B 428181 ! 1 ARTES 1837 SCIENTIA LIBRARY VERITAS OF THE UNIVERSITY OF MICHIGAN PLURIBUS UNUM ! SI QUAERIS PENINSULAM AMOENAM CIRCUMSPICE DEPARTMENT OF ENGINEERING TA 145 R98 40 A GENERAL TEXT BOOK, FOR ARCHITECTS, ENGINEERS, SURVEYORS, SOLICITORS, AUCTIONEERS, LAND AGENTS, STEWARDS, COUNTRY GENTLEMEN, AND OTHERS. 。 3744 A GENERAL TEXT BOOK. FOR THE CONSTANT USE AND REFERENCE OF CF TRE ARCHITECTS, ENGINEERS, SURVEYORS, SOLICITORS, AUCTIONEERS, LAND AGENTS, AND STEWARDS, IN ALL THEIR SEVERAL AND VARIED PROFESSIONAL OCCUPATIONS; ܀ AND FOR THE ASSISTANCE AND GUIDANCE OF COUNTRY GENTLEMEN AND OTHERS ENGAGED IN THE TRANSFER, MANAGEMENT, OR IMPROVEMENT OF LANDED PROPERTY : CONTAINING THEOREMS, FORMULE, RULES, AND TABLES IN GEOMETRY, MENSURATION, AND TRIGONOMETRY; LAND MEASURING, SURVEYING, AND LEVELLING; RAILWAY AND HYDRAULIC ENGINEERING; TIMBER MEASURING; THE VALUATION OF ARTIFICERS' WORK, ESTATES, LEASEHOLDS, LIFEHOLDS, ANNUITIES, TILLAGES, FARMING STOCK, & TENANT RIGHT : THE ASSESSMENT OF PARISHES, RAILWAYS, GAS AND WATER WORKS; THE LAW OF DILAPIDATIONS AND NUISANCES, APPRAISEMENTS AND AUCTIONS, LANDLORD AND TENANT, AGREEMENTS AND LEASES. TOGETHER WITH EXAMPLES OF VILLAS AND COUNTRY HOUSES. BY EDWARD RYDE, CIVIL ENGINEER AND LAND SURVEYOR, AUTHOR OF SEVERAL PROFESSIONAL WORKS. TO WHICH AKE ADDED SEVERAL CHAPTERS ON AGRICULTURE AND LANDED PROPERTY. BY PROFESSOR DONALDSON, AUTHOR OF SEVERAL WORKS ON AGRICULTURE. LONDON: JOHN WEALE, 59, HIGH HOLBORN, MDCCCLIV. LONDON: PRINTED BY GEORGE PHIPPS, RANELAGH Street, EATON SQUARE. 10-5-39 Reclass 1 b m W 1 PREFACE. THE design of this Book is not entirely due to me, but was suggested by the eminent Professional Publisher whose name appears at the foot of the title page. The necessity for its production became apparent from the many enquiries made of him for a work of this character, and when he did me the favor to consult me on the subject, it at once occurred to my mind that the Book should be one which if placed in the hands of my pupils would afford them the materials for the nucleus of that professional knowledge that should govern their pursuits in after-life; a volume to which men of all professions collateral to my own might constantly refer for assistance and information; a volume which would guide the pos- sessor or agent of real property, alike in the transfer as in the improvement or management of his estates; and finally, a volume that would be found acceptable on the table and desk of every practical man and student throughout the kingdom. In the preparation of such a work, an attempt at vi PREFACE. complete originality would be as futile as it is unne- cessary; so many matters of scientific detail, having long since become in a great measure common property; I have therefore in the first five chapters which treat of Arithmetic, Geometry, Mensuration, and Trigonometry, consulted established authorities, but especially I should mention Mr. LAWS' Edition of "Dr. Gregory's Mathe- matics for Practical Men." There are also a few other instances of very minor importance, in which having found material ready to my hand, I have not hesitated to transcribe it (I hope honorably) to these pages, having acknowledged each instance as it occurs. The remaining matter, forming the great bulk of the work, has been an undertaking of immense labour; has occupied the leisure time of several years; and will I trust be found to answer the purposes for which it is intended. If it may sometimes appear to competent persons that too great an importance has been given to trivial things, they must bear in mind that I have been writing for the benefit of all parties; alike for those who may be assumed to know but very little of the subjects treated of, as for those who are well informed upon them. On the other hand I must claim indulgence if any of my observations are not sufficiently in detail for the comprehension of the less skilled portion of my readers, both on account of the PREFACE. vii very limited space at my command for the disposition of so many subjects, and the great difficulty an efficient per- son experiences in describing such things as appear to him so simple that he imagines every one must know them. It is presumed that a very important feature of the work will be found in the numerous Tables with which its pages are interspersed. To the practical man Tables on many of the subjects which are herein contained are of unknown value, by affording much facility for calculation, and by greatly diminishing the chances of error. The chapters upon Engineering, Surveying, Hydrau- lics, and Valuations are extended to a length commen- surate only with the importance of the matters considered, and the necessity of expounding the many and varied rules by which operations of that kind are directed. The Builders' Prices are intended to represent such a scale as will serve to remunerate the master tradesman for the outlay of his capital, his superintendence, and skill; and, although they are published at a time when unfortunately prices are influenced by a variety of oper- ating causes, it is believed they will be found fair expo- nents of average charges. With this view they have been, in some instances, submitted to artificers themselves, for confirmation of my opinions; and the assistance rendered me in this particular by Mr. Powell, a plumber, painter, viii PREFACE. and glazier, and Mr. Hopwood, an ironmonger, both of Pimlico, and men who have my confidence, and such patronage as is at my disposal in their respective busi- nesses, has been such as to merit my acknowledgment here. The chapters on Dilapidations and Nuisances, with the Law of Auction and Appraisements, were origi- nally intended to be supplied by a barrister of emi- nence; but it appeared as the work progressed, that the printed authorities of which the publisher of this book is sole proprietor, aided by that knowledge and experience which fortune has enabled me to acquire, by the exercise of general professional business from a very early age, was sufficient to produce all that could be desired. The examples of Villas and Country Houses are obtained from auxiliary sources: and the chapters on Landed Property, by Professor Donaldson, convey their own description of that gentleman's assistance on the work. I should now conclude, but that I feel the aid of subordinates, when willingly and assiduously accorded in any undertaking, should meet with courteous acknow- ledgment. The names of my assistants, Mr. William Eve and Mr. Frank Harrow, have been already mentioned in PREFACE. ix the book in connection with one of the most useful tables; but, in addition to the services there referred to, upon one or other of them has devolved the tedious and irksome task of reading for the correction of the press; (very often after the ordinary business of the day had been disposed of) so that I feel great pleasure in expressing the sense I entertain of this additional help. I have only to add, that, if any errors are found, and the person who makes the discovery will be at the trouble of communicating with me, the correction shall be made in all future editions, the preparation of which I reserve to myself. UPPER BELGRAVE PLACE, EATON SQUARE, London. 1ST DECEMBER, 1853. EDWARD RYDE. ARITHMETIC SECT. 1 CONTENTS. Notation CHAPTER I. 2 Proof of the First Four Rules 3 Vulgar Fractions 4 Decimals • 5 Duodecimals 6 Powers and Roots. 7 Properties of Numbers 8 Logarithms and Mathematical Tables PAGE 1 to 171 1 2 1 07 ∞ co 3 6 8 9 10 13 to 171 CHAPTER II. PLANE AND SOLID GEOMETRY 172 to 191 SECT. 1 Definitions 172 2 Of Angles and Right Lines, and their Rectangles 173 3 Of Triangles 174 4 Of Quadrilaterals and Polygons 176 5 Of the Circle, and Inscribed and Circumscribing Figures 178 6 Of Planes and Solids 183 • 7 Practical Geometry 186 CHAPTER III. MENSURATION SECT. 1 Comparison of English and French Weights and Measures 2 Mensuration of Superfices 3 Mensuration of Solids 192 to 199 192 194 197 TRIGONOMETRY SECT. 1 CHAPTER IV. Definitions and Trigonometrical formulæ 2 General Propositions 3 Solution of the Cases of Plane Triangles CHAPTER V. CONIC SECTIONS 200 to 215 200 201 203 216 to 218 xii CONTENTS. LAND MEASURING CHAPTER VI. PAGE 219 to 256 226 230 to 256 Table of Decimals of an Acre Table of Land Measure, by dimensions taken in yards • CHAPTER VII. LAND SURVEYING 257 to 296 SECT. 1 Parish and Estate Surveying 2 Trigonometrical Surveying 258 271 3 Traverse Surveying . 280 4 Field Instruments-the Prismatic Compass 283 the Box Sextant 286 the Theodolite 290 CHAPTER VIII. Levelling . 296 to 315 Levelling Instruments-the Spirit Level 299 the Y Level 301 Troughton's Level 307 Mr. Gravatt's Level 308 Levelling Staves 309 Examples in Levelling 314 CHAPTER IX. PLOTTING The Circular Protractor The T Square and Semi-circular Protractor Plotting Sections 316 to 326 319 320 326 CHAPTER X. COMPUTATION OF AREAS 326 to 334 The Pediometer 326 The Computing Scale Computing Tables 328 330 to 334 CHAPTER XI. COPYING MAPS 335 to 338 The Pentagraph 336 CHAPTER XII. RAILWAY SURVEYING 338 to 423 SECT. 1 Exploration and Trial Levels Standing Orders 338 339 CONTENTS. xiii SECT. 2 Proceedings subsequent to the passing of the Act Tables for Setting out Curves Tables for Setting out Slopes Tables of Relative Gradients • PAGE 350 360 375 to 378 379 392 to 419 420 to 423 Specification of Works to be executed in the con- struction of a Railway . Form of Tender COLONIAL SURVEYING CHAPTER XIII. 424 to 439 CHAPTER XIV. HYDRAULICS IN CONNECTION WITH DRAINAGE, SEWERAGE, AND WATER SUPPLY Synopsis of Ryde's Hydraulic Tables Specifications-Iron Pipes and Castings Stone Ware Drain Pipes Pipe Laying Reservoir 440 to 491 443 468 473 477 485 CHAPTER XV. TIMBER MEASURING 491 to 540 Timber Tables-Solid Measure 496 to 515 Unequal Sided Timber 518 to 527 Superficial Measure 529 to 540 CHAPTER XVI. ARTIFICERS' WORK. 541 to 577 SECT. 1 Bricklayers' and Excavators' 2 Slaters' 3 Carpenters' and Joiners' 4 Sawyers' 5 Stonemasons' 6 Plasterers' 7 Ironmongers' 8 Painters' 9 Glaziers' • 10 Paper Hangers'. 541 549 551 566 566 571 573 573 575 576 VALUATION OF ESTATES CHAPTER XVII. 577 to 624 Tables for the Purchasing of Freehold, Copyhold, or Leasehold Estates, Annuities, and Advowsons, and for Renewing Leases for Terms of Years certain and for Lives 589 to 615 xiv CONTENTS. CHAPTER XVIII. PAGE VALUATION OF TILLAGES AND TENANT RIGHT. Tables for Measuring and Valuing Hay Ricks 625 to 646 638 to 646 CHAPTER XIX. VALUATION OF PARISHES 647 to 659 CHAPTER XX. BUILDERS' PRICES. 660 to 706 SECT. 1 Carpenters' and Joiners' 2 Masons' 3 Bricklayers' 4 Plasterers' 5 Ironmongers' 6 Drainers' 660 674 676 676 677 686 7 Plumbers' 689 8 Painters' 694 9 Paper Hangers' and Decorators' 697 10 Glaziers' 699 11 Zinc Workers' 703 12 Coppersmiths' 705 13 Wireworkers' 706 CHAPTER XXI. DILAPIDATIONS AND NUISANCES 707 to 748 SECT. 1 General Definitions 707 счна со до 2 Dilapidations by Tenants for Life and Years 714 • 3 by Mortgagee or Mortgagor 737 4 5 of Party Walls and Fences of Highways and Bridges 738 740 6 Nuisances 746 CHAPTER XXII. THE LAW RELATING TO APPRAISERS AND AUCTIONEERS SECT. 1 The Law relating to Appraisements • 749 to 765 749 752 2 of Auction CHAPTER XXIII. LANDLORD AND TENANT SEOT. 1 Agreements and Leases 2 Notice to Quit 3 Distress 4 Recovery of Possession 765 to 786 765 773 775 782 · CONTENTS. XV CHAPTER XXIV. TABLES. Of Natural Sines and Cosines For Reducing Links into Feet Decimals of a Pound Sterling STAMP LAWS . Stamp Duties Customs' Duties PAGE 787 to 808 788 to 802 803 to 806 807 to 808 CHAPTER XXV. 809 to 832 809 823 EXAMPLES OF VILLAS AND COUNTRY HOUSES 833 to 855 ON LANDED PROPERTY, BY. PROFESSOR DONALDSON. CHAPTER I. LANDLORD AND TENANT-THEIR POSITION AND CONNECTIONS 857 CHAPTER II. LEASE OF LAND, CONDITIONS, AND RESTRICTIONS; CHOICE OF TENANT AND ASSIGNATION OF THE DEED 877 CHAPTER III. CULTIVATION OF LAND, AND ROTATION OF CROPS . CHAPTER IV. BUILDINGS NECESSARY ON CULTIVated Lands-DWELLING HOUSES, FARMERIES, AND COTTAGES FOR LABOURERS CHAPTER V. LAYING OUT FARMS, ROADS, FENCES, AND GATES • • • CHAPTER VI. PLANTATIONS-YOUNG AND OLD TIMBER . • 898 921 941 953 xvi CONTENTS. CHAPTER VII. MEADOWS AND EMBANKMENTS, BEDS OF RIVERS, Water Courses, AND FLOODED GROUNDS. CHAPTER VIII. LAND DRAINING, OPEN AND COVERED-PLAN, EXECUTION, AND ARRANGEMENT BETWEEN LANDLORD AND TENANT • CHAPTER IX. MINERALS-WORKING AND VALUE CHAPTER X. EXPENSES OF AN ESTATE-REGULATIONS OF DISBURSEMENTS—AND RELATION OF THE APPROPRIATE EXPENDITURES CHAPTER XI. VALUATION OF LANDED PROPERTY; OF THE SOIL, OF HOUSES, OF WOODS, OF MINERALS, OF MANORIAL RIGHTS, OF ROYALTIES, AND OF FEE FARM RENTS • PAGE 963 975 988 1003 1013 CHAPTER XII. LAND STEWARD AND FARM BAILIFF: QUALIFICATIONS AND DUTIES 1024 CHAPTER XIII. MANOR BAILIFF, WOODREEVE, GARDENER, AND GAMEKEEPER— THEIR POSITION AND DUTIES CHAPTER XIV, FIXED DAYS OF AUDIT-HALF-YEARLY PAYMENTS OF RENTS- FORM OF NOTICES, RECEIPTS, AND OF CASH BOOKS, GENERAL MAP OF ESTATES, AND OF EACH SEPARATE FARM-CONCLUDING OBSERVATIONS 1048 1058 A GENERAL TEXT BOOK, ETC., ETC. CHAP. I. ARITHMETIC. SECT. I.-Notation. ARITHMETIC is the science of numbers. To the head of notation we may refer the explanation of the principal symbols or characters employed to express operations or results in com- putation. Thus, The sign+ (plus) belongs to addition, and indicates that the numbers between which it is placed are to be added together. Thus, 5 + 7 expresses the sum of 5 and 7, or that 5 and 7 are to be added together. The sign — (minus) indicates that the number which is placed after it is to be subtracted from that which precedes it. So, 9-3 denotes that 3 is to be taken from 9. The sign denotes difference, and is placed between two quantities when it is not immediately evident which of them is the greater. The sign x (into), for multiplication, indicates the product of two numbers between which it is placed. Thus 8 x 5 denotes 8 times 5 or 40. The sign÷(by), for division, indicates that the number which pre- cedes it is to be divided by that which follows it; and the quotient that results from this operation is often represented by placing the first num- ber over the second with a small bar between them. Thus, 158 denotes that 15 is to be divided by 8, and the quotient is expressed thus 15. The sign, two equal and parallel lines placed horizontally, is that of equality. Thus, 2 + 3 + 4 = 9, means that the sum of 2, 3, and 4, is equal to 9. Inequality is represented by two lines so drawn as to form an angle, and placed between two numbers, so that the angular point turns towards the least. Thus, 7 > 4, and A > B, indicate that 7 is greater than 4, and the quantity represented by A greater than the quantity represented by B; and, on the other hand, 3 < 5 and C < D indicate that 3 is less than 5, and C less than D B 2 PROOF OF THE FIRST FOUR RULES OF ARITHMETIC. Colons and double colons are placed between quantities to denote their proportionality. So, 3:5:: 9:15, signifies that 3 are to 5 as 9 are to 15, or 3=15 9 The extraction of roots is indicated by the sign, with a figure occa- sionally placed over it to express the degree of the root; or by a fraction (having unity for its numerator, and the figure expressing the degree of the root for its denominator) placed above and to the right of the quantity to have its root extracted; thus,√4 or 4³, signifies the square root of 4; 3/27, or 27, the cube root of 27; 16 or 16, the fourth or biquadrate root of 16. 4 The raising of powers is expressed by a whole number similarly placed, the figure denoting the power to which the quantity is to be raised; thus, 62, signifies the square of 6; 83, the cube of 8; and 34, the fourth power of 3. The figures thus used to indicate the power, whether whole or fractional numbers, are termed indices or exponents. When both operations are to be successively performed upon a quan- tity, that is, when some root is to be extracted, and then that root to be raised to some different power, the operation is very simply expressed by a fraction placed as before, the denominator of which indicates the root to be extracted, and the numerator the power to which that root is to be afterwards raised. Thus, 273, denotes that the cube root of 27 is to be extracted, and that the root so obtained is to be squared, or raised to the second power. It is immaterial which operation is first performed, for the result would be the same whether we first extracted the cube root, as above, and then squared it, or whether we squared the number first, and then extracted the cube root of the power so obtained. SECT. II.-Proof of the first four Rules of Arithmetic. Simple as these four rules are, it is not unusual to commit errors in working them: it is, therefore, useful to possess modes of proof. 1. Now, addition may be proved by adding downwards, as well as upwards, and observing whether the two sums agree; or, by dividing the numbers, to be added into two portions, finding the sum of each, and then the sum of those two separate amounts. Thus, in the margin, the sum of the four numbers is 7355; the sum of the two upper ones 5857, of the two lower ones 1498, and their sum is 7355, the same as before. 2758 2758 3099 3099 469 1029 5857 7355 469 1029 1498 7355 2. The proof of subtraction is effected by adding the remainder to the subtrahend; if their sum agrees with the minuend the work is right, otherwise not. VULGAR FRACTIONS. 3 3. Multiplication and division reciprocally prove each other. There is also another proof for multiplication, known technically by the phrase casting out the nines. Add together the numbers from left to right in the multiplicand, dropping 9 whenever the sum exceeds 9, and carry on the remainder, dropping the nines as often as the amount is be- yond them; and note the last remainder. Do the same with the multi- plier and with the product; then multiply the first two remainders and cast the nines out of their product; 'if the remainder is equal to the last remainder, this is regarded as a test that the work is right. Thus, taking an example in multiplication, assume the figures in the multiplicand to amount to 6 above two nines, those in the multiplier to 6 above three nines, those in the product to 0 above six nines; the product 6 x 6 of the two first excesses is 36, or 0 above four nines: the coincidence of the two O's is the proof. It is plain, however, that the proof will be precisely the same so long as the figures in the product be the same, whatever be their order: the proof, therefore, though ingenious, is defective*. A similar proof applies to division. SECT. III.-Vulgar Fractions. Common or Vulgar Fractions are so denominated to distinguish them from another kind, hereafter to be mentioned, called Decimal Fractions. A fraction is an expression for the value of any part of an integer, or whole number, such number being considered as unity. Thus, if a pound sterling be the unit, then a shilling will be the twentieth part of that unit, and four pence will be four-twelfths of that twentieth part. These, re- presented according to the usual notation of vulgar fractions, will be and of, respectively. ΤΣ The lower number of a fraction thus represented (denoting the number of parts into which the integer is supposed to be divided) is called the denominator; and the upper figure (which indicates the number of those parts expressed by the fraction) the numerator. Thus, in the fractions 5, 1, 7 and 15 are denominators, 5 and 8 numerators. Vulgar fractions are divided into proper, improper, mixed, simple, compound, and complex. Proper fractions have their numerators less than their denominators, as 2, §, &c. 5 Improper fractions have their numerators equal to, or greater than, their denominators, as 4, 12, &c. 81 M N + * The correctness of this proof, with the exception above specified, may be shewn algebraically, thus:-put M and N the number of nines in the multiplicand and multiplier respectively, m and n their excesses; then, 9 M+ m = the multiplicand, and 9 N + n the multiplier, and the product of those factors will be 9 Mn+ 9 Nm = m n; but the three first terms are each a precise number of nines ; because one of the factors in each is so; these, therefore, being neglected, there re- mains m n to be divided by nine; but m n is the product of the two former excesses : therefore the truth of the method is evident. Q. E. D. 4 VULGAR FRACTIONS. Mixed fractions, or numbers, are those compounded of whole numbers and fractions, as 7, 12, &c. Simple fractions are expressions for parts of whole numbers, as ,, &c. as Compound fractions are expressions for the parts of given fractions, as of, of, &c. Complex fractions have either one or both terms fractional numbers, 5 12 69 24' 143' 123' &c. The value of a fraction is not altered by multiplying or dividing both its numerator and denominator by the same number; thus, 1, 4, 11, 114, are all equal, although successively multiplied by 2, 6, 2 and 12. 2 288, Any number which will divide two or more numbers without re- mainder, is called their common measure. REDUCTION OF VULGAR FRACTIONS. This consists principally in changing them into a more commodious form for the operations of addition, subtraction, &c. CASE I.-To reduce fractions to their lowest terms. Rule.-Divide the numerator and denominator of a fraction by any number that will divide them both, without a remainder; the quotient again, if possible, by any other number: and so on, till 1 is the greatest divisor. Thus, 1178=214 == 11 = 3, where 5, 3, 7, 7, respectively, 2205 are the divisors. 98 147 Or, 1470 = 2, by dividing at once by 735. 2205 Note. This number 735 is called the greatest common measure of the terms of the fraction: it is found thus-Divide the greater of the two numbers by the less; the last divisor by the last remainder, and so on till nothing remains: the last divisor is the greatest common measure required. CASE II. To reduce an improper fraction to its equivalent whole or mixed number. Rule.—Divide the numerator by the denominator, and the quotient will be the answer: as is evident from the nature of division. CASE III. To reduce a mixed number to its equivalent improper fraction; or a whole number to an equivalent fraction having any as- signed denominator. Rule. This is, evidently, the reverse of Case II.; therefore multiply the whole number by the denominator of the fraction, and add the nume- rator to obtain the numerator of the fraction required. Ex.-Reduce 2211 to an improper fraction, and 20 to a fraction whose denominator shall be 274. (22 × 43) + 11 - 957 new numerator, and 257 the 1st fraction. 20 × 274 = 5480 new numerator, and 5480 the 2nd fraction. CASE IV. To reduce a compound fraction to an equivalent simple one. VULGAR FRACTIONS. 5 Rule.-Multiply all the numerators together for the numerator, and all the denominators together for the denominator, of the simple fraction re- quired. If part of the compound fraction be a mixed or a whole number, reduce the former to an improper fraction, and make the latter a fraction by placing 1 under the numerator. When like factors are found in the numerators and denominators, cancel them both. Ex.-Reduce of of of off to a simple fraction. & 2 5 7 1 × 5 × 4 20 1 × 9 × 11¯99 2 × 3 × 5 × 7 x 8 2 × 5 × 8 1 × 5 × 8 3 × 4 × 7 × 9 × 11 4 × 9 × 11 2 × 9 × 11 Here the 3 and 7 common to numerator and denominator are first cancelled; then the fraction is divided by 2; and then by 2 again. CASE V. To reduce fractions of different denominators to equivalent fractions having a common denominator. Rule.-Multiply each numerator into all the denominators except its own, for new numerators; and all the denominators together for a common denominator. Ex.-Reduce, %, and 5, to equivalent fractions having a common denominator. 2 x 7 x 9 = 126 6 × 3 × 9 = 162 the numerators. 5 × 3 × 7 = 105 x 3 × 7 × 9 = 189, the common denominator. 189, 162 42 54 Hence the fractions are 126, 183, 185, or 43, 53, 35, when divided by 3. Hence, also, it appears that exceed, and that exceed. ADDITION AND SUBTRACTION OF FRACTIONS. Rule. If the fractions have a common denominator, add or subtract the numerators, and place the sum or difference as a new numerator over the common denominator. If the fractions have not a common denominator, they must be reduced to that state before the operation is performed. In addition of mixed numbers, it is usually best to take the sum of the integers, and that of the fractions, separately; and then their sum, for the result required. MULTIPLICATION AND DIVISION OF FRACTIONS. Rule 1. To multiply a fraction by a whole number, multiply the nume- rator by that number, and retain the denominator :-Or, divide the de- nominator by the same number, (if a multiple of it,) and retain the nume- rator. 2. To divide a fraction by a whole number, multiply the denominator by that number, and retain the numerator :-Or, divide the numerator by the same number, (if a multiple of it,) and retain the denominator. 6 DECIMALS. 3. To multiply two or more fractions is the same as to take a fraction of a fraction; and is, therefore, effected by taking the product of the numerators for a new numerator, and of the denominators for a new de- nominator. (The product is evidently smaller than either factor when each is less than unity.) 4. To divide one fraction by another, invert the divisor, and proceed as in multiplication. (The quotient is always greater than the dividend when the divisor is less than unity.) SECT IV. Decimals. The embarrassment and loss of time occasioned by the computation of quantities expressed in vulgar or ordinary fractions, have inspired the idea of fixing the denominator so as to know what it is without actually expressing it. Hence originate two dispositions of numbers, decimal fractions and complex numbers. Of the latter, such, for example, as when we express lineal measures in yards, in feet (or thirds of a yard), and inches (or twelfths of a foot), we shall treat in the following section, and shall here confine ourselves to the former. Decimal fractions, or substantively decimals, are fractions always having some power of ten for their denominator; but for the sake of brevity only the numerator is expressed, being written as a whole number with a dot placed on its left hand, which dot determines the value of the denominator, the number of cyphers in the denominator being always equal to the number of figures to the right of the dot, or as it is termed decimal point; if the number of significant figures in the numerator is not sufficient, cyphers are added to the left hand. It is evident that the values of decimals decrease in the same tenfold proportion from the point towards the right hand, as those of integers increase towards the left: thus The vulgar fraction, 0 is written •1 100 •01 "" "" тобо "" "" "" 10000 ·001 ·0001 "" 7 "" "" 10 .7 "" 43 "" "" 100 •43 "" 125 "> 10000 •0125 "" The vulgar fraction, 10 7,3% is written 7.3 "" 42.85 "" "" 57.217 "" 100 1000 42.85 "" 57.217 "" &c. &c. The value of a decimal fraction is not altered by cyphers on the right hand: for 500 or 500, is in value the same as, or 5, that is 1. 1000 When decimals terminate after a certain number of figures, they are called finite, as 1251851, 958058237. ∙125 1000 = 1000 When one or more figures in the decimal become repeated, it is called a repeating or circulating decimal; and a dot is placed over the figure to } DECIMALS. 7 be repeated, if only one, or if more than one, over the first and last figures; thus- •333333, &c. is written ⚫3 •666666, &c. == .6 •428571428571, &c. = 3 •428571 "" •29504504, &c. 131 4 4 4 "" -29504 When the circulating portion of the decimal is preceded by other figures which do not circulate, (as in the last example,) it is called a mixed circulate. Rules for the management of this latter kind of decimals are given by several authors; but, in general, it is more simple and commodious to perform the requisite operations by means of the equivalent vulgar frac- tions, the method of obtaining which is given in Case III. Reduction of Decimals is a rule by which the known parts of given integers are converted into equivalent decimals, and vice versa. CASE I.—To reduce a given vulgar fraction to an equivalent decimal. Rule.-Annex as many cyphers to the numerator as may be necessary then divide by the denominator, and point off in the quotient as many places of decimals as the number of cyphers added to the numerator; if the quotient does not contain so many figures, the deficiency must be made up by cyphers placed on the left hand. CASE II.-Any decimal being given to find its equivalent vulgar frac- tion; or to express its value by integers of lower denominations. Rule.-When the equivalent vulgar fraction is required, place under the decimal as a denominator a unit, with as many cyphers as there are figures in the proposed decimal; and let the fraction so constituted be reduced to its lowest terms. Or, if the value of the decimal be required in lower denominations, multiply the given decimal by the number of parts in the next less de- nomination contained in its integer; and point off, from right to left, as many figures of the product as there were places in the given decimal. Multiply the decimal last pointed off by the value of its integer, in the next inferior order, pointing off the same number of decimals as before; and thus continue the process to the lowest integer, or until the decimals cut off become all cyphers; then will the several numbers on the left of the separating points, together with the remaining decimal, if any, express the required value of the given decimal. CASE III.—To reduce a circulating decimal to its equivalent vulgar fraction. Rule.-Take the figures in the decimal and place them as a whole number for the numerator, and under them for a denominator as many 9's as there are figures in the circulate, and the fraction thus formed will be equivalent in value to the given decimal. If the decimal is a mixed circulate, subtract the finite part (or the figures which are not repeated) from the whole mixed circulate, (both considered as whole numbers,) for the numerator; and for the denomi- nator, take as many 9's as there are figures in the circulating portion of 8 DUODECIMALS. the decimal, with as many cyphers to the right as there are figures in the finite portion of the same. Examples. The circulate .3 91 06 6 " 99 •549 549 >> 999 7-630 2 33 61 TIT 7630 999 7770 = TTT The mixed circulate ·6409 6409-64 141 9900 220 5.29504 = 529504-29 "" = 51 131 444. 99900! SECT. V.-Duodecimals. Fractions whose denominators are multiples of 12, as 144, 1728, &c., are called duodecimals; and the division and sub-division of the integer are understood without being expressed, as in decimals. The method of operating by this class of fractions is principally in use among artificers, in computing the contents of work, of which the dimensions are taken in feet, inches, and twefths of an inch. Rule.—Set down the two dimensions to be multiplied together, one under the other, so that feet shall stand under feet, inches under inches, &c. Multiply each term in the multiplicand, beginning at the lowest, by the feet in the multiplier, and set the result of each immediately under its corresponding term, observing to carry 1 for every 12, from the inches to the feet. In like manner, multiply all the multiplicand by the inches of the multiplier, and then by the twelfth parts, setting the result of each term one place removed to the right hand when the multiplier is inches, and two places when the parts become the multiplier. The sum of these successive products will be the answer required. Or, instead of multiplying by the inches, &c., take such parts of the multiplicand as these are of a foot. Examples. 1. Multiply 12 ft. 7 ins. by 7 ft. 3 ins. ft. ins. 1 12 7 4 7 3 9 88 3 4 ins. 3 1 10 0 3 9 5 6 0 9' 92 2 7 6 0 or, ft. ins. 12 7 4 1 7 ft. 14 14 of 1 ft. of 3 ins. 92 2 7 88 3 4 3 110 9 512 POWERS AND ROOTS. 9 2. Multiply 35 ft. 4 ins. into 12 ft. 3½ ins. ft. ins. 35 4 6 12 3 4 424 6 0 ins. 8 10 1 6 3 11 9 6 0 4' or, || ft. ins. 35 4 6 12 ft. 424 6 0 1 of 1 ft. of 3 ins. 8 10 11 11 91 434 3 11 434 3 11 0 0 The feet in the answers are square feet, but the numbers standing in the place of inches are not square inches, but twelfth parts of square feet, each part being equal to 12 square inches; and the numbers in the third place being twefth parts of these are square inches; in like manner, if the operation be carried further, every successive place will be a twelfth part of that preceding it. SECT. VI.-Powers and Roots. 1.—To Extract the Square Root. Rule.-Divide the given number into periods of two figures each, by setting a point over the place of units, another over the place of hundreds, and so on over every second figure, both to the left hand in integers, and to the right hand in decimals. Find the greatest square in the first period on the left hand, and set its root on the right hand of the given number, after the manner of a quotient figure in division. Subtract the square thus found from the said period, and to the remainder annex the two figures of the next following period, for a dividend. Double the root above- mentioned for a divisor; and find how often it is contained in the said dividend, exclusive of its right-hand figure; and set that quotient figure. both in the quotient and divisor. Multiply the whole augmented divisor by this last quotient figure, and subtract the product from the said divi- dend, bringing down to it the next period of the given number, for a new dividend. Repeat the same process, viz., find another new divisor, by doubling all the figures now found in the root; from which, and the last dividend, find the next figure of the root as before; and so on through all the periods, to the last. Note.-The best way of doubling the root, to form the new divisors, is by adding the last figure always to the last divisor, as appears in the fol- lowing Example.-Also, after the figures belonging to the given number are all exhausted, the operation may be continued into decimals at plea- sure, by adding any number of periods of cyphers, two in each period. 10. PROPERTIES OF NUMBERS. Example. Find the square root of 17-3056 17-3056(4·16 the root: in which the number of 16 decimal places is the same as the number of decimal periods into which the given number was divided. 81 130 1 | 81 826 4956 6 4956 2.-To Extract Cube and higher Roots. The rules for extracting the cube and higher roots, are very tedious. in practice: on which account it is advisable to work by means of logarithms. SECT. VII.-Properties of Numbers. To render these intelligible, we shall here collect a few definitions. Def. 1. A unit, or unity, is the representation of any thing considered individually, without regard to the parts of which it is composed. 2. An integer is either a unit or an assemblage of units; and a fraction is any part or parts of a unit. 3. A multiple of any number is that which contains it some exact num- ber of times. 4. One number is said to measure another, when it divides it without leaving any remainder. 5. And if a number exactly divides two, or more numbers, it is then called their common measure. 6. An even number, is that which can be halved, or divided into two equal parts. 7. An odd number, is that which cannot be halved, or which differs from an even number by unity. 8. A prime number, is that which can only be measured by 1, or unity. 9. One number is said to be prime to another when unity is the only number by which they can both be measured. 10. A composite number, is that which can be measured by some num- ber greater than unity. 11. A perfect number, is that which is equal to the sum of all its divi- sors, or aliquot parts:—thus 6 = § + § + §. Prop. 1. The sum or difference of any two even numbers is an èven number. PROPERTIES OF NUMBERS. 11 2. The sum or difference of any two odd numbers is even; but the sum of three odd numbers is odd. 3. The sum of any even number of odd numbers is even; but the sum of any odd number of odd numbers is odd. 4. The sum or difference of an even and an odd number is odd. 5. The product of any number of even numbers is even; and any power of an even number is even. 6. The product of any number of odd numbers is odd; and every power of an odd number is odd. 7. The product of any number of even numbers, by any number of odd numbers, is even. 8. An odd number cannot be divided by an even number, without a remainder. 9. If an odd number divides an even number, it will also divide the half of it. 10. If a number consist of many parts, and each of those parts have a common divisor d, then will the whole number, taken collectively, be divisible by d. 11. Neither the sum nor the difference of two fractions, which are in their lowest terms, and of which the denominator of the one contains a factor not common to the other, can be equal to an integral number. 12. If a square number be either multiplied or divided by a square, the product or quotient is a square; and conversely, if a square number be either multiplied or divided by a number that is not a square, the product or quotient is not a square. 13. The product arising from two different prime numbers cannot be a square number. 14. The product of no two different numbers prime to each other can make a square, unless each of those numbers be a square. 15. The square root of an integral number, that is not a complete square, can neither be expressed by an integer nor by any rational fraction. 16. The cube root of an integer that is not a complete cube cannot be expressed by either an integer or a rational fraction. 17. Every prime number greater than 2, is of one of the forms 4 n + 1, or 4n — 1. 18. Every prime number greater than 3, is of one of the forms 6 n + 1 or 6 n 1. 19. No algebraical formula can contain prime numbers only. 20. The number of prime numbers is infinite. 21. The first twenty prime numbers are 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, and 67. 22. A square number cannot terminate with an odd number of cyphers. 23. If a square number terminate with a 4, the last figure but one (towards the right hand) will be an even number. 24. If a square number terminate with 5, it will terminate with 25. 12 PROPERTIES OF NUMBERS. 25. If a square number terminate with an odd digit, the last figure but one will be even; and if it terminate with any even digit, except 4, the last figure but one will be odd. 26. No square number can terminate with two equal digits, except two cyphers or two fours. 27. No number whose last, or right-hand digit is 2, 3, 7, or 8, is a square number. 28. If a cube number be divisible by 7, it is also divisible by the cube of 7. 29. The difference between any integral cube and its root is always divisible by 6. 30. Neither the sum nor the difference of two cubes can be a cube. 31. A cube number may end with any of the natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 or 0. 32. If any series of numbers, beginning from 1, be in continued geo- metrical proportion, the 3rd, 5th, 7th, &c. will be squares; the 4th, 7th, 10th, &c. cubes; and the 7th, of course, both a square and a cube. 33. All the powers of any number that end with either 5 or 6, will end with 5 or 6, respectively. 34. Any power, n, of the natural numbers, 1, 2, 3, 4, 5, 6, &c. has as many orders of differences as there are units in the common exponent of all the numbers; and the last of those differences is a constant quantity, and equal to the continual product 1 x 2 x 3 x 4 x x n con- tinued till the last factor, or the number of factors be n, the exponent of the powers. Thus, The 1st powers 1, 2, 3, 4, 5, &c., have but one order of differences 1 1 1 1 &c., and that difference is 1. The 2nd powers 1, 4, 9, 16, 25, &c., have two orders of differences 357 9 2 2 2 of which the last is constantly 2=1 x 2. The 3rd powers 1, 8, 27, 64, 125, &c., have three orders of differences 7 19 37 61 12 18 24 6 6 of which the last is 6 = 1 × 2 × 3. In like manner, the 4th, or last, differences of the 4th powers, are each=24=1×2×3×4; and the 5th, or last differences of the 5th powers, are each 125=1×2×3×4×5. 35. If unity be divided into any two unequal parts, the sum of the square of either of those parts added to the other is the same. Thus, of the two parts and ‡, † + (‡)² = 1 + (1)² = 2}; so, again, of the parts 2 and 3, % + (3)² = 3 + (?)² = 18. 3 2 19 25' 21 For the demonstrations of these and a variety of other properties of numbers, those who wish to pursue this curious line of inquiry may con- sult Legendre "Sur la Théorie des Nombres," the "Disquisitiones Arith- LOGARITHMS. 13 metica" of Gauss, or Barlow's "Elementary Investigation of the Theory of Numbers." Also, for the highly interesting properties of Circulating Decimals, and their connexion with prime numbers, consult the curious works of the late Mr. H. Goodwyn, entitled "A First Centenary," and "A Table of the Circles arising from the Division of a Unit by all the Integers from 1 to 1024." SECT. VIII.-Logarithms. As Logarithms are so fully described in most elementary treatises on Arithmetic, and as a knowledge of their nature and properties is unnecessary to their application to the purposes of calculation, we shall here only explain the manner of using the accompanying tables. By an inspection of Table II., which contains the logarithms of all numbers from 1 to 100, it will be seen that each logarithm consists of two distinct parts, separated by a decimal point; thus, the logarithm of 13 is 1·113943; the number to the left of the decimal point (or 1 in the above example) is called the index or characteristic*, and its value depends only upon the number of digits in the quantity whose logarithm it is, without any regard to the value of that quantity, and it is always 1 less than that number of digits; thus, in the example, the characteristic of the logarithm of 13, which contains two digits, is 1, or one less than that number; and it will be seen from the Table, that 1 is the characteristic of all the loga- rithms from 10 to 99, but that, for numbers below 10, the index is 0, and for 100 is 2, in each case 1 less than the number of digits in the quantity of whose logarithm it is the characteristic. The characteristic, therefore, of the logarithms of all numbers equal to or greater than 1 and less than 10 is 0. 10 "" 100 "" "" "" 100,, 1. 1000,, 2. 1000 "" "" "" 10000,, 3. "" "" 10000 &c. "" 100000 4. &c. &c. When the quantity is less than unity, the characteristic of its logarithm becomes negative, and its value is determined by the number of cyphers which occur between the decimal point and the first significant figure (the fraction being decimally expressed), and is always 1 greater than such number of cyphers; or it is equal to the difference in the number of figures in the numerator and decimal denominator; thus, the characteristic of the logarithm of * In order to avoid confusion from the use of the word index to signify two things, we shall throughout this work employ the term characteristic when speaking of logar- ithms, and index when speaking of roots or powers. 14 LOGARITHMS. ·1 or •01 "" ·001 ·0001 &c. "" Too тобо is T•* 2. "" 3. "" 10000,, 4· &c. &c. The decimal part of the logarithm, or that lying to the right of the decimal point, is called the mantissa, and depends entirely on the relative value of the figures composing the quantity whose logarithm it is, and not at all upon the actual numerical value of that quantity; thus, in the example already given, the decimal part of the logarithm of 13 is ∙113943, which is also the decimal part of the logarithm of 1.3, or 130, or 1300, for in each case the 1 and the 3 have the same relative value. So that the decimal portion of a logarithm is always the same for the same figures, and is not altered by the addition of any number of cyphers either to the right or to the left hand of those figures, or what is equivalent, by the multiplication or division of the quantity by 10, or any power of 10; it is only the characteristic of the logarithm which alters its value, 1 being added to the characteristic for every 10 by which the quantity is multiplied, or subtracted from it for every 10 by which the quantity is divided. Thus, the logarithm of 745800 that of 74580 "" 13 "" "" "" "9 being 5.872622 is 4.872622 7458 3.872622 745.8 2.872622 74.58 1.872622 "" 7.458 0.872622 .7458 1-872622 "" •07458 2-872622 •007458 3.872622 "" It must be borne in mind, that in the logarithm of a fractional quantity, it is only the characteristic which has a negative value, and that the decimal part of a logarithm is always positive. It is, however, sometimes convenient to have the whole logarithm expressed, negatively, both cha- racteristic and decimal; for which purpose, subtract the last right hand figure in the decimal portion from 10, and all the others from 9, and the result will be what is termed the arithmetical complement of the decimal, to which prefix the former characteristic less 1, and the result will be a negative logarithm, equivalent in value to the original logarithm having only a negative characteristic; for example, the logarithm of 07458, as above, is 2-872622, which is equivalent to 1.127378. It is also fre- quently convenient to take the arithmetical complement of the whole logarithm, and this is obtained by subtracting the right hand figure of the decimal from 10, and all the others from 9, including the characteristic * The negative sign (—) is always placed above the characteristic, thus 2, instead of before it, in order to avoid its being misunderstood for the sign of subtraction. USE OF THE TABLES. 15 when positive, but if negative it must be added to 9. Thus, the arithme- tical complement of 3.146128 is 6.853872 2-076276 11.923714 "" "" 5-322839 4.677161 "" "" I-986772 10.013228 "" USE OF THE TABLES. To find the logarithm of any given number. If the number is less than 100, its logarithm will be found in Table II., with its proper characteristic prefixed; but if the number contains more than two figures, its logarithm may be found from Table I. as follows :— If there are only three figures in the number, look for that number in the first column of the table, and on the same line in the next column to the right, under 0, will be found the decimal portion of the required logarithm, to which the proper characteristic must be prefixed, according to the rules which we have just explained. If the quantity contains four figures, look for the first three figures in the first column as before, and the four last figures of the logarithm of the required number will be found on the same line with those three figures, and in that column which has at its head the fourth figure of the given number; the two first figures of the logarithm will be found in the second column (headed O), and which figures being common to all the logarithms inclosed by each pair of horizontal lines, it is unnecessary to repeat. Where these first figures change their value in the middle of a line, the same is indicated by a break in the horizontal line, thus, 139879 | 0194, which shews that the two first figures (13) have changed to 14, and the right hand logarithm is therefore 140194. Examples. Required the logarithm of 734. In Table I., on the same line with 734 and under O, are found 5696, the four last figures of the logarithm, to which the common figures 86 and the proper characteristic 2 being prefixed, we obtain 2.865696, the logarithm required. Find the logarithm of 3476. Here, on the same line with 347 and under 6, will be found 1080, which, with the two first figures and the characteristic prefixed, is 3.541080, the logarithm required. The log. of 5·84 is 0·766413 0932,, 2-969416 "" 10.24,, 1·010300 "" "" 3708,, 3.569140 When the quantity whose logarithm is required contains more than four figures, proceed as follows:-Find the logarithm for the first four figures as above, then look in the first column of the Table of Proportional Parts, at 16 LOGARITHMS. the lower part of each page, for the first four figures, and on the same line in the column having at its head the fifth figure will be found the quantity which must be added to the logarithm already taken out, to give the logarithm of the quantity first required. If the first four figures are not found in the first column of the table, then take the line containing the next less number to it. If the number whose logarithm is required con- tains more than five figures, proceed as above to obtain the logarithm of the first five figures, then, on the same line of the Table of Proportional Parts that the number added to the logarithm for the fifth figure was found, and in the column having at its head the sixth figure, will be found a quantity which, divided by 10 (or what is the same, having its right hand figure taken away*), and added to the logarithm already found, will give the logarithm of the first six figures; again, on the same line and in the column having at its head the seventh figure, will be found a quantity which, divided by 100 (or having two figures cut off from the right hand), and added, will give the logarithm for seven figures. Examples. Required the logarithms of 11488, 621547, 768654, 7642-179. Log. of the first four figures from Tab. I. From Table of Proportional Parts on line with 1148 4.059942 and under 8 } 302 4 Logarithm of 11488, as required = 4.060244 Log. of 6215 From Table of Proportional Parts, on line with 6160, the next less No. in the table to 6215, and under 4. On same line under 7 Logarithm of 621547 = 5·793474 5.793441 28 4 9 Log. of 7686 . 5.885700 From Table of Proportional Parts on same line with 7686 and under 5 } 28 On same line under 4 2 2 Logarithm of 768654 = 5·885730 Log. of 7642 = 3.883207 From Table of Proportional Parts on same line with 7552 and under 1 } 57 On same line under 7 3 99 On same line under 9 513 Logarithm of 7642·179 = 3·883217 * If the figure thus cut off exceeds five, one must be added to the last right hand figure left. USE OF THE TABLES. 17 To find the number answering to any given logarithm. Look in the upper portion of Table I. for the given logarithm, or the next less in value to it that can be found, then on the same line, in the first column, will be found the first three figures, and at the head of the column in which the logarithm was found, the fourth figure of the number sought. If the given logarithm is found exactly in the table, the figures thus obtained will be the required number, care being taken to point off one more figure to the left hand than there are units in the characteristic of the given logarithm, cyphers being attached to the right hand of the number, if requisite. If, however, the given logarithm is not found ex- actly in the table, subtract from it the next less logarithm found, calling the remainder the first difference; then look in the Table of Proportional Parts on the same line with the four figures already obtained from Table I. (or the next less figures which can be found) for this difference, and at the head of the column in which it is found will be the fifth figure of the number sought. If the first difference is not found exactly in the table, look for the next less number to it, which subtract from the first differ- ence for the second difference; then add a cypher to this second difference, and look for it on the same line of the Table of Proportional Parts, as before, and the figure at the head of the column containing the nearest number to it, either greater or less, will be the sixth figure of the number required. Examples. Required the number answering to the logarithm 3·241756. = 3·241756 3.241546 = the log of Given log. Next less log. in Table I. In Table of Prop. Parts on same line with the next less No. to 1744 On the same line 1744. 210 first dif. 199 is found in col. 8 .8 110 second dif. 99 is found in col. 4 ⚫04 The No. required = 1744·84 In this example the next less logarithm which can be found in Table I. is 3-241546, the number answering to which, 1744, is the first four figures of the number sought; then subtracting this logarithm from the given logar- ithm, we obtain for the first difference 210, and looking in the Table of Proportional Parts on a line with 1740 (the next less number to 1744), for the next less number to 210, we find 199, at the head of the column containing which is 8, the fifth figure required; then, subtracting 199 from 210, we obtain the second difference, 11, and adding a cypher, the nearest number which we find on the same line is 99, at the head of the column containing which is 4, the sixth figure required. C 18 DESCRIPTION OF THE Required the numbers answering to the following logarithms: 3.510009, 2.475771, 5-871624. The number answering to the logarithm 3.510009 is found at once to be 3236. Given log. Next less log. 2-475771 2.475671 = the log. of 299-0 100 = 1st dif. From Table of Proportional Parts 87 .06 130 = 2nd dif. 130 •009 No. required = 299.069 Given log. = 5·871624 Next less log. — 5·871573 = the log. of 744000· 51 = 1st dif. From Table of proportional parts 46. 80. 50 52 .. 9. The No. required =744089. It should be observed here, that the number of figures which may be depended upon in any result obtained by logarithms, will be equal to the number of decimal places in the logarithms employed; thus, in using the tables appended to this work, the results obtained will be accurate to six figures, except towards the end of the tables, in which only five figures should be trusted. Mathematical Tables. TABLES III., IV., and V. Mathematicians have computed the lengths of the sines, tangents, and secants (assuming unity for the radius) corresponding to arcs from 1 minute of a degree, through all the gradations of magnitude, up to a quad- rant, or 90°; and the results of the computations are arranged for use in tables called Trigonometrical Tables. As, however, these quantities have to be carried to several places of decimals in order to obtain sufficiently accurate results, their use in calculations is attended with much labour, and therefore it is usual to employ their logarithms instead; but in this case the assumed radius is taken as 10,000,000,000 instead of unity, since with the latter most of the quantities would be fractional, and therefore MATHEMATICAL TABLES. 19 have negative characteristics, the use of which would be inconvenient, and is superseded by taking the radius as above. Table V. is such a table of the logarithms of the sines, cosines, tangents, cotangents, secants, and cosecants, for every minute from 1 minute to 90 degrees, calculated to a radius of 10,000,000,000 as above. It will be observed that the headings of the columns run along the tops of the pages as far as the 45th degree, after which they return along the bottoms of the pages in contrary order, as below:- Sin D. Cosec Tan D. Cot Sec D. Cos Cos D. Sec Cot D. Tan Cosec D. Sin The reason of this will be apparent, if we only consider that the cos, cot, or cosec of an arc is the sin, tan, or sec of the complement of that arc. The intermediate columns headed D, contain the differences of the con- secutive logarithms in the contiguous columns on either side; it will be seen that the same difference is common to the sin and cosec, the tan and cot, and the sec and cos; since, from Table XXI., 1 1 sin= = or 1 sin. cosec; tan= or 1 tan. cot; cot' cosec 1 cos' COS sec= or 1 sec. cos; and consequently, log sin + log cosec = log tan + log cot = log sec + log cos = 2 log rad = 20; there- fore as the sin, tan, or sec increases, so must the corresponding cosec, cot, or cos diminish, and their differences must be equal. The differences of the sines and tangents are not inserted on the two first pages, for the reason explained at page 21. USE OF TABLE V. To find the logarithmic sine, tangent, &c., of a given arc. If the arc contains only degrees and minutes, its sin, tan, &c., will be found simply by inspection, by looking along the top or bottom of the tables for the degrees, and then in the first or last vertical column for the minutes, according as the number of degrees is less or greater than 45°; and on the same line, in the column having for its title (either at the top or bottom, according as the degrees were found) the name of the trigono- metrical quantity required, its log will be found. If the arc contains seconds as well, the logarithm must be found as above for the degrees and minutes; then take the number in the con- tiguous column headed D on the same line, multiply it by the number of seconds, and divide by 100 (which is done by cutting off the two last figures); the quotient must then be added to or subtracted from the log 20 DESCRIPTION OF THE already taken out, according as the same would be increased or decreased by an increase in the arc. Examples. 1. Find the log sin of 37° 47′. As the arc is less than 45°, by looking along the top of the table for the degrees, and in the first column for the minutes, we find in the column having at its top the word sine the figures 9.787232, which is the log sine of the arc required. 2. Find the log tan of 75° 34'. Here, as the arc is greater than 45°, looking at the bottom of the tables for the degrees, and in the last column for the minutes, we find in the column having tan at the bottom, 10-589431, the tan of 75° 34′. 3. Find the log sin of 31° 45′ 5″. The log sin of 31° 45′ is 9.721162 The No. in col. D is 340 x 5" 100 = + 100 17 ... The log sin of 31° 45′ 5″ = 9.721179 4. Find the log cos of 25° 1′ 47″. The log cos of 25° 1′ is 9.957217 The No. in col. D is 98 x 47" 100 100 47 ... The log cos of 25° 1′ 47″ = 9.957170 To find the arc corresponding to any given log sin, tan, &c. :- Look in Table V. for the given log sin, &c., or the next less log thereto, and on the same line will be found the minutes, and at the top or bottom of the page the degrees, of the arc required; if the log thus found is less than the given log, subtract the former from the latter, add two cyphers to the right of the remainder, and divide it by the number found in the contiguous column headed D; the quotient will be the number of seconds to be added to the degrees and minutes in the arc already obtained. Examples. 1. Find the arc whose log tan is 10-577537. Here the arc is found by inspection to be 75° 11′. 2. Find the arc corresponding to the log sin 9-395401. Given log = 9.395401 Next less log = 9.395166 log tan 14° 23' 23500820 29 seconds; ... 9.395401 is the log tan of 14° 23′ 29″. MATHEMATICAL TABLES. 21 In the sines and tangents of arcs less than about 5°, the differences between any two successive values are so great (as will be seen by an in- spection of column D in the table) that the method above given for finding the intermediate values for seconds will not be sufficiently correct; and the same remark applies to the cosines and tangents of arcs greater than about 85°. It will also be observed, that in the cosines and secants of arcs less than 5º, and in the sines and cosecants of arcs greater than 85°, the differences are too small to enable us to calculate accurately the value of any arc from them. The first of these difficulties may be removed by the rules given below for determining the values of the sines and tangents of small arcs, and the tangents of large arcs, and conversely the arcs from the sines and tangents. A table has also been given (Table IV.) of the logarithmic sines for every tenth of a minute as far as a degree and a half, and of the cosines for every tenth of a minute from 88° 29′ to the end of the quadrant. The second difficulty, however, could only be got over by extending the tables to more decimal places, but as this would also require all other quantities employed in the same calculations to be taken to an equal number of decimals, much additional trouble would be occasioned; and it is therefore better for de- termining the value of an arc when near 90°, to employ some other func- tion than its sine, as, for instance, its cosine. In order to render this clearer to those who are not familiar with the use of logarithms, we sub- join an example of such a substitution of the cosine for the sine. For instance, let it be desired from the formula. P₁: P₂ :: sin ß : sin ♪ 1 to determine the value of the angle §, when P₁ = 600·1; P₂ = 669; and the angle ß = 63° 45′. First by multiplying the means and extremes, and dividing both sides by P₁, we obtain sin d= 2 P₁ 1 P₂ sin ß . Then from Table XXI. • (a.) sin ♪ = √1 — (cos §)² P₂ sin ẞ P₁ =√1 = √ 1 — (cos d)²; squaring both sides P₂ sin ß P₁ B) = 1 — (cos d')³, transposing, and extracting the square root. cos d = 2 2 P₁ - (P, sing).. (b.) 1 - We have, therefore, two equations, (a) and (b), from either of which we can obtain the value of the angle d, by substituting the values of the known quantities; but in doing so we shall find that the second equation will give the value of & much more exactly than the first. 22 DESCRIPTION OF THE Thus, by substituting the known quantities in equation (a), we have 669 × sin 63° 45′ 600.1 = sin d. Whence by logarithms, Log sin 63° 45' 9.952731 Log 669 2.825426 12-778157 Log 600.1 2.778224 Log sin & 9.999933 ·. ♪ = 88° 59′ 25″. Proceeding in a similar manner with equation (b), we have 669 × sin 63° 45′\² 1 – (669 600.1 = cos d. Whence by logarithms, taking the radius as unity, for the reasons ex- plained at page 25. Log sin 63° 45′ = 1.952731 Log 669 2.825426 2-778157 Log 600-1 2.778224 1.999933 2 Log ⚫99969 Then 1 •99969 = 1.999866 ·00031, the log of which 4-491362 ÷ 2 2.245681 = cos &; or restoring the radius of the tables, 4-491362, and cos ♪ = 8·245681 = 8-245681 = sin of the complement of §; therefore, by the rule given below for finding a small arc from its sin, we have 8.245681 5.314425 22 3.560128 = 3631.86 seconds = 1° 0′ 31″·86; ♪ = 88° 59′ 28″-14, whence we see that the former value of d obtained from equation (a) is upwards of three seconds too small. MATHEMATICAL TABLES. 23 To find accurately the log sin of an arc less than 5º. Reduce the arc to seconds, and find the log of that number from Table I., to which add 4.685575 (the log sin of 1"), and subtract one-third of the decimal portion of the log sec of the arc taken from Table V.; the remainder is the log sin of the arc required. Examples. Find the log sines of 13′ and of 1° 3′. Log (13′ × 60) = 780″ = 2.892095 4.685575 7.577670 Log sec of 13' = '000003 ÷ 3 = '000001 Log sin of 13′ = 7·577669 Log (63' x 60)=3780" 3.577492 4.685575 8.263067 Log sec of 1° 3′ = '000073 ÷ 3 = ·000024 Log sin of 1° 3′ = 8·263043 To find accurately the log tan of an arc less than 5°. To the log of the number of seconds in the arc add 4.685575, and two- thirds of the decimal portion of its log sec; the sum is the log tan of the arc required. Examples. Find the log tans of 24' and 1° 15′. Log (24′ × 60) = 1440′′ = 3·158362 4.685575 Log sec of 24′ = ·000011 × 3: = '000007 Log tan of 24′ = 7·843944 Log (75′ × 60) = 4500″ = 3.653213 Log sec of 1° 15′ =·000103 × 4.685575 = 000068 Log tan of 1° 15′ = 8·338856 24 DESCRIPTION OF THE To find accurately the log tan of an arc greater than about 85º. Add to the log of the number of seconds that the arc is less than 90°, two-thirds of the decimal portion of the log cosec, and subtract the sum from 15-314425; the remainder will be the log tan required. Examples. 1. Find the log tan of 89° 5′ 13″. 90° 0' 0" 89 5 13 0° 54′ 47″ = 3287 seconds. Constant log Log of 3287 = 15·314425 = 3.516800 Log cosec of 89° 5′ 13″ = '000057 × 1/ = .000038 3.516838 Log tan of 89° 5′ 13″ — 11·797587 2. Find the log tan of 88° 51′ 10″. 90° 0' 0" 88 51 10 1° 8′ 50″ = 4130 seconds. Constant log = 15·314425 Log of 4130 = 3.615950 Log cosec of 88° 51′ 10″ = '000087 × 3 •000058 3.616008 Log tan of 88° 51′ 10″ = 11·698417 To find accurately an arc of not more than 5° from its log sine. To the given log sin, add 5·314425, and one-third of the decimal por- tion of the secant of the nearest arc to that whose log sin is given, the sum, rejecting 10 from the characteristic, will be the logarithm of the number of seconds in the arc. Example. Required the arc whose log sin is 8-314719. Given log sin = 8.314719 Constant log = 5·314425 Log sec of nearest arc = '000093 ÷ 3 = ·000093÷ 3 = 000031 Arc required 1° 10′ 58″ = 4258″ = 3.629175 MATHEMATICAL TABLES. 25 To find accurately an arc of not more than 5° from its log tan. To the given log tan add 5·314425, and from the sum subtract two- thirds of the decimal portion of the log sec of the arc whose log tan is nearest to that given, and the remainder, rejecting 10 from the character- istic, will be the log of the number of seconds in the arc. Example. Required the arc whose long tan is 8-231461 Given log tan 8.231461 Constant log Log sec of nearest arc = '000063 × 5.314425 13.545886 •000042 Required arc = 58′ 34″ = 3514" = 13.545844 To find accurately an arc greater than 85° from its log tan. Add to the given log tan two-thirds of the decimal portion of the log cosec of the nearest arc to that whose log tan is given, and subtract the sum from 15.314425; the remainder is the log of the number of seconds that the arc is less than 90º. Example. Required the arc whose log tan is 11.695900. Constant log 15.314425 Given log tan 11.695900 Log cosec of nearest arc '000088 × •000059 11.695959 3.618466 Required arc = 1° 9′ 14″ = 4154″ . In extracting the root or raising the power of any trigonometrical quantity by means of its logarithm, it will always be found most conve- nient to reduce the assumed radius to unity, by subtracting 10 from the characteristic of the logarithm, which will frequently then become nega- tive; it must, however, be borne in mind that the decimal part of the logarithm is always positive; and, therefore, if it is required to multiply a logarithm with a negative characteristic by any number (as the index of a power), first multiply the decimal part of the logarithm, pointing off as many decimal figures in the product as there were in the logarithm, then multiply the characteristic, and subtract from the product the number (if any) pointed off to the left in the first product: the result will be the ne- gative characteristic, and the decimals pointed off in the first product will be the decimal part of the required logarithm. To divide a logarithm with a negative characteristic by any number: if the characteristic is a 26 DESCRIPTION OF THE mutiple of that number, that is, if it is divisible by it without remainder, proceed as in ordinary division; if not, separate the characteristic from the decimal, and add to the characteristic a number which will make it divi- sible, and prefix to the decimal the same number, then divide both by the given divisor, and the quotients will be the characteristic and decimal of the logarithm required. An example of this alteration of the characteristic is given at page 22. Although Table V. only purports to give the sines, tangents, &c., of angles less than, or equal to 90°, any of these functions of angles greater than 90° may readily be obtained, since any function of an angle greater than 90° is equal to the same function of the supplement of that angle; due regard being had to changing the sign, if requisite, according to Table III., which exhibits the value of each trigonometrical line at the com- mencement of each quadrant, and also the sign with which it is effected in passing through the same. Thus, the log sin of 141° 15' is 9-796521, the same as the sin of its supplement 38° 45'; the log sec of 95° 43′ is 11.001701, or the sec of 84° 17′ with its sign changed; the log cosec of the same is 10-002165, or the cosec of 84° 17', the sign remaining the same; and the log tan of 173° 4′ is 9.084947, or the tan of 6° 56' with its sign altered. TABLE VI. Meridional Parts. In nautical charts, drawn according to Mercator's projection of the sphere, the meridional lines are drawn parallel to each other, or equidis- tant in every latitude, as shewn in fig. 1, so that the distance between any two meridians being assumed as true at the equator would be too great in every other latitude; for whereas the length of a degree of latitude really decreases as we approach the poles, here it is represented as though its length were everywhere the same. If, therefore, the parallels of latitude were drawn at equal distances in representing any country situated in a high latitude, its form would become so much distorted from its breadth being thus increased without its length, that the country would hardly be recognised, and very erroneous views would be occasioned of its form and relative extent. Thus, in the latitude of 60°, a degree of longitude is only half what it is at the equator, and therefore all dimensions east and west would be twice as great as they should be, if drawn to the same scale as those north and south. To correct this distortion, therefore, and preserve the true form of the countries, the distance between the parallels of lati- tude is increased precisely in the same proportion as that between the meridians; so that on a Mercator's chart the relative magnitude of a degree of latitude and longitude is everywhere truly preserved; the parallels of latitude being drawn more and more distant as we leave the equator, as shewn in fig. 1. MATHEMATICAL TABLES. 27 Fig. 1. D Now, the numbers in the table of meridional parts are nothing more than the distances of the several parallels of latitude from the equator, as shewn on a Mercator's chart, expressed in minutes of longitude at the equator. In using the table the degrees of latitude must be sought at the top of the table, and the minutes in the side column, the meridional parts. will then be found at their intersection; thus the meridional parts of 27° 25′ are 1712, and of 76° 3' are 7222. The great use of this table for nautical purposes is to determine the latitude and longitude of a ship at sea, when the course and distance that she has run are known. By the course of a ship is meant the direction in which she sails, estimated by the angle which that direction makes with the meridian. When the course makes the same angle with every meri- dian crossed, it is termed a rhumb, and this course is that usually adopted by navigators, in consequence of the facilities which it affords in ascer- taining the position of their vessels. On a Mercator's chart any rhumb is obviously a straight line, because no other than a straight line would on such a chart cross every meridian at the same angle. Thus, if A and B, figure 1, are any two places between which a vessel sails, then the straight line A B is the rhumb upon which the vessel would sail to preserve the same course or make the same angle with every meridian crossed; A C is the difference of latitude, C B the difference of longitude, and A B the nautical distance run. If now we set off from A towards C, a distance A D equal to the actual difference of latitude measured in degrees at the equator, and draw a line D E parallel to the equator, then will the line A E, measured on the equator, be the true nautical distance, and, being multiplied by 60 (the number of nautical * It is hardly necessary to state that a minute is the 60th part of a degree, and a second the 60th part of a minute. 28 DESCRIPTION OF THE miles in a degree), will give the distance run by the ship, and the line DE is termed the departure or distance run either to the east or west. By inspecting the diagram, we see that A E: rad :: A D: cos < A, or the nautical distance is to radius as the actual difference of latitude is to the cosine of the course; and also A B: rad :: BC: tan ◄ A, or the meridional difference of latitude is to radius as the difference of longitude is to the tangent of the course. If we put d for the nautical distance, c for the course, 7 for the difference of the latitude, λ for the meridional difference of latitude, and L for the difference of longitude, we have, from the above proportions, rad. l = d cos c, And rad. L=λ tan c. From which formulæ either two of the four quantities d, c, l, and L being known, the others may be easily found. For example, a vessel leaving latitude 25° 34′ N. and longitude 61° 24′ w. sails 543 nautical miles on a rhumb line, whose course is N. 42° 5′ E., what latitude and longitude is she then in ? Log cos c (= 42° 5′): = 9.870504 Log d (= 543) Rad. = 2.734800 12.605304 =10·000000 2.605304 = = log of 403 = = 1, then 403 ÷ 60 = 6° 43′ = the ship's difference of latitude to the north; therefore, 25° 34′ + 6° 43′ = 32° 17′ N. is the latitude she is now in. Again, Meridional parts for 32° 17′ = 2048 "" for 25 34 = 1588 Meridional difference of latitude = λ = 560 Log tan c (= 42° 5′) = 9.955707 .. Log λ (= 560) Rad = 2.748188 12.703895 = 10.000000 2-703895 — log of 505·7 — L, then 505·7 ÷ 60 = 8° 25′ 42″ = the ship's difference of longitude to the east; therefore, 61° 24'-8° 25′ 42″ 52° 58′ 28" w. is the longitude she is now in. Example 2.-A vessel sails from latitude 41° 20′ N., and 49° 50′ w., to latitude 64° 25′ N., and longitude 10° 13′ 6″ w., her course and nautical distance? longitude what was MATHEMATICAL TABLES. 29 Meridional parts for 64° 25′ = 5097 for 41 20 = 2728 "" "" 23 5 2369 =λ = 60 Meridional difference of latitude. Difference of lat. = 7 = 1385 49° 50′ 0″ 10 13 6 39 36 54 60 Log L (2376.9) Rad. Log λ (2369). Log (1385) Rad. • 3.376010 = 10.000000 13.376010 = 3.374565 10·001445 = log tan 45° 5′ 44″ = c. = 3·141450 =10·000000 Log cos c ( = 45° 5′ 44″) 13.141450 9-848757 3·292693 = log of 1962 = d. TABLE VII. Length of a Degree of Longitude on each Parallel of Latitude. This table requires no explanation; it exhibits the length of a degree of Longitude in nautical miles (each of which equals 6075.6 feet) at every degree of latitude from the Equator to the Poles. TABLES VIII. AND IX. Dip of the Horizon. The latitude and longitude of a vessel is determined by observations made on the heavenly bodies, which observations consist principally in measuring their altitudes or the angle which they make with the horizon. The altitudes thus taken being compared with certain altitudes given in 30 DESCRIPTION OF THE the "Nautical Almanac," enable the observer to determine both his latitude and longitude. It is, however, requisite to make certain corrections in the observed altitudes in order to obtain the true altitudes. H A K 1 G F F If, in fig. 2, G C D F is a section of the earth, and B the place of an observer, then GE F is the rational horizon, and H CI the sensible horizon. Also, if A is the place of a heavenly body, the angle A E F is its true altitude, A CI its apparent alti- tude, and A B D its observed altitude. If the observer had been on the surface of the earth as C, then the observed altitude would have coincided with the apparent altitude, but when raised above the same, as is always the case at sea when the ob- servations are made from the vessel's deck, the horizon dips, or becomes depressed, as shewn by the line B D, and the observed altitude A B D becomes greater than the apparent altitude A B K or A C I* by the angle K B D: the magnitude of this angle (termed the dip of the horizon) de- pends upon the height of the observer above the surface of the earth; its values for all heights between 1 and 140 feet are given in Table VIII. The angle found in the second column must be subtracted from the ob- served altitude to obtain the apparent altitude. The dip given in Table VIII. supposes that the view of the sea horizon is perfectly unobstructed. Should, however, any object intervene, as a coast, the margin of the sea where it meets the shore must then be taken as the horizon; and in this case the angle to be subtracted from the ob- served altitude will be found in Table IX. under the proper height, and on a line with the distance of the object from the observer, which may always be judged of with sufficient precision by an experienced eye. Thus, if the vessel is about 2 miles from the shore and the observer is 20 feet above the surface of the sea, the angle to be subtracted for the dip will be 6 minutes. TABLE X. Reduction of the Moon's Horizontal Parallax. The difference between the apparent altitude of a heavenly body, or the angle which it makes with the sensible horizon, and its true altitude, or the angle which it forms with the rational horizon, is termed its parallax. The parallax of a body is greatest when it is in the horizon, and it decreases as its altitude increases, until, when it attains the zenith, * The distance B C of the observer above the earth's surface is so inconsiderable, as compared with в A, the distance of the body, that these two angles may be considered as equal without any appreciable error. MATHEMATICAL TABLES. 31 its parallax becomes nothing. Thus, in fig. 3 the parallax at C is greater than that at E, and is nothing at the zenith F. B D The amount of the horizontal parallax depends upon the distance of the body A C and upon the earth's radius A B. The nearer the object, that is, the less A C is, the greater is the angle A C B or the parallax. The moon being much nearer to the earth than any other of the heavenly bodies, its parallax is much greater, and as its distance from the earth varies, so also does its parallax; the amount of its parallax is given in the “Nautical Almanac" for every day throughout the year. The parallax there given is, however, calculated for the earth's greatest or equatorial radius; and since, from the proximity of the moon, the decrease of the earth's radius in higher latitudes diminishes the parallax to such an ex- tent as to require correction, we have given in Table X. the amount to be subtracted from the equatorial parallax to give the true parallax in any given latitude. For example, let the earth's equatorial parallax on any given day, as found in the "Nautical Almanac," be 58 minutes, what will it be for the same day in latitude 52°? Here under 58', and on a line with 52°, we find 7-"2, which must be subtracted from 58', giving 57′ 52″8 for the moon's parallax in that latitude. TABLE XI. Augmentation of the Moon's Semidiameter. In making an observation, it is the position of the centre of the object which is required, but as it would not be easy in practice to judge with sufficient precision of its position, it is usual to measure to the nearest edge (or limb, as it is termed) of the object, and to add the angular value of its semidiameter. In the case of the moon, its apparent semidiameter varies considerably according to its distance from the earth, and also from its great proximity its semidiameter is sensibly increased by the parallax ; for, as her altitude increases, she approaches nearer to the observer, and the apparent semidiameter becomes greater. The value of her horizontal 32 DESCRIPTION OF THE semidiameter for every day is given in the "Nautical Almanac;" and Table XI. shews the augmentation of the same occasioned by an increased altitude. Thus, when the moon's horizontal semidiameter is 15′ 30″, her apparent semidiameter, with an altitude of 51°, will be 15' 42". TABLE XII. AND XIII. Longitude and Time. As the sun apparently revolves round the earth once in every twenty- four hours, with an equal rate, it arrives at each meridian at a different time. And it is on this principle that the longitude of a place is de- termined by the interval of time between the sun's passing the meridian of that place and the meridian of Greenwich. As the whole 360° are equal to an interval of 24 hours, any lesser number of degrees are equal to a proportionate interval of time, and these two tables are for facilitating the conversion of longitude into time, or vice versa. As an example of their use, let it be required to find the interval of time corresponding with a difference of longitude of 43° 13′ 10″. H. M. S. From 2nd column, Table XII. 40° = 2 40 1st "" "" "" 1st 3° = 10′ = 12 "" "" 1st 3' 40 12 "" "" 3rd 10" = 0.667 "" "" 2 52 52.667 The time is therefore Again, if it were required to know the difference of longitude cor- responding with an interval of 4 hours, 31 minutes, and 6 seconds; we have From 1st column of Table XIII. 4 hours 60° 0' 0" "" 2nd 2nd 30 mins. 7 30 0 "" "" "" 1 min. 0 15 0 "" "" "" "" 2nd "" 6 secs. : 0 1 30 "" "" Which gives for the diff. of longitude. 67 46 30 TABLE XIV. Parallax in altitude of the Sun and Planets. The horizontal parallax of the sun and planets depends upon their dis- tance from the earth, and is given for every day in the "Nautical Almanac.” The parallax for any altitude is, as already explained, less than when the object is in the horizon; and Table XIV. is intended to give the amount of parallax for any apparent altitude when the amount of the horizontal parallax is known. In using the Table look for the horizontal parallax at the head of the Table, and in the column at the head of which it stands, MATHEMATICAL TABLES. 33 and on the same line with the apparent altitude, will be found the parallax required. For example, if the sun's horizontal parallax is 9", what is her parallax with an apparent altitude of 48°? Here, in the column having 9″ at its head, and on the same line with 48°, will be found 6", which is the sun's parallax at the time. TABLES XV. and XVI. Refraction of the Sun and Stars. There is another correction rendered necessary in order to reduce the observed altitude of a heavenly body to its apparent altitude; in conse- quence of the optical property of the atmosphere termed refraction. While the effect of the parallax is to make the object appear lower than its true place, that of refraction is to make its altitude appear greater. The effect of refraction is greatest when the object is in the horizon, and it gradually diminishes until at the zenith it becomes nothing; it is not, however, al- ways constant for the same altitude, but varies with the temperature and density of the atmosphere. Table XV. gives the refraction for every ten minutes of apparent altitude, calculated for a mean temperature of 50° Fahr., and a mean pressure of 29.6 ins.; and Table XVI. contains the correction requisite to be made for any other temperature and pressure. For example, what is the refraction of any heavenly body whose observed altitude is 31° 20′ when the temperature is 72°, and the barometer 30-35? In this case we first find, from Table XV., the refraction for a mean state of the atmosphere to be 1′ 35.5", we then find, from Table XVI., that at the temperature of 72° we must subtract 5", and with the barometer at 30-35, that we must add 1", after which we have 1′ 31.5″ for the required refraction. It must be observed, that when the temperature is below the mean, the correction must be added, and when above, the mean subtracted; also, when the barometer is below the mean the correction must be sub- tracted, but when above the same it must be added. The correction for the thermometer is found in the column having the temperature at its head, while that for the barometer is found in that having the pressure at its foot. TABLE XVII. Correction of the Moon's Altitude. As already explained, the effect of the refraction is to raise the object, while that of parallax is to depress it; the parallax, however, being always the greater, the apparent altitude is always less than the true altitude. Table XVII. contains the difference of the refraction and parallax for the moon, which is therefore the correction to be added to the apparent altitude to obtain her true altitude. In using the table, the cor- rection will be found in the column having at its head the moon's hori- zontal parallax, and opposite to the apparent altitude. Should these not be found exactly in the table, we must take the next less values, and to the number thus found we must add or subtract (as the case may be) a pro- D 34 DESCRIPTION OF THE portional part for the requisite number of minutes or seconds wanting, which are given for the altitudes in the left-hand column, and for the parallax in the right-hand column. For example, let the correction be required when the apparent altitude is 29° 37′, and the moon's horizontal parallax is 56′ 24″. In this case the next less numbers to these in the Table are 29° 30′ and 56'. Under 56', and opposite 29° 30', we find 47′ Add proportional parts for parallax 20″ 1" 18 4" 3.5 "" "" >> 47 22.5 Subtract prop. parts for altitude 7' 3 47 19.5 Correction required The moon's true altitude therefore equals 30° 24′ 19″·5. Ex. 2. What is the moon's true altitude when its apparent altitude is 9° 53', and its horizontal parallax is 58′ 20″? Under 58′ and opposite 9° 50' we find . Add proportional parts for parallax 20″ "" 51′ 44″ 20 for altitude 3' 2 52 6 Correction. Therefore the moon's true altitude equals 10° 45′ 6″. TABLE XVIII. Logarithms for finding the Horary Angle or Apparent Time. as The use of this Table is to facilitate the calculation of the Apparent Time at any place, from observations made on the altitude of some known celestial body. The logarithms in the Table are twice the sine of half the arc of longitude corresponding with the number of hours and minutes at which it stands*. The use of the Table is as follows: having obtained this logarithm, look in the table for it, or for the next less logarithm to it, and take out the time in hours and minutes found (if the altitude is decreasing) at the top and in the left-hand column, (but if increasing) at the bottom, and in the right-hand column. Then subtract the logarithm taken in the table from the given logarithm, and having added to the right of the difference thus obtained two cyphers, divide it by the nearest number in the contiguous column headed Diff., and the quotient will be the number of seconds to be added to the hours and minutes already obtained, when the altitude is decreasing, and to be subtracted when increasing. For example, what is the apparent * The manner of performing the calculation by which this logarithm is derived from the observed altitude is fully explained in a Treatise on Navigation, by James Greenwood, B.A.-Weale, Holborn. MATHEMATICAL TABLES. 