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OPINIONS OF THE PRESS. –
“This Essay, by Mr. Blackett, avoids the puerility and
affected philosophy of the common writers of the day. It
openly professes to be an Essay on the Spirit-level, and its
ordinary applications and use, and to this it most strictly
adheres. Hence it is one of the clearest books that we ever
read : and one more useful to the Student or the ordinary ;
ractice of the Surveyor could not have been written. The
nstrument itself, and also the staves and other matters re- ;
quired along with it, are so clearly explained, that nobody
that reads the Essay can fail in understanding them. The A
uses of the Instrument, and the various ways of using it,
together with the best methods of recording the observa- t -
tions and planning them, are given with equal clearness;
nor have we ever seen a book in which the illustrative - |
figures were more accurately and tastefully delineated. -
We feel ourselves constrained to say, that upon a single
subject this is a perfect model, and a model which cannot
be too generally or too closely copied; such being the pro-
perties of the book, we cordially recommend it to all those -
for whose benefit it has been written.”—The Surveyor's, f
Engineer's, and Architect's Journal. .
“Several Years' practical experience in Engineering form -
the ground-work of the Author's literary labours ;
descriptions, rules, elementary and practical examples,
the whole art of Levelling, and the principles upon which
it is founded, make up an Essay which must afford valuable
assistance to the Student, desirous of eminence in the emu-
lative profession of Surveyor or Engineer.”—Literary Ga-
gette.
“We have had much pleasure in reading this work, which
is one of the most useful, practical works that have ever
been published. The necessity of Levelling, and, the re-
quirement of the most extreme nicety on Railroads, we be-
lieve, first brought Mr. B.'s attention to the utility of pub-
lishing a treatise on the subject ; and a very valuable
treatise he has here produced.—Recording levels, keeping
field books, and such-like topics, are well discussed. The
engravings of instruments, also of geometrical figures, plans,
º sections, with the detailed description of the Spirit-
level itself, render this one of the clearest and most inform-
ing works, and also one of the least theoretical, on scientific
subjects, with which we are acquainted. The examples,
and a quantity of information to which we have not time
to refer, add greatly to the importance of the work.”—Tyne
Mercury.
“An Essay on the use of the Spirit-level, seems a valua- *
ble contribution to the scientific library. The tyro will
find a master in this work, while the proficient in his art
will find a valuable companion. The methods are briefly
expounded, and the instructions are easy and readily un-
derstood. It is illustrated with numerous geometrical
figures, plans, and sections.”—Great Northern Advertiser.
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SPIRIT LEVEL.
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ON THE
USE OF THE SPIRIT LEVEL,
AS A PPLIED TO
ENGINEERING AND OTHER PURPOSES
o/”
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&
IBY
gºv .
* OSWALD BLACKETT,
SURVEYOR, &c.
NEWCASTLE UPON TYNE:
PRINTED BY T. AND J. HoDGSON, UNION STREET,
- AND sold By ‘.
E. CHARNLEY, BIGG MARKET ; AND SIMPKIN, MARSHAIPI,
A ND CO., LONDON.
:
1838.
s#º
.:
PREFACE.
lu.
s
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Nº
*
Vo
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t!
Q)
THE great importance of the Art of Levelling, par-
ticularly at the the present day when public en-
terprize is leading to the accomplishment of the
most stupendous undertakings in Railways, and
other important works, will obviate the necessity
of an apology for this attempt to facilitate the
study of one of the most useful branches of sci-
ence. -
There has been little published on this subject,
except detached fragments inconveniently ar-
ranged, and so antiquated, as to be of no utility
to those who seek for practical instruction. Of
these truths every one acquainted with the subject
must be convinced, and that a work systematically
. . . .
" ; ;
. .
.*
-
. .
l
... 3
, sº
arranged was required; I have, therefore, drawn up
the present treatise, which I submit as likely to
be useful to the civil and military Surveyor or
Engineer, and of the greatest advantage to the ju-
nior branches of society who may be designed for
these professions.
iv PREFACE.
The present work comprehends, in addition to
numerous practical examples, proper rules for re-
cording levels; various methods of keeping field
books, and necessary instructions in the several
modes of operation now generally adopted in tak-
ing levels; with such original matter as may lead
to the better elucidation of this important subject,
and in every part of the work I have used such
modes of explanation as I thought would render
the various subjects as plain and concise as pos-
sible.
The first part of this publication contains de-
monstrations of all the principles immediately
subservient to the art of levelling; the work is
also illustrated with carefully executed engrav-
ings of the various instruments used in this art,
with numerous Geometrical Figures, Plans and
Sections. I have also added a detailed description
of the Spirit Level, and the mode of adjusting the
various parts of which it is composed; also the
true form or internal figure of the spirit tube;
I hope therefore that this Essay will be found ac-
ceptable to the practitioner, and useful to the stu-
dent.
It may here be necessary to remark that this
work also embraces a few examples in the sim-
plest form, for measuring inaccessible distances
which may be met with in levelling, such as rivers,
lakes, bogs, &c.
* : *, **E=gssºrºrº , = , . . . "
* ºr ºr º: ,
.” ". . . . . . . .
PREFACE. - º
The information contained in this compendium
is deduced from Geometrical Principles, combined
with several years' practical experience under one
of the first civil Engineers in this kingdom; being
thus arranged, I can with the greater confidence
submit my labours to the candour of the public.
This work has been a considerable time in the
press, in consequence of the author's intention of
publishing with it, Tables for the more readily
finding by inspection the contents of earth-work;
but as this would considerably increase the price
of the work, it has been thought advisablé to pub-
lish them separately.
CONTENTS.
PAGE
Introduction, .......... 0 0 & 0 ° e º e º e º 'º e º 'º e s e º e º e s e e o e º e e s s e e s a e e e a • e l
The Use of the Spirit Level, ... ........ . ................. 4
True Level—Elementary Example, ........................ 6
—--Practical Example,................ ~~~~ 8
Apparent Level—Elementary Example, ~~~~ 10
Reduction of the Apparent Levels, ... 11
•Practical Example, .................... H5
Simple Rules for determining the Depression or Differ-
'ences between the True and Apparent Level, ...... 17
Terrestrial Refraction, .......................................... 20
Description of the Spirit Level with its necessary Ad-
justments, .................... .............................. 23
Graduated Station Staves, &c., ..................... 32 and 105
Simplest form of Spirit Level,.......................... ...... 35
Spirit Tubes, .................... ............................... . 39
Practical Levelling, ... .............. ........... ............... 42
Instructions or Rules for Recording Levels, ........ ..... 43
A new Method of Recording Levels with a Field Book,
being a portion of the Stanhope and Tyne Railway,
near South Shields, ...... ....... ........................ 45
Reduction of Distances, ............................. • * * * * * * e s s 52
A Table to reduce Dimensions taken in Links into Feet,
and Inches, or vice versa, ...... • * * * * * * * * © g º º e º e º O s is e e º gº º 54
A Case of simple Levelling by the Back and Fore Ob-
servations, ................. ........ .................. ..... 55
A Field Book of the above Levels, ....... .............. ..... 59
To Draw or Plot a Profile of the Ground from the above
Levels, ..... “............ ........….......... 60
viii CONTENTS.
PAGE.
A Case of simple Levelling by the Fore Observations only, 61
Field Book to Ditto, and Method of Reducing the Ob-
servations to the true Level,...................... .... .. 64 .
Levels from Thornton Street to Parker's Quay, with a
Field Book and Description, being a peculiar mode
of recording Levels,..... ...................... .......... 66
Another copy and form of Field Book of the above Levels,
but subsecutively arranged, ........................ ...... 78
- To change Depressions into Elevations,............ 74 and 75
t Description of Field Book, .................. ................. 75
. g How two or more Lines of Levels may be taken at one
and the same time,...................................... .... 76
Reference to the Field Book, Plans, and Sections of the
above Levels,........... .............. ...... ............. • 78
Levels taken from Scotswood to Crawcrook Mill Road, 81
Field Book of the above Levels, ......... ................... 88
To Measure inaccessible Distances such as Rivers,
Lakes, Bogs, &c., ............ ............................. 99
To raise a Perpendicular on the Ground with the Chain
onl 9 © tº e º 'º º 0 & 0 & 0 e º e º 'º e º sº e o 0 & e e o e s e e o O & © tº dº ſº tº e e • . . . . . . . . . . © & 105
E S S A Y
ON THE USE OF -
T H E SPIRIT LEVEL.
INTRODUCTION.
The Art of Levelling is that part of Mathema-
tical Geography, aided by the sister sciences,
Arithmetic, Geometry, and Trigonometry,
which enables us to ascertain the height of any
given point or place on the surface of the earth,
above or below that of other given points or
places on the same surface; and which also
enables us to determine the difference in the
distance of these points from the centre and
circumference of the earth. 2
A surface may be said to be truly level, when
all its parts are equally distant from the earth’s
centre of attraction, similar to the smooth sur-
face of lakes uninfluenced by tides, or unruffled
by winds; for the surface of all fluids, when
B
2 ESSAY ON THE
unexposed to external agitation will become
level, for the earth, being a sphere or globe (or
nearly so), the surface of all waters are equally
distant from its centre, which are kept, or sus-
pended, in that state by the laws of gravitation.
As the direction of gravity is in lines which
meet near the centre of the earth; and as the
surface of all fluids is perpendicular to that di-
rection, their surfaces will be portions of a sphe-
roid, similar to the earth ; and when these
surfaces have no great extent, they may be .
considered as planes, but when they have any
magnitude, the curvature of the earth must be
taken into account.
The figure of the earth is now so well known
as scarcely to require any comment; but as we
shall have occasion to refer, for the purpose of
elucidation to its form and dimensions in ano-
ther part of the work, it may, therefore, be ne-
cessary to state, that trigonometrical surveys, or
geodoesic operations, have been undertaken for
the purpose of measuring a degree of meridian
circle in different latitudes, and also by the
pendulum, and from thence determining the
figure and magnitude of the earth, and which
has been effected at several places on its surface
by philosophers under the patronage of different
governments; and I find, by taking a mean of
~~~~~~~~~rº-rº-º-º-º-º-º:
USE OF THE SPIRIT LEVEL. 3
these results, that the equatorial diameter of the
earth is 7919-75, say 7920 miles; and they
have also discovered, that a degree at the poles
is longer than a degree at the equator, so that
the true figure of the earth would appear to be
an oblate spheroid, the polar diameter being
about 22 miles less than the equatorial; but
this difference is so trivial, comparatively
speaking, as to take little from its globular
form, at least so small, as not to affect any of
our operations in levelling; for the ratio of the
polar diameter to that of the equatorial, as
stated by that celebrated philosopher Huygens,
is as 577 to 578, and by our equally celebrated
countryman Newton, as 689 to 692. It is a
fact, that the rotundity of the earth is not
geometrically true; but the inequalities of its
surface are so inconsiderable, that the high-
est mountains bear no greater proportion to the
bulk of the earth than a grain of sand does to a
common globe.
4. ESSAY ON THE
LEVELLING.
THE USE OF THE SPIRIT LEVEL.
VARIous are the methods used in marking
level points, and numerous are the instruments
employed on these occasions, viz. –the Plumb
Level, Water Level (the Chorobates of the
ancients), with various others; but such is the
nature of these instruments, that they are not
at all applicable to scientific purposes.
I shall, therefore, confine my observations to
that invaluable instrument, called the Spirit
Level, by means of which a line may be drawn
parallel to the horizon, describing a lesser circle
of a sphere; for the bubble of air has that pecu-
liar property of always forming a horizontal
plane, and, according to the modern construc-
tion of this instrument, the intersection of the
cross wires of the telescope, which, forms the
line of collimation, must be always parallel
thereto; by this artificial horizon, we are ena-
bled to find whether two or more points be in
the same horizontal plane, or how much they
may deviate therefrom : further particulars of
this instrument I shall reserve for a subsequent
part of the work. My immediate object shall
USE OF THE SPIRIT LEVEL. 5
be to shew the principles upon which the most
approved practical methods used in marking
level points are founded; and, in order to ex-
plain this subject more clearly, it will be neces-
sary to give a few elementary examples.
In the practice of levelling there are two
methods adopted, the one of which gives the
true level and the other only the apparent level.
The first method, which is the most impor-
tant, as being more simple and independent
than any other, is, by the tangent of a circle,
supposed to be applied to the middle point of
the curve of the level, and carried to an equal
distance on each and every side of the point of
contact or instrument station, the extremities of
which will be equally distant from the centre
and circumference of the earth, for the real
curve of the earth is the true level.
The second method is, when the observations
are only taken forward from the point of con-
tact or instrument station, the tangent line will
touch the circle or curve of the level at that
point, and the other extremity will mark the
apparent level; for one of the extremities of
this tangential line will be further from the
centre and circumference of the earth than the
other.
6 ESSAY ON THE
TRUE LEVEL.
ELEMENTARY EXAMPLE.
THE true method of levelling, or marking two
or more level points, as I have already observed,
is, by the tangent of a circle; that is, when the
point of contact is exactly in the middle of the r
tangent line, which is a straight line drawn, so
as just to touch a circle without cutting it; and
the point where it touches the circle is the
point of contact, or true level point; and a tan-
gent cannot touch a circle in more than one
point.—See Prop. 16, 17, 18, 19, 3d Book
Euclid.
Thus supposing theannexed figure to represent
a section of the earth, F = C. L.
the centre, F C the ra- C S.
dius, K L the tangent
(perpendicular to the
radius), C the point of
contact; the two extre-
mities of the tangent
line KL are equally dis-
tant from C (the point of contact), and also
equally distant from the centre F; the angles
at C are right angles, the angles at the centre
USE OF THE SPIRIT LEVEL. 7
#
are equal, the angles K and L are equal, and
the triangles FK C and FLC are equal to one
another, and the radius FC common to both
triangles; therefore K and L are true level
points.-See Prop. 12, 4th. Book Euclid.
This method may, therefore, be practised
without regarding the difference between the
true and apparent level; because the line of
vision is raised equally above the surface of the
earth on the one side of the instrument as on
the other; otherwise both sides may be con-
sidered as apparent levels, and reduced accord-
ingly, for this method rests solely on this circum-
stance, that the Spirit Level is always placed
precisely in the centre of any line, or at an
equal distance from the station staves or gra-
duated rods; for it is evident that if the instru-
ment is set at a certain height, and remains at
that height, a range of level points may be taken
on each and every side of the instrument, which
shall be within the circumference of a circle,
whose centre shall be that of the pivot or cone
on which the Spirit Level turns; consequently,
equi-distant from the eye of the observer, and
also equi-distant from the centre of the earth;
the line of vision being on all sides raised
equally above its centre, as shown in the fol-
lowing figure.
8 ESSAY ON THE
PRACTICAL EXAMPLE.
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. --" :*** sº e s sº 4, sº •ºxy
Let the instrument be placed at C, an equal
distance from A and B, the two points of sight
K and L, as shewn upon the station staves or
graduated rods, set up at A and B, will be level
points, and the difference between the two
f heights, A K and BL, in feet or inches, will
shew how much the one place is higher or lower
USE OF THE SPIRIT LEVEL. 9
than the other; on inspection, it will clearly
appear that the extremity of the line of colli-
mation at L, is as much above F, the centre of
the earth, as K, the other extremity, and are,
therefore, both true level points.
º:
ºr .
*
10 ESSAY ON THE
APPARENT LEVEL.
ELEMENTARY EXAMPLE.
This method is also by the tangent of a cir-
cle, but only carried in one direction from the
point of contact, as the tangent is perpendicu-
lar to the radius, one of the points must there-
fore be further frem the centre and the circum-
ference of the earth than the other, in propor-
tion as it recedes from the point of contact,
encreasing the length of the secant beyond that
of the radius, which constitutes the difference
between the true and apparent level.
Thus in the opposite T} E.
figure, E, on the extremity
of the tangent line, shews
the point of apparent level
only, because the point of C
contact D is not in the
middle of the tangent line,
but at one of its extreme-
ties, and is nearer C, the centre of the earth,
than’E, the other extremity of the tangent line,
for every point of apparent level is higher than
the true level, consequently the error will be
the difference between the length of the radius
USE OF THE SPIRIT LEVEL. I 1
gº
CD, and the secant CE, or whatever E may be
above the periphery of the circle. This method
of taking levels will be found defective in point
of accuracy, if the necessary allowance for the
curvature of the earth is not made. .
- - REDUCTION OF THE APPARENT Level. r
The correction for the curvature of the earth
may be found according to (Prop. 36, 8d.
Book Euclid). “If from any point without a
circle two straight lines be drawn, one of which
cuts the circle, and the other touches it; the
rectangle contained by the whole line which
cuts the circle, and the part of it without the
circle, shall be equal to the square of the line
which touches it.”
Let D be any point
without the circle A B C,
and D C A and D B
two straight lines drawn
from it, of which D C A
cuts the circle, and D B
touches the same ; the
rectangle A D, D C is
equal to the square of DB or (DC+2CE) x DC
* * -- B D2
=B D", and 3CE-EDC =D C the apparent level,
but D C being so indefinitely small compared to
the semi-diameter of the earth, that for all
12 ESSAY ON THE
ical º : , B D* —
practical purposes we may assume it asgö E -
DC. This expression which is simple, and
without any sensible deviation from correctness,
for the semi diameter of the earth being nearly
21 millions of feet, any difference there may be
between the two modes of expression can never
exceed the fraction rrrköz of an inch. There-
fore, the difference between the true and appa.
rent level will be equal to the square of the ... .
distance between the two places, devided by the º .
diameter of the earth. - … < *-
Suppose we take it in numbers, and call the
tangent or the observed level line B D, 5280
feet, equal to 1 mile, square this distance, and
divide by the diameter of the earth A C,
41817600 feet, and the quotient will be the ap-
parent level in feet or decimal parts; thus,
*##### = 666666 decimal parts of a foot
equal to 8 inches, the height of D above the
true level, and this difference will be more or
less in proportion to the length of the tangent;
for this reason it will separate more from the
circumference of a circle in proportion as it
recedes from the point of contact, and the
height of the apparent level will, in conse-
quence, encrease in proportion as the square of
the distance—that is to say, however much it
USE OF THE SPIRIT LEVEL. 13
may rise above the earth’s surface at the dis-
tance of one mile, it will rise four times as much
at the distance of two miles, and nine times as
much at the distance of three miles; thus, in
the annexed figure.
A is the point of
contact or true level
point, B the appa-
rent level at a dis-
tance of one mile,
C at a distance of
two miles, and D at
a distance of three
miles.
