 65
10 45 65||
22.5
19.0 16.4 14.5
10 20 20
25.7 |
21.3 | 18.1
15.510 45 75
22.2
18.8
16.2 14.2
10 20 30
25.1
21.0 17.8
15.4
10 50 50
22.6 19.2
16.6| 14.5
10 20 40
24.6
20.6 17.6
15.2
10 50 60
22.2
18.9
16.3 14.3
10 20 50
24.5
20.4 17.4
15.1
10 50 70
22.0 18.7
16.1 14.1
10 20 60
24.3
20.3| 17.4
15.1
10 55 55
22.3 19.0 16.4 14.2
10 20 70
24.1
20.1 17.2
14.9 10 55 65
21.8
18.5 16.0 14.1
10 25 25
25.1
20.9 17.8
15.5 10 55 75
15.5 10 55 75
21.8
18.5
16.0 14.1
10 25 35
24.6
20.6 17.6
15.2
10 60 60
22.0
18.7 15.9 14.0
10 25 45
24.4
20.5 17.4
15.1
10 60 70
21.6
18.4 15.9 14.0
10 25 55
24.1| 20.3 17.2
|
14.9
10 65 65
21.5
18.2 15.8 14.2
10 25 65
23.9
20.1| 17.2
17.2
14.9
10 65 75|| 21.2
18.0 15.6 13.7
10 25 75
23.7
23.7
19.8| 17.0
19.8 17.0
14.7 10 70 70
14.7 10 70 70 || 21.3| 18.1 15.7 13.8
10 30 30
24.8
20.6 17.6
15.3
15 25 25
24.8 20.8 17.7 15.4
10 30 40
24.3
20.3| 17.4
15.1
15 25 35
24.2 20.3 17.4 15.2
10 30 50
23.8
20.0 17.2
15.0
15 25 45
23.9 20.2 17.2 15.0
10 30 60
23.6
19.8 17.0
14.8
10 30 70
23.5
19.7| 16.9
14.8
15 25 55
15 25 65
23.6 19.9 17.1 14.8
23.4 19.7 16.9 14.7
10 35 35
24.2
20.4 17.5
15.1 15 25 75
10 35 45
23.8
19.9 17.1
10 35 55 23.3 19.6 16.9
10 35 65 23.1 19.5 16.8
10 35 75 23.0 19.4 16.7
14.9 15 35 35
14.715 35 45
14.6 15 35 55
14.6 15 35 65
23.1 19.5 16.7 14.6
23.7 20.1 17.1| 15.0
23.3
19.7 16.9 14.8
22.7 19.3 | 16.6 | 14.6
22.5 19.1 16.5 14.5
EXAMPLE. An Estate, Annuity, or a Lease, to determine on the death of the
longest of Three Lives, aged 10, 35, and 55 years, to pay 3 per cent. and get back
the Principal, is worth 23.3 years' purchase. To make 4 per cent. it is worth 19.6
years' purchase:
VALUATION OF ESTATES.
601
Table 7 continued.
PRESENT WORTH of an ESTATE, AN-
NUITY, or a LEASE, held on the longest of Three Lives, according
to the Northampton Table of Mortality.
Note. The rate of interest shown in this Table is that which a purchaser may
make of his money, and get back the Principal, provided he can re-invest at the
same rate.

Years Purchase at
Years Purchase at
Ages of the
Lives.
3
4 5 6
p.cent.p.cent.p.cent.p.cent.
Ages of the
Lives.
3
4 5 6
p.cent.p.cent.p.cent.p.cent.
15 35 75
15 45 45
15 45 55
15 45 65
15 45 75
22.4 19.0 16.4
22.7 19.1 16.5
22.0 18.8 16.3
21.8 18.6 16.1
21.5 18.3 15.9
15 55 55
15 55 65
15 55 75
15 65 65
13.9 20 40 70
13.8 20 45 45
15 65 75
20 20 20
21.6 18.5 16.1
21.6 18.5 16.1
21.1
21.1
18.0 15.6
18.0 15.6
21.0 18.0 15.6
20.8 17.8 15.5
20.8 17.8 15.5
20.3 17.4 15.1
25.2 20.8 17.8
25.2 20.8 17.8
19.3 16.7 14.6
22.1 18.9 16.4| 14.4
14.0 20 40 60|| 21.7 18.6| 16.2| 14.2
14.4 20 35 55|| 22.1
14.6 20 35 65|| 21.9
14.3 20 35 75 21.8
21.8
14.2 20 40 40 || 22.8 |
22.8
14.0 20 40 50||
18.9 16.4| 14.4
18.7 16.2 14.3
18.6
18.6 16.1 14.2
19.3
21.4| 18.3 15.9 14.
22. 18.7
16.3 14.5
13.9 20 45 55|| 21.4
13.4 20 45 65|| 21.1
15.4 20 45 75| 20.8
18.4
16. 14.2
18.1
15.8| 14.1
17.9
15.5 13.8
20 20 30
24.5 20.6 17.6
15.2 20 50 50 ||
21.4
18.4| 16. 14.1
20 20 40
23.9 20.2 17.3
23.9 20.2 17.3
15.120 50 60||
20.9
18. 15.7 13.9
20 20 50
23.7 19.8 17.1
14.9 20 50 70
20.6
20.6
17.7 15.4 13.6
17.7
20 20 60
23.4 19.7 17.0
23.4 19.7 17.0
14.8 20 55 55
20.9 | 18. 15.6 13.8
20 20 70
23.2 19.5 16.8
14.6 20 55 65
20.3| 17.5
20.3 17.5
15.2 13.6
20 25 25
24.4 20.6 17.6
24.4 20.6 17.6
15.3 20 55 75
20.3| 17.3
20.3 17.3
15.2 13.5
20 25 35
23.8 20.1 17.3
15.1 20 60 60||
20.5
17.7
15.2 | 13.5
20 25 45
23.5 19.9
23.5 19.9 17.0
17.0
14.9 20 60 70 ||
20.
17.3
15.1 13.4
20 25 55
23.119.6
23.1 19.6
16.9
16.9
14.7 20 65 65|| 20.
17.2
15.1 13.6
20 25 65
22.9 19.4
22.9 19.4
16.7
16.7
14.6 20 65 75
19.5
16.8
14.7 13.1
20 25 75
22.6 19.1 16.5
14.4 20 70 70
19.6
16.9
14.8 13.1
20 30 30
24.4 20.1 17.3
24.4 20.1 17.3 15.1 30 30 30 || 23.3 | 19.6
17.
14.9
20 30 40
23.8
23.8 19.7 17.0
19.7 17.0 14.9 30 30 40
22.6
20 30 50
22.8
22.8 19.4 16.8
19.4 16.8
14.7 30 30 50
19.2
21.9 18.8 16.4 14.4
16.6 14.6
20 30 60
22.5
22.5
19.1 16.5
19.1 16.5
14.5 30 30 60
21.5
18.5 16.1 14.2
20 30 70
22.4
19.0 16.5
22.4 19.0 16.5 14.4 30 30 70
21.4
18.4 16. 14.1
20 35 35
23.3
19.8 16.9
23.3 19.8 16.9 14.8 30 35 35
22.5 19.3 16.6 14.7
2035 45
22.7 19.4 16.8 14.7 30 35 45
21.8 18.6| 16.2 14.4
EXAMPLE. An Estate, Annuity, or a Lease, to determine on the death of
the longest of Three Lives, aged 20, 25, and 55 years; to pay 3 per cent. and
get back the Principal, is worth 23.1 years' purchase. To make 4 per cent. it is
worth 19.6 years' purchase.
2 P
602
VALUATION OF ESTATES.
Table 7 continued. PRESENT WORTH of an ESTATE, AN-
NUITY, or a LEASE, held on the longest of Three Lives,
according to the Northampton Table of Mortality.
Note.-The Rate of Interest shown in this Table is that which a purchaser may
make of his money, and get back the Principal, provided he can re-invest at the
same rate.

Ages of the
Lives.
Years Purchase at
4
5
3
p. cent. p. cent. p. cent. p. cent.
6
Ages of the
Lives.
3 4
p. cent. p. cent. p. cent. p. cent.
Years Purchase at
5
6
30 35 55
21.1 18.2
15.9
14.1
40 45 75
18.2 16.
30 35 65
20.9
18.
15.7
14.
40 50 50
19.
14.2 12.8
16.7 14.9 13.3
30 35 75
20.7
17.9
15.6
13.8 40 50 60 ||
18.3
16.2
14.4 12.9
30 40 40
21.8
18.6 16.3
14.3 40 50 70 ||
17.8
17.8
15.7 14.
12.6
30 40 50
21.
18.2 15.9
14.1 40 55 55
18.3
16.2 14.2
12.8
30 40 60
20.6
17.8 15.6
13.9 40 55 65
17.5
15.5 13.8
12.6
30 40 70
20.2
17.5 15.4
13.6 40 55 75
17.3
15.3 13.7
12.4
30 45 45
21.1
18.2 16.
14.2 40 60 60
17.6
15.6 13.7
12.4
30 45 55
20.2
17.6 15.5
13.7 40 60 70
16.9 15.0 13.5
12.2
30 45 65
19.9
17.3
15.2
13.5 40 65 65
16.6 14.7 13.2 12.4
30 45 75 19.6
17. 14.9
13.3 40 65 75
16.2
14.4 12:9
11.8
30 50 50
20.2
17.6 15.5
13.8 40 70 70
16.2
14.5 13. 11.8
30 50 60
19.6
17.1 15.1
13.4 50 50 50
17.9
15.9 14.2 12.8
30 50 70
19.3
16.8 14.8
13.2 50 50 60
17.
15.2
13.6
12.3
30 55 55
19.7
17.2 14.9
13.4 50 50 70|| 16.4
14.6 13.2 12.
30 55 65
18.8
16.4 14.5
13.2 50 55 55 17.
15.2
13.6 12.3
30 55 75
18.7
16.3 14.3 13.
50 55 65
15.9
14.3
12.9 11.9
30 60 60
30 60 70
19.1| 16.7 | 14.6| 13.
18.6| 16.3 14.4
50 55 75
15.6
15.6
14. 12.7 11.6
12.9
50 60 60
16.
14.4 12.8 11.7
30 65 65
18.3 16. 14.1
13.
50 60 70
15.2
13.7
12.4 11.4
30 65 75
17.9 15.7 13.9
12.5 50 65 65
14.8
13.4 12.2 11.5
30 70 70
40 40 40
18.
15.8 14.
12.5 50 65 75
14.3
12.9 11.8 10.9
20.9
18. 15.8
20.
40 40 50
40 40 60 19.4
40 40 70 19.
40 45 45 20.
40 45 55 19.1 16.7 14.9
40 45 65 18.6 16.4 14.5
17.4 15.4
14.
13.7160 60 60||
50 70 70
14.3
14.3
12.9
11.8 10.8
14.6 13.2
12.0 11.0
17. 15.
13.4 60 60 70
13.5
12.4
11.4 10.5
16.6 14.7
13.1 60 65 65
13.2
12.1
11.1 | 10.7
17.5 15.5
13.8 60 65 75
12.4
11.4
10.5
9.8
13.3 60 70 70 || 12.3
12.3
13.
11.3 10.5
9.7
70 70 70 10.5 9.8 9.2
8.6
EXAMPLE. An Estate, Annuity, or a Lease, to determine on the death of the
longest of Three Lives, aged 30, 45, and 65 years, to pay 3 per cent. and get back
the Principal, is worth 19.9 years' purchase. To make 4 per cent. it is worth 17.3
years' purchase.
VALUATION OF ESTATES.
603
Table 8. AMOUNT of FINE to be paid for RENEWING any num-
ber of years lapsed IN A LEASE originally granted for 10 years.
Note.-The rate of Interest shown in this Table is that which a Purchaser may
make of his money, provided he can re-invest the surplus at the same rate, so as to
replace the Fine at the end of his Lease.

3
Years Purchase at
4
5
6
Years.
Years Purchase at
8
10 17.950
per cent. per cent. per cent. per cent.
per cent. per cent. per cent. per cent.
.7
.7
.6
.6
1
.5
.5
.4
1.5
1.4 1.3
1.1
2
1.1
1.
.8
2.3
2.1
1.9
1.8
3
1.6
1.5
1.3
247
+∞
.2
.4
.7
3.1
2.9
2.6
2.4
4
2.3
2.1
1.8
1.
3.9
3.7
3.4
3.1
2.9
2.7
2.4
1.4
4.8
4.5 4.2
3.9
6
3.6
3.4
3.
1.8
5.7
5.3
5.0
4.7
7
4.4
4.1
3.7
2.3
6.6 6.2
5.9
5.5
8
5.2
4.9
4.4
2.9
7.6 7.1 6.8
6.4
9
6.1
5.8
5.2
3.7
8.5
8.1 7.7 7.4
10
7.0
6.7
6.1
4.5
EXAMPLE.-The Fine which a Tenant should pay for the renewal of 5 years
lapsed in his Lease of 10 years, in order that he may make 4 per cent. for the
money he advances, is 3.7 years' purchase of the Net Annual Income.
604
VALUATION OF ESTATES.
Table 9. AMOUNT OF FINE to be paid for RENEWING any
number of years lapsed in a LEASE originally granted for Twenty
Years.
Note.-This Table shows the rate of Interest which a person may make of his
money, provided he can re-invest the surplus at the same rate of Interest, so as to
re-place the Fine at the end of the Lease.

Years Purchase at
3
4
5
6
Years.
Years Purchase at
7
8
10 £12 6 1
per cent. per cent. per cent. per cent.
per cent. per cent. per cent. per cent.
.6
.5
.4
.3
1.1
.9
.8
is co
.6
1.7
1.4
1.2
1.
2.3 1.9
1.6
1.4
2.9 2.5 2.1
1.8
3.6
4.2
4.9
að að +
3.
2.6 2.2
3.6
3.1 2.6
123LO CON
.3
.5
.8
∞O 2000
247
4 1.1
1.
& cr co i
.1
.2
.5
.3
.5
1.5 1.3
.9
.6
6
1.8 1.6
1.1
.8
7
4.2
3.6 3.1
8
5.6
4.8 4.2
3.6
9
6.3 5.5 4.7
4.1
10
7.1 6.2
5.4
4.7
11
ai aż að að +
2.2 1.9 1.4
1.
2.7 2.3
1.7
1.2
3.1
2.7 2.
1.5
3.6
3.1
2.4
1.7
4.1
3.6
2.8
2.1
7.9 6.9
6.
5.3
12
4.6
4.
3.2
2.4
8.6
7.6
6.7 5.9
13
5.2
4.6
3.6
2.8
9.5
8.3
7.4
6.6
14
5.8
5.2
4.2
3.3
10.3
9.1
8.1
7.3
15
6.5
5.8
4.7
3.8
11.2 10.
8.9
8.
16
7.2
6.5
5.3
4.3
12.
10.8
9.7 8.8
17
8.
7.2
6.
4.9
13. 11.7 10.6
9.7
18
8.8
8.
6.8
5.6
13.9 12.6 11.5
10.5
19
9.7
8.9
7.6
6.4
14.9 13.6 12.5
11.5
20
10.6
9.8
8.5
7.3
EXAMPLE. The Fine a Tenant should pay for the Renewal of 12 years lapsed in
a Lease originally granted for 20 years, to make 4 per cent. of the money he
advances, is 6.9 years' purchase of the net Income.
VALUATION OF ESTATES.
605
Table 10. AMOUNT OF FINE to be paid for RENEWING any
number of years lapsed in a LEASE originally granted for Twenty-
one Years.
Note. This Table shows the rate of Interest which a person may make of his
money, provided he can re-invest the surplus at the same rate of Interest, so as to
replace the Fine at the end of the Lease.

Years Purchase at
Years Purchase at
3
4
5
6
7
Years.
816
11.564
10
OR
£11 11 3
per cent. per cent. per cent. per cent.
per cent. per cent. per cent.
per cent.
.5
.4
.4
1.1
.9
.7
47
.3
.6
1.7 1.4
1.1
.9
2.2
1.9 1.5
1.3
2.9 2.4
2.
1.7
3.5 2.9
2.4 2.1
1234 LO CO
.2
.8
∞o ir is
.2
.5
24
.1
.1
.4
.3
.2
.6
.4
.3
1.1
.9
.6
.5
1.4
1.2
.8
.6
6
1.7
1.5
1.
.8
1935∞∞
4.1
3.5
2.9
2.5
2.1
1.8
1.3
1.0
4.8 4.
3.4
2.9
8
2.5
2.1
1.5
1.2
5.5
4.6
4.
3.4
9
2.9
2.5
1.8
1.5
6.2
5.3
4.5
3.9
10
3.3
2.9
2.2
1.7
6.9
5.9
5.1
4.4.
11
3.8
3.3
2.5
7.6
6.6 5.7
5.
12
4.3
3.8
2.9
ai ai
2.
2.4
8.4
7.3
6.4
5.6
13
4.9
4.3
3.3
2.7
9.2
8.
7.
6.2
14
5.4
4.8
3.8
3.2
10.
8.8 7.7
6.8
15
6.1
5.3
4.3
3.6
10.8 9.6
8.5
7.6
16
6.7
6.0
4.9
4.1
11.7 10.4 9.3
8.3
17
7.4
6.7
5.5
4.7
12.6 11.3 10.1
9.1
18
8.2
7.4
6.2
5.4
13.5 12.1 11.
9.9
19
9.
8.2
6.9
6.1
14.4 13.1 11.9 10.8
20
9.9
9.1
7.7
6.9
15.4 14. 12.8 11.8
21
10.8
10.
8.6
7.8
EXAMPLE. The amount of Fine which a Tenant should pay for the Renewal of
12 years lapsed in a Lease originally granted for 21 years, to make 4 per cent. of the
money he advances, is 6.6 years purchase of the Net Annual Income.
606
VALUATION OF ESTATES.
Table 11. AMOUNT OF FINE to be paid for RENEWING any
number of years lapsed in a LEASE originally granted for 40 years.
Note.-This Table shows the rate of Interest which a person may make of his
money provided he can re-invest the surplus, beyond the available interest, at the
same rate, so as to replace the Fine at the end of the Lease.

3
Years Purchase at
4
5
6
Years.
Years Purchase at
7
8
9
10
per cent. per cent. per cent. per cent.
per cent. per cent. per cent. per cent.
.3
.2
.1
.6
.4
.3
.9
.6
1.3
.9
1.6
1.1
.8
∞ ∞ is ¿o i
.1
.2
.4
.3
.6
2.
1.4
1.
2.3
1.6
1.2
.8
∞ 2 år in co io ind
.4
.5
.7
2.7
1.9
1.4
1.
12342 OZ∞
.1
.1
.2
.1
.3
.4
6
.5
7
.6
8
77
.5
3.1 2.2
1.6
1.1
9
.8
.6
3.5
2:5
1.8
1.3
10
.9
3.9 2.8 2.
1.5
11
1.1
4.4 3.1
2.3
1.6
12
1.2
∞ ∞ 2 6 år iA co čo ¿o in jimat Ö
.0
.1
.1
.2
.3
.3
.4
.7
.8
.9
4.8
3.5
2.5
1.8
13
1.3 1.
5.2 3.8 2.8
2.
14
1.5
1.1
.8
5.7 4.2 3.1 2.3
15
1.7
1.2
.9
∞ ∞ & à à ER IA ID ∞ DDHHHÖ
.0
.0
.1
.0
.1
.1
.1
.1
.2
.2
.3
.4
.4
.3
.5
.4
.6
.6
.5
.7
.5
.6
.7
6.2 4.5 3.4 2.5
16
1.9
1.4 1.1
.8
6.7
4.9
7.2 5.3
4.
7.7
5.8
ढाई मं
3.7
4.3
ai as as
2.7
17
2.1
1.6
1.2
.9
12233 TL 20 C7B9
.2
.3
.4
3.
18
2.3 1.7
1.3
1.
3.3
19
2.5 1.9
1.5
1.1
8.2 6.2 4.7
3.6
20
aż
2.7
2.1 1.6
1.3
8.8 6.7 5.1 3.9
21
3.
2.3
1.8
1.4
9.4 7.1
5.5
4.2
22
3.3
2.6
2.
1.6
9.9
7.6
5.9
4.6
23
3.6
2.8
2.2
1.8
10.6
8.1
6.3
4.9
24
3.9
3.1
2.4
11.2 8.7
6.8
5.3
25
4.2
3.4
ai
2.7
11.8 9.2 7.3
5.8
26
4.6
3.7 3.
12.5 9.8 7.8
6.2
27
5.
4.
3.3
13.2 10.4 8.3
6.7
28
5.4
4.4
3.6
13.9 11.
8.9
7.2
29
5.8
4.8 4.
14.6 11.7
9.4
7.7
30
6.3
5.2
4.3
15.3 12.4 10.1
8.2
31
6.8
5.7 4.8
qi ci si ci si að að +
2.
2.2
2.4
2.7
3.
3.3
3.6
4.
16.1 13.1 10.7
8.8
32
7.4
6.2
5.2
4.4
16.9 13.8 11.4
9.5
33
7.9
.6.7
5.7
4.9
17.7 14.6 12.1
10.1
34
8.6
7.3
6.3
5.4
18.5 15.3 12.8
10.8
35
9.2
7.9 6.9
6.
19.4 16.2 13.6
11.6
36
9.9
8.6
7.5
6.6
20.3 17. 14.4 12.4
37
10.7
9.3
8.2
7.3
21.2 17.9 15.3
13.2
38
11.5 10.1
9.
8.
22.1 18.8 16.2 14.1
23.1 19.8 17.2 15.
39
12.4 11.
9.8
8.9
40
13.3 11.9 10.8
9.8
EXAMPLE. The amount of Fine which a Tenant should pay for the renewal of
20 years lapsed in a Lease originally granted for 40 years, to make 4 per cent. of
the money he advances is 6.2 years' purchase of the net annual Income.
VALUATION OF ESTATES.
607

Table 12. AMOUNT of FINE to be paid for RENEWING with ONE LIFE the LEASE of an ESTATE originally
granted on THREE LIVES.
Note.-This Table shows the rate of Interest which a Purchaser may make of his money, provided he can re-invest the Surplus Income, beyond
the Interest on the Purchase Money outstanding, at the same rate of Interest.
Years Purchase.
3
4
per cent. per cent.
Life put in.
Ages of Years Purchase. Years Purchase.
Lives
in posses-
5
6
3
4
sion. per cent. per cent. per cent. per cent.
Life put in.
Ages of Years Purchase. Years Purchase.
Lives
in posses-
·
5
6
3
4
sion. per cent. per cent. per cent. per cent.
Life put in.
Ages of Years Purchase.
Lives
in posses-
sion.
5
6
per cent. per cent.
2.8
3.3
ai ai
2.
25-25 1.5 1.1
2.5
1.8
25-25
1.4 1.
2.2
1.6
25-25
1.2
.9
2.3
25-35 1.7 1.2 2.9
2.1
25-35
1.5
1.2
2.5
1.8
25-35 1.4
1.1
4.1
2.9
25-45 2.
1.5
3.6
2.6
25-45
1.8 1.4
3.1
2.3
25-45
1.6
1.3
4.6 3.4
25-55 2.4 1.8
4.1
3.
25-55
2.3
1.7
3.6
2.7
25-55 2.1
5.2 3.8
25-65 2.8 2.2
4.6
3.4
25-65 2.6
2.1
4.1
3.1
25-65
ல்ல்
1.5
2.4
1.9
5.5
4.1
25-75 3.1 2.4
4.9
3.7
25-75
2.8
2.2
4.4 3.3
25-75 2.6
2.
मं
4.1 2.9
35-35 2.1 1.5
3.6
2.6
35-35
1.8
1.4
3.1
2.3
35-35
1.6
1.3
4.8 3.3
35-45 2.4 1.9 4.3
3.1
35-45
2.2
1.8
3.7
2.8
35-45
2.1 1.6
5.3 3.8
35-55 2.8 2.2 4.7 3.5
35--55 2.6
2.
4.2
3.1
35-55
6.
4.4
35-65 3.3
2.6
20
5.4
4.
35-65 3.1 2.5
4.9
3.7
35-65
ai ai
2.4
1.9
2.8
2.3
6.6
4.9
10 35-75
3.8 3.
6.
4.5
15 35-75
3.5 2.8
5.4
4.1
20 35-75
3.2
2.6
5.7
3.9
45-45 2.9 2.3
5.1
3.5
45-45 2.6
2.2
4.4
3.2
45-45 2.4
2.
6.4
4.7
45-55 3.5 2.7
5.7
4.2
45-55 3.2
2.5
5.1
3.8
45-55
2.9
2.3
7.3
5.4
45-65
4.1 3.2
6.6
5.
45-65 3.8
7.9 5.9
45-75
17.7 5.8
55-55
मंमं
4.6
3.6
7.2
5.5
45-75
4.2
4.4
3.3
7.0
5.3
55-55
4.1
8.7
6.5
55-65
5.
4.
7.9
6.
55-65
4.7
có có có có
3.1
6.
4.5
45-65
3.5
2.9
3.4
6.5
5.
45-75 3.9
3.2
3.1
6.3
4.8
55-55 3.5
2.8
3.8
7.2 5.5
55-65 4.2
3.5
9.8 7.5
10.3 7.9
11.6
55-75 5.9 4.7
9.
7.
55--75
5.5
4.5
8.3 6.5
55-75 5.1
4.2
9.1
65-65 6.2 5.
65-75 7.2 5.9
9.6 7.5
10.8
8.5
65-65 5.9 4.7
65-75 6.8 5.6
8.8
6.9
65-65 5.5
4.4
9.9
7.9
65-75 6.3 5.2
EXAMPLE. The amount of Fine which a Tenant should pay for putting in a new life, aged 15, in a Lease originally granted on three lives,
one of which has dropped, the ages of the lives in possession being 45 and 75, to make 4 per cent. of his money, is 5.5 years' purchase of the
Net Annual Income
608
VALUATION OF ESTATES.
Table 13. PRESENT VALUE of the PERPETUITY of one year's
Rent or Fine, payable at every interval of years stated below.

Years Purchase at
Years Purchase at
3
4
5
Interval
of Years.
6
8
10
per cent.
per cent.
per cent.
per cent.
per cent.
per cent.
16.4
12.3
9.8
2
8.1
6.
4.8
10.8
8.
6.3
3
8.
5.9
4.6
4
6.3
4.6
3.6
5
5.2
3.8
2.9
6
4.3
3.2
2.5
7
~~~
2.9
2.1
1.6
10
2ð að að ai ai –
5.2
3.9
3.
3.8
2.8
2.2
3.
2.1
1.6
2.4
1.7
1.3
2.
1.4
1.1
1.3
.9
.6
2.
1.4
1.
14
.8
.5
1.2
1.2
.4
∞o oo oo
.8
.8
.6
.3
.2
669
20
.5
.3
.2
21
.4
.2
.2
40
.1
.0
.0
64220
.4
EXAMPLE.-The present* worth of the perpetuity of one year's Rent or Fine,
payable every 10 years, is at 4 per cent. 2.1 years' purchase.
* That is to say, immediately after a Fine has been paid for renewal.
VALUATION OF ESTATES.
609
Table 14.
PRESENT VALUE of the REVERSION to a FREE-
HOLD ESTATE, or a PERPETUITY, after any given number of
years not exceeding sixty.

Years Purchase at
Years Purchase at
After these
3
4
5
6
77
8
Years.
per cent. per cent. per cent. per cent.
10
per cent. per cent. per cent. per cent.
9
32.4 24.
19.
15.7
1
13.4
11.6 10.2
9.1
31.4 23.1
18.1
14.8
2
12.5
10.7
9.4
8.3
30.5 22.2
17.3
14.
3
11.7
9.9
8.6
7.5
29.6 21.4
16.5
13.2
10.9
9.2
7.9
6.8
28.8 20.5 15.7 12.5
10.2
8.5
7.2
6.2
27.9 19.8 14.9
11.7
6
9.5
7.9
6.6
5.6
27.1 19.
14.2
11.1
7
8.9
7.3
6.1
5.1
26.3 18.3 13.5 10.5
8
8.3
6.8
5.6
4.7
25.5 17.6 12.9
9.9
9
7.8
6.3
5.1
4.2
24.8 16.9 12.3
9.3
10
7.3
5.8
24.1 16.2
11.7
8.8
11
6.8
5.4
23.4 15.6 11.1
8.3
12
6.3
5.
22.7 15.
10.6
7.8
13
5.9
ti
4.6
22. 14.4
10.1
7.4
14
5.5
4.3
Hi Hi Hi að as
4.7
3.9
4.3
3.5
4.
3.2
3.6
2.9
3.3
2.6
21.4 13.9 9.6
7.
15
5.2
3.9
3.1
2.4
20.8 13.3 9.2
6.6
16
4.8
3.6
2.8
2.2
20.2 12.8
8.7
6.2
17
4.5
3.4
2.6
19.6 12.3
8.3
5.8
18
4.2
3.1
2.4
19. 11.9
7.9
5.5
19
3.9
2.9
2.2
6+2
2.
1.8
1.6
18.5 11.4
7.5
5.2
20
3.7
2.7
2.
1.5
17.9 11.
7.2
4.9
21
3.4
2.5 1.8
1.4
17.4 10.5 6.8
4.6
22
3.2
16.9 10.1
6.5
4.4
23
3.0
16.4 9.8 6.2
4.1
24
2.8
ai ai ai
2.3
1.7
1.2
2.1
1.5 1.1
2.
1.4 1.
15.9
9.4 5.9
3.9
25
2.6
1.8
1.3
.9
15.5
9.
5.6
3.7
26
2.5
1.7
1.2
.8
15.
8.7 5.4
3.5
27
2.3
1.6
1.1
.8
14.6
8.3 5.1
3.3
28
2.1
1.4
1.
.7
14.1 8.
4.9 3.1
29
2.
1.3
.9
.6
13.7 7.7 4.6
2.9
30
1.9
1.2
.8
.6
EXAMPLE. The present worth of the Reversion to a Freehold Estate after 25 years,
to make 4 per cent. interest is 9.4 years' purchase of the net annual rent.
610
VALUATION OF ESTATES.
Table 14 continued.
PRESENT VALUE of the REVERSION to
a FREEHOLD ESTATE, or a PERPETUITY, after any given
number of years not exceeding sixty.

Years Purchase at
After these
3
4
5
6
Years Purchase at
8
9
10
Years.
per cent. per cent. per cent. per cent.
per cent. per cent. per cent. per cent.
13.3
7.4
4.4
12.9
7.1
मं
4.2
si si
2.7
31
1.8
1.1
2.6
32
1.6
1.1
12.6 6.8
4.
2.4
33
1.5
1.
.6
12.2
6.6
3.8
2.3
34
1.4
.9
.6
11.8
6.3
3.6
2.2
35
1.3
.8
.5
11.5
6.1
3.5
2.
36
1.2
.8
11.2 5.9
3.3
1.9
37
1.2
.7
.5
10.8 5.6
3.1
1.8
38
1.1
.7
10.5 5.4
3.
1.7
39
1.
.6
10.2
5.2
2.8
1.6
40
1.
.6
9.9
5.
2.7
1.5
41
.9
.5
9.6 4.8 2.6
1.4
42
.8
.5
9.4
4.6
2.5
1.4
43
.8
.5
9.1 4.5 2.3
1.3
44
.7
.4
8.8
4.3 2.2
1.2
45
7
.4
8.6
मं
4.1
2.1
1.1
46
.6
.4
.2
8.3 4.
2.
1.1
47
.6
.3
8.1 3.8 1.9
1.
48
.6
.3
7.8
3.7
1.8
1.
49
.5
.3
NNNNNWo čo čo čo ip it if år år år å is 2 ∞
.8
.5
.7
.5
.4
.4
.4
.3
.3
.4
.3
.4
.3
.2
.3
.2
.2
.2
.2
.1
.1
.1
.1
.1
7.6
3.5
1.7
.9
50
.5
.3
.1
.1
7.4
3.4
1.7
.9
51
.5
.2
.1
.1
7.2 3.3 16
7.
3.1 1.5
6.8
6.6
as ai
3.
1.4
2.9
1.4
6.4
2.8 1.3
.6
6.2 2.7 1.2
.6
6.
2.6 1.2
5.8 2.5 1.1
5.7 2.4 1.1
.5
·∞∞776 CO CO LO LO
.8
52
.4
.2
.1
.1
.8
53
.4
.2
.1
.1
.7
54
.4
.2
.1
.1
55
.3
.2
.1
·.1
56
.3
.2
.1
57
.3
.2
.1
.0
58
.3
.1
.1
.5
59
.3
.1
.1
60
.2
.1
.1
CHOOOOO
.0
EXAMPLE. The present worth of the Reversion to a Freehold Estate after 60
years, to make 4 per cent. interest, is 2.4 years' purchase of the net annual rent.
VALUATION OF ESTATES.
611
Table 15. PRESENT VALUE of a REVERSIONARY ESTATE
in FEE after the Life of a person of a given age, at the several rates
of 3, 4, 5, 6, 7, and 8 per cent. Interest.

Years Purchase at
Years Purchase at
Age in
3
per cent.
4
per cent.
5
per cent.
6
7
8
Possession.
per cent.
per cent.
per cent.
12.9
7.8
5.2
or
5
3.7
2.8
2.2
12.7
7.5
4.9
10
3.4
2.5
1.9
13.7
8.2
5.4
15
3.8
2.8
2.2
14.7
9.
6.
20
4.3
3.2
2.5
15.5
9.6
6.4
25
4.6
3.4
16.4
10.2
6.9
30
17.4
11.
7.5
35
18.5
11.8
8.2
19.6
12.7
8.9
20.9
13.7
9.7
22.2
14.8
10.6
23.6
16.
11.6
25.
17.2
12.7
26.6
18.6
14.
28.1
20.
15.3
29.6
21.4
16.5
80
30.7
22.5
17.5
31.5
23.2
18.3
33.1
24.8
19.8
KURONJACAJAS
40
6.
20 20 có
5.
3.7
ai ai
2.7
2.9
5.4
4.1
3.2.
4.5
3.6
45
6.6
5.
4.
50
7.2
5.6
4.5
55
8.
6.2
5.
60
8.8
7.
5.6
65
9.8
7.8
6.4
11.
8.9
7.3
75
12.1
9.9
8.3
13.3
11.
9.3
85
14.3
11.9
10.2
15.
12.6
10.9
95
16.4
14.
12.3
EXAMPLE. The present value of a Freehold Reversionary Estate or of an Ad-
vowson subject to the life of a person aged 60, at 4 per cent., is 16 years' purchase.
At 5 per cent., it is worth 11.6 years' purchase.
།
7 612
VALUATION OF ESTATES.
Table 16. Showing the PRESENT VALUE of a REVERSIONARY
ESTATE in FEE after the longest of Two Lives of given ages at
the several rates of 3, 4, 5, and 6 per cent. Interest.

Years Purchase at
Years Purchase at
3
4
Ages.
5
6
per cent.
per cent.
per cent.
per cent.
8.3
4.2
10
9.2
4.8
10
9.9
5.3
10
9280
10
2.4
1.4
20
2.8
1.7
30
3.1
1.9
10.6
5.8
10
40
3.5
2.2
11.3
6.3
10
50
3.9
2.5
11.8
6.8
10
60
4.2
2.8
12.3
7.1
10
70
4.5
3.1
12.5
7.4
10
80
4.7
3.3
10.2
5.5
20
20
3.2
2.
11.
6.1
20
30
3.6
2.3
11.9
6.7
20
40
4.1
2.7
12.8
7.3
20
50
4.6
3.
13.5
7.9
20
60
5.1
3.4
14.1
8.4
20
70
5.5
3.8
14.5
8.8
20
80
5.8
4.1
12.1
6.8
30
30
4.1
2.7
13.1
7.5
30
40
4.7
3.1
14.1
8.3
30
50
5.3
3.5
15.
9.
30
60
5.9
4.
15.7
9.6
30
70
6.3
4.4
16.2
10.
30
80
6.7
4.8
14.4
8.4
40
40
5.3
3.6
15.6
9.4
40
50
6.1
4.1
16.7
10.3
40
60
6.8
4.7
17.6
11.
40
70
7.4
5.3
18.2
11.5
40
80
7.9
5.7
17.2
10.6
50
50
7.
4.9
18.6
11.7
50
60
7.9
5.6
19.7
12.7
50
70
8.8
6.4
20.5
13.3
50
80
9.4
6.9
20.4
13.1
60
60
9.1
6.6
22.
14.5
60
70
10.3
7.6
23.
15.4
60
80
11.1
8.4
24.1
16.4
70
70
11.9
9.
EXAMPLE. A Reversionary Freehold Estate, after the longest of two lives aged
30 and 50, at 3 per cent., is worth 14.1 years' purchase.
At 4 per cent., it is worth 8.3 years' purchase.
VALUATION OF ESTATES.
613
Table 17. PRESENT VALUE of a REVERSIONARY ESTATE
or ANNUITY on a single Life, after any other single Life now in
Possession, at the several rates of 3, 4, 5, and 6 per cent. Interest.

Years Purchase at
Years Purchase at
3
per cent.
4
per cent.
Age of
Life in
Reversion.
Age of
Life in
Possession.
5
6
per cent.
per cent.
6.5
4.9
30
3.8
3.0
7.9
6.
40
4.7
3.7
9.6
7.4
50
5.9
4.7
11.7
9.2
10
60
7.4
6.
14.3
11.5
70
9.4
7.9
17.
14.
80
11.7
10.
5.4
4.2
30
3.3
2.7
6.5
5.1
40
4.1
3.3
8.1
6.4
50
5.1
4.2
10.
8.
20
60
6.5
5.4
12.5
10.2
70
8.5
7.1
15.1
12.6
80
10.7
9.2
4.3
3.5
30
2.8
2.3
5.4
4.3
40
3.5
2.9
6.8
5.5
50
4.5
3.7
8.5
7.
30
60
5.8
4.8
10.9
9.1
70
7.6
6.5
13.4
11.4
80
9.8
8.5
3.3
2.7
30
2.3
1.9
4.1
3.4
40
2.8
2.4
5.3
4.4
50
3.7
3.1
6.8
40
5.7
60
4.8
4.1
9.0
7.6
70
6.5
5.7
11.4
9.9
80
8.6
7.6
2.3
1.9
30
1.7
1.5
2.8
2.4
40
2.1
1.8
3.7
3.2
50
2.7
2.4
50
5.
6.9
9.1
8.
ti có cơ
4.3
60
3.7
3.2
6.
70
5.2
4.6
80
7.1
6.4
1.4
1.2
30
1.1
1.0
1.8
1.5
40
1.4
1.2
2.3
2.0
50
1.8
1.6
60
3.2
2.8
4.6
4.1
6.6
5.9
80
928
60
2.5
2.2
70
3.7
3.3
5.4
4.9
EXAMPLE. A Reversionary Estate on a single life aged 30, after a single life in
possession aged 60, at 3 per cent., is worth in present money, 8.5 years' purchase of
the net Annual Income.
614
VALUATION OF ESTATES.
Table 18. PRESENT VALUE of a REVERSIONARY AN-
NUITY on a Single Life, to be nominated at the death of a person
now in Possession, at the several rates of 3, 4, 5, and 6 per cent.
Interest.

Years Purchase at
Years Purchase at
3
4
per cent.
per cent.
Ages of
Life in
Reversion.
Ages of
Life in
Possession.
5
6
per cent.
per cent.
8.8
6.3
30
4.7
3.6
9.9
7.3
40
5.5
4.3
11.2
8.5
50
6.6
5.3
25
12.6
9.9
60
7.9
6.4
14.2
11.5
70
9.5
7.9
15.8
13.2
80
11.2
9.6
8.3
6.
30
4.5
3.5
9.4
7.
40
5.3
4.2
10.6
8.1
50
6.4
5.1
12.
9.4
30
60
7.6
6.2
13.5
11.
70
9.1
7.7
15.
12.6
80
10.8
9.3
7.8
5.7
30
4.3
3.4
8.8
6.6
40
5.1
4.
10.
7.7
50
6.1
मं
4.9
35
11.3
9.
60
7.3
6.
12.8
10.5
70
8.7
7.4
14.1
12.
80
10.3
8.9
7.3
5.4
30
4.1
3.2
8.2
6.2
40
4.8
3.8
9.3
7.3
50
5.8
4.7
10.5
8.4
40
60
6.9
5.7
11.8
9.8
70
8.3
7.
13.2
11.3
80
9.8
8.5
6.7
5.
30
3.8
3.
7.6
5.8
40
4.5
3.6
8.6
6.7
50
5.4
4.4
9.7
7.8
45
60
6.4
5.4
10.9
9.2
70
7.8
6.6
12.1
10.5
80
9.2
8.1
6.1
4.6
30
3.6
2.8
6.9
5.3
40
7.8
6.2
50
5.
đó
4.2
3.4
4.1
8.8
7.2
50
60
6.
5.
9.9
8.4
70
7.2
6.2
11.
9.6
80
8.5
7.5
EXAMPLE. The present value of a Reversionary Annuity on a Single Life aged
30, to be nominated at the death of a person, now in possession aged 50, to pay 3
per cent., is worth in present money, 10.6 years' purchase of the net annual income.
At 4 per cent. it would be 8.1 years' purchase.
VALUATION OF ESTATES.
615

Table 19. PRESENT VALUE of £1, payable at the death of a person of a given age.
3 PER CENT.
By the
4 PER CENT.
5 PER CENT.
By the
By the
Age.
Northampton
Carlisle
Age.
Northampton
By the
Carlisle
Age.
Tables of
Tables of
Tables of
Tables of
Mortality.
Mortality.
Mortality.
Mortality.
By the
Northampton
Tables of
Mortality.
By the
Carlisle
Tables of
Mortality.
10
.369
.286
10
.287
.208
10
.232
.159
15
.398
.313
15
.315
.232
15
.258
.180
20
.428
.339
20
.345
.255
20
.285
.199
25
.452
.369
25
.368
.283
25
.306
.224
30
.478
.401
30
.393
.313
30
.330
.251
35
.507
.434
35
.422
.345
35
.357
.280
40
.538
.472
40
.454
.382
40
.389
.315
45
.572
.508
45
.489
.419
45
.424
.350
50
.609
.554
50
.528
.466
50
.463
.409
55
.646
.609
55
.569
.527
55
.506
.460
60
.686
.665
65
.729
.711
70
.775
.763
75
.819
.810
80
.861
.843
85
.895
.877
90
.919
.898
CRONIRI
60
.614
.590
60
.553
.527
.663
.642
65
.606
.583
.717
.703
70
.666
.651
75
.771
.760
75
.726
.715
80
.821
.800
80
.785
.761
85
.864
.842
85
.835
.809
90
.894
.869
90
.870
.841
EXAMPLE. £1 payable at the death of a person aged 55 years is worth, in present money at 5 per cent., according to the Northampton
Tables of Mortality .506, or by the Carlisle Tables .460.
E. G.
£100 is worth £50.6 or £46.
£1000 is worth £506 or £460.
616
VALUATION OF ESTATES.
MEMORANDA
As Facts to assist the Memory in matters of Calculations and
Valuations*.
In respect to the value of freehold land, it is
generally considered 30 to 33 years' purchase
Freehold ground-rent, 25 to 30 years' purchase
Freehold houses and buildings, 1st and 2nd class,
18 to 20 years' purchase
Ditto, 3rd and 4th ditto, 16 years' purchase
For leasehold property refer to the Table for the
term of years unexpired for long terms, 1st and
2nd class houses and buildings, 15 to 16 years'
purchase
For do. 2nd and 3rd do.
For do. 3rd and 4th do.
For do. 4th and 5th do.
For do. 5th and 6th do.
14 to 15 years' purchase
12 to 13 years' purchase
11 to 12 years' purchase
10 years' purchase
3 per cent.
•
4 per cent.
5 per cent.
6 per cent.
6 per cent.
7 per cent.
8
per cent.
9 per cent.
10 per cent.
Renewing Leases held under Deans and Chapters.
The Dean and Chapter of Westminster renew their leases,
originally granted for FORTY YEARS, under the 8 per cent.
Tables; the renewing fine of one year's rent payable by the tenant
every fourteen years;-except for very superior houses at the
West-end of the town, which are renewed under the 7 per cent.
Tables. The renewing fine of 1 years being payable by the
tenant every fourteen years.
The Bishop of Winchester's Estates.
11 Years renewing fine for 14 years lapsed in a lease originally
granted for 40 years, 7 per cent. Tables if next the river; or, 11
year's fine in land 8 per cent.
* Chiefly extracted from the 13th Edition of Inwood's Tables.
VALUATION OF ESTATES.
617
City of London Leases, Scale of Ground Rents.
situations} Per foot frontage
S. d.
d.
5 0
Per foot deep
3
2nd do.
ditto
3rd do.
ditto
4th do.
ditto
5th do.
ditto
4 0
ditto
2
3
0
ditto
1/1/
2 0
ditto
1
1 0
ditto
Renewing fine, 7 years' ground rent every 14 years, for a term
of 41 or 61 years.
Lessee to insure, repair, &c.
Purchase of Good Will in Retail Trade, &c.
If retail trade is carried on, giving credit, say, 1 year's purchase.
Ditto, as a ready money concern, say, 1½ year's purchase.
Ditto, trade subject to be annihilated, as public houses, say 2 to
3 years' purchase.
Calculating rent for fixtures, say 12 per cent., or §, being 2s. 6d.
in the pound.
Allowance to Tenants for Repairs.
8 per cent. allow for amount of repairs for 21 years.
7 do.
Or, generally, say, allow—
12 per cent.
10 do.
9 do.
8 do.
7 do.
6 do.
31 do.
for 12 years.
15 do.
18 do.
23 do.
33 do.
above do.
Purchase of Land Tax.
To be made under the Land Tax Act at the price of the 3 per
cent. consols, and to which add one-tenth to the amount, the
income tax being now taken off.
Memorandum relative to the Valuation of Land.
43.560 feet superficial, an acre, at—
d.
per foot
do.
do.
1 do.
14 do.
14 do.
•
£ S. d.
45 7 6 per acre.
90 15 0 do.
136 2 0 do.
. 181 10 0 do.
226 17 6 do.
. 272 5 0 do.
2 Q
618
VALUATION OF ESTATES.
Crown Lands.
The mode adopted in respect to the valuation for renewal of the
crown leases, allowance for repairs as under-
Houses £25 per annum, and under,. 10 per cent.
£25 to £50 .
£50 to £100
£100 and upwards
6 per cent.
7
per cent.
5 per cent.
The rack rent not an overstrained rent on account of crown
property, and to encourage improvements, viz., Calculation.
Rack rent
Deductions
Present repair, £200
£63 per annum.
£
S.
d.
. 14
0
0
Ordinary repairs,
3
3
0
3 3
0
Insurance, £700
. 1 4 0
Outgoings
480
Land tax
25 18 0
£37 2 0
Say, £40 per annum clear rent.
Or, in another case,
Rack rent
Deductions
Present repairs, £250
£150 per annum.
£ S.
d.
17 10
0
Ordinary repairs
7 10 0.
Land tax
5 12 0
Insurance, £1500
3 7 6
Contingencies
7 10 0
41 9 6
42
£108
Crown leases, their custom under act of parliament, is to renew
leases when within 20 years of being expired, not earlier, a new
rent is then assessed taking fine, and
more effectually the rent so reserved.
rent, in order to secure
Increase of Population.
810) 15 per cent.
First 10 years of the century-1800 to 1810
Increase in England and Wales
1810 to 1820 17 per cent.
1820 to 1830 15 per cent.
VALUATION OF ESTATES.
619
Increase in population in England and Wales, 9 millions.
Population of London.
Ditto, including environs
1810 10 millions.
1821
12 millions.
1 millions.
12 millions.
Out of 1000 persons there die annually about 30; and that
the number of inhabitants of every city and county is renewed
every thirty years, or nearly so.
Calculations have been made tending to show that the propor
tion of mortality is diminishing; which fact is confirmed by the
returns in several great cities, proving incontestably the material
amelioration which has taken place in great cities.
Mortality.
100 years since, 1 died in 30.
50 do.
30 do.
20 do.
وو
وو
1
1
1
وو
وو
وو
in 40.
in 48.
in 52.
in 60.
Present time,
1
وو
For Surveys and Valuations
Made in respect to the extensive improvements which have
taken place in London,-Regent-street,-Strand, the Commis-
sioners of Improvements of Westminster, the City and New
London Bridge, St. Katharine's Docks, and other improvements
-the charges have been at the rate of per cent., and 3 guineas
for each surveyor attending to give evidence before a judge and
jury. It is usual to charge 1 per cent. for the first thousand
pounds, and the remainder per cent.
Her Majesty's Commissioners for Building Churches, for tra-
velling expenses, allow 1s. 6d. per mile out, and the same back,
but no expenses; and four journeys, not more, allowed to each
church.
620
VALUATION OF ESTATES.
Rule for determining the Value of a Beneficial Lease for Years, so
that the Purchaser may be able to make a given Interest on the
Price paid, and replace his Capital at the expiration of the Lease.
In every question of this kind, it is evident that two circumstances
may vary considerably: first, the interest which a purchaser may
be considered entitled to make of his money, which in some de-
scriptions of leasehold property, would be as low as 5, and in others
as high as 8 or 9 per cent.; and, secondly, the rate of compound
interest at which he may reckon with certainty upon employing
the money annually laid by to replace his capital at the expiration
of his lease, and which may be considered to range at about 3 or
4 per cent. Any formula, therefore, to be useful, must require
the following data:-
1. The amount of the clear improved rent.
2. The rate of interest required on the purchase-money.
3. The rate of compound interest at which the money annually
laid by to replace capital may be expected to be employed.
4. The length of the lease.
N.B. The two last data being given, tables of compound interest
will give the amount of £1 per annum at the given rate of com-
pound interest for the given number of years.
Now let
a = amount of clear improved rent ;
b =
C =
com-
amount of £1 per annum at ʼn per cent.
pound interest for r years (n standing for the
rate of interest at which money may be expected
to be employed; r standing for the number of
years in the lease);
rate of interest per cent. required on purchase-
money;
x = amount of purchase money;
sum to be annually laid by at n per cent. com-
y=pound interest, to replace capital at expiration of
lease.
by
Then, from this statement, we shall have—
=X
These two are
the unknown
quantities.
These three may, of
course, be considered as
known quantities.
(for the amount of £1 per annum for the number of years
of the lease at the given rate of compound interest multi-
plied by the number of pounds annually laid by, must
equal the purchase-money;
VALUATION OF ESTATES.
621
CX
100
+y=a
for
сх
100
annual interest on purchase-money,
since the annual interest on any sum = that sum
multiplied by the rate of interest, and divided by
100; and the annual interest on the purchase-
money added to the sum annually laid by to replace
capital, must = clear improved rent.
X
From the first of these equations, y, = which, substituted in
the second, gives
с х
100
x =
+
X
b
α
100 a b
100+ b c
X
100 a
100+ b c
and y = b
From the foregoing formula, it follows that the value of any
beneficial lease the product of 100 multiplied into the amount
of clear improved rent, multiplied again into the amount of £1
per annum for whatever number of years the lease may be, at the
given rate of compound interest; the product of this continued
multiplication being divided by 100, added to the product of the
rate per cent. of interest required on purchase-money, multiplied
by the aforesaid amount of £1 per annum, &c.,, &c. Therefore, if
a = £500
وو
b = 28.6765 (supposing n = 3 per cent., rate of comp. interest;
r = 21 years, length of lease;
c=7, rate per cent. of interest required on purchase-money;
we shall have
x=
y
100+ 7 × 28.6765
100 × 500 × 28.6765
=
£4769 15 91;
£166 6 71;
100 × 500
100+ 7 × 28.6765
and £500–166 6 7 = £333 13 4, which is the yearly
interest at 7 per cent. on £4769 15 94, the amount of the
purchase-money; and £166 6 7 annually laid by for 21
years, at 3 per cent. compound interest, will amount to
£4769 15 91; thereby replacing the principal at the end of
the lease.
Where the question is as to the proper sum to be given for
renewing any number of years lapsed in a lease, it is clear that
the party wishing to renew gives up whatever may be the number
of years remaining in his old lease, together with a certain sum
622
VALUATION OF ESTATES.
of money in consideration of receiving a new lease for the time
agreed upon; and the value of the remainder of the old lease
must be therefore deducted from the value of the new lease; and
the remainder will be the proper sum to be given for the renewal.
Thus, supposing it is wished to renew 14 years lapsed in a 21
years' lease, here the value of the remaining part of the lease =
value of a lease for 7 years, and supposing, as before, that
a = £500;
Sn being = 3 per cent. of compound interest;
b = 7·6625 {
c = 7
X
r
99
= 7 years, length of lease;
100 × 500 × 7·6625
100 + 7 x 7.6625
= £2493 13 10; which is the
value of the remaining 7 years of the old lease.
Now, the value of a new lease of 21 years, we shall find thus :
a = £500;
n being 3 per cent. compound interest;
Sn
b = 28·6765 {7
c = 7
x
دو
=
= 21 years.
100 × 500 × 28.6765
100 + 7 × 28.6765
we deduct value of remaining}
7 years of old lease
we shall have.
£4769 15 91; from which, if
2493 13 101,
£2276
1 103 as the proper sum
to be paid for the renewal of the 14 years lapsed.
What Amount of Increased Rent should be given instead of Premium
for the Renewal of any Number of Years lapsed in a Beneficial
lease for Years ?
The same data will suffice for solving this question which were
required for determining the amount of premium to be paid for a
renewal. In the first place, the value of the tenant's remaining
interest in the old lease must be calculated by the first formula;
and this value must be considered as the premium he pays for
renewal; and the increased rent to be paid by him must therefore
be such a sum as, if deducted from the amount of the clear annual
improved rent, will leave a sufficient remainder to afford the
tenant the given rate of interest upon the value of his remainder
of lease, considered as capital, and also enable him to lay by a
certain sum annually, which, at the given rate of compound
interest, will replace this capital at the expiration of the new
lease.
VALUATION OF ESTATES.
623
Supposing...
a = clear improved rent;
b =
amount of £1 per annum for r years at n rate of com-
pound interest, where r = number of years of new
lease, n = rate of compound interest at which money
can be safely employed;
c = rate per cent. required on capital;
d = value of present interest in old lease;
x= increased annual rent to be paid instead of premium;
sum to be annually laid by to replace capital, (i.e.
y=value of the remainder of old lease) at the expiration
of new lease;
then will
by
= d
x=α
c
{od being the
Known
quantities.
Unknown
quantities.
being the interest at the given rate upon
100 the capital sum.
c d
-y
100
d
.. y
b
cd d
x = α
a
100 b
From this formula it follows, that the proper increase of rent
to be paid instead of a premium, for the renewal of any number
of years lapsed in a beneficial lease the amount of the clear
improved rent, after deducting the quotient of the value of re-
mainder of old lease, multiplied by the rate per cent. required on
capital, and divided by 100; further deducting, also, the quotient
of the value of remainder of old lease, divided by the amount of
£1 per annum for the number of years in the new lease, at the
given rate of compound interest; if..
a = £500 amount of clear improved rent;
b = 28-6765 {
n being = 3 per cent., rate of comp. interest
= 21
21 years
length of new lease
γ
c = 7 rate per cent. required on capital;
This is on the supposition that 7 years
= £2493 13 10 remain unexpired of the old lease; the
value being found by the first formula.
d
x = £500
7 × 2493 13 101_2493 13 101
100
28.6765
x = £500 — 174 11 1-86 19 8 = £500 — 261 10 92;
.. x = 238 9 24; which is the proper amount of increased rent
to be paid instead of premium, for the renewal of 14 years lapsed
in a lease of which 7 years remain unexpired, of a property, the clear
improved rent of which is £500 a-year.
624
VALUATION OF ESTATES.
There is only one more way in which renewals may be pur-
chased, and that is, by paying for them partly by premium, and
partly by increased rent; and the foregoing formula will solve
any question of this kind. The amount, however, of one of these
two quantities (i.e. the amount of the premium, or of the increased
rent expected,) must of course be given, as they evidently vary in-
versely to each other. If the amount of premium expected be
given, that amount must be added to the value of remaining part
of old lease; and the last formula will find the additional rent to
be paid.
Ex. gr., if, in the last case, a premium of £500 had been de-
manded, then-
a = £500 clear annual rent;
b = 28.6765, amount of £1, &c.;
C = 7, rate per cent. required on capital ;
d = £2493 13 10+ £500 (amount of prem.) = 2993 13 101;
7 × 2993 13 10 2993 13 101
x = £500
100
28.6765
;
104 7 102 £500 — 313 19 0 =
x = £500 — 209 + 11 1
11 — 104
£186 1 0.
.. if £500 premium is demanded for a renewal of 14 years in a
lease, of which 7 years remain unexpired, of a property, the clear
annual rent of which is £500, the amount of increased rent to be
paid for such renewal (in addition to such premium of £500,) is
£186 1 0 annually.
If the amount of increased rent expected is given, such amount
must, of course, be deducted from the amount of the clear im-
proved rent, and the premium to be paid for the renewal may be
calculated by the formula before given for that purpose; the clear
improved rent being stated at its reduced amount.
VALUATION OF TILLAGES.
625
CHAPTER XVIII.
VALUATIONS OF TILLAGES AND TENANT
RIGHT.
THIS branch of practice attains its greatest importance in Surrey
and parts of the adjacent counties, by reason of the number of
items which the "custom of the country" (as it is technically
termed,) in that neighbourhood, renders subject to the dealings of
the valuator at a change of occupancy.
The following is a list of the various customs prevailing in the
several counties of England, so far as I am acquainted with them,
or they have in any way come under my observation.
Bedfordshire. In this county an outgoing tenant generally has
the option of sowing the wheat crop, if it be a Michaelmas holding,
or of allowing the incoming tenant to enter upon the land suffi-
ciently early to do it himself. And the same with respect to
the spring corn, if the entry be at Lady-day. But in either case,
the corn must be sown by Michaelmas or Lady-day, as may be.
The valuation then takes place upon the labour, seed, and sowing.
If the outgoing tenant exercises this option of sowing the corn
against the wishes of an incoming tenant, the latter may exercise
an option as to taking the crop.
The dung upon the premises at the expiration of the tenancy has
to be left for the use of the incoming tenant without forming any
item in the valuation.
Seed, sowing, and labour upon the grass seeds are valued, and
labour upon the fallows, as well as the labour upon the lands pre-
pared for spring corn not sown by an outgoing tenant at a Lady-
day entry.
Berkshire.—The incoming tenant generally enters upon the land
at Lady-day, to make his fallows and prepare the wheat lands for
the ensuing crop. He pays for hay at a fodder price, and for seed,
labour, and sowing of grass seeds, but not for rent and taxes on the
fallows, which are all paid in full by the outgoing tenant to the end
of his term.
Buckinghamshire.—The incoming tenant pays for labour, seed,
and sowing, but not for dung.
Cambridgeshire. The incoming tenant pays for all kind of
626
VALUATION OF TILLAGES.
labour, seed, and sowing, but not for dung. He also takes to
straw and chaff at a fodder price. There is however a custom by
which the incoming tenant thrashes and draws to market the corn
of the last year's growth, receiving in return the straw and chaff
as remuneration.
Cheshire.—The incoming tenant pays for seed, labour, and sow-
ing, but not for dung.
Cornwall. The incoming tenant pays rent and taxes for the
fallow land, as in Surrey, but generally has the option of pre-entry.
The dung upon the premises is not paid for.
Cumberland.—The incoming tenant at Candlemas-day pays for
seed, sowing, and labour of every description, as well as a propor-
tionate sum of the year's rent and rates on the fallows.
Derbyshire.—The incoming tenant to a farm in this county pays
for very much the same tillages as in Surrey; viz., for full fallows
and full dressings, the value of the labour and manure expended
for seed and sowing, and a year's rent and rates.
For half fallows and half dressings on those lands from which
only one crop has been taken subsequently to the fallow, at the
value of half the labour on such fallows, half the value of the
manure, and a half-year's rent and rates. But with reference to
seeds that may have been sown on the half fallow and failed, the
custom of Derbyshire differs from that of Surrey, inasmuch as the
outgoing and incoming tenant are made to share the loss in equal
moieties. Where the seeds do not fail, seed and sowing is valued
in full. Hay and straw is taken at market price.
Devonshire.—The incoming tenant has a right of pre-entry to
prepare the wheat lands on a Michaelmas tenancy, and the lands
for spring crops of a Lady-day tenancy. In the latter tenancy, he
pays for the wheat crop at valuation. Nothing is paid for manure,
hay, and straw.
Dorsetshire.—The very simple custom of quitting a farm in the
same manner as the tenant entered appears to be the most general.
Durham.-The incoming tenant generally has the right of pre-
entry to fallows, and the use of the unexpended manure arising out
of the last year's crop. Pays for seeds and sowing, and for the
after feed.
Essex. The incoming tenant pays for labour and manure upon
the fallows, seeds, and sowing, and for dung in the yards.
Gloucestershire.—The incoming tenant has generally a right of
pre-entry, and is entitled to the dung arising from the last year's
crop.
Herefordshire.—The incoming tenant has a right of pre-entry,
VALUATION OF TILLAGES.
627
and to the manure from the last year's crop, but pays for seeds
sown.
Hertfordshire. The right of pre-entry to work fallows exists
pretty generally. The incoming tenant is entitled to one-fifth of
the land for fallow, and one-fifth upon which he can sow grass
seeds.
Hampshire.—The incoming tenant pays for labour upon the fal-
lows, and for carting and spreading dung; but is entitled to the
dung without payment.
Huntingdonshire. The incoming tenant pays for labour upon the
fallows, but is entitled to the dung free of cost.
Kent.-The incoming tenant pays for fallows and half fallows,
dressings and half dressings, seed and sowing, clover leys, under-
wood down to the stub, manure upon the premises, and hay and
straw of the last year's growth at a fodder price.
Lancashire.—The outgoing tenant is paid (usually speaking) for
wheat sowing, and is bound generally to leave the farm in the
same state as he found it.
Leicestershire.-The incoming tenant pays for labour, and the
year's rent and rates upon the fallows. For seed, sowing, and full
dressings.
Lincolnshire. The incoming tenant has the right of pre-entry;
pays for clover and grass seeds, and for carting manure, but is en-
titled to the dung free of cost.
Middlesex.—In this county there is a great breadth of land under
culture as market gardens and meadows, to which special agree-
ments generally apply. On the arable lands the incoming tenant
at Michaelmas generally pays for fallows, half fallows, dressings,
half dressings, clover leys, hay, straw, and dung. There are very
few woods and coppices, but where one is met with the underwood
is taken to according to its growth.
Norfolk. The incoming tenant pays for the crop of seeds and
turnips, and for clover leys, but not for dung. He has to draw to
market within reasonable distance the outgoing tenant's corn from
the last year's crop, in return for which he gets the straw and
chaff.
Northamptonshire.—The incoming tenant pays for fallows, seeds
sown, and labour, but not for manure.
Northumberland.-The right of pre-entry allows an incoming
tenant to make his fallows, sow clover and grass seeds, and cart out
the dung of the last year's crop, to which he is entitled. The hold-
ings generally expire at Lady-day, but the outgoing tenant is en-
titled to the crops of the last year; the carting and stacking of
628
VALUATION OF TILLAGES.
which is done by the incoming tenant, who in return is entitled to
the straw when thrashed.
Nottinghamshire.-The incoming tenant pays for fallows, labour,
seed, and sowing, and to a limited extent for unexhausted im-
provements.
Oxfordshire.—The incoming tenant pays for labour on fallows,
seeds, and sowing, and for hay of the last year at a fodder price,
but not for dung.
Rutlandshire.—The incoming tenant pays for labour on the fal-
lows, and for carting the dung. If a Lady-day tenancy, he also
pays for wheat crop, turnips, and seeds, for winter ploughing; and
if the spring corn, is sown for seeds, sowing, and labour.
Shropshire. The incoming tenant pre-enters on the farm. Pays
for the wheat crop and clover seeds upon the land, if they have not
been previously fed off, and for the dung and unconsumed hay and
straw of the last year's growth. (This custom assumes a Lady-
day entry.)
Somersetshire.—The tenancy generally commences at Christmas
or Lady Day. The incoming tenant pays for the crop of wheat,
or for labour, seed, and sowing, for clover seeds and sowing, some-
times for dung, and generally for hay and straw at fodder price.
Staffordshire. The incoming tenant at Lady-day pays for what
in this county is called pin-following, but what in Surrey would be
termed a bastard fallow, and for hay and straw at fodder price,
which here is two-thirds of the market price of the former, and one-
third of the latter. The custom leaves the dung on the farm for
the use of the incoming tenant, but it is equally the custom of this
county that what a tenant pays for when he enters, he is to be paid
for when he leaves. The custom as to the wheat crop is very
undefined.
Suffolk.-The incoming tenant at Michaelmas pays for all the
labour on the fallows, the seeds sown, and labour attending them,
and for the dung and hay. He is required to draw out the out-
going tenant's corn, and in return gets all the straw and chaff of
the last year's crop free.
Surrey.—The county of Surrey is notorious for its high valua-
tions. The tenancies, although frequently entered upon at other
times, are generally computed as from Michaelmas. The valuation
comprises fallows, half fallows, dressings, half dressings, grass
seeds, underwood, clover leys, hay, straw, and manure upon the
premises.
Under the heading of " Fallows" are included all the ploughings,
harrowings, rollings, and couchings, whether judicious or unneces-
VALUATION OF TILLAGES.
629
sary, that the fallow can be shown to have received at the hands
of the outgoing tenant, a year's rent and rates, and if sown with
turnips, the seed and sowing. Half fallows are generally charged
at an agreed sum by the valuators, without going into the details
of the previous fallow. They are said to arise, as has been pre-
viously explained, on lands that have only borne one straw crop
since the full fallow.
Dressings are charged at the full value of the dung, in addition
to the cost of carting and spreading. Half dressings arise in the
same way as half fallows, and are generally treated similarly by
the valuers. Clover seeds are charged at the cost of seed and la-
bour. Clover leys at their estimated value. Underwoods accord-
ing to their growth. Hay and straw sometimes at a fodder price,
and sometimes at a market price; and dung at its measured value.
In those cases that the occupancy commences at a period of
winter or spring, the incoming tenant is charged with the costs of
all the labour, seed and sowing, rates and taxes, that have been
expended upon the farm since the previous Michaelmas (from
which date his rent commences,) in addition to the valuation to
which he would have been subject had he entered at Michaelmas.
When the occupation commences in summer, the incoming tenant
generally takes to the standing crops at a valuation, and the out-
going clears up the rent to the following Michaelmas, excepting
such parts thereof as are taken into account in the valuation of the
fallows. It is an essential feature in the custom of Surrey that a
tenant is entitled to be paid on leaving for all such things as he
paid for when he entered.
The general tenure of Surrey may be said to be leases of 7, 14,
or 21 years, the middle term prevailing. The rentals are almost
without exception half-yearly payments in money. The landlord
generally finds timber rough upon the stem, and bricks, tiles, and
lime at a kiln within seven miles, for the repairs, the tenant finding
cartage and labour. In most cases the restrictions as to cultiva-
tion direct that one-fourth of the arable lands must be in wheat or
beans; one-fourth fallow and turnips; one-fourth barley or oats;
and one-fourth seeds.
I have gone more fully into the customs of this county because
they are familiar to me, and because it will in some measure tend
to illustrate my interpretation of certain technical expressions made
use of by me which bear a different meaning in different counties.
To take but one instance, I understand a "Dressing
to be a
quantity of manure bestowed on the land; whereas I believe in
many parts of England the word "dressing" is applied to one course
""
630
VALUATION OF TILLAGES.
of ploughing, harrowing, &c., and it is very common to say that a
fallow has five dressings.
Sussex. Those portions of the county that adjoin Kent and
Surrey have very similar customs to those of the adjoining counties.
In other parts the labour upon the fallows is charged, but not the
rent and rates. The dung arising out of the crop of the last two
years of the tenancy belongs to the incoming tenant, the only
charge upon it being for carting, casting into heaps, turning, and
spreading. The incoming tenant sometimes carts to market the
corn of the last year's growth belonging to his predecessor, taking
in return the straw and chaff. When this carting is not done, the
straw and chaff is paid for at fodder price.
Warwickshire.—The incoming tenant at Lady-day generally pays
for seed, sowing, rent, and rates on the wheat crop from Michael-
mas; but a custom prevails allowing the outgoing tenant to retain
possession of the wheat lands that are after fallow, not otherwise,
until the following Michaelmas, to get in his wheat crop, in which
case he pays the new occupier the half-year's rent and rates. The
custom as to spring crops allows no right of pre-entry to the in-
coming tenant; if the outgoing occupier prepares and sows the
land, he is paid for so doing at valuation. No fallows are paid for
in this county; but if the turnip crop fails on fallowed land, the out-
goer is allowed one half-year's rent and rates thereon in considera-
tion of the labour he has expended. The dung is not paid for.
Westmoreland.—The incoming tenant pays for seed, sowing, and
labour, previously expended, and a portion of the rent and rates of
fallows. (The expressions waygoing and oncoming are substituted
in the North for outgoing and incoming in the South.)
Wiltshire. The incoming tenant has the right of pre-entry, to
make his fallows and sow his wheat, turnips, and grass seeds. He
is entitled to the dung arising from the crops of the last two years,
and the outgoing tenant consumes the fodder.
Worcestershire.-The chief feature in the custom appears to be,
that a tenant leaves a farm on the same conditions as he entered
upon it.
Yorkshire, East Riding of.-The incoming tenant at Lady-day is
entitled to pre-entry at Candlemas to plough lands for fallow. He
has to pay for clover seeds and sowing, and for the manure arising
from the last year's crop. He also pays for the growing crops of
corn at a valuation, made at suitable times near harvest. The pay-
ments for the amount of the growing crops are (in some cases I am
aware, but whether generally so I am not fully informed) allowed
to be made by instalments, as the corn is thrashed, so that a
VALUATION OF TILLAGES.
631
smaller capital is required to take to a farm under this custom
than is at first sight apparent.
Yorkshire, North Riding of.-The same right of pre-entry exists
as in the East Riding from Candlemas-day, the tenancy com-
mencing at Lady-day. The incoming tenant pays for clover seed
and sowing of the preceding year, and for the manure from the
last year's crop. He also pays for the wheat crop at valuation at
harvest, or allows the outgoing tenant to harvest the crop.
Yorkshire, West Riding of. The tenancy commences at Lady-
day, the tenant having a right of pre-entry at Candlemas. Fallows
and half fallows, dressings and half dressings, are valued in this
Riding in some instances. The wheat crop is sometimes har-
vested by the outgoing tenant; sometimes the incoming occupier
pays for it at valuation; and clover leys are paid for.
I have now gone through the whole of the customs in force in
the several counties of England, so far as they relate to, or form
the subject of, valuations of tenant-right, and as well as I have
been enabled to gather information. It will be obvious to every
practical man that the customs of many counties are exceedingly
difficult to define, varying as they frequently do in different
parishes of the same county, and especially is this the case with
reference to the periods of entry. My endeavour has been to
place together such an amount of information as will convey a
general idea of the whole question; the information is of necessity
imperfect, but at the same time it affords a key to the principal
features.
The following specimen of a Surrey Valuation will sufficiently
elucidate the principle of making them, and writing out the in-
ventory.
Before commencing a valuation, the valuators should always
appoint in writing an umpire, to whom matters of difference may
be referred. If this is not attended to, difficulties sometimes arise
at a subsequent stage in the choice of an umpire, causing great
delay and trouble.
632
VALUATION OF TILLAGES.

SPECIMEN OF FIELD BOOK.
Quantity
in
each Field.
Name of Field.
Quantity
Price
in
each Course.
Items of Valuation. per
Acre.
Value of
Labour and
Tillages.
Value
of
Dressings.
A mount of
Rent and Total Value.
Rates.
Value
of
each Field.
A. R. P.
42 20
Garson.
A. R. P.
40 0 0
5 times Ploughed.@10/
£. s. d.
100 0 0
£. s. d.
£. s. d.
£. s. d.
£. s. d.
Fallow.
2 tine Dragged
,, 1/4
568
Once Rolled
Fallow
Rotation of Crops,
1849 Wheat
Fallow
1850 Tares fed
1851 Wheat
1852 Fallow
(with 4 horses)
», 1/6
300
108 6 8
20 0 0 Dunged 12 Cart
Loads per Acre
Carting and
,, 80/
80 0 0
80 0 0
Spreading
40 0 0 Rent and Rates
,, 35/
70 0 0 70 0 0
258 6 8
20 0 0
Barn Field.
20 0 0
5 times Ploughed.,, 11/
Fallow.
2 tine Dragged
» 1/6
Once Rolled
Rotation of Crops,
55 0 0
300
1 10 0
1849 Wheat
1850 Tares fed
Fallow
1851 Wheat
1852 Fallow
(with 4 horses)
Dunged 12 Cart
Loads per Acre
Carting and
Spreading
Rent and Rates
1/6
", 80/
,, 351
80 0 0
..
59 100
80 0 0
35 00
35 0 0
174 100
VALUATION OF TILLAGES.
633
34 1 6 Guildford Field.
Seeds
Rotation of Crops,
1849 Wheat
1850 Beans
1851 Fallow, Swedes
1852 Wheat, Oats.
Seeds.
33 0 0
7 lbs. of Clover
Seed, per acre
7 lbs. of Trefoil
per acre
2 tine small
Harrowing.
Once Rolling
@ 6d.
5 156
4d.
3 170
6d.
1 130
,,
6d.
0 16 6
Half Fallow.
40s.
66 00
""
78 2 0
18 0 0
Half Dressing.
40s.
36 0 0
""
36 0 0
114 2 0
20 316
Twenty Acres.
20 0 0 Twice Ploughed.
12s. 24 0 0
24 0 0
""
24 0 0
Rotation of Crops,
1849 Wheat
1850 Clover
1851 Oats
1852 Peas.
20 216
Long Field.
Clover Ley
Rotation of Crops,
1849 Tares and Swedes
20 0 0 The Ley
458. 45 00
""
Half Dressing.
35s.
35 0 0
45 0 0
35 0 0
""
80 0 0
8 030 Common Field.
8 00
Half Fallow.
40s. 16 0 0
16 0 0
16 0 0

1850
Peas
1851
Wheat
1852
Clover.
Rotation of Crops,
1849 Clover Ley
1850 Oats
1851 Tares fed
Fallow
1852 Wheat.
2 R
634
VALUATION OF TILLAGES.

29 1 6
Pond Field.
Rotation of Cropping,
1849 Clover Ley
1850 Wheat
1851 Peas
Fallow
1852 Wheat.
28 0 0
Half Dressing.
@ 40s.
56 0 0
56 0 0 || 56 0 0
0
29 3 10 Carthouse Field.
28 0 0
Two tine small
6d.
1 8 0
Seeds
Harrowing.
>>
Rotation of Cropping,
1849 Beans
1850 Wheat
1851 Swedes, Mangold, Tares
1852
Wheat
Seeds.
Once Rolling
200lbs of Clover
Seed
6d.
140
""
6d.
5 0 0
""
10 Bushels of
Rye Grass S
6s.
3 00
""
10 2 0
20 0 0
Half Dressings
40s.
40 0 0
40 0 0
....
20 0 0
Half Fallow
40s.
40 0 0
40 0 0
""
90 2 0
35 2 8 Cross Path Field.
34 0 0
Rotation of Cropping,
16 0 0
Twice Ploughed
* Rent and Rates.
13s.
44 4 0
44 4 0
""
30s.
24 0 0
24 0 0
1849 Peas
""
68 4 0
Fallow
1850 Wheat
1851 Winter Beans
1852 Tares
Tares
fed,
cut,
Fallow.
* The Rent and Rates is
allowed on that portion of
the Field from which the
Tares were fed. This has
been decided by very com-
petent judges as being the
Surrey custom. I cannot
discover the equity of it.
The Tenant should surely
pay the Rent of Land
upon which he has kept
a flock of Sheep
VALUATION OF TILLAGES.
635

SUMMARY.
Quantity
in
each Field.
Name of Field.
Quantity
in each
Course.
Items of Valuation.
Value of
Price. Labour and
Tillages.
Value
of
Dressings.
Amount of
Rent and
Rates.
Value of
Total
Value.
each
Field.
A.
R. P.
A. R. P.
L.
S. D.
L. S. D.
42 2 0
Garson
4000
Fallow
108
68
80 0 0
200 0
Barn Field
2000
Fallow.
59
10 0
8000
I.. S. D.
70 0 0
3500
L.
8. D.
341 6
Guildford Field
3300 Seeds
78
20
36
3600
20 3 16
Twenty Acres
2000 Ploughed after Peas
24
L. S. D.
258 68
17410 0
114 20
24 00
20|2|16|| Long Field
2000
Clover Ley.
45
010
350 0
80 00
•
8030
Common Field.
80
Wheat Ersh
16
ΟΙ Ο
291 6
Pond Field
28 0 0
Wheat Ersh
56 1010
29 3 10
Carthouse Field.
28 0 0
35 2 8
Crosspath Field.
3400
Seeds
Fallow
50 20
40
40 00
44
40
24
010
241 0 12
23100
425
48327 0 0 129
16 O
56 0
90 2
68 40
881 48
A Hill of Dung, 33 yards by 10 yards, and 2 feet high, at 5s. per yard
A Rick of Clover Hay, 10 yards by 6 yards, and 4 yards high, at £4 10s. per load
Three Years' growth in about 3 acres of Underwood
Amount of the Valuation
55 00
162 00
660
1104108
£1104 108
EDWARD RYDE,
JAMES SMITH,
}
Valuators.
636
VALUATION OF TILLAGES.
With reference to the preceding form of Field Book, little need
be said. It will be found convenient in general use, although
perhaps few valuers will adopt it, simply because it appears to
cause extra trouble; such, however, is not the case, and the
information it affords is very interesting. The first column sets
forth the actual quantity of the field, including waste and hedge
and ditch: the outside measure thereof, properly speaking. The
second column contains the name of the field, under which is
written the cultivation, and in the same column there is always
room to make a memorandum of the rotation of cropping, which
should be enquired into. The third column sets forth the inside
measure of the field, or the different quantities included in one
course of husbandry. The fourth column contains the different items
of the valuation. The fifth is set apart for the price. The sixth,
seventh, and eighth contain respectively the amounts of different
charges, distinguishing those for dressings and half dressings, and
the allowance for rent and rates from the valuation of the tillages
and labour. The ninth is a column for the totals of the three
preceding columns and for any extraneous matters that cannot be
ranged under either of the other heads. The tenth and last
column contains the total amount of valuation in each field in
a convenient form for casting.
In writing out the inventory the prices are not given.
The following is the manner in which this is done:—
An INVENTORY and VALUATION of tillages and tenant-
right upon a farm in Surrey, as made between Mr. Daniel Long-
staff and Mr. Richard Smith, this 25th day of October, 1852, by
Edward Ryde, on the part of the said Daniel Longstaff, and James
Smith, on the part of the said Richard Smith.
A. R. P.
42 2 0
Garson-Fallow
40 0 0-5 times ploughing
2 tine dragging
20 0 0
40 0 0
Once rolling
Dunging, carting & spreading
Rent and rates.
20 0 0 Barn Field-Fallow
5 times ploughing
2 tine dragging
Once rolling
Dunging, carting & spreading
Rent and rates.
VALUATION OF TILLAGES.
637
A. R.
P.
34 1 6 Guildford Field-Seeds
33 0 0 Clover seed and sowing
2 tine small harrowing
Once rolling
Half fallow
18 0 0
Half dressing.
20 3 16
The Twenty Acres
20 0 0 Twice ploughing.
20 2 16 Long Field-Clover Ley
20 0 0 The ley
Half dressing.
8 0 30 Common Field-Wheat Ersh
8 0 0 Half fallow.
29 1 6 Pond Field— Wheat Ersh
29 3 10
28 0 0 Half dressing.
Carthouse Field-Seeds
28 0 0-2 tine small harrowing
Once rolling
Clover seed and sowing
20 0 0 Half dressing
Half fallow.
35 2 8 Cross Path Field-Fallow
34 0 0
16 0 0
Twice ploughed
Rent and rates
A hill of dung
A rick of clover hay
3 0 0 Wood-3 Years' growth of underwood.
The tillages, and other acts of husbandry, matters and things
mentioned in the foregoing inventory, are valued at the sum of
one thousand, one hundred and four pounds, ten shillings and
eight pence, by us,
EDWARD RYDE,
JAMES SMITH.
In connection with this subject the following directions and
Tables for Measuring Hay Ricks will be useful.
Let fig. 173" represent a hay stack, the content of which is
required :-
It will be obvious that the mean length, width, and height,
taken at the places indicated on this fig., are the correct dimen-
sions for ascertaining the proper cubic content of the stack.
The density of the stack must then be estimated, and the
remaining operations are supplied by the tables.
638
TABLES FOR MEASURING HAY RICKS.
Table 1.
To be used when the Hay is very close.

Feet
6
77
8
9
10 11
12
13
14
Feet
feet
feet
feet
feet
feet
feet
feet
feet
feet
wide.
high. high.
high.
high.
high.
high.
high.
high.
high.
wide.
67
72
7
84
B88
84
96
108
120
132
144
156
168
98 112
126
140 154
168
182
196
67
7.
96
112
128
144 160
176
192
208 224
9
108 126
144
162 180
198
216
234
252
10 120
140
160
180 200
220
240
260
280
11 132 154
176
198
220
242
264
286
308
13
15
16
17
19
20
21
224 B CO 2 222
12
144
168 192
216 240
264
288
312
336 12
156 182 208
234
260
286
312
338
364
13
14
168
196 224
252
280
308 336
364
392
180
210
240
270 300
330
360
390
420
192
224 256
204 238 272
288 320
306
352
384 416
448
340
374 408
442
476
17
216
252
288
324 360
396
432
468
504 18
228
266
304
342
380 418
456
494
532
19
240
280
320
360
400 440
480
520
560
20
252
294 336
378
420 462
504 546
588
21
264 308 352
396
440 484
23 276
322
368 414
27
24 288 336 384
25 300 350
26 312 364
324 378
400
416
460 506
432 480 528
450 500
550
468 520
432 486 540
528 572
552 598
576 624 672
600 650 700
572 624 676 728
594 648 702 756
616
644
23
24
25
26
27
∞∞ = 22± 2 CFD - 222 * *&&
9
10
11
14
15
16
EXAMPLE. Required the Content of a Hay Stack 23 feet long, 16 feet wide,
and 10 feet high; the Hay being very close.
In Table 1, opposite 16 feet wide, and under 10 feet high, stands the number
320, which is carried to Table 4, to complete the calculation.
Note. A very little practice will show which of the Tables, 1, 2, or 3, should be
made use of for different description of Ricks, as, for example, suppose a person were
to measure a Rick and estimate the content by Table 2, which when cut out proved
to contain more Hay than the Tables gave him, he would know in future, that that
description of Rick must be measured by Table 1, or if it contained less, then
would he know that Table 3 must in future be used; and, having acquainted himself
with the kind of Rick adapted for the two extremes, the mean, or Table 2, will of
course follow.
TABLES FOR MEASURING HAY RICKS.
639
Table 2.
To be used when the Hay is of a mean density.

Feet
6
7
8
9
10
11
12 13
14
Feet
feet
feet
feet
feet
feet
feet
feet
feet
feet
wide.
high.
high.
high.
high. high.
high.
high.
high.
high. wide.
67
8
9
90
105
88888
220
82 88
70
90 100
110
120
130 140
81
93
105
116 128
140
151 163
67
93 106
120
133
146
160
173
186
8
120 135
150
165
180
195
210 9
10
100
116 133
150
166
183
200
216
233
10
11
110 128
146
165
183 201
220
238
256
11
231
12
120 140 160
180
200
220
240
260
280
13 130 151
173
195
216
238
260
281
303
14
140
163
186
210
233
256
280 303
326
221
12
13
14
15
150
175
200
225
250
275 300
325
350
15
210 2 222 3 238 A
16 160
186 213
240 266
293 320 346
373
17
170 198 226
255 283
311
340 368
396
18
180
210
240 270
300
330
360 390
420
19
190 221
253 285
316
348
380 411
443
20
200 233 266
300
333
366
400 433
466 20
21
210
245 280
315
350
385
420 455 490
21
220 256
293 330
366
403
440
476
513
23
230 268 306
345
383
421
460
498
536 23
24
240 280 320
360
400 440
480 520 560 24
25
250 291 333
375
26 260 303 346
416
390 433
458
500 541 583
476 520 563 606
27
270 315 360 405 450 495 540 585 630
9702 222 * *** *
17
18
19
25
26
EXAMPLE
Suppose a Hay Stack, 33 feet long. 18 feet wide, and 12 feet high,
and the Hay of a mean density, what does it contain?
In Table 2, under 12 feet high, and opposite 18 feet wide, stands the Number
360, which must be carried to Table 4, to complete the calculation.
640
TABLES FOR MEASURING HAY RICKS.
Table 3.
To be used when the Hay is very loose.

Feet
6
8
9 10 11
12
13
14
Feet
Feet
Feet
Feet
Feet
Feet
Feet
Feet
Feet
Feet
wide.
high. high.
high.
high.
high.
high.
high.
high.
high. wide.
6
51
7
10
11
∞ DOE & B
8
9
DO 8 N*
60
68
77
85
100
94
110
༄ཧྨ ཙ
828 889
77
85
94
102
111
120
6
90 100
110
120
130
140
7
102
114 125
137
148
160
102
115 128
141
154
167
180
114 128
142
157
171
185
200
10
125
141
157
172
188
204
220
12 102
120
137
154
171
188
205 222
240
12
13
111
130
148
167
185
204
222
241
260
14
120 140
160
180
200
220
240 260
280
15 128 150
171
192
214
235 257 278
300
15
16
137
160
182
205
228
251 274
297
320
16
18
19
*** & ***3 * 285
145
170 194
218 242
267
291
315
340
154 180
205
231 257
282
308
334
360
18
162 190 217
244
271
298
325
352
380
19
171 200 228
257
285 314
342
371
400
180 210 240
270
300 330
360 390
420
21
22
188 220 251
282
314
345
377 408 440
23
197 230 262
295
328
361
394 427 460
24
205 240 274 308
342
377
411 445 480
214
250 285
321
357
392
428 464 500 25
26
222 260 297 334
371
408
445 482 520
27 231 270 308 347 385
424
462 501 540 27
∞ DOE 2 BED FOR 2 723 * Q&A
13
14
17
20
24
26
EXAMPLE.-Suppose a Hay Rick 40 feet long, 18 feet wide, and 12 feet high, the
Hay very loose, what are its contents?
In Table 3, under 12 feet high, and opposite 18 feet wide, stands the number 308,
which carried to Table 4, will complete the calculation.
TABLES FOR MEASURING HAY RICKS.
641
21
22
23
24
25
26
ft. long. | ft. long. | ft. long. | ft. long. | ft. long. | ft. long.
Trusses. Trusses. Trusses. Trusses. Trusses. Trusses.
Numbers.
15
16
17
18
19 20
ft. long. ft. long. ft. long. ft. long. ft. long. ft. long.
Trusses. Trusses. Trusses. Trusses. Trusses. Trusses.
Numbers.
Table 4. Completing the Calculations and showing the Content of
Ricks, in Trusses.
123
1
3
13
1
2
1
3
3
3
4
2
24
2
2
2
4
Q 4
2
4
6
3
7
7
7
6
7
8
9
9
10
10
7
8
8
9
9
10
10
11
11
12
12
13
9
9
10
10
11
12
6
12
13
13
14
15
15
10
11
11
12
13
14
7
14
15
16
16
17
18
12
12
13
14
15
16
16
17
18
19
20
20
9
13
14
15
16
17
18
9
18
19
20
21
22
23
10 15 16
17
18
19
20
10
21
22
20
30
32
34
36
38
40
20
42
44
30
45
48
51
54
57
60
30
63
66
40
60
64
68
72
76
80
40
84
88
9:2
2988
24
25
26
48
50
52
72
75
78
96 100
104
50 75
80
85
90
95
100
50
105
110
115
120
125
130
60
90
96
102
108
114
120 60
126
132
138
144 150
156
70
105 112
119 126
133 140 70
147
154
161
168
175
182
80
120 128 136
144
152
160 80
168
176
184
192 200
208
90
135 144 153 162
171
180 90
189
198
207
216 225
234
100
200
150 160 170 180
190
200 100
210
220
230
240
250
260
300 320 340 360
380
400 200
420 440
460
480 500
520
300 450 480 510 540
400 600 640 680 720
500 750 800 850 900
600 900 960 1020 | 1080
700 1050 1120 1190 1260
570 600 300
630 660
1140
760 800 400
950 1000 500
1200 600
840
1050
1260
690 720 750
880 920 960 1000 1040
1100 1150 1200 1250 | 1300
780
1320 1380 1440 1500 1560
1330
1400 700 1470
1540 1610 1680 1750 1820
EXAMPLE, In Example to Table 1 our calculation was held in abeyance
after finding the number 320.
Now by this Table, under 23 feet long, opposite 300 stands 690 Trusses.
20
46
""
""
""
320 content. 736
1

642
TABLES FOR MEASURING HAY RICKS.
27 28
29
30 31 32
ft. long. ft. long. ft. long. | ft. long. | ft. long. ft. long.
Numbers.
33
34
35
36
37
ft. long. ft. long. ft. long. ft. long. ft. long
38
ft, long
Trusses. Trusses. Trusses. Trusses. Trusses. Trusses.
Numbers.
Table 4 continued. Showing the Content of Ricks, in Trusses.

Trusses. Trusses. Trusses Trusses. Trusses. Trusses.
12
9 &
3
Q7 20 00
3
3
6
6
6
9
123
3
3
3
3
3
6
6
7
7
7
7
9
10
10
10
11
11
4
10
11
11
12
12
12
4
13
13
14
14
14
15
13 14
14
15
15
16
16
17
17
18
18
19
6
16
16
17
18
18
19
6
19
20
21
21
22
22
18
19
20
21
21
22
23
23
24
25
25
26
8
21
22
23
24
24
25
26
27
28
28
9
24
25
26
27
27
28
9
29
30
31
32
8883838
30
34
10
27
28
29
30
31
32
10
33
34
35
36
37
38
20
54
56
58
60
62
64
20
66
68
70
72
74
76
30
81
84
87
90
93
96
30
99
102
105
108
111
114
40
108 112 116 120
124 128 40
132
136
140
144
148
152
50
135 140 145
150 155
160
50
165
170
175
180
185
190
60
162
168 174
180
186
192
60
198
204 210
216
222
228
70 189 196
203
210
217
224
70
231
238
245
252
259
266
232
80 216 224
90 243 252 261
100 270 280 290 300 310
200 540 560 580 600 620
300 810 840 870 900 930 960 300 990
400 1080 1120 1160 1200 1240 1280 400 1320
| |
500 1350 1400 1450 1500 1550 1600 500 1650
600 1620 1680 1740 1800 1860 1920 600 1980
700 1890 1960 2030 2100 2170 2240 700 2310
240
248
256 80
264
272
280 288
296
304
270 279
288 90
297
306
315
324 333
342
320❘ 100
330
340
350
360 370
380
640 200
660
680 700
720
740
760
1020❘ 1050
1360 1400 1440 1480
1700 1750 1800 1850
2040 2100 2160
2380 2450 2520 2590
1080
1110
1140
1520
1900
2220 2280
2660
number 360. In Table 4, under 33 feet long, opposite 300 stands 990 Trusses.
EXAMPLE. In Table 2 our calculation was held in abeyance after finding the
27
60
360 content. 1188
198
79
effort.
have been taken from the Table, and cast together mentally, without the slightest
troublesome at first sight, but on inspection, it will be obvious that the figures might
Note.—This calculation, containing two lines of figures, may appear unnecessarily
TABLES FOR MEASURING HAY RICKS.
643
in others.
Table 4 continued. Showing the Content of Ricks, in Trusses.

45
46
47
48 49
50
ft. long. ft. long. | ft. long. ft. long. | ft. long. | ft. long.
Trusses. Trusses. Trusses. Trusses. Trusses. Trusses.
Numbers.
39
40
42
41
ft. long. ft. long. ft. long. | ft. long.
43 44
ft. long. ft. long.
Trusses. Trusses. Trusses. Trusses, Trusses. Trusses.
Numbers.
1
2
IQ 3
3
7
11
12
4
15
16
19
6
23
24
+0202*8
4
12
16
+020
4
4
4
4
8
8
8
12
12
13
1Q3
4
4
4
4
4
5
2
9
9
9
9
9
10
13
13
14
14
14
15
16
17
17
18
18
18
19
19
20
20
21
21
22
22
23
23
24
24
25
24
25
25
26
6
27
27
28
28
29
30
7
27
28
28
29
30
30
31
32
32
33
34
35
8
31
32
32
33
34
35
36
$6
37
38
39
40
9
35
36
36
37
38
39
9
40
41
42
43
44
45
10
39
40
41
42
43
44
10
45
46
47
48
49
50
20
78
80
82
84
86
88
20
90
92
94
96
98
100
30 117 120 123 126
129
132
30 135
138
141
144
147
150
40
50
156 160 164
195 200 205
210 215
60 234 240 246 252
70 273 280 287 294
80 312 320 328
336
90 351 360 369 378 387
430
168 172
176 40
180
184
188
192 196
200
220
50
225
230
235
240 245
250
258
264 60
270
276
282
288 294
300
301
308 70
315
322
329
336 343
350
344
352 80
360
368
376
384
392
400
396 90
405
414
423
432
441
450
300
400
1560
700
500 1950
600 | 2340
2730
100 390 400 410 420
200 780 800 820 840 860
920
940 960 980
1170 1200 1230 1260 1290 1320 300 1350 1380
1410 1440 1470
1600 1640 1680 1720 1760 400 1800 1840 1880 1920 1960
2000 2050 2100 2150 2200 500 2250 2300 2350 2400 2450
2400 2460 2520 2580 2640 600 2700 2760 2820 2880 2940
2800 2870 2940 3010 3080 700 3150 3220 3290 3360 3430
440 100
450
460
470 480 490
500
880 200 900
1000
1500
2000
2500
3000
3500
EXAMPLE
number 308.
In Table 4, under 40 feet long, opposite 300 stands 1200 Trusses.
By Table 3 our calculation remained in abeyance after finding the
32
8
""
calculating by the Load of 36 Trusses in some counties, and by the Ton of 40 Trusses
Note.-The Contents are given in Trusses on account of the different custom of
308 content. 1232
644
TABLES FOR MEASURING HAY RICKS.
Trusses.
Table 5.
Showing the number of loads and tons which are contained in any
number of trusses.

Trusses.
36 1
0
40 1 4
0 36
1 0
270
280
7 18 6 30 504|| 14 0
7 28 7 0 510 14 6
12 24
12 30 760
756 21
21
0 18 36
4 19 0
50 1 14
1 10
288
8 0
7 8 520
14 16 13 0 792
22
0 19 32
60 1 24
1 20
290
290
8
8 2
7 10 530
14 26 13 10 800
22
8 20 0
820
70 1 34
1 30
300
8 12
7 20 540
15 0 13 20
828
23
0 20 28
72 2 0
1 32
310
8 22
7 30 550
15 10 13 30 840
23
12 21
0
80 2 8
2 0
320
8 32
8 0 560
90 2 18
2 10
324
90
8
100 2 28
2.20
330
9 6
15 20 14 0 864
15 30 14 10 880
16 0 14 16 900
108 3 0
2 28
340
9 16
110 3 2
2 30
350
9 26
120 3 12
130 3 22
3 0
3 10
360 10 0
370 10 10
140 3 32
3 20
380 10 20
8 30 590
9 0 600
9 10 610
9 20 612
144 4 0
3 24
150 4 6
3 30
160 4 16
4 0
390 10 30
396 11 0
396 11 0
400 11 4
9 30 620
16
8 4 570
10 576
8 20 580
9 36 630
9 36 630
10 0 640
16 4 14 20 920
16 14 14 30 936
16 24 15 0 960
16 34 15 10 972
17 0 15 12 1000||
17 8 15 20 1100
17 18
17 28
15 30 1200
24 0 21 24
24 16 22 0
25 0 22 20
25 20 23 0
26 0 23 16
26 24 24 0
27
27 0 24 12
27 28 25 0
30 20 27 20
33 12 30 0
01300
36
36 4 32 20
170 4 26
4 10
410 11 14
10 10 648
18 0 16
81400
81400
38 32 35 0
180 5 0
4 20
190 5 10
4 30
200 5 20
5 0
420 11 24
430 11 34
432 12 0
10 20 650
10 30 660
10 32 670
18 2
16
10 1500
41 24 37 20
18 12
16 201600
44 16 40 0
18 22
16
30 1700
30|1700
47
210 5 30
5 10
440 12 8
11 0 680
18 32
17
216 6 0
5 16
450 12 18
220 6 4
230 6 14
5 20
5 30
460 12 28
468 13 0
240 6 24
6 0
470 13 2
250 6 34
252 7 0
490
6 10 480 13 12
6 12
260 7 8 8
6 20
500
11 10 684
11 20 690
11 28 700
11 30 710
12 0 720
13 22 12 10 730
13 32 12 20 740
19 0 17
0 1800
41900
47 8 42 20
50 0 45 0
52 28 47 20
6
17 10 2000
17 20 2500
17 30 3000
19
19 16
19 26
20 0 18 03500 97 8 87 20
20 10 18 10 4000 111 4100 0
20 20 18 20 5000 138 32125 0
55 20 50 0
69 16 62 20
83 12 75 0
EXAMPLE 1. In 1800 trusses, how many loads or tons?
Opposite 1800 trusses stands 50 loads or 45 tons.
EXAMPLE 2. In 736 trusses, how many loads ?
Opposite 730 stands 20 loads, 10 trusses, to which if we mentally add 6 trusses,
we get the required answer.
EXAMPLE 3. In 736 trusses, how many tons ?
Opposite 730 stands 18 tons 10 trusses, to which if we mentally add the
remaining 6 trusses, we get the required answer.
VALUATION OF HAY RICKS.
645

2s. 4d.
Trusses.
Per Truss,
£4 4s. Od.
Per Load,
£4 138. 4d.
Per Ton.
£ s. d.
£ s. d.
£ s. d.
£ s. d.
30
40
20050
0 10 0
0 10 5
0 10 10
5
0 11
3
0 11
10
1
0 0
1 0 10
1
1 8
10
1 2
1 3
28.
Table 6. Showing the Value of any Number of Trusses at various prices per Truss, Load, or Ton.
Per Truss,
£3 12s. Od.
Per Load,
£4 0s. Od.
Per Ton.
2s. id.
Per Truss,
£3 15s. Od.
Per Load,
£4 3s. 4d.
Per Ton.
2s 2d.
Per Truss,
£3 18s. Od.
Per Load,
£4 68. 8d.
Per Ton.
28. 3d.
Per Truss,
£4 ls. Od.
Per Load,
£4 10s. Od.
Per Ton.
28. 5d.
Per Truss,
£4 78. Od.
Per Load,
£4 168. 8d.
Per Ton.
28. 6d.
Per Truss,
£4 10s. Od.
Per Load,
£5 0s. Od.
Per Ton.
28. 7d.
Per Truss,
£4 138. Od.
Per Load,
£5 38. 4d.
Per Ton.
28. 8d.
Per Truss,
£4 16s. Od.
Per Load,
£5 68. 8d.
Per Ton.
£ s. d.
0 13 4
48
£ s. d.
£ s. d.
£ s.
d.
£ s. d.
8
0 12 1
5
0 12 6
0 12 11
4
1
4 2
10
1 5
5 0
1
5 10
1 6 8
200
2 1
8
2
3
4
20
2 5 0
2 6
8
2
8
4
20
2 10 0
2 11
8
2 13
4
3 0 0
3
26
3 5 0
30
3 7
6
3 10 0
3 12
6
30
3 15
0
3 17
6
4 0
0 0
4 0
0 0
4 3 4
4 6 8
40
4 10 0
4 13
4
4 16 8
40
500
5 3
4
568
50
5
0
0 0
5 4 2
5 8 4
50
5 12
6
5 16
8
6 0 10
50
6 5 0
69 2
6 13 4
60
6 0
0 0
6 5 0
6 10
0
60
6 15
0
7 0 0
7 5
5
0
60
7 10
0
7 15
0
8
0 0
70
7
0 0
7
5 10
7 11
8
70
7 17
8
3
4
8
9 2
70
8 15
0
9
0 10
9
6 8
80
8
0
8 6
8
8 13 4
80
9 0
0
9 6
6
8
9 13 4
80
10 0
0
10 6
10 13 4
90
9 0 0
9 7 6
9 15 0
90
10 2 6
10 10
0
10 17
6
90
11 5
0
11 12
6
12 0 0
100
10 0
0
10 8
4
10 16 8
100
11
5 0
11 13
4
12 1
8
100
12 10 0
12 18
4
13 6 8
200 20 0 0
20 16 8
21 13 4
200
22 10
0
23 6
6
8
24 3
4
200
25 0
0
25 16
8
26 13 4
300
30 0
0
31 5
0
32 10 0
300
33 15
0
35
0
0
36 5
0
300
37 10 0
38 15
0
40
0
0
400 40 0
0
41 13 4
43 6 8
400
45 0
0
46 13 4
48 6 8
400
50 0
0
51 13
4
53
6 8
500
50 0
0
52 1 8
54 3 4
500
56 5
0
58 6 8
60 8 4
500
62 10 0
64 11
8
66 13 4
600
60 0 0
62 10 0
65 0 0
600
67 10 0
70 0
0
72 10 0
600
75 0
0
77 10
0
80 0
0 0
700
70 0 0
72 18 4
75 16 8
700
78 15 0
81 13 4
84 11
8
700
87 10
0
90 8
4
93
6 8
800
80 0
83.6
0
8
86 13
4
800
90
0
93 6
8
96 13 4
800
100
0
0
103 6
6 8
106 13
4
900
90 0 0
93 15 0
97 10
0
900
101 5 0
105 0
0
108 15
0
900
112 10
112 10
0
116
5 0
120 0 0
1000 100 0
200 0 0
2000
3000 300 0 0
4000 400 0 0
104 3
208 6
4
8
312 10 0
416 13 4
EXAMPLE. What is the value of 666 Trusses of Hay at four guineas per Load?
Under £4 4s. per Load, opposite 600 stands £70 0 0
108 6 8
216 13 4❘ 2000
325 0 0 3000
433 6 8 4000
1000
112 10 0
116 13
4
120 16
8
1000
125
0 0
129 3
4
133 6 8
225 0 0
233 6
6 8
8
241 13 4
2000
250
0 0
258 6
8
266 13 4
337 10 0
450 0 0
350 0 0
362 10 0
3000
375 0 0
387 10
0
400 0 0
466 13 4
483 6
6 8
4000
500
500 0 0
516 13 4
533 6 8
60
7 0 0
"9
5
and
1
is
18
666
0 11 8
024
£77 14 0
Note.-Here again Trusses have been used as the measure of quantity
given, that it might serve equally whether Tons or Loads are the custo-
mary measure. Most of the calculations may be made mentally, or at
all events with very little addition.
-646
VALUATION OF HAY RICKS.

Trusses.
3s. 1d.
Per Truss.
£5 118. Od.
Per Load,
£6 3s. 4d.
Per Ton.
£ s. d.
£ s. d.
£ s.
202UNU.
5
0 14 2
0 14 7
5
0 15
0
1 8
4
1 9 2
10
1 10 0
2 16 0
2 18 4
20
3 0 0
4 5
4 7 6
30
4 10 0
5 10 0
5 13 4
5 16 8
40
600
50
6 17 6
7 1
8
7 5 10
50
7 10 0
8 5
0
8 10
0
8 15 0
60
9 0
0
70
9 12 6
9 18 4
10 4 2
70
10 10 0
80 11 0 0
11 6
8
11 13 4
80
12 0
0
90
12 7 6
12 15
0
13 2 6
90
13 10
0
Table 6 continued.-Showing the Value of any Number of Trusses at various prices per Truss, Load, or Ton.
2s. 9d,
Per Truss,
£4 19s. Od.
Per Load,
£5 10s. Od.
Per Ton.
£ s. d.
0 13 9
1 7 6
2 15 0
4 2 6
28. 10d.
Per Truss,
£5 2s. Od.
Per Load,
£5 13s. 4d.
Per Ton.
£ s. d.
28. 11d.
Per Truss,
£5 58. Od.
Per Load,
£5 16s. 8d.
Per Ton.
3s.
Per Truss,
£5 88. Od.
Per Load,
£6 0s. od.
Per Ton.
3s. 2d.
Per Truss,
3s. 4d.
Per Truss,
£6 0s. od.
Per Load,
£6 138. 4d.
Per Ton.
3s. 6d.
Per Truss.
£6
68 Od.
Per Load,
£7 08. Od.
Per Ton.
3 10 0
5 5
700
8 15 0
10 10 0
12 5 0
14 0 0
15 15 0
£5 14s. Od.
Per Load,
£6 6s. 8d.
Per Ton.
3s. 3d.
Per Truss,
£5 17s. Od.
Per Load,
£6 108. od.
Per Ton.
d.
£ s.
d.
£ s. d.
£ s. d.
£ s. d.
0 15 5
0 15 10
5
0 16
3
0 16
8
0 17 6
1 10 10
1 11 8
10
1 12
6
1 13
4
1 15 0
3 1 8
3 3 4
20
3 5
0
3 6
8
4 12 6
4 15 0
30
4 17
6
5 0
0
6 3 4
668
40
6 10
0
6 13 4
7 14 2
7 18 4
50
8 2
6
8 6 8
9 50
9 10
0
60
9 15 0
10 0 0
10 15 10
11 1
8
70
11 7 6
11 13 4
12 6 8
12 13 4
80
13 0 0
13 6 8
13 17 6
14 5 0
90
14 12
6
15 0 0
100
13 15 0
14 13 4
14 11 8
100
15 0
0
15 8
4
15 16 8
100
16 5
0
16 13 4
17 10 0
200
27 10 0
28 6 8
29 3 4
200
30 0 0
30 16 8
31 13 4
200
32 10 0
33 6
8
35 0
0
300 41 5
42 10 0
43 15 0
300
45 0 0
46 5
0
47 10 0
300
48 15 0
50 0
0
52 10 0
400 55 0 0
56 13 4
58 6
8
400
60 0 0
61 13 4
63 6 6 8
400
65 0
0
66 13 4
70 0 0
500
68 15 0
70 16 8
72 18 4
500
75 0
0
77 1 8
79 3 4
500
81 5
0
83 6 8
87 10 0
600
82 10 0
85 0 0
87 10 0
600
90 0
92 10 0
95 0 0
600
97 10 0
100 0 0
105 0
0
700
96 5 0
99 3 4
102 1 8
700
105 0 0
107 18 4
110 16 8
700
113 15 0
116 13 4
122 10
0
800
110 0 0
113 6 8
6
8
116 13 4
800
120 0 0
123 6 8
126 13
4
800
130 0 0
133 68
140 0
0
900
123 15 0
127 10
0
131 5 0
900
135 0 0
138 15
0
142 10 0
900
146 5
0
150 0 0
157 10 0
1000
137 10 0
141 13 4
145 16 8
1000
150 0 0
154 3 4
158 6 8
1000
162 10 0
166 13 4
175 0 0
2000 275 0 0
283 6 6 8
291 13 4
2000
300 0 0
308 6 8
316 13 4
2000
325 0
0
333 6 8
350
0 0
3000
412 10 0
425 0 0
437 10 0
3000
450 0
0
462 10
0
475 0 0
3000
4000
550 0 0
566 13 4
583 6 8
4000
600 0 0
616 13
4
633 6 8
4000
487 10 0
650 0
0
500 0
0
666 13 4
0
525 0 0 0
700 0 0
EXAMPLE. What is the value of 3660 Trusses at £5 10s.
per Ton?
Opposite 3000 trusses is
600
""
60
3660
£412 10 0
82 10 0
8 5 0
£503 5 0
VALUATION OF PARISHES.
647
CHAPTER XIX.
VALUATION OF PARISHES.
In addition to what has been adduced in previous chapters, a very
brief description of the principles that govern Parish Valuations,
made for the purposes of Poor Law Assessment, will be sufficient.
The words of the "Parochial Assessment, Act" are-that no
rate for the relief of the poor in England and Wales shall be al-
lowed by any justices, or be of any force, which shall not be made
upon an estimate of the net annual value of the several heredita-
ments rated thereto, that is to say, the rent at which the same
might be reasonably expected to let from year to year, free of all
usual rates and taxes, and tithe commutation rent charge, (if any,)
and deducting therefrom the probable average annual cost of re-
pairs, insurance, and other expences (if any,) necessary to maintain
them in a state to command such rent.
The instructions issued by the Poor-Law Commissioners with
reference to this particular clause in the Act, run as follow:-
The column headed "Gross Estimated Rental," must be filled
up with the estimated value of the holding, calculated on an esti-
mate of what would be a reasonable rent to pay from year to year,
if there were no tenant's rates and taxes, no tithe, or commutation
rent charge, no repairs to be done by the tenant, nor insurance, nor
other expences to be incurred by him as necessary to keep the pro-
perty in its present condition.
The column headed" Rateable Value," must be filled up thus:-
From the gross rental, ascertained as above, must be deducted the
estimate amount of tenant rates and taxes, of tithe commutation
rent charge, (if any,) of repairs and insurance, and of any other
expences necessary to keep the property in its present condition.
The residue will be the "Rateable Value," or "Net Annual Value,"
according to the first section of the "Parochial Assessment Act."
Now, with reference to the words of the Act, it is quite obvious
that the rent alluded to is not intended to be the rent actually paid
by the tenant, but the rent the property is fairly worth, in compari-
son with other properties in the same parish, and comprised in the
same assessment.
The correct basis of all parish valuations must evidently be
equality and fairness; therefore, it is not possible to make the
648
VALUATION OF PARISHES.
amount of rent that any individual tenant may chance to pay for
his holding the foundation of any calculation for the assessment of
that holding. Yet this is by no means an unusual manner of view-
ing the matter. Men say a thing is worth what it will fetch. If
a farm or a house is not worth the money that is given for it, how
has the tenant been found who will undertake to pay that which
he cannot afford. They urge it is strong presumptive evidence of
the value of the properties, and therefore, as such, the rent so paid,
should be the amount at which the property should be assessed.
A landed proprietor, of considerable intelligence, in a parish I
once surveyed, told me he should have made a better valuation
than I did, for he could have access to the returns of the rentals
made for the Income Tax, at which amounts he would have as-
sessed all properties that were tenanted, and would have valued
those only that were in hand.
I will not go beyond this very parish to refute the arguments
thus adduced. Take the case of one of the farms, which we will
call A. The land is in a high state of cultivation, and is good in
quality. The homestead and residence are above the average cha-
racter. Previous to the present tenancy it was farmed by the
proprietor, who let it without a great portion of the incoming
valuation, that is to say, there were so many acres of fallow upon
the farm, for which the tenant did not pay; he is to leave the same
number on quitting the same, with half fallows, dressings, and
half dressings. The dung arising out of the last year's crops was
left upon the premises for the use of the tenant, and is to be left in
like manner when he quits. Now a farm so taken to, is in a posi-
tion to, and did, command a high rent.
Take an opposite case. A farm we will call B. The incoming
present tenant found no stable nor cow-house upon the premises,
and the landlord too poor to build one. The tenant undertook to
do it, and it cost him £400. He also paid £800 for the incoming
valuation. Now this tenant of course has a lease for 21 years, but
then look what deduction must be made in his rent on account of
his outlay.
year.
To take the valuation sum of £800, first: I have already shown
in the proper place that a tenant should get something like 10 per
cent. for capital thus locked up, so that £800 amounts to £80 a
We must next assume that he puts by about £15 per an-
num to a sinking fund, to accumulate at compound interest at 5
per cent., to replace at the end of the term the capital expended
upon the buildings, upon which he is also entitled to 10 per cent.
interest, so that a further sum of £40 arises under this head.
VALUATION OF PARISHES.
649
To review the question, suppose each farm to be worth £600 per
annum, while the tenant of farm A pays this rent to his landlord,
the tenant of B deducts the three sums of £80, £15, and £40, and
pays his landlord £465.
The following is a tabular view of the case.

Amount of Assessment as
Yearly Rent paid by estimated at the fair yearly
Tenant.
value of each Farm.
£
Farm A.
600
B.
465
£
600
600
If these farms were assessed on their rental, A would pay to-
wards a rate, at 1s. in the pound, £30; while B would pay but
£23 5s., notwithstanding the two farms are of equal value.
Such is the comparison with respect to farms and lands; now
take one as to houses.
Take a row of three houses, all of equal value but belonging to
separate proprietors.
A takes No. 1, which the landlord has placed in good repair,
and undertakes so to maintain it. The rent under these circum-
stances is £50 per annum.
B takes No. 2, which the landlord has also placed in good repair,
but the tenant is to do future repairs and to insure. The rent
under such circumstances is £44 a-year.
C takes No. 3, which is sadly out of repair, and the landlord too
poor to do what is necessary. The tenant undertakes to do the
repairs, and to maintain them afterwards, as well as to pay the in-
surance. The rent under such circumstances is £37.
According to the principle of assessing properties at the rent
paid for them-
£ s. d.
A would pay for No. 1, to a rate at 1s. in the pound
2 10 0
B
for No. 2,
2 4 0
وو
وو
وو
وو
C
for No. 3,
1 17 0
99
وو
وو
وو
an arrangement manifestly unfair, unequal, and incorrect.
I am aware it may be objected to what I have said, that tenants
do not get sufficient allowance made in their rent, under circum-
stances such as I have enumerated; but to this I would reply, that
it is quite a matter of personal moment to themselves only. If
they are not sufficiently acquainted with business of this nature to
2 s
650
VALUATION OF PARISHES.
make an equitable arrangement, there are at all times plenty of
competent professional men, who, for a very small fee, would fur-
nish all the information that is required.
I therefore submit, that in construing the Parochial Assessment
Act, the word rent must always be understood to imply such a
yearly sum as a property may be fairly estimated to be worth in
comparison with other property in the same parish.
To pass to the instructions of the Poor Law Commissioners, as
to filling up the column headed Gross Estimated Rental, and I
must repeat the instructions.
"The column headed Gross Estimated Rental must be filled up
with the gross estimated value of the holding, calculated on an
estimate of what would be a reasonable rent to pay from year to
year, if there were no tenant's rates and taxes, no tithe or commu-
tation rent charge, no repairs to be done by the tenant, nor insur-
ance, nor other expenses to be incurred by him as necessary to keep
the property in its present condition.'
""
It will be obvious, that to fill up the column in this way, the
fair rental of a farm must first be computed in the manner shown
in a previous chapter, to which must be added the amount of the
poor rates, church, highway, and other rates, now paid by the
tenant, because if there were none of these imposts, all tenants
would be able to pay a higher rent than they now pay by just the
amount of these outgoings.
These instructions were adopted by many valuers, myself among
others, in about one instance to each valuer; but it was never re-
peated. The gross value so obtained represented such entirely
fictitious sums, that the greatest dissatisfaction among the rate-
payers resulted; and notwithstanding the additions were all taken
off again before the rateable value was entered, the thing appeared
so grossly inconsistent, that the poor valuer was assumed to know
very little of his profession, if his motives were not characterized by
a harder term.
The practice is, to place in the column of Gross Rental, the sum
at which the property has been valued, and to deduct therefrom an
amount for repairs, insurance on the buildings, and the tithe or
commutation rent charge (if any) for the net rental.
It has been suggested that an allowance should be made for the
repairs of the gates, roads, and fences on a farm; but the practical
difficulties that arise, render futile any attempt to do so. To adopt
the principle fairly, a greater allowance must be made on small
fields than on large ones; and it could never be a per centage de-
duction from the amount of the valuation, inasmuch as a gate costs
VALUATION OF PARISHES.
651
as much to repair, if it belongs to land not worth 10s. an acre, as
one that belongs to land of four times the value. Moreover, in the
valuation of single fields, it would become necessary to ascertain
exactly the length of fence belonging to each field, (for some fields
are bounded entirely by fences belonging to the adjoining fields,)
and whether there is a gate or not.
In entering upon the valuation of a parish, considerable care is
necessary in arriving at a proper standard of value, which should
not be too high; but having determined upon the standard, all the
remainder is easily accomplished by comparison.
The principles enunciated in the chapter on the Valuation of
Estates, will apply in the Valuation of Parishes; so that they need
not be again referred to; but a few brief remarks upon the rating
of railways, gas and water companies, will not be out of place.
If we take the case of a railway, it will serve for the water or
gas companies without further illustration.
A railway, like a farm, cannot be valued on its cost of construc-
tion, since cost is not the measure of value. It is the yearly sum
it is worth to a tenant by way of rent that can alone form the sub-
ject of calculation as to its value.
The first amount to be ascertained is the sum of the annual
earnings, which will answer to the item of produce on a farm.
From this has to be deducted, first, the cost of working the line,
including all outgoings, which is the same thing as the cost of cul-
tivation on a farm; secondly, the sum for renewing the rolling stock
or plant; thirdly, the interest due to the tenant on the value of his
rolling stock; fourthly, a sum for superintendence and manage-
ment; and the remainder is rent, at which the railway should be
assessed.
The cost of construction clearly having nothing to do with the
yearly value of the railway, nor the sum at which it should be
assessed.
There is one item which should possibly be considered in the
case of a railway; an extra allowance for casualties, over which a
tenant may not be able to exercise control; but great caution
must be used in admitting to what extent railway accidents
are beyond control. It is exceedingly likely that if the great
lines of railway were in the occupation of tenants to whom respon-
sibility individually attached, some of the accidents that have
occurred would have been avoided, even if we suppose the present
managers to be the tenants. For there are, doubtless, many things
now sanctioned by managers and boards of directors, of which
they cannot approve, but to which they are partly coerced by their
652
VALUATION OF PARISHES.
desire to retain the satisfaction of the shareholders, who care very
little about anything beyond a large dividend.
It is not at all likely that a railway will be situated entirely in
one parish, hence comes the necessity of dividing the rate, and
fairly apportioning it among the several parishes. Some valuators
have argued that this should be done by an equal mileage
rate, because say they, inasmuch as no money is taken in some
parishes, while large sums are taken in others, an average is all
that can be arrived at. Others there are who say that those
parishes in which no money is taken, cannot possibly lay claim to
any rate, as the earnings there are nothing; or at any rate, they
say, you must either assess them on an estimate of the cost of con-
structing the line, or of the original value of the land. This is all
very fallacious, which there is small difficulty in proving.
We must never lose sight of the fact that the railway is
liable to be rated at what it is worth to rent. Now, to estimate
this rent suppose the portion of the line that is situate in each
parish to be held by a separate tenant; of course in such a case
all the expenses must be borne by a pro-rata mileage charge, and
all the tenants must equitably divide the allowance for superin-
tendence and management. To look at the case of the tenant in
the parish in which no station is situate; what is his position? He
cannot take any money of the public; but would not he take care
that if the other tenants took money of the public in other parishes,
for travelling over his portion of the line, they should, if he allowed
them so to travel, pay him his share of such earnings; and therefore
his portion of the line would become as well worth a rent as any
of the others, upon which rent he should be assessed, and thus
explode the erroneous principles to which I have alluded.
The method of apportioning the rent of a railway among the
several parishes for the purposes of assessment has been much
discussed, and is, as I believe, very little understood. Notwith-
standing it is very simple and clearly demonstrable.
The working expenses I am prepared to admit may be spread
equally over the whole railway according to the earnings, (except
in cases of long lines that are worked in distinct sections, and in
such cases each section may be considered as a separate line,)
the allowance for wear and tear or renewal of the rolling stock
may also be so; the interest on tenants' capital should be made to
follow the same proportion as the allowance for the renewal of the
rolling stock; and the allowance for superintendence should be
evidently greater on those parts of the line where the earnings are
large, than where they are small.
VALUATION OF PARISHES.
653
It is with the division of the earnings or value of the produce of
the railway among the several parishes, I have mostly to deal in
this place. To illustrate this clearly we must draw a Plan.
Fig. 173 m.
Without any reference to scale we will assume, that, from the
terminus at A, there is in the parish No. 1, 5 miles; and that
from terminus A to station B is seven miles, so that two miles of
that length is in parish No. 2.
From B to C we will take to be 5 miles, of which 1 mile is in
parish No. 2, 3 miles in parish No. 3, and 1 mile in parish No. 4.
From C to D we have 2 miles-1 mile in parish No. 4, and 1 mile
in parish No. 5. From D to E is 6 miles, of which 1 mile is
in parish No. 5, and 5 miles in parish No. 6.
The most convenient mode will be to tabulate the details, and
the results will become apparent.
654
VALUATION OF PARISHES.

Names
of
Stations.
Whole Length.
Total
Length
of Line. Earnings.
Parish No. 1.
Parish No. 2.
Parish No. 3.
Parish No. 4.
Parish No. 5.
Parish No. 6.
Total
Length
of
Apportioned
of Apportioned
Line. Earnings. Line. Earnings.
Length
Length
Length
of
of Apportioned
Apportioned
Line. Earnings. Line. Earnings. Line.
Length
of
Length
Apportioned
Earnings.
of
Line.
Apportioned
Earnings.
Miles.
£
Miles.
£
Miles.
£
Miles.
43
Miles.
બ
£
Miles.
£
Miles.
વર
£
A to B
B to A
Ꭰ
MODE AODE ABDE
7
21.000
C
12
42000
14
56000
20 80000
or or or cr
15000
2
17500
20000
20000
☺ ☺ ☺ N
6000
3
10500
3
10500
3
12000 3 12000
3
12000 3
12000
21000
5
15000 2
6000
C
5
15000
1
3000
7
14000
2000
13
32500
1
2500
co co co
9000
6000
7500
122
122
3500
8000
107
8000
2
4000
8000
6
20000
3000
4000
5000
12
10
2000
5000
5 12500
C to A 12
36000
5
LO
15000
5
5000
1
BI
9000
3
9000 1
3000
1000 3
3000 1
1000
3000
1500
16000
11
2000
12
1500
4000
or
10000
ABCE
D to A 14
49000 5
17500 3
7
14000
1
10500 3
2000
10500
3
6000
2
3000
221
7000
1
3500
4000
1
2000
1500
1
1500
6
12000
1
2000
20
10000
E to A
D
ABCA
20
70000
LO
13
26000
5
17500 3
10500
10500
1
2000
3
6000
ww
8
12000
221
7000
4000
1500
6
12000
1
222T
7000
5 17500
4000
10000
3000
2000
or cr
539500
5
137500
89000
102000
64000
49500
7500
10000
97500
VALUATION OF PARISHES.
655
The preceding Table clearly shows the earnings between each
separate station and also in each parish. The following table
shows the fallacy of taking a general average of the receipts to
guide the valuation of a separate parish; it being quite evident
that, if the length of line in each of these parishes were let to a
separate tenant, the length in parish No. 3, would be worth
infinitely more rent than that in parish No. 6:-

Parish.
No. 1
""
99
وو
99
وو
No. of
Miles.
Gross
Earnings.
Earnings
per Mile.
£
5
137,500
27,500
3
89,000 29,666.6
3
LO MM 225
123
5
6
Total
20
102,000 | 34,000
64,000 32,000
49,500 24,750
97,500 19,500
539,500
26,975 General Average.
Union valuations have been spoken of for the purpose of
equalising assessments.
The real fact is that there should be one universal assessment
throughout England and Wales entrusted to the central authority
of one competent surveyor, who should select some 500 or 1000
acres of arable and meadow land, and in the most careful manner
estimate its value according to its productiveness. The average
price of corn upon which this estimate is based should be preserved,
as a standard for regulating the valuation at any future time when
higher or lower prices might prevail. The object of valuing these
1000 acres would be to afford a test to the ideas of the several
valuators who might be engaged in the work, and as a means
whereby uniformity might be attained. Every valuer, upon com-
pleting the valuation of a parish or district, should proceed to the
valuation of the 1000 acres. If his value of it is in excess of the
standard estimate, the valuation he has previously made must be
reduced accordingly. This will be found (it is suggested), a very
sound way of securing equality of rating, far preferable to any
other. Most valuers have impressed upon their minds a certain
scale of prices for all kinds of lands, and it is of little use to show
them any other standard whether higher or lower: for if the doing
so influences them at all, it only has the effect of causing them
to commit irregularities of which they would not otherwise have
been guilty by causing them to put some fields higher or lower as
the case may be, while others they assess at their own standard.
SPECIMEN of the Mode of WRITING OUT the VALUATION
1
2
3
4
5
6
7

Name or Situation of
each Field or
Parcel of Property.
Descrip-
tion or
Mode of No. on
Cultivation Map (if
of each there
Field or be any.)
Parcel of
Property.
Quantity of
each Field
or Parcel of
Property.
Gross
Total Quan- Estimated
tity in each
Holding
which is
separately
Rated.
Rental of
each Hold-
Rateable
Value of
each Hold-
ing which is ing whichis
separately separately
Rated.
Rated.
Barn Field ....
Arable.
16
A. R. P.
9216
A
R. P.
£ s. d. £\s. d.
Long Field . . . . .
Arable.
1910 2
1
Little Mead.....
Grass..
25 13 11
Great Mead....
Grass..
26 19 2 10
Garson.
Arable.
27313 1
Oxted Field
Arable.
28 29 0 6
Barn and Yard ..
29 0030
Cottage and Garden
30
01 0
102 2 || 35 ||150 0 | 0 ||140|0|0
Lane End Field ..
Arable.
3153 2 16
Upper Down. . . . .
Arable.
32 19 110
Middle Down.
Arable.
3322310
Lower Down
Arable.
34 23 110
Drove Lane
35 1 112
Barn and Yard ...
36
0 120
120 2 38 1800 0175 00
Stable Mead...
Orchard ...
Lawn Pasture.
Grass.. 131 5110
Grass.. 132
1120
House and Garden.
Grass.. 133 3110
134
03 20
10 3 20 7000 5500
8
11
9
10
in the Form Prescribed by the Poor Law Commissioners.

Name or Situation of
Description of each
each Holding which
is separately Rated.
Holding which is
separately Rated.
Name of Occupier of
each Holding which
is separately Rated.
No. in
Rate
Book.
Name of Owner of
each Holding which
is separately Rated.
Bunker's Hill
Farm and Lands
Smith, John
Carlow, Earl of
Down Farm Down Land
Smith, John
Derry, William
Manor House House and Land
Smith, John
Himself
SPECIMEN OF FIELD BOOK,
Occupier, Higgins, James

No. on
Plan.
Name of Field.
State of
Cultivation.
Price per
Quantity.
Acre.
A.
16
Barn Field...
Arable.
5
200
20
R. P.
3 30
30s.
17
Furze Brook.
Grass..
2 3 19
12s. 6d,
18
Long Mead ...
Grass..
5 2
0
30s.
23
Hazle Field..
Arable..
4 2
6
25s.
24
Pond Field...
Arable.
21
16
18s.
25
Loampit Field
Arable..
5 1
30
25s.
26
Common Field ...
Arable..
52 10
27s. 6d.
27
Quarry Field .
Arable...
9 1 16
25s.
28
Station Field ..
Arable..
10 2
13
22s. 6d.
29
Windmill Hill ..
Grass.
5 3
30
25s.
30
Garson.
Arable...
9 2
18
22s. 6d.
36
Length Furlong.
Arable...
10 1
13
27s. 6d.
38
First Home Mead .....
Grass..
2 3
16
40s.
39
Second Home Mead.....
Grass..
51 13
40s.
40
Large Home Mead
Grass.
11 2
15
42s. 6d.
41
The Vineyard
Grass..
15 3
3042s. 6d.
42
Cherry Orchard ...
Grass..
10 2
9
45s.
44
Oxford..
Grass..
15
3
1
40s.
45
Lock's Farm...
(Homestead. . .
House & Garden
1
3
10
0 1 10
Allotment Field ...
Arable.
48 1
1 10
32s. 6d.
190 2
5
Deduct for Tithe, Insurance, and
With reference to the form of Valuation, it is necessary to observe that the
three owners, three valuations are required to be stated.
recommended for a PARISH VALUATION.
Owner, Long, John

48
Value.
Gross Rental. Rateable Value.
Remarks.
S.
818
d.
1
1 15 10
8
20
48
5
0
5 13
6
2 2
6
616
0
7 13
0
1113
9
11 18 0
7 8
10 16
20
5
3
Co
14
4 0
S.
d.
514 0
10 13 3
24 12 9
3317 4
23 17 10
31 10 3
48
S.
d.
Rushy and poor.
Unhandy; wet.
Gravelly on brow.
25 0
78 10 1
330 19 10 331 0 0 280 0 0
Repairs.
51 00
Burns.
35/; 32/6; 30/
value of each separate holding must be given. So that, if one occupier hold of
660
BUILDERS' PRICES.
CHAPTER XX.
BUILDERS' PRICES.
SECT. I-Carpenters' and Joiners' Prices.
ROOFS,
At per square of 100 feet superficial.
Common shed roofs, one story high
The same, with purlins
If two stories, add
If three stories, add
Common span or valley, with purlins and rafters, two
stories high
If three stories, add
Framed roofs, with collars, dove-tailed into sides of
rafters, notched to receive purlins, and filled in
with common rafters
Roofs framed, with principals, king posts, purlins,
braces, and common rafters
The same, with kings and queens
Common curb roofs on one side
If two sides, add
If three sides, add
If above two stories, add
Labour.
Nails.
S.
d.
S.
d.
3
3
1
0
4
0
1
6
0
6
0
0
1
0
0
0
5
0
2
0
0
6
0
0
9 6 3 6
13
5
4
0
•
. 15 9
4
0
5
7
2
6
0
6
0
0
1
0
0
0
0
6
0
0
The timber to be measured and taken at per foot cube.
NAKED FLOORS,
At per square.
Labour.
Nails.
Ceiling floors, joists only
2 11
1 6
The same, framed with tie beams
4 2
1
9
The same, with binding and ceiling joists.
5
0
1 11
Ground joists bedded, but not framed
The same, pinned down on plates, and framed to
chimnies
Single-framed floors, trimmed to chimnies and stairs
If above 9 inches deep
Framed with girders and cased bays
Framed with girders, binding, bridging, and ceiling
joists
. 12 6 6 40
2
6
1
6
4
2
1
6
5 3
1
9
7 10
0 0
8
6
3 0
BUILDERS' PRICES.
661
QUARTER PARTITIONS,
At per square.
Common 4 inch braced partitions
Labour.
Nails.
4
Do. 5 inch
do.
5
Do. 6 inch
do.
5
or or + as
S.
d.
S. d.
6
1
3
3
1
6
6
1
6
Truss-framed with king posts
8
8
1
6
Do.
with king and queen posts
10
0
0
0
If oak, extra one-third.
Cube fir bond*
Do.
framed
Do.
LABOUR ON FIR TIMBER,
At per foot cube.
truss framed
Do. framed and chamfered
Do. wrought and framed
Do. wrought, framed, and rebated
Do.
wrought, framed, rebated, and beaded
Do.
Do.
proper door cases
wrought, framed, rebated, and double beaded
Planing fir per foot superficial.
LABOUR ON DEALS,
0
4
0 8
0 10
0
10
1
1
1
3
1
6
8
1
11
0 1
""
""
""
""
plugged
At per foot superficial.
For deals from in. to 12 in. thick—
0
0
edges shot
""
414
༤
jacked
rounded
""
""
HN HN HN HN
""
""
planing on each side
0 1
""
""
grooved
0 1
rebated
0 1
""
35
ploughed and tongued
0 1
framed
0 1
""
""
battened
0 1
""
mitred
0 1
""
""
scribed
0 1
""
""
backed
0 1
""
་
""
throated
0 1
""
""
""
""
clamped
0 1
beaded
0
1
""
""
✦ Bond timbers, wall plates, wood bricks, pole and curb, &c., are all to be under the
head of bond.
662
BUILDERS' PRICES.
Nails.
d.
Labour.
For deals from in. to 1½ in. thick-
S.
d.
S.
cut circular
0 11
""
cut standards
0 21
""
sunk shelves
0 21
""
""
""
""
""
35
scolloped
0 21
""
""
""
""
ledged
dovetailed
For deals from 2 to 3 in. thick—
edges shot
plugged
0 21
0 21
0 1
0 1
""
""
jacked
0 1
rounded
0 1
""
""
""
planing on each side
0 11
grooved
0
11/
""
rebated
0
11/
""
""
ploughed and tongued.
0 11
""
framed
0 12
""
battened
0 11/
""
""
mitred
0 11
""
""
scribed
0 11/
""
backed
0
11
""
throated
0 11
>>
""
""
clamped
0 11/2
beaded
0 12/
""
""
cut circular
0 21
""
cut standards
0 3
""
>>
sunk shelves
0 3
""
>>
""
""
scolloped
0 3
""
""
ledged
0 3
dovetailed .
0 3
""
པ
""
BATTENING TO WALLS,
₫ in. to 14 in., 12 in. from
If plugged to walls, add
Wall hooks add extra
At per square.
centre to centre
3 0
2
0
0 10
1
0
0 0
0
0
0 0
WEATHER BOARDING,
At per square.
Rough
""
Wrought
Wrought and beaded
2 1
2
0
splayed edges
3
5
2
0
5
0
2
0
6
3
2
0
BUILDERS' PRICES.
663
At per square.
ROUGH BOARDING,
Labour.
Nails.
S. d. S. d.
inch deal,
rough
•
2
CO
6
1
6
""
""
Inch deal,
edges shot .
3
4
1
6
ploughed and tongued
3
9
1
6
rough
2
9
2
0
""
edges shot
3
6
2
0
""
ploughed and tongued
4
7
2
0
Whole deal, rough
2
11
3
0
edges shot.
3
9
3
0
""
ploughed and tongued
5
2
3
0
1½ in. deal,
rough
3
4
3
6
edges shot
4 4
3
6
""
""
ploughed and tongued.
5 10
3
6
DEAL FLOORS,
At per square.
Inch deal,
rough edges shot
3
10
1
6
""
wrought, folding
5 11
1
6
""
Whole deal,
straight joint
7 6
1
6
rough edges shot
4
3
2
0
""
wrought folding
6
3
2
0
""
""
""
wrought straight joint, splayed}
do. do. dowelled
1½ inch deal, rough edges shot
wrought folding
8 10
3 0
15 10
4
0
•
4 7
2
6
6
8
2
6
""
""
""
wrought straight joint, splayed heading 10
if ploughed and tongued headings, add
if ploughed and tongued edges, add
for tongues to edges of boards, add .
0
3
0
1
6
0
0
2
7
0
0
4
2
0
BATTEN FLOORS,
At per square.
Inch wrought folding
Inch wrought, straight joint, splayed headings
Inch and quarter wrought folding
Inch and quarter straight joint, splayed headings
The same dowelled
If ploughed and tongued headings, add
. 10 10
2 6
2 6
6
3 6
20 10 5 0
7 6
9 0
8 4
~ ~ ~ ~
2
If ploughed and tongued edges, add
For tongues to edges of battens, add
If battens less than 5 inch, add
2
2
0 0
3
9 0
0
6
3
0
0
1
8
0
0
664
BUILDERS' PRICES.
Common framed grounds
11 inch do.
do.
do.
1 inch do.
do.
do.
FRAMED GROUNDS,
Labour
and Nails.
At per foot super.
S. d.
0
4
1 inch do., ploughed for plastering
0 4
0 5
0 5
SKIRTINGS,
At per foot super.
Plain skirtings
0 2
Do. do.
raking cut to steps
0 4
Torus skirtings
04
Do. do.
raking cut to steps
0 5
GUTTERS AND BEARERS,
At per foot super.
Inch or whole deal
DOOR LININGS,
At per foot super.
Plain, single rebated
Plain, single rebated, and beaded
Plain, double rebated
Plain, double rebated, and double beaded
Square framed jambs, each in 2 panels, and soffit in
1 panel
If bead, butt, or moulded, add
Bead, flush, or quirk moulded, add
Raised panel and moulded, add
For every extra panel, if square
Do. flush or moulded
If double rebated
If double beaded
•
14 rough edges shot
LEDGED DOORS,
At per foot super.
Add, if ploughed and tongued
if ploughed and beaded
if wrought each side
if braced
·
if hung folding.
if 1 inch thicker
0 41
0315
0 32
0 4
0 5
06
0
2/
0
11
0 21
0 11
0 11/
0 11
0
3
COLE
0 4
0 222
0 11
0
0 11/
0 11/
0
3
BUILDERS' PRICES.
665
FRAMED PARTITIONS
Labour & Nails.
S.
d.
04
At per foot super.
1½ inch square framed
2 inch do.
do.
Add, if bead, butt, or moulded
if bead, flush, or quirk moulded
DEAL MOULDINGS,
Common mouldings
Add, if quirked
Fixed complete, at per foot super.
Small mouldings can be measured at per foot run.
DOORS HUNG COMPLETE,
At per foot super.
Two panel square framed
0 41
•
0 11
0 21/
08
2
0 4
Add for every additional 2 panels-
If framed square,
For 1½ inch deal
2 inch do.
21 inch do.
If framed bead, butt, and square,
For 1 inch deal
2 inch do.
If framed bead, flush, and square,
0 1
0 1
0 11
0 11
0
11
1금
​For 1 inch deal
0 12/2
2 inch do.
0 2
21 inch do.
0 21
·
If framed quirk O. G. and bead, and square, or quirk
Ov., and bead and square,
For 1 inch deal
0 11
2 inch do.
0 11
If double marquis, 4 inch wide
0 14
""
""
5 or 6 inch wide
Hung folding
0 21
0
WINDOW LININGS,
At per foot super.
Inch deal, two panel square, framed back linings
""
""
if bead, butt, or moulded, add
if bead, flush, or quirk moulding, add
For each panel above two, if square
if moulded
""
""
>>
if splayed
0 6
0
28
0 11
0 11
0 11
2 T
666
BUILDERS' PRICES.
Do.
WINDOW BACKS, ELBOWS, AND SOFFITS,
At per foot super.
Inch deal, plain keyed, or two panel square backs
two panel square backs, elbows, and soffits
Add, for each panel above three,
""
if splayed.
""
if bead, butt, or moulded
if bead, flush, or quirk moulded
BOXINGS TO WINDOWS,
At per foot super.
Framed, rebated, and beaded boxings
Labour & Nails.
S.
d.
05
06
H COLE KI
220
0
0 11
06
0 7
Splayed, flush, rebated, and beaded boxings
INSIDE WINDOW SHUTTERS,
At per foot super.
inch deal clamped flaps in one height
Inch deal two panel square in one height
For every panel above two,
If framed square
If bead, butt, or moulded
If bead, flush, or quirk moulded
Quirk O. G. and bead, or quirk ov., and bead and
square
For every extra height, add
Sashes-
SASHES AND FRAMES HUNG COMPLETE,
1 inch deal ovolo sashes
At per foot super.
Do. wainscot or mahogany
If 2 or 21 inch sashes deal, add
If do. wainscot or mahogany, add
If astragal and hollow in deal, add
If do. in wainscot and mahogany, add
Frames-
Deal cased frames, oak sunk sills, double pulley, P. B.
and P. S., single hung
If prepared for 2 or 2 sashes, add
If prepared with wainscot or mahogany P. P.Bds.
and P. slips
If for 2 or 2 inch sashes, add
If double hung, add
0 7
0 71
0 11/1
0 1/1/0
0
11
0 11
0 2
3
0 3
04
0 11/10
0 11/
0
2018
10 11
04
0
CORH
2
0 5
0
1
0
32
BUILDERS' PRICES.
667
STAIRCASES,
At per foot super.
Labour & Nails.
s. d.
Common steps and risers, and two fir carriages
Do. moulded nosings and close strings
Do. do. mitred to cut string boards, and
dovetailed to balustres
Add,
0 4
0 6
07
If winders, circular one end
Do. do. circular two ends
carriages
Do. do. both edges
Feather-tongued joints
Add,
Quarter curtail, glued upright, each
0 21/20
0 5
Do. do. geometrical, with wrought and blocked
Riser-tongued to step bottom edge
0 31
0 11
0 21
0 11
3 4
Do. blocked and veneered, each
5 10
Proper curtail, step and riser, each
11 O
Return moulded nosing, each
Return circular, each
Plain cut bracket, each
Circular cut bracket, each
Housing to step and riser, each
1 3
2
1
1
3
2
1
0 6
""
to winders, each
""
to moulded nosings, each
""
to circular ends, each
0 7
0 10
2 31
•
Whole deal plain
Whole deal sunk
OUTSIDE STRINGS TO STAIRS,
At per foot super.
Whole deal sunk and moulded
Whole deal sunk, moulded, and cut
Whole deal sunk, moulded, cut, and mitred to risers
If wreathed, four times the above.
If ramped, once and a half.
0 5
06
0 623
08
0 81
WALL STRINGS,
At per foot super.
Plain and plugging
0 5
If moulded, add.
If rebated for plastering, add
0 1
0 12
•
668
BUILDERS' PRICES.
DADOS,
At per foot super.
Proper dado, with dovetailed keys, joints secured with
slips, and dovetails hung to grounds by grooves
keyed into do., and dado
Add,
If raking, scribed to steps
If raking, scribed to moulded nosings
If base, grooved into floor
Labour & Nails.
s. d.
0 4
0 11
0 11
0 1
For each external mitre beyond two in a room
1 12
If circular on the plan, double the above.
If wreathed, treble the above.
COLUMNS AND PILASTERS,
At per foot super.
14 inch deal plain pilasters, properly glued and
blocked
Do. do.
diminished
•
14 inch deal diminished columns, properly glued and
blocked, under 14 inches diameter
Do. do. above 14 inches diameter
Add, for-
062
09
2 1
1 9
0 11
two inches wide
0 11
three inches wide
0 22
""
01/2
two inches wide
""
three inches wide
0 23
031
""
Arris or deep fluting to pilasters, one inch wide
""
""
""
""
Arris or deep fluting to columns, one inch wide
""
""
""
""
Straight grooves to columns
Headings to flutes to columns.
Straight grooves to pilasters.
Headings to flutes to pilasters.
0 11
0 4
0
424
0 22
In the foregoing list of Carpenters' and Joiners' Prices, all calculations
in respect of materials have been omitted, owing to the very unsettled
state of the market at the present time, (March, 1853,) and the fluctu-
ations to which it is subject. The charges for labour being less affected
by fluctuations of a similar nature, can be more satisfactorily relied on as
permanent approximations to reasonable remuneration to the tradesman, and
may consequently be taken as a basis for estimates for some years to come.
The timber must be added at its measured value, according to market
price at the time being. The method of ascertaining the value of a cube
foot of timber from the prime cost prices is given in the Chapter on Arti-
ficers' Work, and the following Tables will be found useful.
BUILDERS' PRICES.
669

£. s. d. £. s. d. £. s. d. £. s.
s. d.
£. s. d.
2 10 0 2 18 4 3 6 8 3 15 0 4 3 4
£. 8. d.
£. s.
4 11 8
5
0
0
d. £ s. d. £ s. d.
5 8
4 5 16 8
Table showing the price to be charged per foot cube for Fir, or other Timber, used in measured work, calculated at the
various rates of prime cost, standing at the head of the several columns, allowing 5s. for cartage, 10s. for sawing, 10s. for waste,
and £1 5s. for profit, per load.
PRIME COST PER LOAD.
Fir Timber, no labour
Fir Timber, in bond, Plates, Curb, &c.,
labour included.
Fir Timber, framed
Fir Timber, truss framed.
Fir Timber, framed and chamfered
Fir Timber, wrought and framed
Fir Timber, wrought, framed, and rebated
0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 2 10 0 3 0 0 3 20 3 4
0 2 40 2
40 260 2 8 0 2 10 0 3 0 0 3 2 0 3 4 0 3 603 8
0 2 80 2 10 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 3 10 0 4 0
0 2 10 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 3 10 0 4 0 0 4 2
0 2 10 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 3 10 0 4 0 0 4 2
0 3 10 3 3 0 3 5 0 3 70 3 9 0 3 110 4 10 4 30 4 5
0 3 3 0 3 5 0 3 70 3 9 0 3 11 0 4 10 4 3 0 4 50 47
Fir Timber, wrought, framed, rebated, and beaded 0 3 6 0 3 8 0 3 10 0 4 0 0 4 2 0 4 4 0 4 60 4 8 0 4 10
Fir Timber, wrought, framed, rebated and
double beaded
Fir Timber, in proper door cases
•
0 3 8 0 3 10 0 4 0 0 4 20 4 4 0 4 60 4 8 0 4 10 0 5 0
0 3 11 0 4 10 4 3 0 4 5 0 4 7 0 4 90 4 11 0 5 10 5 3
670
BUILDERS' PRICES.

PRIME COST PER LOAD.
Table showing the price to be charged per foot cube for Fir, or other Timber, used in measured work, calculated at the
various rates of prime cost, standing at the head of the several columns, allowing 5s. for cartage, 10s. for sawing, 10s. for waste,
and £1 5s. for profit per load.
£ 8. d. £ s. d. £ s. d. £ s. d.
s. d £ s. d. £ s. d. £ s. d. £ s. d.
6 5 0 6 13 4 7 1 8 7 10 0 7 18 4 8 6 8 8 15 0 9 3 4 10 0 0
Fir Timber, no labour
Fir Timber, in bond, Plates, Curb, &c.,
labour included.