35 time corresponding to the logarithm 9.649321 when the altitude was decreasing? Given log 9.649321 Next less log in Table 9-648913 = log of 5 H. 35 M. 40800 ÷ 3516 = 11 seconds. Therefore, the apparent time required is 5 H. 35 M. 11 s. Ex. 2. What is the apparent time corresponding with the logarithm 9.215630, when the altitude was increasing? Given log 9.215630 Next less log in table 9.214358 = 20 H. 49 M. 127200 7114 18 seconds. Therefore the apparent time is 20 H. 48 м. 42 s. TABLE XIX. Common and Hyperbolic Logarithms. The object of this Table is to facilitate the conversion of common logarithms, into hyperbolic, and vice versa. Its use is as follows:-To convert common logarithms into hyperbolic, write the common logarithm, as shewn in the first example below, and then take from the second column of the Table the equivalent value of each figure in hyperbolic logarithms, taking care that the latter are each moved as many places to the right as the corresponding numbers in the common logarithm are; the sum of the whole will be the hyperbolic logarithm required. To convert hyperbolic logarithms into common, proceed in a similar manner, writing the hyperbolic logarithm as in the second example below, and taking its equivalent value in common logarithms from the fourth column of the Table. Ex. 1. What is the hyperbolic logarithm of 3156? By reference to Table I. we find the common logarithm of 3156 is 3.499137; then- Hyp. Log. 6.907755 | 3 Com. Log. 3. ·4. •921034 0 *09 •207232 7 ⚫009 ⚫020723 3 • •0001. ⚫000230 3 ⚫00003 •000069 1 ·000007 . •000016 1 8.057061 Ex. 2. What is the common logarithm of the number whose hyperbolic logarithm is 5·160731? 36 DESCRIPTION OF THE Hyp. Log. Com. Log. 5. 2.171472 4 •1. ⚫043429 ⚫06 •026057 ·0007. •000304 •00003 ⚫000001 •000013 0 •000000 4 2-241277 TABLE XX. Curvature of the Earth and Refraction. This table is of use in Geodesical operations. Practically, a level line on the earth's surface is a line everywhere equally distant from its centre. It is obviously, therefore, not a straight line, but is a portion of a circle, having the same radius as the earth. When a level, theodolite, or other instrument has the axis of its telescope so adjusted as to be truly level, the prolongation of that axis is not a level line, but is a tangent to that line, coinciding with it only at the point where the instrument stands, and being above it everywhere else. The height of this line above the true level line, if there were no refraction, would be equal to the ver sine of an arc whose radius equalled that of the earth, and whose length was equal to the dis- tance from the instrument: these heights for various distances up to 30 miles are given in the second column of the Table. The effect, however, of the refraction of the atmosphere is to curve the visual ray passing through the centre or axis of the telescope, so that the optical axis is really a curved line which approximates very nearly to a circle, having a radius seven times greater than that of the earth. The heights in the second column require to be reduced by a seventh part, and the numbers thus obtained are given in the third column. To exemplify its use, let us sup- pose that an instrument, placed in an elevated position, has its telescope directed to a church tower 3 miles distant, and that when its telescope is perfectly level the horizontal wires are found to cut a point in one of the windows, which, on direct measurement, is found to be 95 feet from the ground, it is required to ascertain the real difference of level of the two spots. Now, on reference to the Table, we find the correction for 3 miles is 5·14, which, being subtracted from 95 feet, gives 89.86 feet for the actual height of the instrument above the ground on which the tower stands. In taking a series of consecutive observations, as in the ordinary operation of levelling by back and fore sights, to ascertain the relative level of two distant places, so long as no great difference in the range or length of the sights occurs, no correction for curvature or refraction need be made, for when the sights are actually equal no error arises in the ultimate result. MATHEMATICAL TABLES. 37 TABLES XXI., XXII., XXIII., AND XXIV. Trigonometrical Expressions. These Tables require no particular explanation. Table XXI. contains equivalent expressions for sin a, cos a, tan a, cot a, sec a, cosec a, ver sin a, and will be found of considerable use in reducing formulæ containing trigonometrical expressions. Table XXII. contains expressions, the sin, cos, tan, and cot, of mutiple arcs. Table XXIII. contains a variety of formulæ relating to the trigonometrical functions of two angles or arcs. And Table XXIV. contains expressions for the sin, cos, tan, and cot, in terms of the arc, and for the arc in terms of the sin and tan, and also ex- pressions for the powers of the sin and cos. Fig. 4. B C α TABLE XXV. The formulæ given in this Table are intended to enable all the six parts of a plane rectilineal triangle to be determined when three of those parts were pre- viously known. When either a side or angle is wanted it will only be necessary to make A or ẞ the side or angle as the case may be, and to insert in the formulæ the proper values of those letters which are known, which will then ex- press the value wanted. For example, in a triangle, two of whose sides are 23 and 35 feet in length, and the angle included between is 51°, what is the length of the third side? In this case we have given B, C and a, and want to find A, we must, therefore, select a formulæ containing only those letters; we find, accordingly, No. 7 gives A = √(B² + C2-2 B. C. cos a.) We have B = 23, C35, cos 51° 62932; inserting these values, we have A =√(23² + 352-2 x 23 x 35 x 62932) = 27.217, which is the length of the side required. TABLE XXVI. The formulæ given in this Table are to facilitate the solution of quad- ratic and cubic equations, in order to which it is only necessary to substi- tute for p and զ their known values in the formule when the value of x will be determined. By way of example, let it be required to find the value of x in the cubic equation x³ + 3x-536 = 0. We see by reference in the Table, p being to the Table that this corresponds with equation (6) equal to 3, and q to 536. Then, if we substitute these values in the second expression, it becomes. Tan a = 3 3 × 536 100 3 2 2 3 = 536 therefore, a = 0° 12′ 36″, and ½ a = : 0° 6' 18"; 38 DESCRIPTION OF THE then, Tan ẞtan (6′ 18″); therefore, 67° 1' 5", and 26 14° 2′ 10″, and x=2 3. cot (14° 2′ 10″) = 8, which is the true value of x. TABLE XXVII. This Table contains the differential coefficients of some of the most fre- quently-occurring functions of u, and will be found to include all the rules for simple differentiation. TABLE XXVIII. This table contains a variety of constant numbers of frequent use in general calculations; it also contains their logarithms to seven places of decimals, and the arithmetical complements of the same. The latter will be found of use in cases where it is required to divide by the numbers in the Table. TABLE XXIX. To reduce the Sun's Declination to any given Meridian, and to any time under that Meridian. In the "Nautical Almanac" the sun's declination is given for each day at noon at Greenwich; it is, however, necessary for the purposes of navi- gation to ascertain its declination at any other meridian, either at noon or at any other time of the day. In either of these cases, having obtained the declination from page II. of the month, in the "Nautical Almanac," the correction to be either added or subtracted therefrom, according to the directions given below, may be found in the following manner. I. If the sun's declination is required for some other meridian at noon, reckon the difference of longitude between that meridian and Greenwich, then look for this difference in the first left-hand column of the table, and on the line on which the same is found, and in the vertical column having at its head the nearest number to the declination already taken from the “Nautical Almanac," will be found the correction required. It will be seen in the "Nautical Almanac," whether the sun's declination is in- creasing or decreasing; when decreasing, add the correction in east lon- gitude, and subtract it in west longitude; but when the declination is increasing, subtract the correction in east longitude, and add it in west longitude. Example. What was the sun's declination at noon, on the 13th of November, 1850, in longitude 175° w.? MATHEMATICAL TABLES. 39 Here we find, from the "Nautical Almanac," that the sun's declination at noon at Greenwich was 17° 58′ 1″ south, and that it was increasing. We next look in the first column of the table for the given difference of longitude, viz., 175°, but the nearest number that we find is 170°, which is 5º too small, and we must, therefore, add together the corrections found in the proper vertical column on both the lines having 5° and 170° in the first column. Thus, in the present instance, in the column having at its head 18° (the nearest to 17° 58′ 1″,) and on the same line with 5° we find 13″, and on the same line with 170° we find 7′ 22″; these being added together give 7′ 35″ for the required correction, which, as the sun's decli- nation is increasing and the difference of longitude is westerly, has to be added to 17° 58′ 1″, making 18° 5′ 36″ for the sun's declination at noon in longitude 175° west. II. If the sun's declination is required for Greenwich at any other hour than noon, reckon the interval between that time and noon; then look for this interval in the last right-hand column of the table, and on the same line in which it is found, and in the vertical column having at its head the nearest number to the sun's declination (from the "Nautical Almanac "), will be found the required correction, which, when the sun's declination is increasing, is to be added, if the time is after noon, and subtracted if before noon; but when the declination is decreasing must be subtracted if the time is after noon, and added if before noon. Examples. What was the sun's declination at Greenwich on the 4th of July, 1850, at 7 h. 28 m.? From the "Nautical Almanac " we find the sun's declination at noon to have been 22° 54′ 58″ north, and to have been decreasing. Then looking in the last column of the table for the nearest number to 7h. 28 m., we find 7 h. 20 m., and on the same line in the column headed with 23° (the nearest number to 22° 54′ 58″,) we find 1′ 30″, and in the same vertical column on the same line with 8 m. we find 2", therefore the correction is 1′ 32″, which, as the sun's declination was decreasing, and the time after noon has to be subtracted from 22° 54′ 58″, leaving 22° 53′ 26″ north for the sun's declination at the hour required. What was the sun's declination at Greenwich on the 24th of August, 1850, at 20 h. 12 m. ? In this instance the time given, viz., 20 h. 12 m. on the 24th is equi- valent to 3 h. 48 m. before noon on the 25th, for which day the sun's declination is found in the "Nautical Almanac" to have been 10° 48′ 56″ north, and to have been decreasing. Looking then in the column of the table having at its head 11° (the nearest to 10° 48′ 56″,) and on the same line with 3 h. 20 m. we find 2′ 56″, and on the same line with 28 m. we find 25″; adding these two together, we obtain 3′ 21″ for the correction, which, as the sun's declination is decreasing, and the time before noon, 40 MATHEMATICAL TABLES. must be added to 10° 48′ 56″, making 10° 52′ 17″ north for the sun's declination at the time required. III. If the sun's declination is required for some other meridian than Greenwich, at any other hour than noon, we must first make the necessary correction for the difference of longitude in the manner already explained, and then the correction for time according to rule II. Examples. What was the sun's declination on the 17th of May, 1850, at 5 h. 40 m., in longitude 128° E. ? Sun's declination (increasing) at Greenwich, at noon Subtract correction for 120° Subtract correction for 8° Add correction for 5 h. 20 m. 19° 18′ 38″ N. 4′ 46″ 0 19 '} 0 5 5 19 13 33 3' 11" 0 12 J 0 3 23 19 16 56 N. Add correction for 0h. 20 m. Sun's declination at the time and place required What was the sun's declination on the 3rd of June, 1850, at 17 h. 20 m., in longitude 79° w.? 17h. 20 m. on the 3rd, is equivalent to 6 h. 40 m. on the 4th. Sun's declination (increasing) at Greenwich, at noon 22° 25′ 47″ N. Add correction for 70° Add correction for 9° 1' 41" } 0 12 } 0 1 53 Subtract correction for 6 h. 40 m. Sun's declination at the time and place required 22 27 40 . 0 2 24 22 25 16 n. When the sun is near either of the equinoxes its declination may be less than the correction, in which case, when the correction is subtractive, the declination must be subtracted from it, and the remainder will be the sun's declination of a contrary name to that which it was before. Example. What was the sun's declination at noon on the 23rd of September, 1850, in longitude 164° E ? The sun's declination (increasing) at noon, at Greenwich Subtract correction for 160° at noon Subtract correction for 4° . Sun's declination at the place required 0° 1′ 57″ s. 10′ 25″ 0 16 0 10 41 0 8 44 N. MATHEMATICAL TABLES. 41 No. 100 L. 000.] N. Ι 2 LOGARITHMS OF NUMBERS. 3 4 6 7 [No. 109 8 L. 040. 9 N. 5 1000000000434 0868 | 13011734 2166 | 2598 | 3029 | 3461 3891 100 4321 4751 5181 5609 6038 6466 6894 7321 7748 8174 2 8600 9026 9451 9876 0300 0724 1147 1570 1993 2415 I 3 012837 3259 3680 4100 4521 4940 5360 5779 6197 6616 4 7033 7451 7868 8284 8700 6 9116 9532 9947 3252 3664 | 4075 7350 77578164 1408 1812 2216 I 2 3 4 noo 61976616 0361 0775 4486 | 4896 8571 8978 6 2619 3021 5 021189 1603 2016 2428 2841 5306 5715 6125 6533 6942 9384 9789 0195 0600 1004 8033424 3826 4227 4628 5029 5430 5830 6230 6629 7028 7426 7825 8223 8620 9017 9414 9811 7 9 PROPORTIONAL PARTS. | I 2 4 5 | | | 5 78 0207 0602 | 0998 9 6 7 8 9 | 00 N. 3 1000 434 86.8 | 130°2 173⋅6 | 217′0 | 260°4 3038 347°2 390.6 1002 43.3 86.6 129.9 173.2 216.5 259.8 3031 3464 389.7 | | 1004 432 864 129.6 172.8 2160 2592 3024 3456 388-8 | 1006 43.1 86.2 129°3 172.4 2155 258.6 3017 3448 3879 1009 430 86.0 129.0 172.0 2150 258.0 3010 3440 387.0 1011 429 85.8 128.7 1716 214'5 2574 300'3 3432 386.1 | | 1014 42.8 85.6 1284 1712 2140 256-8 299.6 3424 385°2 1016 427 85°4 128°1 | 170·8 213.5 256.2 2989 341.6 3843 | | 1018 42.6 85.2 127.8 1704 2130 255.6 298.2 3408 3834 1020 425 850 1275 1700 212.5 2550 297°5 3400 382.5 1023 424 848 1272 169.6 2120 2544 296.8 3392 381.6 | 1026 42.3 84.6 1269 1692 2115 253-8 296.1 3384 380.7 | | 1028 42.2 84.4 126.6 168.8 2110 2532 2954 3376 | 379.8 1030 42.1 84.2 126.3 168.4 2105 252.6 2947 336.8 378-9 | | 1033 420 840 1260 1680 2100 2520 2940 336.0 378.0 | | | | 1035 419 83.8 125.7 167·6 2095 2514 2933 3352 3771 | | | | | 1038 418 83.6 125°4 167.2 2090 250.8 292.6 3344 376.2 | | | 1040 417 83.4 1251 166.8 208.5 250°2 2919 333.6 375'3 1043 41.6 83.2 124.8 1664 2080 2496 2912 332-8 3744 | | | | 1045 415 830 124°5 1660 2075 249'0 2905 3320 373'5 1048 414 82.8 124°2 1656 | 207′0 248′4 289.8 3312 372-6 | | | | 1050 41.3 82.6 123′9 1652 206.5 247.8 2891 3304 3717 | | 1053 412 824 1236 1648 2060 247.2 288.4 329.6 370.8 1055 411 822 123 3 1644 2055 246-6 287.7 328.8 369.9 | | | 1058 410 820 1230 1640 2050 2460 2870 3280 369.0 | | 1060 409 81.8 122.7 163.6 204 5 2454 286.3 327.2 368.1 | | 1063 40.8 81.6 1224 1632 2040 244.8 285.6 326-4 367.2 | | 1066 407 814 122.1 162.8 2035 244 2 2849 325-6 366.3 1068 40.6 812 121.8 1624 2030 243.6 2842 3248 3654 | | | 1071 405 810 121.5 1620 202.5 243.0 2835 3240 364 5 | | | 1074 404 808 1212 161·6 | 202′0 | 242°4 | 282·8 | 323°2 | 363.6 | | 1076 403 806 1209 161-2 2015 241-8 2821 3224 362.7 1079 402 804 1206 160.8 2010 241-2 2814 321-6 361-8 1082 401 802 120°3 1604 2005 240·6 280.7 3208 360·9 1084 400 800 1200 1600 2000 2400 2800 3200 360.0 1087 399 79.8 119.7 1596 1995 2394 2793 3192 359°1 | | | | | | 1090 39.8 79.6 1194 1592 199.0 238.8 278.6 3184 358·2 | | | | 1093 397 794 1191 158.8 198.5 238.2 2779 317-6 357 3 | | | 1095 39.6 79.2 118.8 1584 1980 2376 277 2 316.8 3564 | | | 1098 39.5 79.0 118.5 1580 1975 2370 276.5 316.03555 | | | | E 42 MATHEMATICAL TABLES. No. 110 L 041.] LOGARITHMS OF NUMBERS. [No. 119 L. 078. N. о I 2 3 4 5 6 7 8 9 N. I I 110 041393 1787 2182 2576 2969 3362 3755 4148 4540 4932 110 5323 5714 6105 6495 6885 7275 7664 8053 8442 8830 2 9218 9606 9993 0380 0766 1153 1538 3 053078 3463 3846 4230 4613 4996 5378 4 6905 7286 7666 5060698 1075 1452 8046 8426 8805 9185 1829 2206 2582 2958 1924 2309 2694 5760 6142 6524 9563 | 9942 0320 3333 3709 4083 4458 4832 5206 5580 5953 6326 6699 7071 7443 7815 7 8186 8557 8928 9298 9668 0038 0407 0776 8071882 2250 2617| 2985 3352 3718 4085 4451 5547 5912 6276 6640 70047368 7731 8094 6 91 PROPORTIONAL PARTS. 2 23 to 4 5 6 70 1145 1514 4816 | 5182 8 8457 8819 9 5 6 7 8 9 N. I 3 4 1101 394 78.8 1182 157.6 1970 2364 2758 3152 354-6 1104 39.3 78.6 1179 1572 1965 235.8 275°1 3144 353'7 1106 392 784 117.6 156.8 1960 2352 2744 313-6 352-8 | | | | | 1109 39.1 78.2 117.3 15641955 2346 | 2737 312-8 351*9 1112 390 780 1170 1560 1950 2340 2730 3120 3510 1115389 77-8 1167 155.6 1945 2334 272-3 311°2 350°1 II18 38.8 77.6 1164 155.2 1940 232.8 2716 3104 349°2 38-877-6 | | | | | 1121 387 77°4 | 116′1 | 1548 1935 232°2 270°9 309.6 | 348°3 1124 38.6 77.2 | 115·8 | 154°4 1930 231.6 | 270°2 | 308.8 | 3474 | | | 1127 385 770 1155 1540 192.5 2310 269.5 308.0346.5 1129 384 768 1152 153.6 1920 2304 268-8 3072 345.6 113238.3 1132 38.3 76.6 1149 1532 191.5 229.8 268.1 3064 3447 1135 382 764 114.6 152.8 1910 229°2 2674 305.6 343.8 | | | | 1138 381 762 114.3 1524 1905 228.6 266.7 3048 3429 1141 380 760 1140 1520 1900 2280 266.0 3040 3420 1144 379 758 1137 151-6 189.5 2274 | 265.3 3032 341*I 1148 378 756 1134 1512 189.0 226.8 2646 3024 340°2 1151 377 754 1131 150-8 188.5 2262 263 9 301-6 339°3 1154 376 752 112.8 1504 1880 225.6 263 2 3008 338.4 | | 1157 375 750 1125 1500 187.5 2250 262-5 3000 337.5 | | 1160 374 748 | 112′2 | 149-6 | 187′0 | 224′4 | 261.8 | 299.2 336-6 1163 373 74-6 1119 1492 186.5 223.8 2611 2984 335'7 1166 372 744 1116 148-81860 223.2 2604 2976 3348 1169 371 742 1113 148 4 185.5 222.6 259.7 296.8 333'9 | | 1172 370 740 1110 1480 1850 2220 259.0 2960 3330 | 1175 369 738 1107 1476 1845 2214 258.3 2952 332.1 1178 36.8 73.6 110'4 147°2 1840 2208 2576 2944 331°2 1182 367 734 1101 146-8 183.5 220 2 2569 293.6 3303 1185 36.6 73.2 109.8 1464 1830 219.6 256.2 2928 3294 | | | 1188 36.5 730 109'5 146'0 182.5 2190 2557 2920 328.5 | | | | 1192 364 72-8 | 109.2 145.6 1820 2184 2548 | 2912 327.6 F195 36.3 72.6 108.9 145 2 1815 217-8 2541 2904 326-7 | | | 1198 362 724 108.6 1448 1810 217-22534 289.6 | 325.8 1202 361 72-2 108-3 1444 1805 216.6 252 7 288.8 3249 1205 360 720 1080 1440 1800 2160 252.0 2880 324.0 1208 359 71.8 107.7 143-6 179°5 2154 251°3 2872 323.1 1212 35.8 71.6 | 107′4 | 1432 1790 2148 250·6 2864 | 322°2 1215 357 714 1071 142.8 178.5 2142 249′9 285.6 321°3 1218 35.671-2 106·8 | 142°4 1780 213.6 249.2 284.8 3204 MATHEMATICAL TABLES. 43 No. 120 L. 079.] LOGARITHMS OF NUMBERS. I 2. 3 [No. 134 L. 130. 6 7 9 N. N.I о 4 ! 5 1 ら 120 079181 9543 9904 0266 | 0626 | 0987 1347 1707 2067 | 2426|120 1082785 3144 3503 3861 4219 4576 49345291 5647 6004 I 6360 6716 7071 7426 77818136 8490 8845 9198 9552 | 9905 0258 0611 0963 1315 1667 2018 2370 2721 3071 | 4 093422 3772 4122 4471 4820 5169 5518 5866 6215 6562 8298 8644 8990 9335 9681 0026 23 5 71 78 | 2091 2434 2777 3119 3462 | | | | 5510 5851 6191 6531 6871 8903 9241 9579 9916 0253 2270 2605 2940 3275 3609 | | 2 34 56 7 8 9 6910 7257 7604 7951 | 6100371 0715 1059 1403 1747 | 38044146 4487 4828 5169 7210 7549 7888 8227 8565 9 110590 0926 | 1263 | 1599 | 1934 3943 4277 4611 4644 5278 5611 | I 7271 7603 7934 8265 85958926 9256|9586|9915 0245 I 2 120574 0903 1231 1560 1888 2216 2544 2871 3198 3525 | 3852 4178 4504 4830 5156 5481 5806 6131 6456 6781 7105 7429 7753 8076 8399 8722 9045 9368 9690 | 130 3 4 PROPORTIONAL PARTS. 2 4 5943 6276 | 6608 | 6940 130 | | 7 2 3 0012 4 N. I 3 5 6 8 9 1222 355 71°0 106.5 142′0 1775 2130 248.5 | 2840 3195 1225 354 70.8 1062 141.6 1770 212 4 2478 283.2 318.6 | 1228 35.3 70.6 1059 141°2 176.5 211.8 2471 2824 3177 | | 1231 352 70'4 105.6 140·8 1760 2112 2464 281-6 316.8 35:2704105.6 | 1235 351 70'2 105°3 1404 175'5 2106 245 7 280.8 315'9 1239 350 700 1050 1400 1750 2100 2450 2800 3150 1243 349 698 1047 139.6 1745 2094 244°3 2792 3141 | | | | 1247 348 69.6 1044 1392 1740 208.8 2436 278.4 3132 1250 347 694 1041 138.8 1735 2082 2429 277·6 312.3 | | | | 1253 346 692 103.8 1384 173′0 207·6 | 2422 276.8 3114 | | 1257 345 690 103.5 1380 172.5 2070 241°5 276·0 | 310′5 1261 344 68.8 1032 137.6 172′0 2064 240.8 2752 309.6 | 1264 343 68.6 1029 1372 1715 205.8 240°1 2744 308.7 1268 342 684 1026 136.8 1710 2052 2394 2736 307.8 | 1272 341 682 102.3 1364 170°5 2046 238.7 272.8 306-9 | | 1276 340 680 102'0 136.0 1700 2040 238.0 2720 306·0 1279 339 67.8 1017 1356 169.5 2034 237 3 2712 305.1 1283 33.8 67.6 1014 1352 1690 202-8 236.6 2704 304.2 1287 337 674 101°1 1348 168.5 2022 2359 269.6 303.3 IOII | | | 100-8 1344 168.0 2016 2352 268.8 302 4 | | | 1291 336 672 1295 335 670 1298 334 66.8 1302 333 66.6 1306 332 664 1310 33166.2 1314 330 66.0 1318 329 658 1322 32.8 65.6 1326 327 654 1330 32.6 65.2 1334 325 65.0 1338 324 64.8 1343 323 64.6 1347 32-264-4 | | | 100'5 1340 1675 2010 2345 2680 3015 | 1002 133.6 167′0 2004 233.8 2672 300-6 999 1332 166·5 | 199·8 | 233′1 | 2664 2997 99.6 132.8 166.0 1992 2324 265.6 298.8 993 1324 1655 1986 2317 2648 2979 | | 990 1320 1650 1980 2310 2640 297.0 | | | 987 1316 1645 1974 230°3 263.2 296.1 | | | | 984 1312 1640 196.8 229.6 262.4 295 2 981 130-8 163.5 1962 228.9 261.6 2943 9781304 163′0 195.6 228.2 260·8 293'4 | | | | 97.5 1300 1625 1950 227.5 2600 292.5 972 | 129.6 | 162′0 | 1944 | 226·8 | 259′2 | 291-6 96.9 1292 1615 1938 226.1 2584 290.7 96·6 128.8 1610 1932 2254257·6 | 289.8 | | 44 MATHEMATICAL TABLES. No. 135 L. 130.] 56 7R 8 140 I 3 5 6 9 I 2 2 LOGARITHMS OF NUMBERS. 4 [No. 149 L. 175. 7 8 9 N. 6 9 1 3815 4120 9868 0168 4424 4728 | 5032 7457 7759 8061 | 0469 0769 1068 2 3 2863 3161 5838 6134 3460 3758 4055 6430 6726 7022 00 456 7 8 9 9 N. 3 5 6 135 130334 0655 0977 1298 1619 1939 2260 2580 2900 3219 135 | 3539 3858 4177 4496 4814 5133 5451 5769 6086 6403 51335451 | 6721 7037 7354 7671 7987 8303 8618 8934 9249 9564 7 9879 0194 0508 0822 1136 1450 1763 2076 2389 2702 8 9 143015 33273639 3951 4263 4574 4885 5196 5507 5818 || 6128 6438 6748 7058 7367 7676 7985 | 8294 8603 8911 140 9219 9527 9835 0142 0449 0756 1063 1370 1676 1982 2152288 2594 2900 3205 3510 5336 56405943 6246 6549 68527154 4 8362 8664 8965 9266 9567 161368 1667 1967|| 2266|| 2564 4353 4650 4947 5244 5541 7 7317 7613 7908 8203 8497 8792 9086 9380 9674 9968 8 170262 0555 0848 11411434 1726 2019 2311 2603 2895 3186 34783769 4060 4351 4641 4932 5222 5512 5802 | | N. I 3 4 5 6 7 8 1351 321 642 96.3 1284 1605 1926 2247 256.8 288.9 1355 320 640 960 1280 1600 1920 2240 2560 288.0 1359 319 63·8 957 127.6 1595 1914 2233 2552 287-1 | 954 127.2 1590 190 8 222.6 2544 286-2 951 126.8 158.5 1902 2219 2536 285-3 948 1264 1580 189.6 2212 252.8 284-4 945 1260 157.5 189.0 2205 2520 283.5 942 125.6 1570 1884 219.8 2512 282-6 939 1252 156.5 187.8 2191 2504 2817 | 93.6 1248 1560 1872 2184 249.6 280.8 | 933 1244 1555 186-6 2177 248.8 279°9 930 1240 1550 1860 2170 248.0 279'0 927 123.6 1545 1854 216.3 247.2 278.1 | | | | 278′1 924 1232 1540 184-8 215.6 246·4 | 277'2 122.8 1535 184-2 2149 245.6 | 276·3 1224 1530 183.6 2142 2448 275°4 | 122.0 | 152°5 1830 213.5 2440 2745 | 121.6 1520 1824 212.8 243.2 273.6 PROPORTIONAL PARTS. 1364 318 63.6 1368 317 634 1372 316 632 1376 315 630 1381 314 62.8 1385 313 62.6 1390 312 624 1394 311 62.2 1398 310 62.0 | 1403 309 61.8 1412 307 614 92.1 | | 1417 30.6 61.2 1422 305 610 1426 304 60.8 918 91.5 912 | 1431 303 60·6 90'9 1436 302 604 90'6 1441 301 60°2 90.3 1446 300 600 1446300 90'0 897 1408 308 61.6 1818 | 212°1 | 242°4 | 272°7 1812 2114 2416 | 271.8 | 121°2 1515 120.8 1510 1204 150°5 180.6 2107 240.8 270.9 1200 1500 1800 2100 2400 270°0 1450 29.9 59.8 119.6 1495 1794 2093 2392 269.1 | | 1455 29.8 59.6 894 1192 1490 178.8 208.6 238.4 268.2 1460 297 594 891 118-8 148.5 178.2 2079 237.6 267.3 | | 1465 29.6 59:2 88.8 1184 148.0 177.6 2072 236.8 266-4 1470 29'5 59°0 88.5 1180 147.5 1770 206·5 | 236·0 265′5 1475 294 58.8 88.2 117.6 1470 176.4 205.8 2352 264·6 1480 29.3 58.6 117-2 146.5 175.8 2051 2344 2637 1485 292 584 87.6 116.8 1460 175.2 2044 233.6 262.8 1490 291 58.2 87.3 116.4 145.5 174.6 2037 232.8 2619 | | | | 1495 290 580 870 116.0 1450 1740 2030 232.0 2610 1500 28.9 57.8 86.7 115.6 144'5 1734 2023 2312 260.1 | 1505 28.8 57.6 864 1152 1440 172.8 2016. 2304 2592 1511287 57'4 8611148 143.5 172-2 2009 229.6 258.3 1516 | 28-6 | 57°2 | 85·8 | 114°4 | 143·0 | 171·6 | 200·2 | 228·8 | 257:4 879 MATHEMATICAL TABLES. 45 No. 150 L. 176.] LOGARITHMS OF NUMBERS. N. о I 2 3 4 5 [No. 169 L. 230. 6 7 8 9 N. 8113 8401 8689 150 I 150 176091 6381 6670 6959 72487536 || 7825 I 234 56 D∞ 7 8 | 8977 9264 9552 9839 0126 0413 0699 0986 1272 1558 2 3 4 5 6 7 8 9 2 181844 2129 2415 2700 2985 3270 3555 3839 4123 4407 4691 4975 5259 5542 5825 6108 6391 6674 6956 7239 7521 7803 8084 8366 8647 8928 9209 9490 9771 0051 | 190332 0612 0892 1171 1451 1730 2010 2289 2567 2846 3125 3403 3681 3959 4237 4514 4792 5069 5346 5623 | | 5900 6176 6453 6729 7005 7281 7556 7832 8107 8382 | | 8657 8932 9206 9481 9755 0029 0303 0577 0850 1124 9 201397 1670 1943 2216 | 2488 | 2761 | 3033 | 3305 | 3577 3848 | 27613033 | | 4120 4391 4663 4934 5204 5475 5746 6016 6286 6556 160 | 6826 7096 7365 7634 7904 8173 8441 8710 8979 9247 9515 9783 | 2 0051 0319 0586 0853 1121 1388 1654 1921 3 212188 2454 2720 2986 3252 3518 3783 4.049 4314 4579 | | 4844 5109 5373 5638 5902 6166 6430 6694 6957 7221 7484 7747 8010 8273 8536 8798 9060 9323 9585 9846 | | 6220108 0370 0631 | 0892 | 1153 1414 1675 1936 2196| 2456 | 2716 2976 3236 3496 3755 4015 4274 4533 4792 5051 5309 5568 5826 6084 6342 6600 6858 7115 7372 7630 7887 8144 8400 8657 89139170 | 9426 | 9682|9938 7887 8144 8400 8657 160 I 2 4 5 7 8 ୨ .00 a PROPORTIONAL Parts. I 2 4 이 7 I 3 4 5 6 78 0193 8 9 9 00 6 5 1140 142.5 1710 1995 2280 256.5 113.6 1420 1704 198.8 227.2 255.6 1132 141-5 169.8 1981 226 4 2547 112.8 1410 1692 1974 225.6 253.8 | | | 1124 1405 168.6 196.7 224-8 252.9 1120 1400 1680 1960 2240 252.0 1116 139.5 1674 1953 2232 251'1 | 1112 1390 166-8 1946 222 4 250°2 110.8 138.5 166.2 1939 221-6 249°3 1104 138.0 165.6 1932 220.8 248.4 | N. 3 1521 285 570 85.5 1527 28.4 56.8 85.2 1532 28.3 56.6 84.9 1537 28.2 56.4 84.6 1543 281 562 843 1548 280 560 840 1554 279 558 83.7 1559 278 556 834 1565 277 554 831 1570 27.6 55.2 82.8 1576 275 550 82.5 1100 137.5 165.0 192.5 | 2200 247′5 | | 1582 274 548 82.2 109.6 1370 1644 1918 2192 246·6 | | | | | 1587 273 546 819 109°2 136.5 163.8 1911 2184 245'7 | | | | | 1593 272 544 81.6 108.8 136.0 163.2 1904 217.6 244.8 272544 1599 27.1 542 813 1084 135°5 162.6 189.7 216.8 243'9 1605 270 540 810 1080 1350 1620 1890 2160 2430 1611 269 53.8 80.7 107.6 1345 1614 1883 2152 242 1 1617 26.8 536 804 1072 1340 1608 187.6 2144 241-2 1623 267 534 801 106.8 133.5 1602 1869 2136 240*3 | 1629 26.6 532 79.8 106.4 1330 1596 1862 212-8 239°4 1635 26.5 530 79′5 | 1060 | 132.5 | 1590 | 185.5 2120 238.5 1641 264 52.8 79.2 105.6 | 132′0 158.4 184-8 2112 237.6 1648 26.3 52.6 78.9 1052 1315 157-8 1841 2104 236.7 165426.252.4 | | 1654 262 52.4 78.6 1048 1310 1572 1834 209.6 | 235·8 | 1660 261 52.2 78.3 1044 1305 156-6 182.7 208-8234'9 | | 1667 260 52·0 | 78′0 | 104°0 1300 1560 182.0 2080 234°0 1673 259 51.8 77.7 103.6 129.5 1554 1813 2072 2331 | | 1680 25.8 51.6 77.4 103.2 129.0 1548 180·6 206·4 | 232°2 1686 257 514 771 102-8 128.5 1542 1799 2056 231°3 | | 1693 256 512 768 1024 1280 1536 1792 2048 2304 | | | 1699 25.5 51.0 76.5 102.0 | 127.5 | 1530 | 178.5 | 2040 | 229.5 | | | | 46 MATHEMATICAL TABLES. I 2 3 5 7 No. 170 L. 230.] N. O LOGARITHMS OF NUMBERS. I 2 3 4 5 6 7 170 230449 0704 0960 1215 1470 1724 2996 3250 3504 3757 4011 4264 5528 5781 6033 6285 6537 6789 8046 8297 8548 8799 9049 9299 1979 [No. 189 L. 278. 89 N. 2234 | 2488 | 2742170 4517 4770 5023 5276 I 7041 7292 7544 7795 9550 9800 | | | 0050 0300 2541 2790 2 3456 9 180 4 240549 0799 1048 1297 1546 1795 2044 2293 3038 3286 3534 3782 4030 4277 4525 4772 5019 5266 5513 5759 | 6006 | 6252, 6499 6745 6991 7237 7482 7728 7973 8219 8464 8709 8954 9198 9443 9687 9932 0176 8 250420 0664 0908 1151 1395 1638 1881 2125 2368 2610 2853 3096 3338 3580 3822 4064 4306 4548 4790 5031 9 | 7 | 8 5273 5514 5755 5996 6237 6477 6718 6958 7198 7439180 7679 7918 8158 8398 8637 8877 9116 9355 9594 9833 I I 2 3+ in 5 2 260071 0310 0548 0787 1025 1263 1501 1739 1976 2214 2451 2688 2925 3162 3399 3636 3873 4109 4346 4582 | | | 4818 5054 5290 5525 5761 5996 6232 6467 6702 6937 7172 7406 7641 7875 8110 8344 8578 8812 9046 9279 | 9513 9746 9980 0213 0446 0679 0912 1144 1377 1609 7 271842 2074 2306 2538 2770 3001 32333464 3696 3927 41584389 4620 4850 5081 5311 5542 5772 6002 6232 6462 66926921 7151 7380 | 76097838 8067 8296 8525 | 789 9 2 3 4 5 6 78 9 9 7 8 177·8 203′2 | 228.6 177°1 2024 227°7 176.4 2016 226.8 175°7 2008 225'9 N. 1 | 2 3 4 5 6 1706 254 50·8 | 76°2 | 101·6 | 127′0 | 152°4 1713 253 50·6 | 75′9 | 101°2 | 126.5 151.8 1719 252 504 75.6 100-8 126.0 1512 1726 251 502 75°3 1004 125°5 150-6 1733 250 500 750 | 1000 | 1250 1500 1750 2000 225.0 1740 249 49.8 747 99.6 1245 1494 174 3 1992 224*1 1747 248 49.6 | 74:4 992 1240 148.8 1736 1984 223.2 1754 247 49′4 | 74'1 98.8 123.5 148.2 1729 1976 222°3 | 1761 246 49.2 73.8 984 123′0 147.6 1722 196.8 2214 | 1769 245 490 735 980 122.5 1470 171′5 196′0 | 220′5 PROPORTIONAL PARTS. 960 1776 244 48.8 | 73°2 97′6 | 122′0 | 146′4 | 170·8 | 1952 | 219′6 1783 243 48.6 | 72°9 972 121°5 1458 170°1 | 1944 2187 1790 242 484 72.6 96.8 1210 1452 169'4 1936 217.8 1798 241 482 723 964 120°5 1446 1687 192.8 216'9 1805 240 480 720 1200 1440 1680 1920 216.0 | | | 1813 239 47-8 717 95.6 1195 1434 167.3 1912 | 215°1 1820 23.8 47.6 714 952 1190 142.8 166.6 1904 || 214°2 1828 237 474 71'I | 948 118.5 142°2 | 165'9 1836 23.6 47.2 70.8 944 1180 141-6 1652 1844 235 470 70'5 940 117.5 1410 1645 189.6| 213.3 188-8 | 2124 1880 2115 | 1852 234 46.8 70.2 93.6 1170 140°4 163.8 187.2 2106 1859 23.3 46.6 69.9 93.2 116.5 139.8 | 163.1 | 1864 209'7 1867 23.2 464 69.6 92.8 116-0 139.2 162.4 185.6 208.8 | | 1876 23′1 46.2 69.3 23.146.2 924 115.5 138.6 1617 1848 2079 1884 230460 690 920 1150 1380 1610 1840 207.0 1892 229 458 68.7 916 1145 1374 1603 183.2 206.1 | | 1900 22.8 456 684 912 1140 136-8 159.6 1824 205.2 | | | 1908 227 45°4 | 68·1 90.8 1135 136.2 158.9 181.6 2043 1917 226 45.2 67.8 90°4 1130 135.6 158.2 180.8 2034 45.2 67.8 MATHEMATICAL TABLES. 47 No. 190 L. 278.] N. о I 2 LOGARITHMS OF NUMBERS. [No. 214 L. 332. 3 4 5 6 7 8 9 N. 2 3 4 5 6 7∞ 8 I 3804 6007 I 1234 SO DO0 5 6 7 8 9 I 2547 2764 2980 200 4706 4921 5136 6854 7068 7282 8991 9204 9417 92049417 |190| 278754 | 8982|9211|9439|9667 | 9895|0123 0351 0578 | 0806 |190 1 281033 1261 1488 1715 1942 2169 2396 2622 2849 3075 3301 3527 3753 3979 4205 4431 4656 4882 5107 5332 5557 5782 6007 6232 6456 6681 6905 7130 7354 7578 7802 8026 8249 8473 8696 8920 9143 9366 9589 9812 290035 0257 0480 0702 0925 11471369 1591 1813 2034 2256 2478 2699 2920 3141 3363 3584 4025 4246 4466 4687 4907 5127 5347 5567 5787 6226 6446 6665 6884 7104 7323 7542 7761 7979 8198 8416 8635 9 8853 9071 9289 | 9507 | 9725 9943 0161 0378 0595 0813 | | 200 301030 1247 1464| 1681 | 1898 2114 2331 3196 3412 3628 3844 4059 4275 4491 5351 5566 5781 5996 6211 6425 6639 7496 7710 7924 8137 8351 8564 8778 9630 9843 0056 0268 0481 0693 0906 1118 1330 1542 311754 1966 2177 2389 2600 2812 3023 3234 3445 3656 3867 4078 4289 | 4499 4710 4920 5130 5340 5551 5760 5970 6180 6390 6599 6809 7018 7227 7436| 7646| 7854 8 8063 8272 8481 8689 8898 9106 9314 9522 9730 9938 9320146 0354 0562 0769 0977 1184 1391 1598 1805| 2012 | | 2219 2426 2633 2839 3046 3252 3458 3665 3871 4077 210 4282 4488 4694 4899 5105 5310 5516 5721 5926 6131 6336 6541 6745 6950 7155 7359 7563 7767 7972 8176 | | 8380 8583 8787 8991 9194 9398 9601 9805 0008 0211 4330414 0617 | 0819 | 1022 | 1225 | 1427 | 1630 | 1832 | 2034 | 2236 4 23+ iO 7∞ 6 210 I 2 3 4 PROPORTIONAL PARTS. I ΙΙΙΟ | 23 456 78 9 I 2 3 4 8 9 N. 3 4 1 | 2 6 5 7 1925 225 450 67.5 900 112.5 1350 1575 1800 202.5 1934 224 448 67.2 89.6 1120 134′4 156·8 179°2 201·6 1943 22.344.6 66.9 89.2 111'5 133.8 156·1 | 178'4 2007 | | 1952 22'2 444 66.6 88.8 1110 1332 1554 177.6 199.8 | 1961 22.I 442 66.3 884 110.5 132.6 1547 176.8 1989 | | 1969 22.0 440 66.0 88.0 1100 1320 1540 176.0 1980 1978 219 43.8 65.7 87.6 109.5 1314 1533 175°2 1971 1987 218 43.6 654 87′2 1090 1308 | 152.6 1744 | 196-2 1996 217 434 651 86.8 108.5 1302 1519 1736 195'3 | | 2005 21.6 43.2 64.8 86.4 1080 129.6 1512 172-8 194'4 2015 215 430 64.5 86.0 107.5 1290 150'5 1720 1935 2024 214 428 642 85.6 1070 128.4 149.8 1712 192.6 2034 213 42-6 639 85.2 106.5 127.8 1491 1704 1917 2043 21.2 424 63.6 84.8 1060 1272 1484 169.6 190-8 | | | 2053 211 42 2 633 844 105'5 126.6 147.7 1688 189.9 2063 21'0 42.0 630 840 1050 1260 1470 1680 189.0 2073 20.9 41.8 62.7 83.6 104.5 1254 146.3 1672 188.1 2082 20.8 41.6 62.4 83.2 1040 1248 145.6 166.4 187.2 2092 207 414 62.1 82.8 103.5 1242 1449 165.6 186.3 | 2103 20.6 41.2 61.8 82.4 1030 123.6 144°2 | 164·8 | 185′4 2113 20.5 400 61.5 82.0 102.5 1230 143.5 1640 1845 2123 204 408 61.2 81.6 102'0 1224 142.8 163.2 183.6 2134 20.3 40.6 60.9 81.2 101.5 121.8 142°1 1624 182.7 2144 20'2 404 60.6 80.8 1010 121°2 | 1414 | 161.6 | 181-8 48 MATHEMATICAL TABLES. No. 215 L. 332.] LOGARITHMS OF NUMBERS. [No. 239 L. 380. N. о I 2 3 4 5 6 7 8 9 N. 6 6 557 215 332438 2640 2842 3044 3246 3447 3649 3850 4051 4253 215 4454 4655 4856 5057 5257 5458 5658 5859 6059 6260 6460 6660 6860 7060 7260 7459 7659 7858 8058 8257 8456 8656 8855 9054 9253 9451 9650 9849 0047 0246 78 220 8 9 340444 0642 0841 1039 1237 1435 1632 1830 | 2028 2225 9 2423 2620 2817 3014 3212 3409 3606 3802 3999 4196 220 4392 4589 4785 4981 5178 5374 5570 5766 5962 | 6157 6353 6549 6744 6939 7135 7330 7525 7720 7915 8110 8305 8500 8694 8889 9083 9278 94729666 | 9860 1 2 3 56 78 9 I 0054 I 2 3456 78 4 350248 0442 0636 0829 1023 1216 1410 1603| 1796 | 1989 2183 2375 2568 | 2761 | 2954 3147 3339 3532 3724 3916 4108 4301 4493 4685 4876 5068 5260 5452 5643 5834 6026 6217 6408 6599 6790 6981 7172 7363 7554 7744 7935 81258316 8506 8696 8886 9076 9266 9456| 9646 9835 0025 0215 0404 0593 0783 0972 1161 1350 1539 9 230 361728 1917 2105 2294 2482 2671 2859 3048 3236 3424 230 3612 3800 3988 4176 4363 4551 4739 4926 5113 5301 I 5488 5675 5862 6049 6236 6423 6610 6796 6983 7169 7356 7542 7729 7915 8101 8287 8473 8659 8845 9030 9216 9401 9587 9772 9958 0143 0328 0513 0698 0883 5 371068 1253 1437 1622 1806 1991 2175 2360 2544 2728 | | 2912 3096 3280 3464 3647 3831 4015 4198 4382 4565 4748 4932 5115 5298 5481 5664 5846 6029 6212 6394 6577 6759 6942 7124 7306 7488 7670 7852 8034 8216 8398 8580 8761 8943 91249306 94879668|9849 0030 9 1234 6 789 PROPORTIONAL PARTS. I 2 3 4 in 5 6 7 8 9 2 3 456 78 N. 2155 20'I 402 603 804 100.5 120.6 1407 160·8 1809 2166 20'0 400 600 800 100.0 1200 1400 1600 180.0 2176 19'9 398 59'7 79.6 99.5 1194 1393 159°2 179°1 39-8597 | | | 2187 19.8 39.6 594 79°2 99'0 118.8 138.6| 1584 178.2 2198 197 394 59°1 78:8 98.5 118.2 137′9 1576 1773 | 118-21379 19.6 392 58.8 78.4 980 117.6 137.2 156.8 176.4 2221 19.5 390 58.5 78.0 97.5 1170 136.5 1560 1755 2232 194 38-8 582 77.6 970 1164 135-8 1552 1746 2210 2244 19.3 38-6 579 772 | 2256 192 384 57.6 76.8 2267 191 382 573 764 2279 19'0 380 57.0 76.0 2291 18.9 37.8 56.7 75.6 2303 18.8 37.6 564 752 18.7 374 56°1 | 74-8 18.6 37.2 55.8 744 2316 2328 2341 18.5370 55°5 | 740 2353 18.4 36.8 552 | 73.6 2366 18.3 36.6 549 732 | 2379 18.2 364 546 | 72-8 2392 18.1 36.2 543 724 2406 18.0 36.0 540 720 2419 179 35.8 537 716 | | 96.5 115·8 | 135°1 | 1544 1737 960 1152 1344 153.6 172.8 | 955 114-6 1337 152·8 | 171-9 950 1140 1330 1520 1710 94'5 1134 | 132°3 | 151*2 | 170*1 940 112.8 131.6 1504 | 169°2 935 112.2 1309 149.6 168.3 930 1116 130′2 | 148.8 | 167°4 925 1110 129.5 1480 166.5 920 1104 128.8 147.2 165.6 915 109.8 128.1 1464 1647 910 109.2 1274 145.6 163.8 90.5 108.6 126.7 144-8 162-9 900 1080 1260 1440 162.0 89.5 1074 1253 1432 1611 MATHEMATICAL TABLES. 49 No. 240 L. 380.] LOGARITHMS OF NUMBERS. [No. 269 L. 431. N. I 2 3 4 5 6 7 8 9 N. 123 5070 I 2 240 380211 0392 0573 0754 0934 1115 1296 1476 1656 1837 240 2017 2197 2377 2557 2737 2917 3097 3277 3815 3995 4174 4353 45334712 4891 5606 5785 5964 6142 6321 6499 6677 6856 7390 7568 7746 7924 8101 8279 8456 8634 9166 9343 9520 9698 9875 0051 0228 0405 || | | | 3456 3636 5249 5428 7034 7212 8811 8989 0582 0759 a 3 + iO DOO a 4 4 5 5 7 8 9 6 390935 1112 1288|| 1464 1641 1817 1993 2169 2345 2521 2697 2873 3048 3224 3400 3575 3751 3926 4101 4277 4452 4627 4802 4977 5152 5326 5501 5676 5850 6025 6199 6374 6548 6722 6896 7071 7245 7419 7592 7766 6 7 8 9 250 9328 9501 250 1056| 1228 Ι 2 3 4 56 7940 8114 8287 8461 8634 | 8808 8981 9154 I 9674 9847 0020 0192 0365 0538 0711 0883 2 401401 1573 1745 1917 2089 2261 2433 2605 2777 2949 3121 3292 3464 3635 3807 3978 4149 4320 4492 4663 4834 5005 5176 5346 5517 5688 5858 6029 61996370 6540 6710 6881 7051 7221 7391 7561 7731 7901 8070 8240 8410 8579 8749 8918 9087 9257 9426 9595 9764 9933 0102 0271 0440 | 0609 0777 0946 1114 1283 1451 8 411620 1788 1956 2124 2293 2461| 2629 2796 | 2964 3132 3300 3467 3635 3803 3970 4137 4305 4472 4639 4806 7 9 260 23 + 23456 78 9 I OHN 2 4973 5140 5307 5474 5641 5808 5974 6141 6308 6474 260 I 6641 6807 6973 7139 7306 7472 7638 7804 7970 8135 8301 8467 8633 8798 89649129 | 9295 | 9460 | 9625 | 9791 9956 0121 0286 0451 0616 0781 0945 1110 1275 1439 | 4 421604 1768 1933 2097 2261 2426 2590 2754 2918 3082 3246 3410 3574 3737 3901 4065 4228 4392 4555 4718 4882 5045 5208 5371 5534 5697 5860 6023 6186 6349 6511 6674 6836 6999 7161 7324 7486 7648 7811 7973 8135 8297 8459 8621 8783 894491069268 | 9429|9591 975299140075|0236|0398 | 0559 | 0720 | 0881 | 1042 | 1203 5 6 78 9 PROPORTIONAL PARTS. I 2 3456 78 9 9 N. 3 4 5 6 7 8 2433 17.8 35.6 534 71°2 890 106.8 124.6 1424 160°2 2446 17.7 354 531 70.8 88.5 106.2 123'9 1416 1593 2460 17.6 352 52.8 704 88.0 105.6 123.2 140·8 158.4 2474 17.5 350 525 70°0 | 87°5 | 105′0 | 122°5 | 140°0 | 157°5 2488 17.4 348 52.2 69.6 | 87·0 | 1044 | 121.8 | 139′2 | 156·6 2503 17.3 346 519 69.2 86.5 103.8 121°1 1384 155'7 2517 17.2 344 51.6 68.8 86.0 103.2 1204 1376 | 154.8 2532 17.1 342 513 68.4 85.5 102.6 119.7 136.8 1539 2547 17.0 340 510 68.0 85.0 1020 1190 1360 | 153.0 2562 169 33.8 50.7 67.6 84.5 2577 16.8 33.6 504 67.2 84.0 2592 16.7 33°4501 50.1 66.8 83.5 2608 16.6 332 49.8 66.4 83.0 2624 16.5 330 495 66.0 82.5 264c 16.4 32.8 49.2 65.6 82.0 2656 16.3 32.6 48.9 65.2 81.5 2672 16.2 32.4 48.5 64.8 81.0 2689 16.1 322 483 644 805 1014 118.3 1352 152.1 100.8 117.6 1344 1512 | | 1002 116.9 133.6 150*3 996 116.2 132.8 149°4 990 115.5 1320 148.5 984 114.8 131.2 147.6 978 114 11304 146.7 972 1134 129.6 | 145.8 96.6 1127 128.8 1449 | 50 MATHEMATICAL TABLES. No. 270 L 431.] I 2 3 4 5 6 440909 1066|| 1224 1381 7 2480 2637 2793 2950 3106 3263 8 4045 4201 4357 4513 N. о LOGARITHMS OF NUMBERS. [No. 299 L. 476. I 2 3 4 5 6 7 270 431364 1525 1685 1846 2007 2167 2328 2488 | 2969 3130 3290 3450 3610 3770 3930 4090 4569 4729 4888 5048 5207 5367 5526 5685 6163 6322 6481 6640 6799 6957 7116 7275 7751 7909 8067 8226 8384 8542 8701 8859 9333 9491 9648 9806 9964 0122 I 2 8 9 N. 2649 2809 |270. 4249 4409 5844 6004 7433 7592 9017 9175 0594 0752 4 3+ 5 78 | 0279 0437 | 1538 | 1695 1852 2009 2166| 2323 6 3419 | | 3576 3732 3889 4669 4825 4981 5137 5293 5449 9 6537 | | 6692 6848 7003 9 280 8088 | 8242 8397 8552 280 9633 I 2 23456 7 3 4 5 6 7 8 9787 9941 0095 1172 1326 1479 1633 2706 2859 3012 3165 4235 4387 4540 4692 | | 5758 5910 6062 6214 7428 7579 7731 | 5604 5760 5915 6071 6226 6382 7158 7313 7468 7623 7778 7933 I 8706 8861 9015 9170 9324 9478 2 450249 0403 0557 0711 0865 1018 | | | 1786 1940 2093 2247 2400 2553 3318 3471 3624 3777 3930 4082 | | | | 4845 4997 5150 5302 5454 5606 6366 6518 6670 6821 6973 7125 7276 7882 8033 8184 8336 8487 8638 8789 8940 | 9091 | 9242 8 9392 9543 9694 9845 9995 0146 0296 0447 0597 0748 9460898 1048 1198 1348 | 1499 | 1649 | 1799 1948 2098 2248 9 290 2398 2548 2697 2847 2997 3146 3296 3445 3594 3744 290 | I 3893 4042 4191 4340 4490 4639 4788 4936 5085 5234 | 2345 7 8 9 5383 5532 5680 5829 5977 6126 6274 6423 6571 6719 6868 7016 7164 7312 7460 7608 7756 7904 8052 8200 | I 2 4. 8347 8495 8643 8790 8938 9085 9233 9380 9527 9675 9822 9969 0116 0263 6471292 1438 1585 1732 2756 2903 3049 3195 4216 4362 4508 4653 56715816 5962 | 6107 | N. 2705 16.0 32°0 2722 15'9 31.8 2740 15.8 31.6 2757 15'7 314 2775 15.6 31.2 2792 15.5 31.0 2810 154 30.8 2833 15.3 30.6 2847 15.2 30°4 2866 15'1 30°2 2885 15.0 30.0 2904 14.9 29.8 2924 14.8 29.6 2944 14'7 29'4 2964 14.6 29.2 2984 14.5 29.0 3005 14'4 28.8 3026 14:3 28.6 3047 142 284 3069 14'I 28.2 3091 14'0 28.0 PROPORTIONAL PARTS. I 234 no 5 6 7 8 9 78 0410 0557 0704 0851 0998 1145 1878 2025 2171 2318 2464 2610 3341 3487 3633 3779 3925 4071 4799 4944 5090 5235 5381 5526 62526397 | 6542 | 6687 | 6832|6976 3 4 5 6 7 8 9 480 640 800 96′0 | 1120 1280 | 1440 47.7 63.6 79.5 954 111.3 1272 143 1 474 632 790 948 110.6 1264 1422 47.1 62.8 78.5 94′2 109′9 | 125.6 | 141′3 46.8 62.4 78.0 93.6 109.2 | 1248 | 140°4 46.5 620 775 930 108.5 1240 139 5 46.2 61.6 77.0 924 107.8 | 123′2 | 138.6 459 61.2 76.5 91.8 1071 1224 1377 45.6 60.8 76.0 91.2 106.4 1216 136.8 453 604 755 90.6 105.7 120.8 135'9 450 600 750 900 1050 | 120′0 | 135°0 447 596 74'5 89'4 104°3 | 119′2 | 134°1 444 592 740 88.8 103.6 1184 133°2 441 58.8 73.5 88.2 | 102.9 117·6 | 132°3 43.8 58.4 73.0 87.6 102.2 116.8 1314 43.5 58.0 72.5 87.0 101.5 116.0 1305 432 576 72.0 864 100-8 1152 129.6 429 572 71.5 85.8 1001 1144 128.7 42.6 56.8 710 | 852 42.3 564 70.5 84.6 42°056·0 700 840 | 994 113.6 127.8 98.7 1128 126.9 98.0 1120 126′0 MATHEMATICAL TABLES. 51 No. 300 L. 477-] LOGARITHMS OF NUMBERS. N. о I 2 3 4 1 6 5 } [No. 339 L. 531. 78 9 N. 300 477121 7266 7411 7555 7700 7844 7989 8133 8278 8422 300 I 23 456 7∞ 8 9 I 123456 9575 9719 9863 I 1012 1156 | 1299 2445 2588 2731 | 3872 4015 4157 5295 5437 5579 6714 6855 6997 8127 8269 8410 9537 23 456 78 9 9677 | 9818 1081 | 1222 2481 2621 310 38764015 I OH 2m 3 4 5 8566 8711 8855 8999 9143 9287 9431 2 480007 0151 0294 0438 0582 0725 0869 1443 1586 1729 1872 2016 2159 2302 2874 3016 3159 3302 3445 3587 3730 4300 4442 4585 4727 4869 5011 5153 5721 5863 6005 6147 6289 6430 6572 7138 7280 7421 7563 7704 7845 7986 7280|7421 | | 8551 8692 8833 8974 9114 9255 9396 9958 0099 0239 0380 0520 0661 0801 0941 310 491362 1502 1642 1782 1922 2062 2201| 2341 | 2760 2900 3040 3179 3319 | 3458 3597 3737 4155 4294 4433 4572 4711 4850 4989 5128 5267 5406 5544 5683 5822 5960 6099 6238 6376 6515 6653 6791 6930 7068 7206 7344 7483 7621 7759 7897 8035 8173 8311 8448 8586 8724 8862 8999 9137 9275 9412 9550 9687 9824 9962 0099 0236 0374 0511 0648 0785 0922 | 7 501059 1196 1333 1470 1607 1744 1880 2017 2154 2291 2427 2564 2700 2837 2973 3109 3246 3382 3518 3655 | | 3791 3927 4063 4199 4335 4471 4607 4743 4878 5014 5150 5286 5421 5557 5693 5828 5964 6099 6234 6370 320 6505 6640 6776 6911 7046 7181 7316 7451 7586 7721 7856 79918126 8260 8395 85308664 8799 | 8934 | 9068 9203 9337 9471 9606 9740 9874 0009 0143 0277 0411 | | | | 4 510545 0679 0813 0947 1081 1215 1349 1482 1616 1750 | | | 1883 2017 2151 2284 2418 2551 2684 2818 2951 3084 | 3218 3351 3484 3617 3750 3883 4016 4149 4282 4415 4548 4681 4813 4946 5079 5211 5344 5476 5609 5741 5874 6006 6139 6271 6403 6535 6668 6800 6932 7064 | | | 7196 7328 7460 7592 7724 7987 8119 8251 8382 9 8514 8646 8777 8909 9040 9171 9303 9434 9566 9697 330 I 9828 9959 009002210353 0090 0221 0353 0485 0615 0745 0876 1007 07450876 | 2 521138 1269 1400 1530 1661 1792 1922 2053 2183 2314 8 9 320 I O123 +56 7∞ 8 9 330 4 ~ 3 + in6 78 | 7855 2444 2575 2705 2835 2966 3096 3226 3356 3486 3616 3746 3876 4006 4136 4266 4396 4526 4656 4785 4915 5045 5174 5304 5434 5563 5693 5822 5951 6081 6210 6339 6469 6598 6727 6856 6985 7114 7243 7372 7501 | | | | 7630 7759 7888 8016 8145 8274 8402 8531 8660 8788 8917 9045 9174 9302 9430 9559 9687 9815 9943 0072 9 5302000328 0456 0584 0712 0840 953020003280456|0584 | | PROPORTIONAL PARTS. | N. 3113 13.9 27.8 41.7 13.8 27.6 414 6 78 a 9 I 2 3456 7.00 8 Ι 23456 7∞ 8 0968 1096 1223 1351 9 I 2 3 4 5 6 7 3135 8 9 55.6 69.5 834 97°3 | 1112 | 125°1 552 690 82-8 96.6 1104 124°2 3158 13.7 27.4 41'1 548 3181 13.6 27°2 40·8 544 3205 13'5 27.0 40'5 540 3228 13'4 26.8 40°2 3253 13°3 3277 13.2 68.5 82.2 959 | 109.6 | 123°3 680 81.6 95.2 108.8 | 122′4 67.5 81.0 94.5 1080 121.5 536 670 80.4 93.8 107.2 120.6 532 66.5 79.8 93.1 106.4 1197 52.866.0 792 | 92°4 | 105.6 | 118.8 52.4 65.5 78.6 91.7 1048 | 1179 520 650 78.0 91.0 1040 1170 25.838.7 387 516645 774903 | 103.2 | 116-1 26.6 39.9 26.4 39.6 39.6 3302 13°1 26.2 39°3 3327 13.0 26.0 39°0 3353 12.9 } 52 MATHEMATICAL TABLES. No. 340 L. 531.] I 2 3456 LOGARITHMS OF NUMBERS. [No. 379 L. 579- I 2 3 4 5 6 7 8 | 1 2 3 4 5 6 N. о 9 N. 340 531479 1607 1734 1862 1990 2117 2245 2372 2500 2627 1340 | | 2754 2882 3009 3136 3264 3391 3518 3645 3772 3899 4026 4153 4280 4407 4534 4661 4787 4914 5041 5167 5294 5421 5547 5674 5800 5927 6053 6179 6306 6432 6558 6685 6811 6937 7063 7189 7315 7441 7567 7693 7819 7945 8071 8197 8322 8448 8574 8699 8825 8951 9076 9202 9327 9452 9578 9703 9829 9954 0079 0204 | | | | 7 540329 0455 0580 0705 0830 0955 1080 1205 1330 1454 1579 1704 1829 1953 2078 | 2203 | 2327 2452 2576 2701 2825 2950 3074 3199 3323 3447 3571 3696 3820 | 3944 4068 4192 4316 4440 4564 4688 4812 4936 5060 5183 350 5307 5431 5555 5678 5802 5925 6049 6172 6296 6419 6543 6666 6789 6913 7036 7159 7282 7405 7529 7652 7775 7898 8021 8144 8267 8389 8512 8635 8758 8881 8 9 350 I 2 3 56 7∞ 8 9 |360 7 8 9 I 2 3 4 5 to 6 7 8 4 9003 9126 9249 9371 9494 9616 9739 9861 9984 0106 5550228 0351 0473 0595 0717 0840 0962 1084 1206 1328 1450 1572 1694 1816 1938 2060 | 2181| 2303 2425 2547 2668 2790 2911 3033 3155 3276 3398 3519 3640 3762 3883 4004 4126 4247 4368 4489 4610 4731 4852 4973 5094 5215 5336 5457 5578 5699 5820 5940 6061 6182 9 6303 6423 6544 6664 6785| 6905 7026| 7146 7267 7387 360 I 7507 7627 7748 7868 7988 8108 8228 8349 84698589 8709 8829 8948 90689188 9308 94289548 | 9667 | 9787 9907 0026 0146 0265 0385 0504 c624 0743 0863 0982 | 5 2 3 4 SO 7∞ a 8 9 370 I 1 2 3456 7∞ a 8 9 I 4 561101 1221 1340 1459 1578 1698 1817 1936 2055 2174 2293 2412 2531 2650 2769 2887 3006 3125 3244 3362 3481 3600 3718 3837 3955 4074 4192 4311 4429 4548 4666 4784 4903 5021 5139 5257 5376 5494 5612 5730 | 5848 5966 6084 6202 6320 6437 6555 6673 6791 6909 7026 7144 7262 7379 7497 7614 7732 7849 7967 8084 8202 8319 8436 8554 8671 8788 8905 9023 9140 9257 370 9374 9491 9608 9725 9842 9959 0076 0193 0309 0426 2570543 0660 0776 0893 1010 1126 1243 1359 1476 1592 1709 1825 1942 2058 2174 2291 2407 2523 2639 2755 2872 2988 3104 3220 3336 3452 3568 3684 3800 3915 40314147 4263| 4379 | 4494 4610 | 4726 | 4841 | 4957 | 5072 5188 5303 5419 5534 5650 5765 5880 5996 6111 6226 6341 6457 6572 6687 6802 6917 7032 7147 7262 7377 7492 7607 7722 7836 7951 8066 8181 8295 8410 8525 8639 8754 88688983 90979212 | 9326|9441! 9555 | 9669 N. 5 6 7 89 3379 12.8 25.6 384 512 640 76.8 89.6 1024 1152 | | 3406 12.7 25°4 381 508 63.5 76.2 88.9 101.6 1143 3433 12.6 25°2 37.8 630 75.6 88.2 100-8 1134 3460 12.5 25.0 62.5 750 87.5 1000 112.5 23456 7∞ a 8 9 PROPORTIONAL PARTS. I 2 ક્ષે 3 4 504 37.5 500 3488 12.4 24.8 372 496 62.0 49.6 62.0 74.4 86.8 3516 12.3 24.6 36.9 49°2 3545 2 3 4 SO 700 5 8 9 99.2111.6 98.4 | 110°7 976 | 109-8 96·8 | 108.9 96.0 108.0 12.2 24.4 3574 12.1 24°2 3604 12'0 24.0 3634 11.9 23.8 36.6 48.8 61.5 73.8 86.1 610 732 854 610 732 854 36.3 484 60.5 72.6 84.7 60·572-6847 | 360 480 600 720 840 35747-659-5714 83.3 95'2 107.1 F MATHEMATICAL TABLES. 53 No. 380 L. 579.] N. LOGARITHMS OF NUMBERS. I 2 3 451 6 7 [No. 414 L. 617. | N. I 8 9 0583 | 0697 | 0811380 1722 1836 1950 2972 3085 4105 4218 41054218 5235 5348 380 579784 9898 0012 0126 0241 0355 0469 1580925 1039 1153 1267 1381 1495 1608 | | | 2063 2177 2291 2404 2518 2631 2745 2858 3199 3312 3426 3539 3652 3765 3879 3992 | 4331 4444 4557 4670 4783 4896 50095122 | 5461 5574 5686 5799 5912 6024 6137 6250 6362 6475 6587 6700 6812 6925 7037 7149 7262 7374 7486 7599 6 7711 7823 7935 8047 8160 8272 8384 8496 8608 8720 4 1 2 3 +56 7∞ | 8 8832 8944 9056 9167 9279 9391 9503 9615| 9726 9838 9950 co61 0173 0284 0396 0507 0619 0730 0842 0953 9 I 1 2 3 4 no 7∞•a 5 8 I 390 591065 1176 1287 1399 1510 1621 1732 1843 1955 2066 390 2177 2288 2399 2510 2621 2732 2843 2954 3064 3175 | | 3286 3397 3508 3618 3729 3840 3950 4061 4171 4282 | | 4393 4503 4614 4724 4834 4945 5055 5165 5276 5386 5496 5606 5717 5827 5937 6047 6157 6267 6377 6487 6597 6707 6817 6927 7037 7146 7256 7366 7476 7586 7695 7805 7914 8024 8134 8243 8353 8462 8572 8681 8791 8900 9009 9119 9228 9337 9446 9556 9665 9774 | | 9883 9992 OIOI 0210 0319 0428 0537 0646 | 0755|0864 9 600973 1082 1191 1299 1408 1517 1625 1734 1843 1951 | | 234567∞ 8 400 I 2 3 4 56 78 9 10 | 2 3 456 78 9 I 2 3 4 no 78 2060 2169 2277 2386 2494 2603 2711 2819 2928 3036 400 3144 3253 3361 3469 3577 3686 3794 3902 4010 4118 | 4226 4334 4442 4550 4658 4766 4874 4982 5089 5197 5305 5413 5521 5628 5736 5844 5951 6059 6166 6274 6381 6489 6596 6704 6811 6919 7026 7133 7241 7348 7455 75627669 7777 7884 7991 8098 8205 8312 8419 8526 8633 8740 8847 8954 9061 9167 9274 9381 9488 9594 9701 9808 9914 0021 0128 0234 0341 0447 0554 8 610660 0767 0873 0979 1086 1192 1298 1405 1511 1617 | | | 1723 1829 1936 2042 2148 2254 2360 2466 2572 2678 9 27842890 2996 3102 3207 3313 3419 3525 3630 3736 410 3842 3947 4053 4159 4264 4370 4475 4581 4686 4792 4897 5003 5108 5213 5319 5424 5529 5634 5740 5845 2 5950 6055 6160 6265 6370 6476 6581 6686 | 6790|6895 3 7000 7105 7210 7315 7420 7525 7629 7734 7839 7943 | | 5 6 7 8 9 590 70.8 82.6 944 106.2 58-570°2 | 81.9 | 93⋅6 | 105.3 58.0 580 69.6 81-2 92.8 1044 57.5 690 80.5 920 103.5 570 68.4 79.8 91.2 102.6 56.567.8791 90'4 101'7 56.0 56.0 67.2 78.4 89.6 100-8 I 1 2 3 + 4 PROPORTIONAL PARTS. N. 3665 11.8 23.6 3696 11'7 23.4 3727 11.6 23°2 I 2 3760 11.5 23.0 3792 11:4 22.8 · 3 4 35.4 47°2 35°1 46.8 34.8464 34'5 46'0 34°2 45'6 3826 33'9 45'2 3860 3895 3930 II'I 22.2 ΙΙΟ 22.0 11.3 22.6 II*2 224 33.6 44.8 33.6448 33°3 44'4 33°0 44'0 3966 IC'9 21.8 32°7 43.6 4002 10.8 21.6 4039 10.7 214 32.4 43°2 32°I 42.8 4077 10.6 21'2 31.8 42'4 4116 21'0 31.5 42.0 10'5 | 1 4 99'9 98.1 55.5 66.6 77.7 88.8 550 66.0 77.0 88.0 99'0 54-5 65.4 76.3 87.2 540 64.8 75.6 86.4 535 642 749 85.6 530 63.6 742 84.8 52.5 630 735 840 97.2 96.3 95'4 94'5 54 MATHEMATICAL TABLES. No. 415 L. 618.] N. о I LOGARITHMS OF NUMBERS. [No. 459 L. 662. 2 3 4 5 6 7 8 9 N. 415 618048 8153 8257 8362 8466 8571 8676 8780 8884 8989 415 | | 9093 9198 9302 9406 9511 9615|9719 9824 6 78 9 420 I 1 2 3 +6 4 8 9 430 123456 4 | 6135 6238 | 7058 7161 7263 8082 8185 8287 9104 9206 | 9308 0224 0326 6 7 8 9 2 3456 78 | 0123 1139 || 1241 1342 2153 | | 2255 2356 3266 3367 9 | I 2 3 4 6 5678 9928 0032 7 620136 0240 0344 0448 0552 0656 0760 | 0864 0968 || 1072 | | | | 1176 1280 1384 1488 1592 1695 1799 1903 2007 2110 || | | 2214 2318 2421 2525 2628 2732 2835 2939 3042 3146 | 3249 3353 3456 3559 3663 3766 3869 3973 4076 4179 420 4282 4385 4488 4591 4695 4798 4901 5004 5107 5210 I 5312 5415 5518 5621 5724 5827 5929 6032 6340 6443 6546 6648 6751 6853 6956 7366 7468 7571 7673 7775 7878 7980 5 8389 8491 8593 8695 8797 8900 9002 9410 9512 9613 9715 9817 9919 0021 7630428 0530 0631 0733 0835 0936 1038 1444 1545 1647 1748 1849 1951 2052 2457 2559 2660 2761 2862 2963 3064 3165 3468 3569 3670 3771 3872 3973 4074 4175 4276 4376 430 I 4477 4578 4679 4779 4880 4981 5081 5182 5283 5383 | | 5484 5584 5685 5785 5886 5986 6087 6187 6287 6388 6488 6588 6688 6789 6889 6989 7089 7189 7290 7390 7490 7590 7690 7790 7890 7990 8090 8190 8290 8389 8489 8589 8689 8789 8888 8988 9088 9188| 9287 | 9387 9486 9586 9686 9785 9885 9984 0084 0183 0283 0382 | 7640481 0581 0680 0779 0879 0978 1077 1177 1276| 1375 | | | | | 1474 1573 1672 1771 1871 1970 2069 2168 2267 2306 2465 2563 2662 2761 2860 2959 3058 3156 3255 3354 3453 3551 3650 3749 3847 3946 4044 4143 | 4242 | 4340 440 | 4439 4537 4636 4734 4832 4931 5029 5127 5226 5324 | 5422 5521 5619 5717 5815 5913 6011 6110 6208 6306 6404 6502 6600 6698 6796 | 6894 | 6992 | 7089 7187 7285 | 7383 7481 7579 7676 7774 7872 7969 8067 8165 8262 | 8360 8458 8555 8653 8750 8848 8945 9043 9140 9237 | 9335 9432 9530 9627 9724 9821 9919 0016 0113 0210 | 7650308 0405 0502 0599 0696 0793 0890 0987 1084 1181 1278 1375 1472 1569 1666 1762 1859 1956 2053 2150 2246 2343 2440 2536 2633 2730 2826 2923 3019 3116 3213 3309 3405 3502 3598 3695 3791 3888 3984 4080 450 4177 4273 4369 4465 4562 4658 4754 4850 4946 5042 5138 5235 5331 5427 5523 5619 | 5715 5810 5906 6002 6098 6194 6290 6386 6482 6577 6673 6769 6864 6960 | | 7056 7152 7247 7343 7438 7534 7629 7725 7820 7916 | | 8011 8107 8202 8298 8393 8488 8584 8679 8774 8870 | 896590609155 9250 9346 9441 9536 9631| 9726 | 9821 9916 0011 0106 0201 0296 0391 0486 0581 0676 0771 8 660865 0960 1055 1150 1245 1339 1434 1529 1623 1718 1813 1907 2002 2096 2191 2286 2380 2475 2569 2663 N. 3 4 78 9 440 1234 in 1 ∞o a 6 8 450 I 2345678 9 PROPORTIONAL PARTS. in ་ 9 I 2 3 4 5 6 7 78 9 9 I 2 3 456 78 9 I 2 5 6 7 8 9 4155 10'4 20.8 31.2 41.6 52.0 4196 10'3 20.6 30.9 41'2 51.5 4237 10'2 20.4 30.6 40.8 51.0 4278 ΙΟΙ 20'2 30.3 40°4 50.5 4321 20.0 10'0 4364 9.9 | 19.8 30.0 40.0 29.7 | 39.6 500 49'5 62.4 72.8 832 | 93.6 61.8 721 824 927 | 612 714 81.6 91-8 60.670.7 80.8 90.9 600 700 800 900 59469.3 79.2 89.1 MATHEMATICAL TABLES. 55 No. 460 L. 662.] I 234 5 7 LOGARITHMS OF NUMBERS. [No. 499 L. 698. I 2 3 4 5 6 | 6 7 8 9 N. I 23456 78 N. о 460 662758 2852 2947 3041 3135 3230 3324 3418 3512 3607460 3701 3795 3889 3983 4078 4172 4266 4360 4454 4548 4642 4736 4830 4924 5018 5112 5206 5299 5393 5487 5581 5675 5769 5862 5956 6050 6143 6237 6331 6424 6518 6612 6705 6799 6892 6986 7079 7173 7266 7360 7453 7546 7640 7733 7826 7920 8013 8106 8199 8293 8386 8479 8572 8665 8759 8852 8945 9038| 9131 9224 9317 9410 9503 9596 9689 9782 9875 9967 0060 0153 8670246 0339 0431 0524 0617 0710 0802 0895 0988 1080 8 9 1173 1265 1358 1451 1543 1636 1728 1821 1913 2005 9 2098 2190 2283 2375 2467 2560 2652 2744 2836 2929 470 I 3021 3113 3205 3297 3390 3482 3574 3666 3758 3850 3942 4034 4126 4218 4310 4402 4494 4586 4677 4769 4861 4953 5045 5137 5228 5320 5412 5503 5595 5687 5778 5870 5962 6053 6145 6236 6328 6419 6511 6602 6694 6785 6876 6968 7059 7151 7242 7333 7424 7516 7607 7698 7789 7881 7972 8063 8154 8245 8336 8427 8518 8609 8700 8791 8882 8973 9064 9155 9246 9337 9428 9519 9610 9700 9791 9882 9973 0063 0154 0245 680336 0426 0517 0607 0698 0789 0879 0970 1060 1151 470 23456 700 8 9 480 I 23456 DO 7 8 9 I I 2 3456 7 8 9 I 2 3 456 78 7 8 9 1241 1332 1422 1513 1603 1693 1784 1874 1964 2055 480 2145 2235 2326 2416 2506 2596 2686 2777 2867 2957 3047 3137 3227 3317 3407 3497 3587 3677 3767 3857 3947 4037 4127 4217 4307 4396 4486 4576 4666 4756 4845 4935 5025 5114 5204 5294 5383 5473 5563 5652 5742 5831 5921 6010 6100 6189 6279 6368 6458 6547 6636 6726 6815 6904 6994 7083 7172 7261 7351 7440 7529 7618 7707 7796 7886 7975 8064 8153 8242 8331 8420 8509 8598 8687 8776 8865 8953 9042 9131 9220 | 9309 9398 9486 9575 9664 9753 9841 9930 0019 0107 490 690196 0285 0373 0462 0550 0639 0728 0816 0905 0993 490 1081 1170 1258 1347 1435 1524 1612 | 1700 1789 1877 1965 2053 2142 2230 2318 2406 2494 2583 2671 2759 2847 2935 3023 3111 3199 3287 3375 3463 3551 3639 3727 3815 3903 3991 4078 4166 4254 4342 4430 4517 4605 4693 4781 4868 4956 5044 5131 5219 5307 5394 5482 5569 5657 5744 5832 5919 6007 6094 6182 6269 6356 6444 6531 6618 6706 6793 6880 6968 70557142 7229 7317 7404 7491 7578 7665 7752 7839 7926 8014 | 8 8100 8188 8275 8362 8449 8535 8622 8709 8796 8883 9 N. 1 2 3 I 4 5 6789 4410 98 19.6 29'4 39°2 49'0 58.8 68.6 78.4 88.2 4454 9'7 19'4 29'I 38-8 485 4500 9.6 19.2 28.8 384 23456 78 9 PROPORTIONAL PARTS. I 2 23 4 5 58-2 58.2 67.9 77.6 87.3 480 57.6 67.2 76.8 86.4 4547 9.5 19.0 28.5 38.0 47'5 57'0 66.5 76.0 85.5 4595 9'4 18.8 28.2 37.6 47'0 56.4 65.8752 84.6 4644 9'3 18.6 27.9 372 465 46.5 55.8 558 651 | 744 83.7 4695 9.2 18.4 27.6 36.8 46.0 55.2 64.4 73.6 82.8 4746 9.I 4798 9.0 18.0 27.0 36.0 45'0 54:0 18.2 27.3 36.4 45'5 546 63.7 72.8 81.9 4852 8.9 17.8 26.7 35.6 4907 8.8 17.6 44'5 53°4 264 352 44.0 52·8 63.0 72.0 81.0 62-371-280*1 61.67041 79°2 56 MATHEMATICAL TABLES. No. 500 L. 698.] N. о I 2 LOGARITHMS OF NUMBERS. [No. 544 L. 736. 3 4 5 6 7 8 9 N. 500 698970 9057 | 9144 | 92319317|94049491 9578 9664 9751 500 9838 9924 0011 0098 0184 0271 0358 0444 0531 0617 I I 23456 7∞ a 2 3 4 5 DOO a 6 2 700704 0790 0877 0963| 1050 1136 1222 1309 1395 1482 1568 1654 1741 1827 1913 1999 2086 2172 2258 2344 2431 2517 2603 2689 2775 2861 2947 3033 3119 3205 3291 3377 3463 3549 3635 3721 3807 3893 3979 4065 4151 4236 4322 4408 4494 4579 4665 4751 4837 4922 5008 5094 5179 5265 5350 5436 5522 5607 5693 5778 7 5864 5949 6035 6120 6206 6291 6376 6462 | 6547 6632 6718 6803 6888 6974 7059 7144 7229 7315 7400 7485 7570 7655 7740 7826 7911 7996 8081 8166 8251 8336 510 8421 8506 8591 8676 8761 8846 8931 9015 9100 9185 Ι 927093559440 9524 9609 9694 9779 9863 9948 0033 8 510 I 2 3456 78 520 I 3 710117 0202 | 0287 0371 0456 0540 | 0625 0710 0794 0879 0963 1048 1132 1217 1301| 1385 1470 1554 1639 1723 1807 1892 1976 2060 2144 2229 2313 2397 2481 | 2566 2650 2734 2818 2902 2986 3070 3154 3238 3323 3407 | | | 3491 3575 3659 3742 3826 3910 3994 4078 4162 4246 4330 4414 4497 4581 4665 4749 4833 4916 5000 5084 9 5167 5251 5335 5418 5502 5586 5669 5753 5836 5920 4 0123 & in 78 9 6 530 I 8 9 23456 7∞ a 8 I 23 456 7∞ a 8 9 I 6003 6087 6170 6254 6337 6421 6504 6588 | 6671 | 6754 520 6838 6921 7004 7088 7171 7254 7338 7421 7504 7587 7671 7754 7837 7920 8003 8086 8169 8253 8336 8419 8502 8585 8668 8751 88348917 9000 9083 9165 9248 9331 9414 9497 9580 9663 9745 9828 9911 9994 0077 720159 0242 0325 0407 0490 0573 0655 0738 0821 0903 0986 1068 1151 1233 1316 1398 1481 1563 1646 1728 | | | | 1811 1893 1975 2058 2140 2222 2305| 2387|2469 | 2552 2634 2716 2798 2881 2963 3045 3127 3209 3291 3374 3456 3538 3620 3702 3784 3866 3948 4030 4112 4194 4276 4358 4440 4522 4604 4685 4767 4849 4931 5013 530 5095 5176 5258 | 5340 5422 5503 5585 5667 5748 5830 5912 5993 6075 6156 6238 6320 6401 6483 6564 6646 6727 6809 6890 6972 7053 7134 7216 7297 7379 7460 7541 7623 7704 7785 7866 7948 8029 8110 8191 8273 8354 8435 8516 8597 8678 8759 8841 8922 9003 9084 9165 9246 9327 9408 9489 9570 9651 9732 9813 9893 9974 0055 0136 0217 0298 0378 0459 0540 0621 | 0702 8 730782 0863 0944 1024 1105 1186 1266 1347 1428 1508 1589 1669 1750 1830 1911 1991 2072 2152 2233 2313 2394 2474 2555 2635 2715 2796 2876 2956 3037 3117 540 3197 3278 3358 3438 3518 3598 3679 3759 3839 3919 3999 4079 4160 4240 4320 4400 4480 4560 4640 4720 4800 4880 4960 5040 5120 5199 5279 5359 5439 5519 5599 | 5679 | 5759583859185998 6078 6157 6237 6317 23456 7∞ a 9 540 1234 PROP. PARTS. N. I 2 3 4 5 6 7 4963 5020 5079 5139 3. 23456 7∞ a 8 9 123 + 4 8 9 8.7 17'4 26.1 34.8 43'5 52.2 609 69.6 78.3 8.6 17.2 25·8 34'4 43°0 51.6 68.8 77'4 60.2 17.0 25'5 34:0 42'5 510 59'5 68.076·5 16.8 25.2 33.6 42.0 50'4 58.8 672175.6 8.5 8:4 MATHEMATICAL TABLES. 57 No. 545 L. 736.] LOGARITHMS OF NUMBERS. [No. 584 L. 767. N. O I 2 3 4 5 6 7 8 9 N. 6 78 9 I 123456 176 9 560 I 2 4 6 78 70 9 I 23456 78 9 I 545 736397 6476 6556 6635 67156795 6874 6954 7034 7113 545 7193 7272 7552 7431 7511 7590 7670 7749 7829 7908 7987 8067 8146 8225 8305 8384 8463 8543 8622 8701 8781 8860 8959 9018 9097 9177 9256 9335 9414 9493 9572 9651 9731 9810 9889 9968 0047 0126 0205 0284 550 740363 0442 0521 0600 0678 0757 0836 0915 0994 1073 550 1152 1230 1309 | 1388 | 1467 1546| 1624 1703 1782 1860 1939 2018 2096 2175 2254 2332 2411 2489 2568 | 2647 2725 2804 2882 2961 3039 3118 3196 3275 3353 3431 3510 3588 3667 3745 3823 3902 3980 4058 4136 4215 4293 4371 4449 4528 4606 4684 4762 4840 4919 4997 5075 5153 5231 5309 5387 5465 5543 5621 5699 5777 5855 5933 6011 6089 6167 6245 6323 6401 6479 6556 6634 6712 6790 6868 | 6945 7023 7101 7179 7256 7334 7412 7489 7567 7645 7722 7800 7878 7955 8033 8110 8188 8266 8343 8421 8498 8576 8653 8731 8808 8885 560 8963 90409118 9195 9272 9350 9427 9504 9582 | 9659 9736 9814 9891 9968 0045 0123 0200 0277 0354 0431 3750508 0586 0663 0740 | 0817 0894 0971 1048 1125 1202 1279 1356 1433 1510 1587 1664 1741 1818 1895 1972 2048 2125 2202 2279 | 2356| 2433 2509|2586|| 2663 2740 2816 2893 2970 3047 3123 3200 3277 3353 3430 3506 3583 3660 3736 3813 3889 3966 4042 4119 4195 4272 4348 4425 4501 4578 4654 4730 4807 4883 4960 5036 5112 5189 5265 5341 5417 5494 5570 5646 5722 5799 5875 5951 6027 6103 61806256 | 6332 | 6408 | 6484| 6560 570 | 61036180 6256|6332|6408 6636 6712 6788 6864 6940 7016 7092 7168 7244 7320 7396 74727548 7624 7700 7775 7851 7927 8003 8079 8155 8230 8306 8382 8458 8533 8609 8685 8761 8836 8912 8988 9063 9139 9214 9290 9366 9441 9517 9592 9668 9743 9819 9894 9970 0045 0121 0196 0272 | 0347 6760422 0498 0573 0649 0724 07990875 0950 | 1025 1101 1176|| 1251 1326 1402 1477 1552 1627 1702 1778 1853 8 1928 2003 2078 2153 2228 2303 2378 2453 2529 2604 2679 2754 2829 | 2904 | 2978 | 3053 | 3128 3203 3278 3353 580 3428 3503 3578 3653 3727 3802 3877 3952 4027 4101 580 4176 4251 4326 4400 4475 4550 4624 4699 4774 4848 4923 4998 5072 5147 5221 | 5296 | 5370 5445 5520 5594 5669 5743 5818 5892 5966 6041 6115 6190 6264 6338 6413 6487 6562 6636 | 6710 6785 6859 6933 7007 7082 6 3tno 7∞ a 8 9 570 I 2 23 7 9 1234 2 3 4 5 6 7OO a 8 9 I 234 56 700 a 8 I 1234 PROPORTIONAL PARTS. N. I 2 3 4 5201 8.3 16.6 5 6 415 498 7 5264 8.2 5328 8.1 16.4 16.2 24933°2 246 32.8 41′0 49°2 574 65.6 73.8 8 9 581 664 74'7 24 3 32.4 40.5 48.6 56-7 648 729 5394 8.0 16.0 24 0 32.0 400 480 560 640 72.0 5462 79 15.8 237 31-6 39.5 47'4 55.3 63.2 71'1 5532 7.8 15.6 23.4 31.2 5603 7'7 15'4 23 I 30.8 5677 7.6 15.2 22.8 30.4 5752 7.5 15.0 22.5 30.0 5829 7'4 14.8 22.2 46.8 54.6 62.4 70°2 38.5 46.2 53.9 61.6 69.3 38.0 45.6 53.2 608 68.4 45'0 52.5 600 67.5 29.6 37.0 44.4 51.8 592 66.6 390 37.5 F 58 MATHEMATICAL TABLES. LOGARITHMS OF NUMBERS. No. 585 L. 767.] N. O 23 I 6 56 78 590 I 1 2 3 456 7∞ a 8 9 600 1 2 [No. 629 L. 799. 4 5 6 7 8 9 N. 6 7 8 9 I 23 +6 7OO 5 8 9 I 585 767156 7230 7304 7379 7453 7527 7601 7675 7749|7823|585 7898 7972 8046 8120 8194 8268 8342 8416 8490 8564 8638 8712 8786 8860 8934 9008 9082 9156 9230 9303 9377 9451 9525 9599 9673 9746 9820 9894 9968 0042 9 770115 0189 0263 0336 0410 0484 0557 0631 0705 0778 03360410 | 05570631 | 0852 0926 0999 1073 1146 | 1220 | 1293 | 1367 1440 1514 590 1587 1661 1734 1808 1881 1955 2028 2102 2175 2248 | | 2322 2395 2468 2542 2615 2688 2762 2835 2908 2981 3055 3128 3201 3274 3348 3421 | 3494 3567 3640 | 3713 3786 3860 3933 4006 4079 4152 4225 4298 4371 4444 4 4517 4590 4663 4736 4809 4882 4955 5028 5100 5173 5246 5319 5392 5465 5538 5610 5683 5756 5829 5902 5974 6047 6120 6193 6265 6338 6411 6483 6556 6629 670167746846 6701 6774 6846 6919 6992 7064 7137 7209 7282 7354 7427 7499 7572 7644 7717 7789 7862 7934 8006 8079 8151 8224 8296 8368 8441 8513 8585 8658 8730 8802 600 8874 8947 9019 9091 9163 9236 9308 9380 9452 9524 9596 9669 9741 9813 9885 9957 0029 0101 0173 9245 780317 0389 046105330605 0677 0749 0821 0893 0965 1037 1109 1181 | 1253 | 1324 1396 1468 1540 1612 1684 1755 1827 1899 1971 2042 2114 2186| 2258|| 2329 | 2401 2473 2544 2616 2688 2759 2831 2902 2974 3046 3117 | | | 3189 3260 3332 3403 3475 3546 3618 3689 3761 3832 3904 3975 4046 | 4118 | 4189 4261 4332 4403 4475 4546 4617 4689 4760 4831 4902 4974 5045 5116 | 5187 | 5259 5330 5401 5472 5543 5615 5686 5757 5828 5899 5970 610 6041 6112 6183 6254 6325 6396 6467 6538 6609 6680 I 6751 6822 6893 6964 7035 7106 7177 7248 7319 7390 7460 7531 7602 7673 7744 7815 7885 7956 8027 8098 8168 8239 8310 8381 8451 8522 8593 8663 8734 8804 85228593 | 87348804 8875 8946 9016 9087 | 9157 9228| 9299 9369 | 9440 | 9510 93699440 | 9581 9651 9722 9792 9863 9933 0004 0074 0144 0215 790285 0356 0426 0496 0567 0637 0707 0778 0848 0918 0988 1059 1129 1199 1269 1340 1410 1480 1550 1620 1691 1761 1831 1901 1971 2041 2111 2181 2252 2322 | | | | 4 mtino 78 9 610 I 123456 78 9 620 1 | | 23456 7∞ a 8 H2 3 4 56 76 a 8 9 2392 2462 2532 2602 2672 2742 2812 2882 2952 3022 620 3092 3162 3231 3301 3371 3441 3511 3581 3651 3721 | 3790 3860 3930 4000 4070 4139 4209 4279 | 4349 | 4418 4488 4558 4627 46974767 4836 4906 4976 5045 5115 5185 5254 5324 5393 5463 5532 5602 5672 5741 5811 5880 5949 6019 6088 6158 6227 6297 6366 6436 6505 6574 6644 6713 6782 6852 6921 6990 7060 7129 7198 | 7268 7337 7406 | 7475 7545 7614 7683 7752 7821 7890 7960 8029 8098 8167 8236 8305 8374 8443 8513 8582 | 9 8651 8720 8789 8651 8720 8789 8858 | 8927 | 8996 | 9065913492039272 234no too a 7 8 PROP. PARTS. N. I 2 3 +4 | 5 29.2 6 7 1234 SO NO0 a 5 7 8 8 9 36.543.8 511 584 65'7 28.8 36.0 43°2 504 57.6 64.8 28.4 35.5 42.6 49.7 56.8 63.9 5908 7:3 14.6 | 21°9 5990 7'2 21.6 14'4 6074 7'1 14.2 21°3 6160 7.0 14.0 21.0 28.0 6248 | 69 | 13.8 13.8 207 27-6 35°0 42'0 34.5 49°056.0 63.0 414 483 55°2 | 62°1 MATHEMATICAL TABLES. 59 i No. 630 L. 799.] LOGARITHMS OF NUMBERS. [No. 674 L. 829. N. O I 2 3 4 5 16 7 8 ŷ N. 234 78 9 2637 2705 3321 3389 4003 4071 4685 4753 5365 5433 I 2 3 4 16 7∞ a 630 799341 9409 9478 9547 9616 9685 9754 9823 9892 9961 630 1800029 0098 0167 02360305 0373 0442 0511 0580 0648 0717 0786 0854 0923 0992 IC61 1129 1198 1266 1335 1404 1472 1541 1609 1678 1747 1815 1884 1952 2021 2089 2158 2226 2295 2363 2432 2500 2568 2774 2842 2910 2979 3047 3116 3184 3252 3457 3525 3594 3662 3730 3798 3867 3935 4139 4208 4276 4344 4412 4480 4548 4616 4821 4889 4957 5025 5093 5161 5229 5297 5501 5569 5637 5705 5773 5841 5908 5976 6044 6112 640 806180 6248 6316 6384 6451 6519 6587 6655 6723 6790 640 I 6858 6926 6994 7061 7129 7197 7264 7332 7400 7467 7535 7603 7670 7738 7806 7873 7941 8008 8076 8143 | | 8211 8279 8346 8414 8481 8549 8616 8684 8886 8953 9021 9088 9156 9223 9290 9358 5 9560 9627 9694 9762 9829 9896 9964 0031 6810233 0300 | 0367 0434 | 0501 0569 0636 0703 | | | 2 2 3 7 8 9 650 I 23456 7∞ a 8 9 660 8 9 I 8751 8818 9425 9492 0098 0165 07700837 4 5 6 7 8 23+ SO DOO a I 23456 TO 7 8 0904 0971 1039 1106 11731240 1307 1374 1441 1508 | 1575 1642 1709 1776 1843 1910 1977 2044 2111 2178 2245 2312 2379 2445 2512 2579 2646 2713 2780 2847 2913 2980 3047 3114 3181 3247 3314 3381 3448 3514 650 35813648 3714 3781 3848 3914 3981 4048 4114 4181 4248 4314 4381 4447 4514 4581 4647 4714 4780 4847 4913 4980 5046 5113 5179 5246 5312 5378 5445 5511 5578 5644 5711 5777 5843 5910 5976 6042 6109 6175 6241 6308 6374 6440 6506 6573 6639 6705 6771 6838 67716838 6904 6970 7036 7102 7169 7235 7301 7367 7433 7499 7565 7631 7698 7764 7830 7896 7962 8028 8094 8160 | 8226 8292 8358 8424 8490 8556 8622 8688 8754 8820 | 88858951 9017 9083 9149 9215 9281 9346 9412 9478 9 9544 9610 9676 9741 9807 9873 9939 0004 0070 0136 660 | 1820201 0267 0333 0399 0464 0530 0595 0661 0727 0792 | 0858 0924 0989 1055 1120 1186 1251 1317| 1382 1448 | | 1514 1579 1645 1710 1775 1841 1906 1972 2037 2103 2168 2233 2299 2364 2430 2495 2560 2626| 2691| 2756 2822 2887 2952 3018 3083 3148 3213 3279 3344 3409 3474 3539 3605 3670 3735 3800 3865 3930 3996 4061 4126 4191 4256 4321 4386 4451 4516 4581 4646 4711 4776 4841 4906 4971 5036 5101 5166 5231 5296|| 5361 5426 5491 5556 5621 5686 5751 5815 5880 5945 6010 | | 6075 6140 6204 6269 6334 6399 6464 6528 6593 6658 670 6723 6787 6852 6917 6981 7046 71117175 7240 7305 7369 7434 7499 7563 7628 7692 7757 7821 7886 7951 | | 8015 8080 8144 8209 8273 8338 8402 8467 8531 8595 | | 8660 8724 8789 8853 8918 8982 9046 91119175 9239 | 23456 too a 7 8 670 I 2 3 4 PROP. PARTS. 1 23456 78 9 2 3 4 8 9 6 7 40.8 47.6 544 61.2 402 | 469 53.6 60.3 39.646.252.8 594 N. I 6340 6.8 6433 6.7 6.6 2 13.6 6530 6630 6.5 6733 6.4 12.8 13'4 20'I 13.2 19.8 13.0 19'5 19.2 3 20'4 27.2 340 26.8 33°5 4 5 26.4 33°0 26.0 32.5 25.6 32.0 39°0 384 45'5 52.0 58.5 448 51°2 57.6 57 60 MATHEMATICAL TABLES. No. 675 L. 829.] LOGARITHMS OF NUMBERS. [No. 719 L. 857. N. о I 2 3 4 5 6 7 8 9 N. 78 9 680 I 12345 7∞ a 8 9 690 I 4 23+36 7∞ a 8 9 700 I | 678 a 9. I 1.2 3456 700 a 8 9 I 123456 N∞ a 7 8 675 829304 9368 9432 9497 9561 9625 9690 9754 9818 9882 675 6 9947 0011 0075 0139 0204 0268 0332 0396 0460 0525 78305890653 0717 0781 0845 0909 0973 1037 1102 1166 1230 1294 1358 1422 1486 1550 1614 1678 1742 1806 1870 1934 1998 2062 2126 2189 2253 2317 2381 2445 2509 2573 2637 2700 2764 2828 2892 2956 3020 3083 680 3147 3211 3275 3338 3402 3466 3530 3593 3657 3721 3784 3848 3912 3975 4039 4103 4166 4230 4294 4357 4421 4484 45484611 | 4675 4739 | 4802 | 4866 | 4929|4993 5056 5120 5183 5247 5310 5373 5437 5500 5564 5627 5691 5754 5817 5881 5944 6007 6071 6134 6197 6261 6324 6387 6451 6514 6577 6641 6704 6767 6830 6894 6957 7020 7083 7146 7210 7273 7336 7399 7462 7525 7588 7652 7715 7778 7841 7904 7967 8030 8093 8156 8219 8282 8345 8408 8471 8534 8597 8660 8723 8786 8849 8912 8975 9038 9101 9164 9227 9289 9352 9415 690 9478 9541 9604 9667 9729 9792 9855 9918 9981 0043 2840106 0169 0232 | 0294 03570420 0482 0545 0608 0671 0733 0796 0859 0921 0984 1046 1109 1172 1234 1297 1359 1422 1485 1547 1610 1672 1735 1797 1860 1922 1985 2047 2110 2172 2235 2297 2360 2422 2484 2547 2609 2672 2734 2796 2859 2921 2983 3046 3108 3170 3233 3295 3357 3420 3482 3544 3606 3669 3731 3793 3855 3918 3980 4042 4104 4166| 4229 4291 4353 4415 4477 4539 4601 4664 4726 4788 4850 4912 4974 5036 9 5098 5160 5222 5284 5346 5408 5470 5532 5594 5656 700 5718 5780 5842 5904 5966 6028 6090 6151 6213 6275 6337 6399 6461 6523 6585 6646 6708 6770 6832 6894 6955 7017 7079 7141 7202 7264 7326 7388 7449 7511 7573 7634 7696 7758 7819 7881 7943 8004 8066 8121 8189 8251 8312 8374 8435 8497 8559 8620 8682 8743 8805 8866 8928 8989 9051 9112 9174 9235 9297 9358 94199481 9542 9604 9665 9726 9788 9849 9911 9972 88500330095 0156 0217 0279 0340 0401 0462 05240585 0646 0707 0769 | 0830 | 0891 0952 1014 1075 1136 1197 9 1258 1320 1381 1442 1503 1564 1625 1686 1747 1809 710 | || | 1870 1931 1992 2053 2114 2175 2236 2297 2358 2419 2480 2541 2602 2663 2724 2785 2846 2907 2968 3029 3090 3150 3211 3272 3333 3394 3455 3516 3577 3637 3698 3759 3820 3881 39414002 4063 4124 4185 4245 4306 4367 4428 4488 4549 4610 4670 4731 4792 4852 4913 4974 5034 5095 5156 5216 5277 5337 5398 5459 5519 5580 5640 5701 5761 5822 5882 5943 6003 6064 6124 6185 6245 6306 6366 6427 6487 6548 6608 6668 6729 67896850 6910 6970 703170917152 | 7212 | 7272 N. I 6839 6.3 12.6 6948 6.2 12.4 7061 6.1 12.2 7178❘ 6.0 123456 7∞ a OH 23 †SO 78 a 9 710 I 4 9 PROP. PARTS. 9 I 23 456 7∞ 8 I 1234 ISO 7∞0 a 6 441504 56.7 434 49.6 55.8 2 12.0 3 4 5 6 189 25°2 31'5 37.8 18.6 24.8 31'0 37°2 18.3 244 30.5 36.6 18.0 24'0 30.0 36.0 7 8 8 42.7 48.8 549 420 480 54'0 | MATHEMATICAL TABLES. 61 No. 720 L. 857.] LOGARITHMS OF NUMBERS. [No. 764 L. 883. N. о I 2 3 4 5 6 7 ៖ 9 N. I 2 1 2 3 4 56 41 78 9 730 I 2 3456 78 0757 0218 0278 0817 0877 1415 1475 2012 2072 2608 2668 3204 3263 I 4 1 2 3 & 56 78 a 9 I 23 +46 78 5 720857332 7393 7453 7513 7574 7634 7694 7755 7815 7875 720 7935 7995 8056 8116 8176 8236 8297 8357 8417 8477 | 85378597 8537 8597 8657 8718 8778 8838 8898 8958 9018 9078 9138 9198 9258 9318 9379 9439 9499 9559 9619 9679 9739 9799 9859 9918 9978 0038 0098 0158 5860338 0398 0458 0518 0578 0637 0697 | | 0937 1996 1056 1116 1176 1231 1295 1355 | 1534 1594 1654 1714 1773 1833 1893 1952 2131 2191 2251 | 2310 | 2370 | 2430 2489 2543 2728 2787 2847 2906 2966 3025 3085 3144 3323 3382 3442 3501 3561 3620 3680 3739 3799 3858 730 3917 3977 4036 4096 4155 4214 4274 4333 4392 4452 4511 4570 4630 4689 4748 4808 4867 4926 4985 5045 5104 5163 5222 | 5282 | 5341 5400 5459 5519 5578 5637 5696 5755 5814 5874 5933 5992 6051 6110 6169 6228 6287 6346 6405 6465 6524 6583 6642 6701 6760 6819 6878 6937 6996 7055 7114 7173 7232 7291 7350 7409 7467 7526 7585 7644 7703 7762 7821 7880 7939 7998 | 8056 8115 8174 8233 8292 8350 8409 8468 8527 8586 9 8644 8703 8762 8821 8879 8938 8997 9056 9114 9173 9 9232 9290 9349 9408 9466 | 9525 9584 9642 9701 9760 740 9818 9877 9935 9994 0053 0111 0170 0228 0287 0345 2870404 0462 0521 0579 0638 0696 0755 0813 0872 0930 0989 1047 1106 1164 1223 1281 1339 1398 1456| 1515 1573 1631 1690 1748 1806 1865 1923 1981 2040 2098 2156 2215 2273 2331 2389 2448 2506 2564 2622 2681 2739 2797 2855 2913 2972 3030 3088 3146 3204 3262 3321 3379 3437 3495 3553 3611 3669 3727 3785 3844 3902 3960 4018 4076 4134 4192 4250 4308 4366 4424 4482 4540 4598 | 4656 | 4714 4772 4830 4888 4945 5003 5061 5119 5177 5235 5293 5351 5409 5466 5524 5582 750 5640 5698 5756 5813 5871 5929 5987 6045 6102 6160 2 6218 6276 6333 6391 6449 6507 6564 6622 6680 6737 3 6795 6853 6910 6968 7026 7083 7141 7199 7256 7314 7371 7429 7487 7544 7602 7659 7717 7774 7832 7889 7947 8004 8062 8119 8177 8234 8292 | 8349 8407 8464 8522 8579 8637 8694 8752 8809 8866 8924 8981 9039 9096 9153 9211 9268 9325 9383 9440 9497 9555 9612 9669 9726 9784 9841 9898 9956 0013 0070 0127 0185 | | 8 9 880242 0299 0356 0413 0471 0528 0585 0642 0699 0756 9 740 I 23 456 78 9 750 I 78 8 760 I 234 I 123456 700 9 I 2 3 4 6 I 2 0814 0871 0928 0985 1042 1099 1156 1213 1271 1328 760 1385 1442 1499 1556 1613 1670 1727 1784 1841 1898 1955 2012 2069|2126 | 2183 2240 2297 2354 2411 2468 2525 2581 2638 2695 2752 | 2809 | 2866 2923 2980 3037 3093 3150 3207 3264 3321 3377 3434 3491 3548 3605 4 | 3 PROP. PARTS. N. I 2 3 4 5 6 ་ 7 8 9 7299 5'9 7423 5.8 7552 5'7 86 11.8 17.7 114 23.6 29.5 11.6 17.4 23.2 17.1 22.8 29.0 41.3472 53.1 34.8 40.6 464 52.2 28.5 34°2 39.9 45.6 51.3 35°4 62 MATHEMATICAL TABLES. No. 765 L. 883.] LOGARITHMS OF NUMBERS. [No. 809 L. 908. N. O I 2 3 4 5 6 7 8 9 N. 6 78 56 7∞ 9 7 4682 4739 5248 5305 5813 5870 8 6378 6434 765 883661 3718 3775 3832 3888 3945 4002 4059 4115 4172 765 4229 4285 4342 4399 4455 4512 4569 4625 4795 4852 49094965 | 5022 5078 5135 5192 5361 5418 5474 5531 5587 5644 5700 5757 5926 5983 6039 6096 6152 6209 6265 6321 | | 6491 6547 6604 6660 6716 6773 6829 6885 9 770 I 2 3 4 iO 8 9 780 I | | | 6942 6998 770 I 2 7505 7561 7054 7111 7167 7223 7280 7336 7392 7449 | | 7617 7674 7730 7786 7842 7898 7955 8011 8067 8123 8179 8236 8292 8348 8404 8460 8516 8573 8629 8685 3 8741 8797 8853 8909 8965 9021 9077 9134 9190 9246 4 9302 9358 9414 9470 9526 9582 9638 9694 9750 9806 5 9862 9918 9974 0030 0086 0141 0197 0253 0309 0365 679 8 I 7 890421 0477 0533 0589 0645 0700 0756 0812 0868 0924 0980 1035 1091 11471203 1259 1314 1370 | 1426 | 1482 1537 1593 1649 1705 1760 1816 1872 1928 1983 2039 9 2095 2150 2206 | 2262 | 2317 | 2373 2429 2484 2540 2595 780 2651 2707 2762 2818 2873 2929 2985 3040 3096 3151 3207 3262 3318 3373 3429 3484 3540 3595 3651 3706 3762 3817 3873 3928 3984 4039 4094 4150 4205 | 4261 4316 4371 4427 4482 4538 4593 4648 4704 4759 4814 | | | 4870 4925 4980 5036 5091 5146 5201 5257 5312 5367 | | 5423 5478 5533 5588 5644 5699 5754 5809 5864 5920 5975 6030 6085 6140 6195 6251 6306 6361 6416 6471 | | 6526 6581 6636 6692 | 6747 6857 6912 6967 7022 7077 7132 7187 7242 7297 7352 7407 | 7462 7517 | 7572 1234 SO T∞ 7 8 9 790 I 3 4 2mt no 7∞ a 6 8 1800 I 123+ SO DO 8 9 PROP. PARTS. 6802 1 2 3 4 5 7∞ a 6 8 I 2 3 4 no 700 a 5 6 8 9 7627 7682 7737 7792 7847 7902 7957 8012 8067 8122 790 8176 8231 8286 8341 8396 8451 8506 8561 8615 8670 8725 8780 8835 8890 8944 8999 9054 9109 9164 9218 9273 9328 9383 9437 9492 9547 9602 9656 9711 9766 9821 9875 9930 9985 0039 0094 0149 0203 0258 0312 | 900367 0422 0476 0531 0586 0640 0695 0749 0804 0859 05310586 | 091309681022 1077 1131 1186| 1240 1295 1349|| 1404 | | 1458 1513 1567 1622 1676 1731 1785 1840 1894 1948 2003 2057 2112 2166| 2221 22752329 2384 2438 2492 | 23842438 2547 2601 2655 2710 2764 2818 2873 2927| 2981 3036 3090 3144 3199 3253 3307 3361 3416 3470 3524 3578 800 | | 3633 3687 3741 | 3795 | 3849 | 3904 | 3958 | 4012 | 4066 | 4120 I 4174 4229 4283 4337 439 4445 44994553 4607 4661 4716 4770 4824 | 4878 | 4932 4986 5040 5094 5148 5202 5256 5310 5364 5418 5472 5526 5580 5634 5688 5742 56345688 5796 5850 5904 5958 6012 6066 6119 6173 6227 6281 6335 6389 6443 6497 6551 6604 6658 6712 6766 | 6820 | | 6874 6927 6981 7035 7089 7196 7250 7304 7358 7411 7465 7519 7573 7626 7734 7787 7841 7895 7949 8002 8056 8109 8163 8270 8324 8378 8431 82708324 | | 7143 7680 8217 N. I 2 3 7686 5.6 7825 5'5 II O 7968 5'4 10.8 II.2 16.8 4 5 22.4 28.0 6 33-6 | 1234 NO 78 a 9 7 8 9 392 448 504 16.5 22'0 27.5 33°0 38.5 440 49'5 16.2 21.6 27.0 32.4 37.8432 48.6 MATHEMATICAL TABLES. 63 No. 810 L. 908.] N. I 2 LOGARITHMS OF NUMBERS. [No. 854 L. 931. 5 6 7 8 9 N. 3 4 810 908485 8539 8592 8646 | 86998753 8807 8860 8914 8967 810 | | I 9021 9074 9128 9181 9235 9289 9342 9396 9449 9503 9556 9609 9663 9716 9770 9823 9877 9930 6984 0037 2 3456 7∞ a 8 9 820 I I 2 4 5 6 7 8 9 ~ 3+nO DO GO Ham +56 7∞ a o I 2 3 910091 0144 0197 025103040358 | 0411 0464 | 0518 0571 0624 0678 0731 0784 0838 0891 0944 0998 1051 1104 | | | 1158 1211 1264 1317 1371 1424 1477 1530 15841637 1690 1743 1797 1850 1903 1956 2009 2063 2116 2169 2222 2275 2328 2381 2435 2488 2541 2594 2647 2700 2753 2806 2859 2913 2966 | 3019 | 3072 3125 3178 3231 3284 3337 3390 3443 3496 3549 3602 3655 3708 3761 3814 3867 3920 3973 4026 4079 4132 4184 4237 4290 820 4343 4396 4449 4502 4555 4608 4660 4713 4766 4819 4872 4925 4977 5030 5083 5136 5189 | 5241 | 5294 5347 | | | 5400 5453 5505 5558 5611 5664 5716 5769 5822 5875 | | | | | 5927 59806033 6085 6138 | 6191 | 6243 6296 6349 6401 | | | 6454 6507 6559 6612 6664 6717 6770 6822 6875 6927 | 6980 7033 7085 7138 7190 7243 7295 7348 7400 7453 7506 7558 7611 7663 7716 7768 7820 78737925 7978 | | 8030 8083 8135 8188 8240 8293 8345 8397 8450 8502 8555 8607 8659 8712 8764 8816 8869 8921 8973 9026 | 9078 913091839235928793409392 | 9444 9496 9549 830 9601 9653 9706 9758 9810 9862 9914 9967 0019 0071 2 3 4 5O Z∞ a 7 8 9 830 I HO 8 9 840 I 23456 7oo a OH 2 m +6 78 9 | 3 4 8 I 1234 SO ZO0 a 6 7 8 9 I 2 920123 0176 0228 0280 0332 0384 0436 0489 0541 0593 0645 0697 0749 0801 0853 0906 0958 1010 1062 1114 1166 1218 1270 1322 1374 1426 1478 1530 1582 1634 1686 1738 1790 1842 1894 1946 1998 2050 2102 2154 2206 2258 2310 2362 2414 2466 2518 2570 2622 2674 2725 2777 2829 2881 29332985 3037 3089 3140 3192 3244 3296 3348 3399 34513503 355536073658 3710 3762 3814 3865 3917 3969 | 4021 | 4072 | 4124 4176 4228 4279 4331 4383 4434 4486 4538 4589 4641 4693 4744 840 4796 4848 4899 4951 5003 5054 5106 5157 5209 5261 5312 5364 5415 5467 5518 5570 5621 5673 5725 5776 5828 5879 5931 5982 6034 6085 6137 6188 6239 6291 | 6342 6394 6445 6497 6548 6600 6651 6702 6754 6805 | | 6857 6908 6959 70117062 7114 7165 7216 7268 7319 7370 7422 7473 7524 7576 7627 7678 7730 7781 7832 | | | 7883 7935 7986 8037 8088 8140 8191 | 8242 | 8293 | 8345 8396 8447 8498 8549 8601 8652 8703 8754 8805 8857 8908 8959 9010 9061 9112 9163 9215 9266 9317 9368 | | 9419 9470 9521 9572 9623 9674 9725 9776 9827 9879 850 9930 9981 0032 0083 0134 2930440 0491 0542 0592 0643 | | | 0949 1000 1051 1102 1153 1458 1509 1560 1610 1661 3 4 5 850 I 234 PROP. PARTS. 123456 7∞ 9 8 I 0185 0236 0287 0338 0389 2 0694 0745 0796 0847 0898 069407450796 | | 1203 1254 1305 1356 1407 | | 3 1712 1763 1814 1864 1915 4 8 6 7 37°1 31.8 9 42.4 47.7 36.441-646-8 4 3 5 21.2 15'9 26.5 5.2 10'4 15.6 20.8 26.0 31.2 N. I 2 8117 5:3 10.6 8271 8432 5'I 10.2 | 15°3 20'4 25.5 30.6 35.7 40.8 459 64 MATHEMATICAL TABLES. No. 855 L. 931.] 6 78 9 860 1234 36 700 8 2 456 7∞ LOGARITHMS OF NUMBERS. [No. 899 L. 954- I 2 3 4 5 6 7 8 9 N. 2322 2829 3335 2372 2423 855 2879 2930 3386 3437 | 3892 3943 | | 4397 4448 678 a I 2 3 4 i 70 a 8 I 23456 7∞ a N. о 855 931966 2017 2068 2118 2169 2220 2271 2474 2524 2575 2626 2677 2727 2778 2981 3031 3082 3133 3183 3234 3285 3487 3538 3589 | 3639 3690 3740 3791 3841 | 3993 4044 4094 4145 4195 4246 4296 4347 4498 4549 4599 4650 4700 4751 4801 4852 4902 4953 860 5003 5054 5104 5154 5205 5255 5306 5356 5406 5457 5507 5558 5608 5658 5709 5759 5809 5860 5910 5960 6011 6061 6111 6162 6212 6262 6313 6363 6413 6463 6514 6564 6614 6665 6715 6765 6815 6865| 6916 6966 7016 7066 7116 7167 7217 7267 7317 7367 7418 7468 7518 7568 7618 7668 7718 7769 7819 7869 | 7919 | 7969 | 8019 8069 8119 8169 8219 8269 8319 8370 8420 8470 8520 8570 8620 8670 8720 8770 8820 8870 8920 8970 9 9020 9070 9120 9170 9220 9270 9319 9369 9419 9469 870 9519 9569 9619|9669|9719|9769 9819 9869||9918|9968|870 1940018 0068 0118 0168 0218 0267 0317 0367 0417 0467 0516 0566 0616 0666 0716 0765 0815 0865 0915 0964 1014 1064 1114 1163 1213 1263 1313 1362 | 1412 || 1462 1511 1561 1611 1660 1710 1760 1809 1859 1909 1958 2008 2058 2107 2157 2207 2256 2306 2355 2405 2455 2504 2554 2603 2653 2702 2752 2801 2851 2901 2950 3000 3049 3099 3148 3198 3247 3297 3346 3396 3445 3495 3544 3593 3643 3692 3742 3791 3841 3890 3939 3989 4038 4088 4137 4186 4236 4285 4335 4384 4433 4483 4532 4581 4631 | 4680 4729 4779 4828 4877 4927 880 4976 5025 5074 5124 5173 5222 5272 5321 5370 5419 | | | 5469 5518 5567 5616 5665 5715 5764 5813 5862 5912 5961 6010 6059 6108 6157 6207 6256 6305 6354 6403 6452 6501 6551 6600 6649 6698 6747 6796 | 6845 6894 | 6943 6992 7041 7090 7139 7189 7238 7287 7336 7385 7434 7483 7532 7581 7630 7679 7728 7777 7826| 7875 7924 7973 8022 8070 8119 8168 8217 8266 8315 8364 8413 8462 8511 8560 8608 8657 8706 8755 8804 8853 8902 8951 8999 9048 9097 9146 9195 9244 9292 | 9341 9390 9439 9488 9536 9585 9634 9683 9731 9780 9829 890 I 9878 9926 9975 0024 0073 0121 0170 0219 0267 0316 2 950365 0414 0462 0511|0560 | 0608 | 0657 0706 0754 0803 3 0851 0900 0949 | 0997 1046 1095 1143 1192 1240 1289 4 1338 1386 1435 1483 1532 1580 1629 1677 1726 1775 1823 1872 1920 1969 2017 2066 2114 2163 2211 2259 2308 2356 2405 2453 2502 2550 2599 2647|| 2696| 2744 2792 2841 2889 2938 2986 3034 3083 3131 3180 3228 | | 3276 3325 3373 3421 3470 3518 3566 3615 3663 3711 3760 3808 3856 39053953 4001 4049 4098 4146 | 4194 8 9 880 Ι 1234 ISO 70 a 6 9 890 6 8 PROP. PARTS. 8 I 23456 7OO 8 9 I 2 5 346 7∞ 8 9 N. I 2 3 4 5 8599 8773 49 8954 4.8 9.6 5'0 ΙΟ 9.8 15.0 147 | 19.6 14'4 192 20'0 6 7 25.0 30°0 35°0 24'5 29.4 34°3 24.0 28.8 33.6 8 9 400 450 39°244'1 38.443.2 MATHEMATICAL TABLES. 65 I .2 23 456 78 9 910 I 2 4 56 78 L. 954.] I LOGARITHMS OF NUMBERS. | | [No. 944 L. 975- I 2 HN 34 no 7∞ 6 8 23456 7∞ a No. 900 N. i | 2 3 4 5 6 ! 7 8 9 IN. 900 954243 4291 4339 4387 4435 4484 4532 | 4580 | 4628 4677 900 4725 4773 4821 4869 4918 4966 5014 5062 5110 5158 5207 5255 5303 5352 5399 5447 5495 5543 5592 5640 | | | | | | 5688 5736 5784 5832 5880 5928 5976 6024 6072 6120 6168 6216 6265 6313 6361 6409 6457 6505 65536601 6649 6697 6745 6793 6840 6888 6936 6984 7032 7080 7128 7176 7224 7272 7320 7368 7416 7464 7512 7559 7607 7655 7703 7751 7799 78477894 7942 7990 8038 8086 8134 8181 8229 8277 8325 8373 8421 8468 8516 | 8564 8612 8659 8707 8755 8803 8850 8898 8946 8994 9 9041 9089 9137 9185 9232 9280 9328 9375 9423 9471 910 9518 9566 9614 9661 9709 9757 9804 9852 9900 9947 I 9995 0042 0090 01380185 0233 0281 0328 0376 | 0423 3960471 0518 0566 0613 0661 0709 0756 0804 0851 0899 0946 0994 1041 1089 1136 1184 1231 1279 13261374 1421 1469 1516 1563| 1611 1658 1706 1753 1801 1848 1895 1943 1990 2038 2085 2132 2180 2227 2275 2322 2369 2417 2464 2511 2559 2606 2653 2701 2748 2795 2843 2890 2937 2985 3032 3079 3126 3174 3221 3268 3316 3363 3410 3457 3504 3552 3599 3646 3693 3741 | | 3788 3835 3882 3929 3977 4024 4071 4118 4165 4212 920 4260 4307 4354 4401 4448 4495 4542 4590 4637 4684 | 4731 4778 4825 4872 4919 4966 5013 5060 5108 5155 5202 5249 5296 5343 5390 5437 5484 | 5531 5578 5625 5672 5719 5766 5813 5860 5907 5954 6001 6048 6095 6142 6189 6236 6283 6329 6376 6423 6470 6517 6564 6611 6658 6705 6752 6799 6845 6892 6939 6986 7033 7080 7127 7173 7220 7267 7314 7361 7408 7454 7501 7548 7595 7642 7688 7735 7782 7829 7875 7922 7969 80168062 8109 8156 8203 8249 8296 8343 8389 8436 8483 8530 8576 8623 8670 8716 8763 8810 8856 8903 930 8950 8996 9043 9090 9136 9183 9229 9276 9323 9369 9416 9463 9509 95569602 9649 9695 9742 9789 9835 9882 9928 9975 0021 0068 0114 0161 0207 0254 0300 4970347 0393 0440 0486 05330579 0626 0672 0719 0765 0812 0858 0904 0951 0997 1044 1090 1137 1183 1229 1276 1322 1369 1415 1461 1508 1554 1601 1647 1693 1740 17861832 | 1879 | 1925 1971 2018 2064 2110 2157 8 2203 2249 2295 2342 2388 2434 2481 2527 2573 2619 2666 2712 2758 2804 2851| 2897 2943 2989 3035 3082 8 9 920 I 2 3456 7 8 9 930 I 2 3 456 7∞ 9 1940 I - 8 9 I 2345O DOO a 6 7 8 1 2 4 5 6 3tno 78 9 3128 3174 3220 3266 3313 3359 3405 3451 3497 3543 940 3590 3636 3682 3728 3774 3820 3866 3913 3959 4005 I 3 4 2 4051 4079 4143 | 4189 4235 4281 4327 4374 4420 4466 4512 4558 4604 4650 4696 4742 4788 4834 4880 4926 4972 5018 5064 | 5110 5156 | 5202 | 5248 | 5294 5340 5386 2 3 4 N. I 2 PROP. PARTS. 9143 4.7 9'4 9339 4.6 9.2 9544 4.5 9'0 3 4 18.8 14'1 13.8 13.5 18.0 5 6 28.2 23'5 18.4 23.0 27.6 32.2 22.5 27.0 31.5 7 8 9 32.9 37.6 42.3 36.8 414 36.0 40.5 66 MATHEMATICAL TABLES. No. 945 L. 975.] N. O LOGARITHMS OF NUMBERS. [No. 989 L. 995- I 2 3 4 5 6 7 8 9 N. 6 78 9 950 I 2 3 4 5 6 7∞ a 960 8 I 23456 too a 7 1184 6 7 8 9 I 2 3 4 SO DO a 5 6 7 8 9 I 3 5 6 2 3 4 SO 7∞ a 945 975432-5478 5524 5570 5616 5662 5707 5753 5799 5845 945 5891 5937 5983 6029 6075 6121 6167 6212 6258 6304 6350 6396 6442 6488 6533 6579 6625 6671 | 6717 | 6763 | 6808 6854 6900 6946 6992 7037 7083 7129 7175 7220 7266 7312 7358 7403 7449 7495 7541 7586 7632 7678 7724 7769 7815 7861 7906 7952 7998 8043 8089 8135 950 8181 8226 8272 8317 8363 8409 8454 8500 8546 8591 8637 8683 8728 8774 8819 8865 8911 8956 9002 9047 9093 913891849230 | 9275 9321 | 9366 | 9412 9457 9503 9548 9594 9639 9685 9730 9776 9821 9867| 9912 | 9958 5980003 0049 0094 0140 0185 0231 0276 0322 | 0367 | 0412 0458 050305490594 0640 0685 0730 0776 0821 0867 0912 0957 1003 1048 1093 1139 1229|| 1275 1320 1366 1411 1456 1501 1547 1592 1637 1683 1728 1773 1819 1864 1909 1954 2000 2045 2090 2135 2181 2226 2271 2316 2362 2407 2452 2497 2543 2588 | 2633 | 2678 960 2723 2769 2814 2859 2904 2949 2994 3040 3085 3130 3175 3220 3265 3310 3356 3401 3446 3491 3536 | 3581 3626 3671 3716 3762 3807 3852 3897 3942 3987 4032 4077 4122 4167 4212 4257 4302 4347 4392 4437 4482 4527 4572 4617 4662 4707 4752 4797 4842 4887 4932 4977 5022 5067 5112 5157 5202 5247 5292 5337 5382 5426 5471 5516 5561 5606 5651 5696 5741 5786 5830 5875 5920 5965 6010 6055 6100 6144 6189 6234 6279 6324 6369 6413 6458 6503 6548 6593 6637 6682 6727 6772 6817 6861 6906 6951 6996 7040 7085 7130 7175 970 7219 7264 7309 7353 7398 7443 7488 7532 7577 7622 7666 7711 7756 7800 7845 7890 7934 7979 8024 8068 8113 8157 8202 8247 8291 8336 8381 8425 8470 8514 8559 8604 8648 8693 8737 8782 8826 8871 8916 8960 9005 9049 9094 9138 9183 9227 9272 9316 9361 9405 9450 9494 9539 9583 9628 9672 9717 9761 9806 9850 9895 9939 9983 0028 0072 0117 0161 0206 0250 0294 8990339 0383 0428 0472 0516 0561 0605 | 0650 0694 0738 0783 0827 0871 0916 0960 1004 1049 1093 1137 1182 9 1226 1270 1315 1359 1403 1448 1492 1536 1580 | 1625 980 1669 1713 1758 1802 1846 1890 1935 1979 2023 2067 | 2111 2156 2200 2244 2288 2333 2377 2421 2465 2509 2554 2598 2642 2686 2730 2774 2819 2863 2907 2951 29953039 3083 | 3127 | 3172 | 3216 | 3260 3304 3348 3392 3436 3480 3524 3568 3613 3657 3701 3745 3789 3833 3877 3921 3965 4009 4053 4097 4141 4185 4229 4273 4317 4361 4405 4449 4493 4537 4581 4625 4669 4713 4757 4801 4845 4889 4933 4977 5021 5065 5108 5152 5196 5240 5284 5328 | 5372 5416 5460 | 5504 | 5547 | 5591 8 970 I 23 456 7∞ 9 980 I 23 tinO DOO a 8 9 I 24456 78 I 2 3 4 56 -7 8 9 PROP. PARTS. N. I 2 3 4 9759 4:4 8.8 9983 4.3 8.6 5 6 13.2 17.6 22.0 26.4 30.8 12.9 17.2 21.5 25.8 30'I 7 *8 9 35.2 39.6 34'4 38.7 MATHEMATICAL TABLES. 