*—#—2
A
The difference between the true and appa-
rent level may also be found according to the
(Prop. 47, 1st. Book Euclid). In any right-
angled triangle, the square which is described
upon the side subtending the right angle is
equal to the squares described upon the sides
which contain the right angle, or, in other
words, in all right angled plain triangles, the
sum of the “squares of the two short sides is
equal to the square of the longest side, called
the hypothenuse; and to find one of the shorter
sides, we have only to subtract the one square
from the other, and extract the square root of
the remainder.
Zº * : *
2% a tº ... . " . * /
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. A
~ *-*** -
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14 ESSAY ON THE
Suppose that the
length of the tan-
gent line B D is
the same as in - C
the preceding ex-
ample, viz. 5280
feet, equal to one T E.
mile, the radius, or
semi-diameter of
the earth, B E 20,-
908,800 feet; square these two numbers, that
is, each number multiplied into itself, and add
the sum of the squares together, extract the
square root; then, from the root thus obtained,
subtract the radius, or semi-diameter of the
earth, which will leave the apparent level;
thus, VB E*-ī-B D*=E 1)—E C=C D, and in
numbers it will stand thus,
The radius, or semi-diameter of the -
earth.E B-20908800°=............ 437.177,91744,0000
Length of tangent line, B D-5280°= 27,878,400
The sum of the squares, V437.177,94531,8400–
20908800'666666, the root and length of the
longest side, E D, from which subtract the
semi-diameter B E, viz. 20908800 will leave
0.666666 for C D in decimal parts of a foot,
equal to 8 inches, the height of D above the true
USE OF THE SPIRIT LEVEL. 15
level I give this proposition a place here, as
we shall have occasion to refer to it hereafter,
in order to explain the method of reducing the
distances measured upon ascending or descend- -
ing planes, viz the hypothen usal to the true
horizontal distance.
PRACTICAL EXAMPLE.
The following example will shew the method
of reducing the apparent to the true level.
/
C
Let the Spirit Level be placed at A, the
point of contact, and over the centre of the
16 - ESSAY ON THE . . ~~~ . . . .
iſ earth, C; at a distance of 1 mile from A, a gra-
duated rod is set up at B; let the line of vision
DE, mark upon the rod 10 feet, which will be
the height of the apparent level, to be reduced
to the true level for the curvature of the earth,
&c. -
Ft. In.
The observed height on station staff,.............. ... 10 0
Ft. In.
The height of instrument, ..... ............ 4 8
In.
The correction for the curvature of
the earth for 1 mile (see #! 8.00
page 22), ........ ....... .........
From which deduct terrestrial re-
fraction (for 1 mile, see Table, X- 66
page 22), ..... -
— 0 7.34
5° 3-34
The true difference of level between A and B
(depression), ..... ............... .............. 4 8.66
It is evident on inspection of this figure, that
one of the extremities of the visual line is fur-
ther from the centre of the earth, C, than the
other, and that the error in the level will be the
difference between the length of the lines CE
and CD, as already stated.
When the observed height is less than the
height of the instrument, take the difference be-
tween the curvature of the earth and refraction
from the observed height, and this last differ-
ence deducted from the height of the instrument
USE OF THE SPIRIT LEVEL. 17
fºr-
-º-wºº. ". . . ºvir,
will give the true difference of level, which will
be elevation.
To find the allowance for the curvature of the
earth and refraction, look in the table (page 22)
for the distance, whether in yards, chains, or
miles ; then in the next column will be found
the correction for the curvature, and in the
third column the quantity of refraction corres-
ponding to that distance.
In the calculations hereafter described for de-
termining the depression or difference between
the true and apparent level; the distances in all
cases are to be squared, whether taken in feet,
yards, chains, or miles, and divided as shewn in
the following simple rules and examples:—
RULE 1.
When the distance or length of any line is
taken in feet, square that distance and divide
by the diameter of the earth in feet, viz-
41817600, and the quotient will be feet or deci.
mal parts; or should 3484800 be taken as a
divisor, then the quotient will be inches and
decimal parts. -
EXAMPLE,
Suppose the length of the line to be 5280
feet, equal to one mile ; 5280x5280=######3–
0.666666 decimal parts of a foot, equal to 8
18 ESSAY ON THE
inches, for the first mile of apparent level, and
to be deducted from it.
RULE 2.
If the distance should be taken in yards, the
divisor in that case will be 4646400, and the
quotient will be in feet or decimal parts of a
foot; or take 387200 for a divisor, and the
quotient will be inches and decimal parts.
EXAMPLE. -
Suppose the length of the line to be 1760
yards, equal to one mile; 1760×1760=######3–
0.666666, equal to 8 inches.
RULE 3.
If the distance should be taken in chains, the
divisor will be 9600, and the quotient will be in
feet and decimal parts; or take 800 for a divi-
sor, the quotient will be inches and decimal
parts.
EXAMPLE.
Suppose the length of the line to be 80
chains, equal to 1 mile; 80x80=#}}=0.666666
equal to 8 inches.
RULE 4.
If the distance should be taken in miles, di-
vide by one and five-tenths, viz. 1-5, and the
quotient will be in feet and decimal parts; or
USE OF THE SPIRIT LEVEL. 19.
multiply the number of miles by the number of
chains in a mile (80), and divide as in the last
example by 9600, the quotient will be in feet
and decimal parts.
EXAMPLE,
Suppose the distance to be 1 mile ; 1x1=#3-
0.666666=8 inches, the height of the apparent
above the true level,
Upon these and the preceding geometrical
principles I have constructed a table, shewing
the quantity of curvature below the apparent
level from 100 yards up to 20 miles; and in
order to secure a greater degree of accuracy in
these operations, I have given in another column
of the table, the quantity of refraction corres-
ponding to those distances. As the effect of re-
fraction in incurvating the rays of light proceed-
ing from objects near the horizon has been
proved to be very considerable, it can by no
means be neglected when the difference between
the true and apparent level is estimated at con-
siderable distances.
20 ESSAY ON THE
TERRESTRIAL REFRACTION.
TERRESTRIAL refraction is that by which ter-
restrial objects appear to be raised higher than
they really are, for the atmosphere being com-
posed of vapours and other matter, which in-
crease in density as they approach the surface
of the earth, when a ray of light is passing from
any object and enters this medium, it is turned
from its rectilineal course into that of a curve,
concave towards the earth, and meeting the eye
in a different direction; thus it is that the ap-
parent or observed elevations of objects are
always greater than the true ones, and conse-
quently must be subtracted from their apparent
altitudes.
In proof of these observations, I beg to men-
tion a circumstance which is related to have
occurred on the great trigonometrical survey of
England. “In measuring the base on Houn-
slow Heath, we had driven into the ground, at
the distance of 100 feet from each other, about
30 pickets, so that their heads appeared through
the boning telescope to be in a right line ; this
was done in the afternoon. The following
morning proved uncommonly dewy, and the
USE OF THE SPIRIT LEVEL. 21
sun shone bright; when, having occasion to
replace the telescope, we remarked that the
heads of the pickets exhibited a curve, concave
upwards, the farthermost pickets rising the
highest; and we concluded they were not pro-
perly driven, till in the afternoon, when we
found that the curve appearance was lost, and
the ebullition in the air had subsided.”
The quantity of refraction contained in the
following table is found by taken an average of
the mean refractions given in the account of the
operations of the great Trigonometrical Survey
of England, and this I find to be equal to 1-12th
of the contained arc. It also appears that the
same average number was occasionally made
use of by Col. Williams, Capt. Mudge, and
others on that survey. But it has been very
justly observed by Mr. Ivory, that it is fruitless
to expect a near agreement in every instance
between observations and any table of refrac-
tions, because it is so affected by the different
states of the atmosphere, and, therefore, can
only be correctly ascertained by simultaneous
observations. See Hutton’s Course of Mathe-
matics, vol. 3, page 186, 7th edition.
22 ESSAY ON THE
TABLE
Shewing the difference between the true and apparent Levels, and also
the quantity of Refraction for distances taken in yards, chains, or
miles. The correction for the curvature of the earth and refrac-
tion will be found in the columns under 1 and 2 in inches, and decis
mal parts; and in the columns, under 3, in feet, inches and parts."
I 2 3
Correction Terrestr. 3|Correction Terrestr. # Corºction|Terrestr.
Hist Curvature, Refraction # cuºure Refraction s Curvature|Refraction
Yds. §: | - — lit.
in. dec. p. in.) dec. p. 5|inſ dec. p. lin.I dec. p. 61 ft. lin'ſ p. ſtin. p.
100 '02582 •02000 || 001 66|| || 0 800|| 0 0-666
| 200 - 10330 •08000| | |0ſ, 666|| 2 || 2 | O; 2.666
| 220 - 1 2500 • 12500 •0104.1 3| 6 || 0 |00|| 0 6|-000
300 -2324.4 • 18000|| || 0 1500|| 4 || 10| 800 0|10|-666
400 - 41322 •32000 ‘02661; 5 I 6, 800 I | 4-666
440 |"50000 •50000 •04,166; 6 24| 000] 2 U-000
500 64,566 ‘72000 •06000; 7: 32| 8||00] 2 S-666
600 92975. •98000 -08 1664, 8, 42| 800 3| 6|-666
700 1 26550 1 j 10666|| 9 54 000; 4, 6-000
| 800 1|-65289 | 62000 13500||10| 66 8|9|| 5|| 6-666
880; 2) •00000: 2|-00000| | 16666|| || 80ſ 800 6, 8-666
900] 2 09 194 2|-42000 20166||12| 96 OIO0 S. O.000
1000; 2 °58264 2| 88000 24000||13||12| 800 9| 4|-666
I 100 3 - 12500 3| 38000 •28 166||14|130| 8 § 10|-666
|200|| 3 | "71900 3} •92000 '32666||15||150 000|T2| 6-0
1320, 4 •50000 4|-50000 ‘87500||16|170; 8|0014, 2-666
1400, 5 -06190 5|- 12000 •42666||17|192| 8|00:16 O 666
1500 5|-81095 5. "Z8000 “48166||18|216 00018 0-000
1600 6, 6ll 57 6 : 48000 ‘54000||19|240 S100|20 O-666
| 700; 7: .46384 7|-22000 •60166||201266 800|22 2-666
1760. 8] -00000 8|-00000 '66666|2|{294 000/24 6-000
This Table may be applied to many other useful pnrposes, particularly
to determine the extent of the visible horizon from any given point.
By this important application we may determine the distance of one ship
'from another, or the distance of any vessel from land when just visible, the
height of the eye of the observer above the level»of the sea or horizontal
*ime being known ; and we may also determine the extent of vision on the
rsurface of the earth, from the top of a mountain or tower.
To find the distance of an object when it first comes in sight, the height
•of the eye of the observer being 96 feet above the level of the sea.
Thus, by inspection, look in the table in the column of correction for
“difference of level, viz. –96 feet, and opposite, in the left hand column will
be found 12 miles for the distance of the object, —
Or thus,
To the height of the eye of the observer add its half, extract the square
root of this sum, and the root thus obtained will be the extent of the visible
horizon in miles.
The height of the eye, 96 feet.
Add its half, ............ 48
A/−
144 = 12 miles.
USE OF THE SPIRIT LEVEL. 23
&
- SPIRIT LEVEL.
SoME of these instruments have plain, or open
sights; and others telescopic sights, constructed
so as to remedy the defects arising from the re-
frangibility of light, and are called Acromatic
Telescopes. These are generally attached to the
best kind of spirit levels, which enable the ope-
rator to distinguish distant objects better, and
obtain a more direct line of sight, affording
a large field of view, and possessing a consi-
derable degree of magnifying power; in the
focus of the eye-glass are two very fine cross-
wires, or hairs (I have generally made use of
the fibres of cotton, which are extremely fine)
fixed in a cylindrical ring at right angles to each
other, connected to screws on the periphery of
the tube, to move and adjust these cross wires
to the axis of the telescope; at the object end
of the telescope is an inner tube, which may be
moved outwards, by turning a tangential screw
on the side of the telescope, to such a distance
as may suit the eye of the observer.
The frontispiece of this work is a correct re-
presentation of one of the best kind of instru-
ments made use of in taking levels, and the fol-
24 ESSAY ON THE
lowing is a detailed account of its parts, by
letters of reference, &c.
A, an acromatic Telescope, nearly 2 feet
long; Fig. 2 is a cross section of the tube at f.
showing the situation of the 4 screws, and the
cross-wires to determine the axis of the telescope.
33, cylindrical rings or collarins on which the
telescope turns: a the eye end, and b the ob-
ject end of the telescope.
B, a tangential screw on the side of the te-
lescope, for moving outwards the inner tube to
such a distance as may suit the eye of the ob-
Serveſ. -
C, the spirit tube, hung collateral to the tele-
scope, containing the column of air, one end of
which rests in a stirrup, with a small screw on
either side to adjust the sydereal motion of the
bubble, and the other is wrought up or down a
male screw by the two capstan-headed female
screws c c, for adjusting the bubble of air paral-
lel to the axis of the telescope.
D, the bar and compass-box. The compass-
box is one piece with the bar, divided into four
quadrants, subdivided into 90 degrees and also
into 360 degrees, with a magnetic needle, trig-
ger and spring to throw it off the centre when
not in use, forming a perfect circumferentor.
E, two supports or rests for the telescope, the
lower ends of which are sunk perpendicularly
*
USE OF THE SPIRIT LEVEL. 25
into each end of the bar D, called wyes, from
their resemblance to the letter Y; these are rais-
ed or depressed by the vertical screws e,f, work-
ing in the upright stem of the wyes, to bring
the instrument to a level: 44, a bow, with a
spring attached to the head of the wyes by a
forked joint at one end and a pin hole at the
other, to fasten down the telescope into its
rest. - - -
F, a conical brass ferule fixed to the under
side of the compass-box (this constitutes the up-
per portion of the instrument), which is fitted
to the bell metal frustrum of a cone attached to
the upper parallel plate.
G, the upper parallel plate. .." &
H, the under parallel plate, fixed to the upper
plate by a strong central pin, ball, and socket.
h h h h, four vertical screws for adjusting the
parallel plates to the parallelism of the column of
air and axis of the telescope, their heads resting
on the under plate H, and working through and
into cylindrical tubes fixed to the upper plate,
G. -
I, a clamping screw to fasten the brass ferule
to the under portion of the instrument.
K, a tangent screw which gives a horizontal
motion to the telescope in order to bring it into
a just line of collimation. -
26 . ESSAY ON THE
L L L, three strong mahogany legs, fitted
with joints, attached to the under side of the
parallel plate H, and on which the whole rests
when in use. -
Telescopes have one defect, that is in short
distances, when the sliding vane of the gra-
duated staves come within 5 or 6 yards of the
instrument, the centre of it cannot be distin-
guished; many cases will occur in levelling
through a country, where only very short dis-
tances can be taken, in passing plantations, deep
ravines, &c.; on these occasions I have gene-
rally made use of a smaller kind of instrument,
but it would be more advisable to have open
sights (perforated pieces of brass) to attach oc-
casionally to each end of the telescope, and to
be placed parallel to its axis: the one at the eye
end of the tube should be a round hole one-
eighth of an inch in diameter, and the one at the
object end a quarter of an inch in diameter, with
a thread or hair across the centre, corresponding
to the cross hairs of the telescope, by which
means near objects would be seen distinctly.
ADJUSTMENTs of THE INSTRUMENT.
The necessary adjustments of this instrument
are three. First—To fix the point of intersection
of the cross wires in a line of collimation that
USE OF THE SPIRIT LEVEL. 27
.
shall exactly coincide with the axis of the tube
of the telescope; but more particularly with the
axis of the cylindrical rings on which the tele-
scope turns. Second—To make the column of
air or bubble parallel to the line of collimation,
or the axis of the telescope. Third—To adjust
the parallel plates for the horizontal motion to
the parallelism of the column of air and teles-
cope. - * … , * • ‘
1st. To adjust the cross wires in order to
obtain a just line of sight.
Having set up the instrument and one of the
graduated station staves, at a distance of 5 or 6
chains (or observe a horizontal line of any kind,
the underside of a window head, or sill, the
frame, &c.), or direct the sight to the brass wire,
across the square hole in the centre of the slid-
ing vane, and observe if the cross wire in the
telescope, but more particularly the horizontal
wire, coincide with it, turn the telescope in a la-
teral direction half round on its axis, and if the
intersection of the wires still corresponds with
the object, they are in their right position, if
not, adjustment is necessary, and which is ef-
ected in the following manner: correct for half
the différence, by moving the wire upwards or
downwards, viz. by easing one of the capstan-
headed screws and tightening the opposite one
28 ESSAY ON THE
(this not being attended to will endanger the
breaking of the threads of the screws, or the
screws themselves), turn the telescope round
into its natural position and adjust the wire
with the object; again turn it half round on
its axis, and continue repeating these opera-
tions, until, in both positions of the telescope,
the wire coincides with the same part of the ob-
ject; the vertical screws 11, moving the hori-
zontal wire; and the horizontal screws 22, the
vertical wire.—See Figure 2, Plate 1.
If the cross hairs or wires are next the eye
glass of the telescope they will appear in a na-
tural position, and will be readily adjusted; but
if the hairs are without the eye-tube they will, in
consequence, be inverted, and require to be
moved in an opposite direction to that in which
they may appear.
Thus, for instance, if the horizontal wire has
been adjusted with some distant object, and the
telescope is turned, in a lateral direction, half
round, the wire appears above the object, it is
too low ; therefore, slacken the then under
screw, and tighten the upper one; bring it again
into a line with the distant, object, and if, on
turning the telescope into its natural"position,
the wire appears below the object, it is now too
high; therefore slacken the upper screw, and
USE OF THE SPIRIT LEVEL. 29
tighten the under one, and repeat these opera-
tions untill you have proof of its adjustment.
2nd. To make the column of air parallel to
the line of collimation or axis of the telescope.
Bring the telescope, with the rims of the wyes
open over a pair of the vertical screws h h, at-
tached to the parallel plates; then, if necessary,
raise one of these screws and depress the other
until the bubble becomes stationary in the mid-
dle of the tube; the telescope must now be
taken out of its rest and laid the contrary way,
if in this situation the bubble of air remains in
the middle, the level has been properly adjusted;
if not, the end to which the column of air runs
will be too high ; therefore the position of the
spirit tube must be so altered as to be equal to
half the difference, by raising or depressing, as
the case may require, the capstan-headed female
screws c c, at one end of the spirit tube, and for
the other half raise or depress the opposite ver-
tical screw d or e in the bottom of the wyes or
h h in the parallel plates; again reverse the te-
lescope by bringing it to its former position, and
if these adjustments have been accurately made
the bubble of air will settle in the middle of the
tube in both positions of the telescope; these
operations must also be repeated until it bears
this proof of accurate adjustment.