Fir Timber, framed
Fir Timber, truss framed
Fir Timber, framed and chamfered
Fir Timber, wrought and framed
Fir Timber, wrought, framed, and rebated
0 3 6 0 3 8 0 3 10 0 4 0 0 4 2 0 4 4 0 4 60 480 5 0
0 3 10 0 4 0 0 4 2 0 4 4 0 4 60 4
8
0
4 10 0
5
0 0
5 4
60
0 4 20 4 4 0 4 6 0 4 8 0 4 100 5
4 10 0 5
0
0
5 20 5
40 5 8
0 4 4 0 4 60 4 8 0 4 10 0 5 0 0 5 2 0 5 4 0 5 6 0 5 10
0 4 4 0 4 60 4 8 0 4 10 0 5 0 0 5 205 40 5 6 0 5 10
0 470 4 9 0 4 11 0 5 1 0 5 3 0 5 5 0 570 590 6 1
0 4 9 0 4 11 0 5 10 5 3 0 5 5 0 5 7 0 5 9 0 5 11 0 6 3
Fir Timber, wrought, framed, rebated, and beaded 0 5 0 0 5 20 5 4 0 5 6 0 5 8 0 5 10 0 6 0 0 6 20 6 6
Fir Timber, wrought, framed, rebated, and
double beaded
Fir Timber, in proper door cases
0 5 2 0 5 40 5 6 0 580 5 10 0 6 0 0 6 2 0 6 4 0 6 8
0 5 5 0 570 5 9 0 5 11 0 6 10 6 30 650 670 6 11
BUILDERS' PRICES.
671
Table showing the Length of Timber of any Scantling contained
in a foot cube.

Scantling. Length.
Scantling.
Length.
Scantling.
Length.
in.
in.
2 - 2
.ମୁଁ ସେ ବବି ବଡ
ft. in.
in.
in.
ft.
in.
in. in.
ft. in.
36
0
4 — 4
9 0
6-10/1
2 3
28
9
4/1/20
8
11
2
2
24
0
5
7
11/1/0
2
31
20
7
5/1/
6
12
2
4
18
0
6
6
0
my _ my
4/
16 0
6/12/
5
6
7/1/20
5
14
5
5/1/20
13
1
6
12 0
6/1/20
11 1
7
10
3
77∞ ∞ ∞
1
8
4
9
8312
8
4
6
9
81/1
4
3
9/1/
9
4
0
10
NNNNNNNNN
1
0
2 11
2 9
2
6
2
5
2
2
321
7 1/1/0
9
7
91/2
3
9
10/1/
1
8
0
10
3 7
11
11
1 10
8/1/1
6
10/1/20
3
9
8
0
11
3
10 00
5
11/1/
1 9
3
12
91/2
7 7
11/1/
3
2
8 — 8
10
7
3
12
3
0
HK
10/1/1
6 10
5 - 5
5
9
9
11
6
6
5/1/
5
3
9/1/2
111/
6 4
6
4 10
10
I Q Q QAT
1
8
3
2
1
2
0
1
10
1
9
12
6 0
6/1/2
4 5
10/1
1
8
3 - 3
16
0
3/1/20
13
8
4
12
778
HK
4/
10
8
8/12/2
5
9
7
9
5/
9 0
9/1/2
6
8
0
10
6/1/20
7
4
7
6 10
10/1/20
11
7/1/
6
4
8
6
0
11/1/
12
5
8
6 - 6
9
4
6
9/1/2
5 0
7
10
4 10
7/
101
4 6
11
4 4
8/1/
11/1/
4
2
12
4 0
9/12/20
10
+∞ ∞ ∞ 0 0 N NNNNTH 03 03 03 M N N NN
HK
4 1
11
1
7
3 10
11/1/20
1 7
3
7
12
1 6
3 5
9 - 9
1
9
3
2
931/
1
8
3
0
10
1
7
2
10
10/1
6
2
9
11
1
5
2
8
111
1
4
2
6
12
1
4
2
4
10 - 10
1
5
4
0
1011
1
4
8
11
1
4
5
11/1/
1
3
2
12
1 2
3
0 11
11
1 2
2 10
8
11/1/2
12
1 2
2
6
12
12
1 1
1
0
2 5
672
BUILDERS' PRICES.
Table showing the Price to be charged per foot run for Scantling
of Fir, or other Timber, calculated at various Prices per foot cube.

Scantling.
2-2
2s. 6d. 3s. Od.
per ft. cube. per ft. cube. per ft. cube.
3s. 6d
Scantling.
2s. 6d. 3s. Od. 3s. 6d.
per ft. cube. per ft. cube. per ft. cube.
0 1 0 1
0 11
5 7
0 7/1/2
0 8/2
0 101
4
21/
H
0
11
0 11
0
12
73
08
0 91/2
0 111
3
0
31/1
1층
​4
0
12
4/2
0
2
5
0
5/1/
0
61
0
0
MH
0
0
3
31
0
9
0
0
10/1/10
0
11
0
11/1/
0
12
0
3-3
0 2
31/
0
9/1/20 0 4
10
0
3
77∞ ∞ ….
8
9
0
HK HK HÊa calen
PH Ha CalCH COLCH
HD HQ M
IIIQNNN Q ∞ ∞ ∞ ∞ ∞ EEE 10 62
∞ ∞ ∞ ∞
HH HQ CS — Hk col
DEH
TC+
HILO LO LO CO
0
1 1/
0
12
8
08/3/2
0 10
1 0
12
21
81/1
09
0 1022
1
03/2
0
2
0
2/
9
091/
0 111
1 11
0
21
0
0
HIHIGA COLCH
0
23
9/2
0 101
1 0
24/
0
3
10
0 10/
1 031
1
31
0 31
10/1
0 11110
1 11
1
32
0 3
031
11
0 11
1
1/2/
1
4
0
31/1
0 4
11/13/
1 0
1
2
1
42
0
31/
0
41
12
1 03/2
1 3
1 5/20
0
3
0
4/1/2
6–6
0 7
09
0 10/
0
4
0
6/1/
081
0 92
0 11
0
41
5
0 83
0 10/1/20
1 01
0
0
51
0
0
144
71/
0
9
0 111
1 11
8
0 93
1 0
2
0
5
0
6
8/1/2
0 10
1 02
4/1/2
0 51
0
61
9
0 111
1
1/
1 32
0 6
9/1/2
1 0
1 21
1
0
0 6
0
0 21 0 29/
0 2/3/1 0 31
31
3/1/2
10
11
4 0 21/0 0 3
41/2
5
0
5/1/ 0
6
7호
​0
0
0 5
8/ 0
9/2/2 0
5
6
0 61
51
0 52
0 6
0
ง
10/12/ 0 632 08
11/1/ 0 71
0
51
3호
​0 31
4
0 332
0
COLH
0
0 731
0
CHHICH HA
H
6723 ∞ ++ LO
HIT CHAT COLER
667 7 ∞ ∞ ∞
10
10/1/20
1
3
15
OT A CO C~
3
4328
101/
1 11
1 32
1 62
11
1 12
1
1 7
111
1 2
1
51
1 81
12
1 3
1 6
1 9
7_7
0 101
1 01
1 2/1/20
7
0 11
1 11
1 3
со
0 112
1 2
1 4/1/2
1 02/
1 3
15
1 11
1 32
16/
9/1/20
1 2
1 432
1 7
10
1 23
15/0
1 81
101/
1 3
1 61
1 9
11
1 4
1 101
11 1/2
1 42
1 81
1 11
12
1 5
1 91
201
8-8
1 1/1/20
1 4
1 7
0
8/1/1
1 21
1
56
1 8
0
0 93
9
1 3
1
1
9
0
HCOLH
0 101
9/12/
1 4
1 7
1 101
12
0 7
0 9
0 10/1/20
10
1 5
1 8
1 1111
4-4
0 3/1/20
0 4
0 43
10/1/
1 6
1 9
2 03
4/1
0
5
5
0
0 5
4445
4 0 4/1/2
0 51
11
1 7
1 10
2 12
41
0 5
0
6
11/
1 71
1 11
2 3
424
0 5/1/20
0
12
1
8
2 0
2 4
0 6
0
9-9
1 5
1 81
1 11½
6/1/10
5
06/12/20
0 73
91
1 6
1 91
2 1
0 6
0 7
0
81
10
1 7
1 10
2 21
7호
​0 6
0
Ha
0 9
101/20
1 8
1 112
2 330
8
0
632
08
0
9
0 81
09
09/21/2
0 10
11
1 83
2 03/
2 5
11/1/0
1 92
93/4
2 2
2 63
0 10/2/20
12
1 10
2 3
2
7
9/1/
0
091/
0 111 10-10
1 10
1
2 7
10
0 8/12/20
0 10
0 112
10/1/20
1 101/20
21
2 7/1/20
101
09
11
0 9
0 101
0 11
1 010
11
1 11
2 3/1/20
2 8
1 1
11 1/
2
0
251
2 9/1/2
11 1
0 92
12
0 10
5-5
5/1/
0 5/1/
0 6
0 11/12/20
1 0
06/0
1 1/
12
2 1
2 6
2 11
1
2
11-11
2 11
6
2 111
0 73
11/1/1
2 2
21/
0 7
0
12
2 3/
2 9
3 2
321/20
6
0
6/1
0 73/2
0 82 12-12
61
0
7
081
0 93
BUILDERS' PRICES.
673
Scantling.
Table showing the Price to be charged per foot run for Scantling
of Fir, or other Timber, calculated at various Prices per foot cube.

5s. Od.
4s. Od. 4s. 6d.
per ft. cube. per ft. cube. per ft. cube.
Scantling.
4s. Od. 4s. 6d. 58. Od.
per ft. cube. per ft. cube. per ft. cube
2-2
0 1/1/20
1글
​21
3
0
4
0
412
0
5
51
6/1/
7
711
8
112
0
0
0 4
05
0 52
0
9
0
1122 N M ∞ M 44 LO LO
0 1/1/0
0 12 0 2 0 21/1
2층
​21
0
3
3
31/
0
4
33/2
0
41
0
051
5 0 532
4
10
10/1/
11
9/1/
063/1
0 63
0 7
11/1 0 72
06/1/20
62
0 71
0
0 7
71
0 8/1/0
0
HCH ODCH
1222 m ∞ * TH10 LO LO CO
Hic eslat Hlas me calet mla cola
0 12/20
3
5-7
1 0
1 1/1/0
1 3
71
1 03/
1
3
1 4
0 21/0
0 3
20
1
1/1/20
1
41
1 5
1 21
1 42
1 6
0
31/12
9
1
3
1
5
1
63
0 332
9/1/
1
41
1
62
1 7
0 41
10
15
7232351
1 9
0 42
10/1/
1
6
1
811
1 93
0 5
11
1 61
1 82
1 10%
05/2
1 1 1/
1
7
1 9
2 112/2
06
12
1
8
1 10/
2 1
061
6-6
1 0
1 1/1/20
1 3
0 622
6
1 1
1
23/
1
41
0
71
1
2
1
3/1
1
5
0
7/1/0
7/10
1
3
1
5
1
62
08
8
1 4
1
6
1
8
08/1
1
5
1 71
1 91
0
9
1
6
1
81
1 10
0 91
91/2
1 7
1 9/2
1 112
12
0 8
0
9
0 93
0 10
10
1 8
1 10/
2 1
10/1/20
1 9
1 112
2 21
3-3
0 3
C++ LO LO CO
12
445
0
31
4
4/2
5
5글
​61
0
0
51
0 6
0 51
0 52
061
0 63 0 7
6/1/ 0 7/
0 7
8
0 3/1/20
0 4
0 3/2/
11
1 10
2 02/2
2 3/
0 4/1/20
11/1/2
1 11
2
2
2 42
04/
0 5
12
20
2 3
26
0 52
7___7
1 41
1 6
18/10
0 61
0
0
0
KIN
0 71
0
0
77∞∞ ∞
HK HABER
7∞
71 1 52
1
8
1 10
8
1 7
1 91
1 111
8/1/20
1 81
1 101
2 2、
1 91
1 112
2 21
91/
1 101
2 11
2 331
931
10
1 11/1/20
2 2/1/20
25
8
8/3/2
0 8
0 81
0 9
0 10
10
2 02/
2 3/2/20
26
0 93
0 102
11
2 12
2 5
2 8
4
9
09
0 101
0 11/1/20
11/1/
2 3
26/2
29/
9/1/2
09/1
0 102/20
1 0
12
2 4
2 7/1/1
2 11
10
0 10
0 111
1 0/21/20
8-8
19
20
23
10/1/
0 101
1 0
1 11
14
8/1/15
1 102
2 1/1/0
2 4
11
0 11 1 03/
1
12
2 0
2 3
2 6
11/1/2
0 11/1/20
1
1
1
2
2호
​91/1
مرادی
2 1/
24/
2 7
12
1 0
1 1/
1 3
10
2 23/1
2 6
29
4-4
0 5/1/
06
0 6
10/1
2 4
2 7/
2 11
41
0
61
0 632
0 73/
11
2051
29
3 09/
5
0 63/
0 7፤
08/1/
0 71
081
0 91
111/
12
2 10/
3 21
3 0
3 4
08
09
0 10
9-9
2 2
26
2 9
61
0 832
0 921
0 11
9/1/
24/
2 8
2111
0 91
0 10
0 112
10
2
2 10
3 1/2
71
0 10/1/20
0 111
1 02/
10
2 7
2 11/21/
3 3
8
0 102 1 0
1 1/
11
2 9
31
351
0 1111 1 01
1 21
111/1
2101/2
3 3
3 7
1 0
1
11
1 3
12
3 0
3 4
3 9
91
1
1
21
1 4
10-10
2 11
3 3/1/20
38
10
1 1/1/20
1
3
1 42
10/1/
3 0
3 4/1/20
3 9
10/1/
1 21
1
3 3/1/
15
11
3 03
3 5
3 93
11
1 2/9/
1 4
1 61
111/
3 24
3 7
4 0
11 1
1 31
1 5
12
5-5
1
4
1 6
1 710
1 8
12
3 4
3 9
4 2
11-11
3 412
39/1/0
4 23
08/
0 10
0 11
51
0 9/1/20
0 102
0 1121
111/
12
3 61
3 11/2
4 43
3 8
4
1
4
7
6
0 10
0 11 1
1
0 12
12
6/1/2
0 11
1
01/0
1 13/14
674
BUILDERS' PRICES.
SECT. II.-Mason's Prices.
s. d.
Labour, squaring and laying New York or Purbeck pav-
ing
per
foot super.
0 11
If in courses, add
0 13/14
LABOUR ON PORTLAND OR SIMILAR STONE.
N.B. Sawing to be taken as half plain work.
Plain work to bond stones
per foot super. 081
""
""
to beds and joints
""
""
rubbed face
circular
""
""
Sunk work
""
""
""
زو
Moulded work rubbed
""
""
""
circular
0 11
""
";
1
1
01/2
51
1
3
"}
1
7
""
1
51
""
2
1
""
Circular work to shafts of columns having the
neck moulding, or part of the base worked
in the same stone
Circular circular or spherical work to domes or balls
If rubbed, add
Taking up, squaring, and relaying old paving
Add, if in courses
1
8
""
2
6
""
0
3
""
0
""
21/
0
1
""
LABOUR ON STATUARY OR VEIN MARBLE, INCLUDING
SAWING, WORKING, AND POLISHING.
Plain work
Circular work
Sunk work
Moulded work
Circular sunk work
•
per foot super.
4
4호
​6
3
""
8 4
""
11 11
""
11 11
""
15
0
39
Circular moulded work
ON OLD WORK.
Old vein marble chimney, reset
0 71/2
""
""
""
squared and reset
0 10
sanded, grounded & squared
1
01/
""
sanded, grounded, squared
and reset
1
3
cleaned and reset, sanded
1 3
>>
""
polished and reset
1 101
>>
""
""
sawed, sanded, polished,
squared, & reset
3 1
The above prices are confined to labour only. The prime cost of stone and marble
varying considerably in different localities, according to the expense of carriage
and other circumstances, it would answer no useful purpose in a book intended for
general circulation, to include any calculation for materials; especially as price
lists of the various kinds can at all times be obtained of the merchants and
dealers.
BUILDERS' PRICES.
675
As an illustration of this difference, the annexed extract from the price list of
Messrs. Randell and Saunders, for Bath stone, is annexed. It will be seen that the
same description of goods varies more than cent. per cent. at different stations.

PRICES.
At Bristol.
Paddington.
Liverpool.
Combe Down, ditto at Bath
BLOCK.
Corsham Down, delivered into
trucks, at Corsham
Box ground stone, ditto at Box
S.
d. s.
d. s.
d. s.
d.
•
per foot cube 0
7 0
9 1
4 1 6
0
80
911 5
""
or Corsham
Farley Down, ditto at Box
Corn Grit, ditto at Corsham
70
914
0 8 0
91 5
""
0 50
71 2
""
Selected Blocks, 1d. per foot extra.
Blocks, of large dimensions, or cut to order,
supplied at a moderate cost.
LANDING.
Four inch, under 24 feet
•
per foot super.0 310
410 61071
Ditto, above 24 feet
0 410
""
510 710 81
51071081
Six inch, under 24 feet
0 410
420 910 101
""
Ditto above 24 feet
33
0 510
610 1010 111
PAVING.
Three inch, corn grit
Ditto ditto, Corsham Down
ASHLAR.
Corsham Down ashlar, 4 inch
""
10 3
со до
2
0 5
0 6
""
Ditto, 5 inch
Ditto, 6 inch
Ditto, 7 inch
Ditto, 8 inch
""
""
""
""
""
This Stone is cut to range in courses, 10, 12, or 14
inches deep; a small allowance being made in
each case for dressing.
0 210 220 50 6
0 210 310 6
0 30 330 70 9
3207109
0 310 410 83
0 40 50 101 0
RANGE STONE.
Sawn range stone
per yard 1 3 1 93 6
This Stone is cut to range in courses, 4, 5, 6, 7, and 8
inches deep, and varies from 3 to 7 inches wide;
5 yards make a ton.
QUOINS. Random sizes
per foot super.0 3
WALL STONES.
per ton 1 0
676
BUILDERS' PRICES.
SECT. III-Bricklayer's Prices.
Concrete-Labour in mixing, wheeling, throwing in from a
stage, and puddling, (where required to be done), including
erection of scaffolding
Brickwork.
Extra labour to maim facings
Labour.
S.
d.
per yard cube
per rod
0
10
37
1
0 1
PAVING.
Brick paving laid flat in sand
per yard 0
4
""
laid on edge in sand
laid flat in mortar
""
""
laid on edge in mortar
0
7
""
0
5
>>
0
8
""
Paving brick paving laid flat in sand
0
4
""
""
laid on edge in ditto
""
091/2
laid flat in mortar
0
7
""
""
laid on edge in mortar
0
11
""
Clinker paving on edge in sand
10 to 12 inch tile paving
1
0
""
0 1
""
Pan tiling laid dry
TILING.
per square
3 2
5 2
""
5 11
""
5
7
""
5
9
""
5
11
""
Pan tiling pointed outside
""
inside and out
Plain tiling laid to a 4 inch guage
laid to a 3½ inch ditto
laid to a 3 inch ditto
""
The prices of bricks, slates, and tiles, vary in price in different locali-
ties, at the present time, (March, 1853), they are very dear, so
that any calculation on account of materials would not be useful in
this place.
Rough render
Floating ditto
Setting
Lathing
SECT. IV-Plasterer's Prices.
If circular work, add on the lathing, and also on each coat of
plastering
If to groins, add as above
0
2
0
21
0 12
0 2
0 1
0
1
BUILDERS' PRICES.
677
SECT. V-Ironmonger's Prices.
AIR BRICKS.
Per Doz.
Per Doz.
S.
d.
s. d.
Hollow sides
6 0
Half bricks
4 0
Hollow sides, heavy
70
Half bricks, heavy
4 6
Full sides
9 0
Half bricks
5
0
Full sides, heavy
12 O
Full sides, heavy
5 6
BRASS BOLTS.
inch flush brass bolts.
2 inches
23
3
4
""
""
33
∞ ∞ + 20 CO E ∞ ·
inch sunk slide.
per doz.
per doz.
§ inch sunk slide.
per doz.
S. d.
1 10 4 inches
5
""
5
6
""
7
8
""
9
10
11
12
""
2
3
4
9
6
5 6
6 4 10
7 3 11
8 2 12
9 0
""
10
0
10
10
""
""
""
""
∞ ∞ ∞ H2O CO
2 3
20
5
6
""
6
""
8
789
8
∞ ∞ or es
S.
d.
S.
d.
0
4 inches
5
4
3
7 6
9
""
10
0
11
3
12
610
5 ∞ ∞ a as cr
6
8
""
8
0
""
9
4
""
8
35
10
8
9
12 0
""
13
4
•
""
13
""
15
911
0 12
14
""
•
8
16
0
2 inch sunk slide.
per doz.
S.
d.
4 inches
6
0
4 inches
7 inch sunk slide.
per doz.
S. d.
1 inch sunk slide.
7 0 4 inches
per doz.
S. d.
8
0
5
7 6
5
8 9
""
""
6
9
0
6
10 6 6
39
""
7
10
6
33
8
9
12
0
13
6
789
""
•
12 3 7
18
14 0
15 9
∞ COL ∞ ∞
5
10
0
•
""
12
0
29
14
0
""
8
16 0
""
9
18
0
""
""
""
10
15
010
17
610
20 0
""
""
""
11
16 6 11
19
311
22 0
""
""
""
12
18 0 12
21
0 12
24 0
""
""
""
NIGHT BOLTS.
6 inch
3s. each. 7 inch
4s. each.
678
BUILDERS' PRICES.
BRASS SOCKET BOLTS,
With iron bolts and back plates.
All brass.
per doz.
per doz.
S. d.
S.
d.
TH 20 CO← ∞ –
3 inches
4
18 0 3 inches
16 O
24 04
20 0
5
6
7
8
""
""
""
30 05
24 O
""
36
06
28 0
""
•
ະ
""
42 07
33 0
""
""
50
08
40 O
""
9
33
60 0 9
48 O
""
STRONG BRASS SOCKET BOLTS,
All brass.
With iron bolts and back plates.
per doz.
per doz.
S. d.
S. d.
6
7
∞ COD ∞ ∞
3 inches
4
5
""
""
23 0
28 0
16 0 3 inches
12 6
19
04
5
15 6
""
LO CO
33
19 O
6
23 0
""
""
34
07
28 0
""
""
8
42 0 8
33 0
""
9
50 0 9
38 0
""
""
3 inches
4
""
20
5
33
3 inches
4
""
5
20
""
SOLID BRASS SHIP BOLTS.
S.
per doz.
d
26
66 inches
32 0 7
""
40
0
SHIP BOLTS, ALL BRASS, SMOOTH SANDED.
per doz.
S.
d.
12 0 6 inches
13
18
68
0
per doz.
S.
d.
45 6
55 O
per doz.
S. d.
22 0
40 O
RACK AND SPRING BRASS BOLTS.
1 inch wide, 12 inches long, 4s. 3d. each.
RACK AND SPRING IMPROVED ESPAGNIOLETTE BRASS BOLTS.
180
§ 3s.
23s. 6d.
BRASS BOLTS FOR BLINDS.
폼 ​48.
From 2s. to 3s. per dozen.
BUILDERS' PRICES.
679
6 inches
7 "
5 inches
6
7
""
""
8
""
IRON NIGHT BOLTS.
per doz.
S. d.
15 0 8 inches
17 O
DOOR CHAIN BOLTS.
per doz.
d.
per doz.
S.
d.
20 0
per doz.
S.
s. d.
8 6
9 inches
15 O
9 6
10
18 O
""
10 6
11
22 0
""
12
0
12
26 0
COTTAGE OR PORTABLE IRON OVENS.
Inside Measure.
9 inches long, 7 inches wide, 64 deep, 11s. 3d. each.
11
""
81
6/1/
14s.
""
""
CASEMENT AND FRENCH WINDOW BRASS FASTENERS.
From 5s. 6d. to 50s. per dozen.
HINGES, BRASS BUTTS.
s. d.
per doz.
s. d.
per doz.
s. d.
s. d.
inch, from
0 10 to 1 0
2 inch, from
29 to 5 9
0 11
1 1
21
3 6
7 6
1
1급
​>>
""
1 1
1 3
2
4 6
90
""
1
3
1
6 6 23/20
5 6
12 0
""
11
1 4
1
9
3
7 3
16 O
""
""
13
1 7
2
0
""
31
90
20 0
""
11/
1 9
3 4
3
11 O
28 0
""
15
20
""
3 932
14 O
34 0
12
2 3
4 3 4
17 6
42 0
"
""
17
2 6
4 9
""
STRONG PROJECTING BRASS BUTTS, WITH POLISHED AND
LACQUERED BACKS.
per doz.
S. d.
per doz.
8. d.
12 inches
2
NNN
""
21
23
21
2g
HHHI MKO TO LOKO
""
5 9 3 inches
20 0
7 031
31 0
""
8 9 3
34 0
""
10 6 32
39 0
""
35
12
6
4
45 0
""
>>
15 O
33
680
BUILDERS' PRICES.
PROJECTING BRASS BUTTS, WITH POLISHED BACKS
AND FRONTS.
per pair.
per pair.
s. d.
s. d.
2 inches
1 0
34 inches
2 6
21
""
1 3
31
3 0
""
"7
21/
2朵
​""
1 6
6
32
3 6
""
1 10
4
4 3
""
3
""
2
2
SKEW BRASS BUTTS, WITH STEEL JOINTS.
From 7s. 9d. to 15s. per pair.
STRONG BROAD PROJECTING BRASS BUTTS, WITH POLISHED
BACKS AND FRONTS,
per doz.
2 inch
21
""
per doz.
s. d.
s. d.
1 4
2 inch
2 2
. 1 7 22
""
2 9
3 inch
31
""
31/12
""
WITH HOLLOW JOINTS.
per doz.
s. d.
per doz.
s. d.
3 0
3 6 4
4 0
32 inch
4 6
""
5 6
3 inch
31
""
BRASS RISING HINGES ON STEEL SCREWS.
per pair.
S. d.
per pair.
S.
d.
11 6 4 inch
15 0
13 6 41
17 6
""
BUILDERS' PRICES.
681

BEST CAST IRON HINGES.
Pew Hinges, Egg joint,
per doz.
Japanned, Japanned, Parliament
per doz.
per doz.
Strong
loose joint
Strong
Knee'd
Butts,
per doz.
Loose Pew Loose Butts
Turned ends
Butts,
per doz.
per doz.
Loose Butts
per doz.
New Skew
Butts,
Turned ends
per doz.
Back Flaps Skew Butts
per doz.
Pew Butts,
per doz.
Japanned,
per doz.
Square
Butts,
per doz.
Edge Butts,
Sizes.
per doz.
s. d.
S. d. S. d. 8.
d.
S.
d.
S.
d.
S.
d.
S.
d.
s. d.
S.
d.
S. d.
S.
d.
S. d.
inches.
3 0
2 8
1 8
1
5
4 6
3 0
1 10
1 9
♡ cr
1
6
0 10
1
1 8
1
0
11
4 6 4
4 0
5
3
6 0
69
6
20 20 CO CT
5 0
5 6 5 6 6 0
TH LO LO Co
9
1 8
3
3
2 0
2 4
2 0
1
3
5
0
2 2
3
9
2
6
3 3
4 0
3
0
1
7
6
2 8
4 6
3 0
3 9
5 0
4 0
2
0
3
3
5
3
3 6
4 6
7
9
5
6
4
6
2
4
21
0
9 0
4
0
5
4
0
10 6
6
6
8
6
6
0
2
8
6 6
8 0
6 6
9
9
3
6
9
8 0
3 2
#
7 0
8
9
11 0
56
7 3
5 6
12 6
10 0
4 2
9
6
8
6 4
11 3
9
3
12 6
7 3
9 0
7 3
16 O
12 6
5 3
10 6
14 0
6 0
18 0
8 9
10 6
89 200
15 6
6 6
11 6
20
0
8 0
12 6
22 0
12 0
13 9
12 0
24 0
19
0
9 6
15 0
16 9
15 0
28
0
24 0
12 0
LO
13 6
13 6
14
6
14 6
35 0
30 0
17
O
20 0
61
23 0
30 0
7호
​36 0
42 0
8/3/2
2 U
682
BUILDERS' PRICES.
size.
BROAD CAST IRON BUTTS.
per doz.
s. d.
size.
per doz.
s. d.
2 by 2
open
2 94
4
by 3
open
8 6
HQ
21
21/2
""
""
""
གྲགས་ཡུས་ ཐུས་པ
239
35
33
2
3
3
31
8 9
>>
""
36
9 0
21
3
9
""
35
4 0
""
32
4
""
96
""
10 O
21
""
""
23
""
པ
22
239
сон
33
"
HKHTY COKH
""
""
""
"}
""
21/2
""
3
""
""
""
2호
​2232
3
31
2호
​232
3
""
""
3 9
3
6
""
""
""
10
6
23
4
4호
​11 O
">
4
11 9
""
>>
4
9
19
5
341
""
4
6
4
23
5
0
5
6
""
5 0
5
༢。ིལ--。
12 6
"
32
10 6
""
11 0
""
11 6
4호
​12 6
""
13 6
33
""
25
23
5
6 41
""
29
3 1/2
12 O
""
25
39
23
56
""
31
""
""
""
""
""
""
""
3
31
320
4
22
31
3호
​32
3
31/12
31/2
3232
4
""
""
6
0
""
6 6
""
322
12 6
4
13 0
14
7 0
""
39
41
13 6
""
COLH
7 6
56
""
4/1/2
14 O
""
7 9
60
""
42
14 6
>:
5
15 O
་
14
""
""
6
6
7
0
7
6
""
80
8 6
""
7 0
7 6
""
25
>>
51
15 9
5/1/2
16 6
""
5
20
31
15 O
""
""
4
16 O
353
""
41
17 0
35
33
""
5
18 O
23
5/1/2
19 O
""
>"
8 0
86
6 5
8 9
""
6
21 0
""
4
17 O
""
>>
""
34
4/1/2
18 O
""
41
9 3
20
5
19 6
""
""
""
41
9 6
51
21 6
""
""
>>
330
COKH
39
16
""
""
""
3
31
3 1/2
3/201
4
7 6
6
""
♡
HKH TO COL
8 0
""
8
66
""
""
9
0
5
""
9
6
""
>>
""
4/1
10 3
6
༩ 。EN
CO
24 0
""
6/1/2
27 0
""
4호
​20 0
""
21 6
""
23 6
""
26 0
""
""
""
3:35
41
11 0
61
29 0
""
>>
22
BUILDERS' PRICES.
683
No.
mai as
1.
10 inch
2.
12
""
3.
14
""
CROSS GARNET AND T HINGES.
per pair.
No.
s. d.
0 5
4.
16 inch
per pair.
s. d.
09
0 6 5.
18
1 0
""
08
6.
20
1 3
""
Strong Cross Garnets, 5d. per lb.
HOOK AND EYE HINGES same price.
CAST IRON PARLIAMENT HINGES.
per doz.
Joint.
Open.
s. d. Joint.
11
by
21
4 9
2
by
Open.
3
per doz.
s. d.
11/
"
12
2
5 3
">
3
5
6
""
39
33
3/1/201
7 0
7 3
""
4
""
CORN
2
""
2
༄༦:
54
33
""
""
""
21
3
33
13
THICY
HIN HA
6
6
6
69
7 0
3
21
+++
7
6
4
8 6
""
""
4/1/2
""
21/
""
>>
""
6 3
567
9 6
10 6
12 0
16 0
""
""
2
14
6 6
""
""
5/1/2
12 6
33
21/1
6 9
3
6
15 0
CAST IRON LATCHES, WITH WROUGHT FURNITURE.
Gate latch, with screws and nuts
s. d.
s. d.
19 0 per dozen.
Common thumb latches
from
2 3 to 4 6
""
New thumb latches
4 6
11 0
""
""
""
Norfolk latches
4 8
14 6
""
""
A
""
Flush latches
5 0
""
Strong fluted Norfolk latches
from 5 6
12 0
""
""
Flush stable latches
9
0
15 0
""
""
""
Jointed handle stable latches
13 6
""
Secret latches, with moving plate
17 6
with drawback bolt
""
""
for gates
20 0
""
10 0
33
§ inch
2
oka w okr
33
39
1
11
1호
​12
""
34
34
·
SCREWS, NAILS, &c.
BRASS HEADED NAILS.
per doz.
s. d.
per doz
s. d.
1
2 2 inch
2 9
1 3 21
3 3
""
•
1 4 2
""
1
1 6
8
22
""
3
""
1
2
2
9
93
31
4
""
""
9
4 3
5 0
7 0
86
3
684
BUILDERS' PRICES.
LOTO COLEH NOO
§ inch
226
>>
་
""
1
11
1/1/20
35
པོ
""
§ inch
20/00 coRH 100
""
1
11
11
17/2
ICT CORH
12
""
>>
""
"
BRASS PLATED HEAD COUNTER-SUNK NAILS.
per doz.
s. d.
1 0 12 inch
1
12
""
1
3
3 21
""
1
3 2
""
1 6
22
per doz.
s. d.
2 0
2 3
2 9
3 0
.
3 6
4 0
1 9
Co
""
BRASS TAPER-HEADED NAILS.
per doz.
s. d.
1 7 2 inch
per doz.
s. d.
3 3
1
8
8
21
3 9
"
1
9
9
·
2
4 6
33
1 10 22
53
""
2
03
6 0
2
3
3 3
7 0
""
2
94
8 6
""
BRASS SASH SCREWS.
From 2s. to 3s. 3d. per dozen.
WROUGHT NAILS.
s. d.
Threepenny per 1000 1 6 | Threepenny
CUT NAILS.
s. d.
per 1000 0 8
Fourpenny
""
1 9 Fourpenny
0 10
"
Sixpenny
2 2
Sixpenny
1 0
""
Tenpenny
3 0
"
Tenpenny
2 0
Twentypenny
""
4 0
Twentypenny
3 0
""
Twentyfourpenny
3d. per lb.
Larger sizes 24d. per lb.
Spikes 3d. per lb.
JOINER'S CUT BRADS.
s. d.
s.
d.
inch
per 1000 0 2 1 inch
per 1000 0 5
228
1
""
""
0 3 11
""
0 42
0 6
1 0
""
CUT FLOOR BRADS.
2, 2, and 3 inches, 2d. per lb.
Cut lath nails, 24s. per cwt.
I
SASH LINE, at per gross of yards.
Cast lath nails, 16s. per cwt.
s. d.
s. d.
No. 1.
2.
3.
4.
5 0
No. 5.
10 O
5 6
6.
14 O
6 6
7.
18 O
8 0
8.
26 0
Common ditto 8d.
per
lb.
BUILDERS' PRICES.
685
LOCKS.
Drawback for Street Doors.
Rim Locks with Brass Knobs,
complete.
6 inch
s. d.
s. d.
each 2 6
8 inch
each
4 6
36
9
6 0
""
""
""
5 0 10
10 0
""
""
""
7
"
8,
MORTICE LOCKS.
Without furniture, from 3s. 6d. to 6s. each.
Brass furniture to ditto, 2s. per set.
China
""
from 2s. upwards.
Cupboard Locks, from 6d. to 2s. 6d. each.
GARDEN ROLLERS, MOUNTED.
s. d.
s. d.
14 inches wide
each 23 0
23 0
22 inches wide
each 64 0
16
18
20
"
"
29 0 24
78 0
""
""
"
36 0 26
""
""
39
99 O
"
50 0
""
Octagon
HAY RACKS, from 7s. to 9s. each.
PILLARS FOR CORN STACKS.
s. d.
each 10 6 Feathered
Circular, 6s. each.
PIPES, GUTTERING, &c.
2
s. d.
each 9 6

23 31/ 4 4 5
5/1/
inches inches inches inches inches inches inches inches
Pipes for Rain Water
s. d. s. d. s. d. s. d. s. d.
1 3 1 6 1 10 2 3 2
31
2 32
s. d. s. d. s. d.
6
2 9 3 3
per yard.
Flat Heads.
2 0 2 3 2 6 2 9 3
0
3 6 4 3
each.
Angle Heads
2 32 6 2 9 3 03
3
4
0 4 6
Angle Shoes
1
01 31
31 6 1 9 2
6
3 0 3 6
Angle Boots
1
6 2 0 2
2
6 3 03
6
4 0 4 6
Guttering, half round
1
01 11
21 4 1 6
Guttering,long angles
1
3 1 6 1
Guttering, O.G. .
Guttering, O.G. angles
Guttering, Lion Head
Clips..
Ditto, plain ditto .
Flange pipes for pumps
Pumps, various
3 0 3 6 4
35 045
3
055 0
9 2 0 2 3
1 7 71 8 2 2
1 10 2 3 2 6
0 10
0 8
1 9 per yard.
2 6 each.
2 6 per yard.
30 each.
each.
per yard.
each.
686
BUILDERS' PRICES.
SECT. VI.-Prices of Materials for Drainage and Water Supply.
GLAZED STONE WARE DRAIN PIPES.
3 inches internal diameter
4
""
""
""
18
""
6
9
12
15
18
""
""
"
""
""
""
""
""
3 inches internal diameter
4
6
9
12
15
18
""
>"
""
""
""
""
""
""
""
3 inch bore of main tube
4
6
9
12
15
""
""
دو
""
""
""
""
BENDS.
•
s. d.
per foot run
0 5
0 6
""
08
""
•
1
>>
11/
1호
​1 10
""
3 0
4 0
""
each
1
3
1 9
>>
2 3
""
13
39
36
5 6
8 0
པ
10 6
""
JUNCTIONS.
each
1 3
1 6
235
2 0
•
>"
3 6
"}
5 6
33
8 0
""
10 6
>>
DOUBLE JUNCTIONS.
3 inch bore of main tube
each
1 8
""
9
3 inch bore
4
6
9
""
4
6
""
""
""
2 0
""
33
25
2 8
•
34
4
6
TRAPS FOR IRON FLAP.
each
1 3
1 6
""
2 0
""
56
3 3
SYPHON TRAPS.
3 inch bore
each
2 6
4
3 6
•
""
""
6
5 0
""
9
7 6
""
""
Water Closet Pans, with Syphon Traps, from 7s. 6d. each.
NOTE. Very large discounts are given by the pipe manufacturers for cash payments.
BUILDERS' PRICES.
687
The Prices, Numbers, Sizes, and Weights, in Cast Iron, of Lowe's Patent
Effluvia Trap Sewer Gratings, or Stench Trap Grids, are as
follow, viz. :-
In. In. In.
Weight.
No. 1 Size 30 by 18-16 deep, about 5 cwt.
No. 2 Size 20 by 12-13 deep, about 2 cwt.
No. 3 Size 14 by
No. 4 Size 11 by
No. 5 Size 9 by
No. 6 Size 6 by
9
9 deep, about 1 cwt.
7— 7 deep, 56lbs.
53-53 deep, 25lbs.
4- 4 deep, 10lbs.
No. 7 Size for Sink Stones, in white metal, square pattern.
No. 7 Size for Sink Stones, in iron, square pattern, with brass
Ditto
ditto
Ditto ditto
Ditto ditto
Ditto ditto
grating and screw plug
in iron, round pattern, with brass
grating and screw plug
all brass, square pattern, with screw plug
all brass, round pattern, with ditto
brass top and grating and lead body, with
screw plug
£ s. d.
1 18 0
0 16 O
090
0 6 9
040
0 3 0
0 2 6
0 19
020
0 3 6
0 3 9
03 0
Glazed or unglazed draining bricks patented by Messrs. RANDELL and
SAUNDERS, can be supplied at the following prices, in any locality where
clay of good quality can be obtained.
BRICKS 12 inches long, 4 inches wide, and 2 inches thick, 1d. each.
12
>>
""
4/1/2
""
31/2
1글​이
​""
The Cost of Bricks to make Drains of various dimensions will be as
follows:-

No. of Bricks Thickness of
Diameter of Drain.
per foot.
Brick.
Cost per foot.
ft.
0
in.
6
in.
8.
d.
4
12321
0
4
0 9
6
2
1
0
8
21
1
3
10
21/1
1
6
12
2321
1
9
14
2 0
16
2 2 2 Y
3
18
3호
​6
20
9
22
3
0
24
4
42/2/2
N N N N Y
N N N N ∞ ∞ ∞ ∞ +
0
6
0
8
0
10
1 .
0
1
9
2
0
2
3
2
6
2
9
3
0
688
BUILDERS' PRICES.
IRON SINK TRAPS.
ROUND JAPANNED TRAPS.
per doz.
per doz.
s. d.
s. d.
4 0
6 inch
12 0
4 6
61
13
6
""
7
15 0
44
73
16 6
""
7 6
8
18 0
""
9 6
9
21 0
""
11
0 10
26 0
""
21 inch
3
31
4
4/
LO
5
5/1/2
""
""
""
""
""
""
5 6
6 6
4 inch
5
CO
6
""
SQUARE JAPANNED TRAPS, WITH BARS OR ROUND HOLES.
per doz.
s. d.
9 07 inch
11 08
""
""
14 09
STABLE DRAINS, JAPANNED.
per doz.
s. d.
. 18 0
23 0
28 0
S.
d.
s. d.
6 inch square
each 0 10 10 inch square
each 2 3
8
1 612
3 6
"
""
>>
""
STRONG GRATES AND FRAMES FOR GRAVEL WALKS,
7 inch square at top, 3s.
SOUGH GRATES, JAPANNED.
per doz.
s. d.
per doz.
4 inch square
s. d.
20
8 inch square
8 6
5
6
""
3 0 9
""
12 0
""
7
"
4 6 10
6 6
""
O
15 O
STRONG SOUGH GRATES WITH BARS, JAPANNED.
per doz.
per doz.
s. d.
s. d.
4 inch square
3 0
8 inch square
9 6
5
4 0
9
13 0
"
""
6
5 6
""
10
16 O
7
7 6
22
BUILDERS' PRICES.
689
SECT. VII.-Plumber's Prices.
Milled lead in sheet, per cwt.
Cut to dimensions
Window lead
£
s. d.
1 8 0
1 9 0
1 17 0
0
1 15 0
0 18 0
Laying Milled lead in gutters, flats, hips, or ridges 1 13
Do. in step or other flashings
DS or P traps, each
Strong service boxes, each
Safes for closets and straps
Solder, per lb.
Plumber, per day
Labourer, Do.
Wall hooks, each
0 10 0
080
0 0 10
0 6 0
04 0
0 0 11
Lead-headed nails
0 0 1
Large do.
0 0 2
Allow for old lead in exchange, 4lbs. to be
deducted for waste, per cwt.
060
DRAWN WATER PIPES.
Middling.
Strong.
s.
d.
s. d.
HOY COKH
inch
per foot
0 5
0 6
0
7
08
""
""
39
1
11
1 1/2
2
21
""
""
""
""
""
09
0 10
0 11
1 1
1 31
1 7
""
1 10
2 3
2
3
28
35
FUNNEL PIPES.
6 lbs.
7 lbs.
4 inch
per foot
2 4
2 9
41
2
9
3 0
20
41
5
51
6
""
""
""
4 inch joints
""
""
""
3 0
3 4
3 4
38
""
38
4 0
""
each
4 3
4 6
""
20
5 0
""
51
5 6
""
6
"
""
61
""
39
60
6 6
2 inch
21
3
3 1/2
""
SOCKET PIPES FOR SINKS.
per foot
""
""
>>
23
1 5
1 7
1
7
1 9
20
2
3
2 3
2 6
690
BUILDERS' PRICES.
RAIN WATER PIPES, INCLUDING FLAPS AND COLLARS.
3 inch
31
""
4
""
inch
1
oo
1/
11
2
21/2
""
""
""
""
""
""
21 inch
3
H
312
4
""
per foot.
""
""
s. d.
s. d.
2 0
2 3
2
3
2 6
•
2 6
2 9
JOINTS, INCLUDING SOLDER AND LABOUR.
each
""
""
པོ
""
•
COMMON LEAD PUMPS.
complete
""
"
""
""
22
2 inch
3
31/12
4
""
FORCE LEAD PUMPS.
complete
""
""
""
""
2135
2 inch
complete
£
s. d.
0
26
0
29
0 3 0
0 3 3
0 3 9
0 4 3
049
1 12 0
•
250
2 15 0
3 50
•
3 0 0
4 0 0
4 15 0
5 15 0
HYDRAULIC PUMPS.
""
4 15 0
5 10 0
700
8 0 0
2-1/2">
3
22
31/2"
4
""
""
9 10 0
23 inch
PUMPS FOR DEEP WELLS.
complete
4 15 0
3
5 15 0
""
"2
3 1/2
6 15 0
""
">
4.
7 15 0
""
""
•
BUILDERS' PRICES.
691
WATER CLOSETS.
Best pan closet with valve, complete
Do. with sunk ivory handle
Do. with shoe valve, extra
Blue painted basin, extra
Bramah's valve closet, complete
Ship Closet with copper basin, complete
Square way
inch
STOP COCKS.
1
cold
2
11
11
""
""
""
""
Large cocks, per lb.
BIB AND BALL COCKS.
Screw ferrules
inch
CO
""
1
11
11/
""
""
£ s. d.
2 5 0
2 15 0
040
04 0
5 10 0
4 10 0
0 3 0
040
076
0 10 6
0 15 6
020
0 3 6
043
08 0
0 11 6
0 18 0
BOSSES, EACH.
inch
0 0 10
1
""
0 1 0
020
COPPER WATER BALLS.
Wrought Rods.
For inch
cock
""
""
1
CONH
11
11/
""
""
""
"
""
""
1
2
11
inch
""
Cobourgs
DRIVING FERRULES.
020
0 2 4
0 4 3
070
. 0 9 0
0 1 1
0 14
0
2 3
0 3 6
+
0 36
692
BUILDERS' PRICES.
LEAD AIR TRAPS,
With Brass Bell Grates.
£ 8.
8. d.
21 inch.
0 2 3
3
31
4
""
""
0 2 9
0 3 6
0 4 6
13 inch
2
21/
3
31
4
41
""
"
,,
""
""
20
""
BRASS GRATES.
1
11
11
2
21
3
inch
""
""
""
""
""
WASHERS AND WASTES, Or plugs.
1
11
11
2
2 3
3
inch
""
"
""
""
33
SHORT SPINDLE VALVES.
LONG SPINDLE VALVES.
1½ inch
2
21/
3
39
92
35
Plain pan closet basin
Hopper
Blue painted basin
""
•
SUNDRIES.
004
0 0 5
0 0 6
008
0 0 10
0 1 0
0 1 2
0 16
•
0
19
0 29
0 3 9
•
0 49
07 0
0 12 0
0 18 O
020
0 29
0 3 3
040
0 6 0
0 13 0
060
0 8 0
•
0 12 0
0 16 0
09 0
0 11 0
0 14 0
BUILDERS' PRICES.
693
Fan and mounting basin
Wash-hand basin with brass washer and chain
Blue printed
do.
Copper tinned basins
Round cistern valves
Shoe
do.
Spring
do.
Spring board and spring
£ s. d.
0 3 0
066
0 8 6
046
059
0 10 6
0 10 6,
066
0 1 0
Cranks each
Stool cocks with plates and handle
Copper wire, per lb.
inch
1
11/
11
""
""
1
24
inch
""
""
0 7 6
0 18
BOILER SCREWS.
0 1 3
018
0 2 6
0 3 6
0 4 3
COCKS FOR SLATE CISTERNS.
0 4 3
0 5 6
0 10 0
inch
SCREWS WITH NUTS AND UNIONS FOR SLATE CISTERNS.
""
1
""
0 3 4
049
0 6 6
WASHERS AND WASTES FOR SLATE CISTERNS WITH UNIONS.
inch
是
​""
1
""
0
2 9
0
5 6
0
7 6
SPINDLE VALVES FOR SLATE CISTERNS WITH UNIONS.
inch
0 5 9
1
0 7 6
694
BUILDERS' PRICES.
SECT. VIII.-Painter's Prices.
COMMON COLOURS, INCLUDING KNOTTING AND STOPPING.
Once in
oil
Twice in
""
Three times in
""
Four times in
""
per yard
Add to every extra coat
If flatted
""
If finished in party colours, add
If sanded
do.
">
""
""
""
""
EXTRA COLOURS.
s. d.
0 31
0
6
08
0 10
0 2
031/2
0
11/
0 6
French grey, fawn, salmon, peach, or like tints
Light green, or olive green.
Patent greens, French greens, yellows or blues
Chinese Vermilion or Lakes
""
twice done on scarlet ground
Imitation granite or splashed work
Mouldings cut in, per foot run, common colours
""
if grained in imitation of woods
Broad lines to form panels
add
0 1
0 3
""
06
""
1 9
2 9
""
0 6
""
0 0212
per foot
0 2
0
11
""
Light and shadowed lines
0 2
""
Cross banded margins
•
""
0 31/12
PLAIN SKIRTINGS, NOT EXCEEDING EIGHT INCHES WIDE.
Once in
Twice
oil
per foot run
0 032
">
""
0 11
Three times
0 12
""
""
Four times
0 21
""
If flatted, add
0 01/
>"
MOULDED SKIRTINGS, EXCEEDING EIGHT INCHES WIDE.
Once in
Twice
oil
•
per foot run
0 1
0 11
""
Three times
0 2
""
""
Four times
""
0 21/1
""
If flatted, add
0
1-194
""
PLAIN CORNICES, NOT EXCEEDING TWELVE INCHES GIRT.
Once in
oil
•
per foot run
0 11
Twice
""
""
0 12
Three times
0 21
""
Four times
0 3
""
If flatted, add
123
0 1
BUILDERS' PRICES.
ENRICHED CORNICES, FRIEZES, OR OTHER ENRICHMENTS.
Once in
Twice
oil
""
695
S. d.
per foot super.
0 11/
0 21
""
031/20
Three times,
Four times
""
""
If flatted, add
""
""
""
If picked in party colours add one half.
REVEALS TO WINDOWS AND DOORS.
0 5
06
Once in
oil
•
per foot run
0 12
Twice
0 12
وو
Three times
0 21
""
""
Four times
0.3
""
""
WINDOW SILLS, STRINGINGS, COPING EDGES, PLINTHS, &c.
Once in oil .
•
per foot run
Twice
0 21/0
0 31
""
Three times
0 5
""
""
Four times
0 6
""
RAIN WATER PIPES AND GUTTERS.
Once in
Twice
oil
per foot run
0 12
""
0 21/20
""
Three times
Four times
0 3
""
""
""
0 31/12
SASH FRAMES AND SQUARES.
Frames once in
oil, not exceeding 25 feet super.
Do. twice
""
Do. three times
""
08
1 0
>>
1 4
""
""
Sash squares
Do. four times
For large Venetian frames, add one-third
once
1
8
per dozen
08
Do.
twice
1 0
""
Do.
three times
1 4
""
Do.
four times
1 8
""
If the squares exceed 30 inches, add per doz. each coat
0 3
If different colour from the frames, add
0 1
If flatted, add
0 4
SASH FRAMES AND SQUARES, GRAINED.
Wainscot oak or mahogany frames, each
1 6
Do.
squares per doz.
1 6
696
BUILDERS' PRICES.
squares per doz.
Rosewood, satinwood, maple, &c.
Varnishing squares per doz. or frames each, in copal
Cleaning old work, rubbing down, or bringing forward, &c., to
be charged day work, ladder work to be charged extra,
according to trouble and labour. The term, party
colours, is applied where the framing is one colour and
the panels another.
DAY ACCOUNT.
Painter, per day
Common colour
per lb.
Putty
""
Hard stopping
""
Brushes
each
Tools
""
Pots
""
Small do.
""
IMITATIONS OF WOODS AND MARBLES*.
s. d.
20
0 6
6 0
0
6
0 3
0 6
36
1 4
0 6
0 4
Wainscot oak
per yard
1 6
Mahogany, maple, or sycamore
1 9
""
Rosewood or Coromandel-wood, and satinwood
2 0
""
Bird's-eye maple or pollard oak
2 6
For enrichments and carved work, add one-fourth
Hand-rail, grained mahogany and varnished
per foot run
0 4
Veined marble, including white ground
per foot super.
0 3
Dove, bardilla, or black and gold
0 5
Sienna, brocatella, Venetian, French, Devonshire
0 6
""
Green verd, or porphyry
Verd antique, oriental, jasper, giolla antico.
Lapis lazuli
If to columns, add
06
08
""
1 0
""
03
""
If to fluted do., add
0 4
Spirit varnish, each coat
Varnishing once in best copal
Do.
Do.
twice do.
""
three times do.
""
""
Cleaning and sizing old work
Hand polishing, per foot super
Do. on columns
VARNISHING.
per yard
06
0 7
1 0
1 4
08
0 6
10
""
Do. do. fluted
1 6
22
French polishing
0 6
""
Do. hand-rails and small articles, per foot run
04
* The prices here given are for work of the very best quality.
BUILDERS' PRICES.
697
£ s. d.
WRITING.
Plain letters
per inch
0 0 012
Do. from 3 to 6 inches girt
""
0 0 21
Sunk or Egyptian
0 0 1
""
Gold plain, under 3 inches girt
0
"
0 1/1/2
Gold sunk or Egyptian do.
0
""
Gold plain, from 3 to 6 inches girt
0 2
0 0 2
""
Gold plain, from 6 to 9 do.
0
""
0 21/
Gold plain, from 9 to 12 do.
0 0 3
""
Gold Egyptian, from 6 to 9 inches girt
0 0 3
""
Gold
do. from 9 to 12 do.
004
If shadowed, add
""
0 0 03/2
If do. double or indented, add
0 0 03
If shaded to appear as projecting letter, add for the double
shadow
Letters enamelled in gold on glass, per inch
Antique or ornamental letters, once and a half the above prices.
0 0 1
0 0 3
GILDING.
Gilding in oil gold, including preparation, per
foot super.
"9
Do. in burnished gold
Carved work, from once and a half to double the
above prices, according to the depth of the
enrichment.
Gilding
inch mouldings, per foot run
Do. & do.
وو
0 3 6
046
Do. 1 do.
""
""
Gilder
per day
002
0 0 3
004
0 7 0
Gold leaf
Oil gold size do.
Pumicing, sizing, and preparing walls,
Lining paper
Do. stout
Canvas lining
per book
Parchment size per lb.
SECT. IX.-Paperhanger and Decorator's Prices.
per piece 0 0 6
0 0 9
01 0
0 3 6
0 20
008
030
Hanging do., including tacks and slipping
0 1 6
22
Do. common papers
do. 4 do.
Hanging lining paper
Do. satin do.
Do. flock or embossed, marbles or granites in blocks
Common papers, 3 colours, or two blocks, per piece 0
Do.
For every extra colour, add
0 0 9
""
0 10
""
0 1 2
""
0 16
"
1
0 to
0
2 0
0
2
0
""
If in rich colours, add
0 2 6
0 0 2
01 0
""
2 V
698
BUILDERS' PRICES.
£ s. d. £
s. d.
Imitation marble
per piece
0 1 6 to 0 2 6
Do. do. done by hand in a superior manner
0
4 6 08 0
""
Do. granite posted
0 2
0
040
""
""
Do. wainscot
0 1
0
"2
Do. do. overgrained
Satin papers, 3 blocks
0
2
6
0 16
0 3 6
22
""
0
4
0,, 0 6 0
""
Do. do. 5 do.
0 6 0
0 10 0
""
Embossed satin
080
0 10 0
""
""
Do. do. bronzed
0 12
0
0 15 0
""
""
Rich crimson flock
0 14
0
0 18 0
""
Do. do. bronzed
0 18
0
""
Panelled decoration
090
29
""
Do. do. including hanging
0 11
0
""
Gothic
Common borders, per dozen yards
Corners to do., each as one yard of border.
Hanging borders, per dozen yards
0 1
0
1 5 0
1 16 0
200
0 3 0
""
do.
0 6
0,,
080
0
0
6,, 0 1 0
Sizing two coats, and varnishing papers per piece 0
2
6 0 3 6
Do.
do.
and do. two coats
0
4
0,, 0 6 0
BORDERS AND MOULDINGS,
INCLUDING
Half-inch wide,
HANGING AND PAPER FIXING.
per yard run
Five-eighths wide,
""
Three-quarters wide,
""
Inch wide,
""
Inch and quarter wide,
""
Inch and half wide,
""
Inch and three-quarters wide,
Two inches wide,
Rich flock borders, 2 inches wide,
Do.
31/1 do.
Old mouldings, up to one inch girt, taken down
regilt and refixed, per yard
For every inch extra width, add .
Ebon lines, drawn out in panels, per foot
Light and shadowed lines,
""
Do. with shaded margin, 3 inches wide
MOULDING.

Black
Gold.
Black
polished gold.
s. d. s. d. s. d. s. d.
0 30 60 9
0 30 70 10
00031091 0
0010 410111 2
0 0 0 6 1 11 6
0 10 71 21 9
0 10 8 1 42 0
0 1010 1 8 2 4
03
04
1 0
0 2
0 01/
0 1
0 2
SCAGLIOLA.
Gray Granite or Porphyry, on slate,
per foot
5 6
Statuary, black and gold
6 0
""
Sienna, Verana, Giallo antico, or Rondara
""
7 0
Brocadilla, or Egyptian green
Verd Antique, or Lapis Lazuli
Columns, including skeleton, extra
7 6
""
80
""
10
""
BUILDERS' PRICES.
699
DISTEMPERING.
Once.
Twice.
s. d.
8. d.
Washing, stopping, and whitening
per yard 0 31
0 5
""
cream tint
0 4
0 6
""
""
drab, fawn, grey
green, lilac, or peach blossom
0
5
08
08
0 10
""
pea green or light blue with
verditer
1
0
1 4
""
""
clouded ceilings
2
0
""
in turps
If one coat of oil color add
Ditto
Plain cornices per foot super., half the above prices.
Enriched ditto, two-thirds.
0 2
""
0 3
""
SECT. X.-Glazier's Prices.
CROWN GLASS IN NEW SASHES.
At per foot super.


Best
Best. Seconds. Thirds. Fourths. Ground.
S. d.
s. d. s. d.
s. d.
s. d.
Squares from 3 ft. 0 in. to 3 ft. 6 in.
1 4
1 2
1 1
0 9
20
2 6
3 0
1 2
1 1
""
0 11 08
1 10
""
2
0
""
2 6
10
0 11
0
90 7 1 8
1
6
2
0
0 11
""
""
0 10 0 8
0 61 6
""
0 90 80 7
under the above
0513
For flatted glass add one third, and for bent two thirds to the above.
PATENT PLATE GLASS IN SQUARES FOR GLAZING.
At per foot super.

BEST.
No. 1. No. 2.
No. 3.
No. 4.
s. d. s. d.
s.
d.
s. d.
6 by 4 and under 9 by 7
1 2 1 3
1 4
1 5
9 by 7 and not above 10 by 8 .
1 3
1 4
1
5
1 6
10 by 8
1 ft.
1 8
1 10
2 0
2 2
""
1 ft.
""
11 ft.
1 11 2 0
2 2
2 4
1½ ft.
2 ft.
2 2 2 4
2 6
2 9
""
2 ft.
3 ft.
2 4 2
7
2 9
2 11
""
3 ft.
4 ft.
2
62
9
2 11
3 1
""
4 ft.
8 ft.
3
0
3 3
3 0
3 0
8 ft.
10 ft.
3 3 3 6
3 9
4 0
""
10 ft.
12 ft..
3 6
3 9
4
0
4
3
""
700
BUILDERS' PRICES.
For seconds up to 1 foot 6 inches deduct 1d. and for all above that size 3d.
No. 1 averages 1-16th of an inch, in thickness and 13 oz. weight to the foot.
No. 2
>>
""
No. 3
1-12th
1-10th
17
22
21
""
""
No. 4
1-9th
24
""
COLOURED GLASS.
Yellow and lemon,
Orange, blue, purple and red
per foot super.
""
Green, flashed ruby, and blue
Embossed glass from
Rosettes per inch
34
36
Best.
Seconds.
8.
d.
s. d.
2 6
1 9
3
3
2 3
3
9
3 0
•
2 6
08
CROWN GLASS STOPPED IN OLD SASHES.

Best. Seconds. Thirds.
s. d. s. d.
s. d.
In squares 3 ft. 0 in. to 3 ft. 6 in. per foot super.
2 01
8
1 3
Ditto 2 6
3 0
1
8 1
5
1 2
""
""
Ditto
Ditto 2 0
under
23
2 6
1 5
1 3
1 1
""
2
0
1 3 1
1
""
1 0
HORTICULTURAL GLASS, IN LIGHTS, GLAZED.

13
16
21
OZ.
Oz.
oz.
s. d. s.
Do.
Not above 12 in. long, and 10 in. wide, per foot super. 0 40
3 ft. super., and not above 40 in. long 0 50
•
d. s. d.
50 7
60 71
FLUTED GLASS, GLAZED.
10 in. by 8 in., and not above 1 ft.
per ft. super. 1 0 1
11 5
11 ft.
do.
2
1 11
31 7
2
do.
2 ft. 6 in.
1 41
61 11
""
""
2호
​do.
3
1 5 1
723
""
""
""
Best flattened crown glass, per foot super., extra
10 4
BUILDERS' PRICES.
701
POLISHED PLATE FOR GLAZING PURPOSES.
£. s. d.
per foot 0 1 9
Under 1 superficial foot
1 ft. and under 2 feet.
0 2 3
2 ft.
3 ft.
026
""
""
3 ft.
4 ft.
02 9
""
""
4 ft.
6 ft.
0 3 0
""
""
6 ft.
8 ft.
0 3 3
""
8 ft.
10 ft.
0 3 6
""
10 ft.
12 ft.
038
""
""
12 ft.
14 ft.
0 3 10
""
""
14 ft.
16 ft.
0 4 0
""
16 ft.
18 ft.
04 2
""
18 ft.
20 ft.
0 4 4
""
""
20 ft.
25 ft.
0 4 6
""
25 ft.
30 ft.
0 49
""
30 ft.
35 ft.
0
4 11
""
""
35 ft.
40 ft.
0 5 2
""
40 ft.
45 ft.
0 5 5
""
45 ft.
50 ft.
0 58
""
50 ft.
55 ft.
0 5 10
""
55 ft.
""
60 ft.
060
"
60 ft.
65 ft.
06 3
""
""
65 ft.
70 ft.
"
35
0 6 6
Glazing 4d. per foot extra.
Ground edges 6d. per foot run.
ROUGH PLATE GLASS.
At per foot super.

1 子
​34.
1 11 11 2
inch. inch. inch. inch. inch.
inch. inches.
s. d. s. d. s. d. s. d. s.
d. s.
d. s. d.
Not above 15 in. long
0
11 1
5 3
0 4
6 5
3 6
0 8 6
Above 15 in. and not above 35
1
01
63
45
06
07
010 0
35
75 1
3 2
04
06
07
7
08
0 8
0 11 0
22
""
75
100 1
52
5 2
14 67
0
""
""
""
100 and upwards.
1
62 65 0
If ground on one side add 6d. per foot.
If smooth on one side and polished the other 2s.
Bending rough plate 28. per foot.
Do. polished plate 3s.
For silvering plate glass add one fifth and for embossing do. 5s. per foot
super. on squares not exceeding 6 feet.
702
BUILDERS' PRICES.
HARTLEY'S PATENT ROUGH PLATE GLASS, INCLUDING GLAZING.
At per foot super.
THICKNESS.


3
444
14
Under 3 ft. superficial
s. d. s. d. s. d. s.
0 8 0 10 0 111
d. s. d.
11 2
""
4
0 90 11 1
01
21 4
دو
5 6
0 10 0 111
11
31 5
""
6
"
011 1 0 1
2 1 41 6
""
010
1 01 11
31
51 7
""
12
1 01 11
41
61 8
ཝ
""
""
15
་
""
1 01 21
51
71 9
20
""
•
1 11
31
61
8 1 10
25
1
41
71
91 11
"
""
30
1
8 1 10 2 0
""
""
Quarries,
0 10 0 11
""
SUNDRIES.
Quarries stopped in old lead lights each
Squares under 7 by 5
7 by 5 and under 8 by 6
New lead lights with squares 6 in. by 4 in., per ft. super.
Do.
do. to 10 by 8
If with quarries add one fourth.
""
""
£ s. d.
. 0 0 11
0 11
002
003
0 0 5
""
""
9 by 7 and under 10 by 8
008
""
New leading old lights, per foot super.
0 0 10
""
Repairing and part leading do.
0 0 6
""
Do.
""
Casements pinned in each
Puttying windows or skylights, each side, per doz. squares
Cleaning windows per dozen squares common size
Moore's moveable glass louvre ventilators, zinc frames and
levers, brass rivets, 16 oz. sheet glass, rough edges, per foot
008
0 0 2
0 0 6
large
0 1 0
0 8 0
Do. 21 oz. sheet glass, rough edges
per foot
0 10 0
Do. patent plate, ground edges
0 16
0
""
Brass frames and levers, British plate, ground and polished edges 1 3 0
BUILDERS' PRICES.
703

THICKNESS.
1
To
$
114
inch. inch. inch. inch. | inch.
s.
d. s. d. s. d. s.
d. s. d.
Glass tiles, each
0 81
01
62
02 6
Do. slates, each 24 in. by 2 in.
•1 10 2
03 104
65 6
Do. do.
20
10
1 01
52
93
33 10
""
""
Do.
do.
16
8,,
0 10 1
32
32
02 2
42 9
SECT. XI.-Zinc Worker's Prices.
Malleable zinc laid with rolls, including labour to laying, complete.

GAUGE.
No. 10 11
12
13
14
15 16
14 16
18
21
24
26
30
Weight per foot superficial
· OZ.
Oz.
OZ.
Oz.
Oz.
Oz.
Oz.
Flats,
Verandahs,
Gutters,
""
s. d. s. d. s. d. s.
0 50 50 60
70 80 9
0 60 70 70 80 8100101
0 510 60 60 70 71081091
d. s.
60
d. s. d. s. d.
GUTTERS AND RAIN WATER PIPES.
At per foot run.

DIAMETER.
O. G.
Gutters.
Square O. G. Octagon
Octagon Shoes
Gutter. Pipes. Heads, Heads, Heads,
each. each.
each.
each.
s. d. s. d. s. d. S.
d. s.
d. s.
d. s. d.
2 inches
0 3 2 0
2 9
3
8 1 4
21
0 4 2 6 3 6
4 8 1 7
99
3
""
31
""
4
""
41
""
cr
""
0 30 5 0 5 2 9
040 510 5 3 3
0 40 610 6 3 10
0 50 70 7 4 2
0 510 710 7 4 10
4 3
5
4 2 0
4 9
5
9 2 4
5
3
6 3 2 8
6 0
6 9 210
6
6
7 3 3 2
704
BUILDERS' PRICES.

Chimney pipes, per foot
Malthouse cowls, each
Lobster back cowls, each
Smoke dispersers
10
DIAMETER.
11 12
inch. inch. inch.
s. d. s. d. s. d.
2 6 2 93 0
4 65 66 6
6 67 68 6
7 68 09 0
SUNDRIES.
48
s. d.
Perforated plates
Do. fitted into squares.
Metal skylights and fan lights
Do. large stout made
•
Ventilating tops according to size up to
Bell tubing, verandah caps and roles
Fan light and skylight bar
Zinc nails for slates
Do. tacks
Soft solder
Zinc worker
Labourer
Plumbic zinc,
·
per foot super. 0 0 41
""
""
•
0 0 6
026
030
1 5 0
per lb. 0 0 6
""
""
0
0 7
0 0 7
01 0
0 0 10
per day 06 0
040
per cwt. 1 14 0
GALVANIZED TINNED IRON,
Per Square.
Plain galvanized tinned iron for roofs or flats laid complete
with
No. 28 gauge
Do.
24
200
2 8 0
""
Do.
22
2 16 0
""
Straight corrugated .
24
2 12 0
""
Do.
22
""
2 18 0
""
Do.
20
3 5 0
""
Do.
18
"
3 18 0
Curved
24
""
2 15 0
"
Do.
22
""
3 3 0
""
Do.
""
20
3 15 0
""
Do.
18
""
""
Do.
16
4 0 0
4 18 0
BUILDERS' PRICES.
705
STEAM AND GAS FITTINGS EXCLUSIVE OF FIXING.



2
1호
​inch. inch.
11
20
1
inch. inch. inch. inch. inch. inch. inch.
1
1
Patent wrought iron
welded tubing, per ft. S
Ditto galvanized
""
Bends and springs,
wrought,
Bends and elbows,
T's equal & diminish-
ing outlets,
s. d. s. d.
s. d. s. d. s. d. s. d. s. d. s. d. s. d.
0 110 8 0 6 0 5 0 420 4 0 31
1 2 0 100 80 7
1 101 1 0 110 9
19 11
2 1
3 10 24
14
each
""
3 6
20
19 1 0 0 9 0 8
3 6
each
20
1910 0 9 0 7
""
4 3
1 4
10
38
Crosses, equal outlets,
Diminishing sockets or
nipples,caps or plugs,
& hexagon nuts, each)
Plain sockets,
""
Connecting pipes or
long screws, each S
0 6 0 510 5
0 8 07 06
0 60 50 4
0 60 50 4
2 9 2 6 1 9 1 6 1 2 1 0 0 9 0 9
0 10 09 07 06 05 04 03 03
0 80 70
0 7 0 6 0 5 0 4 0 3 0 210 2
2 4 2 2 1 8 1 2 0 100 9 0 8 0 7
Iron cocks screwed to 18 0 11 0
fit
Brass main cocks,
Flanges,
وو
5 0 3 0 2 6 2 0
0 10
0 9 0 7 0 6 0 5
1 4 0 100 8 0 7
9 0 5 6 4 6 3 0 2 6 2 0 1 9
each
""
144 0 18 0
13 0 8 0
1 10 17
29 20
1 3 1 0
1 4 1 0
each J
""
10 0 6 0
60 49 3 3 2 3 1 8 1 4
Stout tin pipe, per foot
Union joints for metal
pipes,
Strong do. for iron
3 light gas meters
5 do.
do.
10 do.
do.
SECT.-XII. Coppersmith's Prices.
Copper pipes for main water, with rings and tacks com-
plete, per foot run :—
48
s. d.
200
2 10 0
300
21 inch
3
""
31
. 0 1 2
018
0 19
8
""
4
27
Copper gutters semicircular, arwired, complete :
6 inches girt, per foot run
""
0
1 11
0 1 0
0 1 3
10
0 16
""
""
12
0 19
""
""
Tinned do., 2d. to 3d. extra. Fixing extra.
706
BUILDERS' PRICES.
£ s. d.
Spike and screw prepared with copper ties, 1s. to 1s. 6d. each.
Copper cistern heads, from 7s. 6d. to 12s. 6d.
12 oz. copper for flats and gutters, including seams, labour,
ties, and nails, per ft. super.
16 oz.
""
0 1 3
0 1 8
020
""
20 oz.
""
""
""
For verandahs, add per foot
0 0 2
COPPER PIPES.
Joints
Weight. Price. each.
lbs.
Washing copper
2 inch
21/
3
31
4
4/7/
5
""
""
""
""
22
""
Sheet copper
per foot run
s. d. s. d.
1
2 8 6 0
12 3 86 8
24 07 0
""
21
4
67 6
3
5
490
""
3/2
6
411 0
7
9 13 0
per lb.
""
1 0
1 8
SECT. XIII.-Wire Worker's Prices.
Iron wire for skylight
Strong ditto, inch mesh
Fly wire for safes
Copper do.
Brass trellis wire for bookcases
Octagon
do.
£ s. d.
per foot super.
0 1 1
01 4
""
0 20
""
0 39
""
0 3 3
""
0 3 3
0 5 6
Strong brass trellis for window guard frames
Fine wove wire for blinds
""
Do. in mahogany frames, French polished, and painted
Do. with lines and ornamental corners
Extra for copper wire
0 1 6
028
0 3 6
0 1 2
DILAPIDATIONS AND NUISANCES.
707
CHAPTER XXI.
ON DILAPIDATIONS AND NUISANCES.
SECT. I.-General Definitions.
THE rights of parties with respect to immoveable property
so closely border on each other, and the line of demarca-
tion between them is so indistinct, that one man, in the
fancied exercise of his right, is continually liable to en-
croach upon or disregard the right of another. No person,
however absolute his property in land, can put it to any
use he pleases; his right to use is restrained by the rights
of his neighbour; he is bound to take care that his man-
ner of using does not interfere with the inoffensive and
profitable occupation by his neighbour of his land. Ques-
tions as to the mode in which lands should be used may
arise, either between parties who have different rights to
the same land, and between whom there is a privity or
connection of interest as between landlord and tenant,
tenant for life and remainderman, or incumbent of a bene-
fice and his patron or successor, or between parties who
are strangers to each other in respect of the land used, as
the occupiers of two adjoining tenements. In cases where Distinction
there is a privity in respect of the land, every defect in lapidations &
the condition of the land or house is termed a dilapidation,
and the act or default of the tenant causing or permitting
such defect is termed waste: in cases where tenements,
from misuser or defect of repair, become injurious to a
stranger, the act or default of the party is termed a
nuisance. If a landlord complain that his tenant has
dilapidated the premises leased, he must prove that the
dilapidations in question are such as either the general
nature of the tenure or the particular stipulations of the lease
oblige the tenant to repair; but if the possessor of a house
complain that his neighbour has obstructed his lights or in-
jured his foundation, he must establish his right to the lights
or foundation injured, and by so doing he proves the obliga-
tion of the neighbour not to infringe those rights. The
between Di-
Nuisances.
708
DILAPIDATIONS AND NUISANCES.
Waste de-
fined.
Nuisances
defined,
Obligation
to repair; to
party complaining of a dilapidation must show an original
inherent qualification of the presumed absolute right of
the party possessed; the party complaining of a nuisance
has to prove either that the party complained of has ex-
ceeded his presumed absolute right, or has granted a por-
tion of it to him, and has derogated from that grant.
Waste may be defined as the act or default of one party,
having a right to use a tenement to the injury of another,
having a right to the same tenement.-Nuisances compre-
hend all nuisances which are the acts or defaults of the
possessors of tenements to the injury of strangers, or of
parties interested in the neighbouring tenements.
It is only where the right to use is limited in point of
what Estates duration, and the right of the successor certain to take
attached. effect, that there can be any obligation to repair; thus
tenant in fee simple and tenant in tail are under no obli-
gation in this respect. It is not essential that the right of
succession should be vested in any certain person, if there
be a right of succession which is certain to take effect;
thus, in the case of an ecclesiastical benefice, though the
successor be not known until after the incumbent's estate
is determined, he is under an obligation to repair, which
the successor may enforce against him or his represen-
tatives.
Nature of
Obligation to
repair.
The obligation to preserve from dilapidations, resulting
from the right to use, varies with the nature and extent of
that right; different tenants being bound to different re-
pairs, according to the nature of their estates, and the
covenants and conditions to which they agree. To suffer
Distinction dilapidations, is called Permissive Waste; and to do any
missive and act which will cause dilapidations, is, in legal language, to
Voluntary commit voluntary waste.
between Per-
Waste.
Alteration of
Tenement.
Division of
Waste.
The rule against Voluntary Waste includes an alteration
in the tenement, although it be not thereby rendered less
valuable, or even though the effect of the alteration be to
increase the value.
Hence there are three species of waste,-permissive,
voluntary, and malicious. Permissive waste is of five sorts:
first, the neglect to repair the necessary effects of time and
use; second, the neglect to repair the consequences of in-
evitable accident; third, the neglect to repair the external
or internal coverings of a building; fourth, the omission
to protect the fabric of the building from the consequences
DILAPIDATIONS AND NUISANCES.
709
Of
gation to re-
of dilapidations in the coverings; and, fifth, the omission
to prevent the wrongful act of a stranger. The obliga- of the Obli-
tions of parties with respect to dilapidations may be pair.
ranged into three classes.
Ecclesiastics.
Of the first class, are the obligation to repair, of the Obligation of
incumbent, of an ecclesiastical benefice, the obligation of
the public to repair churches, highways, bridges, and
sewers. The incumbent of a benefice receives the whole
profits of the tenements of which the benefice is endowed,
and is bound to supply the necessary effects of time and
use, and the consequences of inevitable accidents, upon the
buildings attached to the benefice.
repair
Highways,
The public have the sole right to use churches, high- of Public to
ways, bridges, and sewers, and they are all interested in Churches,
having them kept in perfect repair. They must, at all &c.
events, keep them in such a state of repair as is necessary
for the purposes for which they are required.
>
Churches and highways are repairable by the inhabit-
ants of the parish in which they are situate. The obliga-
tion is an obligation of the parishioners towards the public
generally, who all have an interest in the support of
churches and maintenance of highways; and there is also
an obligation of each individual parishioner towards the
general body, to contribute his proportion of the expense.
Bridges being maintained at a greater expense than Bridges.
ordinary highways, and not being situate in every parish,
it tends more to the equality of the burden that the
charge of repairing them should be borne by a larger
district: for this reason, the law has imposed the obliga-
tion of repairing bridges upon the inhabitants of the
county.
Sewers, which include sea walls, and every other erec- Sewers.
tion or device for the protection of lands from the inunda-
tions of the sea or rivers, or for draining off land-waters,
are not, like churches, highways, and bridges, beneficial
to the public generally, but only the proprietors of parti-
cular levels, liable to be damaged by inundations, or
requiring drainage. The inhabitants and proprietors of a
level alone are bound to repair the walls and banks by
which they are protected from floods, and the sewers by
which they are drained; and this is, in its nature, an
obligation of one proprietor towards the other proprietors,
who are subject to a common danger or inconvenience,
710
DILAPIDATIONS AND NUISANCES.
}
Obligation of
Tenants for
Life and
Years.
and rather private than public, though common to many
individuals.
Although the obligations to repair churches, highways,
bridges, and sewers, are equally well ascertained, there is
an observable difference as to the manner in which they
are sanctioned. It is the duty of churchwardens to see
that the church is repaired: but it is left to the parishioners
themselves to determine what repairs shall be done,
and the amount that shall be expended; if they deny
their obligation, the votes of the majority denying the
obligation to repair are considered as thrown away, and
the votes of the minority who admit the obligation, pre-
vail; and if they suffer the church to become dilapidated,
they may be proceeded against by ecclesiastical censures.
At common law, the repairs to be done to highways and
bridges, and the amount to be expended, were equally
under the control of the inhabitants of the parish or
county; though, if they neglected to do sufficient repairs,
they were and still are liable to an indictment. By
statute, the repairs of highways are subject to the control
of a surveyor, and those of bridges to the justices of the
peace. The maintenance of sewers and sea walls was
never voluntary, but was under the direction of commis-
sioners of the Crown.
The second class includes the obligation on all particular
tenants, whose estate is less than an estate of inheritance,
except ecclesiastical incumbents. The law relating to the
general obligation of these tenants to repair is called the
Law of Waste; the law relating to the obligation of eccle-
siastics is called the Law of Dilapidations.
At common law only those tenants whose estates were
created by law were liable for permissive waste in the
absence of express stipulation. If the estate was created
by the party, and there was no condition against waste,
or covenant to repair, it was considered that it was not
intended to place the tenant under any obligation to
repair, and the case was presumed to be of the third class.
The statute of Marlbridge has altered this presumption,
and now tenants for life and for years, whether their
estates are created by act of law or act of the party, are
equally liable for waste, as well permissive as voluntary,
unless it is expressly provided that they shall be without
impeachment of waste.
:
DILAPIDATIONS AND NUISANCES.
711
In these cases, it being presumed that an equivalent
for the occupation is given to the grantor, the tenants are
not bound to repair the necessary and inevitable effects of
time and use. Their obligation is to preserve the tene-
ments from premature decay by reason of exposure to the
weather, and for this purpose to repair the external and
internal coverings of the fabric of the buildings. They
are liable for permissive waste of the fourth sort.
Mortgagees, who, although they have at law an absolute Mortgagees.
estate in the tenements mortgaged, are in equity deemed
to hold them as a pledge merely, are in equity under a
similar obligation to the mortgagors. Of course they are
entitled to be allowed the sums expended in necessary
repairs out of the profits of the premises.
by Covenant.
The obligation of a tenant for life or years may be ex- Obligation
tended by express covenant. Such covenant is construed
with reference to the common law obligation, and unless
an intention to the contrary is manifest, does not render
the tenant liable to repair the necessary effect of time and
use, or the inevitable decay of the fabric of the building.
In ordinary cases the obligation is against permissive
waste of the third sort. They are also liable to repair
dilapidations caused by inevitable accident.
Strangers.
All tenants who are liable for permissive waste are re- Waste by
sponsible for waste committed by strangers, which it is
presumed they are able to withstand, and against whom
they have a remedy. If the strangers are the Queen's
enemies, or felons, their acts of waste are in the nature of
inevitable accidents, for which tenants for life and years,
not under covenant to repair, are not liable.
without Im-
Waste, and
Will.
In the third class may be ranged-tenants without im- Tenants
peachment of waste and tenants at will. Neither of these peachment of
are liable for permissive waste,—the tenant without im- Tenants at
peachment by reason of the expressed intention of the
grantor of the estate; and the tenant at will by reason of
the infirmity of his estate. An estate at will is, in contem-
plation of law, of no value; and therefore whatever services
such tenant renders to his landlord, and it may be presumed
that he renders some, must be more than an equivalent
for his estate.
All tenants, except tenants without impeachment of
waste are liable for voluntary waste; and tenants without
impeachment of waste are liable in equity, but not at law,
712
DILAPIDATIONS AND NUISANCES.
Malicious
Waste.
Tenants in
Common.
Subjects of
Dilapidations
Gardens.
Lands.
for malicious waste. Malicious waste consists in pulling
down the mansion house, or felling timber planted for the
ornament or protection of the mansion-house. The Court
of Chancery considers that it was not the intention of the
grantor to confer the power of destroying such things.
From this waste being solely cognizable in Courts of
Equity, it is called Equitable Waste.
Questions respecting dilapidations occasionally arise
between persons interested jointly or in common in tene-
ments. In such cases there is no obligation by one to the
other to repair any particular dilapidations. One tenant
has a remedy against his co-tenant if he commit voluntary
waste, and may compel him to contribute towards the
necessary repairs of houses and mills.
The general obligation of neighbours as to party walls
and fences dividing their premises is the same as that of
tenants in common, if they are tenants in common of the
wall or fence. One may be, by prescription or contract,
bound to repair a fence so as to prevent cattle in his land
from straying into his neighbour's.
The subjects of dilapidations are houses and other arti-
ficial erections and ways, gardens, land, and trees. Things
made by art demand the exercise of art to preserve them
from decay. It is only as to such things that the law of
permissive waste is applicable. With respect to gardens,
lands, and trees, tenants are by the general law merely
prohibited from committing voluntary waste. But where
lands are let for the purpose of cultivation, as they are
almost universally to tenants for years, they are bound to
cultivate them in a husbandlike manner, and according to
the custom of the country; that is, in the manner in which
farm-lands are usually cultivated in the part of the country
in which the lands leased are situate.
It is voluntary waste in gardens to cut down
the fruit trees, or destroy or remove the shrubs and
plants growing there, except for the purpose of culti-
vation.
It is voluntary waste in land to alter its nature so as to
diminish its value or affect the evidence of title; an altera-
tion in the course of good husbandry, which does not either
diminish the value of the land, or impair the evidence of
title, is not waste. It is also waste to take the substance
of the land, as clay or minerals, except where open
DILAPIDATIONS AND NUISANCES.
713
mines or quarries are leased, in which case there is an
implied authority to continue working them.
Waste as to trees consists in felling timber trees, that Timber.
is, trees which contain, or when mature will contain, wood
useful for building purposes. The property in such trees
belongs to the owner of the inheritance, and in the case
of ecclesiastical property to the Church. No particular
tenant can do any act to destroy or injure their growth, or
fell them, except for the benefit of the inheritance, as to
repair buildings and fences standing on the land demised.
It is not waste to cut down trees not timber, in such a
manner that they will grow again, unless they have been
planted for some particular purpose implying permanence,
such as for the ornament or shelter of a house, or for the
support of a bank or hedge, or in a field for the shade of
cattle. But it is waste to grub up or destroy any trees,
whether timber or not.
There is an important exception to the law against Fixtures.
voluntary waste in the instance of fixtures. By this ex-
ception a particular tenant, who has made erections or
fixed machinery to premises for the purposes of a manu-
facture or trade, or has added to a house any particular
article of ornament or domestic convenience, which may
be removed without injuring the house, is entitled to re-
move the things so fixed. From the occasion and purpose
of the annexation, an authority from the owner of the in-
heritance to fix and remove is inferred, and an intention
of the particular tenant to abandon his property in the
fixture, which would in ordinary cases be presumed, is
negatived.
Neighbour's
A nuisance is an act or neglect of a man on his own Nuisances to
land, the consequences of which extend beyond his pos- Land;
sessions, and encroach upon the possessions or rights of his
neighbour. The general law as to the limits of possessions
is, that he to whom the soil belongs has a right to all the
space perpendicularly above and below; and therefore, so
long as the effects of an act or neglect are confined within
those limits, there is, generally speaking, no nuisance.
But if, in using our land, we encroach upon or disturb our
neighbour in the enjoyment of any part of the space above
or below his land, such act is a nuisance; as if we build
so as to overhang our neighbour's land, and cause the
water from the eaves of our building to fall upon his
2 W
714
DILAPIDATIONS BY
To Easement
Public
Nuisance.
Parties liable
for Waste;
land, or if we carry on a noisome and offensive trade,
so as to corrupt the air over the adjoining land with
noxious effluvia, or disturb it with deafening noises, or
dig under the foundation of a house standing thereon.
It would manifestly interfere with the conveniences
of society, if every noise, or every smell, which the deli-
cate perceptions of a neighbour considered disagreeable,
amounted to a nuisance; the law, therefore, modifies itself
to the exigencies of mankind, and determines that the
noise or stench must be so considerable in degree, and so
long continued, as to destroy the comfort of a person of
ordinary sensibility in the occupation of his property.
Our neighbour may by grant, or by long enjoyment,
which causes a grant to be presumed, acquire an easement
over our land, for the more convenient or profitable occu-
pation of his own, by which his rights spread themselves
into our possessions, and become, as it were, interfused
with ours, and operate to control us in the use of our land;
in such case it is a nuisance to obstruct his enjoyment of
such easement, though we do not encroach upon his terri-
tory: thus, if we give him permission to build upon the
verge of his land, and to open windows looking over our
land, he acquires right to our land for the support of his
house, and to the air over our land for light to his house,
which rights are called easements; and we cannot dig into
our land so as to weaken the foundation of his house, or
build so as to darken his windows, though, if he had ac-
quired no right to those easements, either by grant or
prescription, we might.
If the tenement be used so as to prejudice the whole
neighbourhood, or to injure a public right of way, it is a
public nuisance; and the parties causing it are punishable
by indictment, at the suit of the Queen, and not by action
at the suit of an individual, unless he has sustained some
particular injury over and above that inconvenience
which he has suffered in common with the rest of the
public.
SECT. II.—Dilapidations by Tenants for Life and Years.
By the common law, only tenant in dower, tenant
Tenant by by the curtesy, and guardian, were punishable for waste,
because their estates being created by the law, the law
annexed to them the condition that they should neither do
the curtesy,
&c.
TENANTS FOR LIFE AND YEARS.
715
Marlbridge.
nor permit waste; but a tenant for life or for years, whose
estate was created by act of the party, was not liable for
waste, (that is, for permissive waste,) unless the grantor so
stipulated; the parties being at liberty to contract as to
the manner in which the tenements should be used: the
law did not imply a condition against waste in cases where
they did not so provide. This was remedied by the statute Statute of
of Marlbridge, which provides "that farmers during their
terms shall not make waste or exile of houses, woods, or
men, or of any thing belonging to the tenements that they
have to farm, without special license had by writing of
covenant, making mention that they may do it, which
thing if they do and thereof be convict, they shall yield
full damage, and be punished by amerciament grievously."
The statute of Glocester further enacts, "that a man from of Glocester
henceforth shall have a writ of waste in the Chancery
against him that holdeth by law of England or otherwise
for term of life or for term of years, or a woman in dower;
and he who shall be attainted of waste shall lose the thing
that he hath wasted, and moreover shall recompense thrice
so much as the waste shall be taxed at.'
""
Life and
These statutes extend to every description of tenant for Tenant for
life or years, whether created by grant or devise, to a party Years.
to whom lands are granted for an uncertain period to a
tenant from year to year, for a year, or half a year.
Although a tenant in tail after possibility of issue extinct
is not punishable for waste, yet if he grant over his estate,
his assignee is but tenant for life, and liable therefore.
Every person in whom the estate for life or years becomes
vested as assignee, executor, or occupant of an estate
per auter vie, takes it subject to the condition against
waste.
Soccage.
Will.
A guardian in soccage is liable for waste, voluntary Guardian in
or permissive, but not for waste done by a stranger.
Tenants at will (that is, those who hold merely at Tenant at
the will of the lessor, and whose estate may be determined
at any time, not those who hold under yearly tenancies
determinable by notice, and who are sometimes improperly
termed tenants at will,) are not included in the statute of
Marlbridge or Glocester, and are not bound to do any
repairs; but still they cannot lawfully commit voluntary
waste.
The estate of tenant at will is so infirm, that it is
716
DILAPIDATIONS BY
Liability of
Tenants for
Waste.
reasonable that he should not be bound to do any repairs,
since, if he expend money upon the tenements, his lessor
may immediately determine his interest, and prevent him
from deriving any advantage from such outlay; and if the
tenements are falling into decay, it is always in the power
of the lessor to enter and take measures for their
vation.
preser-
Waste is of two sorts, voluntary and permissive.
permissive According to the old cases, every tenant for life or years
within the statute of Glocester is liable for waste in the
same degree; but in modern times doubts have been en-
tertained, though it would seem without any sufficient
foundation, whether a tenant from year to year, or a
tenant for years, not under covenant, is liable for permis-
sive waste. No distinction can in reason be made between
a tenant for life and a tenant for a year, or for a part of
year. Each is a farmer within the statute of Marlbridge
and a tenant within the statute of Glocester, and each is
made liable by the same words; and there is no provision
that one shall be liable for one sort of waste and one for
another.
Waste in
Buildings.
The statute of Marlbridge prohibits waste or exile
Houses and of houses, woods, or men, or any thing belonging to the
tenements had to farm. These words are large enough to
include every thing that is part of the tenements demised.
The books enumerate buildings, gardens, lands, and woods,
as the subjects of waste. It is proposed to state the law
applicable to each of these subjects separately.
First,
And first, of waste in houses and buildings. It has
Voluntary. been expressly decided that the law of waste extends not
only to dwelling-houses, but to every description of build-
ing, such as outhouses and barns, The word houses in
the statute includes every description of building: but an
incomplete building, such as a pale, a post, or an uncov-
ered wall (which probably means erections not forming
part of a building or a fence), are not subject to the law
of waste.
Voluntary waste is a wilful act committed by the
tenant or by his orders, by which the tenements are de-
stroyed, injured, or altered: it is voluntary waste in a
house to prostrate it, or to destroy or remove any part of
it, as a post, a door, a window, a furnace, a bench, or
TENANTS. FOR LIFE AND YEARS.
717
wainscot fixed to the house. The rule against voluntary
waste extends to additions made to the house by the
tenant himself: thus it has been decided that " glass
annexed to the windows by nails or in any other manner
by the lessor or the lessee cannot be removed by the lessee,
for without glass it is no perfect house. Peradventure
great part of the costs of the house consists of glass,
which if it be open to tempests and rain, waste and putre-
faction of the timber would follow. Wainscot also is
parcel of the house, and it makes no difference whether
fixed by great nails or little nails, or by screws or irons
put through posts or walls (as have been invented of late
time); for if wainscot is by any of the said ways, or by
any other, fastened to the posts or walls of the house the
lessee cannot remove it."
Things merely placed by the tenant on the premises,
but not fixed, however bulky such things may be, are not
within the rule as to voluntary waste: thus a barn placed
upon pattens and blocks of timber lying upon the ground,
but not fixed in or to the ground, may be removed; so if
it rest upon blocks of stone which are fixed in the ground,
but not fastened to the blocks by mortar or otherwise. A
mill removable at pleasure, which was an octagonal wooden
building, raised on a casement of brickwork and anchored
to the ground by shores and land-ties, part of the shores
and the whole of the land ties being one foot under the
surface of the earth, was found by the jury not to be a
fixture. So distillers' vats supported upon brickwork, but
not fastened to the ground, are goods and chattels, and no
part of the premises on which they are placed. And
where certain caps and steps of timber were fixed by a
tenant to a building, and he placed in these caps and steps,
jibs which he fastened there by pins above and below, the
jibs might be taken out of the caps or steps without in-
juring either them or the building; the jibs were held to
be the personal property of the tenant, and no part of the
building, so that he did not lose his right to them by
leaving them there after the expiration of his term.
the rule
voluntary
The right to remove fixtures is an exception to the Exception to
rule against voluntary waste. By this exception a tenant against
for life or years, who during his tenancy has fixed certain waste.
chattels to the premises for the purposes of his trade or as
matters of ornament or furniture, and which can be re-
718
DILAPIDATIONS BY
#
Fixtures.
Tenant may
remove
Buildings
moved without injury to the premises, is entitled to remove
them, and is not guilty of waste in so doing. Although
the cases of tenant for life and of tenant for years are
separately treated of in the books on this subject, there is
no authority for saying that they are not equally entitled to
fixtures. And, as they are made liable for waste without
distinction by the statutes of Marlbridge and Glocester,
it may be inferred that the exception extends in the same
degree to both.
There is distinction between chattels which are substan-
tially of the same character before they are fixed, when
fixed, and after removal, such as engines, pumps, and
grates, which are engines, pumps, and grates, whether
chattels or fixtures; and things the character of which is
altered by their annexation to the land, such as buildings
which, when fixed, exist as buildings, and before and after
severance exist merely as materials, bricks and mortar.
Things of the first class may be removed, whether fixed
for the purpose of trade or of ornament, or domestic con-
venience. Buildings, it seems, may be removed if erected
for the purpose of trade, but agricultural buildings are
not within the same rule as trade buildings.
and Fixtures cc
erected by
him on
Farms,
lord elect to
take to them.
The law as to farm buildings has been recently modified
by the act of the 14th & 15th Vic., c. 25, s. 3, whereby it is
enacted “That if any tenant of a Farm or Lands shall
"after the passing of this Act, with the Consent in
Writing of the Landlord for the Time being, at his own
"Cost and Expense, erect any Farm-building, either de-
unless Land-tached or otherwise, or put up any other Building,
Engine, or Machinery, either for Agricultural Purposes
"or for the Purposes of Trade and Agriculture, (which
“shall not have been erected or put up in pursuance of
"some Obligation in that Behalf,) then all such Buildings,
Engines, and Machinery, shall be the Property of the
"Tenant, and shall be removable by him, notwithstanding
"the same may consist of separate Buildings, or that the
same or any Part thereof may be built in or perma-
nently fixed to the Soil, so as the Tenant making any
"such Removal do not in anywise injure the Land or
Buildings belonging to the Landlord, or otherwise do
"put the same in like Plight and Condition, or as good
Plight and Condition, as the same were in before the
"Erection of any thing so removed: Provided, neverthe-
66
66
TENANTS FOR LIFE AND YEARS.
719
66
"less, that no Tenant shall, under the Provision last
aforesaid, be entitled to remove any such Matter or
Thing as aforesaid without first giving to the Landlord
"or his Agent One Month's previous Notice in Writing
"of his Intention so to do; and thereupon it shall be law-
"ful for the Landlord, or his Agent on his Authority, to
"elect to purchase the Matters and Things so proposed to
“be removed, or any of them, and the Right to remove
"the same shall thereby cease, and the same shall belong
“to the Landlord; and the Value thereof shall be ascer-
"tained and determined by Two Referees, One to be
"chosen by each Party, or by an Umpire to be named by
"such Referees, and shall be paid or allowed in account
"by the Landlord who shall have so elected to purchase
"the same.
Things coming within the building class which are an-
nexed for the purpose of ornament or convenience, it may
be concluded, cannot be removed, such as an out-house.
The right of nurserymen to remove green-houses and Nursery-
hot-houses as trade buildings is left in doubt, it being af Fixtures.
firmed by Lord Kenyon, and doubted, if not denied, by
Lord Ellenborough. On the one hand, it may be said,
that their case resembles those relating to mining fixtures.
It is at least a mixed case between occupying land and
carrying on a trade. If any distinction can be made, it is
in favour of the gardener, green-houses and hot-houses
being erected for rearing of exotics, which are raised by
the gardener's skill, and have not necessarily any connec-
tion with the land demised. On the other hand, it must
be borne in mind that the mining cases were not cases of
simple buildings, but of machinery and of buildings merely
necessary to the machinery, and that green-houses and
hot-houses have a peculiar adaption to the nursery ground
demised; and it may be presumed were intended to form
part of the freehold, unless otherwise agreed.
In consequence of the exception as to fixtures, they have
become a peculiar description of property, and there are
many rules of law relating to them as such, which are not
within the scope of this treatise. It should be noted,
however, that the tenant must remove them during his
term, and that if he omit to do so, they become the pro-
perty of the landlord.
An alteration of the buildings demised is wilful waste Alterations.
720
DILAPIDATIONS BY
Improve-
ments.
Permissive
Waste in
if it be injurious to the inheritance, either by diminishing
the value of the estate, increasing the burden upon it, or
impairing the evidence of title.
There are conflicting authorities as to whether it is
waste to build a new house where none was before. The
conflict is as to the application of the rule of law, not as
to the rule itself. It is not waste simply to alter, but it is
waste to alter to the injury of the inheritance. Some
think that to build a new house is necessarily a benefit to
the lessor, others that it is not. The latter seems to be the
better and prevailing opinion.
the burdens of the lessor by the charge of its repair; and
the act of building a house may be used as evidence that
the builder is the absolute owner of the land.
A new house may increase
Although a landlord may complain of a new erection
as voluntary waste, he may waive this right, and insist
upon the tenant keeping it in repair. But if the lessor,
without the consent of the lessee, build a cottage on the
premises during the lease, the lessee is not liable for waste,
either voluntary or permissive, to such cottage.
If a tenant for life or years choose to alter or im-
prove tenements by erecting buildings, or rebuilding, or
doing extensive repairs to those already erected, whereby
their value is increased, he has no claim at law or in equity
against the remainderman or landlord for the value of the
improvements.
Permissive waste in buildings is the injury happen-
Buildings. ing to them during the term by the permission or neglect
of the tenant; that is, an injury which the tenant might
have prevented, by taking care of the building, and doing
precautionary repairs.
Roof.
The obligation to preserve the tenements from waste
compels the tenant to keep the walls and timbers of the
house from exposure, and renders him liable for any injury
the fabric or skeleton of the house sustains for want of
such repairs as were necessary to preserve it from exposure.
The tenant is bound to keep the external coverings, the
roof, and other outworks, of the building in repair, and to
renew them when they decay, so as to preserve the tim-
bers, walls, and skeleton from premature decay.
obligation to do such repairs is not absolute, but relative,
with reference to the condition of the main timbers and
walls of the house in consequence of his neglect to do
His
TENANTS FOR LIFE AND YEARS.
721
them. Thus, suffering houses to be uncovered, whereby
the
spars, rafters, planchers, or other timbers become rot-
ten, is waste; but barely suffering them to be uncovered
without rotting the timber is not waste. Where a tenant
permitted the standings before the door of his house to be
uncovered and out of repair, whereby the principal timbers
became decayed and in danger of falling, it was held to be
waste.
Glass is an external covering which the tenant is bound Glass.
to keep entire; and if in consequence of the windows being
broken, the interior of the house is injured, he is liable
for waste.
Outer doors must for the same reason be kept in repair Outer Doors.
and entire.
Coverings.
It is also permissive waste if the fabric of the house is Internal
injured by reason of the tenant not keeping in repair the
internal coverings of the walls.
Plastering.
He is also bound to keep filth and water out of the In Drains,
house by repairing the groundsills and drains.
and not
Cleansing.
Repairs.
The repairs which a tenant for life or years is bound to Tenantable
do are usually called tenantable repairs. They extend
only to the finishing, and not to any part of the skeleton
of the house; they include the work of the joiner, plas-
terer, and glazier, but not that of the bricklayer and car-
penter. Stopping out wind and weather, as mending tiles
and chimneys, are included in tenantable repairs, because
such repairs tend to preserve the fabric of the house from
premature decay. They are, therefore, intermediate be-
tween substantial and ornamental repairs; bricklayers' and
carpenters' work being, generally speaking, substantial
repairs; and painting, papering, and whitewashing, orna-
mental repairs.
the House
If the house is ruinous at the time of the lease, that is, Condition of
if the timbers and walls are decayed so that it falls by when leased.
reason of its age and bad condition, and not by the default
of the lessee, it is not waste. If the timbers are standing,
but the rafters are gone, and it falls during the lease, the
tenant is not liable, because he cannot cover the house
without rafters, and he is not bound to find them. On the
point whether if a house is simply uncovered at the time
of the lease, the tenant is bound to cover it, so as to be
responsible for any dilapidations that may ensue by reason
of the want of covering, the authorities are conflicting.
722
DILAPIDATIONS BY
Waste by
Fire.
Waste by
Strangers.
By Under-
Tenant.
Inevitable
Accidents.
Waste by fire, when the fire was caused by the negli-
gence of the tenant, and perhaps when the fire happened
accidentally and without negligence, was accounted per-
missive waste under the statutes; and, according to a
recent decision, waste by fire, occasioned by negligence,
is permissive waste, but the law on this point is not in a
satisfactory state.
If a tenant suffer a stranger to do waste, he shall be
answerable; for it is presumed in law that the tenant may
withstand it, et qui non obstat quod obstare potest, facere
videtur. Another reason given for making the tenant
liable for waste done by a stranger is, that he has a remedy
against the stranger.
Being liable for waste by a stranger, of course the
tenant is liable for waste by his under-lessee, to whom he
has given the opportunity of committing such waste; and
a guardian is liable for waste, by those with whom he is
connected by privity of estate, as where an abbot was
guardian, and one of his monks committed waste; and
where joint tenants are guardians, and one of them does
waste, both are liable.
For dilapidations occurring by inevitable accident a
tenant is not answerable, as where a house is destroyed
by the king's enemies, who are not amenable to the law,
or by superhuman agency, as by lightning or tempest.
And where a house has been blown down by tempest, it
is not waste for the lessee to sell the materials, because
they have become chattels. But if a part of the house
which the tenant is bound to repair is destroyed or injured
by tempest, he is bound to restore it; as if a house is un-
covered by tempest, but the timber is left standing, and
it afterwards fall for want of covering, the tenant is liable
for waste and if a tempest take away a small part of the
thatch, the tenant is bound to repair it; and if he neglect
to do so, and in consequence the house is thrown down by
tempest, he is liable for waste.
Where lands are flooded in consequence of the decay of
a wall of the sea, or the banks of rivers, it is waste in the
tenant; but if the lands be damaged by the sudden rage
and violence of the sea, or by a sudden flood of the river,
it is not waste; and it has been held, that if the banks of
the Trent be unrepaired, it is waste, because the Trent is
TENANTS FOR LIFE AND YEARS.
723
not so violent, but that the lessee, by his policy and in-
dustry, may well enough preserve the banks.
repair;
A covenant to repair is negative as well as positive in Covenant to
its obligation; and the tenant is thereby bound as well not Alterations.
to do an act amounting to voluntary waste as to repair
dilapidations. Thus an alteration of the demised premises
is a breach of a covenant to repair: for example, breaking
a doorway through the house demised into the adjoining
house. So the act of pulling down a brick wall, which
divided one part of the demised premises from another,
was held to be a breach of a covenant to repair and uphold
the brick walls belonging to the demised premises.
But where the covenant was, that the tenant should
leave the premises in as good plight as he found them, and
he pulled down houses, the lessor it was held could have
no action until the end of the term, for the covenant had
relation thereunto; but that if he had wasted the woods,
covenant would have lien, because it would be impossible
to repair such waste.
And if from the language of the lease it appears that
the parties contemplated alterations being made, an al-
teration is no breach of the covenant to repair. Thus,
where the covenant was to repair the demised premises,
together with such buildings, improvements, and additions,
as at any time during the term should be erected, set up,
or made by the tenant, it was decided that the tenant had
not broken the covenant by converting the windows on the
ground floor into shop windows, and stopping up an inter-
nal door in one place, and opening one in another.
Tear.
A covenant to repair obliges the lessee at all events to Wear and
repair and restore those parts of the building which fall
away, wear out, or are destroyed during the term. He is
not bound to repair parts which are merely in progress of
decay. His covenant is to repair all accidents, and to take
all reasonable precautions against the fabric of the building
being exposed to the weather, or becoming more depre-
ciated than it necessarily would from time and ordinary use.
The covenant must be construed with reference to the
age and general condition of the building at the commence-
ment of the term. The covenant to repair is not a cove-
nant to improve, or to keep and yield up the building
demised in as perfect a state as when demised, but to keep
it, as nearly as possible, in the same state as when demised,
DILAPIDATIONS BY
724
}
and to do such repairs as are adapted to the nature of the
building.
The obligation imposed by the covenant to repair differs
from the common law obligation against permissive waste
in this. The common law obligation is merely to guard
the fabric of the building from decay, and is not infringed
by an external dilapidation unless the fabric is injured in
consequence. By the covenant the tenant is uncondi-
tionally bound to repair all dilapidations, whether the
fabric of the building is injured or not. Injuries to the
building caused by inevitable accident are excepted from
the common law obligation, but not from the obligation of
a general covenant.
The obligation of a covenant differs from the obligation
of an ecclesiastic in this. The ecclesiastic is bound to re-
pair buildings and parts of buildings about to fall away
(proximo casuras)—those parts which are nearly but not
quite worn out. The covenantor is only bound to repair
those parts which are actually fallen away and worn out.
If the house falls merely from natural decay, and with-
House falls out default of the tenant, it would seem that he is not
from Decay. bound to rebuild it under an ordinary covenant to repair.
Under a general covenant to repair, the tenant is bound
to keep in repair the inside painting, and this, although he
expressly covenants to paint the outside.
Obligation to
rebuild when
Painting.
Materials.
Accidents.
Where any part has fallen away, the tenant is not bound
to replace it with new materials, but only with materials
of the same value and in the same condition as those defi-
cient ought to have been, had they only been subject to
ordinary decay and wear, except from accident or exposure
to the weather. In determining this, reference must be
had to the age of the building at the time of the lease
granted, and to the duration of the lease; and so much
ought to be deducted from the cost of new materials as it
may be supposed they would be depreciated in value by
ordinary wear during the period the materials to be sup-
plied have formed part of the building. Mr. Woods thinks,
that in hardly any case could the landlord require more
than three-fourths of the new value, and none would occur
in which one-fourth ought not fairly to be demanded.
On a covenant to repair, the covenantor is bound to
repair at all events, and is not excused from repairing de-
fects caused by inevitable accident. An inevitable acci-
TENANTS FOR LIFE. AND YEARS.
725
dent does not render it impossible to perform the covenant.
The covenant is performed by repairing the consequences
of the accident. Where the law infers from circumstances
such obligation as is reasonable, there it limits the obliga-
tion with those qualifications and exceptions, which under
the circumstances are reasonable. It presumes that con-
tract to have been entered into which is just and equal to
both parties. But where the parties have themselves ex-
pressed the contract which they conceive to be just, there
all the law has to do is to apply it to their acts and enforce
its performance; for although it may, with much probability,
be conjectured that a certain contingency was not foreseen,
yet it might have been foreseen, and nothing said about it,
because not intended to be excepted from the generality of
the obligation. For these reasons, where there is a gene-
ral covenant to repair, and the buildings are destroyed by
accidental fire, the lessee is bound to rebuild. It is no
answer to a covenant to repair a bridge, that it was de-
stroyed by an extrordinary flood, such as the covenantor
could not resist, and without default on his part. But
when a house is destroyed by inevitable accident, the lessee
performs his covenant to repair if he rebuild it within a
reasonable time; the covenant to repair not meaning that
the house shall never be out of repair, but that the lessee
will restore all dilapidations which happen during the
term.
dence of
repair and
The general obligation of the covenant to repair is not Indepen-
limited by a covenant to insure in a specific sum. If such Covenants to
sum be insufficient to rebuild the premises, he must supply insure.
the deficiency.
Performance
If the dilapidations are caused by the act or neglect of Excuse from
the landlord himself, or if he renders it impossible for the by Act of
tenant to perform the covenant, the breach of covenant is
excused.
But an act of the lessor which merely impedes but does
not wholly prevent the lessee from performing his cove-
nant, cannot be alleged by him as an excuse for a breach.
And so it is no answer to an action on a covenant for
not repairing and cultivating, that the plaintiff entered on
parcel of the demised premises, and ejected the defendant
therefrom.
Lessor.
And a covenant cannot be discharged by a parol license By License
of the covenantee. If the landlord, by word of mouth, or
of Lessor.
726
DILAPIDATIONS BY
Indepen-
dence of
Covenants to
pay Rent.
pay Rent
ses are
burned.
writing (not being a deed), authorize the lessee to do an
act which is a breach of covenant, the lessee is liable to an
action of covenant notwithstanding.
And the tenant is not excused from the performance of
repair and to a covenant to pay rent by the premises becoming unten-
antable by inevitable accident, as if the house demised is
Obligation to burned down, or land is surrounded by water, or the
when Premi-tenant is evicted by a foreign enemy. And where the
lease contains covenants to pay rent and to repair, and in
the covenant to repair the case of the premises being de-
stroyed by fire is excepted, the tenant must pay the rent
accruing after the premises have been destroyed by fire,
and before they are rebuilt; and he must do so although it
be assumed that it is the duty of the lessor to rebuild, the
covenants being distinct, and he having a sufficient remedy
by action against the lessor for not rebuilding. It has
since been decided that such an exception does not bind
the landlord to rebuild.
Obligation to
pay Rent
ses untenant-
able in
Tenancies
And when premises demised by verbal or written agree-
when Premi- ment, from year to year, or for a shorter time, are destroyed
by fire, in which case the tenant is not bound to rebuild,
without the destruction of the building does not determine the
tenancy, and the tenant still continues liable for the rent.
Covenant.
Covenant to
improve.
It is now settled, notwithstanding some decisions to the
contrary, that the tenant has no right to quit the premises
because they are at the commencement of the tenancy un-
tenantable from dilapidations, which ought to have been
repaired by the landlord, or become so during its conti-
nuance, unless such power is expressly reserved, and ex-
cept, perhaps, in the case of a furnished house, or furnished
apartments, which are taken merely for the purpose of
temporary occupation. It is not a condition implied on the
demise of real property, that it shall be fit for the purpose
for which it is demised, or shall continue fit for such pur-
pose. In this respect the modern and the ancient autho-
rities agree.
Sometimes leases contain covenants to alter and im-
prove: where they do, such covenants must be strictly
performed, and they are not satisfied by substantial and
thorough repairs.
Again, a covenant to make a shop front is not performed
by merely enlarging windows, though such enlargement be
sufficient for the purposes of the tenant's trade; and in
TENANTS FOR LIFE AND YEARS.
727
matters of taste, as to the style and manner in which a
house is covenanted to be rebuilt, equity will enforce a
specific performance; for instance, a covenant to make the
elevation of a house correspond with the elevation of the
adjoining houses.
insure.
Another covenant relating to dilapidations is the cove- Covenant to
nant to insure. The object of this covenant is to compel
the tenant to procure a Joint Stock Insurance Company to
become responsible for the repair of dilapidations by fire.
The covenant to insure binds the tenant to effect an in-
surance directly the covenant is made.
The insurance must be regularly continued without in-
termission, and must be strictly according to the covenant.
By the Building Act of 14 Geo. III., Insurance Offices
are required, on the request of any persons interested in
houses or buildings destroyed or damaged by fire, to lay
out the insurance money in rebuilding or repairing the
premises. The Act is confined to London and West-
minster, and the Bills of Mortality.
In ejectment on the ground that the lease has been for-
feited by not insuring, it lies upon the landlord to prove
that the premises were not insured. The tenant refusing
the landlord information as to insurance, or refusing to
show a policy upon demand, is no evidence of non-insur-
ance. In an action on the covenant it seems that the
tenant would have to prove performance.
In an action for breach of this covenant the damages are
not necessarily nominal. Where the landlord has effected
an insurance on the tenant's default, though such act is not
the necessary consequence of such default, and therefore
the landlord is not as a matter of law entitled to recover
the premiums paid, the jury may, if they please, award the
amount of such premiums, by way of damages, as a sum
reasonably expended to relieve himself from the anxiety
incident to the premises being uninsured. But where the
landlord was a leaseholder under a covenant to insure, and
he demised to the tenant under a similar covenant, the
tenant failed to insure, and the superior landlord brought
ejectment, and recovered, it was held by the Court of
Common Pleas that the sub-landlord was only entitled to
nominal damages in an action against his tenant for breach
of his covenant. He was not entitled to the value of his
estate in the premises, because that had been forfeited by
728
DILAPIDATIONS BY
Extent of
Covenants to
repair.
As to Things.
Persons.
the breach of his own covenant, and not by the breach of
the tenant's.
Besides the degree of care which the covenant to repair
imposes, there are three other points to be attended to in
the construction of such covenants:
On the first point, a general covenant to keep and leave
in repair the premises demised will extend to every part
thereof, and every thing attached thereto, which can be
considered as part of the freehold, and not removable by
the lessee as a tenant's fixture.
The tenant is bound to leave a building erected by him-
self in substantial repair, although the erection was origi-
nally of defective construction.
Extension to On the second point, all covenants relating to the man-
ner of using the premises during the term, as to repair
houses, to cultivate lands, run with the land, and are bind-
ing not only on the lessee, but also on the assignee of his
interest, though he be not expressly named. And such
covenants affect all and each part of the land demised; and
therefore, if the lessee assign his interest in part of the
land, the assignee is bound by the covenants to repair and
to cultivate, so far as they are applicable to the part of the
land which he holds. And they may be taken advantage
of, as well by the assignee of the reversion as by the
lessor himself. And the assignee of the reversion of
part of the premises may sue on a covenant relating to
such part.
The assignee of the lessee is liable by the common law
to perform the covenant. The right of the assignee of the
reversion to enforce performance is founded on the stat.
32 Hen. VIII., c. 4, which only applies where the lease is
by indenture; and therefore when a house is let by verbal
or written agreement, and the tenant agrees to repair, and
the landlord assigns his interest, the assignee cannot sue
the tenant for not repairing; and as there is an express
agreement to repair with the original landlord, an agree-
ment with the assignee to use the premises in a tenant-like
manner cannot be implied. The original landlord, of
course, may sue on the agreement, notwithstanding the
assignment of his reversion. But in such case, if the
tenancy is merely from year to year, and the tenant or his
assignee continue as tenant from year to year of the lessor
or his assignee, an agreement between the new parties will
TENANTS FOR LIFE AND YEARS.
729
be implied that such renewed tenancy shall be on the old
terms.
Notwithstanding some decisions to the contrary, it is
now decided that an assignee in equity of a lease, for in-
stance, a party who has had it deposited with him by way
of equitable mortgage, is not liable on the covenants as
assignee, and that the Court of Chancery will not compel
him to take an assignment.
A covenant to do any thing upon the land, as to build a
wall or a house, or which in any way affects the land, as in
a lease of mines, a covenant to build a smelting mill, is a
covenant which runs with the land, and the benefit there-
of will pass to the assignee of the reversion. But such a
covenant being to do a specific act, and not continually to
be performed during the term, does not bind the assignee,
if not named. Thus, if B covenant for himself, his execu-
tors and administrators, to build a wall, the assignee is not
bound, because the intention appears to be that the wall
shall be built by the lessee before assignment; but if the
covenant be that the lessee or his assigns shall build a wall,
the assignee is bound. If the lessee covenant for himself
and his assigns to build a house within a certain time, and
assign after the expiration of the time, the assignee is not
bound; but if he assign before the covenant is broken, the
assignee is. The assignee of the reversion cannot sue for
a breach of covenant before the conveyance to himself.
A covenant not to build is at all events, in equity,
binding on the assignee, and the Court will restrain the
assignee, who has notice of such covenant, from violating it.
In considering the third point, the time during which Duration of
the obligation of a covenant to repair continues, it is to be
seen, first, when it begins; and, secondly, when it ends.
The obligation to repair usually commences at the date
of the lease, or at the commencement of the term when the
term commences subsequent to the date of the lease. But
when the habendum is from a day prior to the date of the
lease, the covenant binds from the date of the lease.
A covenant to leave in repair at the end, or other
sooner determination of the term, applies when the term
is determined by notice, according to a power reserved to
the lessee.
When a lease is conditioned, that if the lessee does not
repair within six months after notice, the lessor may re-
Covenant.
2 x
730
DILAPIDATIONS BY
Form of Co-
venant.
Waste in
Gardens.
Waste in
Lands; Al-
teration.
enter, the notice to repair must be given to the lessee or
his assignee. A notice to repair given to an under-lessee
will not suffice.
A general covenant to repair is not only obligatory
during the continuance of the lease, but also, where the
lessee continues tenant after its determination, it will be
presumed that he holds under the same terms.
Those covenants alone are implied as continuing in force
which regulate the manner in which the tenements shall
continue to be used.
There are no particular formalities requisite to give
validity to an agreement to repair, as that it should be
contained in a valid lease of the premises.
Waste may be committed in a garden or orchard.
Thus it is waste to cut down apple-trees, or pear trees
growing in a garden or orchard; but not if they grow
scatteringly on divers places of the land. When apple
trees are blown down, the tenant may take them; but
where such trees were abated by a great wind, and fell
upon the crops, and several of the boughs fell into the
ground, and the trees bore fruit two years afterwards, it
was held waste for the lessee to grub them up.
A gardener who cultivates trees for their fruit has no
right to remove them; but a nurseryman who rears them
to sell and transplant has a right to remove.
Nor can the tenant of a pleasure garden remove trees,
ornamental hedges, or shrubs, or a border of box, although
planted by himself, such things being intended to be per-
manent; nor can he plough up a strawberry-bed before it
is exhausted.
There is no authority for saying that a tenant is under
any positive obligation to cultivate a garden or orchard;
the cases only establish a negative obligation against
voluntary waste. The tenant is entitled to cultivate and
to remove or transplant any plants in the fair course of
cultivation, but not to remove things merely for his own
benefit, unless the purpose for which the garden was let
authorizes him to do so, as in the case of a nurseryman;
nor can he alter the character of the garden, or any part
of it, as by ploughing up a strawberry bed and sowing
turnips.
It is waste permanently to alter the character of land,
though its value may be increased, such as to convert
TENANTS FOR LIFE AND YEARS.
731
meadow into arable land by ploughing it up, or arable
land into wood, or a meadow into an orchard, because it
not only changes the course of husbandry, but affects the
proof of title. But it seems that if a meadow is ploughed
for the purpose of improving it as a meadow, and not of
permanently altering its character, as where by the custom
of the country it is good husbandry to do so, it is not
waste to plough it: and so it seems the tenant may root
up bushes, furze, and thorns growing on the land, for me-
lioration: for that is good husbandry, and he is entitled to
such things for fuel. The rule appears to be, that a per-
manent alteration of land, which necessarily affects the
evidence of title, or any alterations which diminish the
value of the land, is waste; but a mere temporary altera-
tion in the ordinary and reasonable course of husbandry
is not: and by reason of the injury to the evidence of title,
it is waste to enclose and cultivate waste land.
It is waste if the tenant take away the substance of the
land, as if he dig and take away clay, because the soil is
impoverished for want of clay; and he cannot open mines, Mines.
quarries, or clay-pits: but if mines, quarries, or clay-pits
are open, and in work, when the estate for life or years is
created, the tenant may continue to work them; because
an intention that he may do so may be presumed; but it
seems that a tenant for life has no right to re-open and
work clay-pits which the grantor had ceased to work be-
fore the creation of the estate. A tenant has no right to
minerals deposited on the land by mountain streams.
As a tenant is entitled to work mines open at the time
the lease is granted, so he may use all means necessary
for working them, and therefore may open new shafts and
pits to follow the same vein of coal. "Otherwise," said
Lord Chancellor King, "working in the same mine would
be impracticable, because the miners would be choked for
want of air, if new holes were not continually opened to
let the air into them; and the same vein of coal frequently
runs a great way, and is very knowable, and easy to be
discerned.
The Court of Chancery will restrain a tenant for life or
years from sowing woad or mustard, they being poisonous
and exhausting plants, by which the vegetative power of
the land is destroyed.
A tenant is bound to keep the fences in repair, and he Fences,
732
DILAPIDATIONS BY
Obligation to
cultivate
Lands.
may cut timber for this purpose; but he has no right to
make fences where none were before. And it would ap-
pear that he is not liable if the fences become dilapidated
from natural decay, and there is no wood on the premises
with which he can repair them.
By the general law a tenant for life or for years is under
no obligation to cultivate lands. Thus it is not waste to
suffer arable land to lie fresh and not manured, so that it
grows full of thorns; it is merely ill-husbandry. To
oblige a tenant to farm according to good husbandry,
there must either be an express contract or a custom of
the country. In most, if not all cases in which lands
have been usually let to farmers, there is a custom of the
country regulating the manner in which the lands are to
be cultivated.
A custom of the country need not have existed from
time immemorial, as must a custom properly so called. It
is the approved habits of good husbandry practised in that
part of the country in which the lands are situate, and is
a means of ascertaining the course of cultivation adapted
to the nature of the lands. It may be proved by cove-
nants usually inserted in farming leases, and need not be
definite and precise.
The obligation to expend manure, and right to remove
must in every case, where there is no express contract, be
governed by the custom of the country. There is no rule
of law on the subject, irrespective of such custom: farm-
ers are more fit than lawyers to decide such a question.
The obligation to cultivate lands according to the cus-
tom of the country does not apply to a garden or to a
meadow let with a gentleman's residence.
•
Where there is a special agreement as to the manner in
which the lands shall be cultivated, the obligation to culti-
vate according to the custom of the country is superseded,
as where the tenant agreed to farm the land in a good and
husbandlike manner, to be kept constantly in grass; and
where the landlord recovers damages for the conversion of
a meadow into arable land, he cannot also recover for re-
moving the straw grown on such land, as contrary to the
custom of the country as to the cultivation of arable land.
If tenant of a park, vivary, warren, or dove-house, de-
Doves, &c. stroy so many of the deer, game, rabbits, or doves, that
sufficient be not left for store, having regard to the num-
Obligation as
to Live Stock,
TENANTS FOR LIFE AND YEARS.
733
ber at the time his estate was created, it is waste. To
stop the holes of a pigeon-house so as to prevent the
pigeons building there, is waste. If the tenant of a park
permit the pales to decay, so that the deer escape, he is
liable for waste. Breaking a wear or suffering the banks
of a fish-pond to decay, so that the water and fish run out,
are respectively acts of waste. But the subversion of
coney-burrows has been held not to be waste.
Emblements are the products of the earth, which a Emblements.
tenant, the determination of whose estate is sudden and
fortuitous, is allowed to take after his interest in the land
has expired, in consideration of his labour and manurance
employed upon the land: "lest the ground should be unma-
nured, which would be hurtful to the commonwealth, he
shall reap the crop which he sowed in peace." The doc-
trine of Emblements has been entirely changed by the
act of the 14 and 15 Vic., c. 25, sec. 1, whereby it is
enacted:
66
nation of
Tenancies
for Life, &c.,
Emblements
hold until
current Year,
"That where the Lease or Tenancy of any farm or on determi-
"Lands held by a Tenant at Rackrent shall determine by Leases or
"the Death or Cesser of the Estate of any Landlord en- under Tenant
"titled for his Life, or for any other uncertain Interest, instead of
"instead of claims to Emblements, the Tenant shall con- Tenant to
"tinue to hold and occupy such Farm or Lands until the Expiration of
Expiration of the then current Year of his Tenancy, &c.
"and shall then quit, upon the Terms of his Lease or
Holding, in the same Manner as if such Lease or
"Tenancy were then determined by Effluxion of Time or
"other lawful Means during the Continuance of his
"Landlord's Estate; and the succeeding Landlord or
"Owner shall be entitled to recover and receive of the
"Tenant, in the same manner as his Predecessor or
"such Tenant's Lessor could have done if he had been
CC
living or had continued the Landlord or Lessor, a fair
"Proportion of the Rent for the Period which may have
"elapsed from the Day of the Death or Cesser of the
"Estate of such Predecessor or Lessor to the Time of the
"Tenant so quitting, and the succeeding Landlord or
"Owner and the Tenant respectively shall, as between
"themselves and as against each other, be entitled to all
"the Benefits and Advantages, and he subject to the
Terms, Conditions, and Restrictions, to which the pre-
ceding Landlord or Lessor and such Tenant respectively
CC
66
734
DILAPIDATIONS BY
Waste as to
Timber.
"would have been entitled and subject in case the Lease
66
or Tenancy had determined in manner aforesaid at the
"Expiration of such current Year: Provided always,
"that no notice to quit shall be necessary or required by
"or from either Party to determine any such Holding and
"Occupation as aforesaid."
Timber trees are parcel of the inheritance, and a tenant
for life or years has only a right to their shade and fruit
during the term. It is waste if he cuts them down, or
does any act to cause them to decay, as if he lops or tops
them. Timber trees are such as are useful for the purpose
of building. Oaks, ashes, and elms are timber in all places.
Thorn-trees, which have stood for sixty or a hundred years,
have been accounted timber. In some countries where
timber is scant, beeches and white-thorns are used for
building, and therefore accounted timber: in such case
it is waste to fell or injure them. In the Countess of
Cumberland's case, birches of a hundred years' growth,
which were serviceable for timber, for sheep-houses, cot-
tages, and other mean buildings, were held to be timber,
which a tenant for life had no right to cut. If by custom
oaks and ashes are seasonable wood, and cut at stated
times, the tenant may cut them at such times; thus, if it
is customary to cut ashes every ten years, the tenant may
cut them.
It is also waste to cut down any trees, though not tim-
ber, such as beeches, maples, willows, &c., which are
planted for the defence or ornament of the house, or in a
pasture-field for the shade of cattle, or on a bank to sus-
tain it, or which form part of a hedge, it being the appa-
rent intention of the landlord or grantor of the estate that
such trees shall continue.
It is not waste to cut down trees which are not timber,
either by law or custom, and are not planted for any of the
above special purposes, in such a manner that they will
grow again. Thus a tenant for years may lawfully cut
down willows, leaving the stools or butts from which they
will shoot afresh. Whitethorns, blackthorns, and hazels
may in like manner be cut down.
Nor is it waste to cut the underwood of hazels, willows,
or thorns, maple or oak. But if the tenant dig up such
trees, or underwood, or suffer the germins to be bitten by
cattle after they are felled, so that they will not grow
TENANTS FOR LIFE AND YEARS.
735
again, or mow the stocks with a wood scythe, it is waste.
Against such waste the Court of Chancery will grant an
injunction. It is not waste for the tenant to fell timber
trees which are completely dead, and bear neither fruit
nor leaves, and have not sufficient timber in them for build-
ings or posts.
If timber trees are blown down by tempest, or severed
from the land by other means, they become the property
of the tenant who takes the first estate of inheritance.
But if dotards, or old trees which have no timber in them,
are blown down, they become the property of the tenant.
And if the landlord fells such trees during the term, the
tenant may take them.
As the tenant is entitled to cut hedges and bushes, the
cuttings belong to him; and if a stranger cut them, the
landlord cannot maintain an action. The trimmings of fir
trees under twenty years old belong to the tenant for life,
and not to the remainderman.
The tenant being entitled, during his term, to the shade
and fruit of timber trees, if the landlord fell them, he may
maintain trespass.
An equitable tenant for life has no right to cut timber
without the consent of the trustees; if he does, he is
bound to account for the timber and its proceeds to the
trustees.
cayed Tim-
When timber is in a state of decay, and will not improve Felling de-
by standing, but is likely to do damage to other trees, and ber.
when the felling of it will be a benefit to all parties con-
cerned, the Court of Chancery will order it to be cut
down, either on the application of the tenant for life or of
the remainderman. When the application is by the re-
mainderman, care will be taken that the tenant for life is
not prejudiced by those trees being taken which are
necessary for repairs. The Court will not order generally
that those trees be cut down which are fit to be cut, and
which a provident owner might think fit for felling. Tim-
ber will on like conditions be ordered to be cut when the
tenant entitled to it is an infant.
When trees are thus felled by order of the Court of
Chancery, the produce of the sale is invested, and the
tenant for life has the interest for his life, such being
equivalent to the fruit and shade of the trees. The first
person entitled to cut timber is entitled to the capital in-
736
DILAPIDATIONS BY
Right to cut
Timber for
vested. Thus, when lands are conveyed in trust for A.,
for life remainder to B., for life without impeachment for
waste, the proceeds arising from the sale of timber belong
to B., on the death of A.
Ornamental timber and trees planted for the defence
and safety of the house will not be allowed to be cut down,
though decaying.
A tenant for life or years may cut timber for the repairs
Repairs, &c. of his house, barns, or fences, for the necessary purposes.
of husbandry, or to be consumed as firewood.. He may
fell timber to repair houses which he is not strictly bound
to repair; for instance, those which were ruinous at the
time of the lease, or those which the lessor covenants to
repair, because the law favours the supportation of houses
of habitation for mankind. But he cannot take timber
for improvements, such as to make fences where none ex-
isted before; or to repair houses which he has wasted, or
suffered to be wasted, nor can he cut timber for the pur-
poses of working mines, such being no benefit to the land.
The right to cut timber for firewood is qualified, and the
lessee can only justify cutting timber trees for that pur-
pose when there is no underwood or deadwood upon the
land.
Covenant as
to Trees.
Timber can only be cut down for the express purpose
of
being used in the repairs of buildings, &c. It cannot law-
fully be sold to raise money for the purchase of other timber;
nor can it be exchanged for other timber better adapted
for the repairs in question. If the timber be cut down
bonâ fide for the purpose of being used in reparations, the
tenant is justified, though he may have over-calculated the
quantity required; but he cannot cut down timber by way
of anticipation, to be used in dilapidations which may hap-
pen at some future time.
Where, by the lease, the lessor is to assign trees to the
lessee for requisite repairs, and a particular tree is assigned
to the lessee by the lessor's bailiff, such assignment
operates as a delivery, and vests the property of the tree
in the lessee, who may fell at any time afterwards.
Where the tenant covenants to deliver up all the trees
standing in an orchard at the time of the demise, reason-
able use and wear only excepted, he is not precluded from
removing trees decayed and past bearing from a part of
the orchard which is too crowded. Where there is a cove-
MORTGAGEE OR MORTGAGOR.
737
nant not to remove or grub up trees, the tenant cannot
remove trees from one part of the premises to another,
unless they are dead, even although he plant more trees
than he removes.
are excepted
Sometimes trees are excepted out of the lease; they are where Trees
then considered as in the possession of the lessor, and are out of Lease.
not subject to dilapidations or waste; but if the tenant
cut or fell them, the landlord may have an action of
trespass against him. Where trees generally are excepted
out of a lease, such exception is construed to relate to
timber trees only, and not to apple or other fruit trees, or
the like; since, if it did, the tenant would not be entitled
to the fruit of such trees. And where the exception was
of timber and other trees, but not the annual fruit thereof,
it was held that apple-trees were not within it, because it
was to be construed strictly against the lessor.
SECT. III.-Dilapidations by Mortgagee or Mortgagor.
Mortgagee to
A mortgagee, who in equity is considered as holding the Obligation on
land as a pledge for the payment of his debt, is bound to repair.
preserve the premises from extraordinary dilapidations ;
but for that depreciation which is caused by gradual de-
cay, the mortgagee is not responsible.
or rebuild.
Although, generally speaking, a mortgagee has no right Right to alter
to alter the mortgaged tenements, yet he may pull down
ruinous houses, and build better ones, to prevent a for-
feiture.
ment of Ex-
He is entitled to be allowed for repairs necessary for the Reimburse-
support of the property, and for the expenses of doing that pense.
which is essential to the maintenance of the mortgagee's
title. But he will not be allowed monies expended in in-
creasing the value of the property, unless the mortgagor
has consented or acquiesced. If he has improved the pro-
perty with the consent of the mortgagor, he is entitled to
be reimbursed the monies expended, with interest, in the
same manner as if it was a new loan.
Mortgagee to
Minerals.
The mortgagee in possession has no right to cut down Right of
timber, except the land is an insufficient security, when it Timber and
seems that the mortgagee may sell the timber. He cannot
open and work mines, or take brick earth; if he does, he
is chargeable with the gross receipts, and not allowed any
of the expenses.
738
DILAPIDATIONS OF
}
Right of
Mortgagor to
Timber.
Property in
Party Walls.
The mortgagor cannot cut down timber to the prejudice
of the security; and therefore if it appear that the security
is scanty, equity will restrain him from felling timber, but
not unless it be clearly shown that the security is deficient,
the presumption being that it is not. If he have cut down
timber to the prejudice of the security, and sold it, he will
be ordered to pay the amount into Court, in trust for the
mortgagee. Underwood, which is in the nature of a crop,
the mortgagor will not be restrained from cutting at sea-
sonable times, and this though the underwood be expressly
mentioned in the mortgage. But where the mortgagor
becomes bankrupt, his assignees will be enjoined from
taking even underwood, because the mortgagee is entitled
to the land in exactly the same plight as it is at the date
of the bankruptcy, and to prove for the residue of his debt.
SECT. IV.-Dilapidations of Party Walls and Fences.
Where a party wall exists between two buildings or gar-
dens, which is used by the occupiers of both buildings
indiscriminately, and it does not appear on whose land it
was built, the presumption is that the parties are tenants
in common of the wall. The presumption of property
arising from acts of ownership must correspond with those
acts; and, as in the case of a party wall, each party equally
makes use of the whole wall, the inference is that they are
equally entitled to the whole wall. It follows that if one
party build against the wall on his side, no action can be
maintained by the other. And if one pull down the wall
for the purpose of rebuilding it, or heighten it, it is not a
trespass against his neighbour; but the neighbour may have
an action on the case for the temporary loss of the protec-
tion of the wall, or for any injury he may sustain from the
increased height, or he may pull down any additional erec-
tion upon the wall. And one tenant in common of a hedge
may have trespass against his co-tenant if he grub it up,
but not if he merely clip it. Whether a party wall stand-
ing between two houses belong half to the owner of one
house and half to the other, or is the common property of
both owners, one has no right to underpin any part of the
wall, unless he can do it without injury to the house of the
other.
The rebuilding and repairs of party walls within London
PARTY WALLS AND FENCES.
739
and a limited district around, are regulated by the Metro-
politan Buildings Act, by which the owner of one of the
houses separated by the party wall may, under the super-
intendence of a district surveyor and official referees, re-
build or repair the party wall when necessary, either with
or without the consent of the owner of the other house,
and recover contribution from other parties benefited by
the works. As this statute is of itself a book, and there
have been as yet no legal decisions on its provisions, this
general reference to it must suffice.
In the case of a party wall out of the limits of the
Building Act, the rights and liabilities of parties with re-
spect to the repairing or rebuilding it will be the same as
those of tenants in common, if they are tenants in common
of the party wall. If half the wall belongs to each party,
then each may repair or rebuild his part.
Fences.
In the case of a fence between two fields, which has a Property in
ditch at its base, the presumption is that the fence belongs
to the party on whose side the ditch is not. It is reasonable
to suppose that, in making the fence by the party who
made it, the ditch was dug on the verge of his own land,
and the earth thrown up on his land, so as to form a bank
on which to plant the fence. And thus, the outer edge or
side of the ditch furthest from the hedge is presumed to be
the boundary of the lands; and if the party to whom the
fence belongs proceeds to widen the ditch, it is prima facie
a trespass on the neighbour's land. Where there are
ditches on both sides the hedge, or where there is no ditch
at all, the proprietorship of the hedge may be proved by
acts of ownership; and if both parties have equally exer-
cised acts of ownership, the right of property will, I appre-
hend, be presumed to be common.
repair Fences
A tenancy in common in a party wall or fence does not obligation to
imply any obligation in one tenant towards his companion
to repair such wall or fence, nor does the existence of a
fence on a man's land impose on him any obligation to re-
pair it as against his neighbour.
to repair.
Though the obligation to repair a fence be annexed to who bound
the fee simple of the land, yet the party bound to do the
repairs is the actual occupier, he being the person whose
immediate duty it is to prevent cattle from straying from
one close into the other; and having the exclusive posses-
sion of the fence, he is the only person who can lawfully
740
DILAPIDATIONS OF
Who to com-
plain of Dila-
pidations.
Inhabitants
of Parish.
repair it, or who can be presumed to know of the
defects.
The obligation to repair is only towards the occupier of
the adjoining close, and not general, as against the public;
and therefore a party seeking to take advantage of that
obligation, either as excusing a trespass, or charging the
obligor for injuries happening to his cattle, must show an
interest in the adjoining close, or a right to have his cattle
there.
SECT. V.-Dilapidations of Highways and Bridges.
Obligation of By the general rule of the common law, the parish
that is, the occupiers of land within the parish—are bound
to repair all the highways therein. Sometimes, by special
prescription, the inhabitants of a township are bound to
repair highways within the township, and sometimes one
parish is bound to repair highways situate in another. A
corporation or individual may be bound to repair highways
by reason of the tenure of some particular lands; an indi-
vidual may also be bound to repair highways by reason of
enclosure. These are exceptions: the general rule is, that
parishioners shall repair the highways; and where the
parties bound by prescription become insolvent and unable
to repair, the charge falls upon the parish. Where the
inhabitants of a township had immemorially repaired high-
ways within the township, and a new road was made by
Act of Parliament, which expressly exempted the inhabi-
tants of the township from the charge of repairing it, it
was held, that, ex necessitate, the rest of the parish were
liable. And where a turnpike road is made by an Act of
Parliament, and placed under the management of trustees,
who are to repair out of the tolls, the parish may be in-
dicted if the road be out of repair, because they are liable
by the general rule of the common law; and the tolls, &c.,
in the hands of the trustees, are only an auxiliary fund;
and if such fund fail, recourse can only be had to the parish.
But where such road is made in a township which, by pre-
scription, is bound to repair the roads within it, the inha-
bitants of the township must repair, because, by the
prescription, the township stands in the place of a parish
as to the repair of highways. It is obvious that the pa-
rishioners cannot discharge themselves from their liability
HIGHWAYS AND BRIDGES.
741
to repair a highway by agreement or otherwise, since such
an agreement would affect the rights and security of the
public, to whom the parish is bound. Where highways are
situate within an extra-parochial hamlet, it has been
doubted whether the inhabitants of such hamlet are, with-
out a special custom, liable to repair; but it would seem,
upon principle, that they are liable to repair, because other-
wise the roads would not be repaired at all; and in the
case of a turnpike road, there could be no persons ulti-
mately liable to keep it in repair, in the event of the tolls,
&c., proving inadequate, because to such road no prescrip-
tion or custom would apply.
Every thoroughfare which is used by the public is a
highway, whether it be a carriage-way, a horse-way, or a
foot-way a navigable river is a highway. In one case
parishioners were indicted for not repairing stairs leading
to the Thames. A way merely leading to a church, a
village, or a private house, and therefore not useful to the
public generally, is not a highway.
A highway may be created by Act of Parliament; and
when it has been recognized in an Act of Parliament as
public, it is a highway, and repairable as such. Where a
highway is created by a temporary Act, it ceases to be
such when the Act expires, and statute duty done upon it
in obedience to the Act is no adoption of it by the public.
When, by Act of Parliament, trustees are empowered to
make a road or roads, no part of them becomes a highway
until the whole are made. But when several roads are
authorized to be made, and it is provided that they shall
not become public until two justices have certified that the
said roads respectively are fit to be travelled on, each road
becomes public so soon as the justices have certified; and
it is not a condition that they shall all be made before any
are public highways.
What is a
Highway.
Highway.
Formerly, wherever a party made a way over his land, Dedication of
and dedicated it to the public, and the public used the way,
it became a public highway, and repairable by the parish.
Now, by the Highway Act, (which came into operation on
the 30th of March, 1836,) "No road or occupation-way
made, or hereafter to be made, by and at the expense of
any individual or private person, body politic or corporate,
nor any roads already set out, or to be hereafter set out,
as a private driftway or horse-path, in any award of Com-
742
DILAPIDATIONS OF
Limited
Dedication.
missioners under an Enclosure Act, shall be deemed or
taken to be a highway, which the inhabitants of any parish
shall be liable to repair, unless the person proposing to de-
dicate such highway to the use of the public shall give
three calendar months' previous notice, in writing, to the
surveyor of the parish, of his intention to dedicate such
highway to the use of the public, describing its situation
and extent, and shall have made, and shall make, the same
in a substantial manner, and of the width required by the
Act, and to the satisfaction of the surveyor and two jus-
tices of the peace, of the division in which such highway
is situate, in petty sessions assembled."
A way may be dedicated for a limited time; it may also
be dedicated for particular periods, as where it appeared
that a bridge was used by the public at all times, on foot
and with horses, but only occasionally with carriages, in
times of flood and frost, when it was unsafe to pass through
the river. In ordinary times the carriages went through
the ford, and the bridge was sometimes barred against car-
riages by a chain, locked to posts. Lord Ellenborough
held that this was a public right of way, limited as to time.
It has been doubted, however, whether there can be a par-
tial dedication of a way, that is, of a right of way for some
carriages and not for others. The argument against such
a dedication is, that it is unjust for the public generally to
be obliged to repair a road which a portion of the public
only are allowed to use.
There cannot be a dedication to a particular part of the
public, as to the inhabitants of a parish; such a dedication
is simply void.
Where lands chargeable with the repair of a highway
are conveyed to several, they are all liable to do the repairs
in proportion to the quantity of land they hold; though if
the way be dilapidated, any one of the proprietors may be
indicted separately, and compelled to pay the whole fine.
He may proceed against those who are jointly liable with
him for contribution. If lands so chargeable come into the
hands of the Crown, they are not discharged.
It is the occupier and not the freeholder of the lands
chargeable with repairs of a highway against whom the
indictment should be preferred. But the occupier is en-
titled to be reimbursed by his landlord the sum expended
in repairs.
HIGHWAYS AND BRIDGES.
743
The surveyor is to make every cart-way leading to any Width.
market-town twenty feet wide at the least, every horse-
way eight feet wide, and every foot-way at the side of any
cart-way, &c., three feet wide, if the space between the
fences will admit thereof.
Gateways across any carriage-way must be ten feet width of
wide, and across any horse-way five feet wide, clear be- Gateways.
tween the posts; and if the owner of any narrower gate
omit to enlarge or remove it after twenty-one days' notice
from the surveyor, he is liable to a penalty not exceeding
10s. per day for so long time as he so neglects.
Snow.
The surveyor is bound to remove any accumulation of Removal of
snow within twenty-four hours after notice from a justice
of the peace. He is empowered to make, scour, cleanse,
and keep open all ditches, gutters, drains, or water-courses, Cleansing
and to make and lay such trunks, tunnels, plats, and Ditches, &c.
bridges, as he may deem necessary, in and through any
lands, adjoining the highway, making the owner or occu-
pier compensation if the lands are not waste or common;
the amount to be settled in the same manner as the amount
of damages for getting materials from enclosed lands.
If any person alter or obstruct the ditches, &c., after
they have been taken under the charge of the surveyor,
he is bound to reimburse the surveyor the expense of re-
instating them, and to forfeit a sum not exceeding three
times such expense.
Posts, &c.
The surveyors of parishes more than three miles from Direction-
the post office are also required, with the consent of the
vestry, or by the direction of the justices at special sessions,
to set up direction-posts or stones in places where two ways
meet, and boundary stones; and on such parts of highways
as are subject to floods, to erect graduated stones to guide
travellers the safest track through the floods, and to secure
horse causeways and foot causeways from being passed
over by waggons, by banks of earth, posts, and stones.
ments.
No tree, bush, or shrub can be planted on any carriage- Encroach-
way within fifteen feet of the centre. And if the owner
do not remove it within twenty-one days after notice from
the surveyor, he forfeits 10s. for every neglect.
Highway.
The highway is that portion of ground which has been Centre of
maintained and repaired by the surveyor for six months
next preceding, and the fifteen feet are to be measured
from the centre of that.
744
DILAPIDATIONS OF
I
Cutting
Hedges.
Materials for
Repairs of
If the surveyor think that a highway is prejudiced by
any hedges or trees (except trees planted for the ornament
or shelter of any hop-ground, house, building, or court-
yard,) he may summon the owner of the land before a
justice, who may determine whether the trees, &c., shall
be cut, pruned, or plashed. If the owner fail to obey the
order of the justice, the surveyor may cut the hedge, and
the owner must reimburse him the expense incurred.
No person can be ordered to cut any hedges between
the last day of September and the last day of March, nor
to fell any timber tree, unless the highway is ordered to
be widened, and then he can only be compelled to grub up
oak-trees in April, May, and June, and ash, elm, or other
trees in December, January, February, and March.
The surveyor may, with the consent of the vestry, con-
Highways. tract for the purchase of materials required for the repair
of highways. He is not to have any interest in such con-
tract without the license of two justices at special sessions,
under a penalty not exceeding £10, and incapacity of being
employed as a surveyor with a salary.