67 No. 990 L. 995] N. I 23456 too a LOGARITHMS OF NUMBERS. I 2 3 4 [No. 999 L. 999. ŷ N. CO I 23 456 78 56 7 990 995635 5679 5723 5767 5811 5854 | 5898 5942 5986 6030 990 58545898 6030990 6074 6117 6161 6205 6249 6293 6337 6380 6424 6468 6512 6555 6599 6643 6687 6731 6774 6818 6862 6906 | 6949 6993 7037 7080 7124 7168 7212 7255 | 7299 | 7343 7386 7430 7474 7517 7561 7605 7648 7692 7736 7779 | || | | 7823 7867 7910 7954 7998 8041 8085 8129 8172 8216 8259 8303 8347 8390 8434 8477 8521 8564 8608 8652 8695 8739 8782 8826 8869 8913 8956 9000 9043 9087 9130 9174 9218 9261 9305 9348 9392 9435 9479 9522 9565 9609 9652 9696 97399783|9826|9870 | 9913 | 9957 TABLE II.—LOGARITHMS OF NUMBERS FROM I TO 100. Log. N. Log. N. 7 8 9 N. Log. N. Log. N. 41 I 0·000000 [21 | 1*322219 161278461 1785330 2 0·301030 ||22| 1°342423 42 1623249|| 62 | 1*792392 30477121|23| 1°361728 || 43 1633468 | 63 1799341 4 0.602060 24 1380211 44 1643453 64 1.806180 50-698970 25 1397940 45 1653213 65 1812913 60-778151 ||26| 1414973 46 1.662758 || 66 | 1819544 70845098 27 1431364 47 1672098 67 1.826075 8 090309028 1447158 48 1.681241 68 1-832509 90954243|29| 1462398|| 49 1690196 69 1-838849 IO 1'000000 30 1'477121 50 1.698970 70 1.845098 11 104139331 1491362 || 51 1707570 71 1-851258 | 12 107918132 1.505150 || 52 1716003 72 1-857332 13 1113943 33 1'518514 53 1724276 || 731-863323 14 114612834 1531479 54 1732394|| 74 1.869232 15 117609135 1544068 55 1740363 75 1875061 16 120412036 1.556302|| 56 1748188|| 76 1.880814 17 1230449 37 1568202 57 1755875 77 1.886491 18 1255273 38 1579784 58 1763428 781-892095 19 1278754 39 1-591065 59 1770852 79 1.897627 20 130103040 1.602060 60 1778151 || | | Log. 9 81 1-908485 82 1-913814 83 1-919078 84 1924279 85 1.929419 86 1.934498 87 1939519 88 1-944483 89 1949390 90 1'954243 91 1'95904.1 92 1-963788 93 1.968483 94 1973128 95 1977724 | 96 1-982271 97 1-986772 98 1991226 991-995635 80 1.903090 || 100 2'000000 TABLE III. Sign Value Sign Value Sign Value | | in-2nd at in 3rd at in 4th at at 90°. Quad. 180º. Quad. 270°. Quad. 360°. Value at oº. Sign in ist Value Quad. Ꭱ R Sin.... Tan.... Sec Versin Cos.... Cot..... Cosec.. ++ R 8 8 ROOF OOROR 8 8 Ꭱ +11 +11+ Ꭱ 2 R R 1 +1 +1 +1 A 8 8 ROOR Ꭱ | 1+++1 | K signifies equal to rad; ∞ signifies infinite; O signifies evanescent. OOROR 8 8 68 MATHEMATICAL TABLES. TABLE IV.—LOGARITHMIC SINES. •I $2 *3 '4 *5 O。 5 6 241877 249056 256118 5°463726 5.764756 5'940847 6·065786 | 6·162696 89 59 1 6.463726 6.505119 6.542907 6.577669 2 764756 785945 806149 825454 3 609854 639817 58 843937 861666 57 56 940847 955088 968876 982240 995205 7007794 47.065786 7.076510 | 7·086975 7097194 7107179 116938 55 162696 171296 179729 188002 196120 204089 54 263066|| 269906|| 276639 53 7 308824 314984 8 366816 372211 377540 321058 327049 332958 338787 52 382804 388005 393145 89 51 O ΙΟ II 9 7417968 7422767 | 7°427513 7°432208 7°436853 | 7441449 463725 468047 472326 476563 480759 484915 505118 509048 512943 516804 520630 524423 50 49 48 12 542906 546511 550085 553630 557147 560635 47 13 577668 580996 584299 587577 590830 594059 46 14 609853 612944 616013 619061 622087 625093 45 15 639816 642702 645568 648416 651245 654056 44 16 667845 670550 673239 675912 678568 681208 43 17 694173 696720 699253 701770 704273 706762 89 42 1 2 2 2 2 2 2 2 2 2 2 3 3 20 21 22 0 18 7.718997 7·721403 | 7723795 | 7-726175 19 742477 744757 747025 749281 764754 766920 766920 769075 771220 785943 788006 790059 792103 794137 806146 808115 810076 812028 7728542 | 7·730896 41 751525 753758 40 773354 775477 39 796162 38 813971 815905 37 23 825451 827335 829211 831079 832939 834791 36 24 843934 843934 845740 847538 849329 851112 852888 35 25 861662 863396 865123 866843 868556 870262 34 26 878695 880362 882023 883678 885326 886968 89 33 28 910879 912428 29 30 31 926119 927614 929104 940842 942287 943727 955082 956481 957875 32 968870 970225 971576 0 277-8950857-8966917-8982917-899884 7.901472 7.903054 32 918566 930589 932068 933543 30 945163 946594 948020 29 959264 | 960650 28 962031 972922 974265 975603 27 33 982233 983547 984857 986164 987466 988764 26 34 995198 996473 997745 9990138.000277 8.001538 25 35 8.007787 8.009026 8010261 8011493 012722 013947 89 24 o 36 8.020021 8021225 8.022427 8.023625 8.024819 8.026011 913970 915508 917039 31 23 38 39 40 4I 37 031919 033092 034261 035426 036589 043501 044642 045781 046916 048048 054781 055893 057003 058109 059213 065776 066861 076500 077558 037749 22 049178 21 42 086965 087997 090056 060314 067942 069021 070098 071171 078613 079666 080716 081764 18 089028 20 19 091081 092104 17 43 097183 098192 099198 100203 101204 102204 16 44 107167 108153 109136 110118 45 116926 117890 118852 119812 111097 120769 112074 15 121725 89 14 ΙΟ *9 .8 '7 .6 5 Log. Cosines. MATHEMATICAL TABLES. 69 TABLE IV.-LOGARITHMIC SINES. •6 .8 *9 I'O 6-241877 6.308824 6-366816 6-417969 6463726 89 59 | I 667846 694175 718999 742480 764756 58 23456 7O 878699 895090 910884 926124 940847 57 7020028 7031928 7043510 7'054791 7.065786 56 126484 135824 144967 153922 162696 55 211914 219601 227154 234578 241877 54 283270 289801 296235 302575 308824 53 344539 350217 355820 361353 366816 52 8 398224 403245 408208 413116 417968 89 51 9 7'445998 7*450497 7'454952 7°459361 7463725 50 10 489031 493109 497149 501152 505118 49 I I 528183 531911 535607 539272 542906 48 12 564096 567529 570935 574315 577668 47 13 597264 600445 603604 606740 609853 46 14 628078 631042 633986 636911 639816 45 15 656849 659624 662382 665122 667844 44 16 683832 68644I 689034 691611 694173 43 17 709237 711697 714144 716577 718997 89 42 o 18 7'733237 7'735566 7737882 7°740186 7'742477 41 19 755980 758190 760389 762577 764754 40 20 777591 779694 781787 783870 785943 39 21 798177 800183 802180 804167 806146 38 22 817831 819749 821658 823558 825451 37 23 836635 838471 840300 842120 843934 36 24 854657 856419 858174 859922 861662 35 o 27 2 2 2 2 2 33 25 871962 873655 875342 877022 878695 34 26 888603 890233 891856 893474 895085 89 33 7.904630 | 7906201 | 7907766 | 7°909326 7.909326 7910879 32 28 920087 921603 923113 924619 926119 31 29 935012 936477 937937 939392 940842 30 30 949442 950859 952271 953679 955082 29 31 963407 964779 966147 967511 968870 28 32 976937 978267 979593 980915 982233 27 33 990058 991349 992636 993919 995198 26 34 8.002795 8.004048 8.005298 8.006544 8.007787 25 35 015168 016386 017601 018813 020021 89 24 0 36 8-0271998-028384 | 8:029566 | 8·030744 8.030744 8.031919 23 41 42 43 44 45 £ £ £ £ £ £ www. 37 038905 040059 041209 042356 043501 22 38 050304 051428 052549 053666 054781 061412 062507 063599 064689 065776 40 072242 073310 082809 093125 103201 074376 083851 084892 094143 095159 104196 105188 075439 076500 085929 086965 113049 114021 122678 123629 114992 124579 096172 097183 106179 107167 115960 116926 125526 126471 89 14 2 2 HHHHHH 21 20 19 18 17 16 15 4 *3 *2 *I Ο Log. Cosines. 70 MATHEMATICAL TABLES. 00 TABLE IV.-LOGARITHMIC SINES. 'O 'I $2 '3 '4 *5 45 8.116926 8117890 8-118852 8.119812 8.120769 8-121725 89 14 46| 126471 127414 128355 129294 130231 131166 13 47 135810 136733 137654 138574 139491 140406 12 48 144953 145857 146759 147659 148557 149453 II 49 153907 I 54793 50 162681 163548 51 171280 172131 155676 156558 164414 172980 157438 158316 ΙΟ 165279 166141 167002 173827 174673 175517 52 179713 180547 181380 182211 183041 183868 in in 55 204070 53 187985 188803 189620 190436 54 8.196102 8.196905 8.197707 8.198508 8.199307 8-200104 204859 205646 206432 191250 192062 89 6 98 76 5 207217 208000 4 56 211895 212670 213443 214215 214986 215755 3 57 219581 220342 221102 221861 222618 223374 58 227134 227882 228628 229374 230118 230861 59 234557 235292 236026 236759 237491 238221 89 ར I 2 I OHN 241855 242578 243300 24402 I 24474I 245459 I 249033 249744 250455 251164 251871 252578 2 10 000 in in I 59 58 9 IO II 3456 7∞ ao - 256094 256794 257492 38·263042 8·263731 | 8·264419 8-265105 | 8.265791 | 8·266475 269881 270559 271236 258190 258887 259582 89 57 56 271912 272587 273260 55 276614 277281 277948 278613 279278 27994I 54 283243 283901 284557 285213 285867 286521 53 289773 290421 291068 291713 292358 293002 52 8 296207 296845 297482 298118 298754 299388 51 302546 303174 303803 304430 305056 305681 50 308794 309414 310033 310651 311268 311885 49 314954 315565 316175| 316784 317393 318001 89 48 I 12 8 321027 8.321629 8.322231 | 8.322832 | 8.323433 | 8.324032 13 14 HH 15 16 17 18 2 346 NO 47 327016 327611 | 328204 328204 332924 333511 338753 33933I 344504 345075 350181 355783 328797 329389 329980 334096 334681 339909 340486 345645 346215 350744 351307 351869 356340 | 356895 357450 19 361315 361864 362413 362961 20 3.66777 367319 367319 367861 368402 368943 1 21 8-372171 8.372707 8.373242 8.373776 8.374310 8.374843 46 335265 335848 341063 341638 44 346784 347352 43 45 352430 352991 42 358004 358558 41 363508 364054 40 369482 88 39 38 23 29 WNNNNNN 24 25 26 27 403199 28 408161 22 377499 378028 378557 379084 382762 383285 383807 384329 387962 388479 388995 393101 393611 394121 394631 398179 398684 399188 399691 403698 404196 408654 409147 379612 380138 37 384850 385370 36 389510 390025 390539 35 395139 395647 34 400194 400696 33 404694 405191 405687 32 409639 410130 410621 31 413068 30 417919 413555 414042 418401 418883 419364 414529 415015 419844 415500 30 420324 88 29 ΙΟ *9 .8 '7 .6 '5 Log. Cosines. MATHEMATICAL TABLES. 71 } '7 ·6 TABLE IV.-LOGARITHMIC SINES. ·8 *9 ΙΟ 45 8.122678 8.123629 8:124579 8-125526 8.126471 89 14 46 I 32099 133030 133959 134885 135810 13 47 141319 142231 143140 144048 144953 12 48 150348 151241 152131 153020 153907 I I 49 159193 160067 160940 161811 162681 10 50 167861 168718 169574 *70428 171280 51 176359 177200 178039 $78877 179713 52 184695 185520 186343 187165 187985 53 192873 193683 194491 195297 196102 89 6 98. 76 • 54 8.200900 8.201695 8.202488 8.203280 8.204070 5 55 208782 209562 210341 211119 211895 4 56 216523 217289 218055 218819 219581 3 57 224128 224881 225634 226384 227133 2 58 231603 232343 233082 233820 234557 I 59 238951 239679 240405 241131 241855 89 I о 246176 246892 247607 248321 249033 59 I 253284 253988 254691 255393 256094 58 2 260276 260970 261662 262352 263042 88 57 I 3 8.267158 4 273933 8.267841 8.268522 274605 8.269202 8.269881 56 275275 275945 276614 55 56 780 280604 281265 281925 282585 283243 54 287173 287825 288475 293645 294287 289125 289773 53 294928 295568 296207 52 300021 300654 301286 301916 302546 51 9 306306 306929 307552 308173 308794 IO 312500 313115 313729 314342 314954 I I 318608 319214 319819 320423 321027 88 48 I 12 8-324630 8-3252288-325825 8.326421 | 8.327016 13 330571 331160 331749 332337 332924 14 33643I 337012 337593 338174 338753 15 342213 342787 343360 343933 344504 16 347919 348485 349051 349616 350180 43 17 353551 354110 354669 355226 355783 18 359111 359663 360214 360765 361315 4I 19 364600 365145 365690 366234 366777 is good fo4$ 7 7 7 ! 50 49 47 46 45 44 42 40 20 370021 370560 371095 371635 372171 88 39 I 21 8-375375 8-375907 8-376438 8.376969 8.377499 38 22 380664 381190 381714 382239 382762 37 23 385889 386409 386927 387445 387962 36 24 25 26 28 29 2 2 2 2 + no no a 391053 391566 392078 392590 393101 35 396155 396662 397168 401198 401699 402200 27. 406183 406679 411112 411601 397674 398179 402700 407173 407668 408161 4.12091 412579 34 403199 33 32 413068 3I 415985 416469 416953 417436 417919 30 30 420804 421283 422762 422239 422717 88 29 4 *3 *2 •I Ο Log. Cosines. 72 MATHEMATICAL TABLES. 0 Deg. TABLE V.-LOG. SINES, ETC. Sine Cosec. Tang. Cotang. Sec. D. Cosine 10'00 0000 o0.000000 Infinite. ooooooo Infinite. 16·463726|13·536274 6·463726 13.536274 0000 2 764756 235244 764756 235244 0000 3 940847 059153 940847 059153 0000 47.065786 12.934214 7065786 12'934214 0000 5 162696 837304 162696 6 241877 758123 241878 7 308824 691176 308825 8 366816 633184 366817 O 0000 0000 02 Deg. 10'000000 60 O 0000 59 58 о 0000 57 о 0000 56 о 8373040000 758122 0001 691175 0001 633183 0001 55 о 9'999999 54 I 9999 53 I 9999 89 52 I o 97417968 12.582032 7°417970 12.582030 0001 10 463725 536275 463727 II 505118 494882 505120 12 542906 457094- 13 577668 422332 14 609853 390147 609857 15 639816 360184 639820 16 667845 332155 667849 17 694173 305827 694179 9'999999 SI I 536273 0002 9998 50 I 494880 0002 9998 49 I 542909 4570910003 9997 48 577672 422328 0003 I 9997 47 I 390143 0004 9996 360180 0004 I 9996 I 332151 0005 9995 I 305821 0005 9995 89 43 I o 187718997 12:281003 7.719003 19 742477 257523 12:2809970006 9*999994 742484 257516 0007 I 9993 4I 20 764754 235246 I 764761 235239 0007 9993 21 785943 214057 I 785951 214049 0008 9992 22 806146 193854 I 806155 193845 0009 9991 24 843934 156066 23 825451 174549 825460 I 174540 0010 9990 I 843944 156056 0011 9989 25 861662 138338 861674 2 138326 0011 9989 26 878695 121305 878708 121292 | 0012 2 2 33 982233 017767 982253 29 926119 073881 926134 30 940842 059158 31 955082 044918 32 968870 031130 968889 0 277.895085 12-104915 7-895099 12 104901 0013 28 910879 089121 910894 35 9988 89 9*999987 2 089106 0014 9986 073866 0015 2 9985 2 940858 059142 0017 9983 30 2 955100 0449000018 9982 2 0311110019 9981 28 2 0177470020 9980 27 ~~wwwwwwwwwww A‡‡ ‡‡‡÷: 46 45 44 42 40 39 38 37 36 34 32 34 995198 004802 995219 004781 0021 2 9979 26 35 8.007787 11-992213 8.007809 11992191 0023 0 36 8.020021 11.979979 8.020045 11'979955 0024 2 9977 89 25 2 9*999976 24 Cosine 40 065776 934224 065806 41 076500 923500 42 086965 913035 086997 43 097183 902817 097217 44 107167 892833 45 116926 90 Deg. 107202 883074 116963 Secant Cotang. 37 031919 38 043501 956499 043527 39 054781 945219 054809 2 968081 031945 968055 0025 9975 23 956473 0027 2 9973 22 945191 0028 2 9972 21 2 934194 0029 9971 20 076531 923469 0031 2 9969 19 2 9130030032 9968 18 2 902783 0034 9966 17 2 892798 0036 9964 3 883037 0037 Tang. Cos. D. 16 9963 89 15 76 Sine 891 Deg. MATHEMATICAL TABLES. 73 0 Deg. TABLE V.-LOG. SINES, ETC. Sine Cosec. Tang. Cotang. Sec. D. 10'00 0458-116926 11.883074 8.116963 11-883037 0037 46 126471 873529 47 135810 864190 135851 33 1 Deg. Cosine 9*999963 15 126510 873490 0039 3 9961 14 864149 0041 9959 13 48 144953 49 153907 855047 144996 846093 153952 • 855004 0042 3 9958 12 846048 0044 3 9956 I I 50 162681 837319 162727 837273 0046 3 9954 ΙΟ 51 171280 I 758145 241921 750967 249102 828720 171328 820287 179763 52 179713] 53 187985 812015 188036 o 54 8.196102 11.803898 8.196156 55 204070 795930 204126 56 211895 788105 211953 57 219581 780419 219641 58 227134 772866 59 234557 765443 234621 1 o 241855 249033 2 256094 743906 743906 256165 11.803844 0054 8.263042 11.736958 8.263115 11736885 | 0073 828672 0048 3 9952 820237 0050 811964 0052 3 9950 ܣܗ 9 8 33 9948 89 7 9*999946 6 795874 0056 788047 0058 780359 0060 227195 772805 0062 765379 0064 758079 0066 9932 59 9929 88 58 I 9'999927 57 4 269881 730119 269956 7300440075 9925 56 7 289773 8 296207 9 302546 10 308794 5 276614 723386 276691 6 283243 716757 283323 710227 289856 703793 196292 723309 0078 9922 55 716677 0080 9920 710144 0082 703708 0085 4 54 9918 697454 302634 697366 0087 +4 53 9915 52 9913 691206 691206 308884 691116 0090 4 51 9910 50 I I 314954 685046 315046 684954 0093 9907 88 49 750898 0068 743835 0071 3344++++++++ 0044 5 9942 4 9940 3 9938 2 9936 I 9934 89 O 1 128.32102711-678973 8.321122 11678878 0095 13 327016 672984 327114 14 332924 15 338753 16 344504 667076 333025 661247 338856 655496 344610 17 350181 649819 350289 18 355783 644217 355895 19 361315 638685 361430 20 366777 633223 366895 1 21 8.37217111*627829 8.372292 11627708 0121 22 377499 622501 377622 672886 0098 666975 0101 661144 0103 655390 0106 649711 0109 644105 0112 638570 0115 633105 0118 +44 + in in in in in ini 9'999905 48 9902 47 4 9899 46 5 9897 45 9894 44 9891 43 9888 42 9885 4I 9882 88 40 9*999879 39 5 622378 0124 9876 23 382762 617238 382889 617111 0127 9873 38 37 24 387962 612038 388092 611908 0130 9870 36 ***70 000 NO 333 M 25 393101 606899 393234 606766 0133 9867 35 26 398179 601821 398315 601685 0136 9864 34 27 403199 596801 403338 596662 0139 9861 33 28 408161 591839 408304 591696 0142 9858 32 29 413068 586932 586932 413213 586787 0146 30 417919 Cosine 582081 418068 Secant Cotang. 5 581932 0149 Tang. Cos. D. 9854 31 9851 88 30 Sine 891 Deg. 88 Deg. G 74 MATHEMATICAL TABLES. 1 Deg. Sine D. TABLE V.-LOG. SINES, ETC. Cosec. Tang. D. Cot. Sec. D. Cos. 21 Deg. 8. II* 8. II* 10'00 9'99 58 535523 6106 6158 59 539186 20542819 I 546422 2549995 3553539 1 30 417919 31422717 32 427462 7909 7823 33 432156 34 436800 7740 35441394 36445941 37 450440 38 454893 I 39459301 40463665 41 467985 42 472263 43 476498 44 480693 45 484848 46 | 488963 47 493040 I 48 497078 49 501080 50 505045 51 508974 52 512867 53 516726 54 520551 55 524343 56 528102 I 57 531828 7996 8002 7914 7828 7745 7657 7663 7577 7499 7422 7346 7583 7273 7200 7129 7505 7428 7352 7279 7206 582081 418068 577283 422869 572538 427618 567844 432315 567685 0159 563200 436962 558606 441560 554059 446110 549560 450613 549387 0173 9827 545107 455070 544930 01776 540699 459481 536335 463849 532015 468172 581932 0149 6 9851 577131 0152 6 9848 572382 0156 6 9844 2 2 2 30 29 28 6 9841 27 563038 0162 558440 0166 69838 26 6/9834 25 553890 0169 6 9831 24 6 23 9823 88 22 540519 0180 536151 0184 6 9820 21 7060 7135 7066 531828 0188 6 9812 6 9816 20 19 6991 6924 6931 6859 6865 6794 6731 6801 6738 527737 472454 523502 476693 519307 580892 519108 01996 515152 585050 511037 589170 506960 593250 527546 0191 6 6998 523307 0195 6 9809 18 9805 17 9801 16 514950 0203 9797 15 7 510830 0207 9793 14 506750 0210 7 9790 88 13 7 6669 6608 6548 6489 6432 6375 6319 6264 6211 502922 597293 6676 498920 501298 494955 505267 491026 509200 502707 0214 9786 12 6615 498702 0218 7 9782 ΓΙ 7 6555 6496 6439 6382 6326 6272 494733 0222 9778 10 490800 0226 9774 7 6055 6004 5 560540 4 557054 5811 5955 5906 5858 460814 539447 6062 457181 543084 6012 453578 546691 450005 550268 446461 553817 464477 535779 6113 486902 0231 487133 513098| 483274 516961 479449 520790 475657 524586 475414 0243 9757 471898 528349 6218 471651 0247 9753 468172 532080 6165 467920 0252 7 9769 483039 0235 7 9765 479210 0239 7 7 7 9761 88 98 76 54 7 9748 3 464221 0256 9740 460553 0260 7 7 9744 2 I 456916 0265 7 9735 88 O 5962 453309 0269 7 9731 59 449732 0274 9726 58 442946 557336 5914 5866 5765 439460 560828 5819 446183 0278 442664 0283 439172 0287 8 9722 57 N 6 563999 7 567431 8 570836 9 574214 5773 ∞ ∞ 9717 8 56 8 9713 87 55 436001 564291 5719 5674 5630 10 577566 5587 II 580892 12 584193 13 587469 14 590721 15 593948 432569 567727 429164 571137 425786 574520 422434 577877 5544 5552 419108 581208 5502 5510 415807 584514 5460 5468 412531 587795 5419 4427 409279 591051 5379 5387 406052 594283 Cos. D. Sec. Cot. D. 5727 5682 5638 435709 0292 432273 0296 428863 0301 8 9708 54 9704 53 9699 52 5595 425480 0306 422123 031I 9694 51 9689 50 418792 0315 9685 415486 0320 9680 8 412205 0325 9675 47 8 408949 0330 9670 49 48 88 Deg. 46 405717 0335 9665 87 45 Tang. Cos. D. Sine 87 Deg. MATHEMATICAL TABLES. 75 21 Deg. Sine D. 8. Cosco. Tang. D. TABLE V.-LOG. SINES, ETC. Cot. Sec. ID. Cos. 3 Deg. II' 8. 1 I' 10'00 9'99 215 593948| 16 597152 17 600332 18 603489 19 606623 20 609734 21 612823 22 615891 23 618937 2 24 621962 25624965 26 627948 27 630911 28 633854 29 636776 30 639680 31 642563 32 645428 2 33 648274 34 651102 35 653911 36 656702 37 659475 38 662230 39 664968 40 667689 41 670393 2 42. 673080 43 675751 44 678405 45 681043 46 683665 47 686272 48 688863 49 691438 50 693998 2 51 696543 52699073 53 701589 54 704090 55 706577 56 709049 57 711507 58 713952 59 716383 60 718800 5339 5300 5261 5223 5186 406052 594283 402848 597492 399668 600677 396511 603839 393377 606978 390266 610094 5347 5308 405717 0335 402508 0340 399323 0345 5270 ∞ ∞ ∞ 8 9665 8 9660 なま 45 44 8 9655 43 5232 396161 0350 9650 42 8 393022 0355 9645 41 5194 5149 387177 613189 5158 389906 0360 9 9640 40 5112 5076 5041 384109 616262 381063 619313 5121 386811 0365 9635 39 5085 383738 0371 9629 38 380687 0376 5050 9624 87 37 9 5006 4972 4938 4904 4871 4839 4806 4775 4743 378038622343 375035 625352 372052 628340 369089 631308 366146 634256| 363224 637184 360320 640093 357437 642982 354572 645853 377657 0381 9619 36 5015 4981 4947 4913 4880 4848 4816 4784 4753 374648 0386 9614 371660 0392 9608 9 368692 0397 9603 9 365744 0403 9597 9 362816 0408 9592 9 359907 0414 9586 9 357018 0419 9 9 9 35 9 34 33 32 31 30 9581 29 351726 648704 4712 4682 4652 4622 4592 4563 4535 4506 4479 445I Cos. D. 872 Deg. 348898 651537 346089 654352 343298 657149 340525 659928 337770 662689 335032 665433 332311 668160 329607 670870 326920 673563 324249 676239 4424 321595 678900 4397 318957 681544 4370 316335 684172 4344 313728 686784 4318 311137 689381 4292 308562 691963 4267 306002 694529 4242 303457 697081 4217 300927 699617 4192 298411 702139 4168 295910 704646 4144 293423 707140 4121 290951 709618 4097 288493 712083 4074 286048 714534 4051 283617 716972 4029 281200 719396 Sec. Cot. D. 4722 4691 348463 0436 354147 0425 9575 87 28 351296 0430 86∞ 9570 27 9564 26 4661 345648 0442 9558 25 4631 342851 0447 9553 24 IO 46c2 I 4573 I 4544 4517 4488 4461 4434 4407 4380 4354 4328 4303 4277 4252 4228 4203 4179 321100 0494 318456 0500 9500 315828 0507 9493 313216 0513 9487 310619 0519 3080370525 ΙΟ IO ΙΟ IO IO 340072 0453 9547 337311 0459 334567 0465 9535 331840 0471 .9529 329130 0476 952487 19 326437 0482 9518 323761 0488 9512 23 954I 22 21 10 20 IO 18 17 9506 16 15 14 13 ΙΟ 9481 12 IO 9475 II ΙΟ 305471 0531 9469 87 10 302919 0537 9463 300383 0544 9456 297861 0550 9450 4062 4040 295354 0557 9443 4155 292860 0563 9437 4132 |290382 0569 9431 4108 287917 0576 9424 4085 285466 0582 IO II II II II II II II 98 76 4 3 283028 0589 II II 9418 9411 2 I 280604 0596 9404 87 O Tang. Cos. D. Sine 87 Deg. 76 MATHEMATICAL TABLES. о 3 Deg. Sine D. 8. TABLE V.-LOG. SINES, ETC. Cosec. Tang. D. Cot. 32 Deg. Sec. D. Cos. I I' 8. II' 10.00 9'99 3 0 718800 6 7735354 8737667 I 721204 2 723595 3725972 4728337 5 730688 733027 3877 4006 3984 281200 719396 278796 721806 4017 3995 276405 724204 3962 280604 0596 9404 870 278194 0602 3941 3919 3898 3857 274028 726588 271663 728959 269312 731317 3930 266973 733663 264646 735996 3974 3952 275796 0609 9391 273412 0616 9384 II II II 9398 59 58 II 57 3909 271041 0622 268683 0629 9378 56 II 266337 0636 3889 II 11 9371 55 9364 12 54 3 9 739969 10 742259 262333 738317 3836 260031 740626 3816 3868 3848 264004 0643 261683 0650 9357 12 53 9350 86 12 52 3827 259374 0657 9343 12 51 II 744536 3796 257741 742922 3756 12 746802 3776 255464 745207 3807 257078 0664 9336 12 50 253198 747479 3787 254793 0671 9329 16 13 749055 3737 14751297 3749 248703 751989 3717 15 753528 246472 754227 3698 755747 3678 244253 756453 17 757955 3661 242045 758668 250945 749740 3768 252521 0678 12 49 9322 48 12 250260 0685 9315 12 47 248011 0692 9308 3729 12 46 3710 245773 0699 9301 45 3692 243547 0706 9294 3673 241332 0714 9286 86 43 12 12 12 44 3 18 760151 19 762337 20 764511 21 766675 22768828 23 770970 24 77310I 25 775223 26 777333 3 27 779434 3642 3624 239849 760872 237663 763065 3655 3606 3588 3570 3553 3535 3518 3501 235489 765246 233325 767417 231172 769578 229030 771727| 3636 239128 0721 236935 0728 12 9279 9272 42 3618 234754 0735 9265 3600 3583 3484 3467 3451 3418 3354 3323 3308 D. 28 781524 29 783605 30 785675 31 787736 3434 32 789787 33 791828 3402 3386 34 793859 35 795881 3370 3 36 797894 37 799897 3339 38 801892 39 803876 40 805852 3293 3278 41 807819 42 809777 43 811726 3249 44 813667 3234 45 815599 3219 Cos. 87 Deg. 186333 814589 3248 184401 816529 3233 Sec. Cot. D. Tang. 224777 775995 222667 778114 220566 780222 226899 773866 3565 3548 3531 3514 218476| 782320| 3497 217680 0795 216395 784408 214325 786486 212264 788554 3447 210213 790613 208172 792662 3415 206141 794701 204119 796731 202106 798752 200103 800763 198108 802765 3337 196124 804758 3322 194148 806742 3307 192181 808717 3263 190223 810683 188274 812641 12 12 232583 0743 9257 12 230422 0750 9250 13 228273 0758 9242 226134 0765 13 9235 13 224005 0773 9227 35 13 221886 0780 9220 86 34 13 219778 0788 9212 13 4I 40 ww 39 38 37 36 333 33 3480 3464 9205 343 I 3399 3383 3368 215592 0803 213514 0811 9189 13 211446 0819 209387 0826 9174 207338 0834 13 9197 13 33 3 32 31 30 9181 29 13 28 13 9166 27 205299 0842 203269 0850 13 9158 26 13 9150 86 25 13 201248 0858 3352 9142 24 199237 0866 13 9134 23 197235 0874 13 9126 22 195242 0882 13 9118 21 3292 3277 3262 13 193258 0890 9110 20 13 191283 0898 9102 13 189317 0906 9094 14 187359 0914 9086 14 185411 0923 9077 14 183471 0931 9069 86 15 Cos. D. Sine 19 18 17 16 861 Deg. MATHEMATICAL TABLES. 77 3 Deg. Sine 8. D. Cosec.❘ Tang. TABLE V.—LOG. SINES, ETC. Sec. D. Cos. 4 Deg D. Cot. II' 8. I I' 10'00 9.99 3 45 815599 46 817522 47 819436 48 821343 3177 3205 3191 49 823240 50 825130 51 827011 52 828884 53 830749 3 54 832607 55 834456 56836297 57 838130 58 839956 59 841774 3163 3149 3135 3122 3108 3095 184401 816529 182478 818461 180564 820384 178657 822298 176760 824205 174870 826103 3219 183471 0931 9069 15 3205 3191 181539 0939 179616 0947 14 14 9061 14 9053 13 3177 3163 3150 171116 829874 169251 831748 172989 827992 3136 172008 0981 9019 14 177702 0956 9044 175795 0964 9036 173897 0973 12 14 I I 14 14 9027 10 9 3123 3108 3082 3069 3056 167393 833613 165544 835471 163703 837321 161870 839163 3096 3083 3070 3043 3057 160044 840998 3030 158226 842825 3045 40843585 3017 I 845387 3005 2 847183 2992 156415 844644 154613 846455 152817 848260 2980 3032 3019 3007 170126 0990 14 168252 0998 14 166387 1007 8993 14 164529 1016 162679 1024 160837 1033 159002 1042 157175 1050 155356 1059 153545 1068 151740 1077 9010 9002 86 14 In4m2 = 0 G8 76 HH ++ 8984 14 8976 14 8967 5 15 8958 15 8950 15 15 8941 86 8932 59 15 8923 58 2995 15 4321 o non 0 4 3 3 848971 2967 4 5 850751 852525 6 854291 2943 7 856049 8 857801 9859546 10 861283 II 863014 4 12 864738 2955 2931 2919 2908 2896 2884 2873 151029 850057 149249851846 147475 853628 145709 855403 143951857171 142199 858932 140454 860686 138717 862433 136986 864173 2970 2958 149943 1086 2982 148154 1095 146372 1104 8914 15 15 2861 14 23 13 866455 2850 868165 15 869868 16 871565 2817 17 873255 18 874938 19 876615 20 878285 4 21 879949 22 881607 883258 24 884903 25 886542 26 888174 27 889801 28 891421 29 893035 30 894643 Cos. 2839 2828 2806 2795 2783 2773 135262 865906 133545 867632 131835 869351 130132 871064 128435 872770 126745 874469 125062 876162 123385 877849 121715 879529 120051 881202 2763 2946 2935 860686 2923 2911 2900 2888 2877 2866 2854 144597 1113 8887 142829 1122 141068 1131 139314 1140 15 15 15 15 137567 1149 8851 135827 1159 15 15 15 1 in 5 in 10 10 10 in 5 8905 8896 10 10 10 57 56 55 54 8878 53 8869 52 8860 51 50 8841 85 49 2843 2832 134094 1168 132368 1177 130649 1187 16 128936 1196 127230| 1205 8832 48 15 566 H H 16 8823 47 8813 46 16 8804 45 8795 16 44 2821 2811 2800 2789 2779 125531 1215 8785 16 123838 1224 8776 16 43 122151 1234 8766 16 42 41 16 120471| 1243 8757 85 40 2752 2742 2731 2721 2711 110199 891112 2700 108579 892742 2690 106965 894366 2680 105357 895984 D. Sec. Cot. D. 118393 882869 116742 884530 115097 886185 113458 887833 2737 111826 889476 118798 1253 117131 1262 2768 2758 2747 16 8747 39 8738 16 2727 2717 2707 2697 115470 1272 113815 1282 112167 1292 110524 1301 8699 108888 131I 8689 16 8728 8718 98 76 m co m m 38 37 36 16 8708 16 16 16 107258 1321 8679 6 I 105634 1331 8669 31 17 104016 1341 8659 85 30 Tang. Cos. D. Sine 35 34 33 32 861 Deg. 85 Deg. 78 MATHEMATICAL TABLES. 4 Deg. O Sine 8. TABLE V.-LOG. SINES, ETC. D. Cosec. Tang. 51 Deg. D. Cot. Sec. D. Cos. II' 8. I I' 9'99 4 30 894643 31 896246 32 897842 33 899432 34 901017 2631 35 902596 2670 2660 2651 2641 105357 895984 103754 897596 102158 899203 100568 900803 2687 104016 1341 8659 17 2677 2667 102404 135I 100797 1361 8649 097404 903987 2622 098983 902398 2648 2658 099197 1371 2638 097602 1381 8619 096013 139F 17 17 17 8629 8639 M2 2 2 2 30 29 28 27 26 860 17 8609 25 36 904169 2612 37 905736 38 907297 4 39 908853 40 910404 41 911949 42 913488 43 915022 44 916550 45 918073 46 919591 47 921103 4 48 922610 49 924112 50 925609 51 927100 52 928587 53 930068 54 931544 55 933015 092703 908719 094264 907147 2620 092853 1411 2603 2629 095831 905570 |094430 1401 8599 17 24 17 8589 23 2610 091281 1422 8578 85 22 17 2593 17 2584 2575 2566 2556 2547 2538 2529 2520 2512 2503 2494 2486 2477 2469 2460 2452 2435 2427 56 934481 2443 065519 936093 2461 091147 910285 089596 911846 088051 913401 086512 914951 084978 916495 083450 918034 081927 919568 080409 921096 078897 922619 077390 924136 075888 925649 074391 927156 072900 928658 071413 930155 069932 931647 068456 933134 066985 934616 2601 2583 2592 086599 1452 089715 1432 088154 1442 8558 8568 21 17 20 17 8548 19 2574 2565 085049 1463 8537 083505 1473 17 18 17 8527 17 2556 081966 1484 080432 1494 8506 17 18 8516 16 98 76 2547 2538 2530 2521 2512 2503 2495 2486 2478 2470 078904 1505 8495 077381 1515 8485 85 13 18 18 18 15 14 1590 5 2411 2403 2394 2387 2379 2371 059704 941952 058262 943404 056826 944852 055394 946295) 053966 947734 052544 949168 2363 063907 1612 8388 85 4 57 935942 064058 937565 062435 1623 8377 062602 939032 18 58 937398 060968 1634 59 938850 2419 061150 940494 059506 1645 o 940296 1941738 2 943174 3 944606 4 946034 5 947456 075864 1526 8474 18 0743511536 8464 18 072844 1547 8453 18 071342 1558 8442 18 069845 1569 8431 18 068353 1579 8421 18 066866 18 18 12 II ΙΟ 8410 065384 1601 8399 2453 2445 2437 2430 2421 2413 18 8366 987654 3 2 2 18 18 8355 I 058048 1656 8344 8 о 056596 1667 19 8333 59 19 055148 1678 8322 58 2405 053705 1689 19 8311 57 2397 19 052266 1700 5 6 948874 7950287 8 951696 9 953100 10 954499 II 955894 12 957284 13 958670 14 960052 15 961429 051126 950597 049713 952021 048304 953441 046900 954856 045501 956267 044106 957674 2335 042716 959075 041330 960473 039948 961866 038571 963255 2355 2348 2340 2332 2325 2317 2310 2302 2295 Cos. D. Sec. Cot. D. Tang. Cos. D. Sine 2329 2321 2314 2390 050832 1711 2382 049403 1723 2374 2366047979 1734 046559 1745 2358 045144 1757 2351 043733 1768 2344 042326 1780 040925 1791 039527 1803 038134 1814 036745 1826 8174 84 45 8300 56 19 8289 84 55 19 8277 54 198266 53 19 8255 52 19 8243 51 19 8232 50 19 8220 19 8209 goog 49 48 19 8197 47 19 19 8186 46 85 Deg. 84 Deg. MATHEMATICAL TABLES. 79 51 Deg. O Sine D. TABLE V.-LOG. SINES, ETC. Cosec. Tang. D. D. Cot. Sec. D. Cos. 6 Deg. 8. II' 8. II' 10'00 9'99 5 15961429 16 962801 17 964170 18 965534 19 966893 20 968249 21 969600 22 970947 23 972289 5 24 973628 25 974962 26 976293 27 977619 28 978941 29 980259 30 981573 2183 31 982883 32 984189 5 33985491 34 986789 35 988083 36 989374 37 990660 38991943 39 993222 40 994497 41 995768 5 42 997036 43 998299 44 999560 45 000816 46 002069 47 003318 48 004563 49005805 2064 50 007044 5 51008278 52 009510 53 010737 54 011962 55 013182 56 014400 57 015613 58 016824 59 018031 60 019235 2288 038571963255 036745 1826 037199 964639 2280 2273 2266 2259 2252 2245 2238 2231 2224 2217 2210 2203 2197 2190 2307 2300 2293 2286 2279 2271 2265 2257 2251 2244 2237 2230 2223 035361 1837 2217 2210 2204 035830 966019 033981 1849 8151 034466 967394 032606 1861 033107 968766 031234 1872 8128 031751 970133 029867 1884 8116 030400 971496 028504 1896 8104 029053 972855 027145 1908 8092 027711 974209 025791 1920 8080 84 37 026372 975560 025038 976906 |023094| 1944 8056 023707 978248 022381 979586 021059 980921 019741 982251 018427 983577 017117 984899 19 198163 8174 45 44 43 19 20 20 20 20 20 20 8139 42 41 40 39 38 024440 1932 8068 20 36 35 021752 1956 8044 020414 1968 8032 019079 1980 8020 017749 1992 8008 016423 2004 20 20 20 20 34 33 32 3I 20 7996 30 2177 015811 986217 2197 015101 2016 7984 013783 2028 20 29 20 2170 2163 2157 2150 2144 2191 20 7972 84 28 014509 987532 2131 2125 2119 2112 2106 013211 988842 011917 990149 010626 991451 009340 992750 2138 008057 994045 006778 995337 005503 996624 004232 997908 002964 999188 001701 000465 2100 2184 012468 2041 7959 27 2178 011158 2053 20 7947 26 20 009851 2065 7935 25 2171 2127 008549 2078 2165 |007250 209o 7910 2158 005955 2103 7897 2152 004663 2115 7885 2146 003376 2128 7872 20 2140 002092 2140 7860 84 19 2134 000812 2153 7847 21 7922 24 21 21 21 21 21 21 21 23 22 21 18 2094 2070 2058 2052 2046 204.0 2034 2029 2023 2017 2012 2006 Cos. D. 842 Deg. 000440 001738 999184 003007 2088 997931 004272 2082 996682 005534 2076 995437 006792 994195 008047 992956 009298 991722 010546 990490 011790 989263 013031 988038 014268 986818 015502| 985600 016732 984387 017959 983176 019183 981969 020403 980765 021620 Sec. Cot. D. 2121 2115 9995352165 7835 998262 2178 17 21 7822 16 2109 2103 996993 2191 995728 2203 21 7809 15 21 7797 14 2097 2091 2085 994466 2216 7784 993208 2229 21 13 21 991953 2242 990702 2255 2080 21 7771 7758 12 II 21 7745 84 10 21 2074 2068 2062 2056 2051 989454 2268 988210 2281 7732 21 7719 96 8 2045 2040 986969 2294 985732 2307 984498 2320 983268 2333 982041 2346 22 21 7706 7 21 22 7693 6 7680 5 22 7667 4 7654 3 2033 2028 980817 2359 7641 979597 2372 22 22 22 2 7628 978380 2386 7614 84 Tang. Cos. D. Sine 84 Deg. 80 MATHEMATICAL TABLES. 6 Deg. Sine O D. 62 Deg. TABLE V.-LOG. SINES, ETC. Cosec. Tang. D. Cot. Sec. D. Cos. 9° ΙΟ 9° IO* 10'00 9'99 6 ΙΙ 0 019235 I 020435 2021632 3022825 4024016 51025203 6 026386 7027567 8 028744 6 9029918 10 031089 II 032257 12 033421 13 034582 14 035741 15 036896 16 038048 17 039197 6 18 040342 2000 1995 1989 1984 1978 1973 1967 1962 1957 1951 1946 1941 1936 1930 1925 1920 1915 1910 1905 980765 021620 979565 022834 978368 024044 977175 025251 2006 975984026455 974797 027655 973614 028852 972433 030046 2023 2017 2011 2000 971256 031237 968763 2493 970082 032425 967575 2507 968911 033609 |966391|2520 967743 034791 966579 035969 965418 037144 964259 038316| 963104 039485 961952 040651 960803 041813 1995 1990 1985 1979 1974 1969 978380 2386 7614 977166 2399 7601 975956 2412 7588 974749 2426 7574 973545 2439 7561 972345 2453 7547 971148 2466 7534 23 969954 2480 60 22 22 59 58 22 2.2 57 56 76 22 22 55 54 7520 53 23 23 33 7507 83 52 7493 51 1964 1958 1953 19 041485 1899 20042625 1895 959658 042973 957027 2631 958515 044130 21 043762 22 044895 1884 955105 047582 1908 952418 2687 23046026 1879 953974 048727 957375 045284 954716 2659 956238 046434 1889 1948 1943 1938 1933 1928 1923 1918 1913 23 965209 2534 7466 23 964031 2548 7452 23 962856 2561 7439 23 961684 2575 7425 23 960515 2589 959349 2603 958187 2617 אא 23 7480 50 49 48 47 46 7411 45 23 7397 44 23 7383 83 43 23 7369 42 955870 2645 23 7355 41 23 7341 953566 2673 23 7327¹ 24 7313 1903 24 047154 1875 25 048279 1870 26 049400 1865 1889 6 27 050519 1860 949481053277 1884 28 051635 1855 29 052749 1850 30 053859 1845 31 054966 1841 32 056071 1836 33 057172 1831 34 058271 35 059367 1822 952846 049869 1898 950131 2715 7285 951721 051008 1893 950600 052144 24 951273 2701 7299 24 24 948992 2729 947856 2743 7271 24 24 7257183 34 946723 2758 7242 948365054407 947251 055535 946141 056659 945034 057781 943929 058900 942828 060016 1879 1874 945593 2772 944465 2786 24 24 7228 wwwwwwww £ £ £ 40 1870 1865 942219 2815 943341 280124 7199 7214 31 24 1827 941729 061130 1855 7170 1860 941100 2830 939984 2844 7185 24 24 24 1851 940633 062240 938870 2859 1846 937760 2873 7156 7141 24 7127 83 25 2 HO 9∞ 765 332 222 30 29 28 27 26 24 6 36 060460 37 061551 38 0626391808 39 063724 1804 40 064806 41 065885 42 066962 1817 1813 938449 064453 939540 063348 1842 936652 2888 7112 24 1799 1794 43 068036 1786 44 069107 45 070176 Cos. 84 Deg. 1781 1790 937361 065556 934444 2917 1833 936276 066655 1828 933345 2932 25 935194 067752 932248 2947 7053 1824 25 934115 068846 1819 931154 2961 7039 25 933038 069938 930062 2976 1815 25 931964 071027 1810 928973 2991 930893 0721131806 927887 3006 929824 073197 926803 3021 1837 935547 2902 24 7098 23 24 7083 22 25 7068 21 20 19 7024 18 7009 17 25 6994 16 25 6979 83 15 98 765 D. Sec. Cot. D. Tang. Cos. D. Sine 831 Deg. MATHEMATICAL TABLES. 81 62 Deg. • Sine D. TABLE V.-LOG. SINES, ETC. Cosec. Tang. D. Cot. Sec. D. Cos. 7 Deg. IO' 9' 7 6 45 070176 46 071242 47 072306 48 073366 49 074424] 50 075480 51 076533 52 077583 53 078631 6 54 079676 55 080719 56 081759 57 082797 58 083832 59 084864 0085894 I 086922 2087947 7 3 088970 4 089990 5 091008 6092024 7093037 8094047 9095056 10 096062 11 097065 7 12 098066 13 099065 14 100062 1777 1772 1768 1763 1759 1755 1750 9* 929824 073197 928758 074278 927694 075356 926634 076432 925576 077505 924520 078576 923467 079644 922417 080710 1746 921369 081773 10° 10.00 9'99 1802 1797 1793 926803 3021 6979 15 925722 3036 6964 25 924644 3051 6949 25 14 13 923568 3066 25 6934 12 1789 25 1784 922495 3081 6919 II 125 1780 921424 3096 920356 3111 1776 125 6889 6904 IO 9 919290 3126 1772 1742 1738 1733 1729 1725 1721 1717 1713 1709 1704 1700 1696 1692 1688 1684 1680 1676 1673 1668 1767 918227 3142 25 6858 83 7 25 6874 8 25 1665 1661 1657 920324 082833 919281 083891 918241 084947 917203.086000 916168 087050 915136 088098 914106 089144 913078 090187 912053 091228 911030 092266 910010 093302 908992 094336 907976 095367 906963 096395 905953 097422 904944 098446 903938 099468 902935 100487 901934 101504 1763 917167 3157 916109 3172 6843 6 25 6828 5 1759 1755 1751 915053 3188 914000 3203 6797 25 6812 4 26 1747 1743 1738 1735 1731 2 2 26 3 26 26 26 2 2 26 26 1727 1722 2 2 2 1719 912950 3218 911902 3234 6766 910856 3249 6751 83 о 909813 3265 6735 59 908772 3280 907734 3296 6704 906698 3312 905664 3327 904633 3343 6782 2 I 6720 82 58 26 57 6688 56 26 26 6673 55 26 6657 54 1715 1711 1707 1703 1699 1695 903605 3359 664I 26 53 902578 3375 901554 3390 900532 3406 26 6625 52 6610 26 5I 26 6594 50 27 899513 3422 657882 49 898496 3438 6562 48 1691 27 15 101056 16 102048 17 103037 1653 1649 1645 900935 102519 899938 103532 898944 104542 897952 105550 896963 106556 18 104025 1642 894990 108560 895975 107559 19 105010 1638 20 105992 1634 7 21 106973 1630 1687 897481 3454 6546 47 27 1684 896468 3470 6530 46 1680 895458 3486 27 1676 894450 3502 27 6514 1672 893444 3518 27 6498 6482 22 107951 23 108927 24 109901 25110873 26 111842 27 112809 1627 1623 1619 1616 1612 1608 28 113774 1605 29 114737 30 115698 1601 Cos. D. 1669 1665 894008 109559 1661 893027 110556 892049 111551 891073 112543 890099 113533 889127 114521 888158 115507 887191 116491 886226 117472 885263 118452 884302 119429. Sec. Cot. D. 892441 3535 891440 3551 27 27 6465 6449 1658 1654 1650 1643 890441 3567 6433 82 889444 3583 888449 3600 887457 3616 1647 885479 3649 886467 3632 27 27 64.17 2 2 2 2 2 27 6400 27 27 སས 6384 6368 27 6351 wwwww.f£ £ £ £ ££ 40 39 38 37 36 98 76 35 1639 1636 1632 1629 884493 3665 883509 3682 27 882528 3698 27 6335 34 27 6318 33 6302 32 881548 3715 28 28 6285 31 880571 3731 6269 82 30 Tang. Cos. D. Sine 831 Deg. 822 Deg. 82 MATHEMATICAL TABLES. 7 Deg. Sine D. Cosec. | Tang. D. TABLE V.-LOG. SINES, ETO. Cot. Sec. D. Cos. 81 Deg. W N Hot 9 7 30 115698 31 116656 32 117613 33 118567 10° 9° 10° 10'00 9'99 1597 1594 34 119519 1583 35 120469 36 121417 37 122362 38 123306 7 39 124248 40 125187 41 126125 42 127060 43 127993 44 128925 45 129854 46 130781 47 131706 7 48 132630 49❘ 133551 50134470 51 135387 52 136303 53 137216 54 138128 55 139037 56 139944 7 57 140850 58 141754 59 142655 8 143555 I 144453 2145349 3 146243 4 147136 5 148026 884302 119429 1625 883344 120404 1622 882387 121377 1618 1590 881433 122348 1587 880481 123317 880571 3731 6269 1615 1611 879531 124284 1580 1608 879596 3748 6252 878623 3765 6235 877652 3781 876683 3798 875716 3815 28 30 28 29 28 1576 878583 125249 1604 877638 126211 874751 3832 873789 3849 1573 1601 876694 127172 872828 3866 1569 1597 2 2 2 2 2 2 2 28 28 ∞ ∞ 6219 27 6202 26 28 ∞ 28 28 ∞ 6185 25 6168 ∞ 24 28 ∞ 6151 23 28 ∞ 6134 82 22 1566 875752 128130 871870 3883 6117 21 1594 28 1562 1559 1556 874813 129087 873875 130041 872940 130994 870913 3900 1591 28 ∞ ∞ 6100 20 1587 869959 3917 6083 19 1552 1545 872007 131944 871075 132893 1549 870146 133839 1584 869006 3934 29 6066 18 96 1581 868056 3951 29 6049 17 867107 3968 29 6032 16 96 1577 866161 3985 29 6015 15 I 542 1532 1529 1525 1522 1519 1516 1512 1509 1506 869219 134784 868294 135726 1539 867370 136667 1535 866449 137605 865530 138542 864613 139476 863697 14.0409| 862784 141340 861872 142269 860963 143196 860056 144121 1574 1571 865216 4002 5998 1567 864274 4020 5980 29 29 29 14 82 13 1564 1561 863333 4037 862395 4054 5963 12 1558 861458 4072 1551 860524 4089 29 1555 859591 4106 2 2 2 2 2 29 5946 II 29 5928 ΙΟ 29 5911 5894 96 8 1548 858660 4124 29 5876 7 1545 1542 1539 855879 4177 857731 4141 856804 4159 5841 29 5859 6 29 5 29 29 582382 4 859150 145044 1503 1500 1496 1493 1490 1487 1484 1481 858246 145966 857345 146885) 856445147803 855547 148718 854651 149632) 853757 150544| 852864 151454 851974 152363 1529 1532 853115 1535 854034 4212 854956 4194 5806 1526 1523 1520 1517 1514 1511 wwwwww 853115 4229 5771 82 I 852197 4247 5753 851282 4265 5735 850368 4283 849456 4301 848546 4319 847637 4336 29 29 5788 2 3 2 29 о 30 59 30 30 30 5717 5699 58 57 30 30 5681 56 5664 81 55 76 8 6 148915 7 149802 8 150686 9151569 ΙΟ 10 152451 II 153330 12 154208 13 155083 14 155957 15 156830 Cos. 82 Deg. 1478 1475 1472 1469 1466 1463 1460 1457 1454 D. Sec. Cot. D. 851085 153269 850198 154174 849314 155077 848431 155978 847549 156877 846670 157775 845792 158671 844917 159565 1508 1505 846731 4354 5646 8458264372 5628 1502 1499 1496 1493 1490 1487 840435 4481 5519 844043 160457 843170 161347 1484 839543 4499 5501 30 30 844923 4390 5610 30 844022 4409 5591 30 843123 4427 5573 130 842225 4445 5555 30 841329 4463 5537 30 30 31 838653 4518 5482 81 45 Tang. Cos. D. Sine 54 53 52 51 50 49 48 47 46 812 Deg. MATHEMATICAL TABLES. 83 81 Deg. TABLE V.—LOG SINES, ETC. Sine D. Cosec. Tang. D. | Cot. | Sec. D.|_Cos. 9'99 9 Deg 9° 815156830 16 157700 17 158569 18 159435 19 160301 20 161164 21 162025 22 162885 23 163743 8 24 164600 25 165454 26 166307 27 167159 28 168008 29 168856 30 169702 31170547 32 171389 10' 9' IO' 10'00 1451 1448 1445 1442 1439 1436 1433 1430 1427 843170 161347 842300 162236 841431 163123 1476 840565 164008 839699 164892 838836 165774 837975 166654 837115 167532 1481 1479 1473 1470 1467 1464 1461 1458 836257 168409 831591 4666 31 5534 834226 4610 31 833346 4628 31 832468 4647 838653 4518 5482 837764 4536 836877 4554 835992 4573 31 835108 4591 45 333 31 5464 44 31 5446 43 5427 42 31 5409 41 5390 40 mmm m 5372 39 31 5353 38 81 37 835400 189284 1424 1422 1419 1416 1413 1410 1407 1405 833693 171029 832841 171899 831992 172767 831144 173634 830298 174499 829453 175362 828611 176224 834546 170157 1455 1453 1450 1447 1444 1442 1439 1436 830716 4684 5316 829843 4703 5297 828971 4722 5278 828101 4740 827233 4759 5241 826366 4778 5222 825501 4797 824638 4816 31 36 31 31 31 31 32 32 32 32 35 34 5260 33 32 823776 4835 5165 1402 1433 32 2 2 2 2 2 31 5203 30 5184 29 81 28 8 33 172230 34 173070| 35 173908 36 174744 37 175578 38 176411 39 177242 40 178072 41 178900 8 42 179726 43 180551 44 181374 45 182196 46 183016 47 183834 48 184651 49 185466 50 186280 1399 1396 1394 1391 1388 1386 1383 1380 1377 1369 1366 1364 1361 1359 1356 8 51 187092 52 187903 53 188712 54 189519 55 190325 56 191130 57 191933 58 192734 59 193534 60 194332 1353 1351 1348 1346 827770 177084 826930 177942 826092 178799 825256 179655 824422 180508 823589 181360 1420 822758 182211 821928 183059 821100 183907 820274 184752 1374 819449 185597 1372 818626 186439 817804 187280 816984 188120 816166 188958 815349 189794 814534 190629 813720 191462 812908 192294 812097 193124 811288193953 810481 194780| 1431 1428 1425 1423 1417 822916 4854 5146 32 822058 4873 5127 32 821201 4892 32 820345 4911 5089 32 819492 4930 5070 818640 4949 27 26 5108 25 24 23 32 5051 22 817789 4968 32 5032 21 1415 1412 1409 1407 1404 1402 1399 1396 32 816941 4987 5013 32 816093 5007 4993 32 815248 5026 4974 32 814403 5045 4955 32 813561 5065 4935 32 812720 5084 4916 33 811880 5104 20 81 19 18 17 16 15 1393 1391 1389 1343 1341 1338 1336 1333 1330 808870 196430 808067 197253 1371 1369 807266 198074 806466 198894 805668 199713 1386 1384 1381 1379 1376 1374 33 809371 5162 4838 33 808538 5182 4818 81 10 33 807706 5202 4798 33 806876 5221 4779 33 806047 5241 4759 805220 5261 33 809675 195606 804394 5281 33 811042 5123 810206 5143 4857 4896 33 4877 14 13 33 12 II 4739 4719 1366 1364 33 803570 5300 4700 33 802747 5320 4680 801926 5340 33 4660 801106 5360 33 4640 800287 5380 33 4620 81 98 76 54 3 2 I Cos. D. Sec. Cot. D. Tang. Cos. D. Sine 81 Deg. 81 Deg. 84 MATHEMATICAL TABLES. 9 Deg. TABLE V.-LOG. SINES, ETC. • Sine D. Cosec. Tang. | D. Cot. 93 Deg. Sec. D. Cos. 9° 10* 9° 1328 1326 1323 1321 90 194332 805668 199713 10* 10.00 9'99 6 9 9 201451 1306 IO 202234 II 203017 12 203797 I304 1299 1294 1280 1278 1275 1273 1271 1268 1264 1259 1257 1255 1253 1250 14205354 15 206131 16 206906 1292 1289 793094 212611 17 207679 1287 792321 213405 9 18 208452 791548 214198 1285 19 209222 1282 790778 214989 20 209992 21 210760 22 211526 23212291 24213055 25 213818 26 214579 1266 9 27 215338. 28 216097 29 216854 30 217609 31 218363 32 219116 33 219868 I 195129 804871 200529 2195925 804075 201345 3 196719 803281 202159 4197511 802489 202971 1318 5 198302 801698 203782 1316 199091 800909 204592 1313 800121 205400 7 199879 8200666 1311 1308 799334 206207 798549 207013 797766| 207817 796983 208619 1301 796203209420 13204577 1296 795423 210220 794646 211018 1361 1359 1356 800287 5380 4620 60 1354 1352 1349 33 33 797841 5440 4560 797029 5460 34 34 796218 5481 4519 799471 5400 798655 5420 4580 33 4600 59 58 4540 1347 1345 34 795408 5501 4499 34 794600 5521 4479 34 1342 793793 5541 34 4459 80 52 1340 792987 5562 4438 1338 1335 1333 34 792183 5582 4418 791381 5603 34 790580 5623 34 4397 4377 789780 5643 34 1331 4357 793869 211815 1328 1326 788982 5664 788185 5684 34 4336 34 1324 1321 1319 34 787389 5705 4295 34 35 785802 5746 4316 45 786595 5726 4274 80 43 4254 42 1317 790008 215780 789240 216568 788474 217356 1312 787709 218142 786945 218926 786182 219710 785421 220492 784662 221272 1261 783903 222052 783146 222830! 782391 223606 781637 224382 780884 225156 785011 5767 35 4233 4.I 1315 1310 1308 1305 1303 1301 1299 784220 5788 35 783432 5809 35 782644 5829 4171 4212 35 4191 38 1297 1294 1292 1290 1246 1244 1242 1239 1237 1235 1233 1231 1228 35 221367 9 36 222115 37 222861 38 223606 39224349 40 225092 41225833 42 226573 43 22731I 772689 233586 44 228048 1226 771952 234345 45 228784 771216 235103 34 220618 1248 779382 226700 780132 225929 778633 227471 772529 6104 777885 228239 777139 229007 776394 229773 775651 230539 774908 231302 774167 232065 771761 6125 36 770993 6146 36 1273 770227 6168 3832 769461 6189 36 35 781858 5850 4150 35 781074 5871 4129 35 780290 5892 4108 35 779508 5913 4087 80 34 35 778728 5934 4066 35 777948 5955 4045 35 777170 5976 4024 35 776394 5997 4003 35 775618 6019 3981 35 1288 774844 6040 35 1286 774071 6061 1284 1281 1279 1277 1275 36 35 32 30 29 28 3960 33 M 35 136 56 26 3918 773300 6082 35 3939 27 3896 80 25 ~ ~ ~ ~ wwwwwwwwwww ✡ ‡ ‡ ‡‡££££✡ue aumen 57 56 55 54 49 48 47 46 44 40 3875 24 3854 23 22 3811 21 768698 6211 36 1271 1269 767935 6232 36 3789 20 773427 232826 1267 1265 1262 765655 6297 36 766414 6275 36 767174 6254 3768 19 3746 18 36 3725 17 764897 6319 36 3703 16 3681 80 15 98 765 Cos. D. Sec. Cot. D. Tang. Cos. D. Sine 81 Deg. 801 Deg. MATHEMATICAL TABLES. 85 9° ΙΟ 9 45 228784| 46 229518 47 230252 48 230984 49 231714 50 232444 51233172 52 233899 53 234625 9 54 235349 55 236073 56 236795 57 237515 58 238235 59 238953 100 239670 1240386 2 241101 10 3 241814 4 242526 5243237 6 243947 244656 8245363 9246069 10 246775 11 247478 10 12 248181 1224 1222 1220 1218 1216 1214 1212 1209 1207 1205 1203 1201 I 199 1197 1195 1193 1191 1189 770482 235859 769748 236614 769016 237368 768286 238120 767556 238872 766828 239622 766101 240371 765375 241118 93 Deg. Sine TABLE V.-LOG. SINES, ETC. D. Cosec. Tang. D. Cot. ୨ 10/1/2 Deg. Sec. D. Cos. 9*99 771216 235103 1260 764897 6319 3681 10° ΤΟ ΟΝ 1258 1256 1254 12:52 1250 1248 1246 764141 6340 36 36 763386 6362 3638 762632 6384 36 761880 6406 36 761128 6428 37 760378 6450 37 759629 6472 37 wwwww 3660 15 14 13 3616 12 3594 II 3572 10 764651 241865 763927 242610 1232 1230 14 249583 15 250282 16 250980 17 251677 18 252373 19 253067 20 253761 10 21 254453 22 255144 23 255834 24 256523 25 257211 26 257898 27 258583 28 259268 29 259951 30 260633 Cos. 80 Deg. 13 248883 1167 1185 1183 1181 1179 1177 1175 1173 1171 1169 757474 249264 756763 249998 756053 250730 755344 251461 754637 252191 1224 1222 1220 1218 1217 762485 244097 761765 244839 761047 245579 754421 6626 37 760330 246319 753681 6649 37 759614 247057 1228 752943 6671 3329 758899 247794 1226 752206 6693 3307 758186 248530 1187 1244 1242 1240 1238 758882 6494 37 3506 80 7 3550 3528 96 9 8 371 763205 243354 756646 6560 37 758135 6516 3484 37 757390 6538 3462 6 5 1234 37 755903 6582 1236 755161 6604 37 3440 4 3418 3 3396 2 3374 I 3351 80 o 751470 6715 3285 750736 6738 3262 750002 6760 3240 749270 6783 3217 748539 6805 38 747809 6828 753931 252920 753225 253648 752522 254374 1215 751819 255100 751117 255824 1165 750417 256547 1163 1161 1159 1158 1156 1154 749718 257269 749020 257990 748323 258710 747627 259429 746933| 260146| 746239 260863 1213 121 I 1209 1207 1205 1203 1201 1200 747080 6851 746352 6873 745626 6896 744900 6919 744176 6941 38 745547 261578 744856 262292 744166| 263005 1152 1150 1148 736283 7194 743477 263717 1146 742789 264428 1144 742102 265138 1142 741417 265847 1141 740732 266555 1139 740049 267261 1137 739367 267967 D. Sec. Cot. D. 1198 1196 1194 1192 1190 1189 1187 1185 1183 1181 1179 1178 1176 743453 6964 742731 6987 38 742010 70IO 741290 7033 740571 7056 7398547079 739137 7102 38 38 ∞ ∞ ∞ ∞ ∞ ∞ MM MM MM MM M 3 3 3 m m M 37 37 37 37 37 59 79 58 57 56 37 55 54 38 3195 53 38 3172 52 38 3149 51 38 3127 50 38 3104 79 49 3081 48 383059 47 3036 46 3013 45 382990 44 2967 43 ∞ ∞ ∞0 MM M 38 2944 42 38 2921 4I 38 2898 79 40 738422 7125 38 737708 7148 736995 7171 391 735572 7217 39 734862 7241 2759 39 ww www W 38 ∞ ∞ 2875 39 2852 38 2829 39 37 2806 36 2783 35 34 734153 7264 2736 39 733445 7287 2713 39 732739 7310 2690 39 732033 7334 2666 79 30 Tang. Cos. D. Sine 33 32 31 791 Deg. 86 MATHEMATICAL TABLES. 10 Deg. Sine TABLE V.-LOG. SINES, ETC. 11 Deg. D. | Cosec. Tang. D. Cot. Sec. ID. Cos. 9' IO' 9* 10° 10'00 9'99 1135 1133 1131 1130 1128 1126 1124 1122 II20 1119 1117 1115 1113 IIII IIIO 1108 1106 1105 1103 4 283190 5 283836 II 1084 1082 1081 1079 1077 1076 1074 6284480 1072 7 285124 1071 8 285766 714234 294017 1069 9286408 713592 294684 1067 10 287048 1066 712952 295349 11 287687 712313 296013 1064 12 288326 711674 296677 1063 13 288964 711036 297339 1061 14 289600 710400 298001 1059 15290236 709764 298662 Cos. D. Sec. Cot. 38 266051 10 39 266723 733277 274269 40 267395 732605 274964 41 268065 731935 275658 42268734 731266 276351 43 269402 730598 277043 44 270069 729931 277734 45 270735 729265 278424 46271400 728600 279113 47 272064 727936 279801 10 48 272726 727274 280488 726612 281174 49 273388 ΙΙΟΙ 50 274049 725951 281858 718142 7810 40 1099 51 274708 725292 282542 1098 52 275367 724633 283225 1096 53 276024 723976 283907 1094 54 276681 723319 284588 1092 55277337 722663 285268 1091 56 277991 722009 285947 1089 10 57 278644 721356 286624 1087 58 279297 1086 720703 287301 59 279948 720052 287977 11 0 280599 719401 288652 I 281248 |718752 289326| 2 281897 718103 289999 3282544 |717456 290671 10 30 260633 739367 267967 39 31 261314 738686 268671 731329 7357 2643 39 32 261994 738006 269375 730625 7381 2619 39 33262673 737327 270077 729923 7404 2596 39 34 263351 736649 270779 2572 729221 7428 39 35 264027 735973 271479 728521 7451 2549 39 36 264703 735297 272178 727822 7475 2525 39 37 265377 734623 2728761162 727124 7499 2501 II74 1172 1170 1169 1167 1165 1164 733949 273573 1160 726427 7522 2478 79 22 732033 7334 2666 30 29 28 27 26 25 24 23 39 40 1158 1157. 1155 725731 7546 1153 1151 1150 1148 1147 1145 1143 1141 1140 1138 1136 2454 40 725036 7570 2430 20 140 |724342 7594 2406 723649 7618 2382 722957 7641 2359 722266 7665 2335 721576 7689 2311 720887 7713 2287 40 720199 7737 2263 79 13 21 b ‡ ‡ ‡ ÷ ÷ ÷ 19 40 18 40 17 40 16 40 15 40 14 40 719512 7761 718826 7786 2239 12 40 2214 II 2190 ΙΟ 717458 7834 716775 7858 2142 716093 7883 2117 1135 1133 1131 1130 1128 1126 1125 1123 716810 291342 716164 292013| 715520 292682 714876 293350 I 122 II20 1118 1117 710001 8103 709329 8127 1873 57 708658 8152 707987 8177 1823 78 55 1115 1114 II 12 IIII 1109 1107 1106 1104 1103 ΙΙΟΙ 701999 8401 1599 79 Deg. 42 42 42 42 42 42 47 $6 701338 8426 1574 78 45 D. Tang. Cos. D. Sine 707318 8201 1799 54 706650 8226 705983 8251 705316 8276 704651 8301 40 40 40 41 715412 7907 2093 41 714732 7931 2069 41 714053 7956 2044 79 4 4I 713376 7980 41 712699 8004 1996 41 712023 8029 41 711348 8053 141 710674 8078 1922 41 41 4.I 41 4I 2166 98 76 in t 5 2020 1971 1947 79 321 3 2 I O 1897 59 58 1848 56 41 1774 53 42 1749 52 42 1724 51 1699 50 1674 703987 8326 1649 703323 8351 1624 702661 8376 49 48 782 Deg. MATHEMATICAL TABLES. 87 111 Deg. Sine D. TABLE V.-LOG. SINES, ETC. Cosec. Tang. D. Cot. Sec. D. Cos. 12 Deg. ŷ' IO* 1058 9 709764 298662 10* ΙΟΟΟ 9'99 1056 1054 1053 1051 1050 1048 1046 1045 1043 1042 1040 1039 1037 1036 1034 1031 ΙΙ 1029 1028 1026 1025 1023 1022 1020 1019 1017 698486 310398 697868 311042 697252 311685 696636 312327 696021 312967 695407 313608 694793 314247 1064 694181 314885 693570 315523 1061 1014 1013 ΙΟΙΙ ΙΟΙΟ 1008 1007 11 15 290236 701338 8426 1574 42 16 290870 709130 299322 700678 8451 1549 42 17 291504 708496 299980 700020 8476 1524 42 18 292137 707863 300638 699362 8502 1498 42 19 292768 707232 301295 698705 8527 1473 42 20 293399 706601 301951 698049 8552 1448 42 21294029 705971 302607 697393 8578 1422 42 22 294658 705342 303261| 696739 8603 1397 42 23295286 |704714 303914 696086 8628 1372 43 II 24 295913 704087 304567 1086 695433 8654 1346 43 25 296539 703461 305218 694782 8679 1321 1084 43 26 297164 702836 305869 694131 8705 1083 43 27 297788 702212 306519. 1081 693481 8730 1270 43 28 298412 701588 307168) 692832 8756 1244 143 29 299034 700966 307815 692185 8782 43 30 299655 700345 308463 691537 8807 1193 143 31 300276 699724 309109 690891 8833 1167 1032 699105 309754 1074 1075 143 32 300895 II 33 301514 34 302132 35 302748 36 303364 37 303979 38 304593 39 305207 40 305819 41 306430 II 42 307041 1016 692959 316159 1060 43 307650 692350 316795 45 1100 44 1098 1096 43 42 1095 1093 1092 1090 4I 40 39 38 1089 1087 78 37 36 35 1295 34 33 32 1080 1078 1218 31 30 1077 29 143 1073 1070 1071 688315 8936 143 690246 8859 1141 78 28 689602 8885 1115 688958 8910 27 43 1090 26 1064 25 1068 687673 8962 143 1038 24 1067 1065 687033 8988 686392 9014 143 IO12 23 43 0986 22 685753 9040 43 0960 21 685115 9066 1062 143 0934 20 684477 9092 0908 78 19 44 44 683841 9118 0882 18 1058 683205 9145 44 0855 17 44 308259 45 308867 46 309474 47 310080 48 310685 49 311289 1005 688107 321222 1048 50311893 1004 691741 317430 691133 318064 690526 318697 689920 319329 689315 319961 688711 320592 682570 9171 44 0829 16 1057 1055 1054 1053 1051 1050 681936 9197 44 0803 15 44 681303 9223 0777 44 680671 9250 0750 44 680039 9276 0724 44 679408 9303 06971 14 13 12 I I 678778 9329 44 0671 78 10 44 II 51 312495 52 313097 53 313698 54 314297 55 314897 56 315495 57 316092 58 316689 59 317284 1003 ΙΟΟΙ IOOO 998 997 996 994 993 60 317879 687505 321851 686903 322479 686302 323106 685703 323733 685103 324358 684505 324983 683908 325607 683311 326231 682716 326853 991 682121 327475 1047 678149 9356 0644 677521 9382 [44] 0618 1045 1044 1043 1041 1040 1039 1037 1036 44 676894 9409 0591 44 676267 9435 0565 44 675642 9462 0538 44 675017 9489 0511 45 674393 9515 0485 45 673769 9542 45 673147 9569 98 765+ 4 3 0458 0431 2 I 145 672525 9596 0404 78 O Cos. D. Sec. Cot. D. Tang. Cos. D. Sine 78 Deg. 78 Deg. 88 MATHEMATICAL TABLES. 12 Deg. 122 Deg. TABLE V.-LOG. SINES, ETC. Sine D. Cosec. Tang. D. Cot. Sec. D. Cos. 9°3 12 0 17879 990 988 986 984 983 982 980 10.6 9° 82121 327474 I 18473 81527 328095 2 19066 80934 328715 987 3 19658 80344 329334 420249 79751 329953 520840 79160 330570 78570 331187 1026 621430 7 22019 77981 331803 8 22607 77393 332418 IO* ΙΟ 1035 1033 1032 1030 1029 1028 1025 979 1024 12 923194 10 23780 II 24366 976 76806 333033 977 12 24950 13 25534 972 14 26117 970 15 26700 969 16 27281 968 17 27862 12 18 28442 1929021 20 29599 21 30176 22 30753 23 31329 24 31903 25 32478 26 33051 12 27 33624 975 76220 333646 75634 334259. 1021 1023 666354 09866 45 9'9 672526 09596 90404 45 671905 09622 90378 59 145 671285 09649 90351 45 670666 09676 90324 45 670047 09703 90297 45 669430 09730 90270 668813 09757 145 90243 45 668197 09785 90215 45 667582 09812 90188 77 52 45 666967 09839 60 90161 90134 1020 665741 09893 45 973 75050 334871 74466 335482 73883 336093 73300 336702 1017 1019 664518 09948 665129 09921 90079 46 90107 ུ༦ལྦུ༦པཉྩ་ 58 57 56 55 54 53 51 50 49 46 48 1016 72719| 337311 966 666aa 965 964 962 961 72138 337919 71558 338527 70979 339133 70401 339739 1012 1015 662689 10030 1013 662081 10058 663907 09975 90025 663298 10003 4690052 47 46 46 46 89997 45 46 89970 44 46 89942 77 43 IOII 661473 10085 89915 660867 10113 46 42 69824 340344| 659656 10168 960 958 957 956 69247 340948| 68671 341552 68097 342155 67522 342757 66949 343358 ΙΟΙΟ 1008 1007 1006 660261 10140 46 89887 4.I 46 89860 40 659052 10196 46 89832 39 1004 658448 10223 46 89804 38 1003 1002 954 1000 657845 10251 657243 10279 656642 10307 46 89777 37 89749 47 47 89721 36 35 28 34195 29 34766 30 35337 31 35906 3236475 3337043 34 37610 35 38176 12 36 38742 37 39306 38 39871 39 40434 40 40996 41 41558 42 42119 43 42679 44 43239 45 43797 953 952 950 949 948 946 66376 343958 65805 344558 65234 345157 64663 345755 998 64094 346353 996 654843 10391 89609 997 654245 10418 656042 10335 89665 999 655442 10363 147 89637 47 89693 77 34 33 32 47 31 63525 346949 994 62957 347545 993 945 62390 348141 944 992 651859 10531 653647 10447 653051 10475 89525 652455 10503 89497 47 47 47 89553 89582 30 29 28 47 27 47 61824 348735 943 990 991 651265 10559 47 89469 26 47 89441 77 25 941 940 939 937 936 935 934 932 931 61258 349329 60694 349922 60129 350514 59566 351106 986 59004 351697 58442 352287 57881 352876 988 987 985 983 982 57321 353465 981 Cos. D. 56761 354053 56203 354640 Sec. Cot. 980 979 650671 10587 89413 650078 10616 47 89384 47 649486 10644 89356 47 648894 10672 89328 47 648303 10700 89300 47 647713 10729 89271 47 89243 647124 10757 646535 10786 645947 10814 645360 10843 D. Tang. Cos. D. 24 23 22 21 20 19 18 47 47 89186 47 89214 17 16 89157 77 15 Sine 78 Deg. 771 Deg. MATHEMATICAL TABLES. 89 12 Deg. o Sine 9° 10° 12 45 | 343797 46 344355 47 344912 48 345469 49 346024 50 346579 51 | 347134 52 347687 53 348240 930 929 927 926 D. Cosec. Tang. D. Cot 9° 656203 354640 655645 355227 655088 355813 654531 356398 TABLE V.-LOG. SINES, ETC. 132 Deg. Sec. D. Cos. 10* ΙΟΟΙ 9.98 977 976 975 653976 356982 974 645360 0843 9157 644773 0872 644187 0900 643602 0929 15 47 48 9100 48 9128 14 13 925 653421 357566 973 643018 0958 642434 0986 48 9071 12 48 9042 II 924 652866 358149 971 922 921 652313 358731 651760 359313 970 641851 1015 8985 48 9014 IO 969 920 968 641269 1044 640687 1073 48 48 8956 96 8 48 8927 77 7 12 54 348792 651208 359893 919 55 349343 56 349893 57 350443 58 350992 59 351540 13 0352088| I 352635 2 353181 13 3 353726 4 354271 5 354815 6 355358 7 355901 8356443 9 356984 650657 360474 967 640107 1102 8898 6 917 916 650107 361053 966 649557 361632 965 915 649008 362210 963 639526 1131 638947 1160 48 638368 1189 48 8869 5 78 8840 4 8811 914 648460 362787 962 913 961 637790 1218 8782 6372131247 8753 3 49 2 911 910 647912 363364 647365 363940 646819 364515 49 49 909 66a 960 959 958 908 907 905 904 903 902 901 10 357524 II 358064 899 644099 367382 953 643557 367953 643016 368524 642476 369094 646274 365090 645729 365664 645185 366237 955 644642 366810 957 954 952 951 898 641936 369663 13 12 358603 | 897 | 640859| 370799 639785 371933 892 891 890 889 888 638713 373064 638178 373629 637644 374193 637111 374756 939 887 885 883 634454 377563 633925 378122 932 633396 378681 931 632869 379239 930 877 Cos. D. 641397 370232 13 359141 896 640322 371367 14 359678 895 15 360215 893 | 639248| 372499|| 16360752 17 361287 18 361822 19 362356 20 362889 13 21 363422 22 363954 636578 375319 636046 375881 23.364485 635515 376442 24 365016 634984 377003 25 365546 26 366075 27 366604 28 367131 884 882 881 880 879 29 367659 632341 379797 30 368185 771 Deg. 631815 380354) 929 Sec. Cot. D. Tang. Cos. D. Sine 950 949 948 634910 1364 8636 634336 1393 8607 633763 1422 8578 633190 1452 8548 632618 1481 8519 632047 1511 8489 631476 1540 8460 630906 1570 8430 630337 1599 49 8401 636636 1276 8724 77 0 49 8695 636060 1305 59 635485 1334 I 49 8666 149 76 58 57 49 49 49 49 49 49 49 56 55 54 53 52 51 50 946 629768 1629 49 8371 76 49 48 945 49 629201 1658 8342 47 944 628633 1688 628067 1718 50 49 8312 46 8282 45 943 942 941 940 938 50 627501 1748 8252 626936 1777 50 626371 1807 625807 1837 625244 1867 44 10 10 10 50 8223 50 8193 43 42 8163 41 50 8133 76 40 50 937 624681 1897 624119 1927 8103 39 50 935 934 933 623558 1957 622997 1987 8013 150 8073 38 96 8043 37 50 36 622437 2017 621878 2047 150 621319 2078 50 7983 35 7953 34 50 7922 33 928 620761 2108 620203 2138 50 619646 2168 50 50 7892 32 7862 31 7832 76 30 76 Deg. H 90 MATHEMATICAL TABLES. 13 Deg. Sine 9° TABLE V.-LOG. SINES, ETC. D. Cosec. | Tang. | D. Cot. 10° 141 Deg. Sec. D. Cos. 10° ΙΟΟΙ 9.98 876 875 874 873 871 13 30 368185 31 368711 32 369236 33 369761 34 370285 872 35 370808 36 371330 870 37 371852 869 38 372373 867 13 39 372894 866 40 373414 865 41 373933 864 42 374452 863 43 374970 862 44 375487 624513 388084 45376003 623997 388631 861 860 9* 631815 380354 631289 380910 630764 381466| 630239 382020 629715 382575 629192 383129 628148 384234 628670 383682 627627 384786 920 927 926 925 924 923 617425 2290 51 619646 2168 619090 2199 7801 618534 2229 617980 2260 7832 922 921 919 616871 2321 7679 616318 2351 615766 2382 615214 2412 627106 385337 626067 386438 626586 385888 625548 386987 625030 387536 918 614663 2443 614112 2474 917 915 914 913 912 856 852 46 376519 859 47 377035 858 13 48 377549 857 621937 390815 622451 390270 49 378063 50 378577 854 620911 391903 621423 391360 51379089 853 620399 392447 622965 389724 911 910 909 613562 2504 7496 613013 2535 7465 612464 2566 51 7434 51 611916 2597 7403 52 611369 2623 7372 52 610822 2659 623481 389178 LA LA LA Ln in in in in in 20 in in 51 29 51 7771 2 28 3000 51 7740 27 7710 26 51 25 51 7649 24 51 7618 23 51 7588 76 22 51 7557 21 51 7526 20 51 19 51 18 96 17 16 15 908 907 906 851 850 618866 394073 52 379601 53 380113 54 380624 619376 393531 606469.2908 905 619887 392989 904 848 845 1384182 2 384687 3 385192 843 842 841 5 386201 839 14 9 388210 6386704 838 7387207 837 612291 401058 8 387709 836 611790 401591 835 611289 402124 613296 399990 615313 397846| 614808 398383 601617 3191 6809 4385697 840 613799 399455 614303 398919 55 381134 849 618357 394614 52 605927 2939 7061 56 381643 605386 2970 7030 76 4 13 57 382152 847 617339 395694 617848 395154 604846 3002 6998 58382661 846 616832 396233 59 383168 140 383675 844 615818 397309 604306 3033 603767 3064 616325 396771 603229 3096 903 902 901 900 899 610276 2690 52 7310 76 13 52 609730 2721 7279 52 609185 2752 7248 52 608640 2783 7217 52 608097 2814 7186 52 607553 2845 7155 52 607011 2876 7124 52 7341 14 12 II IO 7092 52 52 52 898 897 52 52 6967 6936 896 896 12 389711 13 390210 14 390708 15 391206 833 831 832 609790 403718 885 830 609292 404249 608794 404778 53 53 601081 3222 53 600545 3254 53 600010 3286 612793 400524 599476 3317 598942 3349 53 598409 3381 10 388711 597876 3413 834 53 II 389211 610789 402656 597344 3445 610289 403187 596813 3477 53 6491 596282 3509 53 595751 3541 6459 53 6427 75 45 595222 3573 895 602691 3127 602154 3159 6904 76 0 52 6873 53 6841 59 58 57 894 6778 56 892 893 6746 75 55 6714 54 891 53 6683 53 890 889 888 887 886 53 6651 52 6619 5I 53 6587 6555 153 6523 49 48 47 884 883 a∞ to int mano ao non mi to go to 9 8 7 6 5 3 2 I 50 46 Cos. D. Sec. Cot. D. Tang. Cos. D. Sine / 761 Deg. 75 Deg. MATHEMATICAL TABLES. 91 15 Deg. 141 Deg. Sine TABLE V.-LOG. SINES, ETO. D. Cosec. Tang. D. Cot. Sec. D. Cos. 10* IO* ΙΟΟΙ 9° 9* 9'98 14 15 391206 828 16391703 17 392199 826 18 392695 827 825 19 393191 824 20 393685 21 394179 22 394673 23395166 608794 404778 608297 405308 607801 405836 607305 406364 606809 406892 882 881 880 879 878 823 606315 407419 877 595222 3573 6427 594692 3605 6395 594164 3637 6363 593636 3669 6331 593108 3701 6299 54 6266 592581 3734 45 53 44 53 43 54 4.2 54 822 605821 407945 876 592055 3766 54 6234 605327 408471 821 820 604834 408997 875 874 591529 3798 5910033831 54 6202 54 6169 75 37 54 14 24 395658 819 25 396150 26 396641 817 814 813 14 33 400062 34 400549 810 35401035) 36 401520 808 37402005] 807 38402489 39402972 40403455 41 403938 ∞ ∞ ∞ 00 00 00 00 ∞ ∞ 811 27 397132 817 28 397621 816 29 398111 30 398600 31 399088 600912 413179 32 399575 812 600425 413699 599938 414219 865 604342j 409521 603850 410045 818 603359 410569 602868 411092 874 873 872 602379 411615 871 590479 3863 589955 3896 589431 3928 54 588908 3961 6137 54 6104 54 6072 wwwwww B B 41 40 6039 33 870 588385 3993 54 6007 32 868 601889 412137 587863 4026 5974 815 601400 412658 869 54 31 867 866 54 587342 4058 5942 54 586821 4091 55 5863014124 5876 55 585781 4157 5843 30 5909 29 75 28 809 806 598965 415257 864 598480 415775 597995 416293 597511 416810 597028 417326 864 599451 414738 5852624189 5811 55 55 584743 4222 5778 2277 26 25 55 863 584225 4255 5745 24 862 583707 4288 55 5712 23 861 805 860 804 596545 417842 596062 418358 583190 4321 5679 582674 4354 5646 582158 4387 55 22 55 21 803 00 00 859 858 581642 4420 5580 75 19 14 42 404420 802 801 800 799 798 797 796 795 794 794 793 791 790 789 788 787 786 595580 418873 43404901 595099 419387 594618 419901 44 405382 45 405862 594138 420415 46406341 593659 420927 47 406820 593180 421440 48 407299 592701 421952 49 407777 592223422463 50 408254 14 51 408731 52 409207 53 409682 54 410157 55 410632 56 411106 57 411579 58 412052 59 4125241 60 412996 857 581127 4453 55 55 55 5547 5613 20 18 856 855 155 580613 4486 5514 5800994520 17 55 5480 16 855 579585 4553 55 5447 15 854 853 578560 4620 579073 4586 55 5414 14 56 5380 13 852 578048 4653 56 851 591746 422974 850 но 10 10 10 577537 4686 56 5347 12 577026 4720 5280 56 5314 II 591269 423484 590793423993. 590318 424503 792 589843 425011 849 576007 4787 848 575497 4820 848 156 576516 4753 5247 75 10 156 5213 156 5180 847 574989 4854 589368 425519 588894 426027 588421 426534 574481 4887 156 56 5146 846 573973 4921 (56) 5113 845 56 5079 98765+ 4 844 573466 4955 56 5045 3 587948 427041 843 572959 4989 56 5011 2 587476 427547 572453 5022 4978 I 843 587004 428052 571948 5056 4944 75 o 56 Cos. D. Sec. Cot. D. Tang. Cos. D. Sine 75 Deg. 75 Deg. 92 MATHEMATICAL TABLES. 15 Deg. Sine TABLE V.-LOG. SINES, ETC. D. | Cosec. | Tang. | D. | Cot. 15 Deg Sec. D. Cos. 9' IO' 9° 10° ΙΟΟΙ 9'98 15 784 783 783 782 781 6 780 779 778 777 776 775 774 773 773 772 0412996 587004 428052 785 I 413467 586533 428557 2 413938 3 414408 4 414878 5415347 41581 7 416283 8 416751 15 9 417217 10 417684 11 418150 12 418615 13 419079 14 419544 15 420007 16 420470 17 420933 3/ 586062 429062 585592 429566 585122 430070 584653 430573 584185 431075 583717 431577 583249 432079 835 582783432580 582316 433080 581850 433580 00 00 00 00 00 00 00 00 00 842 571948 5056 4944 84I 571443 5090 57 4910 570938 5124 840 57 4876 www) 839 838 838 0100 00 837 836 765 570434 5158 4842 569930 5192 569427 5226 568925 5260 57 568423 5294 57 57 57 4808 57 4774 4740 4706 581385 434080 580921 434579 580456 435078 ∞ ∞ ∞ 00 00 00 834 833 832 832 831 830 770 579993 435576 579530 436073 771 579067 436570 829 828 828 564424 5568 57 563927 5603 563430 5637 58 567921 5328 4672 567420 5363 566920 5397 57 566420 5431 57 565920 5465 57 565421 5500 564922 5534 57 4466 57 57 74 52 4637 4603 4569 4535 57 4500 58 15 18 421395 769 19 421857 20 422318 767 768 21 422778 22 423238 23 423697 24 424156 25 424615 26 425073 762 15 27 425530 761 28 425987 760 29 426443 760 30 426899 31427354 32 427809 33428263 34 428717 35429170 15 36 429623 767 766 578605 437067 578143 437563 826 577682 438059 577222 438554 576762 439048 827 825 58 562933 5672 4328 58 562437 5706 4294 561941 5741 58 4432 4397 4363 74 43 45 42 41 824 765 764 763 576303 439543 575844 440036 822 575385 440529 821 574927 441022 574470 441514 574013 442006 573557 442497 818 573101 442988 823 823 560457 5845 4190 4155 58 559964 5880 4120 4259 58 561446 5776 4224 58 560952 5810 40 39 58 38 37 559471 5915 58 36 4085 820 558978 5950 158 58 ∞ ∞ 4050 74 34 819 558486 5985 557994 6019 819 759 757 572646 443479 816 572191 443968 571737 444458 756 557012 6089 817 4015 3981 58 557503 6054 3946 58 33 32 58 31 556521 6125 758 58 3911 30 8 7+7+7 77 mmmmmmmmm бо 59 58 56 55 54 51 49 48 47 46 44 58 816 556032 6160 3875 29 3840 28 755 571283 444947 815 555542 6195 59 3805 2.7 814 555053 6230 59 754 813 570830 445435 554565 6265 59 3770 26 3735 74 25 59 753 37430075 38430527 39 430978 40 | 431429 41 431879 42432329 43432778 44433226 45 433675 Cos. D. 752 752 570377 445923 569925 446411 569473 446898 812 553589 6336 59 812 554077 6300 3700 24 3664 23 811 751 569022 447384 810 553102 6371 552616 6406 59 59 3629 22 3594 21 750 568571 447870 749 568121 448356 809 749 748 567671 448841 809 552130 6442 59 551644 6477 59 3558 20 3523 19 551159 6513 808 59 3487 18 567222 449326 ·550674 6548 59 747 566774 449810 807 806 550190 6584 59 566325 450294 549706 6619 59 3381 74 15 Sec. Cot. D. Tang. Cos. D. Sine 3452 3416 17 16 98 765 75 Deg. 741 Deg. MATHEMATICAL TABLES. 93 15 Deg. O TABLE V.-LOG. SINES, ETC. Sine D. Cosec. 16 Deg. Cosec. Tang. D. Cot. Sec. ID. Cos. 9° IO' 9* IO' ΙΟ ΟΙ 9'98 46 434122 47 434569 48435016 49 435462 50 435908 51 436353 52 436798 53437242 746 15 45 433675 566325 450294 806 549706 6619 3381 15 745 744 744 565878 450777 565431 451260 805 549223 6655 59 3345 14 564984 451743 804 548740 6691 59 3309 13 743 564538 452225 803 548257 6727 59 60 3273 12 547775 6762 802 60 3238 II 564092 452706 742 802 547294 6798 563647 453187 60 3202 ΙΟ 741 546813 6834 801 563202 453668 60 3166 9 740 800 5463326870 740 562758 454148 60 3130 8 545852 6906 3094 74 7 799 60 15 54 437686 562314 454628 16 55 438129 56438572 57 439014 58 439456 59 439897 0440338 I 440778 2 441218 739 545372 6942 738 737 736 561871 455107 561428 455586 560986 456064 799 798 544893 6978 60 3058 6 603022 5 797 736 560544 456542 796 735 734 560103 457019 559662 457496 796 544414 7014 543936 7050 543458 7086 60 2986 4 733 732 559222 457973 558782 458449 795 794 793 793 60 2950 60 2914 542981 7122 2878 60 542504 7158 2842 74 0 60 542027 7195 2805 60 61 3 2 I 59 541551 7231 276973 58 6 16 3 441658 4 442096 5 442535 442973 7 443410 728 8 443847 9 444284 10 444720 726 II 445155 16 12 445590 731 558342 458925 792 731 730 729 791 790 790 789 727 788 727 788 61 557904 459400 61 557465 459875 540125 7340 2660 61 557027 460349 539651 7376 2624 61 556590 460823 539177 7413 2587 556153 461297 555716 461770 541075 7267 2733 540600 7304 2696 57 56 55 54 61 53 538703 7449 538230 7486 61 2551 52 555280 462242 554845 462714 725 61 2514 51 787 537758 7523 786 537286 7559 61 2477 50 724 723 721 720 720 719 717 715 714 713 713 712 711 Cos. D. 20449054 718 550946 466945 16 21 449485 550515 467413 22 449915 716 550085 467880 23450345 716 549655 468347 777 776 775 775 774 773 Cot. D. Tang. Cos. D. Sine 533992 7817 2183 62 533524 7854 62 533055 7891 532587 7928 532120 7965 531653 8002 24450775 549225 468814 531186 8039 25 451204 548796 469280 530720 8076 26 451632 548368 469746| 530254 8114 27 452060 547940 470211 529789 8151 28 452488 547512 470676| 529324 8188 29 452915 547085 471141 528859 8226 30 453342 546658 471605 528395 8263 Sec. 554410 463186 13 446025 553975 463658 14 446459 553541 464129 723 535871 7669 61 2331 15 446893 553107 464599 722 535401 7706 783 16 447326 552674 465069 534931 7743 17 447759 552241 465539 534461 7780 2220 782 18 448191 551809 466008 781 19448623 551377 466476| 780 61 244 73 49 785 785 536814 7596 536342 7633 66 61 2404 48 61 2367 47 784 46 61 2294 45 783 61 2257 44 62 43 42 2146 41 780 2109 73 4C 62 779 62 *2072 778 778 62 62 2035 1998 1961 333 m 38 A www B B 37 62 36 66 62 1924 35 1886 62 34 62 1849 33 1812 62 32 62 1774 31 1737 73 30 741 Deg. 731 Deg. 94 MATHEMATICAL TABLES. 16 Deg. TABLE V.-LOG. SINES, ETO. 171 Deg. Sine IO* 9° 16 30 453342 31 453768 32 454194 33 454619 34455044 35 455469 36 455893 37 456316 38 456739 710 710 709 708 D. | Cosec. | Tang. | D. 9° 546658 471605 546232 472068 545806 472532 545381 472995 544956 473457 Cot. Sec. D. Cos. 10° ΙΟΟΙ 9*98 773 772 771 771 528395 8263 1737 527932 8301 1699 527468 8338 1662 527005 8375 1625 526543 8413 62 63 63 63 26 1587 ~ N N N W 30 29 28 27 707 770 707 706 705 544531 473919 544107 474381 543684 474842 543261 475303 769 769 526081 8451 1549 525619 8488 63 63 25 768 525158 8526 63 1512 24 704 767 524697 8564 63 63 1474 23 1436 73 22 542838 475763 704 542416 476223 703 541994 476683 702 541573 477142 701 701 700 699 698 698 697 696 688 687 686 16 39 457162 40 457584 41 458006 42 458427 43 458848 541152 477601 5223998753 540732 478059 44 459268 521941 8791 63 45 459688 521483 8829 63 540312 478517 46460108 539892 478975 5210258867 1133 47 460527 520568 8905 539473 479432 16 48 460946 539054 479889 49 461364 538636 480345 50 461782 538218 480801 695 51 462199 537801 481257 695 52 462616 537384 481712 694 53 463032 536968 482167 693 54 463448 536552 482621 693 55 463864 536136 483075 692 56 464279 691 535721 483529 16 57 464694 535306 483982 690 58 465108 600 534892 484435 59 465522 534478 484887 689 17 0 465935 688 534065 485339 I 466348 533652 485791 2 466761 533239 486242 3467173 532827 486693 767 524237 8601 766 523777 8639 631 399 21 63 1361 20 765 523317 8677 765 522858 8715 63 63 1323 19 1285 18 764 63 1247 17 1209 16 763 1171 15 763 14 762 64 761 64 1095 73 13 9∞ 70 in t~ 520111 8943 64 761 1057 12 760 759 519655 8981 1019 64 519199 9019 64 II 0981 ΙΟ 759 758 518743 9058 0942 518288 9096 0904 517833 9134 64 9 8 64 0866 757 64 7 517379 9173 0827 6 757 64 756 755 516925 9211 64 516471 9250 64 0789 5 0750 73 4 516018 9288 755 515565 9327 64 0712 754 515113 9365 64 0673 753 514661 9404 64 0635 32 1 I 753 64 0596 73 0 752 514209 9442 64 0558 59 513758 9481 751 65 0519 58 513307 9520 0480 751 65 57 4 467585 5 467996 685 532415 487143 512857 9558 0442 56 685 532004 487593 750 65 512407 9597 749 65 0403 72 55 17 7468817 683 6468407 684 531593 488043 749 531183 488492 748 511957 9636 511508 9675 65 0364 54 8 469227 683 530773 488941 682 9469637 530363 489390 747 511059 9714 510610 9753 65 0286 0325 53 65 52 0247 | 10 470046 529954 489838 681 II 470455 680 529545 490286 12 470863 680 747 746 510162 9792 65 51 0208 50 746 509714 9831 65 0169 49 65 13 471271 14 471679 15 472086 679 529137 490733 528729 491180 509267 9870 745 508820 9909 65 0130 48 0091 47 744 65 678 744 Cos. D. 528321 491627 527914 492073 Sec. Cot. D. Tang. Cos. D. Sine 508373 9948 0052 46 507927 9988 001272 45 65 731 Deg. 72 Deg. MATHEMATICAL TABLES. 95 171 Deg. TABLE V.—LOG SINES, ETO. Sine D. Cosec. Tang. D. Cot. Sec. D.¦ Cos. 18 Deg. 9'4 17 15 72086 678 16 72492 17 72898 677 676 2274923 672 30 78142 667 10'5 9° 27914 492073 27508 492519 27102 492965 1873304 26696 493410 676 1973710 26290 493854 675 20 74115 25885 494299 674 21 74519 25481 494743 674 25077 495186 673 23 75327 672 24673 495630 17 24 75730 24270 496073 25 76133 671 23867 496515 737 26 76536 23464 496975 670 736 27 76938 23062 497399 669 736 28 7734.0 22660 497841 669 29 77741 668 22259 498282 735 734 21858 498722 IO* 10'0 9'9 507927 19988 80012 45 743 65 507481 20027 79973 44 743 742 741 507035 20066 506590 20105 65 740 740 740 739 738 66 66 506146 20145 79855 66 505701 20184 79816 66 505257 20224 79776 66 504814 20263 79737 66 504370 20303 79697 66 79934 79895 43 42 41 40 39 38 72 37 737 503927 20342 503485 20382 79618 66 503043 20421 66 79579 502601 20461 79539 66 502159 20501 66 79499 501718 20541 66 501278 20580 66 79658 36 35 34 33 32 79459 3I 79420 31 78542 667 21458 499163 734 665 32 78942 666 21058 499603 17 33 79342 20658 500042 733 500837 20620 79380 66 66 733 500397 499958 20700 20660 66 79340 72 79300 732 67 34 79741 35 80140 665 36 80539 663 664 40 38 81334 662 39 81731 661 82128 37 80937 663 20259 500481 19860 500920 19461 501359 19063 501797 499519 20740 79260 76 M32 2 2 2 30 29 28 27 26 18269 502672 17872 503109 661 41 82525 660 17475 503546) 731 731 730 730 729 728 728 727 67 499080 20780 79220 67 498641 20820 79180 67 498203 20860 79140 67 18666 502235 497765 20900 79100 25 24 23 22 67 497328 20941 79059 67 496891 20981 79019 67 496454 21021 78979 72 19 67 21 20 17 42 82921 43 83316 659 659 657 657 656 655 50 86075 654 1751 86467 52 86860 655 17079 503982 16684 504418 727 44 83712 16288 504854 658 45 84107 15893 505289 46 84501 47 84895 48 85289 49 85682 726 495582 21102 496018 21061 78939 18 67 78898 17 67 495146 21142 78858 16 725 67 494711 21183 78817 1.5 14318 507027 13925 507460 725 724 724 723 722 67 15499 505724 15105 506159 493841 21264 14711 506593 494276 21223 78777 14 67 78736 13 67 493407 21304 78696 12 68 492973 21345 68 78655 II 653 53 87251 54 87643 653 652 55 88034 651 651 57 88814 650 56 88424 11576 510054 489946 21630 650 649 11186 510485 58 89204 10796 510916 648 59 89593 10407 511346| 6089982 10018 511776 Cos. D. Sec. Cot. D. 722 721 721 720 719 719 718 718 717 716 492540 21385 13533 507893 492107 21426 68 13140 508326 491674 21467 12749 508759 491241 21507 68 12357 509191 490809 21548 11966 509622 490378 21589 78615 72 10 68 78574 68 78533 78493 78452 489515 21671 489084 21712 78288 68 68 68 68 68 78411 78370 78329 98 76 in + m 2 5 4 3 488654 21753 68 488224 21794 78206 72 o Tang. Cos. D. Sine 78247 I 72 Deg. 72 Deg. MATHEMATICAL TABLES. 96 5491922 6492308 645 18 8 493081 9 493466 10 493851 II 494236 12 494621 7492695 644 644 643 642 fff 508078 513921 507692 514349 507305 514777 506919 515204 18 Deg. Sine 9° 18 0 489982 I 490371 2 490759 TABLE V.-LOG. SINES, ETC. D. | Cosec. | Tang. | D. Cot. 698998 IO' 9° 510018 511776 716 509629| 512206 716 509241 512635 647 3 491147 646 508853 513064 4491535 508465 513493 646 Sec. 18 Deg. D. Cos. 10* 10°02 9'97 488224 1794 487794 1835 8165 68 68 487365 1876 715 486936 1917 8083 69 8042 714 486507 1958 714 486079 1999 69 8206 68 60 59 8124 58 57 56 69 8001 55 713 713 485651 2041 7959 69 54 712 712 485223 2082 7918 484796 2123 7877 69 53 69 71 52 642 641 506534 515631 506149 516057 505764 516484 641 505379 516910 13495005 640 14 495388 639 504995 517335 504612 517761 639 638 637 504228 518185 15 495772 16 496154 503846 518610 17 496537 503463 519034 18 18 496919 637 503081 519458 19 497301 636 502699 519882 20 497682 21 498064 635 633 632 632 28500721 18 27 500342 499658 523259 631 631 499279 523680 29 501099 37 504110 38504485 39504860 40 505234 41 505608 42 505981 625 625 624 495890 527451 495515 527868 495140 528285 479272 2665 70 70 478849 2707 7293 70 478427 2749 7251 70 478005 2791 7209 70 477583 2833 7167 70 477162 2875 7125 70 476741 2917 7083 70 476320 2959 7041 70 498901 524100 630 475900 300I 6999 30 501476 498524 524520 70 629 6957 475480 3043 31 501854 498146 524939 629 475061 3086 70 6914 32 502231 628 497769 525359 474641 3128 70 6872 698 33 502607 628 497393 525778 698 474222 3170 34 502984 497016 526197 627 697 473803 3213 35 503360 496640 526615 626 473385 3255 697 18 36 503735 626 496265 527033 696 472967 3298 483943 2206 7794 483516 2248 7752 69 483090 2289 7711 69 482665 2331 7669 69 4822392372 7628 69 481815 2414 69 481390 2456 7544 70 480966 2497 706 7503 70 480542 2539 7461 480118 2581 70 636 502318 520305 479695 2623 70 501936 520728 22 498444 634 501556 521151 23 498825 634 501175 521573 24 499204 500796 521995 25 499584 500416 522417 26 | 499963 500037 522838 484369 2165 7835 51 711 69 50 710 69 49 710 48 709 47 709 46 708 7586 708 45 44 707 71 43 706 705 705 704 703 703 703 42 7419 4.I 7377 40 7335 39 38 37 36 702 35 71 34 702 701 701 33 32 31 700 30 699 29 699 28 71 6830 27 71 6787 26 71 6745 71 25 71 6702 24 696 695 695 623 494766 528702 694 623 43 506354 622 493646 529950 44 506727 621 493273 530366 494392 529119 622 494019 529535 693 472549 3340 472132 3383 471715 3426 6574 471298 3468 6532 470881 3511 71 6660 23 71 6617 22 171 21 71 20 71 6489 19 71 693 470465 3554 6446 18 693 470050 3596 71 6404 17 692 469634 3639 45 507099 Cos. D. Sec. Cot. 492901 530781 469219 3682 6318 71 15 D. Tang. Cos. D. Sine 71 171 6361 16 72 Deg. 711 Deg. MATHEMATICAL TABLES. 97 18 Deg. Sine D. Cosec. Cosec. Tang. D. Tang. D. Cot. TABLE V.-LOG. SINES, ETC. 19 Deg. Sec. ID. Cos. 9° 10' 9* IO' 10°02 9'97 18 45 507099 620 619 619 616 46 507471 620 47 507843 48 508214 49508585 491415 532439 618 50 508956 491044 532853 618 51 509326 490674 533266 617 52 509696 616 490304 533679 688 53 510065 489935 534092 492901530781 492529 531196 492157 531611 491786 532025 691 691 690 690 467975 3811 72 469219 3682 6318 468804 3725 6275 468389 3768 15 71 14 71 6232 13 6189 12 689 689 688 467561 3854 6146 72 467147 3897 466734 3940 466321 3983 6017 72 II 6103 72 6060 ΙΟ 72 0 900 9 8 72 687 465908 4026 5974 71 7 72 55 510803 56 511172 615 615 614 613 613 612 612 611 611 18 54 510434 489566 534504 489197 534916 488828 535328 57 511540 488460 535739 685 687 465496 4070 5930 6 686 465084 4113 72 5887 5 686 464672 4156 72 5844 464261 4200 72 5800 608 605 58 511907 463850 4243 488093 536150 59512275 487725 536561 19 0 512642 487358 536972 I 513009 486991 537382 2 513375 19 3 513741 610 486259 538202 682 4 514107 485893 538611 682 609 485528 539020681 5514472 609 6 514837 608 485163 539429 681 7 515202 484798 539837 680 8 515566 607 484434 540245 680 9515930 484070 540653 607 10 516294 606 483706 541061 679 II 516657 483343 541468 72 685 684 684 683 462208 4417 486625 537792 683 463439 4286 72 463028 4330 462618 4373 72 5757 5714 5670 71 432 = O I 73 5627 59 73 5583 70 58 73 678 461798 4461 5539 73 461389 4504 73 460980 4548 5452 73 460571 4592 5408 73 460163 4635 73 459755 4679 5321 73 679 459347 4723 5277 73 458939 4767 5233 73 458532 4811 5496 56 765 in in in 57 55 54 5365 53 52 51 50 5189 70 49 73 567 19 12 517020 13 517382 14 517745 15 518107 16 518468 17 518829 482980 541875 605 604 604 603 603 602 601 601 600 600 599 599 598 598 18 519190 19 519551 20 519911 19 21 520271 479729 545524 454476 5252 22 520631 479369 545928 23520990 479010 546331 24521349 478651 546735 25 521707 478293 547138 674 482618 542281 677 482255 542688 677 457312 4943 5057 73 481893 543094 456906 4987 676 481532 543499 676 456501 5031 481171 543905 456095 5075 675 480810 544310 455690 5120 675 480449 544715 674 480089 545119 458125 4855 678 5145 48 73 457719 4899 5101 47 73 46 5013 45 73 4969 74 4925 74 4880 455285 5164 4836 454881 5208 74 41 74 4792 70 40 74 4748 673 741 673 454072 5297 4703 597 596 596 595 Cos. D. 74 74 452862 5430 4570 74 26 522066 477934 547540 671 452460 5475 4525 74 27 522424 477576 547943 452057 5519 670 74 28 522781 477219 548345 451655 5564 670 74 29523138 476862 548747 451253 5609 669 74 30.523495 476505 549149 450851 5653 4347 70 30 672 672 453669 5341 4659 453265 5386 74 4614 wwww . # £ £ £ 44 43 42 39 38 37 36 35 671 34 4481 33 4436 32 4391 31 Sec. Cot. D. Tang. Cos. D. Sine 711 Deg. 704 Deg. 98 MATHEMATICAL TABLES. 19 Deg. TABLE V.-LOG. SINES, ETO. 201 Deg. Sine D. Cosec. Tang. | D. Cot. Sec. D. Cos. 9° 10* 9° 10° 10.02 9'97 19 30 523495 31523852 32 524208 33 524564 34 524920 35 525275 36 525630 37 525984 38526339 595 594 594 593 593 592 591 591 590 590 476505 549149 669 476148 549550 668 475792 549951 668 475436 550352 475080 550752 474725 551152 666 474370551552 666 474016 551952 473661 552351 665 473307 552750 589 589 588 588 587 587 586 471190 555139 662 470839 555536 586 470487 555933 661 585 49 530215 50 530565 51 5309151 52 531265 53 531614 54 531963 55 532312 56 532661 585 584 470136 556329 660 469785 556725 660 469435 557121 450851 5653 4347 75 450450 5698 4302 75 450049 5743 4257 75 449648 5788 667 4212 175 449248 5833 4167 75 448848 5878 4122 75 448448 5923 4077 75 448048 5968 4032 75 447649 6013 3987 75 19 39 526693 447250 6058 665 3942 75 40 527046 472954 553149 664 446851 6103 3897 41 527400 75 472600 553548 446452 6148 664 75 42 527753 472247 553946 446054 6193 3807 663 43 528105 471895 554344 445656 6239 663 44 528458 471542 554741 662 445259 6284 45 528810 444861 6329 3671 46 529161 47 529513 19 48 529864 30 29 28 27 667 26 25 24 665 23 70 22 21 20 3852 19 18 86 75 3761 17 75 3716 16 176 661 444464 6375 444067 6420 76 15 66 77 76 76 3625 3580 70 13 14 584 469085 557517 442483 6602 659 443671 6465 3535 76 443275 6511 3489 442879 6556 12 II 76 76 3444 IO 583 468735 557913 582 582 581 467339 559491 581 468037 558702 441298 6739 467688 559097 657 442087 6648 468386 558308 441692 6693 659 76 3398 659 76 3352 658 76 3307 658 440903 6785 76 657 580 466991 559885 580 I | 534399 465601 561459) 2534745 465255 561851 579 578 577 577 577 576 3 535092 464908 562244 4 535438 464562 562636 5535783 576 464217 563028 653 19 57 533009 440115 6876 76 58 533357 466643 560279 656 439721 6922 3078 76 59 533704 466296 560673 4393276968 77 200534052 465948 561066 2986 70 ° 438934 7014 77 438541 7060 2940 77 440509 6831 76 3169 70 4 76 3261 3215 656 3124 655 3032 655 654 59 653 653 437756 7152 437364 7198 436972 7245 654 438149 7106 2894 58 77 2848 57 77 2802 56 77 2755 69 55 a∞ not mano ao noin 9 8 7 6 5 3 2 I 575 574 574 573 573 7 536474 463526 563811 20 6536129 463871 563419 436581 7291 77 652 2709 54 8 536818 463182 564202 9 537163 462837564592 652 436189 7337 77 2663 53 651 435798 7383 77 2617 52 462493 564983 572 572 461806 565763 571 571 10 537507 11 537851 12 538194 13 538538 14 538880 15 539223 Cos. D. 70 Deg. 461462 566153 649 461120 566542 460777 566932 Sec. Cot. D. 433068 7709 229169 45 Tang. Cos. D. Sine 69 Deg. 4354087430 435017 7476 462149 565373 434627 7522 177 651 2570 51 77 650 2524 50 77 650 2478 49 649 78 433847 7615 77 434237 7569 2431 48 649 2385 78 433458 7662 78 2338 47 46 MATHEMATICAL TABLES. 99 201 Deg. TABLE V.