30 ESSAY ON THE
3d. To adjust the parallel plates for the ho-
rizontal motion. - -
Place again the telescope, &c., over a pair of
the vertical screws, h h, which are attached to
the parallel plates, and cause the column of air
to become stationary in the middle of the spirit
tube, by raising one of the screws and depressing
the other; turn the telescope over the other
two screws, raising one and depressing the other
until the bubble of air rests in the middle ; the
instrument will now become completely adjust-
ed, and may be moved round on the cone at-
tached to the parallel plates, without the column
of air changing materially in its place, and the
observer enabled to take a range of level points
from any side he may judge necessary.
TO PROVE THE ADJUSTMENTS OF THE SPIRIT LEVEL.
Having chosen a level piece of ground, let
each of your assistants, with their graduated
staves, go off for a certain distance, say, 4 chains
on either side of the instrument; and suppose
you find the height on the front staff to be 5
feet 6 inches, and that of the rear staff 6 feet,
making a difference of 6 inches; change the po-
sition of the instrument within 2 or 3 chains of
one of your assistants, and observe the same
USE OF THE SPIRIT LEVEL. 31
points; if the difference should be the same the
instrument has been properly adjusted: it is of the
greatest importance that the instrument should
adjust at an unequal distance in the manner I
have just described, because parts of the instru-
ment may be very far from the truth, and yet
adjust when always placed at an equal distance
from the station staves (situations will frequent-
ly occur in a line of levels where this cannot be
done). Let us suppose, for instance, that the
cross hairs are not properly adjusted to the axes
of the telescope, or the bubble not properly
balanced in the case, then the line of collimation
will be as much inclined on the one side as on
the other, and therefore will give equal results;
but there is another and greater defect than
those now mentioned, and which is not so easily
detected. The defect that I now speak of is in
the mechanical construction of the instrument,
the ends of the telescope not being correctly ba-
lanced; if either end should have the preponder-
ance of weight, it will have the same effect as
that of the cross hairs of throwing the line of
vision upwards or downwards, which would
have a serious effect on a line of levels of 15 or 20
miles extent, where long and short distances
are occasionally and unavoidably taken.
Therefore whenever the telescope is suspected
3. ------~~~~ : - ~~~. . . . ---- ~--------~~~~~ ser---sºmºrrºr-rrºr .
* #
32 ESSAY ON THE
of not being properly balanced, procure a
small ring of sheet lead, nearly the diameter of
the tube of the telescope, to slide upon that end
requiring such counter-balance; or it may be
loaded with pieces of copper (pence or half.
pence) until a proper balance is discovered, and
the bubble turns in every direction without any
material change of position.
The operation of levelling being of a very ac-
curate and important nature, and the best in-
struments, when out of adjustment, being of
little use, we would therefore recommend to
every one, who wishes to rise in his profession,
to make himself perfectly acquainted with, and
skilful in adjusting, the various parts of which it
is composed; without that he must not expect
the instrument to answer the purposes for which
it was intended, nor his observations have that
degree of accuracy which is so requisite.
THE GRADUATED STATION STAVES.
The two Station Staves, or graduated rods,
used in levelling; for the sake of portability,
each rod is made up of two parts, of six feet
each, tongued and grooved, the one made
to slide upon the back of the other; two faces
of the moveable portion of each of these laths
are accurately divided; each face bearing
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USE OF THE SPIRIT LEVEL. 33
two sets of numbers, viz. feet, inches, and tenths,
also feet and hundredth parts; the outer face
numbered upwards to 5 ft. 9 in., and the inner
face, taking up the divisions where the other
left off, numbered consecutively downwards to
11 feet 6 inches, therefore, when the heights ex-
ceed 5 feet 9 inches, the sliding vane must be
fixed at that point, and all the heights above it
will be shown on the inner face, beginning with
5 feet 9 inches, and its parts 5 feet 10 inches, 5
feet 11 in., 6 feet, &c. In Fig. 1 a, Plate 2, it
is shown to stand at 6 feet 6 inches.
* * SLIDING VANES.
: . Each graduated rod has a sliding vane, which
º is made with a groove in the back to slide steady
#' up or down the staff, and to fasten with a spring;
but this is apt to lose its power of action in
dry weather from the pining of the wood, there-
fore a screw is necessary, to work through a
socket in one of the sides of the groove, into a
clutch on the back of the spring, to ease or
tighten, as occasion may require. See Fig. 1 a,
Plate 2.
The length of the vane is about 11 inches,
breadth three and a quarter inches and thickness
nearly half an inch, it has a square hole in the
middle with a brass wire across its centre, to
D
vs.
34 ESSAY ON THE
point out the precise divisions on the staff cor-
responding to the visual line of the telescope.
The face of each vane is veneered, and divided
for the extent of the opening in the centre white,
above and below it for half an inch in width
black, the remainder white. See Fig. 1, Pl. 2.
I have sometimes made use of a lath, 12 feet
8 inches long, dovetailed, with the divisions,
feet, inches, and tenths on one side thereof, with
a circular vane of 4 inches in diameter drawn up
or down with a cord passing over a small sheave
at the top, and another at the bottom. See Fig.
2, and 2 a, Plate 2.
To fasten the vane a small eye'screw of iron
or brass is fixed in the back of the lath at the
height of 5 feet, through which the cord is
drawn and pressed into the eye of the screw, is
a circular wooden pin, slightly flattened on one
side, to gripe the cord, which effectually pre-
vents its slipping.
USE OF THE SPIRIT LEVEL. 35
: … ºr *** - ---------. - - ------, - - - --—----------------------— $º. ------------sº **** * ! -----
SPIRIT L E V E L.
SIMPLEST FORM.
The simplest form of the Spirit Level, for fix-
ing any plane horizontal, is represented in the
following Figure 1. -
It consists of a glass tube set in another one
of brass, about # of an inch diameter, having an
aperture in the middle whence the bubble of air
may be observed; this tube is attached to a flat
bar, 10 inches long, 4 broad, # thick, with two
plain sights A D, B E, fixed at right angles
thereto, of an equal height, and perpendicular to
the tube: in the middle of the eye-end A is a
drilled hole # of inch in diameter, and at the
object end B is an opening of , inch in diameter,
with a hair or wire across its centre to fix the
point on a level with the instrument.
ſ
36 ESSAY ON THE
The glass tube is nearly filled with spirits of
wine, turpentine, or ether; the remaining por-
tion of the tube is occupied with air, which forms
the bubble; it is either hermetically sealed, or
plugged, to keep in the fluid.
The glass tube is not strictly cylindrical, al-
though it may have that appearance; it is slightly
curved, the convex side being upwards.
The method of fixing the glass tube into its
brass case is this, the tube is first fitted into the
case, and if it should be found too wide a few
folds of fine paper are put under it; the tube is
then placed on the forks or wyes of the instru-
ment, called the bubble-trier, which is provided
with a micrometer screw for raising or lowering
the ends of the tube, to bring it into a proper ad-
justment, the bubble C is made to stand between
two marks or scratches on the glass tube at c c,
the ends of the level are now reversed, that is,
the end B is put where A was ; if in this position
the bubble stands in the middle, it proves the le-
vel to be correct and truly horizontal, but if it
should run to either end, it will show the end to
be too much elevated : suppose, for instance, it
were to run to the end B, let a small wooden
wedge be inserted between the upper side of the
glass tube and the brass case, so as to press
that end (B) downwards equal to half the error
USE OF THE SPIRIT LEVEL, 37
or difference, let another small wedge be in-
serted in the other end, between the under side
of the glass tube and the brass case, so as to
press this end (A) upwards equal to the other
half of the error: the level must now be re-
versed to verify these corrections; and when
they are made, so that the bubble stands at the
marks c c, in both positions, the level is correct
If the bubble should have any sideral motion
press a wedge in on that side to which it has a
tendency to run.
The tube is now made fast to the flat bar by
the two screws a and b; at that part of each
screw which will reach about the semi-diameter
of the tube a groove is made to receive, on both
sides and at right angles thereto, the ends of two
very small screws or pins a ar, by which the tube
is supported, and either end elevated or depress-
ed, as the case may require.
The screws a b, are for the purpose of adjust-
ing the under surface of the bar or frame paral-
lel to a tangent supposed to be applied to the
middle point of the curve of the level. This
adjustment is effected without much difficulty,
by placing the level on an adjusting plane or
bench, and then reversing it; if the bubble
should stand exactly between the two marks on
the tube in both situations of the level, it follows
38 Essay ON THE
that neither end of the bubble tube, nor the un-
der surface of the level is elevated ; but if it
should run to one end, we shall suppose the end
A, tighten the adjusting screw a, for one half
the difference, and for the other half raise the
tube by easing the opposite screw b, or raise the
end B of the adjusting plane or bench ; continue
these adjustments until, in both positions of the
instrument, the bubble rests in the middle at the
two marks c c, the level will then be correct,
and may be applied to any surface.
Now to render this simple instrument applica-
ble to field purposes, I had attached, by means
of the screws A B, as shown in figure 2, a ver-
tical arch (milled only), of one and a halfinch in
diameter, and three-eighths of an inch thick; this
arch is wrought by the tangent screw c, by which
means the bubble is accurately and expeditiously
brought into proper adjustment, it is very port-
able and may be used on the head of a walking-
stick; or on the legs of a more perfect instrument,
it will be foundextremely useful, not only in steep
woody grounds, where short sights only can be
obtained, but may be applied to general use, par-
ticularly in draining of lands; its arrangements
being so simple that any one may use it, and it
possesses another important recommendation,
viz., that it is not easily put out of order.
USE OF THE SPIRIT LEVEL. 30
SPIRIT TUBES.
To elucidate the nature and figure of the Spi-
rit Tube more clearly, let the two following fi-
gures represent longitudinal sections of two
tubes, which I have now in my possession and
in use; No. 1. is hermetically sealed, and the
other, No. 2, PLUGGED : the manner in which
this is effected is by corks made to fit the ends
of the tube and covered with gut skin immersed
in a compositon of gum arabic dissolved in wa-
ter and plaster of paris ground together, which
is the best cement for that purpose, and sets in
the spirits of wine almost instantaneously,
It is a fact not generally known that the hard-
est gums, such as gum copal, &c., are soluble in
spirits of wine, whilst the softest gums, which
are readily dissolved in water, as gum arabic,
are not soluble in that spirit. *
Suppose the upper surface of these tubes to be
segments of large circles A CB, then, according
to the laws of hydrodynamics, the surface of any
fluid, influenced by the laws of gravity and in
equilibrium in any vessel, is horizontal, or at
right angles to the direction of gravity; there-
fore, it is plain that the bubble of air, being the
lightest of the contents of the tube, will occupy
the highest part of the circle C, and the two
|
|
40 ESSAY ON THE
points A B, being equally distant from C, will
be in the same horizontal line A D B.
The larger the bubble C, and the radius of the
circle A C B, the more sensible it will be to any
deviation from the horizontal plane, because it
will have to traverse a greater distance along the
tube in proportion to any partial inclination of
either end.
Spirit Levels are too commonly made of the
glass tube in the state in which it is obtained at
the glass-house; but no one can form an idea of
the defects and irregularities of the interior sur-
face of these tubes, unless they are in the habit of
grinding or seeing them ground. No tube ought
to be attached to an astronomical or mathema-
tical instrument unless it has been previously
ground inside to a circle of 800 to 500 feet ra-
dius, according to the length of the telescope to
which it is attached. g
The radius of the tube No. 1, whose bubble
moves about six lines for a minute of inclina-
tion, is 380 feet, and it would require a plumb
line 1520 feet in length to give the same results
with equal precision. tº
In order to give that regular form to the up-
per internal surface of the tube No. 2, I caused
to be made two turned iron mandrils, twice the
length of the glass tube and covered with lead
USE OF THE SPIRIT LEVEL. 41
of the same length ; one of these covered rods
was turned truly cylindrical, and the other rod
to a spindle form, which was made to correspond
with a portion of a circle of 2182 feet radius,
and attached to a telescope 2 feet long.
The cylindlical rod was fixed between the
centres of a lathe, and the glass gently pressed
and continued turning, with the hand, on the
lead, during the operation of grinding with fine
emery, sand, and water, which was fed in at that
end of the tube of the smallest diameter, and
ground until it became perfectly cylindrical,
which was known by a guage made for that pur-
pose: the other mandril or spindle was now ap-
plied, and the glass tube kept in one position
and ground with flour of emery and water; and
it was thought sufficiently ground when every
part of the upper circumference of the tube and
spindle touched each other. -
Spirit Tubes referred to in Page 39.
42 ESSAY ON THE
PRACTICAL LEVELLING.
The methods of Levelling may be divided in-
to simple and compound; what is termed simple
levelling is determining level points from one
|
3.
}
station, or from one point direct to another,
whether the Spirit Level be fixed at one of the
points, or in the intermediate distance, is imma-
terial; but it must be remembered that when
the instrument is placed at one of the extremi-
ties of a line, the result will be the apparent
level only, which will require to be corrected or
reduced to the true level. I would always re-
commend placing the Spirit Level in the inter-
vening space, whenever it can be effected at an
equal distance from the graduated staves, where-
by much time will be saved and unnecessary
trouble avoided; and this reciprocal mode of
levelling is undoubtedly the best and most ex-
peditious, no reduction for the apparent level is
necessary, neither have we occasion to regard
the terrestrial refraction, for whatever be the
quantity it will be equal, and the result of the
practice will be as accurate as if there had been
no refraction, because the density and constitu-
USE OF THE SPIRIT LEVEL, 43
tion of the air and vapour at the same instant
will be the same in each position of the instru-
ment. However, an example in each case will
render this part of the subject quite plain.
INSTRUCTIONS FOR RECORDING LEVELS.
RULE 1.-SIMPLE LEVELLING.
The commencing station, or rear staff, may or
may not have any determined height; but what-
ever height may be shewn on the graduated rod
+-we-ºr----- ~s
or staff, must be entered in the field-book in the
column marked rear heights, and the heights
shewn on the front staff in the column marked
Jront heights, and their difference (whatever it
may be) in the columns of elevation or depres-
sion; therefore the regular station heights from
whence the levels are continued must progres-
sively be added in each column, and deducted
from each other to find the height of the last one
in succession, by this means the Elevations and
Depressions radiate from one general base line.
If the sum of the rear heights exceed the
front heights, the difference will be Elevation;
but if the sum of the front heights exceed the
rear heights, the difference will be depression.
44 ESSAY ON THE
RULE 2.-compound LEVELLING.
Offsets,” bench marks, intermediate and in-
strument heights, are always to be treated as
front heights (which in fact they are), from the
number of the instrument station, or distance
they may be taken from, because the are merely
lines diverging, or let them be considered diverg-
ing, from the rear staff, and they may or may
not be carried to the columns of the general re-
gistry; but when they are so entered, they must
be carried to the column of front heights, and
added to all the heights of that name above
them, and deducted from all the rear heights as
the case may require, by taking the less from the
greater.
When the offsets or intermediate levels are
added to the last observed front heights, they
must also be carried to the other column, be-
cause in this case they become the rear heights
to the next fore observation.
* When these heights are numerous, when taking 3 or 4
lines of levels, to shorten the registry and prevent confusion,
they are frequently recorded on the opposite sheet of the
field-book, and entered in the column of front heights, and
their relative heights are by this means calculated separately.
USE OF THE SPIRIT LEVEL. 45
rºs-rr-, -r-z-ºr-º-º:
RULE 3.—Recording Levels, &c.
To the commencing station or rear height, if
there is a probability of the general line of levels
falling below the base line, add to the rear
heights 100, 200, or 300 feet, by this means all
the observed points become elevations in a
greater or less degree, and the zero mark or
starting point will be 100, 200, or 300 feet
above the base line, consequently whatever sum
be borrowed must be carried to the column of
rise, and also to the column of total rise, as
shewn in the following Field-book (page 48);
and I may further observe that, if the falls are
likely to exceed the rises at any point, any
number of feet may be added to the rear heights
during the progress of these operations, but care
must be taken to carry the same number to the
three columns already mentioned, for the pur-
pose of proving the work in detail. .
If the difference of the sums of the two first
columns, that is the rear and front heights, and
the difference of the sums of the two succeeding
columns, rise and fall, are equal to the sum of
the total rise, the operations have been correctly
performed and afford so many proofs of the ac-
curacy of the additions and subtractions, but if
any of these suus should disagree, re-examine
46 ESSAY ON THE
that column where such difference may arise. As
this rule differs so materially from the preceding
ones, and without arrogating to myself any
merit or claim to this method I beg to say that
this mode of recording the levels and form of
computing was communicated to me by my
friend Mr. T. E. Harrison, civil engineer,
although it is not so simple in its operations as
the two proceeding rules, yet for brevity it has
the decided advantage, and I am so perfectly
convinced of its general utility and efficiency,
that I cannot but give it a place in this work.
I shall now endeavour to explain this rule
more fully, and I have to hope that my readers
will find everything here which will enable them
to undertake any part of the field practice, and
that my detailed explanation will be found as
simple as the nature of the subject will permit.
In the first place then substract the rear
heights from the front heights, which ever are
greatest, and place that difference in its respec-
tive column of elevation or depression, and
proceed until one leaf side or half a page is
completed; add up the sums in the column of
rear heights including the sum borrowed, add
up also the column of front heights, the column
of elevations with the sum borrowed, and the
column of depressions. Now if the difference
USE OF THE SPIRIT LEVEL. 47
between the sums of the rear and front heights
is the same as the difference between the sums
of the elevations and depressions, this much of
the work is correct, and this difference will be
equal to the total rise at that particular point,
but if they should not agree the whole should
be re-examined. If the first difference be-
tween the rear and front heights should be
elevation it must be added to the sum borrowed
in the column of total rise, whatever it may be,
but if the difference should be depression it
must be subtracted from that sum, and as these
operations progress, add each individual rise to
the sum of the total rise, but subtract each in
dividual fall from the sum of the total rise.
~~~~~a a-- ~~~<=-------> --- - - - - - -
.*
i.