Where lands belonging to parishes, or to the surveyor
of highways for the purpose of obtaining materials, become
exhausted, the surveyor may, with the consent of justices
at special sessions, sell the land to the owner of adjoin-
ing land, or, if he refuse, to any other person, for such price
as the justices think reasonable, and apply the money, with
like consent, in the purchase of other lands.
The surveyor may search for, dig, and carry away gravel,
sand, stone, or other materials, in any waste, common, river,
or brook, within the parish; or, if sufficient cannot be ob-
tained in his parish, he may take them from any other
parish, leaving sufficient for the repairs of the highways in
such parish.
Where sufficient materials cannot be had in the waste,
commons, rivers, and brooks, the surveyor may, with the
license of two justices at special sessions, dig and carry
away materials from the enclosed land of any person within
the parish (such land not being a garden, yard, avenue to a
house, lawn, park, paddock, or enclosed plantation, or en-
closed wood not exceeding one hundred acres), or within
any parish adjoining the highway, if sufficient materials
cannot be had within the parish or in the wastes, &c., of
the adjacent parish, and so that sufficient materials be left
HIGHWAYS AND BRIDGES.
745
for the repairs of the highway in the parish where the lands
lie. These questions to be determined by the justices.
The surveyor is to make satisfaction for the materials
taken, and also for the damage done to the lands in taking
and carrying away the same.
Public bridges, if not within a city or town corporate, of Bridges.
are repairable by the inhabitants of the county; if within
a city or town corporate, by the inhabitants of such city or
town. If part in one shire, city, or town, and part in ano-
ther, the inhabitants of the shire, city, or town, are bound
to repair so much of the bridge as lies within their limits.
A bridge may, by custom, be repairable by the hundred or
parish in which it is situate; or an individual may by pre-
scription be bound to repair, by reason of the tenure of
lands.
paired.
Those who are bound to repair bridges, must make them How re-
of such height and strength as shall be answerable to the
course of the water; and if it take a new channel, they must
erect a bridge there. But they are not bound to widen the
bridge, however convenient or necessary it may be to the
public.
Counties are also bound to repair the highways at the Causeways to
ends of bridges for 300 feet.
lic Bridge.
Every bridge which is of public utility is a public bridge, What a pub-
and prima facie repairable by the inhabitants of the county.
Although the bridge is erected by a private individual for
his own private advantage, yet, if it becomes of public be-
nefit, it is a public bridge.
By 43 Geo. III., c. 59, s. 5, no bridge built by an indi-
vidual shall be deemed a county bridge, unless erected in
a substantial and commodious manner, under the direction,
and to the satisfaction, of the county surveyor, or person
appointed by the justices at quarter sessions, or, in Lan-
caster, by the justices at the annual sessions; which sur-
veyor, or person appointed, is to attend and superintend
the erection of the bridge, when required by the party
erecting the same; and if the builder be dissatisfied, the
matter is to be determined at the quarter or annual sessions.
The justices of the peace are to appoint two surveyors,
with salaries, to see bridges amended.
2 Y
746
NUISANCES.
a Nuisance.
SECT. VI.-Nuisances.
Definition of A nuisance may be defined to be a wrongful act or neg-
lect of one man, in the use or management of his land,
which occasions damage to the possession or easement of
his neighbour, or to a public easement.
Acts injuri-
ous to pri-
Any act done by one man on his land which is the cause
vate Posses- of an encroachment on that of another, to his damage, is an
actionable nuisance.
sions,
Offensive
Trades.
If, in consequence of an act done in one colliery, damage
is caused to another, though at some distance, an action
lies by the owner of the colliery injured.
In determining what acts are nuisances, it is necessary
to ascertain the legal extent of the possessions of an occu-
pier of land. He to whom the soil belongs is entitled to
all the space of air above to the sky, and of the earth below
to the centre. His rights extend perpendicularly above
and below his own land, and not laterally, so as to claim
any use from the earth beneath or the air above the adjoin-
ing land. It is therefore not only a nuisance to cause an
encroachment or injury to the soil of a neighbour, as if a
house is built overhanging the land of another; but also if
the air over his land is corrupted or disturbed by noisome
smells or deafening noises, it is a nuisance.
Not every disagreeable smell or noise which spreads
from one man's land to his neighbour's is actionable. The
smell or noise must arise from some permanent cause, and
occasion continual annoyance and discomfort, to a degree
sufficient to depreciate the value of a dwelling-house, and
render it less eligible in consequence of the neighbourhood.
A man is not restricted in the fair and reasonable use of
his land by any delicacy of sense or peculiarity of habit of
his neighbour. A pig-sty, lime-kiln, privy, smith's forge,
tobacco mill, tallow furnace, and glass-house, set up near
a private residence, are nuisances. And so a mill for
steeping sheep-skins, by which the air is corrupted; a
building for manufacturing acid spirit of sulphur, which
occasions noisome and offensive smells; a place for slaugh-
tering horses. It is not essential that the stench raised
should be unwholesome; it is sufficient if it renders the
enjoyment of life and property uncomfortable.
NUISANCES.
747
of occupation
Any wilful and mischievous act of one man which dis- Disturbance
turbs another in the enjoyment of the reasonable profits of of Lands.
his land is a nuisance, though without the inalicious motive
of the agent the act is innocent.
Water.
It is also a nuisance to the occupier of the land over Diversion of
which it flows to obstruct or divert a stream of water. By
this act a natural profit is prevented from coming to the
land. "The proprietor of land on each bank of a stream
is prima facie entitled to half the land covered by the
stream, but there is no property in the water. Every pro-
prietor has an equal right to use the water which flows in
the stream, and, consequently, no proprietor can have the
right to use the water to the prejudice of any other pro-
prietor. No proprietor can either diminish the supply of
water, which would otherwise descend to the proprietor
below, or throw it back upon the proprietor above." By
grant, or by prescription, a proprietor may acquire a right
to take the water, to the prejudice of the other proprietors
of land on the banks of the stream; but by merely appro-
priating to himself water which is not at the time useful to
the other proprietors, he acquires no such right. Thus, a
person who first builds a mill on the banks of a stream has
no right to pen back or divert the water for the supply of
his mill, so as to diminish the quantity of water which
would come to the proprietors below, on the ground that
they have not applied the stream to any particular use.
In public navigable rivers no right can be gained, even
by prescription, to divert or obstruct the stream, to the
prejudice of the public. All that the proprietor of the
land on the banks (and to whom the soil belongs, to the
middle of the river) can do, is to take so much water as
may be necessary for his private purposes by pipes, or
otherwise, so as not sensibly to diminish the quantity, to
the prejudice of the navigation.
Lands from
Where the ancient course of water is to flood certain Protection of
lands at certain seasons, the owners of those lands cannot Inundation.
justify fencing it off their lands, to the prejudice of other
property; though, if such be not the ancient course of
the waters, they may. Thus if a river periodically inun-
dates the surrounding country at certain places, the parties
whose lands are thus periodically subject to floods have no
right to protect their lands against the river, if they there-
by cause the waters to flood the lands of their neighbours,
748
NUISANCES.
Nuisances to
Foundations.
Easements.
By Prescrip-
tion.
Dangerous
Nuisance.
Nuisances:
because by such act they improve and increase the value
of their property at the expense of their neighbours.
A man who builds a house on the verge of his own
land, has no right to the support of his neighbour's land
for the foundation of his house; nor if he build against
the wall of his neighbour's house, has he any right to the
support of such wall; and if he place windows looking to-
wards his neighbour's land, he cannot complain if his
neighbour build so as to obstruct the light.
If the occupier of a house suffers it to be dilapidated so
as to injure the adjoining house, he is liable to an action.
If one has conduit pipes passing by the foundations of the
house, and he neglects to repair them, whereby the house
is injured, it is a nuisance.
So a party having a water course in his land is bound to
cleanse it, at all events so as to prevent its becoming in-
jurious to his neighbour; and is liable for an obstruction,
although he has no notice of it.
The cases as to nuisances caused by fire have already
been stated.
An easement is a right which one man has to use the
land of his neighbour for a special purpose.
A prescriptive right to the easement of light is acquired
by twenty years uninterrupted enjoyment, unless it
appears that such enjoyment was had by some consent or
agreement expressly given for that purpose by deed or
writing. The enjoyment must be by a window or opening
in a building, by which the claimant visibly appropriates
the light flowing through such window to himself.
If a person suffers his tenement to become dangerous to
the public, or exercises an occupation dangerous to health
or life in a public situation, he is guilty of a nuisance.
Thus, if the occupier of a house near a highway suffer it
to become so dilapidated that it is likely to fall on the
passengers, he is indictable.
Remedies for A private nuisance may be abated by the party injured
Abatement. by it, provided he commits no riot in the abatement; but
a public nuisance cannot be abated by an individual, unless
he is specially inconvenienced thereby.
LAW RELATING TO APPRAISEMENTS.
749
CHAPTER XXII.
THE LAW RELATING TO APPRAISERS
AND AUCTIONEERS.
SECT. I.-The Law relating to Appraisements.
duly quali-
can act as
By the Laws regulating Attorneys, no person who is None but
not admitted and enrolled, and otherwise duly qualified to fied persons
act as Attorney or Solicitor, can sue out any writ or pro- Attorneys.
cess, or commence, carry on, or solicit any action, suit, or
other proceeding, in any Court of Equity, or Law, Civil
or Criminal. (6 & 7 Vic., c. 73, s. 2.)
alty of £50.
By 44 Geo. 3, c. 98, s. 14, Every person, who, for, or Under pen-
in expectation of fee, gain, or reward, draws or prepares
any Conveyance or Deed relating to any real or personal
estate, or any proceedings in Law or in Equity, other than
and except a Serjeant-at-Law, Barrister, Solicitor, Attor-
ney, Notary, or Proctor, having obtained a regular certi-
ficate; Special Pleader, Draftsman in Equity, or Convey-
ancer, being a Member of one of the four Inns of Court,
and having taken out a certificate; or a person employed
to engross any Deed, Instrument, or other proceeding,
not drawn or engrossed by himself, as a public officer pre-
paring a public document, in the course of his duty, is
liable to a penalty of £50. The act does not extend to
prevent any person from preparing a will, an agreement
not under seal, or a letter of attorney.
must obtain
By 46, Geo. 3, c. 46, Appraisers are required to obtain Appraiser
licenses from the Inland Revenue Office, for the purpose License.
of carrying on their business; and appraisements are re-
quired to be stamped.
an Appraiser.
Every person who values or appraises any estate or Definition of
property, real or personal, or any interest in possession or
reversion, or any goods, merchandise, or effects, for, or in
expectation of hire, fee, gain, or reward, is an Appraiser
within the act. (s. 4.)
No person
No person can exercise the calling or occupation of an can act as
750
LAW RELATING TO APPRAISEMENTS.
Appraiser
without
License.
Licenses,
when dated.
Penalty of
£50 for act-
ing as
Appraiser
without Li-
cense.
An Auction-
Appraiser without taking out a license, which is granted
by the Commissioners of Inland Revenue. (s. 5.)
Licenses issued between 5th July and 5th August, are
dated 6th July; those issued at other times are dated on
the day of issue. Every license continues in force until
the 5th of July following its issue.
Any person who appraises or values any estate or pro-
perty, &c. for, or in expectation of hire or reward, without
being licensed, is liable to a penalty of £50. (s. 6.)
An Auctioneer duly licensed as such, may act as an
eer can act as Appraiser without an Appraiser's license. (s. 7.)
Appraiser.
Appraiser
must deliver
within four-
stamped pa-
per.
Every Appraiser must set down in words or figures
Valuation every valuation made by him, and the full amount thereof,
teen days on and within fourteen days deliver the same, duly stamped,
to his employer, under a penalty of £50. (s. 8.)
Employer If the employer of an Appraiser receives, or pays, or
an unstamp. makes compensation for making an appraisement, and the
same is not set down on paper duly stamped, he forfeits
£20. (s. 9.)
who receives
ed Valuation
liable to Pen-
alty.
One Sheet of
Paper only
need be
stamped.
License sub-
ject to £2
Stamp.
License to be
taken out
yearly.
Amount of
Stamp Duty
ments.
If more than one sheet or piece of paper is used in
writing an appraisement, that only which contains the ag-
gregate amount of the valuation need be stamped. (s. 10.)
The license to use and exercise the calling or occupation
of an Appraiser in the United Kingdom, is (by 8 & 9 Vic.,
c. 76,) subject to a stamp duty of £2.
It must be taken out yearly by every person (except a
licensed auctioneer) who exercises the calling or occupa-
tion of an appraiser, or who for, or in expectation, of any
gain, fee, or reward, makes any appraisement or valuation
chargeable by law with any stamp duty.
The stamp duty on Appraisements is imposed by 55
on Appraise Geo. 3, c. 184, on an Appraisement or valuation of any
estate or effects, real or personal, heritable or moveable,
or of any interest therein, or of the annual value
thereof, or of any dilapidations, or of any repairs wanted,
or of the materials and labour used, or to be used in any
buildings, or of any artificer's work whatsoever.
Where the amount of such appraisement
or valuation exceeds not
Where it exceeds £50, and exceeds not 100
100
""
200
"
500
""
وو
£. s. d.
£50
. 0 2 6
0 5 0
200
10 10 0
500
0 15 0
100
LAW RELATING TO APPRAISEMENTS.
751
The exemptions from duty are
Appraisements or valuations made in pursuance of the
order of any Court of Admiralty or Vice-Admiralty, or
of any Court of Appeal, from any sentence, adjudication,
or judgment of any Court of Admiralty or Vice-Admiralty.
Appraisements or valuations of any property made for
the purpose of ascertaining the legacy duty payable in
respect thereof.
Exemptions.
how recover-
It should be noted that the above penalties can only be Penalties,
sued for in the name of the Attorney-General, or of the able.
Solicitor of Stamps, or some other officer of the Stamps.
(44. Geo. 3, c. 98.)
cover his
If a person acts as an Appraiser without being licensed, Unlicense
or if an Appraiser omits to write his appraisement on a cannot re-
stamp, his conduct is illegal, and he cannot recover for his Charges.
services. (Palk v. Force, 17, Law Jour., G. B. 299, 12
par. 797.)
do not apply
made for pri-
mation only.
The Stamp Acts do not apply to appraisements made Stamp Acts
merely for private information, but to such only as are to Valuations
intended to be binding between two parties with opposing vate infor-
interests. Thus, a valuation of parish lands made by a
farmer and a basket-maker for the sidesmen of the parish,
with a view to the equalisation of the poor-rate, has been
held not to require an appraisement stamp, and the farmer
and basket-maker recovered compensation for their ser-
vices, although they were not licensed as Appraisers.
(Atkinson v. Fell, 5 Maule & Sel. 240.) And so, where
two partners in a coal mine directed a third person to
balance the profit and loss of the concern, and to value
the materials and utensils, and each party was to take an
article alternately at his valuation, until the whole was
divided, it was held that the valuation so made was for the
mutual information of the partners; and although it was
afterwards adopted as the terms of their agreement, it
was not an appraisement within the stamp laws. (Jackson
v. Stophurd, 4 Tyr. 330.)
ment does
Award
An appraisement or valuation although it is agreed to Appraise-
be and is binding upon the parties as an award, does not not require
require an award stamp. Thus a valuation of the amount Stamp.
due to a builder for building a house was held to be suf-
ficiently stamped with an appraisement stamp. (Perkins
v. Potts, 2 Chit. 399.) So an appraisement of the amount
to be paid by an incoming to an outgoing tenant for stock
752
LAW OF AUCTION.
£10 Stamp
on Auction-
and implements, and of the amount to be allowed by the
outgoing tenant for repairs, is sufficiently stamped with an
appraisement stamp. (Leas v. Burroughs, 12 East. 1.)
SECT. II.—The Law of Auction.
By 8 & 9 Vic., c. 15. The Auction Duty is repealed,
eer's License. and an Excise Duty of £10 is imposed upon every License
to be taken out annually by every person exercising or
carrying on the trade of an Auctioneer, in any part of the
United Kingdom.
Every Auc-
tioneer is re-
quired to
take out Li-
cense.
Every person who exercises or carries on the trade or
business of an Auctioneer, or who acts in such capacity at
any sale or roup, and every person who sells, or offers for
sale, any goods or chattels, lands, tenements, or heredita-
ments, or any interest therein, at any sale, or roup, when
any person or persons become the purchaser of the same,
by competition, and being the highest bidder, either by
being the single bidder, or increasing upon the biddings
made by others, or decreasing on sums named by the
Auctioneer, or person acting as Auctioneer, or other per-
son, at such sale, by any other mode of sale, by competi-
Which must tion, is required to take out the license. The license
annually. should be renewed annually, ten days at least, before the
expiration thereof, on the 5th day of July, in each year.
Every Auctioneer having had such license, who continues
to carry on the business of an Auctioneer in the
year next
ensuing the expiration thereof, and omits to renew his
license as aforesaid, and every person who carries on the
Without Li- business of an Auctioneer as aforesaid, without taking
out such license, forfeits £100.
be renewed
Auctioneer
conducting
business
cense, forfeits
£100.
Persons
exempt from
License.
Auctioneer
can sell any
Persons selling goods or chattels by auction under a
distress, for non-payment of rent or tithes, to a less amount
than £20, or under the authority of any act or acts of par-
liament, in force on 8th May, 1845, in which an exemption
is given to the officer of a court to sell effects seized under
the process of the court, by auction, without taking out or
having any license as an Auctioneer, if the sum for which
the process is enforced, is under £20, need not be licensed
as Auctioneers.
A licensed Auctioneer may sell any description of goods
kind of goods. without having an excise license to authorise him to sell
such goods by retail; and may sell by auction gold and
LAW OF AUCTION.
753
silver plate, patent medicines, and other articles, without a
special license for the sale of such things.
Must post his
The Auctioneer before beginning the auction must affix or Name in Sale
suspend, or cause to be affixed or suspended, a ticket or Room.
board containing his true and full christian and surname, and
residence, painted, printed, or written in large letters, pub-
licly visible or legible in some conspicuous part of the
room or place where the auction is held, so that all persons
may easily read the same, and must keep such ticket or
board so affixed or suspended during the whole time of
such auction being held, under a penalty of £20.
his License
or deposit
The Auctioneer must at the time of any sale by auction Must show
on demand of any officer of excise, customs, stamps, or on demand,
taxes, produce and show to such officer a proper license £10.
granted under the act and then in force, or deposit with the
officer £10. If he fails, he may be arrested and detained
by any officer of the peace. Any officer of the peace, at
the request of the excise officer, &c., may at the termina-
tion of the sale, or sooner, if convenient, arrest and convey
the person acting as Auctioneer, before a Justice of the
Peace, of the county, or place, where the sale has been
held, and the Justice may examine into the fact or facts
charged, and upon proof either by confession of the party
offending, or by the oath of one or more credible witness
or witnesses, (which oath the Justice is empowered to ad-
minister), that the person brought before him did act as
an Auctioneer as aforesaid, and did not produce such license,
or deposit such sum of money, may by warrant made under
his hand commit the offender to the common goal or house
of correction, for the county or place where the sale has
been held, for any time not exceeding one calendar month
from the day of the commitment. Neither the imprison-
ment nor the deposit prejudices or affects any proceedings
afterwards instituted for the recovery of the penalty in-
curred for acting as an Auctioneer, without the license by
the act directed. If the Auctioneer deposits the £10,
and before the expiration of a week from the date of the
sale produces to the officer a proper license to him granted
and in force before and at such sale, the officer must imme-
diately repay the deposit; otherwise, he must, at the expi-
ration of the week, account for it to the Commissioners of
Inland Revenue, or such persons as they may appoint to
receive it.
754
LAW OF AUCTION.
Each Partner If
must be
Licensed.
Auctioneer's
duty to make
productive
Sale.
Conditions of
Sale, Auc-
for omissions.
persons carry on the business of Auctioneers in part-
nership, each partner must take out a separate license.
(6 Geo 4, c. 81, s. 7.)
With respect to the duty of an Auctioneer, he should,
before the sale, take all proper and usual precautions by
advertising, &c., to make the sale as productive as possible
to his client.
If he takes upon himself to frame the conditions of sale,
tioneer liable which, if a solicitor is employed, are usually drawn out
by him, he should insert all usual and proper conditions
which the subject of sale requires. If, in consequence of
his omission to insert proper and usual conditions, the sale
proves ineffectual, he is not entitled to recover anything
from his employer for his services. Dunew was employed
by Daverell to sell a leasehold estate; he omitted to insert
in the particulars of sale a condition that the purchaser
should not inquire into the lessor's title. The purchaser,
as he was entitled to do in the absence of express stipula-
tion to that effect, called for the lessor's title, which Da-
verell being unable to furnish, could not make out his title.
An action having been brought by Dunew for the money
which he supposed to be due to him for endeavouring to
sell the property, Lord Ellenborough held that he was
entitled to recover no compensation for his services be-
cause they had been found to be wholly abortive by
reason of his own neglect. (Dunew v. Daverell, 3
Campb. 451.)
Description
of Property
stantially
correct, or
the sale is
void.
He should describe the property to be sold correctly in
must be sub- the particulars. Any material misdescription will render
the sale voidable by the purchaser, as if a house is de-
scribed to be a free public-house, when the lease contains
a covenant binding the tenant to take beer of a particular
brewer. (Jones v. Edney, 3 Campb., 294.) So if a right
of way is omitted or misdescribed in the particulars and
plan, (Dykes v. Blake, 4 Bing, Q.C., 463,) or if an objec-
tionable projection is omitted, (Pope v. Garland, 4 Y & Z.,
403.) Any extraordinary condition to which the property
is subject, should be described. An annuity payable out
of the tolls of Waterloo-bridge was put up for sale, but
was not described as redeemable, which it was, the pur-
chaser was allowed to repudiate his contract. (Coverley
v. Burrell, Sugden on Vend., 211.) On a sale of lease-
hold property, it was omitted to be mentioned that an Act
LAW OF AUCTION.
755
of Parliament empowered a company to purchase it, the
result was the same. So on the sale of a wood, an incor-
rect description of the average size of the trees prevented
the seller from enforcing the contract. (Lord Brooke, v.
Rownthwaite, 5 Hare, 298.)
that misde-
shall not an-
does not ap-
ulent mis-
Even if there is a condition that misdescriptions shall A Condition
not annul the sale, but that compensation shall be given scription
for the difference in value, it will not apply to a fraudulent nul Sale,
misstatement or a misdescription, so far affecting the sub-ply to fraud-
ject matter of the contract, that it may be reasonably sup- statements.
posed that but for such misdescription the purchaser might
never have entered into the contract. (Flight v. Booth,
1 Bing, Q. C., 377.) Thus, where before the reform in
parliament an estate was described as situate about one
mile from Horsham, (a parliamentary borough,) when it
was between three and four miles from that place, the error
was held fatal. (Duke of Norfolk v. Northy, 1 Campb.,
337.) And so where a lease at a rack rent was described
as held at a ground rent. (Stewart v. Alliston, 1 Mer., 26.)
So where a house which was built partly of brick and partly
of timber—parts of the exterior of which were built of only
lath and plaster, and had no party wall, was described as
a brick-built dwelling-house. (Powell v. Double, Sugden
21.) So where the particulars described a house as No. 4
instead of No. 2, although the name of the occupier was
correctly stated, and the houses No. 2 and 4 were of the
same description, and the latter was rather in better repair
than the former, the purchaser was not bound. (Leach v.
Mullett, 3 C. & P., 115.) So where a house was held
under a lease, and a small yard, which was an essential
part thereof, was held under a yearly tenancy, and the
particulars omitted to notice the difference of tenure.
(Dobell v. Hutchinson, 3 Ad. & E., 355.)
Fixtures, are
at Valuation,
lars must so
If the purchaser is to take timber or fixtures at a valua- If Timber, or
tion it should be so expressed in the particulars or condi- to be taken
tions; if not, he will be entitled to them as part of his the Particu-
purchase without additional payment. (Higginson v. state it.
Clowes, 15 Ves. junr., 516; Colegrave v. Dias Santos, 2
P. & C., 76.)
tion of Goods
spection, is
In the case of goods, which the purchaser sees at the Misdescrip-
time of bidding for them, and buys from inspection, a mis- bought by in-
description is not fatal to the contract, but it may in some not fatal.
cases be considered as amounting to a warranty that the
756
LAW OF AUCTION.
Auctioneer
not liable for
mistakes
arising out of
of opinion.
goods are of the description specified; if they are not,
the auctioneer may be liable to an action for breach of
warranty.
But if from the nature of the subject of sale the descrip-
tion can only be fairly considered as matter of opinion, a
mere matter mistake there being no fraud, does not render the auctioneer
liable. Thus, on a sale of pictures by auction, one was
described in the catalogue as by Claude Loraine, and ano-
ther by Teniers, Lord Kenyon held that the description
was a mere statement of the seller's opinion, and not bind-
ing. (Lendwine v. Slade, 2 Esp. 572.) A different de-
cision was arrived at by a jury, where some pictures were
described in an invoice as the work of Canaletti. The
court refused to disturb the verdict, remarking that he was
a very old painter, (he died in 1798,) and that it was for
the jury to say, under all the circumstances, whether the
words in the invoice implied a warranty of genuineness, or
conveyed only a description or an expression of opinion.
Littledale, J., observed, that all the auctioneers in London
would be alarmed if they thought that words such as those
used were to be understood as a warranty. (Power v.
Barham, 4 A. & R., 470.)
Puffing at
Sales.
Statute of
Frauds ex-
It is illegal to employ puffers, or even one person
to screw up the price, unless the fact is publicly adver-
tised and known. Such conduct is a fraud upon the bid-
ders, and inconsistent with the usual condition that the
highest bidder shall be purchaser; but it seems to be the
better opinion that one bidder may be employed to pre-
vent the property from being sold at an under-value.
(Sugden on Vendors, 8.)
As the Statute of Frauds, 29 Car. 2, c. 3, extends to
tends to Sales sales by auction, it is necessary for the auctioneer to attend
to its provisions.
by Auction.
Contract of
Sale, or
must be in
The 4th section enacts "That no action shall be brought
Agreement, whereby to charge any person upon any contract or sale of
Writing. any lands, tenements, or hereditaments, or any interest in
or concerning them, unless the agreement upon which such
action shall be brought, or some memorandum or note
thereof shall be in writing, and signed by the party to be
charged therewith, or some other person thereunto by him
lawfully authorised."
What cir-
cumstances
binding.
The 17th section is, "That no contract for the sale of
any goods, wares, or merchandize for the price of £10 ster-
LAW OF AUCTION.
757
ling, or upwards, shall be allowed to be good, except the
buyer shall accept part of the goods so sold, and actually
receive the same, or give something in earnest to bind the
bargain, or in part of payment, or that some note or memo-
randum of the said bargain be made and signed by the
parties to be charged by such contract, or their agents,
thereunto lawfully authorised."
Lands.
On a sale of lands by auction, there must be a writing Sale of
signed by the party to be charged, specifying the names of
the vendor and purchaser, and all the particulars and con-
ditions of the contract.
Goods.
On a sale of goods of the price of £10 or upwards, there Sale of
must either be such a writing, or a part payment, or ear-
nest, or acceptance of the goods, or part of them.
is generally
both parties.
The auctioneer is in most cases considered to be agent Auctioneer
of both parties to sign the contract. His employment by Agent of
the vendor to sell gives him authority to sign for him, and
the purchaser by bidding confers on him an authority to
sign for him, unless he otherwise expresses himself. (Ken-
worthy v. Schofield, 2 B. & R., 945; Bartlett v. Parnell,
4 A. & R., 792.) So that if he signs a sufficient memo-
randum in writing, either party may enforce the contract
against the other. But the signature of the auctioneer
will not make him to sue the purchaser on the contract,
because if he appears as principal he is not allowed to say
that he was the agent of the other party. (Farebro-
ther v. Simmons, 5 B. & Ald. 333.)
Clerk Agent
The auctioneer's clerk is the agent of the purchaser, to Auctioneer's
sign the contract, if he signs it in his presence without ob- for purchaser
jection. The auctioneer may sue on a contract so signed.
(Bird v. Boulter, 4 B. & Ad., 443.)
Lot is a
tract.
On a sale by auction, the sale of each lot is a distinct Sale of each
contract, and therefore in the case of goods, if the price of separate con-
each lot is under £10, the Statute of Frauds does not apply.
And the acceptance of or part payment on one lot does not
establish the contract as to the other. (Roots v. Lord
Dormer, 4 B. & Ad. 77.)
of Goods.
amounts to it.
Nice questions sometimes arise as to what amounts Acceptance
to an acceptance of goods within the statute. Some ear- what
rings were put up to auction upon a condition that the
purchaser should pay a deposit of 30 per cent. Bristolli
was the highest bidder, at 88 guineas; the ear-rings were
thereupon handed to him, and he received them without
758
LAW OF AUCTION.
Auctioneer
holds deposit
as a Stake-
holder.
If vendor fail
to perform
Contract,
Auctioneer
deposit to
the pur-
chaser.
objection; after they had been in his hands three or four
minutes he returned them to the auctioneer, saying, that
he had been mistaken as to the price at which they had
been knocked down. The auctioneer refused to receive
them: he did not pay the deposit. Lord Tenterden at the
trial ruled, that there had been an acceptance. The court
granted a new trial, remarking that it was improbable that
the auctioneer intended to part with the property before
payment of the deposit, and that there was very slight evi-
dence of acceptance, which was a question for the jury.
(Phillips v. Bristolli, 2 B. & C., 911.)
If a deposit is paid to the auctioneer, he holds it as
a stakeholder between the parties, and is bound to pay to
the vendor immediately the contract is completed, or to
the purchaser, if the purchase goes off, immediately the
vendor has made default. As he may be called upon to pay
the deposit at any moment, he is not liable for interest, al-
though he may have invested the money and made interest
thereby, (Harrington v. Hoggart, 1 B. & Ad., 577,)
nor is he liable to any expenses which the purchaser has
been put to. But if he has put up the property for sale
without authority, he is liable both to interest and ex-
penses. (Noratt v. Ellis, Sugden, 30.) He is not entitled
to any notice of the purchase being completed or going off,
but must inform himself of the circumstances, and pay
over to the party entitled at his peril. He impliedly un-
dertakes to do so when he receives the deposit. (Duncan
v. Cafe, 2 M. & W., 244.)
If the vendor is not ready to perform his contract at the
stipulated time, the auctioneer is bound at law to return
must return the deposit to the purchaser; and this, although the pur-
chaser is not prepared, and although if the case is within
the Statute of Frauds, negotiations and steps towards com-
pletion have been taken after the time, unless the time has
been enlarged by an agreement, signed by the purchaser
or his agent. (Stowell v. Robinson, 3 Bing, N. C., 928;
Clarke v. King, Ry. & Mood, 394.) He may not be so
bound if proceedings in equity have been taken by either
party. If sued for the deposit, the auctioneer has no right
to compel the vendor and purchaser to interplead. He can-
not be relieved from the performance of his contract which
is to pay the deposit to the party entitled. (Deller v.
Prickett, 15 Ins., 168.)
LAW OF AUCTION.
759
cannot pur-
An auctioneer being employed to sell and obtain the Auctioneer
best price from a third person cannot purchase the pro- chase him-
perty himself. (Esp. Hughes, 6 Ves., 617.)
self.
Purchaser.
As he has an interest in the contract of sale for his May sue'a
commission, he may sue on the contract in his own name.
(Williams v. Millington, 1 H. Br. 81.)
He is also personally liable as principal to the
if he does not disclose the name of his principal.
v. Roberdraw, Peake, 120.)
purchaser
(Hanson
he does not
Is liable if
disclose the
name of his
principal.
to purchaser
Goods he
to do, if he
faith.
on the pre-
If he bona fide sells goods which he has no right to Is not liable
sell, he is not liable to the purchaser, as upon a sale by for selling
auction or other sale of goods there is no warranty of the has no right
title to the goods sold. (Morley v. Attenborough, 3 Ex., acts in good
500.) But he is liable to the real owner of the goods.
Although he is employed by the owner of premises As to selling
to sell on them, he has no right to remain on the premises mises.
if the owner revokes his authority and requires him to quit
even though his remaining there is necessary to complete
his contract with the purchasers of the goods. He must
quit the premises directly he is requested by the owner,
and if he sustains any damage in consequence, must sue
the owner. (Taplin v. Florence, 15 Ins., 402.)
And if
entitled to
tion when
completed.
An auctioneer, as well as every other agent, when Auctioneer
he has performed the stipulated service, is entitled to the remunera-
remuneration agreed to be paid him, or if there is no ex- service is
press agreement to the customary remuneration.
there is an agreement as to the rate of payment, it will be
construed with reference to the custom of the business, if
such custom be so notorious as to render it probable that
the employer knew of it.
Commission,
Sale is not
him.
It is the custom of auctioneers employed to sell estates Entitled to
to claim their commission upon a sale being completed, al- although the
though the sale has not been effected by them, and this effected by
custom has been considered to be incorporated into agree-
ments with their employers, if not expressly excluded.
In Driver v. Cholmondeley (9 C. & P., 559) tried before
Lord Denman and a special jury, in 1835, the plaintiffs
claimed a commission of 1 per cent. on £128,500, the price
of an estate which one of the defendants had sold by pri-
vate contract after the plaintiffs had been employed to sell
it under an agreement, by which they were to have 1 per
cent. on the purchase-money; the defendants contended
that as the plaintiffs had not effected the sale, they were
760
LAW OF AUCTION.
&
not entitled to the commission, but the jury gave them a
verdict. In Rainy v. Vernon, (9 C. & P., 599,) the
plaintiff was employed to sell ground rents by auction, on
the terms of receiving a commission of 1 per cent. on sale.
After he had advertised the property, the defendants sold
it by private contract. Mr. Winstanley proved the cus-
tom to be that if an auctioneer is employed, and a sale ad-
vertised, and before sale the property is sold by the owner
himself, the auctioneer is to be paid his commission. If
the particulars are prepared before the employment of the
auctioneer it makes no difference. If the auctioneer inserts
advertisements and calls the attention of the public to the
property, and brings forward a person who eventually be-
comes the purchaser, he is always paid his commission.
Mr. Shuttleworth confirmed Mr. Winstanley. Mr. Hoggart
said, the usage is for the auctioneer to receive his commis-
sion after he is employed, however the property may be
sold. The amount of commission does not depend upon
whether the auctioneer does much or little. Lord Denman
directed the jury that if they thought that a usage so no-
torious that the defendants must have known it, had been
proved, it was part of the contract. But if the custom was
not so notorious, it was not engrafted on the contract, and
the fair value of the plaintiff's services only ought to be
given. The verdict was for the amount of the commission.
(See Maltby v. Christie, 1 Esp., 340, and see Lawrence, 3,
in Tomkins v. White, 3, Smith, 440.)
In Murray v. Currie, (7 C. & P., 584,) it was proved
to be the custom of land-agents, that where several were
employed to sell an estate, the agent who found a pur-
chaser was entitled to a commission of 2 per cent., whether
he did anything more towards the completion of the pur-
chase or not. It appeared that the purchaser was first
informed that the estate was in the market by the plaintiff,
but he negotiated the terms of the purchase through the
agent employed by the defendant. Lord Denman left it
to the jury to say whether the plaintiff had found the pur-
chaser, in which case he said they were to find for him,
otherwise not; but he told them that they were not bound
to give him all the commission that he claimed. They
found for the plaintiff for part of the commission claimed.
If by the terms of the agreement, commission is to be
mission is to paid on the sum obtained, nothing is due until the contract
If by agree-
ment, Com-
LAW OF AUCTION.
761
obtained,
due until the
completed,
paid.
is completed, and the purchase-money paid to the vendor. on the sum
(Bull v. Price, 7 Bing., 237.) On a negotiation for an ex- nothing is
change of livings the employer agreed to pay the agent his Contract is
commission when the abstract of the conveyance was drawn and money
out. The court held that he was not entitled to be paid
when an abstract of title on one side only had been de-
livered, no abstract having been delivered by the other
party. (Alder v. Boyle, 4 C. B., 635.) But if the em-
ployer, having the opportunity to complete the contract,
wilfully refuses to do so, the agent is entitled to his com-
mission. (Horford v. Wilson, 1 Taunt., 12 W. Tindal,
C. J.; Bull v. Price, 7 Bing., 241.)
By agreement, an auctioneer was to have a commission
of 1 per cent. if the estate was sold by auction, or within
two months afterwards, or per cent. if it was not sold
within two months. The estate was not sold by auction,
but was sold more than two lunar months, but within two
calendar months, afterwards. The court held that it was
not a mercantile contract, in which the term month always
means a calendar month, and that prima facie month meant
lunar month, but that it was for a jury to say whether
there was any usage of trade for month in such cases to
mean calendar month. (Simpson v. Margisson, 11 Q.B., 23.)
Conditions of Sale-On the Sale of Freehold Property.
1. That the highest bidder shall be the buyer: and if
any dispute arise as to the last or best bidder, the lot in
dispute shall be put up at a former bidding.
2. That no person shall advance less at any bidding
than £ or retract his or her bidding.
3. That every purchaser shall immediately pay down a
deposit, in the proportion of £for every £100, of his
or her purchase-money into the hands of the Auctioneer,
and sign an agreement for payment of the remainder to
the proprietor, on the
day of
at
next,
at which time and place the purchases
are to be completed, and the respective purchasers are
then to have the actual possession of their respective lots;
all outgoings to that time being cleared by the vendor.
4. That within
from the day of
the sale, the vendor shall at his own expense, prepare
2 Z
762
LAW OF AUCTION.
and deliver an abstract of his title to each purchaser, or
his or her solicitor; and shall deduce a good title to the
lots sold, commencing with a deed bearing date the
and that no earlier title
A.D.
day of
shall be enquired into or required.
5. That if from any cause the purchase shall not be
completed at the time mentioned in the 2nd condition,
the purchaser shall pay interest on his purchase money at
the rate of 5 per cent., per annum, in addition thereto.
6. That the purchaser of each lot shall pay for all
tenant's fixtures and timber on his lot, at a valuation to
be made by two valuers or their umpire, one valuer to
be named by the vendor and one by the purchaser, within
days after the sale, and if either party shall neglect
to appoint a valuer, the valuation shall be made by the
valuer appointed by the other, and shall be final. That the
amount of such valuation shall be paid at the time and
place mentioned in the 2nd condition in addition to the
purchase-money, or in default of payment, interest shall
be paid thereon according to the 5th condition.
7. That upon payment of the remainder of the pur-
chase-money, the amount of the valuation and interest
as aforesaid, the vendor shall convey the lots to the
respective purchasers: each purchaser, at his or her own
expense, to prepare the conveyance to him or her, and to
tender or leave the same at
for execution by
the vendor.
8. That if any of the purchasers shall neglect or fail
to comply with the above conditions, his or her deposit-
money shall be actually forfeited to the vendor, who shall
be at full liberty to re-sell the lot or lots, bought by him
or her, either by public auction or private contract, and
the deficiency (if any) occasioned by such second sale,
shall immediately after the same sale, be made good to
the vendor by the defaulter at this present sale: and in
case of the non-payment of the same, the whole thereof
shall be recoverable by the vendor, as liquidated damages,
and it shall not be necessary to previously tender a con-
veyance to the purchaser.
Lastly. That if any mistake be made in the descrip-
tion of the premises, or any other error whatever, shall
appear in the particulars of the estate, such mistake or
error shall not annul the sale, but a compensation or equi-
LAW OF AUCTION.
763
valent shall be given or taken as the case may require.
Such compensation or equivalent to be settled by two
referees, or their umpire; each party within ten days after
the discovery of the error, and notice thereof given to
the other party, to appoint one referee by writing; and in
case either party shall neglect to nominate a referee
within the time appointed, the referee of the other party
alone may make a final decision. If two referees are ap-
pointed, they are to nominate an umpire before they enter
upon business, and the decision of such referees or umpire
(as the case may be) shall be final.
Conditions to be inserted where the title deeds cannot be
delivered up.
That as the title deeds which concern this estate relate
to other estates of greater value, the vendor shall retain
the same in his custody, and enter into the usual cove-
nants (to be prepared by his solicitor and at his ex-
pense) for the production of them to the respective pur-
chasers; but all attested copies which may be required
of such deeds shall be had and made at the expense of the
person requiring the same.
Where an estate is intended to be sold in lots, and the title
deeds are to be delivered up, the following condition may be
inserted:
That as the aforesaid lots are holden under the same
title, the purchaser of the greater part in value of the said
estate shall have the custody of the title-deeds, upon his
entering into the usual covenants for the production thereof
to the purchaser or purchasers of the remaining or other
lots: if the largest portion in value of the estate shall
remain unsold, the seller shall be entitled to retain the
deeds upon entering into such covenants as aforesaid; all
such covenants to be prepared by and at the expense of
the person or persons requiring the same, who may have
attested copies of such deeds, at his, her, or their own
expense.
764
LAW OF AUCTION.
Condition to be inserted instead of the fourth-if the property
to be sold is leasehold.
That within
from the day of sale, the
vendor shall, at his own expense, prepare and deliver to
the purchaser, or his solicitor, an abstract of his title to
the property sold, commencing with a lease bearing date
the
; but he shall not
be required to produce the lessor's title, nor shall any en-
quiry be made into the lessor's title.
day
A.D.
Agreement to be signed by the purchaser and to be printed or
written on the conditions and particulars.
I have this day purchased of [name of vendor] by public
auction, lot
mentioned in the above-written
particulars, for the sum of £, and have paid into the
hands of
the sum of £
as a deposit and
in part payment of the said purchase-money; and I do
hereby agree to pay the remaining sum of £
-, at
,
on or before the
unto
day of
; and in all other respects, on my part,
to fulfil the above-written conditions of sale. As witness
my hand, this
day of
185-
Purchase-money
Deposit-money
£
Remainder unpaid
£
Witness,
Conditions of Sale on Sale of Goods.
1. That the highest bidder shall be the buyer, and if
any dispute shall arise, between two or more bidders, the
lot shall be put up again and resold.
2. That no person shall advance less at a bidding than
-, or retract his bidding.
3.
That every purchaser shall immediately pay to the
auctioneer a deposit, at the rate of per cent. on the
amount of his bidding and in part payment.
4. That the remainder of the purchase-money shall
be paid and each lot cleared with all faults at the
expense within
days from the day of sale.
AGREEMENTS AND LEASES.
765
5. That no error of description shall annul the sale,
nor shall any allowance be made for such error.
6. That if the purchaser shall make default either in
payment of remainder of the purchase-money, or in clear-
ing the lot or lots purchased by him, according to the above
conditions, his deposit-money and all his right and interest
in the goods purchased shall be forfeited, and the lot or
lots may be re-sold, either by public auction or private
contract, at any time within
and if any
loss shall arise on such re-sale, the party so in default
shall make good the same.
CHAPTER XXIII.
LANDLORD AND TENANT.
SECT. I.-Agreements and Leases.
Lawyers
only may
"Deed."
sional men
an Agree-
ment."
must be by
Tenancy
1. Ir has been seen, that by 44 Geo. III., c. 98, none prepare a
but the lawyers therein specified, can prepare a deed for Non-profes-
gain, fee, or reward, but that any person not a lawyer, may prepare
may prepare an agreement not under seal.
By the conjoint operation of the Statute of Frauds, what Lease
(29 Car. 2, c. 3, s. 1 and 2,) and the statute 8 & 9 Vict., C. Deed.
106, s. 3, all leases for more than three years from the
making thereof, must be by deed. By the same statute,
the assignment, or surrender in writing of a decree, must
be by deed. A lease for three years or less, from the
making thereof, need not be by deed. An agreement for a Nature of
lease for any term is good without deed; and if a tenant is under an
let into possession under such an agreement, he is at first for a Lease.”
a mere tenant-at-will, and may be turned out upon a
demand of possession, or may quit without notice. If he
occupies and pays rent for an aliquot portion of a year
under such agreement, he becomes tenant from year to
year, upon the terms of the agreement, and can only quit
or be expelled from possession, by giving or receiving a
half year's notice to quit, expiring at the period of his
year when his tenancy commenced. If he remains in
possession during the whole term mentioned in the agree-
"Agreement
766
AGREEMENTS AND LEASES.
Obligation of
the party re-
fusing to
give or take
ment he may quit, or be turned out without notice to
quit.
An agreement for a lease renders the party who neglects
or refuses to give or take a lease according to its pro-
a Lease ac- visions liable to an action at law for compensation in
Agreement. damages or to a bill in equity for a specific performance.
It should provide that the intruding lessees shall not call
for the lessor's title.
cording to
What Agree-
ments are
Leases.
Stamps upon
Any agreement which provides for the tenant having
possession of the land for three years or less from its
date, does not contemplate another instrument being
executed before possession is given, is a lease, and must be
stamped as such.
Agreements. 2. The stamp upon an agreement for a lease is
Or if it contains 2160 words, then for every 1080
above the first 1080, a progressive duty of
The stamp upon a lease of lands at a yearly rent
without premium is—
Stamps upon
Leases.
If the yearly rent does not exceed £5
s. d.
2 6
2 6
06
If it exceeds
£5 and not
£10
1 0
10
15
1 6
وو
وو
15
20
2 0
دو
وو
20
25
2 6
99
وو
25
50
5
0
""
وو
50
75
7 6
وو
""
75
100
10 0
وو
وو
50
5 0
100 then for each 50 and also for
every fractional part of
Leases, on which premiums are paid, and leases of mines
on which Royalties are reserved, are subject to other
duties, for which see the Stamp Act, 13 and 14 Vic., c. 97.
There is a progressive duty of 10s. for every 1080 words
beyond the first 1080, if the lease contains 2160 words or
upwards.
If the duty on the lease is 5s., or less, the duty on the
counterpart is the same as on the lease.
But if the duty on the lease exceeds 5s., the counter-
part may be stamped with a 5s. stamp, and a progressive
duty of 2s. 6d. for every 1080 words beyond the first
1080, if it contains 2160 words. But this counterpart must
have a denoting stamp, and can only be so stamped, on
production of both instruments, duly executed and duly
stamped.
AGREEMENTS AND LEASES.
767
Tenancy
year.
3. The ordinary tenancy of lands, houses, &c., is a Ordinary
tenancy from year to year. This tenancy is implied by from year to
law: 1st, where lands, &c., are let at annual rent, and it is
not expressed how long the tenancy is to last.
2nd. Where a tenant holds over, after the expiration of
a lease, or other tenancy, for a definite term, and pays rent
for a year, or an aliquot part of a year, as a quarter.
3rd. Where a tenant enters into possession under an
agreement to purchase, as an agreement for a lease, and
pays rent in like manner.
In the two last cases, the payment and acceptance of
rent raises an inference that the tenancy is to last for a
definite period, and when no other period is defined, the
presumed term is from year to year.
tion of Ten-
If the tenancy is for a year, or other prescribed Determina-
period, the tenant is bound to quit at the end of the ancy.
the term without notice; but if the tenancy is from year
to year, it can only be determined by a notice to quit
expiring at the period of the year when the tenancy com-
menced, unless it is otherwise expressed in the agreement,
If a tenant holds as tenant from year to year under an
agreement for a lease for a certain term of years, his
tenancy may be determined at the expiration of any year
during the term by a six months' notice to quit ; but at the
end of the term mentioned in the agreement, he is bound
to quit without notice.
If the tenancy is for a year, and so on from year to year
so long as the parties please, it is a tenancy for two years
at the least (Doe d. Chadborn v. Green, 9 A. R., 658;
Reg. v. Chawton, 1 G. B., 247). But a tenancy from year
to year so long as both parties please, may be put an end
to at the end of the first year. (Doe d. Clarke v. Smaridge,
7 G. B., 957; Doe d. Plumer v. Mainby, 10 G. B., 473.)
4. In agreements for leases, the term, the rent, the Covenants of
times of payment, and all the covenants upon which the ment for a
tenant is to hold, should be mentioned. It should also be
stated at whose expense the lease and counterpart is to
be prepared, and that the intended lessees shall not enquire
into the lessor's title.
an "Agree-
Lease."
Leases.
5. In agreements for tenancies, which in law are leases, Covenants of
the latter stipulations as to preparation of a lease, and the
landlord's title, are unnecessary.
6. A lease should specify the time from which the term
768
AGREEMENTS AND LEASES.
ment and
Commence- is to commence, and the term during which the tenant is to
hold the premises; if this is mentioned, the tenant is bound
to quit at the end of the term without notice to quit.
length of
term.
Rent and
times of pay-
ment.
Rates and
Taxes.
Repairs.
Agreement to
cultivate
Lands.
7. The rent payable and the times of payment. If an
annual rent is reserved, and no time of payment mentioned,
it is not payable until the end of the year: therefore, if
the intention is that the rent should be payable quarterly
or half yearly, it is necessary expressly to mention it.
8. The property tax, land tax, and sewers rate imposed
on the rent, are taxes on the rent; and the tenant is entitled
to deduct so much of such taxes as are rated on the rent
from it. But if the premises are rated at a higher value
than the rent, he cannot deduct the whole of such taxes.
An agreement that the tenant shall pay the landlord's
property tax, is not binding; but it is lawful for the tenant
to agree to pay the land tax and sewers rate. The
property tax and land tax must be deducted from the rent,
which is paid next after such taxes have been paid. If
the deduction is not then claimed, the landlord is not
bound to allow such taxes out of a subsequent arrear of
Other taxes and rates, such as the house tax and
parish rates, are payable by the tenant. If the tenant agrees
to pay all rates and taxes or to pay rent clear of all rates
and taxes he is bound to pay the land tax and sewers rate.
rent.
9. There should also be an agreement to repair. If the
agreement to repair is absolute, the tenant is found to
rebuild if the premises are destroyed by fire or other acci-
dent. (Gibbons on Dilapidations, 165.) If this is not the
intention an exception should be introduced into the agree-
ment. He is also to pay rent if the premises are destroyed
by fire, unless the event is provided for in the agreement.
(ib. 168.) A landlord is under no obligation to repair,
except by the custom of the city of London, Norfolk,
and the Isle of Ely, in which places the landlord is bound
to repair in the absence of express agreement binding the
tenant to do so. The Landlord is not understood as war-
ranting that the premises are or will continue tenantable
during the term; and if they become unsafe or uninhabit-
able, the tenant cannot claim compensation from the land-
lord, nor if he quits them in consequence, is he excused
from the payment of rent. (ib. 171.)
10. In a lease of lands an agreement to cultivate should
be inserted. In the absence of express agreement on a
AGREEMENTS AND LEASES.
769
letting of farm lands, an agreement to cultivate according
to the custom of the country is implied. (ib. 201.)
ment and the
particular
11. If it is intended to restrain the tenant from assign- As to Assign-
ing his interest either absolutely or without license, or carrying on
from carrying on any particular trades on the premises, Trades.
an agreement to such an effect should be inserted in the
lease. This is especially necessary if the landlord holds
under a lease by which certain trades are prohibited.
ment of Rent
12. There should also be a proviso of forfeiture, in the Non-pay.
event of non-payment of rent or breach of covenant. or breach of
This will enable the landlord, in the events provided for,
to put an end to the tenancy, and recover possession.
Lease for three years, or less, of a House.
Lease made the
Covenant.
day of
of
of
lets, and the said
of the other part.
18
و
between
of the one part, and
The said
premises numbered
-, in
parish of
takes the messuage or tenement, and
in the county of
street, in the
with the appurtenances, for the term of three years from
the
day and year above-mentioned*.
The rent to be £
a year, payable quarterly, with-
out deduction or abatement, on any account whatever, on
the usual quarter days
: the first quarterly payment to become
due and be made on the
next.
day of
Should the premises be burnt down or rendered unin-
habitable by accidental fire, the rent to be suspended until
they are repaired by the landlord so as to be habitable,
and the tenant on the quarter-day subsequent to the fire,
to pay a proportion of the rent calculated up to the day
of the fire; and on the quarter-day subsequent to the
repair of the premises, to pay a proportion of the rent,
calculated from the day of such repair, up to next subse-
quent quarter-day.
* Or some day before. If it is to hold for three years from the day sub-
sequent to the making the lease must be by deed.
770
AGREEMENTS AND LEASES.
The tenant to keep and leave the premises in as good
repair and condition as the same now are in, reasonable
wear and tear, and accidents by tempest or fire only
excepted.
The tenant to pay all rates and taxes assessed or imposed
on the premises during his tenancy, or on the landlord or
tenant in respect thereof, including land tax, sewers rate,
and water and gas rate, but excepting the landlord's pro-
perty tax.
The tenant not to assign or underlet without the license
in writing of the landlord, nor to carry on any of the fol-
lowing trades
*
*
*
*
*
*
*
If the tenant shall neglect to pay the rent within
twenty-one days after it shall become due, although it be
not demanded, or if he shall desert the same, and leave the
same, without a sufficient distress for a quarter's rent,
whether any rent shall be in arrear or not; and if he shall
make breach of, or fail to perform any of the above agree-
ments, this demise shall be void, and it shall be lawful for
the landlord, his heirs, executors, administrators, or assigns,
to re-enter and re-take possession of the premises.
The tenant has paid to the landlord £
for the
fixtures mentioned in the schedule; and the landlord agrees
to re-purchase the said fixtures at the end of the tenancy,
at their value, not exceeding the said sum of £ such
value to be ascertained, in case of disagreement, by two
brokers, one to be named by each party or their umpire.
Should the tenancy continue beyond the term herein
mentioned, it may be determined by a quarter's notice,
expiring at any quarter day.
Schedule of Fixtures.
[The Schedule should be written on the same paper, or annexed to the
lease. If not, it requires a schedule stamp.]
Agreement for a Farm.
Agreement between
of
in the parish of
of
>
of
and
for letting a farm
in the county
the particulars whereof are mentioned
in the schedule hereunder written.
1. Term to be
-years, to be computed from the
AGREEMENTS AND LEASES.
771
day of
continues beyond that time, the same to be determined on
the
day of-
,
and if the tenancy
in any year, by six
calendar months' notice in writing, to be given by either
party to the other.
the
2. Rent to be £
day of
per annum, to commence from
next, and be paid
quarterly on the usual quarter days.
3. The landlord reserves to himself all timber and
timber-like trees. He also reserves to himself and any
person authorised by him the right of sporting over the
premises.
4. The tenant to pay and discharge all land-tax, rates,
taxes, tithes, and rent-charges in lieu of tithes, and other
outgoings of every description, except the landlord's pro-
perty tax.
5. The tenant not to plough or convert to tillage any
part of the premises described in the said schedule to be
meadow or pasture, without the consent in writing of the
landlord, or his agent; nor sow or plant flax, rape, hemp,
or teasels, upon any part of the said premises, under an
additional sum, at the rate of £20 per acre, per annum, to
be payable quarterly, on the days aforesaid, and to be con-
sidered as rent, and payment thereof to be enforceable
accordingly.
6. The tenant not at any time between the 1st day of
November, and the 1st day of April, to depasture or feed
more than two horses, mares, or geldings, in any one close,
at any one time, after giving or receiving notice to quit
the same.
7. The landlord to keep in repair the roofs, walls, beams,
and stanchions of the dwelling-house and out-houses, be-
longing to the said premises.
8. The tenant not to sell or part with any dung or compost
to be made on the premises, nor any hay, straw, halm, or
stubble, or the fodder that shall arise therefrom, but to
spend and consume the same on the premises.
9. The tenant not to let or in any manner otherwise
dispose of or permit to be occupied by any other person,
any part of the premises, without the landlord's consent in
writing.
10. The tenant to keep in repair the glass of the win-
dows of the dwelling house, and to do all internal repairs
UorM
772
AGREEMENTS AND LEASES.
and painting; and also to repair all gates, posts, stiles,
rails, pales, and backings; and the hedges, walls, and other
fences, and to cleanse the ditches, watercourses, and drains.
11. The tenant not to mow any part of the meadow
lands more than once in any year, or after the 10th day
of August, in every year; and in all respects to manage
and cultivate all the premises in a husbandlike manner.
12. The landlord to have and take immediate possession
of the premises, in case the tenant shall be adjudged bank-
rupt, or in case he shall take the benefit of any act for
the relief of insolvent debtors, or shall permit any writ of
execution to be levied on his effects; or if the rent shall
be in arrear for twenty-one days after any quarter-day,
and there shall not be sufficient distress on the premises,
or if the tenant shall make a breach of, or neglect to per-
form any of the above stipulations.
In witness whereof the said parties to these presents
have hereunto set their hands, the
day of
Witness,
185
The Schedule by the foregoing terms referred to.

No. on
Map.
Description of Premises. Culture.
Quantity.
Observations.
A. B. P.
Maou
NOTICE TO QUIT.
773
SECT. II. -Notice to Quit.
sary.
1. A Notice to Quit is necessary in all cases when the When neces-
tenant holds as tenant from year to year, or from month to
month, or from week to week, or for a continuing term
not precisely defined; but not if he holds for a precise term
or at will.
Notice.
2. If the holding is from year to year, the notice must Length of
expire at the end of the current year. It may either be
given 182 days before the end of the current year, or
prior to, or on the corresponding feast, which happens
two quarters before the feast on which the current year
ends, as on Michaelmas-day, to quit on Lady-day. (Doe d.
Harrop v. Green, 4 Esp., 199.)
If the tenancy is quarterly, or monthly, or weekly, it
may be determined by a quarter's, a month's, or a week's
notice expiring at the end of any quarter, month, or week,
of the tenancy.
ancy is con-
commencing.
3. In general the tenancy is understood as commencing When Ten-
from the time of the tenant's entering, and the notice to sidered as
quit must expire at that period of the year; but if his
quarterly or yearly rent is calculated from the quarter-
day preceding or succeeding his entry, his tenancy will be
taken to commence on such quarter-day. (Doe d. Hol-
comb v. Johnson, 6 Esp., 10.) If the yearly tenancy
arises from a holding over, after the expiration of a lease,
it dates from the time when the lease ended. If different
parts of the premises are held from different times as is
often the case in farms, it is sufficient if the notice is given
a half year before the day on which the first year's rent is
payable, or on which the tenancy of the principal part of
the premises commenced. (Dugget v. Snowden, 2 Black.,
1224; Doe d. Ld. Bradford v. Watkins, 7 East., 551.)
4. A notice to quit may be given by an agent, but he By whom
must have authority at the time he gives the notice. An be given.
agent to let and receive rents has authority to give a notice
to quit; but a mere agent to receive rents has not. One
of several joint tenants may give a notice to quit. But
the notice of one of several co-partners or tenants in com-
mon, without authority from the others, only determines
the tenancy of his share.
Notice is to
be given, and
5. It should be given to the tenant himself or to his To whom to
assignee, not to a sub-tenant. If served on the person in Service.
Uor M
774
NOTICE TO QUIT.
Form of
Notice.
Waiver of
Notice.
Holding over
after the
Landlord's
Notice.
possession of the premises, it will be presumed that he is
assignee of the original tenant in the absence of proof to
the contrary. It may be served on the wife or servant of
the tenant on the premises.
6. The notice should be explicit, and not give the tenant
the option of entering into a new contract. But a notice
to quit, or "I shall insist on double rent," is not bad on
this ground, as it merely intimates the legal consequence of
the tenant holding over. It should also be precise as to
the time of quitting. A notice to quit at "the end of the
current year of your tenancy," when the current year
ends within a half year from the notice, is bad; but a notice
to quit "at the end of the current year of your tenancy,
which will expire next after a half year from the service
of this notice," is good, and the proper form to adopt in all
cases where the time of the commencement of the tenancy
is not known or cannot be proved.
7. A notice to quit is waived by receiving or distraining
for rent accruing due after the expiration of the notice.
8. If a tenant wilfully holds over after the termina-
tion of his term, and after demand made and notice in
writing given for delivering possession by the landlord or
his agent, he is liable to pay to the person kept out of
possession for the time he holds over, at the rate of double
the yearly value of the lands detained. (4. Geo. 2., c. 28.)
This provision applies to a tenant holding over after notice
to quit given by the landlord, and such notice is a suffi-
cient notice and demand of possession under the statute.
Holding over 9. If the tenant holds over after a notice to quit given
by himself, he is liable to pay double rent, which may be
distrained for. (11 Geo. 2, c. 19, s. 18.)
after the
Tenant's
Notice.
Form of Notice to Quit.
Mr.
[Tenant's name.]
day of
I hereby give you notice, to quit and deliver up on the*
the dwelling-house [or
next, the possession of
]with the appurtenances
which you now hold of mef, situate in the parish of
2
in the county of
>
provided
your tenancy originally commenced at that time of the
* Day on which tenancy expires.
+ If notice is signed by an agent, here insert landlord's name.
Maou
DISTRESS.
775
year, or otherwise, that you quit and deliver up the posses-
sion of the said dwelling-house, &c. at the end of the year of
your tenancy, which shall expire next after the end of one-
half-year from the time of your being served with this
notice; and further take notice, that unless you quit at the
expiration of this notice, you will be liable to pay double
the yearly value of the premises held over, for so long as
you shall hold over the same.
Dated this
day of
Yours, &c.
185-.
"
SECT. III.-Distress.
Distress, and
it may
be
1. A Distress is a right to seize goods to enforce pay- Nature of
ment of rent. The landlord distraining must have a in what cases
reversion, that is an interest and right to possess the premi- made.
ses after the determination of the tenancy to which the
rent is incident. There must also be a tenancy for a term
certain, at a rent certain. A person let into possession
under a mere agreement for a lease, who is only tenant
at will and may be ejected at his landlord's pleasure, or
may quit at his own, cannot be distrained on until he has
become tenant from year to year, by payment of rent.
time.
2. A distress must be made during the term, or within At what
six calendar months after its determination, during the
landlord's interest and the tenant's possession (8th Ann,
c. 14, s. 6 & 7.) It must be made in the day-time between
sunrise and sunset. It cannot be made until the day after
that on which the rent is payable.
place.
3. The goods distrained must be taken on the premises At what
from which the rent issues. If the goods of the tenant
are fraudulently removed from the premises after the rent
has become due, the landlord may follow and distrain them
within thirty days after the removal, provided they have
not, before seizure, been bonâ fide sold for a valuable con-
sideration. The tenant and all persons wilfully assisting
him in removing or concealing the goods, are liable to a
penalty in double the value of the goods, and if the value of
the goods does not exceed £50, the penalty may be reco-
vered before two justices. If the goods removed are locked
up in any house or other place, the landlord or his bailiff
may, in the day-time, break open and enter the house or
place, first calling to his assistance the constable of the
776
DISTRESS.
What Goods
are Distrain-
able.
Goods abso-
lutely privi-
leged from
Goods in the
Custody of
the Law.
Distress.
Fixtures.
Things part
of the De-
mise.
Things not
the subject
place, and in the case of a dwelling house, making oath of
a reasonable ground to suspect that the goods are in such
dwelling-house (11 Geo. II., c. 19, s. 1 to 7.)
4. All goods on the premises, with certain exceptions,
may be distrained for rent, also cattle and stock on a com-
mon, appendant appurtenant, or in any ways belonging
to the premises-growing corn, grass, hops, fruits, pulse,
and other produce, may also be distrained and may be cut
when ripe, and laid up in barns on the premises, and in
convenient time may be appraised and sold. Notice of
the place where the crops are lodged must be given to
the tenant within one week after they are lodged. If
the tenant pays or tenders the rent and expenses before
the crops are ripe and cut, cured, or gathered, the distress
is to cease (11 Geo. II., c. 19, s. 8 & 9.)
5. Goods privileged from distress are 1st, goods in the
custody of the law, that is, goods already under distress
or under execution. In this latter case, the execution
creditor is bound to pay the landlord the rent due at the
time of the seizure, not exceeding one year's rent, before
the goods can be removed under the execution (8th Ann,
c. 14.)
6. 2ndly, Fixtures or things fixed to the freehold, such
as grates, doors, windows, and the like: a temporary dis-
union of a fixture does not render liable to a distress, as if
a mill-stone is removed for the purpose of being picked.
7. 3rdly, Things which are part of the demise as the
furniture of a furnished lodging.
8. 4thly, Things which are not the subject of property,
of Property. as wild animals, but tame animals such as cattle, dogs,
tame deer, or deer in an inclosure kept for profit, may be
distrained. (Davies v. Powell Willes, 50.)
Perishable
Things, and
which cannot
9. 5thly, Things which cannot certainly be identified
Things and cannot be returned in the same state, such as loose
be identified. money, meal, or the like, and things which quickly perish,
such as meat and milk, are not distrainable, because they
cannot be returned in the same state. But by W. & M.,
c. 5, s. 3, sheaves of corn, or corn loose or in the straw, or
hay in any barn or granary, or in any hovel, stack, or
rick or otherwise, upon any part of the land may be dis-
trained, and locked up and detained in the place where
found, until replevied or sold.
Goods deli- 10. 9thly, things delivered to a person exercising a
vered for pur-
DISTRESS.
777
public trade to be carried, wrought, or managed in the way
of his trade: under this head, a horse sent to a farrier to
be shoed, goods sent to an auctioneer to be sold, or an ox
sent to a butcher to be slaughtered, are exempt from being
distrained, so the horses and carriages of a guest standing
at an inn are privileged; but horses and carriages at a livery
stables are not. (Parsons v. Gingell, 4 C. B., 545.)
poses of
Trade.
7thly, Things in actual use are privileged, because Goods in use.
to take such things may provoke a breach of the peace,
for instance, an axe in a man's hand, a horse on which
he is riding, a cart in which he is standing, a loom at
which he is working.
their way to
8thly, Cattle on their way to market, put on the land Cattle on
for their necessary refreshment, with the privity of the Market."
lessor or the lessee, are privileged. So cattle which es-
cape into the land because there are not sufficient fences,
unless the owner of the cattle is bound to keep up the
fences, are privileged, until they have been levant and
couchant on the tenant's land (which means until they
have been there a whole night). If the landlord or tenant
of the land into which the cattle escape is bound to keep
up the fences, they are not distrainable unless notice has
been given to the owner of his cattle having strayed,
and he has neglected to remove them for a reasonable
time after such notice. In no case can stray cattle be dis-
trained for rent, if the owner has made fresh pursuit and
endeavoured to bring them back.
leged condi-
Implements of husbandry, and beasts of the plough, Things privi-
saddle horses, poultry, implements of trade, wearing apparel tionally.
and jewels, should not be distrained if there is other suffi-
cient distress.
In making a distress no outer door or window can be
broken, nor can the door of a barn or stable.
Manner of
Distraining,
not to break
outer door.
and tender of
The goods must be seized and impounded; they may Impounding
be, and usually are, impounded and sold on the pre- Rent.
mises (11 Geo. II, c. 19, s. 10,) where this is done, they
are considered as impounded as soon as seized. They can-
not be impounded out of the county in which they are
taken, (stat. Marlbridge, 52, Hen. III, c. 4), nor out of
the hundred except in a pound in the same county, and
not above three miles from the place of the distress, under
a penalty of £5 and treble damages. If the rent is
tendered before the distress is impounded, either to the
3 A
778
DISTRESS.
Sale.
Notice of
Distress and
ment.
landlord or to the bailiff making the distress (Hatch v.
Hale, 15 G. B., c. 10,) it must be accepted. But after
the distress is impounded, the landlord is bound to accept
the rent and costs if tendered.
A distress cannot be sued by stat. 2, W. & M., sess.
1, c. 5, if the tenant does not replevy within five days next
after distress taken, and notice thereof left at the chief
mansion house or other most notorious place on the pre-
mises, the person distraining may, with the sheriff or
under-sheriff of the county, or the constable of the hun-
dred, parish or place, where the distress has been taken,
cause the goods distrained to be appraised by two sworn
appraisers (whom such sheriff, under-sheriff, or constable
must swear to appraise the same truly according to the
best of their understanding,) and after such appraisement,
may sell the same for the best price that can be gotten for
them, for satisfaction of the rent and charges of the dis-
tress, appraisement, and sale, leaving the overplus, if any,
with the sheriff, under sheriff, or constable, for the owner's
use.
The notice must be in writing (Wilson v. Nightin-
Appraise gale, 8 G. B., 1034.) It must specify the goods distrained.
It is sufficient to say that all goods on the premises are dis-
trained (Wakeman v. Lindsay, 19 L. J. G. B., 166), but
not sufficient to say all goods on the premises that may be
required to satisfy the rent and expenses, (Kirby v.
Harding, 6 Ex., 234.) Five clear days must elapse after
the day of the distress and notice given, before the goods
can be appraised or sold. (Robinson v. Waddington, 13 Q.
B., 753.) The appraisers must be two persons having no
interest in the matter, the distraining broker cannot be
one. (Westwood v. Cowne, 1 Stush., 172.) There must be
two appraisers, although the rent is under £20. (Allen v.
Flicker, 10 A. V. E., 640.)
in Distress.
Irregularities The distress should not be excessive. The mere cir-
cumstance of the distress being for more rent than due,
does not render the landlord liable to the tenant unless
some special damage has been sustained by him. (Tancred
v. Leyland, 16 G. B., 669.) There cannot be a second
distress for the same rent, unless the value of the first
distress, is found insufficient. (17th Jas. II, c. 7, s. 4;
Dawson v. Cropp, 1 C. B., 961.)
Costs of Dis-
tress.
By 57 Geo. III, c. 93, no person making a distress
DISTRESS.
779
for rent, when the sum demanded and due does not exceed
£20, can take, either from the tenant or the landlord, any
other or more charges for any matter or thing done in the
distress, than are mentioned in the schedule to the act, or
can make any charge for any act mentioned in the schedule,
unless the act has been really done. If he violates the act,
a justice of the peace may order him to pay treble damages
and costs to the party grieved, which may be levied by
distress warrant; in case of no sufficient distress, he may
be committed to gaol, until he pays or satisfies the order;
if the complaint is unfounded, the complainant may be
ordered to pay costs. The landlord is not liable under
this statute, unless he personally levies the distress.
Every broker who makes a distress must give a copy of
his charges, although the rent demanded exceeds £20.
The schedule of charges are:-
Levying Distress
Man in possession, per day
Appraisement 6d. in the pound on the
value of the goods
Stamp, the lawful amount thereof
All expense of advertisements if any
such
Catalogues, sale and commission, and
delivery of goods ls. in the pound
on the net produce of sale
0 3 0
026
. 0 10 0
The provisions of this statute are extended to distresses
for land tax, assessed taxes, poors rates, church rates, tithes,
highway rates, sewer rates, or any other rates or taxes, if
the sum demanded and due does not exceed £20, and to
all cases in which the whole of several sums sought to be
levied by distresses, taken for different purposes at the
same time, do not exceed the sum of £20. (7 & 8 Geo.
IV., c. 17.)
tress on
or Insolven-
In the event of the bankruptcy or insolvency of the Right of Dis-
tenant, the landlord's remedy by distress is limited to Bankruptcy
one year's rent due at the time of the bankruptcy or in- cy of Terant.
solvency, if more is due he must come in as a creditor. (12
& 13 Vict., c. 106, s. 129; Bankrupt act, 1 & 2 Vict., c. 110,
s. 58; Insolvent debtor's act, persons in prison for debt
who petition for their discharge, 7 & 8 Vict., c. 96, s. 18;
Protection act, insolvents who petition for protection from
process.)
780
DISTRESS.
Warrant of Distress.
To Mr.
goods and chattels of
-, my bailiff.
Distrain the
2
(the tenant,) in
the house he now dwells in, (or on the premises in his
possession,) situate in
county of
for
in the
pounds, being one
year's rent due to me for the same at
day last,
and for your so doing this shall be your sufficient warrant
and authority; and in consideration of your so doing, I
hereby undertake to indemnify against loss, costs, charges,
damages, or expenses which you may thereby incur or
sustain, and against any action or proceeding, lawful or
unlawful, which may be brought against you for acting in
obedience to this warrant. Dated this
day of
Mr.
-185-.
Notice of Distress.
Take notice, that I have this day distrained (or that as
bailiff to
, your landlord, I have this day dis-
trained) on the premises above-mentioned, the several
goods and chattels specified in the inventory hereunder
written, for the sum of
year's rent due to me (or to the said -
at
being one
-₂)
day last, for the said premises, and that
unless you pay the said rent, with the charges of distrain-
ing for the same, or replevy the said goods and chattels
within five days from the date hereof, they will be ap-
praised and sold according to law. Given under my hand
the
day of
-, in the year 18—.
Consent by Tenant to hold over.
Memorandum. That I,
do hereby consent and agree that
my landlord, who hath distrained my goods and chattels
for the rent in a dwelling-house,
situate at
,
in the county of
shall continue in the possession of my said goods and chat-
tels, in the said dwelling-house,
space of
for the
days from the date hereof, the said
having agreed to forbear the sale
of the said goods and chattels for the said space of time, to
DISTRESS.
781
enable me to discharge the said rent; and I, the said
do hereby agree to pay the
expenses of keeping the said possession.
As witness my hand the
in the year of our Lord, 18—.
Witness,
day of-
Notice of Distress of Standing Corn.
Take notice, that I have this day, as bailiff of
, your landlord, taken and distrained on the
premises undermentioned, the several growing crops spe-
cified in the inventory underwritten, for the sum of
-, being one year's rent due to the said
£ -
at
day last, for the said premises, and unless
you previously pay the said rent, with the costs of dis-
training the same, I shall proceed to cut, gather, make,
cure, carry, and lay up the crops, when ripe, in the barn,
or other proper place on the said premises, and in conve-
nient time sell and dispose of the same, towards satisfac-
faction of the said rent, and of the costs of the distress,
appraisement, and sale, according to the form of the sta-
tute in that case made and provided. Given under my
hand this
day of
Appraiser's Oath.
18-.
You and each of you shall well and truly appraise the
goods and chattels mentioned in this inventory (holding it
up in his hand) according to the best of your judgment.
So help you God.
Appraisement.
We, the above-named,
and
Evangelists, by
being sworn upon the Holy
the constable
,
above-named, well and truly to appraise the goods and
chattels mentioned in this inventory, according to the best
of our judgment, and having viewed the said goods and
chattels, do appraise the same at the sum of
pounds. As witness our hands the
-, in the year of our Lord 18—.
day of
Sworn Appraisers.
782
RECOVERY OF POSSESSION.
Right of
Entry.
If Premises
are Deserted.
SECT. IV. Recovery of Possession.
In all cases where the interest of the tenant has ex-
pired, the landlord has a right by law to enter and take
possession, and may do so without resorting to any legal
proceeding, if he can, without disturbing the public peace.
But if the tenant is in possession, and is likely to resist the
landlord's entry, it is advisable to proceed at law, as al-
though the tenant can maintain no action, the landlord
may render himself liable to an indictment for a forceable
entry. (See Davison v. Wilson, 11 G. B., 890.)
If a tenant holding lands, &c., at a rack rent, or a
rent which is full three-fourths of the yearly value of the
demised premises is in arrear for a half-year's rent, and
deserts the premises, and leaves them uncultivated, or un-
occupied, so as no sufficient distress can be had to counter-
vail the arrears of rent, two or more justices of the peace
of the county, riding, division, or place having no interest
in the demised premises, at the request of the landlord, his
bailiff or receiver may go upon and view the same,
and affix, or cause to be affixed, on the most notorious part
of the premises, notice in writing, stating what day, (at
the distance of fourteen days at the least,) they will return
to take a second view thereof, and if upon such second view,
the tenant, or some person on his or her behalf, does not
appear and pay the rent in arrear, or there is not a suffi-
cient distress on the premises, the justices may put the
landlord into possession of the demised premises, and the
lease thereof, as to any demise therein contained, only be-
comes void. This proceeding may be taken, although
there is no right or power of re-entry reserved in the lease
to the landlord upon non-payment of rent. The tenant
may appeal to the next justice or justices of assize of the
county in which the lands lie, or if in London or Middle-
sex, to the judges of the Queen's Bench or Common Pleas,
or if in a County Palatine, before the judges thereof
(11 Geo. 2, c. 19, s. 16 & 17; 57 Geo. 3, c. 52.)
If the premises are within the Metropolitan Police Dis-
trict, a police magistrate, at the request of the landlord,
his bailiff, or receiver, made in open court, and upon proof
given to the satisfaction of the magistrate of the arrear of
rent and desertion of the premises, may issue his warrant
RECOVERY OF POSSESSION.
783
Magistrate, if
more than
directed to the police constable, requiring him to go upon
and view the premises, and affix the notices, and upon re-
turn of the warrant and proof that it has been duly
executed, and that neither the tenant nor any person on
his behalf has appeared and paid the rent, and that there
is not sufficient distress on the premises, the magistrate may
issue his warrant to a police constable, requiring him to put
the landlord into possession. (3 & 4 Vict., c. 84, s. 13.)
If the interest of a tenant holding at will, or for any
term not exceeding seven years, either without rent, Before a
or at a rent not exceeding £20, and upon which no fine Rent not
has been reserved or made payable, has ended or been £20.
duly determined by a legal notice to quit, or otherwise,
and the tenant, or any person by whom the premises or
any part is occupied, neglects or refuses to quit and de-
liver up possession, the landlord or his agent may cause
the person so neglecting or refusing to be served with a
written notice, in form set forth in the schedule; and if
the tenant or occupier does not appear at the time and
place appointed, and show to the satisfaction of the justices
reasonable cause why possession should not be given, and
still neglects or refuses to deliver possession, the landlord
or his agent may give the justices proof of the holding and
of the end or determination of the tenancy, with the time
or manner thereof, and if the title of the landlord has ac-
crued since the letting, the right by which he claims pos-
session, and upon proof of the service notice, and the
neglect or refusal of the tenant or occupier, the justices
acting for the district, division, or place within which the
premises or any part thereof are situate, in petty sessions
assembled, or any two of them may issue a warrant under
their hands and seals to the constables and peace officers
of the district, division, or place, within which the premises,
or any part thereof, are situate, commanding them within
a period therein named, not less than twenty-one nor more
than thirty clear days from the date of the warrant, to
enter by force if needful and give possession thereof to the
landlord or agent. The warrant must be executed be-
tween nine in the morning, and four in the afternoon, and
not upon Sunday, Good Friday or Christmas-day, an
action of trespass may be brought against the party apply-
ing for the warrant, if there is no right of entry. Any
rights which the tenant may be entitled to, as outgoing
784
RECOVERY OF POSSESSION.
In County
Court, if
Rent not
more than
£50.
tenant by custom of the country, or otherwise, are not
affected by the proceeding. The notice of application may
be served either personally or by leaving the same with
some person, being in, and apparently residing at, the
place of abode of the person holding over.
The person
serving the notice must read it over to the person served,
and explain the purport and intent. If the person holding
over cannot be found, and his place of abode is not known,
or admission thereto cannot be obtained for serving the
summons, the posting it up on some conspicuous part of
the premises held over is good service.
If the party to whom the warrant is granted has not at
the time a lawful right to enter, the obtaining of the
warrant is an act of trespass. The execution of the
warrant is to be stayed if the tenant, with two sureties to
be approved of by the justices, enters into a bond to try an
action of trespass and pay the costs if unsuccessful. If he
succeeds in the action, the warrant is suspended. The
bond is to be given to the landlord or his agent, and to be
prepared at his (the landlord's or agent's) costs, and is to be
deemed forfeited, unless the judge at the trial, indorses on
the record that the condition has been fulfilled. The
Court in which the action is brought may relieve the
parties from the bond.
No action can be brought against the justices for granting,
or the constables for executing the warrant (1 & 2Vict. c. 74).
The County Courts have jurisdiction to give posses-
sion to a landlord in all cases when the term or interest
of the tenant of premises the value or the rent payable in
respect of which does not exceed £50 by the year,
and upon which no fine has been paid, has ended or been
duly determined by a legal notice to quit if the tenant or
person in occupation neglects or refuses to quit and deliver
up possession of the premises or any part thereof. The
proceeding in the County Court is by plaint, upon which
a summons issues; and if the tenant or occupier does not
appear and show cause to the contrary upon similar proof,
as is required by 1 & 2 Vict., c. 72, the County Court
may grant a warrant to the bailiff, to the same effect as
the warrant to the constable under the former statute,
which has the same effect and must be executed, or may
be suspended in the same manner as the magistrates'
warrant, (9 & 10 Vict., c. 95, s. 122, 3, 4, 5, 6, 7.)
RECOVERY OF POSSESSION.
785
Form of Notice of Owner's Intention to apply to Justices to
recover Possession, under 1 & 2 Vict. c. 74.
I
owner (or agent to the owner
as the case may be), do hereby give you notice, that, unless
peaceable possession of the tenement, (shortly describing it,)
situate
which was held of me (or of
the said
as the case may be,) under a
tenancy from year to year or (as the case may be) which
expired (or was determined) by notice to quit from the
said
(or otherwise as the case may be,j
day of
on the
و
,
and which
tenement is now held over and detained from the said.
be given to (the owner or agent) on or before the
expiration of seven clear days from the service of this
notice, I,
the
day of
2
shall, on
at
next,
of the clock the same
day, apply to Her Majesty's Justices of the Peace, acting
for the district of
(being the district,
division, or place, in which the said tenement, or any part
thereof, is situate,) in Petty Sessions assembled, to issue
their warrant directing the constables of the said district,
to enter and take possession of the said tenement, and to
eject any person therefrom.
Dated this
To Mr.
(Signed)-
(Owner or Agent.)
Complaint before two Justices.
The complaint of
(owner or agent, &c.,
as the case may be) made before us two of her Majesty's
Justices of the peace acting for the district of
of
did let to
for-
>
in Petty Sessions assembled, who saith that the said
at enement consisting
under the rent of
and that the said tenancy expired (or
was determined by notice to quit given by the said
as the case may be), on the
of
the said
"
day
did serve on
(the tenant overholding) a notice in writing of his intention
786
RECOVERY OF POSSESSION.
to apply to recover possession of the said tenement (a
duplicate of which notice is hereto annexed) by giving, &c.,
(describing the mode in which the service was effected,) and
that notwithstanding the said notice, the said
refused (or neglected) to deliver up possession of the
said tenement and still detains the same.
Taken the
(Signed)
day of
(Signed)
before us.
[A duplicate of the notice of intention to apply is to be
annexed to this complaint.]
Warrant to Peace Officers to take and give Possession.
Whereas, (set forth the complaint,) we, two of Her
Majesty's Justices of the Peace, in Petty Sessions as-
sembled acting for the
of
do authorize and command you on any day within
days from the date hereof, (except on Sunday, Christmas
Day, and Good Friday, to be added if necessary,) between
the hours of nine in the forenoon and four in the afternoon,
to enter (by force if needful and with or without the aid
of
the owner or agent, (as the case
may be,) or any other person or persons whom you mày
think requisite to call to your assistance, into and upon
the said tenement, and to eject thereout any person, and
of the said tenement full and peaceable possession to
deliver to the said
(the owner
or agent).
To
Given under our hands and seals this
and all other
constables and peace officers acting
for the district of
day of
CHAPTER XXIV.
TABLES
OF
NATURAL SINES AND COSINES;
AND
ADDITIONAL USEFUL TABLES.
788
NATURAL SINES & COSIN ES..

0°
1º
2°
N. sin
N. cos N. sin
N. cos
N. sin
N. cos
0
00000
1.00000
01745
99985
03490
99939
60
1
00029
1.00000
01774
99984
03519
99938
59
2
00058
1.00000 01803
99984
03548
99937
58
3
00087
1.00000 01832
99983
03577
99936
57
00116
1.00000
01862
99983
03606 99935
56
00145
1.00000 01891
99982
03635
99934
55
6
00175
1.00000 01920
99982
03664
99933
54
7
00204
1.00000
01949
99981
03693
99932
53
8
00233
1.00000
01978
99980 03723
99931
52
9
00262
1.00000
02007
99980
03752
99930
51
10
00291
1.00000
02036
99979
03781
99929
50
11
00320
.99999
02065
99979
03810
99927
49
12
00349
.99999
02094
99978
03839
99926
48
13
00378
.99999
02123
99977
03868
99925
47
14
00407
.99999
02152
99977
03897
99924
46
15
00436
.99999
02181
99976
03926
99923 45
16
00465
.99999
02211
99976
03955
99922
44
17
00495
.99999
02240
99975
03984
99921
43
18
00524
.99999
02269
99974
04013
99919
42
19
00553
.99998
02298
99974
04042
99918
41
20
00582
.99998
02327
99973
04071
99917 40
21
00611
.99998
02356
99972
04100
99916
39
22
00640
.99998
02385
99972
04129
99915
38
23
00669
.99998
02414
99971
04159
99913
37
24
00698
.99998
02443
99970
04188
99912
36
25
00727
.99997
02472
99969
04217
99911
35
26
00756
.99997
02501
99969
04246
99910
34
27
00785
.99997
02530
99968
04275
99909
33
28
00814
.99997
02560
99967
04304
99907
32
29
00844
.99996
02589
99966
04333
99906
31
30
00873
.99996
02618
99966
04362
99905 30
31
00902
.99996 02647
99965
04391
99904
29
32
00931
.99996 02676
99964
04420
99902
28
33
00960
.99995
02705
99963
04449
99901
27
34
00989
.99995 02734
99963
04478
99900
26
35
01018
.99995
02763
99962
04507
99898
25
36
01047
.99995
02792
99961
04536
99897
24
37
01076
.99994
02821
99960
04565
99896
23
38
01105
.99994
02850
99959
04594
99894
22
39
01134
.99994
02879
99959
04623
99893
21
40
01164
.99993 02908
99958
04653
99892
20
41
01193
.99993
02938
99957
04682
99890
19
42
01222
.99993 02967
99956
04711
99889
18
43
01251
.99992
02996
99955
04740
99888
17
44
01280
.99992
03025
99954
04769
99886
16
45
01309
.99991
03054
99953
04798
99885
15
46
01338
.99991
03083
99952
04827
99883
14
47
01367
.99991
03112
99952
04856
99882
13
48
01396
.99990
03141
99951
04885
99881
12
49
01425
.99990
03170
99950
04914
99879
11
50
01454
.99989 03199
99949
04943
99878
10
51
01483
.99989 03228
99948
04972
99876
9
52
01513
.99989 03257
99947
05001
99875
8
53
01542
.99988 03286
99946
05030
99873
7
54
01571
.99988 03316
99945
05059
99872
55
01600
.99987
03345
99944
05088
99870
56
01629
.99987
03374
99943
05117
99869
57
01658
.99986
03403
99942
05146
99867
58
01687
.99986
03432
99941
05175
99866
59
01716
.99985 03461
99940
05205
99864
60
01745
.99985
03490
99939
05234
99863
210
1
N. cos
N. sin
N. cos
N. sin
N. cos
89°
88°
87°
N. sin
NATURAL SINES & COSINES.
789

30
40
50
N. sin
N. cos
N. sin
N. cos
N. sin
N. cos
1
0
05234
99863
06976
99756
08716
99619
60
123 +
05263
99861
07005
99754
08745
99617
59
05292
99860
07034
99752
08774
99614
58
05321
99858
07063
99750
08803
99612
57
4
05350
99857
07092
99748
08831
99609
56
5
05379
99855
07121
99746
08860
99607
55
6
05408
99854
07150
99744
08889
99604
54
7
05437
99852
07179
99742
08918
99602
53
8
05466
99851
07208
99740
08947
99599
52
9
05495
99849
07237
99738
08976
99596
51
10
05524
99847
07266
99736
09005
99594
50
11
05553
99846
07295
99734
09034
99591
49
12
05582
99844
07324
99731
09063
99588
48
13
05611
99842
07353
99729
09092
99586
47
14
05640 99841
07382
99727
09121
99583
46
15
05669
99839
07411
99725
09150
99580 45
16
05698
99838
07440
99723
09179
99578
44
17
05727
99836
07469
99721
09208
99575
43
18
05756
99834
07498
99719
09237
99572
42
19
05785
99833
07527
99716
09266
99570
41
20
05814
99831 07556
99714
09295
99567
40
21
05844
99829
07585
99712
09324
99564
39
22
05873
99827
07614
99710
09353
99562
38
23
05902
99826
07643
99708
09382 99559
37
24
05931
99824
07672
99705
09411
99556
36
25
05960
99822
07701
99703
09440
99553 35
26
05989
99821
07730
99701
09469 99551
34
27
06018
99819
07759
99699
09498
99548
33
28
06047
99817
07788
99696
09527
99545
32
29
06076
99815
07817
99694
09556
99542
31
30
06105
-99813
07846 99692
09585
99540 30
31
06134
99812
07875 99689
09614
99537
29
32
06163
99810
07904
99687
09642
99534
28
33
06192
99808
07933 99685
09671
99531
27
34
06221
99806
07962 99683
09700
99528
26
35
06250
99804
07991
99680
09729
99526
25
36
06279
99803
08020
99678
09758 99523
24
37
06308
99801
08049
99676
09787
99520
23
38
06337
99799
08078
99673
09816
99517
22
39
06366
99797
08107
99671
09845
99514
21
40
06395 99795
08136
99668
09874
99511 20
41
06424
99793
08165
99666
09903 99508
19
42
06453
99792
08194
99664
09932
99506
18
43
06482
99790
08223
99661
09961
99503
17
44
06511
99788
08252
99659
09990
99500
16
45
06540
99786
08281
99657
10019
99497 15
46
06569
99784
08310
99654
10048
99494
14
47
06598
99782
08339
99652
10077
99491
13
48
06627
99780
08368 99649
10106
99488
12
49
06656
99778
08397
99647
10135
99485
11
50
06685
99776
08426
99644
10164
99482
10
51
06714
99774
08455 99642
10192
99479
9
52
06743
99772
08484
99639
10221
99476
8
53
06773
99770
08513
99637
10250
99473
7
54
06802
99768
08542
99635
10279
99470
6
55
06831
99766
08571 99632
10308
99467
5
56
06860
99764
08600 99630
10337
99464
4
57
06889
99762
08629
99627
10366
99461
3
58
888888
06918
99760
08658
99625
10395
99458
2
59
06947
99758
08687 99622
10424
99455
1
60
06976
99756
08716
99619
10453
99452
0
N. cos
N. sin
N. cos
86°
N. sin
85°
N. cos
N. sin
84°
790
NATURAL SINES & COSINES.

6°
mo
8°
N. sin
N. cos
N. sin
N. cos
N. sin
N. cos
0
10453
99452
12187
99255
13917
99027
60
1
10482
99449
12216 99251
13946
99023
59
10511
99446
12245
99248
13975
99019
58
3
10540
99443
12274
99244
14004
99015
57
4
10569
99440
12302
99240
14033
99011
56
5
10597
99437
12331
99237
14061
99006
55
6
10626
99434
12360
99233
14090
99002
54
7
10655
99431
12389
99230
14119
98998
53
8
10684
99428
12418 99226
14148
98994
52
9
10713
99424
12447
99222
14177
98990
51
10
10742
99421
12476
99219
14205
98986 50
11
10771
99418
12504
99215
14234
98982
49
12
10800
99415
12533
99211
14263
98978
48
13
10829
99412
12562
99208
14292
98973
47
14
10858
99409
12591
99204
14320
98969
46
15
10887
99406
12620
99200
14349
98965
45
16
10916
99402
12649
99197
14378
98961
44
17
10945
99399
12678
99193
14407
98957
43
18
10973
99396
12706 99189
14436
98953
42
19
11002
99393
12735
99186
14464
98948
41
20
11031
99390
12764
99182
14493
98944
40
21
11060
99386
12793
99178
14522
98940
39
22
11089
99383
12822
99175
14551
98936
38
23
11118
99380
12851
99171
14580
98931
37
24
11147
99377
12880
99167
14608
98927
36
25
11176
99374
12908
99163
14637
98923
35
26
11205
99370
12937 99160
14666
98919
34
27
11234
99367
12966
99156
14695
98914
33
28
11263
99364
12995
99152
14723
98910
32
29
11291
99360
13024 99148
14752
98906
31
30
11320
99357
13053
99144
14781
98902 30
31
11349
99354
13081
99141
14810
98897
29
32
11378
99351
13110
99137
14838
98893
28
33
11407
99347
13139
99133
14867
98889
27
34
11436
99344
13168 99129
14896
98884
26
35
11465
99341
13197
99125
14925
98880
25
36
11494
99337
13226
99122
14954
98876
24
37
11523
99334
13254
99118
14982
98871
23
38
11552
99331
13283
99114
15011
98867
22
39
11580
99327 13312
99110
15040
98863
21
40 11609
99324
13341 99106
15069
98858
20
41
11638
99320
13370
99102
15097
98854
19
42
11667
99317
13399
99098
15126
98849
18
43
11696
99314
13427
99094
15155
98845
17
44
11725
99310 13456
99091
15184
98841
16
45
11754
99307
13485
99087
15212
98836
15
46
11783
99303
13514
99083
15241
98832
14
1
47
11812
99300 13543
99079
15270
98827
13
48
11840
99297
13572
99075
15299
98823
12
49
11869
99293 13600
99071
15327
98818
11
50
11898
99290
13629
99067
15356
98814 10
51
11927
99286
13658
99063
15385
98809
9
52
11956
99283 13687
99059
15414
98805
8
53
11985
99279 13716
99055
15442
98800
54
12014
99276
13744
99051
15471
98796
6
55
12043
99272 13773 99047
15500
98791
5
56
12071
99269 13802
99043
15529
98787
4
57
12100
99265 13831
99039
15557
98782
3
58
12129
99262 13860
99035
15586
98778
2
59
12158
99258 13889
99031
15615
98773
1
60
12187
99255
13917
99027
15643
98769
0
N. cos
N. sin
N. cos
N. sin
N. cos
83°
82°
N. sin
81°
1
NATURAL SINES & COSINES.
791

g⁰
10°
11°
!
N. sin
N. cos N. sin
N. cos
N. sin
N. cos
0
15643
98769
17365
98481
19081 98163
60
1 2 3 4
15672
98764
17393
98476
19109
98157
59
15701
98760
17422
98471
19138
98152
58
15730
98755
17451
98466
19167
98146
57
15758
98751
17479
98461
19195
98140
56
5
15787
98746 17508
98455
19224
98135 55
15816
98741
17537
98450
19252
98129
54
15845
98737
17565
98445
19281
98124
53
8
15873
98732
17594
98440
19309
98118
52
9
15902
98728
17623
98435
19338
98112
51
10
15931
98723
17651
98430
19366
98107
50
11
15959
98718
17680
98425
19395
98101
49
12
15988
98714
17708
98420
19423
98096
48
13
16017
98709
17737
98414
19452
98090
47
14
16046
98704
17766
98409
19481
98084
46
15
16074
98700
17794
98404
19509
98079
45
16
16103
98695
17823
98399
19538
98073
44
17
16132
98690
17852
98394
19566
98067
43
18
16160
98686
17880
98389
19595
98061
42
19
16189
98681
17909
98383
19623
98056
41
20
16218
98676
17937
98378
19652
98050
40
21
16246
98671
17966
98373
19680
98044
39
22
16275
98667
17995
98368
19709
98039
38
23
16304
98662
18023
98362
19737
98033
37
24
16333
98657
18052
98357
19766
98027
36
25
16361
98652
18081
98352
19794
98021
35
26
16390
98648
18109 98347
19823
98016
34
27
16419
98643
18138
98341
19851
98010
33
28
16447
98638
18166
98336
19880
98004
32
29
16476
98633
18195
98331
19908
97998
31
30
16505
98629
18224
98325
19937
97992 30
31
16533
98624
18252
98320
19965
97987
29
32
16562
98619
18281
98315
19994
97981
28
33
16591
98614
18309
98310
20022
97975
27
34
16620
98609
18338
98304 20051
97969
26
35
16648
98604
18367
98299
20079
97963
25
36
16677
98600
18395
98294 20108
97958
24
37
16706 98595
18424
98288
20136
97952
23
38
16734 98590
18452
98283
20165
97946
22
39
16763
98585
18481
98277
20193
97940
21
40
16792
98580
18509
98272
20222
97934 20
41
16820
98575
18538
98267
20250
97928
19
42
16849
98570
18567
98261
20279
97922
18
43
16878
98565
18595
98256
20307
97916
17
44
16906
98561
18624
98250
20336
97910
16
45
16935
98556
18652
98245
20364
97905 15
46
16964
98551
18681
98240
20393
97899
14
47
16992
98546
18710
98234
20421
97893
13
48
17021
98541
18738
98229
20450 97887
12
49
17050
98536
18767
98223
50
17078
98531
18795
98218
20478
20507 97875
97881
11
10
51
17107
98526
18824
98212
20535 97869
9
52
17136
98521
18852
98207
20563
97863
8
53
17164
98516
18881
98201
20592
97857
54
17193
98511
18910
98196
20620
97851
55
17222
98506
18938
98190 20649
97845
56
17250
98501
18967
98185
20677
97839
57
17279 98496
18995
98179
20706
97833
8888
58
17308
98491
19024
98174
20734
97827
59
17336 98486
19052
98168
20763
97821
60
17365
98481
19081
98163
20791
97815
3210
0
N. cos
N. sin
N. cos
N. sin
N. cos
N. sin
80°
*790
78°
792
NATURAL SINES & COSINES.

12°
1
13°
14°
1
N. sin
N. cos
N. sin
N. cos
N. sin❘ N.
N. cos
0
20791 97815
22495
97437
24192 97030
60
1
20820 97809
22523
97430
24220
97023
59
2
20848
97803
22552
97424
24249
97015
58
3
20877
97797
22580
97417
24277
97008
57.
4
20905
97791
22608
97411
24305
97001
56
5
20933
97784
22637
97404
24333
96994
55
6
20962
97778
22665
97398
24362
96987
54
7
20990
97772
22693
97391
24390
96980
53.
8
21019
97766
22722
97384
24418
96973
52
9
21047
97760
22750
97378
24446
96966
51
10
21076
97754
22778
97371
24474
96959
50
11
21104
97748
22807
97365
24503
96952
49
12
21132
97742
22835
97358
24531
96945
48
13
21161
97735
22863
97351
24559
96937
47
14
21189
97729
22892
97345
24587
96930
46
15
21218
97723
22920
97338
24615
96923
45
16
21246
97717
22948
97331
24644
96916
44
17
21275
97711
22977 97325
24672
96909
18
21303
97705
23005 97318
24700
96902
21
22723*3
21331
97698
23033
97311
24728
96894
20 21360
97692
23062
97304
24756
96887
43 42 41 40
21388
97686
23090
97298
24784
96880
39
21417
97680
23118
97291
24813
96873
38
21445
97673
23146
97284
24841
96866
37
24
21474
97667
23175
97278
24869
96858
36
25
21502
97661
23203
97271
24897
96851
35
26
21530
97655
23231
97264
24925
96844
34
27
21559
97648
23260
97257
24953
96837
33
28
21587
97642
23288
97251
24982
96829
32
29
21616
97636
23316
97244
25010
96822
31
30
21644
97630
23345
97237
25038
96815 30
31
21672
97623
23373
97230
25066
96807
29
32
21701
97617
23401
97223
25094
96800
28
33
21729
97611
23429
97217
25122
96793
27
34
21758
97604
23458
97210
25151
96786
26
35
21786 97598
23486
97203
25179
96778
25
36
21814
97592
23514
97196
25207
96771
24
37
21843
97585
23542
97189
25235
96764
23
38
21871
97579
23571
97182
25263
96756
22
39
21899
97573
23599
97176
25291
96749
21
40
21928 97566
23627
97169
25320
96742 20
41
21956
97560
23656
97162
25348
96734
19
42
21985
97553
23684
97155
25376
96727
18
43
22013
97547
23712
97148
25404
96719
17
44
22041
97541
23740
97141
25432
96712
16
45
22070
97534
23769
97134
25460
96705
15
46
22098
97528
23797
97127
25488
96697
14
47
22126
97521
23825
97120
25516
96690
13
48
22155
97515
23853
97113
25545
96682
12
49
22183
97508
23882
97106
25573
96675
11
50
22212 97502
23910
97100
25601
96667
10
51
22240
97496
23938
97093
25629
96660
9
52
22268
97489
23966
97086
25657
96653
8
53
22297
97483
23995
97079
25685
96645
7
54
22325
97476
24023
97072
25713
96638
6
55
22353
97470
24051
97065
25741
96630
5
56
22382
97463
24079
97058
25769
96623
4
57
22410
97457
24108
97051
25798
96615
58
22438
97450
24136
97044 25826
96608
59
22467
97444
24164
97037
25854
60
22495
97437
24192
97030
25882
96600
96593
~210
3
N. cos
N. sin
N. cos
N. sin
N. cos
N. sin
ryngo
76°
75°
NATURAL SINES & COSINES.
793

15°
16°
N. sin
N. cos N. sin
N. cos
N. sin
170
N. cos
1
0123 4
25882
96593
27564
96126
29237
95630
60
25910
96585
27592
96118
29265
95622
59
25938
96578
27620
96110
29293
95613
58
25966
96570
27648
96102
29321
95605
57
25994
96562
27676
96094
29348
95596
56
5
26022
96555
27704
96086
29376
95588
55
6
26050
96547
27731
96078
29404
95579
54
789
26079
96540
27759
96070
29432
95571
53
26107
96532
27787
96062
29460
95562
52
26135
96524
27815
96054
29487
95554
51
10
26163
96517
27843
96046
29515
95545
50
11
26191
96509
27871
96037
29543
95536
49
12
26219
96502
27899
96029
29571
95528
48
13
26247
96494
27927
96021
29599
95519
47
14
26275
96486
27955
96013
29626
95511
46
15
26303
96479
27983
96005
29654
95502
45
16
26331
96471
28011
95997
29682
95493
44
17
26359
96463
28039
95989
29710
95485
43
18
26387
96456
28067
95981
29737
95476
42
19
26415
96448
28095
95972
29765
95467
41
20
26443
96440
28123
95964
29793
95459
40
21
26471
96433
28150
95956
29821
95450
39
22
26500
96425
28178
95948
29849
95441
38
23
26528
96417
28206
95940
29876
95433
37
24
26556
96410
28234
95931
29904
95424
36
25
26584
96402
28262
95923
29932
95415 35
26
26612
96394
28290
95915
29960
95407
34
27
26640
96386
28318
95907
29987
95398
33
28
26668
96379
28346
95898
30015
95389
32
29
26696
96371
28374
95890
30043
95380
31
30
26724
96363
28402
95882
30071
95372
30
31
26752 96355
28429
95874
30098
95363
29
32
26780
96347
28457
95865
30126
95354
28
33
26808
96340
28485
95857
30154
95345
27
34
26836
96332
28513
95849
30182
95337
26
35
26864
96324
28541
95841
30209
95328 25
36
26892
96316
28569
95832
30237
95319
24
37
26920 96308
28597
95824
30265
95310
23
38
26948
96301
28625
95816
30292
95301
22
39
26976
96293
28652
95807
30320
95293
21
40
27004
96285
28680
95799
30348
95284 20
41
27032
96277
28708
95791
30376
95275
19
42
27060
96269
28736
95782
30403
95266
18
43
27088
96261
28764
95774
30431
95257
17
44
27116
96253
28792
95766
30459
95248
16
45
27144
96246
28820 95757
30486
95240 15
46
27172
96238
28847
95749
30514
95231
14
47
27200
96230
28875
95740
30542
95222
13
48
27228
96222
28903
95732
30570
95213
12
49
27256
96214
28931
95724
30597
95204
11
50
27284 96206
28959
95715
30625
95195
10
51
27312
96198
28987
95707
30653
95186
9
52
27340
96190
29015
95698
30680
95177
8
53
27368
96182
29042
95690
30708
95168
7
54
27396
96174
29070
95681
30736
95159
6
55
27424 96166
29098
95673
30763
95150
5
56
27452
96158
29126
95664
30791
95142
4
57
27480
96150
29154
95656
30819
95133
3
8888
58
27508
96142
29182
95647
30846
95124
2
27536
96134
29209
95639
30874
95115
1
60
27564
96126
29237
95630
30902
95106
0
N. cos
N. sin
N. cos
N. sin
N. cos
N. sin
74°
73°
72°
3 B
794
NATURAL SINES & COSINES.

18°
19°
20°
N. sin
N. cos N. sin
N. cos
N. sin
N. cos
OIQ3 4O7∞☹
0
30902
95106
32557
94552
34202
93969
60
1
30929
95097
32584
94542
34229
93959
889
59
2
30957
95088 32612
94533
34257
93949
58
30985
95079 32639
94523
34284
93939
57
31012
95070
32667
94514
34311
93929
56
5
31040
95061 32694
94504
34339
93919 55
6
31068
95052
32722
94495
34366
93909
54
31095
95043
32749
94485
34393
93899
53
8
31123
95033
32777
94476
34421
93889
52
9
31151
95024
32804
94466
34448
93879
51
10
31178
95015
32832
94457
34475
93869 50
11
H23:
31206
95006
32859
94447
34503
93859
89
49
12
31233
94997 32887
94438
34530
93849
48
13
31261
94988
32914
94428
34557
93839
47
14
31289
94979
32942
94418
34584
93829
46
15
31316
94970
32969
94409
34612
93819
45
16
31344
94961
32997
94399
34639
93809
44
17
31372
94952
33024
94390
34666
93799
43
18
31399
94943
33051
94380
34694
93789
42
19
31427
94933
33079
94370
34721
93779
41
20
31454
94924
33106
94361
34748
93769
40
21
31482
94915
33134
94351
34775
93759
39
22
31510
94906
33161
94342
34803
93748
38
23
31537
94897
33189
94332
34830 93738
37
24
31565
94888
33216
94322
34857
93728
36
25
31593
94878
33244
94313
34884
93718
35
26
31620
94869
33271
94303
34912
93708
34
27
31648
94860
33298
94293
34939
93698
33
28
31675
94851
33326
94284
34966
93688
32
29
31703
94842
33353
94274
34993
93677
31
30
31730
94832
33381
94264
35021
93667
30
31
31758
94823
33408
94254
35048
93657
29
32
31786
94814
33436
94245
35075
93647
28
33
31813 94805
33463
94235
35102
93637
27
34
31841
94795
33490
94225
35130
93626
26
35
31868
94786
33518
94216
35157
93616 25
36
31896
94777
33545
94206
35184
93606
24
37
31923
94768
33573
94196
35211
93596
23
38
31951
94758
33600
94186
35239
93585
22
39
31979
94749
33627
94176
35266
93575
21
40
32006
94740
33655
94167
35293
93565 20
41
32034
94730
33682
94157
35320
93555
19
42
32061
94721
33710
94147
35347
93544
18
43
32089
94712
33737
94137
35375
93534
17
44
32116
94702
33764
94127
35402
93524
16
45
32144
94693 33792
94118
35429
93514 15
46
32171
94684
33819
94108
35456
93503
14
47
32199
94674
33846
94098
35484
93493
13
48
32227
94665
33874
94088
35511
93483
12
49
32254
94656
33901
94078
35538
93472
11
50
32282 94646
33929 94068
35565
93462
10
51
32309
94637
33956
94058
35592
93452
9
52
32337
94627
33983
94049
35619
93441
8
53
32364
94618
34011
94039
35647
93431
7
54
32392
94609
34038
94029
35674
93420
6
55
32419
94599
34065
94019
35701
93410
5
56
32447
94590
34093
94009
35728
93400
4
57
32474
94580
34120
93999
35755
93389
3
58
32502
94571
34147
93989
35782
93379
2
59
32529
94561
34175
93979
35810
93368
60
32557
94552
34202
93969
35837
93358
0
N. cos
N. sin
N. cos
71°
N. sin
70°
N. cos
N. sin
69°
NATURAL SINES & COSINES.
795

21°
22°
23°
1
N. sin
N. cos
N. sin
N. cos
N. sin
N. cos
0123 +
35837
93358
37461
92718
39073
92050
60
35864
93348
37488
92707
39100
92039
59
35891
93337
37515
92697
39127
92028
58
35918
93327
37542
92686
39153
92016
57
35945
93316
37569
92675
39180
92005
56
5
35973
93306
37595
92664
39207
91994 55
6
36000
93295
37622
92653
39234
91982
54
7
36027
93285
37649
92642
39260
91971
53
8
36054
93274
37676
92631
39287
91959
52
9
36081
93264
37703
92620
39314
91948
51
10
36108
93253
37730
92609
39341
91936
50
11
36135
93243
37757
92598
39367
91925
49
12
36162
93232
37784
92587
39394
91914
48
13
36190
93222
37811
92576
39421
91902
47
14
36217
93211
37838
92565
39448
91891
46
15
36244
93201
37865
92554
39474
91879
45
16
36271
93190
37892
92543
39501
91868
44
17
36298
93180
37919
92532
39528
91856
43
18
36325
93169
37946
92521
39555
91845
42
19
36352
93159
37973
92510
39581
91833
41
20
36379
93148
37999
92499
39608
91822
40
21
36406
93137
38026
92488
39635
91810
39
22
36434
93127
38053
92477
39661
91799
38
23
36461
93116
38080
92466
39688
91787
37
24
36488
93106
38107
92455
39715
91775
36
25
36515
93095
38134
92444
39741
91764
35
26
36542
93084
38161
92432
39768
91752
34
27
36569
93074
38188
92421
39795
91741
33
28
36596
93063
38215
92410
39822
91729
32
29
36623 93052
38241
92399
39848
91718
31
30
36650
93042
38268 92388
39875
91706
30
31
36677
93031
38295
92377
·
· 39902
91694
29
32
36704
93020
38322
92366
39928
91683
28
33
36731
93010
38349
92355
39955
91671
27
34
36758
92999
38376
92343
39982
91660
26
35
36785 92988
38403
92332
40008
91648 25
36
36812
92978
38430
92321
40035
91636
24
37
36839
92967
38456
92310
40062
91625
23
38
36867
92956
38483
92299
40088
91613
22
39
36894
92945
38510
92287
40115
91601
21
40
36921 92935
38537
92276
40141 91590 20
41
36948
92924
38564 92265
40168
91578
19
42
36975
92913
38591
92254
40195
91566
18
43
37002
92902
44
37029 92892
45
37056 92881
46
37083
92870
38617 92243
38644 92231
38671 92220
38698 92209
40221
91555
17
40248
91543
16
40275 91531
15
40301
91519
14
47
37110
92859
38725 92198
40328
91508
13
48
37137
92849
38752
49
37164 92838
38778
92186
92175
40381
40355 91496
91484
12
11
50
37191 92827
38805 92164
40408
91472 10
51
37218
92816
38832
92152
40434
91461
9
52
37245
92805
38859
92141
40461
91449
8
53
37272
92794
38886
92130
40488
91437
7
54
37299 92784
38912
92119
40514
91425
6
55
37326
92773 38939
92107
40541
91414
5
56
37353
92762
38966
92096
40567
91402
4
57
37380
92751
38993
92085
40594
91390
3
58
37407
92740
39020
92073
40621
91378
888
59
37434
92729
39046
92062
40647
91366
60
37461
92718
39073
92050
40674
91355
210
N. cos
N. sin
N. cos
N. sin
N. cos
N. sin
68°
67°
66°
796
NATURAL SINES & COSINES.

24°
25°
26°
N. sin
N. cos
N. sin
N. cos
N. sin N. cos
012345
40674
91355
42262
90631
43837
89879
60
40700
91343
42288
90618
43863
89867
59
40727
91331
42315
90606
43889
89854
58
40753
91319
42341
90594
43916
89841
57
40780
91307
42367
90582
43942
89828
56
40806
91295
42394
90569
43968
89816
55
6
40833
91283
42420
90557
43994
89803
54
40860
91272
42446
90545
44020
89790
53
8
40886
91260
42473
90532
44046
89777
52
9
40913
91248
42499
90520
44072
89764
51
10
40939
91236
42525
90507
44098
89752
50
11
40966
91224
42552
90495
44124
89739
49
12
40992
91212
42578
90483
44151
89726
48
13
41019
91200
42604
90470
44177
89713
47
14
41045
91188
42631
90458
44203
89700
46
15
41072
91176
42657
90446
44229
89687
45
16
41098
91164
42683
90433
44255
89674
44
17
41125
91152
42709
90421
44281
89662
43
18
41151
91140
42736
90408
44307
89649
42
19
41178
91128
42762 90396
44333
89636
41
20
41204
91116
42788
90383
44359
89623
40
21
41231
91104
42815
90371
44385
89610
39
22
41257
91092
42841
90358 44411
89597
38
23
41284
91080
42867
90346
44437
89584
37
24
41310
91068
42894
90334
44464
89571
36
25
41337 91056
42920
90321
44490
89558
35
26
41363
91044
42946
90309
44516
89545
34
27
41390 91032
42972 90296
44542
89532
33
28
41416
91020
42999
90284
44568
89519
32
29
41443
91008
43025
90271
44594
89506
31
30
41469
90996
43051 90259
44620
89493 30
31
41496
90984 *
43077
90246
44646
89480
29
32
41522
90972
43104
90233
44672
89467
28
33
41549
90960
43130
90221
44698
89454
27
34
41575 90948
43156
90208
44724
89441
26
35
41602
90936
43182
90196
44750
89428 25
36
41628
90924
43209
90183
44776
89415
24
37
41655
90911
43235
90171
44802
89402
23
38
41681
90899
43261
90158
44828
89389
22
39
41707
90887
43287
90146
44854
89376
21
40
41734
90875
43313
90133
44880
89363 20
41
41760
90863
43340
90120
44906
89350
19
42
41787
90851
43366
90108
44932
89337
18
43
41813 90839
43392
90095
44958
89324
17
44
41840
90826
43418
90082
44984
89311
16
45
41866 90814
43445
90070
45010 89298
15
46
41892 90802
43471
90057
45036
89285
14
47
41919
90790
43497
90045
45062
89272
13
48
41945
90778
43523
90032
45088
89259
12
49
41972
90766
43549
90019
45114
89245
11
50
41998
90753
43575
90007 45140 89232
10
51
42024
90741
43602
89994
45166
89219
52
42051
90729
43628
89981
45192
89206
8
53
42077
90717
43654
89968
45218
89193
7
54
42104
90704
43680
89956
45243
89180
6
55
42130
90692
43706 89943
45269
89167
5
56
42156
90680
43733
89930
45295
89153
4
57
42183
90668
43759
89918
45321
89140
3
58
42209
90655
43785
89905
45347
89127
59
42235
90643
43811
89892
45373
89114
60
42262
90631
43837
89879
45399
89101
210
0
N. cos
N. sin
N. cos
N. sin
N. cos
N. sin
65°
64°
63°
NATURAL SINES & COSINES.
797

27°
28°
29°
N. sin
N. cos N. sin
N. cos
N. sin
N. cos
0
45399
89101
46947
88295
48481
87462
60
123
45425
89087
46973
88281
48506
87448
59
45451
89074
46999
88267
48532
87434
58
45477
89061
47024
88254
48557
87420
57
4
45503
89048
47050
88240
48583
87406
56
45529
89035
47076
88226
48608
87391 55
6
45554
89021
47101
88213
48634
87377
54
7
45580
89008
47127
88199
48659
87363
53
8
45606
88995
47153
88185
48684
87349
52
9
45632
88981
47178
88172
48710
87335
51
10
45658
88968
47204
88158
48735
87321 50
11
45684
88955
47229
88144
48761
87306
49
12
45710
88942
47255
88130
48786
87292
48
13
45736
88928
47281
88117
48811
87278
47
14
45762
88915
47306
88103
48837
87264
46
15
45787
88902
47332
88089
48862
87250 45
16
45813
88888
47358
88075
48888
87235
44
17
45839
88875
47383
88062
48913
87221
43
18
45865
88862
47409
88048
48938
87207
42
19
45891
88848
47434
88034
48964
87193
41
20
45917
88835
47460
88020
48989
87178
40
21
45942
88822
47486
88006
49014
87164
39
22
45968
88808
47511
87993
49040
87150
38
23
45994
88795
47537
87979
49065
87136
37
24
46020
88782
47562
87965
49090
87121
36
25
46046
88768
47588
87951
49116
87107 35
26
46072
88755
47614
87937
49141
87093
34
27
46097
88741
47639
87923
49166
87079
33
28
46123
88728
47665
87909
49192
87064
32
29
46149
88715
47690
87896
49217
87050
31
30
46175
88701
47716
87882
49242
87036 30
31
46201
88688 47741
87868
49268
87021
29
32
46226
88674
47767
87854
49293
87007
28
33
46252
88661
47793
87840
49318
86993
27
34
46278
88647
47818
87826
49344 86978
26
35
46304
88634
47844
87812
49369
86964 25
36
46330
88620
47869
87798
49394
86949
24
37
46355
88607
47895
87784
49419
86935
23
38
46381
88593 47920
87770
49445
86921
22
39
46407
88580 47946
87756
49470
86906
21
40
46433
88566
47971
87743
49495
86892 20
41
46458
88553 47997
87729
49521
86878
19
42
46484
88539
48022
87715
49546
86863
18
43
46510 88526
48048
87701
49571
86849
17
44
46536
88512
48073 87687
49596
86834
16
45
46561
88499
48099
87673
49622 86820
15
46
46587
88485
48124
87659
49647
86805
14
47
46613
88472
48150
87645
49672 86791
13
48
46639
88458 48175
87631
49
46664
88445
48201
87617
50
46690
88431
48226
87603
49697 86777
49723 86762
49748 86748 10
12
11
51
46716
88417
48252
87589
49773 86733
9
52
46742
88404
48277
87575
49798 86719
8
53
46767 88390
48303
87561
49824
86704
7
54
46793
88377
48328
87546
49849
86690
6
55
46819 88363 48354
87532
49874
86675
5
56
46844 88349
48379
87518
49899
86661
4
57
46870 88336
48405
87504
49924 86646
3
8888888
58
46896 88322
48430
87490
49950
86632
59
46921
88308
48456
87476
49975
60
46947
88295
48481
87462
50000
86617
86603
210
N. cos
N. sin
N. cos
N. sin
N. cos
N. sin
62°
61°
60°
798
NATURAL SINES & COSINES.

30°
31°
32°
1
N. sin
N. cos
N. sin
N. cos
N. sin
N. cos
0
50000
86603
51504
85717
52992
84805 60
1
50025
86588
51529
85702
53017
84789
59
2
50050
86573
51554
85687
53041
84774
58
3
50076
86559
51579
85672
53066
84759
57
4
50101
86544
51604
85657
53091
84743
56
5
50126
86530
51628
85642
53115
84728
55
6
50151
86515
51653
85627
53140
84712
54
7
50176
86501
51678
85612
53164
84697
53
8
50201
86486
51703
85597
53189
84681
52
9
50227
86471
51728
85582
53214
84666
51
10
50252
86457
51753
85567
53238
84650 50
11
50277
86442
51778
85551
53263
84635
49
12
50302
86427
51803
85536
53288
84619
48
13
50327
86413
51828
85521
53312
84604
47
14
50352
86398
51852
85506
53337
84588
46
15
50377
86384
51877
85491
53361
84573
45
16
50403
86369
51902
85476
53386
84557
44
17
50428
86354
51927
85461
53411
84542
43
18
50453
86340
51952
85446
53435
84526
42
19
50478
86325
51977
85431
53460
84511
41
20
50503
86310
52002
85416
53484
84495
40
21
50528
86295
52026
85401
53509
84480
39
22
50553
86281
52051
85385
53534
84464
38
23
50578
86266
52076
85370
53558
84448
37
24
50603
86251
52101
85355
53583
84433
36
25
50628
86237
52126
85340
53607
84417 35
26
50654
86222
52151
85325
53632
84402
34
27
50679
86207
52175
85310
53656
84386
38
28
50704
86192
52200
85294
53681
84370
32
29
50729
86178
52225
85279
53705
84355
31
30
50754 86163
52250
85264
53730
84339
30
31
50779
86148
52275
85249
53754
84324
29
32
50804
86133
52299
85234
53779
84308
28
33
50829
86119
52324
85218
53804
84292
27
34
50854
86104
52349
85203
53828
84277
26
35
50879
86089
52374
85188
53853
84261 25
36
50904
86074
52399
85173
53877
84245
24
37
50929
86059
52423
85157
53902
84230
23
38
50954
86045
52448
85142
53926
84214
22
39
50979
86030
52473
85127
53951
84198
21
40
51004 86015
52498
85112
53975
84182
20
41
51029
86000
52522
85096
54000
84167
19
42
51054
85985
52547
85081
54024
84151
18
43
51079
85970
52572
85066
54049
84135
17
44
51104
85956
52597
85051
54073
84120
16
45
51129 85941
52621
85035
54097 84104 15
46
51154
85926
52646
85020
54122 84088
14
47
51179
85911
52671
85005
54146
84072
13
48
51204
85896
52696
84989
54171
84057
12
49
51229
85881
52720
84974
54195
84041
11
50
51254 85866
52745 84959
54220
84025
10
51
51279
85851 52770
84943
54244
84009
9
52
51304
85836 52794
84928
54269
83994
8
53
51329
85821
52819
84913
54293
83978
17
54
51354 ·
85806
52844 84897
54317
83962
55
51379
85792 52869 84882 54342
83946
5
56
51404
85777
52893
84866
54366
83930
4
57
51429
85762
52918
84851
54391
83915
58
888
51454
85747
52943
84836
54415
83899
59
51479
85732
52967
84820
54440
83883
60
51504
85717
52992
84805
54464
N. cos
N. sin
N. cos
N. sin
N. cos
83867
N. sin
3210
59°
58°
57°
NATURAL SINES & COSINES.
799

33°
34°
35°
N. sin
N. cos
N. sin
N. cos
N. sin
N. cos
0
54464
83867
55919
82904
57358
81915
60
54488
83851
55943
82887
57381
81899
59
2
54513
83835
55968
82871
57405
81882
58
3
54537
83819
55992
82855
57429
81865
57
4
54561
83804
56016
82839
57453
81848
56
54586 83788
56040
82822
57477
81832
55
1
6
54610
83772
56064
82806
57501
81815
54
7
54635
83756
56088
82790
57524
81798
53
8
54659
83740
56112
82773
57548
81782
52
9
54683
83724
56136
82757
57572
81765
51
10
54708
83708
56160
82741
57596
81748 50
11
54732
83692
56184
82724
57619
81731
49
12
54756
83676
56208
82708
57643
81714
48
13
54781
83660
56232
82692
57667
81698
47
14
54805
83645
56256
82675
57691
81681
46
15
54829
83629
56280
82659
57715
81664
45
16
54854
83613
56305
82643
57738
81647
44
17
54878
83597
56329
82626
57762
81631
43
18
54902
83581
56353
82610
57786
81614
42
19
54927
83565
56377
82593
57810
81597
41
20
54951
83549
56401
82577
57833
81580
40
21
54975 83533
56425
82561
57857
81563
39
22
54999
83517
56449
82544
57881
81546
38
23
55024
83501
56473
82528
57904
81530
37
24
55048
83485
56497
82511
57928
81513
36
25
55072
83469
56521
82495
57952
81496
35
26
55097
83453
56545
82478
57976
81479
34
27
55121
83437
56569
82462
57999
81462
33
28
55145
83421
56593
82446
58023
81445
32
29
55169
83405
56617
82429
58047
81428
31
30
55194
83389
56641
82413
58070
81412
30
31
55218
83373
56665
82396
58094
81395
29
32
55242 83356
56689
82380
58118
81378
28
33
55266
83340
56713
82363
58141
81361
27
34
55291
83324 56736
82347
58165
81344
26
35
55315
83308
56760
82330
58189
81327 25
36
55339
83292
56784
82314
58212
81310
24
37
55363
83276
56808
82297
58236
81293
23
38
55388
83260
56832
82281
58260
81276
22
39
55412
83244
56856
82264
58283
81259
21
40
55436
83228
56880
82248
58307
81242 20
41
55460
83212
56904
82231
58330
81225
19
42
55484
83195
56928
82214
58354
81208
18
43
55509
83179
56952
82198
58378
81191
17
44
55533
83163
56976
82181
58401
81174
16
45
55557
83147
57000
82165
58425
81157 15
46
55581
83131
57024
82148
58449
81140
14
47
55605
83115
57047
82132
58472
81123
13
48
55630
83098
57071
82115
58496
81106
12
49
55654
83082
57095
82098
58519
81089
11
50
55678
83066
57119
82082
58543
81072 10
51
55702
83050
57143
82065
58567
81055
9
52
55726
83034
57167
82048
58590
81038
8
53
55750 83017
57191
82032
58614
81021
7
54
55775
83001
57215
82015
58637
81004
6
55
55799 82985 57238
81999
58661
80987
56
55823
82969
57262
81982
58684
80970
4
57
55847
82953
57286
81965
58708
80953
58
55871
82936
57310
81949
58731
80936
59
55895
82920
57334
81932
58755
80919
60
55919
82904
57358
81915
58779
N. cos
N. sin
N. cos
56°
N. sin
55°
N. cos
54°
80902
N. sin
3Q10
2
800
NATURAL SINES & COSINES.

36°
37°
38°
N. sin
N. cos
N. sin
N. cos
N. sin
N. cos
0
58779
80902
60182
79864
61.566
78801 60
1
58802
80885
60205
79846
61589
78783
59
2
58826
80867
60228
79829
61612
78765
58
3
58849
80850
60251
79811
61635
78747
57
58873
80833
60274
79793
61658
78729
56
5
58896
80816
60298
79776
61681
78711 55
6
58920
80799
60321
79758
61704
78694
54
58943
80782
60344
79741
61726
78676
53
8
58967
80765
60367
79723
61749
78658
52
9
58990
80748
60390
79706
61772
78640
51
10
59014
80730
60414
79688
61795
78622 50
11
59037
80713
60437
79671
61818
78604
49
12
59061
80696
60460
79653
61841
78586
48
13
59084
80679
60483
79635
61864
78568
47
14
59108
80662
60506
79618
61887
78550
46
15
59131
80644
60529
79600
61909
78532
45
16
59154
80627
60553
79583
61932
78514
44
17
59178
80610
60576
79565
61955
78496
43
18
59201
80593
60599
79547
61978
78478
42
19
59225
80576
60622
79530 62001
78460
41
20
59248
80558
60645
79512
62024
78442
40
21
59272
80541
60668
79494
62046
78424
39
***
22
59295
80524
60691
79477
62069
78405
38
23
59318
80507
60714
79459
62092
78387
37
24
59342
80489
60738
79441
62115
78369
36
25
59365
80472 60761
79424
62138
78351
35
26
59389
80455
60784
79406
62160
78333
34
27
59412
80438
60807
79388
62183
78315
33
28
59436
80420
60830
79371
62206
78297
32
29
59459
80403
60853
79353
62229
78279
31
30
59482 80386
60876
79335
62251
78261 30
31
59506
80368
60899
79318
62274
78243
29
32
59529
80351
60922
79300 62297
78225
28
33
59552
80334
60945
79282
62320
78206
27
34
59576
80316
60968
79264
62342
78188
26
35
59599
80299
60991
79247
62365
78170 25
36
59622
80282
61015
79229
62388
78152
24
37
59646
80264
61038
79211
62411
78134
23
38
59669
80247
61061
79193
62433
78116
22
39
.59693
80230
61084
79176
62456
78098
21
40
59716 80212
61107
79158
62479
78079
20
41
59739
80195
61130
79140
62502
78061
19
42
59763
80178
61153
79122
62524
78043
18
43
59786
80160
61176
79105
62547
78025
17
44
59809
80143
61199
79087
62570
78007
16
45
59832
80125
61222
79069
62592
77988 15
46
59856
80108
61245
79051
62615
77970
14
47
59879
80091
61268
79033
62638
77952
13
48
59902
80073
61291
79016
62660
77934
12
49
59926
80056
61314
78998
62683
77916
11
50
59949
80038
61337
78980
62706
77897 10
51
59972
80021
61360
78962 62728
77879
9
52
59995
80003
61383
78944
62751
77861
8
53
60019
79986
61406
78926
62774
77843
54
60042
79968
61429
78908
62796
77824
6
55
60065 79951
61451
78891
62819
77806
5
56
60089
79934
61474
78873
62842
77788
4
5888
57
60112
79916
61497 78855
62864
77769
3
60135
79899
61520
78837
62887
77751
2
59
60158
79881
61543
78819
62909
77733
1
60
60182
79864
61566
78801
62932
77715
N. cos
N. sin
N. cos
N. sin
N. cos
N. sin
53°
52°
51°
NATURAL SINES & COSINES.
801

39°
40°
41°
N. sin N. cos N. sin
N. cos
N. sin
N. cos
0
62932
77715
64279
76604
65606
75471
60
1234
62955
77696
64301
76586
65628
75452
59
62977
77678
64323
76567
65650
75433
58
63000
77660
64346
76548
65672
75414
57
63022
77641
64368
76530
65694
75395
56
5
63045
77623
64390
76511
65716
75375
55
6
63068
77605
64412
76492
65738
75356
54
7
63090
77586
64435
76473
65759
75337
53
8
63113
77568
64457
76455
65781
75318
52
9
63135
77550
64479
76436
65803
75299
51
10
63158
77531
64501
76417
65825
75280
50
11
63180
77513
64524
76398
65847
75261
49
12
63203
77494
64546
76380
65869
75241
48
13
63225
77476
64568
76361
65891
75222
47
14
63248
77458
64590
76342
65913
75203
46
15
63271
77439
64612
76323
65935
75184 45
16
63293
77421
64635
76304
65956
75165
44
17
63316
77402
64657
76286
65978
75146
43
18
63338
77384
64679
76267
66000
75126
42
19
63361
77366
64701
76248
66022
75107
41
20
63383
77347
64723
76229
66044
75088
40
21
63406
77329
64746
76210
66066
75069
39
22
63428
77310
64768
76192
66088
75050
38
23
63451
77292
64790
76173
66109
75030
37
24
63473
77273
64812
76154
66131
75011
36
25
63496
77255
64834
76135
66153
74992
35
26
63518
77236
64856
76116
66175
74973
34
27
63540
77218
64878
76097
66197
74953
33
28
63563
77199
64901
76078
66218
74934
32
29
63585
77181
64923
76059
66240
74915
31
30
63608
77162
64945
76041
66262
74896 30
31
63630
77144
64967
76022
66284
74876
29
32
63653 77125
64989
76003
66306
74857
28
33
63675
77107
65011
75984
66327
74838
27
34
63698
77088
65033
75965
66349
74818
26
35
63720
77070
65055
75946
66371
74799
25
36
63742
77051
65077
75927
66393
74780
24
37
63765
77033
65100
75908
66414
74760
23
38
63787
77014
65122
75889
66436
74741
22
39
63810
76996
65144
75870
66458
74722
21
40
63832
76977
65166
75851
66480
74703 20
41
63854 76959
65188
75832
66501
74683
19
42
63877
76940
65210
75813
66523
74664
18
43
63899
76921
65232
75794
66545
74644
17
44
63922
76903
65254
75775
66566
74625
16
45
63944
76884
65276
75756 66588
74606
15
46
63966
76866
65298
75738
66610
74586
14
47
63989 76847
65320
75719
66632
74567
13
48
64011 76828
65342
75700
66653
74548
12
49
64033
76810
65364
75680
66675
74528
11
50
64056
76791
65386
75661
66697
74509
10
51
64078
76772
65408
75642
66718
74489
9
52
64100
76754
65430
75623
66740
74470
8
53
64123
76735
65452
75604
66762
74451
7
54
64145
76717
65474
75585
66783
74431
6
55
64167
76698
65496
75566 66805
74412
5
56
64190
76679
65518
75547
66827
74392
4
57
64212
76661
65540
75528
66848
74373
3
58
64234 76642
65562
75509
66870
74353
59
64256 76623
65584
75490
66891
74334
60
64279
76604
65606
75471
66913
74314
210
N. cos
N. sin
N. cos
50°
N. sin
49°
N. cos
N. sin
48°
802
NATURAL SINES & COSINES.

42°
43°
44°
/
N. sin
N. cos
N. sin
N. cos
N. cos❘ N. sin
N. cos
0
66913
74314
68200
73135
69466
71934 60
12345
66935
74295
68221
73116
69487
71914
899
59
66956
74276
68242
73096
69508
71894
58
66978
74256
68264
73076
69529
71873
57
66999
74237
68285
73056
69549
71853
56
67021
74217
68306
73036
69570
71833 55
67043
74198
68327
73016
69591
71813
54
7
67064
74178
68349
72996
69612
71792
53
8
67086
74159
68370
72976
69633
71772
52
9
67107
74139
68391
72957
69654
71752
51
10
67129
74120
68412
72937
69675
71732 50
11
67151
74100
68434
72917
69696
71711
49
12
67172
74080
68455
72897
69717
71691
48
13
67194
74061
68476
72877
69737
71671
47
14
67215
74041
68497
72857
69758
71650
46
15
67237
74022
68518
*72837
69779
71630
45
16
67258
74002
68539
72817
69800
71610
44
17
67280
73983
68561
72797
69821
71590
43
18
67301
73963
68582
72777
69842
71569
42
19
67323
73944
68603
72757
69862
71549
41
20
67344
73924
68624
72737
69883
71529
40
21
67366
73904
68645
72717
69904
71508
39
22
67387
73885
68666
72697
69925
71488
38
23
67409
73865
68688
72677
69946
71468
37
24
67430
73846
68709
72657
69966
71447
36
25
67452
73826
68730
72637
69987
71427
35
26
67473
73806
68751
72617
70008
71407
34
27
67495
73787
68772
72597
70029
71386
33
28
67516
73767
68793
72577
70049
71366
32
29
67538
73747
68814
72557
70070
71345
31
30
67559 73728
68835
72537
70091
71325
30
31
67580
73708
68857
72517
70112
71305
29
32
67602
73688
68878
72497
70132
71284
28
33
67623
73669
68899
72477
70153
71264
27
34
67645
73649
68920
72457
70174
71243
26
35
67666
73629
68941
72437
70195
71223
25
36
67688
73610
68962
72417
70215
71203
24
37
67709
73590
68983
72397
70236
71182
23
38
67730
73570
69004
72377
70257
71162
22
39
67752
73551 69025
72357
70277
71141
21
40
67773 73531
69046
72337
*70298
*71121
20
41
67795
73511
69067
72317
70319
71100
19
42
67816
73491
69088
72297
70339
71080
18
43
67837
73472
69109
72277
70360
71059
17
44
67859
73452
69130 72257
70381
71039
16
45
67880 73432
69151
72236
70401
71019
15
46
67901
73413
69172
72216
70422
70998
14
47
67923
73393
69193
72196
70443
70978
13
48
67944
73373
69214
72176
70463
70957
12
49
67965
73353
69235
72156
70484
70937
11
50
67987
73333
69256
72136
70505
70916 10
51
68008
73314
69277
72116
70525
70896
9
52
68029
73294
69298
72095
70546
70875
53
68051
73274
69319
72075
70567
70855
54
68072
73254
69340
72055 70587
70834
55
68093
73234
69361 72035
70608
70813
56
68115
73215 69382
72015
70628
70793
4
57
68136
73195
69403
71995
70649
70772
3
58
68157
73175
69424
71974
70670
70752
2
59
68179
73155
69445
71954
70690
70731
1
60
68200
73135
69466
71934
70711
70711
0
/
N. cos
N. sin
N. cos
N. sin
N. cos
N. sin
47°
46°
45°
TABLES FOR REDUCING LINKS INTO FEET.
803

Links.
Feet.
Links.
Feet.
Links.
Feet.
Links.
Feet.
1234
•66
61
40.26
121
79.86
181
119.46
1.32
62
40.92
122
80.52 182
120.12
1.98
63
41.58
123
81.18
183
120.78
2.64
64
42.24
124
81.84
184
121.44
5
3.30
65
42.90
125
82.50 185
122.10
6
3.96
66
43.56
126
83.16
186
122.76
7
4.62
67
44.22
127
83.82 187
123.42
5.28
68
44.88
128
84.48
188
124.08
9
5.94
69
45.54
129
85.14
189
124.74
10
6.60
70
46.20
130
85.80
190
125.40
11
7.26
71
46.86
131
86.46
191
126.06
12
7.92
72
47.52
132
87.12
192
126.72
13
8.58 73
48.18
133
87.78
193
127.38
14
9.24
74
48.84
134
88.44
194
128.04
15
9.90
75
49.50
135
89.10
195
128.70
16
10.56
76
50.16
136
89.76
196
129.36
17
11.22
77
50.82
137
90.42
197
130-02
18
11.88
78
51.48
138
91.08 198
130.68
19
12.54
79
52.14
139
91.74
199
131.34
20
13.20
80
52.80
140
92.40 200
132.00
21
13.86
81
53.46
141
93.06
201
132.66
22
14.52
82
54.12
142
93.72
202
133.32
23
15.18 83
54.78
143
94.38
203
133.98
24
15.84 84
55.44
144
95.04 204
134.64
25
16.50
85
56.10
145
95.70 205
135.30
26
17.16
86
56.76 146
96.36
206
135.96
27
17.82
87
57.42
147
97.02 207
136.62
28
18.48 88
58.08
148
97.68 208
137.28
29
19.14 89
58.74
149
98.34
209
137.94
30
19.80 90
59.40
150
99.00 210
138.60
31
20.46
91
60.06
151
99.66 211
139.26
32
21.12 92
33
21.78
93
34
22.44
94
60.72 152
61.38 153
62.04 154
100.32
212
139.92
100.98
213
140.58
101.64 214
141.24
35
23.10
95
62.70 155
102.30
215
141.90
36
23.76 96
63.36 156
102.96
216
142.56
37
24.42
97
64.02 157
103.62
217
143.22
38
25.08 98
64.68 158
104.28 218
143.88
39
25.74 99
65.34
159
104.94 219
144.54
40
26.40 100
66.00
160
105.60 220
145.20
41
27.06 101
66.66
161
106.26 221
145.86
42
27.72 102
67.32
162
106.92 222
146.52
43
28.38 103
67.98
163
107.58 223
147.18
44
29.04 104
68.64
164
108.24 224
147.84
45
29.70 105
69.30
165
108.90
225
148.50
46
30.36 106
69.96
166
109.56
226
149.16
47
31.02 107
70.62
167
110.22 227
149.82
48
31.68 108
71-28 168
110.88 228
150.48
49
32.34 109
71.94
50
33.00 110
72.60
169
170
111.54 229
151.14
112.20
230
151.80
51
33.66 111
73.26 171
112.86 231
152.46
52
34.32 112
73.92
172
113.52 232
153.12
53
34.98 113
74.58
173
114.18 233
153.78
54
35.64 114
75.24 174
114.84 234
154.44
55
36.30 115
75.90 175
115.50 235
155.10
56
36.96 116
76.56
176
116.16 236
155.76
57
37.62 117
77.22
177
116.82 237
156.42
58
38.28 118
77.88
178
117.48 238
157.08
59
38.94 119
78.54
179
118·14
239
157.74
60
39.60 120
79.20
180
118.80
240
158.40
804
TABLES FOR REDUCING LINKS INTO FEET.

Links.
Feet.
Links.
Feet.
Links.
Feet.
Links.
Feet.
241
159.06
301
198.66
361
238.26 421
277.86
242
159.72 302
199-32
362
238.92 422
278-52
243
160.38 303
199-98
363
239.58 423
279.18
244
161.04 304
200.64
364
240.24 424
279.84
245
161.70 305
201.30 365
240.90
425
280-50
246
162.36 306
201.96
366
241.56 426
281.16
247
163.02
307
202.62
367
242.22 427
281.82
248
163.68
308
203.28
368
242.88 428
282.48
249
164.34
309
203.94
369
243.54 429
283.14
250
165.00 310
204.60
370
244.20 430
283.80
251
165.66
311
205.26
371
244.86 431
284.46
252 166.32
312
205.92
372
245.52
432
285.12
253 166.98
313
206.58
373
246.18
433
285.78
254
167.64
314
207.24
374
246.84
434
286.44
255
168.30
315
207.90
375
247.50 435
287.10
256 168.96
316
208.56
376
248.16 436
287.76
257
169.62
317
209.22 377
248.82
437
288.42
258
170.28
318
209.88
378
249.48
438
289.08
259
170.94
319
210.54
379
250.14
439
289.74
260
171.60 320
211.20 380
250-80 440
290-40
261
172.26 321
211.86 381
251.46 441
291.06
262
263
266
172.92 322 212.54
173.58 323
264 174.24 324
265 174.90 325
175.56 326
382 252.12
442
291.72
213.18
383
252.78
443
292.38
213.84
384
253.44
444
293.04
214.50 385
254.10
445
293-70
215.16
386
254.76 446
294.36
267
176.22 327
215.82
387
255.42 447
295.02
268
176.88 328
216.48 388
256.08
448
295.68
269
177.54 329
217.14
389 256.74
449
296.34
270
178.20 330
217.80 390
257.40
450
297.00
271
178.86 331
218.46
391
258.06 451
297.66
272
179-52 332
219.12
392
258.72
452
298-32
273
180.18 333
219.78
393
259.38
453
298.98
274
180.84 334
220.44
394
260.04
4.54
299.64
275 181.50 335
221.10
395
260.70 455
300-30
276
182.16 336
221.76
396
261.36 456
300-96
277
182.82 337
222.42 397
262.02 457
301.62
278
183.48 338
223.08 398
262-68 458
302.28
279
184.14 339
223.74 399
263.34 459
302.94
280
184.80 340
224-40 400
264.00 460
303.60
281 185.46 341
225.06 401
264.66
461
304.26
282 186.12 342
283 186.78 343
284 187.44 344
285 188.10 345
225.72 402
265.32 462
304.92
226.38
403
265.98 463
305.58
227.04
404
266.64 464
306.24
227.70 405
267.30 465
306.90
286
188-76 346
228.36
406
267.96 466
307.56
287
189.42 347
229.02
407
268.62 467
308-22
288
190.08 348
229.68 408
269.28 468
308-88
289
190.74 349
230.34 409
269.94
469
309.54
290
191.40 350
291 192.06 351
292 192.72 352
293 193.38 353
294 194.04 354
295 194.70 355
296
195.36 356
297 196.02 357
298 196.68 358
231.00 410
231.66 411 271.26
232.32 412 271.92
232.98 413
233.64 414
270-60 470
310-20
471
310-86
472
311.52
272.58 473
312.18
273.24
474
312.84
234.30 415
273.90
475
313.50
234.96 416
274.56
476
314.16
235.62 417
275.22
477
314.82
236.28 418
275.88
478
315.48
299 197.34 359
300
236.94 419
276.54
479
316.14
198.00 360 237.60 420
277-20
480
316.80
TABLES FOR REDUCING LINKS INTO FEET.
805

Links.
Feet.
Links.
Feet.
Links.
Feet.
Links.
Feet.
481
317.46
541
357.06
601
396.66 661
436.26
482
318.12 542
357.72 602
397.32 662
436.92
483
318-78
543
358-38 603
397.98 663
437.58
484
319.44
544
359.04 604
398.64
664
438.24
485
320.10
545
359-70 605
399.30 665
438.90
486
320.76 546
360.36 606
399.96 666
439.56
487
321.42 547
361.02 607
400.62
667
440.22
488
322.08 548
361.68
608 401.28
668
440.88
489
322.74 549
362.34
609
401.94
669
441.54
490
323.40 550
363.00 610
402.60
670
442.20
491
324.06 551
363.66 611
403.26
671
442.86
492
324.72 552
364.32 612
403.92
672
443.52
493 325.38 553
364.98
613
404.58
673
444.18
494 326.04 554
365.64
614
405.24
674
444.84
495
326.70 555
366.30
615
405.90
675
445.50
496
327.36 556
366.96 616
406.56
676
446.16
497
328.02 557
367.62
617
407.22
677
446.82
498
328.68 558
368-28
618
407.88
678
447.48
499
329-34 559
368.94
619
408.54
679
448.14
500
330.00 560
369-60 620
409.20
680
448.80
501
330-66 561
370.26
621
409.86
681
449.46
502
331-32 562
370.92
622
410.52
682
450-12
504
503 331.98 563
332.64 564
371.58
623
411.18 683
450.78
372.24 624
411.84 684
451.44
505
333.30 565
372.90
625
412.50
685
452.10
506
333.96 566
373.56 626
413.16
686
452.76
507 334.62 567
374.22 627
413.82
687
453.42
508
335.28 568
374.88 628
414.48 688
454.08
509
335.94 569
375.54 629
415.14
689
454.74
510
336-60 570
376-20
630
415.80 690
455.40
511 337.26 571 376.86 631
512 337.92 572 377-52
513 338.58 573 378.18
416.46 691
456.06
632
417.12 692
456.72
633
417.78
693
457.38
514 339.24 574
515 339.90 575 379.50
516 340.56 576
378.84 634
418.44 694
458.04
635
419.10 695
458.70
380.16
636
419.76 696
459.36
517
341.22 577
380.82
637
420.42
697
460.02
518
341.88 578
381.48 638
421.08
698
460.68
519 342.54 579
520 343.20 580 382.80 640
521 343.86 581 383.46 641
522 344.52 582 384.12 642
523 345.18 583 384-78 643
524 345.84 584 385.44 644
525 346-50 585 386.10
526 347.16 586 386-76 646
527 347.82 587
528 348-48 588 388-08
529 349-14 589 388.74
530 349.80 590 389.40 650
531 350.46 591 390.06 651 429.66 711
532
351.12 592 390.72 652 430.32
533 351.78 593 391.38 653 430.98
534 352.44 594 392.04 654
535 353.10 595 392.70 655
536
353.76 596 393.36 656
537 354.42 597
538 355.08 598
539 355.74 599
540 356.40 600
382.14 639
421.74 699
461.34
422.40
700
462-00
423.06 701
462.66
423.72 702
463.32
424.38
703
463.98
425.04 704
464.64
645
425.70 705
465-30
426.36 706
465.96
387.42 647
427.02 707
466.62
648
427.68 708
467-28
649 428.34 709
467.94
429.00
710
468.60
469.26
712
469.92
713
470.58
431.64
714
471.24
432.30
715
471.90
432.96 716
472.56
394.02 657
394.68 658
395.34 659
433.62
717
473.22
434.28
718
473.88
434.94
719
474.54
396.00 660
435.60
720
475.20
806
TABLES FOR REDUCING LINKS INTO FEET.