-LOG. SINES, ETO. 21 Deg. Sine D. Cosec. Tang. D. | Cot. Sec. D. Cos. 9° 10° 10° 10.02 9° 9'97 2015 539223 565 570 570 569 569 460777 566932 433068 7709 16 539565 460435 567320 648 17 539907 460093 567709 18 540249 459751 568098 21 541272 22 541613 *9 540590 568 459410 568486 646 20 540931 568 459069 568873 646 458728 569261 567 567 458387.569648 23 541953 566 458047 570035 645 644 566 457707 570422 20 24542293 25 542632 457368 570809 2291 648 647 647 432680 7755 432291 7802 431902 7849 178 45 78 78 645 645 431514 7895 431127 7942 430739 7989 430352 8036 178 429965 8083 429578 8130 78 78 78 178 644 565 564 26 542971 27 543310 456690 571581 457029 571195 643 564 563 563 562 28 543649 456351 571967 643 429191 8177 1823 428805 8224 428419 8271 78 78 78 00 00 00 00 00 00 00 00 ∞ ∞ ∞ 2245 44 2198 43 2151 42 2105 41 2058 40 2011 39 1964 78 1917 69 37 1870 38 36 35 1776 34 1729 33 30 544325 455675 572738| 29 543987 456013 572352 642 427648 8365 1635 642 428033 8318 79 1682 32 79 427262 8412 79 1588 31 544663 455337 573123 642 641 426877 8460 79 1540 32 545000 20 33 545338 561 454662 573892 34 545674 35 546011 562 455000573507 64.I 426493 8507 79 1493 69 28 MMN 2 31 30 29 79 426108 8554 1446 27 640 559 559 558 558 557 38 547019 452981 575810 39547354 452646 576193 40 547689 41 548024 561 560 453989 574660 36 546347 560 453653 575044 37 546683 453317 575427 454326 574276 640 425724 79 8602 1398 26 639 425340 8649 79 1351 25 639 424956 8697 79 1303 24 639 424573 8744 79 1256 23 638 424190 8792 79 1208 22 638 423807 8839 79 1161 21 452311 576576 637 451976 576958 637 423424 8887 423042 8934 80 79 1113 20 79 1066 69 19 20 42 548359 43 548693 44 549027 451641 577341 557 636 422659 8982 1018 18 556 556 555 555 554 554 553 553 552 552 552 551 551 550 550 451307 577723 450973 578104 45 549360 450640 578486 46 549693 450307 578867 47 550026 449974 579248 48 550359 449641 579629 449308 580009 49 550692 50 551024 448976 580389 636 636 635 422277 9030 80 421896 9078 421514 9126 ∞ ∞ ∞ 80 80 ∞ 80 635 634 634 634 633 421133 9173 420752 9221 420371 9269 419991 9317 419611 9365 ∞ 80 ∞ ∞ ∞ ∞ 80 O O O O O 0970 17 0922 16 0874 15 0827 14 0779 13 80 0731 12 80 0683 II 80 0635 69 10 549 549 Cos. D. 20 51 551356 448644 580769| 52 551687 448313 581149 53 552018 447982 581528 54552349 447651 581907 55 552680 447320 582286 56 553010 446990 582665 57 553341 446659 583043 58 553670 446330 583422 446000 583800 59 554000 60 554329 445671 584177 Sec. Cot. D. Tang. Cos. D. Sine 633 632 632 632 631 631 630 630 629 419231 9414 418851 9462 418472 9510 418093 9558 417714 9606 417335 9655 416957 9703 416578 9751 416200 9800 415823 9848 0586 80 80 80 81 81 O O O O ∞∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 0538 80 0490 0442 80 0394 0345 0297 0249 98 76543 N 2 81 0200 I 81 0152 69 o 69 Deg. 69 Deg. Uorm 100 MATHEMATICAL TABLES. 21 Deg. 21 Deg. TABLE V.-LOG. SINES, ETC. Sine D. Cosec.] Tang. D. Cot. Sec. D. Cos. 10* ΙΟ Ο 9'5 10'4 9* 9'9 548 548 547 547 546 44357 585686 627 21 545 545 544 544 543 543 543 542 542 54I 54I 540 540 539 539 957280 42720 587566 628 2154329 45671 584177 415823 29848 I 54658 45342 584555 41544529897 254987 45013 584932 628 415068 29945 81 70055 3 55315 44685 585309 414691 29994 70006 4 55643 414314 30043 69957 5❘ 55971 413938 30091 44029 586062 546 627 6 56299 43701 586439 627 7 56626 43374 586815 626 8 56953 43047:587190 626 629 629 81 70152 81 70103 60 59 58 57 81 56 69909 413561 30140 69860 413185 30189 ∞ ∞ ∞ 81 81 81 81 81 55 54: 69811 53 412810 30238 69762 68 52 538 537 537 536 536 37532 593542 536 535 535 534 534 533 533 532 532 531 531 531 530 530 529 43 528 528 28 63433 495344 31223 29 63755 36245 595027 404973 31272 30 64075 35925 595398 404602 31322 31 64396 35604 595768 404232 31372 32 64716 35284 596138 403862 31422 33 65036 34964 596508 616 403492 31472 34 65356 34644 596878 35 65676 34324 597247 21 36 65995 34005 597616 37 66314 33686 597985 3866632 33368 598354 39 66951 33049 598722 40 67269 41 67587 32413 599459 42 67904 32096 599827 529 68222 613 31778 600194 612 44 68539 31461| 600562 399438 32023 612 45 68856 31144 600929 399071 32073 10 57606 42394 587941 11 57932 42068 588316 12 58258 41742 588691 13 58583 41417 589066 14 58909 41091 589440 15 59234 40766 589814 16 59558 40442 590188 17 59883 40117 590562 21 18 60207 39793 590935 409065 30728 69272 19 60531 39469 591308 408692 30777 69223 20 60855 39145 591681 21 61178 538 22 61501 23 61824 24 62146 25 62468 26 62790 21 27 63112 625 412434 30286 69714 51 81 412059 30335 69665 50 625 81 625 411684 30384 82 69616 49 411309 30433 69567 48 624 82 624 410934 30482 69518 47 82 410560 30531 69469 46 623 82 410186 30580 69420 45 623 82 623 409812 30630 69370 44 82 622 622 622 621 409438 30679 69321 68 43 33 82 42 618 618 37210 593914 406086 31123 83 36888 594285 36567 594656 618 617 617 617 616 620 40 39 38 408319 30827 69173 38822 592054 621 407946 30876 38499 592426 407574 30925 82 38176 592798 407202 30975 69025 37854 593171 406829 31024 68976 406458 3107483 68877 68 34 68926 35 620 619 619 82 82 37 36 82 82 82 82 69124 69075 + + mm mm m 4I 98 765+ 405715 31173 83 68777 68827 33 .∞ ∞ ∞ ∞ ∞ ∞ 183 68728 321 333 32 31 83 68678 30 83 68628 29 83 68578 28 83 616 615 615 615 403122 31521 402753 31571 402384 31621 402015 31671 68528 83 68479 27 83 83 68429 68 25 765 2 2 2 26 68379 24 83 8368329 23 401646 31722 68278 22 614 83 401278 31772 68228 21 614 84 32731 599091 613 400909 31822 68178 20 84 613 400541 31872 400173 31922 399806 31973 68128 19 84 68078 18 84 68027 17 84 16 97977 84 67927 68 15 98 765 Cos. D. Sec. Cot. D. Tang. Cos. D. Sine 681 Deg. 69 Deg. MATHEMATICAL TABLES. 101 50 570435 51 570751 52 571066 53 571380 2r 54 571695 55 572009 56 572323 57 572636 58 572950 59 573263 22573575 I 573888 2 574200 525 525 524 524 48 569804 526 430196 602029 49 570120 526 429880 602395 610 429565 602761 429249 603127 428934 603493 428620 603858 O 21 Deg. Sine 9* TABLE V.—LOG. SINES, ETC. 22 Deg. D. | Cosec. | Tang. | D. | Cot. | Sec. [D.| Cos. | 528 IO' 9° 21 45 568856| 431144 600929 611 46 569172 430828 601296 47 569488 430512 601662 527 527 ΙΟ 10.03 9'96 398704 2124 611 399071 2073 7927 84 15 7876 14 611 3983382174 7826 84 13 84 610 397971 2225 610 397605 2275 7725 3972392326 7775 12 84 II 84 7674 IO 609 609 396873 2376 7624 396507 2427 7573 396142 2478 84 84 84 609 85 7522 68 7 523 523 523 428305 604223 608 427991 604588 427677 604953 427364 605317 608 522 607 427050 605682 522 521 521 520 426737 606046 426425 606410 426112 606773 606 425800 607137 607 395047 2630 607 394683 2681 3943182732 395777 2529 395412 2579 85 7421 7471 9876 85 85 606 393954 2783 606 393590 2834 393227 2885 392863 2936 520 605 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 5555555 in 5 7370 7319 4 3 85 7268 7217 2 I 7166 68 0 7115 7064 67 58 85 22 519 519 3 574512 425488 607500! 4574824 425176 607863 5 575136 605 392500 2987 6 518 518 517 575447 424553 608588 391775 309o 519 424864 608225 604 604 517 516 516 18 19 579470 516 515 515 514 514 513 513 513 512 512 511 511 511 510 510 509 509 509 420530 613281 20 579777 420223 613641 22 21 580085 419915 614000 22580392 419608 614359 23 580699 419301 614718 24 581005 418995 615077 25 581312 418688 615435 26 581618 418382 615793 27 581924 418076 616151 28 582229 417771 616509 29582535 417465 616867 417160 617224 30 582840 Cos. D. Sec. Cot. D. 7 575758 424242 608950 8 576069 423931 609312 9 576379 423621 609674. 10 576689 423311610036 389964 3347 II 576999 423001 610397 602 389603 3398 22 12 577309 422691 610759 602 389241 3450 13 577618 422382 611120 388880 3501 14 577927 422073 611480 601 388520 3553 15 578236 421764 611841 388159 3605 16 578545 421455 612201 387799 3656 86 17 578853 421147 612561 387439 3708 6292 86 579162 420838 612921 387079 3760 6240 86 386719 3812 6188 86 386359 3864 6136 67 40 86 386000 3915 6085 604 392137 3039 6961 391412 3141 603 391050 3192 390688 3244 603 390326 3295 603 602 601 ∞ ∞ ∞ ∞ 00 00 00 00 00 ∞ ∞ 7013 85 85 6910 85 85 6808 6859 85 86 86 6756 6705 6653 86 86 86 6602 67 6550 ེ⊕ ུསྶསྶཔºོ པུ 56 54 49 48 86 6499 47 86 6447 46 601 600 86 6395 45 6344 44 600 43 600 42 41 599 599 39 598 598 598 597 597 597 596 596 596 87 385641 3967 6033 87 385282 4019 5981 87 3849234072 5928 87 384565 4124 5876 87 384207 4176 5824 87 383849 4228 5772 87 383491 4280 5720 87 383133 4332 5668 31 87 382776 4385 5615 67 30 Tang. Cos. D. Sine 38 37 36 35 100 76 in 34 33 32 681 Deg. 67 Deg. 102 MATHEMATICAL TABLES. 22 Deg. Sine D. Cosec. Tang. | D. TABLE V.-LOG. SINES, ETC. Cot. 234 Deg. Sec. ID. Cos. 9* 22 30 582840 417160 617224 10* 9' ΙΟ 10.03 9'96 508 508 507 507 505 505 31 583145 416855 617582 32 583449 416551 617939 33 583754 416246 618295 34 584058 506 415942 618652 35 584361 415639 619008 506 36 584665 506 415335 619364 37 584968 415032 619721 38 585272 414728 620076 595 595 595 382776 4385 5615 382418 4437 5563 87 3820614489 87 30 29 594 594 381705 4542 5458 87 381348 4594 87 5511 28 27 5406 26 594 593 593 593 504 504 503 503 503 502 502 501 501 22 39 585574 414426 620432) 40 585877 414123 620787 41 586179 413821 621142 42 586482 413518 621497 43 586783 413217 621852 44 587085 412915 622207 45 587386 412614 622561 46 587688 412312 622915 47 587989 412011 623269 592 379924 4805 5195 379568 4857 3809924647 5353 88 380636 4699 5301 88 380279 4752 5248 88 87 25 24 23 67 22 88 88 5143 21 592 592 591 591 590 590 590 379213 4910 5090 378858 4963 5037 378503 5016 378148 5069 377793 5121 88 377439 5174 4826 88 377085 5227 4773 20 88 88 19 4984 18 188 88 4931 17 4879 16 15 88 14 376731 5281 589 88 4719 67 13 22 48 588289| 49 588590 50 588890 51 589190 52 589489 53 589789 54 590088 55 590387 56 590686 22 57 590984 501 411711 623623 411410 623976 376377 5334 589 4666 12 89 500 411110 624330 500 589 376024 5387 410810 624683 499 499 410511 625036 374964 5546 588 375317 5493 588 375670 5440 89 89 4613 II 4560 ΙΟ 4507 89 588 499 410211 625388 409912 625741 498 587 374612 5600 89 4454 4400 498 409613 626093 587 374259 5653 89 4347 98 76 89 409314 626445 587 373907 5706 4294 5 89 497 409016 626797 497 497 496 496 58 591282 408420 627501 59 591580 23 591878 408122 627852 408718 627149 555 586 373555 5760 4240 67 4 189 586 373203 5813 4187 586 372851 5867 89 3 4133 2 89 585 372499 5920 4080 I 89 495 495 495 494 494 I 592176 407824 628203 2592473 407527 628554 585 89 585 3 592770 407230 628905 4 593067 406933 629255 5 593363 406637 629606 585 3919 371446 6081 89 4026 67 372148 5974 371797 6028 67 ° 3972 59 584 371095 6135 89 58 3865 584 370745 6189 90 3811 57 56 23 7 593955 493 6593659 406341 629956| 493 406045 630306 583 370394 6243 90 3757 66 55 190 9 594547 493 492 492 491 491 8594251 405749 630656 405453 631005 10 594842 405158 631355 II 595137 404863 631704 00 00 00 00 00 00 10 10 10 10 10 583 370044 6296 3704 54 583 369694 6350 3650 90 53 583 582 582 491 490 12 595432 404568 632053 13 595727 404273 632401 14 596021 403979 632750 15 596315 403685 633098 582 581 581 581 369344 6404 3596 190 368995 6458 3542 90 3686456512 3488 90 368296 6566 3434 190 367947 6621 3379 190 367599 6675 3325 190 367250 6729 3271 190 190 52 51 50 49 48 47 46 Cos. D. Sec. Cot. D. 67 Deg. 366902 6783 3217 66 45 Tang. Cos. D. Sine 662 Deg. MATHEMATICAL TABLES. 103 234 Deg. 24 Deg. TABLE V.-LOG. SINES, ETO. Sine D. Cosec. | Tang. | D. | Cot. Sec. [D. Cos. 9' älú IO* 9* IO' 10.03 9'96 23 15 596315 16 596609 17 596903 18 597196 19 597490 20 597783 21 598075 22 598368 23 598660 490 489 489 489 488 403685 633098 403391 633447 403097 633795 402804 634143 580 580 580 579 579 488 579 487 578 487 578 578 366902 6783 3217 366553 6837 3163 90 366205 6892 3108 91 365857 6946 3054 365510 7001 402510 634490 402217 634838 401925 635185 401632 635532 401340 635879 487 90 45 44 43 42 23 24 598952 486 577 25 599244 26 599536 27 599827 28 600118 486 485 485 485 484 484 484 399300 638302 399010 638647 483 398720 638992 483 398430 639337 482 398140 639682 482 397850 640027 482 397561 640371 481 397272 640716 481 481 396983 641060 396695 641404 480 396406 641747 480 396118 642091 395830 642434 362389 7492 399882 637611 29 600409 399591 637956 30 600700 31 600990 32 601280 23 33 601570 34601860 35 602150 36 602439 37 602728 38 603017 39 603305 40 603594 41 603882 23 42 604170 577 577 577 576 365162 7055 2945 364815 7110 364468 7164 2836 364121 7219 363774 7273 2727 401048 636226 400756 636572 363428 7328 2672 400464 636919 363081 7383 2617 362735 7438 400173 637265 91 91 91 91 91 191 91 91 91 2999 4I 40 2890 2781 66 37 96 33 39 38 36 35 34 2562 91 33 2508 479 395543 642777 479 479 478 477 477 476 476 475 475 392678 646199 392393 646540 392108 646881 474 474 474 473 473 Cos. D. Sec. Cot. D. 662 Deg. 476 392964 645857 394108 644490 49 606179 393821 644832 50 606465 393535 645174 23 51 606751 52 607036 53 607322 54 607607 55 607892 56 608177 93 57 608461 391539 647562 567 352438 9101 93 58 608745 391255 647903 352097 9157 0843 567 94 390971 648243 59 609029 351757 9214 0786 567 194 60 609313 390687 648583 351417 9270 0730 66 O Tang. Cos. D. Sine 91 92 92 361008 7712 2288 66 28 192 360663 7767 2233 92 360318 7822 92 359973 7877 2123 92 359629 7933 2067 92 359284 7988 2012 92 358940 8043 1957 92 358596 8098 1902 92 358253 8154 1846 92 357909 8209 1791 92 357566 8265 1735 43 604457 357223 8320 44 604745 356880 8376 395255 643120 45 605032 356537 8431 478 394968 643463 46 605319 478 394681 643806 47 605606 394394 644148 48 605892 576 362044 7547 191 32 2453 31 576 575 361698 7602 2398 361353 7657 30 2343 29 575 575 574 2178 206 27 26 574 25 574 24 573 23 573 22 573 21 20 572 572 66 19 18 572 572 571 92 92 93 2 2 3 1680 17 1624 16 571 1569 15 571 570 570 570 569 555 393249 645516 569 354484 8765 93 356194 8487 1513 93 3558528542 1458 93 355510 8598 1402 93 355168 8654 1346 93 354826 8710 1290 93 14 13 12 II 66 10 1235 569 354143 8821 569 353801 8877 568 353460 8933 93 1179 93 1123 93 1067 98 76 391823 647222 568 352778 9045 568 353119 8989 93 IOII 5 193 0955 4 0899 3 2 I 66 Deg. 104 MATHEMATICAL TABLES. 242 Deg. 24 Deg. TABLE V.-LOG. SINES, ETC. Sine D. Cosec. Tang. D. | Cot. Sec. D. Coş. 9.6 240 09313 I 09597 2 09880 3 10164 410447 5 10729 6 11012 711294 8 11576 24 9 473 472 472 472 471 47I 10'3 9° 90687 648583 90403 648923 90120 649263 89836 649602 89553 649942 89271 650281 565 ΙΟ 10'0 9'9 566 351417 39270 60730 60 566 351077 39326 566 350737 39382 566 350398 39439 350058 39495 470 470 88706 650959 88424 651297 565 88988 650620 349380 39608 60392 565 349719 39552 94 94 60448 94 60505 94 60674 94 60618 94 60561 59 58 57 28 7 56 55 564 470 564 11858 469 IO 12140 II 12421 12 12702 13 12983 14 13264 469 469 468 468 467 467 17 14105 15 13545 86455 653663| 16 13825 467 86175 654000 88142 651636 87860 651974 87579 652312 87298 652650 87017 652988 563 86736 653326 563 564 563 563 562 562 466 85895 654337 562 561 24 18 14385 19 14665 20 14944 466 466 85615 654674 345663 40232 195 349041 39665 348703 39721 60279 348364 39778 60222 94 60165 348026 39835 94 347688 39891 60109 95 60052 347350 39948 195 347012 40005 59995 95 346674 40062 59938 95 346337 40118 59882 346000 40175 195 94 94 60335 54 53 65 52 94 51 50 49 48 47 46 45 95 44 59825 59768 65 43 465 85335 655011 561 85056 655348 561 561 24 26 16616 465 465 23 15781 84219 656356 464 16060 83940 656692 464 25 16338 83662 657028 464 21 15223 84777 655684 560 344316 40461 59539 22 15502 84498 656020 345326 40289 59711 344989 40346 59654 344652 40404 59596 42 95 195 95 41 40 559 463 83384 657364 559 559 28 17172 29 17450 30 17727 31 18004 32 18281 24 27 16894 463 462 59482 95 59425 195 343308 40632 59368 95 342972 40690 59310 96 342636 40747 59253 196 83106 657699 342301 40805 82828 658034 559 560 343980 40518 560 343644 40575 95 39 38 96 37 36 35 65 34 462 82550 658369. 558 462 461 461 461 460 460 4.60 4221038 43 21313 459 459 459 458 458 457 457 457 D. 33 18558 34 18834 35 19110 24 36 19386 37 19662 80062 661377 38 19938 39 20213 79787 661710 40 20488 79512 662043 41 20763 79237 662376 557 80614 660710 80338 661043 557 557 556 556 556 81719 659373 340627 41092 81442 659708 340292 41150 81166 660042 557 558 558 82273 658704 341296 40977 81996 659039 558 341966 40862 341631 40919 340961 41035 aaa a 96 96 96 96 339958 41208 80890 660376 339624 41266 966 a 96 96 96 196 666OOOOO6 59195 33 96 59138 59081 59023 58965 HO 3332 32 31 30 29 58908 28 58850 27 58792 26 5873465 25 339290 41323 338957 41381 555 555 555 554 554 554 78962 662709 78687 663042 44 21587 78413 663375 336625 41787 58213 16 4521861 78139 663707 336293 41846 58154 65 15 Cos. Sec. Cot. D. Tang. Cos. D. Sine 338623 41439 338290 41497 337957 41555 337624 41613 337291 41671 336958 41729 197 aaa aa a 96 58677 24 96 58619 23 96 58561 22 58503 21 1971 58445 20 97 197 58387 19 58329 18 58271 96 17 197 97 96 66 Deg. 651 Deg. MATHEMATICAL TABLES. 105 24 Deg. о Sine D. 9° IO' 456 456 456 455 455 455 454 454 454 453 453 453 452 452 374594 668013 452 374323 668343 I 1 626219 2626490 451 374052 668672 2445 621861 378139 663707 336293 1846 8154 46 622135 377865 664039 335961 1904 8096 47 622409 377591 664371 335629 1962 48 622682 49 622956 50 623229 51 623502 52 623774 53 624047 24 54 624319 55 624591 56 624863 57 625135 58 625406 59 625677 25 o 625948 TABLE V.-LOG. SINES, ETC. 25 Deg. Cosec. Tang. D. Cot. | Sec. D. | Cos. 9° IO' 10'04 9'95 377318 664703 335297 2021 377044 665035 334965 2079 376771 665366 334634 2137 376498 665697 334303 2196 376226 666029 333971 2254 375953 666360 333640 2313 375681 666691 375409 667021 375137 667352 374865 667682 554 553 553 553 553 552 552 552 551 97 15 14 97 8038 13 97 7979 12 97 7921 I I 97 7863 10 97 7804 97 7746 98 98 7687 65 7 987 บ 551 551 551 333309 2372 332979 2430 98 332648 2489 7511 332318 2548 98 7628 7570 6 98 550 550 550 373781 669002 550 451 45I 373510 669332 549 25 3 626760 4 627030 5 627300 6 627570 7 627840 8 628109 449 9 628378 448 10 628647 11 628916 25 12 629185 549 450 450 450 449 373240 669661 372970 669991 372700 670320 372430 670649 372160 670977. 331987 2607 7393 98 331657 2665 7335 98 331328 2724 7276 65 o 98 330998 2783 7217 98 330668 2842 7158 64 58 98 7452 5432 - O I 59 98 330339 2901 549 98 7099 57 548 330009 2960 548 329680 3019 6981 98 7040 56 98 55 371891 671306 449 371622 671634 448 447 13 629453 14 629721 15 629989 16 630257 17 630524 18 630792 19 631059 445 20 631326 445 25 21 631593 22 631859 23 632125 24 632392 25 632658 26 632923 443 27 633189 28 633454 442 29 633719 30633984 447 447 446 446 446 446 445 444 444 444 443 443 442 442 547 547 370815 672619. 327381 3434 546 370547 672947 546 327053 3494 326726 3553 370279 673274 546 370011 673602 326398 3613 546 369743 673929 326071 3673 545 369476 674257. 325743 3732 545 369208 674584 325416 3792 545 368941 674910 325090 3852 544 368674 675237 324763 3911 544 368407 675564 544 368141 675890 544 367875 676216 543 367608 676543 543 367342 676869 543 367077 677194 543 366811 677520 542 366546 677846 542 366281 678171 542 366016 678496 329023 3138 328694 3197 328366 3256 371353 671963 328037 3316 371084 672291 327709 3375 548 329351 3079 6921 99 54 6862 548 547 99 99 6803 53 52 547 99 6744 51 99 99 6625 64 49 6684 50 99 99 99 100 99 6208 6387 45 6327 44 99 6268 6506 47 99 6447 6566 48 46 43 42 6148 41 100 100 6089 64 40 324436 3971 6029 39 324110 4031 5969 38 323784 4091 5909 323457 4151 5849 323131 4211 5789 322806 4271 5729 322480 4331 5669 322154 4391 5609 321829 4452 100 100 100 100 100 100 1ΟΟ 100 100 37 36 35 34 33 32 5548 31 Cos. D. 651 Deg. Sec. Cot. D. 321504 4512 5488 64 30 Tang. Cos. D. Sine 644 Deg. I 106 MATHEMATICAL TABLES. 261 Deg. 25/ Deg. O Sine TABLE V.-LOG. SINES, ETC. D. Cosec. Tang. | D. | Cot. Sec. D. Cos. 9° ΙΟ 9* IO' 10'04 9'95 441 438 25 30 633984 366016 678496 321504 4512 31 634249 365751 678821 321179 4572 441 32 634514 365486 679146| 320854 4632 440 33 634778 365222 679471 320529 4693 440 34 635042 364958 679795 320205 4753 440 35 635306 364694 680120 439 36 635570 364430 680444 439 37 635834 364166 680768 439 38 636097 363903 681092 438 25 39 636360 438 363640 681416 539 318584 5056 40636623 363377 681740 318260 5117 539 5488 542 100 54I 54I 54I 541 540 540 540 540 5428 ΙΟΙ 5368 32 2 30 29 28 319880 4814 5186 319556 4874 5126 319232 4935 5065 318908 4995 5005 ΙΟΙ ΙΟΙ ΙΟΙ ΙΟΙ ΙΟΙ ΙΟΙ ΙΟΙ 5307 27 5247 26 25 24 23 64 22 4944 2 I ΙΟΙ 4883 20 437 437 437 437 436 436 436 435 435 435 434 434 434 41 636886 363114 682063 317937 5177 4823 539 42 637148 362852 682387 317613 5238 539 43 637411 362589 682710 538 317290 5299 44637673 362327 683033 316967 5360 45 637935 362065 683356 316644 5421 46 638197 47 638458 25 48 638720 361280 684324 315676 5604 49638981 361019 684646 315354 5665 [IOI 19 ΙΟΙ 4762 18 ΙΟΙ 538 538 100 00 00 4701 17 98 7 ΙΟΙ 4640 16 ΙΟΙ 4579 15 538 537 361803 683679 316321 5482 361542 684001 315999 5543 4457 IOI 4518 14 102 64 13 102 4396 12 537 102 433 433 433 432 432 432 431 431 431 430 430 430 537 50 639242 360758 684968 315032 5726 537 51 639503 360497 685290 314710 5787 536 52 639764 360236 685612 536 314388 5848 53 640024 359976 685934 314066 5910 54 640284 359716 686255 313745 5971 55 640544 359456 686577 313423 6032 56 640804 359196 686898 313102 6094 25 57 641064 358936 687219 312781 6155 58 641324 358676 687540 312460 6217 3783 59 641584 358416 687861 3722 312139 6278 26 641842 358158 688182 311818 6340 I 642101 357899 688502 311498 6401 2 642360 357640 688823 311177 6463 3537 3 642618 357382 689143 4335 II 102 4274 ΙΟ 102 4213 9 102 4152 8 102 536 4090 7 102 536 535 535 4029 6 102 3968 5 102 3906 64 4 102 3845 3 430 429 429 429 428 427 427 Cos. D. 64 Deg. 310857 6525 4 642877 357123 689463 310537 6587 5 643135 356865 689783 310217 6648 26 6643393 356607 690103 309897 6710 7 643650 356350 690423 309577 6772 3228 8 643908 356092 690742 309258 6834 3166 9 644165 355835 691062 308938 6896 3104 10 644423 355577 691381 308619 6958 3042 II 644680 428 355320 691700 531 428 355064 692019 531 12 644936 13 645193 354807 692338 14 645450 354550 692656 15 645706 354294 692975 307025 7269 2731 63 45 Sec. Cot. D. Tang. Cos. D. Sine 535 535 534 534 534 534 533 533 533 533 533 532 532 102 102 103 103 103 2 I 3660 64 0 3599 59 58 103 103 103 103 33 3475 57 3413 56 3352 63 55 3290 54 103 103 103 103 532 531 531 308300 7020 307981 7082 307662 7145 307344 7207 103 wwwww 53 52 51 50 2980 49 104 2918 48 104 2855 47 104 2793 46 104 63 Deg MATHEMATICAL TABLES. 107 26 Deg. TABLE V.-LOG SINES, ETC. 27 Deg Sine | D. Cosec. Tang. | D. 9.6 Cot. Sec. | D. Cos. 26 15 45706| 16 45962 427 1746218 18 46474 1946729 426 10'3 9° 54294 692975 54038 693293 426 53782 693612 426 53526 693930 10° ΙΟΟ 9'9 531 530 425 425 425 424 424 424 3049527 424 423 423 423 422 422 422 422 421 26 24 48004 51996 695836 304164 47832 52168 25 48258 51742 696153 303847 47894 26 48512 51488 696470 303530 47957 104 104 104 104 104 104 20 46984 53016 694566 305434 47581 52419 21 47240 52760 694883 305117 47644 52356 22 47494 52506 695201 304799 47706 52294 2347749 52251 695518 530 530 530 529 307025 47269 306707 47331 306388 47394 52606 104 306070 47456 52544 305752 47519 53271 694248 52731 45 104 104 52669 44 43 42 52481 41 40 49713 698685 49461 699001 421 |49208 699316 421 48956 699632 420 420 420 419 419 419 418 48703 699947 3851549 48451 700263 50473 697736 302264 48209 31 49781 50219 698053 301947 48272 32 50034 49966 698369 26 33 50287 34 50539 35 50792 36 51044 37 51297 28 49020 50980697103 30289748083 2949274 50726 697420 302580 48145 27 48766 51234 696787 30321348020 51980 529 529 529 529 528 528 528 528 527 527 527 39 38 304482 47769 52231 63 37 36 105 105 105 52106 35 52043 34 33 105 51917 32 105 51854 31 105 51791 30 105 51728 29 301631 48335 105 51665 63 28 527 105 526 301315 48398 51602 27 526 526 39 51800 48200 700578 299422 48778 418 417 417 417 416 297534 49159 297220 49222 46192 703095 47 53808 296905 49286 48 54059 45941 703409 296591 49350 49 54309 45691 703723 296277 49414 50586 526 525 525 47948 700893 4052052 525 41 52304 47696 701208 51096 63 19 524 26 42 52555 47445 701523 298477 48968 51032 524 43 52806 298163 49032 47194 701837 524 .44 53057 46943 702152 297848 49095 46692 702466 524 45 53308 418 524 46442 702780 46 53558 418 523 523 523 523 | 526/300368 48588 300999 48461 300684 48524 105 105 105 51476 51539 26 25 51412 24 300053 48651 105 51349 106 23 299737 48714 51286 22 106 51222 21 299107 48841 298792 48904 106 51159 20 416 416 416 60 57047 415 415 415 414 414 414 413 Cos. D. Sec. Cot. D. 26 51 54808 |45192 704350 295650 49542 522 52 55058 44942 704663 522 44693 704977 53 55307 522 54 55556 44444 705290 522 55 55805 44195 705603 294397 49798 521 56 56054 43946 705916. 294084 49862 521 57 56302 43698 706228 293772 49926 521 5856551 43449 706541 293459 49990 521 59 56799 43201 706854 293146 50055 42953 707166 521 292834 50119 Tang. Cos. 522 50 54558 45442 704036 295964 49478 50522 63 10 106 106 106 106 106 106 106 106 106 106 18 50968 17 50905 16 50841 15 50778 14 50714 13 50650 12 I I 107 50458 295337 49606 107 50394 295023 49670 294710 49734 107 50330 107 50266 107 50202 107 50138 107 50074 107 50010 107 49945 98 765432 H 107 49881 63 O | D. Sine 633 Deg. 63 Deg. 108 MATHEMATICAL TABLES. 413 413 412 412 412 7 411 410 410 410 409 409 409 408 339009 712146 408 661726 19 20 661970 21 662214 22 662459 408 6 658531 341469 709037 290963 0506 658778 341222 709349 290651 0571 8659025 411 519 340975 709660 290340 0636 27 9 659271 340729 709971 10 659517 340483 710282 289718 0765 11 659763 340237 710593 289407 0830 9170 12 660009 339991 710904 13 660255 339745 711215 14 660501 339499 711525 15 660746 339254 711836 16 660991 409 17 661236 27 18 661481 27 Deg. Sine 9° TABLE V.-LOG. SINES, ETC. D. Cosec. | Tang. D. Cot. 9° IO* 270 657047 342953 707166 272 Deg. Sec. D. Cos. 9'94 10° 10*05 292834 0119 9881 I 657295 342705 707478 2 657542 342458 707790 292210 0248 107 107 108 108 3 657790 342210 708102 291898 0312 9688 4 658037 341963 708414 291586 0377 9623 658284 341716 708726| 291274 0442 412 411 520 520 520 520 519 519 519 292522 0184 9816 107 9752 58 108 9558 108 9494 108 9429 519 518 518 518 518 518 517 ✪ ∞ ∞ ∞ ∞ ∞ t 108 9364 62 52 290029 0700 407 407 4.07 406 405 405 405 404 27 27 663677 28 663920 405 29 664163 30 664406 31 664648 32 664891 33 665133 334867 717401 282599 2269 338519 712766| 287234 1285 8715 338274 713076 407 516 286614 1416109 8584 337786 713696 286304 1481 337541 714005 285995 1546 8454 516 23 662703 337297 714314 285686 161219 8388 406 24 662946 25 663190 26663433 406 515 515 109 337054 714624 285376 1677 8323 336810 714933 285067 1743 336567 715242 515 515 284758 1808 336323 715551 284449 1874 336080 715860 514 338764 712456 287544 1220 ни 517 338030 713386| 516 |286924| 1350 | 517 517 516 289096 0895 9105 |288785 0960 9040 288475 1025 8975 288164 1090 108 8910 287854 1155 108 1155108 108 108 108 108 108 108 9300 9235 45 8845 44 109 8780 62 43 109 8650 42 516 109 8519 109 40 39 38 37 109 8257 36 8126 109 8192 62 34 109 35 44 667786 404 404 403 665375 34 403 35 665617 403 27 36 665859 37 666100 402 402 38 666342 402 39 666583 402 40 666824 401 41 667065 401 42 667305 332695 720169 279831 2864 401 43 667546 332454 720476 279524 2930 401 332214 720783 279217 2996 400 45 668027 331973 721089 278911 3063 Cos. D. Sec. Cot. D. Tang. Cos. D. 63 Deg. 284140 1940 335837 716168 283832 2005 335594 716477 283523 2071 335352 716785 283215 2137 335109 717093 282907 2203 334625 717709 282291 2335 514 514 514 514 513 513 513 513 513 512 512 512 512 512 511 I 511 II 5II 334141 718325 281675 2467 7533 333900 718633| 281367 2533 7467 333658 718940 281060 2599 333417 719248 280752 2665 7335 333176 719555 280445 2731 7269 332935 719862 280138 2797 7203 334383 718017 281983 2400 7600 62 25 O 109 8060 109 110 IIO IIO IIO IIO II 33 wwwwwww↑‡‡ £$£At Abuu muo 59 57 56 49 48 47 46 32 7995 ❤ 7929 7863 7797 7731 7665 26 980 76 MM2 2 2 2 2 31 30 29 28 27 IIO 24 IIO IIO ΙΙΟ 110 IIO 23 7401 22 21 20 19 IIO III 7136 18 7070 17 III III 7004 16 6937 62 15 Sine 621 Deg. MATHEMATICAL TABLES. 109 400 400 399 399 399 399 398 398 398 397 397 397 397 396 396 396 395 395 395 395 394 394 394 394 393 393 393 55 670419 329581 724149 275851 3730 56 670658 329342 724454 275546 3797 6203 57 670896 329104 724759 275241 3864 58 671134 328866 725065| 274935 3931 6069 59 671372 328628 725369 274631 3998 28 0 671609 328391 725674 1 671847 328153 725979 274021 4132 2 672084 327916 726284 273716 4200 28 3 672321 327679 726588 273412 4267 4 672558 327442 726892 273108 4334 27 Deg. Sine 9° TABLE V.-LOG. SINES, ETC. 28 Deg. D. | Cosec. Tang. D. Cot. Sec. D. Cos. IO* 9° IO' 10.05 III III 9'94 2745 668027 331973 721089 278911 3063 6937 46 668267 331733 721396 278604 3129 6871 47 668506 331494 721702 278298 3196 6804 48 668746 331254 722009 277991 3262 49 668986 331014 722315 50 669225 330775 722621 51 669464 330536 722927 52 669703 330297 723232 53 669942 330058 723538 27 54 670181 329819 723844 276156 3663 6337 15 14 98 76 511 511 510 510 510 13 277685 3329 6671 III III 6738 12 II III 277379 3396 510 6604 ΙΟ III 510 277073 3462 6538 509 276768 3529 III 6471 276462 3596 III 6404 62 7 509 III 509 III 6270 509 5 509 508 508 508 508 274326 4065 112 I12 112 112 4 6136 3 2 6002 I 112 5935 62 0 112 508 112 5868 59 507 112 5800 61 58 392 113 113 10 673977 113 326023 728716 271284 4739 5261 113 11 674213 325787 729020 270980 4807 113 28 12 674448 325552 729323 270677 4875 5672795 327205 727197 6 673032 326968 727501 272499 4469 5531 7 673268 326732 727805 272195 4536 5464 8 673505 326495 728109 271891 4604 9673741 326259 728412 271588 4672 5328 392 392 392 391 391 391 391 390 13 674684 325316 729626 270374 4942 14 674919 325081 729929 270071 5010 113 15 675155 324845 730233 269767 5078 4922 113 16 675390 324610 730535 269465 5146 4854 17 675624 113 324376 730838 269162 5214 4786 18 675859 113 324141 731141 268859 5282 4718 19 676094 323906 731444 268556 5350 20 676328 323672 731746 268254 5418 507 507 507 507 506 506 506 506 506 505 5733 112 5666 272803 4402 112 II2 112 5598 5396 5193 61 49 ི་ྲུྨཨºོ༢༦ 56 55 54 53 50 5125 48 113 5058 390 390 390 389 389 389 388 388 388 28 21 676562 323438 732048 267952 5486 4514 22 676796 323204 732351 267649 5554 4446 23 677030 322970 732653 267347 5623 4377 24 677264 322736 732955 267045 5691 4309 25 677498 322502 733257 26 677731 322269 733558 27 677964 322036 733860 503 28 678197 321803 734162 29 678430 321570 734463 30 678663 321337 734764 505 505 505 505 504 504 504 504 504 503 503 113 4990 113 113 114 4650 4582 61 114 114 114 503 503 502 266743 5759 4241 266442 5828 266140 266140 5896 114 114 wwwww.f££££££ 47 46 44 42 40 39 38 37 36 35 98 765 114 4172 4104 34 265838| 5964 114 33 4036 502 265537 6033 114 32 502 Cos. D. Sec. Cot. D. 265236 6101 3899 61 30 Tang. | Cos. D. Sine 114 3967 31 621 Deg. 61 Deg. 110 MATHEMATICAL TABLES. 291 Deg. 28 Deg. Sine TABLE V.-LOG. SINES, ETC. D. Cosec. Tang. D. Cot. Sec. D. Cos. 9° IO* 9* IO* 10.05 9'94 28 30 678663 32 33 34 679128 679360 679592 35 679824 36 680056 37 680288 38 680519 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ mmm en en en M M M 388 387 387 387 387 386 སསསས བ 386 385 41681213 42 43 Www W ∞ ∞ ∞0 385 383 382 382 382 382 381 33 381 381 ∞ ∞ 28 39 680750 319250 737471 262529 6721 3279 40 680982 319018 737771 262229 6790 3210 385 318787 738071 261929 6859 3141 385 681443 318557 738371 261629 6928 384 681674 |318326 738671 261329 6997 3003 384 318095 738971 44 681905 384 45 682135 317865 739271 384 46 682365 317635 739570 383 47 682595 317405 739870 383 28 48 682825 317175 740169 383 49 683055 316945 740468 50 683284 316716 740767 51 683514 316486 741066 52 683743 316257 741365 53 683972 316028 741664 54 684201 315799 741962 55 684430 315570 742261 56 684658 321337 734764 265236 6101 3899 31 678895 321105 735066 264934 6170 3830 320872 735367 264633 6239 320640 735668 264332 6307 3693 115 320408 735969| 264031 6376 115 320176 736269 263731 6445 3555 115 319944 736570 263430 6514 3486 115 263129 6583 3417 386 319712 736871 115 319481 737171 262829 6652 3348 115 30 502 502 502 114 29 114 3761 28 114 27 501 501 501 501 501 500 3624 26 25 24 23 61 22 2I 500 115 20 500 500 500 499 499 499 115 19 115 3072 18 499 499 499 498 59 28 57 684887 58685115 685343 29 685571 I 2 685799 686027 W W W W W 380 380 380 3 686254 380 379 379 379 379 378 29 9 377 377 377 377 376 376 312384 746429 312157 746726 6 686936 313064 745538 254462 8602 378 7 687163 312837 745835 254165 8672 378 8 687389 687616 378 312611 746132 315113 742858 257142 7971 314885 743156 256844 8041 314657 743454 256546 8111 314429 743752 256248 8181 314201 744050 255950 8251 255652 8321 313973 744348 313746 744645 255355 8391 4 686482 313518 744943 255057 8461 5 686709 313291 745240 254760 8531 498 498 498 498 497 497 497 497 497 115 115 261029 7066 115 260729 7136 2864 115 260430 7205 2795 116 260130 7274 2726 116 259831 7344 116 2656 259532 7413 116 2587 259233 7483 116 2517 258934 7552 116 2448 258635 7622 2378 258336 7692 2308 258038 7761 2239 257739 7831 2169 17 2934 16 15 14 61 13 12 II ΙΟ 116 116 116 116 315342 742559 257441 7901 116 2099 61 4 98 76 5t 116 2029 116 1959 3 2 1889 497 496 496 496 496 LO LO LO 117 117 117 1819 61 0 1749 496 117 117 117 1609 1679 57 1539 56 495 117 1469 60 55 1398 ༦ºོཀྵུ་༠ * 59 58 54 495 117 D. 495 495 495 495 494 494 494 494 Sec. Cot. D. 10 687843 II 688069 311931 747023 252977 8954 1046 12 688295 311705 747319 252681 9025 13 688521 252384 9095 311479 747616 14 688747 311253 747913 252087 9166 15 688972 311028 748209 251791 9237 Cos. Tang. Cos. D. 253868 8742 253571 8813 253274 8883 117 1328 53 1258 52 117 1187 51 117 II 17 50 117 118 49 118 118 118 0975 48 0905 47 0834 46 0763 60 45 Sine 61 Deg. 602 Deg. MATHEMATICAL TABLES. 111 291 Deg. TABLE V.-LOG. SINES, ETC. | Sine D. Cosec. Tang, D. Cot. Sec. D. Cos. 30 Deg. 9.6 374 373 373 373 373 372 372 372 371 22 90548 09452 750281 23 90772 |09228 750576 29 24 90996 09004 750872 25 91220 08780 751167 376 376 375 375 375 375 374 374 374 10'3 9° 29 15 88972 11028 748209 251791 59237 40763 16 89198 10802 748505 251495 59307 17 89423 10577 748801 251199 59378 18 89648 10352 749097 19 89873 10127 749393 250607 59520 20 90098 09902 749689 250311 59591 21 90323 09677 749985 250015 59662 IO' 10'0 9'9 494 493 493 493 493 493 118 118 40693 250903 59449 118 118 40622 40551 40480 118 41 77777 45 44 43 42 493 11840409 118 40338 40 39 27 91668 08332 751757 26 91444 08556 751462| 248538 60018 39982 248243 60089 39911 28 91892 08108 752052 247948 60160 29 92115 07885 752347 247653 60232 39768 492 492 492 492 249719 59733 40267 249424 59804 40196 249128 59875 40125 248833 59946 40054 3092339 07661 752642 247358 60303 39697 3994342 371 371 371 370 370 370 05658 755291 370 40 94564 05436 755585 369 41 94786 31 92562 07438 752937 247063 60375 39625 3292785 |07215] 753231 246769 60446 39554 29 33 93008 06992 753526 246474 60518 34 93231 06769 753820 246180 60590 3593453 06547 754115 245885 60661 36 93676 06324 754409 245591 60733 37 93898 06102 754703 245297 60805 38 94120 05880 754997 245003 60877 29 42 95007 3 3 369 368 368 368 367 50 96775 367 367 03446 758224 04993 756172 243828 61164 43 95229 04771 756465 369 44 95450 04550 756759 368 45 95671 46 95892 47 96113 48 96334 49 96554 369 05214 755878 244122 61092 492 492 491 491 491 491 491 491 490 490 490 490 490 490 489 489 489 489 489 |04329| 757052 489 242948 61381 04108 757345 242655 61453 03887 757638 118 118 119 119 119 38 60 60 37 36 35 34 33 119 119 39840 32 31 119 30 119 119 119 29 60 28 39482 27 119 39410 26 119 39339 119 25 39267 24 120 39195 120 23 39123 22 120 244709 60948 244415 61020 39052 21 120 38980 20 120 38908 120 60 19 38836 18 120 243535 61237 243241 61309 38763 17 120 38691 16 120 38619 15 120 488 38547 14 120 488 03666 757931 242069 61598 488 242362 61525 38475 13 120 38402 I2 488 241776 61670 121 38330 II 121 03225 758517 488 241483 61742 38258 60 10 121 29 51 96995 03005 758810 367 488 241190 61815 38185 121 366 54 97654 366 52 97215 5397435 02565 759395 02785 759102 487 240898 61887 38113 86 8 121 366 02346 759687| 487 365 57 98313 01687 760564 487 239436 62251 58 98532 01468 760856 55 97874 02126 759979 487 240021 62105 366 56 98094 01906 760272 365 365 5998751 01249 761148 365 486 238852 62396 60 98970 01030 761439 238561 62469 Cos. D. Sec. Cot. D. Tang. Cos. D. Sine 487 240605 61960 240313 62033 38040 121 37967 121 121 37895 487 239728 62178 37822 121 486 239144 62324 121 37749 37676 76543 2 121 121 37604 3753160 O I 602 Deg. 60 Deg. 112 MATHEMATICAL TABLES. 30 Deg. Sine 9° TABLE V.—LOG. SINES, ETC. D. Cosec. Tang. | D. Cot. 30 Deg. Sec. D. Cos. IO* 9' IO* 10'06 9'93 364 364 300 698970 301030 761439 1 699189 300811 761731 486 364 364 363 2 699407 3 699626 300374 762314 4 699844 300156 762606 486 238561 2469 238269 2542 7531 60 121 300593 762023 486 486 237977 2615 237686 2688 122 122 7458 59 7385 58 7312 363 363 362 362 362 361 361 298198 765224 14 702019 297981 765514 15 702236 297764 765805 361 16 702452 297548 766095 361 30 18 702885 8 700716 30 9700933 299067 764061 235939 3128 10 701151 298849 764352 235648 3201 II 701368 298632 764643 12 701585 298415 764933 362 13 701802 237394 2762 5 700062 299938 762897 237103 2835 363 6 700280 299720 763188 236812 2908 363 485 7 700498 299502 763479 236521 2981 299284 763770 485 |236230 3054 122 485 122 485 122 7238 7165 7092 122 7019 122 485 122 6946 59 52 485 6872 122 484 6799 484 484 235357 3275 235067 3348 122 122 6725 484 484 234776 3422 234486 3495 484 17 702669 360 297331 766385. 483 484 234195 3569 233905 3643 233615 3716 123 6505 123 6431 123 6578 6652 123 6357 19 703101 360 360 359 359 359 359 359 296899 766965 20 703317 296683 767255 232745 3938 123 6062 21 703533 296467 767545 232455 4012 22 703749 296251 767834 232166 4086123 23 703964 296036 768124 231876 4160 5840 24704179 295821 768413 231587 4234 360 297115 766675 233325 3790 123 123 6284 59 43 6210 483 483 483 483 483 233035 3864 123 6136 123 5988 5914 123 482 123 25 704395 295605 768703 26 704610 28 705040 29 705254 30 705469 31 705683 357 32705898 33 706112 34 706326 30 27 704825 358 295175 769281 358 295390 768992 231008 4382 358 358 357 357 357 294960 769570 294746 769860 294531 770148 294317 770437 294102 770726 293888 771015 35 706539 356 30 36 706753 37 706967 38707180 356 356 356 39 707393 40 707606 355 355 41 707819 42 708032 355 43 708245 354 354 44 708458 354 45 708670 Cos. D. 355 482 482 482 482 482 481 481 481 481 481 481 481 480 480 480 480 480 5766 ww ww f ‡ ‡ £££££££4 Jun 56 55 48 46 44 4.2 4.I 40 37 36 231297 4308 124 5692 35 124 124 5618 59 34 291968 773608 480 291755 773896 293247 771880 293033 772168 292820 772457 292607 772745 |292394 773033 226967 5426 125 292181 773321 226679 5501 125 226392 5576 125 226104 5651 291542 774184 225816 5726 125 4274 291330 774471 225529 5801 Sec. Cot. 230719 4457 230430 4531 230140 4605 5395 229852 4680 124 229563 4754 229274 4829 228985 4903 293674 771303 228697 4978 293461 771592 228408 5052 228120 5127 5543 33 124 124 5469 5320 124 124 124 5246 5171 5097 124 5022 124 4943 59 210 9∞ 765 3332 2 2 2 2 32 31 30 29 28 27 26 25 124 4873 24 227832 5202 124 4798 23 125 |227543 5277 227255 5351 4723 22 125 4649 4574 4499 479 479 479 125 D. Tang. Cos. D. Sine 125 4424 4349 4199 59 15 0 000 7 5 2 2 H H 21 20 19 18 17 16 60 Deg. 591 Deg MATHEMATICAL TABLES. 113 30 Deg. TABLE V.-LOG. SINES, ETC. 31 Deg. Sine D. | Cosec. Tang. D. | Cot. Cot Sec.D. | Cos. | 9* ΙΟ 9° 10° 10'06 9'93 354 353 353 353 353 353 352 352 352 35I 351 351 351 350 350 350 350 30 45 708670 291330 774471 46 708882 291118 774759 47 709094 290906 775046 224954 5952 4048 48 709306 290694 775333 224667 6027 3973 49 709518 290482 775621 224379 6102 125 50 709730 290270 775908 224092 6178 5I 709941 290059 776195 52 710153 53 710364 30 54 710575 55 710786 56 710997 57 711208 58 711419 289847 776482 478 223805 6253 289636 776769 352 479 479 479 479 478 478 225529 5801 225241 5877 4123 4199 125 15 14 125 125 13 12 126 3898 II 6 349 349 349 349 349 348 348 348 348 4 712679 287321 779918 476 220368 7162 220082 7238 5 712889 287111 780203 713098 286902 780489 7 713308 286692 780775 8 713517 9713726 10 713935 II 714144 223518 6329 478 478 223231 6404 289425 777055 222945 6480 3520 478 289214 777342 222658 6555 3445 289003 777628 222372 6631 3369 288792 777915 222085 6707 3293 288581 778201 221799 6783 59 711629 288371 778487 221513 6859 3141 31 0 711839 288161 778774 221226 6934 3066 59 0 I 712050 287950 779060 220940 7010 2 712260 287740 779346 477 31 3 712469 287531 779632 126 3822 126 126 IO 3747 3671 96 8 126 3596 59 7 6 478 477 477 477 477 477 126 126 126 126 126 126 5 4 3 3217 2 I 126 2990 476 220654 7086 127 59 127 2914 58 58 2838 127 57 476 2762 56 476 219797 7315 127 2685 476 219511 7391 127 55 2609 476 476 475 475 475 286483 781060 218940 7543 286274 781346 218654 7620 2380 286065 781631 218369 7696 2304 285856 781916 218084 7772 219225 7467 127 54 2533 127 127 127 127 127 53 2457 52 51 50 2228 58 49 347 347 347 347 347 346 31 12 714352| 285648 782201 217799 7849 2151 13 714561 285439 782486 217514 7925 14714769 285231 782771 217229 8002 15 714978 285022 783056 216944 8079 1921 16 715186 284814 783341 216659 8155 1845 17 715394 284606 783626 216374 8232 346 346 18 715602 284398 783910 216090 8309 19 715809 284191 784195 215805 8386 20 716017 346 283983 784479 215521 8463 345 345 345 345 345 344 344 344 344 Cos. D. Sec. Cot. 591 Deg. 31 21 716224 283776 784764 215236 8540 22 716432 283568 785048 214952 8617 23716639 283361 785332 214668 8694 24 716846 283154 785616 214384 8771 25717053 282947 785900 214100 8848 26 717259 282741 786184 213816 8925 27 717466 282534 786468 213532 9002 28 717673 282327 786752 213248 9079 29717879 282121 787036 212964 9157 30 718085 281915 787319 212681 9234 0766 58 30 Tang. Cos. D. Sine 475 475 475 475 475 474 474 474 474 474 474 473 473 473 473 473 473 473 48 127 128 2075 47 128 1998 46 128 45 128 44 1768 128 128 128 128 1691 1614 1537 58 40 1460 128 128 128 1383 1306 1229 wwwwf+++ 43 42 39 38 37 36 98 76 129 1152 35 129 1075 34 129 0998 33 129 129 129 0921 32 0843 31 D. 581 Deg. 114 MATHEMATICAL TABLES. 31 Deg. TABLE V.-LOG. SINES, ETC. 321 Deg. Sine D. Cosec. Tang. | D. Cot. Sec. D. Cos. 9'7 10'2 9' 10' ΙΟ 9'9 31 30 18085 81915 787319 212681 69234 30766 343 343 35 19114 36 19320 37 19525 341 46 21366 340 78634 791846 340 78430 792128 58 23805 76195 795227 5924007 75993 795508 320 24210| 75790 795789 I 24412 75588 796070 4 25017 337 337 337 337 468 203930 71658 337 2 24614 75386 796351 203649 71737 336 3 24816 336 75184 796632 336 74983 796913 340 339 339 339 339 339 53 22791 338 54 22994 338 5523197 338 5623400 338 31 57 23603 76397 794945 205055 71343 28657 469 4721570 31 48 21774 78226 792410 207590 70636 29364 49 21978 78022 792692 207308 70714 29286 50 22181 77819 792974 207026 70793 29207 51 22385 77615 793256 206744 70871 29129 52 22588 77412 793538 206462 70950 29050 206181 71028 77209 793819 28972 77006 79410I 205899 71107 28893 76803794383 205617 71185 76600 794664 31 18291 81709 787603 212397 69312 30688 472 343 81503 787886 32 18497 129 212114 69389 33 18703 81297 788170 211830 69467 343 34 18909 81091 788453 211547 69544 343 472 80886 788736 211264 69622 342 80680 789019 210981 69700 342 130 210698 69777 80475 789302 342 38 19730 80270 789585 210415 69855 30145 342 31 39 19935 80065 789868 210132 69933 40 | 20140 79860 790151 209849 70011 29989 341 41 20345 79655 790433 209567 70089 29911 341 42 20549 79451 790716 209284 70167 29833 341 43 20754 79246 790999 |209001| 70245 4420958 340 79042 791281 208719 70323 340 4521162 78838 791563 208437 70401 208154 70479 207872 70558 29442 472 30 129 29 472 472 129 66 30611 28 30533 27 129 30456 26 129 30378 472 472 471 471 471 471 471 471 471 129 25 30300 24 30223 23 130 58 22 130 30067 21 130 130 130 20 19 18 471 130 130 130 29755 17 29677 16 470 29599 15 130 29521 14 470 130 58 13 470 470 130 12 470 470 470 469 469 469 469 469 205336 71264 HHH 131 131 131 131 131 131 131 131 II IO 9 8 7 6 28815 28736 58 131 5 58 4 4444 469 468 468 204773 71422 204492 71501 204211 71580 131 131 28578 28499 321 I 131 132 132 28420 58 o 28342 59 468 28263 58 468 203368 71817 132 28183 57 336 32 ΙΟ I I 13 26827 14 27027 1527228 Cos. 335 335 335 335 335 334 334 334 334 D. 468 468 468 467 525219 74781 797194 6 25420 74580 797475 7 25622 74378 797755 8 25823 74177 798036, 201964 72213 9 26024 201684 72292 73976 798316 467 10 26225 73775 798596 |201404 72371 467 11 26426 73574 798877 201123 72451 467 12 26626 73374 799157 200843 72530 467 73173 799437 200563 72610 27390 467 72973 799717 200283 72690 27310 467 72772 799997 200003 72769 27231 57 45 Sec. Cot. D. Tang. Cos. D. Sine 468 203087 71896 | 202806 71975 132 28104 56 132 132 28025 57 55 |202525 72054 |202245 72133 27946 54 132 27867 53 132 27787 52 132 27708 51 132 27629 50 132 132 133 133 133 27549 49 27470 48 47 46 58 Deg. 572 Deg. MATHEMATICAL TABLES. 115 321 Deg. Sine. 9' D. Cosec. TABLE V.-LOG. SINES, ETO. Cosec. Tang. | D. Cot. Sec. D. Cos. 33 Deg. IO' 9' 10° 10.07 9'92 32 15 727228 34731009 328 328 328 267413 807527 45733177 47 733569 48 733765 49 73396 50 734157 327 327 334 333 133 333 133 333 133 333 133 6831 333 133 21 728427 271573 801675 466 198325 3249 6751 133 6671 332 22 728626 271374 801955 198045 3329 332 23 728825 271175 802234 197766 3409 6591 332 465 32 24 | 729024 270976 802513 197487 3489 332 465 25729223 270777 802792 197208 3569 331 26729422 270578 803072 196928 3649 331 27 729621 270379 803351 196649 3730 331 465 28729820 270180 803630 196370 3810 465 29 730018 331 269982 803908 196092 3890 330 465 30 730216 269784 804187 195813 3971 330 31 730415 269585 804466 195534 4051 330 32 730613 269387 804745 195255 4132 5868 330 32 33 730811 269189 805023 194977 4212 330 194698 4293 268991 805302 329 35 731206 268794 805580 194420 4374 5626 329 36 731404 268596 805859 464194141 4455 329 37 731602 268398 806137 193863 4535 329 268201 806415 38731799 193585 4616 329 39 731996 268004 806693 328 40 732193 267807 806971 328 41732390 267610 807249 32 42 732587 267216 807805 43 732784 44 732980 267020 808083 327 266823 808361 463 46 733373 266627 808638 463 272772 799997 200003 2769 466 16 727428 272572 800277 199723 2849 7151 466 19972 17 727628 272372 800557 199443 2929 466 18 727828 272172 800836 199164 3009 6991 466 19 728027 271973 801116 198884 3089 6911 466 20 728227 271773 801396 198604 3169 466 7231 133 45 44 7071 43 42 4I 40 39 466 38 465 133 133 134 6431 134 57 37 6511 36 35 98765 465 134 6270 6351 34 134 33 6190 32 134 6110 31 134 465 6029 30 134 464 5949 29 134 464 57 28 134 464 464 464 5788 134 5707 2 2 27 26 134 25 134 135 5545 24 464 5465 23 463 135 5384 22 463 193307 4697 135 5303 21 463 193029 4778 135 5222 20 463 192751 4859 135 5141 57 19 135 463 463 192473 4940 192195 5021 191917 5103 4897 135 191639 5184 4816 5060 18 135 4979 135 17 16 15 327 462 191362 5265 266431 808916 191084 5346 266235 809193 135 136 4735 14 462 327 326 266039 809471 136 462 190807 5428 4572 4654 326 265843 809748 462 190529 5509 462 190252 5591 136 13 12 136 449I II 136 4409 57 10 326 326 325 325 325 325 325 324 324 32 51734353 52734549 265451 810302 53734744 265256 810580 265647 810025 189975 5672 55 735135 264865 811134 189698 5754 189420 5836 54734939 265061 810857 189143 5917 |264670 811410 56 735330 188590 6081 57 735525 264475 811687 188313 6163 58 735719 264281 811964 188036 6245 59 735914 264086 812241 187759 6327 60 736109 263891 812517 187483 6409 462 462 462 462 461 461 461 461 461 1364328 136 4246 86 9 136 4164 7 188866 5999 333 MM M 136 4083 4001 136 136 3919 654 136 3837 3 3755 2 137 3673 I 137 3591 57 o Cos. D. Sec. Cot. D. Tang. Cos. D. Sine 572 Deg. 57 Deg. } 116 MATHEMATICAL TABLES. 33 Deg. Sine 9'7 33 Deg. TABLE V.-LOG. SINES, ETC. D. Cosec. Tang. D. Cot. Sec. D. Cos. 321 321 321 321 60602 817209 320 320 320 320 320 319 319 319 319 319 19 39783 60217 817759 20 39975 60025 818035 181965 78060 21940 21 40167 181690 78143 59833 818310 22 40359 59641 818585 181415 78226 23 40550 59450 818860 181140 78309 2440742 180865 78393 59258 819135 25 40934 59066 819410 180590 78476 26 41125 58875 819684 180316 78559 33 27 41316 58684 819959 180041 78643 318 31 318 32 42271 317 317 317 317 317 57920 821057 33 42462 318 57729 821332 40 43792 3743223 56777 822703 177297 79480 3843413 39 43602 316 56587 822977 316 56398 823250 41 43982 316 56208 823524 316 56018 823798|| 179217 78893 21107 178943 78977 21023 178668 79061 20939 140 20856 57538 821606 178394 79144 34 42652 178120 79228 57348 821880 20772 35 42842 57158 822154 177846 79312 33 36 43033 56967 822429 177571 79396 28 41508 58492 820234 179766 78726 21274 318 29 41699 58301 820508 179492 78810 21190 30 41889 42080 318 58111 820783 459 459 459 459 459 459 458 458 458 458 458 458 458 458 10°2 9° 330 36109 63891 812517 324 324 324 323 323 5 37080 6 37274 323 323 9'9 187483 76409 23591 I 36303 63697 812794 187206 76491 23509 236498 63502 813070 186930 76573 23427 3 36692 63308 813347 186653 76655 4 36886 63114 813623 186377 76737 23263 137 186101 76819 62920 813899 23181 323 62726 814175 137 185825 76902 23098 7 37467 62533 814452 185548 76984 23016 IO' 10*0 461 461 461 460 460 460 460 460 60 137 137 137 137 59 58 23345 57 56 322 460 322 322 322 322 33 9 10 38048 61952 815279 II 38241 61759 815555 12 38434 61566 815831 460 4.60 459 459 137 137 137 137 184721 77232 22768 138 184445 77314 22686 138 184169 77397 22603 13 38627 61373 816107 183893 77480 138 321 61180 816382 459 837661 62339 814728 185272 77067 22933 56 52 9 37855 62145 815004 184996 77149 22851 51 138 14 38820 138 183618 77562 22438 15 39013 |60987 816658 183342 77645 22355 16 39206 60794 816933 183067 77728 138 17 39398 138 33 18 39590 60410 817484 182516 77894 22106 55 54 53 00 00 00 00 00 00 50 49 48 22520 47 46 45 138 182791 77811 22189 22272 44 5643 182241 77977 139 139 139 138 138 138 139 21774 139 21691 139 21607 21524 42 22023 4I 40 21857 333 39 38 37 36 35 2144156 34 21357 33 458 457 457 457 139 139 139 139 139 333 N 32 31 30 29 28 457 457 457 457 27 140 140 140 26 20688 56 25 20604 457 24 140 457 20520 23 456 177023 79564 140 20436 22 456 176750 79648 140 456 176476 79732 140 20352 20268 21 20 44 44550 315 315 Cos. D. 57 Deg. 456 456 456 42 44171 43 44361 316 (55829 824072|| 175928 79901 20099 55639 824345 175655 79985 20015 55450 824619 175381 80069 19931 45 44739 55261 824893 175107 80154 19846 56 15 Sec. Cot. D. Tang. Cos. D. Sine 561 Deg. 456 176202 79816 140 140 20184 19 18 140 140 141 17 16 98 76 MATHEMATICAL TABLES. 117 315 315 315 314 314 314 314 314 313 313 313 313 313 312 312 253941 826805 312 312 312 311 311 311 311 311 310 310 310 310 33 Deg. TABLE V.-LOG. SINES, ETC. Sine D. Cosec. D. Cosec. Tang. D. Tang. D. Cot. 9* IO* 9* 34 Deg. Sec. D. Cos. IO* 10.08 9'91 33 45 744739 255261 824893 175107 0154 9846 12 456 46 744928 255072 825166 456 174834 0238 47 745117 254883 825439 174561 0323 9677 48745306 254694 825713 174287 0407 9593 49|745494 254506 825986 174014 0492 9508 50 745683 254317 826259 173741 0576 51 745871 254129 826532 173468 0661 52 746059 53 746248 253752 827078 172922 0831 9169 56 7 543N HO9∞ 76 8 33 54 746436 55 746624 253376 827624 172376 1000 9000 56 746812 253188 827897 172103 1085 8915 57 746999 253001 828170 171830 1170 58 747187 252813 828442 171558 1255 59 747374 252626 828715 171285 1341 340 747562 252438 828987 171013 1426 I 747749 252251 829260 170740 1511 2 747936 252064 829532 170468 1596 34 3 748123 251877 829805 170195 1682 4 748310 251690 830077 169923 1767 5 748497 251503 830349 169651 1853 6 748683 251317 830621 169379 1938 7 748870 251130 830893 169107 2024 8 749056 250944 831165 168835 2109 9 749243 250757 831437 168563 2195 7805 IO 749429 250571 831709 168291 2281 7719 II 749615 250385 831981 168019 2366 7634 55 49 15 455 455 455 455 455 455 455 455 173195 0746 253564 827351 172649 0915 9085 455 454 454 454 454 454 454 454 454 454 453 453 453 453 453 141 141 141 141 141 141 141 141 141 141 14I 142 8830 142 8745 142 8659 9762 14 13 I I 9424 ΙΟ 9339 9254 5 4 3 2 I 142 142 8489 8574 56 ° 59 142 142 8404 55 58 8318 57 142 8233 56 142 8147 55 142 8062 54 142 7976 53 453 143 143 143 143 7891 52 51 50 453 143 310 309 309 309 309 309 308 308 308 34 12 749801 250199 832253 13749987 250013 832525 14 750172 249828 832796 15750358 249642 833068 453 453 453 16 750543 249457 833339 17 750729 249271 833611 18 750914 249086 833882 19 751099 248901834154 20 751284 248716 834425 34 21 751469. 22 751654 248346 834967 23 751839 308 248161 835238 452 452 452 452 452 308 248531 834696 308 452 452 452 26 307 307 307 307 307 306 24 7520231 247977 835509 25 752208 247792 835780 752392 247608 836051 27 752576 247424 836322 28 752760 247240 836593 29 752944 247056 836864 246872 837134 30753128 452 452 45I 45I 451 45I 143 167475 2538 7462 143 167204 2624 7376 143 166932 2710 7290 166661 2796 143 7204 143 166389 2882 7118 144 166118 2968 7032 144 6946 165846 3054 165575 3141 165304 3227 165033 3313 164762 3400 164491 3486 164220 3573 163949 3659 163678 3746 163407 3833 163136 3919 451 162866 4006 145 167747 2452 7548 48 47 46 45 44 43 42 4I 144 144 6859 55 40 144 6341 144 6427 6773 144 6687 144 6600 144 6514 333 m 39 38 37 36 98 76 35 34 144 6167 144 6254 33 32 145 6081 31 321 5994 55 30 Cos. D. Sec. Cot. D. Tang. Cos. D. Sine 561 Deg. 55 Deg. 118 MATHEMATICAL TABLES. 84 Deg. TABLE V.-LOG. SINES, ETC. 351 Deg. Sine 9° 3430 753128 IO* D. | Cosec. | Tang. | D. 9' Cot. Sec. | D. | Cos. 10' 10.08 9'91 www w 306 306 306 306 50 756782 303 246872 837134 31 753312 246688 837405 32 753495 246505 837675 33 753679 246321 837946 162054 4267 5733 246138 838216 34 753862 161784 4354 305 145 35 754046 245954 838487 161513 4441 5559 305 36754229 145 161243 4528 245771 838757 5472 305 145 37 754412 245588 839027 160973 4615 5385 305 145 38 754595 245405 839297 160703 4703 5297 305 145 34 39 754778 160432 4790 245222 839568 304 40 754960 160162 4877 245040 839838 304 41 755143 244857 840108 450 1598924965 5035 304 42 755326 244674 840378 43 755508 304 244492 840647 44 755690 304 159083 5227 244310 840917 146 45 755872 304 244128 841187 158813 5315 4685 303 46 756054 146 158543 5402 243946 841457 303 47 756236 146 4598 158274 5490 243764 841726 303 34 48 756418 243582 841996 158004 5578 4422 49 756600 303 157734 5666 243400 842266 243218 842535 162866 4006 451 5994 30 45I 162595 4093 145 5907 29 162325 4180 145 451 5820 28 145 451 45I 450 450 450 450 450 27 145 5646 26 25 24 23 55 22 5210 21 145 146 5123 20 450 450 159622 5052 146 19 146 4948 18 159353 5140 4860 302 302 450 449 449 449 449 449 449 449 449 146 17 4773 16 76 15 14 1464510 55 13 543 157465 5754 146 146 147 147 12 4334 4246 II IO 301 301 301 301 300 300 300 300 300 9 299 7 759852 240148 847107 299 148 8 760031 239969 847376 299 148 760211 39789 847644 152356 7434 2566 299 148 10 760390 239610 847913 152087 7523 2477 299 148 11 760569 151819 7612 239431 848181 298 148 12 760748 239252 848449 151551 7701 2299 298 149 13 760927 151283 7790 2210 149 14 761106 298 239073 848717 238894 848986 151014 7879 2121 298 15 761285 238715 849254 150746 7969 Cos. D. Sec. Cot. D. Tang. Cos. D. 55 Deg. 51 756963 243037 842805 157195 5842 4158 52757144 242856 843074 156926 5930 4070 449 53 757326 242674 843343 156657 6018 147 3982 302 302 54757507 242493 843612 55 757688 302 242312 843882 301 56 757869 242131 844151 301 34 57 758050 241950 844420 449 156388 6106 449 448 156118 6194 448 155849 6282 147 448 155580 6370 58 758230 241770 844689 155311 6459 59 758411 241589 844958 155042 6547 35758591 241409 845227 I 758772 241228 845496 2 758952 241048 845764 3 759132 240868 846033 4759312 240688 846302 448 5 759492 240508 846570 35 6759672 240328 846839 147 147 3894 3806 147 3718 55 4 98 765+ 3630 448 147 147 3 354I 2 448 3453 I 448 448 448 154773 6635 154504 6724 154236 6813 147 147 3365 55 0 3276 147 59 448 447 447 447 152893 7256 2744 148 153967 6901 3099 148 153698 6990 3010 148 153430 7078 2922 148 153161 7167 2833 3187 58 57 56 54 55 65 148 54 447 152624 7345 2655 53 52 447 51 44.7 50 447 2388 49 48 447 447 447 47 46 149 2031 54 45 Sine 3 542 Deg. MATHEMATICAL TABLES. 119 58 68871 59 69045 35 Deg TABLE V.—LʊG. SINES, ETC. D. Cosec. Tang. D. Cot. Sine 9'7 35 15 61285 298 17 298 2 2 oo oo 296 296 10'2 9° 445 Sec. D. Cos. IO' 10'0 149 38715 849254 447 150746 87969 12031 16 61464 38536 849522 447 150478 88058 11942 149 11853 61642 38358 849799 446 150210 88147 297 149 18 61821 38179 850058 446 149942 88237 11763 297 149 19 61999 38001 850325 446 149675 88326 11674 297 149 20 62177 37823 850593 446 149407 88416 11584 297 149 2162356 37644 850861 446 149139 88505 11495 297 149 22 62534 37466 851129 446 148871 88595 11405 296 149 23 62712 296 37288 851396 446 148604 88685 11315 150 35 24 62889 37111 851664 446 148336 88774 11226 150 25 63067 36933 851931 446 148069 88864 11136 150 2663245 296 36755 852199 446 147801 88954 11046 150 27 63422 36578 852466 446 147534 89044 10956 28 63600 296 150 36400 852733 445 147267 89134 10866 150 29 63777 36223 853001 445 146999 89224 10776 150 10686 30 63954 36046 853268 146732 89314 445 150 31 64131 35869 853535 445 146465 89404 10596 150 32 64308 35692 853802 445146198 89494 10506 150 35 33 64485 35515 854069 445 145931 89585 10415 150 34 64662 35338 854336 145664 89675 10325 151 35 64838 35162 854603 445 145397 89765 10235 151 36 65015 34985 854870 445 145130 89856 10144 151 37 65191 34809 855137 445 144863 89946 10054 151 38 65367 34633 855404 445 144596 90037 c9963 151 39 65544 34456 855671 444 144329 90127 09873 151 40 65720 34280 855938 09782 144062 90218 444 151 41 65896 34104 856204 444 143796 90309 09691 151 35 42 66072 33928 856471 444 143529 90399 09601 151 43 66247 33753 856737 444 143263 90490 09510 151 4466423 33577 857004 444 142996 90581 09419 151 45 66598 33402 857270 444 142730 90672 09328 152 46 66774 33226 857537 142463 90763 152 47 66949 33051 857803 444 142197 90854 09146 152 48 67124 32876 858069 444 141931 90945 09055 152 4967300 141664 91036 32700 858336 444 50 67475 141398 91127 32525 858602 291 443 35 51 67649 32351 858868 141132 91219 443 52 67824 32176 859134 140866 91310 53 67999 32001 859400 140600 91401 54 68173 31827 859666 140334 91493 55 68348 31652 859932 140068 91584 56 68522 31478 860198 139802 91676 57 68697 31303 860464 139536 91767 295 295 295 295 295 294 294 294 294 294 294 293 293 293 293 293 293 292 292 292 292 292 444 36 Deg. 9'9 45 44 43 42 41 40 39 38 54 37 36 35 34 33 32 31 30 29 54 28 210 a∞ 765 2 2 2 27 26 25 24 23 22 21 20 54 19 18 17 16 15 092.37 14 13 12 08964 II 152 08873 54 10 9856 5 4 3 2 10 152 60 69219 54 Deg. 291 291 291 291 290 290 290 139270 91859 31129 860730 290 30955 860995 290 30781 861261 Cos. D. Sec. Cot. 08781 152 08690 443 443 443 443 443 443 443 443 152 08599 152 152 08507 08416 139005 91951 153 153 153 153 153 08324 98 765+ 4 08233 3 08141 2 08049 I 138739 92042 07958 54 0 D. Tang. Cos. D. Sine 54 Deg. 120 MATHEMATICAL TABLES. 286 | 25 773533 285 285 285 28 774046 285 36 27 773875 285 226125 868416 26 773704 226296 868152 36 Deg. Sine 290 289 289 289 289 ΙΟ Sec. D. Cos. TABLE V.-LOG. SINES, ETC. D. Cosec. Tang.. D. Cot. 9° 9* 36 0 769219 230781 861261 230607 861527 I 769393 2769566 230434 861792 3 769740 230260 862058 4 769913 230087 862323 5 770087 137411| 2502 289 229913 862589 6 770260 137146 2594 229740 862854 7 770433 288 229567 863119 136881 2686 153 154 8 770606 288 229394 863385 136615 2778 7222 154 36 9 770779 288 229221 863650 10 770952 288 229048 863915 II 771125 288 228875 864180 12 771298 228702 864445 287 13 771470 287 228530 864710 228357 864975 442 14771643 287 288 15 771815 287 228185 865240 441 16 771987 228013 865505 287 17 772159287 227841 865770 36 18 772331 286 227669 866035 19 772503 286 227497 866300 20 772675 286 227325 866564 21 772847 286 227153 866829 22 773018 226982 867094 226810 867358 441 23 773190286 24 773361 226639 867623 226467 867887 in in initi 362 Deg. ΙΟ 10'09 9'90 443 138739 2042 7958 60 138473 2134 I53 7866 443 59 138208 2226 153 7774 442 58 442 137942 2318 137677 2410 153 153 7682 57 7590 442 56 153 7498 442 153 55 7406 442 54 442 7314 53 442 53 52 136350 2871 7129 442 442 442 442 51 441 136085 2963 7037 154 135820 3055 6945 154 135555 3148 135290 3240 135025 3333 134760 3425 154 50 49 6852 154 6760 48 154 6667 47 46 154 6575 134495 3518 44I 154 6482 45 44 134230 3611 154 6389 44.I 441 133965 3704 6296 155 53 43 42 441 441 133700 3796 6204 133436 3889155 6111 133171 3982 155 4I 40 155 6018 44I 132906 4075 155 5925 132642 4168 155 5832 44I 132377 4261 155 5739 44I 155 132113 4355 5645 44I www ww 39 38 37 36 9∞ 76 35 131848 4448 155 440 155 5552❘ 53 34 131584 4541 225954 868680 440 5459 29|774217 30 774388 285 284 225783 868945 225612 869209 31 774558 284 225442 869473 32 774729 284 35 775240 284 36 36 775410 283 37 775580 284 156 156 156 130527 4915 5085 130263 5008 225271 869737 33 774899 284 225101 870001 34 775070 224930 870265 224760 870529 440 131320 4634 5366 155 33 32 131055 4728 5272 440 130791 4821 5179 33 31 440 440 440 440 440 30 156 29 129999 5102 4898 156 4992 28 283 283 282 44 776768 282 223232 872903 127097 6136 3864 16 45 776937 223063 873167 Cos. D. Sec. Cot. 54 Deg. 439 157 157 126833 6230 3770 53 15 D. Tang. Cos. D. Sine 531 Deg. 156 4711 53 25 224590 870793 129207 5383 4617 156 128943 5477 224420 871057 156 4523 38 775750 128679 5571 224250 871321 39 775920 224080 871585 283 40 776090 223910 871849 283 41 776259 283 223741 872112 42 776429 43 776598 282 223402 872640 129735 5196 129471 5289 440 156 27 156 4804 26 440 24 440 440 440 439 439 439 439 23 157 128415 5665 4335 157 128151 5759 4241 157 127888 5853 4147 157 127624 5947 223571 872376| 4429 22 21 20 19 127360 6041 157 3959 4053 18 17 98 76 5 MATHEMATICAL TABLES. 121 282 281 281 281 281 281 281 280 O 279 279 279 279 23937 097271 23674 097366 23411 097461 59 79295 20705 76851 23149 097556 37 79463 36 Deg. TABLE V.-LOG. SINES, ETC. Sine D. Cosec. Tang., D. | Cot. Sec. 9'7 10*2 9.8 36 45 76937 282 23063 73167 26833 096230 903770 46 77106 47 77275 48 77444 49 77613 50 77781 22219 74484 25516 096702 158 22725 73694 26306 096419 903581 22556 73957 26043 096513 22387 74220 25780 096608 51 77950 |22050| 74747 52 78119 21881 75010 53 78287 21713 75273 280 36 54 78455 280 21545 75536 55 78624 280 21376 75800 438 5678792 21208 76063 57 78960 280 21040 76326 58 79128 20872 76589 438 280 37 Deg. D. Cos. ΙΟΙ 10° 9' 439 439 439 439 439 22894 73430 26570 096324 157 15 903676 157 14 157 13 903487 12 57 903392 II 439 439 25253 096797 158 903298 ΙΟ 439 438 24990 096892 24727 096986 158 903203 158 903108 158 903014 53 24464 097081 438 24200 097176 158 902919 98 76 158 902824 5 438 158 902729 4 158 902634 3 20537 77114 22886 097651 I 79631 20369 77377 22623 097747 2 79798 20202 77640 22360 097842 438 438 438 438 438 159 902539 2 159 902444 I 159 902349 53 0 159 902253 59 37 3 456 7∞ 80467 80634 279 4 80133 19867 78165 279 80300 278 278 19533 78691 3 79966 20034 77903 438 22097 097937 159 902158 52 58 278 19366 78953 278 278 278 277 13 81634 14 81800 56 78 277 277 277 277 277 276 276 276 159 159 £59 21309 098224 159 21047 098319 901681 8 80801 159 19199 79216 20784 098415 901585 159 9 80968 19032 79478 20522 098510 159 10 81134 18866 7974I 20259 098606 160 901394 11 81301 18699 80003 29997 098702 901298 37 12 81468 18532 80265 29735 098798 902063 438 15 81966 18034 81052 18948 099086 276 16 82132 17868 81314 18686 099182 17 82298 17702 81576 18 82464 17536 81839 19 82630 17370 82101 20 82796 17204 82363 438 437 437 437 437 437 437 437 437 437 437 437 438 19700 78428 21572 098128 901872 57 21835 098033 901967 56 55 901776 54 53 52 901490 51 50 18366 80528 19472 098894 18200 80790 19210 098990 437 18424 099278 18161099374 900626 160 160 901202 160 901106 160 160 900914 160 900818 52 49 48 47 901010 46 45 44 437 37 21 82961 276 275 275 275 27 83953 28 84118 275 275 274 275 16047 84196 436 15882 84457 276 17039 82625 17375 099663 22 83127 16873 82887 17113 099760 2383292 16708 83148 24 83458 16542 83410 16590 099953 900047 25 83623 16377 83672 26 83788 16212 83934 436 17899 099471 17637 099567 160 900722 160 160 900529 43 42 4I 436 161 900433 161900337 52 40 436 436 16852 099856 436 436 436 29 84282 15718 84719 15281 100436 899564 436 30 84447 15553 84980 15020 100533 899467 52 30 Cos. D. Sec. Cot. D. Tang. Cos. ID. Sine 16328 100049 899951 16066 100146 899854 15804 100243 899757 43615543| 100340 899660 38 161 900240 161 900144 161 161 161 161 161 161 39 37 36 35 34 33 32 31 531 Deg. K 52 Deg. 122 MATHEMATICAL TABLES. 37 Deg. Sine TABLE V.-LOG. SINES, ETC. D. Cosec. Tang. | D. Cot. 38 Deg. Sec. D. Cos. 9° IO' 9* IO* ΙΟ ΙΟ 9.89 274 274 274 274 274. 273 273 273 273 273 272 272 272 272 272 272 37 30 784447 215553 884980 215388 885242 31 784612 215224 885503 32784776 33 784941 215059 885765 34 785105 214895 886026 35 785269 214731 886288 36 785433 273 214567 886549 113451 1116 37 785597 214403 886810 113190 1213 8787 38 785761 214239 887072 112928 1311 8689 436 436 436 436 436 436 435 435 115020 0533 162 9467 30 435 114758 0630 162 9370 114497 0727 162 9273 1629273 114235 0824 9176 162 113974 0922 162 9078 113712 1019 8981 162 162 162 162 29 28 27 26 25 8884 24 23 52 22 271 271 37 39 785925 214075 887333 40 786089 213911 887594 41 786252 213748 887855 42 786416 213584 888116 43 786579 213421 888377 44 786742 213258 888639 45 786906 213094 888900 46 787069 212931 889160 47 787232 212768 889421 212605 889682 37 48 787395 49 787557 50 787720 435 435 435 435 435 112667 1408 112406 1506 112145 1603 111884 1701 111623 1798 111361 1896 66 162 163 163 163 163 435 163 435 III100 1994 110840 2092 163 435 163 110579 2190 435 163 271 271 271 271 271 270 270 270 212443 889943 212280 890204 435 435 268 268 268 267 D. 51 787883 212117 890465 109535 2582 52 788045 211955 890725 53 788208 211792 890986 54 788370 211630 891247 55 788532 211468 891507 56 788694 211306 891768 37 57 788856 211144 892028 107972 3172 270 164 58 789018 210982 892289 107711 3271 270 164 59 789180 210820 892549. 6631 107451 3369 270 38789342 210658 892810, 269 107190 3468 I 789504 210496 893070 106930 3567 269 2789665 106669 3665 210335 893331 269 3789827 106409 3764 210173 893591 269 434 106149 3863 4 789988 210012 893851 269 209851 89411I 5 790149 269 38 6790310 209690 894371 268 7 790471 268 209529 894632 8 790632 209368 894892 9 790793 268 209207 895152 10 790954 209046 895412 11 791115 208885 895672 12 791275 208725 895932 267 13791436 208564 896192 267 14 791596 208404 896452 15 791757 208243 896712 Cos. Sec. Cot. 110318 2288 110057 2386 109796 2484 163 163 2 mm en en MMM en 69666 66 8592 8494 21 20 8397 19 8299 18 8202 17 8104 16 8006 15 7908 14 7810 52 13 76 54 m 7712 12 7614 II 434 163 7516 IO 7418 434 434 434 434 109275 2680 164 109014 2778 7222 164 434 108753 2877 164 108493 2975 7025 164 164 7320 7123 434 108232 3074 6926 52 4 98 76 54 164 6828 434 434 434 434 434 6729 2 32 K I 164 6532 52 0 434 434 105889 3962 6 6 6 6 6 1 164 165 6433 59 165 6335 58 165 6236 57 165 6137 56 434 165 6038 51 55 434 433 433 105629 4061 5939 165 105368 4160 5840 105108 4259 5741 104848 4359 54 165 53 165 52 433 433 433 104588 4458 5542 165 104328 4557 166 5443 165 5641 51 50 49 104068 4657 433 166 5343 48 103808 4756 433 166 5244 47 103548 4855 5145 46 433 166 103288 4955 5045 51 45 D. Tang. Cos. D. Sine 52 Deg. 512 Deg. 123 MATHEMATICAL TABLES. 266 265 265 265 265 265 4646 166 101990 5454 166 4546 101730 5554 4446 167 101470 5654 4346 167 23793035 266 206965 898789 101211 5754 4246 167 38 24 793195 206805 899049 100951 5854 25 793354 206646 899308 100692 5954 4046 26 793514 100432 6054 206486 899568 27793673 206327 899827 100173 28 793832 206168 900086 099914 6255 3745 267 16 791917 267 208083 896971 103029 5055 166 4945 17 792077 102769 5154 207923 897231 267 166 18 792237 266 207763 897491 102509 5254 4746 166 19 792397 266 207603 897751 102249 5354 20 792557 266 207443 898010 21 792716 207284 898270 22 792876 266 207124 898530 38 Deg. Sine 9' TABLE V.-LOG. SINES, ETC. D. Cosec. Tang. | D. Cot. 39 Deg. Sec. D. Cos. IO' 9° 3815791757 208243 896712 ΙΟ ΙΟΙΟ 9.89 103288 4955 166 5045 433 433 433 433 455 44 4846 43 42 41 433 40 433 433 433 433 432 51 37 167 4146 333 98 76 39 38 36 35 264 264 | 37 795259 38795417 39 795575 204741 902419 263 263 262 262 262 262 261 261 261 261 261 260 260 260 55 798091 261 201909 907077 431 56 798247 57 798403 58 798560 59 798716 60 798872 Cos. D. 201753 907336 201597 907594 201440 907852) 201284 908111 201128 908369 Sec. Cot. D. 29 793991 265 | 206009 900346| 099654 6355 30 794150 205850 900605 099395 6456 31 794308 205692 900864 099136 6556 3444 168 32 794467 205533 901124 098876 6657 264 168 38 33 794626 098617 6757 264 205374 901383 168 3243 34 794784 098358 6858 205216 901642 264 168 35 794942 264 205058 901901 098099 6959 168 3041 36 795101 204899 902160 097840 7060 2940 264 168 097581 7161 2839 263 168 097321 7261 204583 902679 263 168 2739 2638 097062 7362 204425 902938 263 168 096803 7464 2536 40 795733 263 204267 903197 431 168 41 795891 204109 903455 096545 7565 2435 51 19 263 169 38 42 796049 096286 7666 203951 903714 203794 903973 43 796206 096027 7767 203636 904232 44 796364 095768 7868 45 796521 095509 7970 203479 904491 46 796679 203321 904750 095250 8071 47 796836 203164 905008 094992 8173 48 796993 094733 8274 203007 905267 262 49 797150 202850 905526 094474 8376 202693 905784 094216 8477 50 797307 202536 906043. 38 51 797464 093957 8579 52 797621 093698 8681 202379 906302 53 797777 261 202223 906560 093440 8783 54 797934 261 202066 906819 093181 8885 1013 092923 8987 |092664 9089 092406 9191 092148 9293 432 432 432 432 432 432 432 432 432 432 432 432 432 432 432 167 167 167 6154 3846 3946 34 33 32 167 3645 31 167 167 3544 30 29 3343 51 28 27 3142 26 25 24 23 22 2I 20 431 431 431 431 431 431 431 431 431 431 431 431 431 431 2334 18 169 2233 17 169 2132 16 169 2030 15 169 1929 14 8173169 169 1827 13 1726 12 169 1624 II 169 1523 51 10 170 1421 431 431 431 430 170 170 170 170 170 170 170 1319 1217 1115 OGII 0809 98 7ont m 6 5 4 3 0707 2 091889 9395 091631 9497 0503 51 o Tang. Cos. D. Sine 170 0605 I 170 51 Deg. 51 Deg. 124 MATHEMATICAL TABLES. 39 Deg. O TABLE V.-LOG. SINES, ETC. Sine D. Cosec. Tang.| D. Cot. Sec. D. Cos. 9* 10° 9'9 10'0 ΙΟΙ 39 798872 260 201128 08369 91631 09497 90503 39 Deg. 9.8 60 260 259 259 259 259 259 259 258 258 14 15 258 257 257 257 257 257 257 256 256 197718 14044 23 802436 256 197564 14302 24 802589 25 802743 19 801819 198181 13271 20 801973 198027 13529 86471 11556 21 802128 197872 13787 22 802282 7 799962 8 800117 39 9 800272 199728 10693 10 800427 199573 10951 II 800582 199418 11209 12 800737 258 88533 10729 199263 11467 258 13 800892 172 88276 10832 |199108 11724 258 801047 198953 11982 88018 10936 89064 801201 258 172 87760 11039 198799 12240 88961 16 801356 198644 12498 172 87502 11142 88858 17 801511 172 87244 11245 198489 12756 39 18 801665 198335 13014 86986 11349 430 430 430 I 799028 260 200972 08628 91372 09600 90400 430 200816 08886 2 799184 91114 09702 90298 200661 09144 430 3 799339 |90856 09805 430 4 799495 200505 09402 90598 09907 430 5799651 200349 09660 90340 10010 89990 55 430 6799806 200194 09918 90082 10112 89888 430 200038 10177 171 89823 10215 89785 170 59 171 171 171 171 171 58 90195 57 90093 56 54 53 199883 10435 89565 10318 89682 50 52 430 430 430 430 430 430 430 430 430 429 429 89307 10421 89579 89049 10523 89477 171 171 171 171 88791 10626 89374 49 172 89271 89168 48 47 172 172 86729 11452 172 172 88548 88755 50 43 88651 429 86213 11659 429 429 429 197411 14560 26 802897 39 27 803050 196950 15332 256 256 256 255 255 255 255 255 255 254 254 254 254 197103 15075 429 429 429 85183 12074 256 197257 14817 85956 11763 88237 85698 11866173 88134 173 88030 85440 11970 88444 173 88341 173 £ £ £ £ ‡‡ A+ AAYU one 50 46 45 44 42 4I 40 39 38 37 36 173 87926 35 84925 12178 173 87822 50 34 173 84668 12282 87718 33 195877 17134 40 805039 41 805191 42 805343 43 805495 253 44 805647 253 45 805799 Cos. D. 254 254 253 28 803204 196796 15590 29 803357 196643 15847 30 803511 196489 16104 31 803664 196336 16362 32 803817 196183 16619 33803970 196030 16877 34 804123 35 804276 195724 17391 39 36 804428 195572 17648 37 804581 195419 17905 38 804734 195266 18163 39804886 195114 18420 254 194961 18677 428 194809 18934 428 81066 13743 194657 19191 80809 13848 194505 19448 80552 13953 194353 19705) 80295 14058 194201 19962 80038 14163 85837 50 15 Sec. Cot. D. Tang. Cos. D. Sine 429 84410 12386 173 87614 32 429 84153 12490 173 87510 31 429 429 173 83896 12594 87406 30 83638 12698 174 87302 29 429 174 83381 12802 87198 28 429 429 83123 12907 82866 13011 174 174 87093 27 429 429 174 82609 13115 174 86885 50 25 86989 26 429 82095 13324 429 428 81837 13429 86571 81580 13534 174 81323 13638 174 174 82352 13220 86780 24 86676 23 22 174 428 428 428 428 175 86152 86466 21 86362 20 175 86257 19 18 175 86047 17 175 175 85942 16 51 Deg. 501 Deg. MATHEMATICAL TABLES. 125 39 Deg Sine D. TABLE V.-LOG. SINES, ETC. Cosec. Tang. | D. Cot. Sec. D. Cos. 40 Deg. 9° 10° 9° 10° IO II 9.88 253 253 253 253 252 252 252 252 252 252 252 251 251 251 251 251 251 251 192535 922787 192385 923044 192234 923300 192083 923557 191933 923813 191782 924070 39 45 805799 194201 919962 080038 4163 46 805951 194049 920219 0797814268 193897 920476 47 806103 48 806254 193746 920733 428 079267 4478 | 49 806406 193594 920990 079010 4584 50 806557 175 078753 4689 193443 921247 51806709 193291 921503 078497 4795 52 806860 078240 4900 193140 921760 192989 922017 53 807011 077983 5006 39 54 807163 192837 922274 55 807314 56 807465 57 807615 58 807766 59 807917 400 808067 I 808218 428 428 428 5837 175 15 5732 079524 4373 5627 175 14 175 13 5522 12 175 428 5416 II 428 428 428 428 5311 IO 7 76 17 5205 77 176 5100 98 176 4994 50 7 192686 922530 428 077726 5111 428 428 077470 5217 077213 5323 176 4889 6 428 076956 5428 176 176 4783 4677 5 4 428 2 808368 191632 924327 427 075673 5958 177 250 250 250 250 250 250 249 249 249 249 249 249 177 4254 50 O 59 4042 49 58 40 3 808519 191481 924583 075417 6064 3936 4 808669 191331 924840 075160 6171 5808819 191181 925096 074904 6277 6808969 191031 925352 074648 6383 7 809119 190881 925609 074391 6490 8 809269 190731 925865 9 809419 190581 926122 10 809569 190431 926378 11 809718 190282 926634 427 427 076700 5534 076443 5640 076187 5746 177 075930 5852 4148 176 4572 3 176 4466 176 4360 2 I 427 427 427 427 427 427 427 177 57 3829 177 56 3723 177 55 3617 177 54 3510 074135 6596 3404 073878 6703 177 53 177 52 427 073622 6809 178 3297 51 427 248 248 248 248 248 248 40 12 809868 190132 926890 13 810017 189983 927147 072853 7129 14 810167 189833 927403 072597 7236 15 810316 189684 927659 248 072341 7343 16 810465 189535 927915 0720857450 17 810614 189386 928171 071829 7557 18 810763 189237 928427 071573 7664 19 810912 189088 928683 071317 7771 188939 928940 427 071060 7879 427 073366 6916 178 3191 50 178 3084 49 49 073110 7023 427 427 427 427 427 427 427 178 2977 48 178 178 178 178 178 ∞ ∞ ∞ ∞ ∞ ∞ 2871 47 2764 46 2657 45 2550 44 2443 43 247 247 247 187900 930731 187752 930987 187604 931243 20 811061 40 21 811210 22 811358 23 811507 24 811655 25 811804 26 811952 27 812100 188196 930220 247 188048 930475 247 28 812248 247 29 812396 30 812544 247 246 Cos. D. 501 Deg. 187456 931499 068501 8954 Sec. Cot. D. Tang. Cos. D. Sine 179 179 2336 42 2229 4I 2121 188790 929196 070804 7986 188642 929452 188493 929708 188345 929964 427 427 427 427 49 40 古 179 179 070548 8093 2014 1907 39 38 070292 8201 426 070036 8308 179 426 426 426 426 426 069780 8416 069525 8523 069269 8631 069013| 8739 068757 8847 179 179 180 179 1261 179 1584 1477 1369 179 1692 1799 37 36 35 34 33 32 1153 180 31 1046 49 30 494 Deg. 126 MATHEMATICAL TABLES. 40 Deg. TABLE V.-LOG. SINES, ETC. Sine. D. Cosec. Tang. D. Cot. Sec. 9.8 ΙΟΙ 9° 4030 | 12544 87456 931499 IO' 411 Deg. D. Cos. ΙΟΙ 9.8 245 245 245 245 42 14313 245 244 244 244 244 244 244 244 243 243 243 243 243 242 242 242 242 242 242 242 241 241 41 6 17813 82187 940694 059306 22880 241 7 17958 82042 940949 |059051| 22990 241 8 18103 81897 941204 058796 23101 241 9 18247 81753 941458 |058542 23211 241 10 18392 81608 941714 058286 23322 241 II 18536 |81464 941968 058032 23432 240 12 18681 81319 942223 057777 23543 240 1318825 81175 942478 057522 23653 240 14 18969 240 15 19113 Cos. D. 22660 059817 517668 82332 940438| 059562 22770 246 31 12692 87308 931755 068245 19062 80938 246 87160 932010 32 12840 067990 19170 246 33 12988 87012 932266 067734 19278 246 86865 932522 34 13135 |067478 19387 246 35 13283 86717 932778 067222 19495 80505 246 36 13430 86570 933033 |066967 19603 37 13578 245 86422 933289 066711 19711 86275 933545 38 13725 066455 19820 80180 86128 933800 066200 19928 40 39 13872 40 14019 85981 934056 41 14166 85834 934311 245 85687 934567 43 14460 85540 934823 44 14607 85393 935078 45 14753 85247 935333 46 14900 85100 935589 47 15046 84954 935844 40 48 15193 84807 936100 49 15339 84661 936355 50 15485 84515 936610 51 15632 84368 936866 063134 21234 78766 52 15778 84222 937121 062879 21344 78656 53 15924 243 83931 937632 84076 937376 062624 21453 78547 54 16069 062368 21562 78438 55 16215 243 83639 938142 83785 937887 062113 21672 78328 56 16361 061858 21781 78219 49 40 57 16507 83493 938398 061602 21891 58 16652 83348 938653 061347 22001 59 16798 83202 938908 061092 22110 41 0 16943 83057 939163 060837 22220 I 17088 82912 939418 060582 22330 217233 82767 939673 060327 22440 3 17379 82621 939928 060072 22550 77450 4 17524 82476 940183 426 426 426 426 426 426 426 426 426 426 426 426 426 068501 18954 81046 180 30 29 180 180 80830 28 180 80722 27 180 80613 26 98 76 180 25 426 426 426 426 426 426 426 426 425 425 425 425 425 425 425 425 425 425 425 425 425 425 425 425 425 425 425 425 425 425 425 425 80072 065944 20037 79963 065689 20145 79855 065433 20254 79746 065177 20363 79637 064922 20471 79529 064667 20580 79420 064411 20689 79311 064156 20798 79202 063900 20907 063645 21016 78984 063390 21125 180 181 181 181 181 181 181 181 181 181 181 182 182 182 182 182 182 182 182 182 80397 24 80289 23 49 22 21 20 19 18 17 16 15 98 765 14 49 13 79093 12 II 78875 ΙΟ 10 900 DO 54 8 7 6 4 183 78109 3 ∞ ∞ 183 183 77999 2 77890 I 183 183 77780 49 0 77670 59 183 183 77560 58 57 183 183 77340 56 184 77230 48 55 77120 54 184 77010 53 184 76899 52 184 76789 51 184 76678 50 184 184 76568 49 184 76457 48 76347 47 81031 942733 057267 23764 80887 942988 057012 23875 184 76236 46 185 76125 4845 Sec. Cot. D. Tang. Cos. D. Sine 49 Deg. 48 Deg. MATHEMATICAL TABLES. 127 i 41 Deg. O Sine 9 TABLE V.-LOG. SINES, ETO. 42 Deg. D. Cosec. Tang. D. | Cot. Sec. D. Cos. 10' 9* IO* 10'12 9.87 41 15 819113 16 819257 17 819401 18 819545 19 819689 20 819832 21 819976 22 820120 2 2 238 238 ∞ ∞ ∞ ∞ ∞ ∞ 179021 946299 237 237 237 237 237 237 237 31 821407 32 821550 41 33 821693 178307 947572 052428 5879 34 821835 178165 947826 052174 5991 35 821977 178023 948081 424 051919 6104 36 822120 177880 948336 051664 6216 37 822262 177738 948590 051410 6328 38 822404 177596 948844 051156 6440 39 822546 177454 949099 050901 6552 40 822688 236 177312 949353 050647 6665 41 822830 177170 949607 236 28 820979 238 29 821122 238 178878 946554 053446 5432 30 821265 238 178735 946808 240 240 240 239 239 239 239 239 239 41 24 820406 179594 945281 054719 4874 5126 239 25 820550 179450 945535 238 26 820693 238 179307 945790 27 820836 238 179164 946045 23 820263 179737 945026 054974 4763 5237 48 37 425 425 425 425 425 425 425 424 424 180311 944007 055993 4318 180168 944262 055738 4429 055483 4541 180024 944517 185 179880 94477! 055229 4652 5348 180887 942988 180743 943243 180599 943498 180455 943752 056248 4207 5793 185 057012 3875 6125 185 056757 3986 6014 185 056502 4096 185 ∞ ∞ ∞ 5904 42 7777 45 44 43 185 5682 4I 185 5571 40 5459 39 38 185 185 424 186 36 054465 4986 424 1865014 35 054210 5097 424 186 4903 34 053955 5209 424 186 4791 33 (053701| 5320 424 178593 947063 052937 5656 424 424 424 424 424 186 1864568 4680 32 3I 053192 5544 186 4456 30 186 4344 178450 947318 052682 5768 4232 187 29 48 28 187 4121 27 187 4009 26 236 236 236 235 235 235 235 236177028 949862 050138 6890 424 424 41 42 822972 43 823114 176886 950116 049884 7002 44 823255 176745 950370 |049630 7115 2885 176603 950625 236 188 3110 188 188 45 823397 049375 7228 188 2772 46 823539 176461 950879 049121 7341 2659 188 47 823680 176320 951133 048867 7453 188 2547 48 823821 176179 951388 048612 7566 2434 188 49 823963 176037 951642 048358 7679 188 2321 50 824104 175896 951896| 048104 7792 2208 188 41 51 824245 175755 952150 047850 7905 2095 235 52 824386 175614 952405 047595 8019 1981 235 53 824527 175473 952659 047341 8132 235 54 824668 175332 952913 047087 8245 234 55 824808 175192 953167 046833 8359 234 56 824949 175051 953421 046579 8472 234 57 825090 174910 953675 046325 8586 234 189 58 825230 174770 953929 046071 8699 234 189 174629 954183 045817 8813 1187 234 189 174489 954437 045563 8927 1073 48 0 Cos. D. Sec. Cot. D. Tang. Cos. D. Sine 59 825371 60 825511 483 Deg. 98 76543 424 424 424 424 424 424 4.24 187 3896 25 187 3784 24 187 3672 23 187 3560 22 187 3448 21 050393 6777 187 3335 20 187 3223 48 19 18 2998 17 16 424 424 424 424 424 424 424 424 189 424 424 424 423 423 423 423 423 189 189 1868 189 189 1755 1641 189 1528 1414 1301 2 I 15 14 13 12 II 48 10 48 Deg. 128 MATHEMATICAL TABLES. 42 Deg. TABLE V.-LOG. SINES, ETC. 42 Deg. O Sine | D. Cosec. D. Cosec. Tang.| D. 9.8 Cot. Sec. D. Cos. 42 25511 I 25651 225791 325931 4 26071 5 26211 626351 7 26491 826631 10'I 9'9 74489 54437 10°0 ΙΟΙ 9.8 45563 28927 71073 60 234 423 74349 54691 190 45309 29040 70960 233 423 190 233 74209 54945 74069 55200 45055 29154 70846 58 423 44800 29268 190 70732 233 423 73929 55454 44546 29382 190 70618 གགག་ 59 57 56 233 423 73789 55707 233 423 44293 29496 190 70504 55 73649 55961 233 233 73509 56215 423 423 44039 29610 43785 29724 190 190 70276 70390 54 53 190 73369 56469 4353 29839 70161 47 52 233 423 190 42 9 26770 232 73230 56723 43277 29953 70047 51 423 232 232 232 232 232 232 10 26910 II 27049 12 27189 1327328 14 27467 72533 57993 15 27606 72394 58246 73090 56977 423 43023 30067 191 69933 50 191 72951 57231 42769 30182 69818 49 423 191 72811 57485 42515 30296 69704 48 72672 57739 423 42261 30411 191 69589 47 423 42007 30526 191 69474 46 423 191 41754 30640 69360 45 423 191 16 27745 17 27884 72255 58500 41500 30755 69245 44 232 423 72116 58754 41246 30870 191 69130 47 43 231 423 191 42 18 28023 231 71977 59008 423 40992 30985 69015 42 192 19 28162 71838 59262 40738 31100 68900 4I 231 25 28993 26 29131 71007 60784 70869 61038 42 27 29269 70731 61291 231 231 231 231 230 230 230 230 230 230 230 229 229 229 229 229 229 20 28301 71699 59516 21 28439 71561 59769 22 28578 71422 60023 71284 60277 23 28716 2428855 71145 60531 423 192 40484 31215 68785 40 423 192 40231 31330 68670 423 192 39977| 31445 68555 423 423 39723 31560 192 68440 39469 31676 192 68324 28 76 mmm m 39 38 37 36 423 192 39216 31791 68209 35 423 192 423 38962 31907 68093 47 34 192 31 29821 70179 62306 32 29959 70041 62560 33 30097 69903 62813 34 30234 69766 63067 69628 63320 35 30372 42 36 30509 69491 63574 37 30646 38 30784 39 30921 2829407 2929545 70455 61799 3029683 70317 62052 70593 61545 423 38709 32022 67978 33 38455 32138 193 67862 32 423 193 423 38201 32253 67747 31 37948 32369 19367631 30 423 193 37694 32485 67515 29 423 37440 32601 193 67399 28 423 423 37187 32717 193 67283 27 36933 32833 19367167 26 423 423 36680 32949 193 67051 47 25 193 229 229 228 69354 63827 69216 64081 69079 64335 41 31195 228 42 31332 228 43 31469 228 44 31606 228 45 31742 36426 33065 36173 33181 35919 33297 35665 33414 40 31058 228 68942 64588 35412 33530 68805 64842 35158 33647 68668 65095 423 194 66819 66935 24 23 423 423 423 422 422 422 422 422 194 194 66586 66.703 22 21 194 66470 20 194 66353 19 Cos. D. 34905 33763 68531 65349 34651 33880 68394 65602 34398 33996 6825865855 34145 34113 Sec. Cot. D. Tang. Cos. 194 66237 18 194 66120 17 194 66004 16 195 65887 47 15 D. Sine 48 Deg. 471 Deg. MATHEMATICAL TABLES. 129 422 Deg. TABLE V.-LOG. SINES, ETC. 434 Deg. Sine 9-8 D. | Cosec. Tang.] D. Cot. Sec. D. Cos. 10'1 9'9 IO'O ΙΟΙ 9.8 42 45 | 31742 46 31879 47 32015 48 32152 49 32288 50 32425 51 32561 52 32697 53 32833 42 54 32969 226 228 228 422 422 227 67848 66616 422 68258 65855 34145 34113 68121 66109 67985 66362 65887 15 33891 34230 195 65770 14 33638 34347 195 65653 13 195 33384 34464 65536 12 227 227 227 67712 66869 422 33131 34581 195 65419 II 67575 67123 422 32877 34698 195 65302 10 67439 67376 422 227 67303 67629 422 32624 34815 195 65185 195 32371 34932 65068 98 227 422 67167 67883 195 32117 35050 227 422 195 64950 47 7 O 55 33105 226 56 33241 226 57 33377 226 58 33512 59 33648 43 33783 67031 68136 66895 68389 66759 68643 66623 68896 422 31864 35167 64833 6 422 31611 35284 64716 196 196 5 422 31357 35402 31104 35519 196 64598 4 226 66488 69149 422 196 64481 3 30851 35637 226 66352 69403 422 196 64363 2 226 66217 69656 30597 35755 422 196 64245 I 33919 66081 69909 422 30344 35873 196 64127 47 0 30091 35990 234054 225 225 65946 70162 422 196 64010 59 29838 36108 63892 46 58 422 197 6 10 35134 17 36075 43 12 35403 64597 72694 13 35538 64462 72948 14 35672 64328 73201 15 35807 64193 73454 16 35941 224 63925 73960 64059 73707 225 225 225 225 225 225 224 224 224 43 334189 65811 70416 434325 65675 70669 422 29584 36226 63774 422 29331 36344 197 63656 ༄༦༦༠༥ 5 34460 65540 70922 29078 36462 197 63538 55 422 197 34595 65405 71175 28825 36581 9 34999 65001 71935 64866 72188 II 35269 64731 72441 7 34730 65270 71429 834865 65135 71682 422 28571 36699 197 63419 54 63301 53 422 28318 36817 197 63183 52 422 28065 36936 197 63064 51 422 197 27812 37054 422 198 62946 50 27559 37173 422 198 62827 46 49 224 224 224 224 422 27306 37291 198 62709 48 27052 37410 422 198 62590 47 422 26799 37529 198 62471 46 422 26546 37647 198 62353 45 26293 37766 422 198 62234 44 223 20 36477 223 223 43 21 36611 22 36745 2336878 24 37012 25 37146 26 37279 27 37412 28 37546 2937679 30 37812 18 36209 223 63791 74213 25787 38004 1936343 63657 74466 25534 38123 26040 37885 422 422 422 422 198 62115 43 198 61996 42 63523 74719 25281 38242 198 61877 4I 61758 46 40 199 223 223 223 63122 75479 62988 75732 222 222 222 222 222 222 62188 77250 24521 38600 24268 38720 62854 75985 2401538839 62721 76238 23762 38959 62588 76491 23509 39078 62454 76744 23256 39198 62321 76997 23003 39318 22750 39438 Cos. D. Sec. Cot. D. Tang. Cos. 422 422 422 422 422 422 422 422 422 63389 74973 25027 38362 63255 75226 24774 38481 199 61400 199 61519 61638 39 38 37 199 61280 36 199 61161 35 199 199 61041 34 60922 33 199 60802 199 32 60682 31 200 60562 46 30 D. Sine 471 Deg. 461 Dog. 130 MATHEMATICAL TABLES. 43 Deg. TABLE V.