48 ESSAY ON THE
I have in this field-book given a portion of
the Stanhope and Tyne railway, near South
Shields, with the levels taken at each chain
length, and as there are certain parts of it
steeply inclining ground, I shall take the oppor-
tunity of explaining the mode of reducing the
oblique measurements to the true horizontal
distance, for when we actually measure up or
down a slope of great steepness the line ought
to be shortened in the proportion of radius to
the Co sine of the angle of elevation.
I commence the field-book from the bottom
of each page and write upwards, and the calcu-
lations are extended from left to right; the first
difference that occurs between the rear and
front heights is 0.94 decimal parts of a foot, for
depression or fall, which will be found sub-
tracted from the 100 feet borrowed, making
99ft. 06d. pts. for the total rise at the first chain
distance; the next difference is also a fall of
1:00 one foot, and is also deducted from the
total rise, leaving 98ft 06d. pts. for the second
length, viz. 175; as the falls follow for some
distance we shall pass over them and go to the
approximate distance 3:43, where the first rise
takes place and which is 4:15, viz.-four feet
and fifteen decimal parts which is now added,
making 66 feet 25 decimal parts for the total
FIELD BOOK REFERRED TO.
[To FACE PAGE 48.
- -**- -
i
IDIST, R.E.A.R. FRONT TOTAL | RED,
CH, I HEIGHT, HEIGHT, Rise. ****| Rise. Dist. LOCATIONS. |
350-13] 233-08|167-31 |50-26
26-00 Il-32 8-82. 2'50| – || 17-05|25-39|Mark near Quarry.
25 s 4°52′ 2:40 2-12) —H 14.55|24:39
24- 4°18 4-52 —| 34|| 12:43:23-39
B. M. 5-60 4-18] 1 '42| – || 12.77|B M -
23, 18 12-04, 5-60| 6’44 —ll 11.35|22:57|Surface of ground over
- water-pipes next hedge.
Offset 4-85 12-04| –| 7-19|104-91 offset jace of water in reser-
23. 5'08) 4-85| "13 – 112-1022.39
22 3:40, 5'08 — 1.68||111 -97.21-39
21 - 2-60. 3-40 —| -80 #: Cº.
20:00 2°58' 2-35 °23 —||114.45|l 9-39
J9- 3:40 2.58| -82 114, 22|18-39
18- 4-55 3.40 l’lā 113-40|17-39
17. 4:92] 4:55 37 112.25|16-39
16. 4'45| 4 -92 •37|111.88||5-39 A.
276.64. 16489.15218.898s
15 °45 7:53 4'45| 3:08 112.25||14-84 Y Surface of gr. over
new water pipes.
15:00 10-95| 7-53| 3:42 109-17|14:39
14, 20 3.56 •47 3-09 105-75||13-59
14.00 12-08. 3-56: 8°52 102.66|13:40|r
13-27 4-80 •14|| 4 -66 94-14|12783 tº e
13:00 13.53| 1.80 8-72 s9.48|12-52.É Steeply declining
* ground.
12:33, 7.07 I-52| 5-55 SO-75|| 1 '86 Occupation Road.
12:00 l l 50 7.07| 4:43 75 '20ſ II 54.
I 1 -37 8-72 •31 || 8-4] 70.77|10-91
11-00 IO-25} 8-72; 1 -53 62-36|10-56 J
10-80 l l 50 10.25: 1-25 60-83|10 -36 On oppositeside of
10'75|| 10:25, 11.50 – 1 25, 59.58|10-31 Brook.
- Into centre of brk.
/d 24;" (10 im. water.)
1970 1000. 4325 — 25 60.83|1926., on side orbrook.
10°10| 6-77] 10:00 3.23| 61 08|966|.
10- 1-0|| 6-77 5-76, 64-3)] 9.57|3.
9 80 3:23| 13-60 10:37, 70.07| 9-39. 3
9°50' 4-35| 13-77 9.42| 80'44, 9:13 * *
9-17. 9-80 13.95 4.15 89-86 885 - Steeply declining gr
9. 6-90 9-80 2.90| 94 0 || 8 89
122-84. 25.93| 99.46|| 2:55, 96 9] 887 cross hedge into
| * = **-* | *** *** T = e = | s= . East Dean.
8 ‘80 5-08, 6.9ſ, I 82 8.50; J
8 * 4, 55| 5 08 •53 ; 7-70
7. 4 -35 4. 55 •20 99.26 670
& 5 05 4-35 - 70 99.46|| 5 -70
5°50 1 1 00 5-05 || 5 95 98.76|| 5 20
5°23 6.24 4-52 l'72 – 92-8] 49s. .*::::::: º; into
5 • 1827. 624 7-08 — 91°09| 4:84 #steeply inclining gr.
4, 60] II '86 125 10-61 — 84.06| 4:45 #
4 • 10:45 325| 7:20 — 73°45' 3-88|J on oppo. side of brook
3.43 14'60 10.45| 4-15 – | 66°25' 3-32 Into centre of small]
3°35' 10-45 14-60 – 4-15 62°10' 3-24 brook (6 in. water.)
On side of brook.
3:30 7.10| 10:45 – 3:35, 66:25; 3:19)
3- 1-52 7-10 — 5-58 69.60) 2-89 | ly declini
2-77 .io 1390 —13 so 75 is 2-63 K Steeply declining gr.
- 2-37 5-68 13.96 gº 8-28 88 •98 2-34, | CroSS hedgeinto West
2" | . 4.-88 5-68 — ‘80ſ-97°26′ 2:003. Dean.” -
I-75 3.88) 4-88 — 1.00. 93-06; "I “75
J - 2.94, 3-88 — , -94. 99-06 || -00-
§ 90 100.00 100.00 100 00 00. Borrowed 100 ft.
i_flºan, South Shields, May 27, 1833. . . . . . . . . …"
;Stanhope and Tyne railway commenced Jewels from a mark in a field near Brewery
* - , , ,
3 : 3 / 3
2. 3 3 - d ?
7/7 of
/4, 7 - 5 /
%.'.
:
+.
+
f
,
A.
:
*
º
º
*
t
:
USE OF THE SPIRIT LEVEL. 49
rise at the distauce of 3:48 extending to the
opposite side of the first brook.
I think it would be quite unnecessary to enter
further into this detail, because as the field-
book now stands it is a mere matter of addition
and subtraction, and a little attention to the
preceding instructions will enable any one to
manage the subsequent calculations. I shall
just observe that instead of carrying forward at
any succeeding page the gross numbers at the
head of the four different columns, only carry
forward the total rise and this sum must be
placed at the bottom of the page mnder the
head of rear heights, rise, and total rise, and
whatever may follow must be conducted in the
manner already described. -
Let us now proceed to calculate for the true
horizontal distance,—on examining the column
of total rise and the column of approximating
distances, we shall find four series of numbers
requiring reductions, the 1st series commences
at or between two chains and 2'37, conse-
quently the difference in their distance is 37
links, and their difference of level 8 feet, 28
decimal parts, equal to 12.5 links, which may
be found, according to instructions given in
page 53, and by inspection of the table, page
E
50 ESSAY ON THE
54, or say as 66 ft. : 100 links: 8 ft. 28 pts.=
12.5 links. - - -
Then from the square of (37°)=3169
Subtract the square of (12.5°)= 156:28
Extract the square root of the re-
mainder, ........................Y121275=34:
links for the true horizontal distance, which
added to the 2 chains will give 2:34, and that
must be carried to the column of reduced dis-
tances. The next reduction is between the
2.37 and 277, the difference in their distance is
40 links, and their difference of level 1380 links.
Then from the square of... (40)=1600
Subtract the square of...... (21°)= 441
Extract the square root... v. 1159–84 links for
the horizontal distance, which added to the last
reduced distance 234 will make 268 for the true
distance. The two succeeding distances of the
first series, or declination, also require reduc-
tion, viz. from 3 to 330; but having given two
examples sufficiently explanatory, it would be
superfluous to go further into detail of a sub-
ject so simple.
The second series commences at 8:43 and
terminates at 5:23 inclination--the third ditto
uSE OF THE SPIRIT LEVEL. 51
commences at 8:80 and terminates at 10:10 de-
clination—the fourth ditto commences at 11:00
and terminates at 15:45 inclination. As the re-
maining distances were measured over a surface
nearly level, all that remains to be done is to
find their difference in measurement as they
ascend the column of approximate distance;
thus having reached 15:45, the difference be-
tween that and 16 chains is 55 links, which
added to the last reduced distance leaves 15:39,
and the difference between the two numbers at
the top of the column, 25 and 26 chains, is 1:00
chains, which, added to the other column, leaves
25-39 for the true horizontal measure, making
a difference in the whole distance of 61 links.
As it is my intention to give every informa-
tion I can upon this subject, I beg leave to state
that in a clear open country these reductions
might be avoided, by boning out the line and
erecting poles over the sloping ground, at the
distance of every 10 or 20 links, more or less,
as the surface of the ground may require, and
thereby measuring the distances correctly ; but
in a thickly wooded country this could not be
effected without considernble destruction of
timber and underwood, besides many other dif.
ficulties that we cannot here enumerate.
52 ESSAY ON THE
REDUCTION OF DISTANCEs.
In all operations in levelling we have always
two sides of a right angled triangle given, viz.
the oblique distance measured, or hypothenuse,
and the elevations or depressions, which are
perpendiculars to find the third side or base;
therefore proceed according to the proposition
given in page 18 of apparent level, by substract-
ing the square of the difference of level between
any two points from the square of the oblique
distance, and extracting the square root of the
remainder will give the true length of the
horizontal or base line. -
Suppose the difference of level between two
points should be 100 feet equal to 151 links for
the perpendicular B C, as shewn in the following
figure, and the length of the measured line or
hypothenuse, 6 chains, then VIA B*—B C*=A C.
A.
A B-................. = 6.00% chains =36.0000
B C= 100 feet ... = 1.51* (see table)= 2.2952
v337048–580
five chains and eighty links for the base A C
being the true horizontal distance.
USE OF THE SPIRIT LEVEL, 53
As we have just shewn, the difference between
inclined and horizontal lines vary considerably,
particularly when the inclined lines make large
angles with the horizon, and if plotted to a large
scale the oblique distance will greatly exceed
the true measurement; it is the practice of most
surveyors whenever the ground is slightly in-
clined, to shorten each line a little, for it will
be found next to impossible to measure so many
different lines, and over surfaces of various in-
clinations, with mathematical exactness, there-
fore where great accuracy is required actual re-
duction ought to be resorted to. -
The following Table will materially assist in
reducing dimensions, taken in links into feet,
inches, and decimal parts, and, vice versa, to re-
duce feet, &c., into links.
Suppose I wish to know the number of feet
and inches in 20 links—look in the table for
the number of links and opposite, in the two
right hand columns, will be found 13 ft. 2 inches
and 40 decimal parts.
54
ESSAY ON THE
A TABLE,
TO REDUCE ANY DIM. ENSIONS TAKEN IN L, INKS 1&to
FEET AND INCHEs of vicz versa.
Links. | Feet. Inches.||Links. Feet. Inches. ||Links. Feet. Inches.
l 0 || 7.92|| 34 22 5-28|| 67 || 44 || 2-64
2 1 3-84|| 35 || 23 1-20) 68 || 44 10-56
3 1 || 1-76|| 36 || 23 9-12|| 69 || 45 || 6-48
4 || 2 || 7-68|| 37 24 || 5-04|| 70 || 46 || 2:40
5 || 3 || 3-60|| 38 25 0-96|| 71 || 46 |10-32
6 || 3 |11-52|| 39 25 | 8-88|| 72 47 6-24
7 4 || 7-44|| 40 26 || 4-80|| 73 || 48 || 2-16
8 5 |3:336|| 41 || 27 0.72 74 || 48 || 10.08
9 || 5 |11-28 || 42 | 27 | 8.64|| 75 || 49 || 6-00
10 || 6 || 7-20|| 43 || 28 || 4-56|| 76 || 50 1-92 2.
11 || 7 ||3:312|| 44 29 || 0:48|| 77 50 | 9.84 *
12 || 7 || 1:04|| 45 29 || 8.40|| 78 || 51 | 5:76 .
13 8 || 6.96|| 46 || 30 || 4:32|| 79 || 52 | 1.68
14 9 2.88||47 ||31 || 0:24|| 80 52 9-60
15 | 9 ||10-80|| 48 || 31 8.16|| 81 53 5-52
16 || 10 || 6-72|| 49 || 32 || 4-08|| 82 || 54 1-44 i
17 | 11 || 2-64|| 50 || 33 || 0-00 || 83 || 54 9-36 º
18 11 ||10-56|| 51 || 33 || 7-92|| 84 || 55 5-28
19 || 12 || 6-48 || 52 | 34 || 3-84|| 85 56 1-20
20 | 13 || 2:40|| 53 ||34 |11.76|| 86 56 9:12
21 | 13 |10-32|| 54 35 | 7.68|| 87 57 5.04
22 || 14 || 6-24|| 55 || 36 || 3:60|| 88 || 58 || 0-96 *
23 15 2.16|| 56 || 36 |11-52|| 89 58 888 -
24 15 ||10-08|| 57 37 || 7-44|| 90 59 || 4-80
25 | 16 || 6-00 || 58 38 || 33-6|| 91 60 || 0-72
26 17 | 1-92 || 59 || 38 || 1-28 || 92 || 60 8-64,
27 | 17 | 9-84|| 60 || 39 || 7-20. 93 || 6 || || 4-56
28 18 5-76|| 61 | 40 || 3-12|| 94 | 62 || 0-48
29 || 19 || 1-68|| 62 | 40 |11-04|| 95 62 8-40
30 19 9-60|| 63 41 || 6.96|| 96 || 63 || 4:32
| 31 20 || 5.52|| 64 42 2.88|97 || 64 || 0-24
32 21 | 1.44|| 65 || 42 |10-80|| 98 || 64 8-16 -
33 21 |9-33 43 | 6′72| 99 || 65 | 408
..--
+
H.
USE OF THE SPIRIT LEVEL. 55
A CASE OF SIMPLE LEVELLING BY THE BAck
AND Fore observation.
Suppose it were required to know the height
of a lake of water at A, above the ground floor
# of the bath-house at Z.
At the lake of water A, drive down a stake
(of due length and about 2in. square) until the
. . . head be level with the surface of the water, upon
… which let your first assistant set up one of the
graduated staves,and cause your second assistant
to set up another at a distance of 5 or 6 chains
(each assistant ought to be provided with a small
picket for the purpose of resting the bottom of
the graduated rod, and marking out the precise
point levelled to, the head of which ought to be
pressed into the ground, level with the surface);
56 ESSAY ON THE
place the instrument in the middle, about an equal
distance from each of your assistants, and in a
line with them and the building. Things being
thus prepared, and the Spirit Level properly
adjusted, look through your telescope to your
first assistant or rear staff, and direct him to
move the sliding vane upwards or downwards,
as circumstances may require, until the cross
wire of the vane corresponds with the horizontal
wire in the telescope, and intimate to him, by
some preconcerted sign, that the vane is in its
true position; he must now make fast the slid-
ing vane and observe the number of feet, inches,
and tenths, viz.--2ft. 6in. 4tenths, shewn upon
the graduated rod, which must be entered in the
field-book in the column marked rear heights;
turn the telescope round to your second assist-
ant or front staff, at B, and cause the person
there to move the sliding vane upwards or
downwards, until the cross wire in the vane ap-
pears in the line of collimation as before ; inti-
mate to him that it is in its true position; let
him make fast the sliding vane and observe the
number of feet, &c. viz.-5ft. 3in. 4tenths, shewn
upon the graduated rod, which must be entered
in the field-book in the column marked front
heights; deduct the one from the other, the
less from the greater, and the remainder-will be
USE OF THE SPIRIT LEVEL, 57
the difference of level between A and B, which
is 2ft. 9in. 9tehth below A, and must therefore be
entered in the column marked depression; the
distance being now measured, and found to be
5'10 (5 chains 10 links); enter this also into
your field-book in its proper column (distance
in chains); this done, direct your first assistant
to the station at C, and take up your position in
the middle ground as before; the instrument
being adjusted, look through the telescope to-
wards your rear staff, and cause your assistant
to raise or lower the vane until he has brought
the centre into the visual line of the teles-
cope; direct him to make it fast, and note what
number of feet, &c., viz. –3ft. Oin. 9tenths are
shewn upon the graduated rod, which enter into
the field-book in the column of rear heights:
turn the telescope round and observe the front
staff, and desire your assistant there to raise or
lower the vane until he has brought the centre
also into the visual line of the telescope, desire
him to make fast the vane, and observe the number
offt. viz.-6ft. 6in.9tenths shewn upon his staff,
which enter in your book in the column of front
heights; add the rear heights together, add also
the front heights together, subtract the less from
the greater, and the difference will be fift. 3in.
40teaths, the ground at C being that much below
58 ESSAY ON THE
A, which is entered in the column of depression;
the distance measured up to C makes (11-10)
11 chains 10 links, to be entered in the column
of distances: direct your second assistant to go
forward to D; having taken up your position
with the instrument half way between C and D,
the Spirit Level being adjusted, look back to the
rear staff, and, managing the vane as before, the
visual line will shew the height of the vane on that
staff, viz.-2ft. Oin.9tehths entered in the column
of rear heights, turning the level to look at the
front staff, the visual line will also give the height
of the vane on that staff, viz.—6ft. 3in.0tenthsen-
tered in the column of front heights; add the rear
heights together, and add also the front heights
together, deduct the one from the other, and the
difference will be 10ft. 6in. 9x depression; the
surface at D being that much below A; the
distance measured up to D is 17-10 (17 chains
10 links). Proceed in the same manner with the
remaining stations from D to E and from E to
Z, entering their respective heights, distances,
&c., in the manner shewn in the following field-
book.
Use of THE SPIRIT LEVEL. 59
* *-**** - - -
wºº. .
LEWELS -
FROM THE RESERVOIR TO THE BATH HOUSE.
ID F - i D LOCATIONS
Fr ist º R t || -> €0teS- O -
§. gºn Hits. Hº. Elevation. sio º eS -
- July, 1882.
Z || 32-00 || 14 || 3-1 || 30 || 3-1 || 16 — Level of floor
wº of bath.
3 5-7 || 5 || 87|
E 24-90 10 9°4 || 24 || 6-4 13 || 9-0
3 ||3-0|| 6 || 6-0 -
D 17-10 7 || 6-4 #18 0.4 10 || 6-0
2 : 0-0 || 6 || 3-0
C I 1-10 5 || 6-4 || 1 || || 9°4 6 || 3-0
|| 3 || 0-0 || 6 || 6-0
B 5-10 | 5 || 3-4 2 || 9-0
;
A 2 | 6’4 Water edge.