Links.
Feet.
Links.
Feet.
Links.
Feet.
Links.
Feet.
721
475.86
781
515.46
841
555.06
901
594.66
722
476.52
782
516.12
842
555.72 902
595.32
723 477-18
783
516.78 843
556.38 903
595.98
724 477.84 784
725 478-50
517.44 844
557.04
904
596.64
785
518.10
845
557.70 905
597-30
726 479.16 786
518.76
846
558.36 906
597.96
727
479.82
787
519.42
847
559.02 907
598.62
728
480.48
788
520.08
848
559.68 908
599.28
729'
481.14 789
520.74
849
560.34 909
599.94
730
481.80
790
521.40 850
561.00 910
600-60
731
482.46
791
522.06 851
561.66
911
601.26
732
483.12
792
522.72 852
562.32
912
601.92
733
483-78
793
523.38 853
562.98
913
602.58
734
484.44
794
735
485.10 795
524.04
524.70 855
854
563.64 914
603.24
564.30
915
603.90
736
485.76 796
525.36 856
564.96 916
604.56
737
486.42 797
526.02 857
565.62
917
605.22
738
487.08 798
526.68 858
566.28
918
605.88
739
487.74 799
527.34 859
566-94 919
606.54
740
488.40 800
528.00 860
567.60
920
607.20
741
489.06 801
528.66
861
568-26
921
607.86
742 489.72 802
529.32 862
568.92
922
608.52
743
490.38 803
529.98 863
569.58
923
609.18
744
491.04 804
530.64 864
570-24
924
609.84
745
491.70 805
531.30
865
570-90
925
610.50
746
492.36 806
531.96
866
571.56 926
611.16
747
493.02 807 532.62
867
572.22 927
611.82
748
493.68 808
533.28
868
572-88
928
612.48
749
494.34 809
533.94 869
573.54
929
613.14
750
495.00 810
534.60 870
574-20
930
613.80
751
495.66 811
535.26 871
574-86
931
614.46
752
496.32 812
535.92 872
575.52 932
615.12
753
496.98 813
536.58 873
576-18 933
615.78
759
760
754 497.64
755 498.30 815
756 498.96 816
538.56
757 499.62 817 539.22 877
758 500-28 818 539.88 878
500.94 819 540.54 879
501.60 820 541.20 880
814
537.24
874
576.84 934
616.44
537.90
875
577.50 935
617-10
876
578.16 936
617.76
578.82 937
618.42
579.48 938
619.08
580.14
939
619.74
580.80
940
620.40
761
502.26 821
762
502.92 822
763
503-58 823
541.86 881
542.52 882
543.18 883
581.46 941
621.06
582.12
942
621.72
582.78 943
622.38
764
504.24 824
543.84 884
583.44
944
623.04
765
504.90 825
544.50 885
584.10
945
623.70
766 505.56 826
545.16 886
584.76
946
624.36
767
506.22 827
545.82 887
585.42
947
625.02
768
506.88 828
546.48 888
586.08
948
625.68
769
507-54 829
770 508.20 830
547.14 889
586.74
949
626.34
547.80
890
587-40
950
627.00
771
508.86 831
548.46 891 588.06
951
627.66
772
509.52 832
549.12 892 588.72
952
628.32
773
510.18 833
549.78 893
589.38
953
628.98
774
510.84 834
550.44 894
590-04
954
629.64
775
511.50 835
551.10 895
590-70
955
630.30
776 512.16 836
551.76 896
591.36
956
630.96
777 512.82 837
552.42 897
592.02
957
631.62
778 513-48 838 553.08 898
779 514.14 839 553.74 899
780 514.80 840 554.40 900
592.68
958
632.28
593.34
959
632.94
594.00
960
633.60
DECIMALS OF A POUND STERLING.
807

1/3 062 2/6 125 3/9 187 5/0 25
D
1·001
⚫002
2003
6/3 312 7/6 375
1.064
065
2.066
1.126
127
2.128
1.189
1.251
•19
3.191
4.252
2.253
1 .004
4 067
7129
10 192
•
1 .254
1.005
1.006
3.007
ساهر من انت اهر
1.068
3.069
1.13
193
1.255
1.314
315
2.316
4 317
1.318
4.376
8/9 437
1.439
·377
•44
378
2·441
•
7 379
10 ·442
1.38
1.443
•131
3.194
•256
·319
1.381
444
3.07
•132
2.195
3.257
2.32
3.382
445
HEINKE
2 .008 5 071
1.009
3.01
3.011
3 ⚫012
8 ·133
11 196
2 .258
5 .321
8 .383
11 446
1.072
1.134
•134
197
1.259
1.322
•384
1.447
073
135
198
26
·323
2.385
•448
2.074
2.136
199
261
3.324
.386
449
6 .075
9 137
4/0 2
3 .262
6 325
9 387
1.014
Ha
3·015
3.016
1.076
1.077
3.078
9/0 45
1.139
201
1.264
1.326
1.389
1.451
3.14
2.202
-265
-327
•39
.452
2.141
2.203
3.266
·328
2.391
4 017
2.453
7 079
10 ·142
1 .204
4 +267
7329
10 ·392
1 •454
2018
1.08
•143
1.205
1.268
1.33
1.393
019
1.081
•144
206
.269
331
.394
3.02
2.082
3.145
2.207
2.27
2.332
2395
1.455
456
3.457
5 021 8 .083
11 146
2 .208
5 271
8 .333
11 396
141分​24
1.022
1.023
3.024
6 ·025
2 .458
1.084
1·147
1.209
1.272
1.334
1.397
1.459
1.085
∙148
3.21
1.273
3.086
3.149
3.211
3.274
•335
2.336
.398
2.399
46
2.461
9 087
3/0 ·15
3 .212
6 275
9 337
8/0 •4
3 -462
1.026
1.089
151
1.214
1.276
1.339
·027
·09
152
215
•277
$.028
3.091
·153
77-029
10 092
1 154
2.216
4 ·217
3.278
1.34
2.341
नमनाला
1.401
1.464
402
•465
•403
2.466
7 279
10 ·342
1 404
4 .467
1.03
1.093
1.155
+218
1.28
1.343
·031
094
•156
219
1.281
3.344
3.032
2.095
2.157
3.22
3.282
3.345
1.405
406
2·407
-468
-469
•47
8 033 11 096
2 158
5 -221
8 283
11 346
2 .408
5 -471
1.034
1.097
1.159
1.222
1.284
1.347
1.409
1·035
·098
1.16
.223
-285
3.036
099
161
3.224
3.286
2/0 1
HH|GKAH
9 037
1.039
·04
$.041
10 ·042 1 104 4 167
3 .162
6 .225
9 287
348
2.349
7/0 35
41
2.411
3 ·412
4.101
1.164
1.226
1.289
1.351
1.414
1.472
•473
2.474
6 .475
2.476
1.102
165
227
1.29
352
3.103
166
228
1.291
2.353
415
2.416
7 .229
10 ·292
1 .354
4 ·417
··477
2.478
7479
1.043
1.105
2.168
1.23
1.044
•106
•169
231
3.045
2.107
3.17
232
IPWNUPH
1.293
1.355
•
•294
356
295
-357
1.418
•419
$.42
1.48
•481
.482
11 046
1.047
1.048
$.049
2 108
1.109
∙110
2.111
5 171
8 233
11 296
2 .358
5 421
8 483
1.172
173
2.174
4.234
1.297
1.359
1.422
1.484
•235
.298
•36
423
236
3.299
•361
•424
1/0 -05
•485
2.486
3 112
6 175
9 237
6/03
3 .362
6 .425
9 .487
1.051
1.114
1.176
1.239
4.301
1.364
1.052
1.426
1.489
•115
177
.24
•302
·365
427
053
1 •054
2.116
4 117
3178
7179
2.241
10 242
303
2.366
3.428
1 •304
4 .367
7429
PKNUPL
1·055
118
49
2.491
10 -492
2.18
1.243
1.056
119
181
·057
•12
2.182
·244
2.245
1.305
·306
368
1.43
1.493
369
2.307
2.37
•431
3.432
1.494
2 .058 5 121
8. 183
11 246
2 '308
5 .371
8 •433
2.059
2.495
11 496
4.122
184
1.247
1.309
1.372
3.06
1.123
185
1.248
31
2.061
2.124
·186
3.249
4.311
373
4.374
1.434
435
2.436
1.497
498
3.499
808
DECIMALS OF A POUND STERLING.

•
10/0.5 11/3
11/3 562 12/6 625|13/9 687 15/0 75 16/3 812 17/6 875 18/9 937
1.501
·
1.502
503
1.564
565
2.566
+626
•627
1.689
•69
1.751
1.752
814
1.815
1.876
877
1.939
94
2.628
691
3.753
1 -504 4 567
816
2.878
77629
941
10 ·692
1 754
1.505
4 817
7879
568
4.63
10 942
1.693
1.506
1.755
.569
1.818
631
694
1.756
•
3.507
2.57
819
1.88
1·881
1.943
.632
·
944
695
2.757
3.82
<
⚫882
2.945
2 .508
5 .571
8 .633
11 -696
2 758
5 .821
509
4.572
1.634
4.697
1.759
3.51
1.822
573
635
·698
3.76
823
2.511
8. 883 11 ·946
1.884
885
1.947
2.574
3.636
.948
⚫699
1.761
3 512
6 .575
4.824
.886
9 637 14/07
3.9.9
3 .762
1.514
6 .825
1.576
639
1.701
9 887 19/0 95
515
1.764
1.826
2.577
1.889
951
·64
1.702
.765
2.516
827
89
2.578
952
2.641
2.703
2.766
2.828
891
953
4 .517
7.579
10 ·642
1 704
4 .767
7-829
1.518
1.58
10 ·892
1.643
1 .954
1.705
•519
1.768
581
2.644
1.83
1.893
1.955
1.706
•706
.769
•831
.52
894
2.582
2.645
.956
$707
2-77
⚫832
5 .521
8 .583
2.895
11 646
957
2 708
5 771
522
8 .833
11 -896
1.584
1.647
2 ·958
1.709
1.772
523
2585
1.834
1.897
•648
1.71
773
2.524
2.586
•649
711
774
835
2.836
1.898
1.959
.96
899
3.961
6 .525
9 587 13/0 65
3 712
6 775
4.526
1.589
1.651
9 837 18/0 .9
3 .962
4.714
1.527
1.776
1.839
1.59
1.901
.652
1.964
•964
715
3.528
* ·529
2.591
2·653
2.716
-777
2.778
2.84
1.902
.965
10 ·592
2.841
3.903
1 654
2.966
4 717
1.53
1.593
1.655
718
7 779
1.78
10 ⚫842
1 904
4 ·967
531
1.843
1.905
•594
•656
1.968
719
1.781
532
1.844
.906
-595
969
.657
2.72
782
.845
2.907
2.97
8. 533 11 ·596
2 ·658
5 721
8 783
1.534
11 ⚫846
1.597
2 .908
5 .971
659
722
.535
1.784
•598
1.847
66
723
.785
2.536
2.599
1.848
1.909
.91
4.972
2.661
.724
9 537 12/0 6
2.786
849
3.911
3 662
973
2.974
6 725
1.539
1.601
9 787 17/0·85
3 .912
6 .975
3.54
.602
2.541
603
1.664
665
4.666
726
789
1.851
1.914
.976
1.727
•727
1.79
1.852
.915
977
1.728
4.791
3.853
.916
.978
10 ·542
1 .604
4 .667
1.543
1.605
•668
•544
7 -729
1.73
10 ·792
1 ·854
4 917
7.979
•606
1.793
1.855
1.918
669
1.98
731
2.545
3.794
.856
919
607
981
2.67
11 546 2 ·608
5 -671
4.732
8 733
3.795
2.857
.92
3.982
1.547
1.609
11 -796 2 .858
5 921
3.548
·61
.549
-611
नमनोबलम
1.672
8 .983
1.734
1.797
1.859
1.922
673
1.984
·735
3.798
86
.923
•674
-985
2.736
2.799
861
924
.986
11/0 •55
1.551
1.552
2.553
3 .612
1.614
•615
2.616
6 ·675
1.676
⚫677
9 737 16/08
3 .862
6 .925
9 ·987
1.739
1.801
1.864
3.74
802
865
1.926
.927
989
2.678
1 -554
2.741
4 •617
2.803
2.866
77 679
2.928
10 742
1.555
1.618
1 ·804
4 .867
-929
68
-99
2.991
10 -992
1.743
556
.619
1.805
1.868
681
1.93
•993
4.744
2.557
62
*682
2.745
2 -558 5 -621
806
2.807
1.869
931
2.87
932
8 .683
⚫994
2.995
11 746
2.559
1.622
2 .808
5 871
8 .933
11 -996
1.684
1.747
3.56
1.623
1.809
1.685
748
2.561
.81
1.872
873
1.934
·935
624
$.686
2.749
3.811
.874
$.936
1.997
•
998
2.999
STAMP DUTIES.
809
CHAPTER XXIV.
STAMP LAWS RECENTLY PASSED
In relation to the Duties for the several purposes of Trade, and for the Con-
veyance and Disposal of Property, together with the Duties on Imports.
AN ACT TO AMEND THE LAWS RELATING TO STAMP DUTIES.
FROM and after the tenth day of October one thousand eight hundred and
fifty-three the several stamp duties now payable in Great Britain and
Ireland respectively, under or by virtue of any Act or Acts of Parliament
for or in respect of the several instruments, matters, and things men-
tioned or described (otherwise than by way of exception) in the schedule
to this act annexed, and whereon other duties are by this act granted, shall
respectively cease and determine, and shall be and the same are hereby
repealed; and in lieu and instead thereof there shall be granted, raised,
levied, collected, and paid in and throughout the United Kingdom of
Great Britain and Ireland, for and in respect of things described in the
said schedule, or for or in respect of the vellum, parchment, or paper upon
which any of them respectively shall be written, the several duties or sums
of money set down in figures against the same respectively, or otherwise
specified and set forth in the said schedule, which said schedule, and the
several provisions, regulations, directions and exemptions therein con-
tained with respect to the said duties, and the instruments, matters, and
things charged therewith or exempted therefrom shall be deemed and
taken to be part of this act, and shall be applied, observed, and put in exe-
cution accordingly: Provided always, that nothing herein contained shall
extend to repeal or alter any of the said stamp duties now payable in re-
lation to any deed or instrument which shall have been signed or executed
by any party thereto, or which shall bear date before or upon the tenth
day of October one thousand eight hundred and fifty-three.
Stamps for
drafts.
The duties of one penny by this act granted on receipts and
on drafts or orders for the payment of money respectively may receipts and
be denoted either by a stamp impressed upon the paper whereon.
any such instrument is written or by an adhesive stamp affixed thereto, and
the Commissioners of Inland Revenue shall provide stamps of both descrip-
tions for the purpose of denoting the said duties.
In any case where an adhesive stamp shall be used for the purpose
aforesaid on any receipt or upon any draft or order respectively charge-
able with the duty of, one penny by this act, the person by whom such
receipt shall be given or such draft or order signed or made shall, before
the instrument shall be delivered out of his hands, custody, or power, can-
cel or obliterate the stamp so used, by writing thereon his name or the
initial letters of his name so and in such a manner as to show clearly and
distinctly that such stamp has been made use of, and so that the same may
not be again used; and if any person who shall write or give any such
receipt or discharge or make or sign any such draft or order with any
3 C
810
STAMP DUTIES.
Penalty for
adhesive stamp thereon, shall not bonâ fide in manner aforesaid effectually
cancel or obliterate such stamp, he shall forfeit the sum of ten pounds.
If any person shall fraudulently get off or remove, or cause or
committing procure to be gotten off or removed, from any paper whereon
frauds. any receipt or any draft or order shall be written, any adhesive
stamp, or if any person shall affix or use any such stamp which shall have
been gotten off or removed from any paper whereon any receipt or any
draft or order shall have been written, to or for any receipt, draft, or
order, or any paper whereon any such receipt, draft, or order shall be or
be intended to be written; or if any person shall do or practise, or be con-
cerned in any fraudulent act, contrivance, or device whatever, not specially
provided for by this or some other Act of Parliament, with intent or de-
sign to defraud Her Majesty of any duty by this act granted upon receipts
or upon drafts or orders, every person so offending in any of the said
several cases shall forfeit the sum of twenty pounds.
For better securing the stamp duties by law chargeable on policies of
insurance upon lives, and for preventing frauds in respect of any such
insurances :
Stamps for
policy of
insurances.
Every person who shall make or agree to make, or shall re-
ceive any premium or valuable consideration for making, any
assurance or insurance upon any life or lives, or upon any event
or contingency relating to or depending upon any life or lives, shall, within
one calendar month after the payment or giving of any such premium or
consideration, make out and sign or execute, or cause and procure to be
made out and signed or executed upon vellum, parchment, or paper, duly
stamped, a policy of such assurance or insurance, and have the same ready
to be delivered to the party entitled thereto, and shall upon demand made
by any such party, or any agent in that behalf duly authorized, deliver the
same to him, or in default in any of the cases aforesaid shall forfeit the
sum of fifty pounds:
Articles of
Every person who at the time of the payment or giving of any such
premium or consideration shall be a managing director of or the secretary
to or other principal officer of any society or company receiving any such
premium or consideration, shall be deemed to be a person making or
agreeing to make such assurance or insurance, and shall be subject and
liable to the penalty by this act imposed for any such default as aforesaid.
Whereas by an act passed in the fifty-fifth year of the reign
clerkship to of King George the Third, chapter one hundred and eighty-four
attorneys. certain stamp duties are imposed on any articles of clerkship or
contract whereby any person shall first become bound to serve as a clerk
in order to his admission as an attorney or solicitor in any court; that is
to say, in order to admission in any of the Courts at Westminster, the stamp
duty of one hundred and twenty pounds, and in order to admission in any
of the Courts of the Counties Palatine, the stamp duty of sixty pounds:
And whereas where any person has become bound and has served as a
clerk under any such articles or contract stamped with the said duty of
sixty pounds in order to his admission as an attorney or solicitor in any of
STAMP DUTIES.
811
the Courts of the Counties Palatine, he is capable of being admitted in any
of Her Majesty's Courts at Westminster, but only upon the payment of the
further stamp duty of one hundred and twenty pounds; and it is expedient
to afford relief in such cases :
Where any person shall have become bound as a clerk in order to his
admission as an attorney or solicitor in any of the Courts of the Counties
Palatine by articles or contract stamped with the said duty of sixty pounds,
then upon payment of such further sum of money as with the said duty of
sixty pounds will make up the full stamp duty which, at the date of such
articles or contract, was payable by law on articles of clerkship in order to
admission in any of the Courts at Westminster, it shall be lawful for the
Commissioners of Inland Revenue and they are hereby required to stamp
the said articles or contract with a stamp or stamps to denote such further
duty, and thereupon such articles or contract shall be as valid and effectual
for entitling such person to admission in any of the Courts at Westminster
as if the same had been duly stamped with such full duty in the first
instance.
And whereas by an act passed in the forty-eighth year of the reign of
King George the Third, chapter one hundred and forty-nine, section thirty-
eight, persons intromitting with or entering upon the possession or manage-
ment of any personal or moveable estate or effects in Scotland of any
person dying, are required to exhibit a full and true inventory, duly
stamped, to be recorded as in the said act is provided, of all the personal
or moveable estate and effects of the deceased already recovered or known
to be existing; and if at any subsequent period a discovery shall be made
of any other effects belonging to the deceased, an additional inventory of
the same is in like manner to be exhibited and recorded; and every such
additional inventory is chargeable by law with the full ad valorem stamp
duty payable in respect of the total amount or value of the estate and
effects specified therein, and in any such former inventory; and thereupon
the party exhibiting the same is entitled to receive back the amount of the
stamp duty paid on such former inventory; and it is expedient to prevent
the inconvenience attending the over-payment of the stamp duty in such
cases by charging on any such additional inventory the deficient stamp
duty only.
For inven-
Scotland.
Every such additional inventory to be made and recorded as
aforesaid shall be chargeable only with such amount of stamp tories in
duty as, together with the stamp duty charged upon any for-
mer duly stamped inventory of the estate and effects of the same deceased
person already exhibited and recorded, shall make up the full amount of
stamp duty chargeable by law in respect of the total amount or value of all
the estate and effects of the said deceased specified in the said additional
and any such former inventory.
No license granted to any spiritual person to perform divine service in
any building approved by the bishop in lieu of any church or chapel whilst
the same is under repair or is rebuilding, or in any building so approved
for the convenience of the inhabitants of a parish resident at a distance
812
STAMP DUTIES.
from the church or consecrated chapel, shall be chargeable with any
stamp duty.
And whereas by the said act passed in the fifty-fifth year of the reign of
King George the Third, it is provided that where any property is sold and
conveyed subject to any debt or sum of money to be afterwards paid by
the purchaser, the same shall be deemed to be purchase or consideration
money in respect whereof the said ad valorem duty charged upon the sale
and conveyance of property is to be paid: And whereas it has been held
and determined that the said ad valorem duty is payable in respect of any
such sum or debt only where the purchaser is personally liable or bound,
or undertakes or agrees to pay the same or to indemnify the vendor against
the same; and it is expedient to alter and amend the law in this respect :
Where any lands or other property shall be sold and conveyed
conveyance subject to any mortgage, wadset, or bond or other debt, or to
any gross or entire sum of money, such sum of money or debt
shall be deemed the purchase or consideration money, or part of the pur-
chase or consideration money, as the case may be, in respect whereof the
said ad valorem duty shall be paid, notwithstanding the purchaser shall
not be or become personally liable or shall not undertake or agree to pay
the same or to indemnify the vendor or any person against the same, any-
thing in any act or otherwise to the contrary notwithstanding.
Sale and
of land, &c.
And whereas it has been adjudged and determined by law that upon the
sale of property, where the consideration expressed in the conveyance is a
rent charge or an annuity, made subject to redemption or repurchase, ad
valorem stamp duty is chargeable under the act passed in the Session of
Parliament held in the thirteenth and fourteenth years of Her Majesty,
chapter ninety-seven, only where such redemption or repurchase may be
enforced at the option of the vendor, and it is expedient that such duty
should be chargeable in all cases where such rentcharge or annuity is made
redeemable.
In any case where property shall be sold and conveyed in consideration
of any rentcharge or annuity, or any annual or periodical payment to be
made permanently or for any indefinite period, so that the total amount of
the money to be paid for such property cannot be previously ascertained,
which rentcharge, annuity, or other payment shall be made subject to
redemption or purchase upon terms and conditions specified in the deed or
instrument whereby the property sold shall be conveyed to or vested in
the purchaser, or any person by his direction, the money or the considera-
tion mentioned in the said deed or instrument as that on payment or trans-
fer, delivery or satisfaction, of which the said rentcharge, annuity, or
other payment shall be redeemed or purchased or repurchased, or shall
cease to be payable, shall be deemed to be the purchase money or con-
sideration on the sale of the said property so sold and conveyed, and in
respect of which last-mentioned purchase money or consideration the ad
valorem duty shall be chargeable; and where any such last-mentioned
consideration shall consist wholly or in part of any stock or security men-
tioned in the said act, the value thereof shall be ascertained as in such act
STAMP DUTIES.
813
is in that behalf provided; and where any such annuity, rentcharge, or
other payment aforesaid shall be made subject to redemption or purchase
or repurchase or discontinuance upon payment or satisfaction of any money
or value to be ascertained or calculated in manner provided in the said
deed or instrument, the amount of such money or value shall, for the pur-
pose of charging the said ad valorem duty, be ascertained or calculated
as in such deed or instrument shall be so provided.
And whereas by the said act of the thirteenth and fourteenth years of
Her Majesty, chapter ninety-seven, a stamp duty of five shillings was
granted and imposed upon the duplicate or counterpart of any deed or
instrument chargeable with stamp duty (exclusive of progressive duty) to
the amount of five shillings or upwards; and it is provided that in such
case the duplicate or counterpart shall not be available unless stamped
with a particular stamp for denoting or testifying the payment of the full
and proper stamp duty on the original deed or instrument; and it is ex-
pedient to dispense with the said particular stamp on counterparts of
leases :
Notwithstanding anything contained in the said act, the counterpart of
any lease of lands, tenements, or hereditaments, being duly stamped with
the said stamp duty of five shillings, or any higher stamp duty (exclusive
of progressive duty), and not being executed or signed by or on the be-
half of any lessor or grantor, shall be available as a counterpart without
being stamped with a particular stamp for denoting or testifying the pay-
ment of the stamp duty chargeable on the original lease.
And whereas by the said act of the thirteenth and fourteenth years of
Her Majesty, when any deed or instrument shall be presented to the
Commissioners of Inland Revenue, and the fee of ten shillings shall be
paid to them for their opinion as to the stamp duty with which such deed.
or instrument in their judgment is chargeable, the said commissioners are
required to assess and charge the stamp duty on such deed or instrument,
and, on the same being duly stamped, to impress thereon a particular
stamp to signify and denote that the full amount of stamp duty with which
such deed or instrument is by law chargeable has been paid: And
whereas the said Commissioners are not authorized to impress a particular
stamp upon any deed or instrument not chargeable with any stamp duty
in order to denote that the same is not so chargeable; and it is expedient
that provision should be made for that purpose.
It shall be lawful for any person to present to the said commissioners
any deed or instrument, and upon payment of the fee of ten shillings, as in
the said act is mentioned, to require their opinion whether or not the same
is chargeable with any stamp duty, and if the said commissioners shall be
of opinion that such deed or instrument is not chargeable with any stamp
duty, it shall be lawful for them and they are hereby required to impress
thereon a particular stamp, to be provided by them for that purpose, with
such word or words, or device or symbol thereon as they shall think pro-
per in that behalf, which shall signify and denote that such deed is not
chargeable with any stamp duty; and every such deed or instrument upon
814
STAMP DUTIES.
which the said stamp shall be impressed shall be deemed to be not so
chargeable, and shall be receivable in evidence in all courts of law
and equity, notwithstanding any objection made to the same as being
chargeable with stamp duty, and not stamped to denote the same : Pro-
vided always, that if the said commissioners shall assess and charge any
stamp duty upon or in respect of any such deed or instrument, and the
party presenting the same and paying such duty shall declare himself
dissatisfied with their determination, it shall be lawful for him to appeal
against the same to Her Majesty's Court of Exchequer, on the terms and
in the manner in the said act provided; and the said court shall hear and
determine the appeal, and decide whether the said deed or instrument is
chargeable with any, and if any, what stamp duty; and if the court shall
be of opinion that the same is not so chargeable, or is chargeable with a
less amount of duty than shall have been assessed and charged thereon,
then the amount of such duty or of the excess (as the case may be) shall
be returned to the appellant, together with the sum deposited as in the
said act mentioned; and if the court shall be of opinion that any further
duty is chargeable on the said deed or instrument, such further duty shall
be paid to the said commissioners, and the court shall order and enforce
the payment thereof accordingly.
And whereas it would facilitate the transfer of the bonds and mortgages
given by public companies under the provisions of Acts of Parliament as
securities for money which such companies are by the said acts expressly
empowered or authorized to borrow, if the transfers or assignments of
such-bonds or mortgages were endorsed thereon, and were exempted from
stamp duty, and it is expedient to grant such exemption in consideration
of a composition stamp duty being paid on such bonds and mortgages
on the original making and issuing thereof, in lieu of the stamp
duty with which such transfers or assignments would otherwise be
chargeable :
Transfers of
mortgages.
Where on the original making and issuing of any such bond
bonds and or mortgage as aforesaid, and before any transfer or assignment
thereof, the same shall be stamped with an amount of stamp
duty equal to three times the amount of the ad valorem stamp duty
chargeable thereon by law, and over and above the said ad valorem duty,
then every transfer or assignment thereafter made of such bond or mort-
gage by endorsement thereon shall be deemed to be exempt from the stamp
duty which would otherwise be payable in respect of such transfer or as-
signment: Provided always, that nothing herein contained shall extend to
exempt any such transfer or assignment from any stamp duty to which it
may be liable as a settlement of the money or stock secured by such bond
or mortgage, or any portion thereof.
And whereas it is desirable to facilitate the purchase of stamped paper,
covers, or envelopes, and of other stamps for expressing or denoting the
rates or duties of postage (all of which are hereinafter designated as post-
age stamps), and for that purpose to enable certain persons in the service
of the Post Office to sell postage stamps without having any such license
STAMP DUTIES.
815
as the laws now in force require in that behalf, and without being
subject or liable to any penalty for carrying about postage stamps for
sale:
It shall be lawful for the Postmaster General by writing under Persons au-
Postmaster
General may
sell postage
stamps.
his hand to authorize and appoint any person in the service or thorized by
employment of the Post Office to sell postage stamps at any par-
ticular house or place to be specified for that purpose, and also
any messenger or other person employed in the delivery of
letters sent by post to carry about for sale and to sell at any place postage
stamps, and all such persons shall, during the period that such authority
and appointment shall remain in force and unrevoked, without any license
or any authority other than last aforesaid, be at liberty to sell at any house
or place to be specified as aforesaid, or if so authorized, to carry about for
sale and sell at any place, any postage stamps, and such persons respectively
shall not be subject or liable to any penalty or forfeiture for so doing, any-
thing in any act or acts to the contrary notwithstanding.
sion of the
duties on
playing cards
And whereas by an act passed in the ninth year of the reign For prevent-
of King George the Fourth, chapter eighteen, granting stamp ing the eva-
duties upon playing cards made fit for sale or use in the United
Kingdom, such duties to be denoted on the ace of spades of each
pack of cards, it is enacted that no playing cards shall be sold as waste
cards unless a corner of each card shall be cut off at least half an inch in
depth, and other provisions are therein contained for securing the said
duties: And whereas packs or parcels of cards fit and intended for use
and play, but not containing an ace of spades duly stamped, are commonly
sold under the pretence of being waste cards, each of such cards having a
corner cut off, whereby the said duties are evaded; and it is expedient to
prevent such practice:
No playing cards, except such as shall be bonâ fide spoiled and rendered
unfit for use as playing cards in the process of manufacture, and which
shall have a corner cut off as in the said last-mentioned act is provided,
nor any cards commonly called or known as picture cards or court cards,
shall be deemed to be waste cards; and no playing cards, except waste
cards, shall be sold otherwise than in packs each pack containing fifty-two
cards of the four usual suits of thirteen cards each, including an ace of
spades duly stamped for denoting the duty by the said act granted on a
pack of cards, and tied up together in manner directed by the said act;
and if any person shall sell or expose or keep for sale any playing cards,
not being a pack of cards as aforesaid, and the same not being bonâ fide
waste cards within the meaning of this act, he shall for every pack, parcel,
or separate quantity of cards so sold or exposed or kept for sale forfeit, if
he shall not be a licensed maker of playing cards, the sum of ten pounds,
and if he shall be such licensed maker the sum of twenty pounds; and all
cards so sold or exposed or kept for sale shall be forfeited, and may be
seized and taken by any Officer of Inland Revenue, and be disposed of as
the Commissioners of Inland Revenue shall direct; provided that if in any
proceeding any question shall arise whether any cards are or were bonâ
816
STAMP DUTIES.
fide waste cards or not, proof of the affirmative thereof shall lie on the
party selling the same or having or keeping the same for sale.
And whereas by an act passed in the session held in the seventh and
eighth years of the reign of King George the Fourth, chapter fifty-three,
Officers of Excise and persons employed in the collection or management
of or accounting for the revenue of excise are exempted from serving as
mayor or sheriff, or in any corporate or parochial or other public office or
employment, or on any jury or inquest, or in the Militia; and it is expe-
dient to extend the same to all other officers appointed by or under the
Commissioners of Inland Revenue.
No officer or person appointed by the Commissioners of Inland Revenue,
or employed by them or under their authority or direction in any way re-
lating to any of the duties under their care or management shall, so long
as he shall continue in and exercise such last-mentioned office or employ-
ment, be compelled to serve as mayor or sheriff, or in any of the offices,
employments, or capacities in the said act and herein before in that behalf
mentioned.
Allowance
for receipt
stamps on
hand.
Where any person shall be possessed of any stamps rendered
useless by this act, it shall be lawful for the Commissioners of
Inland Revenue, on application to them or to their proper officer
in that behalf, at any time within six calendar months after the
commencement of this act to cancel and make allowance for the same, as
in the case of spoiled stamps, after deducting the discount by law granted
on the purchase of receipt stamps.
Drafts on
bankers.
Provided always, that any draft or order drawn upon a banker
for a sum of money payable to order on demand which shall,
when presented for payment, purport to be endorsed by the
person to whom the same shall be drawn payable, shall be a sufficient
authority to such banker to pay the amount of such draft or order to the
bearer thereof; and it shall not be incumbent on such banker to prove that
such endorsement, or any subsequent endorsement, was made by or under
the direction or authority of the person to whom the said draft or order
was or is made payable either by the drawer or any endorser thereof.
And whereas by an act passed in the Session of Parliament held in the
fifth and sixth years of Her Majesty's reign, chapter eighty-two, certain
rates and duties denominated stamp duties were granted and made payable
in Ireland for a limited term; and by four several acts passed respectively
in the eighth, eleventh, fourteenth, and fifteenth years of Her Majesty's
reign the same rates and duties were continued for four other several and
successive terms, the last of which will expire on the tenth day of October
one thousand eight hundred and fifty-three; and it is expedient to make
the said rates and duties perpetual:
Stamp duties
in Ireland.
All the several sums of money and duties and composition
for duties granted and made payable in Ireland by the said act
of the fifth and sixth years of Her Majesty, chapter eighty-two,
and not repealed by any subsequent act, and also all duties now payable in
lieu or instead of any of the said duties which may have been so repealed,
STAMP DUTIES.
817
shall be and the same are hereby continued and made perpetual, and shall
be charged, raised, levied, collected, and paid unto and for the use of Her
Majesty, her heirs and successors for ever: The said act of the fifth and
sixth years of Her Majesty, and all and every other act, and acts now in
force in relation to the duties and composition for duties which are con-
tinued by this act, shall severally be continued and remain in full force in
all respects in relation to the said duties and composition for duties hereby
continued and granted, and all and every the powers and authorities, rules,
regulations, directions, penalties, forfeitures, clauses, matters, and things
contained in the said acts or any of them, and in force as aforesaid, shall
severally and respectively be duly observed, practised, applied, and put in
execution in relation to the said duties and composition for duties hereby
continued and granted, for the charging, raising, levying, paying, account-
ing for, and securing of the said duties and composition for duties, and all
arrears thereof, and for the preventing, detecting, and punishing of all
frauds, forgeries, and other offences relating thereto, as fully and effectually
to all intents and purposes as if the same powers, authorities, rules, regu-
lations, directions, penalties, forfeitures, clauses, matters, and things were
particularly repeated and re-enacted in the body of this act with reference
to the said duties and composition for duties hereby granted.
The Schedule referred to by this Act.
Apprenticeship and Clerkship.-Indenture or other instrument or writing
containing the covenants, articles, or agreements for or relating to the
service of any apprentice, clerk, or servant who shall be put or placed
to or with any master or mistress, or to or with any new master or
mistress, either by assignment, transfer, or turn-over, or upon the
death, absence, or incapacity of the former master or mistress, or other-
wise, to learn any profession, trade, or employment whatsoever (ex-
cept articles of clerkship or apprenticeship to any attorney, solicitor,
or other person in order to admission in any court, or in any office in
any court), or any writing whatever (except as aforesaid) whereby any
such assignment, transfer, or turn-over may be effectuated or fas-
certained;
Where no sum of money or other matter or thing shall be paid,
given, assigned, or conveyed, or be secured to be paid, given,
assigned, or conveyed to or for the use or benefit of the master
or mistress, with or in respect of any apprentice, clerk, or
servant
Debenture or certificate for entitling any person to receive any drawback
of any duty or duties, or part of any duty or duties of customs or ex-
cise, or any bounty payable out of the revenue of customs or excise,
for or in respect of any goods, wares, or merchandise exported or
shipped to be exported from any part of the United Kingdom to any
part beyond the sea;
Where the drawback or bounty to be received shall not exceed
ten pounds
Where the same shall exceed ten pounds and not exceed fifty
pounds
•
•
And where the same shall exceed fifty pounds
Duty.
£ s. d.
026
0 1 0
026
050
818
STAMP DUTIES.
Draft or order for the payment of any sum of money to the bearer or to
order, on demand
And the following instruments shall be deemed and taken to be
drafts or orders for the payment of money within the intent and
meaning of this act, and of any act or acts relating to the stamp
duties on bills of exchange, drafts, or orders, and shall be
chargeable accordingly with the stamp duties imposed by this
act or any such act or acts; viz.
All documents or writings usually termed Letters of Credit,
or whereby any person to whom any such document or
writing is or is intended to be delivered or sent shall be en-
titled, or be intended to be entitled to have credit with, or
in account with, or to draw upon any other person for, or
to receive from such other person any sum of money therein
mentioned.
Exemptions from the Duties on Drafts or Orders.
All drafts or orders for the payment of money to the bearer on
demand, drawn upon any banker or bankers, now by law
exempt from stamp duty.
All letters of credit, whether in sets or not, sent by persons in
the United Kingdom to persons abroad authorizing drafts on
the United Kingdom.
Policy of assurance or insurance, or other instrument, by whatever name
the same shall be called, whereby any insurance shall be made upon
any life or lives, or upon any event or contingency relating to or de-
pending upon any life or lives;
Where the sum insured shall not exceed five hundred pounds;
Then for every fifty pounds, and any fractional part of
fifty pounds
Duty.
£ s. d. •
0 0 1
of one hundred pounds
•
006
And where it shall exceed five hundred pounds, and shall not
exceed one thousand pounds;
Then for every one hundred pounds, and any fractional part
0 1 0
Then for every one thousand pounds, and any fractional part
of one thousand pounds
0 10 0
0 0 1
And where it shall exceed one thousand pounds;
Receipt or discharge given for or upon the payment of money amounting
to two pounds or upwards
Exemption.
Receipts given for money deposited in any Bank, or in the hands
of any banker, to be accounted for, whether with interest or not;
provided the same be not expressed to be received of or by the
hands of any other than the person to whom the same is to be ac-
counted for: Provided always, that this exemption shall not extend
to receipts or acknowledgments for sums paid or deposited for or
upon letters of allotment or shares or in respect of calls upon any
scrip or shares of or in any Joint Stock or other Company or proposed
or intended company, which said last-mentioned receipts or ac-
knowledgments, by whomsoever given, shall be liable to the duty
by this act charged on receipts.
STAMP DUTIES.
819
Repeal of certain Stamp Duties, and to grant others in lieu thereof, to
give relief with respect to the Stamp Duties on Newspapers and Sup-
plements thereto, to repeal the Duty on Advertisements, and otherwise to
amend the Laws relating to Stamp Duties.
on instru-
nexed re-
others grant-
thereof.
Whereas it is expedient to repeal the stamp duties now payable in respect
of the several instruments, matters and things mentioned or described in the
schedule to this act annexed, and to impose other stamp duties in lieu thereof,
and also to give relief with respect to the stamp duties on newspapers and
supplements thereto, and otherwise to amend the laws relating to stamp
duties, and to repeal the duty charged on advertisements: Be it therefore
enacted by the Queen's most Excellent Majesty, by and with the advice
and consent of the lords spiritual and temporal, and commons, in this
present parliament assembled, and by the authority of the same, as follows:
From and after the passing of this act the several stamp Stamp duties
duties now payable in Great Britain and Ireland respectively, ments in the
under or by virtue of any Act or Acts of Parliament for or in schedule an-
respect of the several instruments, matters and things mentioned pealed, and
or described in the schedule to this act annexed, and whereon ed in lieu
other duties are by this act granted, shall respectively cease and
determine, and shall be and the same are hereby repealed; and in lieu and
instead thereof there shall be granted, raised, levied, collected, and paid
in and throughout the United Kingdom of Great Britain and Ireland, to
and to the use of Her Majesty, her heirs and successors, for and in respect
of the several instruments, matters, and things described or mentioned in
the said schedule, or for or in respect of the vellum, parchment, or paper
upon which any of them respectively shall be written, the several duties
or sums of money set down in figures against the same respectively, or
otherwise specified and set forth in the said schedule, which said schedule,
and the several provisions, regulations, and directions therein contained
with respect to the said duties, and the instruments, matters, and things
charged therewith, shall be deemed and taken to be part of this act, and
shall be applied, observed, and put in execution accordingly: provided
always, that nothing herein contained shall extend to repeal or alter any
of the said stamp duties now payable in relation to any deed or instru-
ment which shall have been signed or executed by any party thereto, or
which shall bear date before or upon the passing of this act.
The new
duties to be
denominated
stamp duties,
&c.
The said duties by this act granted shall be denominated and
deemed to be stamp duties, and shall be under the care and
management of the Commissioners of Inland Revenue for the
time being; and all the powers, provisions, clauses, regulations,
directions, allowances, and exemptions, fines, forfeitures, pains, and penal-
ties contained in or imposed by any act or acts, or any schedule thereto,
relating to any duties of the same kind or description heretofore payable
in Great Britain and Ireland respectively, and in force at the time of the
passing of this act, shall respectively be in full force and effect with respect
to the duties by this act granted, and to the vellum, parchment, and paper,
820
STAMP DUTIES.
instruments, matters, and things charged and chargeable therewith, and
to the persons liable to the payment of the said duties, so far as the same
are or shall be applicable in all cases not hereby expressly provided for,
and shall be observed, applied, allowed, enforced, and put in execution
for and in the raising, levying, collecting, and securing of the said duties
hereby granted, and otherwise in relation thereto, so far as the same shall
not be superseded by, and shall be consistent with the express provisions
of this act, as fully and effectually to all intents and purposes as if the
same had been herein repeated and specially enacted, mutatis mutandis,
with reference to the said duties by this act granted.
on newspa-
As to duties No higher stamp duty than one penny shall be chargeable on
pers and sup- any newspaper printed on one sheet of paper containing a su-
perficies not exceeding two thousand two hundred and ninety-
plements.
five inches:
A supplement published with any newspaper duly stamped with the
duty of one penny, such supplement being printed on one sheet of paper
only, and together with such newspaper containing in the aggregate
a superficies not exceeding two thousand two hundred and ninety-five
inches, shall be free from stamp duty:
Any other supplement to any such duly stamped newspaper shall not
be chargeable with any higher stamp duty than one halfpenny, provided
it does not contain a superficies exceeding one thousand one hundred and
forty-eight inches:
And any two supplements to any such duly stamped newspaper shall not
be chargeable with any higher stamp duty than one halfpenny on each,
provided each of such supplements be printed and published on one sheet.
of
paper only, and that they contain together a superficies not exceeding
in the aggregate two thousand two hundred and ninety-five inches :
The superficies in all the cases aforesaid to be one side only of the sheet
of paper, and exclusive of the margin of the letter press.
Allowance
per stamps
on hand.
Where any person shall be possessed of any stamps for news-
for newspa- papers rendered useless by this act, it shall be lawful for the
Commissioners of Inland Revenue, on application to them or
to their proper officer in that behalf, at any time within six calendar
months after the commencement of this act, to cancel and make allowance
for the same, as in the case of spoiled stamps
After passing
duties on ad-
And whereas it is expedient to repeal the duties now pay-
of this act all able on advertisements: From and after the passing of this act the
vertisements duties now payable under any act or acts in force for or in respect
to cease. of any advertisement contained in or published with any gazette
or other newspaper, or contained in or published with any other periodical
paper, or in or with any pamphlet or literary work, and all enactments,
clauses, provisions, and regulations for levying, collecting, and securing
the said duties; but so far only as they relate to such duties, shall respec-
tively cease and determine, and shall be and the same are hereby repealed,
save and except as to any of the said duties, which shall have been charged
or incurred on or before the day of the passing of this act, and any arrear
STAMP DUTIES.
821
thereof, and as to all fines and penalties incurred or which may be in-
curred in respect of the said duties or arrears, all which said duties and
arrears, fines and penalties, so excepted as aforesaid, shall respectively be
sued for, recovered, levied, paid, and applied in the same manner as if this
act had not been passed.
signments of
Ireland, and
knowledg-
ment in
Scotland.
Whereas it is expedient to remove doubts which have arisen Duties on as-
as to the stamp duties upon assignments of Judgment in Ire- Judgment in
land; and it is also expedient to reduce the stamp duties now writs of ac-
chargeable in Scotland upon writs of acknowledgment by per-
sons infeft of lands in favour of the heirs or disponees of cre-
ditors: In lieu of the stamp duties now payable upon the instruments
hereinafter mentioned there shall be chargeable (besides any progressive
duties to which the same respectively may be liable by reference to the
head of progressive duty in the schedule to the act of the thirteenth and
fourteenth years of her present Majesty, chapter ninety-seven,) the respec-
tive stamp duties following; (that is to say,)
For and upon every assignment of any judgment in Ireland, one pound fifteen
shillings:
And for and upon any writ of acknowledgment by any person infeft of lands in
Scotland in favour of the heir or disponee of a creditor fully vested in right
of an heritable security constituted by infeftment, ten shillings.
And whereas under and by virtue of certain Acts of Parliament now
in force the governor and company of the bank of Scotland, and the royal
bank of Scotland and the British linen company in Scotland are respec-
tively authorized and empowered to make an issue and re-issue their
promissory notes payable to bearer on demand on unstamped paper, giving
security, and keeping and producing true accounts of all the notes so
issued by them respectively, and accounting for and paying the stamp
duties payable in respect of such notes: And whereas it is expedient to
authorize and empower the commissioners of Her Majesty's Treasury to
compound with the said banks, as well as all bankers in Scotland, for the stamp
duties on their promissory notes payable to bearer on demand, as well as
for stamps payable on their bills of exchange: It shall be lawful for the
Commissioners of Her Majesty's Treasury for the time being, power to
or any three of them, and they are hereby authorized and em-
powered to compound and agree with the said governor and
company of the bank of Scotland, and the royal bank of Scot-
land, and the British linen company in Scotland, and all or
any other bankers in Scotland, or elsewhere, respectively, for a
composition in lieu of the stamp duties payable on the promissory notes
of the said banks and bankers respectively payable to the bearer on de-
mand, as well for stamps payable on their bills of exchange; and such
composition shall be made on such terms and conditions, and with such
security for the payment of the same, and for keeping, producing, and
rendering of such accounts, as the said last-mentioned commissioners may
deem to be proper in that behalf; and upon such composition being entered
into by such banks and bankers respectively it shall be lawful for them to
Treasury to
with bankers
for the stamp
their promis-
compound
in Scotland
duties on
sory notes.
822
STAMP DUTIES.
issue and re-issue all notes and to draw all such bills for which such com-
position shall have been made on unstamped paper, anything in any act
contained to the contrary notwithstanding.
Stamp duty
on scrip cer-
From and after the passing of this act the following stamp
tificates duty shall be chargeable and paid; (that is to say,)
On any scrip certificate, that is to say, any document denoting or in-
tended to denote the right or title of the holder thereof or any
person to any share or shares in any joint stock or other company,
or proposed or intended company, or any certificate declaring or
entitling the holder thereof or any person to be or become the
proprietor of any share or shares of or in any such company, where
such certificate or the right or title to such share or shares shall
be or be intended to be transferable by the delivery of such cer-
tificate, or otherwise than by deed or instrument in writing
Receipts for
land or as-
sessed taxes
or Income
£ s. d.
0 0 1
No receipt given for any sum or sums of money received for
or on account of land tax, or the duties of assessed taxes, or
the duties on profits arising from property, professions, trades,
and offices, by any collecter or receiver of such taxes or duties,
or by any person having authority to collect or receive the same,
shall be subject or liable to any stamp duty.
Tax exempt
from stamp
duty.
Stamps de-
noting the
cies of life
assurance
The duties granted by an act of the present Session of Parlia-
duty on poli- ment on policies of assurance may be denoted either by a stamp
impressed upon the paper whereon any such instrument is
written, or by an adhesive stamp affixed thereto, and the Com-
missioners of Inland Revenue shall provide stamps of both
descriptions for the purpose of denoting the said duties.
may be im-
pressed or
affixed.
Certain par-
written on
adhesive
stamps for
policies.
The adhesive stamps to be so provided for the purpose afore-
ticulars to be said shall be adapted for the writing of the following particu-
lars thereon; (that is to say,) the date and number of the policy,
and the names of the person insured and of one of the direc-
tors of the assurance company, or other person by whom the same shall
be signed; and where an adhesive stamp shall be used or intended to be
used for or upon any such policy, such stamp shall be firmly and securely
affixed and made to adhere to such policy, and all the several particulars
aforesaid shall be fairly and distinctly written upon such stamp at or before
the time of the signing thereof by such director or other person aforesaid,
or in default thereof such director or other person signing such policy
shall forfeit the sum of Fifty Pounds.
The Schedule referred to by this Act.
Duty.
Articles of Clerkship or contract, whereby any person shall first become £ S. d.
bound to serve as a clerk in order to his admission as an attorney or
solicitor in any of Her Majesty's Courts at Westminster or in Ireland,
or in order to his admission as a proctor in the High Court of Admi-
ralty in England, or the Court of Admiralty in Ireland, or in any of
the Ecclesiastical Courts in Doctors Commons or in Ireland
Certificate to be taken out yearly by every person admitted as an attorney
or solicitor in any of Her Majesty's Courts at Westminster or in Ire-
land, or in any other court in England holding pleas where the debt
80 0 0
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
823
?
or damage amounts to forty shillings; and by every person admitted
as a writer to the signet, or as a solicitor, agent, attorney, or procu-
rator in any of the courts in Scotland; and by every person admitted
or enrolled as a notary public in England, Scotland, or Ireland, who
in his own name or in the name of any other person shall commence,
prosecute, carry on, or defend any action, suit, prosecution, or other
proceeding in any of the courts aforesaid, or do any notarial act what-
ever, for or in expectation of any fee, gain, or reward, as an attorney,
solicitor, agent, proctor, procurator, or notary public, although not
admitted or enrolled as such;
If he shall reside within the distance of ten miles from the Gene-
ral Post Office in the city of London, or within the city or
shire of Edinburgh, or in the city of Dublin, or within three
miles thereof;
And if he shall have been admitted for the space of three
years or upwards .
Or if he shall not have been admitted so long
If he shall reside elsewhere, and if he shall have been ad-
mitted for the space of three years and upwards
•
Or if he shall not have been admitted so long
Certificate to be taken out yearly by every person being a member of one of
the Four Inns of Court in England, and by every person in Ireland who
in the character of conveyancer, special pleader, draftsman in equity
or otherwise, shall, for or in expectation of any fee, gain, or reward,
draw or prepare any conveyance of or deed or instrument relating to
any estate or property, real or personal, or any other deed or contract
whatever, or any pleadings or proceedings in any court of law or equity;
If he shall reside within the distance of ten miles from the Ge-
neral Post Office in the city of London, or in the city of
Dublin, or within three miles thereof
•
And if he shall reside elsewhere
Conveyance of any kind or description whatsoever, in England or Ireland,
and charter disposition or contract containing the first original consti-
tution of Feu and Ground Annual Rights in Scotland (not being a
lease or tack for years), in consideration of any annual sum payable
in perpetuity, or for any indefinite period, whether fee farm or other
rent, feu duty, ground annual, or otherwise:
Where the annual sum thereby reserved, secured, or made pay-
able shall not exceed 20s.
And where the same shall exceed 20s. and shall not exceed 127. then
for every 20s. or any fractional part of 20s. of such annual sum
And where the same shall exceed 127. and shall not exceed 241.,
then for every 40s. and for any fractional part of 40s. of such
annual sum
And where the same shall exceed 247. then for every 47. and for
any fractional part of 47. of such annual sum
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
Duty.
£ s. d.
900
4 10 0
600
3 0 0
900
600
0 2 6
0 26
050
0 10 0
Duties now
on under-
Articles to
chargeable
mentioned
The Duties of Customs now chargeable on the articles under-
mentioned imported into Scotland and Ireland shall cease and
determine, and in lieu thereof the following duties shall be
charged from and after the twenty-first day of April One following
thousand eight hundred and fifty-three; viz.
cease, and
duties to be
charged.
824
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
Duties
Spirits or strong waters, for every gallon of such spirits or strong waters, £ s. d.
of any strength not exceeding the strength of proof by Sykes's
Hydrometer, and so in proportion for any greater or less strength
than the strength of proof and for any greater or less quantity
than a gallon, viz.
chargeable
hereafter
mentioned
Spirits or strong waters, the produce of any British possession
in America, not being sweetened spirits or spirits mixed
with any article, so that the degree of strength thereof
cannot be exactly ascertained by such hydrometer:
If imported into Scotland
Ireland
•
the gallon 0 5 0
the gallon 0 3 8
Rum, the produce of any British possession within the limits
of the East India Company's charter, not being sweetened
spirits or spirits so mixed as aforesaid, in regard to which
the conditions of the Act 4 Victoria, Chapter 8, have or
shall have been fulfilled:
If imported into Scotland
Ireland
•
the gallon 0 5 0
the gallon 0 3 8
Rum shrub, however sweeted, the produce of and imported
from such possessions, in regard to which the conditions
of the Act 4 Victoria, chapter 8, have or shall have
been fulfilled, or the produce of and imported from any
British possession in America:
If imported into Scotland
Ireland
•
the gallon 0 5 0
the gallon 0 3 8
The duties of customs chargeable upon the goods, wares, and
on goods, &c. merchandise hereafter mentioned imported into the united king-
dom shall cease and determine on and after the first day of June
imported into
united king- one thousand eight hundred and fifty-three; viz.
dom to cease
on June 1,
1853.
Agates or cornelians, cut or manufactured; albumen; amber, manu-
factures of, not enumerated; anchovies; aquafortis; bandstring twist ;
barytes, sulphate of, ground; bast ropes, twines, and strands; blacking;
books being of editions printed prior to the year 1801, bound or un-
bound; bran; brass, powder of; bricks and clinkers, Dutch and other
sorts; bronze powder; brushes, paint; buttons of metal and other sorts;
cameos, not set; camphor, refined; cantharides; carmine; carriages of
all sorts; casks, empty; catlings; chalk, prepared or manufactured, and
not otherwise enumerated; cider; citron, preserved in salt; cobalt, oxide
of; corks, fishermen's; crayons; crystals, cut or manufactured; cucumbers
preserved in salt; elder flower water; extract of chesnut bark and wood;
quercitron bark; logwood; safflower. Fish, viz.: eels, turbots, of foreign
taking, oysters, salmon, soles, turtle, fresh, not otherwise enumerated;
cured, not otherwise enumerated; frames for pictures, prints, drawings,
or mirrors; furniture woods, excepting ash, beech, birch, elm, oak, wainscot;
gauze of thread; gold, leaves of; gunpowder; hair, manufactures of hair or
goat's wool, or of hair or goat's wool, and any other material not particularly
enumerated or otherwise charged with duty; hams of all kinds; harp
strings or lute strings, silverved; honey; ink, Indian; iron wire; rough
castings; isinglass; latten wire; mead or metheglin; meat, preserved in any
other manner than salted; mercury, prepared; metal, leaf metal; naptha;
oil of resin; olives; orange flower water; orsedew; painters colours, manu-
factured; pencils, of slate and not of slate; perry; phosphorus; pickles, and
vegetables preserved in salt; pollard; pomegranates; pots, viz: melting
pots for goldsmiths, of stone; rose water; saccharum Saturni; sausages or
1
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
825
puddings; seed, viz.: canary, carrot, clover, grass of all sorts, leek, lucern,
mustard, onion, trefoil; all other sorts, not particularly enumerated, or other-
wise charged with duty; silkworm gut; skins; articles manufactured of
skins or furs; smalts; spectacles; spelter or zinc, viz.: rods and oxide of;
stone and slate, hewn; marble sawn into slabs, or otherwise manufactured;
tamarinds; tiles; tobacco pipes, of clay; tongues; turpentine, of a greater
value than 15s. per cwt.; oil or spirit of; twine; vanelloes; varnish, not
otherwise described; verdigris; wafers, wax, sealing; whipcord; waste
wood, viz. billet wood or brush wood, used for the purpose of stowage;
yarn of silk and worsted, spun together and not dyed; raw worsted yarn not
dyed, or only partially dyed, and not being fit or proper for embroidering, or
other fancy purposes.
:
In lieu of the Duties of Customs now chargeable on tea imported into
the United Kingdom, the following duties shall be charged on and after
the first day of June one thousand eight hundred and fifty-three :

5th April 1855
inclusive.
To
5th April 1854
inclusive.
From and after
5th April 1854 to
From and after
5th April 1855 to
5th April 1856
inclusive.
From and after
5th April 1856
£ s. d.
£ s. d.
0 1 10
per Pound.
0 1 3
per Pound.
£ s. d.
0 1 6
per Pound
£ s. d
010
per Pound.
The Duties of Customs chargeable upon the goods, wares, and merchan-
dise hereafter mentioned imported into the United Kingdom, shall cease
and determine on and after the fourth day of June one thousand eight
hundred and fifty-three; viz.
Cables, not of iron, new and old, tarred and untarred; coir rope, twine, and
strands; copper, ore of; regulus of; and brass, old, fit only to be re-manu-
factured; unwrought, viz.: in bricks or pigs, rose copper, and all cast copper;
part wrought, viz.: in bars, rods, or ingots, hammered or raised; in plates
and copper coin; or brass wire; cordage, tarred or untarred, including stand-
ing or running rigging; glass; all plate glass, cast or rolled, of whatever
thickness, however small each pane, plate, or sheet, whether silvered, polished,
or rough, painted or otherwise ornamented, all white flint glass bottles, not
cut, engraved, or otherwise ornamented, and beads and bugles of glass;
wine glasses, tumblers, and all other white flint glass goods, not cut, engraved,
or otherwise ornamented; bottles of glass covered with wicker (not being
cut glass), or of green or common glass; articles of green or common glass,
manufactures, not otherwise enumerated or described, and old broken glass,
fit only to be re-manufactured; lead, pig and sheet; linen, or linen and cotton,
viz.: cambrics and lawns, commonly called French lawns, whether plain or
bordered; lawns of any sort, not French; damasks and damask diaper; sails
of all sorts; mats and matting; pictures; poultry and game, alive or dead;
tin, viz. in blocks, ingots, bars, or slabs; truffles; verjuice; wire, viz.: gilt,
plated, silver and brass; yarn, cable yarn.
In lieu of the Duties of Customs now chargeable on the articles under-
mentioned imported into the United Kingdom, the following duties shall
be charged on and after the fourth day of June one thousand eight hun-
dred and fifty-three; viz.
Apples, raw (not of British Possessions).
dried
Butter (not of British Possessions)
£ s. d.
the bushel 0 0 3
the bushel 0 1 0
the cwt. 0 5 0
3 D
826
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
Cheese (not of British Possessions) to be charged on the landing £
weight
s. d.
the cwt.
0
2 6
Cocoa
the lb.
0
0 1
Husks and shells
the lb.
0
0 0
paste and chocolate
Nuts, small
walnuts
Raisins
Almonds, Jordan
not Jordan, nor bitter
paste of
Arrow root
Barley, pearled
Baskets, viz.:
the lb.
0
0 2
the bushel
0
1 1
0
the bushel
0 1 0
the cwt. 0 10
0
the cwt.
0 10
0
the cwt.
0 10
0
the lb.
0 0 2
the cwt.
0 0 4
the cwt.
0 0
0
0 43
Baskets corresponding with the description commonly called
Berlin
the cubic foot
0 0
7
all others
the cubic foot
0
0 2
Beads, coral
the lb.
0
1
6
arango, crystal, jet, and other sorts not enumerated or de-
scribed
the lb.
the cwt.
0 0
2
0 10 0
Brocade of gold or silver
•
the lb. 0 5 0
the cwt. 0 10 0
Brass, manufactures of, not otherwise enumerated
Bronze, manufactures of, not otherwise enumerated
Candles, viz.:
spermaceti
the cwt. 0 2 4
stearine, till the 5th of April 1858, unless the duty upon
tallow shall be repealed at an earlier time, in which case
this duty shall be reduced to the same rate as tallow
candles
tallow
wax
Canes, viz.:
the cwt. 0 3 6
the cwt. 0 2 4
the cwt. 0 2 4
walking canes or sticks, mounted, painted, or otherwise orna-
mented
umbrella or parasol sticks
Capers, including the pickle
the 100 0 6 0
the 100 0 3 0
the lb. 0 0 1½
Cards, viz., playing cards
·
Cassava powder
Cassia lignea
་
the dozen packs 0 15 0
the cwt. 0 0·42
the lb. 0 0 1
Chicory, or other vegetable matter applicable to the uses of chicory
or coffee, viz. :
raw or kiln-dried, until 10th October 1854 inclusive, the cwt. 0 4 0
from and after 10th October 1854
roasted or ground
the lb.
the lb.
Free.
0 0 4
0 10
0 0 2
China ware, or porcelain, painted or plain, gilt or ornamented, the cwt.
Cinnamon
Clocks, viz. :
Cloves
not exceeding the value of 5s. each
the dozen 040
exceeding the value of 5s. and not exceeding the value of 12s.
6d, each
the dozen 080
exceeding the value of 12s. 6d. and not exceeding the value
of 31. each
each 0 2 0
exceeding the value of 37. and not exceeding the value of 107.
each
exceeding the value of 107. each
Coculus Indicus
Coffee, roasted or ground
each 0 4 0
each 0 10 0
the lb. 0 0 2
the cwt. 0 5 0
•
the lb. 0 0 4
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
827
Comfits, dry, until 5th July 1854 inclusive
from and after 5th July 1854
Confectionery, until 5th July 1854 inclusive
from and after 5th July 1854
•
£ s. d.
the lb. 0 0 2
0 0 11
the lb.
the lb. 0 0 2
the lb. 0 0 1
Copper, manufactures of, not otherwise enumerated or described, and
copper plates, engraved
Corks, ready made
squared for rounding
Dates
Dice
•
Earthenware not otherwise enumerated or described
Feathers, dressed, viz. :
ostrich
paddy bird
not otherwise enumerated or described
the cwt.
0 10 0
the lb.
0 0 6
the cwt. 0 8 0
the cwt.
0 10 0
the pair
1 1 0
the cwt.
0 10 0
the lb.
0 3 0
the lb. 0 3 0
the lb. 0 3
0
the cubic foot
the cubic foot
0 12
0
0 12 0
the bushel
0 0 2
the lb.
0 0 2
the lb.
0
0
1
Flowers, artificial, not made of silk, per cubic foot as packed, no
allowance for vacant spaces
wholly or in part made of silk
Fruit, raw, not otherwise enumerated
•
Ginger, preserved, until 5th July 1354 inclusive
Glass, viz. :
Grapes
from and after 5th July 1854
any kind of window glass, white or stained of one colour only,
(except plate or rolled glass,) and shades and cylinders, until
5th April 1855 inclusive
the cwt.
from & after 5th April 1855 until 5th April 1857 inclusive the cwt.
from and after 5th April 1857
all flint cut glass, flint coloured glass, and fancy ornamental
glass, of whatever kind
•
026
0 1 6
Free.
the cwt.
the bushel 0 0 2
of hair or
0 10 0
Hair articles; manufactures of hair or goat's wool, or
goat's wool and any other material, wholly or in part made up,
not particularly enumerated or otherwise charged with duty
Hats or bonnets, viz.:
of chip
of bast, cane, or horse-hair
of straw
for every 1007. value 5 0 0
the lb. 0 2 6
the lb. 0 2 6
of felt, hair, wool, or beaver
the lb. 0 2 6
each 0 1 0
Hats of silk or silk shag laid upon felt, linen, or other material, each 0 1 0
Iron and steel, wrought or manufactured, viz. :
machinery, wrought castings, tools, cutlery, and other manu-
factures of iron and steel, not enumerated
fancy ornamental articles of iron
of steel
•
the cwt. 0 2 6
the cwt. 0 15 0
the cwt. 0 15 0
Jewels, emeralds, and all other precious stones, set, for every 1007. value 10 0 0
Lead, manufactures of, not otherwise enumerated
Leather, viz.: boot backs
cut into shapes
Liquorice paste (not of British Possessions)
Maccaroni
Mace
powder (not of British Possessions)
root, until 5th April 1857 inclusive
from and after 5th April 1857
Marmalade, until 5th July 1854 inclusive
•
the cwt. 0 2 0
the dozen pairs 0 1 6
0
the cwt. 0 10
the cwt. 1 0 0
the cwt. 1 0 0
the cwt. 0 5 0
Free.
the cwt. 0 1 0
the lb. 0 1 0
the lb. 0 0 2
from and after 5th July 1854
Medlars
•
the lb. 0 0 1
the bushel 0 0 2
828
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
Musical instruments, viz.:
boxes, small, not exceeding four inches in length,
the air 0
£ s. d.
0 3
large
the air 0 0 8
overtures, or extra accompaniments
piano fortes, horizontal grand
the air 0 2 6
each 3 0
0
upright or square
each 2 0 0
harmoniums or seraphines, not exceeding three stops, each 0 12 0
four stops, and not exceeding
seven stops
each
1 4 0
eight stops, and not exceeding
eleven stops
each 1 10 0
exceeding eleven stops each 2 0 0
the 100 notes 0 1 0
accordions, commonly called Chinese
other sorts, including flutinas and common
German square concertinas, the 100 notes 0 5 0
concertina of octagon form, not common German, each 0 4 0
brass instruments, all sorts
instruments, not otherwise enumerated or described, for
Mustard flour
Nutmegs, except those commonly called wild
Nux vomica
Oil, viz.:
the lb. 0 0 9
every 1007. value 10
0 0
the cwt. 0 1 6
the lb. 0
the cwt. 0
1
0
2 0
the lb. 0 0
1
ålmond
bays
essential oil of cloves
Onions
Pears, raw
dried
the lb. 0 0 1
the lb. 0 1 0
the bushel 0 0' 1
the bushel 0 0 3
the bushel 0 1 0
the 1,000 00 1
Percussion caps
Perfumery, not otherwise enumerated, and scented or fancy soap the lb.
Pewter, manufactures of, not otherwise enumerated
Pickles preserved in vinegar
Pimento
Plate of gold
of silver, gilt or ungilt
0 0 2
020
the cwt.
the gallon
0 0 1
•
the cwt. 0 5 0
the oz. troy 1
the oz. troy
1 0
0 1 8
Platting, or other manufactures of straw, chip, or other materials to be
used in or proper for making or ornamenting hats or bonnets, not
otherwise enumerated or charged with duty
cordonet, single, and twist of straw, or of other materials, the lb.
willow squares
Plums, commonly called French plums and prunellos
dried or preserved (except in sugar), not otherwise
preserved in sugar, until 5th July 1854 inclusive,
from and after 5th July 1854
Pomatum
Potato flour
Powder, viz.:
hair powder
perfumed
the dozen
the lb.
0 2 0
0 0 6
00 1
0 15 0
0 15 0
0 0 2
0 0 1
002
the cwt.
described,
the cwt.
·
the lb.
the lb.
the lb.
the cwt.
0 0 41
the lb. 0 0 2
the lb. 0 0 2
not otherwise enumerated or described, that will serve the
same purpose as starch
Prints and drawings, plain or coloured, single
bound or sewn
·
the cwt. 0 0 41
the lb. 0 0 3
the lb. 0 0 3
admitted under treaties of international copy-
right, single
bound or sewn
the lb. 0 0 11
the lb. 0 0 1
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
829
Quassia
Quinces
Rice, not rough, nor in the husk
£
the cwt.
8. d.
010
the bushel 0 0 3
the cwt. 0 0 42
rough, and in the husk
Sago
Scaleboard
Semolina
the quarter
0
0 9
the cwt.
0
0 41/2
the cwt.
01 0
the cwt.
0 0 43
for every 1007. value
for every 100%. value
the cubic foot
500
5
0 0
0 0 6
Ships, foreign ships, to be broken up, with their tackle, apparel and
furniture (except sails),
broken up
Spa ware
Spelter or Zinc, manufactures of, not otherwise enumerated, the cwt.
Spirits, cordials, or strong waters, not being the produce of any
British Possession in America, nor of any British Possession within
the limits of the East India Company's Charter, in regard to
which the conditions of the Act 4 Vict. cap. 8 have or shall been ful-
filled, sweetened or mixed with any article so that the degree of
strength cannot be exactly ascertained by Sykes's hydrometer,
and perfumed spirits to be used as perfumery only, the gallon
Starch
the cwt.
Gum of, torrified or calcined
Succades, including all fruits and vegetables preserved in sugar, until
the 5th July 1854 inclusive
From and after the 5th July 1854
•
Tapioca
Tin foil
0 20
1 0 0
0 0 43
the cwt.
0 0 41
the lb.
0
0 2
the lb.
0 0 1
the cwt.
0 0 41
the cwt.
0 10 0
the cwt.
0 10 0
the cwt.
0 1 0
Manufactures of tin, and not otherwise enumerated,
Toys, viz.:
marbles
all other toys
Turnery, not otherwise described
Varnish, containing any quantity of alcohol or spirit
Vermicelli
Vinegar
Washing balls
the cubic foot 0 0 4
the cubic foot 0 0 4
the gallon 0 12 0
the cwt.
0 1 0
the gallon 0 0 3
the lb. 0 0 2
Water, Cologne water, the flask (thirty of such flasks containing not
more than one gallon)
when not in flasks (as perfumed spirits)
each 008
the gallon 1 0 0
In lieu of the present ad valorem rates of duties of customs charged
upon the importation into the United Kingdom of the undermentioned
articles as not being enumerated in the Tariff, the following duties of
customs shall be charged thereon on and after the fourth day of June one
thousand eight hundred and fifty-three; viz.
Biscuit and bread
Caoutchouc or Indian rubber, manufactures of
Coral negligées
Daguerreotype plates
Fig cake
the cwt. 0 0 41
the lb. 0 0 4
the lb. 0 1 0
the lb.
0 0 3
the cwt.
0 15 0
the cwt.
the lb.
0 5 0
002
Gutta percha, manufactures of, not moulded, such as bands, sheets,
soles, tubing
articles moulded
Lucifers of wood in boxes containing not more than 100 matches,
the gross of boxes
in boxes containing more than 100 matches, the gross of boxes
vesta of wax, in boxes not exceeding 1,000 matches, the
0 0 2
0 0 3
dozen boxes 0 0 6
830
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
£
8. d.
Lucifers in boxes exceeding 1000 matches
the 1000 matches
0
0 0
Mandioca flour
the cwt. 0
0 4
Salacine
Manna croup
Oil cloth, for table covers
Sauces, not otherwise enumerated
the cwt. 0 0 41
Mustard, mixed or manufactured, except flour
the cwt. 0
5 0
•
the square yard
the oz.
0
0 1
0 0 3
the lb.
0 0 1
Soy
the gallon
0
0
6
Sterine, till the 5th April 1858, unless the duty upon tallow shall be
repealed at an earlier time, in which case this duty shall then cease,
After the 5th April 1858
Veneers
the cwt. 0 3 6
Free.
the cwt. 0 1 0
In lieu of the duties of customs now chargeable on the article under-
mentioned imported into the United Kingdom, the following duties shall
be charged on and after the eighth day of June one thousand eight hun-
dred and fifty-three; viz.
Eggs not of British Possessions
the 120 0 0 4
In lieu of the duties of customs now chargeable on the articles under-
mentioned imported into the United Kingdom, the following duties shall
be charged on and after the twelfth day of July one thousand eight hun-
dred and fifty-three; viz.
Soap, not being scented or fancy, viz.:
hard
soft
Naples
the cwt. 0 0 8
the cwt. 7 08
the cwt. 0 0 8
In lieu of the duties of customs now chargeable on the articles under-
mentioned imported into the United Kingdom, the following duties shall
be charged on and after the eleventh day of June one thousand eight hun-
dred and fifty-three; viz.
Oranges and lemons
the bushel 0 0 8
Books, being bound in editions printed in or since the year 1801, bound
or unbound
the cwt. 1 10 0
admited under treaties of international copyright, or if of and
from a British Possession.
Cherries, raw
dried, until 5th July 1854 inclusive
ditto, from and after 5th July 1854
Cotton manufactures, viz.:
fringe
gloves, of cotton or thread
stockings, of cotton or thread
socks, or half hose, of cotton or thread,
the cwt. 0 15 0
the bushel 0 0 2
the lb. 0 0 2
the lb. 0 0 11
the lb. 0 0 2
the dozen pairs 0 0 3
the dozen pairs 0 0 6
the dozen pairs 0 0
articles or manufactures of cotton, wholly or in part made
up, not otherwise charged with duty, for every 1007. value 5 0 0
Embroidery and needlework, viz. :
silk net, figured with the needle, being imitation lace, and ar-
ticles thereof
the lb. 0 10 0
cotton net, figured with the needle, being imitation lace, and
articles thereof
the lb. 0 8 0
curtains, commonly called Swiss, embroidered on muslin or net,
all other embroidery not enumerated,
of and from British Possessions
the lb. 0 1 0
for every 1001. value 10 0 0
for every 1001. value 5 0 0
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
831
Lace and articles thereof, viz. :
mohair or worsted
•
£
8. d.
the lb. 0
1 0
the lb. 1 0 0
thread or cotton pillow lace (not being Brussels point or Saxon
bone lace), not exceeding one inch in width
thread or cotton pillow lace (not being Brussels point or Saxon
bone lace), exceeding one inch in width
the lb. 2 0 0
silk lace, pillow and application, not being Saxon wire ground
lace
the lb. 1 10 0
silk Saxon wire ground lace, and all lace known as Maltese, the lb. 0 8 0
Brussels point, and other lace made by the hand, not other-
wise charged with duty
for every 100l. value 10 0 0
Linen, or linen and cotton manufactures, viz.:
cambric handkerchiefs, hemmed or hemstitched, not trimmed,
the dozen
stays
the dozen pairs
articles, manufactures of linen, or of linen mixed with cotton
or with wool, wholly or in part made up, not particularly
enumerated or otherwise chargeable with duty, for every
Mill boards
Paper, viz.:
026
0 4 0
1007. value 5 00
the lb. 0 0 2
brown paper made of old rope or cordage only, without sepa-
rating or extracting the pitch or tar therefrom, and without
any mixture of other materials therewith
the lb. 0 0 21
printed, painted, or stained paper or paper-hangings, or flock
paper
the square yard 0 0 1
Paper, waste paper, or paper of any other sort not particularly enume-
rated or described, not otherwise charged with duty, the lb.
Pasteboard
Silk manufactures, being
11
velvet, the produce of Europe, plain or figured:
broad stuffs.
0 0 2
the lb. 0 0 21
the foundation of which is wholly composed of
cotton or other materials than silk
the lb. 0 9 0
the lb. 0 3 0
0 10 0
6
ribbons of velvet, or silk embossed with velvet, the lb.
the foundation of which is wholly composed of
cotton, or other materials than silk the lb. 0 3
manufactures of silk, or of silk mixed with any other mate-
rials, the produce of Europe, called plush
black plush, commonly used for making hats,
parasols and umbrellas
the lb. 0 3 0
the lb. 0 1 0
each 0 1 0
damask of silk and wool or other materials, for furniture
China
the lb. 0 0 10
the running yard 0 0 8
corahs, choppahs, Bandannas, and Tussore cloths, viz.: in
pieces not exceeding 54 yards in length,
the piece 0 0 4
exceeding 5 and not exceeding 64 yards, the piece 0 0 6
6
and not exceeding 7
74 and not exceeding 8
yards, the piece 0 0 8
yards, the piece 0 0 9
81 and not exceeding 94 yards, the piece 0 0 10
and for every additional yard in length
China crape shawls, plain and damask
embroidered
the yard 0 0 1
the lb. 0 3 0
the lb. 0 5 0
Pongees, in pieces not exceeding 15 yards in length, the piece 0 20
exceeding 15 yards and not exceeding 21 yards in length, the
piece 0 3 0
exceeding 21 yards and not exceeding 31 yards in length, the
piece 0 5 0
832
AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS.
9 yards in length
Silk handkerchiefs, plain and figured, in pieces not exceeding £ s. d.
the piece 0 1 6
exceeding 9 yards and not exceeding 18 yards in length,
the piece 0 3 0
Watches, of gold, silver, or other metal, exceeding the value of 107.
each
each 1 0 0
other watches, viz. :
gold, open faces
each 0 5 0
hunters
each 0 7 6
repeaters
silver, or any other metal not gold:
open faces
hunters
repeaters
Woollens, articles or manufactures of wool (not being goat's wool) or
each 0 15 0
each 0 2 6
each 0 3 6
each 0 8 0
of wool mixed with cotton, viz.:
carpets and rugs
the square yard
0
0
6
shawls, scarfs, and handkerchiefs, plain and not printed, the lb.
the lb. 0 0
the dozen pairs 0 0
0 0 4
8
printed
gloves
articles or manufactures of wool mixed with cotton, wholly
or in part made up, not otherwise charged with duty, for
every 100%. value 5 0 0
In lieu of the present ad valorem rates of duties of customs charged
upon the importation into the United Kingdom of the undermentioned
articles as not being enumerated in the tariff, the following duties of cus-
toms shall be charged thereon on and after the eleventh day of June one
thousand eight hundred and fifty-three; viz.
Paper, gilt, stained, coloured, embossed, and all fancy kinds, not
being paper-hangings
the lb. 0 0 2
The duties of customs chargeable upon the goods hereafter mentioned, im-
ported into the United Kingdom, shall cease and determine on and after the
twenty-third day of June one thousand eight hundred and fifty-three; viz.
Flock for paper stainers.
On and after the fifth day of July one thousand eight hundred and
fifty-three so much of an act passed in Session of Parliament holden in
the third and fourth years of the reign of His late Majesty King William
the Fourth, chapter one hundred and one, section three, as provides that
the allowance commonly called draft, then made by the Commissioners
of Excise in the weighing of tea, should be made by the Commissioners
of Customs under the authority of the said act, shall be and the same is
hereby repealed; and the allowance of one pound for draft on each chest
of tea exceeding twenty-eight pounds in weight now made by the Com-
missioners of Customs under the authority of the said act shall cease and
determine upon all tea which shall arrive and be reported at the custom
house of any port in the United Kingdom on and after the fifth day of
July one thousand eight hundred and fifty-three.
The duties imposed by this act shall be under the management of the
Commissioners of Her Majesty's Customs, and shall be ascertained, raised,
levied, collected, paid, recovered, and allowed, and applied or appropriated,
under the provisions of any act or acts now in force or hereafter to be made
relating to the customs.
833

HARWICH, DOVERCOURT NEW TOWN.
2ND CLASS.


END ELEVATION.
ELEVATION NEXT GARDEN.


16 by 14
[O]
28 by 16 6
ONE PAIR.
ESTIMATED COST £450.
16 by 14
28 by 16 6
GROUND FLOOR.
3 D
835
VILLAS, CARLTON ROAD, KILBURN PARK.
ROAD,KILBURN

ELEVATION,


10 by
8 6
17 6 by
15 6
14 6 by
12 6
11 by
9 6
10 by
8 6
17 6 by
15 6
22 6 by 146
『 10 by
86
1
20 by 16
20 by 16
17 by 15 6
196 bym
7
17 by 156
ONE PAIR.
GROUND FLOOR.
ESTIMATED COST £850 THE PAIR.
837
WESTBOURN PARK, PADDINGTON.
FULL-SIZED 3RD CLASS.

ELEVATION. 74 FEET.

14 6 by 12
12 by 10 6
14 6 by 12
18 by 13
12 6 by
8 9
12 6 by
8 9
18 by 13
GROUND PLAN.
CHAMBER PLAN.
ESTIMATED COST £800 THE THREE.
ONE PAIR.
[over.
PLAN VARIED.

14 6 by 12
12 by 10 6
14 6 by 12
18 by 13
12 6 by 8 9
18 by 18
839
HILL, ST. JOHN'S WOOD.
No. 2, CARLTON HILL,

ELEVATION.


20 by 16
16 by 13
20 by 16
27 by 16
12 by 12
16 by 13
12 by 12
ONE PAIR.
ESTIMATED COST £475.
GROUND PLAN.
841
33
PADDINGTON ESTATE.
2ND CLASS.

ELEVATION.
H
14 by 13
14 by 13
20 by 18
20 by 18
白宫
​
GROUND PLAN.
ONE PAIR PLAN.
Cost £1000 THE PAIR.
[over.
:

GROUND PLAN.
14 by 13
20 by 18
843
TORIANO AVENUE, KENTISH TOWN.
SMALL 3RD CLASS.

Conser-
vatory.
MRUMIMILA
ELEVATION. 39 FT. 6 IN.


18 by 13
18 by 13
10 2 by
8 9
13 by 8 9
10 2 by
13 by 8 9 8 9
14 by 12
14 by 12
14 by 12
14 by 12
BASEMENT AND GROUND PLAN.
COST £500 THE PAIR.
ONE PAIR PLAN.
[over.



O
rezzak
18 by 13
14 by 12
Conser-
vatory.
BASEMENT AND GROUND PLAN.
845
SAXON VILLA, CLIFTON TERRACE, BRIGHTON.

SA
PERSPECTIVE SKETCH.


16 6 by
17 by 14
17 by 14
16
16 6 by 16
13 by 12
18 by 15
14 by 10
ONE PAIR.
ESTIMATED COST £200.
13 by 12
18 by 15
GROUND PLAN.
[over.

17 by 14
13 by 12
GROUND PLAN.
18 by 15
847
HARWICH, VILLAS AT DOVERCOURT NEW TOWN.
3RD CLASS.

TAVA
NAVA VAYA
ELEVATION.

21 by 12
21 by 12
18 by 12
18 by 12
BASEMENT AND GROUND PLAN.
COST £750 THE PAIR.
849
VILLAS, CARLTON ROAD, KILBURN PARK.

ELEVATION.
14 6 by
11 by
10
11 by
10
12 6
17 by
14 6
lo
T
14 9 by
14 6
14 9 by
14 6
88


17 by 146
17 by 14 6
116 |
11 by
10
10 by
14 9 by
14 6
96
14 9 by
14 6
10 by
96
BASEMENT AND GROUND FLOOR.
ONE PAIR.
TWO PAIR.
ESTIMATED COST £650 THE PAIR.
3 F
851
DOVERCOURT NEW TOWN, NEAR HARWICH.
GARDEN FRONT.
1
ܢܶܐ.
20 0
ELEVATION.
PRINCIPAL FRONT.


13 by 12
16 6 by 12
18 10 by 14
14 by 9 3
14 by
95
GROUND PLAN.
CHAMBER PLAN.
COST £650.
[over.

GROUND PLAN.
I
1
I
16 6 by 12
18 10 by 14

853
DALSTON, NEAR LONDON.

FI


1
190


10
8
8
12
13
12
13
10
15
15
20
10
feet
Cost £340 THE PAIR.
LET AT £23 PER ANNUM.
CONTAINING SIX ROOMS AND CONVENIENCIES.
Thos. Tatlock, Archt., Dalston.]
855
Ο
1
Thos. Tatlock, Archt., Dalston.]
VILLAS IN REGENT'S PARK.

PANE
19 2452049 9310.


clost
Area.
Tardr
Store
Room
Passage
Coals
C
Kitchen
Scullery
12 by 10
6 1
LI
6 2
14
12 11
77
6 6
11
61
8
39 4
20
10
feet.
CONTRACT PRICE £1500.
EACH CONTAINS TEN ROOMS, PANTRY, CELLARS, AND CONVENIENCIES.
RENTAL £75 EACH.
13 3


857
ON LANDED PROPERTY.
CHAPTER I.
LANDLORD AND TENANT-THEIR POSITION AND
CONNECTIONS.
THE landlord is the owner of the soil, whose proprietorship Right of oc-
has been derived chiefly from priority of occupation, and from cupancy
the act of labour subsequently bestowed. To these rights of occupancy a
tacit acknowledgment and virtual acquiescence have been yielded by the
general consent of the human race. Jurists have entangled themselves in
very lengthened disputations and much subtlety of argument in trying to
determine whether the act of labour was necessary to support the right
acquired by priority of occupation; and also, if the public assent be essen-
tial to confirm the two privileges, when joined, in constituting the owner-
ship of property. The question has been long since settled by general
opinion conferring on land the same rights as any other articles confirmed by
which a man can call his own; the same vested interests, and law.
the same inalienable adjuncts. The law of civilized nations, or morality
armed with power, has sanctioned the conferment, and upholds the
continuance.
land.
4
Land has been appropriated in order to make it more generally useful,
and to create a general interest in its favour. An enlightened barbarism
made the first appropriations in large grants of land as the plunder of
conquest, and the reward of services, to be held in tenure for future per-
formances and attendance. The inconvenient superintendence soon induced
the dismemberment of the extensive grants; the uncertain and Grants and
short-lived reigns which prevailed, caused many confiscations; alienations of
and the constant wars and intestine broils of unsettled times,
produced large changes in the possession of the separated portions of the
grants. The no less quarrelsome leisure of peace had a large effect in
leading to fines and confiscations, which still further augmented the distri-
bution of the land as private property. When trade became flourishing,
and money became abundant, land was bought and sold as any other
marketable commodity, the divisions being varied chiefly by chance and
accident; a large part generally remaining with the name of the Rest on ap-
original holder, and still giving the title and rank which accompa-
nied the gift. In this way land has become the property of the present pos-
sessors, who hold by purchase, which rests on the original appropriation.
For a very long period of time the property of land constituted almost
the only form of wealth and power, and carried along with it the sole dis-
propriation.
3 G
858
ON LANDED PROPERTY.
Land the dis-
tinction of
society,
and its power
tinctions of society. The nobles and proprietors formed one part
of the community; and retainers, dependents, and slaves, were
the other portion, which was almost wholly bereft of personal
liberty, and lived on the charity and pleasure of the higher grade. There
was no nobility without property in land—no power, no respect, nor
even the natural gift of personal freedom. Every idea was based upon
the soil: all settlements and associations, isolated or collective, were
founded upon the country, by which the mode of life was regulated, and the
social institutions conformed. In every country where land has been
appropriated, in every form of government, and under every dynasty
which has ruled on earth, in every change and revolution that
has happened, and under every different phase which society has
assumed, the land-owning body has ever had a preponderance in the legis-
lation, and has directed the machinery of government. A certain pres-
tige of independence and patriotism has always in some kind and degree
been found attaching to the owners of the soil, which has not a little con-
tributed to the essential qualification in a member of the legislature, and
of the open recognition of landed property conferring a title to the dis-
tinction in that respect. The early preponderance of the owners of the
soil has not been lost, and little if at all impaired by the upheaving of the
other classes of society-an influence still clings to it, as compared with
other kinds of property, and an earnest desire for the possession of it is
evinced by all persons who can command the means of purchase.
and avidity The durable nature of its essence forms the primary considera-
its influence
of purchase, tion, the current value may fluctuate as that of other commo-
dities, but a total loss never can be sustained by its possession, as no
evanescence takes place of the original matter. This quality confers the
superiority of property in land over other inheritances, and has raised the
estimation both of the article and the possessor. The detached and iso-
lated position of the property confers a power that is of a very useful and
agreeable exercise, and it affords a relaxation not enjoyed by other employ-
ments of capital and time. This leisure gives opportunity for the dis-
charge of public duties, which interfere least with the absence from
business of the habits of life which those duties occasioned and required.
The business of legislation gradually fell into the hands of the party which
had most leisure for the purpose, and inclination for the object. The
and changes
from the
social effect.
gradual increase of numbers soon acquired a preponderating
force, which materially changed the original idea and constitu-
tion of the British House of Commons.
Under the gifts of feudal tenure, the possession of land was conferred on
the condition of military service, and of furnishing a fixed quota of armed
followers, bearing the same relation to the landlord as he did to the sove-
reign. Land under its feudal relations was regarded as a thing out of com-
merce altogether, and no idea was entertained of its being a certain amount
of property appreciable at a money value. It was estimated to be an in-
alienable "entirety" held under the crown, and the gift and the condition
ON LANDED PROPERTY.
859
holding.
of tenure, with the concomitant obligations, passed exclusively Original
to the eldest son, whose prior right in every affair has been re-
cognized from the first dawn of civilization and of social arrangements.
This “backbone" of feudalism has been copied into the laws of real pro-
perty, as the land is termed, along with its immoveable subordinations, in
contradistinction; or of personal property, which consists of moveable goods
of every kind that are evanescent in quality and perishable in the nature.
When the growth of towns, and the influx of money, along with other cir-
cumstances, compelled land to be an article of ordinary bargain and sale,
and of conversion into money and reconversion, the custom primogeni-
was continued of devolving on the eldest son, the inheritance of ture,
the landed property: it was ultimately restricted by law to cases of intes-
tacy only. This law of primogeniture has been much reviled, as “to enrich
one it beggars all the rest of the children," and as making distinctions,
which tend to disarrange and disunite the frame-work of society. But in
the main it has been productive of much good: the landed property has
been preserved in fair and suitable divisions, which uphold the influence
and support the respectability: it has been kept from being use and abuse
partitioned in minute sub-divisions, which derange the general of it;
utility and take away the power of its own improvement by the total want
of means. Feudalism saw that its purposes required the grants of land to
be large rather than small, and civilization finds that to be improved and
its resources developed, land must be in the hands of wealth of an amount
that is able to furnish the sufficient means for that purpose, and also to
make the suitable family provisions that attend the relations of human
nature. In Britain, primogeniture applies in cases of intestacy only, and
most completely differs from the arbitrary laws of continental Europe,
which divide the land among the children, without or with the differs from
parent's consent. This compulsory partition, though seemingly the continent
founded on justice and equity, has been found very injurious to of Europe,
the general interest, and not very profitable to the parties themselves, who
obtain shares of insufficient amount, and which must be assisted by other
pursuits. The evil has been produced by an extreme of the application,
which in a well-meant intenseness overlooks the contingencies that are
near, and the consequences that are remote.
It has been much and less
more hurtful than the use of primogeniture, even in the hurtful.
opinion of its warmest admirers.
the law of
Land-ownership is thus privileged with the application of a law, which
in cases of intestacy conveys the property intact to the eldest son, or heir-
at-law, who receives the patrimony in exclusion of all other claims. It
meets our approbation in so far as it preserves the land in portions suffi-
cient to support its respect and maintain its dignity, and by which the
general utility is developed, and the efficiency remains unimpaired. When
divided estates of land are held in one possession, the parental judgment
must exercise its discretion in devising, by will, the due bequeathments
of the adequate value and amount. And if by intestacy the whole landed
860
ON LANDED PROPERTY.
property goes to primogeniture, the next revolution in the family of pos-
session may correct the discrepancy, and modify the standard of in-
heritance.
Entail of
land.
Stretch of
ture;
A stretch of primogeniture has produced the entail, by which landed
property is devised by one possessor to pass for ever in one line
of possession, as may be defined in the deed of settlement. It
also passed free of all debts, which were obliterated on the successor re-
ceiving the property. This regulation has proved a complete snare to the
commercial dealer, who was debarred from touching the property itself,
and who found his claims wholly extinguished by the exchange of pro-
prietors. The entail of lands of a proper and moderate extent in a direct
line of succession constituted no evil of itself, it was only pri-
primogeni- mogeniture secured by a regulated assignment, which set aside
any other intentions on that point. But very questionable was
annulling of the extinction of debts of all kinds at every change of ownership,
debts hurtful the iniquity was palpable, and the damage to society needed not
any demonstration. The remedy was simple, in leaving the property to
pass intact, and in the law allowing the creditor a fixed annuity till paid
his claim from every successor in the property. As the entail stood, a
barrier was raised against any movement on the property, no improvements
could be done, nor any liability contracted. The hands of the landlord
were fastened, and his willing energies rendered useless. In many cases,
the difficulty of improvement lies far less in the unwillingness or ignorance
restricts im- of the landowner, than in the irrelevance of the proposed advan-
provements. tage to his personal interests in his parental or other capacity, or
in his pecuniary inability to undertake it. The landlord may be the father
of a large family, all unprovided for, except the eldest son, upon whom the
estate devolves, and every outlay on the land only adds to the settled in-
heritance, to the loss of the unportioned part of his family, or he may be a
young proprietor just come into a possession burdened with jointures,
mortgages, and the unpaid portions of younger brothers and sisters charged
upon his estate. Debts, mortgages, and incumbrances will be incurred in
the course of human transactions, and whenever a landed security can be
got, an encouragement is held out to advance money upon it. It is certain
that not more than one-half the income derived from land truly
belongs to its nominal owners, and the proportion has by many
well-informed persons been estimated at not more than one-third. The
remainder belongs chiefly to others, to mortgagees, rent-charge owners,
jointresses, annuitants, and the like; while the nominal owners bear all the
costs of management, and all the accidental or occasional losses which are
necessarily incident to landed property, whether held beneficially or other-
wise. Such cases, and others of a similar nature, form the large majority:
absolute and independent ownership is a rare occurrence.
Burdens by
it.
Disruptions
These impediments have been somewhat removed by the par-
and power tial disruption of large entails, and by a recent act to lay out
money. capital upon the settled estates in such a manner as to constitute
to lay out
ON LANDED PROPERTY.
861
a separate investment, devolving as rent-charge upon the heir-at-law, or
next in the settlement. It remains to be seen whether these measures
shall prove only momentarily advantageous or permanently of the benefits
that have been expected. The borrowing of capital to carry on business
of any kind is not generally to be approved, and it is preferred to reduce
the business to the capital. Loans of money contracted upon the Loans of
provision of the principal and interest being repaid together in money not
a fixed number of years, seem to double the evil which are in- geous,
tended to be modified, by encouraging a course of investment which will
call for artificial aid to support it, and by strengthening and indirectly sub-
sidising a system of family entail, as against purchasers, and thus prevent-
ing the application of free capital to the soil, which should be facilitated by
every wise government.
advanta-
unless due
exercised.
But if there be not a sad deficiency of judgment in the application of
capital in the improvement of landed property, such incumbrances and an-
nual charges as are incurred by the government loans of money are very
trifling in comparison with the quick and lasting benefits that are derived
from the drainage of arable lands that are fitted to repay the cost, from the
erection of suitable and well-designed farm buildings, and from the plant-
ing of waste grounds that are naturally removed beyond any spe-
cies of cultivation. The two latter purposes are only in prospect, judgment is
but must soon be included in the act; and though the profit of
plantations be of a distant nature, it must be reckoned an application of a
most suitable kind as a permanent investment. The raising of embank-
ments and the cutting of water-courses may also be included in the provi-
sions of the act, and thus comprehend the most obvious and tangible im-
provements that can be effected on land. The charge must be reckoned
trifling in respect of the benefits derived, and as the tenant will assist with
the draining of land and the erection of farm buildings, the charge is in
these two points very much lightened to the proprietor of the land. And
the benefit remains with him, for the tenant cannot carry away or undo
the labour he has expended in assisting the drainage of land, or in the
erection of farm buildings. The policy has been questioned of for younger.
securing by the act the outlay of money on settled estates sepa-
rate from the inheritance in investments for younger children, as being a
fresh edition of ostensible ownership, the next heir being a mere rent-payer
for his predecessor's improvements, the rent-charge of which will belong
beneficially to others.
children.
Holders of
and at will.
The position of the landlord who is tenant for life, and of the
farmer who is tenant at will, is strictly analogous. In both cases the land for life
outlay of private capital is discouraged, in both cases the natural
policy of reducing the extent of land to the means that are at command, is
preferable to the expediency of the artificial and temporary aid of loans.
The improvement effected by drainage has been allowed an exception to
two rules of policy-one public and the other private; the first against the
loaning of government funds to individuals, and the other against entering
upon investments with borrowed capital. This compliment has been seen
862
ON LANDED PROPERTY.
to be well deserved by the operations of the Drainage Act. It has been ob-
jected that it goes to keep lands beyond the reach of commerce, which every
policy of law should discourage. But in transfers of land very
both hurtful. much uncertainty prevails-the new comer may have different
views from the old possessor, who may be supposed to have better local
knowledge and more solid views of the wants and capabilities of the land.
In many cases, loans may be much more beneficial when judiciously ap-
plied than an influx of capital, which must seek its way for use, and its
vents for application.
Government
money.
Draining,
The government loans of money can be applied only to the
loans of purposes of improving the land, which enables the proprietor to
provide for his younger family with the rental of the property.
Nor can any heir of land with any reason object to a charge being paid
annually for improvements of which he derives both the immediate and
lasting benefits. Drained lands are of large value over wet
buildings,and grounds, commodious and substantial farm buildings offer a
planting strong enticement to a spirited tenant, and rising plantations are
an encouragement in sheltering cultivated lands for the use of stock.
Such provisions justify the incurring of a rent-charge, which differs wholly
from common debts that have been contracted for other purposes, and ex-
haust instead of renewing the sources of the property. No charge claims
the name of debt, which pays itself by its own action, as in the case of
landed improvements. The peculiar position of many landowners is very
much promoted by the government advances of money, the negotiation of
which is simple and firmly regulated, and admits no jarring or
most useful. tendency to litigation. Much good has been done, and very
comprehensive benefits will accrue from the inevitable enlargement of its
provisions, as has been already suggested in the application to farm build-
ings, plantations, embankments, roads, water-courses, and permanent pur-
poses of every kind.
Encumbered
When an estate of land has got encumbered with debts and
estates, burdens that are absolutely beyond the power of recovery, and
the property is incapable of supporting itself, or of affording a maintenance
to the owners, a power ought to be lodged in the law court of the last re-
sort, by which to sell the property, extinguish the burdens, apply the
residue, and convert the land to the free course of the legitimate purposes.
The want of this remedy has been long felt, and is now applied
how freed. in Ireland, where the just expectations are being realized. Such
a course is essentially necessary for public purposes, and to relieve the pro-
prietors from a burden intolerable to themselves, and most obnoxious to
the future inheritance.
The landowner has been gradually relieved of the encumbrances which
were placed on landed property in order to secure the successive inheri-
tance at a time when the appropriation of it had not discovered the just
purposes of its use, and the true development had not appeared. As
Altered
policy.
population increased, the social organization was enlarged, new
wants arose, and fresh demands clamoured for satisfaction. The
ON LANDED PROPERTY.
863
trammels of feudal policy, and the fetters of selfish monopoly, were com-
pelled to succomb before the rise and growth of free ideas and liberal in-
stitutions; and the changes that were compelled to be adopted contributed
most powerfully to the benefit and aggrandizement of the owners of the
soil. The relaxations have been slow and very gradual, and have been
forced by circumstances, rather than adopted from conviction, of justice and
utility.
and of leases.
Experience soon showed that the owner of a large tract of land, even
when he has the requisite capital or knowledge, could not successfully be-
come the great farming merchant of his own acres, or employ Origin of
them so advantageously in any way as by letting them in sub- farms,
divided portions to others. This very obvious conclusion soon led to the
giving to other persons the use of the lands in definite portions on paying
to the superior a fixed quota yearly: first, of personal services; next, of the
different kinds of produce; and lastly, of money only. The land was long
held by the payment of services and of produce, and the feudal dominion
existed over the goods of the tenant in liability for the debts of the pos-
sessor of the soil. The holding existed only for the life of the grantor,
and for one year during his pleasure. This uncertainty was not removed
till near the end of the fifteenth century, when the goods of the tenant
were declared not liable for the debts of the landlord, and a tenure for a
specified number of years was held good against the successors
in the property, These two acts fixed the basis of the position
of the tenant, and consequently, of the success of British agriculture.
The tenant of land is the holder of a certain extent of ground, for the
use of which, in cultivation, he pays to the owner of it a fixed amount of
money, which is commonly called the yearly rent of the farm, or of the
land that is used. On this quantity of land the farmer employs a capital
that is at first floating, and gradually becomes fixed, by means of being
invested in the soil, by increasing its productiveness, from operations
more or less permanent in their nature. Every operation requires the
means of performance, and results can only come from causes that are
adequate to produce them. The tenant of land who employs.
these means, most naturally expects to enjoy the results, and to
reap the benefit of his operations. He looks to the landlord to grant him
the security of enjoying the reward of his labours, and of reap-
ing the harvest of the seeds which he has sown. The position
of the tenant is based on this primary foundation, which the landlord can-
not with any justice refuse to grant, for he will not himself build a house,
make a road, or plant a tree, till the rights of property are securely
granted him, and he cannot with any reason expect others to do what he
will not do himself under exactly similar circumstances. Capital recoils
with instinctive abhorrence from the want of security; and next to the
preservation of human life, the safety of property constitutes the leading
feature of civilized society. Without this safeguard, capital re- Great value
mains in a useless condition, labour is unemployed, and the of them.
population is deprived of the legitimate enjoyments of their vested inheri-
Policy and
security.
864
ON LANDED PROPERTY.
Length of
most essen-
sary.
""
tance. It is found to be most essentially necessary in every case of rear-
ing a durable superstructure, to find a firm foundation on which to lay the
rests of the construction; if it be unstable and shifting, the aversion will
quickly appear of refusing to expend capital and time in an undertaking
of that precarious and fluctuating constitution. The security must be ex-
tended over a time that is sufficient for the development of the intended
purpose, which must be calculated in strict relation with the elements on
which the action will be exerted. The nature of the productions of land
requires a much longer time than many other employments in which to
repay the cost of cultivation, years are required for each kind of
tenure, produce to contribute a share of the outlay that has been made.
Hence, a short tenure is nothing better than a yearly holding, if there is
more time to expend, there is a very insufficient opportunity to reap the
fruits that are grown.
"Give a man the secure possession of a bleak
rock," says Arthur Young, "and he will turn it into a garden—give him
a nine years' lease of a garden, and he will convert it into a desert. It
is not possible to banish from the mind of the tenant-at-will the very pal-
pable truth, that every improvement he makes on the land is producing a
value to others, and in all probability raising the rent against himself.
Besides, the annual expenditure that is necessary to carry for-
tially neces- ward the current operations, many contingencies occur that are
unavoidable, and which trench upon the capital of the tenant. It
is impossible to cultivate land in any profitable way without incurring an
expenditure more or less beyond the bare necessities of a pinched utility
of the ground. The tenant may have a well-grounded and unbounded
confidence in the owner of the property, that he will not be disturbed by
him, nor denied the fruits of his labours, but he has no knowledge of the
successor—a widow in straitened circumstances, who may be compelled to
use every means to raise money—a minor under unscrupulous guardians,
Danger from who will stickle at no point in order to accumulate the wealth of
want of it, their charge, or some prodigal hunter or lover of the turf, who,
in order to gratify his passions, cares not for to-morrow, nor even for the
afternoon of the present day. These, and many other changes of a similar
kind, stare in the face the tenant who depends on the faith that is not
beyond chance and accident, and convince him of the inconvenience of his
situation, and the irksome apathy to which he is reduced. The conse-
quences never fail to re-act upon the landowner himself, who finds a dimi-
nution of his rental to happen yearly, in order to supply the necessary
demands, of which the situation of the tenant prevents the performance.
He soon finds that it is much easier to uphold than to restore, and that fer-
tility when once abandoned, requires much time and cost to be
repaired. The tenant finds a constant diminution of his sup-
plies, and fears to use the means of increase, as others may obtain the aug-
mentation. Habit and custom may accommodate the minds of men to such
a mode of tenure, as by it the natural indolence is cherished, and exertion
is not required. A rent is raised by certain means which have been long
practised, and are well understood; no prejudices require to be removed
and its evils
ON LANDED PROPERTY.
865
nor any entertainment made of troublesome innovations. Exertion and in-
dependence, which are the life and soul of industry and exertion, are wholly
lost. Not only all great improvements, but even the most common works of
the season will be imperfectly performed, and little can be hazarded beyond
the expenses which the returns of the year will defray, when the farmer
cannot look to the future with security. Capital will be spa- upon every
ringly expended on another man's property when that security kind of pro-
of possession is denied, which is essential to the safe and pro-
fitable application of money; the agriculture of the country will never ar-
rive at the advanced condition of which it is susceptible; and the persons
employed in the occupation will lag behind the other productive classes in
their means of improving their art and acquiring knowledge.
ceedings.
Not only the landlord but the country suffers by the less improved
condition of the public territory, from the want of just and fitting tenures
on his estate. Much land remains uncultivated, or is kept in a very
inferior condition of growing grass, which renders security of comparatively
less value, as the land requires little expenditure, that cannot be re-
placed within the year, and a long possession is not absolutely Cultivation
necessary to enable the rearing and feeding of cattle and sheep. is lessened.
This state of things incurs a large diminution of the general production,
in which every individual of the community is interested, from the pea-
sant at the plough to the peer who legislates for universal satisfaction.
It has been urged against leases of land, that the farmers themselves
set no value upon them; but this argument leads to a very different con-
clusion than the intended contradiction. The absence of security has
engendered an utter ignorance in the cultivation of the soil, of the means
of employing their own capital with advantage, has indisposed them to
the exertion which improvements demand, and has produced a better
contentment, with an easy rent and dependent condition, than with the
prospect of an independence to be earned by an increased labour Ignorance
both of body and mind. The rent is lower and requires less and indo-
exertion, and the eye having been accustomed to behold one produced.
state of things, no other condition can be entertained.
This tenancy
having become the habit of the country, not only re-acts upon the condi-
tion of the occupiers of farms, and the means of perfecting their own art,
but it affects, essentially and directly, the interests of the landowner and
the country.
lence are
The only fitting security for a man who has capital to employ in the
cultivation and improvement of land, is a written covenant subsisting for
a definite and adequate period. The term must be defined, in order that
the property may not seem to be alienated, and the period of time must
be adequate, to draw back by periodical returns, in the lapse of years, the capi-
tal that has been expended. It is the peculiar nature of the returns
from land to be extended over a number of years, and to be
obtained in a succession of crops that are allowed by the sea-
son; and not only is a period required to effect the operation, but a time
likewise to recover the funds expended. The employment completely
Written co-
venant the
best security.
866
Land differs
ON LANDED PROPERTY.
differs from manufactures of perishable articles; the results of one opera-
tion are generally sufficient to reimburse the outlay, and the capital is
restored with recompense. The changes of summer and winter do not
interfere with the proceedings, nor does the want of security affect the
use of the means that are necessary to promote the advancement. The
machine is the property of the person who erects it for the purposes of
trade, and the more perfect it is made, the more profit will be derived by the
owner. But no such assurance rests with the cultivator of the soil,
from Manu- who tills the great machine on which his all depends. It is
factures. the property of another, who will in the end profit by the im-
provements which are made by the temporary possessor. The manufac-
turer receives directly the profits of his stock in trade; the farmer must
share the profits with another, who risks neither money nor labour. The
farmer is fettered by conditions imposed upon no other class of traders, and
the inconvenience of obtaining returns for the current expenditure more
slowly than in any other occupation, are frequently attended with the uncer-
tainty, if the capital advanced can ever be recovered. The employment
of capital on the property of another, must ever be attended with
certain drawbacks that are not easy of adjustment with relation
to the value of the returns: but the insecurity with respect
to the future, and where the possessor cannot employ his funds in the man-
ner which his interest requires, will greatly increase the inconvenience
and perplex the equitable adjustment in an affair where just concessions
are essential to any legitimate compromise.
Longer secu-
rity neces-
sary.
Security the
base of
farming,
The security of possession being the basis of the position of the
farmer, constitutes the foundation on which all the other relations depend:
without it, the very best arrangements, and the most favourable subordi-
nations are impotent and wholly useless. Not that other points of posi-
tion do not bear a part in forming the proper place in which
the cultivator of the soil must be located. The sequel of this
chapter will show the value and necessity of the accompaniments;
but unless they are based on freedom of action and security of possession,
no corresponding benefits accrue from the attendance of the isolated at-
tachments. The action of the whole possessions is paralysed and ren-
dered of none avail, by reason of the want of the lever power to raise
the joint operations. With every propriety and the utmost justice, the
security of tenure in land for an adequate period of time, is made
propriety to occupy the first place in every arrangement of relations
between the owner and occupier of the soil. No sane person
will involve himself in any undertaking without that essential provision.
The capital of the farmer being expended on security of tenure, comes
next to be used upon the capital of the landlord, which is sunk in the
permanent provisions which are required to make the land advantageous
to the occupier. These provisions constitute the furniture of the farm,
Furniture of without which the occupation cannot be converted into the be-
the farm pro- neficial purposes.
The nature of the utensils is durable, as
being fixed upon and growing in the soil, and continue for years
with every
and justice,
vided by
landlord,
ON LANDED PROPERTY.
867
to fulfil the intentions of the formation, consequently they become exclu-
sively the province of the landlord, and are entirely of his concern in the
cultivation of the soil. The outlay of the necessary fixed capital must
be regarded as that which falls peculiarly and primarily upon the owner
of the land, and which cannot be devolved on the temporary occupier
without a more than corresponding sacrifice of the permanent interests of
an estate. The capital being expended by the landlord, who receives in-
terest on the outlay, in the form of the greater rent which the land is
rendered capable of yielding.
The two interests involved in the profitable occupation of the soil, are
the permanent and the temporary, or the owner who holds in perpetuity,
and the farmer who uses the soil for a specified duration. Hence the
provisions that are durable in nature, and which fulfil the purposes of use
for a length of time, are very naturally assigned to the cost of the land-
owner, whose interest in the land accords with the services of the pro-
visions. To the tenant who holds for a fixed period of time, upheld by
there is naturally assigned the temporary upholding of the fur- the tenant.
niture which he uses, on his receiving the raw material of which the fur-
niture is made. This arrangement well coincides with the temporary
interest of the tenant. He uses, but does not afford; he repairs the wear
of application, but not the decays of nature; and maintains the fixed ap-
pendages in the current going order.
Farm,
The first object of attention and necessity in the cultivation of land, is
the adequacy of the houses, or buildings, for the use of the farmer: and of
these erections, the chief attention is the dwelling-house to be inhabited
by the family of the farmer. The comforts and elegancies of life have
descended in Britain to the degrees of capital which have been estab-
lished among the different grades of society, each class challenging
Dwelling-
and expecting that their vocation shall afford equal accom- house on the
modation with similar grades of employment. The reasonable-
ness of this expectation cannot be disputed; the manufacturing classes
have shown the way, and the agricultural employment must necessarily
follow. Scarcely any provision will form a stronger inducement for the
occupation of land than a dwelling of suitable accommodations, at least
to the respectability, which it must ever be a leading object with the
land-owner to induce, to settle upon his property. Several wants and in-
conveniences will be overlooked, and even very necessary demands will
be relinquished in cases where this primary provision is fully complete,
and when attended with a well-stocked garden and orchard, the Garden and
owner of land cannot devise any more alluring objects to the orchard.
eye of inspection. Vegetables and fruits are now indispensable articles
of almost daily consumption, and a rural dwelling loses the name without
them.
The farmer having seen on a farm a suitable accommodation for his
family and domestics, next proceeds to examine the buildings that are
intended for the protection of animals, and the manufacture of produce.
These erections must exist in the corresponding degree of convenience
868
ON LANDED PROPERTY.
ment.
General
buildings
and usefulness, and in the number requisite to the amount of business to
be performed. The inspecting tenant, if he be of the enlightened sort,
will speedily ascertain if the number and arrangement of the buildings
will suit the purposes of cultivation which he intends to adopt, and will
point, at the same time, to the wants that appear, and suggest the amend-
That the greater part of the farm buildings of the present day
are sadly deficient, no person offers to deny; but it is pretended
that no substitution has yet appeared to warrant the removal,
or that no complete form has yet been devised beyond which no advance
can be made. But from deficiency to a completeness of no further pro-
gression, many steps intervene, and very much usefulness is contained;
neither nature or art advances by such extended leaps, but by gradual
steps of progressive ascent. Improved designs of farm buildings are
known which will command five per cent. on the outlay for the lease of
twenty years, separately considered as an item, or will add very consider-
ably to the general rent of the farm. Without the proper accommoda-
tions, the live stock cannot be bred and reared, with the known advantages,
nor can the grain produce be manufactured with the economy
that is requisite in the detailed business of farming. It is idle
to pretend that ideas are undetermined on the subject of farm buildings,
the progression in that point is equal to the general advancement, and the
adoption is only prevented by the general aversion to change. To wait
for a "ne plus ultra" perfection on any point, would delay all human
progress.
are most
necessary.
Labourers'
cottages
The cottage dwellings of the labourers that are required on a farm,
claim a most especial attention both from the landlord and the farmer.
Till of late years, this department found no notice in the general esti-
mate of the furniture of landed property; the old hovels, resembling pin-
folds, were considered sufficiently good, and the horses and dogs.
had more consideration than the labourer, who is the life and
soul of every act and operation. Some considerate landlords have led the
way in erecting very much improved dwellings for the accommodation of
labour; and philanthropy has appealed to the feelings of human nature
in behalf of the hitherto neglected portion of the community. The far-
mer must see that he has got accommodation for the labour he may require,
afforded in the necessary quantity, and placed in the proper convenience.
Any want on that head, will form a very great determent to the embark-
ing of a floating capital to be productive of mutual benefits. Immorality
and disease have been widely propagated from the confinements
sable. in which cleanliness cannot be adopted, nor the decencies of life
maintained. The civilization of the present age demands a wider step
being made at once on this point than on almost any other provision of
the social system. When a moderate exaction in the shape of rent has
been arranged with the farmer, and the land has been amply provided.
with the fixed capital that is necessary for the development of the float-
ing funds of the tenant, the attention of the landlord should descend to
the condition of the labourer, by the employment of whom both his own
are indispen-
ON LANDED PROPERTY.
869
Accommoda-
wages.
station and that of the cultivator of the soil is raised and upheld. Capi-
tal is merely an accumulation of labour, and it is just and reasonable,
morally binding, and religiously imperative, that its attention be directed
to, and its care be bestowed upon, the comfort and maintenance of the source
whence it originates, and by which it is sustained. The owner of the
soil has wholly in his own hands the power and the means of providing
comfort for labour in suitable cottages, garden grounds, bakeries,
pig-styes, and the supply of water: but he is unable to fix the tion and
wages of labour, as it is a marketable article, and liable to the
fluctuations of supply and demand. But it is more stationary, and much
less evanescent than those articles that are strictly perishable in their
nature, and it is capable, if not of a permanent adjustment, at least of a
temporary understanding, as to the amount of the remuneration. With
this view of the matter, the farmer may be understood by the landlord
to pay labour in the highest rate that is known to be given in the district,
and if that amount be low, an advance may be led in a small progression.
The state of society does not yet admit a binding clause to this effect in
an agreement of demise and use, but it is quite possible to introduce a
tacit understanding of the performance, which may soon lead to a public
avowal of the arrangement, than which nothing will more powerfully
conduce to the strength of society. It will rivet fast in affection the con-
tiguous planes of the social organization, and solder the jarring elements
of discord, it will multiply the strength of every chain, and link together
in a firm union all the junctions of the mixed connections. Of all the
plans that have been designed, or that may be intended for the ameliora-
tion of the labouring classes, none is so simple and so effectual as the
increase of the commodity by which are obtained the essential necessaries
of life; and in the case of farm labourers, the landlord must lead the way
in the provision of the fixed articles in dwellings and their appurtenances.
An example must be shown from the highest quarter, and then the next
lowest can be used by treaty to confirm and uphold the arrangement.
Though the figure of the numerical amount of wages be not named, the
sum can, nevertheless, be entertained in a tangible estimate.
Roads, affording a convenient and ready access from the farmery to
the different parts of the farm, are a very essential part of the provi-
sions that are required by an extent of cultivated land. Most farms
adjoin a public road, or are intersected by it, and the private roads will
be much guided by the public line, both in the direction they are made to
take, and in the number of the paths they afford. The roads Roads and
must be durably made by the cost of the landlord, and the keep- gates must
ing in repair devolves on the tenant. The farmer must see that provided.
the quantity of land which he intends to rent is suitably provided with
the necessary intersections of access, or the animal labour will be much
harassed, and the wheel carriages be unnecessarily worn.
amply
If any rivers or large brooks of water run through the farm, or form
the boundary of it on any side, the overflowings of the swollen state must
be prevented by suitable embankments, and the courses assisted by being
870
ON LANDED PROPERTY.
straightened and thrown at the turnings into the proper channel. The
farmer must observe that no damage will happen from overflowings of
sluggish streams, nor from alluvial flats being torn and wasted by impe-
tuous torrents, rushing against the banks and wasting the soft materials.
If neglect has allowed these devastations, the loss must be estimated, and
the recurrence prevented.
Fences a
Fences and gates constitute a part of the fixed capital or furniture of
a farm, that demands a very ample fulfilment on the part of the owner of
the soil. Fences enable the farmer to guard his crops from damage, to
separate the different kinds of beasts, to divide into suitable lots
special care. the grazing animals, and to use the fields of land in the due ro-
tations of cropping. Without divisions, these purposes could not be at-
tained, nor the value of the land realized. Gates are no less necessary to
open and shut on the gaps in the fences that are left for a road into the
fields, and which afford an ingress and egress to the animals, and to the
wheeled carriages and other implements when the fields are cultivated.
The fences must be complete for the purpose of confining the lots of ani-
mals, and the gates must be ready in the action, and strong in the form.
The provision of water for some special fields of the farm may be men-
tioned as an appendage to the necessary furniture of the possession. A
Provision of field or fields may be required for cows' pasture, one for horses
water. or young cattle, to which water may be brought by boring, or
in pipes from a distance. This provision is not general, but may be very
properly hinted in this place.
must
Equitable rents must occupy a large consideration in fixing the position
of the cultivator of the soil. Rent is the surplus of the value of the pro-
duce of the land that remains after every labour is paid, and the farmer's
family maintained. This original and very just definition of rent has been
Rents much encroached upon, and almost wholly overturned by the
be equitable, revolutions of society, which have brought the word to mean
the market price of the soil as an article of commerce for the specified
time, from which the other considerations are wholly excluded. Two
elements in the present day, which cannot be separated in practice, con-
stitute the payment made by the farmer to the owner of the soil, the sim-
ple price paid for the use of the land, and the interest on the fixed capital
in the buildings, enclosures, and other improvements which have added
permanently to the productiveness of the soil. It is not necessary for our
present practical purpose to make any illustration of the theory of these
separate elements, or to pursue the paths of investigation that have been
followed by political writers, in order to explain the nature and
causes of rent. All land in this country capable of cultivation,
justed. yields a rent; and also if it produces the grasses in sufficient
quantity that feed the domesticated animals, the rent will bear a pro-
portion to the fertile or barren quality of the soil, the favourable position
of the farm, and the advantages of occupying it by buildings and other
necessary adjuncts.
and practi-
cally ad-
.
No rules can be established in respect of the proportion of the value of
ON LANDED PROPERTY.
871
the produce that shall be paid in any case as rent. The mode of agricul-
ture that is pursued, and the habits and condition of the tenantry possess
a large degree of influence, the nature of the returns, whether it be corn
or animal produce, the labour that may be required, both in quantity and
quality, and the natural constitution of the land; these are chief objects of
consideration in making an estimate of the probable amount
of rent.
Highest un-
A larger produce is raised by the same labour when der improved
used under an improved system of tillage, and higher rents can tillage.
always be paid where agriculture is most improved. The general varia-
tion of rent is from one-fourth to one-half of the value of the gross pro-
duce, the portion of one-third yet prevails chiefly in the case of perma-
nent grass land. The rent depends on elements that vary with the nature
of the soil, the kinds of produce, and the skill of the farmer.
Per centage
The actual profit to be derived by the farmer must bear a ratio to the
capital employed by him. The best regulated calculations award him
fifteen and even twenty per cent. with which to support himself,
and bear the risks of his trade. The fixed capital which must allowed the
be advanced, should form the first calculation with the farmer
who rents land for use. The landlord's rent and the expenses are left after
allowing fifteen per cent. for interest, the profits of stock, maintenance,
and the risks of trade to the farmer.
farmer.
Rents might be fairly adjusted if the prices of produce remained the
same or nearly the same; but the greater or less supply causes fluctuations,
and also causes that could not be foreseen or provided against at the time of
contract. Fair assumptions with respect to prices and produce form the safest
ground for those who let as well as for those who take land, and founded on
their knowledge of the past, joined with reasonable analogies with respect of
the future: these data will lead to safe conclusions about rent. Fewer mis-
takes would be committed both by landlords and tenants, if more
care was bestowed on the above assumptions. There is a constant to rise rather
tendency in Britain for rents to rise rather than fall, from the
difficulty and necessity of finding employment for capital, and the limited
supply of farms in the market. There is ever a greater hazard that the
landlord shall receive or obtain the promise of too high a rent from the
eagerness of competition, than that he will suffer loss from the land being
underlet.
Rents tend
than fall.
This tendency in the rent of land to rise, and the causes which produce
it, claim an important attention in the management of landed property;
it should be partially checked, rather than keenly encouraged. A land-
owner or any other proprietor never can be able to take an impartial
view of the value of that in which he has so great an interest in render-
ing available as a source of income; but in every view of the Must be mo-
subject, the farmer, must be allowed, such a profit as will ena- derate to al
ble him to cultivate the land, meet the contingencies of trade, tency.
and maintain his family comfortably and respectably. A deficiency of
profit hazards the trenching upon the capital of the farmer, which dimin-
ishes and dries up the source whence is derived the rent and revenue of
al-
low compe-
872
ON LANDED PROPERTY.
the landlord. The loss of the requisite funds is the greatest of all evils
that can afflict the farmer, and the recovery from it is the most difficult.
A retrogression once begun on this point is gradually quickened in speed,
till it ends in total ruin.
Sound policy directs, fair dealing justifies, and good practice supports
the rule, that a fair and lenient exaction shall be made on the industry of
the farmer. The most certain and steadiest revenue is ever derived
where fair and moderate rents are exacted, and not from the sources of
improvident demands and severe treatment. No landlord ever
must be leni- profits by a system of exorbitant rents that is rigidly enforced.
A few years suffice to exhaust the capital stock of the tenants :
the stoppage of improvements, the failure of tenants to fulfil their obli-
gations, and the general deterioration of the property, both in condition
and character, are the certain results of the continuance of rack rents.
Exactions
ent.
Adjustment
of rents,
Acts of great liberality are published in returns of rent being made
to the farmers at the audit days, of ten, fifteen, and twenty per cent. In
special cases of a sudden contingency, such acts are necessary and proper,
but as a general system, the management must be bad that calls for the
constant repetition. The fair adjustment of rents needs no temporary
bounties, it must be able to bear the pressure of low prices and
of deficient crops; and it must allow every tenant the means of
meeting the contingencies of trade that arise from the fluctuations in the
amount and price of his commodities. The rent should be at once re-
duced, when land is seen to be overlet, and the tenant's condition consti-
tuted to meet the demands and engagements. A rack rent, and the relief
or charity of an audit day, create a dependence not to be endured. The
quarter of a century of years that followed the termination of the late
European struggle, has left a lesson to succeeding generations, and one
which may never be equalled, and far less exceeded. Prices of all articles
fell in an unprecedented degree, the landlords clung to the rents as en-
gaged for, the tenants could not pay them, temporary expedients were
adopted, capital was swept away, and more efficient remedies were com-
pelled to be adopted. The necessities of the case being promptly met,
and new arrangements being made with the tenants and suited
to the altered circumstances, no damage ensued to landlord or
tenant, the interests were preserved from the ruin that attended
the denial of justice. A prosperous tenantry, and the improvement of an
estate, will not proceed from the feudal fashion bounty of an audit day,
but from the condition of the tenants, enabling them under a fair and
well-considered covenant to fulfil all obligations, and meet and surmount
every demand that is made upon them.
to suit al-
tered cir-
cumstances.
Local know-
Much local knowledge and correct enquiry are necessary to enable the
forming of an estimate of rent of land. Each district has its peculiar ad-
vantages and drawbacks, which are known to, and can only be
ledge neces- estimated by, enlightened practical men who have resided in the
country, and have learned the calculations. A professional
stranger with a long array of figures and calculations, only leads the land-
sary
ON LANDED PROPERTY.
873
lord into mistakes, anent the real value of the estate, and the means of
entering into equitable contracts with his tenants: he must draw infor-
mation from persons who are better informed than himself, regarding the
letting of land in the district, and the current value of the soil. But local
surveyors are always found of some experience and observation; and if
they have a character of integrity, they can furnish the best local know-
lege of the value of land. These persons being joined with the country
agents of the land-owners, and if both parties are left undisturbed by the
proprietor himself, who is generally the least qualified of any one to form
an impartial judgment, will produce the most correct and best arranged
estimate of the value of the cultivable soil. The improvements that may
be effected, will probably come from a more comprehensive view
and more adventurous judgment and spirit of action. Even in duct im-
that case, an especial attention is ever due to the observations
of local knowledge, and to the practices that have been established by the
experience of ages. The most enlightened judgment will never despise
to hear any truths that relate to its occupation.
even to con-
provements.
Beneficial terms for the management of a farm, constitute a most im-
portant condition in the relations between landlord and tenant. The
temporary occupier of land is necessarily entrusted with the management
of the farm during the period of his possession; and if he consults his
own interests truly, he will conduct the cultivation of the soil Terms of ma-
in the manner best calculated to maintain or increase its produc- nagement,
tiveness. But knowledge may be wanting to adopt the proper means, and
his interest, real or apparent, and even his necessities, may lead and com-
pel him to attempt to take more from the farm than is compatible with
the preservation or increase of its productiveness, and especially towards
the end of the lease, when his interests and those of the landlord begin to
diverge. The written contract is devised to guard against these results,
and to allow the one party the privileges that are necessary to carry on his
business, and to the other, a legal security that these rights shall be em-
ployed only in the purposes contemplated by the parties to the contract.
The essential conditions must be few in number, easily understood, and
as easily complied with. No questions need occur in a well-considered
contract, which must not be made up of a multiplication of con- simple and
ditions, penalties, and restrictions, which only serve to perplex, pointed.
and afford the fruitful source of litigation. The expressions must be so
pointedly obvious in the meaning, that no doubt can arise in the construc-
tion. Two faults are usually committed, a mass of cumbersome and use-
less restrictions fetter the judgment of the farmer, and cramp his energies,
prevent the exercise of judgment, and the powers of adapting the practice
to the circumstances that may arise: the other omission consists in leav-
ing to the farmer an unrestricted power of proceeding to a Two faults
degree of management very hurtful to the landlord, and on
every change of tenants, tending to a deterioration of the farm. The
midland and western counties of England are oppressed with clauses and
enactments that have descended from the practice of olden times, and
common.
3 H
874
ON LANDED PROPERTY.
which either remain a dead letter, or kill the freedom of action that is
demanded by an improving condition of the tenant. In Scotland, where
the lease of land has wrought miracles of the kind, a remarkable degree of
laxity prevails, and whole estates are managed on a simple letter or a
memorandum with constant reference to the custom of the country. The
details so essential to the interest of both parties, are wholly neglected;
towards the end of the lease, land is scourged, buildings are dilapidated;
and in cases where a removal is inevitable on the part of the
tenant, stipulations and restrictions are essentially necessary,
though they must be few: an excess of caution and of laxity, is equally
to be avoided, in order that the interests of both parties may be secured,
the landlord protected, and the tenant disencumbered of useless verbiage
and unmeaning phraseology.
Restrictions.
Not only individual interests are damaged by the neglect of the neces-
sary regulations in the ownership and temporary possession of land, but
the general interests of agriculture do suffer in a very high degree. The
progress of the tenant is retarded by an adherence to obsolete customs and
antiquated practices; the very worst rules are often enforced, and often all
directions are wholly merged in the weighty consideration of the amount
of rent, and the times of payment, not forgetting a penalty in case of
neglect. If good farming cannot be introduced by the stipula-
Bad farming
may be omit- tions of a lease, it may, at least, prevent much that is bad, and
by wholly omitting the notice of exploded practices, room is
left to mention the better rules, and to render them compulsory when
time has fully sanctioned the superiority. The practice of agriculture
clings so very tenaciously to old customs, that every possible means must
be used to unfetter the bonds and loosen the grasp, and many very useful
notices may be made in the small compass of a lease. A mass of stipu-
lations and restrictions, and the total want of conditions, are equally ob-
jectionable: a number may be refused, but some are necessary.
ted.
The condi-
The essential conditions of using land in cultivation, may be recapitu-
lated: 1. Security of possession for a proper length of time. 2. An ade-
quate provision of fixed capital on which to employ the floating
tions that are funds of the farmer, in farm buildings, enclosures, and other ne-
cessary appendages of the land. 3. Equitable rents. 4. Suitable
conditions in respect of the treatment of the land and general manage-
ment.
essential.
All experience has shown that the means of advancing and perfecting
the agriculture of Britain as a branch of public industry, depend essen-
tially upon the relationship which is established between the land-owner
and the farmer. No attainments on the part of the tenant, no varied
and comprehensive professional learning, and no eager willingness to exert
these advantages, are able to compensate for the want of the
not be com- foundation on which the edifice must rest: the structure must
pensated.
be firmly based, or no elevation can be raised. Even the pos-
session of a large capital by the farmer, will not avail for giving to agri-
culture the means of successful cultivation and improvement, the owner
and that can-
ON LANDED PROPERTY.
875
must be given the means of employing it with advantage, by security of
possession, by the privileges required for the proper management of the
business, and by that fair and lenient exactions upon his industry, which
will enable him to employ his capital with a remuneration.
Benefits of
granted.
If these conditions are withheld, the capital employed in the cultiva-
tion of land is exposed to drawbacks in the application of it to the proper
ends, which diminish the possible returns and also the means of improving
the national source of wealth to the degree which is admitted
by the case of adaptation. The improvement of the country, their being
and of its agriculture, follow as a sure consequence, whenever
along with the power of acquiring capital, the means are afforded of apply-
ing it with effect to the legitimate purposes. And wherever these con-
ditions are supplied, agriculture improves, education and intelligence are
extended amongst the large body of the farmers, and each succeeding
generation excels the preceding one in the knowledge acquired, and
the means of employing it for private advantage, and the general wel-
fare. To these benefits must be added the tendency to advance the
wages of labour, and the improvement of the dwellings of the lower
grade of society, which sustains the upper in every stage of elevation.
The utmost
freedom un-
derlies obli-
gations.
“To do as he likes with his own" is a definition of human privileges
that sounds most agreeable to the love of power which so very strongly
actuates on the will of man. But the sound will be found to contain the
whole boast and extravagance of the often quoted phrase. A thousand
obligations and influences surround the will and conduct even of
the most apparently irresponsible and unfettered owner, con- supposed
trolling him by an operation far better and less easily evaded
than legal compulsion, to consult his own interest by consider-
ing that of others. In the capacity of landlord, nothing is wanted but a
knowledge of his own true interest to render this principle effective to a
degree unsurpassed, if indeed equalled, in any other relation which one
man can bear to another. One axiom comprehends nearly the whole that
has been, or which may be said on the relations between landlord and
tenant, that of all of the encouragements to the tenant occupier The grand
that exist, of all the stimulants to individual improvements that axiom of ten-
can be devised, the surest, the most legitimate, and in truth, the
easiest and most permanent in effect, is to make every tenant feel to the
utmost possible degree that the farm to which he devotes his labour and
capital is his "own." If it be true that the best tenant is he who treats
a farm of land as if it was his own, it can scarcely require proof that_the
best landlord is he whose tenant is least made sensible that he is not his
own landlord. Paradox as this has appeared, and may still seem to be, it
is the only statement that approaches the whole truth of the case. The
relation is one of that class which, like the functions of animal life, are
most healthily discharged when they are not felt.
ancy.
The rents and profits of the land are the owner's, and his only: with re-
gard to the soil, in every thing he does with it, and in every thing he
876
ON LANDED PROPERTY.
The rents
"only are.
the owners ;"
abstains from doing, he is bound to make his interest and pleasure con-
sistent with public good. The community still retains of its
original claim to the soil of the planet it inhabits, as much as
is compatible with the purposes for which it has parted with
the remainder. The land-owner inherits or has purchased the superior
interests of the soil and by that possession he takes upon himself the
duties which God and nature have placed upon it. The development of
the resources of the land rests upon the arrangements that are made for
the use of capital in its cultivation, and labour expects employment and
maintenance from the vested interest of its inheritance. The moral
condition of the people is vastly promoted by the ownership of the soil,
which affords to the public use the means and materials of promoting its
respective undertakings. A liberal policy on this point has promoted the
cause of humanity beyond many other seemingly more urgent causes of
impulse. The most selfish and shrewdest utilitarian that ever sought out
the shortest road to his own interest, may take an advice in the shape of a
moral recipe to the owner of land, to realize the feelings of the tenant, to
put himself imaginarily in "his" position, so as to be able to enter into
his wants from "his own" points of view, and never to discard the just
idea, that the well-being of every creature is not only compatible with,
but essentially necessary to, his own. The owner of land is morally
bound and socially obliged, by the performance of many duties, and the
bearing of many charges, which do not fall on other classes, and are not
attached to property of other sorts and constitutions. Though no class of
the people are now held to be " adscriptæ glebæ" or to form part and
parcel of any landed property, yet on the soil, their education and main-
tenance is devolved, and becomes the duty of every land-owner to have
performed. By granting to the farmer the essential conditions
rights in the that have been mentioned, and by refusing no reasonable
demand, by which is acquired a fixed interest in the soil
by the cultivation of it, the land-owner has the power of intro-
ducing into agriculture as great improvements in point of production, as
the invention of the spinning-jenny or the steam engine. To these must
be added the adoption of every new principle that tends in practice to
economise labour, and cheapen the price of articles by which to extend
the sphere of their use. While a population exists, the earth must be
cultivated; and the very first responsibility rests with the virtual owner
who has both the means and the power that are required for that purpose.
No individual in private life possesses the same wide scope of moral ca-
pability with the resident land-owner, in the most variously inviting
field of practical studies and duties. The leizure it affords is a
land owner- high priviledge, and leads to the pursuit of important and
humanizing objects, which lie open in the same degree to no other
condition in life. The pursuit of gain is sufficiently attractive with-
out any over-exactions, and which is allied with and not arrayed against
the enjoyment of natural pleasures, while the love of distinction so natural
to most minds, is indulged by a prominence almost inseparable from the
the other
soil.
The scope of
ship.
ON LANDED PROPERTY.
877
position it confers. Example, almost the effect of law, invests it with a
commission both wider and higher than the magisterial authority which
generally forms one of its leading duties, while the daily recurring sphere
of rural economy in many problems that required solution, and the wide
field of practical and scientific knowledge involved in them, legal and
demand a breadth of varied education, in the fullest sense of social.
the word that is not exceeded by the learning of any other branch of pro-
fessional life. Till the general education happens of the whole body of
the people, the extensive influence of the owner of the soil, and the
commonly great early advantages, form a source of very powerful central
force, from which will emanate a wide dissemination of the most useful
knowledge, and of the accompanying moral and physical blessings to the
human race.
The last to be mentioned-relation of the landlord and tenant-consists
in the case of the non-fulfilment of the terms of the contract. The landlord
pursues for the rent by entering a distress on the goods of the farmer, or
waiving his right of distraint he can proceed by action at law. Landlord's
The tenant can proceed by action against the landlord in default means of re-
of the performance of his part of the contract. But the equit-
able adjustments that should prevail will wholly prevent these disagreeable
resorts.
covery.
Fixtures.
The much agitated uncertainty about fixtures on the soil has been set-
tled by a late act, which directs the farmer to give a month's notice to the
landlord of his intention to remove a fixture that has been
erected by himself with the consent of the landlord, within which
time a negotiation of purchase by the owner of the soil can be effected.
But in all such cases a special agreement settles every point, and on the
simple principle that "conventio vincit legem," all disputes are completely
removed. In making agreements of any kind, the chief point of
attention is the simple plainness of expression, by which all am- simple agree-
biguity is extinguished, and every doubt dispelled.
Validity of
ments.
CHAPTER II.
LEASE OF LAND, CONDITIONS, AND RESTRICTIONS;
CHOICE OF TENANT & ASSIGNATION OF THE DEED.
fined.
A LEASE of land, is the demise, transfer, or letting of the Lease de-
ground by the owner of the soil, by which he grants for a
specified time, the use of its productiveness to another person, on condition
of receiving a fixed amount of money as the consideration due to him for
the value of the temporary occupation. It is a written agreement between
two parties, who engage to perform certain stipulations and restrictions by
mutual consent, and it contains the specified conditions on which the
878
ON LANDED PROPERTY.
agreement is founded, and the times at which they must be fulfilled. The
conditions are obligatory, and even compulsory, and contain the grounds
of proceedings to enforce the observance.
It possesses the power of
making itself respected, and of commanding the obedience of the parties
that constitute the formation of the agreement.
Form to be
cise.
From having contained much useless phraseology and unmeaning and
irrelevant verbiage, the lease of land has been reduced into a
neat and con- neat form concisely worded, and pointedly expressed, calculated
to lead rather than hinder, and to improve rather than deter.
It has been cleared of the feudal tendency to enervate the mind and fetter the
energies of man, and has been converted into an instrument by which to
serve the purposes of the human race in the different grades of which the
mixed society is composed. Necessity compelled very early the assigning
of land for the temporary use of employment, but the advantages never
became extensively beneficial till the goods of the vassal were freed of re-
sponsibility for the debts of the landlord, and a lease from one proprietor
for a specified time, was held good against the successors in the
property. From that time, the lease of land has become the basis
of agricultural improvement, and a very great source of national
wealth. To govern and use landed property without the security
of tenure, and of capital, and without some general stipulations, is the
same thing as if kings and deputies would rule "arbitrarily " without any
laws or written customs, which is wholly repugnant to all just ideas of
modern civilization, and the privileges of natural right. Landed property
is loaded with the burdens which God and nature have imposed upon it
in employing, maintaining, andeducating the people, and in every properly
constituted social system, there must be no dependence of any class of per-
sons upon another, except in the simple affair of exchanging value for
value, or as the Latins expressed it, the "quid pro quo." The love of
dominion, and the inclination to be under masters, are equally to be
dissipated and abolished.
the best
tenure.
The most eligible duration of a lease of land has now been fixed
Twenty years by the best experience in the term of twenty years. Twenty years
length of is a very unusual term in the home counties-7, 14, or 21 has the
preference. This period has been reckoned a long term during
which to part with the control of property, and lose the advantages that may
happen of an increased value—but it has been proved to be in a fair accordance
with the interests of both parties to allow the possessor to adopt and use a pro-
fitable system of management, and the landlord to derive an adequate rent.
Prospective
view.
All the operations on a farm, except those required for the cultiva-
tion of the ground from season to season, have a reference to future
years for the returns to be obtained, and periodical returns after the lapse
of a certain period are required to regain the capital that has been expended,
beyond the funds of the ordinary routine. Unless the farmer can look
forward with a certainty of future recompense for the expenditure that
may be made, no farm can be cultivated in a suitable manner in this
country. The most common executions need a time to be performed, and
ON LANDED PROPERTY.
879
Time for out-
farmer.
the farmer requires a further time to get back his capital with a profit.
The space of eight or ten years is required for the development of long
known applications to land; and more expensive and lengthened
processes, are daily being pushed forward, by the ingenuity of lay by the
science, and the researches of enlightened practice. In many cases
the erection has been done by the tenant of thrashing machines, driven by
steam, which cost a very considerable sum of money, and which never could
have happened unless an adequate time was secured in order to derive the ex-
pected benefits. Owners of land require every security which can be given
to permanent property in order to induce them to improve their lands; and
they must consider that where a lease is denied, no reasonable expectations
can be formed of the tenant deviating from the path adopted by themselves.
No proprietor of land should ever think of withholding some Equitable
equitable share of the privileges he has claimed, and has ob- to be with-
tained, or rather has taken to himself. The general benefit of held.
society and the individual good of his fellow-creature, most earnestly and
justly demand this privilege through his hands. A more liberal policy is
loudly called for in order to second the exertions of genius, and of acces-
sory science, which attempts to promote the advancement of an art on
which national prosperity so very much depends; for without it, societies
may meet, the chemist may analyse, and the philosopher will lecture in
vain. General success in any business depends as much on the Social policy
social policy as on individual exertion, which must be free and necessary.
unfettered, and in every way encouraged. The period of twenty years
cannot be regarded as an extension beyond the nature of the pursuit, nor
in any way unconnected with the interests of both parties. Very rich
lands will sometimes occur, which require little or no expenditure beyond
the ordinary expenses of tillage; and on these soils, a long Shorter ten-
tenure seems less necessary than on improving grounds of more ure for rich
or less extent. But these exceptions are not very general, and
even there the landlord will derive but little benefit from abridging the
lease unduly he will excite the attention of the tenant in closely crop-
ping the land in order to have a guard on his outlay, and to be ready for
a removal with as little as possible lagging behind. Short leases are
worse than none-they provoke an inclination to expend, but afford no
foundation of action-they afford a time to lay out money, but none in
which to recover the amount : so that no advantage is conferred except
that the tenant is not liable to be ousted for the number of years men-
tioned on the rent being duly paid. But in point of inducing improve-
ments by the outlay of capital, a yearly tenancy is just as effectual as
short terms of tenure. Time and experience, the most convincing of all
teachers, and the most despotic of all governors, have long since most
satisfactorily settled the irrefragable truth of the above observations.
The lease of land settles, 1, the time of entry to the farm, the
duration, and the issue of the tenure; 2, the amount, and kind made by the
of rent, and the terms of payment; 3, the stipulations re-
garding the erection and keeping in repair the buildings, fences, and other
lands.
Settlements
lease.
880
ON LANDED PROPERTY.
fixed appertainments of the farm; 4, the rules and conditions of manage-
ment; 5, the reservations made by the landlord; 6, the rights of the
respective parties who contract the agreement.
entry.
The period of entry to farms of land are various, in March, in May, in
September, and in November. The custom of the district generally
establishes the time of entering into the possession of land, and not
being founded on any uniform principle, much embarassment has accrued
Times of in the management of landed property. In March, there remains
much produce unconsumed of the crops of the former year; and
too much interference is occasioned between the outgoing and incoming
tenants, by the former having to use the farmery in manufacturing the
remaining goods of his possession. In September and in November, the
whole crops of the year have been produced by the expense of the out-
going tenant, and they must be manufactured during the winter, by his
own arrangements in the farmery, or sold by auction, or to the incoming
tenant by valuation. The Michaelmas entry prevails much in South
Britain, and is found to be attended with great inconvenience.
The green
crops are on the ground, and the whole expense of raising them must be
repaid to the outgoing tenant: the tillages of the former year are not
exhausted by one crop, and a value is owing: manures otherwise used for
one crop, must be appraised in the forthcoming use: copse woods that
are cut for fuel and sale, are valued in the standing growth, and thus a
large amount of valuations comes against the incoming tenant, and must
be paid in ready money before he enters upon the ground: the grain
crops are lodged in the barns, or built in ricks, and are converted into
money during winter by the outgoing tenant, who may be removed to a
distance the connection is thus continued which should be ended when
the possession is quitted, and a large amount of money is required at the
entry, for which no return is made for some time. This time
very incon- of entry, with all its customs and dues, will be found amply de-
tailed in "Bayldon, on Rents and Tillages," (Longman,) and
in the former part of this work, edited by Mr. Ryde, where valuations
are given as examples, and accurate comparisons are made. The
alteration of the term of entry to the spring, would require a sacrifice on
the part of the landlord of the whole appraisements due to the outgoing
tenant, and thus set clear the entry to the new possessor. The sacrifice
would be very considerable, and the advantages may in some respects seem
distant-but it would prevent the large demand that is made on the in-
coming tenant, and leave the money thus expended, to be used in making
other improvements. The inconveniences of the present system are very
frankly acknowledged, and the benefits of a change largely
changed. anticipated, but custom has got a very firm hold, and habit
exerts its prerogative. An additional evil consists in creating too long a
connection with the farm in the case of the outgoing tenant using the
barns for thrashing the grain crops during the winter, after quitting the
occupation of the land. This is a very fatal objection, as the chief object
in the entry to possession of lands and the quitting of farms, is to sever
Michaelmas
venient.
Must be
ON LANDED PROPERTY.
881
every connection as quickly as possible betwixt the outgoer A stir is now
and the incomer, and to make the change so easy and simple as being made.
to be scarcely perceptible. The autumn entry is worse than that of the
spring, as in the former case, the whole crops of the year are on the ground
for conversion and manufacture, while, at the latter term, only a part
remains to be consumed of the crops of the former year. On these grounds,
both periods of the year are inconvenient for the purpose of taking and
quitting the occupation of lands.
entry.
The most enlightened judgment and the best practical experience,
universally prefer the first of May as the most eligible period May the best
of the year, for the purpose of exchanging an old tenancy for a period of
new possession of the soil in the temporary use.