-LOG. SINES, ETO. Sine D. Cosec. | Tang. D. Cot. Sec. 44 Deg. D. Cos. 9.8 43 30 37812 ΙΟΙ 9'9 62188 77250 10'0 ΙΟΙ 9.8 31 37945 32 38078 33 38211 222 222 221 221 62055 77503 61922 77756 422 22750 39438 60562 30 200 422 22497 39558 60442 29 200 2224439678 61789 78009 422 60322 28 200 21991 39798 60202 27 34 38344 61656 78262 422 21738 39918 200 60082 26 221 35 38477 61523 78515 422 200 221 21485 40038 59962 36 38610 61390 78768 422 25 200 221 21232 40158 59842 24 37 38742 3838875 221 61258 79021 422 200 20979 40279 59721 221 61125 79274 422 23 422 20726 40399 201 59601 46 22 201 48 39 39007 221 40 39140 220 41 39272 220 6099379527 60860 79780 60728 80033 20473 40520 59480 21 422 201 20220 40640 59360 20 422 201 19967 40761 59239 19 4239404 60596 80286 422 201 220 19714 40881 59119 18 86 43 39536 220 60464 80538 422 201 19462 41002 58998 17 44 39668 4539800 60332 80791 422 201 46 39932 47 40064 43 48 40196 220 220 220 219 60200 81044 421 19209 41123 58877 16 201 60068 81297 42 I 18956 41244 58756 15 202 18703 41365 59936 81550 421 58635 14 202 18450 41486 42I 58514 46 13 202 59804 81803 219 18197 41607 49 40328 5040459 59672 82056 42I 58393 12 202 219 17944 41728 58272 II 59541 82309 421 202 219 17691 41849 51 40591 219 59409 82562 421 58151 10 202 52 40722 53 40854 59146 83067 5440985 5901583320 55 41116 58884 83573 56 41247 58753 83826 43 57 41378 218 58622 84079 58 41509 218 58491 84331 59 41640 44 0 | 41771 59278 82814 421 17438 41971 58029 202 219 219 219 218 218 421 1718642092 57908 202 421 16933 42214 57786 42I 16680 42335 202 57665 421 16427 42457 203 57543 42 I 16174 42578 203 57422 46 4 98 7654 203 15921 42700 421 57300 3 1566942822 203 218 218 58360 84584 421 57178 2 I 41902 218 58229 84837 58098 85090 421 15416 42944 203 57056 I 15163 43066 203 421 56934 46 o 218 5 42424 217 217 217 242033 57967 85343 3 42163 57837 85596 4 42294 57706 85848 421 14910 43188 203 56812 421 14657 43310 203 56690 204 14404 43432 421 56568 in in in 59 58 57 204 57576 86101 421 14152 43554 56446 56 421 13899 43677 204 204 56323 45 55 44 642555 742685 217 57445 86354 8 42815 217 57315 86607 42 I 13646 43799 56201 54 204 13393 43922 Cos. D. 942946 57054 87112 10 43076 56924 87365 11 43206 216 56794 56794 87618 12 43336 13 43466 14 43595 216 15 43725 46 Deg. 217 57185 86860 421 56078 53 204 421 13140 44044 55956 52 217 217 12888-44167 204 421 55833 51 421 12635 44289 204 55711 50 216 216 56664 87871 56534 88123 56405 88376 56275 88629 421 12382 44412 205 55588 49 12129 44535 205 42 I 421 421 55465 48 11877 44658 205 55342 47 205 205 11624 44781 11371 44904 55096 45 45 55219 46 Sec. Cot. DTang. Cos. D. Sine 45 Deg. MATHEMATICAL TABLES. 131 441 Deg. TABLE V.-LOG. SINES, ETC. 45 Deg. Sine D. Cosec. Tang. D. | Cot. Sec. D. Cos. ΙΟΙ 216 17 3984 9.84 44 15 3725 56275 9.988629 11371 44904 16 3855 216 56145 9988882 11118 45027 216 56016 9989134 IO'O ΙΟΙ 9.8 19 4243 31 5790 215 215 215 215 215 215 215 215 215 214 214 214 214 214 214 214 214 214 213 213 213 213 213 213 213 213 212 212 212 212 212 212 212 212 211 211 211 211 211 211 211 51909 9'997221 51782 9997473 44 51 8345 51655 9997726 52 8472 51528 9997979 53 8599 51401 9998231 54 8726 55 8852 56 8979 57 9106 58 9232 59 9359 45 7582 52418 9996210 03790 48628 46 7709 52291 9996463 03537 48754 477836 52164 9996715 03285 48879 48 7964 52036 9*996968 03032 49004 49 8091 50 8218 18 4114 55886 9989387 10613 45273 55757 9989640 10360 45397 20 4372 55628 9989893 10107 45520 21 4502 55498 9990145 09855 45644 22 4631 55369 9990398. 09602 45767 23 4760 55240 9990651 09349 45891 44 244889 55111 9990903 09097 46014 25 5018 08844 46138 54982 9991156 26 5147 54853 9991409 08591 46262 27 5276 54724 9991662 08338 46386 28 5405 54595 9'991914 08086 46510 29 5533 54467 9992167 |07833 46634 30 5662 54338 9992420 07580 46758 54210 9992672 07328 46882 32 5919 54081 9992925 07075 47006 44 33 6047 53953 9993178 06822 47131 34 6175 53825 9993430 06570 47255 35 6304 53696 9993683 06317 47380 36 6432 53568 9993936 06064 47504 37 6560 53440 9994189 05811 47629 38 6688 05559 47753 53312 9994441 39 6816 53184 9994694 05306 47878 40 6944 53056 9994947 05053 48003 41 7071 04801 48128 52929 9995199 44 42 17199 52801 9995452 04548 48253 43 7327 52673 9995705 04295 48378 447454 52546 9995957 04043 48503 421 42I 421 421 421 42I 421 421 421 421 421 421 421 421 421 421 421 421 421 421 421 421 421 421 421 421 421 55096 45 205 54973 44 10866 45150 205 54850 43 205 206 54727 42 206 54603 41 206 54480 40 206 54356 39 206 54233 38 206 54109 45 37 206 53986 36 206 206 53738 53862 35 34 53614 33 207 53490 32 207 53366 31 207 53242 30 207 207 53118 29 52994 45 28 207 207 52869 27 52745 26 207 52620 25 207 208 52496 24 208 52371 23 208 52247 22 208 52122 21 208 208 51997 20 51873 45 19 02779 49130 0252749255 02274 49381 C2021 49507 01769 49632 51274 9998484 01516 49758 51148 9998737 01263 49884 51021 9998989 01011 50010 60 9485 211 50894 9999242 00758 50136 50768 9.999495 00505 50262 50641 9999747 00253 50389 421 50515 10.000000 00000 50515 421 421 42 I 421 421 421 421 421 421 421 421 421 421 421 421 421 421 208 51747 18 208 51622 17 51497 16 209 51372 15 209 51246 14 209 51121 13 209 50996 12 209 50870 II 209 50745 45 10 209 50619 209 210 210 210 210 50493 50368 50242 98 76 50116 5 49990 4 210 49864 3 210 49738 2 210 49611 210 49485 45 Cos. D. Sec. Cot. D. Tang. Cos. 45 Deg. D. Sine 45 Deg. 132 MATHEMATICAL TABLES. TABLE VI.—MERIDIONal Parts. 4 7 8 9 0×23 + no t∞ αlo Hamt SO N∞ a O I I 0 2 C 2 O O I I 12 2 3456 78 9 6° 17° | 8° 9 13° | 14° |15" | 16° | 17° | 18° | 19° | 20° | 21° | 22° | 23° | 24° 60 120 180 240 300 361 421 482 542 603 664 725 787 848 910 973 1035 1098 1161 1225 1289 1354 1419 1484 1 61121181 788850911 61 121 181 241 301 362 422 483 543 604 665 726 788 850 911 974 1036 1099 1163 1226 1290 1355 1420 1485 62 122 182 242 302 363 423 484 544 605 666 727 789 851 913 975 1037 1100 1164 1227 1291 1356 1421 1486 63 123 183 243 303 364 424 485 545 606 667 728 790 852 914 976 1038 1101 1165 1228 1292 1357 1422 1487| 64 124 184 244 304 365 425 486 546 607 668 729 791 853 915 977 10391102 1166|1229 1293 13581423 1488 65 125 185 245 305 366 426 487 547 608 669 730 792 854 916 978 1041 1103 1167 1230 1295 1359 1424 1490 6 66 126 186246 306 367 427 488 548 609 670 731 793 855 917 979 1042 1105 1168 1232|1296|1360|1425|1491 7|67|127187|247|307|368|428|489|549|610|671|732 67127 187 247 307 368 428 489 549 610|671 732 794 856 918 980 1043 1106 1169|1233 1297 1361|1426|1492 8 795857 68 128 188 248 308 369 429 490 550 611 672 734 795 857 919 981 10441107 1170 1234 1298 1362 1427 1493 9|69|129|189249309 370 430 491 551 612 673 735 796 858 920 982 1045 1108 11711235 1299 1363 14281494 10 70 130 190 250 310 371 431 492 552 613 674 736 797 859 921 983 1046 1109 1172 1236 1300 1364 1430 1495 10 11 71131191 251 311 372 432 493 553 614 675 737 798 860 922 984 1047 11101173 1237 1301 1366 1431 1496 II 12 72132192 252 312 373 433 494 554 615 676 738 799 861 923 985 1048 11111174 1238 1302 1367 1432 1497 12 13 73 133 193 253 313 374 434 495 555 616 677 739 800 862 924 986 1049 11121175 1239 1303 1368 1433 1498 13 14 74134194 254 314 375435 496 556 617 678 740 801 863 925 987 1050 1113 1176 1240 1304|1369|1434|1499|| 14 618679 741802 15 75 135 195 255 315 376 436 497 557 618 679 741 802 864 926 988 1051 1114 1177 1241 1305 1370 14351500 15 16 76136196 256 316 377 437 498 558 619 680 742 803 865 927 989 1052 1115 1178 1242 1306 1371 1436 1502 16 17 77 137 197 257 317 378 438 499 559 620 681 743 804 866 928 9901053 1116 1179 1243 1307 1372 1437 1503 17 18 78 138 198 258 318 379 439 500 560 621 682 744 805 867 929 991|1054 1117 1181 1244 1308 1373 1438 1504 18 19 79 139 199 259 319 380 440 501 561 622|683745|806|868|930| 993 10551118 1182 1245 1310 1374 1439 1505 19 80 140 200 260 320 381 441 502 562 623 684 746 807 869 931 994 10561119 1183 1246 13111375 1440 1506 20 21 81141 201|261|321 382 442 503 564 624 685 747 808 870 932 995 1057 1120 1184|1248|1312|1376|1441|1507 21 22 82 142 202 262 322 383 443 504 565 625 687 748 809 871 933 996 1058 1121 1185 1249 1313 1377 1443 1508 22 23 83143203263 323 384 444 505 566 626 688 749 810 872 934 997 1059 1122 1186 1250 1314 1379 14441509 23 24 84 144 204 264 324 385 445 506 567 627 689 750 811 873 935 998 1060 1123 1187 1251 1315 1380 1445 1510 24 25 85 145 205 265 325 386 446 507 568 628 690 751 812 874 936 999 1061 1125 1188 1252 1316 1381 1446 1511 25 26 86 146 206 266 326 387 447 508 569 629 691 752 813 875 937 1000 1063 1126 1189 1253 1317 1382 1447 1513 1126|1189|1253|13171382 26 27 87 147 207 267 327 388 448 509 570 631 692 753 815 876 938 1001| 1064 1127 1190 1254 13181383 1448 1514 27 28 88 148 208 268 328 389 449 510 571 632 693 754 816 877 939 1002 1065 1128 1191 1255 1319 1384 1449 1515 28 29 89149209269 330 390 450 511 572 633 694 755817878|941 1003|1066|1129|1192 1256 1320 1385 1450 1 1516 29 ΙΟ II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 2 2 2 2 2 2 2 20 22 MATHEMATICAL TABLES. 133 TABLE VI.-MERIDIONAL PARTS. w 30 31 32 wwwwwww a 40 4I 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 3456 7∞ 37 • I I 12 I 3 220 2° | 3° | 4° | 5° | 6° | 7° | 8° | 9° | 10 14° | 15° | 16° | 17° | 18° | 19° | 20° | 21° 23° 24° 30 90150210270 331 391 451 512 573 634 695 756 818 879 942 1004 1067 11301193 1257 1321 1386 1451 1517 30 31 91151211271 332 392 452 513 574 635 696 757 819 880 943 1005 1068 1131 1194 1258 1322 1387 1452 1518 31 32 92152212272 333 393 453 514 575 636 697 758 820 882 944 1006 1069 1132 1195 1259 1324 1388 1453 1519 32 33 93153213 273 334 394 454 515 576 637 698 759 821 883 945 1007 1070 1133 1196 1260 1325 1389 14551520 33 34 94154214274 335 395 455 516 577 638 699 760 822 884 946 1008 1071 1134 1198 1261 1326 1390 1456 1521 34 95|155|215|275|336|396|456|517578|639|700 35 95 155 215 275 336 396 456 517 578 639 700 761 823 885 947 1009 1072 1135 1199 1262 1327 1392 1457 1522 35 36 96156 216 276 337 397 457 518 579 640 701 762 824 886 948 1010 1073 1136 1200 1264 1328 1393 1458 1524 36 97 157 217 277 338 398 458 519 580 641 702 763 825 887 949 1011 1074 1137 1201 1265|1329 1394 1459 1525 37 38 98 158 218 278 339 399 459 520 581 642 703 764 826 888 950 1012 1075 1138 1202 1266 1330 1395 1460 1526 38 39 99 159 219 279 340 400 460 521 582 643 704 765 827 889 951 1013 1076 1139|1203|1267 1331 1396 1461 1527 39 40 100 160 220 280 341 401 461 522 583 644 705 766 828 890 952 1014 1077 1140 1204 1268 1332 1397 1462|1528| 40 41 101 161 221 281 342 402 462 523 584 645 706 767 829 891 953 1015 1078 1141 1205 1269 1333 1398 1463|1529 41 42|102 162 222 282 343 403 463 524 585 646 707 768 830 892 954 1016 1079 1142 1206 1270 1334 1399 1464 1530 42 43 103 163|223 283 344 404 464 525 586 647 708 769 831 893 955 1018 1080 11441207 12711335 1400 1465 1531 43 44 104 164 224 284 345 405 465 526 587 648 709 770 832 894 956 1019 1081 1145 1208 1272 1336 1401|1467|1532|| 44 45 105 165 225 285 346 406 466 527 588 649 710 771 833 895 957 1020 1082 1146 1209 1273 1338 1402 1468 1533 45 46 106 166 226 286 347 407 467 528 589 650 711 772834 896 958 1021 1084 1147|1210 1274 1339 1403 1469 1535 46 47 107 167 227 287 348 408 468 529 590 651 712 773 835 897 959 1022 1085 1148 1211 1275 1340 1405 1470 1536 47 48 108 168 228 288 349 409 469 530 591 652 713 774 836|898 960 1023 1086 1149|1212 1276 1341 1406 1471 1537 48 49 109 169 229 289 350 410 470 531 592 653 714 775 837 899 961 IC24 1087 1150 12131277 1342 1407 1472 1538 49 50 110 170 230 290 351 411 471 532 593 654 715 777 838 900 962 1025 1088 1151 1215 1278 1343 1408 1473 1539 50 51|111|171231 291 352 412 472 533 594 655 716 778839 901|963|1026|1089 1152 1216 1280 1344 1409 1474 1540 51 52|112|172|232|292|353 413 473 534 595 656 717 779 840|902|964|1027 1090|1153|12171281 1345 141014751541 52 53113173 233 293354414474 535 596 657 718 780 841 903|965|1028 1091 1154 1218|1282|1346 1411|1476|1542 53 54 114 174234294355 415 476 536 597 658 719 781 842|904|966|1029|1092|1155|1219|1283|1347 1412 1477 1543 54 55 115 175 235 295 356 416 477 537 598 659 720 782 843 905 968 1030 1093 1156 1220 1284 1348 1413 1479 1544 55 56| 116 176 236 296 357 417 478 538 599 660 721 783 844 906 969 1031 1094 1157 1221 1285 1349 1414 1480|1546 56 57 117 177 237 297 358 418 479 539 600 661 722 784 845 907 970 1032 1095 1158 1222 1286 1350 1415 14811547 57 58 118 178 238 298 359 419 480 540 601 662 723 785 846 908 971 1033 1096 1159 1223 1287 1352 1416 1482 1548 58 59|119179|239|299|360|420|481|541|602|663|724|786|847|909 972 1034|1097|1160|1224|1288│1353│141814831549 59 134 MATHEMATICAL. TABLES. TABLE VI.-MERIDIONAL PARTS. I OH2M+no z∞ al 6 7 8 I I 25° 26° 27° 28° | 29° | 30º | 31° | 32° | 33° | 34° | 35° | 36° | 37° | 38° | 39° | 40° | 41′ I 0×2M to 78 a 9 ΙΟ II 12 13 42° | 43° | 44° | 45° 1550 1616 1684 1751 1819 1888 1958 2028 2100 2171224423182393 2468 2545 2623 2702 2782 2863|2946 3030 1551 1618 1685 1752 1821 1890 1959 2030 2101 2173 2246 2319 2394 2470 2546 2624 2703 2783 2864 2947 3031 1552 1619 1686 1753 1822 1891 1960 2031 2102 2174 2247 2320 2395 2471 2548 2625 2704 2784 2866 2949 3033 3 1553 1620 1687 1755 1823 1892 1962 2032 2103 2175 2248 2322 2396 2472 2549 2627 2706 2786 2867 2950 3034 4 1554 1621 1688 1756 1824 1893 1963 2033 2104 2176 2249 2323 2398 2473 2550 2628 2707 2787 2869 2951 3036 5 1556 1622 1689 1757 1825 1894 1964 2034 2105 2178 2250 2324 2399 2475 2551 2629 2708 2788 2870 2953 3037 1557 1623 1690 1758 1826 1895 1965 2035 2107 2179 2252 2325 2400 2476 2553 2631 27102790 2871 2954 3038 1558 1624 1691 1759 1827 1896 1966 2037 2108 2180 2253 2327 2401 2477 2554 2632 2711 2791 28732956 3040 1559 1625 1693 1760 1829 1898 1967 2038 2109 2181 22542328|2403 2478 2555 2633 2712 2792 2874 2957 3041 9 1560 1626 1694 1761 1830 1899 1969 2039 2110 2182|2255 2329|2404|2480|2557 2634 2714 2794 2875 2958 3043 IO 1561 1628 1695 1762 1831 1900 1970 2040 2111 21842257 2330 2405 2481 2558 2636 27152795 2877 2960 3044 1562 1629 1696 1764 1832 1901 1971 2041 2113 2185 2258|2332 2406 2482 2559 2637 2716 2797 2878 2961|3046 12 1563 1630 1697 1765 1833 1902 1972 2043 2114 2186 22592333 2408 2484 2560 2638 2718 2798 2880 2963 3047 13 1564 1631 1698 1766 1834 1903 1973 2044 2115 2187 2260 23342409 2485 2562 2640 2719 2799 28812964 3048 141565 1632| 1699|1767|1835 1905 1974 2045 2116 2188 2261|2335 2410 2486 2563|2641 2720 2801 2882 2965 3050 15 1567 1633 1700 1768 1837 1906 1976 2046 2117 2190 2263 2337 2411 2487 2564 2642 2722 2802 2884 2967 3051 16 1568 1634 1701 1769 1838 1907 1977 2047 2119 2191 2264|2338|2413|2489|2566|2644|2723 2803 2885 2968 3053 17 1569 1635 1703 1770 1839 1908 1978 2048 2120 2192 2265 2339 2414 2490 2567 2645 2724 2805 2886 2970 3054 1570 1637 1704 1772 1840 1909 1979 2050 2121 2193 2266| 2340 2415 2491 2568 2646 2726| 2806 2888 2971 3055 1571 1638 1705 1773 1841 1910 1980 2051 2122 2194 2268 2342 2416|2492|2569 2648 2727 2807 2889 2972 3057 19 1572 1639 1706 1774 1842 1912 1981 2052 2123 2196 2269 2343 2418 24942571 2649 2728 2809 2891 2974 3058 1573 1640 1707 1775 1843 1913 1983 2053 2125 2197 2270 2344 2419 2495 2572 2650 2729 2810 2892 2975 3060 1574 1641 1708 1776 1845 1914 1984 2054 2126 2198 22712345 2420 2496 2573 2651 2731 2811 2893 2976 3061 23 1575 1642 1709 1777 1846 1915 1985 2056 2127 21992272|2346|2422 2498 2575 2653 2732 2813 2895 2978 3063 23 24 1577 1643 1711 1778 1847 1916 1986 2057 2128 2200 22742348 2423|2499 2576 2654 2733 2814 2896 2979 3064 24 25 1578 1644 1712 1780 1848 1917 1987 2058 2129 2202 22752349 242425002577 2655 2735 2815 2897 2981 3065 25 26 1579 1645 1713 1781 1849 1918 1988 2059 2131|2203|2276|2350|2425|2501 2578 2657 27362817|28992982 3067|| 25 1580 1647 1714 1782 1850 1920 1990 2060|2132|2204|22772351 2427 2503 2580 2658 2737 2818 2900 2983 3068 27 1581 1648 1715 1783 1852 1921 1991 2061 2133 2205 22792353 2428 25042581 2659 2739 2820 2902 2985 3070 28 29 | 1582| 1649| 1716|1784|1853|1922|1992|2063|2134|2207|2280|2354|2429|2505|2582|2661|27402821|2903|2986|3071 29 18 19 20 21 22 56 7∞ 27 28 14 15 16 17 18 20 21 MATHEMATICAL TABLES. 135 TABLE VI.—MERIDIONAl Parts. 32 33 34 39 40 41 4.4 30 33 43 25° 26° 27° 28° 29° 30° 31° 32° 33° | 34° 35° | 36° 35° | 36° | 37° | 38° | 39° 40° 41° 42° | 43° | 44° | 45° 2135|2208|2281 25842662 30 1583 1650 1717 1785 1854 1923 1993 2064 2135 2208 2281 2355 2430 2506 2584 2662 2742 2822 2904 2988 3073 31 1584 1651 1718 1786 1855 1924 1994 2065 2137|2209|22822356 2432 2508 2585 2663 2743 2824 2906 2989 3074 31 1585 1652 1720 1787 1856 1925 1995 2066 2138 2210 2283 2358 2433 25092586 2665 2744 2825 2907 2991 3075 32 1586 1653 1721 1789 1857 1927 1997 2067 2139 2211 2285 2359 2434 2510 2588 2666 2746 2826 2908 2992 3077 1588 1654 1722 1790 1858 1928 1998 2069 2140 2213 2286 2360 2435 2512 2589|2667|2747 2828 2910 2993 3078 34 2513|2590|2669|2748|2829|2911|29953080 || 35 1589 1656 1723 1791 1860 1929 1999 2070 2141 22142287 2361 2437 2513 2590 2669 2748 2829 2911 2995 3080 35 36 1590 1657 1724 1792 1861 1930 2000 2071 2143 2215 2288 2363 2438 2514 2591 2670 2750 2830 2913 2996 3081 36 37 1591| 1658 1725 1793|1862|1931 2001 2072 2144 2216 2290 2364 2439 2515 2593 2671 2751 2832 2914 2998 3083 37 38 1592 1659 1726 1794 1863 1932 2002 2073 2145 2217 22912365 2440 2517 2594 2673 2752 2833 2915 2999 3084 38 1593 1660 1727 1795 1864 1934 2004 2075 2146 2219 2292|2366 2442 25182595 2674 2754 2834 2917 3000 3085 39 1594 1661 1729 1797 1865 1935 2005 2076 2147 2220 2293|2368 2443 2519 2597 2675 2755 2836 2918 3002 3087 40 1595 1662 1730 1798 1866 1936 2006 2077 2149 2221 2295 2369 2444 2521 2598 2676 2756 2837 2919 3003 3088 | 41 42 1596 1663| 1731|1799|1868 1937 2007 2078 2150 22222296 2370 2445 2522 2599 2678 2758 2839 2921 3005 3090 42 43 1598 1664 1732 1800 1869 1938 2008 2079 2151 2224 2297 2371 2447 2523 2601 2679 2759 2840 2922 3006 3091 1599 1666 1733 1801 1870 1939 2010 2080 2152 2225 2298 2373 2448 2524 2602 2680 2760 2841 2924 3007 3093 1600 1667 1734 1802 1871 1941 2011 2082 2153|2226 2299 23742449 2526 2603 2682 2762 2843 2925 3009 3094 45 1601 1668 1735 1803 1872 1942 2012 2083 2155 2227 2301 2375 2451 2527 2604 2683 2763 2844 2926 3010 3095 46 1602 1669 1736 1805 1873 1943 2013 2084 2156|2228 2302|2376 2452 2528|2606|2684 2764 2845 2928|3012 3097 47 48 1603 1670 1738 1806 1875 1944 2014 2085 2157 2230 2303 2378 2453 2530 2607 2686 2766 2847 2929|3013 3098 48 1604 1671 1739 1807 1876 1945 2015 2086 2158 22312304 2379 2454 2531 2608 2687 2767 2848 293130143100 50 1605 1672 1740 1808 1877 1946 2017 2088 21592232 2306 2380 2456 2532 2610 2688 2768 2849 2932 30163101 1606 1673 1741 1809 1878 1948 2018 2089|2161 2233 2307 2381 2457 2533 2611 2690 2770 2851 2933 3017 3103 1608 1675 1742 1810 1879 1949 2019 2090 2162 2235 2308 2383 2458 25352612 2691 2771 2852 2935 3019 3104 52 53 1609 1676 1743 1811 1880 1950 2020 2091 2163 2236 2309 23842459 2536 2614 2692 2772 2854 2936 30203105 53 54 1610 1677 1744 1813 1881 1951 2021 2092 2164 2237 2311 2385 2461 2537 2615 2694 2774 28552937 3021 3107 55 1611 1678 1746 1814 1883 1952 2022 2094 2165 2238 2312 2386 2462 2538 2616 2695 2775 2856 2939 3023 3108 55 56 1612 1679 1747 1815 1884 1953 2024 2095 2167 2239 2313 2388 2463 25402617 2696 2776 2858 2940 3024 3110 2167|2239|2313|2388|2463|2540|2617|2696|2776|2858 56 57 1613 1680 1748 1816 1885 1955 2025 2096 2168 2241 2314 2389|2464 2541 2619 2698 2778 2859 2942 3026 311I 58 1614 1681 1749 1817 1886 1956 2026 2097 2169 2242 2316 2390 2466 2542 2620 2699 2779 2860 2943 3027 3113 58 59 1615 1682 1750 1818 1887 1957 2027 2098 2170|2243|2317|2391|2467|2544 2621 2700 2780 2862|2944 3029|3114 45 46 47 49 51 52 44 49 50 51 54 57 59 136 MATHEMATICAL TABLES. TABLE VI.—MERIDIONAL Parts. I 2 6 8 II 12 ∞ ∞ | ∞ ∞ • I 2 9 II 12 46° 47° 48° | 49° | 50° 50° | 51 52° | 53° | 54° 54 | 55° | 56° | 57° 57° 58° 59° | 60° | 61° 62° | 63° | 64° | 65° | 66° 3116 3203 3292 3382 3474 3569 3665 37643865 3968 40744183 42944409 4527 4649 4775 4905 5039 5179 5324 41844296 3117 3204 3293 3384 3476 3570 3667 3765 3866 397040764184 4296|4411 4529 4651 4777 4907 5042 5181 5326 3118 3206 3295 3385 3478 3572 3668 3767 3868 3971 4077 4186 4298 4413 4531 4653 4779 4909 5044 5184 5328 3 3120 3207 3296 3387 3479 3574 3670 3769 3870 3973 4079 4188 4300441545334655 4781 4912 50465186 5331 4 3121 3209 3298 3388 3481 3575 3672 3770 3871 3975 4081 4190 4302 4417 4535 4657 4784 4914 5049 5188 5333 3123 3210 3299 3390 3482 3577 3673 3772 3873 3977 4083 4192 4304 4419 4537 4660 4786 4916 5051 5191 5336 3124 3212 3301 3391 3484 3578 3675 3774 3875 3978 4085 4194 4306 4421 4539 4662 4788 4918 5053 5193 5338 7 3126 3213 3302 3393 3485 3580 3677 3775 3877 39804086 4195 4308 4423 4541 4664 4790 4920 5055 5195 5341 3127 3214 3303 3394 3487 3582 3678 3777 3878 3982 4088|4197|4309|4425 4543 4666 4792 4923 5058 5198 5343 93129 3216 3305 3396 348835833680 3779 3880 3984 40904199 4311 4427 4545|4668|4794 4925 5060|5200 5346 10 3130 3217 3306|3397 3490 3585 3681 3780 3882|39854092 4201 4313 4429 4547 4670 4796 4927|5062|5203|5348 | 10 3131 3219 3308 3399 3492 3586 3683 3782 3883 3987 4094 4203 4315 4431 4549 4672 4798 4929|5065 5205 5351 3133 3220 3309 3400 3493 3588 3685 3784 3885 3989 4095420543174433 4551 4674 4801 4931 5067|5207 5353 13 3134 3222 3311 3402 3495 3590 36863785 3887 3991 4097 4207 4319 4434 4553 4676 4803 4934 5069 5210 5356 13 14 3136 3223 3312 3403|3496 3591|3688 3787 3889 3992|4099|4208 4321 4436 4555 4678 48054936|5071 5212 5358 15 3137 3225 3314 3405 3498 3593 3690 3789 3890 3994 4101 4210 4323 4438 4557 46804807 4938 5074 5214 5361 15 16|3139 3226 3316 3407 3499 3594 3691 3790 3892 3996 4103 42124325 4440 4559 4682 4809 4940 5076 5217 5363 16 17 3140 3228 3317 3408 3501 3596 3693 3792|3894 3998|410442144327 4442 4562 4684 4811 4943 5078 5219 5366 | 17 4106|4216 || 3142 3229 3319 3410 3503 3598 3695 3794 3895 3999 4106 4216 4328 4444|4564 4687|4814 4945 5081 5222 5368 | 18 3143 3231 3320 3411 3504 3599 3696 3795 3897 4001 4108 4218 4330 4446 4566 4689 4816 4947 5083 52245371 3144 3232 3322 3413 3506 3601 3698 3797 3899 4003 411042204332 4448 4568 4691 4818 4949 5085 5226 5373 3146 3234 3323 3414 3507 3602 3699 3799 3901 4005 4112 4221 4334 4450 4570 4693 4820 4951 5088 5229 5376 21 3147 3235 3325 3416 3509 3604 3701 3800 39024006 41134223 4336 4452 4572 4695 4822 49545090 5231 5378 22 3149 3237 3326 3417 3510 3606 3703 3802|3904 4008 4115 4225 4338 4454 4574 4697 4824 4956 5092 52345380 23 3150 3238 3328 3419 3512 3607 3704 3804 3906 4010 4117 4227 4340 4456 4576 4699 4826 4958 5095 5236|5383 | 24 3152 3240 3329 3420 3514 3609 3706 3806 390740124119 4229 4342 4458 4578 4701 4829 4960 5097 5238 5385 25 3153 3241 3331 3422 3515 3610 3708 3807 3909 40144121 4231 4344 4460 4580 4703 4831 4963 5099 5241 5388|| 26 27 3155 3242 3332 3423 3517 3612 3709 3809 3911 4015 4122 4232 4346 4462 4582 4705 4833 49655102 5243 5390 27 28 3156 3244 3334 3425 3518 3614 3711 3811 3913 4017 4124 4234 4347 4464 4584 4707 4835 4967 5104 5246 5393 28 293157 3245 3335 3427 35203615 3713|3812 3914 4019 4126 4236 4349 4466 4586 47104837 4969 51065248 5395 | 29 18 19 20 21 22 23 24 25 26 14 19 20 MATHEMATICAL TABLES. 137 TABLE VI.-MERIDIONAL I ARTS. 30 31 33 35 39 40 4I 46° | 47° | 48° | 49° | 50° | 51° | 52° | 53° 54° | 55° | 56° | 57° | 580 | 59° | 60° | 61° | 62° | 63° 64° | 65° | 66° 31 32 34 35 36 16 78 37 3159 3247 3337 3428 3521 3617 3714 3814 3916 4021 4128 4238 4351 4468 4588 4712 4839 4972 5108 5250 5398 30 3160 3248 3338 3430 35233618 3716 3816 3918 40224130 4240 4353 4470 4590 4714 4842 4974 5111 52535401 32 3162 3250 3340 3431 35253620 3717 38173919 40244132 42424355 4472 4592 4716 48444976 5113 5255 5403 33 3163 3251 3341 3433 3526 3622 3719 3819 3921 4026 4133 4244 4357 4474 4594 4718 4846 4978 5115 5258 5406 33 34 3165 3253 3343 3434 3528 3623 3721 3821 3923 4028 4135 4246 4359 4476 4596 4720 4848 4981 5118 5260 5408 3166 3254 3344 3436 3529 3625 3722 3822 3925 40294137 4247 4361 4478 4598 4722 4850 4983 5120 5263 5411 36 3168 3256 3346 3437 3531 3626 3724 3824 3926 4031 4139 4249 4363 4480 4600 4724 4852 4985 5122 5265 5413 37 3169 3257 3347 3439 3532 3628 3726 3826 3928 4033 4141 4251 4365 4482 4602 4726 4855 4987 5125 5267 5416 383171 3259 3349 3440 3534 3630 3727 3827 3930 4035 41 42 4253 4367 44844604 4728 4857 4990 5127 5270 5418 38 3172 3260 3350 3442 3536 3631 3729|3829|3932 4037 4144 4255 4369 4486 4606 4731 4859 4992 5129 5272 5421 | 39 3173 3262 3352 3443 3537 3633 3731 3831 3933 4038 4146|4257 4370 4488 4608 4733 4861 4994 5132 5275 5423 40 3175 3263 3353 3445 3539 3634 3732 3832 3935 4040 4148 4259 4372 4490 4610 4735 4863 4996 5134 5277 5426 41 42 3176 3265 3355 3447 3540 3636 3734 3834 3937 4042 4150 4260 4374 4492 4612 4737 4865 4999 5136 5280 5428 42 43 3178 3266 3356 3448 3542 3638 3736 3836 3938 40444152 4262 4376 4494 4614 4739 4868 5001 5139 5282 5431 43 44 3179 3268 3358 3450 3543 3639 3737 3838 3940 4045 4153 4264 4378 4495 4616 4741 4870 5003 5141 5284 5433 44 45 3181 3269 3359 3451 3545 3641 3739 3839 3942 4047 4155 4266 4380 4497 4618 4743 4872 5005 5143 5287 5436 45 46 3182 3271 3361 3453 3547 3643 3741 3841 3944 4049 4157 4268 4382 4499 4620 4745 4874 5008 5146 5289 5438 46 47 3184 3272 3362 3454 3548 3644 3742 3843 3945 4051 4159 4270 4384 4501 4623 4747 4876 50105148 5292 5441 47 48 3185 3274 3364 3456 3550 3646 37443844 3947 4052 4161 4272 4386 4503 4625 4750 4879 5012 5151 5294 5443 48 49 3187 3275 3365 3457 3551 3647 3746 3846 3949 4054 4162 4274 4388 4505 4627 4752 4881 5014 5153 5297 5446| 49 318832773 50 3188 3277 3367 3459 3553 3649 3747 3848 3951 4056 4164 4275 4390 4507 4629 47 54 4883 5017 5155 5299 5448 50 3190 3278 3368 3460 3555 3651 3749 3849 3952 4058 41664277 4392 4509 4631 4756 4885 5019 5158 5301 5451 3191 3280 3370 3462 3556 3652 3750 3851 3954 40604168 4279 4394 4511 4633 4758 4887 5021 5160 5304 5454 52 3192 3281 3371 3464 3558 3654 3752 3853 3956 4061 4170 4281 4396 4513 4635 4760 4890 5023 5162 5306 5456 53 3194 3283 3373 3465 3559 3655 3754 3854 3958 4063 4172 4283 4398 4515 4637 4762 4892 5026 5165 5309 5459 3195 3284 3374 3467 3561 3657 3755 3856 3959 4065 4173 4285 4399 4517 4639 4764 4894 5028 5167 5311 5461 56 3197 3286 3376 3468 3562 3659 3757 3858 3961 4067 4175 4287 4401 4519 4641 4766 4896 5030 5169 5314 5464 56 57 3198 3287 3378 3470 3564 3660 3759 3860 3963 4069 4177 4289 4403 4521 4643 4769 4898 5033 5172 5316 5466 3200 3289 3379 3471 3566 3662 3760 3861 3964 4070 4179 4291 4405 4523 4645 4771 4901 50355174 5319 5469 | 58 3201 3290 3381|3473 3567|3664|3762|3863|3966|4072 4181 4292 4407 4525 4647 4773 4903 5037 5176 5321 5471 51 52 53 54 55 5555 in in in in 58 59 51 54 55 57 59 L 138 MATHEMATICAL TABLES. TABLE VI.-MERIDIONAL PARTS. O I 2345O ZO a 8 10 I I I 2 80° 67° 68° | 69° 69° 70° 71° 72° 73° 74° 75° | 76° | 77° | 78° | 79° 81° 82° 5474 5631 5795 5966 6146 6335 6534 6746 6970 7210 7467 7745 8046 8375 8739 9145 5477 5633 5797 5969 6149 6338 6538 6749 6974 7214 7472 7749 8051 8381 8745 9153 5479 5636 5800 5972 6152 6341 6541 6753 6978 7218 7476 7754 8056 8387 8752 9160 5482 5639 5803 5975 6155 6345 6545 6757 6982 7222 7481 7759 8061 8393 8758 9167 5484 5642 5806 5978 6158 6348 6548 6760 6986 7227 7485 7764 8067 8398 8765 9174 5487 5644 5809 5981 6161 6351 6552 6764 6990 7231 7490 7769 8072 8404 8771 9182 5489 5647 5811 5984 6164 6354 6555 6768 6994 7235 7494 7774 8077 8410 8778 9189 7 5492 5650 5814 5986 6167 6358 6558 6771 6997 7239 7498 7778 8083 8416 8784 9196 5495 5652 5817 5989 6170 6361 6562 6775 7001 7243 7503 7783 8088 8422 8791 9203 9 5497 5655 5820 5992 6173 6364 6565 6779 7005 7247 7507 7788 8093 8427 8797 9211 5500 5658 5823 5995 6177 6367 6569 6782 7009 7252 7512 7793 8099 8433 8804 9218 5502 5660 5825 5998 6180 6371 6572 6786| 7013 7256 7516 7798 8104 8439 8810 9225 5505 5663 5828 6001 6183 6374 6576 6790 7017 7260 7521 7803 8109 8445 8817 9233 13 5507 5666 5831 6004 6186 6377 6579 6793 7021 7264 7525 7808 8115 8451 8823 9240 5510 5668 5834 6007 6189 6380 6583 6797 7025 7268 7530 7813 8120 8457 8830 9248 5513 5671 5837 6010 6192 6384 6586 6801 7029 7273 7535 7817 8125 8463 8836 9255 5515 5674 5839 6013 6195 6387 6590 6804 7033 7277 7539 7822 8131 8469 8843 9262 5518 5676 5842 6016 6198 6390 6593 6808 7037 7281 7544 7827 8136 8474 8849 9270 5520 5679 5845 6019 6201 6394 6597 6812 7041 7285 7548 7832 8141 8480 8856 9277 19 5523 5682 5848 6022 6205 6397 6600 6815 7045 7289 7553 7837 8147 8486 8863 9285 5526 5685 5851 6025 6208 6400 6603 6819 7048 7294 7557 7842 8152 8492 8869 9292 5528 5687 5854 6028 6211 6403 6607 6823 7052 7298 7562 7847 8158 8498 8876 9300 5531 5690 5856 6031 6214 6407 6610 6826 7056 7302 7566 7852 8163 8504 8883 9307 5533 5693 5859 6034 6217 6410 6614 6830 7060 7306 7571 7857 8168 8510 8889 9315 24 5536 5695 5862 6037 6220 6413 6617 6834 7064 7311 7576 7862 8174 8516 8896 9322 25 5539 5698 5865 6040 6223 6417 6621 6838 7068 7315 7580 7867 8179 8522 8903 9330 26 5541 5701 5868 6043 6226 6420 6624 6841 7072 7319 7585 7872 8185 8528 8909 9337 5544 5704 5871 6046 6230 6423 6628 6845 7076 7323 7589 7877 8190 8534 8916 9345 28 5546 5706 5874 6049 6233 6427 6631 6849 7080 7328 7594 7882 8196 8540 8923 9353 5549 5709 5876 6052 6236 6430 6635 6853 7084 7332 7599 7887 82018546 8930 9360 14 456 15 16 17 18 78 20 21 22 23 27 29 I 0×23 +SO zo a 7 8 83° 84° 85° 9606 10137 10765 9614 10146 10776 9622 1015610788 9631 10166|10799 9639 10175 10811 9647 10185 10822 9655 10195 10834 9664 10205 10846| 9672 10214 10858 9680 10224 10869 9689|10234 10881 ΙΟ 9697 10244 10893 II 9706 10254 10905 12 9714 10264 10917 13 9723 10273 10929 14 9731 10283 10941 15 9740 10293 10953 16 9748 10303 10965 17 9757 10314 10978 18 9765 10324 10990 19 9774 10334 11002 9783 10344 11014 21 9791 10354 11027 22 9800 10364 11039 23 9809 1037411052 24 9817 1038511064 25 9826 10395 11077 26 9835 10405 11089 27 9844 10416 11102 28 9852 1042611115 29 20 MATHEMATICAL TABLES. 139 TABLE VI.-MERIDIONAL PARTS. Он 333 30 31 32 33 39 83° 84° 85° 9861 10437 11127 30 9870 1044711140 31 9879 10457 11153 32 9888 10468 11166 33 9897 10479 11179 34 9906 10489 11192 35 9915 10500 11205 36 99241051c11218 37 993310521 11231 38 9942 10532 11244 39 99511054211257 40 9960 1055311270 41 9969 10564 11284 42 9978 10575 11297 43 9987 1058611310 44 9996 10597 11324 45 67° 68° 69° 70° 710 72° 73° 74° 75° | 76° | 77° 78° 79° 80° 81° 82° 5552 5712 5879 6055 6239 6433 6639 6856 7088 7336| 7603 7892| 8207 8552 8936 9368 5554 5715 5882 6058 6242 6437 6642 6860 7092 7341 7608 7897 8212 8558 8943 9376 5557 5717 5885 6061 6245 6440 6646 6864 7096 7345 7612 7902 8218 8565 8950 9383 5559 5720 5888 6064 6249 6443 6649 6868 7100 7349 7617 7907 8223 8571 8957 9391 34 5562 5723 5891 6067 6252 6447 6653 6871 7104 7353 7622 7912 8229 8577 8963 9399 35 5565 5725 5894 6070 6255 6450 6656 6875 7108 7358 7626 7917 8234 8583 8970 9407 36 5567 5728 5896 6073 6258 6453 6660| 6879 7112 7362 7631 7922 8240 8589 8977 9414 37 5570 5731 5899 6076 6261 6457 6663 6883 7116 7366 7636 7927 8245 8595 8984 9422 38 5573 5734 5902 6079 6264 6460 6667 6886 7120 7371 7640 7932 8251 8601 8991 9430 5575 5736 5905 6082 6268 6463 6670 6890 7124 7375 7645 7937 8256 8607 8998 9438| 40 5578 5739 5908 6085 6271 6467 6674 6894 7128 7379 7650 7942 8262 8614 9005 9445 41 5580 5742 5911 6088 6274 6470 6677 6898 7132 7384 7654 7948 8267 8620 9012 9453 42 5583 5745 5914 6091 6277 6473 6681 6901 7136 7388 7659 7953 8273 8626 9018 9461 43 5586 5747 5917 6094 6280 6477 6685 6905 7140 7392 7664 7958 8279 8632 9025 9469 44 5588 5750 5919 6097 6283 6480 6688 6909 7145 7397 7668 7963 8284 8638 9032 9477 45 5591 5753 5922 6100 6287 6483 6692 6913 7149 7401 7673 7968 8290 8644 9039 9485 46 5594 5756 5925 6103 6290 6487 6695 6917 7153 7406 7678 7973 8295 8651 9046 9493|10005 10608 11337 46 47 5596 5758 5928 6106 6293 6490 6699 6920 7157 7410 7683 7978 8301 8657 9053 9501 1001510619 11351 47 48 5599 5761 5931 6109 6296 6494 6702 6924 7161 7414 7687 7983 8307 8663 9060 9509 10024 10630 11365 48 49 5602 5764 5934 6112 6299 6497 6706 6928 7165 7419 7692 7989 8312 8669 9067 9517 10033 10641 11378 49 50 5604 5767 5937 6115 63036500 6710 6932 7169 7423 7697 7994 8318 8676 9074 9525 10043 10652 11392 50 51 5607 5770 5940 6118 6306 6504 6713 6936 7173 7427 7702 7999 8324 8682 9081 9533 10052 10663 11406 51 52 5610 5772 5943 6121 6309 6507 6717 6940 7177 7432 7706 8004 8329 8688 9088 9541 10061 10674 11420 52 53 5612 5775 5946 6124 6312 6511 6720 6943 7181 7436 7711 8009 8335 8695 9096 9549 10071 10685 11434 53 54 5615 5778 5948 6127 6315 6514 6724 6947 7185 7441 7716 8014 8341 8701 9103 9557 10080 10696 11448 54 55 5617 5781 5951 6130 6319 6517 6728 6951 7189 7445 7721 8020 8347 8707 9110 9565 10089 10708 11462 55 56 5620 5783 5954 6133 6322 6521 6731 6955 7194 7449 7725 8025 8352 8714 9117 9573 10099 10719 11476 56 5623 5786 5957 6136 6325 6524 6735 6959 7198 7454 7730 8030 8358 8720 9124 9581 10108 10730 11490 57 58 5625 5789 5960 6140 6328 6528 6738 6963 7202 7458 7735 8035 8364 8726 9131 9589 10118 10742 11504 58 59 5628 5792 5963 6143 6332| 6531| 6742| 6966| 7206| 7463| 7740| 8040| 8369| 8733| 9138| 9598|10127|10753 11518| 59 57 | 140 MATHEMATICAL TABLES. TABLE VII.-LENGTH OF DEGREE OF LONGITUDE ON EACH PARALLEL OF LATITUDE. Latitude. Nautical miles. Latitude. Nautical miles. Latitude. Nautical miles. о I 59'99 2 59'96 3 59'92 4 59.85 5 59'77 6 59.67 w w w w w w 31 51°43 61 29.09 32 50.88 62 28.17 33 50°32 63 27.74 34 49'74 64 26.30 35 49'15 65 25°36 36 48.54 66 24.40 78 59'55 37 47'92 67 23.44 9 59'42 59.26 IO 59°09 II 58.89 12 58.69 13 58.46 ∞ 2 g 7 q 2 38 47°28 68 22.48 39 46.63 69 21.50 40 45'96 70 20°52 41 45°28 71 19'53 42 44'59 72 18.54 43 43.88 73 17'54 14 58.22 44 43°16 74 16.54 15 57.95 45 42°43 75 15°53 16 57.67 46 41-68 76 14.52 17 57-38 47 40.92 77 13.50 18 57:06 48 40.15 78 12:48 19 56.73 20 56.38 21 56.01 22 55-63 23 55°23 24 54.81 25 54:38 26 53.93 27 53:46 28 52'97 29 52:48 30 51.96 a = = * M * 4 5 6 49 39°36 79 11:45 50 38.57 80 10.42 51 37.76 81 9°38 52 36.94 82 8.35 53 36.11 83 7°31 54 35°27 84 6.27 55 34.4I 85 5°23 56 33°45 86 4.18 57 32.68 87 3.14 3179 88 2.09 59 30°90 89 1'05 60 30.00 90 0'00 MATHEMATICAL TABLES. 141 TABLE VIII. DIP OF HORIZON, CORRECTED FOR REFRACTION. TABLE IX. DIP OF THE HORIZON AT VARIOUS DISTANCES FROM IT. Distance in miles. HEIGHT OF Eye. feet. I feet. I feet. I feet. | feet. | feet. 5 10 15 20 25 30 II 22 34 45 56 68 6++mm OOHHH II 17 22 28 34 4 4 3 3 12 15 19 23 9 12 15 17 7 6 86 9 12 14 IO 12 2186 54 ΙΟ 66 5 5 3 4 4 3 4 4 3 4 4 876 in in in 8 7 6 6 5 6 5 5 5 5 5 in in 4 4 33 3 3 2 2 2 2 2 2 2 Ca 2233 +no feet. feet. "1 IO 1234 SO Z∞ ao • 59 41 6 18 I 24 42 623 1 42 43 627 I 58 4.4 632 5 2 12 45 6 37 6 225 47 6 45' 7 2 36 48 6 50 8 2 47 6 58 9 2 57 53 3 7 56 7 10 7 22 2}} II 12 13 HH 123456 76 O инин X 2 3 16 59 7 34 4 3 25 62 3.49 3 56 14 15 16 17 18 3 33 3 41 4 4 77 4 II 19 4 17 20 4 24 4 31 80 83 86 8 58 9 17 65 7 45 7 56 5 6 68 8 7 71 8 18 74 8 28 78∞∞ 8 38 8 48 TABLE X.-REDUCTION OF MOON'S EQUATORIAL PARALLAX. HORIZONTAL PARALLAX. Lat. 9 8 54 56 58 60 6 | 62 " "1 // 21 89 22 4 37 90 9 22 23 24 25 26 27 28 3456 78 4 43 92 9 26 12 4 49 4 55 a a 95 98 50 9 36 16 48 26 O'I ΟΙ ΟΙ ΟΙ ΟΙ O'2 0'2 0*2 O'2 0'2 0'4 0'5 0'5 0.5 0'5 0.8 0.8 0°9 0'9 0'9 9 45 20 1'3 5 I 100 9 52 24 1.8 300 1.3 1'4 1'4 1'5 1'9 1.9 2.0 2.0 5 7 ΙΟΙ 9 54 5 13 104 10 2 29 5 18 107 IO II 30 5 24 ΙΙΟ 10 19 wwww wwwww 31 5 29 32 5 34 113 10 28 116 44 10 36 33 5 39 119 10 44 52 34 5 44 122 10 52 35 36 37 38 56 7∞ 5 49 6 39 40 125 II о 5 54 128 II 5 59 131 II 16 4 134 II 24 6 9 137 II 31 6 14 140 II 39 8 5666 778 68 72 OON OF OUT* A www 2'4 3°0 3'I 2.5 2.6 2.6 2.7 3.3 3.4 3'5 3°7 4'5 96 on of 3'9 4.0 4.I 4'3 4.6 4.8 5.0 5'1 683 5°2 6.0 6.2 6.7 ino 420 5'4 7.0 7'4 7.7 60 8.1 8.4 8.7 632 O 7∞∞ 5.6 6.3 7°2 457 5.8 6.0 6.6 6.8 7'4 7.6 8.0 8.2 8.5 9.0 9'3 64 8.7 9'3 76 10'2 73∞ N 9'1 9'4 9.8 IO'I 104 10.8 10.6 10.9 11.3 10'0 9'7 9.6 10.0 10'3 10.6 II.2 11'7 80 105 10˚9 II.2 11.6 12'0 142 MATHEMATICAL TABLES. Altitude. TABLE XI. AUGMENTATION OF THE MOON'S SEMIDIAMETER. TABLE XII. FOR CONVERTING LONGITUDE INTO TIME. HORIZONTAL SEMIDIAMETER. "/ 14 30 15 0 15 30 16 0 16 30 17 0 30/15 Long. Time. H. M. M. S. Long. H. M. M. S. Time. Long. Time. Secs. NOT 23 1 2 3 NOHH 22 "/ I O I I 3 3 4 4 4 4 5 5 5 6 mt in iO 3 1 2 3 +SO N∞ 48 30 2 O 40 2 40 I 067 2133 O 12 50 3 20 3 $200 4 o 16 60 4 о 5 O 20 70 4 40 6 O 24 80 5 20 4 7 10 28 80 32 90 36 90 6 O 100 6 40 86 2er f 4/267 5 333 6.400 7467 8533 200j13 20 9.600 5 ΙΟ 10 0 40 300 20 010-667 5 20 I 20 6 Ι I I NOH122 I I I I " NOHH 2 2 O O 122 8 0246∞ 33445 78 9 6 78 a 8 67∞ ∞ a 66 78 9 56 77∞ 166 ^~ I2 14 16 4 18 21 24 27 233 4 5 30 7 3 3 4 4 5 8 233 ++ 02 46 ∞ IO 8 9 9 33 7 9 10 ΙΟ 36 39 4.2 45 48 ΙΟ ∞aaoo 8 9 9 ΙΟ ΙΟ II TABLE XIII. FOR CONVERTING TIME INTO 9 9 ΙΟ II I I 12 IO IO I I 12 13 LONGITUDE. ΙΟ I I 12 13 13 II 12 12 13 14 Time. Long. Time. Long. Min. Time. Long. 51 I I ΙΙ 12 13 14 54 I I 12 13 13 14 57 I I 12 13 14 ++ in 15 15 16 15 60 12 13 63 12 13 14 14 15 14 15 16 16 17 66 12 13 14 15 16 17 69 13 72 75 250 13 14 15 14 15 16 16 17 17 18 18 78 13 13 14 15 16 14 15 16 17 17 18 H. 556 6 34 1 2 3 456 7∞ 78∞ ∞ ∞ H. Sec. Sec. = 18 8 120 8 9 135 1 2 3 +SO 7∞ a ∞ ∞ ∞ 81 14 14 87 84 14 14 90 14 HHHH 15 16 18 15 16 56 17 19 18 19 ΙΙ I 15 30 45 I бо 4 75 5 90 6 105 O 1501 15 0 30 02 30 0 45 03 45 I o 0.4 6:0 1505 7.5 I 30 0.6 9.0 I 45|| 0:710'5 2 o 0.8 12.0 2 15 0913'5 ΙΟ 150 ΙΟ 2 30 11 165 20 5 15 16 17 15 16 17 77 18 19 12 180 30 7 30 18 19 16 240 40 10 о 20 300 50 12 30 MATHEMATICAL TABLES. 143 TABLE XIV. PARALLAX IN ALTITUDE OF THE SUN AND PLANETS. HORIZONTAL PARALLAX IN SECONDS. App. Alt. I 3 5 7 9 II 13 15 17|19|21 23 25|27|29 29 | 31 3 " I 1 3 // 5 = 5 // "1 // // #1 7 9 II 13 15 17 19 21 23 252729 29 31 6 I 3 5 7 9 11 13 15 17 19 21 23 2527 25 27 29 31 9 I 3 5 7 9 II 13 15 17 19 21 23 2527 29 31 29 12 1 3 5 7 9 11 II 13 15 17 19 21 | 22 24 26 28 30 15 I 3 มา 5 7 II 9 13 14 26 28 22 24 26 28 30 18 1 3 5 7 9 10 12 14 16 18 20 22 24 26 28 29 16 18 20 21 I 3 5 7 8 ΙΟ 12 16 18 20 21 14 24. I 3 5 6 8 ΙΟ I2 14 16 17 19 212325 23 25 27 27 29 212325 27 I 3 46 8 ΙΟ 12 13 15 17 19 20 301 3 4 6 8 10 11 13 15 II 16 18 33 I 2 4 8 13 9 II 14 16 18 19 2628 22 24 26 28 20 22 23 25 27 21 23 24 19 21 23 24 26 36 I 2 4 6 7 9 II I 2 14 15 17 19 20 19 2223 2325 39 I 2 4 5 7 9 10 12 13 15 16 18 19 21 23 24 42 I 2 4 5 7 8 10 II 13 14 16 17 17 19 20 22 23 45 I 2 4 5 6 8 9 II I2 13 15 16 18 19 21 22 48 I 2 3 5 6 7 9 10 I I 13 14 15 51 54 57 60 63 66 I 2 3 4 6 7 8 9 I I 12 13 +58 I 2 3 4 6 8 9 IO II 12 I 2 3 4 5 6 7 8 9 ΙΟ 12 II 14 15 15 17 18 19 21 14 16 17 14 15 16 17 18 17 16 17 18 19 18 20 I 2 3 4 5 5 7 8 9|10 12 II 13 14 15 15 16 I 2. 3 4 5 6 7 8 9 10 ΙΟ I I 12 13 14 о I 2 3 4 4 5 6 7 8 9 9 10 II 12 13 69 I 2 3 3 4 5 5 6 7 8 8 9 10 IO I I 72 I 2 2 3 3 4 5 5 6 6 7 8 8 9 10 75 I I 2 2 3 3 4 4 5 5 6 6 7 8 8 78 I I I 2 2 3 3 4 4 4 In 5 6 6 6 81 84 87 '90 I I I 2 2 2 3 3 4 3 4 4 5 5 O I I I I I 2 2 2 2 2 3 3 3 3 I I I I I I I I I 2 2 O O о O о O O 144 MATHEMATICAL TABLES. TABLE XV.-REFRACTION OF THE SUN AND STARS. App. Alt. Refrac- App. | Refrac- App. Refrac- App. Refrac- App. tion. Alt. tion. Alt. tion. Alt. tion. Alt. Refrac- tion. I 10 23 0 24 21′2 9.6 IO 0 5 19.819 02 47.7 28 OI 49°237 OI 17.2 10 5 15°1 102 46°3 10 I 48.4 10 I 16.7 20 22 3.4 205 104 20 2 44.8 20 I 47.6 20 I 16.2 30 21 1.9 305 5'7 302 43°3 30 I 46.9 30 I 15.8 40 20 4.8 40 5 ΙΟ 402 41.8 40 I 46.2 40 I 15'3 50 19 11'5 2 o 18 22.2 10 17 36.3 20 16 53°2 30 16 13:4 II 04 517 || 20 IC 4 47'7 20 4 43'7 50 4 56.3 502 403 304 39 7 10 2 374 20 2 36.0 302 34.6 30 I 42'7 40 15 36.0 404 35.7 402 332 50 15 09 504 31-8 (~) 3 0 14 28.112 04 279 21 10 13 57.3 20 13 28.5 30 13 13 40 12 35.6 10 4 24.5 204 21.1 30 4 17.7 40 4 14.3 50 12 11'3 4 1.5 50 10 10.9 5 6 011 48.313 IO II 26.6 20 II 6.1 30 10 46.7 40 10 28.3 O 9 543 14 938.4 IO O O 9 23.4 50 4 10.5 04 7522 10 4 4.5 20 4 30 3 58.6 40 3 55'7 503 52.7 0 3 49.8 ||23 10 3 47°2 203 44.6 15 0 3 34°3 | 24 02 16.5 32 10 2 15'4 02 10:233 IO 2 9'2 OI 33141 10 I 32.5 10 I 50 I 30°2 OI 0 1 29.642 10 I 29'0 20 I 5'7 30 I 40 I 5'3 50 I 4'9 OI 4.6 ΟΙ ΙΟ Ι 4.2 20 I 3.8 30 I 3'5 5 180 50 2 319 02 30.630 10 2 29.3 20 2 28.1 302 26.9 40 2 25.6 502 244 02 23.231 IO] 2 22′I 202 209 0238.829 50 I 45'5 0 I 44.838 01 10 I 44'1 20 1 43'4 I 40 I 42.0 50 I 413 01 40.639 IO I 39'9 20 I 39°3 I 50 1 14.8 0 I 144 IO I 14'0 20 1 13.5 301 13'1 40 I 12'7 50 I 12.2 OI 11.8 10 I 11.3 20 I 10.9 30 I 38.6 40 I 38.0 50 I 37°3 30 I 10'5 40 I 10'I 50 I 9'7 01 36.740 10 I 36.1 20 I 35°5 O I 9'3 10 I 8.9 20 1 I 8.5 30 2 19.8 30 I 34'9 30 I 8.1 402 18.7 40 I 34'3 40 I 7'7 50 2 17.6 50 I 337 50 I 7.3 I 01 6.9 6.5 20 202 14:4 30 9 40 303 42.0 30 2 13.3 20 I 31.9 30 I 31.3 40 8 553 40 3 39:4 40 2 12.3 40 I 30'7 50 ΙΟ 8 42.3 8 29.9 8 18.2 50 3 36.8 50 2 11.2 20 8 6.6 10 3 32.1 20 3 29.8 30 7 55.6 30 3 27.5 20 2 8.2 302 7.2 20 I 28.4 4.0 7 44'9 403 25'2 50 7 347 503 22.9 402 502 6.2 5°2 2 2 7 ΙΟ O ง 7 247 16 0 3 20725 O 2 4.3 34 7 15:3 10 3 18.5 20 7 6.3 20 3 16.5 10 2 3.4 20 2 2.5 30 I 27.8 40 I 27°3 501 26.7 01 26.243 10 1 25.6 40 I 3.I 50 I O I IO I 2.8 2:4 2'0 30 6 57'7 30 3 14.5 40 6 49.6 40 3 12.5 302 402 1.6 56 20 I 25'1 20 I 1'7 30 I 24.6 30 I 1°3 0'7 50 8 1 2 3 ΙΟ 20 30 O O O OO 6 41.9 50 3 10.5 50 I 59.8 о 6 34417 6 27 I 6. 20.0 03 8.5 26 IO 3 6.6 20 3 4.8 6 13'1 303 3.0 01 58.935 10 I 58.0 20 I 57°2 30 I 56.4 40 I 24.1 50 I 23.6 OI 231 44 10 I 22.6 20 I 22'I 40 I ΙΟ 50 I 0.6 ΟΙ 0'3 ΙΟ Ι O'O 30 1 21.6 40 6 64 40 3 1.2 40 I 55.6 40 I 21'I 50 9 O 10 30 5 35'9 50 5 25.1 5 59'9 5 53.5 18 5 47'4 20 5 41'5 40 5 30'4 502 59°4 50 I 547 02 57-627 01 53-936 102 55'9 202 543 302 52.6 40 2 51°0 502 49°3 50 I 20.6 10 I 53.2 20 I 52.4 OI 20145 10 I 19.6 200 59.6 300 59°2 400 58.9 500 58.5 00 58.2 10 0 57.8 20 I 19°1 200 57'5 301 51.6 40 I 50.8 501 1 500ll 50 1 17.6 30 I 18.6 40 I 18.1 300 57*2 400 56.9 500 56.5 6.1 MATHEMATICAL TABLES. 145 TABLE XV.-REFRACTION OF THE SUN AND STARS. App. Alt. Refrac- tion. App. | Refrac- Alt. tion. App. Refrac- App. Refrac- App. Alt. tion. Alt. Refrac- tion. Alt. tion. "/ 100 55.8 100 40°5 200 55°5 200 40°3 46 0 56.255 00 40864 00 284 73 10 0 28.2 200 28.0 0 17.8 82 10 0 17.6 IO O 200 17:4 20 888 8.2 8.1 7'9 300 55°2 300 40°0 300 27.8 300 17.2 300 7.8 96 400 549 400 39.8 400 27.6 500 54-6 500 39°5 47 054-356 100 54'0 200 53.6 39365 500 27°4 00 272 74 400 17.0 500 16.8 00 16.7 83 400 7.6 50 0 7.4 00 7°2 10 0 39°0 100 26.9 10 0 16.5 200 38.8 200 26.7 200 16.3 ΙΟ Ο 7:0 200 6·9 30 53°3 300 38.5 300 26.5 300 16.1 400 53°0 400 38. 48 500 52.7 100 52.1 500 38.0 00 524157 0 37.8 66 10 0 37.6 200 51.8 200 37°3 200 25.5 400 26.3 500 26.1 00 25.9 75 100 25.7 400 16.0 500 15.8 00 15.6|84 10 O 154 200 15.2 300 6.7 40 o 6.5 500 6.3 IO O 6.1 5'9 200 5.8 300 51.5 300 37°1 300 25°3 300 15.0 300 5.6 40 51.2 50 O 50°9 400 36·9 50 400 25.1 400 14.8 40 0 5.5 36.6 500 24'9 500 14.7 50 5'3 49 00 50.658 100 50'4 0036.4 36467 ΙΟ 36.2 IO O 67 00 247 76 0 0 14 585 0 5'1 100 24.5 100 14:3 ΙΟ 4'9 200 50.1 20 36.0 200 24°3 200 14°2 300 49.8 300 35'7 300 24'1 40 o 49°5 400 35'5 400 23.9 50 O 49°2 500 35°2 500 23.7 50 O 48.959 100 48.6 200 48.3 00 35068 10 0 34.8 ΙΟ 20 O 34-6 OO 23'577 IO O 23'4 200 23.2 300 14.0 400 13.8 500 13.7 0 13.5 86 10 0 13°4 200 13.2 20 O 300 4.6 400 4.5 500 4.3 4'I IO O 3'9 4.8 20 O 3'7 30 O 48.1 300 34°3 300 23.0 300 13.0 30 3.6 40 0 47.8 400 34'1 400 22.8 400 12.8 40 3'4 50 ° 47'5 500 33.8 500 22.6 500 12.6 50 SI oO 47°260 100 46.9 10 O 33'4 IO 200 46.6 200 33 I 300 46.3 300 32.9 40° 46'1 400 32.7 50 • 45.8 52 IO O 45°2 200 45°C 30 0 44.6 400 444 500 44'1 500 31.2 53 O ° 0 43.962 100 43.6 200 43°3 300 43°1 300 304 400 42.8 400 30°2 500 42.6 500 30.0 54 0042.363 100 42.0 200 41.8 oO 29°772 10 O 29'4 200 29.2 300 41.5 400 41.3 500 410 300 29.0 400 28.8 500 28.6 00 45.661 00 33.669 0 0 224 78 500 32.5 00 32.3 70 100 32.0 200 31.8 300 31.6 400 31'4 00 31071 10 0 30.8 200 30.6 IO O 22*2 20 O 22'0 300 21.8 400 21.6 500 21'4 OO 212 79 IO O 21°O| 200 20.8 300 20.6 400 204 500 20°2 00 20.080 10 0 19.8 200 19.6 300 19:4 400 19:2 500 19.0 00 18.9 81 10 o 18.8 200 18.6 20 O 12*0 300 11'9 300 400 II 7 400 50 0 11.5 500 OO 11.3 88 IO O II'2 20 O II'O 300 10.8 4º O 10.7 ΙΟ Ο ΙΟΙ 20 0 10°O] 300 9.8 400 9.6 400 0'3 500 94 300 18.4 300 8.7 oo 12.4 87 IO O 12.2| IO O 200 IO O M32 2 2 2 2 2 - 3'3 3'I 2'9 2.8 2.6 2.4 2.2 2.0 1'9 20 O I'7 300 I'5 40 0 1'3 50 0 10.5 500 I'I 0 0 10.389 00 ΙΟ ΙΟ Ο 0'9 200 0.7 300 0'5 500 ΟΙ O O 9.2 10 0 ΙΟ Ο 9.0 200 8.9 40 0 18.2 500 18.0 40 5010 00 00 00 8.6 8.4 146 MATHEMATICAL TABLES. 80 6503622 7 7 348 34 21 7 6 046 32 20 7 6 57 44 31 18 6 55 42 30 17 6 o Apparent altitude. TABLE XVI.-CORRECTION FOR TABLE OF REFRACTION. о 20 24 28 + + + = I OI 591 43 I 251 101 531 381 211 201 481 33|1 17|1 30 431 291 14|1 401 391 251 110 501 351 211 HEIGHT OF THE THERMOMETER. 32136 40 44 48 52|56|60|64 +++++ 44|48|52|56|60|64 " •2+1= に に 68 = 1800 72 800 761 3 I 17 I 30 I 43 13 1 26| 1 38 91 211 33 6 I 18 1 29 953 38 238 7 2136501 20 34 48 1 OI 19 32 450 57 I 18 31 430 54 I 18 30 410 52 1 4 I 15 I 25 6 6 17 28 390 50 1 I I II I 21 2 01 311 181 50 53 39 29 17 6 5 16 27 370 480 58 I 81 18 20 I 231 III oo 48 37 26 16 5 5 1525350 440 54 I 3 I II 401 17 1 60 550 44 34 24 14 5 5 14 23 320 410 500 58 1 I 6 3 ΟΙ ΙΙΙ 10 510 41 32 22 13 4 4 13 21 300 380 46 54 I I 201 60 570 470 38 29 21 13 4 4 12 20 280 350 430 500 57 40I 20 530 440 36 28 20 12 4 4 11 18 260 33 0 400 470 53 4 4 10 17 240 310 370 440 50 3 10 16 220 300 350 410 46 3 3 9 15 21 0 280 330 38 olo 00 580 490 410 33 26 18 11 4 200 540 460 390 31 24 17 10 3 400 510 430 370 29 23 16 10 5 00 480 410 350 28 22 16 9 300 450 380 320 26 20 149 00 410 350 300 24 19 13 300 340 290 240 2015 II 8 00 320 270 230 19 15 10 14 15 16 56 3 43 3 3 9 14200 260 310 360 40 33813 190 24 0 290 340 38 2 7 12 170 220 260 310 35 2711150 200 240 290 33 26 10 140 19 0 230 27 0 31 269 130 17 0 21 0 250 29 259130 16 0 20 0 240 27 258 110 14 0 18 0 210 24 14 7 100 13 0 16 0 19 0 22 147 90 12 0 15 0 18 0 20 120 150 90 110 13 0 16 0 18 a a∞ Z NO66 6 8 30 380 330 280 22 17 12 7 2 7 00 360 310 260 21|16| 12 7 2 62 6 2 9 oo 280 240 200 16139 2 ΙΟ I I 13 o 260 220 180 15 12 8 00 230 200 170 14 11 8 5 [2 00 210 180 150 13 10 7 74 I 974 864 863 5 2 2 I 46 I I 3 6 I I 35 7 I I 35 7 8 90 8 753 I 53 I I 4 3 I I 35 I34 24 I 24 9 7 42 I I 24 Ο ΙΙΟ ΙΟ Ο 80 7 2 2 2 3M44 in O 235 23 26 28 Ο 60 4 40 70 17 18 19 20 22 24 30 35 40 45 50 55 60 65 70 70 80 00 200 170 140 12 9 7 00 180 160 130 11 8 6 00 170 150 120 10 8 6 00 160 140 120 975 3 I 00 150 130 110 140 120 100 0 130 110 00 130 II O 00 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 55+3M N N 2 - 665 & บา บา O 100 120 150 17 O II O 140 16 00 O O 30 20 ini in 44mMM2 2 2 2 2 2 H 24 I 3 I O I 100 90 4/2 90 70 6 32 80 70 6 90 70 60 80 70 70 60 4 30 30 30 30 20 30 20 20 20 210 20 20 IO ΙΟ IO 10 432 43 I I I I I I 2 3 2 I о 432 32 I I о I 43 33 32 I O о I2 322 22 I I 2 I I I HOOOS1.6z HEIGHT OF O O O I O O I O 2 2 I I о O I O I 20 I I I O O I I O O I I I O O ΙΟ I I I о O о 28.26 OM 28.560 H 28.850 29°45 9 90 110 130 15 80 10 0 12 0 14 80 90 110 13 70 9 0 10 0 12 8 0 10 0 II 9 O II 8'0 10 7 6 80 6 7 6 8 o 6 7 6 985 5 6 7 4 6 3 3 20 3 4 2 21 2 2 2 ΙΟ 2 O O O O O O O O O O O O O O O O O 3 3 3 20 2 2 I O I O ΙΟ ΙΟ I O ΙΟ I I O ΙΟ I +29.750 +30°050 +30·3500 = + 30.64 0 O + 30°93 THE BAROME- TER. MATHEMATICAL TABLES. 147 TABLE XVII.—CORRECTION OF THE MOON'S ALTITUDE. MOON'S Horizontal Parallax. P. P. (Moon's for App. Alt. Alt. 54 55' 56' 57' 58' 60' 59' 61' P. P. for Par. I 2 // 2 + 4 7H 3 II 4 15 5 18 3 6 22 7 26 8 29 9 33 I 7 2 2 2 4 3 5 4 7 4 = = // = // = "1 0 35 36 36 36 37 36 38 36 39 36 40 36 41 36 42 36 10 36 22 37 22 38 22 39 22 40 22 41 22 42 22 43 22|, 20 37 438 439 440 441 442 443 444 41 I'O 30 37 44 38 44 39 44 40 44 41 44 42 44 43 44 44 44 2 2.0 4038 40 38 2039 2040 2041 2042 2043 2044 2045 20 3 3.0 50 38 55 39 55 40 55 41 55 42 55 43 55 44 55 45 554 40 039 28 40 27 41 27 42 27 43 27 44 27 45 27 46 27 5 50 10 39 58 40 58 41 58 42 58 43 58 44 58 45 58 46 586 6.0 20 40 26 41 26 42 26 43 25 44 25 45 25 46 25 47 25 7 7:0 30 40 53 41 53 42 53 43 52 44 52 45 52 46 52 47 528 8.0 40 41 1742 1743 1744 1745 1746 1747 1748 179 90 50 41 42 42 42 43 41 44 41 45 41 46 41 47 41 48 41 0 42 443 444 445 446 447 448 349 3 10 42 25 43 24 44 24 45 24 46 24 47 24 48 23 49 23, 20 42 45 43 44 44 44 45 44 46 44 47 44 48 44 49 44 1 10 30 43 344 345 346 247 2 48 249 250 22 2.0 40 43 21 44 21 45 21 46 21 47 21 48 2049 2050 203 3.0 50 43 38 44 37 45 37 46 37 47 36 48 36 49 36 50 364 4.0 5 95 43 53 44 53 45 53 46 53 47 53 48 53 49 52 50 52 5 5.0 10 44 9 45 9 46 8 47 8 48 8 49 8 50 851 76 6.0 20 44 23 45 23 46 23 47 22 48 22 49 2150 21 51 217 70 30 44 36 45 36 46 35 47 35 48 35 49 35 50 34 51 348 8.0 40 44 49 45 49 46 49 47 48 48 48 49 48 50 48 51 479 9*0 50 45 1 46 I 47 I 48 049 49 59 50 59 51 59 6 II 7 12 8 14 9 16 = ་ LO 6 50 11 51 10 52 IC 50 22 51 21 52 21/ 50 31 51 31 52 311 10 50 41 51 41 52 412 20 50 51 51 50 52 503 30 0 45 12 46 12 47 11 48 11 49 11 10 45 23 46 23 47 23 48 22 49 22 20 45 33 46 33 47 33 48 32 49 32 30 45 43 46 43 47 42 48 42 49 42 40 45 53 46 53 47 52 48 52 49 52 50 46 247 248 I 49 I 50 051 51 59 52 594 40 0 46 11 47 10 48 10 49 10 50 951 952 8 57 53 8 5 5.0 10 46 20 47 19 48 19 49 18 50 18 51 17 52 17 53 166 6.0 | 20 46 28 47 27 48 26 49 26 50 26 51 25 52 25 53 247 70 30 46 34 47 34 48 33 49 33 50 32 51 32 52 31 53 318 8.0 353 40 46 41 47 41 48 40 49 39 50 39 51 38 52 38 53 379 90 50 46 48 47 47 48 47 49 46 50 46 51 45 52 44 53 44 I I 2 2 3 3 4 4 5 6 6 7 7 8 8 9 9 I I I 2 2 1 2 3 4 5 78 9 8 46 54 47 54 48 53 49 53 50 52 51 52 52 51 53 51 IO 47 47 20 47 6 48 59 48 59 49 58 50 58 51 57 52 56 53 56 549 5 50 4 51 "/ 352 353 254 21 IO 853 9 52 754 72 2°0 14 52 14 53 13 54 123 30 30 47 12 48 11 49 10 50 9 51 40 47 17 48 16 49 16 50 15 51 50 47 22 48 21 49 20 50 1951 1952 18 53 17 1853 1754 174 40 047 47 26 48 25 49 25 50 24 51 23 52 22 53 22 54 215 50 10 47 32 48 31 49 30 50 29 51 29 52 28 53 27 54 266 6.0 20 47 35 48 34 49 34 50 33 51 32 52 31 53 31 47.35 353 354 307 7'0 36 52 35 53 35 54 348 8.0 51 41 52 40 53 39 54 54 389 90 51 44 52 43 53 42 54 41 2 5 39 6 3 7 4 4 30 47 40 48 39 49 38 50 37 51 36 52 35 53 35 3949 9 5 40 47 44 48 43 49 42 50 41 50 47 48 48 46 49 46 50 45 . 148 MATHEMATICAL TABLES. TABLE XVII-CORRECTION OF THE MOON'S ALTITUDE. MOON'S HORIZONTAL PARALLAX. P. P. Moon's for App. Alt. Alt. 54' 55' 56′ | 57′ 58' 59' 60' 61' о = // P. P. for Par. + 123456 7∞ a I о 20 47 57 48 57 30 48 I 49 4048 40 48 449 3 50 251 I 50 5 48 6 49 5 50 4 51 //10 47 51 48 50 49 49 50 48 51 10 47 54 48 53 49 52 50 52 51 49 55 50 55 51 49 59 50 58.51 47 52 46 53 45 54 44 50 52 49 53 49 54 47 54 52 52 53 52 54 511 10 57 52 56 53 55 54 542 2.0 052 59 53 58 54 573 2.9 054 594 3'9 152 352 253 I 54 ΙΙΙ 48 9 49 7 50 651 552 4 53 3 54 2 55 5 49 I 10 48 11 49 10 50 8 51 7 52 6 53 5 54 653 4 55 3 6 5'9. I 20 48 13 49 12 50 11 51 9 52 853 7 54 655 55 57 6.9 8 2 2 30 48 15 49 14 50 13 51 12 52 10 53 9 54 855 7 8 7.9 14 51 13 52 II 12 53 11 54 10 55 898.8 50 17 51 15 52 I 3 о 4 с 2 m ti6 DOO 8 9 12 113 40 48 17 49 16 50 50 48 19 49 18 1949 048 21 49 20 10 48 23 49 22 20 48 24 49 23 30 48 26 49 25 40 48 27 49 26 50 48 28 49 27 048 29 49 27 10 48 31 49 29 20 48 31 49 30 30 48 33 49 30 14 53 13 54 11 55 10 54 50 1951 17 52 16 53 15 54 13 55 12 50 20 51 19 52 18 53 16 54 15 55 14 50 22 51 20 52 19 53 17 50 23 51 22 52 21 53 19 50 24 51 23 52 21 53 20 50 25 51 24 52 22 53 21 50 26 51 24 52 23 53 21 50 28 51 26 52 25 53 23 50 28 51 27 52 25 53 24 = 54 16 55 151 10 54 17 55 16 2 20 1755 16|2 1855 17 3 29 54 19 55 18 4 3'9 54 20 55 195 49 54 21 55 19 5'9 54 22 55 207 6.9 6 50 29 51 27 52 26 53 24 54 22 55 208 79 I 7 I I I 40 48 32 49 31 50 48 33 49 31 50 50 14 1 23456 789 ་ I 2345W ZOO a о // O о 15 16 117 29 51 28 52 26 53 24 30 51 28 52 26 53 24 048 34 49 32 50 30 51 29 52 27 53 25 10 48 34 49 33 50 31 51 29 52 27 53 26 20 48 34 49 32 50 31 51 29 52 27 53 25 30 48 35 49 33 50 31 51 29 52 27 53 25 40 48 35 49 34 50 32 51 29 52 28 53 26 50 48 35 49 33 50 31 51 29 52 27 53 25 048 36 49 34 50 31 51 30 52 27 53 25 10 48 35 49 33 50 31 51 29 52 27 53 25 20 48 35 49 33 50 31 51 29 52 26 53 24 30 48 35 49 33 50 31 51 28 52 26 53 24 40 48 34 49 33 50 30 51 28 52 26 53 24 50 48 34 49 32 50 30 51 27 52 25 53 23 54 22 55 219 8.8 54 23 55 21 22/ 54 23 55 21 54 24 55 22 54 24 55 221 10 54 24 55 22 2 19 54 23 55 223 29 54 23 55 21 4 39 54 23 55 215 48 54 23 55 216 5.8 54 22 55 20 7 6.8 54 22 55 208 77 54 21 55 199 87 54 20 55 18 = 048 34 49 31 50 29 51 26 52 24 53 22 54 20 55 17 10 48 33 49 31 50 28 51 26 52 24 53 21 54 19 55 16/ 20 48 32 49 30 50 27 51 25 52 23 53 20 54 1855 151 10 30 48 32 49 29 50 26 51 24 52 22 53 1954 17 55 14 2 19 40 48 31 49 28 50 26 51 24 52 21 53 1854 1655 13 3 29 50 48 30 49 27 50 25 51 23 52 20 53 17 54 15 55 124 3'9 048 29 49 27 50 24 51 22 52 19 53 16 54 14 55 11 5 48 10 48 28 49 26 50 24 51 21 52 18 53 15 54 13 55 106 5.8 50 23 51 20 52 17 53 14 54 12 55 50 22 51 1952 1653 13 54 10 55 50 21 51 18 52 15 53 12 54 9 55 20 48 28 49 25 6 I 7 I 8 I 9 I 40 48 26 49 24 30 48 27 49 24 50 48 26 49 23 97 6-8 88 77 6 8.6 50 20 51 17 52 14 53 11 54 8 55 5 MATHEMATICAL TABLES. 149 I I 5 6 I 7 1234 So to a 2 2 2 8 2 2 2 2 8 1 2 3 4 5 6 7∞ a TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE. P. P. Moon's MOON'S HORIZONTAL Parallax. P. P. Alt. Alt. for App. 54' 55′ for 56' 57' 58′ 59′ 60' 61' Par. = // ་ "1 "/18 I O 23456 7∞ a 048 24 49 21 10 48 23 49 20 20 48 22 49 19 3048 2049 17 50 40 48 19 49 16 50 12 51 50 1851 15 52 12 53 954 655 3 50 17 51 14 52 11 53 854 5 55 2 "/ 50 16 51 13 52 10 53 7 54 355 14 51 10 52 753 4 54 01 0.9 154 582 19 952 6 53 353 59 54 563 2.8 I 50 48 1849 15 50 11 51 8 52 453 3·8 119 048 16 49 12 50 9 51 51 5 52 I 10 48 15 49 11 50 I 20 48 12 49 9 50 8 I 9 I 30 48 11 498 50 4048 40 48 9 49 5 50 50 48 8 49 4 50 20 I I I21 048 549 IO 48 ΙΟ 2048 349 o 851 5 51 4 52 I 53 58 54 554 3.8 2 52 59 53 56 54 535 47 1 52 58 53 54 54 516 57 I 251 59 52 55 53 52 54 497 6.7 4 51 I 51 57 52 54 53 51 54 478 7.6 2 50 58 51 55 52 52 53 48 54 449 8.5 I 50 57 51 54 52 50 53 46 54 43 "/ 2 49 58 50 55 51 51 52 47 53 44 54 40 49 56 50 53 51 48 52 45 53 42 54 38 2 48 58 49 55 50 51 51 47 52 43 53 40 54 361 09 30 48 048 56 49 52 50 48 51 45 52 41 53 37 54 332 1°9 40 47 58 48 54 49 50 50 46 51 42 52 38 53 34 54 303 2.8 50 47 56 48 52 49 48 50 44 51 41 52 36 53 32 54 284 37 047 54 48 50 49 46.50 42 51 38 52 34 53 30 54 265 47 6 5.6 10 47 53 48 48 49 44 50 40 51 35 52 32 53 27 54 23 20 47 50 48 46 49 42 50 37 51 34 52 30 53 25 54 217 6.6 30 47 47 48 43 49 39 50 35 51 31 52 27 53 22 54 198 7:5 40 47 45 48 41 49 36 50 32 51 28 52 24 53 20 54 159 84 50 47 44 48 39 49 35 50 31 51 26 52 22 53 1854 13 22 I 123 047 41 48 37 49 32 50 28 51 24 52 10 47 39 48 34 49 30 50 25 51 21 52 20 47 36 48 31 49 27 50 22 51 18 52 30 47 33 48 29 49 24 50 20 51 15 52 40 47 31 48 26 49 21 50 16 51 50 47 28 48 23 49 19 50 14 51 47 26 48 21 49 16 50 11 51 10 47 24 48 19 49 14 50 9 51 4 5 20 47 21 48 16 49 11 50 6 51 2 51 30 47 18 48 13 49 9 50 3 50 58 51 40 47 16 48 10 49 10 49 5 50 I 50 55 51 50 47 13 48 849 2 49 57 50 52 51 19 53 16 53 15 54 11 12 54 י7 13 53 954 4I 0'9 11 53 654 12 52 653 22 1.8 253 573 2.8 952 5 53 53 554 3.8 652 2 52 57 53 52 5 47 59 52 54 53 50 6 5.6 56 52 51 53 477 65 54 52 48 53 43 8 7'4 50 52 45 53 409 47 52 42 53 37 in Noo 8:3 654 m 24 549 I 3. 5 6 7 8 33 23 + no too a I I 4 I 2 2 225 047 10 48 049 54 50 49 51 44 52 39 53 34 10 47 7 48 2 56 49 51 50 46 51 41 52 35 53 30 20 47 4 47 59 48 54 49 48 50 43 51 38 52 32 53 271 0.9 3047 I 47 56 48 5149 49 46 50 41 51 35 52 29 53 23 2 1.8 40 46 58 47 53 48 47 49 42 50 37 51 31 52 25 53 203 27 50 46 56 47 50 48 44 49 39 50 33 51 27 52 22 53 174 3.6 O 46 52 47 47 48 41 49 36 50 30 51 24 52 19 53 135 45 10 46 49 47 44 48 38 49 32 50 26 51 21 52 15 53 106 54 20 46 46 47 40 48 34 49 28 50 22 51 17 52 11 53 57 64 28 7.2 30 46 42 47 36 48 30 49 25 50 1951 13 52 753 40 46 39 47 33 48 27 49 22 50 16 51 10 52 4 52 589 8.2 58 46 36 47 30 48 24 49 18 50 12 51 6 520 52 54 150 MATHEMATICAL TABLES. TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE. P. P. Moon's! I for Alt. MOON'S HORIZONTAL PARALLAX. App. Alt. 54' 55' 56' 57' "26 I I I 10 2 3 4 5 ZOO a 5 6 7 8 "1 46 33 47 27 48 21 49 10 46 30 47 24 48 1849 20 46 27 47 20 48 14 49 30 46 24 47 1748 11 49 40 46 20 47 13 48 6 49 50 46 16 47 10 48 3 48 227 46 13 47 10 46 9 47 20 46 6 47 30 46 2 46 56 40 45 59 46 52 50 45 55 46 48 2 2 2 3 3 9 3 = ་ 58' 59' 60' 61' = ་ P. P. for Par. = 15 50 9 51 3 51 57 52 51 12 50 6 50 59 51 53 52 47' 8 50 2 50 56 51 49 52 431 0.9 549 59 50 52 51 46 52 392 1.8 49 54 50 47 51 41 52 353 27 57 49 50 50 44 51 37 52 314 35 7 480 48 53 49 47 50 40 51 34 52 27 5 44 3 47 56 48 50 49 43 50 36 51 30 52 23 6 5°3 47 5348 46 49 39 50 33 51 26 52 19 7 6.3 47 48 48 48 42 49 35 50 28 51 21 52 15 8 7'1 47 45 48 38 49 31 50 24 51 17 52 11 19 8.0 47 41 48 34 49 27 50 20 51 14 52 6 MM HO 28 "1 I 2 I 1 045 52 46 45 47 38 48 31 49 24 50 10 45 49 46 42 47 35 48 28 49 21 50 20 45 45 46 38 47 30 48 23 49 16 50 30 45 41 46 34 47 27 48 19 49 12 50 40 45 37 46 31 47 23 48 16 49 8 50 50 45 33 46 26 47 19 48 2/29 045 29 46 21 47 14 48 10 45 25 46 1847 10 48 2 48 16 51 14 51 10 52 3 751 59' 951 2 51 541 0'9 5 50 58 51 512 1-8 I 50 54 51 463 2.6 20 45 22 46 30 45 17 46 40 45 1346 50 45 946 11 49 4 49 6 48 14 47 6 47 58 48 51 49 43 50 36 947 147 54 48 56 50 49 51 414 35 59 49 51 55 49 47 50 44 51 365 44 50 39 51 32 6 5'3 51 28 7 6.2 46 49 38 50 30 51 23 8 7°C 46 18 9 7'9 46 14 30 91 2 2 2 3 3 + 4 8 9 3456 7∞ a I 2345 Doo a O 5 46 58 47 50 48 42 49 34 50 26 51 246 54 47 46 48 38 49 31 50 22 51 4/ 45 5 45 57 46 49 47 41 48 33 49 25 50 17 51 IO 45 45 53 46 45 47 37 48 28 49 21 50 12 51 20 44 58 45 49 46 41 47 33 48 25 49 16 50 851 OI 0.9 I 30 44 53 45 44 46 36 47 28 48 19 49 11 50 3 50 55 2 1*7 46 32 47 24 48 15 49 7 49 59 50 503 2.6 46 27 47 18 48 10 49 I 2 231 6 3 7 3 8 41 9 4 I 2 3 tiO ZOO a O H I 2 32 233 3 4 5 6 7 3 8 4 9 4 40 44 49 45 41 50 44 44 45 36 044 40 45 31 2 49 53 50 45 4 34 46 23 47 15 48 6 48 57 49 49 50 40 5 43 10 44 36 45 27 46 18 47 948 I 48 52 49 43 50 356 52 20 44 31 45 23 46 14 47 5 47 56 48 48 49 39 50 307 6.1 30 44 27 45 1946 10 47 I 47 52 48 44 49 35 50 268 6.8 40 44 24 45 15 46 6 46 57 47 48 48 39 49 30 50 219 7'7 50 44 19 45 10 46 46 52 47 43 48 34 49 25 50 16 I = OI 0.8 044 14 455 45 56 46 47 47 38 48 29 49 20 50 11 10 44 10 45 I 45 51 46 42 47 33 48 23 49 14 50 5 20 44 6 44 56 45 47 46 38 47 29 48 19 49 10 50 30 44 044 51 45 42 46 33 47 23 48 14 49 449 552 17 40 43 57 44 47 45 37 46 28 47 19 48 9 49 049 50 3 2:5 50 43 51 44 42 45 32 46 22 47 13 48 3 48 54 49 454 33 043 47 44 38 45 28 46 18 47 8 47 59 48 49 49 405 42 10 43 43 44 33 45 24 46 14 47 4 47 54 48 44 49 356 50 20 43 39 44 29 45 19 46 9 47 047 49 48 40 49 307 59 30 43 34 44 24 45 14 46 4 46 54 47 44 48 34 49 248 6.7 40 43 29 44 20 45 10 45 59 46 49 47 39 48 29 49 199 75 50 43 25 44 14 45 4 45 54 46 44 47 34 48 23 49 13 MATHEMATICAL TABLES. 151 TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE. MOON'S HORIZONTAL PARALLAX. P. P. Moon's for App. Alt. Alt. 54' 55' 56' 57' 58' 59' 60 | 61' P. P. for Par. "34 1 I I 4 2 1 2 2 334+ in 1 2 3 456 7∞ a 5 335 8 9 5 " I I I 2 4 2 5 3 7 4 4 H23+56 78 a 8 9 36 3 37 5 = I I 38 = Our ŏ = 044 ་ // 11 "1 11 = 12 49 = // 2/ 8 48 571 0.8 248 512 1.6 57 48 46 463 24 13 47 2 47 51 48 404 3:3 8 46 57 47 46 48 355 41 246 51 47 40 48 29 6 5.0 043 20 44 10 45 0 45 50 46 39 47 29 48 1849 8 10 43 15 44 544 54 45 44 46 33 47 23 48 20 43 10 44 44 49 45 39 46 28 47 18 48 30 43 5 43 55 44 44 45 34 46 23 47 12 48 4043 143 50 44 40 45 29 46 18 47 8 47 50 42 55 43 45 44 34 45 23 46 42 51 43 40 44 29 45 18 46 10 42 45 43 35 44 24 45 13 46 20 42 41 43 30 44 19 45 8 45 57 46 46 47 35 48 247 5.8 30 42 36 43 25 44 13 45 245 51 46 40 47 29 48 18 8 6.5 40 42 31 43 20 44 9 45 58 45 46 46 35 47 24 48 139 74 50 42 26 43 14 44 3 45 52 45 40 46 29 47 1748 I 12 48 6 I 042 21 43 9 43 58 44 47 45 35 46 24 47 10 42 15 43 4 43 53 44 41 45 29 46 18 47 6 47 55. 20 42 11 42 59 43 48 44 36 45 24 46 13 47 147 491 0·8 30 42 6 42 54 43 42 44 30 45 18 46 7 46 55 47 432 1.6 4042 1 42 49 43 37 44 25 45 13 46 46 50 47 383 24 50 41 55 42 43 43 31 44 19 45 7 45 55 46 43 47 314 32 041 51 42 39 43 26 44 14 45 2 45 50 46 38 47 26 5 40 265 10 41 45 42 33 43 21 44 8 44 56 45 44 46 32 47 206 48 20 41 40 42 28 43 16 44 3 44 51 45 39 46 27 47 147 5.6 30 41 34 42 22 43 10 43 57 44 45 45 33 46 20 47 78 6·4 40 41 30 42 17 43 14 47 29 72 50 41 24 42 11 42 8 46 56 846 0 41 19 42 10 41 14 42 20 41 I 30 41 5 43 52 44 40 45 27 46 59 43 46 44 34 45 21 46 6 42 54 43 41 44 28 45 15 46 3 46 51 042 48 43 35 44 22 45 9 45 56 46 44' 8 41 54 42 42 43 29 44 16 45 3 45 50 46 371 08 241 48 42 36 43 23 44 9 44 56 45 44 46 30 2 1.6 4 44 51 45 38 46 253 2.3 58 44 45 45 31 46 184 3*1 19 43 6 43 52 44 39 45 26 46 13 5 39 13 42 59 43 46 44 33 45 19 46 40 40 57 41 43 42 30 43 18 44 50 40 51 41 37 42 24 43 11 43 3139 040 46 41 32 42 2 2 3 3445 2 3456 7∞ a 7 4 8 9 5 ་ 40 I I 2 I 2 4 2 5 3141 3+no 7 9 10 40 40 41 26 42 20 40 35 41 21 42 30 40 29 41 15 42 40 40 24 41 10 41 50 40 1841 441 5 6 47 842 54 43 41 44 27 45 14 46 07 5.5 242 48 43 34 44 21 45 7 45 538 6.2 57 42 43 43 29 44 15 45 I 45 489 70 50 42 36 43 22 44 944 54 45 30 0 40 13 40 59 41 45 42 31 43 17 44 30 39 55 40 40 41 26 42 344 49 45 35 10 40 740 53 41 38 42 25 43 10 43 56 44 42 45 28 20 40 I 40 47 41 32 42 1843 4 43 49 44 35 45 211 0·8 11 42 57 43 43 44 28 45 142 15 40 39 49 40 35 41 21 42 6 42 51 43 37 44 23 45 83 23 50 39 44 40 29 41 14 42 042 45 43 30 44 16 45 14 3°C 039 38 40 24 41 9 41 54 42 39 43 25 44 10 44 555 3.8 10 39 32 40 17 41 3 41 48 42 33 43 18 44 344 486 45 20 39 27 40 12 40 5741 42 42 27 43 12 43 57 44 427 5*3 5 40 50 41 35 42 20 43 5 43 50 44 35 8 6.0 6 4 7 4 8 5 30 39 21 40 9 5 40 39 15 40 50 39 9 39 54 40 39 41 23| 42 040 45 41 30 42 543 358 15 42 59 43 44 44 299 6.8 8 42 53 43 38 44 22 152 MATHEMATICAL TABLES. P. P. Moon's TABLE XVII. CORRECTION OF THE MOON'S ALTITUDE. MOON'S HORIZONTAL PARALLAX. for Alt. App. P. P. for Alt. 54' 55' 56′ 57 1 58' 59′ 60' 61' Par. O "1 / "/ "1 ་ "/ I SIHH2mm+nno 123456 78 9 "142 42 0 39 3 39 47 10 38 56 39 41 40 26 41 20 38 51 39 36 40 Ι 30 38 45 39 29 40 40 38 40 39 25 40 3 5 343 39 4 ४ 5 6 40 32 41 17 42 I 42 46 43 30 44 15 8" II 0.7 13 40 57 41 42 42 26 43 10 43 542 15 840 52 41 36 42 20 43 50 38 33 39 17 40 I 40 45 41 29|42 13| 42 57 43 414 29 038 27 39 11 56 40 39 41 23 42 742 51 43 355 3.6 10 38 21 39 5 39 48 40 32 41 16 42 0 42 44 43 276 44 20 38 15 38 59 39 42 40 26 41 941 53 42 36 43 207 51 30 38 8 38 52 39 35 40 19 41 241 46 42 29 43 138 5.8 40 38 3 38 46 39 30 40 13 40 57 41 40 42 23 43 79 6.6 2343 50 37 56 38 39 39 23 40 6 40 49 41 33 42 16 42 59 10 41 54 42 39 43 23 44 20 41 441 49 42 33 43 17 44 4 43 48 3 22 44 2 ~Ham4no 78 9 I I 037 50 38 34 39 10 37 44 38 27 39 20 37 38 38 20 39 1740 10 39 040 53 40 43 41 26 42 10 42 53 36 41 19 42 3641 1942 4 39 46 40 I 30 37 31 38 14 38 3 2 4 3 5 3145 6 4 7 5 39 40 40 40 37 26 38 8 38 51 39 33 40 50 37 18 381 38 44 39 26 40 37 13 37 55 38 38 39 21 40 10 37 7 37 49 38 31 39 14 39 20 37 37 42 38 24 39 6 39 56 2 42 46 29 41 12 41 55 42 38 1 07 22 41 5 41 48 42 31 312 I'4 16 40 59 41 41 42 243 21 9 40 51 41 34 42 174 2.8 340 45 41 28 42 10 5 35 56 40 39 41 21 42 36 4.2 48 40 31 41 13 41 557 49 5 30 36 53 37 35 38 17 38 59 39 41 40 23 41 6 96 3 I I I 23++ no 6 23&io zoo a 541 5 41 48 8 5.6 40 36 47 37 29 38 11 38 53 39 35 40 17 40 59 41 419 6.3 50 36 40 37 22 38 4 38 46 39 28 40 10 40 51 41 33 32 14 15 40 57 3 20 8 40 494 27 46 0 36 35 37 17 37 58 38 40 39 21 40 3 40 45 41 26 10 36 28 37 9 37 51 38 33 39 14 39 56 40 37 41 19 20 36 21 37 3 37 44 38 26 39 7 39 48 40 30 41 III 0°7 30 36 14 36 56 37 37 38 18 38 59 39 41 40 22 41 40 36 9 36 49 37 31 38 12 38 53 39 34 40 50 361 36 43 37 24 38 5 38 46 39 27 40 35 56 36 37 37 17 37 58 38 40 39 20 40 10 35 49 36 29 37 10 37 51 38 32 39 13 39 53 40 34 6 4'1 20 35 42 36 23 37 3 37 44 38 25 39 5 39 46 40 267 48 30 35 35 36 16 36 56 37 37 38 17 38 58 39 38 40 19 8 5.5 40 35 29 36 9 36 50 37 30 38 11 38 51 39 32 40 129 6.2 37 22 38 3 38 44 39 24 40 4 4 3 5 447 6 4 7 8 6 9 I I 4 3 〃 I 2344 no 6 1234 6 7∞ a 50 35 22 36 2 36 42 48 35 16 35 56 36 36 37 449 5 6 4 8 6 9 140 425 34 16 37 57 38 37 39 17 39 57 10 35 9 35 49 36 29 37 9 37 49 38 29 39 939 49/ 2035 235 42 36 22 37 I 37 42 38 21 39 139 411 06 30 34 55 35 34 36 15 36 54 37 34 38 13 38 54 39 33 2 13 40 34 49 35 28 36 8 36 47 37 28 38 7 38 47 39 24 3 19 50 34 42 35 21 36 I 36 40 37 20 37 59 38 39 39 18 4 2.6 0 34 35 35 14 35 53 36 33 37 12 37 52 38 31 39 10 5 32 10 34 28 35 7 35 46 36 25 37 4 37 44 38 23 39 26 39 20 34 21 35 35 39 36 18 36 58 37 37 38 16 38 557 46 30 34 14 34 53 35 32 36 11 36 50 37 29 38 8 38 478 5.2 34 46 35 26 36 4 36 43 37 22 38 138 409 5'9 134 40 35 18 35 57 36 36 37 15 37 40 34 50 34 53 38 32 MATHEMATICAL TABLES. 153 "1 / "/ 37 6 37 45 38 24 36 58 37 37 38 15 36 52 37 30 38 81 0·6 36 44 37 22 38 02 1.2 36 36 37 14 37 523 19 36 29 37 6 37 454 2.5 36 21 36 59 for Alt. App. Alt. 54 55' 56' TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE. P. P. Moon's MOON'S HORIZONTAL PARALLAX. 59' 60' 61' P. P. for Par. 57' 58′ ་ "50 1 4 5 1 2 2 m t in SO Z 23 456 78 a I 3 451 5 5 6 9 7 33 54 34 32 35 11 35 49 36 28 10 33 46 34 25 35 3 35 42 36 20 20 33 40 34 19 34 57 35 35 36 13 30 33 33 34 II 34 49 35 28 36 5 40 33 26 34 4 34 41 35 20 35 58 50 33 19 33 57 34 35 35 13 35 51 33 12 33 50 34 27 35 5 35 43 10 33 5 33 42 34 20 34 57 35 35 20 32 58 33 36 34 13 34 51 35 28 36 30 32 51 33 28 34 6 34 43 35 21 40 32 43 33 21 33 57 34 35 35 50 32 36 33 13 33 51 34 27 35 36 52 I I 2 2 3 2 4 3 453 5 6 5 7 5 8 6 9 7 37 365 31 13 36 51 37 28 286 3·8 6 36 36 43 37 217 45 35 58 36 35 37 128 51 35 49 36 27 37 49 57 435 42 36 19 36 56 12 032 29 33 6 33 43 34 19 34 57 35 33 36 10 36 48 10 32 21 32 58 33 35 34 12 34 49 35 25 36 2 36 40 20 32 15 32 52 33 28 34 5 34 41 35 18 35 55 36 321 06 30 32 7 32 44 33 20 33 57 34 34 35 10 35 47 36 23 2 12 4032 032 36 33 13 33 49 34 25 35 235 39 36 143 18 5031 53 32 30 33 6 33 42 34 18 34 54 35 31 36 74 24 031 46 32 22 32 58 33 34 34 11 34 47 35 23 35 59 5 30 10 31 38 32 14 32 50 33 26 34 34 38 35 14 35 506 3.6 7 32 43 33 19 33 55 34 31 35 735 437 42 032 36 33 11 33 47 34 22 34 58 35 34 8 4.8 40 31 16 31 52 32 28 33 3 33 39 34 15 34 50 35 259 54 50 31 10 31 46 32 21 32 56 33 32 34 7 34 43 35 18 20 31 32 32 30 31 24 32 54 I I 20 30 47 31 30 30 40 31 HN 2 3 4 3 5 455 2 2 3 4566 7 7 8 6 9 7 4 3 1223 to 6 2 1234 SO Z∞0 a 5 2 0 31 2 31 38 32 13 32 48 33 23 33 59 34 34 35 9 10 30 55 31 30 32 5 32 40 33 15 33 50 34 26 35 I/ 22 31 57 32 32 33 7 33 43 34 17 34 521 0·6 14 31 49 32 24 32 59 33 34 34 731 41 32 16 32 50 33 25 34 40 30 32 31 50 30 25 31 30 17 30 52 31 34 32 31 26 32 9 32 44 33 032 35 33 10 30 9 30 44 31 18 31 53 32 27 33 20 30 3 30 37 31 11 31 45 32 19 30 29 55 30 29 31 331 37 32 11 18 33 53 834 432 1.2 34 353 1'7 34 274 2°3 9 33 44 34 185 29 I 33 35 34 9 6 34 32 54 33 28 34 2740 32 45 33 19 33 538 46 40 29 48 30 21 30 55 31 29 32 3 32 37 33 10 33 449 5'1 50 29 41 30 14 30 48 31 22 31 55 32 29 33 3 33 37 56 0 29 33 30 7 30 40 31 457 5 7 6 8 6 9 7 // 13 31 47 32 20 32 54 33 28 10 29 25 29 58 30 32 31 531 38 32 12 32 46 33 19 / 20 29 17 29 50 30 23 30 57 31 30 32 4 32 37 33 101 0'5 30 29 9 29 43 30 16 30 49 31 22 31 55 32 28 33 I2 I'I 40 29 I 29 34 30 7 30 41 31 13 31 46 32 19 32 523 16 50 28 54 29 27 30 0 30 33 31 6 31 39 32 11 32 444 2'1 0 28 47 29 20 29 52 30 24 30 57 31 30 32 3 32 35 5 27 10 28 39 29 11 29 44 30 17 30 49 31 21 31 54 32 266 32 20 28 32 29 4 29 37 30 9 30 41 31 14 31 46 32 18 7 37 30 28 24 28 56 29 28 30 I 30 33 31 5 31 37 32 108 42 40 28 16 28 48 29 20 29 52 30 24 30 57 31 28 32 19 4.8 50 28 9 28 41 29 13 29 45 30 17 30 49 31 20 31 53 M 154 MATHEMATICAL TABLES. TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE. P. P. Moon's] MOON'S HORIZONTAL PARALLAX. for Alt. App. Alt. 54' 55' "1 56' 57′ 58' 59 60' 61' P. P. for Par. // "/ // // // "/ o 28 128 33 29 5 29 37 30 8 30 40 31 12 31 44 10 27 53 28 25 28 56 29 28 29 59 30 31 31 331 34' 8 20 27 45 28 16 28 48 29 19 29 51 30 22 30 54 31 251 0*5 28 40 29 11 29 42 30 14 30 45 31 162 10 028 3129 2 29 34 305 30 36 31 73 15 28 24 28 55 29 26 29 57 30 28 30 594 21 o 27 14 27 45 28 IO 27 627 36 28 20 26 58 27 29 28 58 I 3 4 5 6 2334 56 77 1 2 3 4 SO N∞ a I 30 27 37 28 3 40 27 29 28 3 50 27 22 27 459 7 8 H 60 I 2 3 4 3 61 8 8 ~mmt 56 7∞ 23 456 7OO a 1234 +56 78 1 2 3 4 56 7∞ a I I 4 4 8 62 4/63 53 15 28 47 29 17 29 48 30 19 30 505 2.6 728 38 29 9 29 39 30 10 30 416 3.1 028 30 29 129 31 30 230 337 3.6 30 26 51 27 21 27 51 28 22 28 52 29 22 29 53 30 248 41 40 26 42 27 13 27 43 28 13 28 43 29 14 29 44 30 159 46 50 26 34 27 4 27 34 28 4 28 35 29 5 29 35 30 5 026 26 26 56 27 26 27 56 28 26 28 56 29 26 29 56 10 26 18 26 48 27 18 27 48 28 17 28 47 29 17 29 47' 20 26 11 26 40 27 10 27 40 28 10 28 39 29 9 29 38 1 05 30 26 2 26 32 27 2 27 31 28 I 28 30 29 0 29 29 2 I'O 40 25 54 26 23 26 53 27 22 27 52 28 21 28 50 29 203 14 50 25 47 26 16 26 45 27 15 27 44 28 13 28 42 29 124 19 025 39 26 8 26 37 27 826 6 27 35 28 4 28 33 29 25 2.4 10 25 30 25 59 26 29 26 57 27 26 27 55 28 24 28 53 6 29 20 25 22 25 51 26 20 26 48 27 17 27 46 28 15 28 447 34 30 25 14 25 42 26 11 26 40 27 927 37 28 6 28 358 3.8 40 25 6 25 34 26 625 226 31 27 027 28 27 57 28 259 43 50 24 58 25 27 25 55 26 24 26 52 27 20 27 48 28 16 7 024 50 25 18 25 46 26 15 10 24 42 25 10 25 38 26 6 20 24 34 25 225 30 25 58 30 24 26 24 54 25 22 25 49 40 24 17 24 45 25 13 25 40 26 8 26 35 27 3 27 313 13 50 24 10 24 37 25 4 25 32 25 59 26 26 26 53 27 214 18 o 24 124 28 24 55 25 23 25 50 26 17 26 44 27 11 5 22 IC 23 53 24 20 24 47 25 14 25 41| 26 8 26 35 27 26 27 20 23 45 24 12 24 39 25 6 25 33 26 30 23 36 24 3 24 30 24 57 25 24 25 51 26 43 27 11 27 39 28 26 34 27 3427 2 27 30 27 58, 26 26 26 54 27 22 27 49 1 0‘4 26 17 26 44 27 12 27 402 0.9 26 27 26 547 31 26 17 26 448 3.6 40 23 28 23 55 24 21 24 48 25 15 25 41 26 826 359 4:0 50 23 2123 47 24 14 24 40 25 725 3326 64 0 23 12 23 39 24 I I 3 3 4 4 23456 to a 23446 N∞ 5 7 8 7 9 8 026 26 24 58 25 24 25 50 26 16 24 48 25 16 25 41 26 7 24 3925 5 25 31 25 571 04 5 24 31 10 23 4 23 30 23 56 24 22 20 22 55 23 21 23 48 24 13 30 22 47 23 13 23 39 24 4 24 30 24 56 25 22 25 482 0.8 40 22 39 23 4 23 30 23 55 24 21 24 47 25 12 25 38 3 12 50 22 31 22 56 23 22 23 47 24 13 24 38 25 4 25 294 1*7 65 0 22 22 22 47 23 13 23 38 24 4 24 29 24 55 25 205 2.1 IO 22 14 22 3923 4 23 29 23 55 24 20 24 45 25 106 2.5 20 22 5 22 30 22 55 23 20 23 46 24 10 24 35 25 17 2.9 30 21 56 22 22 22 46 23 11 23 36 24 124 26 24 518 33 40 21 48 22 13 22 37 23 223 27 23 52 24 16 24 419 37 50 21 41 22 5 22 30 22 54 23 18 23 43 24 8 24 32 MATHEMATICAL TABLES. 155 TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE. P. P. Moon's for Alt. MOON'S HORIZONTAL PARALLAX. App. Alt. 54 1 55' 56′ | 57' = // P. P. for 58' 59' 60' 61' Par. I I 2 3 4 5 ISO 70 1234 no too a "66 4 4 5 567 67 6 5 7 6 8 9 8 I I → // "1 ་་ 021 32 21 56 22 21 22 45 23 9 23 34 23 58 24 23 10 21 23 21 48 22 12 22 36 23 0 23 24 23 48 24 13/ 20 21 16 21 40 22 4 16|23 22 28 22 52 23 16 23 40 24 41 04 30/21 721 31 21 55 22 19 22 43 23 723 31 23 542 0.8 40 20 58 21 22 21 46 22 10 22 33 22 57 23 21 23 453 1'1 50 20 49 21 13 21 37 22 022 24 22 48 23 11 23 354 15 0 20 41 21 4 21 28 21 51 22 15 22 38 23 1 23 255 19 10 20 32 20 55 21 19 21 42 22 6 22 29 22 52 23 156 2.3 20 20 25 20 48 21 11 21 34 21 57 22 20 22 43 23 77 27 30 20 16 20 39 21 2 21 25 21 48 22 11 22 34 22 568 3.0 40/20 7 20 30 20 53 21 16 21 38 22 I 22 24 22 479 34 50 19 58 20 21 20 44 21 7 21 29 21 52 22 14 22 37 I 81 04 68 o 19 50 20 12 20 35 20 57 21 20 21 42 22 5 22 27 10 19 41 20 3 20 26 20 48 21 11 21 32 21 55 22 17 20 19 33 19 56 20 18 20 39 21 2 21 24 21 46 22 30 19 24 19 47 20 8 20 30 20 53 21 14 21 36 21 592 07 40 19 15 19 38 19 59 20 21 20 43 21 321 25 21 49|3 I'I 50 19 8 19 30 19 51 20 13 20 34 20 56 21 18 21 404 1'5 o 18 59 19 21 19 42 20 4 20 25 20 46 21 8 21 305 1.8 10 18 51 19 12 19 33 19 54 20 16 20 36 20 58 21 19 21 196 2.2 319 24 19 45 20 6 20 27 20 49 21 18 54 19 15 19 36 19 57 20 18 20 39 21 40 18 24 18 45 19 6 19 27 19 46 20 8 20 29 20 5019 3.3 50 18 16 18 37 18 58 5 4 4 69 234 SO 78 =23&SO N∞ a 6 6 7 6 8 LO 7 8 70 // I I 234566 123456 7∞ a 78 8 I I 2 3 571 23456 78 30 20 18 42 19 18 33 107 25 082.9 19 18 19 39 19 59 20 20 20 41 18 48 19 9 19 29 19 50 20 10 20 31 18 39 18 59 19 20 1 18 20 18 41 19 19 40 20 I 20 21 o 18 7 18 28 10 17 58 18 19 20 17 49 18 10 18 30 18 50 19 10 19 31 19 50 20 111 03 30 17 41 18 I 19 20 19 41 20 1/2 0.7 40 17 33 17 53 18 12 18 32 18 52 19 12 19 32 19 513 10 50 17 24 17 44 18 3 18 23 18 42 19 2 19 22 19 424 13 o 17 15 17 35 17 54 18 14 18 33 18 53 19 12 19 325 17 10 17 6 17 25 17 45 18 4 18 23 18 43 19 2 19 21 2.0 20 16 57 17 16 17 35 17 54 18 14 18 33 19 117 23 30 16 48 17 7 17 26 17 45 18 4 18 23 18 42 19 28 2.6 40 16 40 16 59 17 18 17 37 17 55 18 15 18 33 18 529 30 50 16 31 16 50 17 9 17 27 17 46 18 5 18 24 18 42 72 0 16 22 16 41 10 16 13 16 31 18 52 16 59 17 18 17 36 17 55 18 13 18 32 16 50 17 9 17 27 17 45 18 3 18 22/ 1/2 0.6 2016 4 16 22 16 41 16 59 17 17 17 36 17 54 18 121 0.3 30 15 55 16 13 16 31 16 49 17 7 17 25 17 43 18 40 15 47 16 5 16 23 16 41 16 59 17 17 17 35 17 523 09 50 15 38 15 56 16 14 16 31 16 49 17 7 17 25 17 424 12 o 15 29 15 47 16 4 16 22 16 40 16 57 17 14 17 325 15 10 15 20 15 38 15 55 16 13 16 30 16 47 17 5 17 22 6 1.8 20 15 11 15 28 15 46 16 3 16 20 16 37 16 55 17 127 21 573 6 7 8 9 9 40 14 54 15 11 15 28 15 45 16 50 14 45 15 2 15 18 15 35 15 52 16 9 16 26 16 42 30 15 2 15 19 15 36 15 53 16 10 16 28 16 44 17 2 2824 16 18 16 35 16 529 27 156 MATHEMATICAL TABLES. TABLE XVII.-CORRECTION OF THE MOON'S ALTITUDE. P. P. Moon's for App. Alt. Alt. 54 55' MOON'S HORIZONTAL PARALLAX. ་ 56′ = 57′ P. P. 58′ 59' 60' | 61' Par. = " // = "174 I I 2 2 3 3 5 4 4 5 75 6 7 7 8 8 9 9 .. ـر I I 2 3 3 4 4 1234 io n∞ à 12 0.5 15 523 0.8 14 36 14 53 15 9 15 26 15 42 15 59 16 15 16 32 10 14 27 14 44| 15 O 15 16 15 32 15 49 16 5 16 21 20 14 18 14 34 14 50 15 6 15 23 15 39 15 55 16 III 0°3 615 15 13 15 29 15 45 16 15 4 15 20 15 36 14 54 15 10 15 26 15 424 I'I 14 45 15 O 15 16 15 315 13 14 35 14 50 15 6 15 21 6 1.6 14 25 14 40 14 55 15 107 1.8 08 2.1 14 15 14 30 14 45 15 14 7 14 22 14 36 14 519 24 13 57 14 11 14 26 14 41 30 14 9 14 25 40 14 114 16 50 13 52 14 7 13 43 13 58 10 13 33 13 49 20 13 24 13 40 30 13 15 13 30 40 13 7 13 22 50 12 58 13 13 14 41 14 57 14 33 14 48 14 23 14 39 14 13 14 29 14 4 14 19 13 55 14 10 13 45 14 0 13 37 13 52 13 28 13 42 4 13 13 47 14 1 76 0 12 49 13 18 13 32 14 16 14 31 10 12 40 12 54 13 8 13 23 13 37 13 52 14 6 14 20 20 12 31 12 44 12 59 13 13 13 27 13 41 13 56 14 101 0'2 30 12 22 12 35 12 49 13 4 13 17 13 31 13 46 13 592 05 40 12 13 12 27 12 41 12 55 13 9 13 23 13 36 13 503 07 50 12 4 12 18 12 32 12 45 12 59 13 12 13 26 13 394 09 0 11 55 12 8 12 22 12 35 12 49 13 2 13 16 13 29 5 1'1 10 11 45 11 59 12 12 26 12 40 12 53 13 II 26 12 40 12 53 13 7 13 206 1'4 12 3 12 16 12 30 12 43 12 57 13 107 1.6 08 1.8 12 21 12 34 12 47 13 577 20 II 37 II 51 12 6 6 7 7 8 8 30 11 28 II 41 9 9 II 54 12 II II 7 58 12 11 12 24 12 37 12 499 21 12 1 12 14 12 26 12 39 78 = // I I 2 2 10 58 11 10 3 3 10 49 II 4 4 10 39 10 51 5 579 10 30 10 41 6 6 9 10 21 10 32 7 7 20 O 10 11 10 22 8 8 30 9 39 9 50 10 2 10 13 9 9 40 9 319 42 9 5210 3 50 9 22 9 33 80 ་ = 123456 Zoo a 123456 7∞ a 10 123 O O I I 20 30 3 3 40 4 4 50 8 27 81 8 18 IO 8 9 8 18 7 7 20 8 8 30 8 0 8 9 750 7 59 9 9 40 7 41 7 50 50 7 32 7 41 9 13 9 23 9 39 14 8 54 9 4 9 33 9 44 8 45 9 24 9 34 9 15 9 25 9 5 9 15 8 36 8 56 9 5 40 II 19 11 32 11 45 II 50 II II II 23 II 36 II 49 I * 81 0.2 O II 2 II 14 11 26 11 39 11 51 12 4 12 16 12 29 6 12 19/ 10 10 52 II 5 II 17 II 29 II 42 11 54 12 20 10 43 10 55 II 8 11 20 11 32 11 44 II 56 12 30 10 34 10 46 11 22 11 34 11 46 11 582 04 40 10 26 10 38 II 12 II 24 11 36 11 483 0.6 50 10 17 10 28 II 3 II 14 11 26 11 384 0.8 O 10 7 10 18 10 53 11 4 II 16 11 275 10 ΙΟ 9 58 10 10 43 10 54 II 611 176 12 9 48 10 10 33 10 44 10 56 11 77 14 10 24 10 35 10 46 10 578 1.6 10 14 10 25 10 35 10 469 1.8 10 4 10 15 10 25 10 36 O O O O 8 55 46 9 43 9 53 9 54 10 5 10 15 10 25 9 44 9 55 10 5 10 15 9 35 9 45 9 25 9 35 9 15 9 25 // = 9 55 10 51 0.2 9 45 9 552 03 9 34 9 443 0'5 8 37 8 46 8 56 8 27 8 37 8 46 8 27 8 36 9 5 9 15 8 559 5 9 24 9 14 9 344 0.6 9 245 0.8 8 45 8 55 9 4 9 136 10 8 18 8 27 8 36 8 45 8 54 8 8 8 17 8 26 8 35 8 44 9 37 I'I 8 528 13 7 59 8 7 8 16 8 25 8 33 8 429 15 7 49 7 58 8 6 8 15 8 23 8 32 MATHEMATICAL TABLES. 157 TABLE XVII. CORRECTION OF THE MOON'S ALTITUDE. P. P. Moon's MOON'S HORIZONTAL PARALLAX. for Alt. App. Alt. 54′ | 55′ | 56′ 57' 58' 59' 60' 61' P. P. for Par. = 1182 0723 7 31 7 40 7 48 7 56 8 58 13 10 7 14 7 22 7 30 7 38 7 46 7 55 8 3 - ∞ ∞ ∞ 9 123 + 50 No a 123456 I I 20 7 5 7 13 7 21 7 29 7 37 7 45 7 53 30 655 7 3 7 II 7 19 7 27 7 357 42 40 6 46 6 54 7 2 7 9 7 17 7 25 7 32 4 4 50 6 37 6 45 652 52 7 O 7 7 7 14 7 22 83 o 6 28 6 35 6 42 6 50 6 57 7 47 12 10 6 19 6 26 6 33 6 40 6 47 6 54 7 2 8 21 8 II 8 ΙΙ ΟΙ 7 50 2 0.3 7 40 7 40 3 04 7 294 05 7 19 5 0.6 96 0.8 7 9 7 7 20 6 6 16 9 623 6 30 6 37 6 6 44 51 6 587 09 8 8 30 6 O 6 7 6 14 6 21 6 27 6 6 34 41 6 48 8 10 9 40 5 51 5 58 6 4 6 II 6 18 6 24 6 31 6 37 9 12 50 5 42 5 48 5 55 6 I 6 8 6 14 6 21 6 27 84 0533 5 39 5 45 5 52 5 58 6 4 4 6 10 6 17 → 10 5 23 5 30 5 36 5 42 5 48 5 54 6 6 61 "/ I 5 6 7 2 3 4 5 NO a 1 2 3 + SO Noo a I 20 5 14 5 20 5 26 5 32 5 38 5 44 5 50 5 561 O'I 3º 5 5 5 11 5 17 5 22 5 28 5 34 5 40 5 452 0°2 3 3 40 4 56 5 I 5 7 5 13 5 18 5 24 5 29 5 35 3 03 4 4 50 4 47 4 52 4 57 5 3 5 8 5 14 5 19 5 244 04 85 이 4 37 4 43 4 48 4 53 4 58 5 45 9 5 14 15 05 IO 4 28 4 33 4 38 4 43 4 48 4 53 4 59 5 4 46 0.6 7 20 4 19 4 24 4 29 4 34 4 38 4 43 4 48 4 53 7 0.6 8 8 9 9 304 10 4 14 4 19 4 24 4 29 4 33 4 38 4 38 4 438 0.7 404 0 4 5 4 10 4 14 4 19 4 23 4 28 4 329 0·8 50 3 51 3 56 4 4 44 9 4 13 4 17 4 22 86 0342 3 46 3 50 I I 10 3 33 20 3 24 3 37 3 41 6 61 7 7 20 228 2 2 3 3 4 4 5 587 30 3 14 40 3 5 50 2 56 0246 10 2 37 IO 237 3 27 3 31 3 18 3 22 393 12 2 59 3 2 2 50 2 53 240 2 31 243 2 34 3 55 3 59 3.49 3 45 3 35 3 39 325 3 29 3 16 3 19 3 639 256 2 56 2 59 259 2 46 249 4 3 34 3 53 3 57 3 43 3 47 3 33 3 36 4 7 4 II 4 I 3 50 I 0.1 3 40 2 0°I 3 23 3 26 3 303 0.2 3 12 3 16 3 19 4 0°2 3 2 3 5 3 950*3 252 2 55 2 58 6 04 2 362 39 2 42 2 45 2 48704 8 8 30 2 19 2 21 9 9 40 2 10 2 12 50 2 2 123 224 2 14 2 2 27 2 29 232 2 35 2 17 2 19 2 22 2 24 5 2 7 2 9 2 12 2 14 88 o 1 51 I 53 I 55 I 57 I 59 ΙΟ I 42 I 44 I 46 I 48 I 50 I 51 21 2 2 2 4 I 53 2 1 I 23456 too a 1 2 3 4 SO 7∞ a I 20 I 33 I 34 I 36 I 38 I 40 I 41 I 43 2378 0.5 227905 2 16 6 I 55' I 45 I 0.0 30 I 23 I 25 I 26 I 28 I 30 I 31 I 33 I 342 O'I 40 I 14 I 15 I 17 1 18 89 50 I 5 0 0 56 ΤΟ 0 46 I 6 I 7 I ∞ ∞ I 20 I 21 I 22 I 243 OI 8 I 10 I II I 12 Ι 13 4 ΟΙ • 57 0 58 O 59 I O I I I 2 I 35 O'I 47 • 48 O 49 0 50 0 51 0 52 O 52 6 0.2 20 0 37 0 38 0 38 0 39 0 40 0 41 0 41 O 42 7 0.2 8 8 9 9 30 0 28 O 28 40 0 18 0 29 O 29 50 O 9 O 19 O 9 0 19 Ο ΙΟ O 20 0 30 O 20 0 30 O 20 Ο ΙΟ Ο ΙΟ O IO Ο ΙΟ 0 31 0 318 0.2 O 21 O 21 9 O'2 Ο ΙΟ 158 MATHEMATICAL TABLES. Min. 2 Hours. Diff. 3 Hours. Diff. 4 Hours. Diff. 5 Hours. Hours. Diff. Diff. 6 Hours. 6 Hours. Diff. Diff. 7 Hours. Diff. 4 0 × 23 t 8.825992 9*165679 I 833034 11737 7602 9*397940 9*568894 9.698970 9*798933 60 5457 840015 11635 170240 401214 7555 5428 571358 4107 174773 404471 573811 4088 700861 3152 3138 800384 2418 59 702743 801828 2407 846936 11535 179278 7509 5401 4070 407713 576253 704618 3124 803266 2396 8 9 56 7∞ a 853798 58.860602 11437 183756 7463 410938 5375 578684. 4052 3110 706484 804697 2385 56 11340 7418 5348 4033 3097 2375 9.188207 9'414147 9 581104 9.708342 867349 11245 192631 7373 5322 417340 874040 11152 11061 197028 7329 5296 583513 4015 3083 9.806122 710192 807540 2364 55 54 3997 3070 420517 880676 7285 585911 201399 423679 5270 588299 3980 712034 808952 2353 887258 10970 7241 10880 205745 426825 5243 3962 713868 3057 810357 2342 52 590676 715694 3043 811756 2332 7198 5217 3944 3030 2321 10 8.893785 9'210064 II 10792 900261 12 13 14 234 906684 10706 214358 7156 9'429955 9'593042 9'717512 9.813149 50 5192 433070 10620 218627 7114 436170 5167 595398 3927 3017 719322 814535 2311 49 3910 3005 597744 913055 10536 222870 7073 5142 3892 721124 815915 2300 48 2992 2289 439255 600078 722919 7032 5117 3875 2978 817289 47 919377 227089 10453 6991 442325 602403 5092 3857 724705 2965 818656 2279 2268 46 15 8.925648 9.231284 16 931871 10371 235454 6950 9445379 10290 17 18 78 938045 239600 6910 448419 5067 9.604717 607021 3840 9*726484 9.820017 5043 10210 6870 451445 5018 609315 3823 728255 2952 821372 2258 45 2939 2248 3806 730018 822721 2926 43 944171 243722 10132 6831 454455 611598 731774 824063 2237 42 4993 19 20 950251 956284 247821 10055 251897 6792 457451 4969 613872 3790 2913 733522 825399 2227 41 460433 616135 3772 735262 2900 826729 2217 40 21 Hours. Diff. 20 Hours. Diff. 19 Hours. Diff. 18 Hours. Diff. 17 Hours. Diff. 16 Hours. Diff. Min. TABLE XVIII. LOGARITHMS FOR FINDING THE HORARY ANGLE OR APPARENT TIME. o ammo ime nga no 4 $ MATHEMATICAL TABLES. 159 TABLE XVIII. Logarithms FOR FINDING THE HORARY ANGLE OR APPARENT TIME. Min. 2 Hours. Diff. 3 Hours. Diff. 4 Hours. Diff. 5 Hours. Diff. 6 Hours. Diff. 7 Hours. Diff. 208.956284 9*251897 21 962271 9979 6753 9'460433 9.616135 9°735262 9.826729 255949 22 968213 9904 6715 463400 4945 618388 3756 2887 2206 40 736994 259978 4921 9830 6678 466354 620632 3740 2875 828053 2196 39 23 974111 263985 4898 738719 24 979965 9757 6640 469293 9684 267969 6602 472218 4875 622865 3721 2863 829370 2186 4852 625089 3707 740437 830682 2850 2176 3690 742147 2837 831987 2166 38 37 36 333 en 98 76 45 8.985775 26 9612 9'271930 991543 275870 6566 9'475129 4828 .9.627303 478026 629507 3674 9'743849 2825 9.833287 35 27 997269 9543 279788 0530 4805 28 9002953 9474 283684 6493 480909 631701 4782 3658 745544 834580 2155 2813 29 008596 9405 9338 287558 6457 483779 4760 633886 3642 747232 2800 835867 2145 33 6422 486635 636061 748912 3626 4738 3610 750585 2788 837148 2135 www.g 34 32 2776 838424 2125 31 2115 wwwww 30 9014198 9'291412 019761 9272 6387 9*489478 9.638227 4715 025284 9206 295244 6352 492307 4693 640383 3593 753909 9*752251 2763 9'839693 30 2105 840956 29 299055 030768 914.1 302845 6317 495123 036213 9077 306615 6283 497926 4672 642529 3577 9013 6249 500716 4650 644666 3562 755560 2750 2095 842213 28 2738 2085 757203 843464 4628 646794 3547 2727 2076 27 758840 844710 26 3532 2715 2066 ww ww 36 37 38 no no no 35 9'041621 046991 8950 310364 6216 9'503492 9.648913 4607 8888 314094 052323 057619 8827 317803 6148 6182 506256 651022 3516 9*760469 9.845949 762091 2703 2056 25 4585 509007 4563 653122 3500 39 062879 40 068103 8767 321492 6115 511745 655213 3485 8707 325161 4542 6083 514470 657294 3469 765314 763706 2680 2692 847183 2046 24 848410 2036 23 2668 849632 22 2027 766914 850848 21 328811 517183 4521 659367 3455 768508 2657 2017 852058 20 21 Hours. Diff. 20 Hours. Diff. 19 Hours. Diff. 18 Hours. Diff. 17 Hours. Diff. 16 Hours. Diff. Min. | 160 MATHEMATICAL TABLES. Min. 2 Hours. Diff. 3 Hours. Diff. Hours. Diff. 5 Hours. Diff. 6 Hours. Diff. 4 7 Hours. Diff. TABLE XVIII. LOGARITHMS FOR FINDING THE HORARY ANGLE OR APPARENT TIME. 40 9.068103 8648 9°328811 9°517183 9.659367 6052 9*768508 41 073292 42 078446 8590 332442 6019 519883 4500 661430 3440 2645 9.852058 4479 43 083565 8532 336053 522570 5987 44 088651 8477 339645 4458 663485 3425 771674 770094 2633 853263 2007 525245 5956 8419 343219 527908 4438 665530 3409 2622 854461 1998 1988 773247 5924 4418 667567 3395 2610 855654 774812 1979 3379 2598 856841 20 19 18 17 16 24H 9∞ HH 26 1969 45 9093702 46 098720 8363 9'346773 5893 9'530559 9.669594 4397 47 103706 8308 350309 533197 671613 3365 9*776371 2586 9.858022 777922 48 108658 8254 353827 5863 859198 1959 HK 15 14 8201 357326 5832 535823 4377 673623 3350 49 113579 8148 360807 5802 538437 4357 4338 675621 3336 779467 2575 781005 2563 860367 1949 13 861532 1940 12 541040 5772 4318 677617 3322 782536 2552 1931 862690 II 3307 2541 1921 509*118468 8095 9.364270 9*543630 51 123325 52 128151 8043 367715 5742 546208 4298 9.679601 9'784061 9.863843 ΙΟ 5712 4278 681576 3292 371142 548775 53 132946 7992 5683 4258 683543 3278 785578 2530 1912 374552 551330 7942 5654 685501 3263 787089 2518 864990 9 54 137711 7892 377945 553874 4239 5625 687450 3249 788593 2507 866131 1903 8 2495 790090 4220 3235 2484 868397 867267 1884 1893 o a∞ 76 1874 55 9°142446 56 7842 9*381320 9*556406 9.689391 9'791580 9.869522 147151 384678 5597 57 151826 7793 388018 5568 558926 4.200 561435 4182 691324 3221 793064 2473 870641 1865 5 58 156473 7744 5540 7696 391342 563933 4163 693248 3207 2462 794541 695163 3193 796012 2451 872862 871754 1846 1856 4 59 161090 бо 7648 394650 5512 566419 4144 697071 3179 797476 2440 165679 5484 397940 568894 4125 698970 3165 2428 873964 1837 1828 798933 875061 In+m2 10 21 Hours. Diff. 20 Hours. Diff. 19 Hours. Diff. 18 Hours. Diff. 17 Hours. Diff. 16 Hours. Diff. Min. MATHEMATICAL TABLES. 161 TABLE XIX. COMMON AND HYPERBOLIC LOGARITHMS. Common Logarithms. Hyp. Logarithmus Hyperbolic Com. Logarithms. Logarithms. I' 2' : ☹ m + in ☺ i ∞ å 3° 4* 6. 9* 2*3025851 4.6051702 6.9077553 9°2103404 11.5129255 13.8155106 16.1180957 18.4206807 20.7232658 I' i i in it in ó Å öö ä 9' *4342945 ·8685890 1.3028834 I*7371779 2.1714724 6. 2.6057669 7' 3*0400614 8. 3*4743559 3·9086503 TABLE XX. CURVATURE OF THE EARTH AND REFRACTION. Distance in Chains. Curvature Distance Curvature. and Refraction. in Miles. Curvature. Curvature and Refraction. I 123&56 NO Feet. *OOOIC Feet. *00009 Feet. Feet. *00042 *00036 *00094 *00080 4 *00167 *00143 •00261 *00223 •00375 *00322 *00511 *00438 8 •00667 *00572 9 •00844 *00724 123456 7∞0 a I •67 *57 2.67 2:29 6.00 5'14 10.67 9:15 16.67 14.29 24.00 20.57 32.68 28.01 8 42.69 36.60 54.02 46.30 10 *01042 *00893 ΙΟ 66.70 57'17 II 01261 *01081 II 80.71 69.18 12 •01501 *01286 12 96.05 72°33 13 •01761 01510 13 112.72 96.62 14 ⚫02043 01751 14 130'73 112.05 15 ⚫02345 *02010 15 150.08 128.64 16 *02668 *02287 16 170*75 146.36 17 03012 *02582 17 192'77 165.23 18 *03377 *02894 18 216.10 185°23 19 *03762 *03225 19 240.80 206.40 20 *04169 *03573 20 266.80 228.68 198 40 •16685 *14302 25 416.88 357°32 60 *37519 32173 30 600.30 514-83 162 MATHEMATICAL TABLES. TABLE XXI.—TRIGONOMETRICAL EQUIVALENTS. (Arc c = half the arc a.) (1.) Sin a= cos a. tan a = cos a cot a I √1 — (cos α)² Совес а I tan a - 2 sinc.cos C √ 1 + (cot α)² I cos 2 a 2 cot a + tan c I √1+ (tan α)² 2 tan c I + (tan c)² cot c + tan c = 2 {sin (45°+c)}² — I = I — 2 { sin (⁄ 5° — c) }² {tan (45° - c)}² 1 + {tan (45° — c) }² sin a (2.) Cos a = sin a. cot a = tan a I ✓ I + (tan a)² = 1 − 2 (sin c)² I - (tan c)2 I + (tan c)² - sin (60° + a) — sin (60° — a). √ 1 — (sin a)² I - cot a √1+ (cota) 2 = 2 (cos c)² - I = cot c tan c cote+tan c X sec a (cos c)2- (sin c)? I I + cos 2 a 2 I + tan a. tan c (3.) Tan &= sin a cos a I I I = √(sec a)² I cot a (cos a)2 sec a cosec a 2 tan c NI 2 cot c sin a (sin a)2 sin a. cos a √ I — (cos α)² cos a cot a 2 I CON 2 a I Ap (tan c)2 (cot c)2 I cot c tan c sin 2 a sin 2 a C08 2 a =cot a 2 cot 2 α = I + cos 2 a I + cos 2 a (4.) Cot a = ✔ (cosec a)² - I cos a sin a 1 tan a = the reciprocals of the above expressions for the tangent. I cos a the reciprocals of the above tan a sin a expressions for the cosine. (5.) Sec a = √1 + (tana)³ (6.) Cosec a = I √1+ (cota) 2 sec a = sec a. cot a tan a I the recipro- sin a cals of the above expressions for the sine. (sin a)2 (7.) Versin a = I + cos a | (8.) Coversin a = (cos a)2 I + sin a MATHEMATICAL TABLES. 163 TABLE XXII.