I beg here to state, that on a measured dis-
tance of 5 chains, or 110 yards, with an incli-
nation or declination of 5 feet, the reduction
will only be half an inch for the whole length;
therefore, in the preceding example, we may let
the measurements remain as they are, as only in
one case, the declinations exceed 3 feet.
Having now summed up all the columns se-
parately and collectively, making the sum total
of the rear heights 14ft. 3in. 1:enth, and the sum
total of the front heights 30ft. Sin. Itenth; take
the less from the greater, which will leave 16 ft.
depression for the true difference of level be-
tween A and Z, and the total distance 32
60 ESSAY ON THE
-----ºr--"
chains; making the proportional inclination or
declination from A to Z as 1 to 132, that is for
1 foot altitudinal to 182 longitudinal.
This system of taking and recording levels
will be readily appreciated; for by progressively
adding and subtracting, you have at any time
, the height or depth below the original station,
or zero mark, and it will be found equally ad-
vantageous in making a profile or section of the
ground, being at once easy and expeditious.
Let it be required to draw a profile from the
levels given in the field-book (see page 59.)
Draw a base or horizontal line A Z, as in the
following figure; on this line set off from the
zero mark at A the different distances, viz.-for
B 5:10, for C 11:10, for D 17-10, for E 24.90,
and for Z 32.00 chains, let fall a perpendicular
USE OF THE SPIRIT LEVEL. 61
from each of these distances. The base line
being the level of A, or the water in the lake,
set from B downwards 2ft. 9in.9tenth depression,
from C 6ft. 3in., from D 10ft. 6in., from E 13ft.
9in., and from Z 16ft. Oin. ; connect all those
points together, A and B, B with C, &c., and
you have an exact profile of the ground over
which the levels were taken.
Having thus explained the mode of levelling
by back and fore observations, we shall now
proceed to shew the second method, which con.
sists of levelling from one point direct to ano-
ther by fore observations only, called the appa-
rent level. -
CASE OF SIMPLE LEVELLING
BY THE FORE OBSERVATION,
Let it be required to level from a point at B
to another at X. Instead of placing the instru-
ment between the two staves, as in the preced-
ing example, fix it at one of the extremities of
the line as at B, in the following figure, and
62 ESSAY ON THE
|
}
;
;
t
look forward to the staff at C; request your
assistant then to raise or lower the vane until
it corresponds with the line of vision of the
telescope; enter in your field-book the height
shown on the staff, viz., 10 feet 6 inches in
the column of front height; take the height
of spirit level, 4 feet 4 inches, that is to the
intersection of the cross-hair in the telescope
corresponding to the line of vision, which
must be entered in the column of rear heights—
deduct the one from the other and enter the dif-
ference in its proper column, viz., 6 feet2 inches
depression, because the front heights exceed the
rear heights; measure the distance from B to
C, 10 chains, which enter in the column of dis-
tances; remove the instrument forward and
place it over the mark at C, where your assistant
had previously held his staff, send him forward
to D; having adjusted the level, look towards
the staff at D, the height of the vane above the
surface at that point being 12 feet 4 inches
which enter in the column of front heights as
before, enter also the height of the spirit level,
4 feet 5 inches, in the column of rear heights,
add the rear heights together, add also the front
heights together, subtract the one from the
other, and the difference will be 14 feet 1 inch
depression, which enter in its proper column;
USE OF THE SPIRIT LEVEL, 63
... ------------------, -º-º-º-º-º-º-º-º----, -
measure the distance up to D, which is 22
chains; the instrument is again broughtforward
and placed at the mark D, having adjusted the
spirit level, look forward to the front staff at E,
the height of the vane above the surface is found
to be 8 feet 6 inches, which is entered in the
column of front heights. The height of the in-
strument being 4 feet 3 inches entered in the
column of rear heights, add the rear heights to-
gether, add also the front heights together, de-
duct the one from the other and the difference
will be 13 feet 4 inches depression; measure the
distance up to E, which is 40 chains, proceeding
thus from one staff to another always taking
fore-sights. Having gone through the whole of
the operation, viz., from E to F, and from F to
X, in a similar manner to that which has just
been described and as explained in the following
field-book.
:
§
LEVELS FROM A POINT AT B TO ANOTHER AT X,
BY FORE OBSERVATION ONLY.
July, 1833. Commenced
º
levels from a mark at B.
From Bear-Dist R Front D Correct for Reduced | Reduced gº
ś|Hº Hºli, zººlºr| –
TxTV 39 4 17 | 6 ||—| ‘970| 17 | 5-0 Surface at X below B
21, 10 ſºlo Ta Togo
- 4 || 4 . . . . . . . . .
F|—| 52.00 29 || 0 11 || 6 |-|-890 11| 5 || . .
17 | 6 || 2 || 8 | T80| | | |
{ 4 || 6 || - i &
El— | 40-00 26 || 4 13 || 4 ||—| ‘710| 13 || 3-2 ||
| 13 || 0 ||—— —l
–| 3 || 6 •405
4 || 3 .
P- *|| || |* I tº 14 || 1 |-|-305] 14 || 0 6
-]—| 12 || 4 •180| ||
4 || 5 —l
C-| 10:00 10 || 6 6 || 2 ||—| 125| 6 || 1:8
B|—| -00 || 4 || 4 |. º
Use of THE SPIRIT LVEL. 65
heights, 39 feet 4 inches—take the less from the
greater and the difference will be 17 feet 6
inches depression—apparent level only to be re-
duced to the true level. - -
The distance between B and C on the first
line being 10 chains, square this distance and
divide by 800, the quotient will be inches or
10x10_100
decimal parts *...*=;=125 for the true dif.
erence of level to be deducted from the appa-
rent level, viz., 6 ft. 2 inches. 6 ft. 1 inch 8
tenths, the true level, which enter in the column
of reduced levels; the next distance 22–10=
#=;1803 édited from 14 feet 1 inch=
14 feet 0 inches 6 tenths for the true level at
D; the distance to the third station 40–22=18
chains look in the table (page 22) for the num-
ber and opposite to it, you will find '405(deci-
mal of an inch for the correction)+(505-719 de-
ducted from the next apparent level viz.: 13feet
4 inches, will leave 13 feet 3 inches 2 tenths for
the true level at E, thus the whole may be reduc-
ed by inspection or otherwise, making the true
difference of level between B and X 17 feet 5
inches.and–9—tenths
The advantage of taking the observations at
a short distance from each other is here strik-
ingly illustrated, for the difference between the
F
66
ESSAY ON THE
LEVELS from Nexbit's Cottage, near Thornton Street, to Parker's
Quay, on the River Tyne, taken November 29, 1829, for a then
true and apparent level is so trifling as only in
one instance to exceed a quarter of an inch, but
if the distance of 60 chains had been taken for-
ward at a single observation, the difference or
error would then have been 4 inches and a half.
contemplated Branch of the Newcastle and Carlisle Railway.
OFFSETS, BENCH MARKS AND INTERMEDIATE LEVELS.
| - Offsets TSum of Sum of /ø-i-. A 3-& |
From] Distance. I interm. front rear Eleva- |Depres- |Reduced Red. Locations.
Stat. heights. heights. heights. tion. sion. I Levels. Dist.
round.
34°54 6-8-7-1-114 6-9 |–46 7.2 74| 84 erge of steeply declining] ..
O {; 38.5]+114] 6-9 |—46 || 7-2 71| 8-2 Garden fence.
BM [ . I-6-0|+114|| 6-9 |—46 || 7-2 69 5-7 On Upper-gate Crook.
Il 22-36 || 3:9-0|-|-102|11-9 |—45 || 4-3 61 4-6
m| 30-00 || 3:9.3 + 96, 4-6 ||—44 3.9 55|10-0
28-88 15-1-0|+ 86 6-8 –43 9-6 57|10-2 Bottom of clay-hole.
28.48 || 13.1.0+ 86 6.8 —43 9:6 55|10-2 Surface of water in clay-hole.
27-88 15-1-0|+ 86 6-8 —43 9-6 57|10-2 Bottom of clay-hole 2 feet.
l 27.75 8-7-5]+ 86|| 6-8 —43 9-6 51| 4-7 -
27-43 || 3:9-0|+ 86| 6-8 |—43 9-6 46|| 6-2
26.96 || 2-3-4|+ 86 6-8 |—43 9.6 45' 0.6 Fence.
BM [ 1-6-0+ 86| 6-8 —43 9:6 |44; 3:2 Top of a stake in Fence.
k 25.70 || 3-8-4|+ 82 0.8 –39 2-8 46| 6’4
j || 21:37 || 3-10-0|+ 57|10.1 –32 || 5.6 29, 2-5
i 20-26 3.9-0|+ 50 4-5 –30 5-9: 23| 7.6
h 18-85 || 3-8-3]+ 43 7-3 ||—28 11.4 18| 4-2
g § §: ; § Tº }} º § On a large flat stone in field.
f {; 3-9.9}-H 24, 5-3 —22 || 1:7 6|| 1.5 º
14.88 || 3-9.5|-|- 24 5-3 –22 || 1:7 6|| 1 || Verge of high ground.
e 13:00 || 3:9-04- 2311-0 –15 1-2 12|| 6-8
IBM 5.0-0 + 20, 6-9 – 7 || 5-3 18| 1-6 On stone wall.
11:00 || 7-3-1|+ 20, 6-9 – 7 || 5-3 20|| 4-7 Into gardens.
d { 10-16 || 3:10.6+ 20, 6-9 – 7 || 5-3 17| 0:2 occupation road.
10-06 || 5-0-1|+ 20, 6-9 – 7 || 5-3 18 1-7
C 7-50 || 3-9-5]+ 14 37 – 6 5-1 11| 8-1
b 4-00 || 3-9:54- 610-0 |- 3 || 7-1 7| 0-4
à, 1-00 || 3-8-2}+ 0| 0-0 – 2 | 6-8, || 1-6
Offsets and intermediate levels on line to Thornton Street.
§*.
-
i
g
:
LEVELS FROM THORNTON STREET TO PARKER'S QUAY.
,--Dist. in R Front | El Depres- I Reduce Reduced! —
jbearing...]."|h;,] ... ." |*.* |*::::::::::::: Locations.
º 37-4672 9-8 who, 126| 2-1 Base of Quay.
T5] 0-0|| 15 00 tide.
- 37-43|67 9-8 183|10-9 116| 2-1 High water mark, spring
- r 3 0-9 5| 0-0 on the River Tyne.
24 37-42|64, 8-9 || 178|10-9 114| 2-0 To edge of Parker's Quay,
5|| 0:2 3| 0-9 Lead Factory to Newcastle.
23 36-50 59 8-7 || 175|10-0 116, 1-3 Occupation Road, from
3-3-5 1030
22 36.00|56, 5-2 | 165| 7-0 109 1-8
: 3| 37|12|66
2I 35-60|53. I-5 || 153| 0-4 99|10-9
* e 3|0|5||11 6.2
| 20 - 35-16|50 l’0 || 141| 6-2 91| 5-2
Tal B-8'ſ 15|3.3
19 (34.70|46 7-2 || 127 9.9 81| 2-7
O { Tl29ſ. 13| 3:0
18 34°00'45| 4:3 || 114 6-9 69| 2.6
Il T] 0.4T III 7.0
17 31-38|44; 3.9 || 102.11-9 58| 8-0
In | 6′3| 67.3
*... 16 28-92 43 9-6 || 96|| 4-6 52| 7-0 Edge of Clay-hole }
I { Al 68 g|9-3 #
15 26-7239| 2:8 || 86 6.8 47| 4:0 !
k 3|8-6-4 6-0 -
§ 14 24-25|35, 6-2 || 82 0-8 46|| 6-6
TIB-0|7| 95
#3 23-003310-2 || 74 3-3 40|| 5-1 j
T 4-6 8| 44
12 22.0022. 5-6 || 65||109 33, 5-3 i
j 1|11-7 || 8 0-8 H
11 21:0030) 5-9 || 57|10-1 27| 4-2
- i 1| 6′5 || 7| 5-6
10 19:62|28||114 || 50|| 4-5 21| 5-1 3
h 1| 9°5 || 6 9-2
9 18-39|27| 1.9 || 43| 7-3 16| 5-4 A cross mark in the field. :
8. 3| 6-7 6||11-8 i
8 17.4333| 7-2 || 36|| 7-5 13| 0-3 º
| 5.5 || 7 | 6-2 :
7 16.0022. 1:7 29| 1.3 6||11-6 South Verge of high ground.
&- f { 7| 0.5 ! 4 8:0
6 13-82|15; 1-2 || 24, 5-3 9| 4-1 H
€ 7| 7-9 6-3 -
5 12:00, 7] 5:3] 2311-0 16| 5-7 II •60 Cross fence.
d { | I] 02 || 3| 4:1 - -
4 8-75. 6. 5*I 20 6-9 14| 1-8 Face of stone wall.
O c 2|10-0 || 6 || 3-2 . . . * ~ *
3 6:00 3, 7-1 || 14 37 10| 8-6
* b | 1, 0-5 || 7 5-7
2 2-00 6|10-0 4, 3-4 .
* - 2– s • 4.
1 | " I 00 26.6 ſ ] -
. ... Commmenced at a mark near to Nesbit's Cottage, Thornton-street, Newcastle.
——
* – --> * > . .” -- ~~~~. = a-, -º-º------ * - - - - - -, * * *-* -- <!-- *---- - • *-* - —---------, -
68 Essay ON THE
In explaining the foregoing field-book, of the
levels taken from a stake near Nesbit's cottage,
Thornton Street, to Parker's Quay, the offsets,
bench-marks, and intermediate heights, are en-
tered on the opposite page to the main line of
levels, so that they may either be made use of
or not, as occasion may require, for in the ge-
nerality of cases, exploring levels are only re-
quired to be plotted to a very small scale, and in
all probability wanted at short notice; therefore
the plotting of the intermediate heights might be
omitted, as they would not make any very sensi-
ble difference in the appearance of the profile of
the ground; but under these combined operations
you have two opportunities, the one for com-
pleting the work with the utmost expedition, as
the calculations in the first case are trifling, and
the other (if an estimate, &c. should at any
time be required) of plotting it on a larger
scale, when the intermediate heights would be
essential in delineating the true features of the
country, and having them thus registered, the
calculations can be made at leisure.
This method has many advantages which
practice alone can show in respect of expedition,
convenience, and so forth.
It will be necessary here to observe that the
jirst rear and the last front height are only en-
tered in the general registry, and all the other
DSE OF THE SPIRIT LEVEL. 69
heights which have previously been enumerated
are carried to their proper column (offsets and
intermediate heights) in the opposite page of
the field-book; the calculations are for the
most part made on a slate or waste paper, and
the elevations or depressions only registered,
but for the better explaining the mode of com-
putation I have arranged them under proper
heads in that page, and marking by letters of
reference, as well as by measurements, the po-
sition of these abstract levels; I have also
shewn by plus + and minus —, which are to be
added together, and which subtracted; by this
scheme, it is expected the whole will be more
easily understood.
We may suppose the field-book of the general
line of levels to be already made up, and from
the rules given there can be no difficulty in un-
derstanding it.
The second rule, page 44, says “offsets,
bench-marks, intermediate, and instrument
heights, are always to be treated as front heights,
(which in fact they are), and are therefore to
be added to all the heights of that name, except-
ing the last, and deducted from all the rear
heights as the case may require, by taking the
less from the greater.”
The first observation or rear height is 2 feet
6 inches, 6 tenths, which is carried to its pro-
70 ESSAY ON THE
--~f~ ºr ~ :-rº-. . . .--------- —-- - - - - - - ---— - - - - -, - - - - - - - - - - - -º-º-º-º-º-º-º-º:
- - i - • *- : * Frºz. … - .
per column in the field-book, and in this in-
stance I have also inserted it in the opposite
page under the head of the sum of the rear
heights. Between this and the second station, an
intermediate height, 3 feet 8 inches 2 tenths
was taken, at the distance of one chain, which is
placed in the opposite page of the field-book,
and from its being the first and only front height,
it may be either entered in the column of “off.
sets and intermediate heights,” or in the column
of the sum of the front heights and subtracted
from the sum of the rear heights, (the less from
the greater), and the difference 1 foot, 1 inch,
and 6 tenths is depression, (the sum of the front
heights exceeding the sum of the rear heights).
The rear height at the second station is 1 foot,
0 inches, 5 tenths, making the sum of the rear
heights 8 feet, 7 inches, 1 tenth, (although it
may appear to stand opposite the 3d station,
yet we have progressed no further than the 2d
station with these heights), now between this
and the 3d station, at the distance of 4 chains,
an intermediate height was taken, viz. 3 feet, 9
inches, and 5 tenths, this is to be added to all
the other front heights (excepting the last)
either above or below it according to the method
used in recording these levels; but properly
speaking from its position this is itself the last
observed front height, consequently must be
s:
* * ~ ******-tt-, - . . . ~~~~.m. eas-----1a: "... . . . . . . . . . . . ...
USE OF THE SPIRIT LEVEL. - 71
added to 6 feet ten inches, making 10 feet, 7
inches, and 5 tenths, from which deduct the
sum of the rear heights, 3 feet, 7 inches, 1 tenth,
leaving a difference of 7 feet, 0 inches, 4 tenths,
for depression.
The rear height at the third station was 2
feet, 10 inches, added to the other heights of
that name will make the sum 6 feet, 5 inches,
and 1 tenth ; at the distance of (7.50) seven
chains and a half, on the line between the 3d
and 4th station, an intermediate height was .
taken, 3 feet, 9 inches, and 5 tenths, which add i
to all the other front heights (as before), and .
which you will observe on the third line from
the bottom of the page, in the column of the
sum of the front heights, to be 14 feet, 3 inches,
and 7 tenths, from which deduct the sum of the
rear heights, viz., 6 feet, 5 inches, and 1 tenth,
will leave 11 feet, 8 inches, and 1 tenth, de-
pression. .
- The rear heights at the 4th station was 1
:* foot, 0 inches, and 2 tenths, which added to all
the former heights of that name, viz., 6 feet, 5
inches, and 1 tenth, is equal to 7 feet, 5 inches,
and 3 tenths. Now, between the 4th and the 5th |
station (from the irregularity of the ground,
&c.), there are three intermediate heights, and a
bench-mark taken, the first was at the distance
of 10:06, and its height 5 ft. 0 inch and 1 tenth,
. . . .