At that time,
the whole crops of the previous year have been manufactured by the out-
going tenant, and the new crops are only just sown. The labour of the
year are also best divided at the beginning of May—the preparation of the
ground for the fallow crops of the year is commenced, and the grain crops have
been sown by the outgoing tenant on the fallows of the previous season. In
this arrangement, the whole manure on the farm that has been made from the
straws and root crops of the previous season, belongs to the landlord as the
owner of the soil, and through him to the incoming tenant, wholly free of any
charge whatever. And the condition is most equitable, that the manures that
are produced by any grounds shall be used for their benefit and charged
only with the application. The incoming tenant has had the accom-
modation since 1st of January of the year of entry, of two teams of horses
in the stables of the farmery, for the purpose of carrying the dung from
the yards to heaps in the fields, where to be used for green crops, and to
give the second and third tilths to the lands of the fallow crops of the
ensuing year. The outgoing tenant performs the "first" ploughing during
the winter, of all the lands to be fallowed in the following year, for which
he is paid by the incoming tenant according to the rates of labour in
the district. This essential clause in the lease is devised for the
purpose of securing to the land the benefit of the pulverization it.
done on the surface of the exposed ground by the winter's frosts and rains,
of which no subsequent working of the soil ever can compensate the want.
The incoming tenant pays to his predecessor, the amount of Winter
the bill of grass seeds which were sown the previous year, and ploughing
also the expense of sowing them, as he will derive the whole
benefit in a crop of hay during the first summer of his occupation. The
seeds of the year of his entry, are sown by the teams which are accom-
modated on the farm previous to his arrival. The grain crops of the
year of expiry, are sown by the outgoing tenant, and some two weeks
before full maturity, the standing grains are valued by referees, and the
sum is paid by the incoming tenant to his predecessor, in ready money, or
by a credit accommodation of mutual agreement, when the residences are
not very distantly removed. This enactment prevents the crops Grain crops
being parcelled by auction, and carried to distances by much purchased.
labour, and also the incoming tenant from going to similar occasions, and
bringing what quantity he may require at some considerable cost and trouble.
Conditions of
paid for.
882
ON LANDED PROPERTY.
By the above simple arrangement at this period of the year, the quitting
connection is the easiest and most thoroughly severed, and the incoming
possession is the readiest obtained. On being paid by the new possessor
the value of ploughing the fallow lands in the winter furrow, and for the
grass seeds of the previous year, the quitting tenant leaves the whole
concern without any lag in connection, except the simple operation of
having the grain crops valued, and receiving the money, shortly before
the full maturity. The incoming tenant on fulfillng these few and simple
conditions, obtained at once the free and unfettered possession and use of
Quitting and the houses and lands.
There is no mixture of the employ-
entry easy
and uncon-
nected.
ments as when the thrashing of crops is one person's, and the
cattle in the yards are another's; there are no grounds for brawl-
ings or collisions, in cases of work being done by one man for the benefit
of another, when the entry is in the spring or autumn. The connection
is cut by an absolute removal of all property on the day of separation, and
every settlement is made except in the case of the growing crops of grain,
which must wait the period of attained value.
This general arrangement that has now been detailed, is very generally
used in the North of England, and in much of the South of Scotland. The
clauses anent the winter ploughing of the fallow lands by the outgoing
tenant, and the purchase of the standing grain crops by the new occupier
of the farm, have hardly advanced beyond a bare and scarcely pronounced
notice. Yet both enactments have been introduced and are now used on
the extensive landed estates in Northumberland belonging to the Green-
Mr. Grey's
practice.
wich Hospital, which are under the enlightened management of
John Grey, Esq., Dilston, a gentleman of a very liberal mind,
and judicious understanding, and equally eminent in the practice of agricul-
ture, as in the policy of every connection of the art. It is gratifying that
our recommendation of both provisions is justified by Mr. Grey's opinion,
and sanctioned by his practice.
The arrangements that have been detailed form the prevailing custom
over the whole of Scotland, and two-thirds of the extent of England, being
adopted and used in the widest meaning by the most extensive landed
noblemen of the midland and leading counties. Leases of fourteen years
and even of seven years are most prevalent over the southern counties,
where the arrangements of entry and quitting of farms are not different in
the chief points, and only in the minor details that are occasioned by the
locality and established usages. These lesser points are easily gathered
from local information, and while the primary regulations are maintained.
The very general tendency to adopt on every opportunity the system that
has been recommended is the best proof of the superior utility; and the
wish that is now expressed to introduce the arrangement where not yet
used, shows that the value is appreciated, and that the benefits are
known.
Having fixed the term of entry, the lease next mentions the length of
its duration in the number of years from the determined period of occu-
pation. The most proper and advantageous length of a lease has been
ON LANDED PROPERTY.
long.
883
shown to be twenty years, both for the interest of the landlord Twenty
and tenant; the former by granting an adequate length of years not too
security, gets his property improved, and prosperously managed,
and the tenant obtains a period of years, in which to employ his capital
and his time, with pleasure and advantage. The time is not at all too
long for parting with the control of property, as another person is induced
to take an interest in it, which cannot be accomplished by keeping the
possession, in perpetually moving from hand to hand, and changing occu-
piers who have different views, and practise diverging modes of manage-
ment. A longer period than twenty years has been thought to tend to
an alienation of the property, and consequently objectionable; but "issues"
by mutual consent could be introduced into long leases, and A lease must
thus shorten the duration; and the consent of both parties being have an issue
required to effect a termination, no damage can happen to either party on
account of unrepaid expenditure on lands or buildings. But a determined
issue of the lease is generally preferred which dates from the time of
entry, which are both mentioned in the agreement by the years of the
respective periods. It is essential that a lease have the time of issue
expressly specified, or it may seem a conveyance of property. It is ex-
pedient that the year of expiry be written in the words or figures of the
year in which the lease falls, reckoning twenty from the date of entry.
Though computation can easily ascertain the term of issue, it is better that
the precise time be written, which at once shows the period that is sought.
The amount of the yearly rent is expressed in one sum, Rent defined.
and is most satisfactory in a fixed quantity of money. Corn
rents have been adopted, and partially used; but, a very great objection
consists in the case of deficient crops imposing a heavy rent on the tenant,
when he is least able to pay it, the prices being high and the quantity of
grain being small: hence the necessity has arisen, of fixing a “maximum,”
beyond which the rent shall not rise; as in one single year, of a very
deficient crop, the tenant may be irretrievably ruined, unless he have a
large capital to support him. On the other hand, the rent to the land-
lord
may be
very low, owing to very fruitful seasons, and a "minimum"
of the amount becomes necessary to be fixed, below which the rent shall
not fall. Two points are thus to be ascertained and fixed, a
maximum of rent, and a minimum; and there is just as much sum of
difficulty and chance of error, in fixing these two points as
extremes, as in fixing a point of medium, or in fixing a certain rent in
money. In some few cases of very rich corn-growing districts, this mode
of paying rents in a certain quantity of grain valued in money by the
average prices of the year, may answer a good end—but grain is not the
true measure of rent, which depends very largely upon animal produce
of various kinds. The fairness of the above transaction should have
neither "maximum" nor "minimum ;" and the rent must be regulated, not
according to the prices of a single year, but by the average of a certain
number of years, in five or seven, so that the fluctuations of rent may not
be sudden, but spread over a sufficient period. But even then the
Fixed in a
money.
884
ON LANDED PROPERTY.
Grain rents
useful.
objection is not removed, of an increase of rent in deficient seasons;
for the high prices of that year being included in making the
not generally average, raise the sum to be paid by the farmer beyond the
general amount of the common returns; and the quantity of
grain on which the rent is calculated, cuts heavily into the diminished
stock of the farmer, which may be lessened by one third of the usual
produce.
A fixed payment in money is the most suitable and satisfactory kind of
rent, which is regulated to afford the necessary profits to the farmer,
and to bear the occasional deficiencies of produce and the variations of
price, which are inseparable from the nature of his business. Every in-
telligent tenant of land will prefer this calculation of rent to
any other system, even of rack rents, which ought never to
exist.
Rack rents
never to
exist.
Payments in
kind
abolished.
Payments in kind, as in grain, meals, fowls, and in the labour
of men and animals, are now nearly abandoned, and should be
forthwith exploded. They are the remnants of feudal vassalage
and former connection between landlord and tenant, which cannot exist
in any emancipated country. The public markets of commodities are free
to all classes of society, where sales and purchases are made by fair pay-
ments. To these general resorts all parties must go and sell to meet the
demand, and purchase by the amount of supply. A bare mention is
sufficient as the custom scarcely exists.
Times of pay-
The times of paying rent vary much in different parts of the
ing rents. kingdom: but every where the yearly amount is divided into
equal halves, and paid at half-yearly periods of time. The most common
practice begins the payments at the end of six months after entry, the
second payment after the lapse of a similar interval, so that a year's rent
is paid during the first year of possession. In North Britain, it is very
common to demand no rent till after eighteen months' possession of the
farm, and after the farmer has reaped a crop to enable him to meet the de-
mand. In the last way, a smaller capital is required to take a farm of
land, as the year's crop pays the year's rent; but at the expiry of the
lease, a long connection is maintained between the outgoing tenant, the
Long dates landlord, and the farm which, as formerly observed, should
avoided. cease as promptly as possible at one time. The first method
requires the first year's rent to be paid from the capital of the tenant,
lessened by the proceeds of the animal produce, which has been obtained
during the year. This amount may reach the half-year's rent, so that the
capital of the farmer has to bear only the rent of the other half-year.
the expiry of the lease, the rent is paid when the farmer quits posses-
sion, and the connection wholly ceases. It is the best regulation of paying
rents in the due periods of time-the postponement for one year brings
into the market an host of speculators, who, at less capital, raise the rents
of farms, and ultimately defeat the special purpose. Long usage having
established these two periods of payments of rent, and the general capitals
of farmers having become suited to the conditions, it matters not much
at entry to be
At
ON LANDED PROPERTY.
885
which system is adopted, and the disturbance of either method is not
desired to answer any purpose that is seen to be very beneficial.
delay
When the entry to the farm is made in May, the mode of One year's
delaying the rent for one year, and the usual credit of six
months, fix the first half-yearly payment of rent, at the expiry of
eighteen months after the tenant has taken possession of the farm. In
this time, he has obtained the year's production of the animal department,
and the profits for one and a half years of the grazing stock, which will,
no doubt, largely contribute to the payment of the current going expenses
of cultivation, and of the domestic establishment. But it makes little
provision for the rent of the year—the crop of grain sown by the farmer
has been reaped but not manufactured in the month of November, when
the first half-year's rent is due in eighteen months after the entry. It is
true, that the produce of these crops provides well for the rent of the next
half-year, and the proceeds will repay the deficiency of the animal pro-
ducts in meeting the rent of the first half-year, and thus the rent of the
whole is drawn from the farm, without at all trenching on makes a long
year
the capital of the farmer, whose funds are thus replenished, but calculation.
must still make an advance of money as required during the currency of the
year; low prices and dull markets may prevent the timeous disposal of the
produce, and a deficient crop of grains may demand a store whence to supply
any want that is caused by the failure. The farmer may calculate on a some-
what less capital to take a farm by this mode of paying the rent, but not
in the full amount of the year's rent, by reason of the accidents that may
happen.
The Novem-
similar
ber entry is
When the entry takes place in November, a period of twelve
months has elapsed when the first half-year's rent is demanded,
in the same month of the following year. The farmer has obtained the
proceeds of the animal department for a year, and has reaped "only" the
spring crops of grain, as the autumnal wheats are his predecessor's, being
sown before he quits possession of the farm. In this point of view little
difference is found between the entries of May and November. The pos-
session of the land during the previous summer, enables a better perform-
ance of some parts of the cultivation, and is freed of heavy valuations,
while it is liable to the greater bustle and inconvenience that is attached
to the commencement, than to the fall of the year. As has been observed,
the autumn entry is very objectionable, as it brings the whole crops of the
year to be arranged and manufactured, after the possession of the farm
has passed from the owner of the crops. The Michaelmas entry accumu-
lates a heavy expense on the incoming tenant, the valuation of the and the
unexhausted tillages, the purchase of the outgoing grain crops, Michelmas
if he is bound to do so, and the rent of the year, in half-yearly
payments, before any crop has been reaped of his own property, raise an
expense that is very unsuitable to the extents of possession and the con-
stitutional value of the lands, and very justly condemn that period of the
year as an entry to a farm. The expense is much too great in the first
year to be met by ordinary circumstances, and no adequate result attends
the arrangement, that cannot be obtained by an easier mode of dealing.
one.
886
ON LANDED PROPERTY.
The May
The entry on the 1st of May, to which the best preference is
entry is least given, is by much the least expensive, and by far the most con-
expensive. venient. The first half-year's rent is paid in November of the
year of entry, being six months from that date, and gives the summer
produce of the animal department to the farmer, wherewith to meet the
current expenses, and the first rent, if any surplus remains for that purpose.
The amount of the first year's rent enters into the capital necessary to
manage the farm, but the payment of the rent regularly as the time pro-
gresses, is in keeping with correct business, and at the expiry of the
lease the possession of the farm and the payment of rent cease
convenient together. This method accords with compact movements and
agreeable separations. But an accommodation having been
formed for the postponement of the rent till a crop has been
reaped, the objections have been much reconciled; but, still giving
the preference to the entry in May, rather than in November, on
account of the whole crops of the year being at the latter period
on the hands of transfer, which causes much unnecessary business and
commotion.
and most
when the
lease ex-
pires.
Stipulations
The stipulations of the lease condescend to the upholding and
of the lease. preservation of the buildings on the farm, and of the fences and
roads, and any other fixed appendages that may be on the lands of occupa-
tion. The outgoing tenant is usually bound to keep and leave in good
repair, all the fixed utensils of the farm, and the incoming tenant accepts
them in that condition, and comes under the same obligation as his prede-
cessor. If the latter party has failed in this part of the contract, the duty
falls upon the landlord, that the neglect be repaired by the party who is
liable, or that the utensils be put into the proper order, at his own cost,
in which the incoming tenant can receive them. The landlord can have
the necessary repairs, that have been neglected, to be estimated, and charge
the outgoing tenant with the amount. The necessary repairs must always
be done by the possessing tenant when seen to be required, and it is the
duty of the agent on the estate to inspect the condition of every appen-
dage, examine the stability, and direct the effective maintenance.
When new buildings are to be erected, or extensive alterations to be
made, a separate clause in the lease is required for the special case; and
when the occurrence happens during the lease, a new agreement is
made to suit the business, which is appended to the original document.
In these specialties, the performances and obligations of both parties are
clearly defined, and distinctly expressed. The tenant receives of the
landlord, the raw materials of the repairs.
Support of
buildings.
It is a very equitable condition which requires the tenant to
uphold the buildings in the same good condition in which he
found them, as his fair interest in the use of the houses imposes upon him
the very just demand. The extensive and irreparable decays of nature
are always excepted-the roof of a house, the doors, walls, and gates, may
have lasted beyond the possibility of repair, and no dispute can happen
anent the complete restitution. The tenant is frequently held liable for
ON LANDED PROPERTY.
887
damage to the buildings by fire-but as the houses are the property of the
landowner, equity would direct that the insurance of the buildings be done
by the proprietor's cost, and the farmer pays for the security of his own
property, which is lodged or manufactured in the erections. A clause in
the lease stipulates this arrangement.
fences.
The roads, fences, and watercourses are managed on the same condi-
tions. The incoming tenant examines the state of these appendages, and
accepts them, and is bound to uphold the suitable condition, and to exhibit
it when he quits the farm. If any extensive alteration be ar- Roads and
ranged, it is specially expressed in the lease, and when a wholly
new execution is determined, it is made the subject of a mutual contract,
which is singly entertained and expressed. All these arrangements be-
tween the contracting parties must, and very easily can, be so pointedly
expressed, and easily understood, as never to afford occasion to disagreeable
and unseemly disputes.
The watercourses here mentioned are the beds of small streams that in-
tersect the grounds of the farm, and which at occasional periods will cause
damage to the lands by pulling down and carrying away the alluvial
banks of the stream. The courses of rivers and of all large water-
bodies of water which rise to the name of brooks, and form the courses.
boundaries of estates, or of farms, are the province of the landlord, and are
kept in the proper order by his administration. The means that are to be
adopted, and the execution of the guards against depredations by unruly
bodies of water, will form the matter of a subsequent chapter. The farmer
has only to do with occasional torrents of water which intersect his lands,
tear the soil, and make a waste of ground. The bed may receive the
covered drains of wet grounds, and require a clear discharge at all times,
or it may run alongside a fence, and endanger the stability of it, when the
outrageous torrent is not securely confined. In these cases the duty of
preservation is evidently that of the farmer, but subjected to such assist-
ance from the landlord as will seem to be required from his permanent
and future interests in all such matters. In case of
any violent Landlord's
and extraordinary accident, the landowner will not refuse the aid,
liability of part of the restoration, and sometimes materials rather than
labour will be required, and the former may be readily at his command.
Strong stakes to be driven into the soft bottom of the torrent, and branches
of trees to be woven among the stakes, with the growing end favouring the
direction of the water, are very useful materials in the cases of small brooks
of water, or slender courses that are liable to be much swollen by heavy
rains or sudden thaws, and to become unmanageable by the ordinary
confinements. These articles may well be afforded by the landlord, as the
strong work that is done will add to the future permanence. The under-
standings had better be expressed in the lease which relate to such and
similar points, and also the exemptions, which are expressly and in em-
the duty of the landlord, who must be equally bound with the bankments.
tenant in the mutual obligations. Roads, fences, watercourses, and em-
bankments will undergo a subsequent discussion, and the propriety will
888
ON LANDED PROPERTY.
be considered of almost wholly relieving the farmer of the charge of any
fixed appendages on the farm. A temporary interest ever leads to neg-
lect, which it is the right of the landlord to have redressed, the latter must
have an oversight of the former, which might probably be commuted into
a beneficial charge, when some necessary arrangements are made to suit
the alteration. The hint is merely given here, the adoption remains for
the future expediency.
Rules of
must be spe-
cified
The rules and conditions of management are a very essential branch of
the subject of a lease, and have been generally treated at greater length
than any of the others, from a belief of its vast importance, and being far-
thest removed from the knowledge of those persons who pretend to draw
the stipulations of the lease of land. In the infancy of improved agri-
culture, directions and restrictions were not only justifiable, but
management. very imperatively required; but now that agriculture is every-
where known, much less occasion prevails for the use of conditions in the
management of land. An extreme liberality has pronounced against any
restrictions being imposed upon the exertions of an engagement which
promises to do a certain thing upon enjoying a specified privilege, and
that upon that thing being done, it matters not how or in what way the
privilege be used. To confine the farmer in the sphere of his operations,
or to dictate to him a certain course of proceeding in the cultivation of
the soil in which he has invested a usu-fructuary interest, resembles pre-
scribing to a maltster how many quarters of barley he must
steep in a week, and to a cotton manufacturer how often the
spindles must revolve in a day. But the analogy between the two pur-
poses does not hold, as the circumstances of application are wholly dif-
ferent, the farmer and the manufacturer pay rent to the landlord for the
use of articles that are very different in nature and constitution, variously
adapted, and liable to very opposite susceptibilities. The walls, doors,
windows, and roof of the house which covers the manufacturing operations.
suffer no damage, even from the perpetual motion of the whole machinery
that is employed, accidents being excepted, there is no connection between
the two parties that can impair the value or constitution by the one prey-
ing upon the other. The operations are done by matter working upon
matter by means of an intellectual superiority over brute force, there is no
vitality employed which requires a sustenation from the powers of
another article, and which is damaged by the subtraction of its essence.
The employment of the farmer is engaged upon different ele-
ments, the produce which he acquires is manufactured by the
active powers of life, which are contained and operated in the land for
which the rent is paid, and are there excited by artificial processes and
applications. A very continued use of the soil in certain purposes is found
to deteriorate the quality, and very much to impair the value, and conse-
quently restrictions have been imposed to preserve the value of the original
article which forms the property of the landowner. It is, therefore, still
necessary, that some rules and restrictions be mentioned in the lease for
the purpose of guarding property from spoliation.
are not
analogical.
ON LANDED PROPERTY.
889
ordering.
Any directions given to the farmer should relate rather to Forbidding
what he is not to do than to what he is to perform. The end rather than
proposed must not be to fetter and control the tenant in the
necessary details of his business, but to lay down a few general rules as
will lead to some benefit and prevent what is prejudicial. No particular
directions are to be given of the labours of the farm, as these duties belong
wholly to the farmer himself, but only general stipulations are to be used,
which are seen to be of ready observance, and which do not require to be
enforced by a useless and injurious interference with the legiti-
mate concerns of the tenant. An imperfectly cultivated country
may be much assisted by the directions of a lease, which may be
made a powerful instrument for that purpose; but even in that case, general
principles and rules of management must show the interest to be pursued,
rather than vexatiously disturb and annoy the existing forms of practice.
Suggesting
rather than
annoying.
General
The enlightened knowledge of the present period of agricultural prac-
tice renders unnecessary the insertion of details for the use of the farmer,
and even the general principles must be few, and which appear to be im-
peratively necessary and altogether indispensable. In the case of farms
that are near to a town, and within the convenient distance of one journey
in a day, or of two journeys in the twelve hours of summer, the under-
standing may be expressed in the lease that the land be cultivated in the
course of four years, viz.:-1, fallow or root crops; 2, grain crops; 3,
grasses; 4, grains; and then the hay and straw are allowed to
be exchanged for half-rotted manure brought from the town in scheme;
return. This rotation may be continued in the very favoured situations of
the best lands, where is an extraneous source of obtaining manures. On
the best qualities of soils that are placed beyond the advantages of manure
above the quantity made from the yearly crops, the rotation of five years
is mentioned in-1, fallow or fallow crops; 2, grain crops; 3, clovers;
4, pasture; 5, grains. With some very few exceptions, this course of
cropping may be pronounced to be the most generally suitable for the
British isles. On the most inferior cultivated lands, the course of six years
becomes very appropriate, as—1, fallow or fallow crops; 2, grain crops;
3 clovers; 4, pasture; 5, pasture; 6, grains. It may be mentioned, that
in preparing the grounds for the fallow crops, the land shall receive at least
three clean earths, exclusive of the winter ploughing and the drilling of
the ground for sowing the seeds of the crops. These clauses may but not com-
be inserted or omitted, as the circumstances of each special case pulsory :
may seem to require.
The farmer must agree not to take two crops of grain in succession from
the same ground, and not to mow any grass land for hay twice in the same
year. Any fields of grass land that are of very superior quality, must be
designated by name to be kept in that condition of use, and to be mown or
pastured, as circumstances may require, and without any provision in the
lease for that purpose; but no restrictions must be imposed on the tenant
breaking up and using as arable grounds all inferior grass lands, which at
present yield chiefly very scanty crops of weeds and mosses. It may be
3 I
890
ON LANDED PROPERTY.
varied by cir- mentioned, that all hays and straws are to be consumed on the
cumstances. farm, except in the vicinity of towns, when a special arrange-
ment provides for the alienation by an express clause in the lease. Hay
is in some cases allowed to be sold, and straw is prohibited; potatoes are
sold everywhere, but turnips must be consumed on the farm. These varia-
tions are guided by the peculiar circumstances in which the location of the
land exists.
"Good hus-
bandry de-
fined."
These and similar rules of general adaptation are as few in number as
possible, in order that the farmer may not be converted into a mere ma-
chine, the action of which is altogether directed by an external application.
The much criticised words, "by the rules of good husbandry,"
are appropriate enough, and sufficiently intelligible, and mean
that all the performances of cultivation shall be done in the best
and most approved methods. These operations are well understood in the
present day of practical farming. In the courses of cropping that have
been mentioned, one-fourth, one-fifth, and one-sixth part of the arable
lands will be yearly fallowed, as shown by the number of years in the
rotation. In the end of the lease the tenant must not depart from the
course of cultivation that has prevailed during the currency of the lease,
and a clause is made to contain this enactment, in order that the land is not
scourged by severe cropping to fill the pockets of the outgoing tenant. The
interests of the landlord and farmer are certainly the same in reality, but
they do somewhat differ in the latter years of the lease when the farm is to
be quitted; and fair dealing requires that no interest shall abuse
Last years of the other; and there can be no hardship in binding the tenant to
continue to the end of the lease the system which he has reck-
oned to be the best for his own interest. A sufficient guarantee of good
management does not invariably lodge in the interest of the tenant, the
circumstances of his position may be widely changed during an extended
term of years, and the landlord must not be injured by the casualties or
contingencies that may happen to the private means of the tenant. Public
property should not suffer from private accidents.
tenure.
The root crops and the hay of the previous year will be wholly con-
sumed by the first of May, or the time of entry; but part of the straw will
be remaining in a thrashed state, and all the dung made in the cattle yards
during winter will be on the ground, and best carried out to heaps near to
the fields to which it will be applied. These unapplied productions belong
to the farm, and are used by the incoming tenant free of any charge; but a
tenant right of three years is given for the unexpired value of artificial
Dung and manures, as bones and guano, which are extraneous to the farm,
straw go free. and require a separate consideration. The remaining benefit in
one or two years is valued by referees, and paid by the incoming tenant.
Artificial When three crops have been got since the application of the
have a right manure, the right of compensation ceases. This enactment has
been introduced on the extensive estates of the Greenwich Hos-
pital, in Northumberland, under the direction of John Grey, Esq., Dilston,
whom we have before mentioned, as the agent on that property. It is a
manures
of 3 years.
ON LANDED PROPERTY.
891
most equitable stipulation, as it does not hinder the tenant from making
useful applications, even when he knows he quits the farm from the dread
of losing the full value by the removal. By getting no value Mr. Grey's
for the farm-yard dung, he does not lose any thing, as he gets practices.
the same conditions on the farm to which he removes; but there may not
be any artificial manures in use, and no benefit can be derived from them.
Hence the extra application of artificial manures requires a separate con-
sideration, and are justly entitled to the above recompense. Even under
a lease, the liability does not cease, as it has an issue, just as tenancy at
will expires on a due notice being given.
The landlord reserves for his own use, and witholds from the woods and
occupier of the surface, the workable minerals, as metals, coals Minerals.
and limestone: clay may be added, when the quality of it suit the use in
making bricks and tiles. The farmer is paid for any surface damage that
may be done, by the award of arbitrators, as it cannot be known at the
time of negotiating the lease. Growing wood of all kinds belong to the
landlord, with the provisions of felling and pruning the trees, and car-
rying away the produce. All woodlands enclosed or unenclosed, are the
landlord's reservation, which is not abandoned by the pasturage being used
by the farmer. But the lease must expressly mention the special rights
in these cases. A power is sometimes reserved of taking, to be planted with
trees during the lease, any quantity of ground, on the tenant being abated in
the rent for the estimated value. The rent of one and a half years is generally
deducted, as a set-off for the inconvenience of losing probably an undue
quantity of land, or at least an unexpected choice of the bereavement. It
is best when the landlord reserves at once from the lease, some fixed
quantity of lands to be resumed at any time, and merely defers his power
to do so to a convenient time. Uncertain reservations often lead to misun-
derstandings and disputes.
Hunting and
The right of the landlord to shoot, hunt, fish, and fowl, on the
lands let to the farmer, is generally understood to be of common Fishing;
law, but is best expressly mentioned in the lease. The keeping of ex-
tensive and thickly stocked preserves of game animals, is quite a different
subject from walking over grounds in search of the stray birds that
alight upon the surface from hunger, or from being wearied on the wing:
the former case requires that the cultivated lands which surround the pre-
serves, be used by the landowners themselves, the damage done to the
crops by the animals will fall upon the proper quarter, and complaints and
bickerings will be removed. In common cases of the open farms at a distance
from the seats of landowners, the right to shoot the four-footed animals might
be given to the farmer, reserving to the landlord the privilege of murder-
ing the winged tenants of the air. Some such arrangement might lead to a
settlement or a lull of the vexatious question of game, and damage shooting
to growing crops. The right is not likely to be relinquished by accommo-
the owner of the soil, and therefore should be accommodated.
dated.
The insertion of a clause is quite harmless that the landlord or his
agents have a power, at any time, to enter the grounds and see that the
892
ON LANDED PROPERTY.
conditions are complied with. Such a power must evidently be under-
stood; but a clause to that effect is generally inserted.
Lease is
heritable.
The rights of the contracting parties are capable of being determined
by common law, but are generally fixed and explained by the terms of
the agreement. The farmer and his heirs hold the lease during the stipu-
lated time, on the conditions being fulfilled which were laid down in the
contract. A lease of land is an heritable subject, and in case of
intestacy, goes to the heir-at-law and in England the deed ex-
cludes subtenants, but is directed to heirs and assigns, without any moles-
tation from the landlord. In Scotland, not only are subtenants excluded,
but likewise assignees, legal or voluntary, inferring that the lease shall go
to the heir-at-law alone. This rigid destination of the lease, does not
answer any purpose of utility: it is intended to give to the landlord the
choice of a tenant on the death of the original occupier.
Should not
be strictly
applied:
During the currency of the lease, the farm may pass into the hands of
distant heirs, of whom the landlord can know nothing, or into the hands
of guardians or other legal managers, that are altogether unknown to him.
The "electus personæ," or the choice of the person who shall
occupy his property, has been much insisted upon, as the privi-
lege of the landowner; and it has led to the nomination in the
lease of the parties who shall inherit the farm in the case of changes
occurring in the natural lives of the occupiers. But even with these pro-
visions, the landlord does not obtain the certainty that the heir of the
lease, who may be then unborn, shall choose the farming profession, and
be qualified to conduct the cultivation of land; nor does he know that the
specified members of the family will undertake the conditions of the lease,
with the willingness and ardour that are requisite to ensure success in any
undertaking. The heir-at-law, or the eldest son, may be prevented by
circumstances from becoming a farmer, he may be the least qualified mem-
ber of the family, and various causes may render him unfit for
vised by the the intended occupation. The farmer has no power to rectify
tenant. the evil, by making any other assignation; but there may be
some advantage in getting the eldest son trained to agriculture as a pro-
fession from childhood, from being regarded as the heir of the lease.
Though not many practical inconveniences result from the established
custom, the tenant may, without any damage on the opposite side, have
the power of devising his lease as any other part of property.
might be de-
Choice of a
tenant.
The choice of a tenant or temporary occupier of land, in-
volves several points of very grave consideration. The cus-
tomary acuteness of the Roman people did not overlook the qualifications
that should attend the amenable cultivator of the soil--for Columella in
the book "De Re Rustica," expressly says, that the occupier should be a
person "qui sciet, qui poterit, et volet," or one who knows how to do the busi-
ness, who has the means of doing it, and who has the willing ardour to per-
form the duties of the undertaking. The professional knowledge of the offer-
ing person must be very strictly regarded, and a satisfaction on this point
must be obtained before any advances are made to the other points of ad-
ON LANDED PROPERTY.
893
known.
justment. Ample recommendations must be got of his capability on this
head, from quarters that set aside any expressed doubts. Ignorance will
ruin any property, and render of no avail all the safeguards which a lease
can contain. It may appear a very inquisitorial sort of business, but there
seems to be a necessity, that the landowner shall know the means Means
that are possessed by the offering tenant, to enable him to culti- should be
vate the land in the most approved practice of agriculture. Ex-
tensive damages have accrued to the owners of the soil, and heavy losses
and large inconveniences have attached to the cultivators themselves, from
the perpetual desire of grasping more in the hands than can be firmly
held, and of extending the sphere of operations much beyond the means
of the proper accomplishment. Expansion will ever be much weaker
than compression, and combination of force, of any kind, has ever been
attended with magical results, when directed by the legitimate com-
prehension of its value. The owner of the soil is entitled to have some
understanding on this head—a correct statement of means need not be re-
quested—but a gross estimate may be offered, and confirmed by the proper
marks of validity. The capital required will vary from £6 to Capital
£10 per acre, according to the circumstances of the price of required.
commodities, and the condition of the farm as arable or grazing grounds.
Of the whole amount of capital, at least one-fourth part must be Reserved
reserved in store as a fund at interest for the purpose of meet- capital.
ing the demands of accidents, and unexpected contingencies. Casualties
of every kind must be supplied by the reserves, which must be ready at
command when wanted, promptly administered, and of sufficient power
to fill the gap and repair the disaster. No prudent director of a consider-
able amount of power of any kind, ever expends the whole amount in the
first effort-a part is always reserved to assist the points that may fail from
unexpected resistance, and to supply the wants that may occur, and the
accidents that may happen. Many enterprises miscarry from want of
this reserve-and farming being exposed to many contingencies, requires
such a provision as much as any undertaking of action. Of all the evils
that can affect the farmer, none is more to be dreaded, or more pernicious,
than the want of the requisite funds, and of a reserved capital: without a
sufficient amount of means, every effort is vain and delusive—the absence
of the prime mover sinks every knowledge, and destroys all the attempts
of an eager progression. The landlord is damaged in his property, and
the public are despoiled the legitimate inheritance in the production of the
necessaries of life. Labour is robbed of its patrimony, in not being employed
to the due extent, and the formation and accumulation of capital are
stopped at the very fountain head.
There is also required in a farmer, the wish and the willing- Necessary
ness, to do the business in the proper manner; the ardour which willingness.
creates the zealous emulation, and the enthusiasm which renders success
to be certain in any undertaking. A sluggish, mindless plodding, must
if possible be avoided, which neglects the opportunities that may be lib-
erally offered in the due security of tenure, the very full and adequate
894
ON LANDED PROPERTY.
provision of fixed capital, on which the floating funds of the farmer are
used in the permanent appendages that have been before mentioned, and the
compliance, on the part of the landlord, with every reasonable demand
that is made by the tenant, on his means and his liberal consideration.
The farmer should possess an eager desire to enter into these views, and
to advantage himself, by the use of the endowments which are seen to
exist, and which may in future be granted. The landlord has a right to
be satisfied on these points, as far as enquiry can lead to an opinion.
Expired
When land is out of lease, the general rule should be to treat
leases. with the tenant in possession. He is acquainted with the farm,
and attached to it by habit, and some one of his family or relations may
look on the farm and the lease as their descending patrimony. The feel-
ings of old age and of infancy are torn asunder, by the dispossession of the
old tenant, and doubts and fears may darken the later years of life.
Violence is required to break the long association which even the respect
of place winds round the heart, and the pangs of separation are many and
acute. Cases will arise which forbid the treating with the old tenant—
he may be superannuated, or has been a slovenly cultivator, and has ne-
glected the opportunities that have been offered. Then another person
must be sought by private acquaintance, or by advertising.
When to be The treaty with the tenant in possession, when circumstances
renewed. are suitable, should be ended two or three years before the
old lease expires, as it removes any inducement to scourge the land by
cropping, the ordinary management is uninterrupted, and the land is bet-
ter treated than if the lease had expired. The old tenant is generally
preferred to give the full value of the land, which his experience will
warrant. He will be easier treated with than a stranger on matters of
new outlay, and any requirements that are made, will be more speedily
adjusted with him, than in the case of a new possessor, who will see more
wants, and require more accommodation. The troublesome conditions
will be avoided which attend all changes, even when done under the
easiest and least intrusive conditions. This fact carries with it some
very considerable weight, on the subject of letting farms that are out of lease.
Advertising
When any farm is wholly voided by the late possession, an
of farms.
advertisement may be made of the opportunity of negotiation,
for its use, but no auction should ever be allowed to the highest bidder.
Not the promise of a rent is to be regarded; but the skill, capital, and
character of the tenant, are the chief considerations, and must be found
in existence, or very serious losses will happen to the owners of the soil,
as have already been witnessed in a large abundance. The promise of a
very high rent argues an ignorance of the business, or that no loss can be
sustained; and no evils that can attach to landed property, have inflicted
more serious and lasting damage, than the want of skill and funds by the
tenant. By treating with private offers, the landlord secures the choice of
a tenant, and deserving persons have the means afforded them of procuring
farms. The character and circumstances of the offerers can be privately
ascertained, and a general comparison effected-and it will be learned
·
ON LANDED PROPERTY.
895
if the most likely person that offers is known to exert his professional skill
and his means with an enthusiastic discretion, and if in his private capacity
and social relationship as a man, he maintains the dignity of human nature,
as a responsible moral agent. These observations do not at all Extraneous
tend to introduce any political or religious distinctions-those avoidances.
views are wholly beyond the subject—but the special duties that devolve
on landed property along with its rights, render it imperative that there be
upheld by its station, a careful and nicely scrutinized selection from the
broad phase of human nature, of the agents that are to perform every im-
portant subordinate part in the large operation of fulfilling the mighty
scheme of nature's grand intent. The general course of human nature
demands the provision of the above-mentioned qualities in the station that,
is occupied by the farmer, of capital and intelligence.
in the lease:
The persons are generally mentioned in a lease of land, who Succession
are agreed by the landlord and tenant, to succeed in the occupa-
tion of the farm, in case of the lapse of one or more lives, during the
currency of the period of tenure. These provisions very frequently give
the lease to some person, who may think it a very troublesome incum-
brance, being bred to, and occupied in, a wholly different branch of
business, and he has no power to assign it or give it to another person.
He is compelled to perform the occupation, and whether he succeeds or
fails, he must implement the conditions of the lease. The eldest son, or
some younger member of the family, may be bred to farming, with the
express view of inheriting the lease; and in that case, the lease may pro-
vide, that the farm be transferred to a specially educated son of the farmer,
and in default of his life to a similarly qualified member of the relations
of the family. The farmer, no doubt, should have the power of devising
the lease as any other property-but though the lease be heritable, the pro-
perty in it is not absolute, but fettered with conditions, that relate to other
interests, which must be taken into account, and legitimately considered.
It is most equitable and just, that an assignation of the lease assignation
have the consent of the landlord, and that he be consulted in any
intention of changing the temporary proprietorship of the land. His
own interests will not, or should. not, compel an unwilling occupation by
an incompetent person, and no damage can result to the family of the
farmer, from the friendly interference of the landlord in settling the affairs
of a decease. The words of the lease may allow the farmer to demise
the property to the most qualified son or member of the family—and in
case of another vacancy, it shall go to the next heir who may appear the
most eligible, the heir-at-law being always in reserve, to step in and
settle any interminable disputes. If these directions are thought too vague,
and not sufficiently precise, the lease may be held to be devisable, as any
other property in case of the death of the first holder, and to be assignable
by any living possessor of it with the consent of the proprietor of the land.
The bankruptcy of the tenant must be held as an "ipso facto" Bankruptcy
irritancy of the lease, which will expire the first of May that voids the
follows the event, and the same obligations must be done on
of it.
tenure.
896
ON LANDED PROPERTY,
both sides as are prescribed for the last year of the natural termination of
the agreement. No creditors must be allowed to enter upon the farm, in
any way, for the purpose of reimbursing themselves by a lease of the
property—the moveable goods only are liable for debts, the heritable are
beyond the power of seizure. The farm is vacant, and to be relet, or
granted in possession to the family of the farmer, as circumstances may
direct. The landlord in that case must see a suitable person to continue
A new tenant the farm, and be satisfied that sufficient means exist for that
purpose otherwise a new tenant must be found.
found.
Sketch of a
lease.
The following sketch of a lease is drawn from the principles
that have been stated, and contains the chief points of agreement,
to which may be added the additional clauses which may be rendered
necessary by local and adventitious causes.
A. B. lets, and C. D. accepts, in lease for the period of twenty
years, from 1st of May 18 the farm of land known by the name of
and situated in the parish of
and consisting
of acres, or thereby, partly in grass, and mostly in arable grounds.
A. B. warrants to C. D., the free and unmolested possession and use of
the lands for the time specified, against all intrusion whatsomever. A. B.
reserves as his own property, all the standing timbers on said farm, whe-
ther contained in the enclosed plantations, or standing by the sides of roads
or growing in hedge-rows, with liberty to approach, cut, fell, sell, and de-
liver, the said trees or timber at the proper season of the year. All work-
able minerals below ground, as lime, coals, clay, and metals, are the
property of A. B., and may be used by him at any time on allowing to
C. D. the valued arbitration of the damage done to the surface by the
operations of mining. A. B. has the liberty of shooting and fishing over
the grounds thus let (in the proper seasons,) and by other persons to whom
he may give the permission. A. B. restricts the quantity of game as not
to visibly damage the farmer's crops.
A. B. engages to uphold and maintain in proper condition, all the fences
of plantations which are now formed, or may be afterwards made, and
also to give to C. D. at the place of manufacture, the raw materials, as
felled timber, lime, bricks, and stones, that may be required during the
currency of the lease for the purpose of repairing the partial
decays of the farm buildings, gates, and fences.
Obligations.
On the other hand, C. D. binds and obliges himself, his heirs, and
assignees, to give for the use of said lands, the yearly amount of £
in money; and to be paid to A. B., in equal halves of half-yearly payments,
the first being at the expiry of six months after the term of entry, and to
continue at the end of every six months for the term of the lease; C. D.
agrees to pay to the outgoing tenant the value of ploughing in the winter.
furrow the lands intended to be fallowed during summer, which will be
fixed by referees, according to the price of labour in the district. He
also agrees to buy from the outgoing tenant, the whole standing crops of
grain in the beginning of maturity, which will be valued by two persons
mutually chosen, with an umpire whose decision shall be final.
He also pays to the outgoing tenant the price of the grass seeds
Perform-
ances.
ON LANDED PROPERTY.
897
that were sown the spring before his entry, and of the attendant labour.
He
pays the unexpired value of auxiliary manures, as bones and guano,
but nothing for farm-yard dung.
C. D. engages that during the currency of the lease, the arable lands
shall be cultivated by the most approved rules of husbandry, with the ob-
servance of the following special conditions. Two crops of grain shall not
be grown on the same lands in two successive years, and no grass lands
shall be mown twice for hay in the same year; one fourth, one fifth, or
one sixth part of the lands shall be in fallow preparation yearly, according
as the course of four, five, or six years, be adopted as the rotation of crop-
ping, and the same quantity will be left in the last year of the lease. C. D.
accepts the present condition of the farm buildings, fences, gates, and roads,
and engages to uphold them all in proper order throughout the lease, and
to leave the same condition of these appendages at the termination of his
tenure: he engages not to fell any timber, or growing trees, and
not to shoot or destroy any game animals, except by the express
permission of the landlord. In the case of draining wet lands, C. D. agrees
to perform all carriage work that may be required, and to pay 5s. an acre
for the drained grounds, along with the rent in half-yearly payments.
And also the carriage work for any new buildings that may be agreed to
have erected during the lease by a special agreement: C. D. engages not
to sublet any part of the lands that are in his temporary occupation, and
designates as his successor in the lease, the eldest son [or any other son,] who
may be trained to the business; and in case of accident or non-acceptance
in any case, the lease to be assignable with the consent of the landlord.
Observances.
If C. D. quits the farm at the specified termination on 1st of May,
18-, he engages to quit the possession at that date without any legal
notice or warning whatever. He leaves, as he received at the entry, the
remaining straw and dung in the yards during winter, to the
Quit duties.
incoming tenant free of any charge-he will be paid for unexpired
value of manures as he did on entry; for winter ploughing the fallow
lands, and for the grass seeds of the foregoing spring. His grain crops
will be valued before maturity, and the amount paid to him by the in-
coming tenant. He gives stable room to two pair of horses, after 1st of
January, as he received on entering.
Signed this
Witnesses, {
A. B.
C. D.
day of
"
18-.
The chief attention in the form of a lease, is simplicity and conciseness,
avoiding all multiplicity and complexity of detail, and making the con-
ception of it to be ready to any understanding, and the performance easy
to every knowledge of execution. The above mode of entry and arrange-
ments renders almost imperceptible any change in the tenancy of the land,
and approaches to the much desired perpetuity of occupation. Such a
holding, or the nearest possible similarity to it, is required for Specialties
the benefit of the property, and of all parties concerned. The of a lease.
granting of such a thing becomes a pleasure, and the acceptance of it, a
tribute of willing respect.
898
ON LANDED PROPERTY.
CHAPTER III.
CULTIVATION OF LAND, AND ROTATION OF CROPS.
Cultivation CULTIVATION is the art of tilling, preparing, and improving the
defined. soil by means of labour and manure, so as to render it in a fit
condition for affording plentiful crops, according to the nature of the cli-
mate, situation, and other circumstances in which it is placed. It includes
tillage, in all its branches, in the cultivation of arable lands; the application
of manures on the prepared grounds; the use, sowing, and reaping of
particular crops; and the management of grass lands. But it is more par-
ticularly applied to the preparation of the soil by the implements of culture,
which fits the ground to receive the seeds, and produce the respective crops.
The working of land by the implements and manual labour, along with
the kinds and order of plants which are used for crops, will sufficiently
Notices to be comprehend the sphere of cultivation, accompanied by a notice
of the mode of applying the special manures for the different
made.
plants that are used.
ploughing.
In the present state of agricultural practice, the operations of cultivation
begin after the harvest of the year has been finished, with the view of
the next year's preparations. In Britain, the crops are secured in the
months of August and September, and protracted into October in the nor-
thern parts of the kingdom. The change of season, and the autumnal
rains will have softened the land into a ploughable condition by the month
Winter of November, when the stubble grounds, for the fallows of next
year, are ploughed with furrow of seven or eight inches in depth.
The power of two horses will suffice for the light lands of all kinds;
three will be necessary for heavy stiff loams, and four are required to
plough the obdurate clays, as the plastic and London formations. The
three horses are yoked on the principle of the steelyard; two animals
walk in the furrow in tandem, the foremost drawing from the back shoul-
der of the hind one, by the common chains, lengthened by the stretcher
chains of the two-horse cart; the third horse walks on the unploughed
land, and is made equal to the two in the furrow, by being yoked to the
long end of the main-tree of draught, which gives an advantage of the
power of an animal by means of the point of centre being one foot removed
to the end by which the two horses are attached. A lad is required to
drive the animals, which form a very strong team for ploughing. Four
horses in a plough are yoked as the two in the furrow, as above-mentioned,
and are driven by a lad, or stout boy. It is essential that the winter
ploughing of land be deeply done, in order to afford abundance of loose
soil for the operations of the next summer and spring. An early and deep
ON LANDED PROPERTY.
899
winter ploughing produces a tilth, and imparts a mellowness to the soil,
which late ploughed lands never acquire, and is never to be obtained by
any subsequent workings of the ground. The condition remains cloddy,
rough, and clammy; and the soil never falls from the implements, till the
approach of autumn weakens the adhesion of the particles by diminishing
the contraction of the clayey constituents. With sands and light loams,
the matter is not so very great, but all lands are better in being early
ploughed, in November, December, and not extending far into January.
Turnip lands are ploughed in breadths of many yards, as the Modes of
soil is dry, and no attention is required to the direction of the ploughing:
surface water. But clay lands that are summer fallowed for wheat, are laid
into ridges of four to eight yards, and the furrows are cleanly opened that
the water may freely escape. The ridges may be cleaved by the ploughing,
or cast in two or four together; in either way the furrows are kept open
and cleaned out by the plough. This method retains the furrows in the
present position and form, and is called casting to the gore furrow; two
ridges are gathered, and two are cleaved, and makes a work of much neat-
ness. When the ridges are high in the middle, each single one may be
cleaved out in the winter ploughing-the accumulation of soil in the centre
is exposed to the atmosphere, and the gathering of the ridge is facilitated.
for being sown with the seeds in antumn. Where the whole field is
ploughed, the headlands must be cleared; and the inside furrow, which
receives the water from the longitudinal furrows of the field, must be deeply
and cleanly drawn by the plough, in order that the water may quickly
escape, which requires a cut made by the spade from the ends of the fur-
row into the side ditch of the field. Headlands should not be under six
yards in width, in order to give ample room to the ploughs in turning,
and to avoid the land being trampled by the horses after it is ploughed, a
most unpardonable blunder in the art of ploughing, besides the damage.
done to the land by the prints of the feet of the animals holding water
during winter, and starving the roots of the wheat plants. It is a rule
in the management of clay-lands, that no hollow or stoppage must be neat
be allowed in which water can lodge, but that the furrows are and honest.
clean of earths or clods, and that the corners of the fields have open cuts
made by the spade from the furrows into the land ditches. In the plough-
ing of all lands, and more especially of clay soils, honest work must be done,
or the furrows must be cleanly moved from below, laid at the same height,
and be of a uniform width and depth. No unmoved land, or "rafters,”
must remain between the furrows, nor any flat position, nor the standing
on edge of the slices from the plough. The edge of the furrow that is
cut by the coulter and share must be placed quite perpendicular, and the
same position must be preserved throughout the whole work.
The average of spring seasons will mostly permit the second Spring
tilth of winter ploughed lands to be done in the end of March, ploughing.
or during the month of April. The ploughing is performed at right angles
to the first furrow, or straight across the field; in some cases the ridges are
singly cloven by the spring ploughing, but it is inferior to a cross plough-
900
ON LANDED PROPERTY.
Best cross-
wise.
ing in effecting the required purpose. In cross ploughing clay soils, it is
essentially necessary that narrow furrows be used, in order that the land
be completely stirred, and none be left unmoved between the furrows.
The furrow must be to the depth, or even deeper than the winter plough-
ing, that abundance of soil be raised for the future operations. If the land
be very wet, the furrows must be opened by the longitudinal operation of
the common plough, after the cross ploughing is finished. In some places
the cross ploughing of wet clays is never done, but the lands are wholly
tilled by ploughing longitudinally, from dread of heavy deluges of rain,
inundating the land when all the furrows for the discharge of the water are
choked up. The working of the land is not so complete as by
cross ploughing, but the alternative is preferred.
Previous to the cross-ploughing being commenced, a skilful ploughman
is sent on a day or two previous, for the purpose of drawing straight fur-
rows across the field at the distance of twenty to thirty yards from the
continuous divisions. These furrows serve as marks to the ploughs when
the work is begun, and no time is lost by looking for directions to the pro-
cess. The marking plough goes and returns in the same furrow, and throws
out an open space in which the ploughing begins, and maintains a level
work on the surface of the ground. The two furrows of the commence-
ment of cross ploughing are laid together as a turnip drill, which is readily
done in the widely opened mark by the plough—a narrow comb thrown up
at the commencement of any ploughing, forms a blot on any pretensions
to skill in the art. The open furrows made in the spaces of cross ploughing
by the termination of the work, are to be filled up by ploughing in reverse
for three or four turns of the plough. This reversal prevents any opening
to remain after the land is harrowed and rolled.
Harrowing
The state of the land and of the weather will direct the
and rolling. application of the harrows or of the roll, in the first use of the
implements. In dry seasons, and on hard viscous clays, the harrows will
be unable to make any impression, and the roll must be used, even if four
horses are required to draw it. But the cost must not prevent the most
important purpose of reducing to dust, during dry weather, the hardened
clods of clay, and the masses of soil that are often produced by cross
ploughing. On soft clays, and in moist seasons, the harrows may be
immediately applied, when, with the intervening assistance of the roll,
the land will be reduced and pulverized, and weeds will be extracted.
The weeds and stones that this first operation is capable of
operation. eradicating must be without delay gathered by hand, and
carried away from the field. Little delay must occur in performing these
operations. In mild showery seasons, the weeds will quickly revive and
show a green appearance, of which no vestige must be allowed during
the process of the arable cultivation of land. The last harrowing of
the land and the picking of the weeds may go on simultaneously,
and be nearly finished together. The farm should possess a suf-
ficient quantity of strength to enable the furtherance in conjunction
of the processes of action that are nearly allied in the performance;
The first
ON LANDED PROPERTY.
901
the close connection must be studied, and the regulations correspond-
ingly adapted.
In the end of May, or in the first part of the month of June, Subsequent
the land is again ploughed, and done longitudinally, in casting operations.
together two or four ridges, and keeping open the furrows as the ploughing
is performed. The surface is immediately harrowed, rolled, and harrowed
again, and the weeds and stones are gathered by hand and removed from
the field. This operation constitutes the second cleansing process, and
puts the land into a good cultivated state. When the soil is a friable clay,
and not excessively hard and stubborn, the above ploughing may be
deferred for a time, in order to make the next furrow be the bed of the
dung and lime. But where weeds abound, or the land is very stiff and
viscous, another ploughing is given in the end of July, when the ground
is harrowed, rolled, and harrowed, and cleaned of stones and weeds as
before. This furrow reverses the last ploughing by throwing the ridges
in the contrary direction. The land will now be ready to re- Use of lime
ceive the lime, if any be applied, which is carried to the field in one way;
in hot cinders, and laid on the ground in heaps of one to two bushels on
a square perch, or a space of six yards by five. The quantity used on an
acre will regulate the size of the heaps, but one to two bushels is the
common average. A man with a shovel must be employed to lay the
heaps in a neat form, and cover them with earth, the moisture of which
will gradually reduce the cinders to powder. When this reduction is
effected, the whole of the heaps must be regularly and evenly spread over
the surface of the land, and immediately covered by a double tine of
harrowing. The process of spreading and of harrowing the lime must go
on together, by a combined arrangement, as a high wind will blow away
the lime if left spread and uncovered.
by burying
cinders.
Another method lays the cinders of lime in a longitudinal in another
heap on the headland of the field where it is slowly turned way;
over, and at the same time dissolved into powder by the application of
water; in this powdered state it is carried to the field, and spread from
the carts with shovels, in the space of one ridge, with the cart moving
along the centre. The quantity applied must be regulated by the eye of
the master in the thickness of the strewing on the ground. A new
method directs the hot cinders to be scattered over the ground,
and covered by the ploughing, when the moisture in the soil the hot
will dissolve the shells, and the land will derive much benefit
by the damp exhalations of heat that are evolved during the dissolution
of the cinders. As the powder will lie underground in lumps, a future
working of the land must be understood in order to spread abroad the
lime that is dissolved, and in at least two operations done lengthwise and
across the field. This necessity demands an earlier application of the
lime during the second stirring of the land in the month of June. When
the application is properly done at this period of the year, and the subse-
quent workings of the land are seen to spread the powdered lime in the
soil, this mode of applying calcareous manure must be very superior
902
ON LANDED PROPERTY.
to any other, as the caloric evolved by the hot cinders during the disso-
lution will penetrate the body of clay, sunder the particles, break the
texture, and pulverize the whole mass. It will also impart to the ground
a higher degree of temperature than it before enjoyed, which is the mode
by which lime communicates any benefit to the land.
Dung
applied in
broad cast:
So soon as the process of liming is performed, the dunging
of the land may commence. The heap of dung may be in the
field, having been carted to it during winter, or it may be at
the homestead, having been turned over in the yards. The dung is laid
from carts in small heaps on the ground, and in a row along the single
ridges of land; it is immediately spread evenly over the surface, and
covered by the ploughing of the ground. The dung must be well broken
from lumps, and scattered in small pieces over the surface, and must lie
uncovered for as short time as possible. Farmers who entertain nice
ideas on the subject of evaporation and loss by exposing dung on the
ground to atmospheric influence, appoint a woman or lad to follow each
plough, and with a light fork to throw into the furrow any lumps or clods
of dung that are pushed before the plough, and lie uncovered. This
simple precaution prevents any rough dung being exposed to view,
renders the work more complete, and is fairly worth the expense, though
the principle of loss by exposure yet remains to be proved.
A method has lately been adopted by drilling the land with one furrow
of the common plough, and laying the dung in the furrows. The plough
makes a drill by one furrow or rut in going the length of the field; the
dung is laid and spread along the hollows, the plough in returning covers
a drill of dung with one furrow, and the land presents the appearance of
being ridged with green crops. This method is superior to the broad
cast plan in covering the dung; and drilling the land is less work
than ploughing across. Harrowing will be required to level the
drills before the land is ploughed for being sown.
by drilling.
In ploughing the land this time, some attention is required that the fur-
rows are neatly ploughed out as the season is advancing, and floods of rain
may be expected; the two last furrows on each side of the closing being
always done by a plough drawn by two horses walking in "tandem,” in
order that the horses may not walk upon and damage the ploughed land.
It should be managed by a skilful ploughman, and the closing water fur-
row should be deep and narrow to suit the plough that draws the furrow
afresh after the land is seeded. A wide, open, gaping furrow with flat
sides is a great deformity in finished work: it is often seen, but is not the
less reprehensible on that account. The headlands being neatly gathered
up by the plough, the cuts at the ends and corners must be opened
into the ditches, and in this state the land waits the seed furrowing after
harvest.
Sowing of
wheat.
The month of October is the general season of sowing wheat
in Britain, when the land is neatly ploughed by one furrow and
the ridges gathered. The seed is sown by broad cast or by drill machine,
the water furrows are drawn by the plough, and the cuts made by the spade
ON LANDED PROPERTY.
903
when the process of cultivation is finished, which was begun about the
same period of the previous year.
straight.
A very considerable part of the clay lands in England are lying in
ridges of a crooked serpentine form, of unequal widths at the ends, and
often terminate in a point in the middle of the field. The working of the
land in consequence becomes very awkward; and many attempts have been
made to straighten the ridges, and in some cases successfully, from the
ridges not being very high nor very crooked, but in many attempts with
very great damage, from the contrary circumstances of height and shape.
By reason of the long continued gathering of the ridges in the olden mode
of cultivation, the subsoil has become convex as well as the upper soil, and
when a newly made ridge took a slanting or crossing direction over these
convexities, the water lodged in the hollows, and reduced the full half of
the land to a state of mortar: much loss was in many cases sus- Crooked
tained, and the failures had the usual effect of deterring other ridges made
attempts where the same obstacles did not exist. It has been
recommended to make a complete alteration at once by a levelling with
the spade, removing the too high subsoil to the lower places and then re-
placing the top soil; but this expense would in many cases exceed the
value of the land, and has been little used. When the ridges are not very
high nor very crooked, the alteration is easily effected by the plough, and
the harrows filling up the hollow places; and in extreme cases a very safe
method consists in making with the plough a narrow ridge of four or six
feet in width in the old deep furrows, and increasing it in breadth every
following course of fallowing till it rises and fills the hollows, and levels
the high ridges, when the new ridges may be drawn as nearly as possible
in the direction of the old ones, and then the water will obtain a gradual
flow. This method may be reckoned slow, but it is the safest and most
convenient yet practised, being wholly done by the common plough.
Turnips may be raised on any clay soils in the following way. Turnips on
The land may be wrought in the usual method into July by clay lands.
three ploughings and harrowings, when the dung is applied in broad cast,
and the ridges are gathered by the ploughing. The surface is harrowed
to the utmost possible fineness of tilth, when the turnip seed is sown in
broadcast, or by a drill with long coulters which make ruts in the ground,
and form the crop into rows. The hoeing of the turnips is done in the
usual way. It is supposed that clay lands will produce turnips by this
treatment, or some similar cultivation. The turnips grown on lands
pared and burned without being ploughed, show that the root of the
plant does not require a finely reduced body of soil, provided the surface
is pulverized to the degree that induces the early vegetation and growth
of the tender plant. The encouragement that is given on the surface of
the ground seems to secure the growth of the plant.
Green crop lands require the same early ploughing in winter as clay
soils, in the months of November, December, and January. The furrow
must be round in form and square in the cut, and to the depth Turnip
of seven or eight inches where the soil will possibly allow. Stiff lands.
904
ON LANDED PROPERTY.
loams may require the power of three horses to move the required depth
of soil. The average of seasons usually allows the second ploughing or
the cross furrow to be done in the end of March, or early in April, when
the furrow slices must be narrow, so as to leave no unmoved ground be-
twixt the motions of the plough, and that the earth turned over may not
lie in very large masses. A day or two previous to the ploughing being
commenced, a skilful ploughman is sent with poles to mark out the field
into spaces of twenty to thirty yards, which are made by a furrow of the
common plough, moving twice in the mark that is made. This provision
Working of affords a ready beginning of work, when a number of ploughs
the soils. are sent to the field. When the spaces of ground are finished
in the ploughing, the open furrows are filled to the level of the surface by
the furrows being reversed on each side in the extent of two or three
yards. The harrowing is immediately done and repeated till the clods of
land pass between the teeth of the harrows without being broken, the roll
follows in one application, and the harrows are again used to tear the
weeds and pulverize the squeezed clods. The three processes in the first
harrowing, the rolling, and the second harrowing, may proceed together;
and the hand-picking of stones and weeds can also accompany the opera-
tions. These nuisances are removed from the fields by carts very soon
after being gathered into heaps. The next ploughing is done lengthwise,
and in breadths of about thirty yards as before, and will be finished by the
end of April. The same rolling and harrowing, and picking of stones and
weeds are done as before, when the state of the land will show if the soil
be fitted to be planted with potatoes; if not, another ploughing must be
given without delay. The potato ground should be ready in
the third week of April, when the land is opened into drills of
thirty inches apart by one deep furrow of the common plough. The half-
rotted dung of the farm yards is placed in the intervals, and evenly spread
along by light forks in the hands of women and lads, who are super-
intended by a trustworthy man of the farm. The sets of potatoes fresh
cut are carefully placed by hand over the dung at the distance of eight or
nine inches apart, and pressed into the position by the foot of the person
that deposits the sets of the plant. The plough follows and splits the
drills, throwing a heavy furrow to the right hand over the dung, and in
returning along the opposite side throws another furrow of fresh earth over
the last mentioned, by which the dung is deeply covered with the loose
soil of the ground. A light roll passes along the finished drills and levels
the narrow tops, by which a uniform appearance is secured of the young
plants, and it ends the planting of potatoes.
Potatoes.
Beet-root.
In the second week of May, the land intended to be sown with
beet-root is raised into drills of twenty-eight inches apart; the
half-rotted farm yard dung is spread evenly along the furrows, the drills
are split and reversed by the plough, the seeds are inserted by dibble on
the tops at the distances of four to six inches, and a light rolling finishes
the process. Double drill machines are now fitted with large cups and
proper barrels to deposit the seeds of beet-root along the drills, and in both
ON LANDED PROPERTY.
905
ways a rolling of the tops must follow. It excludes drought and retains
moisture.
The sowing of Swedish turnips follows the planting of beet-root, and is
done in the ways that have been described, the seed being sown along the
tops of the drills by a machine of two rows, drawn by a horse and directed
by a man. The land to be sown with common turnips in June, Swedish
receives the last ploughing after the potatoes, and beet-root are turnips.
planted, being deferred till these operations have been finished. During
that month the turnips are sown with farm yard dung, as has been de-
scribed, and with bones and guano, and other auxiliary manures by the
drop drill, which deposits at fixed distances the manure and seed in mix-
ture. The seed is sown over the farm yard dung by the two drill
implements.
Drilling of
In all these operations of forming and reversing drills with the common
plough, the main tree of draught is five feet in length, which stretches
over the breadth of two drills, and allows the horses to walk widely, and
gives the ploughman a necessary sight of the forward objects. In reversing
the drills to cover the dung, the left-hand horse walks in the furrow of the
last split drill, and the horse on the right hand travels on the top of the
unmoved ridgelet, while the plough splits the intervening drill, and throws
a furrow of earth over the dung. By this method, the dung in
the drills is not disturbed by the feet of the horses as when the all green
animals walk in the intervals, and the advantage is very useful
in not treading on the sets of potatoes which are placed upon the dung.
The common plough is more beneficial in making drills than the imple-
ment with two mould boards. The narrow-pointed share penetrates deeper
and raises more fresh earth than the feathered share of the latter tool, of
which the bottom part of the two mould boards constantly heaves the
plough upwards, and dispossesses the hold of the ground.
crops.
When lime is applied on the green crop fallows, the pulverized material
is spread over the ground before the land is drilled, in the way as de-
scribed for wheat fallows, or the hot cinders are ploughed into the land,
which undergoes one or two subsequent workings in order to mix and dis-
seminate the reduced calcareous substance in the ground. In Lime used.
either way, the lime must come into contact with the soil,
when the former is in the hottest state that is possible.
Turnip soils are very effectually and economically brought to readiness
by the workings of Finlayson's harrow, or a similar grubber. The first
ploughing of the land is done in early winter to the depth of seven or
eight inches, which affords plenty of loose soil for the future operations of
the grubber. The spring working is done across the plough furrow, and
repeated in contrary directions till the proper tilth is produced. In the
intervals between the operations of the grubber, the weeds and stones are
removed by means of the action of the harrow and the roll. The circular
tines of the grubber drag the weeds to the surface, and does not
expose the land to drought as by the ploughing of the ground. working.
The soil is stirred and pulverized by the repeated action of the imple-
Grubber
3 K
906
ON LANDED PROPERTY.
ments, and the moisture is preserved by reason of the land not being
turned up. It promises to be a very great improvement in the working
of turnip lands.
Art of
ploughing
It may not be improper to conclude the notice of cultivation of land with
a few observations on the art of ploughing. The first and most
important thing to be attended to by the ploughman, is the pro-
per adjustment of the implement by means of the coulter and share. If
these parts of the plough be not properly set with a due inclination to the
land sideways, and to the earth downwards, the implement will never
move sweetly nor easily, it will be ever inclining to one side or the other,
go too deep or too light, increase the friction, and distress the animals,
and perform the work in a rough and unsightly manner. This nicety of
adjustment shows the skill of the ploughman; for, if well managed, the
implement should proceed with a very slight touch of the hand. The
plough must be held flat on the bottom, and not obliquely, and leave no
ridges or rafters, or land unmoved between the furrows. The furrow
slices must be all cut of the same width, and be laid at the same height;
if laid too flat backwards, or if the furrow itself and not the edge be per-
pendicular, the harrows cannot raise so much fine mould to cover
described. the seed. The cut made by the coulter in the side of the un-
ploughed land must be as perpendicular as possible, and neat and clean.
The reins extending from the bridle of the horse through an iron ring
fastened on the leather backband, are held on the rounded extremities of
the handles of the plough by means of a plaited groove on the end of the
rope, just before the hands of the ploughman; and with well-trained horses
a plough properly adjusted, and a tolerably skilful ploughman, the use of
the reins will seldom be required, except in turning the horses at the ends
of the field. The headlands must not be under twenty feet in width, so as to
allow room for the horses to turn without treading on the ploughed ground
and leaving footmarks-a most unpardonable blunder in the art of plough-
ing. The ploughman must walk with both feet in the furrow, and with
his body at ease and erect, speak seldom to the horses, and make no blus-
tering noise. Many very good ploughmen walk with one foot in the
furrow and the other on the unploughed land, but it rather spoils the
appearance, and seems intended to guard against any lateral movement of
the implement, which should be wholly prevented by the adjustment. The
horses must be trained to walk at a certain distance of space
from each other, in order that the ploughman may see clearly
forwards to rectify any mistake committed in the preceding furrow. The
horses must be yoked to move freely and easily, and as near to the plough
as not to impede the freedom of step, with a check rope extending from
the inside bridle of each horse to the harness or backband of the other,
in order to keep them fairly opposite to each other. It is better when a
single connection rope from mouth to mouth is only used; but this mode
requires animals of a very uniform temper, and much attention on the part
of the ploughman in training the animals to one rate of pace.
Practical
directions.
It is a very common opinion that any person may be a ploughman, and
ON LANDED PROPERTY.
907
Attention
required.
that the performance of the art requires neither pains nor trouble; but ex-
perience does not enforce the belief that the operations of any art whatever
can be properly performed without attention and trouble. No
doubt some processes are easier performed than others, and some
persons acquire the mode of performing them easier and more quickly
than others; but that aptitude is very far from being a general rule, and
forms no exception to the labour and attention that are universally found
to be necessary to eminence in any branch of business.
The subject of fallowing lands, either for grain or root crops, must not
be dismissed without reminding the cultivator that the proper performance
of fallowing constitutes the basis of all good and profitable husbandry; and
that if it be neglected, not only the crop immediately sown will suffer, but
the damage will extend to all the crops of the rotation. Cultivation means
that nothing grows on land except what is sown; and though this degree
of eminence may never be attained, as there ever may remain a wide dif-
ference between possible and ideal excellence, yet the nearer we approach
to it, the nearer we approach to perfection. The constant and vigilant at-
tention of the cultivator must be incessantly exercised to see that all and
every part of the operations be duly and strictly performed in the proper
season, and to the fullest extent that is required. He must not only give
orders that they should be done, but he must see that they are done; and
if negligently performed, have the process repeated, till satisfaction itself
be satisfied. True economy consists, not in getting things cheaply
done, as many persons erroneously suppose, but in getting them portance of
well done; and the effects of minute care are very great in in-
creasing the produce of land. The goodwill, activity, and energy of the
labourers must be secured and incited by good treatment, which is seldom
or never repaid with carelessness or neglect: exceptions do happen, but
they are few. The implements must be all of the first order, and kept in
full completion, ready when wanted, and never out of repair. The horses
must be spirited and active, well fed, and fierce as lions. The very best
ploughmen may be wholly lost with starved and useless animals; care is
misapplied, and wages are lost in the value. The mind that directs must
attract obedience, and not compel submission-lead his fellow-creatures in
the most noble of arts, from which he and they reap the same fruits, and
experience the same benefits.
Great im-
fallowing,
and of rota-
Rotation of crops, or the order in which the several plants that
are used as crops are made to succeed each other, forms a branch tion of crops.
of the profession of agriculture, than which no other part requires more
judgment, or more conspicuously shows the skill of the farmer; nor is there
any portion of the art on which the profits of the cultivator more certainly
depend. The effects of plants on the soil are very various; some have a
tendency to impoverish it much more than others; some bind and others
loosen it: hence it is necessary to attend to the peculiar nature of each
plant, and to examine in what manner its culture affects the soil. By this
means we shall be enabled to determine in what order we ought to ar-
range the crops one after another, so as to keep the ground always in
908
ON LANDED PROPERTY.
heart, and yet to make it yield the greatest possible produce, which two par-
ticulars form the grand object of a correct and systematic rotation of crops.
Alternation
of plants.
Culmiferous crops are such as have a smooth jointed stalk, and
mostly contain the seeds in chaffy husks. These, especially when
they are approaching the ripe state, draw their nourishment chiefly from
the soil, and derive but very little from the air; therefore, when they are
cultivated for seed, which is most generally the case, the ground cannot
fail to be impoverished by them. On the contrary, the same plants, when
young and clothed with verdure, will derive a considerable portion of their
nourishment from the atmosphere; and, therefore, a culmiferous crop when
cut green, or consumed in that state by animals, does little or no injury to
the land. A crop of hay, cut before the seed is ripe, as it should be, does
not much rob the ground. Leguminous plants, as beans, peas, and vet-
ches, extract, by means of the broad spreading leaves, most of the nourish-
ment from the air, and none of these plants when cut young injure the
ground, but if leguminous plants be allowed to ripen the seed, their effects
Seeded
crops.
Leguminous
plants.
on the ground are still much less severe than of culmiferous
crops in a similar condition. Other remarkable circumstances
distinguish those plants. All the seeds of culmiferous plants ripen at the
same time. As soon as they begin to form, the plant becomes stationary,
the leaves wither, the roots cease to push, and the plant when cut down is
blanched and sapless. The seeds of a leguminous plant are formed suc-
cessively; flowers and fruits appear at the same time in different parts of
the plant. This plant is, therefore, continually growing and pushing its
roots; hence the value of pea and bean straw over that of wheat or oats;
the latter is withered and dry when the crop is cut, the former is green
and succulent. The difference, therefore, with respect to the soil, between
a culmiferous and leguminous crop is very great; the latter growing till
cut down, keeps the ground in constant motion, and leaves it to the plough
in a loose and mellow state; the former ceases growing long
before being reaped, and the ground from a want of motion be-
comes hard and compact. And also dew falling on a culmiferous crop
after the ground begins to harden rests on the surface, and is wholly
evaporated by the next sun. Dews that fall on a leguminous crop are
shaded from the sun by the broad leaves of the plants, and sink at leisure
into the ground. Accordingly, the ground after a culmiferous crop is dry
and hard; after a leguminous crop it is loose, soft, unctuous, and mellow.
Bulbous rooted plants, as turnips, and especially potatoes, are superior to
any other in loosening, dividing, and pulverizing the soil: potato roots
grow generally eight or ten inches below the surface; and by their number
and size they divide and pulverize the ground better than can be done by
the plough; and whatever be the natural colour of the soil, it is black
when the potato crop is dug up. But carrots and parsnips are superior
even to potatoes in this valuable property; for the tap roots penetrate to
a depth of eighteen inches and more, and divide the soil in their
course. Turnips are rather inferior as the bulb grows above
the ground; but it is still much superior to a culmiferous, or a fibrous
Root crops.
ON LANDED PROPERTY.
909
rooted plant. Red clover is similar to the turnip in that respect. From
the properties now mentioned which the plants inherit, culmiferous crops
in a continued succession would render the soil too hard, and leguminous
crops would effect the contrary in making the land too loose; and hence
the necessity of making the one succeed the other in alternation, so as
to keep the land in a proper state, and at the same time produce the
greatest possible quantity of each crop.
ment of crops
In arranging any system of rotations of crops, no invariable rules can
be given which will prove adapted to all cases, because very much depends
on soil, situation, climate, and other circumstances. In the very variable
state of British soil and climate, no very fixed rotations can be prescribed;
but there are some material points to be regarded which no circumstances
must overlook. The crops must be suited to the nature and Arrange-
state of the lands, and the culmiferous and leguminous crops
must be interposed betwixt each other-and this method constitutes
what is called the "alternate husbandry;" but it has been found that the
lighter soils, are not suited even for alternate husbandry, and that they
require a rest in a state of herbage or grass in order to recruit the fertility.
Another general rule may be mentioned, that the same kind of crop or plant
must not be repeated at too short intervals, or both the produce and the
quality will be diminished. And this experience holds as well in green
crops as with the cereal plants.
The basis of every rotation must be held to be the summer fallows, and
the fallows on which the drilled and manured crops are cultivated; and the
conclusion of the course to be with the crop taken in the year preceding a
return of the fallow on the drilled crops when the rotation ceases, and a
new one commences.
cannot be
universal :
In mentioning rotations of crops as a most vital part of the science of
agriculture it is by no means intended to convey an impression of the
necessity that every farmer should and must bind himself to a
slavish routine, but only to direct attention to the study and con-
sideration of that branch of the art from which so many great and lasting
benefits have been found to proceed. A cultivator proceeding without a cor-
rect knowledge, or some knowledge of rotations, is not unlike a ship at sea
without a helm; but even with this knowledge, the real value of every
rotation depends, in a very great measure, upon the fidelity shown in
executing the several processes of labour that belong to it; though, in the
variable climate of Britain, no fixed rotation can be prescribed, yet some
rotations must be viewed as more valuable than others, because the crops
therein included may be most suitable to the particular soils on which
they are cultivated, or the produce may be better adapted to the market
demand of the country, which must ultimately regulate the kinds of pro-
duce that are most deserving of cultivation. Holding these points in view,
alternate husbandry, or the system of having leguminous and culmiferous
crops to follow each other, must be reckoned most judicious and
deserving of commendation, and with some modifications it may
be practised on any soil and in any situation. According to its rules, the
some are
general.
910
ON LANDED PROPERTY.
land would rarely get into a foul or exhausted state; at least, if foul and
exhausted under alternate husbandry, matters would be much worse if any
other system was followed. The rotation may be long or short, as is
consistent with the richness of the soil on which it is executed and other
local circumstances. The crops cultivated may be of any of the varieties
that compose the two tribes, according to the nature of the soil and the
climate of the district where the rotation is used; and where circumstances
render ploughing not so advantageous as pasturage, the land may remain
in grass till these circumstances are obviated, care being always taken
where it is broken up, to follow alternate husbandry during the time it
is under tillage. In this way, it is perfectly practicable to
follow the alternate system in every situation-nor is the cir-
cumstance of the land being in grass for two, three, or four years, any
departure from that system, as it is usually rendered necessary by the
scarcity of manure, poverty of the soil, the want or the distance of markets
for corn or other accidental circumstances. The basis of every rotation,
as before observed, is the bare summer fallow on clay soils, and the fal-
lows on which drilled and manured crops are cultivated; and the
conclusion of the rotation is with the crop taken in the year preceding a
return of the fallow or green crops, when of course a new rotation commences.
We
e now proceed to state the most approved rotations, on strong clays,
loams, on the lighter loams, and on sands and peaty soils.
Alternate
system.
The clay soils which have been found incapable of being reduced in
texture to suit the cultivation of green crops, may be divided into two
kinds the superior class, that produces very abundant crops, and con-
stitute the greater part of the arable lands in some districts; while the
inferior kinds, which much abound in this kindgdom, yield very scanty
and precarious returns. On clays of the best quality, and
in situations where manure is plentiful, a very favourite rotation
has been first year, fallow; second year, wheat; third year,
clover; fourth year, oats; fifth year, beans drilled and hoed; sixth year,
wheat. Manure may be applied on the oat stubble, or in the spring with
the beans, if the nature of the land will admit. In the most favoured
Rotation on
best clay
lands:
six years:
situations, this rotation is well adapted for alternation, and for
keeping the land clean, and in proper tilth. The four years
course of 1, fallow; 2, wheat; 3, clover, peas, beans or tares; 4, oats,
is much esteemed by many eminent cultivators, and may suit very well
on lands of good quality, but the recurrence of the same crop is too
frequent on land of any quality, and it is gradually giving way to a more
extended rotation. Where the land is loamy, and sufficiently mellow to
admit the growth of barley, rotations of six and eight years have
been followed, and they include a larger change of plants from
that circumstance: 1, fallow; 2, wheat; 3, beans, or peas; 4, barley;
5, clover; 6, wheat or oats: or, 1, fallow; 2, wheat; 3, pease; 4,
barley; 5, clover; 6, oats. Here the clover crop is too far removed
from the fallowing process, which supposes the land in the best state of
preparation for the reception of the small and tender seeds of grasses.
eight years.
A
ON LANDED PROPERTY.
911
Barley used.
shorter course is sometimes used: 1, fallow; 2, barley; 3, clover; 4,
beans, pease, or tares; 5, wheat and also: 1, fallow; 2, barley;
3, pease, beans, or tares; 4, wheat: or, 1, fallow; 2, wheat; 3,
pease; 4, oats.
These courses may be varied alternately with clover
in the third year. The longer courses most approved, are:
1, fallow; 2, barley; 3, beans; 4, wheat; 5, tares; 6,
barley, dunged on the stubbles; 7, clover; 8, beans; 9, wheat: and,
1, fallow; 2, wheat; 3, beans; 4, barley; 5, clover, dunged; 6, oats;
7, beans; 8, wheat. This course may be reduced to six years, by
not dunging the clover ley, and by making oats the last crop and
also 1, fallow; 2, barley; 3, clover; 4, beans, dunged; 5, wheat; 6,
tares; 7, wheat; the two wheat crops are here too near to each other,
and the fifth crop may very well take the place of the second. Another
course has been used as: 1, fallow; 2, wheat; 3, beans; 4, barley;
5, clover, dunged; 6, oats; 7, beans, drilled; 8, wheat. If the land
be clean and in tilth for clovers, this rotation claims much merit, and
may be improved by exchanging the fourth and second crops for each
other.
The following course possesses much merit, and joins the very valu-
bean and pasturage farming, a circumstance that is never met able course:
with, and which would rarely be allowed, by the common ideas of crop-
ping: 1st year, fallow, dunged; 2, barley; 3, clovers; 4, grass; 5,
oats; 6, beans, drilled and hoed; 7, wheat. The crops are well varied,
and the land derives the advantage of a rest in pasturage, which refreshes
the ground more effectually and durably than any manuring. Lime
may be applied on the bean stubbles, and the winter ploughing of the
fallow will secure a pulverized surface for the barley tilth, if due advan-
tage be taken of a dry state of the land for sowing. The action of the
lime might be better developed if applied on the barley or bean tilth, in
the spring; but if the climate and soil be precarious, they might prevent
the application. A better course can scarcely be devised; but it supposes
a loaminess in the clay to admit the growth of barley, which is wholly
denied by the viscous marine formations of South Britain. The rotation
originated with Mr. Grey, of Dilston, in Northumberland, whose name
has been already mentioned in the chapter on "Lease." The land on
which it is used is an alluvial clay on the southern bank of Tweed, near
Berwick, and consequently a fresh water formation. The idea arose from
the very frequent failure of the grass seeds when sown on the stale surface
of the winter wheats, and along with the exchange of barley with the wheat
on the fallow. Mr. Grey very judiciously combined the grass from Mr.
of two years, a system wherever adopted and perseveringly con-
tinued in the due performance, is always attended with the same results
of a very superior efficacy.
Grey.
In many places, the land is much too hard and stiff for barley, and then
the course of four and five years with beans and oats may be adopted. On
inferior soils of this description, the following course may be usefully
employed: 1, fallow; 2, wheat; 3, clovers, trefoils, seeds, or cinque
912
ON LANDED PROPERTY.
foils; 4, ditto; 5, wheat, or oats, beans, pease, or tares. The grass
crops may be prolonged if thought fit, and form a course of six years.
Another rotation for inferior clays has been recommended in, 1, fallow;
2, oats; 3, grass; 4, ditto; 5, ditto; 6, beans, drilled; 7, wheat.
And also: 1, fallow; 2, barley, wheat, or oats; 3, clovers; 4, ditto;
5, oats. A crop of winter tares sometimes precedes the fallowing process,
and are eaten on the ground; but the mode is generally imperfect, as a
Legumes
used.
very effectual part of the process is usually performed by the
time the first furrow is given to the land, and the state of
cultivation is always much inferior to the fallows that are effected
by winter ploughings, which have derived the benefits of atmospheric
action. The custom is not unfrequent on turnip soils; but even on
these lands, the fallowing tilth will be inferior, except in some few
particular cases.
Inferior
These courses of cropping suppose lands of good quality, and a capa-
bility in the soil of being drilled with leguminous crops, for the purpose
of preserving the land in a clean and pulverized condition. But on the
inferior clay lands of this kingdom, there is no possibility of drilling any
green plants; the dung may be applied on the autumnal stubble, and a
leguminous crop may be sown in the spring, but it will be
lands. a broad-cast crop, and confers no benefits on the land, and has
no tendency to defer the fallowing process. As it has been found im-
possible to assist the benefits of fallowing to the land by any inter-
mediate operation of dunging and pulverizing the soil, the rotations
of cropping on these lands are more curtailed, as the entire processes of
the rotation depend on the benefits of fallowing; and the quality of the
land will not endure the constancy of cropping that is practised on soils
of richer constituent quality. On all wheat lands, the operation of fallow-
ing constitutes the foundation of the whole course: if that be neglected,
the future produce will in every case be diminished. If the rotation be
formed of alternate cropping, the land is speedily exhausted, and the too
frequent recurrence of the operations of ploughing are known to tine lands
that are weak in texture and composition. These soils are generally of
two kinds,—one of a brick-like nature, and red or black in colour; the
other of a much softer texture; and both rest on a wet clay bottom, and
more or less retentive, and not unfrequently mixed with sands
Sterile clays. and gravels. Of all soils they are the most precarious to manage,
and yield the smallest returns. They are mostly, but not always, found
in inland situations, and distant from the sources of manure, and are unable
in themselves to maintain the animals that are necessary to afford the
requisite materials of that indispensable article. A farm wholly, or mostly,
composed of these sterile clays, is a very heartless concern; but they are
generally interspersed with portions of turnip fields, which very much im-
proves the management, on such soils. Wheat has been proved, in most
cases to be the most profitable crop, though many high-lying situations
will occur where oats may succeed better, from the climate being too late
for an early plant. The rotation of four years: 1, fallow; 2, wheat;
ON LANDED PROPERTY.
913
Four years
judicious.
3, grass seeds, mown or pastured; 4, oats, has been, and is yet very
injudiciously followed on these lands, for the farmer does not
possess manure sufficient to support constant cropping, and con- course in-
sequently a rest in pasturage must be substituted to recruit and
refresh the land. It has been proposed to sow pease, beans, and tares
during the third year in the field alternately; so that clovers may
occur only once in eight years. The following course has been very
profitably employed: 1, fallow; 2, wheat; 3, grass seeds, mown or
pastured; 4, pasture; 5, pease, beans, or tares; 6, oats. A course of
five years may be adopted by sowing any of these plants after pasture,
and would become : 1, fallow; 2, wheat, or oats; 3, grass seeds
mown or pastured; 4, pease, beans, and tares; 5, oats: or, 1, fallow;
2, wheat, or oats; 3, grass seeds; 4, pasture; 5, oats, or pease, beans,
and tares. In high latitudes that are unfavourable to leguminous plants,
the following course may be useful: 1, fallow; 2, oats or barley; 3, grass
seeds; 4 and 5, pasture; 6, oats. Many or most of the soils are physically
inappropriate for barley, and also for leguminous plants; and a Legumes and
failure of the latter crop invariably produces an abundance of grasses used.
weeds, and renders the land very foul. If the tare crop be eaten on the
ground by sheep, it would very much assist the following grain crop; but
the nature of the land is adverse to such a system, unless in some few
cases of soils and of seasons, that are of rare and unfrequent occurrence.
Pasture will preserve the land in a cleaner state, and adds to the vegetable
freshness, that will supply the place of manure, which the farmer does
not possess; and if leguminous crops cannot be obtained in fair quantities,
they had better not be attempted, and the poor quality of the soil prevents
the use of tares and clovers by being consumed on the ground, for the
crops themselves cannot be got in sufficient abundance to confer any
benefit on the land by that mode of manuring, the crop of hay being in
many instances too light to be cut, and must consequently be used in pasture.
A very general opinion prevails that grasses will not grow on these
lands, and certainly for the best of all reasons, because the seeds are never
But experience has proved that a close sward may be produced,
and sheep grazed and fattened without any danger from rot and other
diseases that are so much apprehended on wet lands of that description.
The fresh herbage of the sown grasses afford a wholesome bite, which is
renewed by a fresh sowing of the seeds, before a contagious deterioration
of the herbage takes place. It may not be improper to mention List of
here some plants that have been found to produce the pasturage grass seeds.
that is so very desirable on such lands :
sown.
bushel of rye grass,
bushel of cocksfoot,
6 lbs. of dogstail,
4 lbs. of catstail,
Per Acre,
4 lbs. of meadow fescue,
6 lbs. of red clover,
4 lbs. of white clover.
If the soil be damp and soft, and does not rank among the hard brick-
like clays, the quantity of dogstail may be diminished, and that of the
914
ON LANDED PROPERTY.
clays.
catstail and the meadow fescue increased. A mixture of rare and expen-
sive grasses would be altogether misapplied on such lands; and in case
of soils of any quality, it will be found more profitable to sow a quantity
of the seeds that are known to be best suited to answer the purpose, than
a mixture of plants that may never grow in any sufficient quantity, and
many of which are of doubtful value when obtained. The harder kinds
For barren of these soils should be reduced and pulverized, in the early
season, by the mechanical action of the plough and the roll,
harrowing will be of little use till the later season soften the very adhe-
sive composition of the clay. Lands of any description cannot be too
much reduced and pulverized, but they may be rendered too spongy and
vacant between the particles, which shows the necessity of consolidation
after a complete reduction had been effected. The black and softer kinds
will require less labour, as they will crumble spontaneously by the effects
of the late rains; and if power was applied to reduce the texture in the
early season, the soil would become too fine for wheat, and be apt to
throw out the plants during winter. On some lands, the early reduction
would be very difficult, if at all possible, but it would be attended with
the advantage of consolidating and acquiring a consistency by October for
the seed furrow.
On this latter sort of clay lands, leguminous plants have a better chance
of success than on the bricky kinds, and a crop of peas and tares may
be very profitably used in the rotation. A variation in the kind of plants
that are sown is thus obtained, and a benefit is conferred on the lands by
Legumes the smothering shade of the leguminous crops; but they ought
barely of use. not to be used unless a crop can be produced to cover the
ground closely and evenly, for a thin straggling crop of such plants is
the most pernicious to clean lands that is known. The grass seeds should
be sown on a surface that is pulverized by harrowing and rolling, and
then covered by a lighter application of the same implements.
Draining
Any improvements that may be contemplated to be executed
necessary. on clay lands, must be preceded by complete draining at the
distance of twelve to twenty feet, according to the extreme or partial
wetness of the soil; and may be effected by drains running straight,
oblique, or across the lands, as may suit the inclination of the locality.
Many of the better clay lands are at present in a high state of cultivation
in the neighbourhood of towns, and in favorable districts; but the greater
part is yet susceptible of very much improvement, and probably of more
profitable improvement, than any other kind of land in the kingdom.
The draining should be executed as a permanent improvement chiefly by
the landowner, with a corresponding assistance from the farmer, or it
may be done by the single expense of the farmer, on the proper security
of a lengthened tenure. The circumstance of all wet lands not being
drained, after the obvious and profitable results which have been obtained
by that improvement have been made known to every possessor of the
the soil, reflects a disgrace on those concerned, and who have both the
means and the power, hardly to be wiped away by the future tardy per-
ON LANDED PROPERTY.
915
water-
action of
formance. In the midst of the greatest rage and outward anxiety for
improvements, the most obvious, the most necessary, and the most certain
of any in the result, is much neglected, and without which operations in
that class of soils, all other improvements are in a great measure lost in
effect. The cutting and clearing the courses of brooks and General
rivulets must precede or accompany draining, and also the clearance of
opening of the receiving ditches round the field; and, after courses.
the complete drainage has been effected, the modern improvement of
ploughing the subsoil may be introduced, and followed by an application
of calcareous earths, limes, and chalks, in quantities of 300 to 600 bushels
an acre, in order permanently to alter and improve the texture as the
nature of it may require. Any general benefit that might be derived
from the use of calcareous matters on such soils is lost by reason of the
want of quantity, and from the land not being prepared for the mixture.
It remains to be seen what ultimate effect the complete drainage All neces-
will operate on these stubborn clays, if they will be converted sary for the
in any instance into a fit state for green crops, or only rendered cultivation.
more accessible at the different seasons, and easier of management by the
present mode of cultivation, in addition to the increased productiveness.
Some soils, from an original near alliance, may be rendered fit for green
crops, but the most truly clay lands are probably placed beyond that
possibility. When such improvements are required to be performed, they
should be done at once, promptly and effectually, for not only is more time
gained for reaping the benefits, but the frittering policy is avoided which
squanders the means of action on many points, and effects no object
completely, and by which the produce of each is lessened from want of
concentration to produce any satisfactory results. In no active business
of life has this policy, absurd and puerile as it must appear, been attended
with more mischievous consequences than in agriculture, for with some
very few meritorious exceptions, it pervades every arrangement and detail
of operations, and fetters and prohibits any very great advances in the
improvement of the art. When a quantity of means is allowed to effect
any object, it is very usually exerted on multiplied points of resistance,
and none of which is overcome by reason of the force being too small
that is applied to each, and consequently none of the objects are productive
of the expected results.
Covering
of land.
The general mode of reducing and working clay lands by
exposure during the heats of summer and the vicissitudes of
the weather is well known, and, in most cases, is performed in tolerable
perfection; but observation has shown that the covering of land produces
a fertilizing effect, and kills weeds; and it is probable that, at some future
time, there may proceed from this hint an important and valuable altera-
tion in practice, which may be ascertained by a few decisive trials made
on fair and tangible grounds, which do not in the smallest degree affect
the usual results of cultivation, and at the same time are fitted to justify
the conclusion. The covering that would be afforded by a crop of tares,
or a similar substance, to rot on the ground, might lead to some means of
916
ON LANDED PROPERTY.
accomplishing the purpose. Straw has been applied one inch thick as a
covering to wheat seeds pressed into the soil on untilled lands, and the
crop yielded a very large return of sound and healthy grain. The straw
would afford protection against both cold and drought, and also nutritious
matters by its decomposition, and the weeds will be effectually destroyed.
One good crop of any plant may be got from a single process, and yet be
inadmissible into a system; the means that are required for the purpose
May be of of protection must be carefully considered, and also the bearings
future use. on the future crops, and also on the other parts of the pre-
vailing mode of cultivation, as it may operate more damage in some
quarters than the advantages that are derived in another. Such suggestions
tend to confirm the seemingly very just opinion that all manures are best
applied on the surface, and that plants derive the chief part of their
nourishment from the atmosphere, and that the earth performs only a
secondary part in the process of vegetation. Dung covered in the soil
encourages an exuberance of roots and fibres, whereas all healthy and
soundly productive plants have the roots sharp, hard, and crisp, like the
claws of a bird. Wheat covered with straw on a plate of glass grew well,
which further confirms the theory. The present modes of production
are very laborious and expensive, and our investigations may probably
soon discover much easier and shorter roads, for in the progress of obser-
vation and of science, the necessity is daily felt of surrendering opinions
and maxims which have long been trusted and received on authority;
and we must not suppose that our observation and experience have
explored all the paths, or exhausted all the stores of nature.
Grasses for
cropping.
The grasses may be given which are suitable to be sown, with
the different rotations of cropping.
For a hay crop of one year,
Sow per acre,
bushel of ray grass,
bushel of cocksfoot,
4 lbs. of meadow fescue,
4 lbs. of catstail,
10 lbs. of red clover.
For hay of one crop and one year in pasture,
Sow per acre,
8 lbs. of red clover,
4 lbs. of white clover,
bushel of ray grass,
bushel of cocksfoot,
4 lbs. of meadow fescue,
4 lbs. of catstail.
The grass plants have been already mentioned that are proper to dry
arid clays in permanent pasture of two and three years.
On the subject of clay lands, and the proper rotations, the reader is
referred to "Clay Lands and Loamy Soils," price 1s., published by
Weale, and written by the author of this work. In that treatise, the
various kinds of clay are investigated and described, geologically, chemi-
cally, naturally, and practically, in a very systematic and detailed order ;
the proper cultivation of each kind of land is stated from the best
experience; the rotations of cropping that are suitable to each soil, and
ON LANDED PROPERTY.
917
the grasses adapted to the nature of the grounds. The comprehensiveness
of the little work very much enhances the value.
Turnip land
Best soils.
The second class of soils that was mentioned contains the
better turnip lands and the loamy clays, that are capable of rotations.
being cultivated and planted with green crops. These soils constitute the
most valuable class, and are capable of producing in abundance all the
plants that are held in the highest estimation for the purposes of hus-
bandry. The fallowing crops are: swedish turnips, potatoes, and mangel-
wurzel, being the most valuable plants that are known, and all of
them capable of being raised on these lands with due preparation and
encouragement. On many loamy clays, draining will be required, and
must be performed, before any other expense be incurred. These crops
can be removed to admit wheat being sown at the proper season, and
hence the high value of the land in producing the two crops of the
greatest value in succession. A course of six years is much ap-
proved on these soils: 1, green crops; 2, wheat; 3, clover cut
for hay, or used for soiling, or consumed by live stock on the ground;
4, oats or leguminous plants; 5, winter tares or late turnips consumed
on the ground; 6, wheat. On the four years' course: 1, green crops;
2, wheat; 3, clover; 4, oats. Beans, horse and hand hoed, may be used
along with the winter tares, in portions and alternately, as the rotation
goes on, and the land will then obtain a change of plants, and the green
crops may be varied to suit a similar mode of cultivation. The four
years' course: 1, turnips; 2, barley; 3, clover; 4, wheat is too short, and
the same plants recur too frequently; and it has been proposed to double
the course, and to extend it to eight years, thus: 5, cabbages or mangel-
wurzel; 6, oats; 7, tares or pease; 8, barley: and, for two years more,
9, beans; 10, wheat: and also, 1, turnips or cabbages; 2, barley; 3, clover
or tares; 4, wheat; 5, potatoes or beet; 6, barley; 7, clover; 8, oats or
wheat and also, 1, beet or potatoes; 2, oats; 3, clover; 4, wheat; 5,
turnips and cabbages; 6, barley; 7, beans, pease, and tares; 8, wheat.
The rotation of eight or more years is a repetition of that of four years,
with the object of changing the plants raised as green crops, and substituting
a leguminous and clover crop alternately, so that each occurs only once in
the course of the rotation. But this object may be attained by varying the
four years' course in the fields, as they occur for cropping in succession;
and if the soil be not all alike suitable for similar cropping, a change in the
plants will be necessary. A course of five or six years is most generally
to be preferred, and is found the most commodious, as it affords a full
opportunity of cultivating the most valuable plants, and also of profitable
alternation.
A course of six years has been very usefully employed-1, turnips and
other esculents; 2, wheat; 3, beans, pease, or tares; 4, barley; 5, clover;
6, oats; unless the land is very clean and in high condition, the
clover crop is too far removed from the clearing and manuring process,
otherwise the crops are well arranged. It is desirable that one crop is
918
ON LANDED PROPERTY.
Legumes
used.
eaten on the ground, as an auxiliary manure to support constant
cropping as a leguminous crop is proposed in a similar course
on clay fallows, and then the rotation would stand thus: 1, green crops;
2, barley or wheat; 3, clover; 4, oats; 5, vetches consumed on the
ground; 6, wheat and in five years thus: 1, turnips; 2, barley; 3,
seeds; 4, pease, or tares consumed in the ground; 5, wheat or oats.
Good lands, when well cultivated, will produce two crops of wheat in six
years, and will not require the fallow manuring oftener than once, as it
will have the benefit of a crop consumed on the ground. In some cases
of very favourable situations, the auxiliary manuring may be withdrawn ;
and if the fallowing for green crops occurs twice in six years, it is evident
that the rotation ceases. It is more pleasing to see a field under a crop of
one plant, than of many kinds-and if a farm be suitably divided, alter-
nation may be accomplished without much subdivision in that respect.
Inferior
These rotations apply to clayey loams of the very first quality.
lands. On those of an inferior description, and on the best turnip lands,
rotations somewhat different are used, including grass for two years, where
there are no grass or meadow lands for producing hay and pasturage for
the live stock. A course of six years includes the following crops: 1,
turnips, or other green plants; 2, barley or wheat; 3, clover; 4, grass;
5, beans, pease, or tares; 6, wheat or oats alternately on the fields.
A course of five years is followed by omitting the pease and beans, and
sowing oats as the fifth crop-or pease and beans may be sown in the
fourth year, and followed by oats. A course of eight years has been
recommended: 1, turnips; 2, wheat or barley; 3, clover; 4 and 5,
pasture; 6, oats; 7, tares; 8, wheat: or it may be limited to seven
years' by omitting one year of the pasture. These courses of cropping
are adapted to loamy lands, and it may be very safely affirmed, that no bet-
ter are yet known.
Grass seeds.
The proper grasses are, for hay for one year,
Sow per acre,
bushel of ray grass,
bushel of cocksfoot,
6 lbs. of meadow fescue,
12 lbs of red clover,
8 lbs of white clover,
bushel of ray grass,
6 lbs of catstail,
12 lbs of red clover.
For two years' grass,
Sow per acre,
bushel of cocksfoot,
6 lbs. of meadow fescue,
6 lbs. of catstail.
These soils produce large crops of hay, with a luxuriant pasturage, and
should be very liberally seeded.
Lightest
lands.
The third division of soils that was mentioned, consists of
inferior loams, sands, chalks, and gravels. These lands are chiefly
adapted for green crops, and for sheep feeding, and the quality in many
instances not permitting the production of an average weight of the
heavier roots, herbaceous and leguminous plants have been employed,
which yield a maintenance for sheep, and consequently a manuring to the
ON LANDED PROPERTY.
919
land. On the inferior turnip lands, the following rotations have, for a
long time, constituted a very successful practice: 1, turnips; 2, barley;
3 clover; 4, pasture; 5, oats; and on the lighter qualities of land: 5,
pasture; 6, oats and pease and tares may be sown on the grass turf,
to supply the demands of the farm. The great advantages that are here
derived, consist in the vegetable remains that are accumulated for decom-
position, and it has been found that land cultivated in this manner, yields
greater returns both in grain and in animals, than when used in constant
cropping of more than a usual proportion of the ameliorating crops, and
supplied with all the manures that the crop afforded.
For hay and 2 or 3 years in pasture,
Sow per acre on sands and gravels,
8 lbs. of red clover,
4 lbs of white clover,
bushel of ray grass,
bushel of cocksfoot,
2 lbs. of hard fescue,
bushel of ray grass,
bushel of cocksfoot,
8 lbs. of red clover,
4 lbs. of white clover,
6 lbs. of crested dogstail,
2 lbs of barley-like fescue,
2 lbs. of yellow oat grass,
2 lb. of upright brome grass.
On inferior loams,
Sow per acre,
4 lbs. of meadow fescue,
4 lbs. of crested dogstail,
4 lbs. of hard fescue,
4 lbs. of meadow catstail,
2 lbs. of yellow clover,
2 lbs of rib grass.
The land acquires a freshness and a consolidation from the rest it enjoys
under pasture-but it supposes a dampness in the soil and climate to
induce and favour the growth of grass seeds that are sown for pasture.
In many cases of the very hot and dry soils in South Britain,
Scorching
it is wholly impossible, to procure by any means, a sward of soils.
grass—and hence the necessity of using the green crops for sheep feeding,
and of sowing very few grain crops, and in a very diminished proportion.
On hot burning sands of the iron description, and on some chalks and
gravels, a grain crop very seldom succeeds; if the early months of the
year be dry and hot, a total failure very often ensues, where autumn
sown rye would yield a much greater produce both from its nature,
and from attaining a tall growth, and forming a shade to the
land before the scorching heats commence. The most inferior sorts of
these lands will be most profitably cultivated by a succession of three or
four feeding crops to one of grain for seed: rye, winter tares, and sum-
mer sown rape, may be succeeded alternately by turnips, rape, and spring
vetches, and relieved occasionally by a crop of clover and corn. On
chalks, gravels and sands of the better quality, a course may be adopted
thus: 1, turnips; 2, barley; 3, winter tares, consumed on
the ground; 4, rape, also eaten on the ground; 5, spring
vetches, also consumed on the ground; 6, rye for a seed crop, being four
feeding crops to two of grain: or, 1, turnips; 2, spring vetches; 3,
rye for a seed crop; 4, winter tares; 5, rape; 6, barley—each grain
Rotations:
920
ON LANDED PROPERTY.
crop having thus the benefit of two crops eaten on the ground. A crop of
clover sown at the rate of 30 lbs. an acre, may succeed the barley crop, and
may be cut or consumed on the ground as may be required. The very
inferior soils and burning sands may be well used in a similar manner,
with one crop of seed rye to four of the feeding plants-as, 1, turnips;
2, barley or oats; 3, clover; 4, tares; 5, cole. Thus rye, winter
vetches, turnips, spring vetches, and rye for feed, may be followed at
pleasure by turnips, barley, and clovers-and the lands may be then suc-
cessively cropped with those plants, and kept in good condition.
Peaty soils.
Peaty soils and lands that have been pared and burned may
be cropped in a similar manner, according to quality, and always
with a large and full proportion of the feeding plants. On clayey soils,
pared and burned: 1, turnips or cole; 2, oats or wheat; 3, grasses or
tares; 4, pease or beans; 5, oats; 6, fallow, followed by wheat and
grasses for several years. On thin clays: 1, cole; 2, oats; 3, pease,
beans, and tares, oats or wheat, followed by cole, oats, and grasses, for
several years.
On chalks, sands, and peats: 1, turnips or cole; 2,
barley or oats; 3, grasses; 4, grasses; 5, grasses; 6, oats; 7, tares or
pease; 8, turnips; followed by barley and grasses for a time: or, 1,
turnips; 2, barley; 3, grasses or trefoils; 4, ditto; 5, pease; 6, rye;
7, turnips, followed by barley and grasses.
For a more detailed, and separately arranged enumeration of the ro-
tations of crops, on loamy soils, the reader is referred to “Clay Lands and
Loamy Soils," price 1s., published by Weale, and written by the author
of this work. The various kinds and modifications of loams, are very
fully described, and the use and improvement specified and suggested.
The division of the different soils as above-mentioned, will comprehend
every possible variety-and it is presumed that the above rotations will be
applicable in most cases, with the variations that particular circumstances
and opinions are known to require.
Experience
Experience has now fully established the fact, that in a proper
of rotations. rotation of crops, a plant with a naked stem, and a farinaceous
seed should follow one with a branched stem and a fleshy root, which has
been taken from the ground without bearing seed-and if all these con-
ditions cannot be obtained, that some one of them, at least, must be com-
plied with. Wheat sown after clover, which is allowed to be the best
succession on light soils, fulfils all these conditions when it is sown after
beans, the condition of the preceding crop not ripening the seed is given
up, and consequently this succession is inferior to the other. It is not
possible, however judiciously the land may be manured, to raise the
same crops in regular succession, without loss and detriment both to
the land and in the quantity of the crops. Wheat and clovers answer
well in alternation, but not singly; and this shows that the same effect is
not produced in the soil by these two crops. Experiments have been
made by very eminent chemists, particularly by Macaire of Geneva, at
the request of Decandolle, the celebrated botanist, which lead us to sup-
pose, that in the formation of the seed, or other nutritious parts of plants,
ON LANDED PROPERTY.
921
the sap is digested, and that it takes up certain elements and deposits
others, which are the residue of the process-and these being Exudation
of plants.
no longer necessary for the formation of the seed, are rejected
by the vital action of the plant, and exude by the roots. Thus certain
inferior animals, which in many respects have some analogy with the
vegetables in their growth, as the "polypes," take in nourishment by the
same openings or pores by which the excrements are voided after diges-
tion; and the different constitutions of different animals enables one
class to feed on the excrements of another-whereas, no animal in a
healthy state, can derive nourishment from that which has already
been digested and voided. Our ignorance of the functions of Not fully
vegetable life prevents us from seeing the effects produced recognised.
on the sap, by the expansion of the blossom, or the ripening of the
seed; but experience leads us to perceive, that certain plants thrive
best after certain others—and that in this case, they are always of
distinct and different natures, and of different natural botanic families.
Macaire, and some other scientific men, observed the change that took
place in the water, in which wheat had been made to grow. They
found a deposit in the water of the nature of bitter extract, and this
they considered to be excrementitious. Beans grew well in this water; and
on the other hand, wheat throve in the water in which beans had grown.
The effect of fallowing land is explained on the same principle-the ex-
crement is washed out by the rains, or it is decomposed by the light and
air to which it is exposed by repeated ploughings thus the land is
"sweetened," -an expression very common among the farmers engaged in
fallowing. However interesting it may be to the curious en-
quirer, to ascertain the real causes, it is sufficient for the practical the best
farmer to learn by experience, what crops do succeed best after
each other, and how soon the same kind of seed may be sown again in the
same ground, with a reasonable prospect of its producing a good crop-and
this, after all, can only be learned from actual experiment and observation.
Experience
guide.
CHAPTER IV.
BUILDINGS NECESSARY ON CULTIVATED LANDS,-
DWELLING HOUSES, FARMERIES, AND COTTAGES
FOR LABOURERS.
THE farmer of land having obtained a security for the outlay Farm
of his capital in a lease of the proper duration, and being provi- buildings.
ded with a sufficient quantity of the means for the necessary operations of
cultivation, the attention is next directed to the provisions of the fixed
appendages of the farm, on which his capital is to be used, and his occupa-
tion has to be employed. The tenant uses a number and variety of tools
3 L
922
ON LANDED PROPERTY.
in the cultivation of the soil, some of which are possessed of life, and others
are inanimate, while many are fragile and evanescent, and require a frequent
renovation. All these articles, of whatever denomination, demand a pro-
vision for their use, and done in such a way as will lead to the utmost
fruition of the development. And the first implement to be considered
is the farmer himself.
Dwelling
house.
The increasing opulence, and gradual refinement of the age,
demand a provision of personal comforts, which are suited to the
station in society that is held by the individual representative. The
accommodation of the "Farm House" must be suited to the value of the
farm, and the habits and condition of the occupier. The opulent and exten-
sive farmer will require a very different kind of house from the humble
tenant of a small farm. He will expect personal conveniences suited to
his condition; and a man of good capital, accustomed to the conveniences of
society, will hardly consent to hire a farm which does not possess them,
The uniform progress of things leads to this natural condition, and the
state of the dwelling houses in any country is a very sure indication of an
improving, a stationary, or a non-progressive tenantry. The tenant who
is little superior to the condition of a labourer, will be satisfied with a com-
paratively humble dwelling, and his physical comforts would not be any
way increased by furnishing him with a house superior to his habits and
ideas. Hence the dwelling houses of farmers are to be varied, and uni-
formity is as little admissible in that department of social life, as in any
other branch of occupational business.
Its accom-
Assuming the medium size of farms at 300 acres, the possessor of that
extent must have a capital of £2000 to £3000, and the deriveable annuity
from this sum entitles the receiver to a genteel and comfortable residence.
The accommodation of the house must be respectable, and afford
modation. the proper conveniences to the tenant and his family. In the
present social ideas, a division is required between the master and his ser-
vants; and the sitting and sleeping apartments of both grades must be
separated. This arrangement requires the dwelling house to be two stories
in height, and the ground floor to consist of apartments in which
Apartments. the inmates are separated in employments, and in the places of
abode. The master's family requires a sitting room, in which to live pro-
miscuously, and where the sittings and the conversations are done-and
another room for the purpose of assembling at meals, and which is kept for
that sole use. The farmer will need a room for his business of accounts,
and for the visits of his employés-another room is very useful as a nur-
sery for the children; and where no family is, it may be used as a spare or
lumber room. The accommodation may extend to five rooms, and must
not be under four, in order to meet the extent of capital employed, and which
demands some comfort for its use. There must be a kitchen of suitable
dimensions, and a scullery or back kitchen adjoining, and also a pantry and
dairy. These apartments are most conveniently placed in the back part of
the dwelling house, and to open into the area behind, which contains the
fuel and the ashes, and other minor conveniences. The second floor is di-
ON LANDED PROPERTY.
923
vided into four or more bed rooms and closets, which will accommodate the
family of the farmer, and the occasional visits of a stranger. The sleep-
ing apartments of the servants are reached by a different stair from that by
which the family ascend.
Our limited purpose does not allow a very large advance into General
the subject of farm buildings—a general description and exhi- description.
bition can only be given; but at the end of this chapter, references will be
given to special publications on the subject, which contain a large variety
for selection, and an utility that ever must accompany all such devices.
Two designs are here given of dwelling houses, which will show the intent
of our purpose, and point to the accommodation that is thought to be
required.


K
J
E
L
H
E
D
G
F

Га
M
O
0
C
NMIZ
B
N
A
ס!
سانس
10
20
2-
0
0
80
40
3-30
50 FI
A Sitting Room.
B Best Room.
C Kitchen.
D Scullery.
E Lumber.
F Ashes.
G Yard.
H Fuel.
J Wash-house,
K Privy.
I Dog.
L Dairy.
M Closet.
N Stairs.
O Bed Rooms.
Plan, No. 1, contains two rooms in the length, and is entered by a cen-
tral front door, and by turning to the right and left. The fire-places are
in the gables, and each room has a window in the front. The lobby leads
to the back apartments, and from it the stair springs to the second floor.
The second floor is divided into three bed rooms and a closet, for the family
of the farmer, and a sleeping apartment for the female domestics. The
rooms are all specially marked in the plan.
Extra
buildings.
It is absolutely essential to every habitation of civilized nature,
that there be some back buildings for the performance of dirty
operations, and for keeping articles out of sight that never should be seen.
The position of these accommodations is best right behind the dwelling
houses, in the length of the dwelling, and joining it at the ends. The
dairy occupies the east side, as being a cool exposure; and there are placed
in the small square, as seen in the plan, a wash-house, lumber room, a
house for fuel, ashes, and a privy, and an apartment for a dog. These
erections are low, and stand as lean-tos on a wall that surrounds the en-
closed area.
This house is suited for farms of 200, and to 300 acres, and presents a
924
ON LANDED PROPERTY.
very snug accommodation. The garden may be in front, or on the west
side, as will be afterwards discussed, when mention is made of the general
position of farm buildings in the useful connection.


N
M
•
L
J
K
G
ரு
E
F
P

I
H
F
D
C
D
Q
Q
E
B
R
R
A
R
R
10
20
20
30
40
50 F:
M Privy.
N Wash-house.
A Sitting Room.
E
Stair Closet.
I
Kitchen.
B Parlour.
F
Stairs.
J Yard.
C Passage.
G Larder.
K Fuel.
O Lumber.
D Rooms.
H Scullery.
L Dog.
P Dairy.
House end
for front.
Q Servants'
Rooms.
R Bed Rooms.
Plan, No. 2, is calculated for extents of land in 300 and 400
acres. The end of the house stands for the front, which is entered
by a porch. The house is of double width, and contains two longitudinal
ranges of apartments. which are covered by two tiers of roofing, that meet
in a central valley, along which the water flows to the back end of the
dwelling. The central passage of the house leads to the kitchens, which
stand across the dwelling, and have a side door opening into the back area,
of small accommodations, as in the last design. The sleeping apartments
are arranged and divided for the family and the servants, according to the
ideas already expressed, and the former plan.
The houses are built with mortar, stones or bricks, as the mate-
Materials. rials may abound in the locality. The rooms are floored with
deal, and the kitchens are paved with flags or flooring bricks. The side
walls and ceilings are plastered in the usual way, and in the better
rooms are covered with paper. The second floor is joisted and laid with
deal in the common method of finishing such work. The roofs are covered
with tiles or slates, as the locality may direct.
A good sized garden for growing fruits and vegetables is a most
useful, and, in fact, a most essential appendage to any extent of land
that is intended to be let for cultivation. It must be made into shape,
and very amply provided with fruit trees and shrubs, by the expense
of the proprietor; and when suitably accommodated, it constitutes
ON LANDED PROPERTY.
925
a very great inducement to the occupation of the farm by wealth and re-
spectability: when joined with a commodious and neatly furnished dwel-
ling house, a very large portion has been accomplished in these two
appendages, of the fixed provisions which constitute the necessary furniture
of a farm. The farmer himself must be first accommodated, and then will
look to the maintenance, in comfort and safety, of the live and dead stock
of his employment. The landowner sadly neglects his own interest, who
omits the above-mentioned provisions, on a scale that is rather above than
below the standard which the occupation may seem to require.
Farmeries.
Description.
Farmeries constitute the mass of houses which are grouped to-
gether for the special purposes of the tenant of land, and are a very important
part of the fixed provisions of the farm. The houses are designed to enable
the farmer to thrash, prepare for use, and lay in store, the produce of the
ground to lodge and feed the horses, and other labouring cattle, and to
separate, shelter, and fatten the oxen, and other live stock; to preserve
the implements and machines; to collect manures; and generally to carry
on the works that are required to be performed under the shelter of roofs
and buildings. The principal parts of the farm houses are the barns, the
stables, the feeding houses, the yards or courts, and the shed for containing
the implements and machines of the farm. The barn consists in
a ground floor, on which the thrashed grain falls from the upper
floor, where the machinery is at work, and where it is dressed by fanners
and made ready for use. The straw is thrown by the machinery into an
adjoining house, called the straw barn, in which the straw is lodged, and
whence it is carried as wanted for the different purposes of use.
buildings are required to be two stories high, to lodge the thrashing ma-
chinery on a second floor, and to afford room in the straw barn, for the
accumulation upwards of the thrashed culmy materials. A central position
must be given to the barns, as a very frequent access is required.
shed for implements demands a northern exposure, in order to
preserve the tools from the heats of the sun, and being vacant
below on the ground floor, it affords the best store room over it for the
lodging of thrashed grain. Two stories in height afford a shed, and a
granary over it; and the building most conveniently adjoins the thrashing
barn, in which an inside stair leads to the granary floor. A house for
holding small tools, under lock and key, adjoins the cart shed, and is floored
over with it.
These
The
Sheds and
Stables.
The stables are contrived to lodge the work horses of the
farm; and the house may be only of one story in height, but open
to the top of the roof, and no floor over it. Each animal stands in a trevise
of six feet in width, and is provided with a rack in front, and a manger by
which to be fed with hay and grains. The width of a stable within walls
may be eighteen feet, and the ventilators placed at the ridge of the roof.
A hay house adjoins the stable, and in it the corn chest is placed, into
which the grain descends by a spout from the granary above. Young
horses are kept in yards during winter, and are introduced to the stable
as they are broken to work. The riding stable is fitted for, at least, three
horses, in the same way as the working stable.
.
926
ON LANDED PROPERTY.
Cow shed.
The cows, which breed the fattened animals of beef demand
a very suitable accommodation; and as some part of the milk
will be required for domestic purposes, the position of the cow shed is most
commodious on the west side of the farmery, where it will be near to the
dwelling of the farmer. The animals enter most conveniently by an end
door, and stand in double trevises of two together, and are tied by chains
round the neck. The house for lodging the calves adjoins the cow shed,
where the young animals are confined in single pens of about ten by four
feet, divided by wooden partitions, and on a boarded floor, thickly pierced
with auger holes, in order to convey the moisture into the vacuum under-
neath. If suckled, the calves are led by halter to the cows: if fed by pail,
the door of each apartment is provided with an opening in the centre,
through which the calf puts its head, and drinks the milk.
houses, the riding stable, hay house, and gig house, are one story in height,
and form the west wing of the farmery, which adjoins the dwelling of the
farmer, and are convenient to the special purposes.
Feeding
Yards.
These
Experience not having yet decided the single superiority of
the two modes of fattening cattle, tied in stalls, and loose in
yards, both ways may be adopted; and accordingly a feeding house is
placed in the farmery, in which any backward animals may be forwarded,
and any choice beasts placed for the first selection. The animals stand in
double trevises, and are supplied with roots and hay from houses that adjoin
each end of the feeding apartment. The yards are divided into large and
small extents for young cattle and feeding beasts. Each yard has a shelter
shed, in which the animals repose from colds and heats.
Swine and poultry are so wholly distinct from horses and cattle, that
they are much best kept in separate apartments, of which designs and ex-
planations will be given.
Liquid
draining.
The liquid excrements of the farmery are most beneficially
absorbed by the straws and litter of the yards; but if the
quantity of these articles be deficient for that purpose, oozings may be led
and conducted to a central point, in front of the farmery, and fall through
an iron grate into a covered drain, which conveys the urine to a tank, in
which a mixture is made with earths and vegetable matters. But on farms
that are systematically arranged and conducted, the straws will be in abun-
dance to absorb the urinary feces of the proper quantity of animals. In
very rainy countries, the rain water from the roofs of the houses is inter-
cepted by spouts at the eaves, and conducted from deluging the yards with
moisture. Water is supplied to every part of the farmery, by conducting
water from higher ground to an elevated cistern, where pipes lead it to
troughs, and supply it to them by means of ball cocks or a force-pump
raises water to the cistern, which supplies it as above.
Remarks.
All enlightened practical men have agreed for a long time
past in the opinion, that there is not a wider field to be seen at
present in any branch of rural economy, than appears in the arrangement
and construction of farm buildings. Very great and beneficial alterations
have certainly been made within the last half century, and which are in
some degree corresponding with the extensive improvements in other bran-
ON LANDED PROPERTY.
927
ches of the rural art; but in many parts of the kingdom, it may be said that
any advances on that point have not yet commenced; and even where a
considerable progress has been made, or at least attempted, a suitable effect
has not been produced, from want of the necessary knowledge and judg-
ment in adapting the extent of the accommodation to the purposes required,
and in combining and adjusting the utility of the whole concern with the
proper expenditure. From looking at the present state of farm Bad arrange-
buildings over a great part of the United Kingdom, it would ment.
appear that ingenuity had been employed to devise and erect the most
awkward and useless forms imaginable. Declivities are chosen for the sites
of farmeries in order, it is said, to keep the yards dry, and, at the same
time, to discharge the whole quantity of moisture into ponds and ditches,
or into the ruts of a public road; the straw lies dry and unreduced, and
becomes very unfit for the purposes of manure. The houses are scattered
and disjoined, and require a useless quantity of fencing to connect them—
the yards are large, open, and exposed, and afford a very insufficient ac-
commodation and shelter to the animals, and no proper means of preparing
manure in the most approved and economical manner. The useless expen-
diture in building large timber barns has been long condemned by every
practice of enlightened knowledge-being an expense fully double of what
is required to be used on that point alone. The same latent bar-
barisms of the mind that retard improvements on other points in use.
operate with full force in this respect-an aversion to make the necessary
outlay, and a general and very strong inclination to continue the old usages
and erections at the least possible expense, and to repair and patch up so
long as any possibility exists, and the want of security in the case of any
person, except the landowner, expending capital even for such a necessary
and essential purpose. An improper expenditure, might, no doubt, be in-
curred, by making a number of extensive alterations at one time; but by
gradually introducing the best plans, as occasion may require, and oppor-
tunity offers, either piece-meal or altogether, an important and valuable
change would soon be made, which would show a very different result from
the frittering policy generally pursued, of expending money on many
points, which only serve a temporary purpose, and which, if combined, and
directed to one or more chief objects would introduce some positive bene-
fit in one place, and then in others, as it may be successively applied.
Continued
In consequence of the general aversion to make the necessary New designs
outlay, and the adoption of a temporary system of management, necessary.
few opportunities occur of showing a suitable and economical erection of
buildings on any farm; but few farmers will refuse, and offers are made
to pay the usual interest on the cost of an improved farmery for the lease
of twenty years; and such an erection will always be an inducement to pay
a higher rent, and will become itself a capital in money, paying the usual
revenue of profit. A certain class of cultivators will deny that any im-
provements can be made-and another class, more irrational still, will
acknowledge that the suggested improvements are all very good, but that
they are not required, and are unnecessary-reasons that cannot for a
moment be admitted by any intelligent mind. In many places, where large
928
ON LANDED PROPERTY.
>
Proper
expenditure.
sums of money have been expended in erecting farm buildings,
very glaring blunders have been committed, and much ignorance
has been displayed, even of the most simple and evident details of prac-
tice, arising from the incompetency and conceit of the persons employed
who have never practised the art they pretend to assist, and therefore do
not know the wants they attempt to supply. The land-owner very gener-
ally makes an unprofitable expenditure upon unnecessary erections, and in
useless decorations; or is led away by the plans of architects, who, however
well qualified to plan and build dwelling houses, gothic windows, and spiral
columns, experience has shown to be most miserably deficient in contriving
and placing the accommodations that are required on a quantity of land in
Judgment
required.
cultivation. The economy of labour that is derived from the
juxtaposition of articles that are required to act or to be used in
combination, has been wholly disregarded, if the advantages were fully
known-barns and rick-yards have been placed at opposite sides of a large
farmery-stables and cart sheds in a similar manner, and the
granary placed
at a distance from the barn, for the evident purpose of creating useless
labour in carrying the grain from one place to the other. Farm horses
are often allowed to enter through a cattle yard, and, in many cases, must
travel round the farmery in order to reach the cart shed. Pigs are huddled
into some cold damp corner, and the poultry are similarly treated, and the
door of the house is often found opening to the north, which is the coldest
exposure of any quarter of the heavens. These two kinds of live stock
require much warmth, and a sunny exposure, and their common treatment
is just the reverse. Many similar blunders might be pointed out which
must be obvious to any experienced person, and which abound in the best
Experience publications on the subject. However simple the matter may
necessary. appear, no person is capable of devising plans of convenient
farmeries, without the most intimate knowledge, from long and extensive
experience, of the most minute details of practice; and the first requisite
is to ascertain the number and size of buildings that may be required on
any lands under a certain system of cultivation, without too much curtail-
ment to create inconvenience, and without any useless appendages that
require an unnecessary expense-and then how to connect them, so as to
afford the greatest possible convenience with the least possible labour.
General
mistakes
In planning farmeries, two mistakes are very apt to be committed-to
extend the buildings too much, and make the yards cold and uncomfortable;
or to make them too confined, and consequently deficient in ventilation and
fresh air. It is no easy matter to steer midway of the two extremes : situation
and exposure will claim much of the direction of the arrangement, which
local experience only can know and estimate. Hence arises in a
very great degree, the frequent occurrence of a wrong exposure
and of insufficient accommodation-of one thing very good, and another
very bad, placed side by side-all showing the paucity of ideas on the
subject, and the niggardliness of execution. With the present accom-
modation, as it is most generally found, the farmer cannot use the winter
crops so as to derive the full value; he is consequently discouraged, and
has not the proper inducement to expend his capital on the legitimate object,
ON LANDED PROPERTY.
929
Best forms.
or the cultivation of the soil, and the increase of the quantity of produce.
In the best shapes of farmeries, the form of a parallelogram
is preferred, with the front open to the south, so as to admit the
beneficial effects of the rays of the sun, and without any houses being
placed in front, which would exclude that enjoyment. The building
consequently consists of three sides or wings, with interior accommoda-
tions. For the purpose of illustration, we are able to give three designs
of farmeries for extents of land from 200 to 500 acres, which may be in-
creased or diminished so as to suit any intermediate size of a farm.

K
G
Q
囲
​
I
J
A
R
B
C
H
ЈЈЈЈЈЈ
L
P
S
P
0
-
T
T
T
T
T
M
S
S
D
E
H
p
F
N
A Barn.
B Straw Barn.
C Cart-shed.
D Tool-house.
10
10.
E Stable.
F Box.
G Gig-house.
H Hay-house.
20
I
40
Store-house.
J Gangway.
K Riding-stable.
L Calf Pens.
60
80
M Cow-shed.
N Feeding-house
O Root-house.
P Road.
100 FT
Q Engine.
R Machinery.
S Sheds.
T Yards.
930
ON LANDED PROPERTY.
Farmery
No. 1.
Plan No. 1 exhibits the accommodations ranged in the order that
has been mentioned, and with an interior road between the build-
ings and the yards. The room thus occupied has been made an objection, but
it yet remains for decision if it be not the readiest access to every situation,
and the most convenient arrangement yet devised. The dwelling-house of
the farmer is supposed to stand on the west side of the farmery, and, with the
garden behind it, will equal the extent of the range of conjoined buildings.
The west wing is occupied with a cow shed, calf pens, hay house, riding
stable, and gig house: these appendages will be convenient to the pur-
poses of the farmer's domestic use. The walls are 10 feet high, and made
with mortar, stones, or bricks. The cow shed and stable are pitched with
stones; the other houses have earthen floors. The north wing is formed
of houses of the height of two stories, and are a spare house, gang-way,
thrashing barn, straw barn, cart shed, and tool house. The walls are 24
feet high, and the whole range of buildings is floored with joists and
boards, at the height of 14 or 16 feet from the ground. The floor of the
barn is of boards; the other houses have the floors of earth. The east
wing of the farmery contains a stable for the work horses, a hay house, a
feeding house, and a house for holding roots. The walls are 10 feet high;
and every house, and also of the west wing, are open to the top in the in-
side, and have no floors over the tops of the walls. The horses enter and
leave the stable by an end door, which does not disturb any yard where
cattle are confined.
Arrange-
ments.
The interior room of the farmery that is contained between
the three wings, is diminished by the road, which is 20 feet in
width, and the remainder is divided into yards for store and for feeding
cattle, as shown in the plan. The road is pitched with stones, and the
yards are dug in the bottom to the hard concretion that is beneath the
soft soil. The shelter sheds are twelve feet in width, and low in the
roof. The ricks of grain stand on the north side of the farmery, and are
carted to be thrashed into the gangway, whence the sheaves are
thrown on the second floor of the barn, where the machinery
is at work: they are immediately handed to the person who feeds the
scutchers.
The piggery and poultry yards are made separate designs, and are
placed as shown in the plan: the piggery on the east side of the farmery,
and level with the front of it; and the poultry yard in the centre of the
farmery, and in front of the whole erections. The walls being low will
not intercept the sun from shining on the yards of the farmery. The
piggery breeds and feeds swine on a large scale, as every extent
Piggery. of land in use ought to be held as a manufactory of raw and
finished produce. The boar and brood sows are separately and singly ac-
commodated, and the store pigs have a large yard well littered, with
shelter sheds, and a pond of water in which to roll and wallow. The
feeding hogs are two in a sty, and are there fed with steamed potatoes
mixed with meals, which are prepared in the cooking house, as shown in
the plan. A light iron waggon on four wheels conveys the food along the
ON LANDED PROPERTY.
931
passages, which are laid with flags. The store pigs are fed in the yard
during summer with clovers and vetches, and in winter with potatoes,
turnips, and beet-root, raw or steamed, or in both conditions.
The poultry yard shows a house for each kind of animals, and a hatching
house for all sorts. The young broods are conveyed to small cribs, and
there confined till grown strong to go abroad. A fire-house cooks the
food in steamed or boiled potatoes, which are given to the poultry along
with dry grains, in troughs, in the shelter sheds, which protect Poultry yard.
the animals from rains, storms, and suns. A pond of water in
the centre floats the ducks and geese. Poultry in turkeys and hens are
natives of hot countries, and require much warmth; and hence, the great
fecundity of poultry that roost in labourers' cottages, and enjoy the heat of
the dwelling. In the plan now given, the houses are heated by pipes
from the boiler of the cooking house, that convey heat to stones in cast-
iron pots below the floor, which retain heat for a long time, and impart
warmth to the whole apartment.
Arch.
Pigeon-
house.
An arch may be raised over the south-end of the roadway, on
which a pigeon-house may be placed, and the top surmounted
by a clock. This latter appendage is very useful for maintaining order
and regularity in the operations of business. The floor of the
pigeon-house may be of boards, and hung upon hinges, which
will let fall the floor when necessary and discharge the excrements on the
ground beneath. This provision will save the inconvenience of intruding
on the pigeons, and the trouble of collecting and heaving the quantity
of excrements.
Farmery,
No. 2.
Plan, No. 2, shows the buildings arranged, as in the last design, but a
very wide difference in the interior of the farmery. The road of access is
placed outside the two wings of the buildings, and the feeding yards are
in consequence advanced close to the walls of the houses. The
shelter sheds are placed in two central rows, between which a
railway runs from the stores of roots in the rick-yard through the straw
barn, and conveys potatoes to the cooking house of the piggery and poul-
try yard, and turnips to the cattle in the sheds, which receive the roots
through holes in the wall. This facility of conveyance saves much
labour in cartage and manual work. Straws for litter and hay for pro-
vender are conveyed on the same passage. The piggery and poultry yard
are joined in this plan by which one cooking house serves both departments
with the steamed roots for being mixed with meals. The buildings being
low in the walls, will not much obstruct the rays of the sun from shining
on the yards of the farmery.
Ricks of
grain.
The ricks of grain stand in two rows, which extend the width
of the farmery, and between the rows a railway conveys on a
light waggon of four wheels the unthrashed grain to the machinery, and
is turned into the gangway by a turn-table on the main line of
rail. The ricks may not be thatched, but are covered by a roof
of corrugated iron, which extends over both rows, and rests on cast-iron
pillars, which stand on each side of the rows of ricks. The introduction
Railway.
932
ON LANDED PROPERTY.
of railways is a great improvement, as it strengthens power and dispatches
business. This design of a farmery possesses much merit.

G
H
J
L
E
H
J
G
F
E
B
M
A
K
12
N
Р
mimi
R
T
S
T
S
T
C
D
T
8
p
J
m
n
N
S
Z
a
O
S
10
20
40
S
d
T
f
h
મ
T
+
•


I
I
P
U
T
E

9-3
60
80
100 FT
A Straw Barn.
B Barn.
C Cart-shed.
D Tool-house.
E Root-house.
F Spare-house.
G Ricks.
H Store-shed.
I Stable.
J Railway.
K Gangway.
L Engine.
O Riding-stable. Poultry Yard and f
P Hay-house.
Calf-pens.
R Cow-shed.
S Sheds.
M Machinery. T Yards.
Piggery. g
a Yard.
b Shed.
Sties.
m Roost.
Feeding sties. n Hatch.
h Store-yard.
i Pond.
C Food-house.
j
Cribs.
d Vats.
N Gig-house. U Feeding-house e Fire.
k Ducks.
L
Geese.
o Turkeys.
p Pipes.
ON LANDED PROPERTY.
933

P
N
X
• K
Y
F
B
A
Υ

D
E⚫
W
G
L
T T
2
K
G
T
R
G
20
G
b
n
a
T
Ꮓ
L
H
X
M
G
T
T
b
K
G
ប
G
V


a
F
e
k
F
A Barn.
d
B Engine.
C Machinery.
D Straw Barn.
E Cart shed.
F Spare-house.
G Sheds.
H Box.
го
I Stable.
تسلس
J Tool-house.
K Hay-house
L Yard for
young horses.
M Yard for store
Pigs.
FFFFFF
k
h
2-
20
40
60
80
100 FT
O House for pro- V Root-house.
vender.
b Fire.
j
W Stairs.
C Vats
Turkeys.
k Geese.
P Gig-house.
R Calf-pens.
X Railway.
d Ponds.
e Sheds.
1
Ducks.
m Roost.
Z Roads.
Piggery. h Store-yard.
Q Riding-stable. Y Ricks.
f Feeding-shed. n Hatch.
S Cow-shed. Poultry Yard and g Sties.
T Yards.
N House for bull U Feeding-house a Food-house. i Cribs.
and stallion.
o Pipes.
Plan, No. 3, exhibits all the houses of the farmery ranged in two rows,
having separate roofs, with a longitudinal valley over the central wall.
934
ON LANDED PROPERTY.
No. 3.
The shelter sheds form the inside row of buildings, and the north wing of
Farmery, the farmery is composed of the houses in two rows that usually
occupy that position. A central road leads to the straw barn,
and along it, by cart or railway, roots are conveyed to the yards and pig-
gery, and straws for litter from the straw barn. This house occupies the
width of the two rows of buildings, and is large and roomy: it receives
the straw from the thrashing barn, which stands at right angles with it,
and this position gives opportunity in the straw barn of making any divi-
sions of the kind of straw. The ricks of grain stand in two rows, as in last
plan; the unthrashed grain is conveyed along the railway to the end of the
barn, and is pitched from the waggon to the second floor, on which the
machinery is at work. This arrangement of the rick-yard and barns is
much the most convenient of the designs now given, or probably of any
that may
be devised.
Ricks on a
It is proposed that each rick of grain stands on a square plat-
platform. form of four wheels, which rests on a short branch railway at a
sharp angle of divergence, along which the entire rick runs to the barn when
it is wanted to be thrashed. Any rick may be thrashed that is wanted, as
the way to the barn is wholly unobstructed, and the platform, after its load
is disburdened, is sent back to the position on the branch railway, where it
receives in the end of harvest another rick of grain from the fields. This
plan might deserve a fair trial.
Thrashing
The thrashing of grain is in every case performed by machinery,
machinery. which is best impelled by the power of steam. The absurd
prejudice is here discarded that the use of machinery diminishes labour,
and the latent barbarism of the mind is expelled which continues the
thrashing of grain by means of two sticks tied together, and employs labour
on a non-productive point. Machinery increases labour, and performs the
brutifying parts of the operations, so far as the application is possible. The
thrashing machinery of every farm is provided by the landlord as part of
the fixed furniture of the farm, and upheld in use by the tenant. No fixed
utensil should be removed by the change of occupiers, as when the
machinery belongs to the farmer.
covered as a
It has been proposed to cover a farmery wholly under one roof, like
the terminus of a railway. The dung would be thus protected from rains
and scorching suns, and the animals will live under a uniform temperature.
The roof of corrugated iron would rest on cast-iron pillars, and be extended
in separate tiers along the greatest length of the farmery. In
Farmery exposed situations, hollow cylinders may be formed in the con-
railway ter- cavity of the roof, which will convey the wind harmlessly over
the buildings. It is doubted if it would be beneficial to ex-
clude the influence of the sun altogether from the farmery; the warming
effects may not be compensated in the absence by the exclusion of heavy
rains. Colds and currents of wind are generated under lofty roofs, but
which may be removed in this case by a close walling round the farmery.
minus.
Slates form the best covering that is yet known for roofs of houses;
tiles are the next best article; asphaltum-paper, and some other substi-
tutes have not come into reputation.
ON LANDED PROPERTY.
935
The coarsest glass yet made is too dear for the purpose of roofing; but
as there is a general tendency to cheapen the prices of articles, and extend
the sphere of their use, the time may not be distant when roofs are wholly
made with that article. A most notable specimen is just now exhibited in
the circular roofs of glass resting on rounded rafters of bended deals, like
the springs of a carriage, which stretch the railways at the terminus of the
lines. Those mighty exertions of capital and intellect offer to view very
many lessons to be learned, and performances to be adopted, when pride
will allow imitation, and conceit perceive its ignorance.
Aspect and
exposure.
site: as
The aspect and exposure of farm buildings deserve some con-
sideration. The position of the farmery should evidently be
central, but many hindrances will prevent that selection of the
proximity to a public road, a convenience to water; and shelter will, in
many places, very much influence the choice of the position. The situation
should be dry, or can be easily made so; the approach not difficult, or can
be made convenient without any heavy expense. The exposure should be
low rather than high, and have an open front, whence there come enliven-
ing heats and currents of refreshening air. The aspect may be fixed
to the south, as being the most benign quarter of the heavens in the
British isles; the west is boisterous and wet; and the east, though cold and
dry, is favoured with the rising sun; and on that account be- South-east
comes preferable as a deviation from the south. The subjoined preferable.
quotation will show that, even in the benign climate of Italy, the proper
aspect of the farmeries did not escape the notice of the Roman people :-
"Edificium meridianam partem respiciat, in primo angulo excipiens
ortum solis hyberni, et paululum ab occidente avertatur hybernali. Ita
proveniet, ut per hyemen sole illustretur, et calores ejus æstate non sen-
tiat." Palladius de Re Rustica. Lib. I., cap. viii.
The front of the buildings being low in the walls and turned to the east,
the low suns of winter will shine upon the yards; and during the fierce
and scorching heats of summer, the meridian blaze will have lost its power
over the extent of the farmery by reason of the averted position. The best
aspect ranges from west to east, and the intermediate points will accom-
modate almost any situations in Britain.
Cottages or dwelling-houses for labourers, are an object of Cottages.
very great importance, and form a point of much consideration.
Labour is the source of every gain; and it is most just and equitable that
wealth, which is the accumulation of labour, be used in providing comfort
and competence to the springs of its existence. But the very slow and
gradual upward progress of the social system has not yet brought labour
and the actors of it into the proper degree of the very just estimation ; and
the condition of labour yet rests almost wholly dependent on the benevo-
lence of the wealth of the upper grades of society; and that power never
can be more beneficially or agreeably employed than in affording comfort
to its fellow-creatures.
The present accommodation of the agricultural labourers forms a very
great blot on the rapidly improving social economy of the present day.
Till of late years the hovels of the working class never attracted any
936
ON LANDED PROPERTY.
of them.
notice, large families being confined in a single apartment of sixteen feet
square, where the common decencies of life cannot be preserved. The pro-
miscuous intercourse of age and sex at all times and on every occasion
violates the feelings of propriety and decorum, and engenders immorality
that is seldom forgotten during the after-life. Filth and stench abound
Deficiencies where cooking and sleeping are done in conjunction, and the
roofs being low, a foul air is constantly respired, and the very
healthy enjoyment is denied of breathing in a large volume of the sur-
rounding atmosphere. Such dwellings resemble the stalls of a stable,
where the animal performs all the functions of life in one apartment. A
house with one door for ingress and egress of every article never can be
clean, and will be very deficient in ventilation from the want of a current
of air that is produced by openings in the opposite sides of a house.
These very glaring deficiencies are now being noticed, and the remedies
suggested and applied. The decent separation of age and sex is the first
step in the arrangements of civilization among human beings that are
located in permanent dwellings. This very obvious truth requires that
any human dwelling consists of at least two apartments on the ground floor.
The same necessity of separation demands that the sitting and sleeping
apartments be distinct; and experience has shown that bedrooms are much
more dry and comfortable when placed on a second floor from the ground:
hence, every cottage must have a second floor.
Improve-
ments
gradual.
It would be a very useless undertaking to make dwellings be-
yond the means of being supported, or to raise expectations
beyond the power of being realized. The present ideas must
only lead a step in the progress, and point the way to a further advance-
ment; the conditions of the social arrangement must always be considered,
and the upward progress must be ahead rather than behind the state of the
system. The present state of things will sufficiently warrant the essential
requisites of a labourer's cottage, that every habitation have two apart-
ments on the ground, of which one serves for the sitting and cooking de-
partment, and the other for better purposes and occasions, that the bedrooms
are placed on a second floor of joists and boards, and that there
be some small back buildings as minor accommodations for the
purpose of works that would incommode the dwelling, and also to conceal
articles that never should be seen. These principles, in three requisites,
form the basis of the following details, in which are implied the cottage
having a door in front, and another opening backwards, and a height of
wall that admits a large volume of air to traverse the habitation.
Stated.
Subjoined are the plans of three cottage dwellings that are arranged on
the above principles, and which are not attended with any unsuitable
decorations or a lavish expenditure.
Plan, No. 1.
Plan of cottage, No. 1, is a single dwelling for one family,
with the proposed accommodations. The ground floor contains
two rooms with opposite fire-places, and the stair rises from the kitchen to
the second floor. A porch in front breaks the uniformity of bare walls,
and affords some little inside room. The walls of the cottage are 14 feet
high, leaving 10 feet for the height of the ground floor, and 4 feet to the
ON LANDED PROPERTY.
937

E
Р
bakililim (NAIADA

יך.

F
G
Η
K
C
D
K
10 5 0
A
N
B
10
M
I
2-
20
30
40F?
L
A Room.
B Kitchen.
C Yard.
E Pig.
F Poultry.
G Wash-house.
I Privy.
K Garden.
L Road.
M Porch.
N Fires.
O Stairs.
P Bed Rooms.
D Dog.
H Ashes.
The second floor is divided
The back area contains small
sleeping floor, which is placed in the roof in the remaining height to make
apartments. The windows are in the roof.
into three bed rooms, as shown in the plan.
buildings as lean-tos on a surrounding wall of 8 feet high, in a privy,
ash-house, wash-house, fuel-house, poultry-house, and pig-sty. The con-
tents of the privy and wash-house pass into the ash-pit, and form a good
mixed manure for the surrounding garden, which contains or parts
of an acre. This appendage is most necessary to the cottage for growing
vegetables, and to afford an agreeable recreation to the cares and toils
of life.
3 M
938
ON LANDED PROPERTY.

A
B
AA
自​康
​
A Garden.
B Road.
M
Tx
C
10
A
L
K
K
Ι
Ι
H
H
F
F
E
G G
E
G
D
H
D
G
.........
E Kitchen:
F Stairs.
M
N
B
A
10
20
90
40
H Fuel.
I Wash-house.
K Ashes.
L Privy.
M Poultry.
N Pig.
No. 2.
C Porch,
D Room.
G Fires.
Plan, No. 2, shows two cottages that are joined longitudinally,
and have the ends for front. The porch is in the side of the
house, and enters through the garden. The accommodation and arrange-
ment are the same as in last design, and the back area has the same small
buildings. The garden surrounds the cottages, and a road leads to each
dwelling through the garden.
ON LANDED PROPERTY.
939

H
ID
10
田
​P
I
10
E

D
Р
20
3,0
40F3

F
M
L
K
E
T
N
A
F
D
G
B
H
20
30
40 FT
A Room.
E Yard.
I Fowl.
B Kitchen.
F Wash-house.
K Dog.
C Poultry.
G Road.
L Pig.
D Stairs.
H Garden.
M Ashes.
N Privy.
O Bed Closet.
P Bed Rooms.
No. 3.
Plan, No. 3, shows the design of a single cottage, with the
poultry-house placed under the roof of the dwelling, and be-
twixt the fires, of which the heat will convey a very agreeable warmth to
the animals. This provision will largely contribute to the laying of eggs
and the hatching of chickens throughout the year. The other accommo-
dations are similar to the last plans.
The entire site of the cottages is excavated to the depth of two feet,
which is filled with stones of the convenient size and flatness to form the
foundation of the building; and below the brick floor of each apartment
there is one foot in depth of broken stones, which will render the cottage
very dry underneath.
940
ON LANDED PROPERTY.
Expense.
The cost of the single cottages in each dwelling will vary
from £80 to £100, according to circumstances, and the two
that are joined will cost about £180.
Groups of
cottages.
Groups of cottages have been devised-square, circular, and
polygonal, and containing six to twelve dwellings in one con-
gregation, with a garden attached to each habitation, and having a pump
of water and a bakery to serve the whole of the families that dwell in the
house. But lazy assemblages are created, and much idle gossiping is en-
couraged; and it is preferred to have not more than two cottages in con-
nexion, and the fronts averted from any close communication of business.
The gardens are best when closely joined to the dwellings, both for plea-
sure and usefulness.
Books of
For a variety of choice and selection on the subject of farmeries and
cottages, the reader is referred to "Donaldson's Improved Farm Build-
ings," and "Designs of Cottages," by the same author. This
reference. work may be had of the publisher of this book.
farmeries contains designs for farms of 50 to 1000 acres
and polygonal, and embracing much variety of design.
accompany the farmeries, and also a number of cottages.
designs of cottages comprehends these habitations only, and
and useful variety of design and invention.
The book of
square, circular,
Farmer's houses
The book of 40
exhibits a large
The cost of the erection of farm buildings varies from two to five years'
rent of the land; the calculation being liable to the usual variations by cir-
cumstances that affect all such arrangements. Employers very much neg-
lect their own interest who omit the provision of affording the labourer
pleasure after pain, and of giving some little solace to the cares of poverty
and toil. A commodious lodging is equally required with the
Necessity of
comfortable payment of the wages of labour, as without it the value does
dwellings. not appear, nor is the desire properly excited to the future de-
velopment. The spirit sinks when the relish is withheld of enjoying the
hard-earned rewards of toil, however small they may be, and no earnest-
ness can be reasonably expected, nor can any anxiety be manifested, when
the small indulgence is denied the labourer of having a comfortable
fireside and a warm bed in which to recruit the body and refresh the spirits
for the coming exertions. Negligence and inconvenience aggravate
the filth of poverty, and put to flight every idea of living in the vicinity.
Land-owners lose the value of their property by not pro-
by the want viding the ample fixed appendages of the farm on which the
tenant uses his floating capital, and the labourer exerts his share
in the bodily performances. In the former case he loses the present
value, and in the latter he fails to obtain the attachment and esteem of the
ground-work of society, on which the whole superstructure leans for sup-
port. It is only to be got by just rewards and kind treatment, and must
not be neglected if the higher grade of existence be contemplated to
endure.
Value is lost
of them.
ON LANDED PROPERTY.
941
CHAPTER V.