-EXPRESSIONS FOR MULTIPLE ABOS. (1.) Sin a=. α cos a 2 (2.) Sin 2 a 2 sin a. cos a. (3.) Sin 3 α= 3 sin a 4 (sin a)³. (4) Sin 4 a = cos a {4 sin a—8 (sin a)³}. (5.) Sin 5 a = 5 sin a — 20 (sin a)³ + 16 (sin a)5. sin (3 (6.) Sin na = 2 sin ẞ. sin • (8 + 1). sin (6+2)+ &c n 2 I (2 sin a)”−3. n—1 (7.) = cos a { (2 sin a) (n-3). (n-4) + I.2 (2 sin a) "-5 (n−4). (n-5). (n − 6) (2 sin a)”—' + &c. 78-7 1.2.3 (8.) Cos &a= I + cos a 2 (9.) Cos 2 a=2 (cos a)³ — I. (10.) Cos 3 α=4 (cos a)3-3 cos a. (11.) Cos 4 4 a = 8 (cos a)¹ — 8 (cos a)²+ 1. (12.) Cos 5 a = 16 (cos a)5 — 20 (cos a)³+5 cos a. (13.) Cos na={{(2 sin a)” — n (2 sin a) N-2 **+ n (n − 3) (2 sin a)”~4 n (n 4). (n − 5) I.2.3 (2 sin a) 7. n-6 I 2 • + &c.}. (14.) Tan α 2 (15.) Tan 2 α= (16.) Tan 3 α = tan a I+ √1+ (tan a) I 2 tan a 1 — (tan a)²º 3 tan a (tan a)3 I 3 (tan a)² (17.) Tan 4a= 4 tan a 4 (tan a)³ I (18.) Tan 5α= a (19.) Cot 2 2 (20.) Cot 2 α = (21.) Cot 3 a = (22.) Cot 4 α = (23.) Cot 5 a = 6 (tan a)² + (tan a)* 5 tan a I 1 — 10 10 (tan a)³ + (tan a)5 (tan a)² + 5 (tan a)ª¯ I √ 1+ (cot a)² — cot a (cot a)2 - I 2 cot a (cot a)³ — 3 cot a 3 (cot a)² - I (cot a) - 6 (cot a)²+1. 4 (cot a)3-4 cot a (cot a)5 - 10 (cot a)3 + 5 cot a 5 (cot a) 10 (cot a)²+1 164 MATHEMATICAL TABLES. TABLE XXIII.-FORMULA RELATING TO TWO ARCS OR ANGLES. (1.) Sin (a+ß) sin a. cos ẞ+cos a. sin ß. = -cos a. sin ß. (2.) Sin (a -ß) = sin a. cos ß cos ẞ - cos a (3.) Cos (a+ß) = cos a. cos ẞ — sin a. sin ß. (4.) Cos (a —ß) = (5.) Tan (a+b) (6.) Tan (a -ß): (7.) Cot (a+ß) (8.) Cot (a-B) cos a. cos ẞ+ sin a . sin ß. tan a+tan ẞ I tan a. tan ẞ tan a-tan B I tan a. tan ẞ cot a. cot ẞ — I cot ẞ+ cot a cot a. cot ẞ + I cot ẞ- cot a (9.) Sin (a+ß). sin (a — ß) = (sin a)² - (sin ẞ)² = (cos 6)² — (cos a)². (10.) Cos (a+ß). cos (a — ß) = (cos a)² — (sin ß)² = (cos ß)² — (sin a)². · Sin (a+B) tan atan B cot ẞ+cot a (11.) Sin (a-ß) tan a tan B cot ẞ-cot a Cos (a + B) cot ẞ tan a cot a- tan 3 (12.) Sin (a — ß) cot ẞ+tan a cot a+tan B - (13.) Sin a+ sin 3 = 2 sin § (a+ß) . cos § (a — ß). (14.) Sin a- sin ß = 2 sin § (a− ß) . cos § (a + B). (15.) Cos a+cos B = 2 cos & (a + B). cos (a — ß). (16.) Cos acos B = 2 sin § (a — B). sin § (a +ß). (17.) Tan a+tan ß : sin (a+B) cos a. cos B (18.) Tan a sin (a-ß) -tan B (19.) Cot a+cot ß (20.) Cot a- cot B (21.) 2 sin a. (22.) 2 cos a (23.) 2 cos a. (24.) 2 sin a a. cos ß . = : - cos a . cos ẞ sin (a+B) sin a. sin ẞ sin (a -ß) sin a. sin B sin (a+ẞ) + sin (a —ß). - sin ß = sin (a + ß) — sin (a — ß). cos B = cos (a+B) + cos (a -B). sin B — cos (a — ß) — cos (a+B). = (25.) Tan (a+B+g) If a+ß+y=x. = I tan (a+ẞ)+tan y I-tan (a + B). tan y tan atan ẞ +tan y tan a. tan ẞ. tan y tan a. tan ẞ-tan a. tan ß- tan ß. tan y = (26.) Tan a+tan ẞ+tan y tan a. tan ß. tan y. MATHEMATICAL TABLES. 165 TABLE XXIV.-TRIGONOMETRICAL EXPRESSIONS. Expressions for the sin, cos, tan, and cot, in terms of the arc a. a5 a7 I.2.3 I.2.3.4.5 a³ (1.) Sin a = a + = a( (z.) Cosa = 1 (3.) Tan a I a2 I 2 • + a² = (1 - 402) I (4.) Cot a = = 8 a 4a² a g-2 · • I 3.4.5.6. + &c. 7 a² I I 4 a I.2.3.4 I -)·(1 + 2 a a2 I I g² 8 a a? • &c. 92 q8 .2.3.4.5.6 402). (1- 972 8 a + &c. 27). &c. + 25 x² - 4 a² + &c. 4 Ju² &c. α a² 4a² 2 a Expressions for the arc in terms of the sin and tan. (sin a)3 I. 3. (sin a)5 I Ι • (5.) Arca = sin a + + + &c. • I 2.3 2.3.4.5 (tan a)³ 3 (tan a) + &c. 5 (6.) Arc a = tan a Expressions for the powers of the sin and cos. (7.) 2 (sin a)2 (8.) 4 (sina)3 = (9.) 8 (sin a)4 (10.) 16 (sina)5 cos 2 a, 3 sin a sin 3 a, 4 cos 2a + cos 4a, 3 sin 5 a 2" (sin a)" = ± 2 sin na (II.) 2n 5 sin 3a +10 sin a, 2n. sin (n − 2) a + 2n (n I) sin (n—4) a I 2 • 2n (n + 1). (n 2) I 2.3 sin (n < 6) a + &c. (12.) Or, 27 (sin a)" - ±2cosna+2n.cos (n − 2) a± — 2 n (n − 1). (n − 2) + I.2.3 2n (n-1) cos (n—4) a I.2 cos (n 6) a + &c. When n is of the form 4m + 1, use series (11) with the upper signs. N n "" "" n 99 4m I, "" 4m, "" (II) (12) lower signs. upper signs. "" 2 (13.) 2 (cosa)² = (14.) 4 (cos a a)3 cos 2a + 1, cos 3 a + 3 cos a, 4m + 2, (12) lower signs. (15.) 8 (cos a)4 cos 4a + 4 cos 2a + 3, (16.) 16 (cos a)5 (17.) 2" (cos a)" cos 5a + 5 cos 3 a + 10 cos a. = 2 cosna + 2n. cos (n − 2) a + 2 n (n I 2 • · 1) cos (n — 4) a Game 2n (n 1). (n − 2) + cos (n 6) a + &c. 1.2.3 2n (n - 1). (n The formula ending in · 2). &c. I.2.3. &c. cos (n — n) a, or in 2 n (n − 1). (n I 2.3 3. &c. 1). (n-2). &c. cos a, according as n is an even or an odd number, and in the former case half the expression is to be taken for the last term. 166 MATHEMATICAL TABLES. TABLE XXV. FORMULA FOR SOLVING ALL THE CASES OF A RECTILINEAL TRIANGLE, OF WHICH THREE PARTS ARE KNOWN. Value of any side, as A. B. sin a (1.) A -- sin ẞ C. sin a (2.) (3.) sin y B + C (4.) cos y sin y. cot a cos ẞ+ sin ẞ. cot a (5.) == B. cos y B. sin y. cot ß. y.cot B. (6.) = C. cons ß + C. sin B. cot y (7.) ✔ (B² + C² 2 B. C. cos α). (8.) = B. cosy {C² - B². (sin y)}. ± √ (9.) = C. cos ß ± √ {B² — C². (sin ß)²} Value of the sin of any angle, as ß. B. sin a A (10.) Sin B (II.) B. sin y C (12.) = sin (y + a). (13.) = sin y. .cos a + cos y sin a. B. sin a (14.) ✔ B² + C² 2 B. C. cos a) (15.) (16.) (17.) B. sin y ✓ (B² + A² — 2 B. A. cos y) I = A² C² + 07 - B²) ? 2A.C sin a {C. cos a± √ò C¹³ . (sin a²) } A (18.) siny {A.cosy± √ ѳ A². (sin y)} C a B MATHEMATICAL TABLES. 167 TABLE XXVI.-TRIGONOMETRICAL FORMULA FOR THE SOLUTION OF QUADRATICS AND CUBICS. (1.) x²+px=q. Let tan a= Root = √q. tan § a, 2nd Root = √q. cot & a. (5.) x³+px+q=0. P Let tan a = 39 Let tan 6 = ³/ tan § a, =³/ Only real root x = — 2, . cot 2 B. EQUATIONS OF THE SECOND DEGREE. √q. tan § a, 2.8 ´(2.) x·³ —px= q. (3.) x²+p I - .. 2 Tan a = Sin α = P P ✔g. tana, X √q. cotta. √q. cota. EQUATIONS OF THE THIrd Degree. (6.) x³ + px − q =o. P Tan a = 2 Tanak 39 tan ß = ³/tan ½ a, x = ; p cot 2 ẞ. 3 (7.) x³−px+q=0. P Sin a= p 2 39 3 3 tan α = ✓ tana, P 2 3 sin 2 B z is imaginary. If p² <49, When 4p³ <27 q². (4.) x² -px — px = — q. -√ Sin a= T = Ρ √q. tan § a, x = √ q. cot § a. (8.) x³-px-q=0. Sin a = P 39 tan a = ³/ tan } a, 2 3 3 (9.) x³ − px + q = 0. 39 Let sin 3 α= Ρ When 4p³ > or = 27q², the fol- lowing will be the solution of the two last cases. I P 213 +3 = (10.) x³ 39 Sin 3 α = P X 2 - 2 sin 2 ß = xp -q=0. I 量 P. sin a. 3 3 sin (60° — a). √. sin (60° + a). Root x = 2 sin a. 3 P 2nd root x = 2 sin (60°—a). 3 3rd root = - 2 x P. sin (60°+a). x = 2 V 168 MATHEMATICAL TABLES. TABLE XXVII.-DIFFERENTIAL COEFFICIENTS. Value of u (1.) x. (2.) nx (3.) x¹. I. n. du Value of dz m (4.) log, x. (5.) log z. (6.) ax. in which m is the modulus of the {in system of logarithms. I [= 2.7182818.] I ar log, a. (7.) sin x. (8.) cos x. COS X. sin z. I (9.) tan x. (cos x)2 (Io.) cot2. (11.) (sin x)2. (12.) (cos x)2. (13.) (tan x)². (14.) (cot x)2. (15.) sin-1 x. (16.) cos-1x. I (sin x)2 2 sin z. cos X. 2 sin z.cos X. 2 tan x (cos x)2 2 cot z (sin x)2 I I (17.) tan-¹x. -VI-2 I I + 2.2 (18.) px ± 4x. d (px) dx d (4x) dx d (ø x) d (4x) 4x. ФХ a x d x (19.) 4 x (x)2 d (fx) (20.) fx. Qx. 4 x. Qx. 4 x +fx.4x. dx d (ø x) dx +fx.qx • d (4 x) d x (21.) v, in which d. (4 x) dx (ø v) v = 4 x. d x a v MATHEMATICAL TABLES. 169 TABLE XXVIII. USEFUL NUMBERS, WITH THEIR LOGARITHMS. Circumference of a circle whose dia. I Number. 3.1415927 Logarithm. Complement Logarithm. of Logarithm. 0'49714999*5028501 Area of the same • 0-7853982 1-8950899 10*1049101 4 Diameter of a whose area circle I •} = √ Surface of a sphere whose dia. I • Solidity of the same Diameter of a sphere whose solidity=1 +16 216 1*1283792 0.0524551 9'9475449 3.1415927 0'4971499 9*5028501 05235988 17189986 10-281CO14 Length of arc 2"= sin 2″ (rad. being unity) 1*2407010 0.0936672 9.9063328 Length of arc 1″=sin 1″ (rad. being unity) Į 0000004848 6-6855749 15.3144251 0*000009696 6·9866049 15.0133951 Length of arc 3"— sin 3″ (rad. being unity) =0'000014544 5·1626961 14.8373039 0000290888 44637261 13'5362739 Length of arc 1′= sin 1′ (rad. being unity) Length of arc 1° (rad being unity)=0017453293 22418774 117581226 Length of sin 1° (rad being unity) Radius reduced to seconds "" • to minutes · to degrees • 0.017452406 22418553 117581447 206264.8 5*3144251 4.6855749 3437 74677 35362739 | 6·4637261 57°295780 17581226 8.2418774 360 degrees expressed in seconds 12 hours expressed in seconds 24 hours expressed in seconds No. whose hyperbolic loga- } rithm is I Modulus of common logarithms 1296000 6.1126050 3.8873940 46354837 53645163 86400 49365137 50634863 43200 ==2718281829 04342944 9'5437056 = *434294482 | 1·6377843 10-3622157 I'949040 02898127 97101873 2*1315308 0*3286916 9.6713084 No. of French metres in a toise No. of English yards in a French toise No. of English feet in a French toise No. of English yards in a French metre. No. of English feet in a French metre No. of English inches in a French metre. = 6·394592508058128 | 9*1941872 No. of English feet in a French foot = No. of English acres in a French are = No. of imp. lbs. Troy in a French gramme • 1093633100388716 9-8611284 3.2808992 05159929 94840071 39°37079 15951742 84048258 10657654 00276616 | 9′9723384 0'02471143 23928978 11.6071022 0.00268098 3.4282936 |12:5717064 N 170 MATHEMATICAL TABLES. TABLE XXVIII. USEFUL NUMBERS, WITH THEIR LOGARITHMS. No. of imp. lbs. Avoird. in a French gramme No. of English cwts. in a French kilogramme · No. of imp. gallons in a French litre No. of Sexagesimal degrees in a Centesimal degree. Number. Logarithm. of Logarithm. Complement } 0*00220606 3*3436173 12·6563827 0'0196969 2*2943979 117056021 022009687 13426137 10.6573863 0'9 19542425100457575 No. of Sexagesimal minutes in a Centesimal minute 0'54 1-7323938 19:2676062 No. of Sexagesimal seconds in a Centesimal second C'324 15105450 104894540 Weight of a cubic foot of pure water in lbs. Avoird. the Bar. being 30, and the Ther. 62° Length in inches of a pendulum which vibrates seconds in the latitude of Greenwich 62.3210606 17946348 8.2053652 39°1393 15926130 8.4073860 Velocity (in feet per second) acquired in a second by a body falling in vacuo in g= 32.19084 1*5077222 | 8·4922778 the lat. of Greenwich No. of cubic inches in an im- perial gallon 277*274 • No. of feet in a statute mile 5280 2'4429092 3.7226339 6·2773661 7*5570908 No. of feet in a geographical or nautical mile 6075.6 37835892 | 6·2164108 235*9093 2*3727441 8.6272559 Diurnal acceleration of stars (=3m 55°•9093) expressed in mean solar seconds Sidereal day (=23h 56m 48.09) expressed in mean solar days Mean solar day • (=24h3m 56°5554) expressed in sidereal days Sidereal revolution of Earth ex- pressed in mean solar days Tropical revolution of Earth ex- pressed in mean solar days. Earth's equatorial radius ex- pressed in feet. Earth's polar radius expressed in feet Compression of the Earth Length of a degree of latitude in feet at the Equator Length of a degree of latitude in feet in latitude 45° • } 099726967 1-9988127 10'0011873 100273791 0.0011874 9.9988126 365·25636 2.5625978 74374022 365-242242-5625910| 74374080 20921665 73205963 2.6794037 20852394 7'3191559 2.6808441 I 3'5199931 12:4800069 302 362732 5'5595859 44404141 364543'5 5'5617494 44382506 MATHEMATICAL TABLES. 171 1ABLE XXIX. Long. O I 2 O % 40 8 0 O 40 4° 6° 8° 〃 . SUN'S DECLINATION. 13° | 14° | 15° 10° 11° 12° 40 40 4 0 41° Ο = = 40 310 30 310 Time from 16° | 17° | 18° | 19° | 20° | 21° | 22° 23° 23° 15′ Noon. h * ! ". " 36 310 30 30 310 60 60 60 510 510 20 410 20 410 310 510 4/0 ΙΟ I O 1 O 6 223+ TO 77∞ O I O 8 4∞ 2 O 12 2 O 16 3 20 4 o 24 0 28 O 32 8 o 8 O 80 80 70 70 70 70 610 30 12 O 12 12 O II O II O II Ο ΙΙ Ο ΙΟΟ ΙΟΟ 910 910 910 80 80 70 6/0 40 4 0 160 16 0 16 0 15 0 15 0 14 0 14 0 140 130 120 120 120 110 100 100 80 80 60 50 20 O 20 O 20 0 190 190 180 18 0 170 160 150 150 150 140 130 120 110 910 710 4 60 240 24 0 240 23 0 240 230 230 22 O 21 0 200 200 180 180 180 160 160 140 130 100 80 4 O 270 260 26 0 250 250 240 230 220 210 210 190 190 170 150 130 100 0 310 300 300 290 290 270 270 260 240 240 220 210 190 170 150 110 70 270 27 80 310 31 9 350 35 10 390 0 39 39 20 I 19 I 18 30 I 58 57 40 2 37 2 36 50 3 16 3 15 60 3 55 3 54 70 4 351 4 33 80 5 14 5 12 35 34 O 39 38 I 17 I 16 O O • ° 56 I 14 I 12 Ι ΙΟ I 81 6I 4 Ι 20 590 560 520 480 430 370 290 16 O II I 481 451 431 391 361 321 281 231 181 III 40 550 430 250 17 I 340 320 320 310 300 280 270 270 240 240 210 190 160 120 37 36 35 340 330 320 310 290 280 260 240 210 180 140 8 3 35 3 3 I ΙΟ 4 12 I 561 54 51 2 35 2 32 2 28 2 24 2 20 2 17 2 132 82 3 13 3 10 3 6 3 O 256 2 512 462 412 3 52 3 52 3 48 3 43 3 25 3 193 133 4 31 4 264 20 4 6 3 593 533 453 5 10 5 4 4 57 4 48 4 41 4 344 264 174 90 5 531 5 521 5 48 5 42 5 34 5 23 5 5 16 5 100 6 32 6 31 6 27 6 21 6 11 II 5 59 5 51 H 0 36 6 0 40 I 20 2 130 580 33 580 330 22 311 120 410 28 491 260 49 0 34 2 40 3 20 81 410 58 • 39 4 40 6044 5 20 50 6 • 56 6 40 I I I 7 7 20 ୪ о 8 40 31 571 511 441 351 251 342 272 192 101 591 471 52 562 472 362 23 2 81 363 253 153 22 47 2 29/2 73 553 433 283 112 512 261 551 84 594 494 37 4 254 103 543 343 122 442 91 14 5 5 5 425 325 215 94 534 384 203 583 33 3 3 2 241 22 IIO 7 II 7 10 7 6 6 6 48 6 6 59 6 26 6 166 55 535 40 5 235 6 64 35 4 464 233 553 212 381 30 120 7 51 7 49 I 6 51 7 44 7 37 7 25 7 II 7 6 396 256 105 535 345 124 464 163 392 531 39 130 8 30 8 27 8 23 8 15 8 27 477 36 7 257 12 6 57 6 416 216 25 38 Ι 114 37 3 583 71 47 I 12 140 9 9 9 91 9 7 79 2 8 53 8 40 8 23 8 12 7 59 7 457 307 126 516 306 45 34 4 59 163 211 55 1 18 150 9 48 9 45 9 40 9 30 9 17 8 58 8 47 8 338 188 27 427 216 576 305 57 5 204 333 352 4 I 24 160 10 28 10 25 10 20 10 348 13 8 137 497 256 566 215 414 523 502 12 170 II 611 410 58 10 47 10 68 458 197 53 8 197 537 226 466 25 114 52 22 180 11 46 11 4311 37 11 25|11 389 15 8 49 8 21 7 48 7 9/6 245 29|4 192 28 9 9 54 9 35 9 22 9 88 528 31 10 II 9 57 9 429 259 8/10 32|10 10 46 10 32 10 169 589 O 9 20 10 O I 29 10 40 I 34 II 20 I 40 12 O ז' 172 GEOMETRICAL DEFINITIONS. CHAP. II. PLANE AND SOLID GEOMETRY. SECT. I.-Definitions. 1. GEOMETRY is that department of science, by means of which we de- monstrate the properties, affections, and measures of all sorts of magnitude. 2. Magnitude is a term used to denote the extension of any thing, and is of three kinds; as the magnitude of a line, which is only in one direc- tion, viz., length; the magnitude of a surface, which is in two directions, viz., length and breadth; and the magnitude of a solid, which is in three directions, viz., length, breadth and depth. 3. A point has no parts or magnitude; neither length, breadth, nor thickness, and serves only to assign position. 4. A line has length without breadth or thickness, and indicates direc- tion and distance. Cor. The extremities of a line are, therefore, points. 5. A right line is that which lies evenly, or in the same direction, be- tween two points. A curve line continually changes its direction. Cor. Hence there can only be one species of right lines, but there is an infinite variety in the species of curves. 6. An angle is the inclination of two lines to one another, meeting in a point, called the angular point. When it is formed by two right lines, it is a plane angle, as A; if by curve lines, it is a curvilineal angle, as B. (Fig. 1.) 7. A right angle is that which is made by one right line A B falling upon another C D, and making the angles on each side equal, that is, A B C A B D: so that the line A B does not incline more to one side than another: it is then said to be perpendicular to the line C D. All other angles are called oblique angles. (Fig. 2.) 8. An obtuse angle is greater than a right angle, as R. (Fig. 3.) 9. An acute angle is less than a right angle, as S. (Fig. 3.) 10. Contiguous or adjacent angles, are the two angles formed by one line falling upon another, as R, S. (Fig. 3.) 11. Vertical or opposite angles, are those made on contrary sides of two lines intersecting one another, as A E C, DE B. (Fig. 4.) 12. A surface has length and breadth, but no thickness, and shews extension. The area of a figure is the quantity of space which its sur- face occupies. Cor. The boundaries or limits of a surface are lines. 13. A plane is that surface which lies perfectly even between its ex- tremes; or which, being cut by another plane in any direction, its section would be a straight line. ANGLES, AND RIGHT LINES, AND THEIR RECTANGLES. 173 14. A solid is a magnitude extended every way, or which has length, breadth, and depth. Cor. The boundaries or extremes of a solid are surfaces. 15. The square of a right line is the space included by four right lines equal to it, set perpendicular to one another. 16. The rectangle of two lines is the space included by four lines equal to them, set perpendicular to one another, the opposite ones being equal. 17. One right line is said to be parallel to another, when both lines, being extended to any length, will never meet, but always preserve the same distance between them. SECT. II.—Of Angles, and Right Lines, and their Rectangles. PROP. I. If to any point C in a right line A B, several other right lines D C, E C are drawn on the same side; all the angles formed at the point C, taken together, are equal to two right angles; thus, A C D + DCE + ECB the two right angles ACP + PCB. (Fig. 5.) [Euclid, Book I. Prop. 13.] Cor. 1. All the angles made about one point in a plane, being taken together, are equal to four right angles. Cor. 2. If all the angles at C, on one side of the line A B, are found to be equal to two right angles; then A C B is a straight line. (Fig. 5.) [Euc. B. I. Prop. 14.] II. If two right lines, A B, C D, cut one another, the opposite angles CE B and A E D will be equal. (Fig. 4.) [Euc. B. I. Prop. 15.] III. A right line, B I, which is perpendicular to one of two parallels, is perpendicular to the other. (Fig. 6.) IV. If a right line C G, intersects two parallels A D, F H; the alternate angles, A B E, and B E H, will be equal. (Fig. 6.) [Euc. B. I. Prop. 29.] Cor. 1. The two internal angles D BE and BEH on the same side are equal to two right angles. (Fig. 6.) Cor. 2. The external angle C B D, is equal to the internal angle on the same side B E H. (Fig. 6.) [Euc. B. I. Prop. 28.] V. Right lines, parallel to the same right line, are parallel to one another. [Euc. B. I. Prop. 30.] VI. If a right line A C be divided into two parts A B, B C; the square of the whole line is equal to the squares of both the parts, and twice the rectangle of the parts; or A C² = A B² + B C² + 2 A B × BC. (Fig. 7.) [Euc. B. II. Prop. 4.] VII. The square of the difference of two lines A C, B C, is equal to the sum of their squares, wanting twice their rectangle; or A B² = A C² +BC2 2 ACX B C. Or A B² + 2 A C × B C = A C² + B C² (Fig. 7.) [Euc. B. II. Prop. 7.] VIII. The square of the sum of two lines is equal to the sum of their squares, together with their rectangle. 174 TRIANGLES. IX. The rectangle of the sum and difference of two lines is equal to the difference of their squares. X. The square of the sum, together with the square of the difference of two lines, is equal to twice the sum of their squares. SECT. III.—Of Triangles. DEFINITIONS. 1. A triangle is a plane figure bounded by three right lines, called the sides of the triangle. 2. An equilateral triangle is one in which all the three sides are equal. 3. An isosceles triangle has only two sides equal. 4. A scalene triangle has all its three sides unequal. 5. An equiangular triangle is one which has three equal angles; and two triangles are said to be equiangular, when the angles in the one are respectively equal to those in the other. 6. A right-angled triangle is that which has one of its angles a right angle. The side opposite to the right angle is called the hypothenuse, and the other two sides the legs. 7. An oblique angled triangle has all its angles oblique. 8. An obtuse angled triangle has one of its angles obtuse. 9. An acute angled triangle has all its angles acute. 10. In a triangle, the lowest side, as A B, is called the base, and the opposite angle C the vertex: the altitude of a triangle is the perpendicular height (CD) from the base, or its extension to the vertex. (Fig. 8.) 11. Similar triangles are those whose angles or sides are respectively equal, each to each. And homologous sides are those lying between equal angles. PROPOSITIONS. PROP. I. In any triangle A B C, if one side B C be produced or drawn out; the external angle A C D will be equal to the two internal opposite angles A B C and B A C. (Fig. 9.) [Euc. B. I. Prop. 32.] II. In any triangle, the sum of the three internal angles is equal to two right angles. [Euc. B. I. Prop. 32.] Cor. 1. If two angles in one triangle be equal to two angles in another: the third will also be equal to the third. Cor. 2. If one angle of a triangle be a right angle, the sum of the other two will be equal to a right angle. III. The angles at the base of an isosceles triangle, are equal. [Euc. B. I. Prop. 5.] Cor. 1. An equilateral triangle is also equiangular; and the contrary. Cor. 2. The line which is perpendicular to the base of an isosceles triangle, bisects both it and the vertical angle. IV. In any triangle, the greatest side is opposite to the greatest angle, and the least to the least. [Euc. B. I. Prop. 18.] TRIANGLES. 175 V. In any triangle A B C, the sum of any two sides B A, A C, is greater than the third B C, and their difference is less than the third side. (Fig. 10.) [Euc. B. I. Prop. 20.] VI. If two triangles A B C, a b c, have two sides, and the included angle equal in each; these triangles, and their correspondent parts, shall be equal. (Fig. 11.) [Euc. B. I. Prop. 4.] VII. If two triangles A B C and a b c, have two angles and an in- cluded side equal, each to each; the remaining parts shall be equal, and the whole triangles equal. (Fig. 11.) [Euc. B. I. Prop. 26.] VIII. Triangles of equal bases and heights are equal. [Euc. B. I. Prop. 37.] IX. Triangles of the same height, are in proportion to one another as their bases. [Euc. B. VI. Prop. 1.] X. If a line D E be drawn parallel to one side B C, of a triangle; the segments of the other sides will be proportional; that is, A D: DB:: A E: EC. (Fig. 12.) [Euc. B. VI. Prop. 2.] Cor. 1. If the segments be proportional, A D : DB::AE:EC; then the line D E is parallel to the side B C. (Fig. 12.) Cor. 2. If several lines be drawn parallel to one side of a triangle, all the segments will be proportional. Cor. 3. A line drawn parallel to any side of a triangle, cuts off a triangle similar to the whole. XI. In similar triangles, the homologous sides are proportional; that is, A B: AC::DE: DF. (Fig. 13.) [Euc. B. VI. Prop. 4.] XII. Like triangles are in the duplicate ratio, or as the squares of, their homologous sides. [Euc. B. VI. Prop. 19.] XIII. In any triangle, the difference of the squares of the two legs A B and A C, is equal to twice the rectangle contained by the base B C, and the distance D 0, of its middle point from the perpendicular D A. (Fig. 14.) XIV. In a right-angled triangle B A C, if a perpendicular be let fall from the right angle upon the hypothenuse, it will divide it into two triangles, similar to one another and to the whole, A B D, A D C. (Fig. 14.) [Euc. B. VI. Prop. 8.] Cor. 1. The rectangle of the hypothenuse and either segment is equal to the square of the adjoining side. XV. The distance A O of the right angle, from the middle of the hypothenuse is equal to half the hypothenuse. (Fig. 14.) XVI. In a right-angled triangle, the square of the hypothenuse is equal to the sum of the squares of the two sides. [Euc. B. I. Prop. 47.] XVII. If the square of one side of a triangle be equal to the sum of the squares of the other two sides; then the angle comprehended by them is a right angle. [Euc. B. I. Prop. 48.] XVIII. If an angle A, of a triangle B A C be bisected by a right line. A D, which cuts the base; the segments of the base will be proportional to the adjoining sides of the triangle; that is, BD:DC::AB: A C. (Fig. 10.) [Euc. B. VI. Prop. 3.] 176 QUADRILATERALS AND POLYGONS. XIX. If the sides be as the segments of the base, the line A D bisects the angle A. (Fig. 10.) [Euc. B. VI. Prop. A.] XX. Three lines drawn from the three angles of a triangle to the middle of the opposite sides, all meet in one point. XXI. Three perpendicular lines erected on the middle of the three sides of any triangle, all meet in one point. XXII. The point of intersection of the three perpendiculars, will be equally distant from the three angles; or, it will be the centre of the cir- cumscribing circle. XXIII. Three perpendiculars drawn from the three angles of a triangle, upon the opposite sides, all meet in one point. XXIV. Three lines bisecting the three angles of a triangle, all meet in one point. XXV. If D be any point in the base of a scalene triangle, A BC: then is A B² x D C + A C² × B D = A D² × B C + B C × B D × D C. (Fig. 10.) SECT. IV.-Of Quadrilaterals and Polygons. DEFINITIONS. 1. A quadrangle or quadrilateral, is a plane figure bounded by four right lines. 2. A parallelogram is a quadrangle whose opposite sides are parallel, as AG BH. The line A B drawn to the opposite corners is called the diameter or diagonal. And if two lines be drawn parallel to the two sides, through any point of the diagonal, they divide it into several others, and then C and D are called parallelograms about the diameter; and E and F the complements; and the figure E D F a gnomon. (Fig. 15.) 3. A rectangle is a parallelogram whose sides are perpendicular to one another. 4. A square is a rectangle of four equal sides and four equal angles. 5. A rhombus is a parallelogram, whose sides are equal, and all its angles oblique. 6. A rhomboid is a parallelogram in which only the opposite sides are equal, and all its angles oblique. 7. A trapezoid is a quadrangle, having only two sides parallel, as Fig. 16. 8. A trapezium is a quadrangle that has no two sides parallel, as Fig. 17. 9. A polygon is a plane figure enclosed by many right lines. If all the sides and angles are equal, it is called a regular polygon, and denomi- nated according to the number of sides or angles, as a pentagon having five sides, a hexagon, having six sides, a heptagon, having seven sides, &c. 10. The diagonal of a quadrangle or polygon is a line drawn between any two opposite corners of the figure, as A B. (Fig. 15.) QUADRILATERALS AND POLYGONS. 177 11. The height of a figure is a line drawn from its vertex, perpendicular to the base, or opposite side on which it stands. 12. Like or similar figures, are those whose several angles are equal to one another, and the sides about the equal angles proportional. 13. Homologous sides of two like figures are those between two angles, respectively equal. 14. The perimeter or circumference of a figure, is the compass of it, or sum of all the lines that enclose it. 15. The internal angles of a figure are those on the inside, made by the lines that bound the figure, as A B C, D C B, &c. (Fig. 18.) 16. The external angles of a figure are the angles made by each side of a figure, and the adjoining side drawn out, as B A F, A E G. (Fig. 18.) PROPOSITIONS. PROP. I. In any parallelogram the opposite sides and angles are equal; and the diagonal divides it into two equal triangles. [Euc. B. I. Prop. 34.] II. The diagonals of a parallelogram intersect each other in the middle point of both. III. Any line B C passing through the middle of the diagonal of a parallelogram P, divides the area into two equal parts. (Fig 19.) IV. Any right line BC drawn through the middle point P of the diagonal of a parallelogram, is bisected in that point; or BP = P C. (Fig. 19.) V. In any parallelogram A G H B, the complements E and F are equal. (Fig. 15.) [Euc. B. I. Prop. 43.] VI. Parallelograms of equal bases and heights are equal. [Euc. B. I. Prop. 36.] VII. The area of a parallelogram is double the area of a triangle having the same base and height. [Euc. B. I. Prop. 41.] VIII. Parallelograms of the same height are to one another as their bases. [Euc. B. VI. Prop. 1.] IX. Parallelograms of equal bases are as their heights. X. Parallelograms are to one another, as their bases and heights. XI. In any parallelogram the sum of the squares of the diagonals is equal to the sum of the squares of all the four sides. XII. The sum of the four internal angles of any quadrilateral figure, is equal to four right angles. XIII. If two angles of a quadrangle be right angles, the sum of the other two amounts to two right angles. XIV. The sum of all the internal angles of a polygon is equal to twice as many right angles, abating four, as the polygon has sides. Cor. Hence all right-lined figures of the same number of sides, have the sum of all the internal angles equal. XV. The sum of the external angles of any polygon is equal to four right angles. Cor. All right-lined figures have the sum of their external angles equal. 178 CIRCLES, ETC. XVI. In two similar figures A C, PR; if two lines B E, Q T, be drawn after a like manner, as suppose, to make the angle C B E=RQT; then these lines have the same proportion as any two homologous sides of the figure; viz., BEQT BO: QR: AB: PQ:: AD: PS. (Fig. 20.) XVII. All similar figures are to one another as the squares of their homologous sides. XVIII. Any figure described on the hypothenuse of a right-angled triangle, is equal to two similar figures described the same way upon the two legs; that is, B F CALC+AG B. (Fig. 21.) [Euc. B. VI. Prop. 31.] XIX. Any regular figure A BCDE, is equal to a triangle whose base is the perimeter ABCDEA; and height the line O P, drawn from the centre, perpendicular to one side. (Fig. 22.) XX. Only three sorts of regular figures can fill up a plane surface, that is, the whole space round an assumed point, and these are six triangles, four squares, or three hexagons. SECT. V. Of the Circle, and Inscribed and Circumscribed Figures. DEFINITIONS. 1. A circle is a plane figure described by a right line moving about a fixed point, as A C about C: or it is a figure bounded by a curved line, every part of which is equidistant from a fixed point. (Fig. 23.) 2. The centre of a circle is the fixed point about which the line moves, as C. (Fig. 23.) 3. The radius is the line that describes the circle, as C A. (Fig. 23.) Cor. All the radii of a circle are equal. 4. The circumference is the line described by the extreme end of the moving line, as ABDEA. (Fig. 23.) 5. The diameter is a line drawn through the centre, from one side to the other, as A D. (Fig. 23.) 6. A semicircle is half the circle, cut off by the diameter, as A B D. 7. A quadrant, or quarter of a circle, is the part between two radii per- pendicular to one another, as CDE. (Fig. 23.) 8. An arc is any part of the circumference, as A B. (Fig. 24.) 9. A sector is a part bounded by two radii, and the arc between them, as A CB. (Fig. 24.) 10. A chord is a right line drawn through the circle, as D F. 11. A segment is a part cut off by a right line, or chord, as DEF, or DABF. (Fig. 24.) 12. Angle at the centre is that whose angular point is at the centre ACB. (Fig. 24.) 13. Angle at the circumference is when the angular point is in the cir- cumference, as BA D, or B C D. (Fig. 25.) CIRCLES, ETC. 179 14. Angle in a segment, is the angle made by two lines drawn from some point of the arc of that segment to the ends of the base; as B CD is an angle in the segment B CD. (Fig. 25.) 15. Angle upon a segment is the angle made in the opposite segment, whose sides stand upon the base of the first; as B A D, which stands upon the segment B C D. (Fig. 25.) 16. A tangent is a line touching a circle, which, produced, does not cut it, as G A F. (Fig. 23.) 17. Circles are said to touch one another, which meet, but do not cut one another. 18. Similar arcs, or similar sectors, are those bounded by radii that make the same angle. 19. Similar segments are those which contain similar triangles, alike placed. 20. A figure is said to be inscribed in a circle, or a circle circumscribed about a figure, when all the angular points of the figure are in the circum- ference of the circle. (Fig. 26.) 21. A circle is said to be inscribed in a figure, or a figure circumscribed about a circle, when the circle touches all the sides of the figure. (Fig. 27.) 22. One figure is inscribed in another, when all the angles of the in- scribed figure are in the sides of the other. (Fig. 28.) PROPOSITIONS. PROP. I. The radius C R, bisects any chord at right angles, which does not pass through the centre, as A B. (Fig. 29.) [Euc. B. III. Prop. 3.] Cor. 1. If a line bisects a chord at right angles, it passes through the centre of the circle. Cor. 2. The radius that bisects the chord also bisects the arc. II. In a circle equal chords are equally distant from the centre. [Euc. B. III. Prop. 14.] III. If several lines be drawn through a circle, the greatest is the diameter, and those that are nearest the centre are greater than those that are farther off. [Euc. B. III. Prop. 15.] IV. If from any point three equal right lines can be drawn to the cir- cumference, that point is the centre. [Euc. B. III. Prop. 9.] V. No circle can cut another in more than two points. [Euc. B. III. Prop. 10.] VI. There can be only two equal lines drawn from any exterior point, to the circumference of a circle. VII. In any circle, if several radii be drawn making equal angles, the arcs and sectors comprehended thereby will be equal; that is, if the angle A C B = BCD, then, the arc A B = BD, and the sector ACB = B CD. (Fig. 30.) [Euc. B. III. Prop. 26.] VIII. In the same or equal circles, the arcs, and also the sectors, are proportional to the angles intercepted by the radii. IX. The circumferences of circles are to one another as their diameters. 180 CIRCLES, ETC. X. A right line, perpendicular to the diameter of a circle, at the ex- treme point, touches the circle in that point, and lies wholly without the circle; or is a tangent to the circle. XI. If two circles touch one another, either inwardly or outwardly, the line passing through their centres shall also pass through the point of contact. [Euc. B. III. Prop. 11 and 12.] XII. In a circle the angle at the centre is double the angle at the cir- cumference, standing upon the same arc; or B D C = 2 BAC. (Fig. 31.) [Euc. B. III. Prop. 20.] XIII. All angles in the same segment of a circle are equal, as DAC = DBC, and D G C DHC. (Fig. 32.) [Euc. B. III. Prop. 21.] • — · XIV. If two right lines D C, A B, be drawn from the extremities of two equal arcs DA, BC, they will be parallel. (Fig. 32.) XV. The angle ABC in a semicircle is a right angle. (Fig. 33.) [Euc. B. III. Prop. 31.] XVI. The angle F BG, in a greater segment FABCG, is less than a right angle; and the angle DBE, in a less segment DBE, is greater than a right angle. (Fig. 33.) [Euc. B. III. Prop. 31.] XVII. If two lines cutting a circle, intersect one another in A; and there be made at the centre,▲ ECF = ▲ BAD; then the arc BD + GH = 2 EF, if A is within the circle; or the arc BDG H = 2 EF, if A is without. (Fig. 34.) XVIII. If from a point without, two lines, A B, AD be drawn to cut a circle; the angle made by them is equal to the angle at the centre, standing on half the difference of the two arcs of the circumference GH, BD. (Fig. 34.) XIX. The angle A= ▲ BHD + HD G, when A is within; or A = BHD-HD G, when A is without the circle. (Fig. 34.) XX. In a circle, the angle made at the point of contact between the tangent and any chord, is equal to the angle in the alternate or opposite. segment; ECF = E BC, and E CA=EGC. (Fig. 35.) [Euc. B. III. Prop. 32.] XXI. A tangent to the middle point of an arc, is parallel to the chord of it. XXII. If from any point B in a semicircle, a perpendicular B D be let fall upon the diameter, it will be a mean proportional between the seg- ments of the diameter; that is, A D:DB::DB: DC. (Fig 36.) [Euc. B. VI. Prop. 13.] XXIII. The chord is a mean proportional between the adjoining seg- ment and the diameter, from the similarity of the triangles: that is, A D : AB::AB: AC; and CD: CB:: CB: CA. (Fig. 36.) XXIV. In a circle, if the diameter AD be drawn, and from the ends of the chords AB, AC, perpendiculars be drawn upon the diameter; the squares of the chords will be as the segments of the diameter; that is, AE:AF: A B2: A C². (Fig. 37.) B² XXV. If two circles touch one another in P, and the line PDE be drawn through their centres; and any line PA B is drawn through that } CIRCLES, ETC. 181 point to cut the circles, that line will be divided in proportion to the diameters; that is, PA: P B :: PD: PE. (Fig. 38.) XXVI. If through any point F in the diameter of a circle, any chord, C F D be drawn, the rectangle of the segments of the chord is equal to the rectangle of the segments of the diameter; CF × F D = AF × FB also G F x F E. (Fig. 39.) [Euc. B. III. Prop. 35.] XXVII. If through any point F out of the circle in the diameter B A produced, any line F C D be drawn through the circle: the rectangle of the whole line and the external part is equal to the rectangle of the whole line passing through the centre, and the external part; D F x FC= AFX FB also F Ex F G. (Fig. 40.) XXVIII. Let H F be a tangent at H; then the rectangle C F × F D = square of the tangent F H. (Fig. 40.) [Euc. B. III. Prop. 36.] XXIX. If from the same point F, two tangents be drawn to the circle, they will be equal; that is, F H = FI. (Fig. 40.) XXX. If a line P F C be drawn perpendicular to the diameter A D of a circle; and any line drawn from A to cut the circle and the perpen- dicular; then the rectangle of the distances of the sections from A, will be equal to the rectangle of the diameter and the distance of the perpen- dicular from A; that is, A B x A CAP x A D. Also, A BACA K². (Fig. 41.) (Fig. 41.) XXXI. In a circle E D F whose centre is C, and radius C E, if the points B, A, be so placed in the diameter produced, that C B, C E, CA be in continual proportion, then two lines B D, A D drawn from these points to any point in the circumference of the circle will always be in the given ratio of B E to A E. (Fig. 42.) XXXII. In a circle, if a perpendicular D B be let fall from any point D, upon the diameter C I, and the tangent D O drawn from D, then A B, A C, A O, will be in continual proportion. (Fig. 43.) XXXIII. If a triangle B D F be inscribed in a circle, and a perpen- dicular D P let fall from D on the opposite side B F, and the diameter D A drawn; then, as the perpendicular is to one side including the angle D, so is the other side to the diameter of the circle; that is, D P : DB:: DF: DA. (Fig. 44.) XXXIV. The rectangle of any two sides of an inscribed triangle is equal to the rectangle of the diameter, and the perpendicular on the third side; that is, BD X D F = AD × DP. (Fig. 44.) XXXV. If a triangle B A C be inscribed in a circle, and the angle A bisected by the right line A E D, then as one side is to the segment of the bisecting line within the triangle, so is the whole bisecting line to the other side; that is, A B: A E:: A D : A C; and A B × A C = BE. ECA E2. (Fig. 45.) XXXVI. If a quadrilateral A B C D be inscribed in a circle, the sum of two opposite angles is equal to two right angles; that is, A DC+ A B C two right angles. (Fig. 46.) [Euc. B. III. Prop. 22.] 182 CIRCLES, ETC. XXXVII. If a quadrangle be inscribed in a circle, the rectangle of the diagonals is equal to the sum of the rectangles of the opposite sides; or CAX BD CBX DA+ CD x A B. (Fig. 46.) XXXVIII. A circle is equal to a triangle whose base is the circum- ference of the circle; and height, its radius. XXXIX. The area of a circle is equal to the rectangle of half the cir- cumference and half the diameter. XL. Circles (that is, their areas) are to one another as the squares of their diameters, or as the squares of the radii, or as the squares of the circumferences. [Euc. B. XII. Prop. 2.] XLI. Similar polygons inscribed in circles, are to one another as the circles wherein they are inscribed. XLII. A circle is to any circumscribed rectilineal figure, as the circle's periphery to the periphery of the figure. XLIII. If an equilateral triangle A B C be inscribed in a circle; the square of the side thereof is equal to three times the square of the radius; that is, A B² = 3 A D². (Fig. 47.) XLIV. If from any point D in the circumference of a circle, having inscribed in it an equilateral triangle, chords be drawn to the three angles A, B, C; the longest chord A D, is equal to the sum of the two lesser chords, B D and C D. (Fig. 48.) XLV. A square inscribed in a circle, is equal to twice the square of the radius. XLVI. The side of a regular hexagon inscribed in a circle, is equal to the radius of the circle. XLVII. If two chords in a circle mutually intersect at right angles, the sum of the squares of the segments of the chords is equal to the square of the diameter of the circle; that is, A P² + P B² + P C² + P D² = diam.² (Fig. 49.) XLVIII. If the diameter P Q be divided into two parts at any point R, and if R S be drawn perpendicular to P Q; also R T applied equal to the radius, and T R produced to the circumference at V: then, RT= RV = PR+RQ; or RT is the arithmetical mean, 2 ; or RV is the harmonical mean, between the two segments of the diame- ter PR, QR (Fig. 50.) RS =√ PRX RQ; or RS is the geometrical mean, 2 X PRX RQ PR+RQ XLIX. If the arcs P Q, Q R, R S, &c., be equal, and there be drawn the chords PQ, P R, P S, &c., then it will be P Q: PR:: PR: P Q +PS:: PS: PR+PT::PT:PS+P V, &c. (Fig. 51.) L. If the arcs PQ, QR, RS, &c., be equal, the angles Q P R, R P S, SP T, &c., will be equal; or in equal circles, equal angles stand upon equal arcs, whether they be at the centres or circumferences. (Fig. 51.) [Euc. B. III. Prop. 26.] LI. The centre of a circle being O, and P a point in the radius, or in the radius produced; if the circumference be divided into as many equal PLANES AND SOLIDS. 183 parts A B, B C, C D, &c., as there are units in 2n, and lines be drawn from P to all the points of division; then shall the continual product of all the alternate lines, viz., P A PCX PE, &c., be = r² xn when P is within the circle, or = x ™ when P is without the circle; and the product of the rest of the lines, viz., P B × PD × P F, &c., = p² + x²: where r = A O the radius, and x = 0 P the distance of P from the centre. (Fig. 52.) — SECT. VI.-Of Planes and Solids. DEFINITIONS. 1. THE common section of two planes, is the line in which they meet, or cut each other. 2. A line is perpendicular to a plane, when it is perpendicular to every line in that plane which meets it. 3. One plane is perpendicular to another, when every line of the one, which is perpendicular to the line of their common section, is perpen- dicular to the other. 4. The inclination of one plane to another, or the angle they form be- tween them, is the angle contained by two lines, drawn from any point in the common section, and at right angles to the same, one of these lines in each plane. 5. Parallel Planes are such as being produced ever so far in any direc- tion, will never meet, or which are everywhere at an equal perpendicular distance. 6. A solid angle is that which is made by three or more plane angles, meeting each other in the same point. 7. Similar solids, contained by plane figures, are such as have all their solid angles equal, each to each, and are bounded by the same number of similar planes, alike placed. 8. A prism is a solid whose ends are parallel, equal, and like plane figures, and its sides, connecting those ends, are parallelograms. (Fig. 53 and 54.) 9. A prism takes particular names according to the figure of its base or ends, whether triangular, square, rectangular, pentagonal, hexa- gonal, &c. 10. A right or upright prism, is that which has the planes of the sides perpendicular to the planes of the ends or base. (Fig. 53.) When such is not the case it is called an oblique prism. (Fig. 54.) 11. A parallelopiped, or parallelopipedon, is a prism bounded by six parallelograms, every opposite two of which are equal, alike, and parallel. (Fig 55.) 12. A rectangular parallelopipedon is that whose bounding planes are all rectangles, which are perpendicular to each other. (Fig. 56.) 13. A cube is a square prism, being bounded by six equal square sides or faces, which are perpendicular to each other. (Fig. 57.) 184 PLANES AND SOLIDS. 14. A cylinder is a round prism having circles for its ends; and is conceived to be formed by the rotation of a right line about the circum- ferences of two equal and parallel circles, always parallel to the axis. (Fig. 58.) 15. The axis of a cylinder is the right line A B joining the centres of the two parallel circles, about which the figure is described. 16. A pyramid is a solid whose base is any right-lined plane figure, and its sides triangles, having all their vertices meeting together in a point above the base, called the vertex of the pyramid. (Fig. 59.) 17. Pyramids, like prisms, take particular names from the figure of their base. 18. A cone is a round pyramid having a circular base, and is conceived to be generated by the rotation of a right line about the circumference of a circle, one end of which is fixed at a point above the plane of that circle. (Fig. 60.) 19. The axis of a cone is the right line, A B, joining the vertex, or fixed point, and the centre of the circle about which the figure is de- scribed. 20. When the axis of a cone or pyramid is perpendicular to the base, it is called a right cone or pyramid; but if inclined it is called oblique. 21. Similar cones and cylinders, are such as have their altitudes and the diameters of their bases proportional. 22. A sphere is a solid bounded by one curve surface, which is every- where equally distant from a certain point within, called the centre. It is conceived to be generated by the rotation of a semi-circle about its diameter, which remains fixed. (Fig. 61.) 23. The axis of a sphere is the right line about which the semi-circle revolves, and the centre is the same as that of the revolving semi-circle. 24. The diameter of a sphere is any right line passing through the centre, and terminated both ways by the surface. 25. The altitude of a solid is the perpendicular drawn from the vertex to the opposite side or base. PROPOSITIONS. PROP. I. If any prism be cut by a plane parallel to its base, the section will be equal and like to the base. II. If a cylinder be cut by a plane parallel to its base, the section will be a circle, equal to the base. III. All prisms and cylinders, of equal bases and altitudes, are equal to each other. [Euc. B. XI. Prop. 31.] IV. Rectangular parallelopipedons, of equal altitudes, are to each other as their bases. [Euc. B. XI. Prop. 32.] V. Rectangular parallelopipedons, of equal bases, are to each other as their altitudes. VI. Because prisms and cylinders are as their altitudes, when their bases are equal: and, as their bases when their altitudes are equal. There- PLANES AND SOLIDS. 185 fore, universally, when neither are equal, they are to one another as the product of their bases and altitudes: hence, also, these products are the proper numeral measures of their quantities or magnitudes. VII. Similar prisms and cylinders are to each other as the cubes of their altitudes, or of any like linear dimensions. [Euc. B. XI., Prop. 33.] VIII. In any pyramid a section parallel to the base is similar to the base; and these two planes are to each other as the squares of their dis- tances from the vertex. IX. In a right cone, any section parallel to the base is a circle; and this section is to the base as the squares of their distances from the vertex. X. All pyramids and cones of equal bases and altitudes are equal to one another. XI. Every pyramid is the third part of a prism of the same base and altitude. [Euc. B. XII., Prop. 10.] XII. If a sphere be cut by a plane, the section will be a circle. XIII. Every sphere is two-thirds of its circumscribing cylinder. XIV. A cone, hemisphere, and cylinder of the same base and altitude are to each other as the numbers 1, 2, 3. [Euc. B. XII., Prop. 10.] XV. AH spheres are to each other as the cubes of their diameters; all these being like parts of their circumscribing cylinders. [Euc. B. XII., Prop. 18.] XVI. There are only three sorts of regular plane figures which can be joined together, so as to form a solid angle; viz., three, four, or five triangles, three squares, and three pentagons: thus giving five different species of solid angles, which are those of the five regular or Platonic bodies; viz. :- 1. The tatraedon, (Fig. 62,) bounded by four equilateral triangles, each solid angle of which is formed by three triangles. 2. The hexaedron, or cube, (Fig. 57,) contained by six squares, each solid angle of which is formed by three squares. 3. The octaedron, (Fig. 63,) bounded by eight triangles, each solid angle of which is formed by four triangles. 4. The dodecaedron, (Fig. 64,) bounded by twelve pentagons, each solid angle of which is formed by three pentagons. 5. The icosaedron, (Fig. 65,) bounded by twenty triangles, each solid angle of which is formed by five triangles. XVII. Only one sort of the foregoing five regular bodies, joined at their angles, can completely fill a solid space, without leaving any vacuity; viz., eight hexaedrons, or cubes. XVIII. A sphere is to any circumscribing solid B F, (all whose planes touch the sphere,) as the surface of the sphere to the surface of the solid. (Fig. 66.) XIX. All bodies circumscribing the same sphere, are to one another as their surfaces. XX. The sphere is the greatest or most capacious of all bodies of equal surface. 186 PRACTICAL GEOMETRY. SECT. VII.-Practical Geometry. It is not intended in this place to present a complete collection of Geometrical Problems, but merely a selection of the most useful, espe- cially in reference to the employments of Mechanics and Engineers. The instruments for the purposes of geometrical construction, are too well known to require any description here; and their use is much easier learned by an examination of the instruments themselves, than by any written explanation. PROB. I. From a given point B in a given straight line A C, to draw a line perpendicular to the same. From B as a centre, with any radius, describe arcs cutting A C in a and c, then from a and c with any larger radius describe arcs cutting each other in d and e; then the straight line d Be will be perpendicular to AC. (Fig. 67.) PROB. II. To erect a perpendicular at the end of a given line. With any radius, and from a point somewhere above A B, describe a semicircular arc passing through the point B, at which the perpendicular is to be erected, and also cutting A B in C; then, through C and the centre of the arc produce the right line CD, cutting the arc in D, and a line joining D and B will be the perpendicular required. (Fig. 68.) PROB. III. To bisect any given angle A C B. From C as a centre, with any radius, describe an arc cutting the sides in D and E; then from D and E, as centres with the same radius, describe arcs cutting each other in F; then the straight line joining C and F will bisect the angle ACB. (Fig. 69.) PROB. IV. To bisect a given angle B A P; then to bisect its half; and so on. Through any point B draw B E parallel to AP, and upon B E set off the distance B C equal to B A; then join A. C, and it will bisect the angle ВАР. Again, set off, upon BE, from C, CD = CA; join A D, and it will bisect CA P, or quadrisect BA P. Again, set off, upon BE, DE = DA; join EA; and E A P will be of BA P: and so on. (Fig. 70.) PROB. V. At a given point A in a given line AB, to make an angle equal to a given angle C. From the centres A and C, with the same radius, describe the arcs DE, FG. Then, with radius D E, and centre F, describe an arc, cutting FG in G. Through G draw the line A G; and it will form the angle required. (Fig. 71.) PROB. VI. To divide any given angle ABC into three equal parts. From B, with any radius, describe the circle ACDA. Bisect the angle A B C by BE, and produce A B to D. On the edge of a ruler mark off the length of the radius A B. Lay the ruler on D, and move it till PRACTICAL GEOMETRY. 187 one of the marks on the edge intersects B E, and the other the arc A Cin G. Set off the distance C G from G to F: and draw the lines BF, and BG, they will trisect the angle ABC. (Fig. 72.) PROB. VII. To divide a given line A B into any proposed number of equal parts. 1st Method. Draw any other line A C, forming any angle with the given line A B; on which set off as many of any equal parts, A D, D E, E F, FC, as the line A B is to be divided into. Join BC; parallel to which draw the other lines FG, EH, DI: then these will divide A B in the manner required. (Fig. 73.) 2nd Method, without drawing parallel lines. Let A B be the line which is to be divided into n equal parts. Through one extremity A draw any right line AD, upon which set off n + 1 equal parts, the point D being at the termination of the (n + 1)th part. Join D B and produce it until the prolongation B E = B D. Let F be the termination of the (n - 1)th part. Join F E, and the right line of junction will cut the given line A B in the point P, such that BP = A B; and of course n distances each equal to BP set off 1 - n upon BA, will divide it, as required*. (Fig. 74.) PROB. VIII. To cut off from a given line A B, supposed to be very short, any proportional part. Suppose, for example, it were required to find the,,, &c., of the line A B, fig. 75. From the ends A and B draw A D, B C, perpen- dicular to A B, and divide A D into twelve equal parts; then through these divisions 1, 2, 3, &c., draw lines 1 f, 2 g, &c., parallel to A B. Draw the diagonal A C, and 1 d will be the of AB; 2 c,, and so on. The 12 same method is applicable to any other part of a given line. PROB. IX. To make a diagonal scale, say, of feet, inches, and tenths of an inch. Draw an indefinite line A B, on which set off from A to B the given length for one foot, any required number of times; and from these divi- sions A, C, H, B, draw A D, C E, &c., perpendicular to A B. On A D and BF set off any length ten times, and through these divisions draw lines parallel to A B; then divide A C and D E into twelve equal parts, each of which will be one inch. Draw the lines A 1, g 2, &c., and they will form the scale required; viz., each of the larger divisions from E to G, G to F, &c., will represent a foot; each of the twelve divisions between D and E, an inch; and the several horizontal lines parallel to R C in the triangle ECR, will be equal to fo, fo, fo, &c., of an inch. (Fig. 76.) Note.-If the scale be meant to represent feet, or any other unit, and tenths and hundredths, then D E must be divided into ten instead of twelve equal parts. * The truth of this method is easily demonstrated. point of division, on a D, between F and D, draw IB. DIIF, IB is parallel to F P. Consequently, BP: BA:: Through 1 the intermediate Then, because D B — B E, and IF:IA::1: n, by construction. 188 PRACTICAL GEOMETRY. PROB. X. To find the centre of a circle. Draw any chord A B, and bisect it perpendicularly with the line R D. Then bisect R D in C, which will be the centre required. (Fig. 29.) PROB. XI. To divide a given circle into any number of concentric parts, equal to each other in area. Draw the radius A B, and on it describe the semicircle Aƒ e d B. Divide A B into the proposed number of equal parts, 1, 2, 3, &c., and erect the perpendiculars 1 d, 2 e, 3f, &c., meeting the semicircle in d, e, f, &c. Then from the centre B, and with radii Bd, Be, &c., describe cir- cles; so shall the given circle be divided into the proposed number of equal concentric parts. (Fig. 77.) PROB. XII. To divide a given circle into any number of parts, equal both in area and perimeter. Divide the diameter QR into the proposed number of equal parts at the points S, T, V, &c.; then, on one side of the diameter describe semicircles on the diameters QS, QT, QV, and on the other side of it describe semi- circles on RV, RT, RS; so shall the parts 17, 35, 53, 71, be all equal, both in area and perimeter. (Fig. 78.) PROB. XIII. To describe the circumference of a circle through three given points, A, B, C. From the middle point B draw chords B A, B C, to the two other points, and bisect these chords perpendicularly by lines meeting in O, which will be the centre. Then from the centre O, at the distance of any of the points, as O A, describe a circle, and it will pass through the two other points BC, as required. (Fig. 79.) The same method may be employed for finding the centre of a circular arc, by taking any three points in the same, as A, B, and C. PROB. XIV. To describe mechanically the circumference of a circle through three given points, A, B, C, when the centre is inaccessible; or the circle too large to be described with compasses. Place two rulers MN, RS, cross ways, touching the three points, A, B, C. Fix them in V by a pin, and by a transverse piece T. Hold a pencil in A, and describe the arc BA C, by moving the angle RAN, so as to keep the outside edges of the rulers against the pins B C. Remove the instrument R.V N, and on the arc described mark two points, D, E, so that their dis- tance shall be equal to the length B C. Apply the edges of the instrument against D E, and with a pencil in G describe the arc B C, which will com- plete the circumference of the circle required. (Fig. 80.) Otherwise. Let an axle of 12 or 15 inches long carry two unequal wheels A and B, of which one, A, shall be fixed, while the other, B, shall be susceptible of motion along the axle, and being placed at any assigned distance, A B, upon the paper or plane on which the circle is to be de- scribed. Then will A and B be analogous to the ends of a conic frustum, the vertex of the complete cone being the centre (0) of the circle (CDEF) which will be described by the rim, or edge, of the wheel A, as it rolls upon the proposed plane. Then it will be, as the diameter of the wheel A is to the difference of the diameters of A and B, so is the radius of the PRACTICAL GEOMETRY. 189 circle proposed to be described by A, to the distance, A B, at which the two wheels must be asunder, measured upon the plane on which the circle is to be described. The wheel B will evidently describe, simultaneously, another circle (GHIK) whose radius will be less than that of the former by A B. (Fig. 81.) PROB. XV. On a given chord A B to describe mechanically an arc of a large circle that shall contain any number of degrees. Place two rulers, forming an angle A CB, equal to the supplement of half the given number of degrees, and fix them in C. Place two pins at the extremities of the given chord, and hold a pencil in C; then move the edges of this instrument against the pins, and the pencil will describe the arc required. (Fig. 82.) Suppose it is required to describe an arc of 50 degrees on the given chord A B; subtract 25 degrees (which is half the given angle,) from 180, and the difference, 155 degrees, will be the supplement. Then form an angle A C B of 155 degrees with the two rulers, and proceed as has been shewn above. PROB. XVI. To describe the segment of a circle of large radius, of which the chord A B and versine CD are given. Through D draw H I parallel to A B; then join A D and D B, and draw A H perpendicular to A D and BI perpendicular to B D, also draw A d and B d perpendicular to A B. Then divide A C, B C, H D, and I D, into any number of equal parts, 1, 2, 3, &c., and draw lines joining the corresponding numbers in HI and A B; also divide A d, B d, into the same number of equal parts, a, b, c, &c., and draw lines from the point D to these last divisions, then will the points where the lines a D, b D, c D, &c., cut the lines 11, 22, 33, &c., be so many points in the required seg- ment. (Fig. 83.) PROB. XVII. To find the length of any given arc of a circle, A B. From A and B, as centres, with radius equal to a quarter of the chord of the arc A B, describe arcs cutting the given arc in C, and its chord in D; join C D, which will equal half the length of the arc A B nearly. (Fig. 84.) PROB. XVIII. To draw a straight line equal in length to any given portion of the circumference of a circle. Let A BCD be the circle, and let A a, a b, b B, be the portions of the circumference of which the length is required; draw the two diameters BD and AC at right angles to each other, and at the end of the latter draw the tangent line A e; then divide the radius EC into four equal parts, and set off three of them from C to F on the diameter produced; then draw lines from F through the points a, b, B, cutting the tangent line A e, in c, d, e; so shall the lines A c, cd, de, be equal in length to the arcs A a, ab, b B, and the whole line A e equal to the quadrant A B. (Fig. 85.) PROB. XIX. To bisect any given triangle A BC. Upon any one of the sides, as A B, describe a semicircle, which bisect in the point D; then from B as a centre with radius BD describe an arc 190 PRACTICAL GEOMETRY. cutting A B in E, through which point draw the line EF parallel with the side AC; then will the line EF bisect the given triangle A B C. (Fig. 86.) PROB. XX. To reduce a given rectilinear figure, ABCDEFGA, of any number of sides, to a triangle of equal area. Join any two alternate angles, as A C, and through the intermediate angle B, draw BH parallel to A C, cutting one of the adjoining sides in H, and join C H, then will the triangle C B a, added to the figure, be equal to the triangle a A H taken out of the same; in like manner join H D, and draw GI parallel to the same through the intermediate point G, producing it to cut the side A G (also produced) in I, and join ID. Next join D F, and through E draw a line parallel thereto, cutting the side G F produced in K, and join D K; lastly, join D G, and draw parallel to the same through the point K a line cutting the side A G produced in L, then join D L, and the triangle ID L will be equal in area to the given rectilinear figure ABCDEFGA. (Fig. 87.) PROB. XXI. To form a rectangle of the largest area, in a given triangle, A B C. Bisect any two sides A B and B C in D and E, and from those points draw lines D F and E G perpendicular to the third side AC and join D E, then will the rectangle D E F G be the largest which can be inscribed in the given triangle. (Fig. 88.) PROB. XXII. To form a square equal in area to a given triangle, A BC. On the longest side produced set off CD, equal half the perpendicular height BE; and at C erect the perpendicular C F; then on A D describe a semicircle cutting C F in G, and on C G form the square C G H I, which will be equal in area to the given triangle. (Fig. 89.) PROB. XXIII. To find the side of a square equal in area to a given rectangle, A B CD. Produce the lesser side A B of the rectangle till A E equal the longer side A D; then describe upon A E a semicircle cutting B C in F, and join A F, which will be the side of the square required. (Fig. 90.) PROB. XXIV. To find the side of a square equal to the difference be- tween two given squares. Let the sides of the two given squares be A and B. Then draw the line C D equal to the lesser line B, and at one of its extremities erect the indefinite perpendicular D E; then with radius equal to A, and from Cas a centre, describe an arc cutting this perpendicular in E; then D E will equal the side of the square required. (Fig. 91.) PROB. XXV. To find the side of a square equal in area to any number of given squares. Let the lines A, B, and C, be the sides of the given squares. Draw D E equal to A, and at the end of it erect the perpendicular E F equal to B; join D F and perpendicular to it, from the point F, erect the perpendicular G F equal to C; then join D G, which will be equal to the side of a square equal in area to the three squares on A, B, and C. (Fig. 92.) PRACTICAL GEOMETRY. 191 PROB. XXVI. To find the side of a square nearly equal in area to a given circle, A BCD. Draw the two diameters, A C, BD, at right angles to each other; then bisect the radius E C in F, and through D and F produce the straight line D G cutting the circle in G, then will D G equal the side of the square required. (Fig. 93.) PROB. XXVII. Given the side of a regular polygon of any number of sides (not exceeding twelve), to find the radius of the circle in which it may be inscribed. Multiply the given side of the polygon by the number which stands in column b, opposite its proper name in the annexed Table of Polygons; the product will be the radius required. Thus, suppose the polygon was to be an octagon, and each side 12, then 1.3065628 × 12 = 15.6687536 would be the radius sought. Take 15.67 as a radius from a diagonal scale, describe a circle, and from the same scale, taking off 12, it may be applied as the side of an octagon in that circle. PROB. XXVIII. Given the radius of a circle, to find the side of any regular polygon (not having more than twelve sides) inscribed in it. Multiply the given radius by the number in column c, standing opposite the number of sides of the proposed polygon; the product is the length of the side required, Thus, suppose the radius of the circle to be 5, then 5 × 1·732051 = 8-66025, will be the side of the inscribed equilateral triangle. Table of Polygons. No. of Names. sides. Multipliers for areas. (a.) Radius of circum. cir. Factors for sides. (ხ.) (c.) 3 Trigon 0.4330127 0.5773503 1.732051 4 Tetragon, or Square 1.0000000 0.7071068 1.414214 5 Pentagon 1.7204774 0.8506508 1.175570 6 Hexagon 2.5980762 1.0000000 1.000000 7 Heptagon 3.6339124 1.1523824 0.867767 8 Octagon 4-8284271 1.3065628 0.765367 9 Nonagon 6.1818242 1.4619022 0.684040 10 Decagon 7.6942088 1.6180340 0.618034 11 Undecagon 9.3656399 1.7747324 0.563465 12 Dodecagon 11.1961524 1.9318517 0.517638 192 WEIGHTS AND MEASURES. CHAP. III. MENSURATION. SECT. I.-Comparison of English and French Weights and Measures. THE following is a comparative Table of the Weights and Measures of England and France, which was published by the Royal and Central Society of Agriculture of Paris, in the Annuary for 1829, and founded on a Report, made by Mr. Mathieu, to the Royal Academy of Sciences of France, on the bill passed the 17th of May, 1824, relative to the Weights and Measures termed "Imperial," which are now used in Great Britain. Measures of Length. ENGLISH. 1 Inch (1-36th of a yard) 1 Foot (1-3rd of a yard) Yard Imperial Fathom (2 yards) Pole, or perch (5½ yards) Furlong (220 yards) Mile (1760 yards) 1 Millimetre 1 Centimetre FRENCH. 1 Decimetre 1 Metre Myriametre 1 Yard square ENGLISH. 1 Rod (square perch) 1 Rood (1210 yards square) 1 Acre (4840 yards square) FRENCH. 1 Metre square 1 Are 1 Hectare Il ti || || FRENCH. 2.539954 centimetres. 3.0479449 decimetres. 0-91438348 metre. 1-82876696 metre. 5.02911 metres. 201.16437 metres. 1609-3149 metres. ENGLISH. 0.03937 inch. 0.393708 inch. 3.937079 inches. 39.37079 inches. 3.2808992 feet. 1.093633 yard. 6.2138 miles. Square Measures. ENGLISH. 1 Pint (1-8th of a gallon) 1 Quart (1-4th of a gallon) 1 Gallon imperial • Solid Measures. FRENCH. 0.836097 metre square. 25.291939 metres square. 10-116775 ares. 0.404671 hectare. ENGLISH. 1.196033 yard square. 0.098845 rood. 2.473614 acres. FRENCH. 0.567932 litre. 1.135864 litre. 4.54345794 litres. WEIGHTS AND MEASURES. 193 ENGLISH. 1 Peck (2 gallons) 1 Bushel (8 gallons) 1 Sack (3 bushels) 1 Quarter (8 bushels) . 1 Chaldron (12 sacks) • FRENCH. 1 Litre 1 Decalitre 1 Hectolitre || FRENCH. 9-0869159 litres. 36-347664 litres. 1.09043 hectolitre. 2.907813 hectolitres. 13.08516 hectolitres. { ENGLISH. 1.760773 pint. 0-2200967 gallon. 2.2009667 gallons. . 22.009667 gallons. ENGLISH TROY. Weights. FRENCH. 0.06477 gramme. 1.55456 gramme. 1 Grain (1-24th of a pennyweight) 1 Pennyweight (1-20th of an ounce) 1 Ounce (1-12th of a pound troy) 1 Pound troy imperial ENGLISH AVOIRDUPOIS. 1 Drachm (1-16th of an ounce) 1 Ounce (1-16th of a pound) 1 Pound avoirdupois imperial 1 Hundred-weight (112 pounds) 1 Ton (20 hundred-weight 1 Gramme 1 Kilogramme FRENCH. 31.0913 grammes. 0-3730959 kilogramme. FRENCH. 1.7712 gramme. 28.3384 grammes. 0.4534148 kilogramme. 50-78246 kilogrammes. 1015-649 kilogrammes. ENGLISH. 15.438 grains troy. 0-643 pennyweight. 0.03216 ounce troy. {{ 2.68027 pounds troy. Angular Measure. 2.20548 do. avoirdupois. In France, the centesimal division of the circle is frequently employed, in which the whole circumference is divided into 400 degrees, each de- gree into 100 minutes, each minute into 100 seconds, &c. 1 Degree CENTESIMAL. 1 Minute 1 Second 1 Degree 1 Minute 1 Second ENGLISH. || || ENGLISH. 54 minutes. 32.4 seconds. •324 second. CENTESIMAL. 14 degree. 1.85185 minute. 3.08641 seconds. 194 MENSURATION OF SUPERFICIES. SECT. II.-Mensuration of Superficies. TRIANGLES. Let b, c, and d, represent the three sides of a triangle (see fig. 95); ß, y, and ♪, the angles opposite those sides respectively; and h the per- pendicular height from the vertex to the base b; then the area= = bh, or = 1 bc. sins = 1 c d. sin ß = db. sin y. d² — c² b) 2 b Or, = ✓ d² - (d² 26 the least. + where b is the greatest side and c 2 If half the sum of the three sides or log of area = area= b + c + d b+c+ 2 =s, then the √ s (s — b). (s — c) . (s — d), and the {log s + log (s — b) + log (s — c) + log (8 — d) }. QUADRILATERALS, OR FOUR-SIDED FIGURES. Square, Rectangle, Rhombus and Rhomboid:-To obtain the area, multiply the perpendicular height (h, fig. 96) by the base (b) on which it falls. The area of a Trapezium is best found by dividing it into two triangles (as fig. 17), the areas of which may be found by the foregoing rules. The area of a Trapezoid (fig. 16) may either be found in the same way, or by multiplying half the sum of the two parallel sides (a + b) by the perpendicular distance between them (h). POLYGONS. To obtain the area of any regular polygon, having less than twelve sides, multiply the square of one of the sides by the number found in column a, of the Table of Polygons, page 191. Or, generally, if the length of one of the equal sides, and n the number of them; then the area=12 tan. The area of an irregular into triangles, as in fig. 97. it, by Prob. XX., page 190. n 4 n (90 On - 180). N polygon may be determined by dividing it Or by forming one triangle equal in area to CIRCLES. Let d represent the diameter, c the circumference, a the area, and p = 3.14159; then the с Diameter = d 4 a <=2 a Ρ с p 4 a Circumference = c = c = pd Area = a= p d² 4 d = 2√ pa. c² dc = '7854 d². 4p 4 с 4 a c² and P p =- • d2 4 a MENSURATION OF SUPERFICIES. 195 Circular Arcs.-If r represents the radius, and d the diameter of the circlè; s the sine, and v₁ the versed sine of the arc; c the chord of half the arc, v, the versed sine of half the arc; and m the measure in degrees of the whole arc; then the length of the arc 0174533 r m ; or = 2 d ✓ 3 3v₁ nearly; 3 d V2 5 v1 or · Z { 5 d +4√ dv₂} nearly; 5d-3 v₂ 8c-2s or = nearly. 3 And the following relations between the several quantities, from which any one of them may be obtained, will be found useful, viz. :— V₁ = r √ p² — s² c = √ s² + 8 = √ r² d = $2 01 +21 v v₂ ² 1 2 ... (r — v₁)² (1.) (2.) (3.) (4.) Circular Sectors.-Let d represent the diameter of the circle, 7 the length of the arc of the sector, and m its measure in degrees; then the area = Zrl. or = ·00218 d² m. Circular Segments.-Let d represent the diameter of the circle, v the versed sine, c₁ the chord of the whole arc, and c₂ the chord of half the arc; then the area = {√ (dv — v²) + √ dv} nearly; or = v(dv - v²) nearly; or=&v (c₁ + c₂) nearly; 2 or = √(c+v²) nearly. V Or the area of any segment, as fig. 98, may be obtained by finding the area of the sector A B C D, and subtracting from it the area of the triangle A C D. The area of a circular zone, as E F G H, may be found by subtracting the area of the segment G H I from the area of the segment E GIH F. PARABOLA. The area of a parabola is equal to two-thirds of the product of the base x the perpendicular height. Parabolic Arcs.-Let x be the abscissa a b, fig. 99, measured from the vertex a, and y the corresponding right ordinate cb; then the length of the arc c a d is = 2√ (y² + $x²) nearly; or = } { √ (y² + # x²) y² + z x² y } Parabolic Frustum, or Zone.-The word zone is here used to denote the space c d e g (fig. 99), contained between the two parallel double ordi- 196 MENSURATION OF SUPERFICIES. nates c d and e g. Let y₁ = the length of the double ordinate c d, and y2 = the length of eg, and d = the perpendicular distance between them bf; then the Y2 area of the zone = f d Y 2³ — y i Y ₂² — Yı 3 3 2 2 ELLIPSE. The area is equal to the product of the transverse diameter x the con- jugate diameter x 785398. The periphery or circumference is equal to the sum of the transverse and conjugate diameters x 1.57079. The foregoing is only an approximation to the periphery, although suf- ficiently near the truth for ordinary purposes; but where greater accuracy is required the following series may be employed. Let t represent the C2 transverse axis, c the conjugate, p = 3.14159, &c., and d = 1 – ; then d 3 d² pt {1 22 22.42 will be the periphery. 32.5 ď³ 22.42.62 32.52.7 dt 22. 42. 62. 82 &c.} Elliptic Segments-To find the area of the elliptic segment abc (fig. 100), find the area of the corresponding circular segment, dbe, described on the same axis (bƒ) to which the cutting line or base of the segment a c is perpendicular. Then, as this axis (bf): the other axis (gh): the circular segment (dbe): the elliptic segment (abc). Elliptic Arcs.-Let t represent the semi-transverse, and c the semi- conjugate diameters of the ellipse, and d the distance of the ordinate from the centre, then the length of the arc contained between the ordinate and the parallel semi-axis will be =d{1+ ď² + c? 4t2 c² 2 d+ + 6 t 40 to +2 c² or make 8 tª c² — 4t² ct + co 112 t¹2 =r; then the d® + &c.} 12 t² — fr d² length of the arc = d nearly. t2 ť² - d² HYPERBOLA. The area of an hyperbola or hyperbolic segment may be found as follows:-let t and c represent the semi-transverse and semi-conjugate diameters, 2y the double ordinate which cuts off the segment, and x its abcissa; also q = area = 2 x y {3-325 {}} X 2t+x ; then the 9 92 3.5.7 93 3.5.7.9 &c.} or 4 cx 15 {4√ (2tx + & x²) + √2tx} nearly. Hyperbolic Arcs.-The notation being the same, the following approx- imation may be employed to obtain the length of an hyperbolic arc. 120 ct + (19² + 21 c²) 4 x Arc +y, nearly. 120 c² t +(91² + 21 c²) 4 x MENSURATION OF SOLIDS. 197 SECT. III.-Mensuration of Solids. PARALLELOPIPEDON, PRISM, OR CYLINDER. Surface. Multiply the perimeter of one end by the length or per- pendicular height, to which add the area of the two ends, the sum will be the surface. Solidity = the area of the base x the perpendicular height. PYRAMID OR CONE. Surface. Multiply half the perimeter by the slant height, to which add the area of the base, the sum is the surface. Solidity the area of the base x one-third the perpendicular height. Frustum of a Pyramid or Cone. Surface.-Multiply half the sum of the perimeters of the two ends by the perpendicular height. Solidity.—Add a diameter or side of the greater end to one of the less, and from the square of the sum subtract the product of the said two diameters or sides; then multiply the remainder by one-third of the height, and this product by 785398 for circles, or by the proper multi- plier for polygons; the last product will be the capacity. That is, let D equal the greater diameter, d the less, h the perpendicu- lar height, and p=785398 for cones, or for any pyramid the proper multiplier from column (a) in the table at page 191, then Solidity=ph (D² + D d + d²). SPHERE. Surface the diameter x the circumference, the square of the diameter × 3.14159, — the square of the circumference × 3183. Solidity = the cube of the diameter × ·5236, the cube of the cir- cumference x ·01688. Spherical Segment.-Let d equal the diameter of the aphere, r the radius of the base of the segment, and h its height; then the curved sur- face = 3.14159 d h. Solidity=0·5236 h² (3d-2 h); or = 0·5236 h (3r² + h²). The surface and solidity of a spherical zone may be obtained by taking the difference between the two segments. CONOIDS. A conoid is the solid generated by the revolution of a conic section about one of its axis, and is called a spheroid, paraboloid, or hyperboloid, according to the section from which it is produced. Spheroids. When the ellipse revolves about its transverse axis, it is called an oblong or prolate spheroid; when about its conjugate axis, an oblate spheroid; and when about any other of its diameters, a universal spheroid, in which latter case its figure is somewhat resembling a heart. To obtain the solidity of a spheroid, multiply the square of the revolving axis by the fixed axis, and the product by 0-5236. 198 MENSURATION OF SOLIDS. Paraboloid.-Let y be the radius of the circular base, and x the alti- tude of the solid; then Surface 0·5236y {(y² + 4x²)* — y³} . х2 Solidity = 1.5708 y² x. Hyperboloid. Let t equal the transverse axis, r the radius of the base, a the altitude, and p the parameter; then the Solidity = p² 1 t + // a t + a THE REGULAR OR PLATONIC SOLIDS. The regular or Platonic bodies are five in number, and have already been described at page 185. 1. To find either the surface or the solid content of any of the regular bodies. Multiply the proper tabular area or surface (taken from column (a) in the following table,) by the square of the linear edge of the solid, for the superficies. And Multiply the tabular solidity in column (b) of the table by the cube of the linear edge for the solid content. Surfaces and Solidities of Regular Bodies, the side being unity or 1. No. of sides. Name. Surface. (a) Solidity. (6) 46 Tetraedron 1.7320508 0.1178513 Hexaedron 6.0000000 1.0000000 8 Octaedron 3.4641016 0.4714045 12 Dodecaedron 20.6457288 7-6631189 20 Icosaedron 8.6602540 2.1816950 2. The diameter of a sphere being given, to find the side of any of the Platonic bodies, that may be either inscribed in the sphere, or circum- scribed about the sphere, or that is equal to the sphere.-Multiply the given diameter of the sphere by the proper or corresponding number, in the following table, answering to the thing sought, and the product will be the side of the Platonic body required. The diam. of a sphere being 1; That may be inscribed in the sphere, is That is equal to to the sphere, is the side of a That may be cir- cumscribed about the sphere, is Tetraedron 0.8164966 2.4494897 1.6439480 Hexaedron 0.5773503 1.0000000 0.8059958 Octaedron 0.7071068 1-2247447 1.0356300 Dodecaedron 0.3568221 0.4490279 0-4088190 Icosaedron 0.5257309 0.6615845 0-6214433 MENSURATION OF SOLIDS. 199 3. The side of any of the five Platonic bodies being given, to find the diameter of a sphere, that may either be inscribed in that body, or circum- scribed about it, or that is equal to it.-As the respective number in the table above, under the title inscribed, circumscribed, or equal, is to 1, so is the side of the given Platonic body to the diameter of its inscribed, cir- cumscribed, or equal sphere. 4. The side of any one of the five Platonic bodies being given, to find the side of the other four bodies, that may be equal in solidity to that of the given body.—-As the number under the title equal in the last column of the table above, against the given Platonic body, is to the number under the same title, against the body whose side is sought, so is the side of the given Platonic body to the side of the body sought. Besides these there are thirteen demiregular bodies, called Solids of Archimedes. They are described in the Supplement to Lidonne's Tables de tous les Diviseurs des Nombres, &c., Paris, 1808; twelve of them were described by Abraham Sharp, in his Treatise on Polyedra. TO FIND THE CONTENTS OF SURFACES AND SOLIDS NOT REDUCIBLE TO ANY KNOWN FIGURE, BY THE EQUIDISTANT ORDINATE METHOD. The general rule is included in this proposition, viz. :-If any right line be divided into any even number of equal parts, 1, 2, 3, 4, &c., (fig. 101,) and at the points of division be erected perpendicular ordinates 1 A, 2 B, 3 C, &c., terminated by any curve A C G: then, if a be put for the sum of the first and last ordinates, 1 A, 7 G, e for the sum of the even ordinates, 2 B, 4 D, 6 F, &c., viz., the second, fourth, sixth., &c., and o for the sum of all the rest, 3 C, 5 E, &c., viz., the third, fifth, &c., or the odd ordinates, excepting the first and last: then, the common distance 1, 2, 2, 3, &c., of the ordinates being multiplied into the sum arising from the addition of s, four times e, and twice o, one third of the product will be the area 1 A, G 7, very nearly. That is, s + 4e + 2o 3 D= D = area, D being = A C = CE, &c. The same theorem will equally serve for the contents of all solids, by using the sections perpendicular to the axis instead of the ordinates. The proposition is quite accurate, for all parabolic and right lined areas as well as for all solids generated by the revolutions of conic sections or right lines about axes, and for pyramids and their frustums. For other areas and solidities it is an excellent approximation. The greater the number of ordinates, or of sections, that are taken, the more accurately will the area or the capacity be determined. But in a great majority of cases five equidistant ordinates, or sections, will lead to a very accurate result. 200 TRIGONOMETRY. CHAP. IV. TRIGONOMETRY. SECT. I.-Definitions and Trigonometrical Formulœ. 1. Plane Trigonometry is that branch of mathematics by which we learn how to determine or compute the unknown parts of a plane, or rectilinear triangle, from those which are known, when that is possible. Every triangle consists of six parts, viz., three sides, and three angles opposite those sides. And any three of these being given (excepting only when the three angles are given,) the others may always be determined from them. The determination of the mutual relation of the sines, tangents, secants, &c., of the sums, differences, multiples, &c., of arcs or angles; or the in- vestigation of the connected formulæ, is also usually classed under plane trigonometry. 2. Let A C B (fig. 102,) be a rectilinear angle: if about C as a centre, with any radius C A, a circle be described, intersecting C A, C B, in A, B, the arc A B is called the measure of the angle A C B. 3. The circumference of a circle is supposed to be divided or to be divisible into 360 equal parts, called degrees; each degree into 60 equal parts, called minutes; each of these into 60 equal parts, called seconds; and so on to the minutest possible subdivisions. Of these, the first is indicated by a small circle, the second by a single accent, the third by a double accent, &c. Thus, 47° 18′ 34" 45"", denotes 47 degrees, 18 minutes, 34 seconds, and 45 thirds. The number of degrees, minutes, seconds, &c., contained in the arc A B of the circle described from the angular point C, and which is contained between the two legs A C, A B, is called the measure of the angle A C B, which is then said to be an angle of so many degrees, minutes, seconds, &c. Thus, since a quadrant or quarter of a circle, contains 90 degrees, and a quadrantal arc is the measure of a right angle, a right angle is said to be one of 90 degrees. 4. The complement of an arc is its difference from a quadrant, as B E; and the complement of an angle is its difference from a right angle, as EC B. 5. The supplement of an arc is its difference from a semicircle, as A' E B; and the supplement of an angle is its difference from two right angles, as A' C B. 6. The sine of an arc is a perpendicular let fall from one extremity upon a diameter passing through the other, as B D. 7. The versed sine or versine of an arc is that part of the diameter which is intercepted between the foot of the sine and the arc, as D A. 1 PLANE TRIGONOMETRY. 201 8. The tangent of an arc is a right line which touches it in one extre- mity, and is limited by a right line drawn from the centre of the circle through the other extremity, as A T. 9. The secant of an arc is the radial line which thus limits the tangent, as CT. 10. These are also, by way of accommodation, said to be the sine, tan- gent, &c., of the angle measured by the aforesaid arc, to its determinate radius. 11. The cosine of an arc or angle, is the sine of the complement of that arc or angle, as GB: the cotangent of an arc or angle is the tangent of the complement of that arc or angle, as E M. And the co-versed sine E G, and cosecant C M, are similarly the versed sine and secant of the complement. 12. The suversine of an arc is the versed sine of its supplement, as A D. Note.-The following contractions are employed to express the fore- going terms, viz. :— For the radius of the arc A B we write rad A B, sine tangent ditto sin A B, ditto tan AB, secant ditto sec A B, versine. ditto versin A B, cosine ditto cos AB, cotangent... ditto cot A B, cosecant ditto cosec A B, coversine.... ditto covers A B. SECT. II.-General Propositions. I. The chord of any arc is a mean proportional between the versed sine of that arc and the diameter of the circle. II. As radius is to the cosine of any arc, so is twice the sine of that arc to the sine of double the arc. III. The secant of any arc is equal to the sum of its tangent, and the tangent of half its complement. IV. The sum of the tangent and secant of any arc, is equal to the tan- gent of an arc exceeding that by half its complement. Or, the sum of the tangent and secant of an arc is equal to the tangent of 45° plus half the arc. V. The chord of 60° is equal to the radius of the circle; the versed sine and cosine of 60° are each equal to half the radius, and the secant of 60° is equal to double the radius. VI. The tangent of 45° is equal to the radius. VII. The square of the sine of half any arc or angle is equal to a rect- angle under half the radius and the versed sine of the whole arc; and the square of its cosine is equal to a rectangle under half the radius and the versed sine of the supplement of the whole arc or angle. VIII. The rectangle under the radius and the sine of the sum or the difference of two arcs is equal to the sum or the difference of the rectangles under their alternate sines and cosines. Р 202 PLANE TRIGONOMETRY. IX. The rectangle under the radius and the cosine of the sum or the difference of two arcs, is equal to the difference or the sum of the rect- angles under their respective cosines and sines. X. As the difference or sum of the square of the radius and the rectangle under the tangents of two arcs, is to the square of the radius; so is the sum or difference of their tangents, to the tangent of the sum or difference of the arcs. XI. As the sum of the sines of two unequal arcs, is to their difference; so is the tangent of half the sum of those two arcs to the tangent of half their difference. XII. Of any three equidifferent arcs, it will be as radius is to the cosine of their common difference, so is the sine of the mean arc, to half the sum of the sines of the extremes; and, as radius is to the sine of the common difference, so is the cosine of the mean arc to half the difference of the sines of the two extremes. (A.) If the sine of the mean of three equidifferent arcs (radius being unity) be multiplied into twice the cosine of the common difference, and the sine of either extreme be deducted from the product, the remainder will be the sine of the other extreme. (B.) The sine of any arc above 60°, is equal to the sine of another arc as much below 60°, together with the sine of its excess above 60°. Cor. From this latter proposition, the sines below 60° being known, those of arcs above 60° are determinable by addition only. XIII. In any right-angled triangle, the hypothenuse is to one of the legs, as the radius is to the sine of the angle opposite to that leg; and one of the legs is to the other as the radius is to the tangent of the angle oppo- site to the latter. XIV. In any plane triangle, as one of the sides is to another, so is the sine of the angle opposite to the former to the sine of the angle opposite to the latter. XV. In any plane triangle it will be, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. XVI. In any plane triangle it will be, as the cosine of the difference of the angles at the base, is to the cosine of half their sum, so is the sum of the sides about the vertical angles to the third side. Also, as the sine of half the difference of the angles at the base, is to the sine of half their sum, so is the difference of the sides about the vertical angle to the third side, or base*. XVII. In any plane triangle it will be, as the base is to the sum of the two other sides, so is the difference of those sides to the difference of the segments of the base made by a perpendicular let fall from the vertical angle. * These propositions were first given by Thacker in his Mathematical Miscellany, pub- lished in 1743; their practical utility has been subsequently shown by Professor Wallace, in the Edinburgh Philosophical Transactions. PLANE TRIGONOMETRY. 