J.--> *-ºs-----º-º-º-º-º-º-º-º-º-º-º-º-º-º-º-º:* -- . . . . . . . . -, -, -i-. … . . . . . . . . . - - . . . . .
72 g ESSAY ON THE
#--
added to the sum of the front heights, namely,
20 ft. 6 inches and 9 tenths, is equal to 25 feet,
7 inches, from this subtract the sum of the rear
heights, 7 feet, 5 inches, 3 tenths, and the re-
mainder will be 18 feet, 1 inch, and 7 tenths,
depression.
Now the sum of the rear heights and the sum
of the front heights are the same as in the last
case, up to the 5th station; the second inter-
mediate height 3 feet, 10 inches, and 6 tenths,
taken at the distance of 10:15, a few links fur-
ther than the last, in an occupation road (now
known by the name of the Scotswood Road),
which added to the sum of the front heights,
20 ft. 6 inches, and 9 tenths, is equal to 24 feet,
5 inches, and 5 tenths, from which deduct the
sum of the rear heights, 7 feet, 5 inches, and 3
tenths, the difference will be 17 feet, 0 inches,
2 tenths, depression. The third intermediate
height was 7 feet, 8 inches, and 1 tenth, taken
at the distance of 11:00 (in the garden ground),
to this add the sum of the front heights, 20 feet,
6inches, and 9 tenths, will give 27 feet, 10 inches,
from which subtract the sum of the rear heights,
7 feet, 5 inches, 3 tenths, as before, their dif.
ference will be 20 feet, 4 inches, and 7 tenths,
depression. -
The last height of this series is the bench-
mark, 5 feet, 0 inches, 0 tenths, taken upon a
~, | º,
Zº . . . , 's
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31 ºf
LEVELS from Thornton Street to Parker's Quay collec-
tively, as a proof to former Field Book.
From Distances Rear Front Eleva- || Depres- e
Stat. in Chains. Heights. Heights. tion. sion, Locations.
#jº T Qſ
37-48] 2 0-0 2 +. 126) fl:1 Base of Quay.
3 *, *, *| 5 || 0-0|| 15| 0:0
37:44, 211| 0-0|| 327 I •l 116 'll |High water mark spring tides.
3| 0-9| 5 || 0-0 e
G ſº * > the River Tyne.
24, 37-42 sº 11 *l 322] I'l 114 2-0 |Tö edge jºrs quay on
5| 0 |2| 3| 0-9
23 36-50; 202 10-9) 319|| 0 |2| 116 l'8 |Occupation road from factory.
3| 3•5| 10 3-0
22 36:00 199| 7-4, 308| 9-2 109|| 1:8
3| 3-7| 12 6-6
21 35,60|| 196|| 3-7| 296 2.6 99||10.9
3| 0-5 11| 6′2
20 35° 16, 193 3-2 284 8-4, 91 5-2
3| 5-8| 13 8-3
19 34-70, 189| 9.4| 271 (). 1 81| 2-7
ſ *-
: 6|| 8-7| 13| 3:0 round
34:54, 183 0.7| 257 9.1 '74, 8.4 vš. of steeply declining
e 3| 8-5, 6, 8 ~7
o - 34.25 179| 4,2| 251 0°4. 71 | 8°2 learden fence.
| *
1 6-0|| 3| 8-5
BMſ 177|10-2 247 3-9 69| 5’7 ||On upper gate crook.
U 1| 2.9ſ 1 || 6-0 -
176|| 7-3] 245| 9.9 69| 2.6
l8 34 00 sº
3| 9-0|| 1 || 7-0
172 10-3] 234 2-9 6|| 4-6
Il 32°36|—||—|-|--
1 || 0 °4. 3| 9-0
17 31 38 171 || 9.9| 230 5-9 58| 8-0
3| 93 67.3
Ill 30.00) 168|| 0 6 223| 10:6 55|10-0
... 6'3| 3| 9-3
16 ſ 28:92] 167| 6′3 220 1 3 52| 7-0 |Edge of clay-hole.
15| || 0 | {}| 9.8
28:88) 152| 5'3| 210 3-5 57|10-2 |Bottom of clay-hole.
13| 1.0l 15, 10
28° 48' 139|| 4°3| 195| 2-5 55|10-2 |Surface of water., c. h.
15| | |0|| 13 1.0 -
27-88 124|| 3:3| 182 1 -5 57|10-2 |Bottom of clay-hole.
8| 7.5 J5|| 1:0
27.75] 1 15| 7-8| 167| 0:5 5]| 4-7
3| 9-0|| 8 || 7-5
l 27-43| 1 || || 10°8| 158 5-0 46|| 6’2
2 3'4| 3| 9 0
26.96] 109|| 7-4 154 8-0 45| 0:6
|| 6-0 2| 3-4 * *
U BMI 108 l'4, 152 4-6 44|| 3:2 |Top of stake in fence.
4, 6-8 || 6-0
15 26-72; 103 6'6|| 150| 10.6 47| 4:0
3| 8°4| 4 || 6-0
k 25.70| 99| 10:2| 146|| 4-6 46|| 6’4
3| 8-6 3| 8 °4,
l 4. 24, 25 96 l'6|| 142| 8-2 46; 6.6
iſ so 79.5
13 23 00. 94, 5-6|| 134 10-7 40|| 5 ||
1| 4'6|| 8 || 4-4.
12| 22:00. 93 1-0 126|| 6′3 33| 5'3
3|10-0 8|| 0-8
j 21:37: 89) 3-0|| | 18| 5-5 29| 2'5
| | | 1.7 3 l ():0
| | 21:00 87| 3'3| || 14, 7-5 27| 4-2
3| 9:0| 7| 5-6
i 20°26′ 83| 6′3| 107 1-9 23| 7:6
|| 6-5 3| 9 ()
I () 19.62| 8 || 11.8| 103| 4-9 2|| 5 “I
3| 8°3| 6 || 9 °2
h 18-S5, 78; 3-5] 96 7.7 18| 4-2
||| 9-5 3| 8 3
Q 18-39, 76, 6-0 || 92] 1 1-4 16| 5'4 |A cross mark in the field.
3| 6-7| 6 || II •8
§ 17.70 72|ll 3| 85| 11-6 13| 0-3
3| 67 3| 6.7
8 17:43| 69| 4'6| 82| 4'9 13| 0-3
I 5'5| 7| 6-2 t
7 16:00 67 l l ‘l 74 10-7 6|ll'6 To Verge of high ground.
2| 0:0 4| 8-0
ſ BMT 65||11.1| 70 2-7 4|| 3:6 |Cross on large flat stone in field.
- 3| 9°9| 2 0-0 - \
f 15:41, 62. 1 °2| 68| 2-7 6| l'5
| 3| 9°5 || 3 9-9
U 1488, 58] 3-7, 64 4-8 6| l'I
7| 0'5| 3 9 5
6 13.82 5 l 3'2' 60 7.3 9| 4 •l
a 9-ol. 63
e 13.00. 47| 6’2 60 1 0 12| 6-8
7| 7-9| 3| 9-0
5 12:00 39| 10:3| 56 4'0 16| 5-7
5|| 0-0|| 3| 4, 1 *
ſ IBM 34|10:3| 52 11-9 18| l'6 |Cross mark on stone wall. -
7| 3•l 5|| 0-0
II .00) 27| 7-2 47 11.9 20|| 4-7 |Cross into garden ground.
d sº 8 10.6 7 3.1 Scot d d.
10-15, 23| 8-6, 40 8.8 17| 0:2 Iº *:::::::: road, now
5|| 0:1 3| 10:6
10-06| 18 8-5 36|| 10-2 18| 1.7
U 1 || 0:2 5|| 0-1
4. , 8.75] 17 8°3| 3 || 10:1 14|18 ||Face of stone wall.
3.95 6' 3-2
C 7.50; 18|10-8|| 25 6-9 II. 8-1
2| 10-0|| 3| 9.5
3 6:00 l l () 8 21 || 9'4. 10| 8*6 -- ~.
3| 9-5 7| 5-7
b 4.00| 7| 3:3| 14 37 7| 0 °4.
1| 0 °5| 8 9-5
2 2°00' 6' 2-8 10| 6-2 4| 3:4 || –
3. 8-2 6|| 10:0
à, 1.00; 2 6-6 3| 8-2 I | 1.6
...] ...| 3| 8:8
I •00] 2 6-6
Commenced levels from a mark near Nesbitt's Cottage, Thornton Street,
ewcastle.
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USE OF THE SPIRIT LEVEL. 73
f
t;.
projection of a thorough-stone in a wall, on the
left hand side of the line (as a point to return
to upon any occasion), this also add to the sum
of the front heights, viz., 20 feet, 6 inches, 9
tenths, equal to 25 feet, 6 inches, and 9 tenths,
from this also deduct the sum of the rear heights,
7 feet, 5 inches, and 3 tenths (it being the least
number), and the difference will be 18 feet, 1
inch, and 6 tenths for depressions (see profile
plate 8).
The method of performing the remaining ex-
amples is precisely the same as those just detailed,
and is the most advantageous manner in which
they may be performed, and I hope will be found
sufficiently comprehensive : but to render the
subject more easy and intelligible I have given in
the annexed Table, another copy and form of
Field Book, the same levels, but subsecutively ar-
ranged, which will serve as a sort of connecting
chain, and will enable the learner more readily to
understand and review the whole of these cases,
and the results will be found the same in every
particular; therefore I conceive that further
explanation would be unnecessary. It would
certainly have given me great satisfaction if I
could have curtailed this matter, or made use of
language less tautologous, but in describing a
subject of this kind it is quite unavoidable.
Having in a former part of this work explained
74 ESSAY - ON THE
the method of plotting, I shall only now, there-
fore, refer to the profile of the ground between
Thornton Street and Parker's Quay, for the
purpose of stating that the whole of the cases
are depressions, which was intentional : now in
practice it is preferable to have them elevations,
that the figures shewing the heights should be
sufficiently below the surface line so as to leave
it, and the space above it, clear for further ope-
rations, such as describing the line of road with
its inclinations (per mile, yard, or proportion-
ate), also the depths of cuts and heights of em-
bankments, &c.
Now to reverse these depressions, and suppose I
borrow, subsequent to my calculations, the sum
of 200 feet, then my starting point or first station
is that much above an assumed base line ; then
proceeding up the columns of the field book
I deduct each individual depression from this
sum and their difference will be elevation,
thus:–
DEPRES-1 SUM | ELEWATIONS,
STAT, - SIONS, BOR,
ft. in. x| feet.
3d or at 6:00 10 8 6, 200 | 189 3 4,
b or at 4:00 intermediate point. 7 0 4 200 | 192 11 6
2d or at 2:00 4, 8 4, 200 | 195 8 6
a or at l’00 intermediate point. I l 6, 200 198 10 4
|lst for starting point. - 0 0 0| 200 | 200 feet.
So proceed in a similar manner to the end,
entering these elevations in the column of re-
duced levels opposite their respective counter
USE OF THE SPIRIT LEVEL. 75
º
i.
parts; and they may also be reversed by start-
ing from the opposite end of the line or termini,
as at Parker's Quay, and returning down the co-
lumn of depression to Thornton Street; now, the
fall at the former place is the greatest at the base
of the Quay, 126 feet, 1 inch, 1 tenth, there-
fore deduct each individual fall from this sum
and their difference will be elevation, thus:–
|-------------------rz--—-----------— ----------------------,
the end. DEPRES-ITOTAL FALL. ELEVA-
DIST. So continue to l SIons. BASE of PAR-1 Tions.
KER’s QUAY.
36-00 109 1 1 126 1 1 16 11 3 &c. &c.
36-50 tº-rººmsº 116 I 8: 126 l l 9 11 8|Occupation Road.
37-42 114 2 0 126 l l 11 11 1 Edge of Parker's Q.
37°44'. ' 116 1 1 126 l l 10 0 0|Level of high water.
37-48||New Zero mark. 126 l l 126 l l | 0 0 0|Base of Parker's Q,
DESCRIPTION OF FIELD BOOK.
The pages of the Field Book are divided into
ten columns, or may be less than that number as
may suit the taste of individuals.
The first column is for the number of the
station from which the operations may com-
mence, the second is for the bearings of one
station from another, the third is for the pro-
gressive distance or surface measure, the fourth
for the heights observed on the rear staff, the
fifth for the heights observed on the front staff,
the sixth for the elevations, the seventh for the
depressions, the eighth for the reduced levels,
--------
76 ESSAY ON THE
- |
(that is when the difference of the observed
heights requires to be reduced to the curvature
of the earth by allowing for the curvation and
refraction,) the ninth reduced distances, (as the
surface measure is generally oblique, it is abso-
lutely necessary for the accuracy of the work to
reduce them either in the field or in doors to
the true horizontal distances), the tenth loca-
tions; this column is for noting down such re-
marks and observations as may be requisite for
the better explaining the progress of the work
and the crossing of fences, roads, rivers, &c.,
and may be entered from top or bottom of each
page as may be found most convenient.
The characters used to denote observations,
taken on the right or left to the main line, thus:—
T to the right hand, and right angled thereto;
} oblique, on the right; T to the left hand and
right-angled thereto; # oblique to the left being
to some particular mark.
HOW TWO OR MORE LINES OF LEVELS MAY
BE TAKEN AT ONE AND THE SAME TIME.
In describing the method of taking several
lines of levels, at one and the same time, and to
convey a correct idea of the operations, I have
*... .
i
PLATE II: ZZZZ.
6/roſſ MD P/AM of 3 lines of Zevels, ºwing the mode aſ operation with the heights on the stares at the various points of the surface.
-- - - - Z - - A.
% See * o/recordºy the Zevels in Pºeza Book payezs.
-
--
-
---
- -
---
*7%. 2.
Zowc/7/72/MAZ SEC 770V sheriny Zºe Alerations of 3 lines of Zevels taken collectively
AT. To prevent confuszon Zºe Aegyhts on the nameº.ca/Zºzze orzine-AB are on/y skewn see &oana Pan/and Aze/ZAook 24/e 73/
-
s s § § S. § s S. s s s s
- s * º s s * § s s § § s
!----------------------------------------- ----------------------------------------- --- ----------- -----------------
3 3. 3. s º: = : : : 3. $: 3. -
- - -
c - c - 2 c 3. - - ~ 3.
- - -
Fºy, 3. */4. -
cross section of the grow wid Cross SECTION of the 6RotºWD
aſ a al-b b az +500 s.t.
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USE OF THE SPIRIT LEVEL. 77
introduced an appropriate example with a field
book, a plan, and longitudinal and transverse
sections. (See plate, No. 4.) -
I am not aware that such a method has been
practised by any surveyor or engineer; how-
ever it will be found to possess peculiar advan-
tages, particularly when the operations are ex-
tended to the exploring of a country intended
for Public Works; it offers a choice of so many
different lines either for canals, railways, turn-
pike roads, or for draining extensive tracts of
boggy or marshy lands. -
In detailing these operations I beg to observe
that I have shewn the levels to have been takens.
only on one side, viz., on the left hand of the
line A B, which I shall in this instance call the
main line, and on which the distances appear to
be taken, although they were actually carried
forward on the operative line A Y; my object
in this arrangement was to make the subject
more explicit, and to destroy the appearance of
confusion which the frequent crossing and re-
crossing of the centre line might create; when a
method is properly understood, any alteration
may be made according as the necessities of the
case may require, for practice in all cases will
suggest improvements.
The longitudinal line of levels is taken at
78. ESSAY ON THE
:----, six---> . ;- -,-,-,-,-,-,-,-,- -- " " - - - - a
five chains, and the transverse levels at ten
chains apart, making the total distance in the
lateral direction a quarter of a mile; but in
operations of this kind the transverse distances
may be assumed. When the distance of these
level points exceeds ten or fifteen chains it will
be found advisable to place staff holders on each
line, as so much time is occupied in travelling
backward and forward.
In reference to the field book, plan and sec-
tion—to commence with I borrow 20 feet, which
is entered in the column of rear heights, conse-
quently the base line will be that much below
the starting point; the instrument stations on
the central line are marked thus o on the plan ;
each station on the main line is marked by
numbers with a x, and the transverse level
points by letters of reference with a x, and their
distance from the line A B.Şall the observed
and-heights. The first observed which is a rear
height is at a stake mark surface level near A=
7:50 viz, 7 feet and 50 decimal parts, which is
entered in the column of rear heights, and ad-
ded to the 20 feet borrowed, making 27°50 pro-
ceeding from right to left. The next height is
on the central line at a-5 feet, entered first in -
the column of front heights, and added to all
the heights of that name (if any), and it must
FIELD BOOK,
SHEWING THE ENTRY OF THREE LINES OF LEVELS,
Rear
(From
Dist,
Stat. ings.
\
inch,
Back
Sights.
Fore
Sights.
eTElevaſ
tion.
Depres-
S1011,
Reduced
Levels.
| Red.
|Dist.
Locations,
278|90
600
27290
12
260
25
65
254165
2100
25265
600
24665
75
259/90
4.175
255] 15
13
242
00
l6
1225
234|40
*
75
233.65
4|75
228|90
RH
50
65
4.
237
13
215
00
90
8
229
00
65
00
65
14
215
5
210
8
202
00
90
00
90
16
199
25
40
oo
90
14
188
75
65
4.
194
16
I'72
25
65
R.H
12|50
18215
4|75
16790
Tsº
179|15
12|50
155|40
00
15
7
172
11
160
O
º
4.
156
25
90
00
90
75
15
2|50
15290
00
90
25
65
7
145
11
134,
00
O
134|65
00
is
I0
146
RH
200
144|15
6100
138||15
11|25
12690
4.
129
75
90
1000
| 1990
2
117
25
65
00
65
6
I 11
—125
12665
1 1/25
100/40
4.
121
75
90
–25||
100 15
10
80
12
109
R. H
2
107
00
80
4.
95
12
83
75
40
10
30
00
80
7
100
|50
SO
3
79
12:00
88.80
7
72
00
80
90
87.90
1200
6080
90
00
4.
83
0
59
90
90
12
70
75
25
90
00
RH
3|00
67|25
75
25
00
25
6
6]
50
75
13
47
50
75
00
75
00
75
50
25
50
25
00
25
25
00
50
75
50
8250
25
50
5
27
00
50
50
00
7
20
50
00
:
00
—l-
24
20
14
25
21
18
12
10
22
14
23
16
24.