LAYING OUT FARMS, ROADS, FENCES,
AND GATES.
farms.
IN old inhabited, thickly peopled, and highly improved countries as
Great Britain now presents in the cultivable surface, no opportunities
occur, except in the few cases of enclosing large commons, of making an
original formation of farms. The form should be as compact as possible
from the attending circumstances, for time is saved in the til- Position of
lage, the expenses are lessened in several ways, and the super-
intendence is rendered more easy; the boundaries should be as straight as
can be obtained, and curved only to suit the bends and sinuosities of the
surface of the ground. The courses of rivers and of large brooks of
water, the line of roads that are drawn for public use, the access to
water, and the provision of shelter, will all be entitled to due considera-
tion, and must have much weight in determining the division of land into
fields, the size of the enclosures, and the exposure of the grounds. A va-
riety of soils will also happen to disturb a regular uniformity; it is very
highly eligible to join with clay lands a portion of turnip soils, Much varied.
and these again must be divided by the fences of the farm in
order that the same field may not undergo two processes of cultivation,
nor produce crops of different kinds. It is convenient, when a public road
intersects or runs along some part of a farm of land, when the access is
convenient to the business of the occupation, and the road may very
beneficially form the boundary of two contiguous farms. Rivers, roads,
plantations, and stripes of trees constitute the divisions of lands in culti-
vation, as the passage is generally troublesome, and the distance inconve-
nient. High and low grounds are often required to be joined in the
occupation, in order to attach grazing grounds with arable lands, and
to afford the shelter of the valley to the exposure of the hills. Many
variations must have attention, and much consideration and weighing of
circumstances are deserved by the very important purpose of allotting
grounds for the convenient and effectual cultivation.
Few or no general rules can be laid down with respect to the size of
farms. In practice the size of farms must be made to suit
the demand, the condition of the tenantry, and other circum-
stances.
Size very
various.
In the vicinity of towns, the quantity of lands will tend to be small in
the single occupations. The cultivation is market-gardening rather than
farming, and the demand is for articles, in the raising, transport, and dis-
posal of which a minute care is necessary. The rent is high, which
942
ON LANDED PROPERTY.
Nearer towns
represses the size of the extents of land, as the articles sell dearly, the
sale is ready, manure is at command, the produce is quick
in succession, and a smaller capital is required. But when land
is removed from a convenient distance from towns or marts of small
quantities of produce, which are sold in retail, the rent will be very much
less, and the management will be conducted under very different circum-
stances; the produce will be chiefly in grain and live stock, which will be
more cheaply produced, and sold in considerable quantity.
One very general rule may be stated, that no farm of lands shall be less
than employs one plough with two horses to perform the yearly labour.
This quantity will be forty or fifty acres, as the soil may be clay or turnip
land. Below that extent the condition of a tenant of land descends to
the common labourer, and even that quantity does not raise the occupier
above the servile employment of bodily labour, as the quantity of capi-
tal that is used cannot command a profit that is sufficient to maintain an
idleness. The quality of the soil, the opulence of the district, and the
benignity of climate, and the geographical position, will very much deter-
mine the size of farms; and while no doubt can exist, of the
General rule. general superiority of farms of sufficient magnitude, it is not
by any means advocated, that the size of farms must be increased and in-
definitely, either for the individual interest of the land-owner, or for the
public benefit. It is quite certain, that the example of beneficial improve-
ments has always been set by extensive farmers, who are persons of capi-
tal and education, and enjoy a station that places them above vulgar pre-
judices and local conceit. But a variety in the extent of farms is suited
to the variety of demand, which is generally greatest for small possessions ;
and landlords often do not much heed these regulations, provided a good
rent is conveniently obtained. The spirit and enterprize of the larger
farmer are often outweighed by the greater frugality and attentive detail
of the smaller tenant; and the compensation is often surprising when the
disadvantages are considered under which the smaller tenant labours.
The dimensions of farms are frequently increased from large extents
requiring less expenditure for buildings and enclosures than small pos-
sessions; but there is danger by so doing in placing the lands
beyond the reach of the farmers around. A continued exten-
sion of this kind may place particular farms beyond the reach of the
common capital of farmers, and the demand may be very much lessened
when they are brought into the public market.
Large farms.
Pastoral or hill grazing farms must be extensive because a large sur-
face is necessary to yield a good return, and different animals require to
be kept on the grounds, which cannot be done without sufficient space.
The expense is less in managing these large congregations; a greater
number of animals can be bought and sold at a time, and few or many
shepherds are equally capable of being managed, and of bestowing their
superintendence.
The tendency of farms to increase in size, shows the improving con-
dition of a tenantry and a sub-division of lands implies a declining
ON LANDED PROPERTY.
943
tends to in-
crease the
size of farms.
condition, or a defective connexion between them and the land-owners ;
capital is shown to be wanting for the purposes of cultivation, Condition of
and the tenantry to descend into a worse condition. A regularly tenantry
continued progress of sub-division of lands will ruin any coun-
try, as is seen in the case of France, on the score of ownership;
and in tenancy, in a great part of Scotland, in many remote districts of
England and Wales, and over the whole kingdom of Ireland. Such a
state of things is most peculiarly unfavourable to the progress of agricul-
ture; and the increase of the farms in size will be the first symptom of
revival, for it will show that funds have begun to be acquired, and that a
superior class of tenantry will be established. Every progress Minute sub-
of agriculture has increased the extent of the holdings of land, division al-
and if ever the tenantry of Ireland rise above their present
condition of starved and ill-requited labourers, the existing possessions of
land must be formed into extents that can be cultivated with effect. Such
changes are gradual, and require much time; the evil has been extending
for generations, and as many more may pass away before a suitable allot-
ment is seen of the land for cultivation, and the substitution of a class of
spirited and independent yeomanry for the present unfortunate occupants
of the cabin and the bog.
ways hurtful.
Roads.
Materials.
Roads are artificial pathways formed on the surface of the earth for the
transport of heavy bodies, and as the natural ground is soft and
yielding, it becomes necessary to protect the tracks from pres-
sure and attrition by a covering of some harder matter, as pavement, small
stones, or gravel. The first article is costly, and not to be found in many
places; gravels are worn round by the action of water, and the small peb-
bles never bind together to form a compact bed of road, and consequently
stones broken small by the hand-hammer, which are got from a
quarry or from surface stones, are the most useful materials in
the making of roads. The disunited fragments present many angular
points, which when acted upon by pressure, are fitted into the alternate
shapes, and become almost a solid mass of small particles possessing a
broken continuity. These angular points are wanting in gravels, which
require to be broken by hammer, and even then the remaining round side
prevents the junction so well as in quarried materials. Hence stones of
any hard kind have been long established as the most suitable materials
for making roads, and broken to the size of passing through a ring of two
inches in diameter.
The direction of roads is an object of very great importance, whether
the line be a public thoroughfare, or a cross-road of communication, or
a private farm outlet. The inclination of the surface, and the hardness,
smoothness, and durability of the covering, constitute the chief properties
of a road, the highest of which is a plane with a surface resist-
ing the pressure of bodies, and opposing the least resistance to
their motion. Steep acclivities must be avoided in the direction of roads,
when high grounds cannot be ascended by a rise of one foot of slope to
thirty-five of base, and from that figure to fifty, the line of road must be
Direction.
944
ON LANDED PROPERTY.
Cross
mences.
Roads.
Grass turf
tom.
diverted round the hill, and to skirt the base of the high ground, rising or
descending in its course, according as the object to which it
leads is situated above or below the level whence the road com-
A circuitous line is certainly produced in this way, but it is
unavoidable, as the hills cannot be climbed, nor deep vallies crossed with-
out an overwhelming inconvenience. The vallies that intersect a country
are to be crossed by roads at the narrowest point which can be approached,
when a bridge will be generally necessary. The cutting of the upper side of
a road that skirts the side of high grounds, very conveniently
affords the materials for embanking the lower side, and the
expense is less than when a road is made on a level plain, where the whole
formation is made of raised materials. This line of a road affords a drier
bed generally than when the direction lies along low grounds, which may
be wet and swampy, and exposed to inundations. A ditch along the high
side of the road intercepts the waters from the high grounds, and conveys
it to stone culverts which cross the road at the proper places for discharge.
In every case where the advantage can be obtained, the hard materials
that compose a road, should be laid upon the grass turf, as it presents a
tough and matted surface which resists the pressure, and pre-
the best bot-vents the broken stones from sinking into soft ground. But
when excavations are made, and embankments formed for the
passage of a road, that advantage is not got, and the materials are com-
pelled to be laid on the newly-formed bed of fresh earths, which are
mostly soft, and yield to the pressure. In that case, the hardest and
driest materials that can be got, are selected and laid in an even surface
below the track of the road and broken to a small size. Over it is laid
a body of broken stones, which were before mentioned, in the depth of
twelve inches, and width of twenty feet; and this space is bounded on
each side by a sloping ground of twelve to fifteen feet reaching to the
side ditches which run along the front of the boundary fence. This width
of sixty feet is not beyond the use of a public thoroughfare;
and the hard materials of twenty feet in width, allow the car-
riages to change the tracks, and not to follow, as in narrow roads, the
same path of wheels, which is a most pernicious accompaniment of a con-
fined space, and very soon destroys the consistency of the road. Convex
roads, or having a high centre with sloping sides, are discontinued from
an excess of the method of formation, but as much convexity is eligible
as will throw the water to the side ditches. Roads must be kept dry, and
Draining of where wet grounds must be passed, drains are necessary to be
placed below the road in three longitudinal cavities filled with
broken stones, one in the centre of the road, and the others at the division
of the hard materials with the sloping sides of earth. Cross drains are
necessary in the hollow places, to convey the water to the side ditches.
Width.
Roads.
The most public roads are turnpike trusts, with which the land-owner
has only a small joint concern, and over which his property control does
not extend; but the private roads are his jurisdiction, jointly or singly;
and the roads on his farms are exclusively his undivided patrimony and
ON LANDED PROPERTY.
945
Surveyor-
ship.
employment, and deserve an especial attention. When money is collected
from the farmers by a rateage, and applied in the making and repairs of
roads of a general use, some competent person must be appointed as the
permanent overseer, who shall employ labour and collect materials, at the
times and places, which shall appear to be most eligible and generally
beneficial. The custom is not yet abandoned of the farmers serving in
the yearly rotation as overseers of parish roads, and of bestowing so low
a minimum of attention as scarcely ever to see the object of their
care. The tenure of office is far too short to allow any ideas
on the subject, and as it must occupy some time, less or more, an utter
carelessness is evinced towards an object of the most primary attention.
These district and parish roads are the first divergence from the main
trunks, or parliamentary trusts; they are the arteries, and the farm or
private roads form the veins of the ramified intersection of a country by
the means of communication. The parish roads may be one-third below
the width of the turnpike lines, and the farm roads may be one-fourth
narrower than the district tracks, making the breadths to be forty feet and
thirty feet respectively. The first extent will be divided into sixteen.
feet of hard materials in the centre, with twelve feet of sloping ground
on each side, and the farm road will be fourteen feet in the centre of bro-
ken stones, and eight feet in the sides of sloping surface. These widths
will be sufficient for all ordinary purposes.
Private
roads.
All roads must join each other at right angles, with an arc or circular
sweep on each side of the junction, in order to indulge the constant ten-
dency of animals and carriages to turn in the intended direction before
the whole equipment has reached the road that has been Junction of
approached. Ample room is better than pillars or railings roads.
placed at these points, as the carriages run against the securities in a con-
fined passage, and break the outposts of safety. A strong railing
recommended on the extreme edge of the circular sweep, after a very ample
ground has been allowed to render the use of it very seldom required.
Parish and district roads have the same object in view as the main trunks,
to reach the point of attention in the most convenient and eligible manner :
the location of farm roads is directed by the position of the
farmery, the formation of the intervening grounds, and to afford
access to the adjoining fields of land. The square or parallelogram
form of fields must be preserved, if at all possible; if beyond the reach,
then a bended or curvilinear shape must be preferred to a polygonal cir-
cumference of corners and abutments. In other cases, two sides, or one
side, of a field, may possibly be got in a straight—and the others will be
directed by the adjoining lines of road, or formations of the ground. It
is best when each field of land opens into a hard road, and which prevents
the travelling over the soft surface of any field in order to reach the other
beyond it, which is often very inconvenient. For this purpose, the breadth
of two fields must intervene between two roads, and when this arrangement
cannot be obtained, the headlands of the field that adjoins the
road, must be made into a road, and kept for that use. There
Between
every two
fields.
946
ON LANDED PROPERTY.
is a greater necessity that straight lines be preserved in the placing
of farm roads than in the direction of the main trunks; the latter
have only one object in view, while the private purposes have several
contemplations. Still the roads may be located in places such as are found
to be low grounds, and at such distances as will shape the fields in the
oblong direction, along the line of the private road, or stretching across
between the two roads. The equal size of fields of land is also to be pre-
served as much as possible; and the best experience has fixed the size of
twenty acres, or varying from fifteen to thirty, as the most suitable extent
of divided lands, for the purposes of arable or grazing husbandry. Small
enclosures create too many fences and gates, and incur an expense in the
upholding and repair; and large fields are in many instances much
exposed from want of shelter, and require too large a number
Ready access.
of animals for the pasturage, and small flocks of beasts always
thrive best. The access to water will have much influence in determining
the extent and position of fields, and the most essential article may be
procured by forming a pond in the lowest ground, by boring as a well,
or by bringing the water from one place to another in a rill, in a covered
drain, or in metallic pipes. In the latter case, a trough being placed
across a subdivision fence, will supply two fields, and when the grounds
are very high in the position, the pasture must be used by sheep, which
require little or none of the element of water for the organized develop-
The shape of fields must not depart far from the square form, or
the grounds will become formed into a number of longitudinal slips, that
Corners to are both unsightly and inconvenient. Corners are in all cases
be planted. to be avoided; but when the situations are unavoidable, the nar-
row angle must be planted with trees, and thus make a straight fence of
the field. The junction of roads, as was before mentioned, must be at
right angles which will direct the joining of the fields to be in the same
position in all cases of a contiguity.
ment.
Roads a
provement.
It may be very safely affirmed that the making of roads as
primary im- convenient lines of communication are the first improvements
to be done in any country, and the keeping of the tracks in a
sufficient repair, is a point of little less importance than the original for-
mation. When roads are in bad repair, the wheel carriages are broken, the
animals of draught are distressed, and small loads are transported; cir-
cumstances which operate against the prosperity of agricultural under-
takings. The landowner has the power of enforcing the proper condition
of the parish roads, and the tracks for farm purposes are wholly and
absolutely his own performance. No fixed appendage of the farm possesses
a higher useful value than an ample sufficiency of well-made roads, nor will
any enlightened practical man neglect to examine and estimate the con-
venience which his floating capital will enjoy in that respect: he will use
his judgment in comparing the advantages which are presented by different
great value situations, and make his choice by the greatest number of
to any farm. facilities that are offered for the employment of his money and
his time. The approach to the main trunks of communication is the first
ON LANDED PROPERTY.
947
noticed.
attention, and then the access to each field from the farmery, which is the
focus of the whole movements. The finest farmery that can be devised
and erected, may be rendered of small utility when the application of its
merits is withheld by the want of the ways of traffic; when the loads must
be restricted in weight, and the frequency of the transits is limited.
Practical men know full well the drawback of these prohibitions, and will
not fail to place them on the proper side of the account in reckoning the
sum of the intended offer for land to be used in cultivation. It becomes
the interest, and also the duty of the landowner, to have the Always
farms of land unobjectionably provided with convenient and
well-made roads, as well as with buildings for habitations. The means of
transit must be very ample and ready, and no want must appear that can
hinder the full per centage being given to the owner of the soil for the
interest be has purchased in it, from allowing the floating capital of the
tenant the beneficial and prosperous opportunity of use, and from employ-
ing and maintaining labour, which is the paramount and overruling con-
sideration of every object and design. Any neglect on these points baffles
the fulfilment of the intended purpose, and destroys the arrangement of
the joint performances.
The maintenance of farm roads in the proper repair devolves on the
farmer, who must support the bed of hard materials, and keep Good repair
the side ditches clear as currents for water. This charge is indispensable
seldom expensive; the field stones that are periodically gathered, serve as
broken materials, and the earthy scourings of the side ditches are generally
useful in compost with lime for making a manure of very considerable
value. The farmer's own interest must ever induce him to perform these
operations. The smoothness of roads for his carts and horses, and soaked
earths for manure, are worth the attention of every cultivator that deserves
the appellation.
Enclosed
Fences are barriers raised betwixt the fields of land for the purpose of
protecting the crops that are growing in an enclosure from injury done by
the animals which are grazing in the adjoining division. They also serve
the purpose of separating the flocks of animals, and enable the production
of different plants and crops in the required divisions without any mixture
or confusion. Lowland arable farms require to be closely and
permanently subdivided by lasting boundaries, while upland grounds.
farms and hill grazings are only provided with a general fence which
surrounds the whole farm, so as to protect the grounds, and save the sheep
and other animals from disturbance. Large flocks of mountain sheep do
not require any minute subdivision, but are spread over an extensive range
of surface. Lower pastures that have some tillage lands, are divided in the
crops from the grazing grounds; and near to the homestead, there will be
two or three paddocks or small enclosures for the rams of the flock, for weak
ewes, and similar purposes. The comparative small value of the surface
ground prevents the extension of enclosures in a practical view; Open farms.
but where the ground increases in value, a greater use of en-
closures is required, and will be admissible on the score of profit. Sometimes
948
ON LANDED PROPERTY.
the quantity of arable lands in these possessions is so large that another
farm is constituted distinct from the grazing ranges, and then the enclosing
of the cultivated parts is similar to lowland farms.
Stone walls.
Fences are made with stones from the quarry of rocks, or with the
gatherings of the field in boulders and slaty fragments. These stone walls
stand either wholly above ground in the entire height, or are sunk in an
excavation, and form a fence in the front having the top level with the
ground behind the slope that has been dug. This last is
called a sunk fence. Mortar walls are erected on the sides of
highways in the vicinity of towns and other situations that are much ex-
posed to trespass and injury. They are the most complete and durable of
all fences; but the cost is beyond a very extended application. The
foundation is made with broad flat stones in a firm subsoil-the width of
eighteen inches at the base slopes to one foot at the top, which is covered
with rough stones set on edge, and projecting over the wall on both sides.
The height is from four and a half to five feet.
walls.
Dry stone Dry stone walls, admit a much larger application than the
erections with mortar as a common masonry. But even that
provision of fences is confined to certain districts which contain suitable
rocky formations that are near to the surface of the ground, and easy of
access. Schistoze formations are the most eligible, as the laminar fracture
produces a form of the fragments that is adapted to the purpose of build-
ing walls in which no mortar is used as a cement. The foundation is dug
to a firm depth on which flat sided stones are laid in the width of nearly
four feet; the wall to be raised is laid on these stones in the width of three
feet; the top at the height of five feet from the ground is narrowed to
eighteen inches, over which is laid a tier of long narrow rough stones
placed on edge, and projecting over the wall on both sides. The sides
of the wall are built with the best shaped stones in the manner of the
common walling, and the small lumps are firmly packed in the centre.
A cope of stones is much preferable to turf which soon moulders away; and
it adds to the solidity of the fences in the weight of the stones that are
laid on the top of the wall.
Boulders.
Boulders or field stones are very abundant in many parts of
North Britain, and very good fences are formed with these
materials, the shape is rounded, and seem to be a large formation of
primitive gravel, and are difficult to be built into walls. The hand-ham-
mer is applied to break the lumps into at least one square side, which is
placed outwards in the wall, and the centre is very closely filled with the
smaller boulders. There being no large stones to form a coping, the top
is rounded with the unbroken stones into a narrow apex, which is ter-
minated with one row of the largest lumps that are found. The
sunk fence of these stones consists of only one facing of boulders,
as the back rests against the solid bank of earth, which has been excavated
in the depth of the fence. Plantations are well fenced in this way, and the
top of the fence is level with the surface of the cultivated land and of the
planted ground. The top of the wall is covered with turf, as part of the
surface of the plantation.
Sunk fences.
ON LANDED PROPERTY.
949
useful.
Stone walls are called dead fences, and under peculiar circumstances the
preference is justly due to these erections as the boundaries of lands, and
for the separation of grounds. Less space is occupied by the stone wall
than by the live fences; it does not harbour vermin of any kind, and less
expense is required in keeping up the dilapidations. But the appearance
is dull, and wants the enlivening and cheerful aspect of the blossoming
hawthorn, and less shelter is afforded to animals by the wall than by the
hedge. Dry grounds which do not require ditches as outlets for water, are
best adapted for stone walls, and always with the understanding Walls when
that the rocks are adjacent to the grounds that are to be fenced;
that the access is easy, the rock conveniently dug, and the whole operation
capable of being done at a moderate expense. On high exposed grounds,
where the climate is outrageous and the soil unfavourable, no care or at-
tention is able to raise live fences, and then walls of some kind are the
necessity of the case. Turf walls will last for a very considerable time,
when well built at first, and where the climate is moist, and the grassy ve-
getation ample and strong. But they form no obstacle to the trespass of
sheep over the soft materials; cattle rub upon them, and hot suns induce
the mouldering and dilapidation.
Thorn fences
Live fences are the most common boundaries of fields over the
greater part of the British isles; and for the purpose of raising
the fence of growing shrubs, the most approved plant is the common haw-
thorn of white blossom. It is a perennial plant, of much durability, and
has a large adaptation of growth in different soils and situations. This
last quality constitutes a very large recommendation to the use of its
application, and where a varied utility is required, the last importance is
attached to that property of the article that is selected. Experience has
long ago shown most incontrovertibly that the common white thorn is the
most generally useful plant for forming hedges: it grows quickly, and on
a great variety of soils, and the prickles or spines are very annoying to
stragglers that trespass from field to field. The plant is raised in nur-
series to the age of three or four years from the haws or ripened fruit of
the aged plants, which are sown in beds of fine earths that are prepared
for the purpose. The sets are raised for use, and cut to the length of six
to twelve inches, as new shoots from the cut end are ever more vigorous
than the continuation of the stem produced in the nursery. The Erection.
line of new fence being determined and marked with planted
stakes, a turf is cast by the spade along the line and inverted upon the
ground, with one side touching the cord, and the other sloped by the
spade from the middle of the turf to the surface of the ground. On this
sloped earth of turf, the cut thorn sets are very carefully placed by hand
at the distance of four inches from each other, the upper end being even
with the high end of the slope. A ditch, in the case of wet grounds, is
dug at the width of three feet, and the depth of two feet; and the earth
that is excavated is thrown backwards to form a mound. The best earth
on the surface of the ditch is placed over the roots of the thorns, the upper
ends being left in sight, whence the shoots will proceed. On dry lands no
ditch is required, and the sets are placed deep in order to enjoy the benefits
950
ON LANDED PROPERTY.
Care when
young.
of moisture. The mound of loose earth is raised to a height be-
hind the row of thorn sets, and upon it is placed a fence of
strong dead thorns, or better in a paling of three bars of sawn timber,
which will last for many years. The front of the young hedge is pro-
tected by a similar fence, which is placed in a slanting manner along the
side of the ditch, and in this way defends the young shoots from injury.
These fences must be upheld and repaired with a very vigilant and con-
stant care, in order that the young thorns are securely protected during
the years of tender growth.
Weeds re-
During the first two or three years of the growth of young thorns, so
many weeds must be pulled away by the hand as will afford room for the
young plants, and no more need to be destroyed, as the covering of weeds
defends the bank of earth from drought, retains moisture, shel-
moved. ters the plants, and is beneficial to the growth of the thorns.
On no account are spades to be applied, as is usually done, to pare away
the bank of earth by gradual operations, and expose the roots and stems of
the thorns to the influence of sun and drought. After three years, or in
less time, the thorn shoots will overtop the weeds, and then no more care
is necessary on that point. Some shoots of the thorns will rise much
above the other growths, both in height and sideways; these overgrowths
are lopped by the pruning knife, but no other cutting or slashing is done;
as wherever an incision is made in any vegetable growth, a bundle of
feeble shoots are protruded, which divert the juice from the main purpose,
Training of and enfeeble the special growth. Hedges must be allowed to
the hedge. grow in the wild luxuriance of nature to the height of full five
feet, when the form may be fashioned into any shape that may be wished;
and generally, in the period of eight years, the fence will be complete,
and need no protection from accessory aid. A sufficient regularity of height
and straightness of sides can be obtained by lopping the overgrowths that
appear; and with this small application hedges are best allowed to remain
without any cutting or plashing; and the luxuriant blossom of nature's
forms is much more pleasing than the dull uniform sameness that is pro-
duced by the shears of the clipper. Gaps are to be very carefully filled
up from the first year of the growth by planting young sets in the open
space, or better by pulling across the gap the young shoots on each side of
it, which are fixed in that position by means of hooked pegs of wood
driven into the ground. This precaution is necessary in order to procure
a close hedge, and unless it be thick in stems and foliage, passages will be
made at the weak places, which destroy the utility and impair the value of
No cutting of the performance. Hedges never should be cut in any stage of
the growth. growth in a young state, the progress is retarded by it, and in
the advanced condition an expense is incurred which is wholly useless and
unnecessary. It only remains to raise a hedge to the required height,
and then to keep it in that condition of existence.
Furze.
Furze forms a very good fence in some places, but the plant
flourishes only on dry banks, under warm early climates. When
the growth rises high, it is apt to become open below, which objection is
ON LANDED PROPERTY.
951
partly remedied by having the hedge in two parallel rows, and by cutting
the rows alternately, so that one row forms the fence while the other is
growing after being cut.
Beech.
Beeches grow well on some damp cold soils, and form a good
fence, but the plant is of slow growth, and it wants the formidable
prickles of the thorn, which constitute the weapons of defence against the
trespass of animals. The hornbean tree is of a similar nature and value.
The sloe thorn, or black thorn, from its very sharp and nu-
merous prickles, forms a strong and durable fence, but the plant
is both slow and shy of growth.
Sloe.
Thorn hedges never grow well at gateways, and it is very advantageous
to raise a piece of stone wall on each side of the passage, and to insert the
thorn roots between the stones, with the shoot end projecting outwards,
and from the young shoots growing upwards, very strong fences are often
obtained from this mode of inserting the thorns.
All fences
raised by the
land owner,
and upheld
by the farmer
Fences of every kind must be first raised by the proprietor of
the land, and subsequently kept in repair by the farmer; and
nothing more clearly shows a farmer in every sense of the word
than a range of fences in a thorough and complete condition of
use and efficiency, without any gaps or weak places. Good husbandry
never understands a carelessness to be evinced in any one single depart-
ment on the farm; the most attentive vigilance is to be adopted even in the
most minute articles of utility, and the habitual custom must be exercised
of keeping all things in use and every thing in order.
New fences of thorns are to be placed, if possible, on the grassy surface
of turfy ground, in which the roots of the thorns spread in search of sus-
tenance. The length of the thorn-set fits the sloped side of the inverted
turf that was laid to form the base of the fence; one end sends Sets laid on
upwards the shoots which form the hedge, and the under end grass turf.
which is covered with earth, projects the roots which nourish the plants.
The operations of life are on the surface of the ground, and these processes
are engendered by the life and decomposition of the animal and vegetable
existences that are in being on the surface of the earth. The roots of the
thorns spreading among the decomposition of these minute portions of life,
receive a food that is of all others the most favourable to life of any kind,
for no manure yet known can be compared with decaying vegetables when
in connection with the quicker elements of animal bodies. No ploughing
or digging of the ground is required on which a new fence is to be placed.
A number of trees growing in a hedge-row is no doubt very Hedge-row
objectionable, but a few 'standards in scattered distances enliven
the scenery and improve the landscape, and the damage to the hedge is
inconsiderable. The distance of 50 or 60 yards seems a proper distribu-
tion. It has been proposed to make a plantation in the sharp corners of
the fields, and to round the inner fence, so that the ploughs in ploughing
the headlands do not turn, but go round the field and lay the headland in
one direction. These clumps of trees will add to the scenery, and in some
places be a useful shelter.
trees.
952
ON LANDED PROPERTY.
Gates.
((
Gates are a part of the fence or boundary which is raised for
the purpose of dividing land into portions that are convenient
for its use, in the state of arable or pasturing applications. The judicious
arrangement and proper maintenance of these boundaries form a very im-
portant department of modern agriculture; and, consequently, a value is
attached to the consideration of the best materials and the fabrication that
are adapted to the special purpose. The fences are stationary and fixed,
and as the use of the enclosed portion of land requires the ingress and
egress of the tools that cultivate and convert the produce into value, an
entry is necessarily selected, which shall be opened for admission and closed
for prohibition. A bar or hindrance in this entry was very early con-
trived, and has been long used, called a Gate," which is formed of bars
of timber fastened together, and being hung or suspended on a fixed post
or pillar by means of turning appliances of iron, which join together the
parts of the timber frame, the gate moves on either side of the entry, and
opens the road, or it remains across the way and shuts the passage. In
every case two timber posts are required: one on which the gate is hung
or suspended, and another on which it shuts, and to which it is fastened
to remain across the road. The entry to the field or the gateway admits
only one form of gate in an oblong square, as some objects in
nature are limited to certain forms and applications. But the
interior parts of this square form admit a great variety of ap-
plications with which to fill the vacant space, and it is chiefly this portion
of the article that constitutes the differences of which the implement is sus-
ceptible. An adherence to practical utility must be rigidly attended to,
and at the same time a neatness must be produced, which denotes a simi-
larity with other refined objects. Every article of use must bear a cor-
responding degree of refinement: strong without being clumsy, and neat
but not gaudy, or fancifully ostentatious.
Can only be
square in
form.
Two gates to
every field.
Every field of land should be provided with at least two gate-
ways on the opposite sides, so as to make it approachable from
each side of the ground. The width of the gateway should not be below 12
feet, nor the gate itself under 9 feet in length, so as to afford a free passage to
the loaded vehicles. Gateways should be placed on dry grounds, and are
most convenient when opposite to the headlands of the field, at either or
both ends. The carts, empty or loaded, travel to the ends of the field, and
find a straight road along the headland to the gateway, and pass to the
road outside the field. The gate posts of oak, or some durable timber,
should not be under nine feet in length, three feet below ground, and six
feet above the earth. The part under ground should have a thick butt
end, and be well fixed by means of closely rammed moist clay; the hole
must be filled in that manner from the bottom to the top, with the post
upright in the centre, and a turf of grass laid over the surface. The utility
and stability of the gate wholly depends on the secure fixation
of the hanging post; if it is unable to carry the weight of the
gate, or if it yields to the frequency of the opening and shutting by the
traffic, the fore end will soon fall to the ground, and the implement is
Posts to be
firm.
ON LANDED PROPERTY.
953
rendered useless. Some little labour and attention is required to make
secure the foundation of the gate, which is best done in the first perform-
ance, and not to require a repetition, which is never so effectual.
Gates are formed of five longitudinal bars about four inches wide and
one inch thick; the wood may be larch, ash, willow or the durable firs,
and dressed by the plane to receive the covering of paint. The bars are
mortised at the ends into upright small square posts of hard timber, and
fastened by a wooden pin. The back end post of the gate is heavier than
the fore end, as it is next to the hanging post, and is fitted to receive the
iron work by which the gate is suspended. The gate is best hung by
crooks and thimbles of iron; the former being driven into the Clap gates
hanging post, and the latter being clasped on the upper and most lasting.
lower bars of the gate. It is best attached to the catch post by means of a
small iron catch driven into the post, and a small chain attached to the
hand-bar of the gate. This fastening never can be opened, except by the
hand of man. Swing gates that pass to either side are ever liable to fall
too deep or rise too shallow in the iron latch that is sunk in the catch
post, and spring fastenings are very liable to be undone by the animals
rubbing against them. The gate must be of a height sufficient to
prevent any animals getting their heads over it, and pushing with the animal's
their breast against the upper bar, otherwise it is quickly broken.
The posts of a gate look well when they are octagonal shaped and rounded
to a top. All gateways should be deeply laid with small broken stones, as
animals always congregate at the gates and convert soft ground into a pud-
dle. No better sign need be required of a good farmer than having every
gate in proper order, and every gateway affording a dry and firm passage
at any season of the year.
High above
reach.
The reader is referred to "Designs of Gates for the Park, the Policy,
and the Farm," by the author of this work, and to be had of the publisher,
where a large variety of gates is delineated, with a strict regard to economy
and the useful convenience.
CHAPTER VI.
PLANTATIONS-YOUNG AND OLD TIMBER.
A PLANTATION is formed of trees that are placed in the ground at such
distances as allow room of the full growth being attained. The object
is to raise timber for artificial purposes; to convert into a profitable use
the barren grounds, and irregularly formed lands; to adorn the surface,
beautify the landscape, and enliven the scenery, and in unpro-
pitious climates, to afford shelter to the cultivated portions of
the earth. A tree seems to have been among the earliest productions of
Woods:
3 N
954
ON LANDED PROPERTY.
nature destined for the purpose of clothing the ground with vegetation;
tall, shrubby, or fruticose, the stem is seldom absent in any latitude that
permits the existence of any degree of organized life. The bulk is regu-
lated by the quality of the soil and climate, and the foliage undergoes the
same modifications. In most parts of Britain, a very equable medium is
established; the bulk attains a useful standard, and the growth is gene-
rally ready, and sufficiently progressive.
ren lands,
The rearing of timber is an object of much value to the owner of the soil,
and of a very considerable interest to the national community, in relation to
only on bar- the vested right which is enjoyed anent the purposes to which the
surface of the earth is appropriated. In arranging these distribu-
tions of use, the rule may be held as absolute, that all lands be planted with
trees, which are inaccessible to the plough by reason of elevation, declivity,
or other insuperable establishment of nature. And where a grassy surface
on a kindly subsoil yields a grateful herbage to animals, the position of
plantations must be so arranged as to afford shelter to the grounds that
produce the value in pasturage. The profit of the grazing will determine
if the use continues for animals, or may be better converted into a plan-
tation. Very high elevations deny the growth of any vegeta-
nient to cul- tion; grasses will grow where trees cannot live, and conse-
or inconve-
tivation. quently such a value must come from these situations as nature
is pleased to allow. Plantations are best made on moderate elevations, on
sloping grounds that deny cultivation, and on low situations where for
special reasons a congregation of trees may be eligible. Use and orna-
ment will always determine the establishment of plantations, and regu-
lated and modified by the contingent circumstances that ever attend the
purposes of active intention.
Trees of use are naturally divided into two large assortments of hard
and soft timber, the former bearing the seeds in imbricated cones, and the
latter in shells, nuts, and drupes, which form coverings of a greater or
less hardened consistence. At the periods of full ripeness, the seeds are
gathered, and safely reserved for being sown in the proper seasons on finely
prepared grounds, that are fenced round, and duly cultivated for the pur-
Young
plants.
pose of nursing the young vegetations. The seedling plants
are moved from the bed of one year, and placed in rows, where
the weeds are killed by hoeing the intervals, and only the moderate growth
of the plant is encouraged. At the end of two years, the trees are ready
for the use of the plantation, or to be placed in wider rows in the nur-
sery, there to wait the demands of sale.
Grounds intended to be planted with trees, must be completely fenced
during the year previous to the planting, and thoroughly laid dry by open
drains, if the nature of the land requires the removal of water. These
ditches are placed in the lowest grounds, and follow the sinuosities of
the surface in every direction, however crooked or awkward the appearance
may become. The general discharge must lead to a large ditch, brook,
or rivulet, into which the water escapes. The conveyance must be clear
and uninterrupted to the outside of the plantation, if at all possible to be
ON LANDED PROPERTY.
955
got. If a flat surface occur, an artificial level must be sought and made for
the special use.
Two methods are adopted in planting trees: one way opens circular
pits in the ground, three to four feet apart, about one foot deep, and one
foot and a half in diameter. The tree is placed upright in the centre of
the hole, with the rootlets carefully spread abroad by the hand; Planting of
the excavated earth is turned into the pit, and trodden firmly trees in pits;
round the trees by the foot, and then the grassy turf is placed as before
over the pit, and cut in two parts with the tree in the incision. The earth
being trodden firmly by the foot, and the turf being compressed by the
back of the spade, finishes the planting of the tree. This mode is adopted
for plants of the largest size, which are placed at the widest distances on
the ground. The second way of planting trees, makes two incisions with
the common spade, centrally crossing each other at right angles; the tree
is placed in the ground at the point of intersection, the spade holding up the
turf till the plant is fixed, and then depressing it to secure the position.
The roots of the plant are neatly dressed by knife, and the feathers are
arranged in the new position before the fixture is accomplished. This
method is cheap and expeditious, and leaves the roots among the best soil
on the surface of the ground, among which to spread horizontally, and
establish its abode; whereas in pits, by the first way, the roots are placed
in the subsoil, which is often very pernicious and inimical to by incisions
vegetation; the growth is stopped, till new roots emerge from in the ground.
the stem, and draw subsistence from the upper soil. Trees are fibrous
rooted plants, and spread horizontally along the surface of the earth; no
tap root descends to require a depth of humified earths, and consequently
the insertion may be more shallow, and the labour less costly. The last
mentioned method is therefore the preferable way of planting young trees
in the ground.
The distance between the plants and the number of trees that are
required to cover an acre of ground, are very much varied both in opinion
and practice. Hard timber trees, as oak, ash, and elm, are usually planted
at four feet apart, on the calculation that the one-half of the trees are
taken out when risen to one-third of the full growth, in order to make
room for the standing crop, and that these remaining trees need Trees on an
the space of eight feet between them. But experience has acre of ground
shown that a full crop of timber trees can stand in four feet apart, and
consequently the first planting must be thicker on the ground. The larch
and Scotch fir are found the most suitable plants on the highest exposures,
and even on the sheltered slopes of these elevations, these trees maintain
the greatest worth: on the lowest declivities, and upon the best grounds,
the oak, ash, and elm, usurp the preference: and on low flooded lands which
cannot be amended, the willow and alder will be the chosen plants. The
beech on chalks, the hazel on rocky banks, and the birch on barren gravels,
will be useful introductions; and in some situations, the Spanish chesnut
will equal in value the most esteemed tree in Britain. In every case of
planting trees on high or low grounds, and of firs or hard tim-
varied by
situation.
956
ON LANDED PROPERTY.
ber, the distance between the plants will be two feet, and the number
on an acre will vary from eight to ten thousand. The plants of hard
timber may stand at two feet and a half apart, and in certain expo-
sures, the firs may be so close as eighteen inches. These close distances
are required to create a mutual warmth, and to promote the upright shoot-
ing of the plants by preventing the lateral expansion.
Time of
planting.
The planting of trees is best done in the months of November, Decem-
ber, and January, and during the mild fresh weather that occurs betwixt
the frosts and snows of these wintry divisions of the year. So
soon as the setting of the plants is accomplished, the gates are
shut, and as the fencing has been previously done, the performance is
wholly completed. Roads of twenty feet in width are left in the conve-
nient directions over the planted grounds, and so arranged as to afford a
ready and convenient access to the working requirements, and to the ve-
hicles of export when the felled timber is removed. This con-
venience is never to be omitted being made in all cases of
plantations of trees. Open ditches are to be dug along the sides of
the road in all places where water may overflow the passages, and are di-
rected to discharge the contents into some one of the main outlets.
wet lands only these drains are necessary.
Roads in
woods.
On
Our system of close planting allows the trees to grow altogether unmo-
lested, save the insertion during two years of fresh sets in the places where
a failure of the growth is seen to happen. The most vigorous and thriving
trees take the lead, and carry the pre-eminence, and strive to reach the
benefit of sunshine, which is necessary to a prosperous vegetation. A cer-
Thick
planting
tain number of plants attain that station, and form an umbra-
geous canopy of leaves and branches that join in the contact;
beneath this covering, all vegetation is killed, and almost every life ex-
tinguished, at least that rises upwards in any considerable height. The
trees that cannot rise upwards into the sunshine, are killed, and when seen
to be fairly mastered, are usefully removed for fencing purposes; the lateral
branches of the trees that succeed in obtaining the permanent elevation,
die away, from a beginning at the bottom of the stem, and are killed pro-
gressively upwards, according as the tree rises in height. The decay fol-
lows closely on the ascent of the stem, and there is left on the top of the
tree "only" a round canopy of green branches and leaves, of a small ver-
tical extent, and so far laterally as the contiguous formations will allow.
The stem of the tree becomes a straight bole without any knots or blem-
ishes; the upward struggle of growth prevents any bendings or lateral
inclinations, and the efforts of nature are directed to one chief point. By
this method, nature exhibits the finest timber in the world;
pruning not in the wilds of America, in the straths of Scotland, and on the
necessary. Alpine cliffs of Norway, the seeds are sown by the wind, and
the roots are struck into the uppermost stratum of decayed vegetable earth
-a lesson which forbids the pruning or lopping of branches, and the inser-
tion of the young plants deeply into the ground.
renders
The pruning of trees, or the cutting away of the branches, by a saw
ON LANDED PROPERTY.
957
Expense
avoided.
or chisel, is a mangling process, which very much damages the timber of
the stem. Sap flows to an incision, and very often protrudes a number of
young shoots; or a struggle is made to cover the wound, which forms a large
blemish when the timber is sawn for use. When the tree prunes itself by
means of a killing confinement of the lower parts, as by thick planting,
no such accident happens; the decay is gradual and progressive, and the
sap flowing upwards by the attraction of heat, leaves the branches to a
complete annihilation: there is no wound to be covered with
bark, the branch drops off, and the junction with the stem is
soon imperceptible: the expense of pruning is avoided, and also the
labour and cost of thinning, which is seldom repaid by the value of the
clearances. The trees grow to a full maturity, and have no attention, ex-
cept in keeping the fences good against trespass, and in removing the
stems that are undergrown, before rottenness destroys the use for fencing.
About one-fourth of the number of trees planted will remain for crop,
and will average about two thousand on an acre, standing at four to six
feet apart. The other portion of the original plants is sacrificed to the
purpose of .raising the standing crop into a prosperous condition.
Quality of
timber im-
proved.
The observant eye that looks into a congregation of trees which have
been grown from nature's care, or that have escaped the havoc of the thin-
ning and pruning performances, cannot fail to discover the truth of all
the above statements, and that the system is also supported by the most
rigid adherence to established laws. In these places are seen the stems
of trees, tall and straight, without branch, knot, or excrescence
of any kind, and the bark slippery and smooth without any
interruptions. Wherever the sun and light are allowed to pe-
netrate the branches of trees will seek it laterally as well as vertically, and
the number of shoots will be proportioned to the free access that is given
to these necessary elements of growth. The vegetation is thus directed
to many points, the tree becomes a bush, and fails to reach the height of a
timber provision; the stem is knotty and rifty, and worthless in the hands
of the workman; and the wider standing of the trees reduces the number
on an acre of ground. On low grounds which approach the residence of
demesne, a luxuriant foliage may be wished, and then the trees are thinned
to the distances that may be required. An undergrowth of bushes may
be wished to shelter the beasts of game, when the openings betwixt the
trees must be wide to admit the sun and light to nourish the evergreens
that form the cover. In such cases, a distance of ten to twenty feet may
intervene betwixt the trees, and the first planting may be in the half or a
third of that distance, and the supernumerary quantity of plants are re-
moved at different stages of the growth, leaving the number to stand for
crop.
trees.
The fir tribe of trees generally reach maturity in about thirty years, and
the hard timbers in forty to sixty. Fellings and sales are then Maturity of
made according to the wants of the locality, and the purposes
that require to be supplied. In every case the trees are felled, topped, and
lopped by the owner's expense, and drawn outside the plantation, and
958
ON LANDED PROPERTY.
Sales.
laid in convenient lots for sale, whence the removal is made by the pur-
chaser. Every tree must be cut down, save some few choice
standards that are left in the outside to adorn the scenery, and
the empty ground is immediately filled with the suitable plants, as before
directed. No trees are to be left standing in the interior of the wood;
the ground must be clear, as young trees never thrive under the shade
and drip of the full grown forerunners. The custom is most pernicious
that mixes growing trees of different ages; the younger always
clean cut and suffer from the older, and the general appearance is never thriv-
ing or satisfactory. In this way the cutting and planting of
trees go on in an uninterrupted succession, and the ground is never empty
of production.
Woods to be
none left.
Neglected
woods to be
wholly re-
newed.
When plantations have been neglected, and allowed to grow in old tim-
bers, younger trees, and a bushy underwood, the evil becomes very appa-
rent of such a mixed system. By cutting and removing the full grown
trees, a very great damage is inflicted on the smaller growths of every
kind, and the younger trees when put in full possession of the
ground, form only the half crop which the land is able to bear.
In this way the evil is perpetuated, and each succeeding gene-
ration grows to damage the following vegetable increase. The most effec-
tual way is to cut everything completely from the ground, and to plant
afresh with the suitable plants, and attending for some two or three years
that the young trees that are planted be not overpowered by the thick
and rapid growth of the underwood, and the shoots from the old stools
which possess the vivacious principle. These exuberances are very use-
ful in sheltering and drawing into a tall growth, the plants that are in-
serted in the ground, provided the density be not allowed to choke the
growth of the young trees-this danger exists only for a short time, and
is easily avoided.
Felling tim-
bers, and
barking oaks.
Hard timbers and firs are best felled in the end of the year, and removed
before the spring growth is commenced. The ground is planted with
young trees in the same winter. Oaks being cut for barking in the early
summer, the planting of the land with fresh growths is delayed
to the next winter, when the process is repeated, as above de-
scribed. In every case the clearing of the ground must be
complete, save some few choice trees in the corners or fences of the
plantation, which may adorn the scenery and enliven the landscape. The
remnants must be few, and all others are indiscriminately removed.
Copse woods.
Copse or coppice is a plantation of trees that rise to a certain.
growth of years, when the stems are all cut and sold for the re-
spective purposes of use. The trees are of the vivacious kinds, that send
forth shoots from the old stools after the growth is cut, and the most rapid
in vegetation are necessarily preferred. The whole tribe of fir trees, or the
coniferous division of plants is wholly excluded, and the choice falls on the
oak, ash, elm, willow, and chesnut. The fir plants are deficient in the
vivacious principle, and those trees are most eligible which shoot readily
from the stools and prosecute a vigorous growth.
ON LANDED PROPERTY.
959
Inferior lands are generally converted into copses, as banks, Various in
rocky declivities, barren wastes, and flooded grounds. In the the situation.
first formation the plants are inserted as for a timber plantation that has
been already treated, and the stems are immediately cut close by the
ground. Sometimes a year is deferred between the planting and cutting,
but with no convincing advantage. The growths are ever more rapid and
vigorous from a cut stem than in the natural stalk from the nursery. This
fact is generally well understood, and the practice adopted in the case of
a new copse wood being formed, and the strongest plants in the nursery
are used, as they, when cut, send out the most healthy and vigorous shoots,
which in the shortest time are led into the form of the useful purposes that
are required. The sets are two feet apart as for timber, the near
contiguity being equally required in order to induce the quick
and upright vertical growth. The vegetations that are not able to attain
the height of the upper reach, are dwindled into the inferior purposes, as
will be afterwards detailed.
Planting.
the produce.
Copse woods mostly prevail in the hop-growing districts of England,
and these localities are chiefly situated on the chalk formations, where
coal is not found as fuel. The hop plant requires a pole to support the
twining stem, around which it climbs and fastens by means of tendrils.
This purpose uses the tallest and stoutest growths of the coppice. Fuel
demands for its most urgent purpose the use of all the inferior stems,
branches, and bushes, or all the growths that are inapplicable to any other
purpose by reason of want of strength and bulk. The intermediate growths
occupy the middle purposes of stakes for fencing and for making sheep
hurdles, and this use becomes in many places the principal application.
Copses generally attain the full growth of the purposes for Purposes of
which the articles are used in the time of ten to fourteen years,
when the produce is sold by auction or private bargain in a fixed sum of
money by the acre of land. The purchaser cuts the timber in every shoot
or bush of any kind, applies it to his own purposes, and removes the whole
articles outside the plantation by the first of May, when the young shoots
from the stools will sustain damage by the trespass of any intrusion. The
brushwood that grows on the earthen mound or fence belongs to Manufacture
the purchaser, who plashes a new fence with the thorns which of the woods.
he cuts for his purpose. The fence is not included in the measurement of
the ground, and the purchaser gets the stems that grow upon the mound
for the trouble of plashing the new fence. The growths are cut from the
stems by an upward slanting cut of the axe, and the face of the cut must
be clean and even, that no roughness occur to lodge wetness and lead to
decay. The new shoots rise from the seam of the wood and bark, and the
more sloping extent of cut will produce a greater number of fresh vege-
tations. But a medium is to be observed, as the stool will not support to
maturity a disproportionate number of shoots. The eye of experience will
easily fix the proper elevation of the cut.
In the southern counties of England a quantity of woodlands belongs to
most farms, which are cut at the proper season, and used by the farmer as
960
ON LANDED PROPERTY.
氤
​Best pro-
any other crops on his lands. This arrangement supplies the farmer with
firewood, and also with fencing and hurdle stakes, and the de-
perty of them mand for hop poles in his vicinity will add to the accommoda-
tion afforded by the woodlands. But it may be better policy that the
landlord manages all the woods as his own care, and the farmer can buy
the fuel and stakes he may want at the periodical sales of the articles. The
landlord would thus employ a fixed number of special workmen under an
experienced and trusty foreman, who will be employed during the year in
cutting copses, felling timber, barking oak, and upholding fences. The
cuttings will be duly separated into the purposes of use carried outside the
plantation, whereon a fixed day the disposed lots are vended by auction,
or previously sold by private treaty, and the time of removal is expressly
certified. The landlord has thus the certainty of the lasting object being
duly provided, and can make what alterations he pleases at any time.
Old stools to A long continued cutting of the stools of copse wood forms a
be removed. dense tuft or collection of the ends of the shoots upon the old
stool, in the cavities of which the water lodges and induces decay. In
these overgrown cases, the whole collection is best removed by cutting the
old stem close by the ground with a saw, and slanting the cut upwards, so
as to prevent a lodgment of any kind being made upon the incision. This
operation presents a fresh source of shoots, and very often most wonder-
fully renovates the condition of the stools. When a lengthened age has
wholly debilitated the production of suitable growths from the stools, it is
the best way, as in the case of full grown timber trees, to dig and remove
the old stumps wholly from the ground, and to plant with nursery sets, as
at first, the entire area of the plantation. The sets must be placed in fresh
ground, and not in the holes whence the stools are removed. This reno-
vation is the same as making a new coppice.
Copses and
Though it is very customary, it is still highly objectionable,
timbers to be to grow together the trees for timber, and the undergrowth for
separate. coppice purposes. The timber trees stand widely, and the
branches spread in an extensive lateral expansion, the stem never rises to a
height of bole to constitute utility, and covers a large shade, under which
the copse wood does not thrive, but dwindles into an inferior growth. This
is an object of daily observation, and requires to be removed by copse
woods occupying the ground in the one purpose, and timber trees to have
the same privilege with any underwood that may rise, being cut for use at
the seemingly proper periods. This arrangement is very simple and easy,
and provides each purpose separately, as they do not thrive in union, and
suffer mutually by the intrusion on each other's abode.
Best trees
for copses.
In the hop growing districts, and on the copse lands of the
best quality, the most eligible trees are oak, ash, and Spanish
chesnut. The ash is quickest in growth, but not very durable as a hop-
pole, the oak rises slower but lasts longer, while the chesnut very often
excels both these plants, in being more durable than the ash, and wanting
the fault of the oak,in being brittle and unwooded in the upper end of the
stem. On dry banks and on rocky declivities, the birch and the hazel
ON LANDED PROPERTY.
961 ·
Varied ac-
cording to
soil.
form a good undergrowth of stakes and fuel, but never rise into hop-poles,
for which purpose the oak, ash, and chesnut are the most valuable trees.
On lands that are damp and moist, even after a complete surface draining,
the alder grows well, and affords hop-poles of the first quality, and stakes
for the fence and hurdles. On the lowest grounds, the willow
tree yields the largest produce, and hop-poles are often obtained
of the best sort. The ash obtains the widest range of growth,
as it thrives well on all soils, from the flooded ground to the sandy waste;
but the inferior growths of it are not equal in quantity to that of the hazel
and birch, and on chalky lands the beech exceeds all others in bulk and
produce, though it is chiefly adapted for fire-wood. It seldom rises to the
height of good stakes. The trees now mentioned are adapted for any va-
riety of soils that may occur, and present a selection which suit the occu-
pation of any lands in Britain.
Digging of
land not
necessary.
Copses not
pruned.
No advantage attends any preparation of the ground for trees
by being dug or trenched, especially on high situations; expe-
rience has shown that the growth may be superior on trenched
lands for the space of five or six years, when it falls to the standard of the
unprepared grounds. The sole attention in making plantations of any
kind for timber or copses, is directed to complete fencing, open draining
of the surface where wetness prevails, and roads of twenty feet in width
traversing the grounds in the convenient directions, by which to obtain
access for any purpose. The only work to be done till the timber is full
grown is to remove occasionally the trees that are smothered by the taller
growths, and use the stems for some purpose before the decay performs a
total uselessness. No pruning or thinning is to be done in copse
woods, as the thick growth is necessary to promote the tall and
straight form of the poles and stakes, which would spread laterally into
branches if room was given for that purpose. The full growth is reached
in ten to fourteen years; and the value of copses varies from £8 to £20 per
acre, according to the quantity and quality of the produce, and the price
of the different articles in the locality. In many places, the poorer lands.
of all sorts pay as much rent as the cultivated grounds, where the small
necessary attention is bestowed. Many wastes in the districts value of the
wanting coal might be well used in copse woods, and especially
rocky declivities, on which no other improvement ever can be done. The
first expense is comparatively small, and though the times of payment are
far between, the return is more certain than yearly crops of vegetables,
and the casualties are much less numerous. The yearly cost is something,
and is covered by a very small produce and a low price.
woods.
Seeds of trees that fall to the ground germinate and strike roots into the
soil, from which timber arises that is better in quality than the trees that
grow from the plants of the nursery. This fact is well known in every
timber growing quarter of the known world. When the timber is used by
the saw and chisel of the workman, the operator can tell if the materials
had grown from the seed or the plant, the former being cleanest in the
fibre, and presenting a smoother surface from the action of the tools. It
962
ON LANDED PROPERTY.
from seeds.
Timber best follows that the seeds of trees be thickly scattered on the land
which is to be planted and allowed to germinate and strike roots
into the ground as in nature's way. The seeds are mixed in a large va-
riety, so that success be the more certain, and sown by hand in at least
four bushels on an acre. It will be advantageous that the grass on the
surface be not consumed by any animals for some years before the seeds are
sown, but allowed to fall and decay yearly, which will afford a bed of ve-
getable earth for the germination of the seeds and attaching of the roots to
the ground. The young plants will grow in a thick condition as from the
inserted stems; the thriving individuals will rise and form the crop;
and the inferior growths will dwindle into underwood, or be altogether
extirpated. The quantity of seeds must be very ample, and
when a failure is observed in the first and second years, another
sowing must be done in a smaller quantity, and every means
used to obtain a full crop on the ground. All vermin that eat tender
shoots and gnaw the barks of trees must not be present; and the fencing of
the sown grounds must be very secure. The collection of seeds for use
will supersede the nursery, and a very considerable expense will be saved.
Nature has shown the way; and the results are superior to the mode that
is now followed, which employs much more time, and expends a larger
cost. The stem of the nursery being cut close by the ground when the
tree is planted, sends forth a vigorous shoot, which grows far more luxu-
riantly than the old stem; and this shows the superiority of every growth
from the position where the vegetation is to be permanent, and the seed is
more vivacious than any stem.
To be sown
on the
ground.
Portland;
his authority
The above detailed system of very thick planting, which promotes an
upright straightness of growth, and kills the under-branches without the
mangling of the pruning process, is founded on nature in the first place,
Duke of and has been illustrated by the practice of the Duke of Portland
on his extensive landed estates, in the counties of Nottingham
and Northumberland, and in Ayrshire, in the west of Scotland. His Grace
is known as the originator of several most correct practical maxims on
various agricultural subjects, which are introduced and practised
with a most extensive benefit, and are never disturbed by any of
the evanescent theories of the day. Our opinion has ever admired the
planting of trees, as now detailed, and for which an appeal is made to his
authority; the system has an unerring law of nature for its base, and reason
for its guide. On the subject of planting acorns and placing young trees,
his Grace writes in a private letter on the matter :—
“Fine large
acorns produce very superior plants for some years; but I do not
think I have seen that superiority disappear till after the expiration of
more than seven years.
Communica-
tion.
"I am quite satisfied that the effect of double trenching is to operate a
permanent benefit. I did not see this effect in a plantation till it was
twenty years old. It was by mere accident I discovered that effect; but I
have since acted upon it extensively, and subsequent experience has con-
firmed the truth of the appearances. The roots of the plants work more
ON LANDED PROPERTY.
963
easily, get sooner out of reach of the effects of the sun, and the rain sinking
deeper into the earth, is not so soon evaporated."
In the matters of planting and draining, our work has adopted his
Grace's practice, as the most just in principle, and efficacious in the result.
CHAPTER VII.
MEADOWS AND EMBANKMENTS, BEDS OF RIVERS,
WATER COURSES, AND FLOODED GROUNDS.
Meadows,
or low
grounds.
LANDS that are low in position and flat on the surface are exposed to
floods of water, which usurp the dominion of the ground, and
damage the productive quality of the soil, owing to the time
of the possession by the watery element. This damage equally ensues,
whether the ground be in an arable condition or used in a state of grass,
for the starvation of the land by the water, produces a low state of tem-
perature in the soil, which continues for some time, and very
much retards vegetation. These grounds are mostly grazed
by animals, during the periods when the inundations of water are abser ';
but in many cases, the arable condition would be very profitable, it the
presence of the water could be averted. The low position of the inundated
grounds, presents a formidable barrier to the removal of the water, as the
descent induces a sluggish motion, and retards the escape after the liquid
has been directed into a proper channel. This obstacle has exerted much
influence on the operations of embanking, and has very much Embanking.
perplexed the arrangements for the purpose. Where the fall of
the ground affords a quick descent of the water, the process is com-
paratively very easy, as it only remains to provide a channel and turn
the water into it. In other cases, the channels are over-charged and burst
by the bulk of water, or are always full, and throw back the water into the
smaller outlets.
Embanking may be justly termed the first branch of engineering that
has been practised by the human race. Observation soon showed to the
eye, that low grounds were the most fertile that were situated along the sea
shore, and on the banks of rivers, and that the quality was damaged by
the inundations of water on the surface, and that the area was gradually
lessened by the invasion of rivers, seas, and lakes. Measures were not
long in being used, for the purpose of averting the damage; and the
monuments yet remain over all the countries of the ancient The first
world, where arts and sciences were brought into life, and engineering ;
cradled into use. The alluvial shores, wide plains, and fertile deltas, are
found to be protected against waste and temporary damage, and the
confined water is directed in small channels for the purpose of conferring
964
ON LANDED PROPERTY.
in Holland;
the benefits of irrigation on the grounds that are secured from the ravages
of nature. Every country of modern Europe exhibits the marks of this
ancient art—the dikes of Holland, are marvels of human industry
—and the embankment of the river Po in Italy shows a skill
and application of the practice that excites universal admiration. In
the former country, the ocean, inland seas, and rivers, are prevented
and confined within proper limits: the sediment of mud that is
carried by the rapid torrents from the higher grounds, sinks in the
channel of the rivers and raises the course of the water above the
surrounding level, where the inhabitants have their homes,
in Italy;
and cultivate the grounds. A rupture of these banks
would inundate a whole region of country, devastate the property, and
probably drown many thousands of people: yet such is the feeling of
security produced by the skill and labour of centuries, in devising and
repairing these artificial mounds, that no dread is ever expressed, and a
bank of mud is felt sufficient to repel the floods of rivers and the storms
of the ocean. The river Po rushes impetuously from high grounds into
the valley of Lombardy, and runs during the half of its course of 300
miles into the Adriatic sea, over a country of alluvial flat, where the
descent is small, and the course is slow and sluggish; the bulk of the
water is much swollen by the dissolved snows of the Alps, and the torrents
carry along vast quantities of fine earth that is torn from the high grounds
which, on reaching the low country where the water moves slowly, or
almost stagnates, sinks to the bottom as sediment, consolidates, and elevates
the bed of the river. This natural course of centuries has raised
river Po; the channel of the water above the surrounding country, and
embankments were raised at an early age in order to guard the labours of
man from the ravages of the unloosened waters. These banks are models
of skill and industry-of ingenuity in the plan, and of perseverance in the
maintaining of the bulwarks.
with the
in Britain.
In Britain, the embanking of grounds exposed to damage and
degradation, seems to have been begun at an early period of
time, though probably not before the Roman conquest. The Romney
marsh and the flat grounds of the estuary of the Thames, may have been
the work of the Romans, who had attained much knowledge of the art,
and were ever ready to communicate their acquirements to the victims of
their conquering policy. After the retreat of these improving adventurers,
the art of embanking slept in the general slumber of the human mind
for the dark period of one thousand years, and revived in the sixteenth
century, along with the universal resurrection of arts and sciences, men
and manners: foreign intercourse showed the policy of Holland, which
country sent engineers to Britain, who commenced with the draining and
embanking of the fens of Lincolnshire, where the sea comes far inland by
reason of the flatness of the alluvial formation of the country, and the de-
scending rivers are prevented the discharge of the waters into the sea which
are consequently thrown back upon the surface of the ground. Two centuries
of repeated attempts have scarcely sufficed to complete the emancipation
ON LANDED PROPERTY.
965
of these overflowed districts; but the operations have very much conduced
to advance the skill of the art of embanking, and have shown the principles
in many different forms.
Three uses
There are three applications of the use of embankments, in
guarding the encroachments of the sea, in turning away occasional of embank-
floods of water from the surface of flat lands, and in preventing
ing;
rare with the
the waste of alluvial lands by the invasion of rapid streams or torrents
that tear, waste, and carry away the soft and unresisting earthy accumu-
lation of tender ingredients. The shores of the sea are most generally
either rocky or sandy, which are useless for cultivable purposes of any
kind, and the cases are not many where the ocean intrudes on grounds
that are worth any cost and labour in the defence. There are
some few instances of such an occurrence, but the greater part Ocean.
happens in the case of inland seas or estuaries that penetrate the
country, and on the sides of which the alluvial flats have been formed
that require to be protected. In these situations, the force of the sea is
much less than of the open ocean-the tides rise gently, and the winds
have a very diminished effect. The tides are not impelled by furious
winds blowing in the same direction, and the mixture of fresh water very
much lessens the power of the briny liquid. But the barriers to be
opposed are the same in both cases, as the resistances come forward in the
same manner, and are formed of similar elements.
Embanking is based upon very simple principles, but the application of
them to practice requires both skill and experience. The fundamental
principle is, that a liquid presses upon any resisting solid, not by any
dimensions, or general properties of the fluid, but solely with a General prin-
force proportionate to its depth. Hence when a perpendicular ciples.
bank is opposed to a body of water, it has to sustain the pressure of the
depth of the body, and undiminished by any assistance that can be given
at it. This is a fixed law of fluids, and carries along with it the simplest
conviction of practice. It only remains to convert the deep pressure
laterally into a shallow depth vertically, and thus reduce the opposition
from an impinging force into a rolling harmlessness of motion. On this
principle, soft materials being hardened into a body, are equally useful
with the hardest rocks, or even walls of cemented masonry; and have
the surface so levelled and crusted, as that the ripple of the rolling water
does not make a breach, or form any beginning of damage. Banks are
made with compacted earth, in the dimensions of three feet of base to one
of perpendicular height. The slope is set to the sea, and covered with
turf, the pieces of which are fastened to the surface by means of hooked
wooden pegs. This growth of grassy surface presents the best of all
materials on which waters roll without doing damage, and it
is fed by the alternate benefits of being dry and having a watery
covering. The mound may be six or eight feet wide on the top, and have
a slope to the land of one and a half feet of base to one of height, or about
one-half of the seaward slope; the whole construction being quickly and
carefully covered with turf, and being duly attended and repaired, will
Best mate-
rials.
966
ON LANDED PROPERTY.
very soon become a grassy barrier of much strength, which will bear an
intrusion beyond its appearance.
It is a law both of theory and of experience that the greater slope of a
Slope of bank, the more effectually it performs the object of its purpose,
banks. and its end as a resisting surface. There is no precise rule for
the degree of slope, because it depends on the nature of the materials of
the bank, and on the degree of exposure to the winds, waves, and currents
of the tide; but it should rather be above than below the average now
stated, of three feet of base to one of height, and in no case below two to
one, even where the resistance appears to be very much reduced in force.
The height must be above the highest known rise of waters, which must
not wash over the top of the bank, and the slope height may be six feet
above the water line. Much care is required in forming the slope of the
bank to the sea, in order to prevent any breach, or abrasion of the surface;
the earth is beaten hard with mallets, and the grassy turf is best taken
from the sea shore, when the plants will be proper to the maritime
situation, and may be chiefly the sea carex, the upright sea lyme grass, the
sea rushy wheat grass, and certain kinds of the sedge. The creeping
roots of the plants extend beneath the surface, bind the loose earth of the
bank, so as to enable it to resist the continued action of the waves. A thin
coating of straw, and sometimes fascines of osiers, or branches of any kind
are pinned down on the bank to form a kind of thatch; but
How secured. the simple turf, when laid with care on a well prepared bank, is
the most sufficient.
Front pro-
Where banks are exposed to high rolling tides that are driven in fury
by storms of straight in-blowing winds, the necessity occurs of driving
into the ground two rows of piles in three or four yards between, and
filling the empty space with the largest stones that can be found. This
front barrier being placed in twenty feet distant from the grassy bank,
will act as a breakwater; the fury of the waves is broken by it, the water
passes through the loose mass of stones, gathers in a placid body between
the barrier and the bank, and rolls upon the latter like a standing pool that
is gently moved by a force that is distant and little troublesome. Where
stones are scarce and wood abounds, the piles may be driven into the ground
almost close together, when the quantity of them will constitute
tection: the barrier, but stones are preferable where found within a
reasonable distance. The bottom of the grassy bank will be in no danger
of being undermined from the quiet re-assemblage of broken waters as by
the furious lashings and peltings of the merciless beat of briny waves that
search every access, and explore every crevice. To prevent the very
smallest entrance into the bank being obtained, in case of there being no
breakwater erected, the bottom of the bank in the grassy turf, must
underlie the slimy ground of the shore, and the hardened mud on which
the water rolls must overlap the turf of the base of the mound, and conduct
the roll of the water from its own slope to the grassy bank without any
obstacle intervening at the junction of the mound with the shore. If the
water beats against any resistance, it will soon make its way, and an entry
ON LANDED PROPERTY.
967
banks:
once found will quickly lead to an overwhelming destruction. The whole
secret lies in making water always roll upon the resistance, but never to
impinge against it. Where streams of water from the country must pass
through the bank into the sea, a suitable opening must be left in openings in
the mound, and built with solid masonry, of the size to permit the
free egress of the largest quantity of water ever known to demand ad-
mittance; when the tide is ebb, the discharge is free and easy through
this opening of the fresh water from the land; and when the tide rises, it
will, if unrestrained, pass through the orifice and inundate the flat lands
which the bank was erected to defend. To prevent this intrusion, a gate
of thick boards strengthened with iron bars, is suspended by hinges to
shut the opening as closely as the wood and stone wall can be fitted to join.
The running water from the country pushes the gate before it, and keeps it
open, and runs freely into the sea-when the tide rises, a heavier force of
water rolling against the gate shuts it, by which the sea water is excluded, and
the fresh water from the land is confined inside the bank till the tide recedes,
when the gate is opened by its superior weight against the
receding tide, and the congregated waters escape through the
opening. This arrangement provides a bed inside the barrier in which the
assemblage of fresh water rests without doing harm during the presence of
the tide outside; but, except during very heavy land floods, the quantity
will be vastly inferior to the tides that were formerly admitted, and there-
fore much surface will be secured from overflowing.
This simple
mechanism is applied to one river flowing into another as well as running
into the sea; the inferior stream is overpowered by the greater pressure
of the main river, but being collected inside a mound, and a gate being
provided, it will open the sluice when it equals in weight the
quantity of water outside, and flow away. But the waiting con-
gregation of waters is often inconvenient.
gates or
sluices:
open and
shut with
the tide.
A more costly, but a generally more effectual mode, consists in leaving no
opening in the bank; but collecting the inside waters, and erecting a
steam pump, by the constant working of which the river is hoisted over
the barrier in continued discharges. This mode is essential in cases
where the country is below the level of the sea, as is frequent in Holland
and in the fenny districts of England. The steam is superior to the
windmill, or to any power yet known, by reason of the steadiness and
constancy with which it acts: and the pump is preferable to
wheels and buckets, in being less cumbersome, easier managed,
and less liable to accident.
Pumps.
When the raising of an embankment occurs on ground that is covered
by every tide that flows, the difficulty is very perplexing in securing the
works as it proceeds, against the tides, and also against the storms and
gales that may occur. The near completion of the work is frequently
thrown back to a beginning by some slight breach, which leads to an over-
throw of the whole structure. Practical skill and resources are im-
peratively necessary in the chief operator who directs the works, and
caution and foresight are nowhere more in request. The most secure
968
ON LANDED PROPERTY.
way is to make a temporary fence by means of piles and stones in front of
the mound being erected, which will break the storms, and guard from
damage the erection till the work be completed, when the protection may
be removed. The dam, if not wholly close, will at least turn away the
chief parts of the water. Such a guard is almost indispensable where the
water is a regular attendant.
Alluvial
valleys.
These descriptions guard against the overflowings of land by tidal
estuaries, that are often augmented by fresh water floods of the streams
or rivers that flow into the arms of the sea. The flatness of the alluvial
valley permits the ascent of the tide, and the lateral low surface
of the ground allows the spreading of the commingled waters.
Where the tide of the sea cannot rise the ascent of the country, the allu-
vial valleys still remain very flat, and the rivers that flow through them
are slow and sluggish in the course, and when swollen by heavy falls of
rain, or by melted snows, the adjacent meadows are overflowed by the
excess of water, and damaged by the cold application. The protection of
these grounds from damage, occupies the next attention.
Beds of
rivers.
Rivers are the great natural channels for conveying the surplus waters
of the globe to the ocean, which is the general receptacle. The hollows
and sinuosities of the earth generally regulate their course, depth, and
width of channel, and are all dependent upon physical laws, which are as
usual seen to be connected with a purpose or design. The channels are
variously excavated: when it is wide, the velocity of the water is reduced;
when contracted, the water runs faster, and the depth increases; the
current is retarded by a tortuous channel, and quickened by a straight
course: when the water undermines a bank, it is only hewing out a more
suitable channel, and the tide is sought to be shut out by a bar of mud
being thrown across the mouth of the outlet. These adaptations are
termed the regimen by engineers, and so far from being the result of
chance, is dependent upon laws that permit the usual investigation. When
these operations of the river interfere with the works of man,
reason instructs him to facilitate the natural operations, or
present obstacles to their accomplishment as shall suit his own purposes.
A trough is the natural channel of a river, and the deviations from this
form are occasioned by steep banks, a barrier of rocks, or greater or less
resistance of the surface strata, when the stream of water is diverted into
pools, shallows, and eddies, and excavation of the banks. The solidity and
permanence of the banks depend in part on the inclination of the surface,
the hardness, tenacity, and smoothness of the materials, and on the degree
of parallelism that is preserved between the course of the bank and the
impinging current. Tortuous courses of bodies of water pre-
sent an angle of resistance to the moving fluid, which being
enlarged in volume acts with violence against an earthy accumulation, tears
the mass, and carries away the dissolved materials. The flat soils of
alluvial formation are gradually wasted and reduced in the superficial
area by these invasions of watery bodies, and the protection of the cul-
tivated lands becomes a business of constant attention. In waters of any
Tortuous
courses.
ON LANDED PROPERTY.
969
banks.
considerable depth, the most efficient protection of the banks, is made by
driving one or more rows of strong and lengthy poles deeply into the
bottom of the river, at the distance of about eight or ten feet from the
bank, and filling the intervening space with very large stones. The row
of piles must be placed in a direction of presenting to the moving waters
as sharp an angle of contact as can be obtained, as this provision very
much relieves the pressure, and throws off the impending weight. In the
absence of large stones, baskets of strong osiers are filled with small stones
and sunk in the bed of the vacant space behind the piles, and in Defence of
other cases, bundles of brushwood are placed behind the piles,
and held in the position by ligaments of some kind being fastened around
the stakes in this position, the sediment lodges among the twigs, and
consolidates into an earthy bank. The large piles of wood by which the
whole provision is sustained, must be used in quantities as may appear to
be necessary from the materials that can be obtained. The weight of large
stones very soon finds a bed of repose-it only remains to have two rows
of piles fronting the river, which will prevent the rolling of the stones into
the deep trough of the channel-small stones will require the front piles to
be thickly planted, and also cross rows at no great distances extending to
the bank. The placing of the piles must be thicker for brush-
wood, the bundles of which are pressed and held down by planks modes.
that are joined to the driven piles. A very effectual defence is erected by
forming a slope bank of stones and planks, extending from the top of the
bank of the river forwards to the bottom of the water, of which the surface
is lozenged with cross and longitudinal planks of timber. The water rolls
upon this sloping surface, as upon the grassy banks that have been de-
scribed, and though it be costly, it forms the most complete barrier that
can be furnished. But in the most cases, the rows of piles, with some hard
or consolidating materials, placed behind, will be adopted.
Various
Straight and
courses.
When waters run in a straight course, little or no damage is
done to the banks which confine the current: but when the bed circular
is narrow and the line crooked, the water is broken or displaced
in the particles, and the agitation that is produced carries forward violence
and destruction to all opposing obstacles. The course of rivers must be
straight, or as nearly so as possible, and all attempts to alter or improve
the line of currents must approach to that design. All bends of rivers must
be assimilated to the straight line by using the largest circular sweep that
can be got, and the barriers that are presented to an impinging current,
must not offer a right-angled resistance, but receive the force in a sharp
divergence, and throw off the brunt of the violence. This adoption forms
an approach to the straight line, and though not straight itself, it throws
the water into straight course till it meets a similar obstacle, when it is
similarly treated. In making new courses for water, or in improving old
ones, it is a grand blunder to confine the current; water spread abroad is
very harmless, and damage arises from large collections that are confined
in the movement and agitated in the course. A tendency must Beds must be
ever be manifested to widen rather than contract the beds of widened.
30
970
ON LANDED PROPERTY.
rivers, and to straighten the lines of course whenever a bare possibility exists.
Necks of land may be often cut through with advantage in order to obtain
a straight course, even at a present sacrifice of value in the land that may
be used: the gradual damages of future waste will reach the amount and
exceed the present expenditure.
Flooded
grounds.
Mounds.
The notice now made provides against the damage done by the force of
currents of water rushing against the banks of soft earths that are unable
to resist the pressure; an injury is also sustained by meadow lands being
occasionally flooded by swollen rivers, which overflow the banks and stag-
nate the waters on the adjoining grounds. Summer floods will often come
during hay harvest and sweep away the cocked and tedded hays, or mix
with sands and mud the unmown herbage, and render it useless for any
purpose. These floods being spread abroad are not violent in
the action or large in force; the intrusion is easily averted, and
the direction controlled. A bank is raised of the materials of the ground
on the perpendicular height of three feet, which will overtop the highest
flood that may occur. The base will extend ten feet towards the river,
which will afford a very gradual slope of vertical height. The
mound may be almost perpendicular on the field side, as the
bank has not to sustain a force pressing directly upon it, as in the case of
the tides of the sea that rise with a constant appointment; it lies in the
direction of the current of the river, and has only to support the weight of
a fluid body that glides along its exterior, but does not exert an action
upon its constructed strength. It has only to show the course to the water,
and not to impede or obstruct it; the outspread water is restrained, but
not denied any prescribed course. The bank must recede some little dis-
tance from the bank of the river, and be so directed along its course as to
avoid any abrupt turning or hollows where the waters can lodge and press
with weight; the exterior slope must be convex, and the line must be uni-
formly gradual in the bendings, and afford the water an easy rolling
motion, without any ripple or displacement of the particles. The bank is
constructed of hard rammed earths, that are covered with grassy turfs,
and may be one yard in width on the top. Care must be used that the
embankment is continued to the first current of the overflowing, in order
that the water does not get behind the mound and render it of little avail.
In alluvial countries, as now described, the grounds are flat,
Hilly lands.
and the currents of water are slow, and hence the means of pre-
vention of harm are adapted to these qualities. Rivers of greater or less
magnitude, that flow from hilly countries, are rapid in the course from the
fall of the ground, and liable to very sudden risings of water, by reason of
heavy rains in the mountains: the impetuous course continues till the
flat country is reached, and before that period, much damage is done by
the raging waters rolling against the banks, tearing away the loose soil in
the narrow alluvial valleys through which the river flows, which very
often amounts to a total alteration of the course, when a bed of gravel is
left for the new bed that is taken from the cultivated lands.
These hilly grounds and narrow valleys produce more bendings
Much wasted
ON LANDED PROPERTY.
971
than happen in wide plains, and the soil being mostly of gravelly loam,
the waste is easy, and the demolition very quick. The gravel which is
carried along by the torrent is usually heaved against one side of the
channel, which being obstructed, the water is driven to the other side, and
with the whole force and weight it undermines and tears the soft alluvium
of which the flat lands are formed. The power of the water is most pro-
digiously augmented by the narrow channels which are formed between
the natural banks and the mounds of rolled gravel which shifts with the
floods and lies where deposited.
The furious rush of these impetuous torrents requires to be opposed by
the strong erection of very hard materials. Solid stone work is the best
resistance, built of squared blocks, with or without mortar, and raised to a
height beyond the highest rise of the waters. The form of the bulwark is
square, and longer in the face to the river than in the breadth to the land,
and must be very firmly based on the solid substratum that is reached by
digging through the alluvial mass of gravels and loose earths. The bar-
rier is called a jetty, and is placed to receive the current of the Stone jetties
water at a sharp angle of divergence, and to throw it off easily,
and almost without seeming to stop the direction of the stream. An ob-
tuse angle of divergence will throw the force of the water against the
opposite bank; and if the bed of the stream be narrow, the water will break
it, and probably cause a damage equal to that which is sought to be pre-
vented. The jetty must throw the current of water into a mid-channel,
and not against either bank; and consequently, the face of the stone work
must be in a straight line with the mid-channel, into which the water is
wished to be directed. The force of the current being broken against the
jetty, the water will require to flow for a considerable distance to break the
ere a new force is acquired, unless the fall of the country be current.
very great; and when a fresh current is formed which threatens danger to
the bank, a jetty is there built, which turns the stream as before into mid-
channel and clear of either bank. In this way the stream is conducted
from jetty to jetty in a harmless torrent till it reaches the placid flow of
the level country, when it is directed by the embankments of the former
description.
It is useful to protect jetties in front where the streams are very power-
ful, by placing large stones in a loose position at the base of the wall, and
raised to the height of the ordinary quantity of water. The bottom of the
heap may extend to three or four yards into the stream, and taper to one
stone at the top where the loose aggregation leans against the jetty. The
weight of each single block must be sufficient to secure for itself an im-
moveable bed, and defy the force of the water to change the position. In
the substratums of clay and alluvial earths, strong and lengthy wooden
piles may be driven into the bed of the stream, as has been men- Piles of tim-
tioned before, and a defence formed between them and the jetty;
but in many substrata the driving of piles is difficult, and the loose aggre-
gation of stones will be preferred. Both ends of the jetty must taper
backwards into the bank with a wall like itself, in order to prevent at the
ber.
972
ON LANDED PROPERTY.
upper end the ingress of water behind the building, and at the under end
the eddying of the stream into a corner, which may become the receptacle
of waters that may seek a new channel. The whole volume of the stream
must be directed into a mid-channel, and without any scattering of the
sheet of water towards either of the banks. The collected stream will
wear a channel for itself by the weight of its volume, and for that purpose
every encouragement must be given to direct it in a mass. This direction
is very peculiarly applicable to streams that descend an alluvial valley
from higher grounds, where the banks are in composition soft and easy of
demolition, and where the rapidity of the torrent soon excavates
to be always a bed for the water. It is not here meant to confine the bed of
kept.
any river of water, but in certain cases to direct the body of
water in a mid-channel, which will keep it from running against the
banks and tearing away the land.
Mid-channel
Water-
courses
Watercourses are beds of rivers on a small scale, that traverse estates,
farms, and plantations, on their way to join the main rivers that lead to
the ocean.
A surface of undulations and sinuosities very often compels a
tortuous course of the waters, and a formation of gravel or of soft alluvium
of ground gives way to the floods and torrents that run in the bended
course that has been excavated. These torrents are chiefly from floods of
rain and the melting of snows, and are confined from doing harm at the
bendings of the course by driving into the ground with heavy mallets a
row or two of strong stakes in one to two feet distant, and weaving a fence
with the branches of trees in the manner of a basket. The space between
the row of stakes and the bank is filled with the largest stones
that can be found, among which the water passes and deposits a
sediment, which in time fills the crevices, and the mass becomes a solid.
The wicker work having the tail of the branches in the direction of the
current, directs the water very quickly and smoothly along the
guarded,
wattled fence, and the wall being open to the passage of the
water through it, no solid resistance is offered to the current, but rather a
breakwater, which directs but does not obstruct the course. Small rivu-
lets that are only periodical streams of any size, are fenced in
and rivulets. this way by upright walls of wicker work backed with stones;
and larger brooks are guarded with a sloped wall, as has been before de-
scribed. This slope is well formed with strong stakes driven into the
ground, the vacuities being filled with stones from the shingly bed of the
stream, and the top covered with long branches of trees, with the tails
pointing with the current, and fastened to the stakes by the natural hooks
of the branches, or by ligaments, or by cross beams nailed to the stakes.
Heavy stones being laid upon the top will add much to the solidity of the
structure. In the course of time, the proper grasses will grow and form a
matted turf, along which the floods of water will run with much ease and
tranquillity. Very good walls are formed in this way; the materials are
generally ready, the performance requires little skill and the expense is
not great.
4
ON LANDED PROPERTY.
973
embanking.
The principles of embanking are few and very simple, and Simple prin-
admit an easy application. Water should run in a course as ciples of
straight as can be obtained, and have a wide channel rather
than a narrow bed. The bendings of rivers are guarded by barriers of
piles and stones, and the impetuous currents of mountain streams are
diverted into a mid-channel by jetties of stone masonry, against which the
water rushes at a very sharp angle of divergence. The risings of tides and
floods into deep formations of water are averted from doing harm by means
of earthen mounds covered with grassy turf, on which the waters roll, but
against which they do not impinge and press with the weight of their
depth. This last principle forms the chief remembrance of embanking.
The difficulties of execution will be proportionate with the circumstances
of the locality, in position, materials, and labour.
Irrigated
Irrigated grounds constitute a very beneficial adaptation of
lands that are situated to undergo the special application. In ground.
dry hot countries the artificial supply of moisture was early adopted as a
mode of increasing the fruits of the ground, and the practice has been in
some degree continued in many countries in which circumstances permitted
the use. The Romans used water extensively both on arable and grass
lands, and from them the application has descended to the present day.
In Britain, irrigation attracted much notice within the last hundred years;
and there was scarcely left a brook, rill, or stream that was not converted
to that purpose wherever it could possibly be used.
The advantages consist in raising an early grass in the spring, Great advan-
in growing a large crop of hay, and in producing an abundant tages.
lattermath for the grazing of animals. In some places these advantages
are very great, and compensate the heavy expenses of formation and up-
holding. The full benefit of flooding suppose a dry hot climate, and an
easy command of water, and a position of the lands to admit the ingress
and egress of the water, and an application at a moderate expense. These
indispensable requisites will show that, comparatively speaking, few situa-
tions admit that mode of improvement.
dows.
Irrigated lands are divided into two kinds—catch and flow meadows :
the former lying on a declivity, and catching the water in its descent from
the higher grounds; and the latter raised artificially, to allow the water to
flow over them. In catch work, the water is conducted by a Catch mea-
level course to the higher part of the ground, and divided into
rills, which are stopped at intervals to make the water flow with a rip-
ling motion over the surface, for which purpose all inequalities must be
levelled, and the stops duly regulated, in order to throw an equal quantity
over the whole space. If the declivity be considerable, the rills must be
cut in a diagonal direction to follow the fall of the ground, so as to convey
the water most regularly, and with a uniform motion, and in an equal
quantity over the surface; if the ground be more flat and even, straight
and parallel cuts will answer the purpose. When the water has passed
over the whole space, it is conveyed away in an open ditch into a brook
974
ON LANDED PROPERTY.
or river; or if the ground admits, it may irrigate another division of catch
or flow meadow before it be finally lost.
Flow mea-
dows.
In flow meadows, the land is generally flat or nearly so, and
must be raised into ridges of ten to fifteen yards in width, with
open drains between them, and rills cut along the top of the ridges, with
a longitudinal fall to cause the water to flow along them, and with a de-
clination of the sides of the ridges to the catch drains sufficient to make
the water run briskly over the surface. The main or conducting drain
passes along the head or upper end of the flow work, and discharges a
quantity of water into the rills along the tops of the ridges, regulated by
the volume they can contain, and which is thrown by the artificial stops
in the rills evenly and regularly over the sides of the ridges. It passes
into the catch drains, which convey it into an open ditch, brook, or river,
where it is carried away. The expense of forming watered
meadows has been stated at £5 to £20 and upwards per acre;
the latter kind being much more expensive than the former, which in
many situations can be done at a moderate cost. The annual
expense has been stated at £6 an acre, and the produce at £9;
leaving a profit of £3 an acre, after paying £2 10s. for rent, included in
the expenses.
Expense.
Returns.
watering.
In the general management of irrigated lands, the water is admitted in
November, after the surface has been eaten very bare, and the gates,
sluices, drains, and rills have all been put into working order. Practice varies
in the time the land is allowed to be under water during the winter
months; some allowing ten to fourteen days; others, two, three, or four
weeks; gradually lessening the time to a few days till the beginning of
Seasons of March. A month's watering may be given in November and
December, with some days between each time, and in January
and February for a week at a time, and latterly for four or five days. The
lands should be laid as dry as possible between the waterings, and it has
been much recommended to avoid raising a white scum by too much water-
ing, and to turn off the water instantly, as damage ensues from a noxious
quality in the scum, and the risk of the meadow being exposed to frost in
that state. But many experienced irrigators never found any damage
from that cause. In the beginning of March, there is generally sufficient
grass to admit sheep to feed, and the meadow will be allowed a time to
dry and consolidate before the admission of any stock. It is customary to
fold the flocks on adjoining arable lands, and to graze the meadows from
ten o'clock to five, when the dews will be off the grass. The herb-
age may be eaten close till the first of May, when the water is
admitted for a few days, and again laid dry for hay. After the crop is
removed, dairy cows and young cattle are admitted to graze till October,
as summer watering has long been supposed to rot the sheep. The second
crop of hay has been cut, but it is generally weak and flaccid in quality;
and even the first crop, if not cut quickly in the season, often becomes
coarse and unpalatable.
Use of the
herbage.
Irrigation is a very beneficial way of using land in places that suit the
ON LANDED PROPERTY.
975
results.
application, and where water can be led to the grounds, and the surface of
the land made uniformly level at a reasonable expense. The chief benefits
attend a dry soil and a warm climate, though advantages are not wanting
in cold latitudes and under watery climes. The fertilization that is im-
parted arises principally from the protection of the ground during winter
from colds and frosts, and to the higher temperature which the ground
obtains. Anlysis of soft and hard waters gave no result on which to found
a preference, and no difference could be observed between the clear water
of the spring and the sedimentary liquids of a still water brook. No doubt
thirsty lands under a dry climate will imbibe very beneficial moisture from
the waters that run over the surface, but which must not stag- Various
nate upon the ground so as to cause starvation and excess; the
movement must be constant and uniform, and neither loitering nor mean-
dering. The use of irrigation on cold lands and under stormy climates
produced an overgrowth of rushes and aquatic herbs; the practice retro-
graded, and is now confined to the select localities, where the proper eligi-
bilities are found. The stream of water must be constant and abundant,
capable of being commodiously applied, and also having a ready escape
from the grounds after the purpose has been effected. All these provisions
will be examined and ascertained before an irrigation is attempted. The
soil and its capabilities must be duly accounted: if it be strong General
in nature and will be grateful of a higher temperature, or thirsty
and will be benefited by a large application of moisture. The probable
expense will be also estimated, and the expected result will be placed
in opposition. It is not a general use of the land, as so many attendances
are required to be present. When these requisites abound, the use of
water has very largely repaid the application.
capabilities.
CHAPTER VIII.
LAND DRAINING, OPEN AND COVERED,-PLAN, EXE-
CUTION AND ARRANGEMENT BETWEEN LANDLORD
AND TENANT.
lands.
It was very early observed by the cultivators of the earth, that moisture
formed one of the essential elements of vegetation, and another obser-
vation was not much longer in being made, that an excess of it pro-
duced the opposite effect, retarded vegetation, and ultimately Draining of
caused sterility and barrenness. In the early ages of agricul-
ture, little or no attention was paid to the remedy of this damage which
the land sustained: but as population increased, the wants to be supplied
became more urgent, and application was made to remove the cause of
this damage among the other operations of improvement. The first at-
976
ON LANDED PROPERTY.
First concep-
tions.
Stones for
filling the
trenches.
tention was directed to the removal of springs, which are formed by out-
bursts of water from the under strata of the earth, forced upwards by pres-
sure from a higher quarter. It is found that water flows in the permeable
strata of the earth, as sands and gravels, and as these strata lie irregularly,
unevenly, and interruptedly, the water finds or forces outlets upwards,
as it is stopped in its course by impervious substances, and impelled by
the pressure of its own body from a more elevated quarter. Attention
was early directed to the interception of these outlets, and con-
venience suggested the mode of making trenches in the ground,
and thus conveying away the water underneath the operations that were
acted upon the surface. In order to afford a current room for the water,
stones were used to make a small square culvert in the bottom of the
trench, and over it was laid a quantity of smaller stones which were covered
by a turf and earth, and this operation finished the process. In places
where stones were not abundant, or could not be found at all, other mate-
rials have been used for being laid in the bottom of the trench, to afford a
vacuum in which the water may flow, as stubble, straw twisted into ropes,
and brushwood; and when the latter substance is put into neat bundles,
and firmly tied together, and well trodden into the trench, which is sloped
in the sides and narrowed downwards, drains have been found to run very
well for many years, when filled with that material: but stones
are in every case preferable, being the strongest material, and
the most durable. Very many and most valuable improve-
ments were made by this process; springs were intercepted and diverted;
bogs and quagmires were rendered firm ground. Much waste land was re-
claimed which was previously rendered nearly useless by the repeated inter-
ruptions caused by watery outlets. The observation of these causes and
remedies was afterwards extended to the damage inflicted on land by at-
mospheric wetness, from the clayey nature of the land retaining too long
the moisture that falls from the heavens, and thereby retarding the opera-
tions of cultivation, and lessening the quantity and quality of the vege-
table productions. It was early known that clay is not permeable to water,
and consequently water will not flow into the trenches but from a short
Frequent
distance on either side of them, on the very wet and tenacious
drainage.
clay lands which abound in this kingdom. On this principle is
founded the modern system of frequent draining, in which the drains are
placed at short distances from each other in order that the water may
flow
into some one of them and not remain on the land. The wetness caused by
the rains from the heavens has been too often attributed to springs from
below; an insufficient number of drains has been made in order to divert
them: the cause lay in a different quarter, and the land remained wet as
before. The knowledge of the true cause of wetness has crept very slowly
into the agricultural world; in many instances it is yet unknown, and very
far from being generally acted upon. The very general desire of doing
things with little trouble, and at little cost, has added much to the belief
of water rising from below the ground being the cause of wetness; a few
drains were reckoned sufficient, which gave little trouble to the mind or to
ON LANDED PROPERTY.
977
the purse. A better knowledge is now being obtained, but not rejecting
the former where found to be prevalent and necessary.
Tapping of
A system of draining wet lands by tapping the springs, was much esti-
mated some few years ago. It consisted in boring large auger holes in low
grounds into the tail of the stratum in which the water flowed, and from which
it burst upwards in higher grounds and drawing the water to the auger holes.
The plan succeeded or failed according as the strata in which
the water flowed were regular or irregular, continuous or inter- springs
rupted. Failures were most frequent, as might be expected; and for the pur-
pose of carrying away surface water the plan was wholly useless. Even where
it succeeded, it was seldom very strikingly more beneficial than the old
mode of running a drain to each spring, for this drain in its course fre-
quently intercepted other sources of wetness, or the surface water that
flowed near its course. The specific success was confined to the
springs flowing in sands and gravels, and where they formed
the sole source of wetness. Draining of lands on that system has been
altogether discontinued for a long time past.
now disused.
The modern system of draining differs from the old only in making a
greater number of drains, and hence it is often called the frequent sys-
tem. The same shape of the drains, the same mode of digging, and mostly
of filling, yet prevail. The frequency of the drains carries off all the
surface water, and intercepts the springs on the land, if any exist, and
thus effectually answers both purposes.
In the modern system of draining, three things are chiefly to be con-
sidered: the frequency of the drains, the depth, and the mode of filling.
The frequency of the drains will depend on the tenacity of the upper
soil, and the nature of the subsoil, if it be pervious, impervious, or mixed.
In pervious and mixed subsoils, the water will flow into a cavity from a
distance in the permeable strata, and consequently the drains may be
farther apart; but in tenacious soils, and in compact impervious subsoils,
the water will not percolate or flow to any distance, and conse- Frequency of
quently the drains must be nearer to each other in order to afford drains,
a ready egress to the superabundant moisture. The most tenacious clay
soils may not require a nearer distance than four yards: some writers
state five yards as the closest draining that any lands may require; but in
pure plastic clays which form the extreme cases, it is better to err on the
safe side, and to have rather more drains than too few, and thus repeat
the old error of a non-effective performance. A distance of five yards
will drain very wet lands, but instances are not wanting where four yards
may
be required. A distance of not more than eight yards will be required
to drain the most permeable soils and subsoils, and the general distance of
four to eight yards may be stated as being required for the soils and cli-
mate of Britain, ranging between these two numbers, according to soil
and situation. Of these circumstances, the practitioner must judge from
appearances; in many cases the herbage will give a fair idea of
the nature of the soil; aquatic plants indicating the superabun-
dance of moisture from below, and the altitude or hilly nature of the
how indi-
cated.
978
ON LANDED PROPERTY.
country will give intimation of the quantity of rain that may be expected
to fall, and of the number of drains that may be required when both cir-
cumstances are considered. The skill and judgment of the chief operator
must be duly and very fully exercised on these points. A local knowledge
is best; but as it is very seldom to be got, the next best, or that of practice
and experience must be used. Mistakes are often committed from want
of the observation and consideration which these two points
Much judg-
ment re- require the two essential points on which the whole matter
quired. rests. On no point in the practice of agriculture is there more
room for the exercise of skill and judgment, for a mistake is productive of
much more mischief than in most other cases, being widely spread in its
effects, and difficult of remedy.
Depth of
The depth of the drains must also be regulated by the nature of the
soil, and the dryness or humidity of the climate. In pure clays, where
the effect of the drain is wholly confined to the carrying away of surface
water, the drains cannot be too shallow, provided they are not disturbed
by the plough or the feet of the animals. All the moisture or water to
be carried away lies on the surface, and consequently the readier access it
finds to the drains the better. But impervious and mixed subsoils, where
the under-water flows in horizontal or vertical strata, the drains may be
deeper, in order to find a firm foundation for the materials with which the
drain is filled; though the propriety is questioned, and is certainly very
questionable, of cutting drains any deeper than where the water
drains, is first found, and there to commence filling the drain, always
supposing a firm foundation to be first found. Deep drains require more
materials to fill them, and create more expense, both in filling and in dig-
ging; but in permeable soils, they may be useful in draining water which
may flow in a stratum that edges or throws water upwards between the
drains. Drains removed to a depth beyond the reach of the surface water,
are wholly useless for the purpose of removing it, and much money and
useless labour have been expended in digging downwards to cure the evil,
when the remedy lay wholly upon the surface. In our climate, and upon
the generality of our soils, a depth of two to three feet may be stated as a
two to three fair average; water lying or flowing below that depth can in-
flict no damage on the upper soil, and if the drains are made
deeper, they may be removed beyond the reach of the surface water.
Various depths have been mentioned by writers, and even by practical
men, which are not worth much discussion, as they seem to have pro-
ceeded more from fancy and bare matter of opinion, than to be grounded
on experience or on any specific solid fact. The depth now stated is
sufficient to intercept the permeable strata, and does not require any
large quantity of materials to fill it to a proper depth from the top, or
render it accessible to the surface water, and these are the very special
purposes of draining, viz., to carry away the surface water, and at the
same time drain the under-water that lies within the reach of damaging
the
upper soil.
feet.
Stones have ever been universally preferred for the purpose of filling
ON LANDED PROPERTY.
979
drains, but in many countries they are not found, and other materials have
been used, as brushwood, stubble, and twisted straw. Modern invention
has supplied the place of stones, and by the substitution of tiles, which are
composed of puddled clay moulded into the proper shape, and then baked
in an oven or kiln, to a hardness that resists the action of the Materials of
vicissitudes to which they are exposed. This invention must be filling.
reckoned one of the most valuable of modern times, for it converts matter
into the means of improving itself, and the most tenacious clay into a
mode of making itself productive. The ductile quality of clay allows
it to be moulded into any form, which in the present case is about twelve
inches long, and arched into a span of four inches. Other dimensions
are used, but the shape now given has been found to be well adapted
for the purpose. The width of the drains at the top may be about two
feet, sloping to six inches in width at the bottom, in which the tile of
four inches is laid. It has been found by experience that the
constant percolation or oozing of water on the bottom of a drain,
even of a hard and tenacious clayey nature, creates a softness in which the
thin edge of the tile gradually sinks and obstructs the arched passage, as-
sisted by the superincumbent weight of the filling materials. This cir-
cumstance has rendered necessary the use of soles or flat tiles that are
laid below the arched tile to prevent the sinking, and in common practice,
a piece of a broken sole is laid below the meeting corners of the arched
tiles, and bears the pressure of both. A quantity of straw, or a turf laid
with the grassy side downwards, is put over the tile, and the excavated
earth being thrown promiscuously to fill the drain, the process is
finished.
Width of
drains.
used.
In the filling of drains with stones, the materials are broken with ham-
mers, to the size of the largest road metal, either in the quarry where the
stones are dug, or on the sides of the drains where the unbroken materials
are laid. Stones dug from a quarry are preferable to stones gathered on
the surface of the ground, as they afford more angular points, stones, how
and consequently a greater number of interstices in the drains;
when the stones are broken on the sides of the drains, the bruised materials
are very conveniently lifted into the drains by means of baskets, without
any earth getting intermixed. When they are dug and broken in a
quarry, earth or rubbish of some sort will generally get mixed with them,
and it is essential that no earth get into the drains. A screen is very
easily constructed and placed on a wheelbarrow to be moved along the
side of the drain as it is filled, provided with a wide screen to turn the
stones into the drain, and a narrower one to throw on the ground the rub-
bish that passes through the wider bars of the upper screen. The carts
come alongside the screen, into which the stones are thrown from the
carts by hand shovel, the large bulks run into the drain, and the rubbish
falls on the land; and with care and attention very sufficient work is made.
But in general it may be recommended, that the stones be laid unbroken
on the sides of the drains; that they be broken on a platform of boards,
filled into baskets, and placed into the drains, and immediately covered
980
ON LANDED PROPERTY.
them.
Covering of with turf and earth. It is necessary that the drains be not
allowed to remain long open and unfilled, nor the stones be al-
lowed to lie uncovered after being put into the drains. In this operation,
as in all others of a similar nature, systematic dispatch must be studied,
the different operations must go on simultaneously, and be so arranged,
that the execution of one part does not overreach the other, in order that
the unfinished portion may sustain no damage. The earth crumbles into
drains lying open, and causes labour in shovelling it out before the stones
are put in and the same objection holds with stones placed in drains and
lying uncovered.
It is very convenient when land can be drained in a state of grass, on
account of the superior cleanliness and neatness with which the work can
be performed. This very great advantage will most amply compensate
Grassy turf for any additional expense incurred in digging the drains during
useful. the hard season of summer, which may sometimes happen, and
sometimes not. The lines of the drains being first marked by pegs or
turves, the unbroken stones may be laid alongside at convenience; the
grassy turf must be pared off thinly, and laid aside, and carefully pre-
served for covering the broken stones; the drains may then be dug to the
full depth, and immediately filled with the broken stones to the height of
twelve to sixteen inches from the top; the stones levelled with an iron
rake, and the grassy turf laid neatly over them, and the earth shovelled
in upon it. The broken stones should be put into baskets, and handed to
a man standing in the drain, who will empty them in the proper place,
level the stones, and lay the grassy turf neatly over them; and it is essen-
tial that this part of the business shall be performed by a confidential
person specially appointed for the purpose, and whose contract bears a
greater remuneration for the proper execution of it. The quarrying and
breaking of the stones, the digging of the drains and the filling of the
earth, may be let to be done by contract; but the filling of the drain
with stones, and the laying of the turf over them, should be performed by
a fixed daily or weekly remuneration, where there is no induce-
ment to hurry over the work imperfectly, as is generally the
case in contract work. Work that is exposed to view may be
mended when seen to be imperfectly performed, but a drain when covered
is hid for ever, and the mischief remains. Much draining has been spoiled
and money uselessly expended by the work being improperly executed on
an erroneous system: contract work requires a sharp oversight, and in what-
ever way draining is performed, it claims much attention, being easy to
spoil, and difficult to remedy.
Filling most
carefully
done.
In digging drains it is advantageous that the cavity is sloped to a very
narrow bottom, as the stones, in being put into the drain, catch on the
sloped sides, and form a kind of artificial arch, and afford a greater cavity,
or more interstices below. When tiles are used, the bottom of the drain may
be made the breadth of the tile, or a little more.
Broken stones laid in a drain over the tile about a foot in depth, has
been called the “ ne plus ultra" of draining, as it affords a clear pas-
ON LANDED PROPERTY.
981
"Ne plus
ultra" of
draining.
Tiles.
sage for water in the tile, and the upper space occupied by the
stones is open and porous for extracting and conveying the
water downwards. In the case of the tile alone being used, and covered,
as it generally is, with straw, or a thin grassy turf, these substances are
soon compressed and decay, and then there is only the space occupied by
the tile, about four inches in height, to form a drain, both to extract and
carry away the water. When stones are used, the half of the depth of
the drain is filled, and thus affords an interstitial cavity of fifteen inches,
for the purpose of receiving and discharging water. This circumstance
constitutes the superiority of stones over tiles for the purpose of draining :
they also form a stronger drain, and are more durable. Tiles
are preferred where there is a constant current of water; in
such cases, where stones are used, a square culvert should be set with
broken stones, of a size proportioned to the quantity of water it may
have to contain. It is necessary that a constant current of water have a
free unbroken course. The receiving drain at the lower end of the field,
must be wide, and have ample space both in width and depth-a depth of
some inches below the common drains, and a width sufficient to contain a
square set culvert of large unbroken stones to convey the whole quantity
of water from the drainage; if one culvert be insufficient, two may be
made; and in the case of tiles, if one large tile, which are made for the
purpose, be insufficient, two may be placed, if necessary. These re-
ceiving drains must be conducted with great care, where the common
drains are discharged into them, built with solidity, and have a covering
of broken stones and grassy turf over them. If the current of water be
large or rapid, care must be taken that the bed of the current is secured
by laying soles or thin stones.
.
filling.
When drains are being dug, it may be advantageous to lay on one side
of the drain the porous upper soil which is first 'excavated, and on the
other side, the subsoil which will be of a different nature. After the
grassy turf or straw is laid neatly over the stones or tiles, this earth
may be shovelled into the drain, and may be mixed, or the one Earthy
preferred to the other. Where the subsoil is very clayey and
tenacious, the upper soil may be first put in, and the subsoil put on the
top, as the action of the air and the operations of cultivation may pre-
vent its consolidating and denying a passage to the water downwards, as
often happens when it is put undermost in the drain. But no damage
may happen from both kinds being put in promiscuously, unless the clay
be very tenacious. A depth of fifteen inches of earth, over the stones or
tiles will be sufficient to admit subsoil ploughing, and may not be too deep
and deny a passage to the water.
Digging.
When the pressure of other business over the farm does not allow the
full combination of the operating force on the point of draining, it will
be very convenient to dig the drains to half the depth, and to
excavate the part that is left at the time when the materials are
brought forward and broken, and then the two operations of digging and
filling can go on together. It is of very great consequence that a drain
982
ON LANDED PROPERTY.
be filled with stones immediately on being dug, on the same day, if
possible.
Direction.
Drains are generally run in three directions, upright, aslant, and across;
and each mode has its advocates, according as circumstances have favoured
the operations. Cross draining can only be done when the de-
clivity of the land favours the descent of the water in that
direction, and then it becomes a kind of upright draining, being upright
to the fall of the water. The across and slant directions have an advantage
in the ruts of the plough crossing the drains, and thus conveying the water
to be carried off, while in the upright direction the ruts and the drains run
parallel, and consequently the water may remain longer on the land before
reaching the drains. A preference may be justly given to that direction,
which causes the ruts of the plough to cross the drains, for it seems natural
to suppose that the water will, by that means, make a quicker escape. But
much land has been and is yet drained, by placing a drain in each furrow
Furrow between the ridges, at distances of four to twenty yards, and
keeping the open furrow over the drain; and it is contended
that it forms the most effectual mode of drainage on pure clay lands, and
that the drains must be no deeper than places them beyond disturbance
by the plough and the horses' feet. The ridges are shaped and raised to a
convexity to throw the water to the furrows, and it is there quickly let
into the drains. This mode is still largely practised in many places, and
it has proved both effectual and durable.
draining.
The Duke of Portland was among the first practitioners in Britain, of
the furrow draining, or frequent system; and the mode of placing the
Duke of
Portland's
method.
drain in the open furrow made by the plough, and sinking the
cavity no deeper than beyond disturbance by the implements
of cultivation, has always been used, and is yet followed over
all His Grace's estates, and was seen in full operation by the author of this
work on the stiff alluvial clays in Ayrshire, in the west of Scotland, on the
estate of that nobleman. After all that has been done, spoken, and written
on the subject of frequent draining, the above practice may form the sim-
plest and most effectual mode that is yet known; and His Grace's very
true and most just opinion on the subjects, is very deserving of
being recorded:—“That on all purely clay soils, the drains can-
not be too shallow, provided they are not disturbed." Place the drains in
point of number within the quick reach of the water, and afford to the
water as quick a descent to the cavity after it has reached the surface of
the drain. These two provisions constitute complete drainage, and both
must exist, as one is useless without the other.
His maxim.
Circular or pipe tiles have lately been introduced, which
Pipe tiles.
fit into each other at the ends, and thus form an uninterrupted
channel. The diameter has been reduced so low as one inch-much too
small an orifice to form a drain. The largest tiles are sometimes deficient
in forming a cavity large enough to form a drain, and experience has taught
all drainers to increase rather than diminish the size and capacity of the
open portion of the drain. It is on this account that stones are so very
ON LANDED PROPERTY.
983
much preferable to tiles, in forming an interstitial cavity of broken stones
in place of four inches afforded by the tile, for the purpose of draining and
carrying away the water.
Pure clay soils admit the stones to be small broken, as there is no
current or muddy oosing of water to require large passages. But in mixed
subsoils of sands and gravels, where are found outlets and oozings of water,
the stones may be of a larger size, as they form larger openings and in-
terstices for the passage of the muddy liquid. On soft bottoms where the
stones sink by their own weight, it is necessary that some flat substance
be laid underneath them. Soles are used in tile-draining; and for stones,
slates have been very much recommended, and no doubt will prove to be
very effectual, but the expense will be considerable, and flat shaped stones
may be used, or any rough unbroken stones may be thrown into the drain
till a bottom be formed by their weight sinking them, and then the broken
materials may be put into the drain as usual. These points require much
attention in draining; a neglect even in one single place may
defeat the purpose of an entire length of drains, cause obstructions,
and much expense and labour in removing them.
Soles for
sands and
gravels.
The very first object to be considered in commencing the operation of
draining, is an outlet for the collected water, and for this purpose, the
brooks or rivulets must be very carefully examined, deepened, and
straightened, where it is necessary; the second consideration is the large
drain, whether covered or open, that receives the water from the small
field drains, and conveys it to the brook. It must be of sufficient width
and depth, and convey the water freely away, without any stoppage or
obstructions. An experienced operator will commence with these exami-
nations, on which depends in a very great degree the success of the
intended scheme.
Hill drain-
ing.
Very much good has been effected on the Cheviot mountains
and the Southern Highlands of Scotland in improving the sheep
pastures, by cutting open drains for surface water with the spade, in large
sods from sixteen to eighteen inches wide, and laying them on the under
side, as the drains are chiefly run along the slanting sides of mountainous
grounds. The cut is then cleared out to the depth of about fifteen inches,
and the loose earth is likewise thrown to the lower side, so as to make a
bank.
These drains by removing the surface water, have proved of essential
service in preventing the rot among sheep in moist pastures. An early
bite of grass may be procured for the sheep by throwing the water over
convenient grounds by way of irrigation, and these two advantages make
this kind of draining one of the most useful improvements of the present
day.
When springs of water are found in land to be drained, it will happen
that the straight lines of the drains will pass on each side, and leave the
outlet untouched; in that case, a drain must be cut, and run with the
necessary declivity from the set drain to the spring, and a tile must be
laid, or a square culvert set with stones, to convey the current to the drain ;
984
ON LANDED PROPERTY.
Springs of
water inter-
cepted.
and if the current of water be strong and constant, it will require
a tile, or a stone culvert to convey it to the receiving drain at
the end of the field. An oozing of water will find a way among
broken stones; but it is much better that a current have a free course in a
tile or culvert. The ends of all drains that remain open should be built
up firmly with square stones to the height of the drain, leaving a square
mouth of discharge for the water. The joining of small drains with re-
ceiving drains must be made of the same height, and covered with the
same turf and earth; and all such work must be done by an experienced
confidential person, and the whole carefully overlooked and superintended
by the chief operator. In no agricultural business whatever is more care
and attention necessary than in draining, and nowhere does carelessness
and neglect operate more forcibly and to greater disadvantage.
All drains
covered.
It is advantageous that all drains or ditches be covered, that
no open drains remain anywhere visible within the enclosure of
a field. Covered drains admit the plough close to the fence, and allow
the live stock to obtain the shelter of the hedge by standing close to it.
The expense of draining, like that of every other operation and per-
formance, will vary according to circumstances as the cost and distance of
the carriage of the materials, and the price of labour required to apply
and adapt the materials to the purpose. A variation in draining will also
happen from the greater or smaller number of drains that are required on
an acre of land, and this circumstance itself must vary according to the
extreme or moderate wetness of the soil. All these circumstances com-
bined require a wider range of figure than at first sight would appear to
be necessary, and to the reasons above given there must be added the
nature of the soil, if it be hard or soft for digging. The expense will
range from £4 to £8 per acre, according as the favourable or unfavourable
circumstances may predominate; an average may be stated in £5 or £6
Expense of an acre, when the drains are five or six yards apart, which
draining; width will drain moderately wet lands. This estimate is con-
fined within the hedges of the field to be drained, all exterior operations,
as the cutting of open ditches, and of water courses, must be charged to the
account of general expenditure.
The expense of draining being very considerable, and the nature of the
improvement being permanent, it is both natural and reasonable that it be
performed at the expense of the party who has a permanent interest in the
land on which the improvement is performed. A yearly tenant of land
is debarred by common sense from making any outlay of which he cannot
reap the full fruits in the year of tenure; a farmer with a short lease is
not much better situated. A lease of not less than twenty years,
falls. at least, is required to justify such a costly improvement as
draining at the expense of the tenant, that he may have a fair chance of
being reimbursed for his outlay of capital. A farmer, even with a lease,
has only a temporary interest in the land he occupies-it is contrary to
human nature to expect that he will take as much trouble in the per-
formance as if he had an interest at stake, and consequently the cost of the
on whom it
ON LANDED PROPERTY.
985
improvement reverts on the proprietor who enjoys the perpetuity of the
value. Accordingly, the most equitable arrangement seems to be that the
improvement be effected at the cost of the proprietor, the tenant paying a
yearly interest for the money expended, and the cartage of the materials
as an equivalent for the benefit he may derive from the improvement
that has been effected. The work being done by the proprietor's own
workmen, he has the greater security that it is properly done; a vast
advantage over the draining being entrusted to persons who have only a
temporary interest in the performance. Various arrangements Various ar-
have been made between landlord and tenant; as the former rangements.
giving the tiles, and the latter digging the drains and filling them; and
otherwise each party paying half the expense. The most common, and
the most equitable arrangement consists in the landowner making all the
outlay, and the farmer paying five per cent. interest on the outlay, during
the period of twenty years: and otherwise, the tenant pays 5s. or 6s. an
acre for the drained lands, along with the rent, in half-yearly payments.
This last mode will give the landowner three-and-a-half to four per cent.
yearly, for the money expended, which may be sufficient when the national
funds are taken as a model. This last arrangement was from the first
adopted, and is still used by the Duke of Portland, whose excel-
lent practice has been already mentioned on several rural under-
takings. His methods and calculations are never exceeded by
any subsequent attempts, but remain as rocks fixed in the bottom of the
sea, that are never lifted up and down by tides. In all arrangements, the
proprietor must have the work done by his own agency both in labour and
superintendence, as he has the security of its being permanently effected.
The farmer by doing a stated portion of the performance, buys the yearly
fruits of the improvement, and at the end of twenty years, the negotiation
is terminated, and the improved ground becomes an article of commerce
in the altered condition which has been imposed upon it. A wealthy
tenant may be induced by a lease of twenty or twenty-five years to drain
lands at his own cost which are the property of another person; but the
cases are few, and there is yet a great aversion to grant the necessary
security which is essential to the business. Security begets confidence, and
confidence promotes that thirst and eager desire of remuneration which
does not exist unless self-interest be enlisted in the cause, and which so
effectually ensures the advancement and economical termination of any
intended scheme. Terms of agreement regulate the moral ex-
citement, which is keen or blunt as the conditions may be
encouraging or unfair between the parties.
Duke of
Portland's
method
of all ways
the most
equitable.
The draining of lands that are wet, either from springs of water from
below the ground, or from the aluminous composition of the soil holding
the moisture too long, and causing damage to vegetation, or as often
happens from both causes must precede all other improvements that may
be intended to be undertaken under the circumstances now described.
Experience will direct whether a thorough frequent draining be necessary
to prevent the damage of a general wetness, or a less frequent drainage
3 P
986
ON LANDED PROPERTY.
Value of
to carry away the hurtful effects of springs, aided by a partial wetness of
the soil; but in every case the drainage should be more frequent than less
frequent, in order to produce at once a sure and certain result. No pro-
prietor of land ever can find a more profitable or a safer invest-
draining, ment for money-he has the security on his own property, in
addition to the improvement of it; and it has been stated, as an average
calculation, that land thoroughly drained, and properly managed other-
wise produces three crops in two years, in comparison with the former
produce. The farmer has the advantage of more produce from his lands,
the texture improved, and more easily wrought and accessible, and a more
grateful and a sweeter herbage. The circumstance of draining rendering
lands easier and sooner accessible at the different periods of working, is a
recommendation of itself sufficient to show the great value of the improve-
ment, besides the increase of produce in every crop that grows. Experience
has not yet recorded the fact, if draining has in any case converted stiff
clay lands into turnip loams: if it has happened any where, it may
have
arisen from a constitutional near alliance of the soil, or from
the nature of it approximating to loam, and wanting only the
abstraction of the water, and but little alteration in the texture. Clay
soils may probably be placed beyond that degree of alteration.
on any lands.
It has been objected to draining that it destroys the viscous tenacity in the
land, so necessary to the production of wheat and beans, and may carry off
in the shape of water the saline and soluble salts in the soil. But these
evils may exist only in imagination and anticipation, and may in effect be
only partial, and may not detract much from the general value of draining.
The effects of it have been found so very superior to that of the viscous
tenacity and that of the soluble salts in the wet state of the land, that
little hesitation will be entertained which of the two conditions of the land
must be preferred for practice.
Objections
It is certain that draining has not in every case been attended
not tenable. with success, and that in many instances it has been accompanied
with loss of capital. This result may be ascribed to two general causes:
the want of knowledge or caution in the application of the system to prac-
tice, and to the defective execution of the works, in cutting and filling the
drains, and in the materials used. True economy consists in getting work
well done, not in the cheapness of execution; and a very general mistake
is constantly committed in placing the tiles too deep, and too small a
quantity of porous materials over them; thus repeating the old error of
having useless drains deeply imbedded in compact clay, and beyond the
reach of the surface water. But the occasional failures of draining are not
more frequent than other miscarriages, the chance of which attaches to
proceedings of every kind. A neglected execution will mar any
purpose, and a careless application almost renders a failure to be
Failures few.
certain.
In order to derive the full effects of draining, it must be followed by an
improved treatment of the land in every respect, as to cropping and ma-
nuring, in order to repair the damage they may sustain by the supposed
ON LANDED PROPERTY.
987
of draining.
General,
loss of tenacity and of saline soluble matters. When land is drained in a
state of grass, there will be fresh matters in the soil for decomposition,
and then the liberal application of calcareous matters becomes very highly
necessary and desirable. It has been admitted in all ages of the world,
that the draining of marshes and of stagnant waters is highly Consequences
conducive to health and salubrity; and we may very reasonably
suppose that the close draining of wet lands, though performed on a
smaller scale, will operate in a similar manner. It carries away or pre-
vents the generation of the pestilential miasms that originate in distem-
pered and poisonous bodies, and lime arrests the noxious effluvia that tend
to rise more or less from every soil at certain seasons of the year, and de-
composes them, or causes the elements to assume new forms of chemical
combination, in which they no longer exert the same injurious influence
on animal life. How beautiful a consequence of agricultural skill that the
health of the community should be promoted by the same methods which
most largely increase the produce of the land! Can it be doubted that
the All-benevolent Creator of the world places this consequence so plainly
before mankind as a stimulus to further and more general improvements,
to the application of other knowledge still to the amelioration of the soil?
What noble employment for the mind of man! By the use of
his reason, his energies, and his capital, he affords in the first
place, employment for his fellow-creatures, then an increase of food and of
health to the human race; and lastly, a remuneration to himself. What
more can his heart desire? There is nothing wanting to satisfy either the
selfish or the philanthropic mind. A very heavy and unextinguishable
responsibility rests on those persons who possess the means and the
of conferring such invaluable benefits on the human race, and neglect the
very valuable opportunity of lightening the debts of property to poverty ;
and who continue ignorant and unwilling, or incapable of action, in spite
of the warnings of science and the sanctions of experience. Under the
wide expanse of heaven there is not and cannot be a more gratifying em-
ployment than the improving the condition of the human race; Universal,
and as the physical condition must ever precede the moral, the
improvement of which we are now treating, must claim a prominent place
among the agencies that may be employed in effecting that object. There
is a huge difference between the employment we are now describing and
the many fooleries that engage the attention of the human race, that de-
grade the intellect, vitiate the morals, and debilitate the bodies of men.
Here is employment, food, and health, to be derived from a source the
most rational under heaven-from the cultivation of the earth, the inalien-
able patrimony of the human race. It is not a little surprising that any
draining should remain unperformed, the proofs of the beneficial effects
being so many, so strong, and undeniable. The results, as we have shown,
are not confined to the benefit of the individual who performs the opera-
tion; they swell into national importance, and claim the attention of the
philosopher and statesman, as well as of the cultivator and
owner of the soil. Every interest must give way to the general
power
to every
grade of
society,
988
ON LANDED PROPERTY.
<
interest; but here is no opposition, or any jarring contention, for
every party is benefited, and the general good promoted. The labourer
finds employment; the farmer obtains an increase of produce; and the land-
owner gets his property improved in value, and a remuneration for his
capital; the nation enjoys a climate improved and salubrified by
and compre- the process, and an increase of food, the essential element of life,
hensively.
on the regular and ample supply of which articles the prosperity
of any social community almost wholly depends.
individually
CHAPTER IX.
MINERALS-WORKING AND VALUE.
MINERAL property is very frequently the most valuable part of a landed
estate. The income is generally steady and secure, and not so uncertain
as the revenue of the capitalist and the trader. Extensive mining infers
the advancement of a large capital; and an adequate knowledge of the sub-
ject should be present before commencing too rashly in the works of dig-
Minerals.
ging minerals. There are many cases in which the land-owner
may profitably embark his capital in mining; but in most cases
it is preferred to lease out this species of property to others, who advance
the capital and follow mining as a profession.
The metals of Britain are-copper, tin, lead, and iron. The useful
minerals are-lime, coal, clay, and building stones. Copper lies chiefly
in the older rocks of primary and transition, and is found in many con-
ditions, but chiefly in the ores of sulphurets. The most important of the
ores of copper is copper-pyrites or yellow copper ore, which is a compound
of sulphuret of copper, and sesqui-sulphuret of iron. It is found in
granite, the trap rocks, and even in the lava of recent volcanoes. Although
more difficult to be reduced than iron, it was more extensively
employed by the ancients, who understood the art of hardening
it, so as to form cutting instruments, by mixing it with tin and other
metals.
Copper,
The primary and transition deposits of Cornwall, that are intersected by
porphyries and other plutonic rocks, afford the richest mines of copper
that are now worked, which lie in the tract of country between Truro and
the Land's End. The veins traverse the slaty rocks or killas of the pro-
vincial nomenclature, and are collected into groups, and do not cover a
large extent of surface. The directions are various in which the veins run
their course, which is never vertical, but at an angle with the horizon.
The depth is not known, the search being generally abandoned on account
of the poverty of the vein, or the increased expenses of sinking.
The average width is three feet, some are six and even ten or
in Cornwall;
ON LANDED PROPERTY.
989
twelve, with smaller ramifications. The length is under two miles, though
some reach to seven. The depth is great, extending to 1650 feet below
the surface of the ground, and many cases approach to that level. The
driftways and levels under ground amount in the aggregate to hundreds of
miles. The mines extend under the bed of the sea; and the dashing of the
waves, and the rolling of the pebbles and fragments of rock, are heard by
the workmen in the excavations below.
A very rich mine of copper was wrought in Anglesea, which for twelve
years, from 1773 to 1785, lowered the price of the metal throughout
Europe. The produce diminished, and the mine is now only moderately
productive. Some other places afford copper in limited quantities—as
Devonshire, Derbyshire, and Staffordshire, the Wicklow Mountains, and
the Isle of Man. The transition mountains of Scotland show a in Argyle-
small quantity; and a mine has been opened in the Zetland shire.
Islands. No rock above the coal in Britain contains copper; but in Ger-
many, beds of what are called copper-slate exist in the new red sandstone.
The brass of the Romans meant copper, which must have been very
early worked in this country. The Crown gave up its right to all the
baser metals in 1688, when England did not produce sufficient copper for
its own use; and the copper coinage of native metal did not appear till
1717. From this period the increase of copper has been amazing, and
now exceeding 14,000 tons, being in the one-half exported, and over one
million of money in value.
Smelting.
Sulphur, iron, and other substances are associated with cop-
per, and require, in being separated from it, a much more com-
plicated series of operations than iron or lead. The smelting establish-
ments are quite distinct from the digging of the metal, which is sent to the
former as a raw material, to be prepared by a different division of labour
and of firm. The same hands do not often possess both undertakings.
The metal of copper is very malleable, and may be hammered into plates
of great fineness. The substance is of great value in the arts.
Iron only
exceeds it in tenacity, which is superior to that of gold, silver,
and platinum. The alloy equals the single value-three parts of
copper and one of zinc form brass; one hundred parts to ten of tin, it
forms bronze and gun-metal; with twenty-five of tin, it forms
bell-metal; with thirty-five of tin, it forms optical speculæ,
which were formerly used as mirrors.
Quality.
Value.
Very few localities can be expected to yield copper in any workable
quantity. The value is inferior only to the precious metals, and the
mineral is very profitable on an estate of land; but much caution is due
to the engagement in working it, and must ever be done under the direc-
tion of a skilful engineer.
Tin is a scarce metal, yet was early known to the nations of Europe,
who seem to have derived the supply from the inhabitants of Tyre. It
occurs in the primary rocks, in veins, or disseminated, and in two mineral
species, the peroxide, called tin stone, or tin ore, and the cupreous, sul-
phuret or bell-metal ore. The metal is abundant in Cornwall, and is
990
ON LANDED PROPERTY.
found on the continent of Europe, and in the East Indies. In Cornwall
Tin.
the veins extend from a line to several feet in thickness, and are
of unknown depth, being wider in the softer rocks than in the
granite. The veins are wrought by vertical shafts and by drifts under-
ground that extend for many leagues. Stream tin or grain tin is gathered
in the ravines and valleys, where it lies mixed with sand and gravel in
grains or larger fragments up to twenty pounds in weight. The ore is
separated by washing, and sells at a lower price than the block tin of the
veins.
The purifying of tin is a tedious process; the ore is first reduced to
powder by stampers, and washed and sifted, so as to separate the tin from
the other mixtures. The heat of a furnace then banishes the sulphur and
arsenic from their combinations, and washing separates the substances.
The ore is then fused by lime and coal; the lime combines with the earthy
matters, and the coal reduces the oxide to the metallic state. It
Working. is again further purified by fusion, and cast into blocks, which
are stamped for commerce. About 4300 tons of tin are produced in Corn-
wall, of which the one-half is exported. The locality of tin is
very limited, and forbids any hope of a successful search in
Britain. Some deposits of stream-tin may probably occur in the primary
districts of the west of Scotland and Ireland.
Quantity.
Lead :
Lead exists only in one abundant ore, which is the sulphuret
or galena, or lead glance. The mineral occurs in veins of va-
rying thickness, in the primary or transition districts, partially in the old
red sand stone, abundantly in the mountain limestone, but sparingly in
the coal measures, or the superior formations. The chief positions in
Britain are the slaty and greywacke hills, which stretch across the island
from St. Abb's Head to the Irish sea; in Derbyshire, Shropshire, Devon-
shire, and Cornwall; in the Isle of Man; in Denbighshire and Flintshire;
and in some parts of Ireland. The mines have been worked in Scotland
since 1540 with considerable profit, in the slaty and greywacke rocks of
the counties of Dumfries and Lanark. The thickness of the veins varies
from four to ten feet and upwards.
where found.
The elevated country near the Cheviot hills, in the north of England,
around Crossfell, where the meeting happens of the counties of Northum-
berland, Durham, North Riding of Yorkshire, Cumberland, and
Westmoreland, contains the mines of lead that are the richest in
England. The number is 175, and have been, or are now worked. The
rock of mountain limestone, with its accompanying strata of sandstone and
slate, contains the mines which are situated in the five counties. The
directions of the veins are various, and are sometimes very slender, and at
other times thick, as fifteen feet or more. The best are in the limestone;
and the quantity and quality are contracted in the slate and sandstone.
Trap in dikes intersect the veins, which are very productive, and have much
increased the value of the landed property.
The oldest mines are in Derbyshire, and the richest in North Wales,
which yield fully one-fourth of all the lead in the kingdom. Many or all
ON LANDED PROPERTY.
991
Quantity.
these mines have been worked out or destroyed by inundations. The aver-
age yearly produce of lead in Britain is about 50,000 tons, and
at £20 per ton the value is about one million sterling. About
one-third of the produce is exported.
Lead-glance is the chief ore, and the extraction of the metal is not very
difficult. The sulphur is driven off as acids, and the metal is Working.
oxidated by the action of a powerful heat; a part of the sulphuric
acid combines with the metal, and forms sulphate of lead, to reduce which
quicklime and coal are added during the process; the lime combining with
the sulphuric acid, and the carbon of the coal abstracting the oxygen of
the metallic oxide. The metal being reduced, is collected in vessels, from
which it is cast into large ingots termed pigs, and is ready for commerce.
Silver, iron, and copper, are in a small quantity mixed with common
lead. The silver is extracted, when the quantity defrays the expense; but
the amount and value are inconsiderable in this country.
Risk of
Mining.
The hazards are large of mining and smelting, and metal-
liferous veins are irregularly disposed, sometimes disappear, and
are cut off when the indications appear of the largest returns. They are
consequently placed beyond the calculation of coal and stones, which lie in
beds, and admit an approximate relation of the raw material with the ex-
terior approach. The number and thickness of the veins must determine
the expediency of working, and the proprietor will be guided by the best
advice on the subject.
Iron.
Iron is the most useful of all the metals, and enters every-
where into the composition of the larger masses of mountain
rocks, and in combination with oxygen, sulphur, silica, and other sub-
stances, forms many mineral species. The ores are numerous, but two of
them furnish the useful metal in magnetic iron and clay ironstone. The
former yields the iron of Sweden and Norway, and occurs in beds or single
crystals in the older rock formations, and combines the two oxides of red
and black. The ironstone is found in the coal measures of Britain, of which
the whole consumption is supplied from that quarter. It is a happy ad-
vantage, the coal and lime necessary for the smelting the ore are found
together, as the geological deposit has placed the formations.
Iron occurs in beds, that are from one inch to a foot in thickness, and
alternate with shale, limestone, and coal. The ore is put into large fur-
naces, where a powerful heat is raised by common coal mixed with lime as
a flux. The oxygen is banished by the heat, while the lime Where found
combines and carries off the foreign matters in a fusible com-
pound called slag. The melted metal by its density sinks to the bottom,
where it escapes by a hole plugged with sand and clay; the slag
floats upon the surface, and escapes by an aperture in the side of
the furnace. The process of fusion goes on continually, as fresh matter is
constantly supplied from above. The liquid matter received from the
furnace is run into moulds of sand, and then it forms the pig-iron of
commerce.
Working.
The furnaces are square at the bottom, where the metal collects, and
992
ON LANDED PROPERTY.
Smelting.
then swell outward to their greatest diameter, when they contract to the
commencement of the chimney. They are built with bricks or stone, and
lined with fire bricks; the hearth at the bottom being a hard infusible
stone. A tunnel head, or an external gallery, at the beginning of the
upper part of the chimney, contains square openings with iron
doors, by which the furnace is charged with materials. A most
intense degree of heat is raised by blowing pipes, which are driven by
steam power, and holes introduce the streams of air in the lower and nar-
rower part of the furnace. The fuel is coke or common bituminous coal;
and a saving of these matters in the one-third to one-half is effected by
heating the air before entering the furnace, by passing it through heated
pipes that are placed between the furnace and the blowing apparatus :
iron is more brittle produced in this way than by means of coke and
cold air.
Before being put into the furnace, the ore has been exposed
Furnaces. in heaps to the air, for the purpose of banishing water, carbonic
acid, and sulphur. Ironstone, coal, and limestone, are then introduced in
twenty cubic feet of coal to the corresponding quantities of iron and lime.
The liquid metal is usually drawn off every twelve hours; and the furnace
being once ignited, is never again extinguished till it needs reparation.
The metal is conveyed into its moulds under a shed by the side of the
furnace.
The iron is impure as it comes into the first melted condition, containing
foreign bodies, chiefly carbon, and is hence regarded as a carburet. It is
fusible, and may be moulded into many fabrics. It becomes tenacious and
ductile, but more infusible, and formed into soft or malleable iron by a
further series of processes, by which it is freed of its carbon and other
impurities.
Pig-iron.
The pig-iron is fused in a peculiar kind of furnace, and
formed into a slab, which is rendered brittle by throwing water
upon it. Being broken into pieces, a reverbatory furnace subjects it to
the operation of puddling, which consists in stirring it while in a liquid
state, when a large disengagement will happen of carbonic oxide, as is
known by the blue flame. Balls are then formed of the iron, and forged
by heavy hammers, or are passed while hot between a series of grooved
rollers. This condition is called mill-bar iron. The forging is continued
by welding pieces of it together, and the properties are further acquired of
malleability, ductility, and cohesiveness.
Steel.
The iron thus prepared is the valuable substance of malleable
iron, fusible only by the most intense heat that can be produced
by any artificial means. The malleability is of any temperature, and in-
creases with the heat applied; when red hot, it may be hammered into any
forms, and welded or joined in any fashion. It is very ductile, and may
be drawn into thin wires, when the supporting power exceeds all other
metals. Combined with carbon, iron forms steel.
Iron is generally melted where it is found, as coals and lime are in
contiguity. The mines of Britain are in North and South Wales,
ON LANDED PROPERTY.
993
Shropshire, Staffordshire, and Derbyshire; and in Scotland, in
the vallies of Forth and Clyde.
Mines in
Britain.
The improvements of the smelting processes, and the use of the steam
engine, have increased the iron trade most amazingly, from the middle to
the close of last century, and the facility of an increased production had
the usual effect of diminishing the price, and this result enlarged the con-
sumption by introducing iron into many other purposes of use. The de-
mand now must limit the production, as Britain seems capable of supplying
the entire consumption of the world.
Rent or
royalty.
The mines of iron are let upon lease for a stipulated rent or
royalty. The royalty is not reducible to rule, but must vary
with the nature and richness of the mine, and other circumstances that
affect the value of the produce. The land-owner may sink the new mine,
and work it till the value can be approximated, when a tenancy can be
negotiated. Very long leases are generally granted to companies or
wealthy individuals, who make every erection, and perform all business at
their own cost, without any demand on the original inheritance.
Coal
Coal is a very inflammable body, composed chiefly of bitumen
with other matters, with much carbon in the hard varieties.
The formation lies in great irregular basins, the strata dipping to some
common centre, or general axis, and are found in the sandstones of the
secondary class of rocks, which succeed the unstratified deposits. Where
this rock is not deeply covered by the upper formations, the coal approaches
the surface, and was early discovered for the purpose of fuel. It forms
the chief mineral wealth of Britain, and employs a large portion of the
shipping and mariners of the island. The regularity of the strata of coal
is very often disturbed and intersected by dikes, fissures, and irruptions
of igneous rocks, as traps, basalt, porphyries, and interjected argillaceous
matters, which are found in every geological deposit from the granite to
the chalk. These barriers run in various directions, vertical, oblique, and
often right-angled to the stratum of coal; and are known by
different names as dikes, slips, faults, and troubles, according as
the dislocation of the stratum is greater or less, and affects the proceedings
of the mine largely or in a small degree.
mines.
Boring.
Coal is best discovered by boring, and the natural indications
must be such as to induce that trial being made. Professional
borers contract for the work, and are paid 5s. for the first five fathoms;
10s. or more for the second; 15s. or more for the third, and so on, in the
same proportion for every five fathoms, or thirty feet in depth. The
essential purpose of boring is to ascertain the depth and thickness of the
mineral seams in the tract to be surveyed. The depth of the covering
over the coal and the thickness of the strata, must be ascer-
tained, and also the dip or inclination, which the coals assume
in the extent of the surface ground. Declivities admit a day-level being
made, which will draw off the water into lower ground, when it is best five
or six feet in height, and four feet wide, built and arched with stones or
bricks. Water will flow into every excavation made in the ground,
Depth.
994
ON LANDED PROPERTY.
Levels.
either from the looser earth of alluvial covering, or from the seams of
solid strata through which it may permeate. In level situations, no in-
clination can be found, and pumps are necessary in order to raise
the water from the bottom of the excavation to the surface, on
which it is floated away into brooks or rivers; or it is discharged into
a day-level, which has been described. In great depths, there is a large
mechanical stress in the length of the piston rods, and the increase of
weight and strength in other parts of the pump, when water
is raised from the bottom, and therefore it is necessary to have a
series of pumps, the lowermost throwing the water into a cistern, whence
another higher pump draws it to a second cistern, and so on to the dis-
charging orifice. The cylinders of the pumps are fifteen and eighteen
Pumps.
inches diameter.
Engine pits.
Coals are reached by an engine pit, circular in form, and divided by
partitions into parts, as the purposes may require, in placing the pump,
for ventilation, and for raising the coals. The engine pit is
frequently placed at the tail or lowest dip of the inclined strata
below ground, to which the water flows, and the coals are raised at other
places that are pointed by convenience. The coal pits are circularly lined
with masonry, through the depth of the loose covering of the surface; the
rocks below afford a solid boundary, and not unfrequently the wall is continued
from top to the bottom, or planks of wood or thick boards are substituted.
Sheathings of cast iron prevent the influx of quicksands, which were
formerly thought to be fatal and altogether insurmountable. A peculiar
arrangement joins the different segments.
Water pre-
Water will flow into the pit that is being sunk, which must
vented. be removed by pumps that are successively lowered downwards
as the works proceeds. A pump will very conveniently raise water to
the height of twenty-five fathoms, so that three pumps will be required
for the depth of seventy-five fathoms. The cisterns that receive the water
at the stated distances, are fixed in the excavations made to receive them
in the sides of the pit, as the excavation goes on; and the pumps are used
in the first place to raise the water that flows into the pit that is being
dug: they are afterwards placed in the position which they are to occupy.
In some pits, the water is carried to the fixed cisterns by means of spiral
boxes carried round the sides; but in all larger pits, the entry of water
is prohibited by the cast iron sheathing that has been mentioned. The
sinking of the engine pit constitutes the first grand work of the mine, and
is termed the winning of the colliery. When the mine is won, the further
operations consist in working the mineral, the division and economy of
labour, the ventilation of the mine, and the removal of the water. In the
vast coal field of the Tyne, the mineral lies deep under a bed of alluvial
debris, and large depths must be sunk to reach and excavate the workable
One engine pit with the necessary machinery, has
expended, £50,000; and even £80,000 and £100,000 have been
in special cases, used in these purposes. Nothing could justify such large
outlays, but the high value of this rich coal, which it has maintained for
Cost of sink- seams.
ing.
ON LANDED PROPERTY.
995
centuries, and the seemingly inexhaustible source of the supply, which
appears to meet the continued and increasing demand. In that locality,
mining is seen in the perfected science, and engineering is exhibited on a
scale of grandeur.
coal,
The coal lies in seams that are more or less inclined from the horizontal
direction and which are parted by strata, which are more or less argilla-
ceous, siliceous, or calcareous; the lower is floor, and the upper the roof,
and the coal is parted from each, by thin seams of dry powder Seams of
or clay; and the coal itself is intersected by series of subordinate
partings, parallel to the main ones, consisting of a soft carbonaceous matter
which blackens the fingers, and varying in thicknesss from a line to an
inch and half. The mass is also cut by backs and cutters, which extend
transversely at right angles to the line of dip, and longitudinally in the
line of dip, and these divisions facilitate the working of the coal, and affect
the methods of working.
Two methods are used in working coals-one way leaves Ways of dig-
pillars to support the roof, and which remains in permanency, ging.
or being removed, the roof falls in and fills the mine; the second mode
allows the roof to fall in regularly as the work proceeds. The first
mode is the most common, and the most generally applicable. The engine
pit is at once sunk to the most extreme depth, from which a mine is run
which is termed the dip head level, and to it all the water in the mine s
directed. A series of excavations is conducted in the line of ascent
upwards, and another at right angles to these. The pump raises the
water from the lowest level, roads are directed in various quarters, and
one fourth part or more is left of the standing mass in order to support
the roof. The progressive excavations of the coal divide the mine into
numerous passages, which are called rooms or thirlings, and communicate
with one general passage, that leads to the place in the bottom of the pit,
by which the coal is to be elevated. This road is a double railway of cast
iron, on which are run low trucks on four wheels, called rolleys, Roads and
and are dragged by one horse, several trucks being hooked
together. The excavated coal is placed in tubs, technically termed corves,
made of osiers, or of hammered iron. They are put on small trucks with
low wheels called trams, which are dragged through the low and narrow
passages by manual labour. Each truck carries a tub or corf, con-
taining four to six cwts. Boys drive the corves from the workings
to the mainway, and lads drive the trucks along the mainway to
the shaft.
trucks.
The miners, or hewers, work separately in assigned portions of work.
The coal is brought down with light picks of iron, by wedges and drills,
and sometimes with gunpowder. The room being scanty for work, the
body reclines or sits, and in narrow seams, the back is flat on the pave-
ment. The hire is by the quantity excavated, and the miner Hired-
assists in loading the corves, which on reaching the mainway,
are examined by the superintendent, and being passed his sanction, several
corves are hooked together, the train is drawn by a horse rapidly along
quantity.
996
ON LANDED PROPERTY.
the railway. Where the inclination is great, inclined planes, with ma-
chinery are substituted for animal power.
The corves having reached the bottom of the shaft, a strong rope with
hooks and chains attaches a certain number, which are raised to the pit
mouth by means of the rope being coiled round a beam which is revolved
by a horse walking in a circular pathway; in all large mines, steam power
Elevation by relieves the use of animals. The corves are unhooked by at-
machinery. tendants at the mouth of the pit, and dragged on rails to the
place of deposition of the load. The empty corves are lowered by the
elevating power working in another direction.
Ventilation is very necessary in every work underground, and fresh
air must be made to circulate in every part of the excavation. Air pits
are provided in the shape of wooden boxes, which communicate with the
open air, or with some large opening that receives from it the necessary
respirations.
Coal mines are very dangerously infested with destructive vapours
that
issue from the pores and fissures of the coal, and which accumulate in two
dangerous gases, of carbonic acid gas, and light carburreted
hydrogen. The former receives the name of coal damp, or
choke damp; and the latter of fire damp, or foul air.
Gas in pits.
Carbonic acid being heavy, falls to the ground, and rolls along like
water, in the lower part of the works, rising by degrees to the higher. It
issues abundantly from the seams and fissures, forming a stratum of a foot
or two at the bottom of the excavation, while a pure air is respirable above
it. In the air above it, a candle burns clear; in the stratum, it is instantly
extinguished. This gas is pernicious to human life, either pure or mixed
with atmospheric air: when a candle will not burn in it, it is instantly
fatal. Hence the precaution of lowering a candle to try the quality of
the gas, and also the modern safe-guard of the miner carrying a
Safety lamps. lamp which by the faint burning warns the approach of danger.
The general air of mines has a quantity of this gas, but does not prove
deleterious.
Fire damp.
The fire damp of mines is sub-carburreted hydrogen, and
burns with a strong yellow flame. When abundantly present, it
detonates with violence, and hence the danger of the explosion. Being
light it flies to the higher part of the works, and hangs like a canopy over
the heads of the workmen. A small quantity of it mixed with the
common air, creates no inconvenience; but when pure, and without
almost any mixture, respiring life does not exist in it. If ignited by the
contact of a burning lamp, a terrible explosion takes place, attended with
much devastation and loss of life. The gas is not ignited by any tem-
perature below that of flame, and flame cannot be communicated through
narrow tubes of metal. Hence a lamp was constructed by Sir H. Davy,
the celebrated chemist, which is covered with a tall cylinder of fine wire
that from the fineness of the texture does not greatly obstruct the light,
while it admits sufficient air from without to support the combustion.
When brought into contact with the inflammable air of the
Now less
dangerous.
ON LANDED PROPERTY.
997
mine, the air enters the lamp and supports combustion, but the flame
of the lamp does not pass through the covering of wire gauze, and
inflame the explosive atmosphere without. In extreme cases, air which
enters the lamp will take fire, and the intense heat will oxidate the wires,
and cause them to fall into pieces. This safeguard of a lamp against
explosions, is not wholly perfect-but it has greatly reduced the number
of explosions, and would still lessen the accidents, if due caution was
observed. Miners are careless, and often open the lamps to trim them in
spite of every admonition and the many fatal examples.
coals
Private gain and public interest are equally concerned in the working
of coal mines. A just rent can always be got for coal in proportion to
the quantity of saleable produce, and the royalty varies from Royalty on
one-sixth or more, to one-fifteenth, according as the mine is level
free, or requires an engine pit. When other minerals, as ironstone, are
wrought along with the coal, a separate royalty is charged on the special
article. The lease must describe the situation and extent of the mine,
with a map made and signed by both parties. The mode of working the
mine, the maintenance of the levels, and other general regulations, are
also agreed, the landlord builds the specified accommodations, the lessee
upholds them, and leaves all in tenantable order when he vacates the
possession. The moveable machinery is erected by the tenant, and the
landlord can buy it at the valuation of mutual referees.
known from
sale.
The royalty is ascertained from the sworn books of sale by
the tenant, and the owner may appoint his own agents as checks the books of
for his interest: and he can send into the mine at any time,
surveyors to see that the mine is properly wrought, and all things are
attended. The working must not touch any other mine by ten fathoms,
nor go underneath any specified buildings; all pits must be arched over,
and surface damages paid. Other conditions will arise from local circum-
stances, and occurring attachments.
When coals are discovered, the proprietor of the ground sinks the pit,
makes the levels, and puts all into current going order for operations. The
mine is then let for a yearly rent: or a long lease on very Lease is long.
equitable terms is given to the wealthy individual, or a public
company, which uses the possession nearly as its own. In other cases, the
proprietor is the sole agent, works the mine, and gets all profits. The charge
of royalty is the most just and equitable for both parties, as it depends on
the quantity sold, and does not rob one to pay another in an uncertainty.
The quantity of coals excavated yearly in Britain reaches 35,000,000 of
tons, and at 10s. of an average price the value amounts to £18,000,000. The
one-half of the price belongs to the labour that has brought the coal to
the mouth of the pit, and the other for the carriage to the port of delivery.