203 XVIII. In any plane triangle it will be, as twice the rectangle under any two sides, is to the difference of the sum of the squares of those two sides and the square of the base, so is the radius to the cosine of the angle contained by the two sides. Cor. When unity is assumed as radius, then if A C, A B, B C, are the sides of a triangle, and C the angle opposite the side A B, this A C² + BC2 A B2 : and similar expressions for Prop. gives cos C= the other angles. 2CB.CA XIX. As the sum of the tangents of any two unequal angles is to their difference, so is the sine of the sum of those angles to the sine of their difference. XX. As the sine of the difference of any two unequal angles is to the difference of their sines, so is the sum of those sines to the sine of the sum of the angles. These and other propositions are the foundation of various formulæ, for which the reader who wishes to pursue the inquiry may consult the best treatises on Trigonometry. SECT. III.—Solution of the Cases of Plane Triangles. Although the three sides and three angles of a plane triangle, when combined three and three, constitute twenty varieties, yet they furnish only three distinct cases in which separate rules are required. CASE I. When a side and an angle are two of the given parts. The solution may be effected by Prop. XIV. of the preceding section, wherein it is affirmed that the sides of plane triangles are respectively.pro- portional to the sines of their opposite angles. In practice, if a side be required, begin the proportion with a sine, and say, As the sine of the given angle, Is to its opposite side; So is the sine of either of the other angles, To its opposite side. If an angle be required, begin the proportion with a side, and say, As one of the given sides, Is to the sine of its opposite angle; So is the other given side, To the sine of its opposite angle. The third angle becomes known by taking the sum of the two former from 180°. Note. It is usually best to work the proportions in trigonometry by means of the logarithms, taking the logarithm of the first term from the 204 PLANE TRIGONOMETRY. sum of the logarithms of the second and third, to obtain the logarithm of the fourth term. Or, adding the arithmetical complement of the logarithm of the first term to the logarithms of the other two, to obtain that of the fourth. CASE II. When two sides and the included angle are given. The solution may be effected by means of Props. XV. and XVI. of the preceding section. Thus: take the given angle from 180°, the remainder will be the sum of the other two angles. Then say, As the sum of the given sides, Is to their difference; So is the tangent of half the sum of the remaining angles; To the tangent of half their difference. Then, secondly say, Or, As the cosine of half the said difference, Is to the cosine of half the sum of the angles; So is the sum of the given sides, To the third, or required side. As the sine of half the diff. of the angles, Is to the sine of half their sum; So is the difference of the given sides, To the third side. Example.—In the triangle A B C (Fig. 9) are given A C = 450, B C 540, and the included angle C = 80°; to find the third side, and the two remaining angles. Then, Log (BC-AC 90) Log tan (A + B = 50°) = 1.954243 ='10.076187 12.030430 Log (BO+AC 990) 2.995635 Log tan (½ A – B = 6°11′) 9.034795 Then, Log cos († A + B = 50°) Log (BC+A C 9.808068 990) 2.995635 12.803703 Log cos († A – B = 6°11′) 9.997466 Log (AB 640·08) = 2.806237 (A Also, ½ (A + B) + † (A — B) = 56° 11′ = A; and † (A + B) — 1 B) = 43° 49′ = B. Here, much time will be saved in the work by taking log cos (A + B) from the tables, at the same time with log tan (A + B); and log cos PLANE TRIGONOMETRY, 205 (A — B) as soon as log tan ½ (A - B) is found. Observe, also, that the log of B C + AC is the same in the second operation as in the first, Thus the tables need only be opened in five places for both operations. Another solution to Case II. . Supposing C to be the given angle, and C A, CB, the given sides; then the third side may be found by this theorem, viz. :— C² AB=√ (A C² + BC-2AC. CB. cos C). Thus, taking A C='450, BC = 540, C = 80°, its cos 1736482 AB=√(450 +5402 - 2 x 450 x 540 × 1736482) ={902 (52 + 622 × 5 × 6 × 1736482)} X 90 ✓ 50.58118 = 90 × 7·112 = 640·08, as before. CASE III. When the three sides of a plane triangle are given, to find the angles. 1st Method.—Assume the longest of the three sides as base, then say, conformably with Prop. XVI., last section, As the base, Is to the sum of the two other sides; So is the difference of those sides, To the difference of the segments of the base. Half the base added to the said difference gives the greater segment, and made less by it gives the less; and thus, by means of the perpendicular from the vertical angle, divides the original triangle into two, each of which falls under the first case. 2nd Method.—Find any one of the angles by means of Prop. XVIII. of the preceding section; and the remaining angles either by a repe- tition of the same rule, or by the relation of the sides to the sines of their opposite angles, viz. :— cos C = A C²+ BC2 - A B² ; cos B = 2 AC. BC BA² + AC² - BC2 A B² + BC² - A C² 2 AB. BC and cos A 2AB.AC RIGHT-ANGLED PLANE TRIANGLES. Right-angled triangles may (as well as others,) be solved by means of the rule to the respective case under which any specified example falls; and it will then be found, since a right angle is always one of the data, that the rule usually becomes simplified in its application. When two of the sides are given, the third may be found by means of the property in Geom., Prop. XVI., Sect. II. Hypoth. =√(base² + perp.²) Base =√(hyp.2 — perp.²) = √ (hyp. + perp.). (hyp. — perp.) Perp. (hyp.2 - base2)=√(hyp. + base).. (hyp. - base.) There is another method for right-angled triangles, known by the phrase making any side radius; which is this. 206 PLANE TRIGONOMETRY. "To find a side. Call any one of the sides radius, and write upon it the word radius; observe whether the other sides become sines, tangents, or secants, and write those words upon them accordingly. Call the word written upon each side the name of each side: then say, As the name of the given side, Is to the given side; So is the name of the required side, To the required side." "To find an angle. Call either of the given sides radius, and write upon it the word radius; observe whether the other sides become sines, tangents, or secants, and write those words on them accordingly. Call the word written upon each side the name of that side. Then say, As the side made radius, Is to radius ; So is the other given side, To the name of that side, which determines the opposite angle.” When the numbers which measure the sides of the triangle are either under 12, or resolvable into factors which are each less than 12, the solution may be obtained, conformably with this rule, easier without logarithms than with them. For, Let A BC (Fig. 103) be a right-angled triangle, in which A B, the base, is assumed to be radius; BC is the tangent of A, and A C its secant, to that radius; or, dividing each of these by the base, we shall have the tangent and secant of A respectively, radius being unity. Tracing in like manner the consequences of assuming BC (as fig. 104), and AC (as fig. 105), each for radius, we shall readily obtain these expressions. 1. perp. base = tan angle at base. (Fig. 103.) 2. hyp. = sec angle at base. (Fig. 103.) base base 3. tan angle at vertex. (Fig. 105.) perp. hyp. 4. sec angle at vertex. (Fig. 105.) perp. 5. perp. = sin angle at base. (Fig. 104.) hyp. base 6. sin angle at vertex. (Fig. 104.) hyp. SECT. IV.—On the application of Trigonometry to measuring Heights and Distances. Trigonometry receives its principal practical application in the opera- tions of surveying, and measuring heights and distances; as, however, the methods of its application (depending on the peculiar circumstances of PLANE TRIGONOMETRY. 207 each case) are exceedingly various, we cannot lay down any general rules, but must content ourselves with giving a selection of such examples as are most likely to occur; and the principles developed in which will be sufficient to guide any person in its further application to other cases. Example 1. In order to find the distance between two trees, A and B (Fig. 9), which could not be directly measured because of a pool which occupied much of the intermediate space, I measured the distance of each of them from a third object, C, viz., A C588, B C 672, and then at the point = C took the angle ACB between the two trees 55° 40. Required their distance. This is an example to Case II. of plane triangles, in which two sides, and the included angle, are given. The work, therefore, may exercise the student: the answer is 593.8. Example 2. Wanting to know the distance between two inaccessible objects, C and D (fig. 106), which lay in a direct line from the bottom of a tower on whose top I stood, I took the angles of depression of the two objects, viz., of the most remote 2510, of the nearest 57°. What is the distance between them, the height of the tower A B being 120 feet. HAD = 25° 30′, hence B A D=BAH-HAD = 64° 30′. HAC 57° C, hence BAC =BAH BAH-HAC = 33° 0. Hence the following calculation, by means of the natural tangents. For, if A B be regarded as radius, BD and BC will be the tangents of the respective angles BAD, BA C, and C D the difference of those tan- gents. It is, therefore, equal to the product of the difference of the natural tangents of those angles into the height A B. Thus, nat. tan 64° 30′ = nat. tan 33° difference 2.0965436 0.6494076 1.4471360 120 multiplied by height, gives distance CD=173.6563200 * *The natural sines, tangents, &c., are easily obtained from Table IV. by subtracting 10 from the characteristics, and then finding the natural number answering to the logarithms with their characteristics so altered. 208 PLANE TRIGONOMETRY. Example 3. Standing at a measurable distance A B (Fig. 103), on a horizontal plane, from the bottom of a tower, I took the angle of elevation of the top (C); it is required from thence to determine the height of the tower. In this case there would be given A B and the angle A, to find BC= ABX tan A. By logarithms, when the numbers are large, it will be log BC= log A B + log tan A. Note.-If angle A = 11° 19′ then BC A B very nearly. BC= AB "" A=16 42 BC=AB "" A=21 48 "" "} "" A=26 34 BC = 1 A B "" A=30 58 "7 "" A35 0 "" "" A 38 40 BC "" "" "" A=45 = 45 0 BC "" BC= & AB BC=7AB 10 AB A B, exactly. To save the time of computation, therefore, the observer may set the instrument to one of these angles, and advance or recede, till it accords with the angle of elevation of the object; its height above the horizontal level of the observer's eye will at once be known, by taking the appro- priate fraction of the distance A B. Example 4. Wanting to know the height of a church steeple, to the bottom of which I could not measure on account of a high wall between me and the church, I fixed upon two stations at the distance of 93 feet from each other, on a horizontal line from the bottom of the steeple, and at each of them took the angle of elevation of the top of the steeple, that is, at the nearest station 55° 54', at the other 33° 20′. steeple. Required the height of the Recurring to figure 106, we have given the distance CD, and the angles of elevation at C and D. The quickest operation is by means of the natural tangents, and the theorem A B CD cot D-cot C Thus cot D=cot 33° 20′ = 1·5204261 C=cot 55 54 = 6770509 Their difference = ·8433752 Hence A B = 93 -8433752 =110.27 feet. Example 5. Wishing to know the height of an obelisk standing at the top of a regularly sloping hill, I first measured from its bottom a distance of 36 PLANE TRIGONOMETRY. 209 feet, and there found the angle formed by the inclined plane and a line from the centre of the instrument to the top of the obelisk 41°; but after measuring on downward in the same sloping direction 54 feet farther, I found the angle formed in like manner to be only 23° 45'. What was the height of the obelisk, and what the angle made by the sloping ground with the horizon? there are given in the to find BC. It will be B-A): A B (= 54) The figure being constructed (see fig. 107), triangle A CB, all the angles and the side A B, obtained by this proportion, as sin C (= 17° 15' :: sin A (= 23° 45′): BC = 73-3392. Then, in the triangle D B C are known BC as above, BD=36, CBD 41°; to find the other angles and the side CD. Thus, first, as CB+BD: CB-BD : : tan ½ (D+C) = ½ (139°) : tan † (D — C) — 42° 24. Hence 69° 30′ + 42° 241 1 112° 541 = CD B, and 69° 30' 42° 24127° 5 BCD. Then, = sin B CD: BD :: sin C BD: CD = 51·86 height of the obelisk. The angle of inclination D A E=HDA=CD B-90° = 22° 541'. Remark. If the line B D cannot be measured, then the angle DAE of the sloping ground must be taken, as well as the angles CA B and C B D. In that case D A E + 90° will be equal to CD B: so that, after C B is found from the triangle A CB, CD may be found in the triangle CBD, by means of the relation between the sides and the sines of their opposite angles. Example 6. Being on a horizontal plane, and wanting to ascertain the height of a tower standing on the top of an inaccessible hill, I took the angle of ele- vation of the top of the hill 40°, and of the top of the tower 51°, then measuring in a direct line 180 feet farther from the hill, I took in the same vertical plane the angle of elevation of the top of the tower 33° 45′. Required from hence the height of the tower. The figure being constructed (see fig. 108), there are given, A B = 180, C A B = 33° 45′, A C B = CBE-CA E = 17° 15′, C B D = 11°, BDC 180° — (90° — D B E) = 130°. And CD may be found from = the expression C D . rad¹ = A B. sin A. sin C B D. cosec A C B . sec. D BE. Or, using logarithms, log A B = 180° + log sin A + log sin CBD = + log cosec A CB = +log sec DBE 2.255273 9.744739 9.280599 33° 45' 11° 0′ = 17° 15′ = 10·527914 40° 0′ = 10·115746 41.924271 - log rad = 40.000000 log CD = 83.9983 1.924271 210 PLANE TRIGONOMETRY. * Example 7. In order to determine the distance between two inaccessible objects A and B (Fig. 108), on a horizontal plane, we measured a convenient base, CD, of 536 yards, and at the extremities C and D took the following angles, viz., DCB = 40° 16′, BC A = 57° 40′, CD A = 42° 22′, A D B = 71° 7'. Required the distance A B. First, in the triangle CD A are given all the angles, and the side C D to find A. D. So, again, in the triangle CD B, are given all the angles, and CD to find D B. Lastly, in the triangle D A B are given the two sides AD, BD, and the included angle A D B, to find A B = 939-52 yards. Remark.-In like manner the distances taken two and two, between any number of remote objects posited around a convenient station line, may be ascertained. Example 8. Suppose that in carrying on an extensive survey, the distance between two spires A and B (Fig. 109) has been found equal to 6594 yards, and that C and D are two eminences conveniently situated for extending the triangles, but not admitting of the determination of their distance by actual admeasurement: to ascertain it, therefore, we took at C and D the fol- lowing angles, viz. :— s ACB=85° 46' BCD = 23° 56′ Required CD from these data. ADC=31° 48' ADB= 68° 2′ In order to solve this problem, construct a similar quadrilateral A c db, assuming cd equal to 1, 10, or any other convenient number: compute Ab from the given angles, according to the method of the preceding ex- ample. Then, since the quadrilaterals Acdb, A C D B, are similar, it will be, as Ab :cd::AB:CD; from which CD is found to be equal to 4694 yards. Example 9. Given the angles of elevation of any distant object, taken at three places in a horizontal right line, which does not pass through the point directly below the object; and the respective distances between the stations; to find the height of the object, and its distance from either station. Let AEC (Fig. 110) be the horizontal plane, FE the perpendicular height of the object above that plane, A, B, C, the three places of obser- vation, FA E, F BE, FCE, the angles of elevation, and A B, B C, the given distances. Then, since the triangles AEF, BEF, CEF, are all right angled at E, the distances A E, BE, CE, will manifestly be as the cotangents of the angles of elevation at A, B, and C. *"hine are two big to be tu PLANE TRIGONOMETRY. 211 Put ABD, B Cd, E F = x, and then express algebraically the theorem given in Geom., which in this case becomes, A E². BC+C E². A B = BE². AC + AC. A B.BC. The resulting equation is dx² (cot A)² + D x² (cot C)² = (D + d) x² (Cot B)² + (D + d) D d. From which is readily found x = ✓ (D + d) D d - d (Cot A)² + D (cot C)² (D + d) (cot B)² * Thus E F becoming known, the distances A E, BE, CE, are found, by multiplying the cotangents of A, B, and C, respectively, by E F. Remark. When D = d, or D + d 2D = 2d, that is, when the point B is midway between A and C, the algebraic expression becomes, x=d÷√(cot A)² + (cot C)² — (cɔt B)², which is tolerably well suited for logarithmic computation. The rule may, in that case, be thus expressed. Double the log cotangents of the angles of elevation of the extreme sta- tions, find the natural numbers answering thereto, and take half their sum ; from which subtract the natural number answering to twice the log cotan- gent of the middle angle of elevation: then half the log of this remainder subtracted from the log of the measured distance between the first and second, or the second and third stations, will be the log of the height of the object. The distance from either station will be found as above. Note.—The case explained in this example, is one that is highly useful, and of frequent occurrence. An analogous one is when the angles of elevation of a remote object are taken from the three angles of a triangle on a horizontal plane, the sides of that triangle being known, or measurable : but the above admits of a simpler computation, and may usually be employed. Example 10. From a convenient station P (Fig. 111), where could be seen three objects, A, B, and C, whose distances from each other were known (viz. A B 800, A C600, BC= 400 yards), I took the horizontal angles APC = 33° 45', BPC = 22° 30′. It is hence required to determine the respective distances of my station from each object. Here it will be necessary, as preparatory to the computation, to describe the manner of Construction.-Draw the given triangle A B C from any convenient scale. From the point A draw a line AD to make with AB an angle equal to 22° 30′, and from B a line BD to make an angle DBA = 33° 45'. Let a circle be described to pass through their intersection D, and through the points A and B. Through C and D draw a right line to meet the circle again in P: so shall P be the point required. For, drawing PA, PB, the angle APD is evidently = A B D, since it stands on the 212 PLANE TRIGONOMETRY. same arc AD: and for a like reason BPD=BAD. So that P is the point where the angles have the assigned value. The result of a careful construction of this kind, upon a good-sized scale, will give the values of PA, PC, P B, true to within the 200th part of each. Manner of Computation.-In the triangle ABC, where the sides are known, find the angles. In the triangle A B D, where all the angles are known, and the side AB, find one of the other sides AD. Take BAD from BAC, the remainder, D A C, is the angle included between the two known sides, AD, AC; from which the angles ADC and ACD may be found, by Case II., p. 204. The angle C A P=180° (A PC+ACD). — Also, BCP BCA-ACD; and PBC=ABC+PBA=ABC + sup. A DC. Hence the three required distances are found by these proportions. As sin APC: AC :: sin PAC: PC:: sin PCA: PA; and lastly, as sin BPC: BC:: sin BPC: BP. The results of the com- putation are, PA = 709.33, P C = 1042·66, P B = 934 yards. *** The computation of problems of this kind, however, may be a little shortened by means of an analytical investigation. Those who wish to pursue this department of trigonometry may consult the treatises by Bonnycastle, Gregory, and Woodhouse. Note. If C had been nearer to P than A B, the general principles of construction and computation would be the same; and the modification in the process very obvious. DETERMINATION OF HEIGHTS AND DISTANCES BY APPROXIMATE MECHANICAL METHODS. 1. For Heights. 1. By shadows, when the sun shines.-Set up vertically a staff of known length, and measure the length of its shadow upon a horizontal or other plane; measure also the length of the shadow of the object whose height is required. Then it will be, as the length of the shadow of the staff, is to the length of the staff itself; so is the length of the shadow of the object, to the object's height. 2. By two rods or staves set up vertically.-Let two staves, one, say, of 6 feet, the other of 4 feet long, be placed upon horizontal circular or square feet, on which each may stand steadily. Let A B (Fig. 112) be the object, as a tower or steeple, whose altitude is required, and AC the horizontal plane passing through its base. Let CD and E F, the two rods, be placed with their bases in one and the same line C A, passing through A, the foot of the object; and let them be moved nearer to, or farther from, each other, until the summit B of the object is seen, in the same line as D and F, the tops of the rods. Then by the principle of similar triangles, it will be, as DH (=CE): FH:: DG (CA): BG; to which add A GCD, for the whole height A B. PLANE TRIGONOMETRY. 213 3. By reflection.-Place a vessel of water upon the ground, and recede from it, until you see the top of the object reflected from the smooth sur- face of the liquid. Then, since by a principle in optics, the angles of inci- dence and reflection are equal, it will be as your distance measured horizontally from the point at which the reflection is made, is to the height of your eye above the reflecting surface; so is the horizontal distance of the foot of the object from the vessel to its altitude above the said surface*. 4. By means of a portable barometer and thermometer.-Observe the altitude B, of the mercurial column, in inches, tenths, and hundredths, at the bottom of the hill, or other object whose altitude is required; observe, also, the altitude, b, of the mercurial column at the top of the object; ob- serve the temperatures on Fahrenheit's thermometer, at the times of the two barometrical observations, and take the mean between them. Then 55000 × B-b B+b height of the hill, in feet for the temperature 440 of 55° on Fahrenheit. Add 10 of this result for every degree which the mean temperature exceeds 55°; subtract as much for every degree below 55°. This will be a good approximation when the height of the hill is less than 2000 feet; and it is easily remembered, because 55°, the assumed tem- perature, agree with 55, the significant figures in the co-efficient; while the significant figures in the denominator of the correcting fraction are two fours. 5. By an extension of the principle of page 208.-Set the sextant, or other instrument, to the angle 45°, and find the point C (Fig. 103) on the horizontal plane, where the object A B has that elevation: then set the instrument to 26° 34', and recede from C, in direction B C D, till the object has that elevation. The distance CD between the two stations will be = A B. So, again, if C = 40°, D = 24° 31, CD will be = if C = 35°, D = 22° 23′, CD if C = 30°, D = 20° 6'′, CD or, "" or, "" or, "" or, generally, if cot D if C = 20°, D A B. A B. "" A B. "" A B. "" cot C = rad, C D = A B. = 14° 56′, CD 6. For deviation from level.-Let E represent the elevation of the tan- gent line to the earth above the true level, in feet and parts of a foot, D the distance in miles: then E = ½ D². first * Leonard Digges, in his curious work, the Pantometria, published in 1571, proposed a method for the determination of altitudes by means of a geometrical square and plummet, which has been described by various later authors, as Ozanam, Donn, Hutton, &c. But, as it does not seem preferable to the methods above given, I have not repeated it here. 214 PLANE TRIGONOMETRY. This gives 8 inches for a distance of one mile; and is a near approxima- tion when the distance does not exceed 2 or 3 miles. 2. For Distances. 1. By means of a rhombus set off upon a horizontal plane.-Suppose O (Fig. 113) the object, and O B the required distance. With a line or measuring tape, whose length is equal to the side of the intended rhombus, say 50 or 100 feet, lay down one side BA in the direction BO towards the object, and BC another side in any convenient direction (for whether B be a right angle, or not, is of no consequence); and put up rods or arrows at A and C. Then fasten two ends of two such lines at A and C, and ex- tend them until the two other ends just meet together at D; let them lie thus stretched upon the ground, and they will form the two other sides of the rhombus AD, CD. Fix a mark or arrow at R, directly between C and O, upon the line A D; and measure R D, R A upon the tape. Then it will be as RD:DC::CB: BO, the required distance. Otherwise. To find the length of the inaccessible line Q R. At some convenient point B (Fig. 114) lay down the rhombus B ADC, so that two of its sides, BA, BC, are directed to the extremities of the line QR. Mark the intersections, O and P, of A R, CQ, with the sides of the rhombus (as in the former method): then the triangle ODP will be similar to the triangle R B Q; and the inaccessible distance R Q will be found Thus, if B A B C, &c. = = OP=13 ft. 7 ins., then Q R 2 OP × BA² * OD X DP 100 ft., OD=9 ft. 5 ins., DP11 ft. 10 ins., 10000 × 1372 = 9_5 × 1110100 12 = 1219 feet. 2. By means of a micrometer attached to a telescope.-Portable in- struments for the purpose of measuring extremely small angles, have been invented by Martin, Cavallo, Dollond, Brewster, and others. In employing them for the determination of distances, all that is necessary in practice is to measure the angle subtended by an object of known dimen- sions, placed either vertically or horizontally, at the remoter extremity of the line whose length we wish to ascertain. Thus, if there be a house, or other erection, built with bricks, of the usual size; then four courses in height are equal to a foot, and four in length equal to a yard: and distances measured by means of these will be tolerably accurate, if care be taken while observing the angle subtended by the horizontal object, to stand directly in front of it. A man, a carriage-wheel, a window, a door, &c., at the remoter extremity of the distance we wish to ascertain, may serve for an approximation. But in all cases where it is possible, let a foot, a *For PD: DA::AB: BR: A B2 PD and OD: OP::BR:RQ A B2. O P OD.DP' PLANE TRIGONOMETRY. 215 yard, or a six-feet measure, be placed vertically, at one end of the line to be measured, while the observer with his micrometer stands at the other. Then, if h be the height of the object, either h× cotangle subtended or hx cot angle will give the distance, according as the eye of the observer is horizontally opposite to the middle, or to one extremity of the object whose angle is taken. When a table of natural tangents is not at hand, a very near approxi- mation for all angles less than half a degree, and a tolerably near one up to angles of a degree, will be furnished by the following rules. If the distant object whose angle is taken be 1 foot in length, then 3437·73 ÷ the angle in minutes will give the distance in or 206264 ÷ the angle in seconds } feet. If the remote object be 3, 6, 9, &c., feet in length, multiply the former result by 3, 6, 9, &c., respectively. Ex. 1. What is the distance of a man 6 feet high, when he subtends an angle of 30 seconds? 206264 × 6÷ 30= 206264 ÷ 5= 41252.8 feet 13750.9 yards, the distance required. Ex. 2. In order to ascertain the length of a street, I put up a foot mea- sure at one end of it, and standing at the other found that measure to subtend an angle of 2 minutes: required the length of the street. 3437·73 ÷ 2 = 1718.86 feet = 572.95 yards. 3. By means of the velocity of sound.-Let a gun be fired at the re- moter extremity of the required distance, and observe, by means of a chronometer that measures tenths of seconds, the interval that elapses between the flash and the report: then estimate the distance for one second by the following rule, and multiply that distance by the observed interval of time; the product will give the whole distance required. At the temperature of freezing, 32°, the velocity of sound is 1100 feet per second; for lower temperatures deduct, or for higher temperatures add, half a foot per second for every degree of difference from 32° on Fahr. thermometer; the result will shew the velocity of sound, very nearly, at all such temperatures. Thus, at the temperature of 50° the velocity of sound is, 1100 × (50 — 32) = 1109 feet. 1 : At temperature 60°, it is 1100 + ½ (60 −32) = 1114 feet. 216 CONIC SECTIONS. CHAP. V. CONIC SECTIONS. SECT. I.-Definitions. 1. Conic Sections are the figures made by a plane cutting a cone. 2. According to the different positions of the cutting plane there arise five different figures or sections, viz., a triangle, a circle, an ellipse, an hyperbola, and a parabola: of which the three last are peculiarly called Conic Sections. 3. If the cutting plane pass through the vertex of the cone, and any part of the base, the section will be a triangle, as A B. (Fig. 115.) 4. If the plane cut the cone parallel to the base, or make no angle with it, the section will be a circle, as A B. (Fig. 116.) 5. The section is an ellipse when the cone is cut obliquely through both sides, or when the plane is inclined to the base in a less angle than the side of the cone is, as A B C D. (Fig. 120.) 6. The section is a parabola when the cone is cut by a plane parallel to the side, or when the cutting plane and the side of the cone make equal angles with the base, as P₁ A P₂. (Fig. 138.) 7. The section is an hyperbola when the cutting plane makes a greater angle with the base than the side of the cone makes, as P₁ A P₂. (Fig. 130.) Note. In all the above definitions the cone is supposed to be a right cone. 8. If all the sides of the cone be continued through the vertex, forming an opposite equal cone, and the plane be also continued to cut the opposite cone, this latter section is called the opposite hyperbola to the former, as S, B S. (Fig. 130.) 9. And if there be two other cones, with their axes in the same plane and their sides touching the sides of the former cones, then will the same plane cut all the cones and form four hyperbolas, as P, A P₂, R, C R2, S₁ B S2, Q1 D Q₂ (fig. 118), each opposite pair of which are similar; these hyperbolas are said to be conjugate to each other, and the figure thus formed is called the figure of the conjugate hyperbolas, as fig. 118. Note.—In the following definitions, the letters refer to fig. 117 for the ellipse; fig. 118 for the hyperbola; and fig. 119 for the parabola. 10. The vertices of any section are the points where the cutting plane meets the opposite sides of the cone, as A and B. Cor. Hence the ellipse and the opposite hyperbolas have each two vertices; but the parabola only one; unless we consider the other as at an infinite distance. 11. The major axis, or transverse diameter of a conic section, is the line or distance A B between the vertices. CONIC SECTIONS. 217 Cor. Hence the axis of a parabola is infinite in length, A B being only a part of it. 12. The centre O is the middle of the axis. Cor. Hence the centre of a parabola is infinitely distant from the vertex. And of an ellipse, the axis and centre lie within the curve: but of an hyperbola, without. 13. The minor or conjugate axis, is the line C D, drawn through the centre perpendicular to the transverse axis, and bounded each way by the curve. Cor. Hence the parabola has not any conjugate axis, unless we suppose it at an infinite distance, and infinite in length. 14. A tangent to a curve at any point, is a line as A, T₁, which touches the curve in that point; but being produced either way does not cut it. 15. A diameter is any right line, as A, B₁, drawn through the centre, and terminated on each side by the curve; and the extremities of the diameter, or its intersections with the curve, as A, and B₁, are its vertices Cor. Hence all the diameters of a parabola are parallel to the axis, and infinite in length. Hence, also, every diameter of the ellipse and hyper- bola has two vertices; but of the parabola, only one; unless we consider the other as at an infinite distance. 16. The conjugate to any diameter is the line drawn through the centre, and parallel to the tangent of the curve at the vertex of the diameter. So, C₁ D₁, parallel to the tangent at A₁, is the conjugate to A₁ B₁. 17. An ordinate to any diameter is a line parallel to its conjugate, or to the tangent at its vertex, and terminated by the diameter and curve. So, K I and K₂ A, are ordinates to the axis A B; and K, I and E₁ I, ordi- nates to the diameter A, B₁. 1 Cor. Hence the ordinates of the axes are perpendicular to it; but of other diameters, the ordinates are oblique to them. 18. An abscissa is a part of any diameter, contained between its vertex and an ordinate to it; as A K or B K, and A, E, or B, E₁. Cor. Hence, in the ellipse and hyperbola, every ordinate has two abscissæ; but in the parabola only one; the other vertex of the diameter being infinitely distant. 19. The vertex from which the abscissæ are measured is called the origin of those abscissæ, and any abscissa and its ordinate are called co-ordinates, as A K and K I. 20. The parameter of any diameter is that double ordinate which is a third proportional to the transverse and conjugate axes in the ellipse or hyperbola, and to any abscissa and its ordinate in the parabola. The parameter of the transverse axis is called the principal parameter, or the latus rectum; thus, if A, B, C, D₁ :: C, D, : I, I, then I, I, is the para- meter of A₁ B₁; and if A B : C D : : C D : I½ I3, then I, I, is the latus rectum. 21. The point where the parameter cuts the transverse axis is called the focus, as E, F; and the distance of the focus from the nearest vertex of the same axis is called the focal distance, as A E, B F. 1 1 Cor. Hence, the ellipse and hyperbola have each two foci, but the 218 CONIC SECTIONS. parabola only one. The foci (or burning points) were so called because all rays are united or reflected into one of them, which proceed from the other focus, and are reflected from the curve. 22. The point E is also frequently called the pole; and a line drawn from any point in the curve to the pole, is called the radius vector as E I. And the angle B E I, contained between the radius vector and the transverse axis, is called the traced angle. 23. The directrix is a right line drawn perpendicular to the transverse axis of a conic section, through an assignable point in the prolongation of that axis; such that lines drawn from any points in the curve parallel to the axis to meet the directrix, shall be to lines drawn from the same points to the focus, in a constant ratio for the same curve. 2 Thus, if A E: AT:: EI₂: I½y : : E 1: I, x:: EI:IX, then X Y is the directrix. In the ellipse A E is less than A T. In the parabola A E is equal to A T. In the hyperbola A E is greater than A T. 24. The subtangent to any point in a curve, is that portion of the trans- verse axis which is contained between the tangent and ordinate to the same point, as K₂ T1. 25. A normal at any point is a line drawn from that point perpen- dicular to the tangent, to meet the transverse axis, as A, L. 26. The Radius of Curvature of a conic section or other curve, is the radius of that circle which is precisely of the same curvature as the curve itself, at any assigned point, or the radius of the circle which fits the curve and coincides with it, at a small distance on each side of the point of con- tact. The circle itself is called the osculatory circle, or the equicurve circle; and if the curve be of incessantly varying curvature, each point has a distinct equicurve circle, the radius of which is perpendicular to the tangent at the point of contact. 27. An asymtote is a right line towards which a certain curve line ap- proaches continually nearer and nearer, yet so as never to meet, except both be produced indefinitely. The hyperbola has two asymptotes, as U V, W Z. LAND MEASURING. 219 CHAPTER VI. LAND MEASURING. We cannot enter upon any calculation connected with Land that is not more or less dependent upon the admeasurement of its surface, or, in more technical terms, its "superficial area;" how much more important then, than is ordinarily supposed, does it be- come that the very simple operations necessary to arrive at a correct result should be properly understood by those who affect to practise this particular branch of science. No extraordinary ability or power of genius, nothing out of the common way in point of education and mental attainments, no laborious application to study, nor any great amount of previous practice, is requisite to produce a competent "Land Measurer." I do not mean to say that all these are not advantages which will give a man possessing them superiority over another who does not possess them; but they are not at all indispensable; and I will endeavour to expound in simple language the rules requisite to be understood to enable any person, though of mean ability, who can perform the four fundamental rules of arithmetic, (or by the aid of Tables I pub- lished ten years since, or the Tables I will annex to this article, addition only), to measure accurately any piece of land that may come in his way although he may not be able to do it quickly, so as to turn to profitable pecuniary account the knowledge he has thus acquired. I must not here be misunderstood. While all I have said above applies to “ Land Measuring,” not one word is applicable to "Land Surveying;" that is a totally different branch of science, requiring long practice and a thoroughly perfect scientific education. By "Land Surveying" I mean the admeasurement, by an infinity of instrumental and other contrivances, of the geographical and physical features of the earth's surface, embracing in their widest scope the operations of " Surveying, Mapping, and Levelling.” In extensive operations, land is generally measured with a chain of 100 links, known as Gunter's Chain, from the name of its in- ventor, the Rev. Edward Gunter, who was born in 1680, and died in 1726, so that it must have been in use upwards of 125 years. The chief advantage of the use of this chain is the facility it affords in squaring or casting the dimensions, 100,000 square links, or 10 square chains, being equal to one statute acre. If, however, the 220 LAND MEASURING. results of operations in other measures are conveniently tabulated, this advantage of Gunter's Chain is superseded, and the non-pro- fessional "Land Measurer" is at liberty to take the dimensions in that measure with which he is most familiar. Country gentlemen, farmers, and indeed all classes of the community, being more gene- rally acquainted with the standard yard, it is my intention to lay down the principles of Land Measuring without reference to any particular kind of measure used, and then to annex thereto a cor- rectly computed Table of results, in statute acres, of dimensions taken in yards. These Tables will, as I have previously stated, entirely obviate the necessity of all calculation in cases when the pieces of land do not exceed 100 yards square, and will render dimen- sions in yards equally as convenient as those in chains and links. RULES. 1. If the piece of land to be measured is in the form of a square or rectangle, that is, having four right angles, and all its sides parallel, its area is found by multiplying its length by its width. (Vide Mensuration of Superficies.) 2. If the piece of land to be measured is triangular, the length of the base multiplied by one-half the perpendicular, or one-half of the base multiplied by the perpendicular, will give the area; or, what is the same thing, the full base multiplied by the perpen- dicular, will give twice the area of the triangle. (Vide Mensuration of Superficies.) 3. If the piece of land has two of its sides parallel and at right angles with the base, add the two parallel sides together, and multiply one-half their sum by the base or side running at right angles to them, the product will be the area; or multiply the sum of the two sides by the base, and take half the product for the area. Example 1. A square piece of land is 4 long and 4 wide, what is its area? (Fig. 125.) 4 long multiplied by 4 wide gives . 16 superficial area. I have endeavoured to render this result plainly apparent by dividing the figure into squares and numbering them, from which it will at once be seen that the area of the figure must be 16 squares of whatever measure the dimensions were taken in. LAND MEASURING. 221 Ex. 2.-What is the content of the triangular piece of land whose base is 8 and perpendicular 4? (Fig. 126.) 8 base multiplied by 2 half perpendicular gives 16 superficial content. or 8 base 4 perpendicular 2)32 twice area gives 16 required area. or 4 half base 4 perpendicular 16 area. This is also rendered clearly apparent on the figure, by which it is shewn that the triangle ABC contains 12 perfect squares and 8 half-squares. It also shews that the two triangles wanting to form a rectangle of the same dimensions contain, in the aggre- gate, the same number of squares and half-squares as the triangle; thus illustrating, in the plainest manner, that one-half the area of the rectangle is the area of the triangle. Ex. 3.—Required the area of the rhomboid whose base is 4, and its parallel sides 4 and 8 respectively. (Fig. 127.) added to. 4 height of one side 8 height of opposite side divided by 2) 12 gives 6 mean height multiplied by 4 base gives . 24 area. or, added to . 4 8 12 sum of the sides multiplied by 4 base divided by 2)48 gives 24 area. The figures shew that 6 must be the mean height, the square A and the two half squares a a, rejected, being equal to the square B, and the two half squares b b, taken in. The previous rules form the fundamental ones for measuring land, but it is very unusual indeed to meet with just such figures 222 LAND MEASURING. in practice; it does not unfrequently happen that a four-sided field is met with, but then it scarcely ever occurs that the sides are parallel to each other, or if so, that the angles are right angles; even should that be the case, it is not possible to be certain of the fact, without verifying it by some process that would take as much time as would be required to measure the field; the rule then is to divide the field into several imaginary mathematical figures, and to take such dimensions as may be required to produce the area. The triangle will be found to be the most useful of all others for this purpose, or a trapezium divided into two triangles by the "diagonal," which thus becomes a base common to both tri- angles, and will consequently give the area of the trapezium if mul- tiplied into half the sum of the two perpendiculars of the triangle. Ex. 4.-Required the Content of the Field in the form of a Trapezium, whose dimensions in Links are as given in Fig. 128. Note.-In measuring the base AB, it was found that the first perpendicular to the corner E, sprang at the point C 422 links from A, and a mark was there left until the perpendicular could be measured; (it is very dangerous to the accuracy of the work to dis- continue measuring on one line, to measure another, before the first line is completed; the insertion of the figures in the wrong places, and mixing the arrows which denote the number of chains, are among the most fruitful sources of error to an unpractised person in such cases.) Continuing the diagonal the perpendicular to the corner, F was found to spring at the point D 830 links from A*. Continuing the total length, the base A B was found to be 1142 links. The chain was then taken to F, and the perpendicular FD was measured, equal 460 links; and then the perpendicular from C to E, and found to be 480 links, which completed the operation. add { 460 480 Calculation. divide by 2) 940 sum of perpendiculars 470 half sum of perpendiculars. * The insertion of the distances on the diagonal at which the perpendiculars rise are not at all required in the computation of the area, but it is always worth while to enter them in the Field Book, as they enable an approximate plot of the field to be drawn, if at any future time such may be desirable. I once measured field by field the parish of Walton-upon-Thames, containing 7300 acres, and by attending to this particular in keeping the Field Notes, I was enabled some two or three years subsequently, at my leisure, to plot a very tolerable map of that parish.-E. R. LAND MEASURING. 223 multiply by acres 1142 diagonal 470 half sum of perpendiculars 79940 4568 5,36740 product in square links 4 rood 1,46960 40 perches 18,78400 The area 536740 square links is reduced into acres, roods, and perches, by dividing by 100,000 the number of square links in an acre; this is readily done by cutting off the five right-hand figures; the figure 5 remaining on the left-hand being acres, and those on the right decimals of an acre, which by multiplying by 4 (the number of roods in an acre) and again cutting off five figures, leaves one rood on the left of the decimal dot-the decimals of a rood being multiplied by 40 (the number of perches in a rood), and the five decimals again pointed off, leave 18 perches and 78400 decimals of a perch. The answer, therefore, is 5A. 1R. 18.7r. To facilitate this reduction of square links, a Table is annexed, shewing the several roods and perches in any decimal of an acre. It is very easy to reduce them mentally by committing the fol- lowing particulars to memory. .00625 is 1 perch •01250 is 2 •02500 is 4 •05000 is 8 " وو وو •10000 is 16 •20000 is 32 •25000 is 1 rood •50000 is 2 roods 75000 is 3 roods In our previous example, this is the kind of mental calculation we should have to carry on. We see that the given decimal •36740 is more than one rood; there- fore, we set down one rood, and at a glance we discover we have left •11740 10000 of which we know to be .. 16 •01250 2 and the remainder nearly 1 19 percs nearly By the assistance of some Tables published by me in 1842, 224 LAND MEASURING. under the title of "Ryde's Pocket Companion and Ready Reckoner," the calculation of the previous example would have been as under. The Tables rising in value, every separate link up to 1000, the half of the diagonal or odd number would have been taken (to bring it within the scope of the Tables, and thus save one line of addition,) and the sum of the perpendiculars. Thus, at page 115 A. R. P. 1142 571 by 900 = 5 0 22.2 2 وو by 40 = 0 0 36.5 5 1 18.7 otherwise it would have stood at page 94 470 by 1100 = 5_0_27·2 by 40 = 0 0 30. وو by 2 = 0 0 1.5 5 1 18.7 The only advantage of the former arrangement over the latter being, the saving of one line, effected in the addition of the quantities. Ex. 5.-What is the Content of the piece of Land whose dimensions are marked upon figure 129? AB First, we have the diagonal A B = 1034, and the two perpen- diculars CE and D F = 411 and 395 respectively; then on the line BE, between it and the curved fence, we have, first, a triangle BIK, whose base BI is 100, and perpendicular I K 66; next a rhomboid HIKL, whose base IH is the difference between 300 and 100, and whose perpendiculars HL and IK are 6 and 20 respectively; then a rectangle G H L M, whose base HG is the difference between 700 and 300, and whose perpendiculars HL and GM are 20; and lastly, we have a triangle EG M, whose base GE is the difference between 960 and 700, and whose perpen- dicular G M is 20. Calculation. 1034 2 517 × (411 + 395 806) 2) 100 50 half-base 6 perp. 300 Tri. BIK. LAND MEASURING. 225 400 base 20 6 20 perp. 2) 26 8000 13 1-perp. 200 260 2600 2600 10 1-perp. 517 -diagonal. 806 sum of perp. 3102 41360 4.16702 area of trapezium AEBF. 300 Triangle BIK. 2600 Rhomboid HIK L. 8000 Rectangle G H L M. 2600 Triangle E G M. 4.30202 Total area of field. At By the Table of Decimals of an acre ·30052 = lr. 8p. Answer 4a. 1r. 8p. By "Ryde's Pocket Companion and Ready Reckoner." page 104, 517 by 806 وو وو P. 26.6 Trap. A E B F. A. B. = 4 0 10, 50 6 0 = 0 0.4 Tri. BIK. "" 3, 13 80, 400 200 = 0 0 4.1 Rhom. HIKL. 39 20 = 0 0 12.8 Rec. G HLM. 52, 260 10 = 0 0 وو 4.1 Tri. E G M. Answer 4 1 8. Other Examples might be added, with all the fences crooked, but it is considered unnecessary, as every distinct fence would have to be treated in a similar manner to the fence BKL ME, in our last Example. 226 DECIMALS OF AN ACRE. R. P. Dec. R. P. Dec. R. P. Dec. R. P. Dec. 0 1 .00625 1 1 .25625 2 1 .50625 3 1 .75625 0 2 .01250 1 2 .26250 2 2 .51250 3 2 .76250 0 3 .01875 1 3 .26875 2 3 .51875 3 3 .76875 0 4 .02500 1 4 .27500 2 4 .52500 3 4 .77500 0 5 .03125 1 5 .28125 2 5 .53125 3 5 .78125 0 6 .03750 1 6 .28750 2 6 .53750 3 6 .78750 0 7 .04375 1 7 .29375 2 7 .54375 3 7 .79375 08 .05000 1 8 .30000 2 8 .55000 3 8 .80000 09 .05625 1 9 .30625 2 9 .55625 3 9 .80625 0 10 .06250 1 10 .31250 2 10 .56250 3 10 .81250 0 11 .06875 1 11 .31875 2 11 .56875 3 11 .81875 0 12 .07500 1 12 .32500 2 12 .57500 3 12 .82500 0 13 .08125 1 13 .33125 2 13 .58125 3 13 .83125 0 14 .08750 1 14 .33750 2 14 .58750 3 14 .83750 0 15 .09375 1 15 .34375 2 15 .59375 3 15 .84375 0 16 .10000 1 16 .35000 2 16 .60000 3 16 .85000 0 17 .10625 1 17 .35625 2 17 .60625 3 17 .85625 0 18 .11250 1 18 .36250 2 18 .61250 3 18 .86250 0 19 .11875 1 19 .36875 2 19 .61875 3 19 .86875 0 20 .12500 1 20 .37500 2 20 .62500 3 20 .87500 0 21 .13125 1 21 .38125 2 21 .63125 3 21 .88125 0 22 .13750 1 22 .38750 2 22 .63750 3 22 .88750 0 23 .14375 1 23 .39375 2 23 .64375 3 23 .89375 0 24 .15000 1 24 .40000 2 24 .65000 3 24 .90000 0 25 .15625 1 25 .40625 2 25 .65625 3 25 .90625 0 26 .16250 1 26 .41250 2 26 .66250 3 26 .91250 0 27 .16875 1 27 .41875 2 27 .66875 3 27 .91875 0 28 .17500 1 28 .42500 228 .67500 328 .92500 0 29 .18125 1 29 .43125 2 29 .68125 3 29 .93125 0 30 .18750 1 30 .43750 2 30 .68750 3 30 .93750 0 31 .19375 1 31 .44375 2 31 .69375 3 31 .94375 0 32 .20000 1 32 .45000 2 32 .70000 3 32 .95000 0 33 .20625 1 33 .45625 2 33 .70625 3 33 .95625 0 34 .21250 1 34 .46250 2 34 .71250 3 34 .96250 0 35 .21875 135 .46875 2 35 .71875 3 35 .96875 0 36 .22500 1 36 .47500 2 36 .72500 336 .97500 0 37 .23125 038 .23750 1 38 0 39 .24375 1 0 .25000 1 37 .48125 2 37 .73125 3 37 .98125 .48750 2 38 .73750 3 38 .98750 1 39 .49375 2 39 .74375 3 39 .99375 20 .50000 30 .75000 LAND MEASURING. 227 Required the content of the field whose dimensions in yards are as shewn upon fig. 130. Yards. 14 = 7 1-perp. 198 2 99 half-base 37 = base. 2 88 perp. 259 Tri. B. 792 792 198 2 160 38 8712 Triangle A. = 19=-base 2 259 Tri. B. 19 361 Tri. C. 1932 Rhom. D. 171 1026 Tri. E. 27+ 19 46 2 2 19 361 Tri. C. 23-perp. 160—76 = 84 base 12290 area in square yards. 4840) 12290 (2 acres. 9680 2610 4 92 184 1932 Rhomboid D. 4840) 10440 (2 roods. 9680 760 40 76 =38-base 4840) 30400 (6.28 perches 2 29040 27 perp. 13600 266 9680 76 39200 1026 Tri. E. By the new Tables:- 88 yards by 99 = 1 7 37=0 0 8.56 19=0 0 11.93 38720 480 A. R. P. 3 8 19 "" 23 840 1 23.87 دو 38 Answer 27=0 0 33.92 2 2 6.28 228 LAND MEASURING. Note.-The reduction of square yards into acres, roods, and perches is given in this case to illustrate the method of doing it by figures; for the future we shall only employ the Tables. Required the Area of the Field whose dimensions in yards are as marked upon fig. 131. By the Tables. 198 × 116 + 46 = 99 × 162* 2 99 × 100 = 2 99 × 62 = 1 1 0 7·27 2.91 Trap. A. 186 × 127 + 68 = 93 × 195* 2 93 × 100 = 1 93 × 95 = 1 2+8 × 55 = 3 27·44 3 12·07 5 × 55 = 0 0 9.09 Trap. B. 9.09 Rhom. C. 2 8+4 × 134 – 55 – 6 × 79 = 0 0 15.67 Rhom. D. 2 7+5 + × 27 = 6 × 27 = 0 0 5.36 Rhom. E. 2 66 × 11 = 33 × 11 = 0 0 12.10 0 12.10 Tri. F. 2 157-87 70 ×4=35 × 4 = 0 0 4.63 Tri. G. 2 2 Total Contents . . 7 1 16.54 What are the respective quantities of four pieces of Harvest Work, whose dimensions in yards are severally, as marked on fig. 132? Note.-We may here remark, that in narrow slips of land, such as is represented in this field, it is sufficiently accurate for ordinary purposes, if the mean length is ascertained by measuring up the middle of the slip, and the width is taken as near to either end as possible, about at right angles with the centre length, and averaged for a mean width. * The Tables being limited to 100 yards in extent an extra line in the casting is required in each of these two figures. †This figure is not strictly a mathematical one; it will be observed, the mean length is taken and the mean width: the field represented, is an actual field, in the parish of Walton. Here is another little irregularity of small importance; the 11 yards may not be quite at right angles with the base, but not sufficiently at variance to produce any practical consequence. LAND MEASURING. 229 By the Table. A. R. P. = 28 × 97 = 0 2 9.79 Trap. A. 25 + 31 56 2 2 33 + 43 76 38 × 94 = 0 2 38·08 Trap. B. 2 2 48 + 46 2 94 2 32 + 34 2 66 = 33 × 97 = 0 2 = 47 × 96 = 0 3 29.16 Trap. C. Total Contents 2 25·82 = 0 2 25·82 Trap. D. 2 3 22.85 The little instrument used for erecting perpendiculars is called a Cross. The most simple one that can be constructed, and the most convenient because the most portable, consists of a round piece of box-wood, about four inches in diameter, and three-quar- ters of an inch in thickness; it has a hole in the centre, through which it may be slipped on to the offset rod, to a suitable height when stuck in the ground for a man's eye to look into. Two grooves at right angles with each other are cut into it, as shewn on Fig. 133; a thin piece of vernier is stuck on to the top of it, and when on the staff it appears as Fig. 134. To prove the accuracy of the Cross, look into groove AB, Fig. 135, and direct an assistant to set up a stick C; look through the other groove D E, and have another stick set up at F: twist the Cross round on the offset rod until the stick at F can be seen through the groove A B; then if the stick at C is seen through the groove D E, the Cross is obviously correct. Tables of Land Measure, by dimensions taken in yards. Dimensions. Statute content. Dimensions. Statute content. Dimensions. Statute content. Yards. A. R. P. Yards. A. B. P. Yards. A. R. P. 1 by 1 0 0 0.03 1 by 65 0 0 2.15 2 by 30 0 0 1.98 2 0 0 0.07 66 0 0 2.18 31 0 0 2.05 3 0 0 0.1 67 0 0 2.21 32 0 0 2.12 4 0 0 0.13 68 0 0 2.25 33 0 0 2.18 5 0 0 0.16 69 0 0 2.28 34 0 0 2.25 67 0 0 0.2 70 0 0 2.31 35 0 0 2.31 0 0 0.23 71 0 0 2.35 36 0 0 2.38 8 0 0 0.26 72 0 0 2.38 37 0 0 2.45 9 0 0 0.3 73 0 0 2.41 38 0 0 2.51 10 0 0 0.33 74 0 0 2.45 39 0 0 2.58 11 0 0 0.36 75 0 0 2.48 40 0 0 2.64 12 0 0 0.4 76 0 0 2.51 41 0 0 2.71 13 0 0 0.43 77 0 0 2.55 42 0 0 2.78 14 0 0 0.46 78 0 0 2.58 43 0 0 2.84 15 0 0 0.5 79 0 0 2.61 44 0 0 2.91 16 0 0 0.53 80 0 0 2.64 45 0 0 2.98 17 0 0 0.56 81 0 0 2.68 46 0 0 3.04 18 0 0 0.6 82 0 0 2.71 47 0 0 3.11 19 0 0 0.63 83 0 0 2.74 48 0 0 3.17 20 0 0 0.66 84 0 0 2.78 49 0 0 3.24 21 0 0 0.69 85 0 0 2.81 50 0 0 3.31 22 0 0 0.73 86 0 0 2.84 51 0 0 3.37 23 0 0 0 0.76 87 0 0 2.88 52 0 0 3.44 24 0 0 0 0.79 88 0 0 2.91 53 0 0 3.50 25 0 0 0 0.83 89 0 0 2.94 54 0 0 3.57 26 0 0 0.86 90 0 0 2.98 55 0 0 3.64 27 0 0 0.89 91 0 0 3.01 56 0 0 3.7 28 0 0 0.93 92 0 0 3.04 57 0 0 3.77 29 0 0 0.96 93 0 0 3.07 58 0 0 3.83 30 0 0 0.99 94 0 0 3.11 59 0 0 3.9 31 0 0 1.02 95 0 0 3.14 60 0 0 3.97 32 0 0 1.06 96 0 0 3.17 61 0 0 4.03 33 0 0 1.09 97 0 0 3.21 62 0 0 4.1 34 0 0 1.12 98 0 0 3.24 63 0 0 4.17 35 0 0 1.16 99 0 0 3.27 64 0 0 4.23 36 0 0 1.19 100 0 0 3.31 65 0 0 4.3 37 0 0 1.22 2 by 2 0 0 0.13 66 0 4.36 38 0 0 1.26 3 0 0 0.2 67 0 0 4.43 39 0 0 0 1.29 4 0 0 0.26 68 0 0 4.5 40 0 0 0 1.32 0 0 0.33 69 0 0 4.56 41 0 0 0 1.36 6 0 0 0.4 70 0 0 4.63 42 0 0 0 1.39 7 0 0 0.46 71 0 0 4.69 43 0 0 1.42 8 0 0 0.53 72 0 0 4.76 44 0 0 1.45 9 0 0 0.6 73 0 0 4.83 45 0 0 1.49 10 0 0 0.66 74 0 0 4.89 46 0 0 1.52 11 0 0 0.73 75 0 0 4.96 47 0 0 0 1.55 12 0 0 0.79 76 0 0 5.02 48 0 0 1.59 13 0 0 0.86 77 0 5.09 49 0 0 1.62 14 0 0 0.93 78 0 0 5.16 50 0 0 1,65 15 0 0 0.99 79 0 0 5.22 51 0 0 1.69 16 0 0 1.06 80 0 0 5.29 52 0 0 1.72 17 0 0 1.12 81 0 0 5.36 53 0 0 1,75 18 0 0 0 1.19 82 0 0 5.42 54 0 0 1,79 19 0 0 1.26 83 0 0 5.49 55 0 0 1.82 56 0 0 1,85 57 0 0 1.88 58 0 0 1,92 59 0 0 1,95 22222 20 0 0 1.32 84 0 0 5.55 21 0 0 1.39 85 0 5.62 0 0 1.45 86 0 5.69 23 0 0 1.52 87 0 5,75 24 0 0 1.59 88 0 0 5.82 60 0 0 1.98 25 0 0 1.65 89 0 0 5.88 61 0 0 2.02 26 0 0 1.72 90 0 0 5.95 62 0 0 0 2.05 27 0 0 1,79 91 0 0 6.02 63 0 0 0 2,08 64 0 0 2.12 88888 28 0 0 1.85 92 0 0 6.08 29 0 0 1.92 93 0 0 6.15 TABLES OF LAND MEASURE. 231 Dimensions. Statute content. Dimensions. Statute content. Dimensions. Yards. A. R. P. Yards. A. R. P. Yards. Statute content. A. R. P. 2 by 94 0 0 6.21 3 by 60 0 0 5.95 4 by 27 0 0 3.57 95 0 0 6.28 61 0 0 6.05 28 0 0 3.7 96 0 0 6.35 62 0 0 6.15 29 0 0 3.83 97 0 0 6.41 63 0 0 6.25 30 0 0 3.97 98 0 0 6.48 64 0 0 0 6.35 31 0 0 4.1 99 0 0 6.55 65 0 0 0 6.45 32 0 4.23 100 0 0 6.61 66 0 0 0 6.55 33 0 0 4.36 3 by 3 0 0 0.3 67 0 0 0 6.64 34 0 0 4.5 4 0 0 0.4 68 0 0 0 6.74 35 0 0 4.63 0 0 0.5 69 0 0 0 6.84 36 0 0 4.76 6 0 0 0.6 70 0 0 6.94 37 0 0 4.89 7 0 0 0.69 71 0 0 7.04 38 0 0 5.02 8 0 0 0.79 72 0 0 7.14 39 0 0 5.16 9 0 0 0.89 73 0 0 7.24 40 0 0 5.29 10 0 0 0.99 74 0 0 7.34 41 0 0 5.42 11 0 0 1.09 75 0 0 7.44 42 0 0 5.55 12 0 0 1.19 76 0 0 7.54 43 0 0 5.69 13 0 0 1.29 77 0 0 7.64 44 0 0 5.82 14 0 0 1.39 78 0 0 7.74 45 0 0 5.95 15 0 0 1.49 79 0 0 7.83 46 0 0 6.08 16 0 0 1.59 80 0 0 7.93 47 0 6.21 17 0 0 1.69 81 0 0 0 8.03 48 0 0 6.35 18 0 0 1.79 82 0 0 0 8.13 49 0 0 6.48 19 0 0 1.88 83 0 0 0 8.23 50 0 0 6.61 20 0 0 1.98 84 0 0 0 8.33 51 0 0 6.74 21 0 0 2.08 85 0 0 0 8.43 52 0 0 6.88 22 0 0 2.18 86 0 0 0 8.53 53 0 0 7.01 23 0 0 2.28 87 0 0 0 8.63 54 0 0 7.14 24 0 0 2.38 88 0 0 0 8.73 55 0 0 7.27 25 0 0 2.48 89 0 0 0 8.83 56 0 0 7.4 26 0 0 2.58 90 0 0 0 8.93 57 0 0 7.54 27 0 0 2.68 91 0 0 0 9.02 58 0 0 7.67 28 0 0 2.78 92 0 0 0 9.12 59 0 0 7.8 29 0 0 2.88 93 0 0 0 9.22 60 0 0 7.93 ུ 30 0 0 2.98 94 0 0 0 9.32 61 0 0 8.07 31 0 0 3.07 95 0 0 0 9.42 62 0 0 8.2 32 0 0 3.17 96 0 0 0 9.52 63 0 0 8.33 33 0 0 3.27 97 0 0 0 9.62 64 0 0 8.46 34 0 0 3.37 98 0 0 0 9.72 65 0 0 8.6 35 0 0 3.47 99 0 0 0 9.82 66 0 0 8.73 36 0 0 3.57 100 0 0 0 9.92 67 0 0 8.86 37 0 0 3.67 4 by 4 38 0 0 3.77 39 0 0 3.87 456 0 0 0 0.53 68 0 0 8.99 0 0 0.66 69 0 0 9.12 0 0 0 0.79 70 0 0 9.26 40 0 0 3.97 7 0 0 0 0.93 71 0 0 9.39 41 0 0 4.07 8 0 0 0 1.06 72 0 0 9.52 42 0 0 4.17 9 0 0 0 1.19 73 0 0 9.65 43 0 0 4.26 10 0 0 0 1.32 74 0 0 9.79 44 0 0 4.36 11 0 0 0 1.45 75 0 0 9.92 45 0 0 4.46 12 0 0 1.59 76 0 0 10.05 46 0 0 4.56 13 0 0 1.72 77 0 0 10.18 47 0 0 4.66 14 0 0 1.85 78 0 0 10.31 48 0 0 4.76 15 0 0 1.98 79 0 0 10.45 49 0 0 4.86 16 0 0 2.12 80 0 0 10.58 50 0 0 4.96 17 0 0 2,25 81 0 0 10.71 51 0 0 5.06 18 0 0 2,38 82 0 0 10.84 52 0 0 5.16 19 0 0 2.51 83 0 0 10.98 53 0 0 5.26 20 0 0 2.64 84 0 0 11.11 54 0 0 5.36 21 0 0 2.78 85 0 0 11.24 55 0 0 5.45 22 0 0 2,91 86 0 0 11.37 56 0 0 5.55 23 0 0 3.04 87 0 0 11.5 57 0 0 5.65 24 0 0 3.17 88 0 0 11.64 58 0 0 5.75 25 0 0 3.31 89 0 0 11.77 59 0 0 5.85 26 0 0 0 3.44 90 0 0 11.9 232 TABLES OF LAND MEASURE. Dimensions. Yards. Statute content. A. R. P. Dimensions. Statute content. Dimensions. Statute content. Yards. 4 by 91 0 0 12.03 5 by 59 92 0 0 12.17 60 A. R. P. 0 0 9.75 0 0 9.92 Yards. A. R. P. 6 by 28 0 0 5.55 29 0 0 5.75 93 0 0 12.3 61 0 0 10.08 30 0 0 5.95 94 0 0 12.43 62 0 0 10.25 31 0 0 6.15 95 0 0 12.56 63 0 0 10.41 32 0 0 6.35 96 0 0 12.69 64 0 0 10.58 33 0 0 6.55 97 0 0 12.83 65 0 0 10.74 34 0 6.74 98 0 0 12.96 66 0 0 10.91 35 0 0 6.94 99 0 0 13.09 67 0 0 11.07 36 0 0 7.14 100 0 0 13.22 68 0 0 11.24 37 0 0 7.34 5 by 5 0 0 0.83 69 0 0 11.4 38 0 0 7,54 6 0 0 0.99 70 0 0 11.57 39 0 0 7.74 7 0 0 1.16 71 0 0 11.74 40 0 0 7,93 8 0 0 1.32 72 0 0 11.9 41 0 0 8.13 11 13 15 17 POHERCRONO 9 0 0 1.49 73 0 0 12.07 42 0 0 8.33 10 0 0 1.65 74 0 0 12.23 43 0 0 8.53 0 0 1.82 75 0 0 12.4 44 0 0 8.73 12 0 0 1.98 76 0 0 12.56 45 0 0 8.93 0 0 2.15 77 0 0 12.73 46 0 0 9.12 14 0 0 2.31 78 0 0 12.89 47 0 0 9.32 0 0 2.48 79 0 0 13.06 48 0 0 9.52 16 0 0 2.64 80 0 0 13.22 49 0 0 9.72 0 0 2.81 81 0 0 13.39 50 0 0 9.92 18 0 0 2.98 82 0 0 13.55 51 0 0 10.12 19 0 0 3.14 83 0 0 13.72 52 0 0 10.31 20 0 0 3.31 84 0 0 13.88 53 0 0 10.51 21 0 0 3.47 85 0 0 14.05 54 0 0 10.71 22 0 0 3.64 86 0 0 14.21 55 0 0 10.91 23 0 0 3.8 87 0 0 14.38 56 0 0 11.11 24 0 0 3.97 88 0 0 14.55 57 0 0 11.31 25 0 0 4.13 89 0 0 14.71 58 0 0 11.5 26 0 0 4.3 90 0 0 14.88 59 0 0 11.7 27 0 0 4.46 91 0 0 15.04 60 0 0 11.9 28 0 0 4.63 92 0 0 15.21 61 0 0 12.1 29 0 0 4,79 93 0 0 15.37 62 0 0 12.3 30 0 0 4.96 94 0 0 15.54 63 0 0 12.5 31 0 0 5.12 95 0 0 15.7 64 0 0 12.69 32 0 0 5.29 96 0 0 15.87 65 0 0 12.89 33 0 0 5.45 97 0 0 16.03 66 0 0 13.09 34 0 0 5.62 98 0 0 16.2 67 0 0 13.29 35 0 0 5.79 99 0 0 16.36 68 0 0 13.49 36 0 0 5.95 100 0 0 16.53 69 0 0 13.69 37 0 0 6.12 6 by 6 0 0 1.19 70 0 0 13.88 38 0 0 6.28 7 0 0 1.39 71 0 0 14.08 39 0 0 6.45 8 0 0 1.59 བ 72 0 0 14.28 40 0 0 6.61 9 0 0 1.79 73 0 0 14.48 41 0 0 6.78 10 0 0 1.98 74 0 0 14.68 42 0 0 6.94 11 0 0 2.18 75 0 0 14.88 43 0 0 7.11 12 0 0 2.38 76 0 0 15.07 44 0 7.27 13 0 0 2.58 77 0 0 15.27 45 0 0 7,44 14 0 0 2.78 78 0 0 15.47 46 0 7.6 15 0 2.98 79 0 0 15.67 47 0 0 7.77 16 0 0 3.17 80 0 0 15.87 48 0 0 7.93 17 0 0 3.37 81 0 0 16.07 49 0 0 8.10 18 0 0 3.57 82 0 0 16.26 50 0 0 8.26 19 0 0 3.77 83 0 0 16.46 51 0 0 8.43 20 0 0 3.97 84 0 0 16.66 52 0 0 8.6 21 0 0 4.17 85 0 0 16.86 53 0 0 8.76 22 0 0 4.36 86 0 0 17.06 54 0 0 8.93 23 0 0 4.56 87 0 0 17.26 55 0 0 9.09 24 0 0 4.76 88 0 0 17.45 56 0 0 9.26 25 0 4.96 89 0 0 17.65 57 0 0 9.42 26 0 0 5.16 90 0 0 17.85 58 0 0 9.59 27 0 0 0 5.36 91 0 0 18.05 TABLES OF LAND MEASURE. 233 Dimensions. Statute content. Yards. A. R. P. Dimensions. Yards. Statute content. Dimensions. Statute content, A. R. P. Yards. A. R. P. 6 by 92 0 0 18.25 7 by 62 0 0 14.35 8 by 33 0 0 0 8.73 93 0 0 18.45 63 0 0 14.58 34 0 0 0 8.99 94 0 0 18.64 64 0 0 14.81 35 0 0 9.26 95 0 0 18.84 65 0 0 15.04 36 0 0 0 9.52 96 0 0 19.04 66 0 0 15.27 37 0 0 9.79 97 0 0 19.24 67 0 0 15.5 38 0 0 10.05 98 0 0 19.44 68 0 0 15.74 39 0 0 10.31 99 0 0 19.64 69 0 0 15.97 40 0 0 10.58 100 0 0 19.83 70 0 0 16.2 41 0 0 10.84 7 by 7 0 0 1.62 71 0 0 16.43 8 0 0 1.85 72 0 0 16.66 9 0 0 2.08 73 0 0 16.89 *** 42 0 0 11.11 43 0 0 11.37 44 0 0 11.64 10 0 0 2.31 74 0 0.17.12 45 0 0 11.9 11 0 0 2.55 75 0 0 17.36 46 0 0 12.17 12 0 0 2.78 76 0 0 17.59 47 0 0 12.43 13 0 0 0 3.01 77 0 0 17.82 48 0 0 12.69 14 0 0 0 3.24 78 0 0 18.05 49 0 0 12.96 15 0 3.47 79 0 0 18.28 50 0 0 13.22 16 0 0 3.7 80 0 0 18.51 51 0 0 13.49 17 0 0 3.93 81 0 0 18.74 52 0 0 13.75 18 0 0 4.17 82 0 0 18.98 53 0 0 14.02 19 0 0 4.4 83 0 0 19.21 54 0 0 14.28 20 0 0 4.63 84 0 0 19.44 55 0 0 14.55 21 0 0 4.86 85 0 0 19.67 56 0 0 14.81 22 0 0 5.09 86 0 0 19.9 57 0 0 15.07 23 0 0 5.32 87 0 0 20.13 58 0 0 15.34 24 0 0 5.55 88 0 0 20.36 59 0 0 15.6 25 0 0 5.79 89 0 0 20.6 60 0 0 15.87 26 0 0 6.02 90 0 0 20.83 61 0 0 16.13 27 0 0 6.25 91 0 0 21.06 62 0 0 16.4 28 0 0 6.48 92 0 0 21.29 63 0 0 16.66 29 0 0 6.71 93 0 0 21.52 64 0 0 16.93 30 0 0 6.94 94 0 0 21.75 65 0 0 17.19 31 0 0 0 7.17 95 0 0 21.98 66 0 0 17.45 32 0 0 7.4 96 0 0 22.21 67 0 0 17.72 33 0 0 7.64 97 0 0 22.45 68 0 0 17.98 34 0 0 7.87 98 0 0 22.68 69 0 0 18.25 35 0 0 8.1 99 0 0 22.91 70 0 0 18.51 36 0 0 8.33 100 0 0 23.14 71 0 0 18.78 37 0 0 8.56 8 by 8 0 0 2.12 72 0 0 19.04 38 0 0 8.79 9 0 0 2.38 73 0 0 19.31 39 0 0 9.02 10 0 0 2.64 74 0 0 19.57 40 0 0 9.26 11 0 0 2.91 75 0 0 19.83 41 0 0 9.49 12 0 0 3.17 76 0 0 20.1 ***** 42 0 0 0 9.72 13 0 0 3.44 77 0 0 20.36 43 0 0 9.95 14 0 0 3.7 78 0 0 20.63 44 0 0 10.18 15 0 0 3.97 79 0 0 20.89 45 0 0 10.41 16 0 0 4.23 80 0 0 21.16 46 0 0 10.64 17 0 0 4.5 81 0 0 21.42 47 0 0 10.88 18 0 0 4.76 82 0 0 21.69 48 0 0 11.11 19 0 0.5.02 83 0 0 21.95 49 0 0 11.34 20 0 0 5.29 84 0 0 22.21 50 0 0 11.57 21 0 0 5.55 85 0 0 22.48 51 0 0 11.8 22 0 0 5.82 86 0 0 22.74 52 0 0 12.03 23 0 0 6.08 87 0 0 23.01 53 0 0 12.26 24 0 0 6.35 88 0 0 23.27 54 0 0 12.5 25 0 0 6.61 89 0 0 23.54 55 0 0 12.73 26 0 0 6.88 90 0 0 23.8 56 0 0 12.96 27 0 0 7.14 91 0 24.07 57 0 0 13.19 28 0 0 7.4 92 0 0 24.33 58 0 0 13.42 29 0 0 7.67 93 0 0 24.6 59 0 0 13.65 30 0 0 0 7.93 94 0 0 24.86 60 0 0 13.88 31 0 0 0 8.20 95 0 0 25.12 61 0 0 14.12 32 0 0 8.46 96 0 0 25.39 Ꭱ R 234 TABLES OF LAND MEASURE. Dimensions. Statute content. Dimensions. Statute content. Dimensions. Statute content. Yards, A. R. P. Yards. + A. R. P. Yards. 8 by 97 0 0 25.65 9 by 69 0 0 20.53 10 by 42 A. R. P. 0 0 13.88 98 0 0 25.92 70 0 0 20.83 43 0 0 14.21 99 0 26.18 71 0 0 21.12 44 0 0 14.55 100 0 0 26.45 72 0 0 21.42 45 0 0 14.88 9 by 9 0 0 2.68 73 0 0 21.72 46 0 0 15.21 10 0 0 2.98 74 0 0 22.02 47 0 0 15.54 11 0 0 3.27 75 0 0 22.31 48 0 0 15.87 12 0 0 3.57 76 0 0 22.61 49 0 0 16.2 13 0 0 3.87 77 0 0 22.91 50 0 0 16.53 14 0 0 4.17 78 0 0 23.21 51 0 0 16.86 15 0 4.46 79 0 0 23.5 52 0 0 17.19 16 0 4.76 80 0 0 23.8 53 0 0 17.52 17 0 0 5.06 81 0 0 24.1 54 0 0 17.85 18 0 0 5.36 82 0 0 24.4 55 0 0 18.18 19 0 0 5.65 83 0 0 24.69 56 0 0 18.51 20 0 0 5.95 84 0 0 24.99 57 0 0 18.84 21 0 0 6.25 85 0 0 25.29 58 0 0 19.17 22 0 0 6.55 86 0 0 25.59 59 0 0 19.5 23 0 0 6.84 87 0 0 25.88 60 0 0 19.83 24 0 0 7.14 88 0 0 26.18 61 0 0 20.17 25 0 0 7.44 89 0 0 26.48 62 0 20.5 26 0 0 7.74 90 0 0 26.78 63 0 20.83 27 0 0 8.03 91 0 0 27.07 64 0 21.16 28 0 0 8.33 92 0 0 27.37 65 0 0 21.49 29 0 0 8.63 93 0 0 27.67 66 0 0 21.82 30 0 0 8.93 94 0 0 27.97 67 0 0 22.15 31 0 0 9.22 95 0 0 28.26 68 0 0 22.48 32 0 9.52 96 0 0 28.56 69 0 0 22.81 33 0 9.82 97 0 0 28.86 70 0 23.14 34 0 0 10.12 98 0 0 29.16 71 0 0 23.47 35 0 10.41 99 0 0 29.45 72 0 0 23.8 36 0 0 10.71 100 0 0 29.75 73 0 0 24.13 37 0 0 11.01 10 by 10 0 0 3.31 74 0 0 24.46 38 0 0 11.31 11 0 0 3.64 75 0 0 24.79 39 0 0 11.6 12 0 0 3.97 76 0 25.12 40 0 0 11.9 13 0 0 4.3 77 0 25.45 41 0 0 12.2 14 0 0 4.63 78 0 0 25.79 42 0 0 12.5 15 0 0 4.96 79 0 0 26.12 43 0 0 12.79 16 0 0 5.29 80 0 0 26.45 44 0 0 13.09 17 0 0 5.62 81 0 0 26.78 45 0 0 13.39 18 0 0 5.95 82 0 0 27.11 46 0 0 13.69 19 0 0 6.28 83 0 0 27.44 47 0 0 13.98 20 0 0 6.61 84 0 0 27.77 48 0 0 14.28 21 0 0 6.94 85 0 0 28.1 49 0 0 14.58 22 0 0 7.27 86 0 0 28.43 50 0 0 14.88 23 0 0.7.6 87 0 0 28.76 51 0 0 15.17 24 0 0 7.93 88 0 0 29.09 52 0 0 15.47 25 0 0 8.26 89 0 0 29.42 53 0 0 15.77 26 0 0 8.6 90 0 0 29.75 54 0 0 16.07 27 0 0 8.93 91 0 0 30.08 55 0 0 16.36 28 0 0 9.26 92 0 0 30.41 56 0 0 16.66 29 0 0 9.59 93 0 0 30.74 57 0 0 16.96 30 0 0 9.92 94 0 0 31.07 58 0 0 17.26 31 0 0 10.25 95 0 0 31.4 59 0 0 17.55 32 0 0 10.58 96 0 0 31.74 60 0 0 17.85 33 0 0 10.91 97 0 0 32.07 61 0 0 18.15 34 0 0 11.24 98 0 0 32.4 62 0 0 18.45 35 0 0 11.57 99 0 0 32.73 63 0 0 18.74 36 0 0 11.9 100 0 0 33.06 64 0 0 19.04 37 0 0 12.23 11 by 11 0 0 4. 65 0 0 19.34 38 0 0 12.56 12 0 0 4.36 66 0 0 19.64 39 0 0 12.89 13 0 0 4.73 67 0 0 19.93 40 0 0 13.22 14 0 0 5.09 68 0 0 20.23 41 0 0 13.55 15 0 0 5.45 TABLES OF LAND MEASURE. 235 Dimensions. Statute content. Yards. A. R. P. Dimensions. Yards. Statute content. Dimensions. A. R. P. Yards. Statute content. A. R. P. 11 by 16 0 0 5.82 11 by 80 0 0 29.19 12 by 55 0 0 21.82 17 0 0 0 6.18 81 0 0 29.56 56 0 0 22.21 18 0 0 6.55 82 0 0 29.92 57 0 0 22.61 19 0 0 0 6.91 83 0 0 30.28 58 0 0 23.01 20 0 0 7.27 84 0 0 30.65 59 0 0 23.4 21 0 0 0 7.64 85 0 0 31.01 60 0 0 23.8 22 0 8. 86 0 0 31.37 61 0 0 24.2 23 0 8.36 87 0 0 31.74 62 0 0 24.6 24 0 8.73 88 0 0 32.1 63 0 0 24.99 25 0 9.19 89 0 0 32.46 64 0 0 25.39 26 0 0 0 9.56 90 0 0 32.83 65 0 0 25.79 27 0 0 9.92 91 0 0 33.19 66 0 0 26.18 28 0 0 10.28 92 0 0 33.56 67 0 0 26.58 29 0 0 10.65 93 0 0 33.92 68 0 0 26.98 30 0 0 11.01 94 0 0 34.28 69 0 0 27.37 31 0 0 11.37 95 0 0 34.65 70 0 0 27.77 32 0 0 11.74 96 0 0 35.01 71 0 0 28.17 33 0 0 12.1 97 0 0 35.37 72 0 0 28.56 34 0 0 12.46 98 0 0 35.74 73 0 0 28.96 35 0 0 12.83 99 0 0 36.1 74 0 0 29.36 36 0 0 13.19 100 0 0 36.46 75 0 0 29.75 37 0 0 13.56 12 by 12 0 0 4.76 76 0 0 30.15 38 0 0 13.92 13 0 0 5.16 77 0 0 30.55 39 0 0 14.28 14 0 0 5.55 78 0 0 30.94 40 0 0 14.65 15 0 0 5.95 79 0 0 31.34 41 0 0 15.01 16 0 0 6.35 80 0 0 31.74 42 0 0 15.37 17 0 6.74 81 0 0 32.13 43 0 0 15.74 18 0 0 7.14 82 0 0 32.53 44 0 0 16.1 19 0 7.54 83 0 0 32.93 45 0 0 16.46 20 0 0 7.93 84 0 0 33.32 46 0 0 16.83 21 0 0 8.33 85 0 0 33.72 47 0 0 17.19 22 0 0 8.73 86 0 0 34.12 48 0 0 17.56 23 0 9.12 87 0 0 34.51 49 0 0 17.92 24 0 0 0 9.52 88 0 0 34.91 50 0 0 18.28 25 0 0 9.92 89 0 0 35.31 51 0 0 18.65 26 0 0 10.31 90 0 0 35.7 52 0 0 19.01 27 0 0 10.71 91 0 0 36.1 53 0 0 19.37 28 0 0 11.11 92 0 0 36.5 54 0 0 19.74 29 0 0 11.5 93 0 0 36.89 55 0 0 20.1 30 0 0 11.9 94 0 0 37.29 56 0 0 20.46 31 0 0 12.3 95 0 0 37.69 57 0 0 20.83 32 0 0 12.69 96 0 0 38.08 58 0 0 21.19 33 0 0 13.09 97 0 0 38.48 59 0 0 21.56 34 0 0 13.49 98 0 0 38.88 60 0 0 21.92 35 0 0 13.88 99 0 0 39.27 61 0 0 22.28 36 0 0 14.28 100 0 0 39.67 62 0 0 22.65 37 0 0 14.68 13 by 13 0 0 5.59 63 0 0 23.01 38 0 0 15.07 14 0 6.02 64 0 0 23.37 39 0 0 15.47 15 0 0 6.45 65 0 0 23.74 40 0 0 15.87 16 0 0 6.88 66 0 0 24.1 41 0 0 16.26 17 0 0 0 7.31 67 0 0 24.46 42 0 0 16.66 18 0 0 0 7.73 68 0 0 24.83 43 0 0 17.06 19 0 0 0 8.17 69 0 0 25.19 44 0 0 17.45 20 0 0 0 8.6 70 0 25.56 45 0 0 17.85 21 0 0 0 9.02 222 71 0 25.92 46 0 0 18.25 22 0 0 9.45 72 0 0 26.28 47 0 0 18.64 23 0 0 9.88 73 0 0 26.65 48 0 0 19.04 24 0 0 10.31 74 0 0 27.01 49 0 0 19.44 25 0 0 10.74 75 0 0 27.37 50 0 0 19.83 26 0 0 11.17 76 0 0 27.74 51 0 0 20.23 27 0 0 11.6 77 0 0 28.1 52 0 0 20.63 78 0 0 28.46 53 0 0 21.02 79 0 0 28.83 54 0 0 21.42 888 28 0 0 12.03 29 0 0 12.46 30 0 0 12.89 236 TABLES OF LAND MEASURE. Dimensions. Yards. Statute content. Dimensions. Statu e content. Dimensions. Statute content. A. R. P. Yards. A. R. P. Yards. A. R. P. 13 by 31 0 0 13.32 13 by 95 0 1 0.83 14 by 72 0 0 33.32 32 0 0 13.75 96 0 1 1.26 73 0 0 33.79 33 0 0 14.18 97 0 1 1.69 74 0 0 34.25 34 0 0 14.61 98 0 1 2.12 75 0 0 34.71 35 0 0 15.04 99 0 1 2.55 76 0 0 35.17 36 0 0 15.47 100 0 1 2.98 77 0 0 35.64 37 0 0 15.9 14 by 14 0 0 6.48 78 0 0 36.1 38 0 0 16.33 15 0 0 6.94 79 0 0 36.56 39 0 0 16.76 16 0 0 7.4 80 0 0 37.02 40 0 0 17.19 17 0 0 7.87 81 0 0 37.49 41 0 0 17.62 18 0 0 8.33 82 0 0 37.95 42 0 0 18.05 19 0 0 8.79 83 0 0 38.41 43 0 0 18.48 20 0 0 9.26 84 0 0 38.88 44 0 0 18.91 21 0 0 9.72 85 0 0 39.34 45 0 0 19.34 22 0 0 10.18 86 0 0 39.8 46 0 0 19.77 23 0 0 10.64 87 0 1 1 0.26 47 0 0 20.2 24 0 0 11.11 88 0 1 1 0.73 48 0 0 20.63 25 0 0 11.57 89 0 1 1.19 49 0 21.06 26 0 0 12.03 90 0 1 1.65 50 0 21.49 27 0 0 12.5 91 0 1 2.12 51 0 21.92 28 0 0 12.96 92 0 1 2.58 52 0 0 22.35 29 0 0 13.42 93 0 1 3.04 53 0 0 22.78 30 0 0 13.88 94 0 1 1 3.5 54 0 0 23.21 31 0 0 14.35 95 0 1 1 3.97 55 0 0 23.64 32 0 0 14.81 96 0 1 4.43 56 0 0 24.07 33 0 0 15.27 97 0 1 4.89 57 0 0 24.5 34 0 0 15.74 98 0 1 5.36 58 0 0 24.93 35 0 16.2 99 0 1 5.82 59 0 0 25.36 36 0 0 16.66 100 0 1 6.28 60 0 0 25.79 37 0 0 17.12 15 by 15 0 0 7.44 61 0 0 26.21 38 0 0 17.59 16 0 0 7.93 62 0 0 26.64 39 0 0 18.05 17 0 0 8.43 63 0 0 27.07 40 0 18.51 18 0 0 8.93 64 0 0 27.5 41 0 0 18.98 19 0 0 9.42 65 0 0 27.93 42 0 0 19.44 20 0 0 9.92 66 0 0 28.36 43 0 0 19.9 21 0 0 10.41 67 0 0 28.79 44 0 0 20.36 22 0 0 10.91 68 0 0 29.22 45 0 0 20.83 23 0 0 11.4 69 0 0 29.65 46 0 0 21.29 24 0 0 11.9 70 0 0 30.08 47 0 0 21.75 25 0 0 12.4 71 0 0 30.51 48 0 0 22.21 26 0 0 12.89 72 0 0 30.94 49 0 0 22.68 27 0 0 13.39 73 0 0 31.37 50 0 0 23.14 28 0 0 13.88 74 0 0 31.8 51 0 23.6 29 0 0 14.38 75 0 0 32.23 52 0 0 24.07 30 0 0 14.88 76 0 0 32.66 53 0 24.53 31 0 0 15.37 77 0 0 33.09 54 0 0 24.99 32 0 0 15.87 78 0 0 33.52 55 0 0 25.45 33 0 0 16.36 79 0 0 33.95 56 0 0 25.92 34 0 0 16.86 80 0 0 34.38 57 0 0 26.38 35 0 0 17.36 81 0 0 34.81 58 0 0 26.84 36 0 0 17.85 82 0 0 35.24 59 0 27.31 37 0 0 18.35 83 0 0 35.67 60 0 O 27.77 38 0 0 18.84 84 0 0 36.1 61 0 28.23 39 0 0 19.34 85 0 0 36.53 62 0 0 28.69 40 0 0 19.83 86 0 0 36.96 63 0 0 29.16 41 0 0 20.33 87 0 0 37.39 64 0 0 29.62 42 0 0 20.83 88 0 0 37.82 65 0 0 30.08 43 0 0 21.32 89 0 0 38.25 66 0 0 30,55 44 0 0 21.82 90 0 0 38.68 67 0 0 31.01 45 0 0 22.31 91 0 0 39.11 68 92 0 0 39.54 93 0 0 39.97 94 0 1 0.4 71 228: 0 0 31.47 46 0 0 22.81 69 0 0 31.93 47 0 0 23.31 70 0 0 32.4 48 0 0 23.8 0 0 32.86 49 0 0 24.3 TABLES OF LAND MEASURE. 237 Dimensions. Statute content. Yards. A. R. P. Dimensions. Yards. Statute content. Dimensions. Statute content. A. R. P. Yards. A. R. P. 15 by 50 0 0 21.79 16 by 29 0 0 15.34 16 by 93 0 1 9.19 51 0 0 25.29 30 0 0 15.87 94 0 1 9.72 52 0 0 25.79 31 0 0 16.4 95 0 1 10.25 53 0 0 26.28 32 0 0 16.93 96 0 1 10.78 54 0 0 26.78 33 0 0 17.45 97 0 1 11.31 55 0 0 27.27 34 0 0 17.98 98 0 1 11.83 56 0 0 27.77 35 0 0 18.51 99 0 1 12.36 57 0 0 28.26 36 0 0 19.04 100 0 1 12.89 58 0 0 28.76 37 0 0 19.57 17 by 17 0 0 9.55 59 0 0 29.26 38 0 0 20.1 18 0 0 10.12 60 0 0 29.75 39 0 0 20.63 19 0 0 10.68 61 0 0 30.25 40 0 0 21.16 20 0 0 11.24 62 0 0 30.74 41 0 0 21.69 21 0 0 11.8 63 0 0 31.24 42 0 0 22.21 22 0 0 12.36 64 0 0 31.74 43 0 0 22.74 23 0 0 12.93 65 0 0 32.23 44 0 0 23.27 24 0 0 13.49 66 0 0 32.73 45 0 0 23.8 25 0 14.05 67 0 0 33.22 46 0 0 24.33 26 0 0 14.61 68 0 0 33.72 47 0 0 24.86 27 0 0 15.17 69 0 0 34.21 48 0 0 25.39 28 0 0 15.74 70 0 0 34.71 49 0 0 25.92 29 0 0 16.3 71 0 0 35.21 50 0 26.45 30 0 0 16.86 72 0 0 35.7 51 0 0 26.98 31 0 0 17.42 73 Ꮳ 0 36.2 52 0 0 27.5 32 0 0 17.98 74 0 0 36.69 53 0 0 28.03 33 0 0 18.55 75 .0 0 37.19 54 0 0 28.56 34 0 0 19.11 76 0 0 37.69 55 0 0 29.09 35 0 0 19.67 77 0 0 38.18 56 0 0 29.62 36 0 0 20.23 78 0 0 38.68 57 0 0 30.15 37 0 0 20.79 79 0 0 39.17 58 0 0 30.68 38 0 0 21.36 80 0 0 39.67 59 0 0 31.21 39 0 0 21.92 81 0 1 0.17 60 0 0 31.74 40 0 0 22.48 82 0 1 0.66 61 0 0 32.26 41 0 0 23.04 83 0 1 1.16 62 0 0 32.79 42 0 0 23.6 84 0 1 1.65 63 0 0 33.32 43 0 24.17 85 0 1 2.15 64 0 0 33.85 44 0 0 24.73 85 86 0 1 2.64 65 0 0 34.38 45 0 25.29 87 0 1 3.14 66 0 0 34.91 46 0 0 25.85 88 0 1 3.64 67 0 0 35.44 47 0 0 26.41 89 0 1 4.13 68 0 0 35.97 48 0 0 26.98 90 0 1 4.63 69 0 0 36.5 49 0 0 27.54 91 0 1 5.12 70 0 0 37.02 50 0 28.1 92 0 1 5.62 71 0 0 37.55 51 0 0 28.66 93 0 1 6.12 72 0 0 38.08 52 0 0 29.22 94 0 1 6.61 73 0 0 38.61 53 0 0 29.79 95 0 1 7.11 74 0 0 39.14 54 0 0 30.35 96 0 1 7.6 75 0 0 39.67 55 0 30.91 97 0 1 8.1 76 0 1 0.2 56 0 0 31.47 98 0 1 8.6 77 0 1 0.73 57 0 32.03 99 0 1 9.09 78 0 1 1.26 58 0 0 32.6 100 0 1 9.59 79 0 1 1.79 59 0 0 33.16 16 by 16 0 0 8.46 80 0 1 2.31 60 0 0 33.72 17 0 0 8.99 81 0 1 2.84 61 0 0 34.28 18 0 0 9.52 82 0 1 3.37 62 0 0 34.84 19 0 0 10.05 83 0 1 3.9 63 0 0 35.4 20 0 0 10.58 84 0 1 4.43 64 0 0 35.97 21 0 0 11.11 85 0 1 4.96 65 0 0 36.53 22 0 0 11.64 86 0 1 5.49 66 0 0 37.09 23 0 0 12.17 87 0 1 1 6.02 67 0 0 37.65 24 0 0 12.69 88 0 1 1 6.55 68 0 38.21 25 0 0 13.22 89 0 1 1 7.07 26 0 0 13.75 90 0 1 7.6 27 0 0 14.28 91 0 1 1 8.13 28 0 0 14.81 92 0 1 8.66 SCEN 69 0 0 38.78 70 0 0 39.34 0 0 39.9 72 0 1 0.46 TABLES OF LAND MEASURE. 238 Dimensions. Statute content. Dimensions. Statute content. Dimensions. Statute content. Yards. A. R. P. Yards. A. R. P. Yards. A. R. P. 17 by 73 0 1 1.02 18 by 54 0 0 32.13 19 by 36 0 0 22.61 74 0 1 1.59 55 0 0 32.73 37 0 0 23.24 75 0 1 2.15 56 0 0 33.32 38 0 0 23.87 76 0 1 2.71 57 0 0 33.92 39 0 0 24.5 77 0 1 3.27 58 0 0 34.51 40 0 0 25.12 78 0 1 3.83 59 0 0 35.11 41 0 0 25.75 79 0 1 4.4 60 0 0 35.7 42 0 0 26.38 80 0 1 4.96 61 0 0 36.3 43 0 0 27.01 81 0 1 5.52 62 0 0 36.89 44 0 0 27.64 82 0 1 6.08 63 0 0 37.49 45 0 0 28.26 83 0 1 6.64 64 0 0 38.08 46 0 0 28.89 84 0 1 7.21 65 0 0 38.68 47 0 0 29.52 85 0 1 7.77 66 0 0 39.27 48 0 0 30.15 86 0 1 8.33 67 0 0 39.87 49 0 0 30.78 87 0 1 8.89 68 0 1 0.46 50 0 0 31.4 88 0 1 9.45 69 1 1.06 51 0 0 32.03 89 0 1 10.02 70 0 1 1.65 52 0 0 32.66 90 0 1 10.58 71 0 1 2.25 53 0 0 33.29 91 0 1 11.14 72 0 1 2.84 54 0 0 33.92 92 0 1 11.7 73 0 1 3.44 55 0 0 34.55 93 0 1 12.26 74 0 1 4.03 56 0 0 35.17 94 0 1 12.83 75 0 1 4.63 57 0 0 35.8 95 0 1 13.39 76 0 1 5.22 58 0 0 36.43 96 0 1 13.95 77 0 1 5.82 59 0 0 37.06 97 0 1 14.51 78 0 1 6.41 60 0 0 37.69 98 0 1 15.07 79 0 1 7.01 61 0 0 38.31 99 0 1 15.64 80 0 1 7.6 62 0 0 38.94 100 0 1 16.2 81 0 1 8.2 63 0 0 39.57 18 by 18 0 0 10.71 82 0 1 8·79 64 0 1 0.2 19 0 11.31 83 0 1 9.39 65 0 1 0.83 20 0 0 11.9 84 0 1 9.98 66 0 1 1.45 21 0 0 12.5 85 0 1 10.58 67 0 1 2.08 22 0 0 13.09 86 0 1 11.17 68 0 1 2.71 23 0 0 13.69 87 0 1 11.77 69 0 1 3.34 24 0 0 14.28 88 0 1 12.36 70 0 1 3.97 25 0 0 14.88 89 0 1 12.96 71 0 1 4.6 26 0 0 15.47 90 0 1 13.55 72 0 1 5.22 27 0 0 16.07 91 0 1 14.15 73 0 1 5.85 28 0 0 16.66 92 0 1 14.74 74 0 1 6.48 29 0 0 17.26 93 0 1 15.34 75 0 1 7.11 30 0 0 17.85 94 0 1 15.93 76 0 1 7.74 31 0 0 18.45 95 0 1 16.53 77 0 1 8.36 32 0 0 19.04 96 0 1 17.12 78 0 1 8.99 33 0 0 19.64 97 0 1 17.72 79 0 1 1 9.62 34 0 0 20.23 98 0 1 18.31 80 0 1 10.25 35 0 0 20.83 99 0 1 18.91 81 0 1 10.88 36 0 0 21.42 100 0 1 19.5 82 0 1 11.5 37 0 0 22.02 19 by 19 0 0 11.93 83 0 1 12.13 38 0 0 22.61 20 0 0 12.56 84 0 1 12.76 39 0 0 23.21 21 0 0 13.19 85 0 1 13.39 40 0 0 23.8 22 0 0 13.82 86 0 1 14.02 41 0 0 24.4 23 0 0 14.45 87 0 1 14.64 42 0 0 24.99 24 0 0 15.07 88 0 1 15.27 43 0 0 25.59 25 0 0 15.7 89 0 1 15.9 44 0 0 26.18 26 0 0 16.33 90 0 1 16.53 45 0 0 26.78 27 0 0 16.96 91 0 1 17.16 46 0 0 27.37 28 0 0 17.59 92 0 1 17.79 47 0 0 27.97 29 0' 0 18.21 93 0 1 18.41 48 0 0 28.56 30 0 18.84 94 0 1 19.04 49 0 0 29.16 31 0 19.47 95 0 1 19.67 50 0 0 29.75 32 0 0 20.1 96 0 1 20.3 51 0 0 30.35 33 0 0 20.73 97 0 1 20.93 52 0 0 30.94 34 0 0 21.36 98 0 1 21.55 53 0 0 31.54 35 0 0 21.98 99 0 1 22.18 TABLES OF LAND MEASURE. 239 Dimensions. Statute content. Dimensions. Statute content. Dimensions. Statute content. iards. A. R. P. Yards. A. R. P. Yards. A. R. P. 19 by 100 20 by 20 0 1 22.81 20 by 83 0 1 14.88 21 by 67 0 1 6.51 0 0 13.22 84 0 1 15.54 68 0 1 7.21 21 0 0 13.88 85 0 1 16.2 69 0 1 7.9 22 0 0 14.55 86 0 1 16.86 70 0 1 8.6 23 0 0 15.21 87 0 1 17.52 71 0 1 9.29 24 0 0 15.87 88 0 1 18.18 72 0 1 9.98 25 0 0 16.53 89 0 1 18.84 73 0 1 10.68 26 0 0 17.19 90 0 1 19.5 74 0 1 11.37 27 0 0 17.85 91 0 1 20.17 75 0 1 12.07 28 0 0 18.51 92 0 1 20.83 76 0 1 12.76 29 0 0 19.17 93 0 1 21.49 77 0 1 13.45 30 0 0 19.83 94 0 1 22.15 78 0 1 14.15 31 0 0 20.5 95 0 1 22.81 79 0 1 14.84 32 0 0 21.16 96 0 1 23.47 80 0 1 15.54 33 0 0 21.82 97 0 1 24.13 81 0 1 16.23 34 0 0 22.48 98 0 1 24.79 82 0 1 16.93 35 0 0 23.14 99 0 1 25.45 83 0 1 17.62 36 0 0 23.8 100 0 1 26.12 84 0 1 18.31 37 0 0 24.46 21 by 21 0 0 14.58 85 0 1 19.01 38 0 0 25.12 22 0 0 15.27 86 0 1 19.7 39 0 0 25.79 23 0 0 15.97 87 0 1 20.4 40 0 0 26.45 24 0 0 16.66 88 0 1 21.09 41 0 0 27.11 25 0 0 17.36 89 0 1 21.79 42 0 0 27.77 26 0 0 18.05 90 0 1 22.48 43 0 0 28.43 27 0 0 18.74 91 0 1 23.17 44 0 0 29.09 28 0 0 19.44 92 0 1 23.87 45 0 0 29.75 29 0 0 20.13 93 0 1 24.56 46 0 0 30.41 30 0 0 20.83 94 0 1 25.26 47 0 0 31.07 31 0 0 21.52 95 0 1 25.95 48 0 0 31.74 32 0 0 22.21 96 0 1 26.64 49 0 0 32.4 33 0 0 22.91 97 0 1 27.34 50 0 0 33.06 34 0 0 23.6 98 0 1 28.03 51 0 0 33.72 35 0 0 24.3 99 0 1 28.73 52 0 0 34.38 36 0 0 24.99 100 0 1 29.42 53 0 0 35.04 37 0 0 25.69 22 by 22 0 0 16. 54 0 0 35.7 38 0 0 26.38 23 0 0 16.73 55 0 0 36.36 39 0 0 27.07 24 0 0 17.45 56 0 0 37.02 40 0 0 27.77 25 0 0 18.18 57 0 37.69 41 0 0 28.46 26 0 0 18.91 58 0 0 38.35 42 0 0 29.16 27 0 0 19.64 59 0 0 39.01 43 0 0 29.85 28 0 0 20.36 60 0 0 39.67 44 0 0 30.55 29 0 0 21.09 61 0 1 1 0.33 45 0 0 31.24 30 0 0 21.82 62 0 1 1 0.99 46 0 0 31.93 31 0 0 22.55 63 0 1 1.65 47 0 0 32.63 32 0 0 23.27 64 0 1 2.31 48 0 0 33.32 33 0 0 24. 65 0 1 2.98 49 0 0 34.02 34 0 0 24.73 66 0 1 3.64 50 0 0 34.71 35 0 0 25.45' 67 0 1 4.3 51 0 0 35.4 36 0 0 26.18 68 0 1 4.96 52 0 0 36.1 37 0 0 26.91 69 0 1 5.62 53 0 0 36.79 38 0 0 27.64 70 0 1 6.28 54 0 0 37.49 39 0 28.36 71 0 1 6.94 55 0 0 38.18 40 0 29.09 72 0 1 7.6 56 0 0 38.88 41 0 0 29.82 73 0 1 8.26 57 0 0 39.57 42 0 0 30.55 74 0 1 8.93 58 0 1 0.26 43 0 0 31.27 75 0 1 9.59 59 0 1 0.96 44 0 0 32. 76 0 1 10.25 60 0 1 1.65 45 0 0 32.73 77 1 10.91 61 0 1 2.35 46 0 0 33.45 78 0 1 11.57 62 0 1 3.04 47 0 0 34.18 79 0 1 12.23 80 0 1 12.89 81 0 1 13.55 65 82 0 1 14.21 66 3+38 63 0 1 3.74 48 0 0 34.91 64 0 1 4.43 49 0 0 35.64 0 1 5.12 50 0 0 36.36 0 1 5.82 51 0 0 37.09 240 TABLES OF LAND MEASURE. Dimensions. Statute content. Dimensions. Statute content. Dimensions. Statute content. Yards. A. R. P. Yards. A. R. P. Yards. A. R. P. 22 by 52 0 0 37.82 23 by 38 0 0 28.89 24 by 25 0 0 19.83 53 0 0 38.55 39 0 0 29.65 26 0 0 20.63 54 0 0 39.27 40 0 0 30.41 27 0 0 21.42 55 0 1 0. 41 0 0 31.17 28 0 0 22.21 56 0 1 0.73 42 0 0 31.93 29 0 0 23.01 57 0 1 1 1.45 43 0 0 32.69 30 0 0 23.8 58 0 1 2.18 44 0 0 33.45 31 0 0 24.6 59 0 1 2.91 45 0 0 34.21 32 0 0 25.39 60 0 1 3.64 46 0 0 34.98 33 0 0 26.18 61 0 1 4.36 47 0 0 35.74 34 0 0 26.98 62 0 1 1 5.09 48 0 0 36.5 35 0 0 27.77 63 0 1 5.82 49 0 0 37.26 36 0 0 28.56 64 0 1 6.55 50 0 0 38.02 37 0 0 29.36 65 66 67 68 70 71 72 88508RENOLE 0 1 1 7.27 51 0 0 38.78 38 0 0 30.15 0 1 8. 52 0 0 39.54 39 0 0 30.94 0 1 8.73 53 0 1 1 0.3 40 0 0 31.74 0 1 9.45 54 0 1 1.06 41 0 0 32.53 69 0 1 10.18 55 0 1 1.82 42 0 0 33.32 0 1 10.91 56 0 1 2.58 43 0 0 34.12 0 1 11.64 57 0 1 3.34 44 0 0 34.91 0 1 12.36 58 0 1 4.1 45 0 0 35.7 73 0 1 13.09 59 0 1 4.86 46 0 0 36.5 74 0 1 13.82 60 0 1 5.62 47 0 0 37.29 75 0 1 14.55 61 0 1 6.38 48 0 0 38.08 76 0 1 15.27 62 0 1 7.14 49 0 0 38.88 77 0 1 16. 63 0 1 7.9 50 0 0 39.67 78 0 1 16.73 64 0 1 8.66 51 0 1 1 0.46 79 0 1 17.45 65 0 1 9.42 52 0 1 1 1.26 80 0 1 18.18 66 0 1 10.18 53 0 1 2.05 81 0 1 18.91 67 0 1 10.94 54 0 1 2.84 82 0 1 19.64 68 0 1 11.7 55 0 1 1 3.64 83 0 1 20.36 69 0 1 12.46 56 0 1 1 4.43 84 0 1 21.09 70 0 1 13.22 57 0 1 1 5.22 85 0 1 21.82 71 0 1 13.98 58 0 1 1 6.02 86 0 1 22.55 72 0 1 14.74 59 0 1 1 6.81 87 0 1 23.27 73 0 1 15.5 60 0 1 1 7.6 88 0 1 24. 74 0 1 16.26 61 0 1 1 8.4 89 0 1 24.73 75 0 1 17.02 62 0 1 9.19 90 0 1 25.45 76 0 1 17.79 63 0 1 1 9.98 31 0 1 26.18 77 0 1 18.55 64 0 1 10.78 92 0 1 26.91 78 0 1 19.31 65 0 1 11.57 93 0 1 27.64 79 0 1 20.07 66 0 1 12.36 94 0 1 28.36 80 0 1 20.83 67 0 1 13.16 95 0 1 29.09 81 0 1 21.59 68 0 1 13.95 96 0 1 29.82 82 0 1 22.35 69 0 1 14.74 97 0 1 30.55 83 0 1 23.11 70 0 1 15.54 98 0 1 31.27 84 0 1 23.87 71 0 1 16.33 99 0 1 32. 85 0 1 24.63 72 0 1 17.12 100 0 1 32.73 86 0 1 25.39 73 0 1 17.92 23 by 23 0 0 17.49 87 0 1 26.15 74 0 1 18.71 24 0 0 18.25 88 0 1 26.91 75 0 1 19.5 25 0 0 19.01 89 0 1 27.67 76 0 1 20.3 26 0 0 19.77 90 0 1 28.43 77 0 1 21.09 27 0 0 20.53 91 0 1 29.19 78 0 1 21.88 28 0 0 21.29 92 0 1 29.95 79 0 1 22.68 29 0 0 22.05 93 0 1 30.71 80 0 1 23.47 30 0 0 22.81 94 0 1 31.47 81 0 1 24.26 31 0 0 23.57 95 0 1 32.23 82 0 1 25.06 32 0 0 24.33 96 0 1 32.99 83 0 1 25.85 33 0 0 25.09 97 0 1 33.75 84 0 1 26.64 34 0 0 25.85 98 0 1 34.51 85 0 1 27.44 35 0 0 26.61 99 0 1 35.27 86 0 1 28.23 36 0 0 27.37 100 0 1 36.03 87 0 1 29.02 37 0 0 28.13 24 by 24 0 0 19.04 88 0 1 29.82 TABLES OF LAND MEASURE. 241 • Dimensions. Yards. Statute content. A. R. P. Dimensions. Yards. Statute content. Dimensions. Statute content. 