20
15
26
21
14
24
21
27
28
15
2]
14
26
es
19
26
22
20
25
25
00
50
75
75
50
00
50
25
25
50
25
25
75
40
50
00
00
10
10
25
00
50
00
50
00
25
00
50
00
Z
60-00
45-00
Q
40’00
85 °00
25'00
10:00
C
5-00
Height of instrument.
On Main line A B.
20" ch. T of Main line A B
10" ch. T of Main line A B
House.
mark at A, near Herd's
Commenced at a stake.
Borrowed 20 feet which added to the R.H., or rear heights, will make all the points elevations.
!
USE OF THE SPIRIT LEVEL. 79
also be carried to the other column, because it
becomes the rear height to the next fore obser-
vation; deduct the one sum from the other and
the difference will be 22:50 elevation, because
the sum of the rear heights exceeds the front
heights, therefore the mark at a will be that
much above the base line. The next height is
on the third line, at b-1'50, and is likewise car-
ried to the columns just mentioned, making the
sum of the rear heights at this point =32:50,
and the sum of the front heights 6:50, leaving a
difference of 26 feet for the elevation of b,
which is 20 chains to the left of A. (See ground
plan.)
We now turn again to our assistants, on the
main line, who have measured out a distance of
5 chains, the instrument remaining as before,
the observed height which is the fourth 8:25.
The fifth is the instrument height, at c=4'50;
the sixth is at d=1-0; the seventh is at 10
chains on the main line = 13.50; the eighth is
at e=6-0 feet, all of these are carried to the two
columns in the manner already described; first
to the front heights and then to the rear heights.
The ninth is on the third line at ſ=#5 feet,
and being the last observation of the first series
this sum, therefore, is only carried to the co-
lumns of front heights, and added to all the
80 ESSAY ON THE
heights of that name : a picket must be put
down here to rest the staff and mark the precise
spot levelled to. As the instrument is to be
removed from this position to another at g, the
person carrying the staff must remain here un-
til a height has been obtained for the next series
of level points; that the whole may be consecu-
tively arranged. The sum of the rear heights, up
to this station, is 67°25, and the sum of the front
heights 42:25, leaving a difference of 25 feet for
the elevation of f.
The instrument being now removed to g,
point the telescope to the staff at ſ, and observe
the height thereon, viz., 3 feet, which must be
carried to the column of rear heights only (see
R H on plan), and added to the heights of that
name. The telescope is next directed to a
point on the main line, at 15 chains, where the
observed height is 1275, this is first added to
the sum of the front heights and afterwards to
the sum of the rear heights as before directed
as the subsequent cases are all similar to those
already enumerated, it would be quite superflu-
ous to proceed further in the detail of this sub-
ject, and I shall suppose that my readers have
by this time, acquired some knowledge of the
art, so as to understand these instructions;
observe, however, to enter every thing in their
USE OF THE SPIRIT LEVEL. 81
respective columns, particularly the heights
which are to be added, alternately, to the one
and then to the other, excepting the first and
the last of each series. See Field Book, (Plan,
and Section Plate 4.)
LEVELS TAKEN FROM SCOTSWOOD TO
CRAWCROOK MILL ROAD,
BEING A PART of THE NEWCASTLE AND CARLISLE RAIL-
WAY, a PORTION OF WHICH IS ALSO IN THE LINE. or
THE ONCE PROJECTED CANAL BETWEEN THIS PLACE
AND MARYPORT. -
My object in giving the section (See Plate 5),
is to shew, that, in the crossings of Rivers,
Brooks, &c., the soundings or depths of water
may be taken, and added to the general line of
Levels, without any apparent break in the
chain. -
These Levels commence at a stake in an oc-
cupation road leading from Scotswood to Ben-
well, and to this add 100 feet, which is car-
ried to the Field Book (page 88), and entered
in the column of rear heights, also in the column
of elevations, which is to raise that object 100
feet above the assumed base line. (See section).
The first observation or rear height (is from
the stake just mentioned), and is entered in that
G
82 ESSAY ON THE
---,--- ~~~~~-ºr---
column 4 feet 6 inches and 1-tenth of an inch,
(4, 6, 1) the next is an intermediate level (4,2,2)
this is carried first to the column of front heights,
and then again to the column of rear heights,
the distance 40 links, the fore observation is a
bench mark on a cantch cut in a tree, in the
centre of a fence, and standing a little to the
right of the line, at the head of Mold’s Meadow,
and nearly its level, and corresponds with a dis-
tance of 70 links on the main line, the height ,
of which is 9, 10, 8, entered in the column of
front heights only. The instrument being re-
moved to the next station, and as nothing parti-
cular occurs until we reach the edge of the ri-
ver, I shall just give the different heights as
they were taken, without preface; and, there-
fore, beg to refer my readers to the entries in
the field book, wherein they will find the suc-
ceeding observations to be, first, a rear height
(2, 9, 7,) and its front height (4, 1,6,) distance
2:50. Rear height (7, 6,2,) and its front height
(4, 7, 9,) distance 4.25. ; the next rear height is
(1, 4,0,) and its front height (8, 3, 4,) distance
5:50; again, the rear height (1, 7, 5,) and
its front height (6, 9, 0,.); distance, 7:50, to
the low water line" on the North, or Scotswood
* If the depth is taken at High Water Spring Tide, then
deduct the full rise of ordinary Spring Tide from the Depth
USE OF THE SPIRIT LEVEL. 83
side of the River Tyne, where a stake has been
driven, or some other mark made, such as a
large flat stone laid level with the water. Place
the instrument at some convenient distance from
this mark, and observe how far the opposite
side of the stream agrees with that on the nor-
thern shore (for in rivers of considerable width
and where the current sets strong to one side,
or a boisterous wind blowing athwart the chan-
nel, the water will be raised on one side and de-
pressed on the other); therefore, if any difference
should be found, and the water higher on the
north than on the south side, add one-half of the
found, and the remainder will be the depth to be inserted in
the Draught. (At low Water.)
3 ſ 1st Hour before and after high water, deduct #} \ ºf
# 2d Hour before and after high water, deduct # #
3 J 3d Hour before and after high water, deduct # 5 *
# 4th Hour before and after high water, deduct # ſº;
# 5th Hour before and after high water, deduct tº ###
# leth Hour before or about low water, deduct & J 5°º
If the depth is taken at High Water Neap Tide, from each
depth deduct # of the full rise of Spring Tide, or the whole
rise except one-fifth part.
ſ 1st Hour before and after high water, deduct #
2d Hour before and after high water, deduct #
| 3d Hour before and after high water, deduct #
|; Hour before and after high water, deduct #
i
:
5th Hour before and after high water, deduct #
6th Hour before or about low water, deduct # J 5
These allowances are not given as quite precise, for they
will vary a little from several causes; but as a general rule,
will be found sufficiently exact on most occasions.
º Mackenzie's Maritime Surveying
i
84 ESSAY ON THE
difference to the first and subtract one-half of the
difference from the last observed height, (viz.
that at the edge of low water), and let a
stake be driven to within low water mark on
the opposite edge of the stream, equal to the
other half of the difference; it will be necessary
to observe, that in tidal rivers, when the wa-
ter is ebbing or flowing, an assistant ought to
be placed at one of the extremities of the low
water line whilst the soundings are taken, to
notice whether the water rises or fahls, above
or below the stake head, which must be added
or substracted to or from the soundings as the
case may require, so as to reduce the whole to
one horizontal plane; previous to taking the
depths, let a strong line or cord be stretched
across the stream, from one stake to the other,
having small cork-floats attached to it at every
10 links, painted white on one side, and num-
bered 10, 20, 30, 40, &c.; these, will keep
the line on the surface of the water, and pre-
vent its getting foul with any thing at the bot-
tom, and being thus numbered, will answer
every purpose of the chain, but the cord must
be hauled perfectly tight, and in the direction
of the intended line. A boat must be provided,
and which will require to be pulled along the
cord line, the principle surveyor will occupy
USE OF THE SPIRIT LEVEL. 85
the head of the boat, to record the depths, and
two assistants the stern, the one to take the
numbers or distances, and the other the sound.
ings, which are to be taken at 50 links apart,
and the depths may be ascertained, either with
the levelling staff, or a staff provided for that
purpose, with a trencher foot, of three or four
inches diameter, to prevent its sinking in the
sand or silt (when they exceed two or three fa-
thoms, a ship's line ought to be used); now as
those soundingsprogress, they willalternately be-
come rear and front heights to each other, with
the exception of the first and last; at low water
mark, the depth is nought, and is entered in the
field-book accordingly (0.0.0.) in the column of
rear heights; at 50 links from the shore, mak-
ing 8 chains from the starting point, the sound-
ing is found to be 5 feet, entered in the column
of front heights, it is also carried to the opposite
column, because, it becomes the rear height to
the next sounding; particular attention should
be paid to these operations, as an error may very
easily be committed; the third sounding is 4
feet, entered in the column of front heights,
and again, in the column of rear heights, dis-
tance, 8'50; and the fourth sounding which is
2 feet, becomes its front height, distance, 9
chains; the fifth sounding is 1 foot, distance,
86 ESSAY ON THE
9:50 ; the sixth is 1 foot, distance, 10 chains;
the seventh is 1 foot, distance, 10.50; the eighth
is only 6 inches, distance, 11 chains, (these are
to be recorded in the manner described above,)
and the ninth or last, brings us up to the ter-
mini or low water mark, on the south side
(0, 0, 0,) entered in the column of front heights
only, and the elevation of which, will be found
to agree with the opposite extremity of the low
water line, viz. 84, 0, 8, and the distance 11
chains, 50 links. Ordinary spring tides rise
from 7 to 8 feet above this mark. The next series
of levels are over a portion of the bed of the ri-
ver, the rear height is 10, 10, 9, an interme-
diate height 9, 9, 3, entered first as a front
height (distance 14 chains); and, again, as a
rear height 9, 9, 3, and its front height 2, 2, 0,
distance 1460 upon the bank of the river or
towing path. Nextin succession is, a rear height
5, 11, 0, and its front height 4, 8, 3, distance
18 chains. As the subsequent operations and
process for determining the relative heights
of the remaining portion of the line are similar
to those already described, therefore, I con-
ceive it would be unnecessary to go further with
the detail, but at once refer my readers to the
field book, commencing in page 88, in which
they will find the whole entered according to
USE OF THE SPIRIT LEVEL. 87
the observations taken in the field, and conform-
able to the rule given in page 44. It is almost
impossible to avoid the appearance of intricacy
and labour in the construction of such exam-
ples, however, the student will do well to con-
sider attentively, so that he may perfectly com-
prehend the principles on which these opera-
tions are founded, and thereby be enabled to
employ the leading lines when required, without
regard to the minuter divisions of them, which
may in some cases be omitted.
88 ESSAY ON THE
LEVELS FROM ScotswooD TO CRAWCROOK MILL RoAD.
From Bear- BET Rear Front Eleva- i Dep Red. *
Stat. : chains. heights. lº. : * Levels. |# Locations.
| | 18:00 16s, 0.969 orb 93 04 ſ Carried forward.
- 5||11-0 || 4 || 8-3 * towing path.
14-60 157] I '9|64. 4-2 92 9.7 * Bºer, or
º
9| 9-3 i
& | | | 14:00 147 4-6 85 24 -- Bed of river.
- 10110.9 -
|. e pººr . e a.ol | South side of Twne.
+ 11 50 136 5-7 84 0-8 Edge of i. *::::
& ſº ſº 6-0|. 4
| 11-09) 135||11 7 83; 6 S #
1| 0-0 9
| 10-50) 13411"/ 83 0-8 §
ºf . ºº rt;
|| 0-0 - #
10:00 133|II •7 83| 0-8 ##
*= 'sº
I | 0-0 || || 0-0 .#
9 •50 1821.7 49| 10-9. 83 0-8 §§
“º ſ = - -º Eg
2| 0-0 || 1 || 0-0 5:
9:00 130ill 7|48] 10-9 82 0-8 #
4|| 0-0 |2|| 0-0 *
8-50) 12611 -7|46 10-9 80 0-8 #
gº ºn O
5|| 0-0 || 4 || 0-0 CD
8:00 121|II •7|42; 10-9 '79 0-8
0|| 0-0 || 5 || 0 (. Tyne.
: 7-50. 121|11 -7|37| 10-9 84| 0-8 north side of river
i. A Edge of low water,
: iſ 7-5 6' 9-0 -
5-50l 120 4-glgil i-9 39| 2.8
: 4-0 || 8 || 3°4
4-25, 119 0-2 |22 10-5] 96 l'7 Road to Lemington.
# *== gº
t * 7| 6-2 || 4 7.9 p
* 2-50 111 || 6-0 il8 i: 93 3-4 Mold's meadow.
>- 2| 9-7 || 4 || 6
BM | 108 8-3 |14|| 1 |0| 94 7.3 F Cantch cut on tree.
4 2-2 3. 10-8
* •40 104 6-1 || 4 2-2 100 3-9
- - me ºn I - *:::::... ood t
Onº SCOESW O
º - º 6-1 || 4 22 * in the road leading
*. Borrowed, 100]. ... [...] ... 100. From top of a stake
Levels of a portion of the Newcastle and Carlisle rail-road. from Scotswood to Crawcrook: 1827.
USE OF THE SPIRIT LEVEL. 89
|
I,EWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD.
From | Bear-i Dist. º Rear. Front Eleva- |Pº. Red. I Red. L —
Stat.I ings.] chains. I heights. I heights. tion. Sion. I levels, ſist. Locations.
48:00, 176 7-181| 92 94 9-9 Carried forward.
- 3 :
46.00. I'72| 9 •
9|
45.75 16;
78 5-9 94 4-0 Verge of New cut.
l
2 º
•7| 88|Il 3 - Ditto opposite side.
º
88! I 1-3 Bottom of Cut.
!
9
45 °15' 154.
8
;
:
-
3.
. 45:00 146 89| 10:6
*
ment.
97 6-0 BM On side of embank-
44, 50l 145
;#.
:
l
44'25] 143 99| 4, -9 Ditto opposite side.
º
i
2
i
43.00. 140 99 4-9 Surface of Turnpike.
2 4 3 - “$:
39| 2-5 94; 3-6 Bottom of slope.
7
42-4ſ) 133
7
To
º
3
1
3.
§
42:00 125 93| 10-3
—;
º-
;
:
2
7
39-00 | 121 94| 3:0
*
== F *
4.
36:00 118 6.9l 95|10-4
0. tº
33-00 113 6-8|19|| 0-2 94 6-6
30.00. 109' 5'5|15. 6-3, 93 l 1-2
27:00 105|10:41, 8.8l. 94| 2:1
2-9
24-00 | 101 || 7-5, 7, 8.5 93 l l =0
I
21:00. 97 6 5) 3| 9-7 93 8.8
I º
•4 Brought forward.
90
ESSAY ON THE
LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD.
Stat.
From [Bear-ll)ist. in Rear
Front | Eleva- |* | 1.* | : Locations.
ings. chains. heights. ſh; tion. sion.
84-00 186| 4-789) 5 0, 96 || 1 || 7 Carried forward.
5|| 1 °6|| 4 || 4-7
81 00 181| 3•185 $3.
96] 2-8
4, 10°5' 5|| 0-5 {80-001 mile.
7800. 176 4.67911 s 96 4.6
4 10-1| 7| 8-1
77.00 17]] 6-572, 3-7, 99 2-8
I •l || 4 || 10°]
5°467 B-6 95] 11 -8
8
75-00. 163
:
73°25 157
8
3•959 5-2| 97 10-7 Road to Beaumont’s
0-0 6, 1-5
72°50 149, 3.953 3-7 96|| 0:2
3| 8-7| 8 || 6-7 west side.
7200 145|| 7-2|44. 9-0|| 100 10-2 |siºsewoºd,
4| 0°2' 4 0°4. in centre.
69-00 | 14|| 7-0|40 so 100 10-4 Surface of New road,
3
37
# : 0°4. - Lead wharf.
7.2 l east side.
I •4, 100 62] Surface of New-road,
3| II •4.
67.00. 137, 7-6
7| 3•5; 3 T 1-4
66:30 130 4-133 2-0. 97 2-1
6 II •9| 7| 3-5
66-00 128 4-2|25 | 10-5 97 5-7
4|| 1 */ 4| 0°2
68–00: 119| 2-521) 10-8
####|
60-00 II5 0°5|18| 2-4. 96 10-1
6, 11-0|| 6 || 8 -- |
57:00 10s IB|12| 0-6 96 0-9
5||7.4|4| 6.5 -
54.00. IO2 6-1 || 7| 6-1. 95–
3| 6-4, 311-3
51*00. 98 11-7| 3| 6-8: 95) 4-9
3||s|3| 6′s
94. 9.9 Brought forward.
|USE OF THE SPIRIT LEVEL. 91.
LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD.
From] Bear-IDist. i R * leva- Red. | Red. - •,
|º i. ği. hºis. #. º Pººl 1. |† Locations.
110°00| 195] 11 299||10-0 99|| 1 °2 - Carried forward.
- - New Quay.
6|II •3| 7 8-7 bow, top of Stella
BM. 188||11.9189 1-8 99||10–6] ſ Iro cramp in the El-
2 o'el 4 o'9
106:00 186||11785, 04 101|118 East end of cottage.
| --|11-3 2 oz
104°00' 186|| 0:483| 0-2 103|| 0-2
- 5l 0-4 5 º -
101 00 l81| 0-0|77|| 6-2 lo& 5-8 lstella Old Quay.
10| 7-0, 6, 2-2
100.00. 170 5-0|7|| 4-0. 99 l =0
9 I •5 10 7-0 wharf.
99°50' iól 8:350 9-0 100. 6-5 West end of Lead
7| 1.7| 9| 3-5 º º
99°25' 154, 1-8||5|| 5-5 º 8-3 Highest ground in do
8 º: 7 1-7 wharf
sº e ſº § - º
98-25 || 145|| 3-2|44, 3-8| 100 11-4 - London Company’
6 5 °5 3| I •4 wharf.
96-40 138 9-7|4|| 2-4| 97, 7-3 BM and East end of Lead
7| 5-8| 1 || 6-7
95-00. 131 35;} 7-7 91} 8-2
7|10-5] 3| 7-1 •
94-36|| 123| 5-436|| 0 6| 87| 4-8 Into Blaydon Burn.