The capital engaged in coal mining exceeds £10,000,000. The single
seams of coals vary in thickness from one foot to forty, and the aggregation
of a coal bed from that to 200 feet. The condition of the mining
population has been much improved by private benevolence, and special
acts of legislation.
998
ON LANDED PROPERTY.
Lime.
Lime exists in many combinations, but mostly as a car-
bonate, or an earthy base in combination with carbonic acid
gas. The highly indurated and crystalline kinds form marbles; and the
softer constitute the common compact limestone, magnesian stone, oolite
limes, and chalk. All these rocks, being subjected to a strong heat above
redness, yield the gas which holds the stone together, and becomes a light
cinder, which on being slaked with water falls into fine powder. The
mixture with sand becomes mortar for building walls of stones and bricks
and the powder is used as manure for land.
Lime is mostly a flat rock, and lies in horizontal beds, that are divided
by seams, and cross fissures, and differs largely from the veins from which
minerals are extracted. Where the rock is uppermost in position without
any stratified body being superimposed except the alluvial covering, the
excavation of the stone is done by open cast, that is, in the manner of a
quarry. An outlet for the water is first to be found in the natural descent
of the ground-if none exists, a low point must be formed, and a pump
placed over it, which will discharge the water into some opening or out-
let. The earthy covering of the rock must be raised by spade,
and wheeled by barrows to some side where no interference
will be made with the works. When the limestone lies deep, the mining
of the rock proceeds in the manner of coals. The rock of lime generally
yields to the pick, hammer, and wedge: otherwise, it is bored and blasted
with gunpowder.
Working.
Burning.
Furnaces are built for the purpose of calcining limestone, in the ellip-
tical form, narrowing to the bottom where the calcined lime is withdrawn.
The egg-shape is used, when the wider end must be at the top, in order
to receive the raw materials of broken stones. The exterior wall of the
furnace is of thick masonry, and the inside lined with fire brick, or stones
capable to resist a high temperature, and erected on a convenient ground
to receive the stones that are intended to be burnt. It should stand at
the bottom of a slope if possible, and the top level with the
mixed stones, which are put at once into the furnace, and the
low ground gives access to the removal of the cinders of the lime as they
are drawn from the opening at the bottom of the furnace. When a
suitable situation is at a moderate distance, a railway will convey upon
trucks, the stones to the furnace. The stones are broken by hammer into
a convenient size, and put into the furnace with alternate layers of coals
or wood. The fire being applied below ascends upwards, consumes the
fuel, and banishes the gas from the stone, which is drawn and carried from
the eye of the kiln, in a constant regularity with the filling of the stones
into the top of the furnace. In this way the work never stops, and the
supply is constant. It is computed that, in a well-constructed kiln, one
bushel of the best coal will produce three of lime, and from one-third to
Drawing of one-half, according to the constitution of the lime, may be
withdrawn every day. These proportions will vary, and as
much as two-thirds may be withdrawn by extending the height of the
kiln, lessening its diameter, and diminishing the width of the top. But
cinders.
ON LANDED PROPERTY.
999
the calcination will be less gradual and perfect than when more time is
allowed, and a smaller quantity withdrawn.
Royalty.
The proprietor may keep in his own hands the working of limestones;
but it is generally let at a royalty that varies from one-sixth to
a fourth of the proceeds, according to the quality and sale of the
lime, and the distance and cost of fuel. When the royalty is extended
to show an average of years, a lease may be granted, as for a farm of land,
upon the moderated calculation that should direct the assumptions of
value.
Building stones are sufficiently strong to resist the pressure of any force
applied to them, and durable to oppose disintegration from the power of
chemical changes and external agents. Hardness and tenacity compose
the first quality, and the texture forms the second. The closeness of the
grain, the homogeneity of the mass, and in certain cases the specific
gravity, indicate durability, and afford the only direction of judgment,
independently of experience. A loose earthy texture is very unfavourable
to durability.
Building
stones.
Building stones are of all kinds, from the primitive granite to the upper-
most formation of chalk. The secondary formation of flat rocks affords
the most useful articles, as the beds are flat and horizontal, and are tra-
versed by seams and fissures, which very much facilitate the excavation of
the stones. Sandstones and limestones are the best rocks for mak-
ing walls; and the varieties are many, and the qualities discordant.
They are certainly inferior to the crystalline rocks in a very long dura-
bility; but the use is more general from the facility of being raised, and
formed into any shape of blocks. Limestones are of better practical value
than sandstones.
quarry
quarries.
Beds of rocks that are workable, will lie on flat grounds, or in the sides
of declivities. In both cases, the lowest point must be sought where to
begin the excavation, and to it the water will flow and be discharged. A
road must be made to lead into the opening from the nearest approach of the
common thoroughfare, of which the ascents must be easy, and Working of
the inclinations gentle. Where a permanent use of the
for stones is anticipated, the earthy covering must be removed and wheeled
to some convenient deposition, in which no interference will be made with
the future operations. If the quality allows, the earthy matters may be
mixed with lime for a compost manure: at least, the uppermost stratum
may suit this purpose. Where a short purpose is required in digging
stones, the earth may be laid behind the operations, and thus fill up the
excavation, which will again become arable ground. A depth and width
of face of rock will be preserved according to the dip and inclination of
the strata. When the beds sink downwards, and no outlet can be Shaping for
dug to vent the water, a pump must be erected to raise the li- use.
quid, and discharge it over the intervening height into a running declivity.
The stones are separated and raised in blocks by sledges, picks, wedges,
and hand-levers; and in case of the harder rock, gunpowder is applied to
burst the rock into fragments. The nature of the rock, the direction of
1000
ON LANDED PROPERTY.
the strata, and the lines of cleavage, adapt the modes of working to the
peculiar conformations.
Quarries of stones are but little valued, except in some few cases where
favourable circumstances concur to demand the use. The quality then must
be
very superior, the transport ready, and the sale constant and permanent.
These junctions very seldom meet. When a stone quarry is worked in
ordinary circumstances, the royalty varies from one-third to two-
fifths of the sales, leaving two-thirds to three-fifths for the
expenses and profit of the lessee. A yearly rent may be imposed, after an
approximation has been learned of the probable value from the bygone
practice.
Royalty.
Slates are a primary formation of rocks, crystalline, hard, and durable,
Slates.
and are laid in vertical strata, thin and fissile, with laminar
openings. They are used for roofing houses and are very ex-
tensively quarried in Wales, and in the west of Scotland. The larger
rocks are parted by wedges and levers, and the fragments by hand tools
into smaller sizes. Slates are only found in the primary districts, and are
wrought on a royalty, as may be due to the demand.
Flagstones,
wrought.
Clay.
Flagstones are used for laying pavements, private roads, and the floors
of houses. The rock is found from the primary schist to the
uppermost sandstone, in which formation it chiefly abounds, and
constitutes a very useful article. The bed is raised in the natural divisions,
which are afterward separated into use, as can be effected, The
quarry is conducted as formerly described for building stones,
and the royalty or yearly value is fixed in the same way. The stone is
mostly siliceous, with a base of clay and sometimes with limestone.
Clay is an alluvial formation that is of vast extent in some flat countries,
and the presence of it can be traced from the decomposition of soft felspar
in the primary rocks, to the sub-ærial deposit of fresh water
alluvium, attending every formation, and contributing very large-
ly to mark the connections that serve to exhibit the various stages of the
ascending series of deposits. Argillaceous schistus is the first type of
the body of clay, and from that primary rock, in the form of shale of
very various qualities and conditions, clay is an accompaniment of every
deposit, and a very strong indication of the increasing existence of soft
materials in the structure of the globe. The first deposits of clay that are
exposed to view, are very viscous and tenacious in the texture, from hav-
ing been suspended in, and deposited by marine water, as is clearly indi-
cated by the presence of the spoils of the ocean. Other beds are much
more friable, having been washed by fresh water, and deposited by its
agency.
Finer kinds.
The finer clays, or those that are most pure in silica and alumina, are
used in making porcelain and pottery, and the more mixed sorts are manufac-
tured into bricks and tiles. For both purposes, the essential
quality is the kneadable property, by which when moistened, the
clay can be led into any shape by hand or tool. Porcelain clay is the
finest; pottery is made of the second quality; and bricks and tiles pro-
ON LANDED PROPERTY.
1001
ceed from the inferior qualities. The first kinds of clay are the decompo-
sitions of the older rocks, in veins or small beds, whence the substance is
excavated like metals, and sent to the special manufactory. It forms a
very distinct employment, and is not of great extent in Britain.
Inferior
qualities.
The inferior clays are mixed with other substances, from having been
exposed to different combinations, and to the affections of external agencies.
The foreign substances are lime, iron, manganese, potassa, and bitumen,
in very different quantities and combinations, most of which
substances tend to make the clay fusible. A certain degree of
fusibility is required both in pottery and bricks, in order that the ma-
nufactured article may be rendered capable of resisting the absorption of
moisture; and in all the natural clays, even the purest employed in the
arts, the foreign bodies exist in them to the degree of producing fusion.
at certain temperatures.
Very early ages of the world used vitrified or fused clay in the forma-
tion of vessels, and the use of brick as a substitute for stone in building
seems to have had a very early date.
Clay for
bricks.
Clay that is fit for bricks is found in many parts of Britain: it must
be free of stones, plastic, and capable of forming a stiff paste with water.
Lime is added to some clays to produce a tendency to fusion,
and is used as powdered chalk, or marl. Sand also is used for
the purpose of preventing too great a contraction of the clay in the fur-
nace, and it must be as siliceous as possible. The quantity is soon deter-
mined by experience, and must not make the bricks brittle. The best clays
are those which already contain the portions of lime and sand that are
necessary for the above purposes. Coal cinders are added to clay, and
prevent the contraction of clay in burning, in the same manner as sand;
the iron of the clay is de-oxidised, and the bricks are yellow, a colour
which is valued in building, and the durability is increased. Certain clays
resist high temperatures, and constitute fire bricks, as the constituent mat-
ters exist in some definite proportion. This clay is scarce, and is chiefly
found in the shales of the coal formation.
Digging.
The beds of manufactured clay are several feet thick, or lie in very ir-
regular deposits. In certain cases, it is dug and used at once; but most
generally and beneficially, it is raised from the bed or clay pit,
laid in shallow heaps before winter and in quantity enough for
the work of one year. The harder matters will be reduced by exposure
to the air, the parts will be blended together, and the whole mass will
be mollified. In most cases, one winter's exposure will prepare the
clay; but in some instances, two, and sometimes three, are required;
and in all cases, a long exposure is beneficial. The clay is several
times turned over and moistened with water, and if sand or lime be re-
quired, this is the best stage of the process for mixing them intimately
with the clay. Straw or turf is frequently laid over the clay after being
prepared in this way. Soil and stones are carefully removed when the
clay is moved from the bed.
The clay mill or pug mill next cuts the clay into minute shreds, as it
3 Q
1002
ON LANDED PROPERTY.
Working.
passes downwards through the action of arms and knives, which are im-
pelled by the power of horses or steam. The clay is then ready for being
moulded into any shape, either by manual labour, or by ma-
chinery. The clay is thrown with some force into the mould,
smoothed over the top by a ruler of wood, which compresses the clay, and
fits it to the mould. This is the mould for flat articles; for bended and
arched purposes, a slice of clay is fitted over the mould, and pressed down
upon it: the moulds being removed, the shaped clay is placed on the
shelves of a drying shed. An expert moulder will form 5000 bricks in a
day, and 1500 to 2000 draining tiles. Bricks for drying are
Drying.
built in walls with alternate interstices, which allow the circu-
lation of air: but for drying tiles, shelves are used in long sheds of
various sizes, as the extent of works may require. An ordinary
work will need a shed of 150 feet long, 18 feet wide, and 6 feet high.
The sides of the shed are hung with canvas cloth, which is run up
on rollers, when the screen is not wanted to prevent the effects of frost.
The roofing may be of slates, tiles, thatch, or boards, as the climate
may require.
The tiles must remain in the shed till sufficiently dry to bear the heat of
the kiln. This time will vary from four to eight days, according as the
weather may be dry or moist. Baking kilns are of two kinds; clamps for
preparing common bricks, and close kilns which harden tiles for roofing
and draining. The clamp is an oblong heap of bricks placed above each
Burning.
other longitudinally and transversely, leaving intervals for the
passage of the air: fuel chambers are formed on the ground
of fire-bricks, entering from the opposite sides of the heap: from these
flues, cross ones are carried at right angles into the intervening spaces.
The fuel is put into the chambers, ignited, and the clamp is gradually
heated from the bottom upwards. More or less fuel, and the enlarging
or diminishing the orifices of the fire-places, will regulate the combustion,
which is slow at first, and gradually increased to the required intensity,
and after a suitable time, the furnaces are closed, the fires extinguished,
and the bricks allowed to cool.
Kilns.
The close kilns act upon the same principle, and the heat being con-
fined within walls, can be raised to a greater intensity by an equal expen-
diture of fuel. An oblong building with a set of fuel chambers
along the sides, which are prolonged into flues, contains the tiles
placed interstitially from the bottom to the arched roof, and best when set
on end. Cross flues of fire-bricks convey the heat uniformly over the
extent, and the vapour or heated air escapes at the top by vents for the
special purpose. The fire is put into the chambers, and the heat ascend-
ing warms, dries, and bakes the tiles of clay, by the rising current of air,
and by the contact of the tiles with one another. The slow fire is gradu-
ally increased, and kept burning till the tiles are baked, which will require
about seventy-two hours, according to the construction of the kiln, and
the degree of heat maintained. When the tiles are baked, the fires are
extinguished, and the mass is allowed to cool. Different constructions and
ON LANDED PROPERTY.
1003
operations are used in making kilns which are more or less perfect, and
may yet be much improved.
Tiles.
Draining tiles are now mostly made by machines, of which the most
approved are those of Mr. Anislie and Mr. Etheredge. The clay passes.
between rollers, and hence into apertures which contain the
mould that is wished, and from which the clay comes in the
shape of the intended use. Some differences exist in the construction of
the machines, but the purpose is effected as above mentioned. It is doubt-
ful if any advantage is gained by the use of machinery in this respect.
The article is not so well manufactured, and cheapness never can consti-
tute true economy. For draining tiles a good article is essential, as the
damage is removed from view, and is placed beyond repair. An insuf-
ficient preparation is beyond all other things to be avoided.
Quantity.
The manufacture of bricks, in Britain, exceeds fifteen hundred millions
yearly. The production in England, and the economy of la-
bour exceed all other countries, but not the quality of the article,
being inferior to Holland. Brick grounds are rendered useless by the dig-
ging of clay for any future application, at least for a long period of time;
and the land may be sold for that use, a lease granted for a cer-
tain extent of ground, or a royalty claimed on a specific num-
ber of manufactured articles.
Rent,
CHAPTER X.
EXPENSES OF AN ESTATE-REGULATIONS OF DIS-
BURSEMENTS—AND RELATION OF THE
PRIATE EXPENDITURES.
APPRO-
Expenditure
on a landed
estate.
It is a fixed law of nature that all bodies tend to change con-
dition, which terminates in a total decay and disappearance
from a state of being. This tendency exists in all formations,
whether organic or devoid of functional progressions; and is quick or
slow, according as the natural constitution may be soft and pervious, or
compact, hard, and durable. Inorganic bodies are slow in decay, but are
liable to a disintegration of the parts, which impairs the quality and de-
feats the purpose of use. Vegetable bodies are quicker to decompose from
the greater number of component parts, and the natural quality of the
different kinds that are produced. Slow growths are the most durable, as
the parts are more exposed in the congregation, and hardened by the ex-
ternal influences of affection. The inorganic creation does not allow these
circumstances, and the condition is less changeable, but still liable to nature's
general law.
When these materials are used for the purposes of utility, the Materials for
best quality that can be procured is chosen for the special appli- repairs.
1004
ON LANDED PROPERTY.
cation, and adapted as the most experienced knowledge is able to
direct.
Stones and
For the building of houses and walls of any kind, stones are preferred
to bricks, in all cases where the former materials can be got within the
bounds of a reasonable expense. But in alluvial countries, and where the
distance of carriage and other circumstances render difficult the provision
of stones, the use of bricks is adopted; and being an artificial production,
that material for walls becomes more easily decomposed, especially if the
clay be indifferent in quality, and the manufacture into bricks has been
improperly executed. Not only the getting of these materials forms a
chief consideration, but the quality as to fitness and durability must con-
stitute a very large item in the estimate that is being made of
bricks. any undertaking that requires the use of the materials. Expense
being equal, or so nearly balanced, as that the superior eligibility of stones
is able to cover the difference, no hesitation can happen which of the ar-
ticles will be used; and a consideration may be added of the extended
superiority which the harder material will evince beyond the present cal-
culation of the applied utility. Where the cost of stones does not exceed
fifty per cent. more than bricks, the choice will be justified of the rocky
body, as the durability will recompense the surplus in requiring less re-
pairs, and in constituting a better erection in every point of view. But
where the balance of cost amounts to nearly one hundred per cent., the
brick must be chosen, as that amount may never be repaid during a long
currency of the necessary repairs. If the stone be sandy, and
belong to the soft deposit of rocks, the decay will soon com-
mence; exposure very much affects earthy aggregations that have not
been removed beyond the influence of its power by the force of fire or a
very minute cement. This quality is soon determined by experience, and
has a very large effect in determining the eligibility of building materials,
as the choice may happen in different localities. Bricks must be calcu-
lated in the same way, not only in the primary cost, but in a strict rela-
tion of the future value, as shown in the quality of duration. This
attachment to any article will very much adjust the equilibrium against a
greater original expense of purchase.
Sandstones.
Timbers.
The use of timbers is regulated by the same rules of consi-
deration as the choice of stones and bricks. The hard woods
are used for purposes that are exposed to external actions which promote
decay, and the softer qualities are adapted for use in situations that are
covered from damage, and sheltered from violence. The timber roofing of
houses being covered from exposure, is constructed of firs, which, being
kept dry, are nearly equal to the hard woods. Timbers kept in one state,
wet or dry, will last long; it is the change of conditions, from wet to dry,
and from dry to wet, that tries the constitution of the timber, and which
marks the quality of quick and soft decay. Friction, or the attriting con-
tact of other bodies, in constant or frequent applications, imposes on tim-
ber the special adaptation of purposes, as it requires a quality similar to
that which resists decay. All posts sunk into the ground are required to
ON LANDED PROPERTY.
1005
Decays and
be of hard timbers, and very much of the inside furniture of barns, stables,
and cow-sheds, and also of cottages and dwelling houses. In all
cases of exposure, or a more frequent use, hardness must be repairs.
applied, and the best quality of it selected.
Reason and conventional agreement have established the relation be-
twixt landlord and tenant, or the permanent and temporary occupier of
the soil, that the former affords the raw materials with which to uphold
the decays of nature, and the farmer puts the articles into form, and places
the adaptations into use; and also that general decays, or a universal
failure of any permanent articles, are wholly replaced by the landlord ;
the farmer doing such a part of the work as the agreement has understood,
or a posterior arrangement may dictate. But for the purpose of restoring
and upholding all the small decays and tendencies to damage that may
occur during the lease, the farmer gets, without price, from the owner of
the soil, felled timber, lime, stones, and bricks, at the respective places of
manufacture, which are carried to the required uses and timeously applied.
On a neglected estate, where decays and dilapidations have been Total dilapi-
allowed to progress, and to escape observation and attention,
this expense to the landlord will amount to a sum; but under all correct and
systematic management, the item will be trifling, except it may be for
once in ten or fifteen years, when a wholly new erection of buildings, or
some part of a farmery becomes necessary; then a due allowance must be
made by scattering the special sum expended on that point over the lease
of the farm, and distributing it on the general outlay. A notice of it must
be taken before and after the event, and by contracting the outlay of some
years, prevent the expenditure of the special year from exceeding the
average of the general arrangement. In this way an equitable distribu-
tion is created and maintained.
The upholding and restoring of decays of perishable materials,
includes the preservation and restoring of watercourses and beds
dations.
General
repairs.
of rivers, the repairing of roads, the repairing of very old fences, or the
making a new one in its place, and all purposes of repair in which any
wholly new undertaking is not performed. Such expenses will inevitably
occur in every case of using the surface of the earth, and the more vigi-
lantly the wants are noticed and supplied, the expense will be less, and
the general benefit will be greater. The very beginning of a want must
be checked, that it may not grow into a gap of wide dimensions, in which
more means may be spent than would have repaired many beginnings.
These things require an active and vigilant superintendence, and a prompt
and spirited execution.
Circumstances of locality and special position will very much influence
the amount of expenditure that may be required for the purpose of up-
holding in current-going order of a proper and sound condition all the
articles of decay which a landed estate will present to that department.
The size of the farms, in being small or large, will affect the cost of the
repairs of houses; the intersection of the estate by brooks or rivers will
require a greater or less expense, as the courses are few or many, Prompt exe-
cution.
1006
ON LANDED PROPERTY.
and the roads are sometimes so arranged as to make a sum of some
magnitude in the upholding. Very much will depend on the activity
of management that is displayed, and the orderly system that is adopted
in the vigilance of detection, and the promptitude of supplying the inci-
pient deficiencies that may occur. The economy of this management con-
sists not in withholding the outlay that is necessarily required in order to
save expense, but in doing promptly what must be done in due time and
in the proper place. No greater fault than neglect can occur in the
management of business, especially when the growth of the evil proceeds
increasing as time progresses.
Per centage
In all ordinary cases of circumstantial attachments, and where
of cost. a tolerable exact system of management has been adopted and
prevailed for some time, the sum of five per cent on the rental of the estate
is found sufficient to uphold the retrograding condition that attends the
articles of use in realizing the value of the ground. But where a dilapi-
dated condition has been allowed, and where local circumstances demand a
corresponding attention, a variation rises to ten per cent., denoting an
average of seven or eight in cases of the medium circumstances of attach-
ment and position. If a sum near to ten per cent. be required for a time,
it may soon be reduced by a vigilant attention and enlightened system of
management; and if that figure be exceeded by reason of some previous
negligence, the extent may soon be curtailed within that sum; and the
better way may be not to exceed it in any case, but to proceed gradually, and
accomplish yearly what can be done with that amount of money, always
executing in the first place the most necessary requirements. This mode
may answer better than to make a very large expenditure in one year, and
do nothing in the next, except when imperative circumstances require
such a course of proceedings as has happened, and no doubt will again
In these cases, the average expenditure must be regulated by the
occur.
In a course
of years.
course of five years; beyond which time no extra amount beyond
the allowed medium should be carried forward to embarrass the
next period of that amount of years. Each year must be kept as nearly
as possible to the sum that is allowed and fixed for the special purpose;
and no proceedings of any kind are to be left to uncertainty where they
can be fixed. Extras and accidents will require deviations which are soon
ascertained by the lapse of experience, and reduced to the original regu-
lation, and made a part of it. As was before observed, the replacing of
an old erection of any kind by a new structure, falls under the department
of upholding the decays, for a similar thing stood there before, whereas a
new erection understands that nothing of the kind had ever before appeared.
The execution of wholly new undertakings on a landed estate
takings. deserves a consideration that is widely different from the repairs
that are required to uphold the value that is being derived. That depart-
ment of outlay admits no dispute, it only needs a regulated disposal.
Original executions will be various: in making new roads, new planta-
tions of trees, cutting watercourses, or new beds for rivers, consolidating
farms, and erection of dwelling-houses for tradesmen and mechanics-these
New under-
ON LANDED PROPERTY.
1007
Waste
grounds.
Plantations.
objects require a very careful and attentive consideration of the concomi-
tant and combining circumstances which may seem to justify the execution.
It must be very readily granted that all grounds that cannot be ploughed,
or any way improved, and which do not yield a natural pasturage of some
little value, should be planted with trees, as a crop of timber may be got
of some degree of quality, and the land is improved for the future arable
cultivation, if wished to be restored, and if the surface formation will allow
the use of the ground for the use of aration. If water can be conveyed to
irrigate the surface, the value may be well used in that way; or if the
ground can be improved by a top-dressing with composts, the
planting with trees may not be eligible. But precipitous grounds,
rocky declivities, and slopes that are beyond practical use, do not admit
one moment's hesitation in being converted into a plantation of timber or
copse wood, according as the nature of the ground and the demand of the
locality may direct. A coppice will return a value in eight or ten years,
when the circumstances are mediately favourable, and at most in fourteen
years, when the best use of the growths requires a lengthened duration to
attain the necessary maturity. The quickest return in value
from timber trees comes in about thirty years from the fir tribe
of plants: the hard timbers will require a period of nearly sixty years be-
fore any part of the expense is returned which has been incurred. During
that time the outlay lies dormant at compound interest, and in sixty years
will be quadrupled in amount, and doubled in thirty years. All these
considerations must be duly and very carefully weighed in estimating the
propriety of an undertaking in planting trees, and discover if the use of
money could not be more beneficial in some other expenditure. But many
situations will occur where no other use of the ground can be devised, or
is rationally possible, and then the calculation comes to be the extent to
which the execution may proceed at one time, or at distant intervals. A
large performance may throw a burden on the property that is too heavy
for its position, and the improvement may be too extensive to form a pro-
portionate part of the aggregated extent. The amount must be New things
duly regulated by the circumstances of the proprietor, and the special
capital that can be spared to the purpose of general improvements. A
certain quantity of money should be allowed for this special purpose, in
all cases where the requirements are in existence; and but few situations
are found where the wants do not happen. New plantations are not by
any means to be included in the charge of five to ten per cent. for the pur-
pose of upholding the current-going value of landed property; that allow-
ance only supports a value, and does not create any source of deriving an
income. All creations that are wholly new, are to be entered in an ac-
count that is altogether disconnected with any other rendition, and distinct.
the outlay is sunk for many years, and a heavy interest charge.
comes against the proceeds that may be realized. It is true, that a trifling
expense is incurred yearly in carrying forward the increase of plantations,
in keeping clear the courses of water, and maintaining the fencible con-
dition of the boundary walls. This balance, though small, assists in ren-
1008
ON LANDED PROPERTY.
1
dering more tolerable the long period of time during which no value is
derived from plantations of trees.
Loans of
money used
in three
ways-drain-
It may be again observed, that all grounds that are physically beyond any
other purpose of application, cannot be too soon planted with trees, in tim-
ber or copses, which may be very beneficially mixed in the position of
enclosures, but not in the plants being placed in mixture. There is no
doubt that loans of money now granted by government to drain
wet lands will soon be extended to the two purposes of erecting
farm buildings and planting waste grounds, and both uses are
ing, planting, fully as necessary as the removal of superabundant water; and
no more just and beneficial burden can be imposed on landed
property than the performance of these three purposes, which increase the
quantity of the necessaries of life, salubrify the air, add to the lasting value
of the property as an article of commerce, encourage the letting of it for
temporary use, shelter the country, adorn the scenery, and contribute in a
variety of ways to the comforts of the people.
and building.
Extra pur-
The raising of new embankments, and the cutting of water-
poses. courses in an original direction, forms another item of general
expenditure to be charged to the account of improvements. The return
arises from the estimated advantage that will accrue from the performance
in a larger abundance of some articles in a certain quarter than would have
been produced or were grown if the new work had not been done. This
calculation must go beyond a barely ideal existence if at all possible to be
attained; the accruements must be clearly obvious, and almost firmly tan-
gible, in order to justify the expenditure on points that require to show
certainties in the returns. These executions require a yearly charge in
upholding the useful condition, and consequently, the inducements of per-
formance must be stronger on that account than where one action suffices
for a long period of time. These occasional or probably constant repairs
are included in the charge of upholding the current revenue of the pro-
perty, and must be put under the regulation that apportions the yearly
amount of that expenditure. The cutting a river course may be
divided by two parties that possess the opposite sides of the
river, and will be mutually benefited by the alteration, when each side of
the banks will be defended by the proprietor, and the cost included in the
charge of yearly repairs. The building of new jetties of stone works, in
order to throw the course of waters into a mid-channel, and save the banks
from being wasted, will go to the charge of upholding, as the want of the
article may incur a much greater outlay in erecting the same protection
after an extensive evil has been done. These structures for the purpose of
preventing future evils that may be of a great, but are still of an uncertain
magnitude, differ from the requirements that are needed for the purpose of
warding off constant occurrences, as floods of water and rise of tides; the
latter operation being once done, the repetition is unnecessary; in the for-
mer case, the uncertainty of coming storms renders a constant employment
in the protection of the alluvial banks. Such employments are to be
added to the account of protections, as distinguished from total alterations,
Rivers.
ON LANDED PROPERTY.
1009
which first confer a benefit, and then require a yearly charge to enable the
continuance.
Roads
The making and maintenance of roads does not in every case
form a separate charge on landed property. The turnpike roads are
managed by commissioners, who need no local assistance: the public roads
of local use are, or intended to be, supported by a fixed charge on the ren-
tal of each farm, which is to this day, in most places, badly arranged, and
imperfectly executed. But when a new road is formed, or an old one re-
constructed, the proprietor of the land is always expected to bear a chief
part of the expense; when the item must be charged to an expenditure for
which no value may ever be got, but an improved passage of use, and a
benefit conferred on the public at large. It would be a very superior
arrangement that all the roads on any estate of land be managed by the
chief direction of the agent on the property, and the acting power under the
delegated by him to a subordinate in office under his surveil- agent's care.
lance. In that case, the whole expense would fall on the landlord and the
farmers; the latter bearing the one-half of the expenditure, and the other
moiety attaching to the owner. This outlay on the property must be charged
to the yearly per centage of use, as it goes to uphold the current value of
the property in the provision of roads, which form the first consideration
in the lasting improvements in any country or division of territory. Ano-
ther arrangement will charge the land-owner with making all the A beneficial
roads, and that the farmers uphold them; but most of the neces- arrangement.
sary roads are now made in Britain, and the landlord would escape the
fair contribution. But where new roads are required, the owner must
bear the original outlay, and also the future share of the necessary repairs.
The charge made on the rent of each farm for the purpose of roads, will
be paid to the agent at the half-yearly audits of rent. The mode is used
in some few instances of the roads being managed by the estate agent, and
the benefits are very evident and frankly acknowledged. The farmers
being only temporary occupiers of the ground, no part of their funds must
be applied to the structure of permanent erections; the land-owner is the
liable person, and also for a fair share of the future requirements to up-
hold the value. The landlord gives a share in upholding buildings on a
farm by giving raw materials in lime, stone, and timber; so in upholding
roads, after his cost has made them, a share must come from his property
to maintain the articles in use. This charge, where it is come into use,
will be included in the per centage of repairs.
Bridges.
The building of bridges is generally a private concern of the
land-owner, or of subscription among the neighbouring pro-
prietors, when the possession of it evidently assists their advantage. At
all events, such a thing is wholly beyond the province of the farmer, and
it is also removed beyond the charge of repairs: it is an original edifice,
and needs no future amendments that can form a charge. The owner of
the property is always expected to make the largest contribution, and very
justly in many cases, as his property will be most largely benefited by
the erection. But instances are not wanting where the public will be
1010
ON LANDED PROPERTY.
equally, if not more, advantaged than the property itself by the projected
means of traffic, when the owner of the soil may be allowed an equality
Singly or
with other subscribers. If any landed property does not exist
doubly useful
on both sides of the bridge, the advantages are not so large to the
benefit of the patrimony; the bridge is only a public transit through the
estate; but when both sides belong to the same property, it is a means of
communication, and becomes doubly valuable. All these considerations
occur in estimating every kind of outlay on the estate of land; the private
advantage to the owner, the general benefit to the country, the charge re-
quired to derive undiminished the current-going yearly revenue, the
amount that can be allowed to general improvements which promise a
distant return, and what sums the extent and value of the property are
able to give in extras, as contributions and subscriptions, for objects of
public utility.
It is an important point to fix the relation of the several points of ex-
penditure on an estate of landed property, or the respective amount of the
items which constitute the gross outlay over the whole extent. For this
purpose it is necessary to ascertain the most valuable points of outlay, or
those which return the quickest value for the money that is ex-
Purposes of
outlay.
pended, and the steadiness of the source which forms the spring
of revenue. Two items constitute the chief outlay on landed property——
farms and the plantations. The last point is contained in two departments,
or the making of plantations, and the cost of protecting those that have
been made, dividing the outlay into two accounts, which must not be con-
founded together, but separately arranged; the two amounts being added
together will show the gross outlay in the department of plantations. The
growing of timber makes slow returns, and at distant periods of time;
the thinnings, if any, consist of worthless under-growths, which fetch little
money, and do not repay any part of the original cost, if the value upholds
the current item of expense. But on most estates, a quantity of timber
will be found that is full grown and ready for sale, and by a
certain quantity of yearly value from that source, the current-
going expense will be covered, and a surplus be derived for the rent of
the land. When oak timber is produced, a double chance occurs in the
wood and bark as articles of value, in obtaining a revenue from the plan-
tations, which contributes very much to the value of the grounds. A
yearly fall of timber is to be recommended in all cases where the articles
are found; if not yearly, then in the time of two or three years, a sum of
money, less or more, must be got from that use of the land. The regula-
tion is imperative, that on all estates which contain woods of the proper
age, an income be derived from the sales of timber which shall cover the
cost of upholding, and if possible, a surplus be accumulated that will de-
fray the expense of making new plantations, in some part, if not the whole
of the outlay. From the revenue of the plantations a per cent-
from them. age must be deducted for the current-going expenditure, which
will not be large, but still forming an item. The very varying conditions
of estates of land in quantity and quality of timber, and the uncertainty of
Woods.
Revenue
•
ON LANDED PROPERTY.
1011
the value of the article, render impossible any nomination of the amount of
the
per centage; the sale being large or small, adds to the difficulty, and
the figure must be left to the circumstances of each particular case that
occurs. Where no timber exists that can be sold, then the cost falls upon
the rental of the estate, when the average per centage for the purpose of
plantations will not exceed two to three per cent., or about one- None but an
third of the cost in upholding the current value of the farmed outlay.
lands; and it will require an estate of some magnitude, and woods of very
considerable extent, to use that allowance, except in cases of making altera-
tions and improvements beyond the currency of procedure. In this calcu-
lation there are not included the timber of pleasure grounds, or of parks
and policies; these places are isolated from common touch, and are not de-
pended on by any estimate of value. All hedge-row timbers over the
estate are contained in the calculation, and the same purposes of use are
attached. Copse woods, if any, are comprehended in the account, and
ranked with timbers in the general estimate.
On estates of old improvement that are proportionately Young plan-
wooded and enclosed, a yearly rental should be derived from the tations.
produce sold, or at least the current expenses should be paid by the arti-
cle which requires the protection of cost. Cases will occur of under-age
plantations, when no value can be got, but must be waited for till the tim-
ber is matured for use. A yearly item will then be expended in the pro-
tection of the plantations, which will vary with the many circumstances of
extent of grounds, situation, locality of the fields, and the exposure of
situation.
Rent of lands
The yearly revenue that is steadily derived from the lands
that are let in farms of temporary occupation, requires an atten-
tion much wider than that of plantations, and a larger allowance in pro-
portion to the value of the source of income. The produce of land being
yearly in its nature, the value is annually derived; and as the recurrence is
steady, and not liable to any omissions, the more attention is required that
no wants be allowed which may impair the yearly revenue in the necessary
attachments. Plantations are in general an improving department, at least
to a certain age; the appurtenances of a farm are decaying from the very
day of erection, and demand the care of upholding in order to continue the
income that is got from their use. This very essential difference renders
necessary a much larger allowance for the support of the most valuable
department, and as it constitutes the chief part of the property, it must be
first considered, and have the proper estimation. A per centage
on the gross rental of the estate in five per cent. has been found to uphold the
sufficient in cases of well-regulated estates, and of business judi-
ciously administered, where former carelessness creates no large demands,
and fortuitous circumstances have no large possession. A variation to ten
per cent. has been allowed to meet the cases of extraordinary demand that
arise from natural causes, and from the bad administration of former offi-
cials, or from some undefinable or incontrollable cause which may have
ceased after a time, and then the work of regeneration must commence.
Per centage
value.
1012
ON LANDED PROPERTY.
But these extremes of extra charge are not to be included as common de-
mands, and should be noticed as examples to be avoided rather than models
of imitation. Few or no cases should reach the medium figure of seven
and a half per cent., which shows an outlay beyond the justness of good
regulations and a sound apportionment. At the same time, few or no
Not to be ex- estates will need less than five per cent., unless a niggardly par-
simony be allowed to exercise its sway, and create many wants
to demand on some future day an expenditure much beyond the amount of
savings which it is able to show at the present time. This policy but too
often prevails, and is attended with much loss and inconvenience.
ceeded.
By taking seven and a half per cent. as the average allowance for
upholding an estate, and the cost of the plantations at one-third of that
sum, there is got the figure of ten per cent. as the amount of these two
expenditures on landed property.
Cost of gar-
Gardens, policies, and pleasure grounds, form a part of the
dens, policies appropriated use of an estate of land, and require a proportionate
and pleasure allowance for the maintenance. These establishments form an
grounds.
article of luxury rather than use, and no tangible revenue is de-
rived from them; yet a burden is created on the landed estate, and a con-
sideration is due to the department when the parts of any estate of land
are regulated in calculation. Plantations make a return in some annual
sums, or in more years' amount, or a large value is obtained from a general
fall of grown timber, which must be distributed over the years in which
no income was derived. But gardens and reserve grounds never show a
return of any value; the whole produce disappears, and the cost of pro-
duction must come from another source, or the rental of the property. The
extent of these appropriations will depend on the extent of the property,
the family of the owner, and if the domestics are constantly resident; but
in general cases, a per centage of two and a half per cent. will suffice for a
genteel and moderate establishment, where prudence and economy are duly
entertained. Thus, two and a half per cent., added to ten per cent., as
shown before, makes twelve and a half per cent. for the current-going
yearly cost of supporting the yearly value of a landed estate, and
allowing two and a half per cent. for extras in contributions and
subscriptions for purposes connected with the property, there is got the
sum of fifteen per cent., as the gross estimate of maintaining a landed
estate. The average may be stated at ten to fifteen per cent.
Whole per
centage.
ON LANDED PROPERTY.
1013
CHAPTER XI.
VALUATION OF LANDED PROPERTY; OF THE SOIL, OF
HOUSES, OF WOODS, OF MINERALS, OF MANORIAL
RIGHTS, OF ROYALTIES, AND OF FEE FARM RENTS*.
valued.
LAND having become an article of commerce is raised and depressed in
value by the same laws and contingencies as other commodities that are
used for profit and advantage. The value of a landed estate, as Land how
the subject of sale or purchase, is primarily determined by the
free rent which is produced from the use of it. This rent may be calculated
from certain assumed rates of farm produce-but the simple determination
proceeds from the marketable value of the land, or the amount which can
be got for it by the farmers of occupation.
The probable rent is diminished by all the burdens which affect the land,
as land-tax, poor's rates, tythes, and any other burdens which fall upon the
land, and not upon any other securities. The net rent thus obtained,
is to be multiplied by such a number of years' purchase as land produces
at the time in the market. This expression shows the amount of interest
which the buyer calculates upon receiving from his purchase- Interest of
money. Thus, if the number is twenty-five, or if the purchaser
pays twenty-five for every £1 of free rent, being in common language
twenty-five years' purchase he will receive four per cent. for
25 : 1 :: 100: 4.
purchase.
If the market price be three years' purchase, he will receive three and
one-third per cent. for
30 : 1 :: 100 : 31.
The common rate of interest should determine the number of years' pur-
chase; but the demand for land, as compared with other securities exerts
the same influence, as in all other cases of transactions in selling property.
When the sum of five per cent. constituted the rate of interest in this
country, the common calculation reckoned land to sell at twenty-five years'
purchase, or, in other words, that it should yield four per cent. of interest.
But this proportion is not now upheld by land—the market rate of interest
scarcely exceeds three per cent., and land is sold at prices which does not
even reach that figure.
When it is wished or fixed to have a certain rate of interest Per centage
from land, the number of years that will yield the amount being expected.
multiplied into the net rental, the product will exhibit the amount of
the purchase-money, which must be increased by the estimate of woods,
mines, or other adjuncts, and diminished by all incumbrances that may
exist. The present value must be ascertained, as in the case of annuities,
and the amount deducted. An annuity of £100 yearly for ten years,
* See also examples of practice, pp. 620-631.
1014
ON LANDED PROPERTY.
Leases of
much con-
sideration.
payable half-yearly, and at the rate of three and a half per cent. interest,
is worth £837 12s. 10d. to be deducted, and so on with all similar cases.
A heavy consideration is due to the leases of land, if the rents
seem equitable, or low, that no advantage may be expected,
when the holdings expire, or that a rise of rental is evident.
Leases which are long in expiry are generally reckoned adverse to the
selling of land, as the chance is distant of deriving any advantage that may
occur. But no large calculation can be founded on these probabilities,
which are at best uncertainties, unless the rental be very palpably under
the average of the common estimate. In that case, and where several
cases are found, an inducement may be formed to advance the offer of
purchase, as a realization is evident of the increased amount. Farms that
are underlet, and which are held by lease, constitute an annuity in the
amount of the yearly deficiency, and the same thing as if the money was
paid to a recipient quarter, instead of not receiving it from a source of
proper value. If a farm have ten years of lease unexpired, and the rent
be evidently £100 too low, then the sum of £837 12s 10d. is to be
deducted from the purchase-money which was shown before to be the
present value of £100 for ten years paid half-yearly, and reckoning in-
terest at three and a half per cent. These deficiencies on the wants of the
Encum-
brances.
realized value, are encumbrances upon the property, and tell
heavily against the market value of land. But such cases do not
often occur, as values of every kind have now been well ascertained, and
in a period of time and under circumstances which exclude the rational ex-
pectation of any great change.
Condition of
The general condition of an estate of land will very largely
the estate influence the amount of the value, in its being forward in con-
dition, well regulated, and under the due administration. If the appur-
tenances of the farms show extensive dilapidations, and will immediately
require a large outlay of money to execute the necessary repairs; if the roads.
show an incommodious condition, and need any considerable restoration; if
the plantations exhibit a state of neglect, are open and exposed to depreda-
tions; and if the fences are broken down, damaged, and misthriven, too
few in number, and ineffectual in the purpose, a very large drawback will
be formed by the aggregation of such items, and the money that has been
saved by the parsimony of neglect, will now be deducted in a greater sum
from the expected amount of sale. Articles that are exposed to view for
the purpose of vendition, must be exhibited in the very soundest possible
condition, as the flaws are the objects of observation, and are always
magnified rather than lessened, or even fairly estimated. A hurried
preparation does not exhibit the proper and necessary train of enticing
appearances, that are necessary to secure an approbation of willing invest-
ment: the newly raised exhibitions are seen through, and raise a suspicion
of other coverings being purposely used. Only a long and continuously
persevered administration of care and economy, can exhibit a
landed property to the eye of purchase in the garb that will
both suit the fancy and please the judgment: show an article
must be
sound and
pleasurable.
ON LANDED PROPERTY.
1015
for the delight of the mind, as well as profit to the pocket. In making
these preparations, it is only necessary to consult the current condition, in
articles of lasting utility, and of durable pleasure. These purposes suit
both views, of present possession and of future dismemberment.
Many, or nearly all estates of land that are of any considerable extent,
possess houses that pay rent, either in single tenements, or in congregated
villages. The property is more perishable than the land Houses pay-
which is cultivated, and repairs are regularly required to sup- ing rent.
port the tenantable condition. The per centage on the rent of houses to
uphold decays, is to be deducted from the yearly amount: but it is
generally included in the general per centage over the estate, and is not
separated in a distinct account, except the village be large, and yields a
revenue that deserves a classified consideration. In that case, a distinct
view is shown of the different values got from land and houses-the
expense of maintaining the serviceable condition of each species of property,
and the net revenue from each source, when the purchase cost can be
distinguished. The decaying nature of houses requires a larger interest
than lands, and consequently a smaller number of years' purchase. The
interest being calculated at seven and a half per cent. in the common
estimate, the number of years will be about thirteen and a half on the
purchase number. The general number is below that figure, and falls even
so low as one-third of the calculation in diminution.
Villages
In many situations, houses pay a very encouraging rent of a property
in land. In manufacturing districts, in convenient fishing stations on the
sea coast, and in places where mechanics abound, the erection of cottage
dwellings becomes a good outlay of money-the rents are small,
and easily raised, and are generally well paid. The source of
employment and the means must be first discovered, and the permanency
of the undertakings. When these provisions exist in a moderate degree, no
more beneficial ornament can be conferred on a landed property than a
number of conveniently located and suitably provided cottage dwellings,
showing health and contentment, and nursing the bonds of union, and the
sinews of the nation's strength. All such habitations must be under the
management of the landlord, and not placed under the dominion of any
farmer, except where the domiciles answer the express purpose of lodging
the labourers of the farm. In that case, the property ranks as a
provision of the farm, and is merged into the value of that de- mer's care.
partment. In sequestered localities that are removed from the conveniences
of the parish village, and where farms of land are regularly constituted, it
would be very advantageous and beneficial to establish a village by the
means of the proprietor, import the raw materials, export the produce,
employ labour, and circulate money. A value would be given to the
property, and if circumstances are moderately favourable, the adverse ones
may be turned into sources of nutrition.
not the far-
The foregoing remarks only apply to houses that yield a rent, or are
capable of yielding a revenue, and not all to the houses of the farm, which
instead of being placed to the value of the land in the proper number, are to
1016
ON LANDED PROPERTY.
Separate
be deducted from the purchase-money, when they are seen to be
deficient in the necessary provision. The amount that may be
estimated to erect the required habitations must be deducted from the
number of years' purchase.
Woods are determined in value on several data: full-grown timbers are
estimated by the selling price, lessened by the cost of felling, and the ex-
penses of sale. The improved condition of the land may be reckoned, when
an arable state of the ground is intended to be done; but it is mostly replanted
with young trees. A calculation can be formed of the number of trees on an
acre of ground, and local experience will be able to form a value of the single
trees, and thence of the acre, and of the total number of acres in the
plantation. It is best that the seller has the trees felled by his own work-
men; and in some cases, an eligibility may occur, that the trees be dragged
outside the wood by the same employment; but if this last per-
formance be not done by the seller's execution, the felling of the
trees is very properly done by that part of the transaction. Distinctive
marks separate the trees, so that no confusion happens. Lots of bulk to
suit a variety of purchase, may be laid outside the wood, and sold in
divisions, or by the measured foot. And as before observed, it is much
best, that the owner has the trees brought to that position, and that no
purchaser enters the plantation.
woods.
When woods are not full grown, but vary in age from the year of being
planted to the time of maturation, a different mode of valuation must be
adopted. The cost of producing woods is usually applied as a mode of
valuing young trees, and when the age of timbers approaches the full
growth of use, the value of the wood when felled may be learned from
Young plan- the knowledge of the value of timber, and the corresponding
tations. deduction must be made in the number of years that will elapse
till the maturity be attained. The land will be improved for the
purpose of pasturage; and this consideration may form an item of some
value in the estimate. The amount of the original expense of forming a
plantation is increased by the accumulated interest from the time of out-
lay to the time of sale, the amount of the annual rents, with interest from
the period of planting to the time of sale, and the value of the land on
which the wood is growing, because the cost of the land on which the
wood is planted, is part of the cost of production.
If land worth 10s. an acre has been planted with trees for twenty years,
at £5 an acre of original cost, the value of the timber in this
way will be as under :-
Valuation.
£.
s. d.
The sum of £5 principal and interest at 3 per cent for
twenty years
9 19 0
The amount of 10s. per annum at the same interest and time
The value of the land at 10s. an acre, at thirty years' purchase
Value of the wood in twentieth year, per acre
14
2 10
15
0 0
39
1 10
This mode of valuing woods is not eligible, unless the age of the trees
ON LANDED PROPERTY.
1017
be very young, or under ten years, when the approximation can be better
made from the existing circumstances than from the distant value of the
matured article. The calculation only shows what the cost has been to
the seller of the land to bring into the present condition the article which
is offered for sale; but it affords no index to the value of the materials
after the lapse of many years, during which time the purchaser gets no
revenue, and has to wait the expected return.
The age of Age of thirty
thirty years will bring to maturity the general average of plan- years.
tations of fir trees, and sixty years may be allowed for the use of the
hard woods, as oak, ash, and elms. In unmixed congregations of trees,
the calculation will be based on these simple periods of time; but where
the woods are of mixed kinds, an opinion must be formed of the relative
quantities of each sort, and then assume an average number of years in
which the maturity will be reached. This assumption may be forty-five
years, which may be divided into three periods: 1, of simple growth;
2, of accelerated growth; 3, of matured growth: and each period must
be attached with a definite portion of the ultimate value. The simple
division of the return into three parts would not be a fair apportionment,
for the trees during the first period of time will not attain any-
thing like one-third of the matured value, and consequently a periods.
reduced item must be attached. The middle division of time will in-
crease the most rapidly, and will push the trees to the full height, and
commence the hardening of the timber into the useful consistence. The
third, or last period, will bear the largest value, as the timber gradually
attains the matured state. A notice must be taken of the quality of the
soil to carry out the growths of the earliest periods, and of the exposure
to allow the statures; for not unfrequently the first growths are encou-
raged by favourable circumstances which do not exist when an advanced
stage of existence is attained. Observation will not fail to intrude the
necessary deductions on this point.
Three
General
objects.
The first object is to compute the number of trees on an acre of ground,
which may be averaged by observing the distance between each standard
that prevails over the extent of the plantation. Then the probable value
must be ascertained of the timbers when full grown, and felled
for sale. The age of the plantation being known, and the time
of full maturity fixed, as before explained, there may be given to the latter
division of time, seven-tenths of the aggregated value of the timbers
when sold, one-fifth of the same sum to the middle division of time, and
one-tenth to the first fifteen years of the growth of the trees; and if the
sale happens when the age is about thirty-five years, or nearly to seven
or eight, then one-tenth is to be taken from the third division of the age,
and added to the first apportionment. This becomes necessary, from the
greater value which has been attained by the young growths in seven or
eight years, than if the valuation happened at the time of three or four
years; and the last stage of maturity is less in value at thirty-five years
than if the calculation was made between forty and forty-five years. Be-
sides these data, other contingencies will occur to influence the calcula-
3 R
1018
ON LANDED PROPERTY.
tions, which must be alive to every observation, and open to every
suggestion.
use.
Growing woods of any age that is below the condition of immediate use
Woods below seldom or never in this country realizes the full value in case of
sale, being reckoned a dead stock which the proprietor cannot
use, or remove, or cut down without damaging his estate in the very essen-
tial provisions of shelter and embellishment. Such acts would inflict
a damage on the general value of landed property that would many times
exceed the amount of any sum that may be shown by calculation, even
the most correct and the most substantially founded, and hardly would
any diminution of value compensate the loss or want of one of the chief
ornaments of nature, as shown in clothing the earth with vegetable growths
of low and high dimensions. In most cases of young woods, the plan-
tations are generally reckoned a most necessary appendage to
them. any extent of landed property, of which the value is scarcely
entertained; but if wanting, the value would be largely accounted and
urged as an abatement. The justness of the complaint cannot be denied,
and urges the demand on all proprietors that the provision be not in any
case neglected. The price of growing woods, however it may be
estimated, resolves itself into a simple bargain, of what the seller can
get for it, and on what sum the purchaser is inclined to give, after he has
consulted his convenience, and has prudently weighed the combination
of circumstances which occurs to justify the purchase of the property.
The cultivated lands and woods constitute the solid basis of landed pro-
Price of
Land and
wood, chief
sources.
perty; the other sources of revenue are only attachments, that
are evanescent in the nature, less durable in the fixity, and more
exposed to chances and accidents of disruption. The chief at-
tention must be paid to these two sources of revenue, as they form the
only permanent foundation of any sound procedure. The intrinsic qual-
ity of any soil, and the value derived from it, are no doubt, the primary
points of regard, as by them is fixed the sum of the revenue; but many
cases will occur, where an extended view must be taken of the capabilities
of the natural provisions as inducing the probability of profitable under-
takings beyond the present realizations. The susceptibility of future
Susceptibi-
lity of im-
provement.
improvements is a quality in landed property that is often more
valuable than the present condition of profit, for it holds out
the chances that may occur during the progress of undertakings
which frequently much exceed the original calculations. The presence of
woods and of dwellings on the estate are essential to its existence as a
patrimonial inheritance, or a source of revenue; without them, land is
only a dreary waste possessing neither shelter against the storm, or food
against the natural cravings. The strength of a nation is founded on the
number of its people, and an estate rests for value on the number of its
appurtenances, and the state of the establishment which is maintained.
The existing state or manner in which lands lie, makes all the differences
imaginable in the estimates of value and produce. The situation has very
great influence, being near to towns, convenient to manufactures, or con-
ON LANDED PROPERTY.
1019
nected with an advancing condition of elements. The temperature of
situation is also a matter of notice, as it affects very much the value both
of lands and woods. The social position of an estate of land Social posi-
must also be considered, if the community be liberal-minded, tion of an
or prejudiced, frugal in habits, or lax and dissipated. The habits
estate.
of industry and of social affection must not be overlooked, and if the
capable improvements of the district be fully performed, or are only being
commenced, or half-way progressed. In a case of large improvements
being done, the supply of labour, and the demand for produce will be
taken into account, and the conveniencies that are seen of making these
provisions, as is possible in many cases, where the necessity may dictate.
The probability of creating a revenue, as well as the certainty of getting
an income ready-made, will weigh the scale of judgment in the ratio of
the considerations that are brought to bear upon the subject, and a greater
number of these items occur in the purchase and value of landed Probability
property than in most other human transactions. The seller of a revenue.
must be aware of the circumstances that will bring forward these consi-
derations, and have the articles for sale in the best possible condition that
can remove objections which act in any way to detract from the value of
the commodity. Woods and buildings are the foremost of the appur-
tenances of landed property, and no reasonable expenditure must be with-
held, in order to make the provision of these two articles, that is conform-
able with the property and the attending circumstances. Buildings are
required to uphold the current going value of the land, and timbers are
needed to construct and uphold the buildings, and both objects being ar-
tificial productions, can be raised on almost any lands in Britain. Articles
of fancy and show are not required beyond the precincts of the
pleasurable demesne; the provision over the estate must suit
the circumstances of use, and lead to advancement. In making planta-
tions, care is to be used that no encroachment is made on arable purposes,
as the value of woods is posterior to the growing of yearly crops, which
supply the daily wants of recurring use. A due proportion must be ob-
served of the present with the future purposes, unless the grounds show a
large amount of useless surfaces over cultivable lands, when the expe-
diency admits no doubt of the speedy conversion of wastes into some
shape of utility.
No articles
of show.
Mineral property of any kind is always reckoned a valuable Mineral pro-
appendage to an estate of land. If none of the valuable metals perty.
are found to enhance the value of the surface ground, and even coals being
altogether absent, there may still exist a sufficient quantity of clay and
building stones with which may be supplied the current wants of the pro-
perty in the manufactured article of bricks and stones for walling. The
presence of these articles, though none are sold to raise a yearly revenue,
is a very large convenience to any estate of land, as it abrogates the neces-
sity of foreign purchase, and tends to the constitution of the property as
being self-contained. A self-supporting property conveys a title to eligi-
bility, and the necessary articles being present, will form a pre-eminence.
1020
ON LANDED PROPERTY.
A mine and
land of a
similar
value.
over those that must be wrought for foreign use, and which have to supply
the want of the materials that are constantly required. The value of these
adventitious articles of property is variously affected by the ascertained
continuation of the mineral substances, or the apprehended exhaustibility,
View of the the prospect of the value being maintained, and if the support
articles. of the undertaking rests upon the solid grounds of suitable ac-
companying provisions. If the foreign export be none, the value of coal,
clay, and building stones will be very considerable; and with the total
want of coal, which is the most general case, the attachment of building
materials will have a due attention. The quantity and quality of surface
ground, which may be destroyed for use in working the minerals, must not
escape the notice of valuation; the allowance in money for the destruction
will detract a something from the value in all cases where the use of the
surface infers a price of any amount. The annual revenue that is derived
from a mine, is held to pay the same interest on the purchase-
money as the soil of the earth, and it is liable to the same de-
duction in a per centage for the yearly upholding of the current
going order. In some cases, this charge will exceed that of land
that is let in farms, as the movements of action are quicker and more fre-
quent, and the frictions and collisions are much more numerous of the
different bodies that are in use. This consideration, the probable ex-
haustion of the article, and the uncertainty of demand, impose upon mineral
property a cheaper purchase than of land in the full proportion of one-half
the amount. The surface of the ground can be seen, examined, and esti-
mated, and the possible and probable capabilities are estimated in prospect,
the use of it can never fail while the human race exists, and all the artifi-
cial repositories of money are trifling safeguards in comparison with the
improved utility of the natural patrimony. Minerals are an adjunct to it,
and a very valuable one; but the use is much hidden, and the continuation
but differ uncertain. Hence, though the net produce of mines does add to
in prospect. the aggregated sum of the purchase-money of a landed estate,
the reckoning must be separately made, and the entertainment different.
The chief consideration rests upon the continuation of the rent at the pre-
sent reported value; the extension is a matter of choice in any improve-
ments that may be contemplated to make on the property. The probability
of this object, however, will conduce to flatter the prospects of purchase,
if not over-estimated by the selling party, and put forward at an extrava-
gant estimation. A thing that may be done is of uncertain amount,
as the doing of it is exposed to many contingencies that are beyond all cal-
culation; on these points, any fixed data give way to the best assumptions.
Calculating land to fetch at present twenty-four years' pur-
purchase in chase, which may be beyond the average, except in very prime
qualities of soil and circumstances, minerals may be put down
at twelve years' purchase, and the net revenue being multiplied by that
figure, will give the amount to be added to the proposed offer for the pos-
session of the estate.
Years of
mines.
Manorial
rights.
Manorial rights or claims exist over lands that are not en-
closed, but have been left open to the purposes of different
ON LANDED PROPERTY.
1021
usages. When the disruptions happened of the large congregations of
landed purposes that had long existed in Britain, large tracts of ground
were appropriated to general use, with reservation of certain rights to some
superior person who adjoined the property, and who contemplated his own
possession of it at no very distant time, by granting the use of it upon re-
tainable conditions. Some lands were used in common pasturage that was
open to the adjoining grounds of cultivation, and the lord of the manor
had the mines and quarries reserved for his use. Wooded grounds yielded
the pasturage to the adjoining tenants, and the growing timbers are the
property of the lord; and as manors of land came originally from the
crown, the lords who held them gave away to lesser lords the similar pos-
sessions, and retained the claims over them, which have been called mano-
rial rights. Quit-rents, escheatments, and heriots were established, which
yet exist in a very diminished degree. Quit-rents, or quiet-rents,
is a certain small rent, payable by the tenants of manors in token
of subjection, and by which the tenant goes quiet and free. It was an-
ciently called white-rent, because paid in silver money, and differing from
rent-corns. Escheatments are a fall of the land to the lord of the manor,
by reason of the extinction of the blood of the tenant in the want of heirs,
or by the commission of treason or felony. The original conditions being
broken, the gift resulted back to the lord who gave it. Heriot
is a personal chattel, due to the lord on the death of the tenant,
and is no charge on the lands, but merely on the goods and chattels : the
lord chooses any article that may appear good. Fines were also imposed
by the higher lords upon their dependents for the alienation of the land
that was given them.
Quit-rents.
Heriots.
These feudal relics are yet found in South Britain, where ancient usages
drag a lengthened existence beyond the rest of the kingdom. Heriots will
depend on the probable chances of human life, and on the value of the ar-
ticles that can be taken. One seizure in thirty years may ap- One in thirty
proximate the chance of the property, which may place the pur- years.
chase in that of ten to fifteen years. It is uncertain what articles are liable,
and the value cannot be named. The timber trees that grow on pastured
lands are counted and valued by the age, as in the enclosed plantations ;
and there must be taken into account the probability of how many may
succeed in growing in future years, as the young shoots are constantly ex-
posed to browsing animals. The value does not form a large figure in the
estimate of property in land.
Royalty.
Royalty is the claim of the crown over the mines that were
wrought as its property, and was continued by the owners who
succeeded as possessors. It consists of a fixed part of the value of each
article that is sold by weight or measure, and was charged for the liberty
to work and sell the materials. It was a prerogative of the crown, which
descended to the next in power, or the owners of the soil, as they existed
in titled or inferior gradations; the distinction was continued, as it implied
both the profit and pride of superiority. When mines are dug and carried
into a current-going condition by the landlord's expense, and the approxi-
mated value has been ascertained, a fixed yearly rent may be agreed be-
1022
ON LANDED PROPERTY.
tween the parties; but when speculation enters upon the undertaking, a
royalty on the sales constitutes the safest ground of action, and must have
a lease of suitable duration to warrant the outlay. After the expiring of
the first lease, which will generally fix the future value, a yearly rent may
supersede the royalty, or it may be continued by mutual option.
A free rent.
A royalty is a revenue that is free of all deductions, as the costs
of every kind in working and upholding the currency of action
falls upon the tenant, and the landlord gets the stipulated part by the
trouble of receiving it. But the exhaustible nature of the property, and
the uncertainty of demand, fall equally upon both parties; and the pur-
chase value of the owner's share is reduced to the number of twelve years
in the half of property in surface ground. Royalty is the net rent, calcu-
lated posterior to the cost to the tenant of upholding materials, and there-
fore both ways arrive at the same value to the owner, and do not alter the
amount of the purchase-money.
Fee-farm
value.
Fee-farm rents are due from tenures without homage, and
rent is a free which belonged to the heirs for ever. The feoffment contained
very special articles of agreement, one of which was the power
of the feoffer and his heirs to enter into the possession of the lands upon
the rent not having been paid for two years. The rent was one-third or
one-fourth of the value, and some conditions of performance were imposed,
as upholding churches and chaplains; but no fealty or service was done to
the superior, as it was a removal of burdens from himself, and for which
he allowed a means of performance. This trifle is free of any deduction,
and may be added in the yearly amount of the unincumbered rent of the
land. The likings of superiority yet continue these relics, though they
are now both few and unimportant.
The foregoing modes and items of valuation may be illustrated by an
example of the statements that have now been given,
General va-
An estate of land is let into farms, which yield a gross rental
luation of an of £15,000 yearly. The net-rent must be shown on which to cal-
culate the purchase-money after the burdens have been deducted:
Gross rental
estate.
Burdens-Allow 12 per cent. for upholding the current-
going order, as previously shown
Net rental
£15,000
1,875
£13,125
Which is formed wholly from the surface ground, and is augmented by
the following items :—
Royalty of mines, which is free of burdens
Manorial rights by estimate
Fee-farm rents
Surface-rents
Rent
Yearly.
£350
150
50
550
13,125
£13,675
ON LANDED PROPERTY.
1023
The net-rent, with the manorial rights and fee-farm rents, is
the sum of £13,325, at twenty years' purchase
Royalty of £350 yearly, at ten years' purchase
Purchase-money
Purchase-
money.
£266,500
3,500
£270,000
Land
bears a low
interest.
The woods are included in the surface-rents of the ground, and estimated
as shown before, and placed under the reduction that has been explained.
Land is computed to fetch the lowest interest of any stock in
this country with relation to the purchase-money. The burdens,
outlay, and trouble, anent the possession of it, are very considerable; and
though the former may be ascertained with a very fair exactness, there
are other expenses attending it which escape the common estimates of de-
duction. The nature and extent of the estate, its present and
past condition, the state of the tenantry, the conditions of leases,
and other circumstances, will exert an indirect influence, and not very
small, on the eligibility of an investment in land. Annual hold-
ings and short leases incur more expense than where long leases
prevail: frequent changes produce wants and desires by reason of the ob-
jects being exposed to view. In addition to the regular expenditure which
can be estimated, there is always a calculation of casual matters and un-
avoidable accidents, which fall upon landed property beyond any other
kind of capital. It is very common to hear complaints of the great expenses
of landed property, which are in many cases very true, and are much
owing to the careless attention and system of neglect with which the pos-
session is managed. The full value of landed property can only be derived
by maintaining it in good order, and for this purpose the requisite Must be in
expenditure must not be withheld, and the judicious and rela- good order.
tive application of it is to be preserved with the most scrupulous attention.
If a small revenue is derived from a well-ordered and replenished estate
of land, much less will be obtained from a neglected property, which is
daily sliding downwards, and will soon arrive at total worthlessness. An
improvident management will soon destroy any property without a trace
of the fortune that has been lost, while a foreseeing and ready outlay for
all necessary objects will always secure a well-paid present in- Is easily de-
come, and promote ultimate improvement of the estate. Incom- stroyed.
petency is never more clearly shown than in the so-called economy of
withholding the means to repair deficiencies and make them durable, when
larger gaps will arise from the neglect, and in refusing an expenditure which
would add some new sources, and also prevent the casualties of recurrence.
In this way much of the expenses on land is heedlessly incurred.
The inducements to acquire landed property ever remain to
be very strong, notwithstanding the low interest that accrues,
and the expenses that are attached. It possesses a more durable security
than other kinds of capital; there is a fair expectation of a future increase
of value, and there are many pleasing associations connected
with the solid and enduring possession of a landed estate.
Land much
desired.
Is a firm
security.
1024
ON LANDED PROPERTY.
However much the thirst of gain may frequent the crowded ports of com-
merce, and haunt the walks of trade, no sooner has a large fortune been
realized than it looks towards the land as the safest security. A rural re-
tirement has ever formed a chief delight of the human race, and no wealth
is able to find an equal, or to substitute the enjoyments. Superiority is
ever pleasing to the mind, and there is more room in the vacant country
than in the crowded town, where to show the exercise of power and the
influence of wealth. The possession of land conveys with it very peculiar
associations of inherited liking and pleasing recurrence, and there are at-
A gratifying tached to it many feelings of some little importance, which
employment. employ the fancy and divert the judgment. A proprietor of land
is pleased to employ a happy labour, and to pay it; gratification associates
with the learning of the clergy and teachers of the neighbourhood, and the
justice and the magistrate are delighted to assist in dispensing rationality
as law on disputed points, and to contribute in the advancement of morality.
The residence becomes highly pleasing, and the employment most truly
useful.
CHAPTER XII.
LAND STEWARD AND FARM BAILIFF: QUALIFICATIONS
AND DUTIES.
Land
THE land steward is a comparatively new official employment, having
superseded the old manorial courts of audit, in which lawyers were
necessarily employed. The post now requires a well educated
steward and enlightened civilian, who is divested of the trammels and
prejudices of a dogmatic craft, and whose mind has been very largely
liberalized by a varied and comprehensive education. In the present
days of enlightened and very rapidly progressive improvement of every
kind, degree, and quality, it is most essentially necessary, that “the”
person to whom the possessor of land has delegated the power of superin-
tendence and direction over his property, be very intimately acquainted
with the most approved modes of cultivating the possession, drawn from
a systematic education and a regularly confirmed experience. For this
purpose, the education must be commenced from boyhood; and especial
His educa- care must be used, that the prejudices and trammels of the
antiquated customs of a craft be not allowed to usurp the place
of liberal ideas, and of reasonable and enlightened entertainments. In
addition to the utmost extent of the usual education called "schooling,”
which is necessary to any profession, there is to be recommended for
practical use and ornamental possession, a pretty extensive classical edu-
cation, by which is meant a very considerable knowledge of, and ac-
tion.
ON LANDED PROPERTY.
1025
Classical.
quaintance with, the ancient writers of Greece and Rome; from the
perusal of which may be drawn the most liberal sentiments, and also
the most elegant and ingenious, and which never fail to exert a most
favourable influence on the professional transactions of any kind or degree
with which they come into contact. They also tend very powerfully to
create and promote that graceful affability of manner which is necessary
for every person engaged in general business of a superior kind, where
proper courtesy to inferiors, and the deferential respect that is due to
superiors, are most imperatively required to constitute a negotiating
"medium," for arranging and carrying on the business of the
property. The use of a knowledge of these languages is un-
deniable in producing the aptitude of correct speaking and writing, than
which there is not a more useful or ornamental part of a polite education.
And no qualification more clearly shows the fitness of any person for a
business" occupation than the readiness with which ideas and concep-
tions are entertained, and the correctness with which they are quickly
clothed with a becoming verdure of language, that is at once Command of
clear and intelligible, expressive and decorous, and which sends language.
afloat in the commercial world as a current coin the very commonest
transactions of business. Nothing more effectually contributes to the
agreeable and faithful discharge of a mixed duty, than a graceful and
pleasing affability of manner, and the prompt and correct use of the
tongue and of the pen at all times, and on any occasions that may occur;
and to produce these requisites, no branch of learning is more efficacious
than an intimate acquaintance with the language and ideas of Greece and
Rome, the two great theatres of human glory, from whom every succeeding
enlightened nation has very unwillingly borrowed, and which many more
have not yet equalled or approached. The common conversation of
every person that is employed in the higher world of business, his inter-
course with society, both vulgar and refined, his epistolary and business
correspondence, and even his daily communications with servants and
domestics, will be elevated and dignified, and even rendered more clear
and intelligible, by being largely interspersed and ornately commingled
with the "lactea ubertas" of Livy, and the "immortalis velocitas" of
Sallust.
curator
Physical
sciences
Among the branches of education which are necessary to be cultivated
by the person to perform the office of land steward, or the
and administrator" of landed property, an especial notice is due to
chemistry, botany, geology, and natural history, as being
all of them more or less intimately connected with the nature
and organization of the particular species of property with which the
management is charged. The studies and a fair knowledge of each branch
are very often required to be exercised in the specific application where
the use is attended with very beneficial effects. But if occasions never
happen to call forth the use of them, the general knowledge that is created
never fails to have a very beneficial effect on the other branches
that are exercised. Such studies enlarge the circle of know- able.
very value-
1026
ON LANDED PROPERTY.
!
ledge, ennoble the sentiments, refine and exalt the ideas, and insensibly
lead the mind to form elevated conceptions of every object and transaction
that is presented to its comprehension and negotiation. The mind is
whetted to vivacity of conception and action by the attrition of exciting
causes; by the number and power of the mental stimulants that have
been poured into the intellectual "sensorium," where by the action of
fusion and amalgamation, a current of refined matter is produced and
emitted, which improves every object that is touched, and burnishes with
a brighter polish every transaction which is performed. It promotes every
affair, and brightens every business.
A most powerful incentive to the acquisition of general learning is, that
Learning it gives to the possessor of it a commanding position in society;
gives power. power is most gratifying to the mind of man, and the mental is
so much more pleasurable than the material form of it, that it is exercised
without the infliction of pain, and in its development it is innocuous, and
meets with opportunities of conveying benefits to others, than which
latter employment no exercise can be more agreeable to human benevolence.
A corresponding station in society is essentially necessary for every person
who is engaged in a respectable and useful employment; and it can neither
be attained nor upheld without that enlargement and refinement of the
mind which flows from a general education, and which alone can entitle
Professional any individual to the proud distinction. The position in society
education ; must be graced by the man, and not the man by the position.
A general education points unerringly to the paths of eminence; it infuses
virtue into every sentiment, and imparts a grace to every action.
The fundamental part of a professional education, must be that of the art or
practice which is intended to form the occupation of the individual, and as the
business of a land steward will be chiefly confined to the superintendence
and direction of agricultural matters, it is most imperatively necessary that
the person receives a practical education of the first order, and thus get ac-
quainted with every detail and all the minutiae of the art. This education must
be the most improved, the most enlightened, and the most approved, which
the age and country can afford; and care is necessary that this practice be
not instilled at any age too young for the discrimination of ideas, and when
the pliant ductility of the mind is too apt to receive and set down as the
most incontrovertible truths the practices which only constitute the
trammels and antiquated prejudices of the craft. The mind is thus
stamped from without, instead of being moved from within, and
enlightened: becomes a passive recipient instead of an active exponent.
Originality is wholly destroyed. To prevent this very common result of
the general system of education, the study of practical agriculture is made
to form the last part of a general education; and the branches formerly
mentioned are previously acquired, in order that they may, by the power
of their influence, liberalize the sentiments, and tend to neutralize the usual
effects of an early infusion of prejudices and dogmas, which very often
completely defy all future eradication, and produce very baneful results.
On the other hand, equally as much care and caution must be used, that
liberal and
ON LANDED PROPERTY.
1027
the overheated fancies of scientific lore be not allowed to take the place of
"rational" practice, and overturn the best laid schemes of scientific
prudence and discretion. The one part of learning must balance & moderate;
and improve the other; practice must show the results of every rational,
and well conceived theory-and general learning will enlighten the con-
ceptions, and by deduction show the feasibility of every scheme. Thus
the two seemingly opposite elements of learning tend most materially to
benefit each other; the meeting of the materials in the mind produce the
the scintillations and coruscations that are so very necessary for the
arrangement and transaction of affairs, and which illuminate every path
and brighten every progress. If the mind be not stored to plenitude
with valuable learning, it will quickly be occupied with lumber, trash,
and trifles.
mathematic;
A general education never can be mentioned, without a very “special
recommendation being always given to the study of mathematics properly
so called. The word comprehends a wide range, and the branch
must be extensively studied; for no education can be reckoned
in any way complete without it; by it the mind is early accustomed to
strict discipline: it learns to distinguish between causes and effects, to
demand evidence for every fact, and a demonstration for every truth;
and it dispels that very ignoble and infectious art of "believing "
without evidence. Mathematics infuse a systematic order into every
arrangement, and arrive by a strict method to every conclusion. No con-
fusion is allowed; every thing is clearly placed, and produced from a
regular concatenation. And so it must be in business, the arrangement
must be methodical and clear, and the performance will be orderly, and
the dispatch of it will be regular. A correct and wholesome discipline of
the mind, is imparted by the studies of mathematics: it re- discipline of
strains the vagaries of fancy, and curbs the licentiousness of an
unbridled impetuosity at the same time, very pleasant truths are
unfolded, and a trustworthy confidence derived in the ultimate results of
any undertaking. These observations will apply to the practice of any
liberal profession.
the mind.
Two stages of life will acquire the practical knowledge of agriculture;
the first will be previous to the acquisition of the polite and liberal learn-
ing, and the other after that valuable acquisition has been made. Not less
than two years should be allowed to each term of the apprenticeship. The
first period will teach the mechanical drudgery of the business; and the
second will look at agriculture with liberal views, and enlightened optics.
Some years must then elapse in the acquisition of varied scientific know-
ledge, and in maturing and ruminating the practices that have been
witnessed. No person must commence the office of land steward under
the age of thirty years, or more; at which time the ideas will Age of busi-
be matured, the experience extended, and the habits confirmed. ness.
An early age only employs a raw inexperience and an immaturity of
intellect that can add dignity to no employment, and is productive of much
mischief.
1028
ON LANDED PROPERTY.
During the first term of the apprenticeship, the juvenile attention will
be employed in the operations of daily farming, in the participation of the
manual and bodily labours, of which an intimate knowledge is requisite.
The second period of learning, will direct and superintend the employ-
ments, attend markets, fairs, and shows, at which much general knowledge
may be acquired. A very material part consists in gathering a correct
knowledge of the breeding and use of the improved animals of the farm,
which now forms a very prominent part of the rural occupation.
the juvenile No branch of practical knowledge can be found more useful, or
more conducive to the interest of landed property, and to the
advancement of cultivation: no part of the employment is more rational
or more truly delightful.
Tyroship of
course.
Varied
learning.
After the mind has been opened and liberalized by the study of the
polite arts and of elegant literature, the attention must be most earnestly
directed to the acquisition of the varied branches of knowledge, which
will not only reflect a lustre on the profession, but will conduce most
powerfully to the beneficial and satisfactory progress of the professional
undertakings. The practical ideas must be concentrated and fixed; the
habits of business must be chosen and formed; and the whole character
must be graced with affability of manner and frankness of behaviour,
which engage the attention of all who may approach, and always leave a
very pleasing prepossession of remembrance. In the multiform
varieties of a general business, no quality of the mind is attended
with more beneficial impressions; it disarms hostility, and often wholly
changes the frowns of opposition and the appearances of conflict. It is a
quality of inestimable value; by it professional ignorance is often shrouded
in a veil, and mistakes are slurred over, and pass unnoticed. When
exerted along with other necessary acquisitions of office, it adds a brilliancy to
every conception; and in business it gives a relish to every employment,
and a passport to every intrusion. In promoting this very useful quality,
a general education will be found to exert very powerful effects; and also
in giving to the mind a stretch of liberality that is so necessary
Courtesy. to every person who is engaged in the busy world, and whose
attention is more particularly directed to the fruitful progress of a specific
description of property. Early inculcated prejudices and rooted anti-
pathies exert a most baneful influence on every human affair, and very
often completely baffle all attempts of removal. For this purpose, a com-
prehensive and varied education should be very early introduced, which,
by presenting to the mind the most varied assemblage of objects and
opinions, will accustom it to the very useful task of analyzing and choosing,
and will prevent the pernicious extremity of one idea or practice usurping
the undisputed possession of the mind. Most men, or rather all men,
have their crotchets, and the sooner and the more earnestly they set about
the removal of them, the better. The mind is not sufficiently
trained, nor the habits confirmed, for arranging and conducting
an extensive and responsible business, till nearly the age of forty
years, or considerably turned of thirty. Till that age, the constant
Crotchets
must be
avoided.
ON LANDED PROPERTY.
1029
employment must be to gather information, and provide a Age of forty
stock of knowledge for future use, by acting in subordinate suitable.
capacities.
years
A chief agent that has been thus qualified resides upon the estate of land,
and not very distant from it; and in addition to the duties of the agency,
may be charged with the direction of a practical farm, which the proprietor
may or should carry forward, in order to show to the tenantry an example
of the most enlightened practice. On this farm, all new theories, and
rational experiments are proved on a suitable scale, as will not interfere
with general results, and at the same time are sufficient to test the
feasibility of the schemes that may be propounded. Such an establishment
is very necessary in order to develope the resources of the pro- A farm
perty which is entrusted to the charge and possession of indi- necessary.
vidual capacity. The powerful spur of self-interest will also come into
action; for wherever labour is judiciously employed, the recompense is
certain from such quarters.
The duties of a chief agent on the days of audit in the receipt of rents,
will be found in the last chapter of this work, along with the forms of
notices, receipts, and cash books. The salary of such an agent
Salary fixed.
is generally at £300 or £400 yearly, according to the extent of
the charge. A fixed sum is better than a per centage on the intromissions:
it establishes a certainty which is useful in all cases. It also prevents
any attempts on the part of the agent to increase unduly the amount of
the rental, in order to raise his own emolument, than which insidious
mode of managing any business, nothing can be more detrimental to the
property, and disgraceful to the individual. All such temptations must
be very carefully removed.
All monies are paid by the chief agent, and no arrangements are made,
nor any undertaking carried forward without his privity and direction.
The fixation and direction of all undertakings must be centered in one
person, along with all subordinate departments; confusion will otherwise
ensue, attended with clashings and collisions, and attempts at independence,
which invariably produce damage to every concern that is interested. All
accounts must be reduced into one collection, where the accounts are easily
examined and viewed in connection. A properly adjusted establishment
of a chief agent and his subordinates, resembles the staff of the general
of an army, where the duties are most clearly chalked out for each depart-
ment, and the means allowed for accomplishing the orders that
Regulations.
are given. In the conferences with subordinate officers, the
agent must listen attentively to every suggestion that comes from the de-
partments of office, and form an opinion from the statements that are given
and joined with his own reflection on the separate points. He must
always appear to be superior to the need of advice, and at the same time
be open and willing to receive the hints and observations that may occur
in the course of discussion. A friendly urbanity of disposition goes very
far to promote that degree of willing cheerfulness, which so very power-
fully advances the onward progress and fruitful termination of every un-
1030
ON LANDED PROPERTY.
dertaking to which unity of purpose and cordiality of support are essen-
tially requisite.
Visits fre-
quent.
An agent must not be far distant from an estate of land, in order to
enable a frequent and personal inspection of every proceeding,
and of getting acquainted with the characters of individuals,
and of directing every subordinate department. A constant and very mi-
nute surveillance must be exercised by him in every particular affair; and
upon no account and in no affair must he rest satisfied with reports, nor
allow the interested motives of those persons who approach him to influence
his opinions or bias his judgment. To act upon hearsay, even on the
most trivial occasion, shows a very great weakness in the powers of per-
ception, and a disposition much too easy in the nature of compliances to
enable the manly part to be called forth, than which no qualification is
more required in the arduous situation of being placed between opposite
and very often conflicting elements. A very vigorous enquiry must be
made into the bearings of every affair, the truth must be discovered, and the
decision and the future proceedings must be thereon made and directed.
Nothing more effectually degrades a man placed in a responsible situation,
than opinions crudely formed with hasty decisions, and actions impru-
Steadiness dently executed, which are soon found to be wrong in tempe-
of purpose. rament, and hurtful in the consequences. Perhaps in few or no
offices of employment is there greater occasion for affability of manner,
courtesy of bearing, calmness of judgment, and decisive energy of action
when the resolution has been coolly formed. Hastiness and vacillation
are equally the proofs of imbecility, that is most truly disqualifying for
such an office.
It must be laid down, and most tenaciously and inflexibly upheld as a
fundamental maxim, that an estate agent must be an agriculturist of the
most improved grade. Land-owners have committed most prodigious
mistakes in employing lawyers, commercialists, or some similar persons,
often of a nondescript character, whose sole object is ever to levy a sum
of rental at any risk, and at the same time are utterly regardless of the
source whence the profit is derived. Professional ignorance prevents any
attention being paid to the furtherance of the art which supplies the
revenue, and other engagements distract the necessary attention, even were
it available and useful. The estate is seen only when the rents are due,
and not again till that period returns: a manor bailiff is seldom kept, and
no inspecting visitations are used. Under such treatment, all perishable
articles fall into a state of ruin, as buildings, fences, roads, and
the land itself; the rent is drawn so long as it can be got, and
when the collection is no longer possible, a considerable sum of money is
required to put the property into a vendible condition, which might have
been wholly prevented by judicious regulations, and a timely interference,
with a constant and vigilant surveillance. Very different must be the
results to any landed property from the labours of a specially educated
and duly constituted agent, whose time must be constantly occupied in the
business of his remunerated employment, keeping accounts within doors,
Ignorance
ruinous.
ON LANDED PROPERTY.
1031
where also will be devised the schemes of improvement, and the means of
accomplishing every undertaking. The personal inspection, very fre-
quently repeated, will include the farms, plantations, and roads, and also
the interior policies, except where the resident family take that depart-
ment under a special direction. Faults and mistakes must be put right
without delay, and the whole exercise is a most agreeable occu- Exercise
pation for a rational being, and very necessary for upholding
pleasant.
the value of the property. Even when a manor bailiff is kept, the visita-
tions of the chief agent, are no less necessary; reports are apt to produce
an improper bias, and misstatements are best removed by the evidence of
the senses.
In such inspections, a very patient and polite attention is re-
quired to all opinions and suggestions that may be given and stated, in pro
and con; hints are got from such sources, and information needs every
source of obtaining a proper knowledge. No person is degraded by listen-
ing to remarks from any quarter; something may be gained, and nothing
is lost, and common civility is exercised.
The due authority of the chief agent controls the inferior departments
on the estate, and there must be impressed the proper sense of that ar-
rangement. Much confusion will ensue from this subordination
not being properly understood and acted upon; co-operation Authority.
will be disarranged, and malevolence and lurking hostility will be engen-
dered. The chief agent must use his power "discreetly;" make his ar-
rangements "judiciously and practicably;" give his orders "civilly," but
"firmly and energetically;" convey the necessary censures "authoritatively,
but blandly;" commend "freely, but duly restrictive;" and in every case.
to judge coolly and dispassionately, and act decidedly and firmly. An
ample supply of prudent discretion and a very great command of temper,
are most essential requisites in such an employment, in order to meet the
very frequent rebuffs and mortifications, arising from the perpetual colli-
sion of jarring interests, which naturally converge to the agent's position,
This point very often forms the most arduous part of the official duty.
Department.
In such situations, nothing is more necessary and becoming than the
propriety of appearance and behaviour that belongs to the grade of society
in which any individual may be placed. The land agent is exposed to
the frequent contact of superiors and inferiors, and to both these grades,
the
proper deportment must be correctly exercised. To the for-
mer, a respect is due from the station in society, which expects
opinions and proofs to be rendered with professional firmness, and sugges-
tions offered with caution and prudence, as each special case may require.
In such cases, an over-eagerness and heatedness are much to be avoided,
which serve to produce irritation, and mar the face of proceedings. To-
wards inferiors, courtesy and affability are absolutely indispensable, in
order to secure the goodwill and affection of the operatives in every un-
dertaking, and who form the muscles and sinews of every active operation,
Harshness must in all cases be avoided, even though the amount of pro-
vocation may apppear to justify the exercise: conciliation must form and
cement the attachment; harshness will sever it.
-
1032
ON LANDED PROPERTY.
Correspon-
The last, but not the least important, part of the duty of a land steward,
is the correspondence, or communication with his employer, who is the
owner of the property. The position in society often removes
dence. the land-owner wholly beyond any notice of the concern, and
even his constant or temporary residence does not enable him to enter into
any considerable knowledge of the business: the drudgery forbids it. The
knowledge and judgment of the agent come into full play, as upon his
opinions and course of proceedings, the prosperity of the property, and
necessary welfare of the subordinate parts do in a great measure depend.
The most enlightened professional knowledge must be joined with a cool
and reflective judgment, and used with equal energy on trivial matters
as on large undertakings. A varied education has been largely recom-
mended in order to raise the ideas and elevate the conceptions above the
mole-eyed plodding in the mud of vulgar practices and of obsolete pre-
judices, and of the clay-born sympathies that keep within the gin-horse
track of daily routine. Judgment must systemize the conceptions, and
steadiness must direct the attainment of every business and objects that
may be contemplated.
Correctness.
The owner of a landed property being necessitated to rely on the esti-
mate and representations of the land-steward, and to give his sanction
almost wholly to his calculations, there occurs the most pressing necessity
that these estimates of opinion be composed on a very firm
basis, and after a most mature reflection. Hasty decisions and
crude calculations must be most carefully avoided, for the consequent mis-
carriages do much mischief, both directly and indirectly; they are exposed
to contempt, and tend to prevent any future attempts of a similar nature;
they also induce the proprietor to distrust the trustworthy confidence that
Trustworthi- ever should be reposed in an agent, and to think his own inter-
ference becomes the more necessary, and also to hear and con-
sider other opinions on the subjects that come under consideration. The
agent thus loses his proper "status" on account of these former misgivings,
and also the confidence that is necessary to the undertaking and executing
the beneficial improvements on the property. Envy and malevolence are
ever ready to exert their evil offices whenever the least opening occurs.
To prevent these gaps of offence, the most careful attention is required.
ness.
The general and professional education of the agent must enable him
to form ideas and concoct plans which will bear a severe investigation, and
stand the test of the most rigid scrutiny. The language of conveyance
must be clear, and easily understood, pithy and short: the answers will
consequently be the quicker obtained and the easier followed. The agent's
mind must be wholly occupied with his occupation, devising modes of
necessary improvements, arranging the execution, and obtaining the con-
sent and sanction of the proprietor, after there have been bestowed upon.
them the necessary explanations and elucidations. In this way, the uni-
versal benefit will be most usefully promoted.
The farm bailiff is a most useful person in the management and culti-
vation of landed property. It has been observed that there may be, or.
ON LANDED PROPERTY.
1033
Farm bailiffs.
should be, a farm conducted practically on most estates of land
by the proprietor, and of which the charge will devolve on the
agent. He delegates the resident power to a practical person for the pur-
pose of executing the orders he may receive, and conducts every practical
business from these orders, and his own special judgment. This person
must have been bred from boyhood in the constant exercise of agricul-
tural operations: at least to have acquired a most thorough knowledge of
the nature and extent of each. It is most essentially necessary that he is
a perfect master of every practical process in cultivation; for when a per-
son is thus acquainted with any performance from personal expe- His qualifi-
rience, he is much better qualified to describe it, and to give
directions on the subject, than if the recommendations were the mere re-
sults of observation, however acute and penetrating. In addition to these
primary qualifications, the farm bailiff must possess as much education
as enables him to keep a correct account of the daily labour on the farm,
and of the corns in the granary as it is thrashed and sold. The form of
the wages book is subjoined.
cations.
•
3 s
1034
WAGES BOOK.

| Number.
Names
of
Wages
Business.
per
Persons.
Employed.
Day.
WAGES BOOK.
An Account of the Names of Persons in the employment of
and Weekly Labour and Wages for Four Weeks, from the
day of
Monday.
Tuesday.
Wednesday.
Thursday.
Friday.
Saturday.
Amount
per
Week.
£ s. d.
Wednesday.
| Thursday.
| Friday.
Monday.
Tuesday.
Saturday.
Amount
per
Week.
£ 's. d.
~
Wednesday.
Thursday.
Monday.
Tuesday.
Friday.
Saturday.
, at
to the
Amount
per
Week.
£ s. d.
day of
and of their Daily
185
| Wednesday.
Thursday.
Monday.
| Tuesday.
Saturday.
Friday.
Amount
per
Week.
£ s. d.
Observations
showing how
each Person
is Employed.
ON LANDED PROPERTY.
1035
The account is rendered monthly: the amount of the money is given to
him, which he pays to the respective parties. The other accounts are
given in as the transactions take place, and entered in the general farm
account in which the weekly wages are entered in one sum,
of wages.
Duties.
as per bill"
In order to ensure sobriety and steadiness as much as possible, it is better
that a farm bailiff be a married person; for of all requisites in
such an office, steadiness may be termed the very first, both in
kind and degree; and in order to give encouragement to attention and
activity, the wages given must be liberal, and constitute a sufficient re-
ward for the tear and wear of the body and mind that are exerted in such
an office. The dwelling house must be suitable, with a garden attached,
and the keep of a cow is part of the salary, with a stye for pigs. The sa-
lary is usually £60 to £80 in money, the use of a saddle horse, and the
usual appendages.
The duty of the farm bailiff is to arrange and direct the whole pro-
cesses of the farm, after consultation and concurrence of the chief agent
who may have the chief direction. It is necessary that he is in the stables
in the summer mornings soon after five o'clock, from 1st of March to 1st
of October, when the harvest will be concluded. The necessary orders
are given to the ploughmen, and the feed of oats is given to the horses
from a locked chest, of which he keeps the key; and the same quantity
is put into nose bags, and hung in the stables to be given to the horses
during the interval of two hours for dinner. The bailiff sees all the teams
of horses leave the stables at a quarter before six o'clock, which
allows the work in the field to be commenced at six precisely.
Labours.
The time stops at eleven, begins again at one, p. m. stops at six, and so on;
after that hour the bailiff is again in the stables, and feeds the horses
with oats from the locked chest as in the morning. This finishes the
necessary attention to the horses' labour.
Inspections.
After every order is given in the mornings and seen to be acted upon,
the bailiff proceeds at seven o'clock to take the charge of the weeders of
the crops, or hoers of turnips, in lads and women, and by a very constant
attendance, he procures the duty of this branch of operators as
firmly, as steadily, as conciliatory lenity will allow. From this
employment, however, he must steal a march, once or twice in the day, to
inspect the other works that may be proceeding, as ploughing, digging of
ditches, road making, or any other business on the farm. His absence
must be short, as "trifling" day-labourers require much care.
A steady
sense of duty will not allow any harshness beyond the proper obtaining of
value for value. When due explanations are given, and no suitable return
is made, the total separation is much better than the adoption of any coer-
cion or vindictive proceedings. The bailiff sees the teams leave the
stables at a quarter before one, p.m., when he takes his post with the daily
labourers till the hour of six o'clock. In the evenings, after that hour,
the bailiff may arrange with the servants the work of the morrow,
always allowing the probable disarrangement by the weather, and other
1036
ON LANDED PROPERTY.
An under
bailiff
accidents. On large farms, in order that the bailiff may have greater
liberty of moving about, and inspecting the works of the farm, a steady
labourer is selected to attend the gang of women and lads ; and
during winter, this person feeds the thrashing machine, and per-
forms all the barn work. He leads the sowing of the grain crops, sows
the turnips, and in harvest, he becomes the chief builder of the ricks of
grain. This person is a most useful addition on farms of 300 acres, and
upwards. He frees the chief bailiff of the most troublesome part of the
farming drudgery, and usually gets one-fourth more wages than the
ploughman.
The hay and corn harvests will require the constant attendance of the
manager of every farm, and the turnip season is equally imperative in its
demands for his presence. He must not be confined to any spot, or parti-
cular department of notice, but must move constantly about, and see that
all operations are progressing, and are duly executed. During these times,
all foreign business is laid aside, and the home matters are the sole concern,
A very chief care of the farm bailiff consists in his keeping every tool
of the farm in the best acting order, the dead stock always in complete
readiness, and the living implements in high spirits, and full of
order. life and activity. The former is done by a vigilant attention,
and the latter by kind treatment and conciliation. A harsh bailiff
will lose his employer many acts of returning kindness: encouragement
leads mankind; but harshness and brutality produce obduracy and
retaliation.
Tools in
ON LANDED PROPERTY.
1037
FARM ACCOUNT BOOK. 1852.
INDEX.

A.
Folio.
B.
Barn
2
Cattle
Cash
•
Expenses for Labour
Farm Servants
Granary
C.
D.
9
4
E.
5
LO
F.
13
G.
3
Horses
H.
8
1038
FARM ACCOUNT BOOK,
1852.
DR.
Rick Yard.
(1)

Wheat. Barley.
Oats.
Beans.
Peas.
Date.
Folio.
Ricks.
Ricks.
Ricks.
Ricks.
Ricks.
Nov.
To Crop, 1852 .
7
10
16
4
3
1852.
Date Folio.
This account shows the ricks that are thrashed,
DR. Barn.
(2)
Wheat. Barley. Oats.
Beans.
Peas.
Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus.
Nov. 16 1
To Rick Yard .
15 6
1852.
Date.
Folio.
Nov. 20 2
To Barn
This account shows the progress o
DR.
Granary.
(3)
Wheat. Barley. Oats. Beans.
Peas.
£ s
d.
Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus.
15 6
This account will, at any time, sho
FARM ACCOUNT BOOK,
1039
1852.
Date.
Folio.
Contra. CR.
(1)

Wheat. Barley.
Oats.
Beans.
Peas.
Ricks.
Ricks. Ricks.
Ricks.
Ricks.
Nov. 16 2
By Barn .
1
and those that remain of each grain crop.
1852.
Date.
Folio.
Contra. CR.
(2)

Wheat. Barley. Oats.
Beans.
Peas.
Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus.
Nov. 20
3
By Granary.
15 6
thrashing and storing the crop of grain.
1852.
Contra.
CR.
(3)

Wheat. Barley. Oats. Beans. Peas.
Date. Folio.
£ s. d.
Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus.
Nov. 304 & 14
By Sale
30 0 0 10 0
the quantity of grain on hand.
1040
FARM ACCOUNT BOOK.
1852.
Date.
Folio.
DR.
Cash.
(4)

£
S.
d.
Nov. 30 3 & 14
To Cash for 10 qrs. of Wheat, at 60s. .
30
0
0
8
وو
""
To Cash for One Foal.
15
0
0
1852.
Date.
The balance of this general cash account will
DR.
Expenses for Labour.
Folio.
(5)

£
S.
d.
This account shows the expenses of labour only, and saves
1852.
DR.
Petty Expenses.
Date.
Folio.
(6)

વા
£
8.
d.
This account shows the smaller incidental expenses, and the amount

FARM ACCOUNT BOOK.
1041
1852.
Date.
Folio.
Contra. CR.
(4)
48
£
S.
d.
Dec. 1.
5
10
By Cash paid Monthly Wages Bill .
23
14
3
8
""
""
By Cash paid for One Horse .
25
0
0
show the final balance of all transactions.
1852.
Date.
Folio.
Contra.
CR.
(5)
£
S.
d.
Dec. 1.
4
By Monthly Bill of Labour
23
14
3
time in examining the general cash account for that
1852.
Date.
Folio.
purpose.
Contra.
CR.
Dec. 8.
4
By Expenses at Market
is carried to the general cash account quarterly or half yearly.
£
જે
S.
(6)
હું
d.
0
7 6

1042
FARM ACCOUNT BOOK.
1852.
Date.
Folio.
1852.
Date.
Folio.
DR.
Manure Account.
£
48
S.
(7)
d.
This account shows the money
DR.
Horses.
(8)
48
£
S.
d.
Horses. Mares.
Foals.
:
To Stock on Farm
300
0
0
8
2
3
4
To Purchase
25
0
0
1
0
0
1852.
Date. Folio.
:
0:
:
DR.
Cattle.
£
S.
d.
This account shows the dealings
(9)
Bulls. Cows. Oxen. Heifers.
To Stock on Farm
500
0
0
1
14
18
15
To Purchase
16
0
0
0
2
0
This account shows the numbers and value
FARM ACCOUNT BOOK.
1043
1852.
Date.
Folio.
Dec. 10.
Contra. OR.
(7)

£
8.
d.
By Cash for 10 loads of Dung, at 4s.
2
0
0
spent for any manures.
1852.
Date. Folio.
:
Contra.
CR.
(8)

£
S.
d.
Horses. Mares.
Foals.
4
By Sale
15
0
0
0
0
1
By Death.
20
0
0
1
0
0
among horses, the number and values.
1852.
Date.
Folio.
:.
:
:
Contra. CR.
(6)

વા
£
8.
d.
Bulls.
Cows.
Oxen. Heifers.
By Sale
24
0
0
0
0
0
3
By Death
14
0
0
1
0
0
of the transactions among cattle.
1044
FARM ACCOUNT BOOK.
1852.
Date. Folio.
:
DR.
Sheep.
£
રે
(10)

8.
d.
Rams.
Ewes. 1 year's 2 years'
To Stock on Farm
0 0
0
2
300
150
120
To Purchase
60
0
0
60
0
This account shows every
1852.
Date.
Folio.
DR.
Swine.
(11)

મે
£
8.
d.
Boars.
Sows.
Pigs.
Hogs.
To Stock on Farm
60
0
อ
1
3
16
10
...
1852.
Date.
Folio.
General Loss on Stock.
(12)

Horses. Cattle. Sheep. Swine.
£
S.
d.
By Death.
1
1
1
2
38
00
This acccount collects all losses on dead and live stock, and shows the amount.
FARM ACCOUNT BOOK.
1045
1852.
Date.
Folio.
:
:
:
:.
(10) Contra.
CR.

£
8.
d.
Rams.
Ewes. 1 year's. 2 years'.
By Sale
60
0
0
0
0
0
40
By Death
1
10
0
0
1
0
0
lealing among sheep.
1852.
Date.
Folio.
....
1852.
Date.
:
:
Contra. CR.
(11)

£
4+
S.
d.
Boars.
Sows.
Pigs.
Hogs.
By Sale
3
0
0
0
0
0
2
By Death
0
10
0
0
1
0
Goods from Farm as below.
House.
Stables.
Folio.
Beef.
Mutton.
l'ork.
Hams.
Cheese.
Poultry.
Eggs.
Milk.
:
st.
40
Butter.
Price.
£ s. d.
Oats.
Hay.
Straw.
Price.
(12)
Garden.

£ s. d.
£ s. d.
qrs. tns.
4s. 800 100
20s. 10 00
Load
2
80s.|| 8| O | 0 ||10 Dung||2|0|0
This account shows the goods sent from the farm for the use of a resident family.

1046
FARM ACCOUNT BOOK.
1852.
Date.
Folio.
1852.
Date.
Folio.
DR.
A. B., Farm Servant.
48
To Payment.
2
•
S. d.
Wheat. Barley.
(13)
Oats.
qrs. bus. qrs. bus. qrs. bus.
00041016
This account is fitted for payments in kind; when the wages
DR. J. D., Corn Factor.
(14)
બ
£
8.
d.
Nov. 30
3
To 10 qrs. of Wheat at 60s.
30
0
0
This account shows all debts that may exist in business when no
This form of Farm Book-keeping may be enlarged or contracted to
suit any circumstances of use, and columns may be added as required.
Double entry is adopted, as it affords the most clear and effectual check
FARM ACCOUNT BOOK.
1047
1852.
Date.
Folio.
:
Account Current. CR.
By 1 yr's conditions
£
S. d.
Wheat.
Barley.
(13)
Oats.

bus.
qrs.
qrs. bus.
qrs. bus.
10000 34 40 10 6
are wholly in money, they appear in the monthly bill.
1852.
Date.
Folio.
His Account Current.
Nov. 30.
4
By Cash.
•
•
credit is given for the goods sold. Each dealer requires a column.
(14)

4+
£
8.
d.
ས
30
0
0
and exposition of business. A simple entry merely states a bare fact;
the double entry certifies the negociation, and vouches the transaction of
the business.
1048
ON LANDED PROPERTY.
F
CHAPTER XIII.
MANOR BAILIFF, WOODREEVE, GARDENER, AND GAME-
KEEPER THEIR POSITION AND DUTIES.
Manor bailiff.
WHERE landed property is extensive, and lies in a wide circuit, the head
agent of superintendence is removed beyond the drudgery of the inferior
work, and retires to the higher duties. A constant residence is not made
on the estate, but only the necessary visits, or an occasional abode for a
period of the year. A subordinate authority and management is delegated
to the manor bailiff, who lives in the centre of the estate, and
performs all the lower duties, and attends the minor concerns.
Such a person is essentially required wherever there is attempted to show
a well-managed estate of land, as the detailed works of any undertaking
constitute the perfection which is formed by the seeming trifles of attach-
ment. All large establishments demand a staff of action that is efficiently
constituted and systematically organized; and a methodical exactness must
pervade every branch of the departments, even to the minutia that nearly
escape observation. The profitable development of every large under-
taking mainly depends on the constitution of the managing authority, and
the mode and manner by which the action can be exerted, or is allowed to
show an efficiency. The arrangement must be made with judgment, and
directed with much care.
The manor bailiff resides in some convenient central part of
Residence. the estate, where a suitable house is provided, with the necessary
attachments, and attended with a quantity of land sufficient to maintain a
saddle horse and a couple of cows. The money salary is usually £80
yearly. He must be a steady trustworthy person, respectable, and well
educated, thoroughly acquainted with the most enlightened agriculture in
every branch and detailed appurtenance, and equal to any keeping of ac-
counts. His time will be constantly occupied with the business of the
estate, in arranging the performances with the chief agent, and
Occupations.
superintending the execution. The wants of the farmers will
first be made known to him, when he will hear the statements that are
made, examine the grounds of validity, and judge the feasible sufficiency
of being laid before the head agent for his approval or rejection. His own
opinion must accompany every proposition; and it is most highly necessary
that he is raised above partiality of representation, and the listening to re-
ward. The vigilance of the chief agent must be ever awake on this point.
An over-intimacy with any person or persons is to be discouraged, as it
begets jealousy and destroys confidence. The preference is never to be
shown to any individuals in priority of being served, except upon some
ON LANDED PROPERTY.
1049
Qualifica-
tions.
Proposals.
very sufficient grounds, such as superior management, the greatest number
of wants, or the want of repairs for the longest time. As all the buildings
and repairs of houses will be entrusted to the manor bailiff, his knowledge.
must comprehend these performances, and be able to point im-
perfections, and check abuses. Measurement of works of all
kinds must be familiar to him, and also of lands on the small scale of fields
and pieces of land. If the farmers or workmen have complaints of wrong
in the bailiff, the chief agent hears and decides the case; and if he prefers
complaint against any person of the estate, the case is settled by the same
arbitrament. The agent must exercise a keen enquiry and a sound dis-
cretion in deciding what may be purposely concealed from his knowledge.
For the purpose of new buildings and repairs, the manor
bailiff proposes plans and receives estimates from workmen, un-
less the estate be large enough to keep in employment the necessary oper-
ators of every department. These plans and estimates being sanctioned
and signed by the chief agent, the works are commenced, carried on, and
finished under the bailiff's superintendence, who draws money from the
superior, with which to pay the subsisting money of the employed labour,
and the balance that may be owing when the work is finished, measured,
calculated, approved, and balanced with the money received. The value
of the timber used is paid to the woodreeve on the estate, or bought from
abroad, if none is grown that is suitable. The operations and items of de-
tail will much employ the time of one person on an estate of land of the
medium extent.
Visits to
farms.
A very particular part of the employment of a manor bailiff
consists in his visiting twice in the year every field of land on
each single farm on the estate, and noting the management which is
practised by the farmer. One visit is made in March or April, when the
spring operations are being done, and the other in October, when the
harvests are all finished, and the sowing of wheats is progressing. By
riding round each field the condition of the gates and fences is observed,
the neglects are noticed, and the improvements commended. An entry-
book, carried in the pocket, contains these notices and memorandums,
which require a convenient pen-case and ink-holder to be provided for the
purpose, and to form a constant company. The rotations of cropping on
each field of land must be very carefully noticed and entered in a book
that is specially provided and adapted for the use of the bailiff:
the size is a pocket folio of convenient bulk, containing on the
left-hand leaf a plan of the farm on a reduced scale, with the fields num-
bered in a regular order and coloured, to distinguish grass from arable
grounds, and woods from meadows. The right-hand leaf which is opposite
the former, contains the number of years in single columns, which form
the lease of the farm, in which is written the crop which the land bears in
that year, as marked by the figure in the regulated order of seasons. This
book is contrived and used for the express purpose of the chief agent and
owner of the estate being able to know at any time the system of cropping,
which is practised without the necessity of a personal inspection. A copy
Uses of a
field-book.
3 T
1050
ON LANDED PROPERTY.
of the book being sent the owner of the estate to any distance, the know-
ledge is transmitted of the arable management on which the prosperity of
the estate is chiefly dependent. The use of the book is best made in the
autumn visit of the manor bailiff, as at that time the land will most clearly
show the effects of the system of cropping, if any injurious rota-
Twice-a-year
tion has been followed and allowed, or a good one adopted and
persevered. The introduction of any improper management is checked at
once, and the manor bailiff must be able to judge of the admission or re-
jection of the proposed innovation, report to the chief agent, receive the
matured opinion, and return the verdict to the farmer; not that the farmer
is to be confined within the narrow limits that may be chalked out by any
superintendents, or checked by their ideas, but there is a most imperative
necessity that the intrinsic worth and quality of the property receive no
damage, and that the policy be not retrogressive, if it is not advancing.
This is the duty of all persons who are in charge of property, and land has
the very peculiar attachment of being easily damaged, but not recovered
Correctly
kept.
without much time and expense. The manor bailiff comes into
the room of the chief agent in observing and reporting the
changes of use, and the benefits or damage of progress.
The visits of the manor bailiff will discover if the open drains, or large
cuts for the conveyance of water, are duly opened to answer the purpose,
Is a general and if the receiving outlets of frequent drained lands are in the
inspector. proper discharge of the purpose. As was before observed in
this chapter, the fences will form an object of interest, as ruined fences
seldom admit being recovered, and new ones are long in being reared into
use. In fact, every proceeding on the surface of the ground comes within
the notice of the manor bailiff, who is a general inspector of every business,
and performs a special part that is marked for his personal execution.
Though the plantations are under the management of a special director,
who is entrusted with that department, yet an observation must be taken
of the condition of that branch of property, and of the mode in which it is
managed and protected. The manor bailiff can observe and report of these
and similar concerns, without exciting any malevolence or hostility, always
observing a prudent discretion, and a courteous demeanour. As these de-
partments are all under the jurisdiction of the chief agent, the delegation
of the manor bailiff invests him with the surveillance of the whole parts of
the landed concern.
All roads
under his
charge.
The few cases of putting under the management of the manor
bailiff the making and repair of all the roads on the estate where
he is located, have proved the beneficial effects of the arrange-
ment in the improved condition of the roads, and the lessened charge of
expenditure. The necessities of the paths of transit create a charge on the
rent of the farmers, which is fixed on the pound of payment by the chief agent,
who collects the money at the half-yearly audit, and places it in a fund to
be used as the manor bailiff may require. He will appoint the number of
workmen, as the work to be done will demand, and station them in dwel-
And are well lings upon or near to the localities on which the work is re-
done.
ON LANDED PROPERTY.
1051
quired. The digging of materials may constitute an extra item, and
engage a contract agreement, or by special bargain; but the upholding
of roads will employ a quantity of fixed labour throughout the year, which
will mainly apportion the charge on the pound of rent to the farmer. The
inspection of roads and farms is done at the same time, and becomes a
business at once valuable and agreeable. This employment will form a
distinct account in the hands of the manor bailiff, in which he will be debtor
for all monies received, and creditor for all amounts paid. The making
of new roads will be distinct from repairs, and must have a separate page,
and a distinct consideration.
The manor bailiff conveys to the farmers all notices of infor- Gives notice
mation that are necessary, and that by special delivery of hand. of rent days,
Even where fixed rent days prevail, the chief agent prepares and signs
with his own hand a letter of notice to each farmer some two or three
days previous, and sends the whole bundle to be singly delivered to each
tenant by the manor bailiff. The form of these circulars will be given
elsewhere. This delivery of notice is a part of the official routine of
business, which is never to be neglected, even though the omission may
seem to be harmless: it keeps attention alive, awakens interest, and by
exhibiting care on one side of any concern, generally obtains a similar re-
turn from the opposite quarters. On the rent days, the manor bailiff sits
closely by the chief agent, who receives the money, counts it after him,
places the parcels in proper order, and keeps a separate account of the
amount. If time allows, any observations on either side betwixt the agents
and the farmer may be mentioned and settled, but affairs of any magnitude
are best discussed at a meeting of special appointment. At all and attends
these occasions the manor bailiff is an essential presence, as he punctually.
has seen the grounds of the request, and has heard all the urgencies and
remonstrances that can be advanced.
The duties of the manor bailiff are separated from practical farming, yet
the person must be capable of surveying that department; and if he does
not intermeddle, his observations may still be useful. The roads and fences
of any farm that is used by the landlord are equally under his care, as if
let to a tenant, and he must exercise the same diligence to promote the
advantage and sustain the utility. The young fences that are being reared
on the estate till grown for the use of the farmer, are under the manage-
ment of the manor bailiff, who has workmen located conveniently for the
purpose, or the day-labourers on the roads may act in both capacities, and
be separately accounted. Both purposes may be served by one arrange-
ment, as one surveillance comprehends the objects to be done.
When the draining of lands is being done on the estate, the
whole charge of the execution may devolve on the manor bailiff, draining his
unless the extent of the property and the nature of it is able to
afford, and requires a special appointment for the purpose. A gang of
workmen may be kept for the separated purpose of draining, or the other
workmen under the bailiff's jurisdiction may be used for draining when
the performances can be so arranged so as not to get into contact and
Fences and
charge.
1052
ON LANDED PROPERTY.
create confusion. The bailiff must be competent on the subject of draining,
and actively acquire and promote intelligence on that very important point
of rural management. The leader of the workmen must be trustworthy in
the absence of the bailiff; the course of the drains will be directed by their
opinion, and the cavities filled as they direct. Where a manufactory of
tiles is placed on the estate, the chief management may rest
with the manor bailiff, with competent foremen to direct every
separate branch of the business. These appointments will render the per-
son a very responsible individual, and who has the power of very much
promoting both practical utility and social contentment. These two objects
constitute the chief aim of every human employment.
And tile
making.
Is the prac-
The office of manor bailiff now described, lodges on the properties of
land that are extensive, to employ and maintain the highest orders of
agency, and the value can afford the deduction of the cost. All estates
should have a practical person constantly resident, and large extents pos-
sess that requisite in the manor bailiff, as the chief agent may be
tical agent. distant, and have similar employments, of which he incurs the
responsibility without performing the drudgery. On smaller extents of
landed property, the practical resident may perform every duty, assisted
by a servant to carry messages and deliver written notices. The manor
bailiff must be possessed with a sound judgment, enlightened views, and a
conduct that rises above every symptom of partiality or under-cloak deal-
ing. Every thing must be fairly and faithfully represented, and no reser-
vation made of any points that require an open disclosure. He is better
when free of any social connections with the population of the estate, and
removed beyond mixing in any dealings with the farmers. An independent
Must be in- position must be maintained which can equal the appearance of
dependent. superiors, and escape the unbecoming familiarity of inferior
grades. Very much of the smooth and agreeable management of an estate
of land will depend on the manor bailiff, who is placed on large extents
for the express purpose of maintaining the connexion between the chief
agent and the departments of operation. A very steady activity is re-
quired, which assigns each work the necessary portion of time, and upholds
the performance of every duty in the proper period of appointment. Steadi-
ness is almost the first of virtues in such employments, no display of un-
common energies on some particular occasions, and no momentary fits of
unusual performances, though probably very valuable in themselves, can
compensate for the derelictions of laxity and carelessness which succeed
the periods of exertion. A vigilant observation and a steady execution
constitute the foremost qualities of recommendation in any charge of
operative performances.
Woodreeve.
Woodreeve is a person who acts as steward of any woodlands,
and the defender and manager. The term is nearly obsolete,
and comes from a word of the Saxon language, which conveys the above
meaning. In former times, the woods were mostly planted by the seeds of
nature, and the woodreeve merely ranged the grounds in order to debar
any intrusion, and to preserve the wild beasts for the purposes of pleasure
ON LANDED PROPERTY.
1053
and of the chace. Improvements were totally unheeded, and the reeve
merely took the charge of protecting and defending the spontaneous pro-
ductions of nature. A more settled order of society introduced other ideas
of wooded property, and the system gained ground of making wholly new
plantations of trees, and of much improving the old grounds that were
occupied as forests. The reeve now became a regularly employed attach-
ment of the landed property, and his duties were marked and
defined as a subordinate in office to the chief agency. The
feudal superiority was sunk into a useful appendage, and the haughty air
of independence was lowered into the economical arrangement of a gra-
duated subordination.
His office.
duties.
fences.
On large estates, and on those which do not employ a manor bailiff, the
woodreeve is placed in charge of the whole plantations on the property
and of the nurseries where such things exist. The dwelling must adjoin
the largest portion of the woods, or be central as possible to the divisions
of wooded lands, and have the accommodation of the grounds to keep a
saddle horse and two cows, with the necessary small buildings. The money
salary is £80 yearly. He will direct the felling and selling of Position and
timber in the proper seasons, receive all monies, and account for
it to the chief agent. The planting of new grounds is a chief employ-
ment during the fresh months of winter; and the fencing of the grounds,
and the protection of the young trees, constitute a part of professional duty
that is not exceeded in value by any other department in the management
of landed property. Whole growths of trees may be destroyed beyond
recovery by the trespass of cattle during one single day, and no remedy
can be found except by planting afresh the ground with trees in the quan-
tity destroyed. The whole plantation fences over the estate In woods and
belong to the province of the woodreeve; for, as observed in the
article “Lease,” the farmer has only to protect his fields, and the landlord
who makes a plantation of young trees must protect the property he has
enclosed for his own purposes. These fences require a most vigilant at-
tention, and a constant outlook for the commencement of dilapidations,
which may lead to gaps and entries of intrusion. A supply of ready ma-
terials in stakes and bars is a very necessary preparation, and so located
as to be easily applied when needed for the neighbouring woods. The
judgment of the woodreeve will be exercised in making these preparations,
than which there can be no better fitness for office. The felling of oak
trees and of peeling the bark will, on some estates, form a busy time with
all woodmen, and is generally very profitably employed. The sale of these
articles is managed by the woodreeve, and the receipts duly accounted.
The winter sales of other timbers are similarly done, and rendered in the
amount. The accounts kept by the woodreeve are only a debtor and cre-
ditor pages of receipts and payments, and rendered periodically to the chief
agent, and placed by him in the proper department.
It has been adopted to place under the charge of the wood-
reeve all the road-side fences on the estate, in order that they
may add to the beauty of the scenery, from being better kept
Roadside
fences his
care;
1054
ON LANDED PROPERTY.
than the cares of the farm might contemplate. The arrangement is good,
only it will add some little item to the expense of the department of woods,
but which will be inconsiderable in comparison with the improvements
that
may be effected. The gates of these roadside fences will be under the
same care as the hedges, and both objects being kept in neat and efficient
order will form an object of much pleasure and utility. It relieves the
farmer of some part of the many burdens of his situation, and forms a step
towards the suggestion in the article "Lease," that all the fences on an
estate be managed by the care of the land-owner. The roadside fences
have exhibited a very marked improvement from being under the charge
of the woodreeve, in the few cases where the arrangement has been adopted,
and it is reasonable to expect a similar condition of all other
fences that are placed under the same authority. Whenever
permanent objects are discussed, the land-owner's interest is ever
foremost, and must take the brunt of the required expenditure in upholding
the condition. A farmer patches a permanent article to make it serve his
temporary purpose; the landlord erects and maintains the objects to serve
the present time, and to extend the utility to future usages.
and probably
all other
fences.
A nursery of some extent is very usefully kept on most estates of land
that have a moderate extent, and though trees sufficient to supply exten-
sive wants may not be raised, some number will be ready to meet moderate
demands, and young thorns may be raised in any quantity to supply the
wants of the estate. The nursery is the peculiar province of the wood-
reeve, and is best managed by labourers specially designed for the purpose.
His day
workers,
The arrangements of the estate will allow the woodreeve a number of
workmen which experience may find to be adequate to accomplish the quan-
tity of work that has to be performed. The number will be altogether
dependent on the extent and condition of the plantations; if the positions
be distant and enclosures small, and need much planting, and if the timbers
be old, and much felling is to be done. In many cases, much
work is done by contract, and the number of day labourers is
reduced; but some operations do not admit being contracted, and are best
done by daily oversight. The felling and topping of timber trees may
be contracted, as the work is visible, and does not admit being imperfectly
performed, and then concealed from view; and the raising of new fences
may also be contracted, and let to the constantly employed labourers under
the woodreeve, and these persons will be alternately paid by the day, or
by the job, as the nature of the different works may require or allow.
The gang of labourers must always be headed by a trustworthy indivi-
dual, who receives the commands of the woodreeve, and who is mainly
responsible for the proper execution of every job of performance, whether
done by contract or day labour. Before contract work is exten-
sively embraced, a confidence must be established between the
parties, and a belief that neither one is overreaching the other, but that
the establishment is made and carried on for mutual benefit. These under-
standings contribute very powerfully to the furtherance and prosperous
result of any undertaking, and society is soldered and cemented by the
and job men.
ON LANDED PROPERTY.
1055
kind treatment and adequate remuneration which are practised by the
employers to the employed, which has ever formed, and yet constitutes
the heavy burden which remains to be discharged. The labourers must
be all conveniently lodged in cottages over the estate, and not assembled
in one place, but scattered singly, or in two dwellings together, and so
placed as to exercise a surveillance over the woods, detect trespass, inspect
the fences in the daily walks, and report promptly to the woodreeve, who
will as readily issue the necessary directions to have the remedies supplied.
The living of labourers in villages is very objectionable, idle single cot-
congregations are encouraged, and gossiping assemblages spend tages useful.
time and divert the attention. The dwellings must be placed so as to
communicate readily, and afford an inspection of some utility whenever
the labourer leaves his home, whether he traverses a bye-way, or walks
along the public road: the eye cannot be opened, without looking on
some object of interest. A woodreeve with four or six men should man-
age the woods of a pretty extensive estate; but the number is wholly
dependent on the quantity of wooded lands and the age of the timbers,
and the extra work that may be attached to the department of the wood-
reeve. In the event of the land-owner assuming the management of the
fences on the sides of the roads, as has been suggested, and probably of
the whole fences of the estate, the charge of the woodreeve will His foremen.
be most prodigiously increased, and a delegation of authority
will accrue to some trustworthy foremen, who will act under him, and un-
dertake the charge and management of an assigned portion of work. The
localities must be divided with judgment, and appointed with discretion.
As before observed, all the dwellings must be planted with the view and
for the express purpose of enabling a surveillance of some kind or degree
being done by every operator in whatever capacity he may act, and
under whatever charge his labour is exerted. Very much toil and trouble
may be saved to the chief agents by arranging every subordinate as a
part of the employment, and not as a driven slave, who toils for a grudged
pittance, but as a willing actor, who is stimulated by motive, and impelled
by gratitude. This is the only way of rendering human nature useful,
and willing to apply its energies, by showing an interest in being em-
ployed, and a reward for exertion. Discontent should be wholly removed,
and contentment is not at all beyond the reach of attainment.
In the notice of woods as a part of landed property, it was observed
that the expense of that department rested wholly with the nature of the
estate, as it may be stocked with old timbers, or half-grown plantations,
or is in an incipient condition, and require much original expen- Woods,
diture. In the two latter cases, no revenue will be derived young or old.
from the wooded grounds, and the whole cost of the woodreeve's depart-
ment will fall upon the estate as a primary outlay. A stock of full-grown
timbers on any estate is an item of very considerable value, and enhances
the price of the property more than the presence of it might suppose.
Where a moderate quantity of timbers is ready for sale, such a portion
should be yearly vended, as will cover the expense of the Sale of tim-
ber.
1056
ON LANDED PROPERTY.
Gardeners.
woodreeving, in the current-going item of outlay for repairs and ne-
cessary upholding; but the raising of new fences, and the making of new
plantations, and all original work, must form a part of the general ex-
penditure, unless a special fall of timber can be made to meet the outlay
of money. If the yearly sale does not cover the whole cost of the wood-
men, the greater part, or some portion being paid, will proportionally
relieve the general burdens of the estate. Whenever a bare possibility
exists, some relief must be given, but not to detract from future values by
a premature use of the articles. This blunder may and has been done,
and requires to be guarded against. Where no timbers are found for sale,
the establishment of woodreeve will be reduced correspondingly, unless
large doings are contemplated, and ample extraneous funds are at command.
Gardener's office is wholly confined to the inside walled grounds, and
the pleasure walks, roads, and shrubberies, that surround the gardens, and
manorial residence. The department is most usually excluded
from the inspection of the land agent, and wholly directed by
the family of the estate. Nevertheless, a notice may be made of the ar-
rangement which may seem just and equitable of that item in reference
to a landed property. The expense of luxuries is seldom calculated and
never regarded, consequently a much larger cost is attached to that depart-
ment than appears in any part of the property. A garden of four acres
is a provision for an estate of a very respectable extent, and allowing one
man to an acre of ground, the head gardener will require four men em-
Duties and ployed within the walls; and if the outer appendages are large,
expense. as roads, walks, lawns, and shrubberies, two or three more
hands will be required to keep all things in the state of trim neatness,
which the practice of gardening understands. The average of six men
with a head gardener, will require the sum of £300 yearly of maintenance
only, exclusive of wants of seeds and flowers, which are uncertain and
contingent. The employment of land in gardening, pays no rent in return
for outlay, and is only to be placed to the account of unpaid luxury, that
is both necessary and useful.
Gamekeeper is an appendage of landed property, which is reckoned
to be equally required with the other charges of protection. There is no
doubt that the preservation of game animals, and a tolerably abundant
supply of the different articles of that kind, forms, and even may consti-
tute, a very great inducement to the possession of land, and
Gamekeeper. were the arrangement not carried to a provoking extreme, no
challenge would be given to the right of possession in the passing flights of
rest on the grounds where the animals alight. Both pleasure and profit
can easily be derived from that source of occupation, provided a relaxa-
tion and forbearance were extended to conciliate and not exasperate the
feelings of a jealous inferiority. The department of gamekeeping is most
generally managed by the landlord's own special arrangements, but like
gardening, it may be noticed, and the relation stated with the other estab-
lishments on landed property.
One head gamekeeper will require about £100 a year, for his mainten-
ON LANDED PROPERTY.
1057
ance, a pony, cow, house, and garden. Two assistants will be needed in
£100 more, which will make £200 to be the yearly cost of maintaining
the protection of game. The erection of extra establishments, and food
for the animals that is given in the plantations, will form another calcu-
lation: the above is given as a medium thing, and to suit mo- Arrangement
derate views on that point. The estimate now given for that and expense.
purpose, and likewise for the establishment of gardening, will no doubt
fall very short of the general costs that are incurred on these points; but
as they are matters of fancy rather than use, and promoted by whim
rather than utility, a moderate approximation is stated, without regard of
special arrangements.
Agent's
judgment,
The establishments of gardening and gamekeeping do not always, or
rather very seldom, fall under the direction of the chief agent on an
estate of landed property; but as the expenses are part of his disburse-
ments, the notice is not to be omitted of the uses to which the money is
applied. It may sometimes be his requested duty to give his opinion of
the amount which should be incurred on each particular point
of outlay, to make the arrangements, and to settle the estab-
lishments; and then his judgment will be called into action, in disposing
the parts to suit the particular purposes, and in allotting the distribution
of the general charge on the property as the different values may require.
It is true that the two departments now mentioned, are almost a domestic
concern, and need not the inclusion in the estate concern, but as the
landed value supports every department, the very household arrangements
must be made conformably and partake the same regulations with the
other branches of the landed economy. The land and woods must have
the first care, as they form the source of revenue which upholds all con-
cerns: the other branches must be contented with such appor-
tionments as the respective values and necessities may seem
to require, and are able to justify. The chief agent must pre-
pare an advice on all these points, which if used, may lead to pleasurable
results; and if not adopted, it may not be less valuable, to be honored
with a rejection.
in making
arrange-
ments.
Whatever arrangements may be made in the case of the gardener and
gamekeeper on any landed property, the chief agent must have the whole
direction of the manor bailiff and woodreeve, as these offices do not form
an independent separation, but are merely delegations of the business of
the chief agent, and of which he retains the responsible execution. Hence
a very regular subordination must be established and maintained by an
understood dependence upon him, except in cases of last resort, when an
appeal may be necessary to the owner of the property. These
deputies are appointed by the approving knowledge by the
landlord for their qualifications, and are moved by his convenience. No
despotism must be exercised by the agent, but his authority must be
supported in all reasonable jurisdictions, which are equitably dispensed.
His just
authority.
1058
ON LANDED PROPERTY.
CHAPTER XIV.
FIXED DAYS OF AUDIT-HALF-YEARLY PAYMENTS
OF RENTS-FORM OF NOTICES, RECEIPTS, AND OF
CASH BOOKS, GENERAL MAP OF ESTATES, AND
OF EACH SEPARATE FARM-CONCLUDING OBSER-
VATIONS.
Days of
FIXED days of audit are best adapted to the systematic management of
landed property, where nothing must be left to uncertainty that can be
fixed, but all proceedings go on in the most undisturbed order.
Audit The times of receiving rents are of considerable import in the
management of a landed estate, and the fixed periods are not less desirable.
The days of audit are most generally arbitrary, and conveyed to the
notice of the tenantry, in a precept from the receiving agent on the
property. No doubt the known period of the year lets the farmer under-
stand that the time of payment is approaching, and warns him to make a
timeous preparation for the coming damage. Still he may trust to some
little postponement of the day of audit, and neglect his diligence, and he
may plead an excuse of not knowing the exact time for the neglect of
fixed and
observed.
readiness. Some other business of the agent may interfere, and
induce the putting aside the rent-day for some time, and a vague-
ness is by this means introduced which is hurtfully extended into the
other ramifications of business. Alterations of the day may follow, and
lead into a month posterior to the customary time of clearing obligations.
Such shufflings very much impair the efficiency of business, and totally
disqualify any person from acting in the capacity of receiver of rents.
Business hangs in suspense, uncertainty is prolonged, and accounts of
every kind are kept behind, and fail to show the exact currency of affairs,
in the purpose for which they are established. The closely kept state of
accounts is the chief recommendation of any establishment, and no dilato-
riness must be allowed in the very least tittle of amount. Activity is the
soul of business, and punctuality with dispatch carry forward the
whole machinery at the proper speed and rate of advancement.
payments.
The best experience has established the payment of money rents half-
Half-yearly yearly, or in equal halves, at the end of every six months, after
the entry to the farm, and during the currency of the lease. No
better mode of management has been devised, and it obtains the approba-
tion of both parties in the giver and receiver. The best time of entry
has been shown to be in May, in the middle of the month, or on the
first day of the summer quarter of the year. The first half-year expires
ON LANDED PROPERTY.
1059
in November, and in that month the first moiety of the rent is due. But
to avoid the appearance of an anxious eagerness, and to indulge the con-
fidence in the mutual transactions, that neither party expects any trickery
or demur, a quietus of one month is given to the tenantry, and short as it
may be, the utility, is not below an estimate. The middle of December,
or the fifteenth day of the month, is fixed as the permanent day of audit,
with the postponement till Monday, when the fifteenth day is a Sunday,
and also if it falls upon a Saturday. Such assemblies give rise to hilarity
which is sometimes extended to late hours, and all occasions should be
avoided of unfitting the mind for the day of holy rest. The same day of
the month of June, will be six months distant, and divides the year into
equal portions.
purpose of
December
and June.
In June
These times of the year, June and December, do not seem to
be exceeded in fitness by any other periods, for the
rendering the value that is derived from the use of the land.
the farmer has received the sales of the grain crops, thrashed and vended
during winter, and also the proceeds of the winter-fed beef, which will
meet the half-yearly rent, and leave a surplus to aid the next payment.
In December, the clip of wool, and the sales of all the summer-fed animals,
will come into hand, and under particular circumstances, these receipts
will exceed the values of the winter half-year. In grass-land districts,
almost the whole proceeds of the season will be obtained at this time of
the year, from cheese, wool, and grass-fed beef and mutton. And Best periods
the period of the month of December, gives an ample time to
the necessary transactions being done to meet the demand upon the farmer.
No disadvantage is imposed upon him, of disposing any stock under
value in order to meet the rent-day; and in June, he has had sufficient
time to convert into money the grains of corn farms, and the winter values
of beef and mutton, upon the lands that form the mixed cultivations of
Britain. No faults have ever been urged against these periods of the year,
where the times are duly observed, and regularly attended. Omissions
and neglect may disturb, but not destroy the eligibility.
of the
year.
Arrears,
The times of paying the rent of lands being fixed, and a month's quietus
being given, it is very necessary that it be understood that no arrears are
allowed, but that the full amount of the rent is expected on the
day appointed, as all arrangements are made with that express
view: nothing more contributes to embarrass any business than a number
and a multiplicity of payments, which equally annoy and disturb both
parties; the landlord never knows his income, and the farmer is per-
petually bustling with payments. A mistaken lenity often leads to these
confusions, and the demanding rents at improper seasons; the over-renting
of farms, and an improper choice of tenants, tend to the embarrassments
which involve much disagreeable communication, and create a very un-
profitable state of affairs. To promote the non-existence of any back dues,
an especial care must be used to place the tenant in a position to meet the
exactness that is required, and to choose tenants who are capable and
willing to use the necessary exertion under the circumstances that permit
1060
ON LANDED PROPERTY.
not to be
allowed.
the attainment. Arrears of rent are a certain index of bad management,
probably on both sides of the business; but if other exactitudes are per-
formed under the same circumstances, a suspicion may be inferred that the
tenant is failing in duty, and requires to be observed: the land under
his temporary use will be in arrear of management, and defalcations will
spread into every branch of the undertaking. Nothing is more to be
avoided in the management of any landed property; when the
cash-book shows few or no arrears, the assurance is certain of
the prosperous and thriving condition, that the landlord enjoys his
income, and the tenants share the fruits of the arrangement. But when
the contrary happens, when the column of arrears equals the receipts,
and stands constantly filled with a full amount of figures, the sus-
picion is just, that the property is on the back ground, and the value
and condition is diminishing. In a general view, arrears are most dis-
graceful to the superintendency of an estate, and many evils grow out of
them. They encourage idleness and extravagance among indolent and
thoughtless tenants, and are a disheartening burden to the industrious.
To a receiver they are the cause of much trouble, and to a proprietor they
are doubly embarrassing, as being the cause of intricate accounts, and of an
uncertain income.
The remedy for arrears, as of every other malady, is to be suited to the
Causes and cause. If it arises from over-renting, reduce the rent to an
remedy. estimated fairness. If it be owing to over-indulgence, or to
real misfortune, or to the known poverty of an ill-chosen tenant, and there
is no prospect of the arrears ever being paid up-wipe it off. On the
contrary, if the defaulter has substance, and there is a probability of his
being able, one day or other, to clear the debt, lay it aside, and wait
until a good year of fruits, or other favourable incident, occur for enforcing
the payment. Standing arrears must be expunged, and current arrears
prevented: the former by using means of due consideration, and the latter
by establishing strict regulations to insure the punctuality of every pay-
ment. But when extraordinary circumstances do occur, judgment will
be immediately called into action, and matured into an arrangement by
the exact circumstances of the case. The occurrences of this nature
require a just compensation, which no reasonable proprietorship ever can
deny, or think of refusing. When the tenants are exact on the rent days,
and pay the value of the farms readily and cheerfully, an equal willingness
of promptitude must meet the occurring wants, and thus ensure
the continuance of the strict and well-regulated system of de-
portment. Fire, tempests, loss of stock by accident, and other unavoidable
calamities may befall the lower class of tenants, when it may be not only
cruelty, but a very bad policy to demand the whole rent in the usual ful-
ness of payment. Such cases are easily managed; a very bad crop of
grains, or a large decline of prices, even though temporary, will, and
must, induce a relaxation of the fixed rules, which are again observed,
when the occasion of their being loosened, has passed away. Exceptions
occur in every arrangement, and fixities are all liable to be shaken in their
Prompt
doings,
ON LANDED PROPERTY.
1061
and no
arrears.
position. Arrears are a defilement to the rental of an estate, and con-
stitute a stain both on the proprietorship and management of the pos-
session. Every payment that is in arrear shows a want of
arrangement in some quarter to meet the demand; it may be
too large for the means, or the latter are not duly provided for the
occasion; neglect is seen on both sides, too much is asked and cannot be
found, and a fair value is not provided by reason of improvidence and an
aversion to an honest exactness.
A month before the day of audit, the chief agent will address to each
individual farmer on the estate, a circular note signed by his own hand,
reminding the tenant of the rent-day, and requesting his attendance. The
bundle of letters goes to the manor bailiff, who delivers from his own
hand, each letter to the special direction, which very much enforces the
official notice contained in the circular. A trusty servant on Written
small estates, acts for a manor bailiff, as such a person is occa-
sionally employed in carrying orders and messages. The note runs
thus:-
Sir,
notice.
Fordhall House, 12th May, 1852.
or
Esq., falls
I beg to remind you that the day of audit for the receiving the
rents of your landlord, Earl of
on the usual day of Tuesday, 16th of June, of this year, on which day
the half-yearly rents due on 15th May, will be gathered in the King's
Hotel, Wayford, at ten o'clock, A.M., when your punctual attendance is most
respectfully requested, by, sir,
Your very obedient servant,
A B.,
Accredited agent and receiver.
To Mr. G. F-
Tenant in Fordhouse.
This notice is delivered to every person on the estate, who pays a rent
of any amount.
Day ap-
all parties,
Precisely at the place and hour appointed, the chief agent arrives with
his clerk, who has prepared the proper stamp receipts for each payment
of money, and has had them signed by the receiver. The
manor bailiff and woodreeve join the company in a suitable pointed for
apartment, to which the farmers are introduced singly and in
succession: a seat for a few minutes, gives the money rent to the receiver,
who counts it, gives it to the manor bailiff, who also counts it, and if they
both find the same amount, the clerk hands the stamped receipt to the
farmer, who makes a suitable obeisance of mutual satisfaction, and retires.
Another tenant is introduced, and is similarly treated, and so on till the
number is exhausted. The clerk makes a scroll note of each receipt of
money with the name of the payer; the money is put into parcels of twenty
paper notes and of twenty gold sovereigns, which are all again counted by
the agent and bailiff, after the business of receiving is over, and when the
amount which they count agrees with the sum of the clerk's scroll account,
1062
ON LANDED PROPERTY.
Proceedings.
the business is complete. When they disagree, a repetition is done, and
the mistake discovered. It is very convenient when the banker of the
proprietor lives in the town in which the rents are received, as he attends
with his clerk, counts and receives the money, and gives the agent the
note of transfer of the amount to the credit of his employer.
When this arrangement cannot be done, the money remains
with the agent till next day, when it is carried by him to the bank of the
property in the special locality. The security of the money for one night
rests with the agent, manor bailiff, and woodreeve, sleeping in adjoining
rooms, the former being central, and having the cash in the apartment.
The cases are most numerous where the latter way is adopted, as only large
properties and contiguous market towns afford the convenience of a bank.
But most landed estates of any considerable extent will employ this
arrangement.
Receipts.
The receipts given in return for money rents, are worded
thus:-
Received on account of Earl of
Wayford, 16th June, 1852.
or
Esq.,
the sum of eighty pounds sterling, from Mr. G. F., tenant in Fordhouse
Farm, being the half-year's rent of that farm due on 15th May last, by
the said Mr. G. F.
£80
Signed A. B.,
Accredited agent and receiver.
When partial payments are made and arrears do occur, a stamp is not
required, and an acknowledgment is given on plain paper, stating the
particulars, and writing on the left hand corner, the rent of the farm, the
sum received, and the arrears due.
Thus:
Rent £180
Paid 100
Arrears £80
This note will agree with the agent's book, and prevents the possibility
of any mistakes.
The receiving agent fills up the general cash-book of the estate from the
scroll pages of the day of audit, placing every receipt of money in the
proper assignment, and any disbursements to the proper account of use.
Cash-book
and copy
sheet.
These are the employments of his home retirement, where with
his clerk he adjusts the items, and schemes the regulated ex-
penditures. Where it is not convenient for the proprietor to
see the general books of the estate, a copy sheet of each year's proceedings
is regularly sent him.
It is not unfrequent that the landlord treats the tenants with a dinner
at least once a year; and it may happen in June or December, as may
ON LANDED PROPERTY.
1063
Dinner.
No business
audit-day.
be arranged. In that case, when the farmer is bowing retire-
ment from the audit-room with the receipt for the rent in his
hand, the agent will be glad to see him again at four, five, or six o'clock,
as the hour may be fixed for dinner. At the other half-yearly audit when
a dinner is not given, a glass of wine is handed to the tenant in the audit-
room, when the money has been paid, and the receipt delivered; and this
acknowledgment ends the intercourse for that day. It is best
arranged that little or no public business is done by the agent on the
on the days of audit; the money matters will very sufficiently
occupy the attention, and the memory must not be crowded with a multi-
tude of proposals, which may be too hastily considered, and improperly
regarded. On such occasions, advantage may be taken of a hurried em-
ployment to convert into promises the probably unguarded words of
passing observation, and which require a much more grave consideration
than can be bestowed upon any subject in these hurried moments of occu-
pation. But on the last-mentioned day of audit a leisure may be got for
the hearing and answering the appeals and proposals of the tenantry; and
in long cases, the answer can be afterwards returned through the manor
bailiff. Separate days, or one in every half-year, may be appointed for
the purpose of hearing proposals, and meeting demands, which may
be fixed as are the audit-days, and have the same consideration given to
their importance. In some instances, the days of audit are held at the
mansion of the proprietor, when the same forms of business are observed
as at the public resorts.
The subjoined form of a cash-book for an estate of land, may
be altered in any way to suit the circumstances of attachment,
and may afford the grounds of adoption in most cases.
Books.
1064
ESTATE CASH BOOK.
Crop 1852.]
Posses-
Names of
sors'
Rent.
Farms.
Names.
4
DR.
Estate Cash Book.

s.d. Date.
Cash
Received.
£
48
s. d. £ s. d. Arrears.
£ s. d.
s.d.
Newstead A. B. Money 280 0 0 15th Half
Burdens,
June Year's
if any
Rent...140 O 0
15th
Dec. Ditto... 140 0 0
280 0 0
280 00
Grange
E. F.
Money 600 0 0 15th
Half
Burdens,
June Year's
if any
Rent... 300
300 0 0
15th
600 0 0
Dec. Cash... 240 00
540 0 0
By E. F. 60 00
This Book shows the rents received, the arrears, the expenses on each
farm, and the whole charge of upholding the estate. It may be continued
to any extent, and have attached to it the general receipts of money from
ESTATE CASH BOOK.
1065
Crop 1852.]
Contra. CR.

Date.
Expenses.
£
S. d.
બે
£
S. d.
£
8.
d.
18th July By Cash paid the Carpenter's
Bill for Repairs, as by Ac-
count rendered…………..
55 17 0 55 17 0
16th Sept. By Cash paid the Mason's Bill
for Repairs by account......
15 6 6
By Cash paid the Carpenter's
Account
10 8 0
80
25
14 6
Total .......
81 11 6
other quarters, and also the general expenses. Abstracts of each de-
partment being joined together will show the result of the whole
proceedings.
3 U
1066
ON LANDED PROPERTY.
Brevity and simplicity of arrangement constitute the essence of the art
of keeping accounts, which are to be so designed as to afford at any time
from a slight inspection, a clear and satisfactory view of the existing state
of affairs. There must be no dilatoriness of entry of the very minutest
trifle; every transaction must be recorded within twenty-four hours after
being done, and show the negotiation in the place of proper exhibition.
Nothing is left till to-morrow which can be done to-day, and each night
must show the business of every kind arranged as it has been done, and
duly noted. No other way is able to direct the current of affairs in the
proper channel, or control the tendency to go awry.
Short and
The following very concise and simple form of a book of receipts and
payments, may be found useful in certain places of an extent
clear. not very large, and where the proceedings require to be closely
shown, and narrowly guarded. Its chief use consists in giving a view of
gross receipts and disbursements, and showing the balance of money that
remains in hand. It is a concise abstract of general proceedings, and has
been found very useful under circumstances which require an understand-
ing of that nature.

Account in respect of Receipts and Payments at
month, or from weeks ending
for one
1852.
Dr.
Cr.
Receipts.
Dates.
Particulars of sums paid and received.
Payments.
4+
£
S. d.
બે
£
S.
d.
It is conveniently and very beneficially arranged that there be attached
to the residence of the manor bailiff, an office-room of public resort, at
which the bailiff is found on most days of the week and settles the business
of the estate that requires the transaction of being put into the form of
writing. This office of two apartments in the outer and inner rooms,
may be joined with, or placed at a small distance from, the dwelling-
Bailiff's
office.
house of the bailiff, and to it the chief agent may be appointed
to come on the fourth Wednesday of every month, or any
other day or week as may be eligible. The farmers and all the subordi-
nate agents know this appointment, and attend it, when reports are made
and suggestions heard and settled. The manor bailiff and woodreeve
ON LANDED PROPERTY.
1067
Where to
meet and
consult,
refer all matters to be settled at this meeting, and the tenants look to it
as the termination of all cogitations and proposals. In this office are kept
all the books of general reference, and the maps, which require very often
to be consulted. On estates of the smaller extent, the agent
will be of the minor grade, and perform the whole business of
agency and of the bailiff; the office will be attached to his own
dwelling, and answer the purpose above described. When he resides at
a distance, an occasional residence may be found on the estate, when the
monthly attendance at the bailiff's office will be more convenient, and more
easily attended.
may be the
place of
audit.
In some cases of landed property on which the idea of hospitality is
not entertained or largely distributed, the office at the residence of the
manor bailiff or inferior agent, may serve as the place of audit,
and the rents can be received in the two rooms of office. This
arrangement does not abandon the monthly day of meeting at
the office, as it is exclusively devoted to the receipt of money, and the
other time to the transaction of contingent business. The residence of
the proprietor may have an office attached, where every agency is done:
on largely extended estates, the offices of business may be two or three
in number, in order to suit the distances of detachments. At each place
the agency must occasionally attend in order to inspect the demands that
are made, and to diffuse a spirit of good order and emulation. In these
offices, there must be lodged the necessary provisions for the transaction
of business, as maps, rentals, books of accounts, registers, and receptacles
of business that has been transacted. No person must carry away on any
occasion, or for any purpose, a paper of any kind from the office, without
leaving in its place, a memorandum, stating by whom it was taken, and for
what purpose, and when it will be returned, in order that it may be traced
in case it should not be brought back. This regulation should be written
in large letters, and suspended in the most conspicuous place of the office.
Such an injunction requires a positive enforcement.
Rent-roll.
A rent-roll is required on every estate of land, or a statement of the
gross value of the property, ranged in the order of the farms,
and other sources of revenue, as woods, mines, rights, and fines.
This general view of increase is best arranged in columns, as being most
perspicuous; and for a schedule of farms the following are proper :—
1. The mark of the farm in the general map.
2. The names of the farms.
3. The contents, or admeasurements of each.
4. The names of the present tenants of each.
5. The amounts of the existing rents.
6. The outgoings, if any, by the proprietor.
7. The expiration of the lease.
The farms are best arranged geographically, in the natural order in which
they lie on the estate, and thus appear on the rent-roll. The general roll-
map of the estate, the book of maps, the large rotation book of maps, and
the pocket-book of maps, must all agree in having the farms similarly
1068
ON LANDED PROPERTY.
marked, and arranged in the same order, and also in the receiver's general
cash-book, and in fact, on every occasion of the farms being placed in order
of any kind, a systematic mode of proceeding must be adopted, prac-
tised, and enforced; and when neglected or infringed, it has to be imme-
diately restored.
Maps of
Books and
Estates of land must be mapped in the whole extent by a compe-
tent surveyor, or of the districts, or officiaries into which
estate. a large extent may be divided. These provisions will be lodged
on rollers, and unfolded on the floor of the office when a general consul-
tation is required. On a reduced scale from this map, there is constructed
a book of maps, in which each separate farm is contained on a leaf which
extends over the whole book when opened, and the middle of it bends into
the centre of the book when it is folded. This volume forms a ready re-
ference to each single farm, and can be carried to any place to
single be examined on the spot for the purpose of certification.
In
the reduced scale of one-half of these maps of estates, the general
book of rotations is made, having on the right-hand side the plan of the
farm, and on the left the rotations of cropping during the currency of the
lease, as has been shown in the duties of the manor bailiff. And on all
suitably reduced scales from these plans, the pocket-book of maps and ro-
tations is constructed, so as to be convenient, and easily portable. All
these plans being fitly done in one copy by a professed surveyor, can be
copied into any useful number by an official who has received an educa-
tion that enables the performance. At every office on an estate of land,
there must be lodged within its walls, the book of maps, and the rota-
tion books of the districts which lie within the circuit of the officiary;
reference will be constantly necessary, and the provisions must be had.
The original copies of professional skill will remain at the chief office, the
others are copied as substitutes.
maps of
The plantations are separately mapped, and shown in the office or offices
to which the position of the woods appertains. And when a new planting
of trees has been done, a plan is made of the plantation ground,
plantations. in order to answer the special purpose of necessary references.
The woods are ranged in the numerical order, and a book with columns con-
tains the extent of each plantation, the age of the timbers, the time of last
cuttings, and the money got from sales, with the respective dates attached.
The quantity of hedge-row trees on each farm may be entered in a simi-
lar book, and accounted as they may be cut down and disposed for use, or
sold. The manor bailiff and the woodreeve prepare and keep
these books, and the chief agent examines and approves. On
the inferior agencies, these performances fall upon the steward himself.
These cases often join the duties of bailiff and woodreeve in one person,
who will assist in upholding the provisions that have been mentioned.
Accounts.
On every estate of land there must be established laws and usages, to
which both parties are liable, though no written contract subsist on the
subject. Though these laws may be imperfect, they ought to be strictly
observed, until better regulations are found: moral justice demands the
ON LANDED PROPERTY.
1069
exactness.
performance of these duties, and the example must be set of integrity and
good faith to the tenants. The proprietor and agent must show the model;
for if these persons break customs and covenants, what can be said to a
farmer who follows the example? It is no more than common prudence
to fulfil with scrupulous exactness every covenant and agreement, A scrupulous
and every promise that has been made, even to the meanest cot-
tager or labourer on the property, in order to inspire the same principle
into the conduct of every person that is concerned. Not only good faith
must be preserved, but good offices; and frequent acts of kindness must
liberalize the minds of the tenants, and not with any loss, but with a posi-
tive advantage to the estate. Spirited improvers must be denied no rea-
sonable request, and should have favors voluntarily conferred upon them.
Estates, like men, acquire good or bad characters, and not from Character
the quality of the soil, but from the conduct that is observed in
the arrangement and treatment of the negotiations. A skilful farmer of
capital will rarely fix his abode on an estate of bad repute; while on the
contrary, a contest will happen to obtain a footing on a property of estab-
lished character. Nothing can well add more to the permanent respect-
ability of a family of rank and fortune than having the estates occupied by
a wealthy and respectable tenantry.
established.
The good management of a landed estate requires the assistance of a law
officer, as solicitor, or attorney. This person is employed as an assistant
when required, as is medical aid when specially necessary. Judicious re-
gulations and timely advice without interference will almost prevent any
serious divisions on the estate; yet cases will occur from the frailties of
human nature, and in a state of civilized society, and of established pro-
perty. The lawyer is best engaged on large properties to manage all
legal affairs for a yearly stipend, which may be sometimes exceeded, but
oftener below the mark. The land surveyor is employed when the pro-
fessional service is required, and is often a useful person as an arbitrator or
referee.
of business.
In every business between man and man, the affairs must be No arrear
made pleasurable, and transacted cheerfully, as the matters oc-
cur, and never delayed, till by accumulation the performance is difficult
and irksome. Dispatch is essential before misunderstandings; idle tales,
and groundless surmises have time to intervene, sour the mind, and pro-
duce a distant coolness. Barriers are thus raised, which nothing but the
mystic law may remove. No tricks or artifice to take advantage like
gamblers round a table, but an honest desire to find the point of equity and
right, must be the chief motive; and when honest men, who have character
to lose, meet to settle any business, the difficulty very quickly vanishes.
An umpire may be necessary at times, but the occasions will be few.
On the part of persons in power, a conduct of a somewhat
peculiar mark has to be observed, in order to give no offence to
superiors, to please the equals, and to conciliate inferiors. A
demeanour at once respectful and firm must be exhibited by agents, in
order to procure respect and observance of regulations. No arrogant
Conduct of
persons in
power.
1
1070
ON LANDED PROPERTY.
haughtiness nor austerity of manner must debar the approach of solicita-
tion, nor must an improper familiarity allow the intrusion of every petty
squabble or request that may suppose itself worthy to be heard. The for-
mer line of conduct prevents the necessary access of presence, and the
latter crowds every avenue with trifling advances. No quality is more
Firm decision hurtful in an agent of any kind than the want of a firm decision;
essential, the resolves must be decided and adhered to with pertinacity.
Inferiors must be taught into a respectful submission, but no slavish
cringing, which wholly destroys the independence of mind which must
ever accompany the use of any rational faculty. A courteous affability
must be very largely entertained with every person, of whatever rank or
station, that requires to use the agency of the estate in any way; no cold
repulsion is to be used, nor a feeling of disdain be manifested, unless on
the proper occasions, which must be well settled and authenticated. A
demeaning familiarity must be very carefully avoided, as it tends most
powerfully to lose esteem, to sink respect, and never fails to beget con-
tempt for the object of its exercise. There is a happy medium of conduct
which pleases superiors and conciliates the lower stations of life; it is a
most valuable acquisition, as it procures confidence from the for-
memory. mer and attaches the latter, who form the supporting ground-
work of society. In the days of audit, or at any other times, the agent of
extensive business must not trust to promises in a crowded memory, but
reduce every business into writing, when it is of the possible import. An
occupation being arranged in this way, and the habits of transaction being
adapted to the circumstances of the position, and a systematic organization
being on every point established, there is only wanting the polite affability
and courteous demeanour which gilds every object and burnishes every
business, gives oil to the wheels of affairs, and lubricates every transaction.
and a clear
Moral re-
Such an important subject as the charge of landed property cannot be
dismissed without a parting admonition to the holders of these offices. In
many cases the total absence, only a temporary residence, and the occupa-
tion of the land-owner in legislature, leaves to the agent the almost uncon-
trolled direction of the estate; while in almost every instance of an agency
of repute, the advice of the professional adviser is as it ought to be-deci-
sive of the system that is adopted. The agent will see that he is entrusted
with the physical and moral condition of a portion of his fellow-
sponsibility creatures, who have a claim or vested right to be employed,
of an agent; maintained, and educated by the property of which he has the
administration. His employer has bought a certain part of the develope-
ment of its resources, and this being the acting portion, must have its
every direction made to tend to the chief points of attachment. This em-
ployment becomes a very serious concern to a rational being, who must
assume a corresponding lofty standard of morality in every sense and mean-
ing of the word. The agent has to hold in constant perspective the
employment of the people, and a competency of support; the education,
moral and religious, accompanied with such a remuneration to his employer
ON LANDED PROPERTY.
1071
and most
important
charge.
as will justify the progress of the undertakings. These purposes form a
most important charge to be invested in any one person, and re-
quire a thoughtfulness the most serious, and a calculation the
most profound. It is no every-day affair, or passing concern,
but a matter the most valuable of all the varieties of occupation. Those
persons who write about man, and the different states and stages of his
existence-moral, social, and political-would do well to remember two
things: the cultivation of the earth, and the supply of the necessaries of
life; for they uphold or overturn all their ideal fabrics.
INDEX.
A.
Abutments, wings, and spandrils
Accommodation land, valuation of
of labour on land.
Accounts of subordinate land agency
Acre decimal table
Addition of vulgar fractions
proof of
Adjustment of rents (On Landed
Property)
Advertising of farms
Age for business men
Agent's judgment (On Landed Pro-
perty)
Age of plantations
Agreement between auctioneer and
purchaser at sale by auction
Agreements and leases, law re-
lating to
•
Agreement for a farm
PAGE
PAGE
•
406 Appraisements, law relating to
749
586
under distress
781
869
Appraisers' oath in cases of distress
781
1068
Approaches to bridges
409
226
Appropriation of land
857
•
5 Arches and Counterforts
405
2
backing to
405
over reservoir
489
872
Arch over road of the farm yards
931
•
894
Areas, computation of
326
1027
Arithmetic
1
1057
proof of first four rules
Arrangement of crops on land
2
909
1017
estate expenses
1057
farmeries
930
764 Arrears of rent of landed property
Artesian wells and springs
1059
467
765
Artificers' work
541
770
Artificial manures
890
857
984
Art of ploughing
Ashlar work.
968 Aspect of farmeries
906
403
935
•
895
752
1031
Alienation of land
All drains should be covered.
Alluvial valleys
Altered policy (On Landed Property)
Alternate system of cultivation of
land.
862
Assignation of lease
Auction, law of
Alternation of plants
Amount of fine to be paid for renew-
ing any number of years lapsed
in a lease originally granted for
ten years
Amount of fine to be paid for renew-
ing any number of years lapsed
in a lease originally granted for
twenty years
Amount of fine to be paid for renew-
ing any number of years lapsed
in a lease originally granted for
twenty-one years
Amount of fine to be paid for renew-
ing any number of years lapsed
in a lease originally granted for
forty years
Amount of fine to be paid for renew-
ing with one life the lease of an
estate originally granted on three
lives.
Angles and right lines, and their
rectangles.
603 Back drainage of houses
Backing to Arches
Bad farming.
arrangment of farmeries.
604 Bailiff's business office
Baking of tiles
•
Ballasting and laying permanent
sidings of a railway
605 Ballasting and laying permanent
way of a railway
Bankruptcy, its effect on a lease
Barley used in rotation of crops
606 Bedfordshire, agricultural custom
910
908
Authority of a land agent
B.
455
405
874
927
1066
1002
417
413
895
911
of
625
Beds of rivers
Beech trees
968
•
951
607❘ Beet root
904
Benefit of leases on landed property
875
173
Berkshire, agricultural custom of
625
•
Angular mensuration
193
Best forms of farmeries.
929
Apartments of agricultural dwellings
922
materials of embankment
965
1074
INDEX.
Books of estate agency
Best soils, cropping of
times of paying rent of land
trees for copses
Block in course work
PAGE
917 Concrete foundation
PAGE
487
1059
489
960 Condition of lease of land
403 Conditions of sale, freehold property
881
761
1034
leasehold property
764
reference on farmeries and
goods and chattels
764
cottages
Boring of coal
940 Condition of tenantry
993
943
a landed estate
1014
Boulders, or field stones
948 Conic sections
216
Box sextant
•
286 Consent by tenant to hold over un-
Bricks, quality of
488
der distress
780
Bricklayers' prices
676 Constant water supply
465
quantities &c.
work
547
Construction of water closet
459
541
Contents of railway cuttings and
Brickwork
402
489
embankments, methods of com-
puting the
380
Bridges
1009
Continued use of badly arranged
culverts, &c.
402
farmeries
927
and highways, dilapida-
tions of
Buckinghamshire, agricultural cus-
Coping and string courses
406
740 Copper
988
Coppersmiths' prices
705
Burdens on land
tom of
Builders' prices
Building stones
Burning of lime
•
Butt jointed pipes.
•
625
Copse woods.
958
660
not formed.
961
•
999 Copying maps
860 Corners of fields should be planted
998 Cornwall, agricultural custom of
461 Cost of sinking coal pits
pleasure grounds
335
946
626
•
994
1012
•
Cottages
935
C.
Cambridgeshire, agricuitural cus-
tom of
designs for
833
on farm, valuation of
586
Counterforts and arches
405
Capacity of sewers
625
451
Covering of drains
980
land
915
453
Cow shed
926
Capital required in farming
893 Cross staff
229
Capping top of reservoir
486
Crooked ridges on land to be made
Carpenters and Joiners' work
551
straight
903
prices
660
Cube root, extraction of
10
Casting of iron pipes
468
Cultivation of land lessened
865
Catch-water meadows
973
defined
898
Causes of arrears of rent of land
1060
Culverts
411
Cement, Roman
Centring of arches
404 Cumberland, agricultural custom of
489 Curvature of the earth and refrac-
626
Cesspools
468
tion, table of
161
Character of estate established
1069
Curvature of the earth and refrac-
Cheshire, agricultural custom of
626
tion, the use of the table of
36
Choice of a tenant of land
892
•
Customs duties
823
Circles, &c.
•
178 Custom of the County of Bedford
625
Circular protractor
319
Berks
625
Clap gates
953
Bucks
625
Classical education of land steward
1025
Cambridge
625
Clay
1000
Cheshire
626
for bricks
1001
Cornwall
626
•
Cleansing sewers by manual labour
454
Cumberland
626
Coal
993
Derby
626
Cocks for water supply
•
470
Devon
626
Collected reference to maps
324
Dorset
626
Colonial surveying
424
Durham
626
Complaint before justices to recover
Essex
626
possession
785
•
Glo'ster
626
Computation of areas
326
•
Computing scale
tables
•
328
330
Hereford
Hertford
Hants
626
•
627
627
·
Concrete, composed of
404
Huntingdon 627
INDEX.
1075
PAGE
PAGE
Custom of the County of Kent
Lancaster
Leicester
bridges
627 Dilapidations of highways and
627
740
627 Dip of the horizon, table of
141
Lincoln
627
the use of the
•
Middlesex. 627
tables of
29
Norfolk
Northamp-
•
627
Direction of roads on estates
943
drains
982
ton
627
Discharge of water flowing through
Custom of the County of Northum-
pipes.
442
berland
627
Disposal of material
401
Custom of the County of Nottingham
628
Distress, appraisement
781
Oxford
628
appraisers' oath
781
Rutland
628
consent by tenant to hold
Shropshire
Somerset
628
over.
780
•
628
Distress, notice of
780
Stafford
628
notice of, standing corn
781
Suffolk
Surrey
628
warrant of
780
628
Diversion of roads in constructing a
Sussex
630
railway
412
Warwick
630
Division of fractions
5
Westmore-
proof of
3
land
•
630
Dorsetshire, agricultural custom of
626
Custom of the County of Wilts
630
Dr. Angus Smith's preparation for
Worcester.
York, East
630
coating pipes
470
Drainage outfall
446
Riding
630
sewerage, and water sup-
Custom ofthe County of York, North
ply of towns
440
Riding
631 Draining necessary on clay lands
914
Custom of the County of York, West
Riding
of land
975
631
roads
944
Drain pipes, tender for
475
Drainage and water supply, prices
D.
of materials for
686
Drains, house
455
Danger from uncertainty of tenure
in land
Decays of houses
junctions for
458
864
main
446
1005
pipe
445
•
Decimals
of an acre
6
447
226
of a pound sterling.
reduction of
•
Declination of the sun, tables of
807
7
size of
trapping of
under bridges
450
459
407
171
Drawing of lime cinders
998
the use of
Drilling of green crops
905
•
the tables of
38
Drying of bricks
1002
Decorators' and paperhangers' prices
697
Dry stone walls
948
Defence of banks
969
Dung, free to incoming tenant of
Deficiencies of cottages
936
farm.
890
Depth of drains
978
Dung used in broad cast and drilling
902
Derbyshire, agricultural custom of
626
Duodecimals
8
Description of a farmery
925 Durham, agricultural custom of
626
entails
860
Duties of farm bailiff
1035
Designs for houses, villas, cot-
tages, &c.
Dwelling house
922
833
of the farm
867
Devonshire, agricultural custom of
626
Differential coefficients, tables of
168
the use of
E.
the tables of
38
Digging of clay
1001
drains
981
Earthy filling of drains
land
961
Dilapidations by mortgagee or
Earthenware pipes
Elevation by machinery
Embanking
460
981
•
996
486
mortgagor
737
963
Dilapidations and nuisances
707
Embankments
400
•
by tenants for life
Enclosed grounds
947
•
and years
714 Encumbered estates
862
1076
INDEX.
541
•
cottages
940
Encumbrances
Engine pits
Entail of land
Equitable privileges of farmers
Erection of hedge fences
Essex, agricultural custom of
•
Exactions from a farmer should be
Estate valuation
lenient
Excavations and embankments
for pipe laying
•
of foundation
Excavators' work
•
Expense of pruning trees avoided
PAGE
1014 | Flooded grounds
994 Flow meadows
PAGE
970
974
860 Fluids, motion of, passing through pipes 442
879 Form of lease
94.9
626
577
872
398
479
408
957
sewers
tender for railway works
Formulæ for solving all the cases of
a rectilineal triangle, of which
three parts are known, tables of .
Formulæ for solving all the cases of
a rectilineal triangle, the use of
the tables of
Formulæ for the solution of quad-
ratics and cubics, tables of .
Formulæ for the solution of quad-
878
453
420
166
37
167
irrigation
974
draining
984
ratics and cubics, the use of the
tables of
37
•
Expenditure on landed property
1003
Experience of rotations.
920
Formulæ relating to two arcs or
angles, tables of
164
Expired leases
895
Formulæ relating to two arcs or
Exploration and trial levels
338
Extra buildings
923
Foundation of concrete.
Extraction of cube root
10
square root
9
•
Exudation of plants
921
vulgar
F.
Facts to assist the memory in mat-
ters of valuation
Failures, few in draining land
Farm account book
angles, the use of the tables of
Fractions, addition & subtraction of
sion of
Fractions, reduction of .
Functions of sewers
Furniture of farm.
Furnaces
Furrow draining
37
487
LO
5
multiplication and divi-
5
4
3
•
451
866
992
982
•
616
986
1037
buildings
921
G.
Farmeries
925
Farmer's dwelling, its accommo-
Game
891
•
dation
922
Gamekeeper
1056
Farmery covered
934
No. 1
930
Gardener
Garden and Orchards
1056
867
No. 2
931
Gas in pits
996
•
No. 3
934 Gas works, rating of
651
Farm homesteads, valuation of
583
Gates
952
labour, valuation of
•
587
Feeding yards
926
Gathering grounds, for water supply
General Board of Health, on sur-
462
Fee farm rent
1022
veys and maps
447
•
Felling timber
958
General buildings on farms
868
Fences
870
•
clearing of water-courses
915
in charge of the manor
description of farm buildings
923
bailiff
1051
mistake in farmeries.
926
Fencing and ditching
393
objects in valuing plantations
1017
Field book for farm bailiff
1049
principle of embanking
965
levelling
311
repairs of houses
1006
setting out slopes
374
rule of size of farms
942
surveying
270
scheme of crops
889
valuation of tillages
value of draining
987
and tenant right
632
valuation of an estate
1022
Filling in after pipe laying
480
Geometry, plane and solid
172
•
of drains to be carefully done
980
practical
186
•
Filter, the best one for water
464
Glaziers' prices
699
Fire damp
996
work
575
·
Fishing
Fixed sum of money for rent
Fixtures on farms.
Flagstones
Flat measure, tables of .
891 Gloucestershire, agricultural cus-
877 Good husbandry defined
Government loans of money
883
tom of
626
890
1000
•
528 Grain rents
862
884
·
INDEX.
1077
Grain crops purchased
Grand axiom of tenancy
Grants of land
Grass turf the best bottom of roads
for covering drains.
Grasses for cropping
PAGE
881 | Interest of purchased estates
875
low of land
857 Intermittent supply of water
PAGE
1013
1023
465
944
Inventory and valuation of tillages
980 and tenant right
636
916 Iron
991
Gravatt's level
308 Ironmongers' prices
677
Gravel.
488
Ironmongery
573
Great importance of fallowing
907
Iron pipes and castings, specifica-
advantages of irrigation
973
tion for
468
value of leases
863
Iron, quality of
468
Grey, Mr., his practice in agriculture
882
Ironwork
407
891
Irrigated grounds.
973
911
Groined arches
489
Groups of cottages
940
J.
Grubber working
905
•
Gully gratings
481
Joiners' prices
660
Joints for pipes
461
Judgment required in planning
H.
farmeries
928
•
Junctions for house drains
458
Hampshire, agricultural custom of
627
Junction of roads
945
•
Hedge-row trees
951
Herefordshire, agricultural custom
of
Heriots.
626
K.
1021
Hertfordshire, agricultural custom
of
Kent, the agricultural custom of
627
627 Kilns
1002
Highways and bridges, dilapida-
tions of
740
Hill draining
983
L.
Holders of land for life.
861
Horizon, tables of the dip of .
14]
Labour, hours
1034
the use of the tables of the
Labourers' Cottages
868
dip of
29
Lancashire, agricultural custom of
627
House drains
455-456
Land and wood, chief sources
1018
junctions for
458
trapping of
459
Houses, designs for
833
bears a low interest
differs from manufactures
how valued
•
1023
866
1013
paying rent
1015
Huntingdonshire, agricultural cus-
is a firm security
is easily injured
1023
1023
•
tom of
627
is much desired
1023
Hydrants and screw cocks
480
measure, tables of
230
Hydraulics
440
measuring
219
Hydraulic tables (Ryde's), synopsis
must be in good order
1023
of, second edition of
443
•
plans for railways
380
Hydraulic tables (Ryde's), speci-
men of
surveying
257
444
the distinction of society
858
Hydrostatic bellows
Hyperbolic and common logarithms,
table of
Hyperbolic and common logarithms,
the use of the table of
440
valuation
577
Landlord and tenant
765
161 Landlord's aid in accidents
Large farms.
887
942
35 Last years of tenure
890
Law of auction
752
I.
Ignorance ruinous in agency
relating to agreements and
leases
765
Law relating to appraisements
749
1030
Laying and ballasting permanent
Improved house drains.
Improvements gradual in dwellings
Inferior lands in rotation of crops
455
sidings of a railway
417
936
Laying and ballasting permanent
912
way of a railway
413
918
Laying drain pipes
479
Inferior qualities of clay
Inspections by bailiffs
1001 Lead
990
1035 Lease defined
877
1078
INDEX.
Lease for three years, or less, of a
house
Lease is heritable
•
is long of coal mines
must have an issue
of much consideration
Leases and agreements
Legumes and grasses used
hardly of use.
PAGE
PAGE
Maps and surveys for sanitary pur-
769
poses
447
892 Maps of estates
1068
997 Masonry
490
883 Masons' prices
674
1014 Materials for building houses.
924
765
filling drains
979
913
roads
943
914 Mathematical tables, use of
18
•
used
912 Maturity of trees
957
918 May entry on farms
881
Leguminous plants
908
Meadows
963
Leicestershire, agricultural custom of
627
Means of farming should be known
893
Length of tenure
•
864
Level, Gravatt's
Measures and weights, mensura-
308
tion of
192
spirit.
299 Measuring bricklayers' work.
541
Troughton's
307
carpenters' and joiners'
Y
301 work.
551
Levels
994 Measuring excavators' work
541
Levelling
296
glaziers' work
575
practical specimen of
314
hay ricks, tables for
638
staves
•
309
iron work
573
the operation of
310
land
219
Lime
489
painters' work
573
998
paper-hangers' work
576
used
905
plasterers' work
571
Lining of puddle for reservoir
Liquid draining of farmery
List of grass seeds
Loans of money
Lincolnshire, agricultural custom of
627
sawyers' work
566
487
stonemasons' work
566
926
timber.
491
913
Memoranda to assist the memory
861
in matters of valuation
616
1008
Mensuration, angular
193
•
bolic, table of
Logarithms
Logarithms, common and hyper-
•
Logarithms, common and hyper-
bolic, the use of the tables of
Logarithms for finding the horary
angle or apparent time, table of.
Logarithms for finding the horary
angle or apparent time, the use
of the table of
Logarithms of numbers, tables of
Logarithms, use of the table of
Logarithmic sines, tangents, &c.,
tables of
•
Logarithmic sines, tangents, &c.,
use of the tables of
Long dates at entry on farm
Longer security necessary
Longitude and time, tables of
13
of solids
197
of superfices
194
161
weights and measures
192
hyper-
Meridional parts, tables of
132
35
the use of the
tables of
26
34
41
158 Metropolis, subterranean survey
Michaelmas entry on farms
Mid-channels of water must be used
Middlesex, agricultural custom of .
Mineral property
vey of
454
880
972
627
1019
•
15
Minerals
891
988
68 Mines of coal
993
Modes of ploughing
899
19
884
•
Moon's altitude, tables of the cor-
rection of
147
866
Moon's altitude, the use of the
142
tables of correction of
33
the use of the
Moon's parallax, tables of
141
tables of
32
the use of the
Longitude, tables of
140
the use of the tables of
29
tables of
Moon's semidiameter, tables of the
augmentation of
30
142
M.
Main drains
Moon's semidiameter, the use of
the tables of the augmentation of
Moral responsibility of an agent
31
1070
•
•
446 Mortar
404
Mains and pipes for water supply,
488
size of
466
Manor bailiff.
1048
Manorial rights
Mortgagee or mortgagor, dilapida-
tions by
737
1021
Manufacture of the copse woods
Motion of fluids passing through
959
pipes
441
INDEX.
1079
Motion of water
Mounds
Much judgment required in draining
Much varied position of farms
Multiple arcs, tables of expressions
for
•
PAGE
453 Parish valuation, written in the
PAGE
970
978
form prescribed by the Poor Law
Commissioners
656
941
Parish valuation, Field Book re-
commended for .
658
163 Parishes, valuation of
•
647
Multiple arcs, the use of the ta-
bles of
Parliamentary plans and sections
345
37
Paved crossings
409
Multiplication, proof of
of fractions
3
Paving.
547
5 Peaty soils
920
Pediometer
327
•
N.
Natural sines and cosines
for agricultural labourers
Pentagraph
Permanent fencing
336
394
Piggery
930
787
Pig iron
992
Notice of distress
Necessity of comfortable dwellings
Neglected woods
New designs of farm buildings
necessary
Norfolk, agricultural custom of
Northamptonshire, agricultural cus-
tom of
Northumberland, agricultural cus-
tom of
Notation in arithmetic
distress of standing corn.
owner's intention to apply
Piles of timber
971
940
Pipe drains
445-447
958
•
laying, specification for
477
tender for
484
•
927
Pipes and castings, tender for
472
627
mains for water supply,
size of
466
627 Pipes, coated
470
earthenware
460
627
iron
469
·
1
stoneware, tender for
475
780
Plane and solid geometry
172
781
trigonometry
200
Planes and solids
183
to justices to recover possession
785
Plans and sections, parliamentary
345
Notice to quit
774
Plantations
1007
Notices to be made of cultivation
898
Planting of trees
955
Nottinghamshire, agricultural cus-
copses
959
tom of
628
Plasterers' prices
676
Nuisances
746
work
571
•
and Dilapidations.
•
Numbers, the properties of
Numerical reference to maps
10
707 Plotting, sections
323 | Plumbers' prices
326
surveys
316
689
Policy and security of tenant of
land.
863
0.
Polygons and quadrilaterals
176
Portland's, Duke of, mode of planting
962
Obligations of a lease
896
draining
982
Observances of a lease
897
•
arrangement with
Old timber stools removed
960
his tenants
985
•
Opening in banks .
967 Possession, recovery of
782
•
Origin of farms and leases
863
Potatoes
904
Original holding of land
859 | Poultry yard
931
Outfall drainage
446
•
Practical geometry
186
Oxfordshire, agricultural custom of
628
Present worth of an estate, lease, or
P.
Painters' prices
694
work
573
Paperhangers' work
576
•
Paperhanger and decorators' prices
697
Parallax in altitude of the sun and
planets, tables of
143
Parallax in altitude of the sun
and planets, the use of the ta-
bles of
32
Parapet walls
406
Parish and estate surveying
258
annuity, for any number of years
certain and in perpetuity, at the
several rates of interest which a
purchaser may thereby make of
his money.
Present worth of property held on a
single life, as of a person in pos-
session of a living or benefice, or
the holder of a lease, estate, or
annuity, according to the Nor-
thampton table of mortality.
Present worth of property held on a
single life, as of a person in pos-
session of a living or benefice, or
the holder of a lease, estate, or
590
594
1080
INDEX.
annuity, according to the Carlisle
table of mortality
Present worth of an estate, annuity,
or a lease on two joint lives, ac-
cording to the Northampton table
of mortality
Present value of an estate, annuity,
or a lease, held on the longest of
two lives, calculated according to
the Northampton table of mortality
Present worth of an estate, annuity,
or a lease, held on the longest of
three lives, according to the Nor-
thampton table of mortality
Present value of the perpetuity of
one year's rent or fine, payable at
intervals of years
Present value of the reversion to a
freehold estate, or a perpetuity,
after any given number of years
not exceeding sixty
Present value of a reversionary
estate in fee after the life of a
person of a given age, at the
several rates of 3, 4, 5, 6, 7, and
8 per cent. interest
Present value of a reversionary
estate in fee after the longest of
two lives of given ages, at the
several rates of 3, 4, 5, and 6 per
cent. interest
Present value of a reversionary
estate or annuity on a single life,
after any other single life now
in possession, at the several rates
of 3, 4, 5, and 6 per cent. in-
terest
Present value of a reversionary an-
nuity on a single life, to be
nominated at the death of a per-
son now in possession, at the
several rates of 3, 4, 5, and 6 per
cent. interest
PAGE
•
-stone-ware drain pipes
PAGE
Q.
596
Quadrilaterals and polygons
176
•
Quality of copper
iron
989
•
468
598
473
water
462
Quantity of bricks
1003
599
lead
water
991
•
464
•
547
882
600
Quantities in brick-work, &c.
Quitting and entering farms
cuttings and embankments,
methods of computing the con-
R.
608 Rack rents
Railway
609
tents of
·
Railway surveying
works, tender for
Railways, rating of
Rain fall
611
guage
Rating of railways, gas, and water
works
Receipts, form of
•
Recovery of possession
612 Rectangles, right lines, and angles
Reduction of vulgar fractions
•
Refraction and curvature of the
earth, the use of the tables of
Refraction of the sun and stars, ta-
bles of
Refraction of the sun and stars, the
884
931
380
338
420
651
452
439
651
1062
782
173
4
Decimals
7
Reference to maps, collected.
324
numerical
323
613
Refraction and curvature of the
earth, tables of .
161
36
•
144
614
use of the tables of
33
•
Regulations on land
1029
Relative gradients, table of
379
age
615
Remarks on the construction of farm
Price of young woods
1018
buildings
926
·
Prices of builders' work
660
Rents must be equitable
870
materials for drainage and
Rent defined
883
water supply
686
of lands
1011
Primogeniture
859
of woods
1010
Prismatic compass
283
roll
1067
Private roads
945
tends to rise rather than fall.
871
Proof of first four rules of arith-
upon bricks
1003
•
metic
2
Reserved capital of farmers
893
Properties of numbers
Prospective view of farming opera-
tions.
Protractor, circular
semi-circular
Provision of water
Puddle.
Pumps
•
Purposes of outlay
10 Reservoir
967 Risk of mining
994
1010 Roads
•
464
specification for
485
878 Residence of land agent
1048
319 Restrictions in farming
874
320 Right_lines, angles, and their rect-
870
angles
173
487 Rights of land
857
991
Rivers
1008
887
Present value of £1, payable at
the death of a person of a given
INDEX.
1081
PAGE
PAGE
Roads in mines
woods
995
•
956
Skewbacks
489
on farm
to be provided
under the agent's care
Slaters' work
869 Sloe
943 Slope of banks -
549
951
966
•
1009 Slopes
486
•
Roadside fences
Roman cement
Root crops
Rotation of crops
•
Royalty
1053
Social position of an estate
1019
404
policy necessary in the man-
908
agement of an estate
879
910
Socket pipes
461
919 Soffits of arches
489
993
Soles for sands and gravels
983
1011
Solid geometry
172
Rubble.
Rules of management of a farm
Rutlandshire, agricultural custom of
Ryde's Hydraulic tables, synopsis
404
measure, tables of
495
888
Solids and planes
183
•
628
mensuration of
197
•
Somersetshire, agricultural custom of
628
of second edition of
Ryde's hydraulic tables, specimen of
•
443
Sowing of wheat
902
444
Spandril of arches
487
Spandrils, abutments, and wings
406
Specialties of a lease
897
S.
Specification for construction of
railway works
392
•
Salary, fixed of a land agent.
1029
Specification for iron socket pipes
Sale by auction, conditions of sale
of freehold property
and castings
468
761
Specifications for pipe laying
477
Sale by auction, conditions of sale
reservoir
485
of leasehold property
764
Specifications for stone-ware drain
Sale by auction, conditions of sale
pipes.
473
of goods
764
Spirit level
299
·
Sale by auction, agreement
764
Springs and artesian wells
467
Sales of timber
Sawyers' work
Scorching soils
958
of water intercepted
984
566 Spring ploughing .
919 Square root, extraction of
899
9
Screw cock and hydrants
480
Stables.
925
•
Seams of coal
995
Staffordshire, agricultural custom of 628
Seasons of watering
974
Stamp duties
809
Section, working
·
361
Standing orders
339
Security the base of farming
866
Sterile clays
912
Seeded crops.
908
Stipulations of a lease
886
Semi-circular protractor
320
Stone
402
Sets of thorns laid on turf
951
imposts
406
•
Setting out centre line of railway
350
-jetties
971
curves
351
Stonemasons' work
566
tables for.
Setting out slopes.
362
specimen field
book .
374
360 Stone-ware drain pipes, specification
for
Stone-ware drain pipes, quality of .
tender for
473
473
475
•
Setting out slopes, tables for
•
375
Stones for filling trenches
976
widths of railways,
how used
979
•
canals, &c.
Settlements made by the lease
362
Storage reservoir
464
879 Straight courses of water
969
Sewerage of towns
446
Stretch of primogeniture
860
drainage, and water sup-
String courses and coping
406
ply of towns
440
Subterranean survey of the me-
Sewers
451
•
tropolis
454
cleansing of
454 Subtraction of vulgar fractions
5
form of
453
proof of
2
Sewer gratings
460
Succession in a farm lease
895
Short tenure for rich lands
879
Suffolk, agricultural custom of
628
Shropshire, agricultural custom of
628
Sunk fences
948
•
Simple principles of embanking
973
Sun's declination, tables of
171
Single cottages useful
1055
the use of the ta-
Size of drains
450-452-456
bles of
38
farms various
941
Superfices, mensuration of
194
water mains and pipes
466 Superficial or flat measure, tables of
528
3 V
1082
INDEX.
PAGE
PAGE
Supply of water
461 Tables of logarithms and numbers.
41
Support of buildings
886
logarithms, use of.
15
Surplus earth
481
logarithmic sines, tan-
Surrey, agricultural custom of
628
gents, &c. .
68
Surveying, colonial
424
Tables of logarithmic sines, tan-
land
257
gents, &c., the use of
19
parishes and estates
258
Tables of Longitudes
140
railway
338
the use of
29
traverse
280
longitude and time
142
trigonometrical
271
the
Surveyorship of roads
945
use of
32
•
Surveys and maps for sanitary pur-
Tables of Meridional parts
132
poses.
447
the use of
26
Sussex, agricultural custom of
630
moon's parallax
141
Swedish turnips
905
the use of
30
•
Synopsis of second edition of Ryde's
natural sines and cosines
787
hydraulic tables
443
parallax in altitude of the
sun and planets.
143
Tables of parallax in altitude of the
T.
sun and planets, the use of
Tables of refraction of the sun and
32
Tables for computing areas
measuring hay ricks
valuing hay ricks
setting out curves
setting out slopes
330
•
stars.
144
638
Tables of refraction of the sun and
645
•
stars, the use of
33
360
375
Tables of relative gradients
solid measure
379
495
•
Tables, hydraulic, synopsis of 2nd
superficial or flat measure
528
edition of
443
the sun's declination
171
Tables, hydraulic, specimen of
mathematical, use of.
444
trigonometrical equivalents
162
18
trigonometrical formulæ
of augmentation of the
moon's semidiameter.
142
for the solution of quadratics and
cubics
167
Tables of augmentation of the
moon's semidiameter, the use of
Tables of common and hyperbolic
logarithms
Tables of trigonometrical expres-
31
sions.
165
Tables of unequalsided timber
516
161
Tables of common and hyperbolic
logarithms, the use of
useful numbers, with
their logarithms
169
Tables of correction of the moon's
altitude
Tables of correction of the moon's
altitude, the use of
Tables of curvature of the earth
and refraction
Tables of curvature of the earth
35 Tables showing the amount of fine
to be paid for renewing any num-
ber of years lapsed in a lease
originally granted for 10 years
147
161
and refraction, the use of
36
Table of decimals of an acre.
decimals of a pound
226
sterling
Table of differential co-efficients
dip of the horizon.
·
the use
of
Table of expressions for mutiple arcs
formulæ for solving all
the cases of a rectilineal triangle,
of which three parts are known
Table of formulae relating to two
arcs or angles
•
Tables of land measure
logarithms for finding the
horary angle or apparent time
Tables of logarithms for finding the
horary angle or apparent time,
the use of .
807
168
141
33 Tables showing the amount of fine
to be paid for renewing any num-
ber of years lapsed in a lease
originally granted for 20 years
Tables showing the amount of fine
to be paid for renewing any num-
ber of years lapsed in a lease
originally granted for 21 years
Tables showing the amount of fine
to be paid for renewing any num-
ber of years lapsed in a lease
originally granted for 40 years
Tables showing the amount of fine
to be paid for renewing with one
life the lease of an estate origi-
nally granted on three lives
Tables showing the length of tim-
ber of any scantling contained in
a foot cube
29
163
•
166
164
230
158
•
Tables showing the number of
years' purchase upon the net
rental, required to return a given
rate of interest
•
603
604
605
606
607
671
589
34 Tables showing the present worth
INDEX.
-1083
of an estate, lease, or annuity, for
any number of years certain and
in perpetuity, at the several rates
of interest which a purchaser may
thereby make of his money
Tables showing the present worth
of property held on a single life,
as of a person in possession of a
living or benefice, or the holder
of a lease, estate, or annuity, ac-
cording to the Northampton table
of mortality
Tables showing the present worth
of property held on a single life,
as of a person in possession of a
living or benefice, or the holder
of a lease, estate, or annuity, ac-
cording to the Carlisle table of
mortality
Tables showing the present worth
of an estate, annuity, or a lease
held on two joint lives, according
to the Northampton table of mor-
tality
Tables showing the present value
of an estate, annuity, or a lease
held on the longest of two lives,
calculated according to the Nor-
thampton table of mortality
Tables of the present worth of an
estate, annuity, or a lease, held
on the longest of three lives, ac-
cording to the Northampton table
of mortality
Tables showing the present value of
the perpetuity of one year's rent
or fine, payable at every interval
of years
Tables showing the present value of
the reversion to a freehold estate,
or perpetuity, after any given
number of years not exceeding
60
Tables showing the present value
of a reversionary estate in fee
after the life of a person of a
given age, at the several rates of
3, 4, 5, 6, 7, and 8 per cent.
interest
Tables showing the present value
of a reversionary estate in fee
after the longest of two lives of
given ages at the several rates
of 3, 4, 5, and 6 per cent. in-
terest
Tables showing the present value
of a reversionary estate or annuity
on a single life, after any other
single life now in possession, at
the several rates of 3, 4, 5, and 6
per cent. interest
Tables showing the present value
of a reversionary annuity on a
single life, to be nominated at
the death of a person now in
PAGE
590
possession, at the several rates of
3, 4, 5, and 6 per cent. interest.
Tables showing the present value
of £1, payable at the death of a
person of a given age
Tables showing the price per foot
run of scantlings of fir or other
timber
Tables showing the price to be
charged for fir or other timber,
in measured work
594 Temporary fencing
Tapping of springs
Tenants for life and years, dilapi-
dations by .
598 Threshing machinery
Tiles for draining
Tortuous courses of water
•
PAGE
614
615
672
669
394
977
714
Tender for iron pipes and castings
472
pipe laying
railway works
484
•
420
596
stone-ware drain pipes
475
•
Terms of management of a farm
873
Theodolite
290
Thick planting
956
Three periods of the growth of woods
1017
934
981
Tiling
545-548
•
Timber measuring
491
tables, solid measure
495
599
superficial or flat
measure
528
Timber tables, unequalsided timber
Time for outlay by the farmer
516
879
of entry on farms
880
600
planting
956
•
paying rents of farms
884
Tin
990
968
608 Total dilapidations on an estate
Trapping house drains
1005
459
Traverse surveying
280
955
•
338
•
174
271
200
307
391
903
903
tenure
878
Twenty years not too long
883
Two gates to every field of land
952
612
U.
Unequalsided timber, tables of
516
Use of herbage from irrigation
974
lime
901
•
613
the mathematical tables
18
sun's declination
38
Use of the table of common and
hyperbolic logarithms
35
Trees on an acre of ground
Trial levels and exploration
609 Triangles
Trigonometrical surveying
Trigonometry, plane
Troughton's level
Tunnels
Turnip lands
611 Turnips on clay lands
Twenty years the best length of
table for reducing the
1084
INDEX.
for
Use of the table of correction of the
moon's altitude.
•
Use of the table of curvature of the
earth and refraction
Use of the table of dip of the
horizon
Use of the tables of logarithms
PAGE
Valuation of wood lands
33 Value of copper
•
draining
woods
Valuing hay ricks, tables for .
Various modes of protecting banks
results of watering lands
arrangements of executing
PAGE
586
989
986
36
961
645
29
969
15
975
•
finding the horary angle or ap-
parent time
drainage
985
34
Velocity of fluids passing through
Use of the table of logarithmic
pipes
441
sines, tangents, &c.
19
Villages
1015
Use of the table of longitudes
29
Vulgar fractions
3
longitude and
addition and sub-
time
32
traction of.
5
Use of the table of meridional parts
moon's parallax
semidi-
26
30
Vulgar fractions, multiplication and
division of .
Vulgar fractions, reduction of
54
ameter
31
Use of the table of parallax in alti-
tude of the sun and planets
Use of the table of refraction of the
sun and stars
Use of the table of trigonometrical
expressions
32
W.
33 Walls, how useful
949
Warrant of distress
780
37
to peace officers to take
and give possession
786
Warwickshire, agricultural custom
V.
of
630
Waste grounds
1007
Validity of simple agreements
Valuation memoranda to assist the
877 Water-closet, construction of
459
courses
972
memory
616
887
Valuation of a parish, written in
filter.
464
the form prescribed by the Poor
Law Commissioners
flowing through pipes, dis-
656
charge of
442
Valuation of a parish, Field Book
recommended for
Water in motion
453
•
658
in pits
994
Valuation of accommodation land
586
•
mains and pipes, size of
466
bricklayers' work
545
pipes, tender for
472
carpenters' and joiner'
quality of
462
•
work
556
quantity of
464
Valuation of cottages
586
supply
461
estates
577
and drainage, prices
excavators' work
548
of materials for
686
farm homesteads
583
Water supply, drainage, and sew-
farm labour
587
erage of towns
440
glaziers' work
•
575
Water works, rating of.
651
ironmongery
•
573
Ways of digging pits
995
land.
painters' work
paper hanging
parishes
•
plasterers' work
sawyers' work
577
Weeds in hedges
950
1016
Weights and measures, mensura-
575
tion of
192
576 Westmoreland, agricultural custom
647 of
630
572 Width of drains
979
566 Widths of ground required for
slaters' work
550
railways and canals
362
stonemasons' work
569
•
Width of roads
944
tillages and tenant
Wiltshire, agricultural custom of
630
•
right
625
Wings, abutments, and spandrils
406
Valuation of tillages, specimen of
Field Book
Winter ploughing
898
632
Wireworkers' prices
706
Valuation of tillages, specimen of
inventory and valuation
Wooden sleepers
416
636 Wood lands, valuation of
586
INDEX.
1085
Woodreeve
Wood work
•
Woods and minerals
below use
clean cut
Worcestershire, agricultural cus-
PAGE
1052
tom of
Working of clay
•
iron
•
lead
lime
quarries
soils
tin
Working section
•
Y.
PAGE
407
891 Y level
301
958 Years' purchase on net rental, table
1018 of
589
958 Years of purchase in mines
Yorkshire, agricultural custom
1020
630
1002
of
Young plantations
630
1010
991
1011
991 Young plants of trees
954
998
999
904
Z.
990
361 Zinc-workers' prices
703
LONDON:
PRINTED BY G. PHIPPS, RANELAGH STREET, EATON SQUARE.
ERRATA.
Page 224 line 24, for IK 66 read IK 6.
Page 467 line 9, for AA, fig. 194 read A A, fig. 187.
LIST OF PLATES.
2
4
13 +
General Diagrams.
5 Diagram Plan of the Parish of Sunbury.
6
} Diagrams for setting out Slopes.
8 Parliamentary Plan of a proposed Railway.
9 Parliamentary Section of a proposed Railway.
10 Land Plan of a proposed Railway.
11 Working Section of a proposed Railway.
12 General Diagrams.
13)
Plans of House Drainage.
145
Plate.1.
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4
Fig. 5.
D\ P.
E
-B
Fig.6.
Fig. 7.
G
H
I
D
B
E
D
Fig. 8.
Fig.9.
Fig.10.
Z 1 2 7 V MLA

A
Fig.ll.
B
R/S
B
D
a
Fig.12.
A
Fig. 13.
D
Fig.14.
A
C
Fig.15.
$
E
A
F
F
A-
-B
C
G
Fig.16.
G
Fig.17.
H
A
В C
D
B
D
B
Fig.18.
Fig.20.
Fig.19.
D
P
D B
D
Fig.21.
C

D
B
B
Fig.22.
D
G
Fig. 23.
B
E
B
C
C
Fig. 24.
Fig.25.
A
B
E
F
E
D
B
D
C H
b.
Fig.26.
Fig.27.
Fig.28
Fig.29
D
Fig.30.
E
Fig. 31.
Di
B
Fig.32.
B
Fig.33.
R
B
Fig.34.
F

E
C
Р
D
B
B
E
E
Fig.35.
Fig.36.
B
Fig.37.
B
C
Fig.38.
E
Fig.39.
R
Fig.41.
A B
D
D
C
F
D
D
H
B
B
B
E
G
E
H
A
Fig.40.
Fig.42.
Fig.4.3.
Fig.44.
D
Fig.45.
Fig 46.
C
Fig.47.

A
I
D
E K
B
F
B
E
D
G
Bk
F
E
IC
B
A F
B
Fig.48.
F
D
Fig.49.
B
P
E
Fig.50
T
Fig. 51.
1 6 0 2
B
C
D
D
Fig.63.
P
Fig.64.
R
Fig.65.
B
Fig.66
10
Р
D
D
P
E
B C
BA
P
D E
D
D
G
Fig.52.
C
E
B
D
B
B
A
D
E
Fig.53.
Fig.54.
Fig.55.
Fig.56.
Fig.57
Fig.58.
Fig.59
Fig.60.
Fig.61.
Fig.62
t
B

B
T
B
P
P
W K
H
G
G
B
H
B
Fig.67.
Fig.68.
Fig.69.
Fig. 70.
B
C
D
Fig. 72.
Fig. 71.
E-

E
E
F
A
D
F
B
A
-C
a
F
Fig. 73.
E
C
Fig. 74.
A
Fig.75.
Ad
B
D
RC
F
3
Fig.76.
H
B
1
1
B
P
I
H G
B
7
8
와
​E
10
D
1 2
E
G
F
ZA
12
D
C
Fig.77
4
C
D
E
Fig. 78.
F.
7
3
A
R
B
Q
1. IS
.3
3
5
7
B
London, John Weale, Architectural Library:59 High Holborn 1853.
A
Fig. 7.9
B
D
Fig. 80.
M
S
P
F
B
I
E
T
R
N
B
Fig. 81.
F
D

K
B
G
H
D
II.A. Beever. sc.
Plate 2.
A-
B
AR
Fig. 82.
C
di
2
3
Fig. 83.
D
3
2
d I
Fig. 84.
Fig.85.
B
Fig.86.
C
Fig. 87.
D
Fig. 88.
G
C
B
Fig. 89.
Fig.90.
A-6 Å Ä Ä Ë

B
#
2
3
C
3
2
1 B
E
D
B
D
D
A E
B
K
F
A
D
B
A
E
I
A H
G
C DI
D
Fig.91.
E
Fig.101.
D
E F
A B C
D
G
1
2
4 5
7
C
Fig.lll.
P
Fig.92.
Fig.93.
A
B
B
G
C-
G
B
F
C
E
Fig.103.
Fig.94.
C
Fig.95.
-b..
E
D
A
Fig.104.
Fig.106.
A
H
sec
tan
A
rad
B
A
T
Fig.102.
E
M
G
B
Fig.105.
rad
COS
B
see
Crad B
tan
Fig.113.
Fig.112.
B
A
A
A
R
D
F
H
D
« ด
B
C
C E
A
Fig.117.
x
Cz
T
A
Π
Br
Pi
W
R¹
Fig.107.
Fig.96.
C
C
Fig.108.
A
0 1
H
B
E
Fig.115.
Fig.114.
A
Fig.116.
D
B
E
Fig.120.
AAB
E
B
D
F
R2
E
H
E
Bi
Fig.118.
C²
Y
C
D
Fig.97.
Fig.98.
B
Fig.108*
IC2
D
E
I
Fig.99
Fig.109.
b
AB
d
a
Fig.100.
b

Fig.110.
B
Fig.121.
I
P
Fig.122.
C
M
Τ
A F K
0
F
B
172
X
772
D
Fig.119.
13
Xx
Q
T
A
Pl
I
α
e
F
K2
K
I
T
K?
E
K
L
F
K2
B
T¹
E
A
T
T
B F
TE
B
A
E
K
K3
D
14
P2
X
13
D
x
K
Jolm Weale, Architectural Library, 59, fligh Holborn, 1853.
$2
Ꮓ
Y
-B2
E1
P2
h
B
WA.Beerer sc.
Plate 3.

C-
Fig. 125.
t
Fig.126.
B
NIH
1
A
A
Fig. 127.
B
height
a
A
mean
B
460
Fig. 128.
1142
830
422
480
a
Fig. 148.
Fig.149.
Fig.150.
Fig.151.

A
B
A
C
B
G
d
B
E
AC
H
E
G
H
D
D
a
A
Κ
I
Fig.147.
F
A
E
D Hƒ
B
Fig.145.
E
'L
I
Fig. 130.
Kẹ
A
E
\130;
411
960
C
Fig. 129.
750
395
F
A
27
034
G 700
H 300 T100
M
L K B
20
76
E
20
46
G
157
87
Fig. 131.
66
193
198
45
4
A
Edward Ryde Del.
55
134
127
286
144
B
116
21
68
Fig.133
Fig. 135.
B
D
K-
88
138 160
Ꭰ
Fig.132.
46
198
E
Fig. 134.
970
C
A
A
B
Fig.144.
-
Fig. 143.
&
Fig. 136.
d
b
Fig. 137.
a
A
A
38
Bø
Fig. 146.
G
I
H
Fig.142.
D
C
Ꭰ
m
~
A
Fig.154.
11
Fig.140.
A
Line 1.
B
Fig. 138.
a
b
d
1
C
B
A
a
d'
Fig. 139.
h
d
B
Fig.152.
C
Fig.155.
B
23
72
1600-12
36
1636
13
End
|1250
Fig.123.
1136
|1115
1050
3
a
+ &
H
<--230op-->
Fig. 153.
730
19a
19
590P 29 a
1636–12
680
10 | 520
16 430
280
210 12
Q 2
326.5 Theod.
146.5 Bear.
13
1290-11
Line 2.
D
Line 3.
Line 1.
Line 4
E
B
Fig.141.
A
Main line
London John Weale, 1853.
C
8
Fig.124.
K
H
P2
X
51
W. A. Beever. Sc.
Plate 4.

F
Fig 156.
A
B
D
E
G
Fig.165.
E
C
H
Fig.157.
Fig. 158.
F
L
I
K
B
A
B
K
I
Fig.166.
E
D
Fig. 167.
A
C
B
Fig.169.
G
A
B
Fig.168.
B E
Fig.170.
E
C
G
Fig.172.
T
Fig. 174.
F
A
B
ž 1 ź
N
♡
13
20
4
Edward Ryde, del.
ž 3 ž
G
B
D
C
Fio.171.
-
4을
​5
152
ź
6
Ź
7
42
8
호 ​10
11
호 ​12
13
214
201-
7
18 9 10
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Fig.159.
B
A
D
B
C
Fig.160.
B
D
C
A
B
H
Fig.161.
D
A
C
E
F
D
Fig.162.
D
Ex
C
A
Limb
Vernier
South
Magnetic Meridian
-North
C
D
B
Fig.176.
B
D
Fig.175.
5
EDWARD RYDE
44 FEET TO ONE INCH
PIMLICO
5
London, John Weale, 1853 .
B
Fig.163.
L
A
M,
F
44 FEE
O
OFFSET
C
D
B Fig. 177.
Fia.164.
B
A
D
9 Fig. 173.
E
A
C
A
4
3
2
4
2
V
8
IV. A. Beever, $c .
Plate 5

PARISH OF SUNBURY
M
LETON
PARISH
1
a
SHE PP
E
RT
d
ASHFORD
a
PARISH
PARISH
12
FELTHAM
10
CHARLTON
e
1
1
N
PA
t
f
13:
VI
Ꮓ
&
HALLIFORD
且
​S
H
R
SCALE.
5 10 15 20 25 30
60
90 Chains
n
d
Edw Ryde, del .
H
A
N
០៧
གཤེའང་གངས་
m
W
ORTH
W
PARISH
V
u
M
A
L
T
N
London John Weale, 1853.
E
11
P
A R
S
AMPTON
B
H
S
PARISH
t
1385. 1. 24.
943. I. 4.
313.0.25.
REFERENCE.
ARABLE LAND.
MEADOW LAND.
HOMESTEADS WOODS &c.
TOTAL CONTENT 2641.3. 13.
WA. Beever, Sc..
Plate 6..
A
B
A
Fig. 1.
02
1
Dz
a3
3
IC
1
Fig. 2.
B
ал
bi
az
+
B₂
a3
W4
b4
a5
bs
06
16
b
a4
аг
az
al
B
bi
bz
A
B₂
bs
a
1
ag
Fig. 3.
F
0.6
dz
b3
E
Published by John Weale.59 High Holborn London 1853.
ba
V 6
(1.7
a6
as
a4
it 3
Di
b6
b5
124
13
12
a2
01
bi
D
AM.Lowry Se
Plate 7
A
B
0.1
az
by b z
Fig. 4.
i 6
Va
G
bs
a
15
a 3
bz
04
bs
D6
E
(6
as
a3
a2
bó
v3
~
bz
bi
F
a
az
b2
13
رم
at
BA
..
10
ว 06
bo
ат
bi
、
H
100
իգ
as
be
15
x W
d.4
b
az
a2
be
a 1
bi
C
D
A
B
A
B
Published by John Weale. 59 High Holborn. London 1853.
Fig. 5.
a 4
a 3
Fig. 6.
di
(1.2
a 3
F
F
a 4
a

れる
​C
C
D
D
JW. Lowry Sc.
PARISH OF
OF IDS WORTH
3.
RAD
FUR
&
Edr Ride Del.
PARISH OF
6 Miles
CHALTON
4.
RAD. 4 FUR.2 CH.
7
#
R
a
7
7 Mites
RAD.3 FUR,
0
Parish Boundary
P
R
ISH
3
10
RAD.
FUR.
Limit of Deviation
O
F
RAD. 4
7
FUR.
8 Miles
MILE
2
Limit of Deviation
Scale
for General Plan.
20
40
60
3
80, Chains 1 Mile.
J
Scale
for Enlargements.
1
2
3
4
.f 6 7 8 9 10 I 12 13 14 15 16 17 18
19 20
Chains - 4 of a Mile.
London, John Weale, 1853.
BURITO N
4
Tunnels
RAD. SIFUR
9 Miles
1
2
5
0
BURITON
Plate 8.

Ïd. Beever, Sc.
Edward Ryde, Del.
3
4
6
Cross Section. No 1.
1
1
+
1
1
Tin
66
Level
Level of Rails
1 in 101
Greatest Inclination or present road 1 in 66.
Greatest Inclination or road when altered. Level.
t
I IN 100
6 Miles
1
I
273
Public Road to be crossed on the Level.
Level unaltered.
f
1
I
1
I
1
}
I
DATUM LINE 200 feet below the Apex of the Mile Stone (marked 50 miles from London) shown on Plan
2
3
4
5
6
I IN 8 O
7
Public Road to be crossed on the Level.
Level unaltered.
7 Miles
1
2
Horizontal o
Public Road to be crossed on Level.
Level unaltered.
Occupation Road
1
1
!
1
I
!
1
|
1
I
1
1
1
1
34
339
Under Bridge, 20 reet span 16 feet high.
Public Road. Level unaltered.
30
73
I IN 96
الله
3
4
5
6
Seales
20
400
60
It
Vertical 9 10 20 30 40 _00_80__700
London, John Weale, 1853.
200 Feet
?
8 Miles
Cross Section, No 2.
1
I
1 in 30
1 in 55
1 in 30
1
1 in 198
Level of Rails
Greatest Inclination of present road 1 in 55.
Greatest Inclination of road when altered 1 in 30.
381
2
30_Chains = 1 Mile
14
26
3
4
5
10
9
74
TUNNEL 462 Yos
IIN 122
Public Road.
197
Level unaltered.
73
24
Pond
Under Bridge, 20 feet span,
Public Road, Level unaltered.
16 feet high
18
1
1
1
!
Under Bridge, 20 reet span,16 rt. high
Public Road. Level unaltered.
9 Miles
1
2
3
4
5
G
Scales for Cross Sections.
Horizontal e 7
2
3
70
15 Chains
Vertical p 20
20
30 4
50
60 Feet
II.A. Beever, Sc -
1
303
Public Road, to be raised 2 reet, and
crossed on Level. See Cross Section N.“I.
Public Road to be diverted
Public Road to be diverted
14
Occupation Road
1
!
1
1
1
1
|
t
1
1
}
1
Plate 9.
See Cross Section Nº 2.
Turnpike Road to be raised
9reet and passed over Bridge.
30 feet Span, 16 feet High

LAND PLAN.
II
11
11
THE
!!
11
||
!!
}}
Testim
11
11
11
11
11
13
14
15
16
17
18
19
20
21
22
23
24
25
26 27
28
29 1
31.
32
33
34 35
36
12
0.3.33
9 MILES
0.2.13
37-
1
38.
2
39
30
#1
10.0.14
43
47
45
Diversion of Road
46
47.
48
11
0
49
9
7
8
1
30
30
3
0.1.13
52
53
54 55 56 57
58
1
59
0 2
14
61
6
29
62
63
64
65 66
5
0.1.11
67 68 69 5
71
0234
0.2.31
72
73
7.4 75 76
77
78
3.1.33
479
77
Edward Rrde, del.
London John Weale, 1853.
Plate 10.


A
11
11
11
11
11
11
11
6
81
82
83 -84-
0.0.8
0.0.37
85--
go
87
88
89
7
791
نظام علم
WA.Beever. Sc.
above Datum Line
Formation Level
Heights of
Edward Ryde Civil Engineer & Surveyor.
697 698
699
DATUM LINE
Datum Line
of Ground above
Heights of Surface
· 315.10
Embankment
and Heights of
Depths of Cutting
30.02
344.68
303.10
41.58
344.14
317.10
27.04
345.12
6
701
702
323.60
19.47
343.60
31.9.80
23.80
342.54
.54
323.00
19.54
342.01
341.48
323.60
18.41
324.10
17.38
340.95
323.80
17.15
340.42
322.80
17.62
-343.07
703
704
705
706
707
708
709
71
339.89
17.36
322.20
17.69
339.36
322.00
338.83
319.10
338.30
321.00
337.77
320.90
19. 73
Formation Level
Upper Surface of Rails
17.30
16.87
337.24
320.50
16. 74
336.71
320.30
16 .41
336.18
320.00
16.18
335.65
319.50
16.15
335.12
319.10
16.02
334.59
318.90
334.06
318.50
15. 69
15.56
333.53
317.90
333.00
317.00
332.48
3.16.00
331.96
315.50
331.44
314.80
330.92
313.50 |
330.40
312.00
RATE
329.88
3.11.28
329.36
3.11.50
328.84
| 312.50
328.32
314.02
327.80
315.70
Pond
15.63
16.00
OF
Under Bridge
Foot Way!
Under Bridge
Public Road!
16 .48
16.46
16 .64
327.26
317.00
326.72
317.72
326.18
319.50
17.42
18.40
18.60
17.86
16.34
INCLINATION
325.64
321.10
325.10
322.00
324.56
322.00
324.02
322.80
London, John Weale, 1853.
14.30
12.10
10.26
Under Bridge
Public Road!
9.00
6.68
4.54
3.10
2.56
1.22
IN
/ 22
0.00
322.94
323.94
1.00
322.40
323.90
1.50
323.48
323.48
WORKING
SECTION.
321.86
322.50
0.64
321.32
321.10
0.22
Public Road
320.78
3.19.18
1.60
(Level Crossing)
324.24
318.00
2.24
319.70
317.00
2.70
319.16
316.10
3.06
318.62
315.50
3.12
318.08
3.15.30
2.78
317.54
315.00
2.54
317.00
315.10
1.90
316.46
316.46
0.00
315.92
318.22
2.30
315. 38
320.00
4.62
712
713
714
715
716
717
718
719 9 MILES 721
722
723
724
725
726
727
728
729
7.31
732
733
734
735
736
737
738
739
2
741
742
743
744
745 746
747
748
749
3
751
752 753
754
755
756 757
758
759
4
761
762
763
764
765
766
767
768
769
5
771
772
773
774
775 776
777
778
779
6
781
782
783
784
785
786
787
788
314.84
320.84
6.00
314.30
321.10
6.80
313.76
320.76
7.00
313.22
320.00
6.78
312.68
318.68
6 .00
312.14
316.70
4 56
30. 66
315.26
3.60
3IL. 10
315.70
4.60
310.60
315.90
5.30
310.10
317.10
7.00
309.60
318.60
9.00
309.10
320.50
П. 40
308.60
323.50
14.90
308.10
326.10
18.00
307.60
330.60)
23.00
Over Bridge
307.10
333.10
26.00
Occupation
Road!
306.60
333.60
27.00
306.10
335.10
29.00
305.61
336.61
31.00
305.12
338.12
33.00
304.63
339.23
34.60
304.14
340.64
36.50
303.64
342.00
38.36
303.14
343.14
40.00
302.64
343.62
41.02
302.14
343.14
41.00
301.64
343.40
41.76
301.10
342.90
41.80
300.56
341.10
40.54
300.02
299.48
338.02
38.00
330.0
30.52
298.94
315.00
16.06
300.50
298.40
30.00
WA. Beever, Sc.
789
7
791
12.60
297.86
302.20
if
34
297.32
285.50
Π
11.82
296.78
281.70
15 .08
296.24
281.60
14
64
295.70
281.90
13. 84
Over Bridge
Plate II.




Fia. 173. a.
Fio. 179.
( ་
Fig.180.
!
1
1
1
L
B
A
B
A
Fia. 182.
Fig.183.
Fig.173c.
E
A
F
A
B
Fig. 187.
parents
IMPERMEABLE
D
Porous
b
Fig.173.b.
IMPROVED SYSTEM OF BACK DRAINAGE.
OLD SYSTEM OF HOUSE DRAINAGE.
E
A
F
B
Fig.173k
Fig.181.
Fig. 184. Fig. 185.
Fig. 173.d.
d
00
H
Edward Ride. Del .
A
B
Di
E:
(
e
Fig.186.
Fig. 173.1.
M
SIZ
1
N
B
F
C
Plan
Section
Fig.173.e.
Fig. 189.
to
C
Fig. 188.
Fia. 190.
STREET
Sewer
Fig. 173. m.
PARISH NO. 2.
PARISH ALINE
A
PARISH
PARISH NO.4.
SEWER
NO.3.
Section
PLAN
SECTION
Fig. 192
Fia. 193.
B
Fig. 194.
PLAN
Fig. 173. n.
PARISH
RAILWAY
NO. 6.
PARISH NO. 5.
Plan
Fig.191.
STREE T
C
London, John Weale, 1853.
DR
B
A
A
SECTION
Fig. 195.
Fig. 173. f.
E
RADIUS
A
70
Fig.196.
20
B
C
Fig.173.h.
Centre Stake
·36
18
-X-
-40
12x
Fig.173.i.
Fig. 173.g
F
E
B.
NER
SINE
SINE
D
C
M
RADIUS
Plate.12.







E
F
In
D
d
Α
'M'
B
IA. Beever. Sc .
B
a
m
N
N
Plates
!
1
1
ST
1
1
"
1
1
1
A N
1
}
i
10
1
SEPARATE
12./
11.4
12.0
1
1
1
1
1
DRE
1
1
1
量
​1
1
}
1
1
1
}
DRAINAGE.

06
B.M
11.92
ST
TREET
ST
JOHN
10.3
10.8
1
12.0
44
1
W
S
R
1
1
1
1
1
1
1
!
1
1
1
1
1
1
1
1
1
1
1
1
о
1
1
1
ན
!
1
1
1
1
11.8
A
D
}
1
1
1
1
1
1
1
1
W.S
1
}
:
1
1
1
}
1
NOTE.
W.S. WATER SUPPLY.
S. SINK STONE.
R.S. RAIN SPOUT.
O. CLOSET.
EDWARD RYDE, DEL.
1
1
1
1
1
Sa
1
1
量
​Sa
DS
So
S
HARGING ON THE
ST
JOH
100
11.0
0000
TAN
ココロ
​N S
PL
A CE
YARD
10.5
9.3
10.0
D
D
O
هد
་་་
t
www
The
bo
ST
A
ND R
E
E W
W S
TE RR A C
耳
​O
ច
SCALES.
FEET 10
10
20 30 40 50
100 FEET
Τ
LINKS 100 90 80 70 60 50 40 30 20 10
0
I CHAIN
W. A. BEEVER.SC.
London, John Weale, 1853
Plate 14.
1
1
1
1
1
1
ST
1
1
1
t
1
1
ANDR
1
1
1
E
W
1
1-
1
1
S
1
IMPROVED BACK
DRAINAGE.

12.2
II.4 ST
JOHN S
10.8
S
12.1
12.0
1
ROAD
1
1
1
1
1
1
1
12.0
W.S
1
1
1
1
1
1
NOTE.
W.S. WATER SUPPLY.
S. SINK STONE.
R.S. RAIN SPOUT.
O. CLOSET.
EDWARD RYDE, DEL.
1
薯
​1
11.8
1
1
1
#
R.S
R.S
OS
W.S
10.3
TB.M RE E T
11.92
ST
JO
H
NS PLACE
10.5
9.3
10.0
1602
Lolos
미
​미
​000
11.10
TAN
Y
ARD
R.S
R.SI
R.S
R.S
R.S
R.S
R.S
R.S
DR.S R.Sh
R.S
120 123) 124 125 124|126|125 12 3|1727120
12.5
ST
000
ANDREWS TERRACE
R
SCALES.
FEET 10
0
10 20 30 40 50
LINKS 100 90 80 70 60 50 40 30 20 10 0
London, John Weale, 1853.
V
E
R
100 FEET
I CHAIN
W. A. BEEVER.SC.
NEW LIST
LIST OF WORKS
RECENTLY PUBLISHED,
OR IN PREPARATION FOR PUBLICATION IN 1853,
BY JOHN WEALE, 59, HIGH HOLBORN, LONDON.
GREAT EXHIBITION BUILDING.
The BUILDING erected in HYDE PARK for the GREAT EXHIBITION
of the WORKS of INDUSTRY of ALL NATIONS, 1851:
Illustrated by 28 large folding Plates, embracing plans, elevations, sections, and details, laid
down to a large scale from the working drawings of the Contractors, Messrs. Fox, HENDER-
SON, and Co., by CHARLES DOWNES, Architect; with a scientific description by CHARLES
COWPER, C. E.
In 4 Parts, royal quarto, now complete, price £1. 10s., or in cloth boards, lettered, price £1. 11s. 6d.
***This work has every measured detail so thoroughly made out as to enable the Engineer or Architect to erect
a construction of a similar nature, either more or less extensive.
The following is a List of the Subjects and Plates:
CONTENTS.
Origin of the Great Exhibition build- Main gutters and rain-water connec- | Louvres.
ing.
General description of the building.
Columns.
Girders and trusses.
Wooden trusses.
Cast-iron girders.
Glass roof.
Wrought-iron trusses.
Plan of ground floor.
Plan of galleries.
Plan above galleries.
South elevation.
East elevation.
Transverse section.
Longitudinal section.
Details of columns.
Details of vertical diagonal bracing.
Wood trusses and cast-iron girders.
Wrought-iron trusses under roof.
tions.
Galleries.
Staircases.
Gallery railing.
Transept.
Lead flats.
Outer walls, or sides of building.
Ends of transept.
LIST OF PLATES.
Glass roof and Paxton gutters.
Main gutters.
Details of gallery, and ornamental
bands on columns.
Plans and section of staircases.
Details of staircases.
Ditto, and gallery railing.
Details of transept roof.
Details of lead flats.
Setting out the building and fixing
the columns.
Proving girders and trusses.
Hoisting girders and trusses.
Hoisting transept ribs.
Manufacture of the sash-bars.
Miscellaneous details.
Paxton's latest improvements in roofs.
Outer walls, or sides of building.
Details of ditto.
Details of panels and joint-plates at
ends of building.
External elevation of semicircular
head of transept end.
Internal elevation of ditto.
Details of ditto, and pedestals at south
entrance.
Wrought-iron trusses under transept Details of machinery for moving
roof and lead flat.
In octavo, cloth boards, price 9s.
louvres.
HYDRAULIC FORMULE, CO-EFFICIENTS, AND TABLES,
For finding the Discharge of Water from Orifices, Notches, Weirs, Short Tubes, Diaphragms,
Mouth-pieces, Pipes, Drains, Streams, and Rivers.
BY JOHN NEVILLE,
ARCHITECT AND C. E., MEMBER ROYAL IRISH ACADEMY, MEMBER INST. C. E. IRELAND, MEMBER GEOLOGICAL
SOC. IRELAND, COUNTY SURVEYOR OF LOUTH, AND OF THE COUNTY OF THE TOWN OF DROGHEDA.
This work contains above 150 different hydraulic formulæ (the Continental ones reduced to
English measures), and the most extensive and accurate Tables yet published for finding the
mean velocity of discharge from triangular, quadrilateral, and circular orifices, pipes, and rivers;
with experimental results and co-efficients;-effects of friction; of the velocity of approach; and
of curves, bends, contractions, and expansions;—the best form of channel;—THE DRAINAGE
effects of long and shorT WEIRS, AND WEIR-BASINS;-extent of back-water from weirs ;
contracted channels;-catchment basins;-hydrostatic and hydraulic pressure;-water-power,
&c. &c. &c.
2
JOHN WEALE'S
SIR JOHN RENNIE'S WORK
ON
THE THEORY, FORMATION, AND CONSTRUCTION OF BRITISH
AND FOREIGN HARBOURS. 2 V
Copious explanatory text, illustrated by numerous examples, in 2 Parts, at 128. cach,

in-half-moroc007 price 312. 123.
Vol
Vols. very neat
The history of the most ancient maritime nations affords conclusive evidence of the
importance which they attached to the construction of secure and extensive Harbours, as
indispensably necessary to the extension of commerce and navigation, and to the successful
establishment of colonies in distant parts of the globe.
To this important subject, and more especially with reference to the vast extension of our
commerce with foreign nations, the attention of the British Government has of late years been
worthily directed; and as this may be reasonably expected to enhance the value of any
information which may add to our existing stock of knowledge in a department of Civil
Engineering as yet but imperfectly understood, its contribution at the present time may become
generally useful to the Engineering Profession.
The Plates are executed by the best mechanical Engravers; the Views finely engraved under the direction of
Mr. Pye: all the Engineering Plates have dimensions, with every explanatory detail for professional use.
The following is a list of the Subjects engraved :
MOLE, HARBOUR, and BREAKWATER of CHERBOURG,
with details. 5 plates.
Views of the ROYAL DOCKYARD at SHEERNESS. 4
plates.
HARBOUR and Town of SHEERNESS, store-houses, &c.
2 plates.
Graving and other docks, with details, pumping engines,
and machinery, at SHEERNESS.
14 plates.
CHATHAM DOCKYARD and the River Medway.
Proposed NORTHFLEET DOCKS.
PORTSMOUTH DOCKYARD and HARBOUR. 2 plates.
WOOLWICH and DEPTFORD DOCKYAards.
General view of PLYMOUTH and DEVONPORT.
Chart of PLYMOUTH SOUND.
DEVONPORT and KEYHAM DOCKYARds.
DEVONPORT and PEMBROKE DOCKYARDS.
View and plans of the VICTUALLING ESTABLISHMENTS
at PLYMOUTH. 2 plates.
RAMSGATE HARBOUR, plans and sections, lock-gates,
slips, engine-house, and workshops. 6 plates.
DOVER HARBOUR at various periods, and Harbour of
Refuge. 4 plates.
NEWHAVEN, RYE, and SHOREHAM HARBOURs.
HULL DOCKS and HARBOUR,
BRIDLINGTON HARBOUr.
SCARBOROUGH HARBOUR. 2 plates.
HARTLEPOOL BAY, HARBOUR, DOCKS, and Lock-
GATES. 16 plates.
CORK HARBOUR and MILFORD HAVEN.
SUNDERLAND HARBOUR, and driving piles and dredg-
ing. 3 plates.
Mouth of the RIVER TYNE.
LEITH DOCKS, harbour, pier, Martello tower, and ware-
houses. 4 plates.
BERWICK HARBOUR.
BELL ROCK LIGHTHOUSE.
TOWN and HARBOUR of PETERHEAD, and proposed
harbour of Fraserburgh.
GREAT GRIMSBY DOCKS and Wharfs.
BAY of ARDROSSAN, proposed docks on the Broomie-
law, and GREENOCK HARBour.
PORT PATRICK HARBOur.
DONAGHADEE HARBOUR.
TOWN and HARBOUR of BELFAST.
CARRICKFERGUS HARBOUR.
DUBLIN BAy.
DOUGLAS HARBOUR, Isle of Man.
KINGSTOWN HARBOUR.
HOWTH HArbour.
HOLYHEAD HARBOUR.
ABERDEEN.
HOLYHEAD and PORTLand.
HARBOURS of the DEE and MERSEY.
LIVERPOOL.
WHITEHAVEN.
DELAWARE.
Ponta-Delgarda.
YARMOUTH, HARWICH, and Lowestoft.
VENICE.
3 plates.
ANCONA, TARENTUM, ANTIUM, BRINDISI, and Malaga.
NAPLES.
MESSINA and SYRACUSE.
PORT PEIRæus.
EGINA, GUMISHLA, STANCHIO, and BOURDRoon.
TUNIS, SIDON, and TYRE.
PALERMO and GIRGENTI.
GENOA and CIVITA VECCHIA.
CALAIS and DUNKIRK.
BREST.
CARLSCRONA and COPENHAGEN.
CADIZ.
TOULON and MARSEILLes.
CORUNNA and FERROL.
HAVRE and DIEPPE.
CARTAGENA and CETTE.
ALGIERS.
CRONSTADT.
DUNDEE, &c. &c.
NEW LIST OF WORKS.
3
TREDGOLD ON THE STEAM ENGINE.
Published in 74 Parts, price 2s. 6d. each, in 4to, illustrated by very numerous engravings and wood-cuts, a new and
much extended edition, now complete in 3 vols. bound in 4, in elegant half-morocco, price Nine Guineas and a
Half.
THE STEAM ENGINE,
IN ITS PROGRESSIVE AND PRESENT STATE OF IMPROVEMENT;
Practically and amply elucidating, in every detail, its modifications and applications, its duties
and consumption of fuel, with an investigation of its principles and the proportions of its parts
for efficiency and strength; including examples of British and American recently constructed
engines, with details, drawn to a large scale.
The well-known and highly appreciated Treatise, Mr. TREDGOLD's national Work on the
STEAM ENGINE, founded on scientific principles and compiled from the practice of the best
makers—showing also easy rules for construction, and for the calculation of its power in all
cases—has commanded a most extensive sale in the several English editions, and in Translations
on the Continent. These editions being now out of print, the proprietor has been induced to
enlarge and extend the present edition by practical examples of all kinds, with the most recent
improvements in the construction and practical operations of the steam engine both at home and
abroad.
The work is divided into the sections named below, either of which may be purchased
separately: working engineers will be thus enabled to select those portions which more
especially apply to the objects upon which they may be respectively employed.
Several scientific men, extensively and practically employed, have contributed original and
really practical papers of the utmost utility; by which the value of this extended edition is much
increased. A copious INDEX for reference is added.
DIVISION A. Locomotive Engines, 41 plates and 55 wood-cuts, complete, making Vol. I. In half-morocco
binding, price £2. 12s. 6d.
DIVISION B. Marine Engines, British and American, numerous plates and wood-cuts, making Vol. II.; bound in
2 vols. half-morocco, price £3. 13s. 6d.
DIVISION C to G. making Vol. III., and completing the work, comprising Stationary Engines, Pumping Engines,
Engines for Mills, and several examples of Boilers employed in the British Steam Navy, in half-morocco,
price £3. 13s. 6d.
LIST OF PLATES. DIVISION A.-LOCOMOTIVE ENGINES.
Elevation of the 8-wheeled locomotive engine and tender,
the IRON DUKE, on the Great Western Railway.
Longitudinal section of ditto.
Plan, ditto.
Transverse sections, ditto.
Details of ditto: transverse section through working
gear, transverse section and end view of tender; plan
and section of feed-pump; plan and elevation of hand-
pump; details of inside framing, centre axle, driving
axle-box, regulation-valve, centre-beam stay, &c.
Elevation of Crampton's patent locomotive engine and
tender.
Longitudinal section of ditto.
Plan of ditto.
Transverse sections of ditto.
Elevation of the PYRACMON six-wheeled goods' engine
on the Great Western Railway.
Half-plan of the working gear of ditto.
Elevation of a portion of the working gear of ditto.
Diagrams, by J. Sewell, L. E., of resistances per ton of
the train; and portion of engines of the class of the
GREAT BRITAIN locomotive, including tender, with
various loads and at various velocities; also of the
additional resistance in tbs. per ton of the train, when
the engine is loaded, to be added to the resistance per
ton of the engine and tender when unloaded.
Side and front elevation of an express carriage engine,
introduced on the Eastern Counties Railway by James
Samuel, C. E., Resident Engineer.
Longitudinal and cross section of ditto.
Plan of ditto; with plan and section of cylinders, details
and sections, piston full size.
Elevation of the outside-cylinder tank engine made by
Messrs. Sharpe Brothers & Co., of Manchester, for
the Manchester and Birmingham Railway.
Section of cylinder and other parts, and part elevation
of ditto.
Longitudinal section of ditto.
Plan of ditto.
Transverse sections of both ends, with sectional parts.
Mr. Edward Wood's experiments on the several sections
of old and modern valves of locomotive engines,-viz.
fig. 1, stroke commences; fig. 2, steam-port open;
fig. 3, steam-port open; fig. 4, steam-port open; fig. 5,
stroke completed, steam cut off, exhaustion com-
mences; fig. 6, stroke commences; fig. 7, steam-port
full open; fig. 8, steam cut off; fig. 9, exhaustion
commences; fig. 10, steam completed.
Ditto, drawn and engraved to half-size: fig. 1, old valve,
-inch lap; fig. 2, 3-inch lap; fig. 3, 4-inch lap;
fig. 4, 3-inch lap, Gray's patent; fig. 5, 1-inch lap.
Elevation of a six-wheeled locomotive engine and tender,
No. 15, constructed by Messrs. Tayleur, Vulcan,
Foundry, Warrington, for the Caledonian Railway.
Longitudinal section of ditto.
Plan of ditto, engine and tender, with cylindrical part
of boiler removed.
Elevations of fire-box, section of fire-box, section of
smoke-box of ditto.
Elevations and sectional parts of ditto.
Sectional parts, half-plan of working gear, ditto.
Elevation of Messrs. Robert Stephenson and Co.'s six-
wheeled patent locomotive engine and tender.
Longitudinal section of ditto.
JOHN WEALE'S
TREDGOLD ON THE STEAM ENGINE.
Plan and details of Stephenson's patent engine.
Section of fire-box, section of smoke-box, front and back
elevations of the same.
Plan of a six-wheeled engine on the Birmingham and
Shrewsbury Railway, constructed by Messrs. Bury,
Curtis, and Kennedy, Liverpool.
Longitudinal section of ditto.
Sectional elevation of the smoke-box of ditto.
Sectional elevation of the fire-box of ditto.
Elevation of the locomotive engine and tender, PLEWS,
adapted for high speeds, constructed by Messrs. R. &
W. Hawthorn, of Newcastle-upon-Tyne, for the York,
Newcastle, and Berwick Railway Company.
Longitudinal section of ditto. This section is through
the fire-box, boiler, and smoke-box, showing the
tubes, safety-valve, whistles, steam and blast pipes, &c.
Plan of ditto.
Plan of the working gear, details, &c. &c.
Forty-one plates and fifty-five wood engravings.
DIVISION B.-MARINE ENGINES, &c.
Two plates, comprising figures 1, 2, and 3, Properties
of Steam.
Plan of H. M. screw steam frigate DAUNTLESS, con-
structed by Robert Napier, Esq.
Longitudinal elevation and transverse section of ditto.
Longitudinal section at A B on plan, longitudinal section
at CD on plan of ditto.
Engines of H. M. steam ship TERRIBLE, constructed by
Messrs. Maudslay, Sons, and Field, on the double-
cylinder principle. Longitudinal sections of engines.
Transverse section and end view of ditto.
Transverse section through boilers of ditto.
Plan of engines, showing also bunkers, paddles, &c.
Oscillating engines of the Peninsular and Oriental Com-
pany's steam vessel ARIEL, constructed by John Penn
and Sons. Longitudinal section.
Section at engines of ditto.
Section at boiler of ditto.
Plan at boiler of ditto.
Section at air-pump-section at cylinder of ditto.
Annular cylinder engines of the iron steam vessels PRIN-
CESS MARY and PRINCESS MAUDE, constructed by
Maudslay, Sons, and Field. Longitudinal section.
Transverse section at engines of ditto.
Section at boilers of ditto.
Plan of engines of ditto, showing bunkers, paddles, &c.
Plan of engines of H. M. steam vessel SIMOOM, Con-
structed by James Watt & Co., of London and Soho.
Longitudinal section of ditto.
Cross section of ditto.
Engine of the RED ROVER, side view and plan.
Longitudinal section of ditto.
Cross sections of ditto.
Sheer draught and plans of vessel.
Plan of the engine of H. M. steam frigate PHŒNIX.
Longitudinal section of engine of ditto.
Cross section of ditto.
Engine of the RUBY steam vessel, elevation and plan.
Sheer draught and plan of vessel.
Plan of engine of the WILBERFORCE, Hull and London
packet.
Cross section of ditto and vessel.
Longitudinal section of engines of ditto.
Elevation of engines of ditto.
Engines of the BERENICE, Hon. E. I. Co.'s steam vessel.
Section of ditto.
Sheer draught and plan, stern view, and body plan of
vessel.
View of the BERENICE, whilst at sea.
Boilers of H. M. ships HERMES, SPITFIRE, and FIREFLY.
Kingston's valves, as fitted on board sea-going vessels
for blow-off injection, and hand-pump sea valves.
Boilers of H. M. steam vessel AFRICAN.
Morgan's paddle-wheels, as fitted in H. M. S. Medea.
Side elevation of ditto.
Plans of upper and lower decks of H. M. S. MEDEA.
Sheer draught and profile of ditto.
Morgan and Seaward's paddle-wheels, comparatively.
Positions of a float of a radiating paddle-wheel in a
vessel in motion, and positions of a float of a verti-
cally acting wheel in a vessel in motion.
Cycloidal paddle-wheels.
Sailing of steamers in five points from courses.
Experimental steaming and sailing of the CALEDONIA,
VANGUARD, ASIA, and MEDea.
Engines of H. M. steam ship MEGÆRA.
Engine of the steam boat NEW WORLD, T. F. Secor &
Co., Engineers, New York. Elevation and section.
Elevations of cylinder and crank ends.
Steam cylinders, plans, and sections.
Details.
Several sections of details.
Details and sections.
Details of parts.
Plans and sections of condenser, bed-plates, air-pump
bucket, &c.
Details and sections, injection valves.
Details, plan and elevation of beams, &c. &c.
Details, sections of parts, boilers, &c. of the steam boat
NEW WORLD.
Sections, details, and paddles.
Engines of the U. S. mail steamers ОHIо and GEORGIA.
Longitudinal section.
Elevations and cross sections of ditto.
Details of steam-chests, side-pipes, valves, and valve
gear of ditto.
Section of valves, and plan of piston of ditto.
Boilers of ditto, sections of ditto,
Engine of the U. S. steamer WATER-WITCH. Sectional
elevation.
Steam-chests and cylinders of ditto.
Boilers, sections, &c. of ditto.
Boilers of the U. S. steamer PowHATAN.
Front view and sections of ditto.
Elevation of the Pittsburg and Cincinnati American
packet BUCKEYE STATE.
Bow view, stern view.
Plan of the BUCKEYE State.
Model, &c. of ditto, wheel-house frame, cross section at
wheel-house, and body plan.
Plan and side elevation of ditto.
Sheer draught and plan, with the body plan, of the U.S.
steam frigate SARANAC.
Longitudinal section of ditto, cross section.
Engines of the U. S. steamer SUSQUEHANNA.
Elevation of the U. S. PACIFIC steam packet engine.
Plan of ditto.
Boilers of ditto, end views.
Ditto
ditto.
Eighty-five engravings and fifty-one wood-cuts.
NEW LIST OF WORKS.
TREDGOLD ON THE STEAM ENGINE.
DIVISION C. TO G., FORMING VOL. III.
STATIONARY ENGINES, PUMPING
Side elevation of pumping engine, U. S. dock, New York.
End elevation of ditto.
Elevation and section of the pumps, ditto.-2 plates.
Boilers of pumping engines, ditto.
Boilers, Details, &c. of pumping engines, ditto.
Plan of the boilers, ditto.
Isometrical projection of a rectangular boiler.
Plan and two sections of a cylindrical boiler.
Brunton's apparatus for feeding furnace-fires by means
of machinery.
Parts of a high-pressure engine with a 4-passaged cock.
Section of a double-acting condensing engine.
Section of a common atmospheric engine.
On the construction of pistons.
Section of steam pipes and valves.
Apparatus for opening and closing steam passages.
Parallel motions.-2 plates.
Plan and elevation of an atmospheric engine.
Elevation of a single-acting Boulton and Watt engine.
Double-acting engine for raising water.
Double-acting engine for impelling machinery.
Maudslay's portable condensing engine for impelling
machinery.
Indicator for measuring the force of steam in the cylin-
der, and diagrams of forms of vessels.
Section of a steam vessel with its boiler, in two parts—
diagrams showing fire-places-longitudinal section
through boiler and fire-places.
Isometrical projection of a steam-boat engine.
Plan and section of a steam-boat engine.
Ten horse-power engine, constructed by W. Fairbairn
and Co.-4 plates.
Forty-five horse-power engine, constructed by W. Fair-
bairn & Co.-3 plates.
Plan and section of boiler for a 20-horse engine, at the
manufactory of Whitworth & Co., Manchester.
Messrs. Hague's double-acting cylinder, with slides, &c.
Sixty-five-inch cylinder, erected by Maudslay, Sons, and
Field, at the Chelsea Water-works.-5 plates.
Beale's patented rotary engine.
Double-story boilers of H.M.S. DEVASTATION, 400 H. P.
Refrigerator feed and brine pumps.
Feed and brine apparatus, as fitted on board the West
India Royal Mail Company's ships.
Boilers of H. M. steam sloop BASILISK, 400 H.P.
Boilers of the SINGAPORE, 470 H. P., Peninsular and
Oriental Company.
Original double-story boilers of the GREAT Western,
Telescopic chimney, or sliding funnel, of H. M. ship
HYDRA, 220 H. P.
Seaward's patent brine and feed valves.
Boilers of H. M. mail packet UNDINE, (Miller, Raven-
hill, & Co.) 100 H. P.
Cross sections of engines of H. M. mail packet UNDINE.
Longitudinal elevation of ditto.
Brine-pumps as fitted on board H. M. S. Medea, 220
H. P. (Maudslay, Sons, and Field.)
Boilers of H. M. S. HYDRA, 220 H. P.
1
ENGINES, MARINE BOILERS, &c.
5
Plan of the four boilers, with the supplementary steam-
chests and shut-off valves, of the AVENGER.
Boilers of H. M. steam ship NIGER, 400 H. P., fitted by
Maudslay, Sons, and Field.
Experimental boiler, Woolwich Yard. [Sons, and Field.)
Boilers of H. M. S. TERRIBLE, 800 H. P. (Maudslay,
Boilers of the MINX and TEASER, 100 H.P. (trans-
ferred to WASp.)
Boilers of the SAMSON, 450 H. P.
Daniel's pyrometer, full size.
[and Field.)
Boilers of the Desperate, 400 H. P. (Maudslay, Sons,
Boilers of the NIGER (2nd plate).
Boilers of H. M. S. BASILISK (2nd plate).
Boilers of the UNDINE.
Boilers of the Royal Mail steam ships ASIA and AFRICA,
768 H. P., constructed by R. Napier, Glasgow.
Longitudinal and midship sections of ditto.
Boilers of H.M.S. LA HOGUE, 450 H.P. (Seaward & Co.)
H. M. S. SIDON, 560 H. P. Plan of telescope funnel.
Boilers of H. M. S. BRISK, 250 H. P.
Copper boilers for H. M. S. SANSPAREIL, 350 H. P.
(James Watt & Co.)
American marine boilers, designed and executed by C.
W. Copeland, Esq., of New York, as fitted on board
the American packets.
Midship section of the hull of the steam packet PACI-
Fic, New York and Liverpool line.
Elevation of pumping engines of the New Orleans Water-
works, U. S., arranged and drawn by E. W. Smith,
Engineer, constructed at the Allaire Works, New York.
Elevation of pumps and valves, chests, gearing, &c.
Elevation at steam cylinder end.
General plan of a turbine water-wheel in operation at
Lowell, Massachusets, U. S., by J. B. Francis, C. E.
Elevation of ditto.· Section of ditto.
Plan of the floats and guide curves, ditto.
Large self-acting surfacing and screw-propeller lathe,
by Joseph Whitworth & Co., Manchester.
Longitudinal section, showing arrangement of engine-
room for disc engine applied to screw propeller, and
Bishop's disc engine, by G. & J. Rennie, with details.
Arrangement of engine-room for engines of 60 horse-
power, for driving propellers of H. M. steam vessels
REYNARD and CRUISER, constructed by Messrs.
Rennie. Longitudinal section and engine-room.
Ditto. Transverse section at boilers and at engines.
Very claborate diagrams showing experiments and
results of various paddle-wheels.--8 plates.
Steam flour-mills at Smyrna, constructed by Messrs.
Joyce & Co. Double cylinder pendulous condensing
engine, side elevation.
Side elevation, horizontal plan, ditto.
Longitudinal section.
Horizontal plan of mill-house and boilers.
Transverse section through engine-house and mill.
Boilers, longitudinal and transverse sections, front view.
| Section through mill-stones, elevation of upper part,
section of lower part, plan of hopper, &c.
SUMMARY OF THE ILLUSTRATIONS.
Vol. I.
Locomotive Engines
Plates.
41
Wood-cuts.
55
II.
Marine Engines
85
51
III.
Stationary Engines, Pumping Engines, Engines for
Flour-Mills, Examples of Boilers, &c., &c.
100
58
Total
226
164
6
JOHN WEALE'S
A NEW SURVEY OF LONDON:
FULLY DEVELOPING
Its Antiquity, History, and Architecture-Palatial and Ecclesiastical Structures-Public Build-
ings-and its Social, Literary, and Scientific Institutions-various Galleries of Art-Parks,
Pleasure Gardens, and Conservatories-Trade and Manufactures-Government and Municipal
Arrangements-Railways, Canals, and Water Supply-and its Geography, Geology, and
Natural History. Illustrated by a newly constructed whole sheet Map, and more than Two
Hundred finely executed Engravings, from Original Drawings by the best Artists, of the most
interesting subjects in the Metropolis and its Vicinage.
Third edition, in 2 vols., 910 pages, small 8vo., in cloth boards lettered, price 10s. 6d., or in half-morocco elegant,
148., and in half-calf gilt, 12s.
The following is a list of the Subjects more particularly treated of:
Physical Geography of the Basin of Bridges.
the Thames.
Climate.
Geology.
Geology of the water-courses.
Natural history.
Statistics.
Canals.
Cemeteries.
Club-houses.
Colleges.
Corporation of the City of London.
Customs, dock and port of London.
Spirit of the public journals-'The Royal dockyards.
Times.'
Legislation and government.
Municipal arrangements.
Police.
Postal arrangements.
Banking.
Assurances.
Duties on articles imported into Eng-
land.
Architecture of London-its history,
&c.
Ancient London.
Temple church, St. Saviour's, and
other ancient churches.
Westminster Abbey church.
Westminster Palace.
Westminster Hall.
Sepulchral architecture.
Tudor churches.
Ancient churches.
Modern churches.
Lincoln's Inn hall, and the other inns
of court.
St. Paul's cathedral.
Sir Christopher Wren's churches.
The public buildings of Inigo Jones
and of Sir William Chambers.
Arts, manufactures, and trade.
Tables of the names, actuaries, and
business terms of the several as-
surance companies.
Asylums.
Bank of England.
Baths and wash-houses.
Bazaars and show-rooms.
Model buildings for the poor.
Breweries.
Electric telegraph.
Education.
Engineers' workshops.
Sir Thomas Gresham and the Royal
Exchange.
Galleries of Pictures: those of
Lord Ashburton.
Barbers' Hall.
Bridewell Hospital.
Thomas Baring, Esq.
Society of British Artists.
British Institution.
British Museum.
Duke of Buccleuch.
Chelsea Hospital.
Duke of Devonshire.
G. Tomline, Esq.
Dulwich College.
Earl of Ellesmere.
Foundling Hospital.
School of Design.
Greenwich Hospital.
Vernon Gallery.
Grosvenor Gallery.
Guildhall, City.
Hampton Court Palace.
T. Holford, Esq.
H. T. Hope, Esq.
St. James's Palace.
Kensington Palace.
Marquis of Lansdowne.
National Gallery.
National Institution.
Duke of Northumberland.
Lord Overstone.
Mr. Sheepshanks.
Lord Garvagh.
Galleries of Pictures: those of
Earl de Grey.
Earl Normanton.
Sir Robert Peel.
Queen's Gallery, Buckingham Pa-
lace.
Samuel Rogers, Esq.
Royal Academy.
Society of Arts.
Society of Painters in Water Co-
lours.
Duke of Sutherland.
Lord Ward.
Duke of Wellington.
Whitehall Chapel.
Windsor Castle.
Gas-works and gas-lighting in Lon-
don.
Gardens, conservatories, and parks.
Halls.
Hospitals.
Jews' synagogues and schools.
Learned societies.
Museums.
Public libraries.
Lunatic asylums.
Markets.
Mercantile marine.
Mint.
Music, opera, oratorios, musical socie-
ties, &c.
Observatories.
Panoramas.
Patents for inventions in England.
Public and private buildings.
Prisons.
Railway stations.
Sewers of London.
Thames tunnel.
Union workhouses.
Water supply of London.
Excursions to the vicinity of London.
Castle and stables at Windsor.
Colleges of Cambridge and Oxford.
&c., &c
In one large Volume, with numerous Tables, Engravings, and Cuts, price me tramed,
A TEXT
BOOK
For Agents, Estate Agents, Stewards, and Private Gentlemen, generally, in connection with
Valuing, Surveying, Building, Letting and Leasing, Setting out, Disposing, and particularly
describing all kinds of Property, whether it be Land or Personal Property. Useful to
Assurance Companies
Builders
Landed Proprietors
Stewards
Auctioneers
Appraisers
Agriculturists
Architects
Civil Engineers
Estate Agents
Te-be published in the cours of the Spring of 1953,
Surveyors
Valuers, &c.

NEW LIST OF WORKS.
THE WORK ON
BRIDGES OF STONE, IRON, TIMBER, AND WIRE.
7
In 4 Vols. bound in 3, described in pages 8, 9, 10 of the larger Catalogue of Publications; to which the following
is the Supplement, now completed, entitled
SUPPLEMENT TO THE THEORY, PRACTICE, AND ARCHITECTURE OF
BRIDGES OF STONE, IRON, TIMBER, WIRE, AND SUSPENSION,'
In one large 8vo volume, with explanatory text and 68 Plates, comprising details and measured dimensions,
in Parts as follows:
Part I.
""
II.
""
III.
IV.
68.
68.
68.
10s.
20s.
V. & VI.
Bound in half-morocco, uniform with the larger work, price £2. 108., or in a different pattern at the same price.
LIST OF PLATES.
Cast-iron girder bridge, Ashford, Rye and Hastings
Railway.
Details, ditto.
Elevation and plan of truss of St. Mary's Viaduct,
Cheltenham Railway.
Iron road bridge over the Railway at Chalk Farm.
Mr. Fairbairn's hollow-girder bridge at Blackburn.
Waterford and Limerick Railway truss bridge.
Hollow-girder bridge over the River Medlock.
Railway bridge over lagunes of Venice.
Viaduct at Beangency, Orleans and Tours Railway.
Oblique cast-iron bridge, on the system of M. Polonceau,
over the Canal St. Denis.
Blackwall Extension Railway, Commercial Road bridge.
Ditto, enlarged elevation of outside girders, with
details.
Ditto, details.
Ditto, ditto, and sections.
Ditto, ditto,
ditto.
Richmond and Windsor main line, bridge over the
Thames.
Ditto, details.
Ditto, ditto, and sections.
Orleans and Bordeaux Railway bridge.
Ditto, sections and details.
Rouen and Havre Railway timber bridge.
Ditto, details.
Ditto, ditto, and sections.
Viaduct of the Valley of Malauncey, near Rouen.
Hoop-iron suspension bridge over the Seine at Suresne,
department de la Seine.
Hoop-iron suspension foot bridge at Abainville.
Suspension bridge over the Douro, iron wire suspension
cables.
Ditto, details.
Glasgow and South-Western Railway bridge over the
water of Ayr.
Ditto, sections and details.
Plan of the cities of Ofen and Pesth.
Sections and soundings of the River Danube.
Longitudinal section of framing.
No. 1 coffer-dam
Transverse framing of coffer-dam.
Sections of Nos. 2 and 3 of coffer-dam.
Plan of No. 3 coffer-dam and ice-breakers.
Plan and elevation of the construction of the scaffolding,
and the manner of hoisting the chains.
Line of soundings,-dam longitudinal sections.
Dam sections.
Plan and elevation of the Pesth suspension bridge.
Elevation of Nos. 2 and 3 coffer-dams.
End view of ditto.
Transverse section of No. 2 ditto.
Transverse section of coffer-dam, plan of the 1st course,
and No. 3 pier.
Vertical section of Nos. 2 and 3 piers, showing vertical
bond-stones.
Vertical cross section of ditto.
Front elevation of Nos. 2 and 3 piers.
End elevation of ditto.
Details of chains.
Ditto.
Ditto and plan of nut, bolt, and retaining-links.
Plan and elevation of roller-frames.
Elevation and section of main blocks for raising the
chains.
Ditto, longitudinal section of fixture pier, showing
tunnel for chains.
Plan and elevation of retaining-plates, showing machine
for boring holes for retaining-bars.
Retaining link and bar.
Longitudinal plan and elevation of cast-iron beam with
truss columns.
Longitudinal elevation and section of trussing, &c.
Plan of pier at level of footpath.
Detail of cantilevers for supporting the balconies round
the towers.
Elevation and section of cantilevers.
Detail of key-stone and Hungarian arms.
Front elevation of toll-houses and wing walls.
Longitudinal elevation of toll-house, fixture pier, wing
wall, and pedestal.
Vertical section of retaining-piers.
Section at end of fixture pier, showing chain-holes.
Lamp and pedestal at entrance of bridge.
Lamp and pedestal at end of wing walls.
Separately sold from the above in a volume, price half-bound in morocco £1. 128.
AN ACCOUNT, with illustrations, of the SUSPENSION BRIDGE ACROSS
the RIVER DANUBE,
BY WILLIAM TIERNEY CLARK, C.E., F.R.S.
With Forty Engravings.
8
JOHN WEALE'S
THE AIDE-MÉMOIRE TO THE MILITARY SCIENCES,
Framed from Contributions of Officers of the different Services, and edited by a Committee of
the Corps of Royal Engineers. The work is now completed.
Abattis.
Ammunition.
Anemometer.
Anti-Corrosion.
Sold in 3 vols., or in 6 Parts, as follows:
£. 3. d.
Part I.
A. to D., NEW EDITION
0 14 0
II.
D. to F.
0 16 0
•
III.
F. to M.
0 16 0
IV. M. to P.
•
0 14 0
V.
P. to R.
0 16 0
VI.
R. to Z.
1 0 0
4 16 0
The subjects amply and practically treated of are as follows:
PART A. B. C.
SKETCH OF THE SCIENCE AND ART OF WAR.
Bombardment.
Boom.
Breach.
Bridge, Masonry, Demolition of.
Buffalo.
Artillery.
Attack of Fortresses and Posts.
Appendix-Assault.
Barometer.
Bridge, Field.
Pontoon.
Boat.
Rope.
Boat and Rope.
Cask.
Trestle.
Raft.
Flying, Swing.
Bullock.
Cable, Chain.
Camel.
Hemp.
Camp, Intrenched.
Caponière.
Capstan, Field.
Carriages (Land and Sea Service).
Castrametation.
Chevaux-de-Frize.
Combustion, Spontaneous.
Command.
Barricade.
Barrier.
Battery.
Blindage.
Block.
Blockade, Military.
Blockhouse.
Boat.
Pile and Spar.
Flying, Trail.
Reconstruction of.
Field, Demolition of.
PART D. E. F.
Dam, temporary.
Defence of buildings and villages.
Defensive elements.
Defence of fortresses.
Defensive precautions.
Defence of coasts.
Defilade.
Demolition of works and buildings.
Demolition of artillery.
Depression carriages.
Derrick (sheers, &c.)
Dialling
Disembarkation and embarkation.
Diving dress and apparatus.
Draining.
Electricity:
Lightning conductor.
Electrotype.
Explosion of powder.
Electric telegraph.
Elephant.
Embarkation.
Engineer, military.
civil.
Epaulement.
Eprouvette.
Equipment of Artillery.
Engineer.
PART F. G. H. I. K. L. M.
Compass.
Contouring.
Equipment, Naval.
American.
Musket-ball Cartridge.
Escalade.
Evolutions of infantry.
artillery.
cavalry.
Fascine.
Field sketching.
Fire, vertical.
precautions against.
cart.
Forage, bulk and weight of.
Ford.
Fortification, field.
Fort, permanent.
Fort, field.
Fortress, permanent.
Fraise.
Furnace, shot.
Fuze for mines.
Gabion.
Horse.
Hurdle.
Hut.
Ice.
Forts, detached.
Fortresses, field, or places du moment. Galvanism.
Fortification, permanent.
Geognosy and Geology.
Kyanizing and Burnettizing.
Laboratory.
Grenade.
Levelling
""
Coehorn's system.
Guard-house, defensible.
Loophole.
Bastion do.
Guerite.
Machicoulis.
""
Montalembert's do.
Gun cotton.
""
""
Magazine.
Carnot's do.
Gunner.
"
""
German
do.
""
""
relative value of.
""
Fougass.
Gunnery.
Gunpowder.
Heat,
Mantlet.
Manœuvres of cavalry.
Marine artillery.
horse artillery.
NEW LIST OF WORKS.
9
Meteorology.
Mining, military: Part 1.
AIDE-MÉMOIRE TO THE MILITARY SCIENCES.
Part II.-Practical operations.
III.-Charges of mines.
IV.-Counter or defensive
mines.
v.-Attack and defence of
countermines.
Appendix 1.-Mines for field ser-
vice.
II.-On breaching ex-
periments.
PART M. N. O. P.
Appendix III. -On Ventilation.
Mountain artillery.
Mountain barometer.
Mule for burden.
Musket.
Musketry fire and practice.
Observatory, astronomical: Part 1.
Part II.-Chronometers, &c.
III.-Portable observatories.
Iv.-Astronomical instru-
ments.
Observatory, Magnetical.
PART P. Q. R.
Appendix:-On the books and
forms used.
Ordnance, British.
,
construction of.
Part 1.-Casting of iron ordnance.
11.-Brass do.
III.-Machinery, Woolwich.
Ordnance department.
Oven, field.
, permanent.
Pah.
Palanque.
Palisade.- Parapet.
Palæontology.
Passage of rivers.
Part 1.-Military operations, and
the construction of tem-
porary bridges.
-Permanent bridges.
III.-Ditto.
Pendulum.
Roads:
Part II.-Maintenance of Mac-
adamized roads.
Rocket artillery.
Sanitary precautions :
-Fever as an army disease.
II.-Cholera.
Sap.
Shrapnell shells, or spherical case.
Shot garlands.
Siege operations in India.
-, irregular.
and engineer equipment.
Sod-work.
Staff.
Statistics.
Steam engine.
locomotive:
I. On the consumption of fuel
Penetration of projectiles.
Petard.
Planting trees.
Point-blank.
Pontoon.
Position, military.
retrenched.
Pyrotechny, military.
Quarry.
Quartering of troops.
Railway.
Reconnoitring.
Reports, military.
River and inland navigation.
Prisons, military: discipline and ma- Roads:
nagement.
PART R. S. T. V. W. Z.
II. Resistances to Railway
III.
Trains.
Qualifications of Engine
Drivers and Fire-men.
Iv.-Description of the LORD of
THE ISLES and the LIVER-
POOL locomotive engines.
V. The Locomotive Engine
Boiler.
Stockade.
Street fighting.
Surveying :
Trigonometrical survey.
Ordnance survey of Great Britain
and Ireland.
Swimming.
Tactics of the three arms.
Tambour.
Telegraph, field.
and the evaporation of water.
universal.
1
INDEX, AND LIST OF CONTRIBUTORS.
Part 1.-Tracing and construction.
Tête de pont.
Trous de loup.
Voltaic electricity:
I.-Invention of the electric tele-
graph.
II.-Transmission of electricity to
a distant place.
III.-Patents granted prior to the
year 1838.
-Various telegraphs in use in
England.
The submarine telegraph.
Water meadows, or irrigation:
1.—Historical sketch.
II.-Machines for raising water.
Water supply.
Water-wheels.
Weather.
Wells.
Zig-zag.
THE ENGINEER'S AND CONTRACTOR'S POCKET BOOK,
WITH AN ASTRONOMICAL ALMANACK,
REVISED FOR 1852 1858 In morocco tuck, price 6s.
1854
CONTENTS.
AIR, Air in motion (or wind), and wind-mills.
Alloys for bronze; Miscellaneous alloys and composi-
tions; Table of alloys; Alloys of copper and zinc,
and of copper and tin.
Almanack for 1852 and 1953,
American railroads; steam vessels.
Areas of the segments of a circle.
Armstrong (R.), his experiment on boilers.
Astronomical phenomena.
Ballasting.
Barlow's (Mr.) experiments.
Barrel drains and culverts.
Bell-hanger's prices.
Blowing a blast engine.
Boilers and engines, proportions of; Furnaces and
chimneys; Marine.
Bossut's experiments on the discharge of water by hori-
zontal conduit or conducting pipes.
Brass, weight of a lineal foot of, round and square.
Breen (Hugh), his almanack.
Bricks.
Bridges and viaducts; Bridges of brick and stone; Iron
bridges; Timber bridges.
Burt's (Mr.) agency for the sale of preserved timber.
10
JOHN WEALE'S
THE ENGINEER'S AND CONTRACTOR'S POCKET BOOK.
Cask and malt gauging.
Cast-iron binders or joints; Columns, formulæ of;
Columns or cylinders, Table of diameter of; Hollow
columns, Table of the diameters and thickness of
metal of; Girders, prices of; Stancheons, Table of,
strength of.
Chairs, tables, weights, &c.
Chatburn limestone.
Chimneys, &c., dimensions of.
Circumferences, &c. of circles.
Coal, evaporating power of, and results of coking.
Columns, cast-iron, weight or pressure of, strength of.
Comparative values between the present and former
measures of capacity.
Continuous bearing.
Copper pipes, Table of the weight of, Table of the bore
and weight of cocks for.
Copper, weight of a lineal foot of, round and square.
Cornish pumping engines.
Cotton mill; Cotton press.
Current coin of the principal commercial countries, with
their weight and relative value in British money.
Digging, well-sinking, &c.
Docks, dry, at Greenock.
Draining by steam power.
Dredging machinery.
DWARF, Table of experiments with H. M. screw steam
tender.
Earthwork and embankments, Tables of contents, &c.
Experiments on rectangular bars of malleable iron, by
Mr. Barlow; on angle and T iron bars.
Fairbairn (Wm.); on the expansive action of steam, and
a new construction of expansion valves for condensing
steam engines.
Feet reduced to links and decimals.
Fire-proof flooring.
Flour-mills.
Fluids in motion.
Francis (J. B., of Lowell, Massachusets), his water-wheel.
French measures.
Friction.
Fuel, boilers, furnaces, &c.
Furnaces and boilers.
Galvanized tin iron sheets in London or Liverpool, list
of gauges and weights of.
Gas-tubing composition.
Glynn (Joseph), F.R.S., on turbine water-wheels.
Hawksby (Mr., of Nottingham), his experiments on
pumping water.
Heat, Tables of the effects of.
Hexagon heads and nuts for bolts, proportional sizes
and weights of.
Hick's rule for calculating the strength of shafts.
Hodgkinson's (Eaton) experiments.
Hungerford Bridge.
Hydraulics.
Hydrodynamics.
Hydrostatic press.
Hydrostatics.
Imperial standard measures of Great Britain; Iron.
Indian Navy, ships of war, and other vessels.
Institution of Civil Engineers, List of Members of the,
corrected to March 15, 1852.
Iron balls, weight of cast; bars, angle and T, weight
of; castings; experiments; hoop, weight of 10 lineal
feet; lock gates; roofs; tubes for locomotive and
marine boilers; weights of rolled iron.
Ironmonger's prices.
Just's analysis of Mr. Dixon Robinson's limestone.
Latitudes and longitudes of the principal observatories.
Lead pipes, Table of the weights of,
Leslie (J.), C.E.
Lime, mortar, cements, concrete, &c.
Limestone, analysis of.
Liquids in motion.
Locomotive engines; Table showing the speed of an
engine.
Log for a sea-going steamer, form of.
Machines and tools, prices of.
Mahogany, experiments made on the strength of Hon-
duras.
Mallet's experiments on overshot wheels.
Marine boilers; engines.
Masonry and stone-work.
Massachusets railroads.
Mensuration, epitome of.
Metals, lineal expansion of.
Morin's (Col.) experiments.
Motion; motion of water in rivers.
Nails, weight and length.
Navies-of the United States; Indian Navy; Oriental
and Peninsular Company; British Navy; of Austria;
Denmark; Naples; Spain; France; Germanic Con-
federation; Holland; Portugal; Prussia; Sardinia;
Sweden and Norway; Turkey; Russia; Royal West
India Mail Company's fleet.
New York, State of, railroads.
Numbers, Table of the fourth and fifth power of.
Paddle-wheel steamers.
Pambour (Count de) and Mr. Parkes' experiments on
boilers for the production of steam.
Peacocke's (R. A.) hydraulic experiments.
Pile-driving.
Pitch of wheels.
Table to find the diameter of a wheel
for a given pitch of teeth.
Plastering.
Playfair (Dr. Lyon).
Preserved timber.
Prices for railways; paid by H. M. Office of Works,
smith and founder's work.
Prony's experiments.
Proportions of steam engines and boilers.
Pumping engines; pumping water by steam power.
Rails, chairs, &c., Table of.
Railway, American, statistics; railway and building
contractor's prices; carriages.
Rain, Tables of.
Rammell's (T. W.) plan and estimate for a distributing
apparatus by fixed pipes and hydrants.
Rennie's (Mr. Geo.) experiments; (the late J.) estimate.
Roads, experiments upon carriages travelling on ordinary
roads; influence of the diameter of the wheels;
Morin's experiments on the traction of carriages, and
the destructive effects which they produce upon roads.
Robinson (Dixon), his experiments and material.
Roofs; covering of roofs.
Ropes, Morin's recent experiments on the stiffness of
ropes; tarred ropes; dry white ropes.
Saw-mill.
Screw steamers.
Sewage manures.
Sewers, castings for; their estimates, &c.
Signs and abbreviations used in arithmetic and mathe-
matical expressions.
Slating.
Sleepers, quantity in cubic feet, &c.
Smeaton's experiments on wind-mills.
Smith and founder's prices.
Specific gravity, Table of.
Steam dredging; Navigation; Tables of the elastic
force; Vessels of war, of America; of England; of
India; of several maritime nations.
NEW LIST OF WORKS.
11
THE ENGINEER'S AND CONTRACTOR'S POCKET BOOK.
Steel, weight of round steel.
Stone, per tb., stone, qr., cwt., and ton, &c., Table of
the price.
Stones.
Strength of columns; Materials of construction.
Sugar-mill.
Suspension aqueduct over the Alleghany River; Bridges.
Table of experiments with H. M. screw steam tender
DWARF; of gradients; iron roofs; latent heats;
paddle-wheel steamers of H. M. Service and Post-
Office Service; pressure of the wind moving at given
velocities; prices of galvanized tinned iron tube;
specific heats; the cohesive power of bodies; columns,
posts, &c., of timber and iron; the comparative
strength, size, weight, and price of iron-wire rope
(A. Smith's), hempen rope, and iron chain; cor-
responding velocities with heads of water as high as
50 ft., in feet and decimals; dimensions of the prin-
cipal parts of marine engines; effects of heat on
different metals; elastic force of steam; expansion
and density of water; expansion of solids by in-
creasing the temperature; expansion of water by
heat; heights corresponding to different velocities, in
French metres; lineal expansion of metals; motion
of water, and quantities discharged by pipes of
different diameters; power of metals, &c.; pressure,
&c., of wind-mill sails; principal dimensions of 28
merchant steamers with screw propellers; of steamers
with paddle-wheels; progressive dilatation of metals
by heat, &c.; proportion of real to theoretical discharge
through thin-lipped orifices; quantities of water, in
cubic feet, discharged over a weir per minute, &c.;
quantity of water discharged per minute; relative
weight and strength of ropes and chains; results of
experiments on the friction of unctuous surfaces;
scantlings of posts of oak; size and weight of iron
laths; weight in ths. required to crush 14-in. cubes
of stone, and other bodies; weight of a lineal foot of
cast-iron pipes, in tbs.; weight of a lineal foot of flat
bar iron, in lbs.; weight of a lineal foot of square
and round bar iron; weight of a superficial foot of
various metals, in tbs.; weight of modules of elasticity
of various metals; velocities of paddle-wheels of dif-
ferent diameters, in feet per minute, and British
statute miles per hour; showing the dimensions, cost,
and price per cubic yard, of ten of the principal
bridges or viaducts built for railways, and also the
height of the boiling point at different heights;-to
find the diameter of a wheel for a given pitch of
teeth.
Tables of squares, cubes, square and cube roots.
Teeth of wheels.
Temperature, of the relative indications of, by different
thermometers.
Thermometers, Table of comparison of different.
Timber for carpentry and joinery purposes; Table of
the properties of different kinds of.
Tin plates, Table of the weight of.
Tools and machines, prices of.
Traction, Morin's experiments on.
Tredgold's Rules for Hydraulics, from Eytelwein's
Equation.
Turbines, Report on, by Joseph Glynn and others.
Values of different materials.
Water-wheels.
Watson's (H. H.) analysis of limestone from the quar-
ries at Chatburn.
Weight of angle and T iron bars; of woods.
Weights and measures.
West India Royal Mail Company.
Whitelaw's experiments on turbine water-wheels.
White's (of Cowes) experiments on Honduras mahogany.
Wicksteed's (Thos.) experiments on the evaporating
power of different kinds of coal.
Wind-mills, of air, air in motion, &c.
Woods.
Wrought iron, prices.
Zinc as a material in house-building.
In One Volume 8vo, extra cloth, bound, price 9s.
THE STUDENT'S GUIDE TO THE PRACTICE OF DESIGNING,
MEASURING, AND VALUING ARTIFICERS' WORKS;
Containing Directions for taking Dimensions, abstracting the same, and bringing the Quantities
into Bill; with Tables of Constants, and copious memoranda for the Valuation of Labour and
Materials in the respective trades of Bricklayer and Slater, Carpenter and Joiner, Sawyer,
Stonemason, Plasterer, Smith and Ironmonger, Plumber, Painter and Glazier, Paper-hanger.
Thirty-eight Plates and Wood-cuts.
The Measuring, &c., edited by Edward Dobson, Architect and Surveyor. Second Edition,
with the additions on Design by E. LACY GARBETT, Architect.
CONTENTS.
PRELIMINARY OBSERVATIONS ON DESIGNING ARTI-
FICERS' WORKS.
Preliminary Observations on Measurement, Valuation,
&c.- On measuring-On rotation therein
therein-On
abstracting quantities-On valuation-On the use
of constants of labour.
BRICKLAYER AND SLATER.
DESIGN OF BRICKWORK-technical terms, &c.
Foundations-Arches, inverted and erect-Window
and other aperture heads-Window jambs-Plates
and internal cornices-String-courses-External
cornices-Chimney shafts-On general improve-
ment of brick architecture, especially fenestration.
MEASUREMENT.
Of diggers' work-Of brickwork, of facings, &c.
DESIGN OF TILING, and technical terms.
Measurement of Tiling-Example of the mode of
keeping the measuring-book for brickwork.
ABSTRACTING Bricklayers' and Tilers' work.
Example of bill of Bricklayers' and Tilers' work.
VALUATION of Bricklayers' work, Earthwork, Con-
crete, &c.
Table of sizes and weights of various articles-Tables
of the numbers of bricks or tiles in various works
-Valuation of Diggers' and Bricklayers' labour—
Table of Constants for said labour.
12
JOHN WEALE'S
DESIGNING, MEASURING, AND VALUING ARTIFICERS' WORKS.
EXAMPLES OF VALUING.
1. A yard of concrete.-2. A rod of brickwork.-
3. A foot of facing.-4. A yard of paving.-5. A
square of tiling.
DESIGN,
SLATING.
MEASUREMENT,
AND
VALUATION OF
CARPENTER AND JOINER.
DESIGN OF CARPENTRY-technical terms, &c.
Brestsummers, an abuse: substitutes for them
Joists, trimmers, trimming-joists-Girders, their
abuse and right use- -Substitutes for girders and
quarter-partitions-Quarter-partitions-Roof-fram-
ing-Great waste in present common modes of roof-
framing-To determine the right mode of subdi-
viding the weight, and the right numbers of bearers
for leaded roofs-The same for other roofs-Prin-
ciple of the truss-Considerations that determine
its right pitch-Internal filling or tracery of trusses
-Collar-beam trusses-Connection of the parts of
trusses-Variations on the truss; right limits
thereto To avoid fallacious trussing and roof-
framing-Delorme's roofing; its economy on cir-
cular plans-Useful property of regular polygonal
plans-On combinations of roofing, hips, and valleys
On gutters, their use and abuse-Mansarde or
curb-roofs.
DESIGN OF JOINERY-technical terms, &c.
Modes of finishing and decorating panel-work-Design
of doors.
MEASUREMENT of Carpenters' and Joiners' work-Ab-
breviations.
Modes of measuring Carpenters' work-Classification
of labour when measured with the timber-Classifi-
cation of labour and nails when measured separately
from the timber.
EXAMPLES OF MEASUREMENT, arch centerings.
Bracketing to sham entablatures, gutters-Sound-
boarding, chimney-grounds, sham plinths - Sham
pilasters, floor-boarding, mouldings - Doorcases,
doors, doorway linings Dado or surbase,
its best construction · Sashes and sash-frames
(examples of measurement) - Shutters, boxings,
and other window fittings - Staircases and their
fittings.
ABSTRACTING Carpenters' and Joiners' work.
Example of Bill of Carpenters' and Joiners' work.
VALUATION of Carpenters' and Joiners' work, Memo-
randa.
Tables of numbers and weights.
TABLES OF CONSTANTS OF LABOUr.
Roofs, naked floors Quarter-partitions, Labour on
fir, per foot cube-Example of the valuation of
deals or battens Constants of labour on deals,
per foot superficial.
CONSTANTS OF LABOUR, and of nails, separately.
On battening, weather boarding-Rough boarding,
deal floors, batten floors.
LABOUR AND NAILS together.
On grounds, skirtings, gutters, doorway-linings-
Doors, framed partitions, mouldings — Window-
fittings- Shutters, sashes and frames, staircases-
Staircase fittings, wall-strings-Dados, sham co-
lumns and pilasters.
VALUATION OF SAWYERS' WORK.
MASON.
DESIGN OF STONEMASONS' WORK.
Dr. Robison on Greek and Gothic Architecture
Great fallacy in the Gothic ornamentation, which
led also to the modern monkey styles ''Resto-
ration' and Preservation.
MEASUREMENT of Stonemason's work.
Example of measuring a spandril step, three methods
Allowance for labour not seen in finished stone
-Abbreviations, Specimen of the measuring-book
-Stairs, Landings, Steps, Coping-String-courses,
Plinths, Window-sills, Curbs-Columns, Entabla-
tures, Blockings-Cornices, Renaissance Niches.
ABSTRACTING AND VALUATION.
Table of weight of stone Table of Constants of
Labour Example of Bill of Masons' work.
PLASTERER.
DESIGN OF PLASTER-WORK in real and mock Archi-
tecture.
Ceilings and their uses Unnecessary disease and
death traced to their misconstruction - Sanitary
requirements for a right ceiling Conditions to
be observed to render domestic ceilings innoxious
- Ditto, for ceilings of public buildings - Bar-
barous shifts necessitated by wrong ceiling —
Technical terms in Plasterers' work.
MEASUREMENT of Plaster-work.
Abbreviations --Abstracting of Plasterers' work
Example of Bill of Plasterers' work.
VALUATION.
Memoranda of quantities of materials - Constants of
Labour.
SMITH AND FOUNDER.
ON THE USE OF METAL-WORK IN ARCHITECTURE.
Iron not rightly to be used much more now than in
the middle ages
Substitutes for the present
extravagant use of iron- Fire-proof (and sanitary)
ceiling and flooring- Fire-proof roof-framing in
brick and iron-Another method, applicable to
hipped roofs - A mode of untrussed roof-framing
in iron only-A principle for iron trussed roofing
on any plan or scale-Another variation thereof
On the decoration of metallic architecture.
MEASUREMENT of Smiths' and Founders' work.
PLUMBER, PAINTER, GLAZIER, &c.
DESIGN, &C. OF LEAD-WOrk.
MEASUREMENT OF PAINT-WORK- Abbreviations.
Specimen of the measuring-book-Abstract of Paint-
workExample of Bill of Paint-work.
VALUATION of Paint-work.
Constants of Labour Measurement and Valuation
of GLAZING Measurement and Valuation of
PAPER-HANGING.
-
APPENDIX ON WARMING.
Modifications of sanitary construction to suit the
English open fire-More economic modes of warming
in public buildings-Ditto, for private ones--Warm-
ing by gas.
NEW LIST OF WORKS.
In 12mo., price 5s. bound and lettered,
13
THE OPERATIVE MECHANIC'S WORKSHOP COMPANION, AND
THE SCIENTIFIC GENTLEMAN'S PRACTICAL ASSISTANT ;
Comprising a great variety of the most useful Rules in Mechanical Science, divested of mathe-
matical complexity; with numerous Tables of Practical Data and Calculated Results, for
facilitating Mechanical and Commercial Transactions.
BY W. TEMPLETON,
AUTHOR OF SEVERAL SCIENTIFIC WORKS.
Third edition, with the addition of Mechanical Tables for the use of Operative Smiths, Mill-
wrights, and Engineers; and practical directions for the Smelting of Metallic Ores.
GEOMETRY.
To erect a perpendicular on a right line.
To erect a perpendicular at the end of a line.
To bisect a given angle.
CONTENTS.
To describe a circle through three given points out of a
right line.
To find the centre of a given circle.
To find the length of any given arc of a circle.
To draw a tangent to a circle.
To draw lines towards the centre of a circle, the centre
being inaccessible.
To describe an arc of a circle.
To describe an ellipse or oval.
To describe an elliptic arch.
To describe a parabola.
To measure an intercepted line.
To obtain the distance of an inaccessible object.
To find the distance between two inaccessible objects.
To design a beam of strongest section.
To find the proper position for the eccentric in a steam
engine.
To determine the proper length of valve levers.
To inscribe any regular polygon.
To construct a square upon a right line.
To form a square equal to a given triangle.
To form a square equal to a given rectangle.
To form a rectangle equal to a given square.
To bisect any given triangle.
To describe a circle in a given triangle.
To form a rectangle in a given triangle.
To make a rectangle equal to a given triangle.
To make a triangle equal to a given quadrilateral.
To form a square equal to a given circle.
To form an octagon from a given square.
To form a square equal to two given squares, or a circle
equal to two given circles.
To draw a line equal to any portion of a circle's circum-
ference.
To draw a spiral with uniform spaces.
To draw a volute for the Ionic column.
To draw a scroll for hand-rails.
To find the angles and lengths of materials for pyramidal
frustums.
To describe the proper form of material by which to form
a cone.
Sector by which to obtain angles.
GEOMETRY APPLIED TO MECHANICS.
To delineate a vee-threaded screw.
To delineate a square-threaded screw.
To determine the proper forms for a pair of bevel wheels.
Proportions for the construction of toothed wheels.
To delineate wheels by orthographic projection.
Delineation of an undershot water-wheel.
DECIMAL ARITHMETIC.
Definitions.-Reduction.
Applied examples.
Definitions of Arithmetical Signs.
British Standard Measures.-British Special Measures.
Decimal Approximations.-Decimal Equivalents.
MENSURATION.
To measure the surface of a square, rectangle, rhom-
boid, &c.
Two sides of a triangle given, to find the third side.
Utility of triangles.
To find the area of a triangle.
Table of Polygons.
Definitions of the circle.-Rules in relation to the circle.
To find the diameter of a circle when any chord and
versed sine are given.
To find the length of any given arc of a circle.
To find the area of the sector of a circle.
To find the area of a circular ring.
To find the area of an ellipse.
To find the area of a parabola.
To find the solidity or capacity of any cubical figure.
To find the convex surface and solidity of a cylinder.
To find the length of any cylindrical helix.
To find the convex surface and solidity of a cone.
To find the solidity or capacity of any frustum of a cone
or pyramid.
To find the solid contents of a wedge.
To find the convex surface and solidity of a sphere
or globe.
To find the convex surface and solidity of the segment
of a globe.
To find the convex surface and solidity of a cylindrical
ring.
To determine the proper length of iron for a ring of
given diameter.
To determine the length of angle iron to form a ring of
given diameter.
To measure the capacity of a locomotive tender tank.
Table of Specific Gravities and Properties of Metals.
Table of Specific Gravities and Properties of Timber.
Table of Specific Gravities of Liquids, Gases, &c.
Weights of various measures of water.
Table of the Weight of Square and Round Bar Iron.
Table of the Weight of Flat Bar Iron.
Table of the Circumferences of Circles, from 1 inch to
20 feet ths of an inch; advancing by an eighth.
Table showing the Weight of a lineal foot of Malleable
Rectangular or Flat Iron, from th of an inch to
3 inches thick; advancing by an eighth, and quarter
of an inch, in breadth.
Table showing the Weight of a lineal foot of Round
Bar Iron, in avoirdupois qrs. tbs. oz., from 1th of an
inch to 12 inches in diameter; advancing by an
eighth of an inch.
Table showing the Weight of a lineal foot of Square
Bar Iron, in avoirdupois qrs. tbs. oz., from th of an
inch to 12 inches; advancing by an eighth.
Table containing the Circumferences for Angled Iron
14
JOHN WEALE'S NEW LIST OF WORKS.
THE OPERATIVE MECHANIC'S WORKSHOP COMPANION.
Table of Inclined Planes.
Hoops, from 6 inches to 6 feet in diameter; ad-
vancing by an eighth of an inch.-Angle outside.
Table containing the Circumferences for Angled Iron
Hoops, from 6 inches to 6 feet in diameter; ad-
vancing by an eighth of an inch.-Angle inside.
Proportional breadths for six-sided nuts.
Table of the Weights of Sheet Iron, Copper, and Brass.
Comparative weights of different bodies.
Table of the Weights of Cast-Iron Pipes.
Weights of leaden pipes.
To find the weights of pipes of various metals.
Weight of a cubic inch of various metals.
Table of the Weights of Cast-Iron Balls.
Table to facilitate the Measure of Timber.
Table of Cubic or Solid Measure.
To measure battens, deals, and planks.
Table of Scantling Timber.
INSTRUMENTAL ARITHMETIC.
Explanation of the slide rule.-Numeration.—To mul-
tiply by the slide rule.-Proportion.-Rule of Three
Inverse.-Square and cube roots.-Measure of squares,
rectangles, &c.-Measure of circles and polygons.
Tables of Gauge-Points for the Slide Rule.
Mensuration of solidity and capacity.-To compute the
power of steam engines. Of steam engine boilers.
COMMERCIAL TABLES.
Tables by which to facilitate the Calculation of British
Money.-Table of Equivalent Prices.
Definitions.
STRENGTH OF MATERIALS.
Table of Tenacities, Resistance to Compression, &c. of
Various Bodies.
Table of Comparative Strength of Ropes and Chains.
Table of Metallic Alloys.
Resistance of bodies to lateral pressure.
Table of Practical Data.
To find the dimensions of a beam of timber to sustain a
given weight.-To determine the absolute strength
of a rectangular beam of timber.
To determine the dimensions of a beam with a given
degree of deflection.
Cast-iron beams of strongest section.
Of wooden beams, trussed.
Absolute strength of cast-iron beams.
Table of Dimensions for Cast-Iron Beams.
To find the weight of a cast-iron beam.
Resistance to flexure by vertical pressure.
To determine the dimensions for a column of timber.
Table by which to determine the Dimensions of Cast-
Iron Columns.
Resistance of bodies to twisting.
Relative strength of metals to resist torsion.
On the Smelting of Metallic Ores.
Table of Squares, Cubes, &c. of Numbers.
Definitions, &c.
MECHANIC POWERS.
Rules. First kind of lever. Second ditto. Third ditto.
Lever on a safety-valve, &c.-Wheel and pinion, or
crane.-Rules, &c.-The pulley, with applications.—
Inclined plane.
Table of Inclinations and Amount of Opposing Re-
sistance.
A. Delineation of Screws.
The wedge. The screw.-The endless screw, or screw
applied to a wheel.
CONTINUOUS CIRCULAR MOTION.
Definitions, &c.-Proportional diameters of wheels to
the number of revolutions.-Of a train of wheels and
pinions.-Diameters or number of teeth in wheels in
proportion to their velocities.-To determine the
proper diameters of wheels to given peculiarities.-
To find the proportional wheels for screw cutting by
a lathe.
Table of Change Wheels for Screw Cutting.
Diameters of small wheels.
Table of the Strength of Wheels of Cast Iron.
Table of the Diameters of Wheels to contain a given
number of Teeth.
FRICTION.
PROPERTIES OF WATER AND AIR.
Effects produced by water in its natural state.
The pressure of fluids.--The hydraulic press.--The
weights of bodies obtained by displacement of fluids.
-The resistance of water to bodies passing through
it.--Of water flowing through orifices.-Discharging
of water by rectangular apertures.-Flowing of water
through pipes.
Table of the Diameters of Pipes for the Discharging of
Water.
Laws of the gravity of water.--Rules relating to water-
wheels.-Turbines, their effects, &c.--Rule to calcu-
late the powers of turbines.-Overshot water wheels,
notice of.
Effects produced by steam.
Table of the Elastic Force of Steam.-Of the latent heat
in steam.-Steam as a motive power.-Temperature
of steam.- Expansive force of steam. Table of
Hyperbolic Logarithms.-Condensation of steam.-
Boiling points of impure water.
Effects produced by air.
Table of the Expansion of Air by Heat.-Table relating
to Pumps.-Oxygen of the atmosphere.-Resistance
of the atmosphere.-Table of Atmospheric Force.-
Effect of wind-mills.
STEAM ENGINE BOILERS.
To determine the amount of heating surface in a boiler.
-Of waggon-shaped boilers.-Of cylindrical boilers.
- Marine boilers. Locomotive boilers. Heating
powers of combustibles.
Observations on the giving an order for a steam engine.
Table of Dimensions for Steam Engine Cylinders.
Units of nominal power.-To estimate the power of an
engine. To determine the velocity for the piston of
a steam engine.
Table of Approximate Velocities for Pistons.
Table for Parallel Motions.
LOGARITHMS.
Table of Logarithms.
Table of Circumferences and Areas of Circles.
Table of Square and Cube Roots of Numbers.
Table of Per-Centage and Discount.
LIST OF PLATES.
B. Illustration to the Drawing of Bevel Wheels.
C.
Orthographic Projection.
D. Applications of Mechanic Powers.
E. and F. Parallel Motions.
G. Elevation and Section of an Overshot Water-Wheel,
constructed by Messrs. Donkin and Co.
Details.
H.
K.
Boilers of the 'Braganza' steam vessel, by Messrs.
Bury, Curtis, and Kennedy.
L. Locomotive Boiler.
SERIES OF
MR. WEALE'S
RUDIMENTARY WORKS
FOR THE USE OF BEGINNERS.
1s.
•
2.
NEW LIST FOR 1853.
1. Rudimentary Chemistry, by Prof. Fownes,
F.R. S., including Agricultural Chemistry,
for the use of Farmers. 4th edition.
Natural Philosophy, by Charles
45. Rudimentary Treatise on Limes, Cements,
Mortars, Concrete, Mastics, &c., by Geo. R.
Burnell, C.E.
•
1s.
46.
the Art of Con-
Tomlinson
1s.
3.
Geology, by Lieut.-Col. Portlock,
F.R.S., &c. 3rd edition
structing and Repairing
by H. Law, C.E.
Common Roads,
1s.
•
4, 5.
6.
1s. 6d.
Mineralogy, by D. Varley, 2 vols. 2s.
Mechanics, by Charles Tomlin-
47, 48, 49.
the Construction
•
38.
son
1s.
50.
•
7.
Electricity, by Sir William Snow
Harris, F. R.S. 3rd edition.
•
•
18.
8, 9, 10.
11, 11*.
12.
1s. 6d.
Magnetism, by the same, 3 vols. 3s. 6d.
History of the Electric Tele-
graph, by E. Highton, C. E., double Part 28.
Pneumatics, by Charles Tomlin-
son.
and Illumination of Lighthouses, by Alan
Stevenson, C.E., 3 vols.
the Law of Con-
tracts for Works and Services, by David
Gibbons, Esq.
51, 52, 53.
54.
1s.
13, 14, 15.-- Civil Engineering, by Henry
Law, C. E., 3 vols. : and 15*. Supplement, 4s. 6d.
Architecture (Orders of), by
W. H. Leeds. 2nd edition.
1s.
Architect
Naval Architec-
ture, Principles of the Science, by J. Peake,
N.A., 3 vols.
•
3s.
Masting, Mast-
making, and Rigging of Ships, by R. Kipping, 16
N.A. (in the press)
55, 56.
•
Navigation: the
Sailor's Sea-Book.-How to keep the log.
and work it off-Latitude and longitude-
Great Circle Sailing-Law of Storms and
Variable Winds; and an Explanation of
Terms used, with coloured illustrations of
Flags, 2 vols.
57, 58.
the Principles of
the Art of Warming and Ventilation, by
Chas. Tomlinson, 2 vols.
16.
17.
Ditto (Styles of), by T. Bury,
1s.
18, 19.
Ditto (Principles of Design in),
by E. L. Garbett, Architect, 2 vols.
28.
20, 21.
Perspective, by G. Pyne, Artist,
2 vols. 3rd edition
28.
22.
Art of Building, by E. Dobson,
C.E.
1s.
59.
23, 24.
Brick - making,
Tile-
R. Armstrong, C.E.
making, &c., by the same, 2 vols.
28.
60, 61.
25, 26.
Masonry and Stone-cut-
ting, by the same, with illustrations of the
preceding, in 16 4to. atlas plates
62.
28.
27, 28.
Painting, or a Grammar
63, 64, 65.
of Colouring, by George Field, Esq.,
2 vols.
28.
29.
Draining Districts and
Lands
1s.
30.
Draining and Sewage of
66.
Towns and Buildings
1s.
31.
Well-sinking and Boring,
67, 68.
by G. R. Burnell, C.E.
1s.
32.
the Use of Instruments,
33.
by J. F. Heather, M.A. 3rd edition.
Constructing Cranes, by
15.
69, 70.
J. Glynn, F.R.S., C.E.
1s.
71.
•
34.
Treatise on the Steam Engine,
by Dr. Lardner
1s.
35.
28.
28.
•
Steam Boilers, by
1s.
Land and Engi-
18.
neering Surveying, by T. Baker, C. E., 2 vols. 2s.
Introductory patches of Rail-
way Details, by R. M. Stephenson, C.E.
Treatise on the Construction of
Agricultural Buildings; on Motive Powers,
and the Machinery of the Steading; and on
Agricultural Field Engines, Machines, and
Implements, 3 vols. (vol. 8 in the press)
on Clay Lands and
Loamy Soils, by Prof. Donaldson, A. E.
on Clock and Watch-
making, and on Church Clocks, by E. B.
Denison, M. A., 2 vols.
-
•
and Practical Treatise on Music,
by C. C. Spencer, 2 vols.
•
Instruction for Playing the
Piano-Forte, by the same
•
38.
1s.
28.
•
28.
•
1s.
72, 73, 74, 75. — Treatise (A Manual of the
Mollusca) on Recent Fossil Shells, by S. P.
Woodward, and illustrations, 4 vols. (vols.
3 & 4 in the press)
on Descriptive Geo-
metry, by J. F. Heather, M.A., 2 vols.
on Economy of Fuel,
particularly with reference to Reverberatory
Furnaces for the Manufacture of Iron and
Steam Boilers.
•
4s.
2$.
1s.
Treatise on Steam as applied
to General Purposes and Locomotive En-
gines, by J. Sewell, C. E., 3 vols.
79**. Atlas of Plates illustrative of the 3 vols.,
in folio, and as a Drawing Book of Loco-
motive Engines, price 7s.
80, 81. Rudimentary Treatise on Marine Engines,
and on the Screw, &c., by R. Murray, C.E.,
2 vols.
•
3s.
28.
40.
Art of Blasting Rocks and Quar-
rying, and on Stone, by Lieut.-Gen. Sir J.
Burgoyne, K.C.B., R.E. 2nd edition
36, 37, 38, 39.- Dictionary of Terms used by
Architects, Builders, Civil and Mechanical
Engineers, Surveyors, Artists, Ship-builders,
&c., 4 vols.
Art of Glass-Staining, by Dr.
1s.
76, 77.
77*.
4s.
•
M. A. Gessert
1s.
•
•
41.
Essay on Painting on Glass, by
78, 79, 79*.
E. O. Fromberg
ls.
42.
Treatise on Cottage Building
18.
•
43.
Tubular and Girder
Bridges, and others, more particularly de-
scribing the Britannia and Conway Bridges,
with Experiments
44.
by E. Dobson, C.E.
1s.
Foundations, &c.,
18.
16
MR. WEALE'S SERIES OF RUDIMENTARY WORKS.

80*, 81*. The Practice of Embanking Lands from
the Sea, treated as a Means of Profitable
Employment of Capital, by John Wiggins,
F. G.S., Land Agent and Surveyor, 2 vols. .
82, 82*. Rudimentary Treatise on the Power of
Water, as applied to drive Flour-Mills, by
Joseph Glynn, F.R.S., C.E.
83.
Haddon, M. A.
82**, 83*.
83**.
Book-Keeping, by James.
and Practical Treatise on
the Manufacture and Distribution of Coal
Gas, by Samuel Hughes, C. E., 2 vols.
Treatise on the Construction
of Locks, by A. C. Hobbs, Mechanician,
with illustrations
MATHEMATICAL SERIES.
28.
28.
18.
•
· 38.
1s.
•
84. Rudimentary and Elementary Treatise on
Arithmetic, the Theory, and numerous Ex-
amples for Practice, and for Self-Examina-
tion, by Prof. J. R. Young
1s. 6d.
1s. 6d.
84*. Key to the above, by Prof. J. R. Young
85. Rudimentary Equational Arithmetic: Ques-
tions of Interest, Annuities, and General
Commerce, by W. Hipsley, Esq.
105. Rudimentary and First Mnemonical Lessons
in Algebra, Geometry, and Trigonometry,
by the Rev. Thomas Penyngton Kirkman,
M.A.
NEW SERIES OF LONDON.'
1-10. LONDON described and illustrated,
10 vols.
NEW
18. 6d.
18. each.
SERIES OF EDUCATIONAL
WORKS.
1, 2. CONSTITUTIONAL HISTORY OF ENGLAND,
2 vols.: vol. ii. in the press
28.
•
3. View of the HISTORY OF GREECE: in the press 18.
4. HISTORY OF ROME: ditto
•
5, 6. A Chronology of Civil and Ecclesiastical
History, Literature, Science, and Art, from
the earliest time to 1850, 2 vols.: ditto
7. Grammar of the English Language, for use in
Schools and for Private Instruction, by
Hyde Clarke, Esq.
8, 8*. Dictionary of the English Language, by
the same, 2 vols.: in the press
9. Grammar of the Greek Language: ditto
10, 11. Dictionary of the Greek and English Lan-
guages, 2 vols.: vol. ii. in the press
English and Greek Lan-
guages: in the press
13. Grammar of the Latin Language: ditto
14, 15. Dictionary of the Latin and English Lan-
guages, 2 vols.: ditto
guages: ditto
18.
2s.
•
1s.
2s.
18.
1s.
86, 87.
Elements of Algebra, for the
use of Schools and Self-Instruction, by
James Haddon, M.A., 2 vols.
28.
28.
•
12.
88, 89.
Principles of Geometry, by
Henry Law, C. E., 2 vols..
1s.
•
2s.
1s.
•
90.
Analytical Gemetry, by James
Hann, Professor
1s.
2s.
91, 92. Treatises on Plane and Spherical irigʊ-
nometry, by the same, 2 vols.
16.
English and Latin Lan-
28.
1s..
•
•
93. Rudimentary Elements and Practice of Men-
suration, by T. Baker, C.E.
17. Grammar of the French Language, by a distin-
1s.
•
guished Linguist: in the press
1s.
•
94, 95.
Treatise on Logarithms, and
Tables for facilitating Astronomical, Nauti-
cal, Trigonometrical, and Logarithmic Cal-
culations, by H. Law, C.E., 2 vols.
18. Dictionary of the French and English Lan-
guages, by the same: ditto
18.
19.
•
28.
96.
and Elementary Treatise on
Popular Astronomy, by the Rev. Robert
Main, M. R. A. S.
English and French Lan-
guages, by the same: ditto
20. Grammar of the Italian Language, by Alfred
1s.
Elwes
1s.
•
1s.
•
•
97.
Principles and Practice of Sta-
tistics and Dynamics, by T. Baker, C.E. 1s.
98,98*.
Elements of Mechanism, and
Practical Construction of Machines, by the
same, 2 vols.
21. Dictionary of the Italian, English, and French
Languages, by the same: in the press
1s.
·
22.
•
English, Italian, and French
Languages in the press
1s.
23.
28.
99, 100. Theory and Practice of Nautical Astro-
nomy and Navigation, by H. W. Jeans,
R. N. C., Portsmouth, 2 vols.
28.
101. Rudimentary Differential Calculus, by W. S.
B. Woolhouse, F. R.A. S.
26.
1s.
•
24. Grammar of the Spanish Language
25. Dictionary of the Spanish and English Lan-
guages: in the press
guages: ditto
French, Italian, and English
Languages: ditto
18.
•
1s.
•
1s.
English and Spanish Lan-
1s.
•
102.
Integral Calculus, by Homer-
sham Cox, M. A.
27. Grammar of the German Language, by G. L.
1s.
Strausz, (Ph. Dr.)
1s.
103.
104.
28. Classical German Reader, from the best Authors 1s.
29, 30, 31. Dictionaries of the English, German,
and French Languages, 3 vols.: in the
press
Collection of Examples of the
Integral Calculus, by Professor James Hann. 1s.
Collection of Examples of the
Differential Calculus, by J. Haddon, M. A. 1s.
SUPPLEMENTARY TO THE SERIES.
•
3s.
DOMESTIC MEDICINE; or complete and comprehensive Instructions for Self-aid by simple and efficient Means for
the Preservation and Restoration of Health; originally written by M. Raspail, and now fully translated-and
adapted to the use of the British public. This work is addressed to the heads of families and also to
professional and working men, who, from sedulous application, are particularly susceptible of morbid
affections. 1s. 6d.

Mr. Weale's General Catalogue, to which this forms a Supplement, may be had gratis on application, or will be
forwarded by post on the receipt of four penny-stamps. The Supplement may also be had by forwarding two
penny stamps.
JOHN WEALE, 59, HIGH HOLBORN.
apf gel


UNIVERSITY OF MICHIGAN
3 9015 06718 4914