5 sºlºſio’s
9375] 117 sºft's 2-1 39 6-8
5 ; 5| 8-5
92.50|| 11 || 11 922. 5-6, 89. 6-3
4| 1-4 5| 9°4 -
89.25] 107|10-bilé 8.2 911 2-3
3 #-O 8: 8°5
88.25 104 5-5 7|11 7| 96 5-8 -
2 11-1] 3 5-0
86-50 101: 6-4, 4 6-7 96 11-7
| 6-7 4|| 6-7
96l 11-7 - JBrought forward.
92 ESSAY ON THE
LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD.
from Bear Dist. in TR FTEITTEETRTRT —
º #. ...' him. hiº. #. º Lº. º Locations.
- 18600 1981-19s sº los 78 Carried forward.
- 9| 0-3 || 5-5 -
| | |13475, 187|10-891|10-0. 96 0.8 - iRoad to boatlanding.
9| 3-5] 2 2-0 || }
133-00 178| 7-389 8-0 88 11-3 i
*- : + *m. 4
7|3's 7 5-3 I of river. .
129'50' 171| 3.5182] 2-7| 89 0.8 | |siºound, bank!
* 7| 9-1 r
126'75, 163| 6-4. i
1 7-8 d
126'25] 161 || 10:6 t
*– !
w 4ſ 2-6
§ 125°00; IBW 8-0
- 5| 8-6
124°50' 15||11-4 |
3||12|3|8-6|
122:50, 148 0-241; 5-3. 106| 6.9
simpams sºme mm . * gate.
1 8-2 6 9-8 - depôt below On-
121 "W5| 146|| 4-0||34 7.5; Ill: 8°5 . Mark on Flag's coal
3| 5 6' 4 4-5
119.25 142|10-430 3-0. 112 74
9| 3-9| 3| 5-6
I 18.00. 133| 6′526 9-4 106, 9°l
|| 3:3| 9| 3-9] .
| 16.70| 132: 3-2|17| 5-5] 114 9-7
4|10-2 6 11-5 Stella coal staith.
1 16-40 127| 5-0|10| 6-0|| 11 6 11-0 Mark on the Offgate,
g|1-0|2| 2.2
I 15.25 i IS 4-0 8. 3-8 110 0°2
3| 7-1 2 4-8
| 14-50 l 14 8-9] 5| 11 0 108 9-9
tº dº | *-mº wºº ºh-ºº-º- º
10| 9 2 3 7-1 -
| 13-00 || 103 l l 7|2| 3-9| 101 || 7-8
4|10 5|2| 3-9
99] I -2 JBrought forward.
USE OF THE SPIRIT LEVEL.
98
LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD.
From! Bear-[Dist. in
Stat.) ings.] chains.
Rear Front
heights. | heights.
|
Red. I Red.
levels. J dist.
165 •00
160-00
158-00
157°00
155-00
BM.
17: āīā
3| II •3 3: 8°5
168 7.5||70 10.9
imºmº I ºmºmi º -ºms
6-0|| 4 || 5-8
I68] 1 °5|66|| 5-1
2 3•5 tº e -
165|10-0|65
6-0
11-1
s|10-0|3|113
162| 0-0||61||11-3
4|II 2 3|10-0
157 0-8||58] 1-3
153-00
5| 6:6; 4
15|| 6-253
11 2
2-l
151 °00
2.8
11.8
3| 8-0|| 5
I47
149-00
147-00
10-2|47
6|| 6 || 3
141| 4°ll44
8-0
•3
3
5°ll 4
II •0
3
137
3
9
‘.
145.00
3
o
}
4.
133
:
2
143'00
5
127
l
I
§
:
141 00
140 00
189-00
BM.
BM.
2
125
;
º
:
I
l
:
l
6
|
2
:
1.
Eleva- Depres-
tion.
S10Il.
| Locations.
97| 11 °4.
97| 8-6
IOI 8-4,
99| 10-9
100 0-7
98
99| 10-9
0-8
4's
2-6
0.7
99 2-8
101| 9:6
101| 5-2
101| 1.6
11-5
Carried forward.
miles.
Post.
Mark, bottom Gate
Newburn.
Road from Stella to
Townley, Esq.
|Inclosed Pºp. E.
Kiln.
Flagging, Stella Lime
Stella.
Level of quay, High
Brought forward.
94 Essay on THE
LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD.
From Bear-IDist. in | . Rear Front | Eleva-. Pºº- . Red.
Stat. ings. chains. heights: ſh; tion. sion. evels. dist. Locations.
- 20400. Its 10°3 78 4-0|| 99| 6′3| | - Carried forward.
3| 9 || 3 5.9
201-00 IT2| 1 2.72|10-1| 99 3•I
5
198°00' 166
2-1 || 5 || 4-2
11-167| 5-9 99 5-2
- 3| 8'1| 3| 4-1
195-00. I63 3-0|64. I-8| 99 I •2
4|| 3-8| 3 || 0-5
I92.00. I58||11 260 3-8 98 ºf -9
6||11-7 , - * 4.
53 3-6, 105] 0-6| | | | | | Into plantation.
-- 158
7-8
7-8 IO5| 3-4
:
:
:
9 •
4.
3
I86-00 i. I
6.
I
10°4
:
183.00. 148
t
102| 3-0
:
4.
|
4.
180:00 143 98 6.5
7 - >
178°50′ 135 98 8-0|| | | | Grass land.
;
:
§
;%§
|2
6
|
i. 178-80) 128 99|| 4-0|| | | ||Water course.
;º
- mound.
102 4-4 Top of Caomb, hedge
§
;%
17823, 125||
2
&
hedge.
99||10-3| 4. |Base of Caomb of
6
;
:
178°16' 118
I
}
177:00 112 100 0°4
:
i
2
174-00 º 100) 7.9
I
:
171*00 105 99 º
i
:
; : 168-00) 102
º;:;
|
97
3.
9.
s
|Brought forward.
Use of THE SPIRIT LEVEL. 95
LEWELS FROM, SCOTSWOOD TO CRAWCROOK MILL ROAD.
|Fºr Bear=|Dist. i R | | | Front Eleva-. ID Red. | Red. •
º º: i. hºis. liš. . | * i. dist. | Locations.
| | |2600||1857.781 tº 104 1-1 || |Carried forward.
II 3-2 || 5-9
245:00 184. 4-580 0-7| 104.3-8.
8, 9.7| 4 4-6
243-00 180 6-8|75|| 8-1 104|10-7|
4. 9-6|| 8 9-7 . | |
240-00 17; 9:2|7|10-4 103|10-8| | | | | 3|Miles.
5| Bºls 92 . . . . "
237-00 I'70 4-068|| 1.2| 102 2-8
5 4-0|| 3: 6-8| i side of Gut. :-
234°00 165| 0-0|64 6-4 100 5-6 || ||Water edge, opposite|
9| 0-0 6||3.3 -
230-50, 156|| 0-0|58] 2-6 97 9.4| " - Centre of Gut.
6|| 3-8 f 0-0 Gut.
227-00) 149| 82.49 2.6] 100 5-6 water edge, Ryton
| 4| 3•7| 4 || 4-2
223-00 || 145|| 4-5144|| 10-4 IOI 6-1
4| 9-3, 7, 2-3
21900 140 72.87 sq. 102nd
6|| 9 |3| 8 || 5-2
217.00, 188! 99|29| 2.9| 1041 7-0
2 #| 6| 9-3 |
214:00. 131|| 8-822. 5-6 109. 3-2
3| 9-0 || 5 || 1 °3| .
BM. 127|11.8|17| 4-8 109] ".5| stake toporcsome
to Newburn.
• 7| 0-0 8 9-0 Road, from Ryton
218-75) 120 11-8|13| 7-3. 107 4-5|| Centre of Peth Lane
6| 7-4 7| 0-0
213:00 114|| 4-4 6|| 7-3. 1071. 9-1
6||77|| iſ 2-1
210.00. 107| 8-7| 5 || 5-2 102 3-5
4 5-0|2 ; .
207-00 IO3| 3-7 3| 0-0 100, 3.7 *
3| 9-4 3| 0-0 -
99. 6-3 . . . Brought forward.
96 - ESSAY ON THE
|
:
*
LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD.
|FromiRear-IDist. * Rear Front Eleva- * Red. |: Locatio
Stat.) ings.] chains. heights. heights. tion. sion. Levels. dist. Catlong.
266°00| 217 || 4 || || 10 sºlos 7-8
- stake in Hall's field.
1|ss 611.9
265-00. 215| 7-3|103 8-4|11 || 10-9
8|| 6-0|| 1 §:
264.60. 207: 1-3|10||11 -6|105] 1 7
s|| 6-0
93 5-6||12| 1-0
7| 8-3| “.. 7-5 |
260-50, 197|10-3] 92|10-1|105] 0-2
ford and ferry boat.
Water Lane Road to
1 || 6-7
264-25, 205] 6-6
* | 10-4
91 || 1 -7|102, 9-0
257-50, 194
|03|| 10-6)
254°00' 185 84| 0-0|101 || 8-9
21
255 00 isi
6|| 5-5 side of Creek.
77|| 6-5| 94| 9.4 Water edge, opposite
8
7
l
0
•8
§#.§
253-50 IT2
Bottom of Creek.
252.75 15s 3-5 64 6-5 89| 9.4
l
9
0.
0
252°00' 140 94| 9.4| Water edge in Creek.
45
6
5
251-00 || 130 98|| 0-0
7
:
:
249-50|| 127 102 8-0
:
96
- 9
249 •00| 117 4°l
2
4.
247°50' 114
I
7
:
%
7
l
i
246.75|| 106 .93| 3-6 Broken ground.
:
• - e.%
:
l
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99|| 3-0
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i
ar—----------
---wº
º
USE OF THE SPIRIT LEVEL.
97
LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD.
|From] Bear-| Dist. |
Stat.], ings. chains.
Front
Rear
heights. |
heights. |
SIOIA,
Eleva: Depres:
tion. |
Red.
levels.
- |...}
dist.
Locations.
317-00
l9 |
4.
2
S4
48 106
314-0ſ)
31 1-00
5
185
I
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5 •
}
8
80
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181| 7
º
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305-00
302-00
3||
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4.
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6
166
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8-3
5-6
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103
102
2
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299-00
4.
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I
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60
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296-00
5
156
5
54
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290 00
287-00
15]
2
149
146
4.
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102
4.
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9
103
4.
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284.00
141
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37
3.
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105
;
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283.00
131
:
10
26
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130
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105
&
112
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10
119
1
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274-00
6
I 13
.
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106
270-00
4.
109
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l
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2
106
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5-8
10-8
8.4
3. 1
2-6
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II •]
7.7
I •6
2.7
10-9
2-8
5-8
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Carried forward.
Stanners.
Stake, west end of the
Stanners.
*
*
•
º
*
|
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Stake, east end of the
Brought forward.
Essay on the
LEVELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD.
Stat.
From º: Uist. in Rear
Front | Eleva- |Depres- | Red. | Red. tº
ings." chains. heights. h; tion. | | | | Locations.
sion. evels. | dist.
longs, 22 yds.
ford, 4 miles, 3 fur-
- Mill to Stanner’s
351-00 167| 6-660) 2-9. 107 3-7 _* To stakein road from
4, 7-6] 2 9 0
349.00 162] 1 1-0|57| 5'9| 105 5-1
3| 7-0
34700 155 tº
52] I l 5, 107 4-5
§
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4.
9
6
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344-00| 1561 i 107| 4-8
;
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3
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§
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-_-|-
USE OF THE SPIRIT LEVEL. 99
:
jº-}As --
i
$
s
.&
INACCESSIBLE DISTANCES.
To MEASURE INACCESSIBLE DISTANCEs, such
AS RIVERS, LAKES, BOGS, &c.
As a variety of obstacles of this "kind are
frequently met with in surveying and levelling
through a country, I purpose to give a few
examples for the more readily surmounting these
difficulties, and I shall confine my illustrations to
problems or such examples as bear the simplest
form ; but whose calculations depend upon pure
geometrical principles, and particularly the si-
milarity of triangles. -
To FIND THE BREADTH OF A RIVER WITH THE.
CHAIN ONLY. -
}
ID
Having placed a staff at the point A as near
the edge of the river as convenient, fix up ano-
4
---
i
100 ESSAY ON THE
ther at C on the opposite shore to that on which
you stand; then with the aid of a cross staff or
chain at A, raise A B perpendicular to A C;
make also A E equal to E B, erect the perpen-
dicular Bf5, and produce that line until it meets
at D, the direction of the line C E ; then the
distance B D will be equal to A C the breath
of the river.
For the angle A E C=B E D and A E=E B
(and A C = BD) the angles A and B are right
angles; and the triangles A C E, E B D are
therefore identical and equal in all respects.
This problem may be applied to any inacces-
sible distance, for example let EB=4, B D=8,
and AE = 12, chains; then by similar triangles
as E B : B D :: A E : A C.
Thus, A C = ** =# = 24 chains, the width
of the river.
+i
~.*
USE OF THE SPIRIT LEVEL. 101. ;
: TO OBTAIN THE MEASUREMENT OF AN IN-
* ACESSIBLE DISTANCE AS THE BREADTH OF
THERIVER WITH THETHEODOLITE, SECTANT,
CIRCUMFERENTOR, OR COMPASS.
.”Wi
ºt
EXAMPLE II.
Place your instrument near the edge of the
Aº river at A, desire your assistant to plant a
| staff at B, and direct the sights and the zero
i. point of your instrument to that object, then, fix-
* ing it tight, move the sights round until they
form an angle of 45 degrees; now desire your
assistant to draw the line B C (perpendicular to
A B) and let him carry a staff along that line
until he has brought it into your line of collima-
tion at D, measure the distance from B to the
point of intersection at D, and you will obtain
the width of the river A B.
For B D = A B.
102 ESSAY ON THE
-
TO MEASURE THE BREADTH OF A RIVER
OBLIQUE TO ITS COURSE.
EXAMPLE III.
Suppose the line to be running in the direction
of AB, them, as in the preceding example, plant
the instrument near the edge of the water at A, set
up a staff at B, on the *posite side of the river,
having your theodolite properly fixed with the
telescope direct upon B, turn the moveable in-
dex round until it forms an angle of 26° 34,
draw the line B C perpendicular to A B, and let
your assistant move a staff along that line until
he brings it to the line of collimation at D as
before, then measure the distance from B to the
point of intersection at D, which will be equal
to one-half the length of the line A B.
Therefore, 2 B D = A B the breadth of the
river in that direction.
USE OF THE SPIRIT LEVEL. 103
To MEASURE THE BREADTH OF A LAKE.
zºº.”
as ºr
• 㺠= : º T.
C D
*=-
Fº-T-S-Eºs::==
--Sºrrºs \
|
B S.
NSS3 --> * *
ſº- - ºn Nº.
N
Nº.
EXAMPLE IV.
Plant the theaolite at A, and direct your as-
sistant to set up a pole or staff on the opposite
side at B ; set the index to zero or 360 degrees
on the limb, turn the theodolite round till
through the telescope you observe the pole at
B; screw the instrument fast in that position ;
then turning the index round until it form
an angle of fourteen degrees two minutes,
your assistant in the mean time having raised
B C (perpendicular to A B), let him now move
along that line with a staff until that object ex-
actly corresponds with the vertical wire of the
telescope, and there let him plant the staff D;
measure the distance B D, which, it must be ob.
:*
.
... *-
- -º.
--.-
104 ESSAY ON THE
served, will be only equal to one fourth of the
breadth of the lake A B. ºf
. Therefore, 4 B D = A B.
Now let us suppose the lake to be 100,Chains
in breadth. Having two angles given, viz. A
and B, the sum of which is 14:02 + 90–104-02
—180 will leave 75-58 for the angle D. •
Then as radius is to the natural co-tangent of
the Z. A so is B D to A B.
The following table of angles and multipliers
will greatly assist these operations.
Supposing the instrument to be always placed
in a similar situation to A, and the sights direct-
ed to the object on the opposite side at B, move
the index round to any of the angles in the
table, and multiply the length of the line B D
by the multiplier standing opposite to the angle
applied to the observation, and the product will
be equal to the breadth of the river or lake.
ANGLES. MULTIPLRS.
459,00’
269-34'
180.26%
149-02,
119-19ſ
99.287
7o-08.
59.437
l
USE OF THE SPIRIT LEVEL. 105
}
When the instrument or staff cannot be plant-
ed near the edge of the water, deduct the dis-
tance between these points from the total width,
and the difference will be the true width of the
TiVer.
To RAISE A PERPENDICULAR ON THE
GROUND WITH THE CHAIN ONLY.
With the numbers 3, 4, and 5, or any multi-
ple thereof. Set
off from C to D
on the line A B
40 links, and -
planting a staff at }-Hz
#–
each of those places, fasten one end of the chain
at C, and the other at D, stretch the chain tight,
and with 30 links in one hand extending from
the point C, and 50 links in the other extending
from the point D ; set up a staff in the angle of
meeting at E, then the line C E will be perpen-
dictilar to A. B.
In conclusion, I think it necessary to say that
having in another part of this work given a plate
and description of levelling staves, I omitted to
notice the valuable invention of Mr. Gravatt as
being the best adapted for expedition; the feet
are divided into hundredth parts up the cen-
L
106 Essay on THE USE of THE SPIRIT LEVEL.
tre of the staff in the form of a scale in alternate
black and white streaks, and the tenths in each
foot are numbered alternately 1, 3, 5, 7, 9,-10
30, 50, 70, 90, the top of the figure completing
the number, and the bottom of these figures are
substituted for the intervening ones, viz., 20,
40, 60, 80, so that each figure is one-tenth of a
foot in height; on the left hand side of the divi-
sions is the number of each foot (from ſ to 14),
the whole of those figures are of such a size as
to be distinguished through the telescope at a
considerable distance. By this arrangement, the
whole responsibility rests with the person super-
intending these operations; but where great
accuracy is required, and where attentive and
skilful assistants are employed, I certainly would
prefer those with, sliding vanes, manufactured
by Messrs. Troughton, W. and S. Jones, Elliott,
and other eminent Mathematical Instrument
Makers, in London. - -
ERRATA.
Page 24 line 17 for sydereal read lateral.
– 30 – 14 after materially, dele in.
— 37 — . 9 for syderal read lateral.
– 44 – 5 for the read they. -
— 50 – 12 for 1380 links read 13.80 feet.
– 78 – 19 after A B insert and.
In Field Book at page 48 on line 8-80 instead of 18'504
read Î 96-91 f8:50 .
&
* >
# . . . NEWCASTLE:
# PRINTED BY T. AND J. Hodgson, UNION STREET.
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