24 by 89 0 1 30.61 25 by 77 A. R. P. 0 1 23.64 Yards. A, R. P. 26 by 66 0 1 16.73 90 0 1 31.4 78 0 1 24.46 67 0 1 17.59 91 0 1 32.2 79 0 1 25.29 68 0 1 18.45 92 0 1 32.99 80 0 1 26.12 69 0 1 19.31 93 0 1 33.79 81 0 1 26.94 70 0 1 20.17 94 0 1 34.58 82 0 1 27.77 71 0 1 21.02 95 0 1 35.37 83 0 1 28.6 72 0 1 21.88 96 0 1 36.17 84 0 1 29.42 73 0 1 22.74 97 0 1 36.96 85 0 1 30.25 74 0 1 23.6 98 0 1 37.75 86 0 1 31.07 75 0 1 24.46 99 0 1 38.55 87 0 1 31.9 76 0 1 25.32 100 0 1 39.34 88 0 1 32.73 77 0 1 26.18 25 by 25 0 0 20.66 89 0 1 33.55 78 0 1 27.04 26 0 0 21.49 90 0 1 34.38 79 0 1 27.9 27 0 0 22.31 91 0 1 35.21 80 0 1 28.76 28 0 0 23.14 92 0 1 36.03 81 0 1 29.62 29 0 0 23.97 93 0 1 36.86 82 0 1 30.48 30 0 0 24.79 94 0 1 37.69 83 0 1 31.34 31 0 0 25.62 95 0 1 38.51 84 0 1 32.2 32 0 0 26.45 96 0 1 39.34 85 0 1 33.06 33 0 0 27.27 97 0 2 0.17 86 0 1 33.92 34 0 0 28.1 98 0 2 0.99 87 0 1 34.78 35 0 0 28.93 99 0 2 1.82 88 0 1 35.64 36 0 0 29.75 100 0 2 2.64 89 0 1 36.5 37 0 0 30.58 26 by 26 0 0 22.35 90 0 137.36 38 0 0 31.4 27 0 0 23.21 91 0 1 38.21 39 0 0 32.23 28 0 0 24.07 92 0 1 39.07 40 0 0 33.06 29 0 0 24.93 93 0 1 39.93 41 0 0 33.88 30 0 0 25.79 94 0.2 0.79 42 0 0 34.71 31 0 0 26.64 95 0 2 1.65 43 0 0 35.54 32 0 0 27.5 96 2 2.51 44 0 0 36.36 33 0 0 28.36 97 0 2 3.37 45 0 0 37.19 34 0 0 29.22 98 0 2 4.23 46 0 0 38.02 35 0 0 30.08 99 0 2 5.09 47 0 0 38.84 36 0 0 30.94 100 0 2 5.95 48 0 0 39.67 37 0 0 31.8 27 by 27 0 0 24.1 49 0 1 0.5 38 0 0 32.66 28 0 0 24.99 50 0 1 1.32 39 0 0 33.52 29 0 0 25.88 51 0 1 2.15 40 0 0 34.38 30 0 0 26.78 52 0 1 2.98 41 0 0 35.24 31 0 0 27.67 53 0 1 3.8 42 0 0 36.1 32 0 0 28.56 54 0 1 4.63 43 0 0 36.96 33 0 0 29.45 55 0 1 5.45 44 0 0 37.82 34 0 0 30.35 56 0 1 6.28 45 0 0 38.68 35 0 0 31.24 57 0 1 7.11 46 0 0 39.54 36 0 0 32.13 58 0 1 7.93 47 0 1 0.4 37 0 0 33.02 59 0 1 8.76 48 0 1 1.26 38 0 0 33.92 60 0 1 9.59 49 0 1 2.12 39 0 34.81 61 0 1 10.41 50 0 1 2.98 40 0 0 35.7 62 0 1 11.24 51 0 1 3.83 41 0 0 36.6 63 0 1 12.07 52 0 1 1 4.69 42 0 0 37.49 64 0 1 12.89 53 0 1 5.55 43 0 0 38.38 65 0 1 13.72 54 0 1 6.41 44 0 0 39.27 66 0 1 14.55 55 0 1 7.27 45 0 1 0.17 67 0 1 15.37 56 0 1 8.13 46 0 1 1.06 68 0 1 16.2 57 0 1 8.99 47 0 1 1.95 69 0 1 17.02 58 0 1 9.85 48 0 1 2.84 70 0 1 17.85 59 0 1 10.71 49 0 1 3.74 71 0 1 18.68 60 0 1 11.57 50 0 1 4.63 72 0 1 19.5 61 73 0 1 20.33 74 0 1 21.16 75 0 1 21.98 76 0 1 22.81 UNI15 0 1 12.43 51 0 1 5.52 62 0 1 13.29 52 0 1 6.41 63 0 1 14.15 53 0 1 7.31 64 0 1 15.01 54 0 1 8.2 65 0 1 15.87 55 0 1 9.09 242 TABLES OF LAND MEASURE. Dimensions. Statute content. Dimensions. Statute content. Dimensions. Statute content. Yards. A. R. P. Yards. A. R. P. Yards. A. R. P. 27 by 56 0 1 9.98 28 by 47 0 1 3.5 29 by 39 0 0 37.39 57 0 1 10.88 48 0 1 4.43 40 0 0 38.35 58 0 1 11.77 49 0 1 5.36 41 0 0 39.31 59 0 1 12.66 50 0 1 6.28 42 0 1 1 0.26 60 0 1 13.55 51 0 1 7.21 43 0 1 1.22 61 0 1 14.45 52 0 1 8.13 44 0 1 2.18 62 0 1 15.34 53 0 1 9.06 45 0 1 1 3.14 63 0 1 16.23 54 0 1 9.98 46 0 1 4.1 64 0 1 17.12 55 0 1 10.91 47 0 1 5.06 65 0 1 18.02 56 0 1 11.83 48 0 1 6.02 66 0 1 18.91 57 0 1 12.76 49 0 1 7.98 67 0 1 19.8 58 0 1 13.69 50 0 1 8.93 68 0 1 20.69 59 0 1 14.61 51 0 1 9.89 69 0 1 21.59 60 0 1 15.54 52 0 1 10.85 70 0 1 22.48 61 0 1 16.46 53 0 1 11.81 71 0 1 23.37 62 0 1 17.39 54 0 1 12.77 72 0 1 24.26 63 0 1 18.31 55 0 1 13.73 73 0 1 25.16 64 0 1 19.24 56 0 1 14.69 74 0 1 26.05 65 0 1 20.17 57 0 1 15.64 75 0 1 26.94 66 0 1 21.09 58 0 1 16.6 76 0 1 27.83 67 0 1 22.02 59 0 1 17.56 77 0 1 28.73 68 0 1 22.94 60 0 1 18.52 78 0 1 29.62 69 0 1 23.87 61 0 1 19.48 79 0 1 30.51 70 0 1 24.79 62 0 1 20.44 80 0 1 31.4 71 0 1 25.72 63 0 1 21.4 81 0 1 32.3 72 0 1 26.64 64 0 1 22.36 82 0 1 33.19 73 0 1 27.57 65 0 1 23.31 83 0 1 34.08 74 0 1 28.5 66 0 1 24.27 84 0 1 34.98 75 0 1 29.42 67 0 1 25.23 85 0 1 35.87 76 0 1 30.35 68 0 1 26.19 86 0 1 36.76 77 0 1 31.27 69 0 1 27.15 87 0 137.65 78 0 1 32.2 70 0 1 28.11 88 0 1 38.55 79 0 1 33.12 71 0 1 29.07 89 0 1 39.44 80 0 1 34.05 72 0 1 30.02 90 0 2 0.33 81 0 1 34.98 73 0 1 30.98 91 0 2 1.22 82 0 1 35.9 74 0 1 31.94 92 0 2 2.12 83 0 1 36.83 75 0 1 32.9 93 0 2 3.01 84 0 1 37.75 76 0 1 33.86 94 0 2 4.9 85 0 1 38.68 77 0 1 34.82 95 0 2 4.79 86 0 1 39.6 78 0 1 35.78 96 0 2 2 5.69 87 0 2 0.53 79 0 1 36.74 97 0 2 6.58 88 0 2 1.45 80 0 1 37.69 98 0 2 2 7.47 89 0 2 2.38 81 0 1 38.65 99 0 2 2 8.36 90 0 2 3.31 82 0 1 39.61 100 0 2 2 9.26 91 0 2 4.23 83 0 2 0.57 28 by 28 0 0 25.92 92 0 2 5.16 84 0 2 1.53 29 0 0 26.84 93 0 2 6.08 85 0 2 2.49 30 0 0 27.77 94 0 2 7.01 86 0 2 3.45 31 0 0 28.69 95 0 2 7.93 87 0 2 4.4 32 0 0 29.62 96 0 2 8.86 88 0 2 5.36 33 0 0 30.55 97 0 2 9.79 89 0 2 6.32 34 0 0 31.47 98 0 2 10.71 90 0 2 7.28 35 0 0 32.4 99 0 2 11.64 91 0 2 8.24 36 0 0 33.32 100 0 2 12.56 92 0 2 9.2 37 0 0 34.25 29 by 29 0 0 27.8 93 0 2 10.16 38 0 0 35.17 30 0 0 28.76 94 0 2 11.12 39 0 0 36.1 31 0 0 29.72 95 0 2 12.07 40 0 0 37.02 32 0 0 30.68 96 0 2 13.03 41 0 0 37.95 33 0 0 31.64 97 0 2 13.99 42 0 0 38.88 34 0 0 32.6 98 0 2 14.95 43 0 0 39.8 35 0 0 33.55 99 0 2 15.91 44 0 1 0.73 36 0 0 34.51 100 0 2 16.87 45 0 1 1 1.65 37 0 0 35.47 30 by 30 0 0 29.75 46 0 1 2.58 38 0 0 36.43 31 0 0 30.74 TABLES OF LAND MEASURE. 243 Dimensions. Statute content. Dimensions. Statute content. Dimensions. Yards. 30 by 32 A. R. P. 0 0 31.74 Yards. A. R. P. Yards. Statute content. A. R. P. 96 0 2 15.21 31 by 90 0 2 12.23 33 0 0 32.73 97 0 2 16.2 91 0 2 13.26 34 0 0 33.72 98 0 2 17.19 92 0 2 14.28 35 0 0 34.71 99 0 2 18.18 93 0 2 15.31 36 0 0 35.7 100 0 2 19.17 94 0 2 16.33 37 0 0 36.69 31 by 31 0 0 31.77 95 0 2 17.36 38 0 0 37.69 32 0 0 32.79 96 0 2 18.38 39 0 0 38.68 33 0 0 33.82 97 0 2 19.4 40 0 0 39.67 34 0 0 34.84 98 0 2 20.43 41 0 1 0.66 35 0 0 35.87 99 0 2 21.45 42 0 1 1.65 36 0 0 36.89 100 0 2 22.48 43 0 1 2.64 37 0 0 37.92 32 by 32 0 0 33.85 44 0 1 3.64 38 0 0 38.94 33 0 0 34.91 45 0 1 4.63 39 0 0 39.97 34 0 0 35.97 46 0 1 5.62 40 0 1 0.99 35 0 0 37.02 47 0 1 6.61 41 0 1 2.02 36 0 0 38.08 48 0 1 7.6 42 0 1 3.04 37 0 0 39.14 49 0 1 8.6 43 0 1 4.07 38 0 1 0.2 50 0 1 9.59 44 0 1 5.09 39 0 1 1.26 51 0 1 10.58 45 0 1 6.12 40 0 1 1 2.31 52 0 1 11.57 46 0 1 7.14 41 0 1 3.37 53 0 1 12.56 47 0 1 8.17 42 0 1 1 4.43 54 0 1 13.55 48 0 1 9.19 43 0 1 5.49 55 0 1 14.55 49 0 1 10.21 44 0 1 6.55 56 0 1 15.54 50 0 1 11.24 45 0 1 7.6 57 0 1 16.53 51 0 1 12.26 46 0 1 8.66 58 0 1 17.52 52 0 1 13.29 47 0 1 9.72 59 0 1 18.51 53 0 1 14.31 48 0 1 10.78 60 0 1 19.5 54 0 1 15.34 49 0 1 11.83 61 0 1 20.5 55 0 1 16.36 50 0 1 12.89 62 0 1 21.49 56 0 1 17.39 51 0 1 13.95 63 0 1 22.48 57 0 1 18.41 52 0 1 15.01 64 0 1 23.47 58 0 1 19.44 53 0 1 16.07 65 0 1 24.46 59 0 1 20.46 54 0 1 17.12 66 0 1 25.45 60 0 1 21.49 55 0 1 18.18 67 0 1 26.45 61 0 1 22.51 56 0 1 19.24 68 0 1 27.44 62 0 1 23.54 57 0 1 20.3 69 0 1 28.43 63 0 1 24.56 58 0 1 21.36 70 0 1 29.42 64 0 1 25.59 59 0 1 22.41 71 0 1 30.41 65 0 1 26.61 60 1 23.47 72 0 1 31.4 66 0 1 27.64 73 0 1 32.4 67 0 1 28.66 74 0 1 33.39 68 0 1 29.69 75 0 1 34.38 69 0 1 30.71 76 0 1 35.37 70 0 1 31.74 77 0 1 36.36 71 0 1 32.76 78 0 1 37.36 72 0 1 33.79 79 0 1 38.35 73 0 1 34.81 80 0 1 39.34 74 0 1 35.83 81 0 2 0.33 75 0 1 36.86 888 82 0 2 1.32 76 0 1 37.88 83 0 2 2.31 77 0 1 38.91 84 0 2 3.31 78 0 1 39.93 INNJ88RRARIS2 1 24.53 62 0 1 25.59 63 0 1 26.64 64 0 1 27.7 65 0 1 28.76 0 1 29.82 67 0 1 30.88 0 1 31.93 69 0 1 32.99 70 0 1 34.05 71 0 1 35.11 0 1 36.17 73 0 1 37.22 85 0 2 4.3 79 0 2 2 0.96 74 0 1 38.28 86 0 2 5.29 80 02 1.98 75 0 1 39.34 87 0 2 6.28 81 0 2 2 3.01 76 0 2 0.4 88 0 2 7.27 82 0 2 4.03 77 0 2 1.45 89 0 2 8.26 83 0 2 5.06 78 0 2 2.51 91 2UNKHA 90 0 2 9.26 84 0 2 6.08 79 0 2 3.57 0 2 10.25 92 0 2 11.24 93 0 2 12.23 87 94 0 2 13.22 95 0 2 14.21 168888888 85 0 2 7.11 80 0 2 4.63 0 2 8.13 81 0 2 5.69 0 2 9.16 82 0 2 2 6.74 0 2 10.18 83 0 2 2 7.8 89 0 2 11.21 84 0 2 8.86 244 TABLES OF LAND MEASURE. Dimensions. Yards. Statute content. Dimensions. Statute content. Dimensions. Statute content. A. R. P. Yards. A. R. P. Yards. A. R. P. 32 by 85 0 2 9.92 33 by 81 0 2 8.36 34 by 78 0 2 7.67 86 0 2 10.98 82 0 2 9.45 79 2 8.79 87 0 2 12.03 83 0 2 10.55 80 2 9.92 88 0 2 13.09 84 0 2 11.64 81 0 2 11.04 89 0 2 14.15 85 0 2 12.73 82 0 2 12.17 90 0 2 15.21 86 0 2 13.82 83 0 2 13.29 91 0 2 16.26 87 0 2 14.91 84 0 2 14.41 92 0 2 17.32 88 0 2 16. 85 0 2 15.54 93 0 2 18.38 89 0 2 17.09 86 0 2 16.66 94 0 2 19.44 90 0 2 18.18 87 0 2 17.79 95 0 2 20.5 91 0 2 19.27 88 0 2 18.91 96 0 2 21.55 92 0 2 20.36 89 0 2 20.03 97 0 2 22.61 93 0 2 21.45 90 0 2 21.16 98 0 2 23.67 94 0 2 22.55 91 0 2 22.28 99 0 2 24.73 95 0 2 23.64 92 0 2 23.4 100 0 2 25.79 96 0 2 24.73 93 0 2 24.53 33 by 33 0 0 36. 97 0 2 25.82 94 0 2 25.65 34 0 0 37.09 98 0 2 26.91 95 0 2 26.78 35 0 0 38.18 99 0 2 28. 96 0 2 27.9 36 0 0 39.27 100 0 2 29.09 97 0 2 29.02 37 0 1 0.36 34 by 34 0 0 38.21 98 0 2 30.15 38 0 1 1.45 35 0 0 39.34 99 0 2 31.27 39 0 1 2.55 36 0 1 0.46 100 0 2 32.4 40 0 1 3.64 37 0 1 1.59 35 by 35 0 1 0.5 41 0 1 4.73 38 0 1 2.71 36 0 1 1.65 42 0 1 1 5.82 39 0 1 3.83 37 0 1 2.81 43 0 1 6.91 40 0 1 4.96 38 0 1 3.97 44 0 1 8. 41 0 1 6.08 39 0 1 5.12 45 0 1 9.09 42 0 1 7.21 40 0 1 6.28 46 0 1 10.18 43 0 1 8.33 41 0 1 7.44 47 0 1 11.27 44 0 1 9.45 42 0 1 8.6 48 0 1 12.36 45 0 1 10.58 43 0 1 9.75 49 0 1 13.45 46 0 1 11.7 44 0 1 10.91 50 0 1 14.55 47 0 1 12.83 45 0 1 12.07 51 0 1 15.64 48 0 1 13.95 46 0 1 13.22 52 0 1 16.73 49 0 1 15.07 47 0 1 14.38 53 0 1 17.82 50 0 1 16.2 48 0 1 15.54 54 0 1 18.91 51 0 1 17.32 49 0 1 16.69 55 0 1 20. 52 0 1 18.45 50 1 17.85 56 0 1 21.09 53 0 1 19.57 51 0 1 19.01 57 0 1 22.18 54 0 1 20.69 52 0 1 20.17 58 0 1 23.27 55 0 1 21.82 53 0 1 21.32 59 0 1 24.36 56 0 1 22.94 54 0 1 22.48 60 0 1 25.45 57 0 1 24.07 55 0 1 23.64 61 0 1 26.55 58 0 1 25.19 56 0 1 24.79 62 0 1 1 27.64 59 0 1 26.31 57 0 1 25.95 63 0 1 28.73 60 0 1 27.44 58 0 1 27.11 64 0 1 29.82 61 0 1 28.56 59 0 1 28.26 65 0 1 30.91 62 0 1 29.69 66 0 1 32. 63 0 1 30.81 67 0 1 33.09 64 0 1 31.93 68 0 1 34.18 65 0 1 33.06 69 0 135.27 66 0 1 34.18 70 0 1 36.36 67 0 1 35.31 71 0 1 37.45 68 0 1 36.43 72 0 1 38.55 69 0 1 37.55 73 0 1 39.64 70 0 1 38.68 74 0 2 0.73 71 0 1 39.8 75 0 2 1.82 72 0 2 0.93 76 0 2 2.91 73 2 2.05 77 0 2 4. 74 0 2 3.17 78 2 5.09 75 0 2 4.3 79 0 2 6.18 76 0 2 5.42 80 0 2 7.27 77 0 2 6.55 JFINIJ:****FCC28 0 1 29.42 0 1 30.58 62 0 1 31.74 0 1 32.89 0 1 34.05 0 1 35.21 0 1 36.36 0 1 37.52 0 1 38.68 69 0 1 39.83 70 0 2 0.99 0 2 2.15 72 0 2 3.31 0 2 4.46 2 5.62 0 2 6.78 TABLES OF LAND MEASURE. 245 Statute content. Dimensions. Statute content. Dimensions. Statute content. Dimensions. Yards A. R. P. Yards. A. R. P. Yards. A. R. P. 35 by 76 0 2 7.93 36 by 75 0 2 2 9.26 37 by 75 0 2 11.74 77 0 2 9.09 76 0 2 10.45 76 0 2 12.96 78 0 2 10.25 77 0 2 11.64 77 0 2 14.18 79 0 2 11.4 78 0 2 12.83 78 0 2 15.4 80 0 2 12.56 79 0 2 14.02 79 0 2 16.63 81 0 2 13.72 80 0 2 15.21 80 0 2 17.85 82 0 2 14.88 81 0 2 16.4 81 0 2 19.07 83 0 216.03 82 0 2 17.59 82 0 2 20.3 84 0 2 17.19 83 0 2 18.78 83 0 2 21.52 85 0 2 18.35 84 0 2 19.97 84 0 2 22.74 86 0 2 19.5 85 0 2 21.16 85 0 2 23.97 87 0 2 20.66 86 0 2 22.35 86 0 2 25.19 88 0 2 21.82 87 0 2 23.54 87 0 2 26.41 89 0 2 22.98 88 0 2 24.73 88 0 2 27.64 90 0 2 24.13 89 0 2 25.92 89 0 2 28.86 91 0 2 25.29 90 0 2 27.11 90 0 2 30.08 92 0 2 26.45 91 0 2 28.3 91 0 2 31.31 93 0 2 27.6 92 0 2 29.49 92 0 2 32.53 94 0 2 28.76 93 0 2 30.68 93 0 2 33.75 95 0 2 29.92 94 0 2 31.87 94 0 2 34.98 96 0 2 31.07 95 0 2 33.06 95 0 2 36.2 97 0 2 32.23 96 0 2 34.25 96 0 2 37.42 98 0 2 33.39 97 0 2 35.44 97 0 2 38.64 99 0 234.55 98 0 2 36.63 98 0 2 39.87 100 0 2 35.7 99 0 2 37.82 99 0 3 1.09 36 by 36 0 1 2.84 100 0 2 39.01 100 0 3 2.31 37 0 1 4.03 37 by 37 0 1 5.26 38 by 38 0 1 7.74 38 0 1 5.22 38 0 1 6.48 39 0 1 8.99 39 0 1 1 6.41 39 0 1 7.7 40 0 1 10.25 40 0 1 1 7.6 40 0 1 8.93 41 0 1 11.5 41 0 1 8.79 41 0 1 10.15 42 0 1 12.76 42 0 1 9.98 42 0 1 11.37 43 0 1 14.02 43 0 1 11.17 43 0 1 12.6 44 0 1 15.27 44 0 1 12.36 44 0 1 13.82 45 0 1 16.53 45 0 1 13.55 45 0 1 15.041 46 0 1 17.79 46 0 1 14.74 46 0 1 16.26 47 0 1 19.04 47 0 1 15.93 47 0 1 17.49 48 0 1 20.3 48 0 1 17.12 48 0 1 18.71 49 0 1 21.55 49 0 1 18.31 49 0 1 19.93 50 0 1 22.81 50 0 1 19.5 50 0 1 21.16 51 0 1 24.07 51 0 1 20.69 51 0 1 22.38 52 0 1 25.32 52 0 1 21.88 52 0 1 23.6 53 0 1 26.58 53 0 1 23.07 53 0 1 24.83 54 0 1 27.83 54 0 1 24.26 54 0 1 26.05 55 0 1 29.09 55 0 1 25.45 55 0 1 27.27 56 0 1 30.35 56 0 1 26.64 56 0 1 28.5 57 0 1 31.6 57 0 1 27.83 57 0 1 29.72 58 0 1 32.86 58 0 1 29.02 58 0 1 30.94 59 0 1 34.12 59 0 1 30.21 59 0 1 32.17 60 0 1 31.4 60 0 1 33.39 61 61 0 1 32.6 61 0 1 34.61 62 62 0 1 33.79 62 0 1 35.83 63 0 1 34.98 63 0 1 37.06 64 0 1 36.17 64 0 1 38.28 65 0 1 37.36 65 0 1 39.5 66 0 1 38.55 66 0 2 0.73 67 0 1 39.74 67 0 2 1.95 68 68 0 2 0.93 68 0 2 3.17 8UNIHUS583 60 0 1 35.37 0 1 36.63 0 1 37.88 63 0 1 39.14 64 0 2 0.4 65 0 2 1.65 66 0 2 2 2.91 67 0 2 4.17 0 2 5.42 69 0 2 6.68 69 0 2 2.12 69 0 2 4.4 70 0 2 7.93 70 0 2 3.31 70 0 2 5.62 71 0 2 9.19 71 0 2 4.5 71 0 2 6.84 72 0 2 10.45 72 0 2 5.69 72 0 2 8.07 73 0 2 11.7 73 0 2 6.88 73 0 2 9.29 74 0 2 12.96 74 0 2 8.07 74 0 2 10.51 75 0 2 14.21 246 TABLES OF LAND MEASURE. Dimensions. Statute content. Dimensions. Statute content. Dimensions. Statute content. Yards. A. R. P. Yards. A. R. P. Yards. A. R. P. 38 by 76 0 2 15.47 39 by 78 0 2 20.56 40 by 81 0 2 27·11 77 0 2 16.73 79 0 2 21.85 82 0 2 28.43 78 0 2 17.97 80 0 2 23.14 83 0 2 29.75 79 0 2 19.24 81 0 2 24.43 84 0 2 31.07 80 0 2 20.5 82 0 2 25.72 85 0 232.4 81 0 2 21.75 83 0 2 27.01 86 0 2 33.72 82 0 2 23.01 84 0 2 28.3 87 0 2 35.04 83 0 2 24.26 85 0 2 29.59 88 0 2 36.36 84 0 2 25.52 86 0 2 30.88 89 0 2 37.69 85 0 2 26.78 87 0 2 32.17 90 0 2 39.01 86 0 2 28.03 88 0 2 33.45 91 0 3 0.33 87 0 2 29.29 89 0 2 34.74 92 0 3 1.65 88 0 2 30.55 90 0 2 36.03 93 0 3 2.98 89 0 2 31.8 91 0 2 37.32 94 0 3 4.3 90 0 2 33.06 92 0 2 38.61 95 0 3 5.62 91 0 2 34.31 93 0 2 39.9 96 0 3 6.94 92 0 2 35.58 94 0 3 1.19 97 3 8.26 93 0 2 36.83 95 0 3 2.48 98 3 9.59 94 0 2 38.08 96 0 3 3.77 99 0 3 10.91 95 0 2 39.34 97 0 3 3 5.06 100 0 3 12.23 96 0 3 0.6 98 0 3 6.35 41 by 41 0 1 15.57 97 0 3 1.85 99 0 3 3 7.64 42 0 1 16.93 98 0 3 3.11 100 0 3 8.93 43 0 1 18.28 99 0 3 4.36 40 by 40 0 1 12.89 44 0 1 19.64 100 0 3 5.62 41 0 1 14.21 45 0 1 20.99 39 by 39 0 1 10.28 42 0 1 15.54 46 0 1 22.35 40 0 1 11.57 43 0 1 16.86 47 0 1 23.7 41 0 1 12.86 44 0 1 18.18 48 0 1 25.06 42 0 1 14.15 45 0 1 19.5 49 0 1 26.41 43 0 1 15.44 46 0 1 20.83 50 0 1 27.77 44 0 1 16.73 47 0 1 22.15 51 0 1 29.12 45 46 47 48 0 1 18.02 48 0 1 23.47 52 0 1 30.48 0 1 19.31 49 0 1 24.79 53 0 1 31.83 0 1 20.6 50 0 1 26.12 54 0 1 33.19 0 1 21.88 51 0 1 27.44 55 0 1 34.55 49 0 1 23.17 52 0 1 28.76 56 0 1 35.9 50 0 1 24.46 53 0 1 30.08 57 0 1 37.26 51 0 1 25.75 54 0 1 31.4 58 1 38.61 52 0 1 27.04 55 0 1 32.73 59 0 1 39.97 53 0 1 28.33 56 0 1 34.05 60 0 2 1.32 54 0 1 29.62 57 0 1 35.37 61 0 2 2.68 55 0 1 30.91 58 0 1 36.69 62 0 2 4.03 56 0 1 32.2 59 0 1 38.02 63 0 2 5.39 57 0 1 33.49 60 0 1 39.34 64 0 2 6.74 58 0 1 34.78 61 0 2 0.66 65 0 2 8.1 59 0 1 36.07 62 0 2 1.98 66 0 2 9.45 60 0 1 37.36 63 0 2 3.31 67 0 2 10.81 61 0 1 38.64 64 0 2 4.63 68 0 2 12.17 62 0 1 39.93 65 0 2 5.95 69 0 2 13.52 63 0 2 1.22 66 0 2 7.27 70 0 2 14.88 64 0 2 2.51 67 0 2 8.6 71 0 216.23 65 0 2 3.8 68 0 2 9.92 72 0 2 17.59 66 0 2 5.09 69 2 11.24 73 0 2 18.94 67 0 2 6.38 70 2 12.56 74 0 2 20.3 68 0 2 7.67 71 0 2 13.88 75 0 2 21.65 69 0 2 8.96 72 0 2 15.21 76 0 2 23.01 70 0 2 10.25 73 0 2 16.53 77 0 2 24.36 71 0 2 11.54 74 0 2 17.85 78 0 2 25.72 72 0 2 12.83 75 0 2 19.17 79 0 2 27.07 73 0 2 14.12 76 0 2 20.5 80 0 2 28.43 74 0 2 15.4 77 0 2 21.82 81 0 2 29.79 75 0 2 16.69 78 0 2 23.14 82 0 2 31.14 76 0 2 17.98 79 0 2 24.46 83 0 2 32.5 77 0 2 19.27 80 0 2 25.79 84 0 2 33.85 TABLES OF LAND MEASURE. 247 Dimensions. Statute content. Dimensions. Statute content. Dimensions. Statute content. Yards. A. R. P. Yards. A. R. P. Yards. A. R. P. 41 by 85 0 2 35.21 42 by 90 0 3 4.96 43 by 96 0 3 16.46 86 0 236.56 91 0 3 6.35 97 0 3 17.88 87 0 237.92 92 0 3 7.74 98 0 3 19.31 88 0 2 39.27 93 0 3 9.12 99 0 • 3 20.73 89 0 3 0.63 94 0 3 10.51 100 0 3 22.15 90 0 3 1.98 95 0 3 11.9 44 by 44 0 1 24. 91 0 3 3.34 96 0 3 13.29 45 0 1 25.45 92 0 3 4.69 97 0 3 14.68 46 0 1 26.91 93 0 3 6.05 98 0 3 16.07 47 0 1 28.36 94 0 3 7.4 99 0 3 17.45 48 0 1 29.82 95 0 3 8.76 100 0 3 18.84 49 0 1 31.27 96 0 3 10.12 43 by 43 0 1 21.12 50 0 1 32.73 97 0 3 11.47 44 0 1 22.55 51 0 1 34.18 98 0 3 12.83 45 0 1 23.97 52 0 1 35.64 99 0 3 14.18 46 0 1 25.39 53 0 1 37.09 100 0 3 15.54 47 0 1 26.81 54 0 1 38.55 42 by 42 0 1 18.31 48 0 1 28.23 55 0 2 2 0. 43 0 1 19.7 49 0 1 29.65 56 0 2 2 1.45 44 0 1 21.09 50 0 1 31.07 57 0 2 2 2.91 45 0 1 22.48 51 0 1 32.5 58 0 2 2 4.36 46 0 1 23.87 52 0 1 33.92 59 0 2 5.82 47 0 1 25.26 53 0 1 35.34 60 0 2 2 7.27 48 0 1 26.64 54 0 1 36.76 61 0 2 8.73 49 0 1 28.03 55 0 1 38.18 62 0 2 10.18 50 0 1 29.42 56 0 1 39.6 63 0 2 11.64 51 0 1 30.81 57 0 2 1.02 64 0 2 13.09 52 0 1 32.2 58 0 2 2.45 65 0 2 14.55 53 0 1 33.59 59 0 2 3.87 66 0 2 16. 54 0 1 34.98 60 0 2 5.29 67 0 2 17.45 55 0 1 36.36 61 0 2 6.71 68 0 2 18.91 56 0 1 37.75 62 0 2 8.13 69 0 2 20.36 57 0 1 39,14 63 0 2 9.55 70 0 2 21.82 58 0 2 0,53 64 0 2 10.98 71 0 2 23.27 59 0 2 1.92 65 0 2 12.4 72 0 2 24.73 60 0 2 3.31 66 0 2 13.82 73 0 2 26.18 61 0 2 4.69 67 0 2 15.24 74 0 2 27.64 62 0 2 6.08 68 0 2 16.66 75 0 2 29.09 63 0 2 7.47 69 0 2 18.08 76 0 2 30.55 64 0 2 8,86 70 0 2 19.5 77 0 2 32. 65 0 2 10.25 71 0 2 20.93 78 2 33.45 66 0 2 11.64 72 0 2 22.35 79 0 2 34.91 67 0 213,02 73 0 2 23.77 80 0 2 36.36 68 0 2 14.41 74 0 2 25.19 81 0 2 37.82 69 0 2 15,8 75 0 2 26.61 82 0 2 39.27 70 0 2 17.19 76 0 2 28.03 83 0 3 0.73 71 0 2 18,58 77 0 2 29.45 84 0 3 2.18 72 0 2 19.97 78 0 2 30.88 85 0 3 3 3.64 73 0 2 21,36 79 0 2 32.3 86 0 3 5.09 74 0 2 22.74 80 0 233.72 87 0 3 6.55 75 0 2 24,13 81 0 2 35.14 88 0 3 8. 76 0 2 25.52 82 0 2 36.56 89 0 3 9.45 77 0 2 26.91 83 0 2 37.98 90 0 3 10.91 78 0 2 28,3 84 0 2 39.4 91 0 3 12.36 79 0 229.69 85 0 3 0.83 92 0 3 13.82 80 0 2 31.07 86 0 3 2.25 93 0 3 15.27 81 0 2 32.46 87 0 3 3.67 94 0 3 16.73 82 0 2 33.85 88 0 3 5.09 95 0 3 18.18 83 0 2 35.24 89 0 3 6.51 96 0 3 19.64 84 0 2 36.63 90 0 3 7.93 97 0 3 21.09 85 0 2 38.02 91 0 3 3 9.36 98 0 3 22.55 86 0 2 39.4 92 0 3 10.78 99 0 3 24. 87 0 3 0.79 93 0 3 12.2 100 0 3 25.45 88 0 3 2.18 94 0 3 13.62 45 by 45 0 1 26.94 89 0 3 3·57 95 0 3 15.04 46 0 1 28.43 248 TABLES OF LAND MEASURE. Dimensions. Yards. Statute content. Dimensions. Statute content. Dimensions. A. R. P. Yards. A. R. P. Yards. A. R. Statute content. P. 45 by 47 0 1 29.92 46 by 56 0 2 5.16 47 by 66 0 222.55 48 0 1 31.4 57 0 2 6.68 67 0 2 24.1 49 0 1 32.89 58 0 2 8.2 68 0 2 25.65 50 0 1 34.38 59 0 2 9.72 69 0 2 27.21 51 0 1 35.87 60 0 2 11.24 70 0 2 28.76 52 0 1 37.36 61 0 2 12.76 71 0 2 30.31 53 0 1 38.84 62 0 2 14.28 72 0 2 31.87 54 0 2 0.33 63 0 2 15.8 73 0 2 33.42 55 0 2 1.82 64 0 2 17.32 74 0 2 34.98 56 0 2 3.31 65 0 2 18.84 75 0 2 36.53 57 0 2 4.79 66 0 2 20.36 76 0 2 38.08 58 0 2 6.28 67 0 2 21.88 77 0 2 39.64 59 0 2 7.77 68 0 2 23.4 78 3 1.19 60 0 2 9.26 69 0 2 24.93 79 3 2.74 61 0 2 10.74 70 0 2 26.45 80 3 4.3 62 0 2 12.23 71 0 2 27.97 81 3 5.85 63 0 2 13.72 72 0 2 29.49 82 0 3 7.4 64 0 2 15.21 73 0 2 31.01 83 0 3 8.96 65 0 2 16.69 74 0 2 32.53 84 0 3 10.51 66 0 2 18.18 75 0 2 34.05 85 0 3 12.07 67 0 2 19.67 76 0 2 35.57 86 0 3 13.62 68 0 2 21.16 77 0 2 37.09 87 0 3 15.17 69 0 222.64 78 0 2 38.61 88 0 3 16.73 70 0 2 24.13 79 0 3 0.13 89 0 3 18.28 71 0 2 25.62 80 0 3 1.65 90 0 3 19.83 72 0 2 27.11 81 0 3 3.17 91 0 3 21.39 73 0 2 28.6 82 0 3 4.69 92 0 3 22-94 74 0 2 30.08 83 0 3 6.21 93 0 3 24.5 75 0 2 31.57 84 0 3 7.74 94 0 3 26.05 76 0 2 33.06 85 0 3 9.26 95 0 3 27.6 77 0 234.55 86 0 3 10.78 96 0 3 29.16 78 0 2 36.03 87 0 3 12.3 97 0 3 30.71 79 0 2 37.52 88 0 3 13.82 98 0 3 32.26 80 0 2 39.01 89 0 3 15.34 99 0 3 33.82 81 0 3 0.5 90 0 3 16.86 100 0 3 35.37 82 0 3 1.98 91 0 3 18.38 48 by 48 0 1 36.17 83 0 3 3.47 92 0 3 19.9 49 0 1 37.75 84 0 3 4.96 93 0 3 21.42 50 0 1 39.34 85 0 3 6.45 94 0 3 22.94 51 0 2 0.93 86 0 3 7.93 95 0 3 24.46 52 0 2 2.51 87 0 3 9.42 96 0 3 25.98 53 0 2 4.1 88 0 3 10.91 97 0 3 27.5 54 0 2 5.69 89 0 3 12.4 98 0 3 29.02 55 2 7.27 90 0 3 13.88 99 0 3 30.55 56 0 2 8.86 91 0 3 15.37 100 0 3 32.07 57 0 92 0 3 16.86 47 by 47 0 1 33.02 93 0 3 18.35 48 0 1 34.58 94 0 3 19.83 49 0 1 36.13 95 0 3 21.32 50 0 1 37.69 96 0 3 22.81 51 0 1 39.24 97 0 3 24.3 52 0 2 0.79 98 0 3 25.79 53 0 2 2.35 99 0 3 27.27 54 0 2 3.9 100 0 3 28.76 55 0 2 5.45 46 by 46 0 1 29.95 56 0 2 7.01 47 0 1 31.47 57 0 2 8.56 48 0 1 32.99 58 0 2 10.12 49 0 1 34.51 59 0 2 11.67 50 0 1 36.03 60 0 2 13.22 51 0 1 37.55 61 0 2 14.78 52 0 1 39.07 62 0 2 16.33 53 0 2 0.6 63 0 2 17.88 54 0 2 2.12 64 0 2 19.44 55 0 2 3.64 65 0 2 20.99 ZZZZZZZIXARAC*****: 0 212.03 59 0 2 10.45 2 13.62 60 0 2 15.21 0 2 16.79 62 0 2 18.38 63 0 2 19.97 64 0 2 21.55 65 0 2 23.14 66 0 2 24.73 67 0 2 26.31 68 0 2 27.9 0 2 29.49 70 0 2 31.07 71 0 2 32.66 72 0 2 34.25 73 0 2 35,83 74 0 2 37.42 75 0 2 39.01 76 0 3 0.6 TABLES OF LAND MEASURE. 249 Dimensions. Statute content. Yards. A. R. P. Dimensions. Yards. Statute content. Dimensions. Statute content. A. R. P. Yards. 48 by 77 0 3 2.18 49 by 89 0 3 24.17 51 by 52 A. R. P. 0 2 7.67 78 0 3 3 3.77 90 0 3 25.79 53 0 2 9.36 79 0 3 3 5.36 91 0 3 27.4 54 2 11.04 80 0 3 3 6.94 92 0 3 29.02 55 0 2 12.73 81 0 3 3 8.53 93 0 3 30.64 56 0 2 14.41 82 0 3 10.12 94 0 3 32.26 57 0 2 16.1 83 0 3 11.7 95 0 3 33.88 58 0 2 17.79 84 0 3 13.29 96 0 3 35.5 59 0 2 19.47 85 0 3 14.88 97 0 3 37.12 86 0 3 16.46 98 0 3 38.74 87 0 3 18.05 99 1 0 0.36 88 0 3 19.64 100 1 0 1.98 89 0 3 21.22 50 by 50 0 2 2.64 90 0 3 22.81 51 0 2 4.3 91 0 3 24.4 52 0 2 5.95 92 0 3 25.98 53 0 2 7.6 93 0 3 27.57 54 0 2 9.26 94 0 3 29.16 55 0 2 10.91 95 0 3 30.74 56 0 2 12.56 96 0 3 32.33 57 0 2 14.21 71 97 0 3 33.92 58 0 2 15.87 98 0 3 35.5 59 0 2 17.52 99 0 3 37.09 60 0 2 19.17 100 0 3 38.68 61 0 2 20.83 49 by 49 0 1 39.37 62 0 2 22.48 50 0 2 0.99 63 0 2 24.13 IZLAFIZZJOBRPAR3828: 0 2 21.16 61 0 2 22.84 0 2 24.53 0 2 26.21 0 2 27.9 0 2 29.59 66 0 2 31.27 67 0 2 32.96 0 2 34.64 0 2 36.33 70 0 2 38.02 0 2 39.7 72 0 3 1.39 0 3 3.07 74 0 3 4.76 0 3 6.45 0 3 8.13 77 0 3 3 9.82 51 0 2 2 2.61 64 0 2 25.79 78 0 3 11.5 52 0 2 2 4.23 65 0 2 27.44 79 0 3 13.19 53 0 2 2 5.85 66 0 2 29.09 80 0 3 14,88 54 0 2 7.47 67 0 2 30.74 81 0 3 16.56 55 0 2 2 9.09 68 0 2 32.4 82 0 3 18.25 56 0 2 10.71 69 0 2 34.05 83 0 3 19.93 57 0 2 12.33 70 0 2 35.7 84 0 3 21.62 58 0 2 13.95 71 0 2 37.36 85 0 3 23.31 59 0 2 15.57 72 0 2 39.01 86 0 3 24.99 60 0 2 17.19 73 0 3 0.66 87 0 3 26.68 61 0 2 18.81 74 0 3 2.31 88 0 3 28.36 62 0 2 20.43 75 0 3 3.97 89 0 3 30.05 63 0 2 22.05 76 0 3 5.62 90 0 3 31.74 64 0 2 23.67 77 3 7.27 91 0 3 33.42 65 0 2 25.29 78 0 3 8.93 92 0 3 35.11 66 0 2 26.91 79 0 3 10.58 93 0 3 36.79 67 0 2 28.53 80 0 3 12.23 94 0 3 38.48 68 0 2 30.15 81 0 3 13.88 95 1 0 0.17 69 0 2 31.77 82 0 3 15.54 96 1 0 1.85 70 0 2 33.39 83 0 3 17.19 97 1 0 3.54 71 0 2 35.01 84 0 3 18.84 98 1 0 5.22 72 0 2 36.63 85 0 3 20.5 99 1 0 6.91 73 0 2 38.25 86 0 3 22.15 100 1 0 8.6 74 0 2 39.87 87 0 3 23.8 52 by 52 0 2 9.39 75 0 3 1.49 88 0 3 25.45 53 0 2 11.11 76 0 3 3.11 89 0 3 27.11 54 0 2 12.83 77 0 3 4.73 90 0 3 28.76 55 0 2 14.55 78 0 3 6.35 91 0 3 30.41 56 0 2 16.26 79 0 3 7.97 92 0 3 32.07 57 0 2 17.98 80 0 3 9.59 93 0 3 33.72 58 0 2 19.7 81 0 3 11.21 94 0 3 35.37 59 0 2 21.42 82 0 3 12.83 95 0 3 37.02 60 0 2 23.14 83 0 3 14.45 96 0 3 38.68 61 0 2 24.86 84 0 3 16.07 97 1 0 0 0.33 62 0 2 26.58 85 0 3 17.69 98 1 0 1.98 63 0 2 28.3 86 0 3 19.31 99 1 0 3.64 64 0 2 30.02 87 0 3 20.93 100 1 0 5.29 65 0 2 31.74 88 0 3 22.55 51 by 51 0 2 5.98 66 0 2 33.45 S 250 TABLES OF LAND MEASURE. Dimensions. Statute content. Yards. A. R. P. Dimensions. Yards. Statute content. Dimensions. Statute content. A. R. P. Yards. A. R. P. 52 by 67 0 2 35.17 53 by 83 0 3 25.42 54 by 100 1 0 18.51 68 0 2 36.89 84 0 3 27.17 55 by 55 0 2 20. 69 0 2 38.61 70 0 3 0.33 71 0 3 2.05 72 0 3 3.77 ∞ ∞ ∞ ∞ 85 0 3 28.93 56 0 2 21.82 86 0 3 30.68 57 0 2 23.64 87 0 3 32.43 58 0 2 25.45 88 0 3 34.18 59 0 2 27.27 73 0 3 5.49 89 0 3 35.93 60 0 2 29.09 74 0 3 7.21 90 0 3 37.69 61 0 2 30.91 75 0 3 8.93 91 0 3 39.44 62 0 2 32.73 76 0 3 10.64 92 1 0 1.19 63 0 2 34.55 77 0 3 12.36 93 1 0 2.94 64 0 2 36.36 78 0 3 14.08 94 1 0 4.69 65 0 2 38.18 7.9 0 3 15.8 95 1 0 6.45 66 0 3 0. 80 0 3 17.52 96 1 0 8.2 67 0 3 1.82 81 0 3 19.24 97 1 0 9.95 68 0 3 3.64 82 0 3 20.96 98 1 0 11.7 69 0 3 3 5.45 83 0 3 22.68 99 1 0 13.45 70 0 3 7.27 84 0 3 24.4 100 1 0 15.21 71 0 3 9.09 85 0 3 26.12 54 by 54 0 2 16.4 72 0 3 10.91 86 0 3 27.83 55 0 2 18.18 73 0 3 12.73 87 0 3 29.55 56 0 2 19.97 74 0 3 14.55 88 0 3 31.27 57 0 2 21.75 75 0 3 16.36 89 0 3 32.99 58 0 2 23.54 76 0 3 18.18 90 0 3 34.71 59 0 225.32 77 0 3 20. 91 0 3 36.43 60 0 2 27.11 78 0 3 21.82 92 0 3.38.15 61 0 2 28.89 79 0 3 23.64 93 0 3 39.87 62 0 2 30.68 80 0 3 25.45 94 1 0 1.59 63 0 2 32.46 81 0 3 27.27 95 1 0 3.31 64 0 2 34.25 82 0 3 29.09 96 1 0 5.02 65 0 236.03 83 0 3 30.91 97 1 0 6.74 66 0 2 37.82 84 0 3 32.73 98 1 0 8.46 67 0 239.6 85 0 3 34.55 99 1 0 10.18 68 0 3 1.39 86 0 3 36.36 100 1 0 11.9 69 3 3.17 87 0 3 38·18 53 by 53 0 2 12.86 70 3 4.96 88 1 0 0. 54 0 2 14.61 71 3 6.74 89 1 0 0 1.82 55 0 2 16.36 72 0 3 8.53 90 1 0 0 3.64 56 0 2 18.12 73 0 3 10.31 91 1 0 5.45 57 0 2 19.87 74 0 3 12.1 92 1 0 7.27 58 0 2 21.62 75 0 3 13.88 93 1 0 9.09 59 0 2 23.37 76 0 3 15.67 94 1 0 10.91 60 0 2 25.12 77 0 3 17.45 95 1 0 12.73 61 0 2 26.88 78 0 3 19.24 96 1 0 14.55 62 0 2 28.63 79 0 3 21.02 97 1 0 16.36 63 0 2 30.38 80 0 3 22.81 98 1 0 18.18 64 0 2 32.13 81 0 3 24.6 99 1 0 20. 65 0 2 33.88 82 0 3 26.38 100 1 0 21.82 66 0 2 35.64 83 0 3 28.17 56 by 56 0 2 23.67 67 0 2 37,39 84 0 3 29.95 57 0 2 25.52 68 0 2 39.14 85 0 3 31.74 58 0 2 27.37 69 0 3 0.89 86 0 3 33.52 59 0 2 29.22 70 0 3 2.64 87 0 3 35.31 60 0 2 31.07 71 0 3 4.4 88 0 3 37.09 61 0 2 32.93 72 0 3 6.15 89 0 3 38.88 62 0 2 34.78 73 0 3 7.9 90 1 0 0 0.66 63 0 2 36.63 74 0 3 9.65 91 1 0 2.45 64 0 2 38.48 75 0 3 11.4 92 1 0 4.23 65 0 3 0.33 76 0 3 13.16 93 1 0 6.02 66 0 3 2.18 77 0 3 14.91 94 1 0 7.8 67 0 3 4.03 78 0 3 16.66 95 1 0 9.59 68 0 3 5.88 79 0 3 18.41 96 1 0 11.37 69 0 3 7.74 80 0 3 20.17 97 1 0 13.16 70 0 3 3 9.59 81 0 3 21.92 98 1 0 14.94 71 0 3 11.44 82 0 3 23.67 99 1 0 16.73 72 0 3 13.29 TABLES OF LAND MEASURE. 251 Dimensions. Yards. Statute content. A. R. P. Dimensions. Yards. Statute content. Dimensions. Statute content. A. R. P. Yards. A. R. P. 56 by 73 0 3 15.14 57 by 93 1 0 15.24 59 by 72 0 3 20.43 74 0 3 16.99 94 1 0 17.12 73 0 3 22.38 75 0 3 18.84 95 1 0 19.01 74 0 3 24.33 76 0 3 20.69 96 1 0 20.89 75 0 3 26.28 77 0 3 22.55 97 1 0 22.78 76 0 3 28.23 78 0 3 24.4 98 1 0 24.66 77 0 3 30.18 79 0 3 26.25 99 1 0 26.55 78 0 3 32.13 80 0 3 28.1 100 1 0 28.43 79 0 3 34.08 81 0 3 29.95 58 by 58 0 2 31.21 80 0 3 36.03 82 0 3 31.8 59 0 2 33.12 81 0 3 37.98 83 0 3 33.65 60 0 2 35.04 82 0 3 39.93 84 0 3 35.5 61 85 0 3 37.36 86 0 3 39.21 87 1 0 1.06 88 1 0 2.91 89 1 0 4.76 90 1 0 6.61 91 1 0 8.46 68 92 1 0 10.31 69 93 1 0 12.17 NOBRARA382 0 2 36.96 83 1 0 1.88 62 0 2 38.88 84 1 0 0 3.83 63 0 3 0.79 85 1 0 5.79 64 0 3 3 2.71 86 1 0 7.74 65 0 3 4.63 87 1 0 9.69 66 0 3 3 6.55 88 1 0 11.64 67 0 3 3 8.46 89 1 0 13.59 0 3 10.38 90 1 0 15.54 0 3 12.3 91 1 0 17.49 70 0 3 14.21 92 1 0 19.44 94 1 0 14.02 71 0 3 16.13 93 1 0 21.39 95 1 0 15.87 72 0 3 18.05 94 1 0 23.34 96 1 0 17.72 73 0 3 19.97 95 1 0 25.29 97 1 0 19.57 74 0 3 21.88 96 1 0 27.24 98 1 0 21.42 75 0 3 23.8 97 1 0 29.19 99 1 0 23.27 76 0 3 25.72 98 1 0 31.14 100 1 0 25.12 77 0 3 27.64 99 1 0 33.09 57 by 57 0 2 27.4 78 0 3 29.55 100 1 0 35.04 58 0 2 29.29 79 0 3 31.47 60 by 60 0 2 39.01 59 0 2 31.17 80 0 3 33.39 61 0 3 0.99 60 0 2 33.06 81 0 3 35.31 62 0 3 298 61 0 234.94 82 0 3 37.22 63 0 3 4.96 62 0 2 36.83 83 0 3 39.14 64 0 3 3 6.94 63 0 2 38.71 84 1 0 1.06 65 0 3 8.93 64 0 3 0.6 85 1 0 0 2.98 66 0 3 10.91 65 0 3 2.48 86 1 0 0 4.89 67 0 3 12.89 66 0 3 4.36 87 1 0 6.81 68 0 3 14.88 67 0 3 6.25 88 1 0 8.73 69 0 3 16.86 68 0 3 8.13 89 1 0 10.64 70 0 3 18.84 69 0 3 10.02 90 1 0 12.56 71 0 3 20.83 70 0 3 11.9 91 1 0 14.48 72 0 3 22.81 71 0 3 13.79 92 1 0 16.4 73 0 3 24.79 72 0 3 15.67 93 1 0 18.31 74 0 3 26.78 73 0 3 17.55 94 1 0 20.23 75 0 3 28.76 74 0 3 19.44 95 1 0 22.15 76 0 3 30.74 75 0 3 21.32 96 1 0 24.07 77 0 3 32.73 76 0 3 23.21 97 1 0 25.98 78 0 3 34.71 77 0 3 25.09 98 1 0 27.9 79 0 3 36.69 78 0 3 26.98 99 1 0 29.82 80 0 3 38.68 79 0 3 28.86 100 1 0 31.74 81 1 0 0.66 80 0 3 30.74 59 by 59 0 2 35.07 82 1 0 2.64 81 0 3 32.63 60 0 2 37.02 83 1 0 4.63 82 0 3 34.51 61 0 2 38.98 84 1 0 6.61 83 0 3 36.4 62 0 3 0.93 85 1 0 0 8.6 84 0 3 38.28 63 0 3 2.88 86 1 0 10.58 85 1 0 0.17 64 0 3 4.83 87 1 0 12.56 86 1 0 2.05 65 0 3 6.78 88 1 0 14.55 87 1 0 3.93 66 0 3 8.73 89 1 0 16.53 88 1 0 5.82 67 0 3 10.68 90 1 0 18.51 89 1 0 7.7 68 0 3 12.63 91 1 0 20.5 90 1 0 9.59 69 0 3 14.58 92 1 0 22.48 91 1 0 11.47 70 0 3 16.53 93 1 0 24.46 92 1 0 13.36 71 0 3 18.48 94 1 0 26.45 252 TABLES OF LAND MEASURE: Dimensions. Statute content. Dimensions. Statute content. Dimensions. Statute content. Yards. A. R. P. Yards. A. R. P. Yards. A. R. P. 60 by 95 1 0 28.43 62 by 80 1 0 3.97 64 by 69 0 3 25.98 96 1 0 30.41 81 1 0 6.02 70 0 3 28.1 97 1 0 32.4 82 1 0 8.07 71 0 3 30.21 98 1 0 34.38 83 1 0 10.12 72 0 3 32.33 99 1 0 36.36 84 1 0 12.17 73 0 3 34.45 100 1 0 38.35 85 1 0 14.21 74 0 3 36.56 61 by 61 0 3 3.01 86 1 0 16.26 75 0 3 38.68 62 0 3 5.02 87 1 0 18.31 76 1 0 0.79 63 0 3 7.04 88 1 0 20.36 77 1 0 2.91 64 0 3 9.06 89 1 0 22.41 78 1 0 5.02 65 0 3 11.07 90 1 0 24.46 79 1 0 7.14 66 0 3 13.09 91 1 0 26.51 80 1 0 9.26 67 0 3 15.11 92 1 0 28.56 81 1 0 11.37 71 IIIIIFINIJ88: 0 3 17.12 93 1 0 30.61 82 1 0 13.49 0 3 19.14 94 1 0 32.66 83 1 0 15.6 70 0 3 21.16 95 1 0 34.71 84 1 0 17.72 0 3 23.17 96 1 0 36.76 85 1 0 19.83 72 0 3 25.19 97 1 0 38.81 86 1 0 21.95 73 0 3 27.21 98 1 1 0.86 87 1 0 24.07 74 0 3 29.22 99 1 1 2.91 88 1 0 26.18 75 0 3 31.24 100 1 1 4.96 89 1 0 28.3 76 0 3 33.26 63 by 63 0 3 11.21 90 1 0 30.41 77 0 3 35.27 64 0 3 13.29 91 1 0 32.53 78 0 3 37.29 65 0 3 15.37 92 1 0 34.64 0 3 39.31 66 0 3 17.45 93 1 0 36.76 80 1 0 1.32 67 0 3 19.54 94 1 0 38.88 81 1 0 3.34 68 0 3 21.62 95 1 1 0.99 82 1 0 5.36 69 0 3 23.7 96 1 1 3.11 83 1 0 7.37 70 0 3 25.79 97 1 1 5.22 84 1 0 9.39 71 0 3 27.87 98 1 1 7.34 85 1 0 11.4 72 0 3 29.95 99 1 1 9.45 86 1 0 13.42 73 0 3 32.03 100 1 1 11.57 87 1 0 15.44 74 0 3 34.12 65 by 65 0 3 19.67 88 1 0 17.45 75 0 3 36.2 66 0 3 21.82 89 1 0 19.47 76 0 3 38.28 67 0 3 23.97 90 1 0 21.49 77 1 0 0.36 68 0 3 26.12 91 1 0 23.5 78 1 0 2.45 69 0 3 28.26 92 1 0 25.52 79 1 0 4.53 70 0 3 30.41 93 1 0 27.54 80 1 0 6.61 71 0 3 32.56 94 1 0 29.55 81 1 0 8.69 72 0 3 34.71 95 1 0 31.57 82 1 0 10.78 73 0 3 36.86 96 1 0 33.59 83 1 0 12.86 74 0 3 39.01 97 1 0 35.6 84 1 0 14.94 75 1 0 1.16 98 1 0 37.62 85 1 0 17.02 76 1 0 3.31 99 1 0 39.64 86 1 0 19.11 77 1 0 5.45 100 1 1 1.65 87 1 0 21.19 78 1 0 7.6 62 by 62 0 3 7.07 88 1 0 23.27 79 1 0 9.75 63 0 3 9.12 89 1 0 25.36 80 1 0 11.9 64 0 3 11.17 90 1 0 27.44 81 1 0 14.05 65 0 3 13.22 91 1 0 29.52 82 1 0 16.2 66 0 3 15.27 92 1 0 31.6 83 1 0 18.35 67 0 3 17.32 93 1 0 33.69 84 1 0 20.5 68 0 3 19.37 94 1 0 35.77 85 1 0 22.64 69 0 3 21.42 95 1 0 37.85 86 1 0 24.79 70 0 3 23.47 96 1 0 39.93 87 1 0 26.94 71 0 3 25.52 97 1 1 2.02 88 1 0 29.09 72 0 3 27.57 98 1 1 4.1 89 1 0 31.24 73 0 3 29.62 99 1 1 6.18 90 1 0 33.39 74 0 3 31.67 100 1 1 8.26 91 1 0 35.54 75 0 3 33.72 64 by 64 0 3 15.4 92 1 0 37.69 76 0 3 35.77 65 0 3 17.52 93 1 0 39.83 77 0 3 37.82 66 0 3 19.64 94 1 1 1.98 78 0 3 39.87 67 0 3 21.75 95 1 1 4.13 79 1 0 1.92 68 0 3 23.87 96 1 1 6.28 TABLES OF LAND MEASURE. 253 Dimensions. Statute content. Yards. A. R. P. Dimensions. Yards. Statute content. Dimensions. Statute content. A. R. Ρ Yards. A. R. P. 65 by 97 1 1 8.43 67 by 92 1 1 3.77 69 by 91 1 1 7.57 98 1 1 10.58 93 1 1 5.98 92 1 1 9.85 99 1 1 12.73 94 1 1 8.2 93 1 1 12.13 100 1 1 14.88 95 1 1 10.41 94 1 1 14.41 66 by 66 0 3 24. 96 1 1 12.63 95 1 1 16.69 78 CIZIJAF≈≈NJ882 67 0 3 26.18 97 1 1 14.84 96 1 1 18.98 3 28.36 98 1 1 17.06 97 1 1 21.26 3 30.55 99 1 1 19.27 98 1 1 23.54 70 0 3 32.73 100 1 1 21.48 99 1 1 25.82 0 3 34.91 68 by 68 0 3 32.86 100 1 1 28.1 0 3 37.09 69 0 3 35.11 70 by 70 1 0 1.98 0 3 39.27 70 0 3 37.36 71 1 0 4.3 74 1 0 1.45 71 0 3 39.6 72 1 0 6.61 1 0 3.64 72 1 0 1.85 73 1 0 8.93 76 1 0 5.82 73 1 0 4.1 74 1 0 11.24 77 1 0 8. 74 1 0 0 6.35 75 1 0 13.55 1 0 10.18 75 1 0 8.6 76 1 0 15.87 1 0 12.36 76 1 0 10.84 77 1 0 18.18 80 1 0 14.55 77 1 0 13.09 78 1 0 20.5 81 1 0 16.73 78 1 0 15.34 79 1 0 22.81 82 1 0 18.91 79 1 0 17.59 80 1 0 25.12 83 1 0 21.09 80 1 0 19.83 81 1 0 27.44 84 1 0 23.27 81 1 0 22.08 82 1 0 29.75 85 1 0 25.45 82 1 0 24.33 83 1 0 32.07 86 1 0 27.64 83 1 0 26.58 84 1 0 34.38 87 1 0 29.82 84 1 0 28.83 85 1 0 36.69 88 1 0 32. 85 1 0 31.07 86 1 0 39.01 89 1 0 34.18 86 1 0 33.32 87 1 1 1.32 90 1 0 36.36 87 1 0 35.57 88 1 1 3.64 91 1 0 38.55 88 1 0 37.82 89 1 1 5.95 92 1 1 0.73 89 1 1 0.07 90 1 1 8.26 93 1 1 1 2.91 90 1 1 2.31 91 1 1 10.58 94 1 1 1 5.09 91 1 1 4.56 92 1 1 12.89 95 1 1 7.27 92 1 1 6.81 93 1 1 15.21 96 1 1 9.45 93 1 1 9.06 94 1 1 17.52 97 1 1 11.64 94 1 1 11.51 95 1 1 19.83 98 1 1 13.82 95 1 1 13.55 96 1 1 22.15 99 1 1 16. 96 1 1 15.8 97 1 1 24.46 100 1 1 18.18 97 1 1 18.05 98 1 1 26.78 67 by 67 0 3 28.4 98 1 1 20.3 99 1 1 29.09 68 0 3 30.61 99 1 1 22.55 100 1 1 31.4 69 0 3 32.83 100 1 1 24.79 71 by 71 1 0 6.64 70 0 3 35.04 69 by 69 0 3 37.39 72 1 0 8.99 71 0 3 37.26 70 0 3 39.67 73 1 0 11.34 72 0 3 39.47 71 1 0 1.95 74 1 0 13.69 73 1 0 1.69 72 1 0 4.23 75 1 0 16.03 74 1 0 3.9 73 1 0 6.51 76 1 0 18.38 75 1 0 6.12 74 1 0 8.79 77 1 0 20.73 76 1 0 8.33 75 1 0 11.07 78 1 0 23.07 77 1 0 10.55 76 1 0 13.36 79 1 0 25.42 78 1 0 12.76 77 1 0 15.64 80 1 0 27.77 79 1 0 14.98 78 1 0 17.92 81 1 0 30.12 80 1 0 17.19 79 1 0 20.2 82 1 0 32.46 81 1 0 19.4 80 1 0 22.48 83 1 0 34.81 82 1 0 21.62 81 1 0 24.76. 84 1 0 37.16 83 1 0 23.83. 82 1 0 27.04 85 1 0 39.5 84 1 0 26.05 83 1 0 29.32 86 1 1 1.85 85 1 0 28.26 84 1 0 31.6 87 1 1.4.2 86 1 0 30.48 85 1 0 33.88 88 1 1 6.55 87 1 0 32.69 86 1 0 36.17 89 1 1 8.89 88 1 0 34.91 87 1 0 38.45 90 1 1 11.24 89 1 0 37.12 88 1 1 0.73 91 1 1 13.59 90 1 0 39.34 89 1 1 3.01 92 1 1 15.93 91 1 1 1 1.55 90 1 1 5.29 93 1 1 18.28 254 TABLES OF LAND MEASURE. Dimensions. Statute content. Dimensions. Statute content. Dimensions. Statute content. Yards. A. R. P. 71 by 91 1 1 20.63 Yards. 74 by 74 A. R. P. Yards. A. K. P. 1 0 21.02 76 by 87 1 1 18.58 95 1 1 22.98 75 1 0 23.47 88 1 1 21.09 96 1 1 25.32 76 1 0 25.92 89 1 1 23.6 97 1 1 27.67 77 1 0 28.36 90 1 1 26.12 98 1 1 30.02 78 1 0 30.81 91 1 1 28.63 99 1 1 32.36 79 1 0 33.26 92 1 1 31.14 100 1 1 34.71 80 1 0 35.7 93 1 1 33.65 72 by 72 1 0 11.37 81 1 0 38.15 94 1 1 36.17 73 1 0 13.75 82 1 1 0.6 95 1 1 38.68 74 1 0 16.13 83 1 1 3.04 96 1 2 1.19 75 1 0 18.51 84 1 1 5.49 97 1 2 3.7 76 1 0 20.89 85 1 1 7.93 98 1 2 6.21 77 1 0 23.27 86 1 1 10.38 99 1 2 8.73 78 1 0 25.65 87 1 1 12.83 100 1 2 11.24 79 1 0 28.03 88 1 1 15.27 77 by 77 1 0 36. 80 1 0 30.41 89 1 1 17.72 78 1 0 38.55 81 1 0 32.79 90 1 1 20.17 79 1 1 1.09 82 1 0 35.17 91 1 1 22.61 80 1 1 3.64 83 1 0 37.55 92 1 1 25.06 81 1 1 6.18 84 1 0 39.93 93 1 1 27.5 82 1 1 8.73 85 1 1 2.31 94 1 1 29.95 83 1 1 11.27 86 1 1 4.69 95 1.1 32.4 84 1 1 13.82 87 1 1 7.07 96 1 1 34.84 85 1 1 16.36 88 1 1 9.45 97 1 1 37.29 86 1 1 18.91 89 1 1 11.83 98 1 1 39.74 87 1 1 21.45 90 1 1 14.21 99 1 2 2.18 88 1 1 24. 91 1 1 16.6 100 1 2 4.63 89 1 1 26.55 92 1 1 18.98 75 by 75 1 0 25.95 90 1 1 29.09 93 1 1 21.36 76 1 0 28.43 91 1 1 31.64 94 1 23.74 77 1 0 30.91 92 1 1 34.18 95 1 1 26.12 78 1 0 33.39 93 1 1 36.73 96. 1 1 28.5 79 1 0 35.87 94 1 1 39.27 97 1 1 30.88 80 1 0 38.35 95 1 2 1.82 98 1 1 33.26 81 1 1 0.83 96 1 2 4.36 99 1 1 35.64 82 1 1 3.31 97 1 2 6.91 100 1 1 38.02 83 1 1 5.79 98 1 2 9.45 73 by 73 1 0 16.17 84 1 1 8.26 99 1 2 12. 74 1 0 18.58 85 1 1 10.74 100 1 2 14.55 75 1 0 20.99 86 1 1 13.22 78 by 78 1 1 1.12 76 1 0 23.4 87 1 1 15.7 79 1 1 3.7 77 1 0 25.82 88 1 1 18.18 80 1 1 6.28 78 1 0 28.23 89 1 1 20.66 81 1 1 8.86 79 1 0 30.64 90 1 1 23.14 82 1 1 11.44 80 1 0 33.06 91 1 1 25.62 83 1 1 14.02 81 1 0 35.47 92 1 1 28.1 84 1 1 16.6 82 1 0 37.88 93 1 1 30.58 85 1 1 19.17 83 1 1 0.3 94 1 1 33.06 86 1 1 21.75 84 1 1 2.71 95 1 1 35.54 87 1 1 24.33 85 1 1 5.12 96 1 1 38.02 88 1 1 26.91 86 1 1 7.54 97 1 2 0.5 89 1 1 29.49 87 1 1 9.95 98 1 2 2.98 90 1 1 32.07 88 1 1 12.36 99 1 2 5.45 91 1 1 34.64 89 1 1 14.78 100 1 2 7.93 92 1 1 37.22 90 1 1 17.19 76 by 76 1 0 30.94 93 1 1 39.8 91 1 1 19.6 77 1 0 33.45 94 1 2 2.38 92 1 1 22.02 78 1 0 35.97 95 1 2 4.96 93 1 1 24.43 79 1 0 38.48 96 1 2 7.54 94 1 1 26.84 80 1 1 0.99 97 1 2 10.12 95 1 1 29.26 81 1 1 3.5 98 1 2 12.69 96 1 1 31.67 82 1 1 6.02 99 1 2 15.27 97 1 1 34.08 83 1 1 8.53 100 1 2 17.85 98 1 1 36.5 84 1 1 11.04 79 by 79 1 1 6.31 99 1 1 38.91 85 1 1 13.55 80 1 1 1 8.93 100 1 2 2 1.32 86 1 1 16.07 81 1 1 11.54 TABLES OF LAND MEASURE. 255 Dimensions. Statute content. 1 ards. A. R. P. Dimensions. Yards. Statute content. Dimensions. Statute content. A. R. P. Yards. A. R. P. 79 by 82 1 1 14.15 82 by 86 1 1 33.12 85 by 99 1 2 38.18 83 1 1 16.76 87 1 1 35.83 100 1 3 0.99 84 1 1 19.37 88 1 1 38.55 86 by 86 1 2 4.5 85 1 1 21.98 89 1 2 1.26 87 1 2 7.34 86 1 1 24.6 90 1 2 3.97 88 1 2 10.18 87 1 1 27.21 91 1 2 6.68 89 1 2 13.02 88 1 1 29.82 92 1 2 9.39 90 1 2 15.87 89 1 1 32.43 93 1 2 12.1 91 1 2 18.71 90 1 1 35.04 94 1 2 14.81 92 1 2 21.55 91 1 1 37.65 95 1 2 17.52 93 1 2 24.4 92 1 2 0.26 96 1 2 20.23 94 1 2 27.24 93 1 2 2.88 97 1 2 22.94 95 1 2 30.08 94 1 2 5.49 98 1 2 25.65 96 1 2 32.93 95 1 2 2 8.1 99 1 2 28.36 97 1 2 35.77 96 1 2 10.71 100 1 2 31.07 98 1 2 38.61 97 1 2 13.32 83 by 83 1 1 27.74 99 1 3 1.45 98 1 2 15.93 84 1 1 30.48 100 1 3 3 4.3 99 1 2 18.55 85 1 1 33.22 87 by 87 1 2 10.21 100 1 2 21.16 86 1 1 35.97 88 1 2 13.09 80 by 80 1 1 11.57 87 1 1 38.71 89 1 2 15.97 81 1 1 14.21 88 82 1 1 16.86 89 83 1 1 19.5 90 84 1 1 22.15 91 1 2 NNNN 1 2 1.45 90 1 2 18.84 1 2 4.2 91 1 2 21.72 1 2 6.94 92 1 2 24.6 2 9.69 93 1 2 27.47 85 1 1 24.79 92 1 2 12.43 94 1 2 30.35 86 1 1 27.44 93 1 2 15.17 95 1 2 33.22 87 1 1 30.08 94 1 2 17.92 96 1 2 36.1 88 1 1 32.73 95 1 2 20.66 97 1 2 38.98 89 1 1 35.37 96 1 2 23.4 98 1 3 1.85 90 1 1 38.02 97 1 2 26.15 99 1 3 4.73 91 1 2 0.66 98 1 2 28.89 100 1 3 7.6 92 1 2 3.31 99 1 2 31.64 88 by 88 1 2 16. 93 1 2 5.95 100 1 2 34.38 89 1 2 18.91 94 1 2 8.6 84 by 84 1 1 33.26 90 1 2 21.82 95 1 2 11.24 85 1 1 36.03 91 1 2 24.73 96 1 2 13.88 86 1 1 38.81 92 1 2 27.64 97 1 2 16.53 87 1 2 1.59 93 1 2 30.55 98 1 2 19.17 88 1 2 4.36 94 1 2 33.45 99 1 2 21.82 89 1 2 7.14 95 1 2 36.36 100 1 2 24.46 90 1 2 9.92 96 1 2 39.27 81 by 81 1 1 16.89 91 1 2 12.69 97 1 3 2.18 82 1 1 19.57 92 1 2 15.47 98 1 3 5.09 83 1 1 22.25 93 1 2 18.25 99 1 3 8. 84 1 1 24.93 94 1 2 21.02 100 1 3 10.91 85 1 1 27.6 95 1 2 23.8 89 by 89 1 2 21.85 86 1 1 30.28 96 1 2 26.58 90 1 2 24.79 87 1 1 32.96 97 1 2 29.36 91 1 2 27.74 88 1 1 35.64 98 1 2 32.13 92 1 2 30.68 89 1 1 38.31 99 1 2 34.91 93 1 2 33.62 90 1 2 0.99 100 1 2 37.69 94 1 2 36.56 91 1 2 3.67 85 by 85 1 1 38.84 95 1 2 39.5 92 1 2 6.35 86 1 2 1.65 96 1 3 2.45 93 1 2 2 9.02 87 1 2 4.46 97 1 3 5.39 94 1 2 11.7 88 1 2 7.27 98 1 3 8.33 95 1 2 14.38 89 1 2 10.08 99 1 3 11.27 96 1 2 17.06 90 1 2 12.89 100 1 3 14.21 97 1 2 19.74 91 1 2 15.7 90 by 90 1 2 27.77 98 1 2 22.41 92 1 2 18.51 91 1 2 30.74 99 1 2 25.09 93 1 2 21.32 92 1 2 33.72 100 1 2 27.77 94 1 2 24.13 93 1 2 36.69 82 by 82 1 1 22.28 95 1 2 26.94 94 1 2 39.67 83 1 1 24.99 96 1 2 29.75 95 1 3 2.64 84 1 1 27.7 97 1 2 32.56 96 1 3 5.62 85 1 1 30.41 98 1 2 35.37 97 1 3 8.59 256 TABLES OF LAND MEASURE. Dimensions. Yards. Statute content. Dimensions. Statute content. Dimensions. Statute content. A. R. P. Yards. 90 by 98 1 3 11.57 92 by 99 A. R. P. 1 3 21.09 Yards. A. R. P. 95 by 98 1 3 27.77 99 1 3 14.55 100 1 3 24.13 99 1 3 30.91 100 1 3 17.52 93 by 93 1 3 5.92 100 1 3 34.05 91 by 91 1 2 33.75 94 1 3 8.99 96 by 96 1 3 24.66 92 1 2 36.76 95 1 3 12.07 97 1 3 27.83 93 1 2 39.77 96 1 3 15.14 98 1 3 31.01 94 1 3 2.78 97 1 3 18.21 99 1 3 34.18 95 1 3 5.79 98 1 3 21.29 100 1.3 37.36 96 1 3 8.79 99 1 3 24.36 97 by 97 1 3 31.04 97 1 3 11.8 100 1 3 27.44 98 1 3 34.25 98 1 3 14.81 94 by 94 1 3 12.1 99 1 3 37.45 99 1 3 17.82 95 1 3 15.21 100 2 0 0.66 100 1 3 20.83 96 1 3 18.31 98 by 98 1 3 37.49 92 by 92 1 2 39.8 97 1 3 21.42 99 2 0 0.73 93 1 3 2.84 98 1 3 24.53 100 2 0 3.97 94 1 3 5.88 99 1 3 27.64 99 by 99 2 0 4. 95 1 3 8.93 100 1 3 30.74 100 2 0 7.27 96 1 3 11.9795 by 95 1 3 18.35 100 by 100 20 10.58 97 1 3 15.01 96 1 3 21.49 98 1 3 18.05 97 1 3 24.63 THESE TABLES have been computed by my Assistants, MR. A. R. SOWDON and MR. W. EVE, and the proofs from the press most carefully examined by MR. W. EVE and MR. FRANK HARROW, whose assistance I have much pleasure in acknowledging. LAND SURVEYING. 257 CHAPTER VII. LAND SURVEYING. UNLIKE Land Measuring, the Science of Land Surveying, to be practised successfully, requires that the person who uses it should be well educated in the several branches of Arithmetic, Algebra, Logarithms, Trigonometry, and Geometry; and to carry on Surveys of extensive and varied character, several years of previous practice is necessary. Under the heading of Land Surveying, is properly included every description of Mapping and Levelling, in whatever manner performed. As great, if not greater improvements have been effected in this particular science within the last few years than in any other, and many costly works have been published, but as I believe, with very few exceptions, those works, while they profess to do every- thing, contain nothing, comparatively speaking, of the practical methods adopted by skilful surveyors of the present day. The little work in Mr. Weale's Rudimentary Treatises* is written by a practical Surveyor, and contains many very useful remarks, which will, doubtless, conduce to promote its circulation; but with this exception, I am not acquainted with any Treatise exclusively penned by a practical man. They are, for the most part, the pro- duction of schoolmasters and other mere theorists; and some of them are but enlarged editions of original works, written previous to the introduction of those improvements into the practice of Surveying of which I have spoken. Perhaps the greatest stimulant Civil Surveying ever received was, the passing of the Tithe Commutation Act in 1836, under which all titheable lands in England and Wales were required to be surveyed and mapped. In accordance with the provisions of that Act and the new Poor-Law Assessment Act of a previous session, I, in my own personal practice, surveyed and mapped parishes to an aggregate extent of about sixty thousand acres within a period of ten years. It has long been my desire to publish fully the practical knowledge experience has taught me in that and subse- quent works; but a want of time, coupled with the very great expense of such a publication, and its usually unprofitable cha- racter (at all events to an author) has deterred the intention. * Land and Engineering Surveying, by T. Baker, C.E. 258 LAND SURVEYING. The following Synopsis is intended to contain such information as will afford an insight into the best principles of the science, in character with the nature of the present work. SEC. 1.-Parish and Estate Surveying. The first step in the practice of Surveying is to learn to chain a line with accuracy and dispatch; the former of which being ac- quired, the latter will be sure to follow, with practice. An active man who has a good eye is invaluable to a surveyor as a chain- man: such a one is very difficult to be obtained, and is not often to be met with in a purely agricultural district. Many of the most active men being wholly incapable of sticking out a straight line, while on the contrary, men with excellent eyes are frequently too cloddy in their motions to get across a country. A little attention in the selection of a chain-man will amply repay the trouble. The best way to direct a chain is for the person who follows it to stand perfectly upright behind the arrow which has been left in the ground; his heels touching each other, his toes pointed out on either side of the arrow, and his feet forming something like an angle of 30 degrees with the chain line. His chain-man should also stand erect, and so soon as he is placed nearly in his position, should take care that his heels touch, and that his feet form the reverse position of his director, who is then enabled, by the motion of the thumb of the right-hand in which he holds the handle of the chain, to bring him into an exact line between himself and the fore mark, which, if of good size and well chosen, will then appear to rise directly above the centre of the man's head. The man, if he understand his business, will at the same time discover if any par- ticular object which he may have noticed to have been either in a direct line with the chain, or bearing a relative position therewith in former sets, still occupies the same position, and thus becomes a guarantee that no mistake has been made in the foremark. He will then be careful to tighten the chain so soon as the director has his handle to the arrow; when he has so done, will stick his arrow down between his feet, and will then be ready to proceed on his line when directed. The director of the chain having the handle in his right-hand, will stoop down as soon as his chain-man is in the right direction; and putting his thumb through the bow or eye of the arrow, will cause the handle of the chain to touch the arrow ; and seeing that while in that position his chain-man places his ar- row properly in the ground, will, as soon as that is accomplished, close his hand without withdrawing his thumb, and in rising will LAND SURVEYING. 259 way be very draw the arrow up with him. Five arrows can in this conveniently carried, their points always sticking out to the right, the obvious consequence of the hand being closed upon them, and the back of the hand being kept in a perfectly horizontal position, otherwise the points will be found to be sticking in the ground when the attempt is made to put the thumb through the eye of the arrow. According to the height of the person directing a chain will be the distance from the arrow at which his feet will require to be placed, so that when he stoops to touch the wire with the handle, the chain may exactly reach the required spot without sub- sequently requiring to be moved either backwards or forwards: this also is one of those mechanical performances in which practice will produce the greatest proficiency. The chain-man should carry the arrows in his left hand, the chain in his right, and while walking along should draw one arrow out of the bundle with his right hand in readiness for use at the termination of the chain. He should also pay attention to the length of a chain, so as to judge approximately the point at which he will have to stop, that no sudden jerk may be experienced by the chain (which does it great harm) and that the operation of turning round and getting in line be effected as quickly as possible; to which end he should be instructed to be always on the look out for his back mark, and by moving about to place himself as nearly as he can do in the same relative position with it and the director (who is standing at the last arrow) as he occupied in setting the previous chains. A chain-man's attention should be called to the necessity of observing, as soon as the first chain on a line is set, the position of some one or more objects to serve as a back mark; it will save much loss of valuable time, and no end of trouble, and there are seldom cases when something cannot be noticed, at all events, if not directly in line, so little removed from it that its position can be approximately determined. Before commencing to chain a line, the director of the chain should stand at the point at which the line commences, and look- ing at the most distant fore mark, should observe if any remark- able object, a green spot in a field, a gap or a bush in a hedge, a tree, a bough, or a thistle, is directly in his line; if so, he should frequently notice while traversing the line, that his position with reference to it becomes unaltered; and by the exercise of care in this manner, a line 30 or 40 chains in length, may be chained with perfect straightness without any artificial setting out. But if there is no intervening object, and the line is a long one with off-sets, it will be better to direct one or two sticks to be stuck up at inter- 260 LAND SURVEYING. mediate distances, for the best men will sometimes wind a line if they have but a single mark at the end of it to guide them. Very competent surveyors vary in their practice as to the num- ber of arrows they use. I have had experience in the several methods, both from necessity (caused by the occasional loss of an arrow) and design, and have no hesitation in recommending the number ten as the most practical, surest, and best. The chain-man proceeds with his eleventh chain precisely in the same manner as though he had a handful of arrows, the only difference in his opera- tion being, instead of sticking down that of which he has none left, he lays his handle of the chain on the ground and places his foot. upon it, in which position he remains until the ten wires are brought up to him by the director, of whom he takes them, imme- diately places one in the ground, and then proceeds on his way. The pointed end of the swivel in the centre of the chain should always determine the end which should go first; if attention is not paid to this, the abrupt angles at the other end of the swivel hang in the bushes in passing through hedges, and frequently meet with other obstructions which jerk and stretch the chain, and which are passed harmless if the other end is driven first. To ensure expedition, a surveyor's field staff should include a man to draw and another to follow the chain, a boy to carry sticks and make marks and stations; and if the work is very thick, a com- petent person to measure the offsets, himself keeping the book; if not very close work, he can save the offset man by using the rod himself: the great desideratum being (always assuming the prac- tice is followed for a profit) to keep the chain continually moving. Throughout the course of every line an infinity of marks should be made at intervals, certainly not exceeding ten chains, and if at five the better. These marks will be found exceedingly useful in determining the position of other lines falling near them, and in the detection of an error, an event which will happen occasionally to the most careful. This induces a notice of a few of the most fruitful sources of error to young surveyors. First may be mentioned, want of at- tention to the change of arrows at the end of ten chains; then the omission in long naked lines to make any note in the book of the number of changes as they successively occur; the mistake of the 40 brass mark for 60; the 20 for 80; the confusion of the fore mark with some other object similar, but out of direction; cases in which it is impossible to set an arrow down at the end of the chain that perhaps occurs in the centre of a pond or a deep ditch, in con- sequence of which several parts of a chain are obliged to be used, LAND SURVEYING. 261 and require to be set to rights when the obstruction is passed; and last, though not of least importance, the too common practice of allowing a chain-man to hold his own handle of the chain to the point which terminates the line, instead of hauling beyond it, by which means the chain is frequently read from the wrong end, or an offset is booked at the wrong place. The best marks to be made on a line in grass lands are such as can be cut out with a small spade in one of the forms of fig. 136, and if many of them are made in one piece of ground, they should be distinguished from one another, as shewn in the fig., where the different position of the detached diamond, which is entered in the book as marked on the land, readily effects it. In arable land nothing more can be done than driving in a peg; but every fence should be marked, either by a race mark on a quickset or bough, or in any ready way which may present itself. All pale fences should be rased on passing, and every post which may be in line. The length of the offset rod in most general favour is ten links, but fifteen links will be found preferable; and the one used by me is twenty links. It is made of a straight piece of ground-ash. It has no figures on it; but the links are marked by characteristic colouring; an arrangement which allows either end to be used without chance of error. In "sticking out a line," particular care should be taken that at least three (as many more as possible) of the ranging rods or pickets are seen at the time of planting a fresh one; an obvious precaution against a deviation of the line, which the slightest inac- curacy would produce if only two were used. In crossing the sharp apex of a hill great care is also required to preserve the straightness of a line, and in many cases which occur in large sur- veys, the use of an instrument, if not absolutely indispensable is very desirable. It sometimes happens that a line may be ranged across a series of hills, from apex to apex, and the intermediate spaces across the valleys subsequently managed, but no regular rule can be laid down; generally, the great consideration is, to get some permanent and very prominent back and fore mark, if pos- sible, beyond the limits of the work. As an illustration of this method, in conducting a survey of the parish of Horsell, in Surrey, about two years since, I found the church, in the heart of the vil- lage, to occupy a very prominent position on a hill; and I imme- diately obtained permission to use the tower (a square one) as a station. Upon the top of this I erected a large flag pole, and from that pole laid out a line towards every remarkable object on the 262 LAND SURVEYING. surrounding hills, regardless of where it would terminate, and then connected them by base lines. These lines were all patterns of straightness-houses and farm buildings offered small obstacles with such a mark behind and before; and although it frequently happened that for eight or ten fields we could see neither, no in- stance occurred in which the end of our line was not proved beyond doubt as being in the same direction in which we started. A knowledge of the principles of what is technically called "taking up the details" of a survey, next claims our attention. This is done by means of what are called "offsets," or short lines measured from any given point on a chain line to an angle or point in a hedge, fence, or building, to fix the position of that point upon the plan. These offsets are measured with the offset rod already spoken of, and are generally taken at right angles with the chain line, simply because that is an angle that may be very approxi- mately determined upon the ground and as readily upon the plan, without the aid of an instrument in either case; short distances. only being used. It is not however at variance with sound prin- ciples if a sextant or any angular instrument is used, if these off- sets are made to take any other angle which special circumstances may require; but then it involves the noting of the angle, and so forth, and occasions an inconvenience and trouble to the surveyor, which he will always avoid if he can. All offsets not specially de- noted by any angle are understood to be right angles, whether under a variety of circumstances that may have occurred in the field they are so drawn in the book or not. There is another species of offsets called "opposites," and dis- tinguished from the ordinary offsets by the letters "op" annexed to them. They are such as these: supposing two chain lines A B and A C, (fig. 137,) to pass on either side the house D, and that in chaining those lines the points a and d, at which the line of the front of the building b c would, if produced, intersect, had been noticed; then would the distance a b become an "op." at the point a on the line A C to the corner of the house D, and the distance c d would become an op" at the point d on line A B to the same house D, the position of which, if the points are correctly taken, a proof of which is afforded by measuring bc, must be obviously better fixed than by any other method of offsetting. When the distance between any two points on a given line of fence or building is taken, it is called an "along," and is entered in the book with an "a" attached to the figures, thus 24 a placed on a line between two points denotes it is 24 along that line from point to point. LAND SURVEYING. 263 The accuracy of an offset depends upon the care with which it is taken; but after all it is generally little more than an approxi- mation to truth, and becomes more and more liable to error as it is increased in length; for it may be measured on the ground with a little inclination from the perpendicular in one direction, and plotted on the paper with an inclination in the opposite direction. Slight inaccuracies may also occur in measuring with the rod; hence, what is of but trifling importance in small operations in- creases with a significant ratio, and renders it necessary to sub- scribe a limit to the length of the offset. This limit has been usually fixed by writers on the subject at "one chain;" but that is too much, except for very small scales, and as applied to the scale of 44 feet to an inch, adopted by the General Board of Health for all plans made under the "Public Health Act 1848," totally im- practicable. To that scale two lengths of the rod used is quite as long as any offset can be safely taken, and then great care is re- quired to make them plot nicely, as every half link makes a percep- tible difference. The length of the offset must therefore be a dis- cretionary point with the surveyor, as ranging from about 30 to 80 or 100 links, according to circumstances; special points and sharp angles being as much as possible fixed by short offsets, while fences running nearly parallel to the chain line in which a departure from the perpendicular will neither affect the length of the offset nor the position of the fence on the paper, may form exceptions for the exercise of a little indulgence. To illustrate the method of taking up the details, we will con- sider the fence A abcd B (fig. 138), is to be taken up by the offset line A B. Looking along the fence from the point A, we discover that a bend occurs at the point a, and therefore in chaining along the line from A towards B, we carry the point a in our mind's eye, and determine when we arrive at the point a', from which the per- pendicular d'a arises; noting the distances A a and a'a, we proceed to measure until we arrive at b', where we note the respective dis- tances A b and b'b, and chain on to c; here the chain line touches the fence, and therefore we have only one distance to denote, viz., Ac; hence, we go on to d, noting in a similar manner the dis- tances A d' and d'd, and complete our work by entering the length of the line AB. A little consideration and study will convey to the mind of the enquirer the application of this principle to every crooked fence which can possibly occur in a survey. Had there been a fence on the opposite side of the line in fig. 138, as in fig. 139, offsets would have been required, as there shewn; and again, if one line had been insufficient to take up the fence, more must 264 LAND SURVEYING. have been taken, as shewn in Figures 140 and 141; the several ends of the lines being fixed by triangulation, as hereafter to be spoken of. We now come to the consideration of the method of laying out the fundamental lines of a survey. In order to do this effectually, the surveyor must acquaint himself with the boundary of the land to be surveyed, and if he can make one triangle encompass the whole without going too far out of the work, of course that is the best method that can be adopted; because if he can only get the sides of that triangle accurately set out and measured, all other lines within it may be made to depend thereon, and the chances of error are consequently confined to the internal detail thereof, which is easily detected and rectified. A large triangle, comprising the boundary of an estate, is gene- rally sufficiently proved by the secondary lines that traverse it from side to side in every possible direction; but it is a very great ad- vantage where it can be done to take the angles formed by the several sides of the triangle. This enables the straightness of the sides to be tested by casting the internal angles together and ascer- taining if they amount to 180 degrees, as the sum of the internal angles of all triangles should do. It also enables a surveyor to run a proof line from any one of the points of the triangle, so as to fall at a right angle on the opposite side. For instance, let us suppose the angles of the triangle represented in fig. 142 were taken, and that the angle B A C is 38 degrees, we require to let fall the proof line BD, so that the angles BD A and B DC may be each right angles. Taking the angle B A D=38° and the angle B DA = 90°, we know of course that the angle ABD must be such as will make when cast with the two known angles 180 degrees; hence, in this case, we have to lay off 52 degrees at B as the measure of the angle A B D. If any one of the sides is not straight, the aggregate sum of the observed angles will be either greater or less than 180 degrees, according to the nature of the error. (See fig. 143.) It is hardly to be supposed, with the irregular shapes which boundaries of fields and landed properties assume, that many estates exist which can be enclosed in one triangle, as above stated, although it does sometimes happen, and has within my experience. The estate alluded to is situate on Sunbury Common, between three roads. It is now divided among several owners, but twenty years ago it formed one property, it is represented in fig. 144. When an estate cannot be entirely encompassed by one triangle, then the desideratum is to enclose as much of it as possible within the triangle, leaving the outskirts to be provided for by secondary LAND SURVEYING. 265 constructions. In the estate represented by fig. 145, having laid out the primary triangle A B C, and the proof line B D, the lines CE, EF, and FG, are severally determined on as necessary, as fundamental lines for that corner of the estate, and to fix their *position beyond all doubt with reference to the large triangle the line F G is produced to H, a line is taken from E through G to K, and from C through I to F. To provide for the remaining portion of the estate, a line is run from B to O, from 0 to M, and from M to N, and then their positions are securely fixed by the lines PLM, BQM, and LQ O. The great beauty of the method of construction just described is, that if any one of the lines be wrong, the remaining lines are sufficient not only to detect the mistake, but to point out beyond doubt the line in error, and to plot the work accurately without its aid. For example, suppose an error had been contained in either of the lines CE or E F, by plotting the lines CIF, F G H, and EIGK, it would have been apparent at once which was in error, as the other would scale the measured length. It may be as well to observe, that the constructions herein re- commended for estates or blocks of land containing many enclo- sures, apply equally to single fields of similar proportions, examples of which our space will not admit. When the limits of the estate to be surveyed assume other forms than those of a triangle, it is generally desirable to divide it into two principal triangles, and provide for the outskirts as most expedient. Fig. 146 is an illustration of my meaning. Here A B C and C D A are the two principal triangles, and the accu- racy of the two opposite points B and D is securely tested by the proof line BED; then by using E as a common point, and laying out E FG, HIE, AG, G H, and HD, AEG becomes a triangle with AF as a proof line; E G H a triangle with F I a proof line; and E HD is a triangle with DI as a proof line; while the lines A G, G H, and HD, severally act as proofs to each other and the whole work. Sufficient having been said to enunciate a principle so far as theory is concerned, it is now proposed to see by a reference to an instance of actual practice, how far this principle can be carried out in practice; for it must be remembered, that in all professions, mere theories, when attempted to be put in practice, are assailed by an infinity of difficulties. Hence, it is totally impossible to prescribe a rule from which no deviation shall be made; the only practical mode is to point out correct tenets, and require as close an approximation thereto as possible. T 266 LAND SURVEYING. ► Plate 5 represents a reduced plan of the parish of Sunbury, surveyed by me about five years since. Several difficulties pre- sented themselves during the laying out of the fundamental lines, of which the close proximity of the River Thames to the village, on the south side of the parish, the number of houses and gardens * scattered about its area, and the very flat nature of the country, formed some of the most prominent. Advantage was first of all taken of the straight piece of road from F to M, and a line ranged down it to A; a second line was then laid out from B to R, escaping as much as possible of the village of Sunbury, but en- countering a great portion of the Thames and the tributary streams; a third line was then laid out from R to M, avoiding the villages of Halliford and Charlton, but extending some distance beyond the parish to meet the main line. These three lines formed the fundamental triangle B M R. The next step was to lay out the proof line R I, about which the only difficulty encountered was at Y. A line was then found practicable from D to W, and at W another line was laid off to fall on the base at right angles at H. A line down the straight road from X through Y to P, completed the principal lines within the large triangle. Lines were then started from R and O, and from their interception at the point c, a tie-line was laid out so as to fall at right angles on the base of the triangle at Q. From Q a line was laid out through a to l, and from Q through f and h to i; 10 and 7b being joined the triangles ROc and Ob l became fundamental triangles, well and securely fixed and proved. The small triangle dek, with the lines kh and ig completed the boundary on the south-west. The triangle T t B, with proof lines tV and s U, and the triangle Sn R, with lines R M Q, no, op, np, p q, qr, r S, and r T (some of which were obliged to be calcu- lated) completed the fundamental lines for the survey of the boundary on the river side; and the triangles A Cu, CG w, G K 3, G3 w, w Cu; with proof lines Cv; Ex; Fy; F1; z5; 1, 4, 9; 2,3; and tie and secondary lines 6,7; 7,5; 7,8; 8, 9; 9,3; 10, 12: and 11, 12, 13 formed all the lines necessary for the triangulation of the parish. Upon examination, theory might suggest that the triangles to the north of the line A M, should have been fewer in number, and that at all events the line between points u and 3 should have been one continuous one; but the local difficulties intervening would have caused a far greater loss of time than any advantage gained * The houses and gardens are not shewn in detail on the plan owing to the diminu- tive size of the scale; it has been thought better to block in the sites built upon. LAND SURVEYING. 267 would justify, and therefore the attention was chiefly directed to the formation of a series of triangles, the sides of which would check one another, and be useful as offset lines, in the which we were very successful. It was not deemed expedient to extend c Q into the large triangle, the safety of the triangle R o C being per- fectly secure without it. The lines in the south corner are such as it were possible to obtain; the theodolite being used in all cases where it became necessary to compute the sides of triangles by means of the contained angles. On the whole, the triangulation of this parish is offered as a good practical illustration of the best principles of surveying, carried out without the smallest view to the purposes to which it is now about to be applied; executed, moreover, to produce professional remuneration under the influence of a very bad bargain; and now selected by chance from a number of others equally good, but with less convenient dimensions for the size of our intended work. Note.-It should be here stated that the lines, and not the sta- tions, were all numbered in the actual survey. The lettering has been adopted in the plate as offering greater facility of reference. Having laid out the fundamental lines of a survey, and chained them, the next process requiring attention is what is technically termed “filling in ;" that is, laying out, and chaining such a num- ber of internal or secondary lines, as may be required, with the offsets upon them, to take up all the fences, houses, buildings, and other features upon the land. Here it must be observed, that the lines taken for this purpose should be what are called "through lines," that is, lines running from any one already fixed line to another line already fixed, so that no distortion of the internal features of the survey, with reference to the external ones can take place. It is not imperatively necessary to the accuracy of the map that these lines are to follow consecutively from one fixed line to another; they may be taken in this way: Let A B, B C, and C A (fig. 147) be the lines of a triangle, already fixed; and a line is required from D to E to take up the neigh- bouring fence, which at the point E turns to the right. A line is then run from F, crossing E to G, where the fence again deviates its course; and lastly, the line from H, through G to I, completes the filling in of the fence. This is manifestly as correct an opera- tion as though the order of the lines had been reversed (as they will be when they come to be plotted), and H I had been first chained, then G F, and then E D, and equally so as though the line D E had been extended to e, that a line had then been car- ried from E to f, and then from G to i. The position and direc- 268 LAND SURVEYING. tion of these secondary lines entirely depend upon local circum- stances; it is often more expeditious to run two or three lines on the ground, than encounter the local difficulties of laying out one line which would look best upon paper. It is desirable that as many lines as possible should proceed from one station, by reason of the excellent check they become to each other. I will here notice a few of the methods by which obstructions in the admeasurement of chain lines may be overcome; but it must not for a moment be understood that the plans here sug- gested are the only efficient ones; on the contrary, an infinite number will present themselves to the mathematician, who will of course adopt that one that may be best suited to the special cir- cumstances for which some expedient is required. In figure 148 the chain line A B crosses a river, and it is to be premised that the surveyor has no instrument for taking angles with him, he is therefore desirous of getting the inaccessible dis- tance c d, in the readiest manner possible. Let the points a c re- present the extremities of the last perfect chain before arriving at the river, and let b be a mark at the centre link of that chain, then let one handle of the chain be held at a, and the other at b ; and by laying hold of the centre of the chain, let the point ƒ of the equilateral triangle a bƒ be marked in a similar manner set out the triangle b c e, then will fe⇒ a bor b c = 50 links; let the lines d e and bf be made to intersect in g; and let the distance fg be accurately measured in links, and tenths of links by reason of its shortness; then say as the side f g of the triangle ƒge is to the side fe, so is the side e c of the similar triangle c d e to the required side cd; for example, let ƒg = 22.6 links; then fg = 22·6 : ƒ e = 50 : : e c = 50 : c d = 110 links. = : Suppose A B C D, fig. 149, to be the site of a house crossed by the chain line E F G H, which has been previously laid out, either from high ground or by means of good back and fore marks. Measure the distance F D, and set off the same from D to I: in like manner set off C K equal to C G, then will the distance I K equal the required distance F G. Had FD and G C been equal, the line would have crossed the house at right angles, and the width D C would consequently have been equal to the required distance. Fig. 150 represents a house crossed by the chain line E F G H in a different manner. In this case make D I equal F D, and then because the triangles GDI and F D G are similar and equal, the side G I will be equal to the required side G F. Rec- tangular hay and corn ricks are generally so nearly right angled LAND SURVEYING. 269 as to admit of this process with sufficient approximation to truth. If the obstruction is a pond, lay off a b (Fig. 151) and c d, each equal 50 links on the chain line on either side of the pond; con- struct the equilateral triangles a be, a b f, c d g, and c d h, by holding the handles of the chain at the points a b and c d, and marking the points e f g h, with the centre of the chain in manner described in the first example; produce a e, and g d to k, and a f and d h to i; then because all the triangles are similar and equi- lateral the sides a k, k d, di, and i a, are all similar to the re- quired side a d. If the pond is small the operations need only be carried on on one side of it, which even then affords a check upon the accuracy of the work, inasmuch as a k and k d should exactly correspond; but if the equilateral triangles, whose sides are 50 links are very disproportioned to the required side; it is better to repeat the work on both sides, and average the length of the four sides (supposing they do not quite agree) for the length of the required side. If the surveyor had with him, as every surveyor should have when filling in a survey, a pocket sextant, he would have set out the angles ka d, k da, i ad, i da, each equal 60 degrees with the sextant. Some surveyors, in matters of this kind, lay off the angle d a k = 60 degrees, and then walking along the line a k lay off the angle a k d therefrom, also equal 60 degrees. This practice is open to grave objection-for if the slightest inaccuracy is com- mitted in laying off the first angle, it is not only repeated but in all probability increased in the second; whereas in the plan herein recommended, each angle depends solely upon the base line. One great advantage in the use of a sextant over the chain only, for purposes of this kind, is, that the operations are not re- quired to be of quite such large dimensions, and consequently the liability to error is proportionately diminished; for instance, in the example we have quoted the angles might have been taken at b and c, the equilateral triangle confined to the actual unknown distance bc, and the lines to be measured been reduced to b l, l c, c m, and m b. If an instrument is at hand, when the obstruction of a river (or any other feature) impedes the admeasurement of a line, it is easily overcome in this way-let A and B (fig. 152) be known points in the chain line already measured, and noted in the field book in ordinary course. At B erect a perpendicular, upon which at any point D observe the angle AD B; lay off the angle B D C equal 270 LAND SURVEYING. thereto; then because the triangles A B D and BCD are similar and equal; the unknown base B C equals the known base A B. The method of keeping a Field Book is varied by different surveyors to a great extent; but in the course of my practice I have made a trial of most methods, and think I may safely chal- lenge all others to a comparison with the one used by myself which is herein recommended. Fig. 153 illustrates one page of this Field Book, and Fig. 154 the lines therein referred to. 13, at the foot of the column, signifies that line 13 is the one referred to by the notes. 1636-12, placed at the foot of the page, on the left hand, represents that line 13 starts from the point denoted by the admeasurement 1636, on line 12; and the position of those figures illustrates approxi- mately the relative positions of the two lines. 1290--11, on the right hand side of the page, denotes the point to which line 13 proceeds, and again illustrates, by the position of the figures, the relative positions of the lines 13 and 11. The theodolite bearing is entered to shew the mode of doing it. The correct bearing of the line is entered at top, the opposite bearing beneath it. The offsets to the neighbouring fence speak for themselves: at zero it is two links to the right of the chain line; at 210, on the line, it is twelve to the right; at 280, the line crosses it; at 430, it is 16 to the left; at 520, 10 to the left; at 680, the line crosses it again; and at the same point on the line, it is 59, opposite to the corner of the house, the dimensions of which are given; but to positionise which an op. on another line is required: at 730 another fence, running to the corner of the house is crossed, at 19 a, or 19 along which the first fence terminates: at 1050 a point is crossed, which represents zero on line 6 (or 0-6), the posi- tion of which line is also relatively shewn: at 1115, the line is opposite the straight portion of another fence, to which is noted an op. of 230: at 1136 it crosses that fence wihch proceeds 3 a, and then turns; and at 1250 the line terminates. If the actual starting point of line 13 had not been known when 12 was measured, so that when 13 was chained, it had become ne- cessary to measure from any given known point on 12 to ascer- tain such starting point, such distance would have to be expressed in the Field Book, and added to or subtracted from the given point, as the case might be. Fig. 155 illustrates this: 1600-12 is the known point, beyond which 36 links had to be measured to the starting point of—13, and being measured beyond the known point on the given line had to be added thereto. 1350-11 is the nearest known point to which the line proceeds; and falling on TRIGONOMETRICAL SURVEYING. 271 that line between the known point and zero the remeasured dis- tance 60 had to be subtracted from the known quantities, leaving 1290 as the point of junction. The point to which a line proceeds cannot generally be filled in until the line is measured. By a strict observance to this mode of entering the field notes, and trusting nothing whatever to memory, it becomes as easy to plot the work ten years subsequent to the survey as at the time. I surveyed in or about the year 1842 a parish containing upwards of fourteen thousand acres, and did not lay down a line of it until the work was completed, and I had returned to my office-a cir- cumstance necessitated by the impossibility of getting a room sufficiently large for the map (which was eighteen feet by twelve feet) within the parish surveyed. And as a further proof of the excellence of this kind of Field Book-requiring very recently a replot of this very survey, I placed the Field Books in the hands of two of my pupils, who produced, notwithstanding the circum- stances that they had never seen the parish, and knew nothing of the survey, as good a map as my own plot; indeed the operation of plotting from such a Field Book is perfectly mechanical SECT. II.-Trigonometrical Surveying. In very extensive surveys, such as the Survey of the United Kingdom, now being carried on by the scientific branch of the Ordnance Corps, or (to illustrate a case within my practice) the Survey of the Island of Guernsey, which I am conducting, the methods previously described would not be at all applicable. It would neither be possible to lay out the lines of construction, nor to measure them with a sufficient degree of accuracy. It there- fore becomes necessary to adopt some more certain mode of opera- tion by an extended system of triangulation, on the data of one very correctly measured base, and the sides calculated therefrom, and the angles trigged at the vertices of the respective triangles. In such a system the first attention must be turned to the selection of the base, which should be as long as it possibly can be, in proportion to the extent of the country, and should be situate in a level plain, from either end of which some suitable trigonometrical points can be seen. In the Survey of the Island of Guernsey the base line was chosen in a straight level road. In cases requiring more than ordinary accuracy, glass, deal, and platinum rods have been used, laid in a level trough purposely erected for the occasion, and brought into contact by the most deli- 272 TRIGONOMETRICAL SURVEYING. cate and careful operations; but for all ordinary purposes, a careful admeasurement by the chain, taken twice in contrary directions, will produce results, the mean of which may be very safely taken as the correct length of the base. I have said that the base should be measured in a level plain, but I do not intend to imply that no other will do. So that the site chosen for the base does not contain irregularities and undulations of surface, a gentle fall in either direction can ob- viously cause no other inconvenience than to require the base to be levelled, and from the hypothenusally measured base, and its perpendicular height at one end above the other, the true hori- zontal base can be readily obtained by any of the Rules of Right Angled Triangles. AC (fig. 103,) being the line measured; A B being the base whose length is required; B C the ascer- tained height of C above A: or the angle of elevation or depres- sion can be taken with the theodolite from each end of the base, and the calculation will resolve itself into the case of a right angled triangle, in which the hypothenuse and the angles are given to find the base. But the base so found evidently requires some further reduction to render it mathematically correct, ac- cording to the degree of elevation at which it is situated above the level of the sea. The annexed figure will serve to illustrate the nature of this reduction. a b is the level of the sea, or an arc of the earth's circumference. A B is the reduced level base or a parallel arc, the distance between which is the height above the level of the sea, to which the base has already been reduced. a A B b Now, the length of the arc A B being known, though obviously longer than it should be, at the level of the sea, and the radius of the earth a C being assumed as 21,008,000 feet; it is evident that by ascertaining the height of a above A the correct length of ab may be ascertained; from which as a base, we can calcu- late the sides of a number of triangles, and from the sides of these triangles, forming so many fresh bases, can safely determine other trigonometrical points, until the whole country to be surveyed is covered with a net work of triangles, which can be correctly delineated upon paper in their true geographical positions. C The following is the formulæ for making this correction :— From the sum of the log of the altitude A a, and the log of the TRIGONOMETRICAL SURVEYING. 273 base A B, subtract the log of the sum of the radius and altitude (a C + A a) and the remainder will be the log of a number of feet, (all the dimensions being taken in feet) to be subtracted from the base AB, to produce the true base a b. This correction will not be required in ordinary surveys, unless the base measured is at great elevation. It sometimes happens that the length of a base, or distance between two points eminently qualified as stations to form the extremities of a base, cannot be entirely ascertained by actual admeasurement. The base used for the Ordnance Survey of Ire- land was lengthened two miles by calculation beyond the mea- sured distance. I will shew how this can be done, and at the same time be made to test the accuracy of the measured base. Let A and B (fig. 156,) be two elevated positions, which it is desirable to constitute extremities to the base, and let it be pos- sible to ascertain by admeasurement the length of the line C D E. First the line between A and B is correctly staked out by the theodolite or transit instrument, and permanent marks are made at C D E F and G. Secondly, the line is measured from C to D, and from D to E; and lastly, the following angles are taken :- At A. FA B and B A G. At C. ACF; FCB; BCG; and G C A. At D. ADF; FDB; BDG; and G D A. At E. AEF; FEB; BEG; and GE A. At B. ABF; and A B G. At F. AFC; CFD; DFE; and EF B. And at G. AGC; CGD; DGE; and E G B. Now by calculation we have first the triangle C D F, in which are given the base C D, and all the angles, to find the sides C F and D F. Secondly, the triangle D E F; given the base D E, and all the angles, to find the sides D F and F E. Thirdly, the triangle C E F; given the base CE, and all the angles, to find the sides C F and E F. Now the side D F being common to the first and second triangles, if the admeasurement of the base and angles have been correctly taken, the result in each case should correspond. And the side C F being common to the first and third triangles, and the side E F to the second and third, the results of the cal- culations should also correspond, and if they do the admeasure- ment of the two sections of the base C E is proved to be correct. 374 TRIGONOMETRICAL SURVEYING. The same operation takes place on the opposite side of the base with the several triangles C DG; DEG; and CE G. And thus we obtain lots of data for the calculation of the per- fect base AB. First, we have the triangle C F A, with base C F, and all the angles known, to find A C. Secondly-The triangle D FA, with base DF, and all the angles, to find A D. Thirdly-The triangle E F A, with base E F, and all the angles, to find E A. Fourthly-The triangle EF B, with base EF, and all the angles, to find E B. And fifthly-The triangle AF B, with base AF, and all the angles, to find A B. It will be obvious that the calculations and tests can be carried on through several other triangles, on the same side of the base, and a corresponding number on the opposite side; but sufficient has been said to elucidate the principle, and if A D, as found in the second triangle, is equal to the measured length CD, plus A C, as found in the first triangle; and A E, as found in the third triangle, is equal to the measured length C E, plus A C, there can be no doubt as to the accuracy of either A C; CD; or DE. And if the length A B, as found by the fifth triangle, is equal to E B, as found by the fourth, plus A C, plus C D, plus DE, there is sufficient proof of the accuracy of the whole base without reference to other triangles. The best triangles in the example before us, from which to compute the base, would have been ADF and ADG for the length AD; and D F B, and D G B for the length D B, the sides D F and D G being taken as the mean result of the calculations of the triangles CDF and C D G, and DEF and DE G. Those who would pursue the subject of bases, beyond these re- marks, will find the accounts of the admeasurement of the base lines for the Ordnance Surveys of England and Ireland very in- teresting. The account of the former operation was published in 1801; and of the latter very recently by Captain Yolland, Royal Engineers. Detailed accounts of the methods adopted at various times upon the Continent may be found in many standard works-" Recueil des Observations Géodesiques, par Biot et Arago." "Puissant, Traité de Géodesie.” "Base du Système Métrique Decimal ;" and the works of Cassini, Colonel Lampton, &c. TRIGONOMETRICAL SURVEYING. 275 Triangulation. The second process in a trigonometrical survey is to select a number of conspicuous stations on the highest hills as trigonome- trical points, which may either consist of prominent objects such as churches, windmills, towers, and trees, or they may be artificial erections of poles, flag staves, &c. ; the latter possessing the advan- tage, if the points are intended as theodolite stations, from which to trig other angles, inasmuch as they can be moved to allow the theodolite to be placed over the exact point; but the former are preferable as the stations of scondary triangles, in which it is not considered necessary to trig the third angle. The nearer the triangles are equilateral the less will be the error produced by any fault in taking the angles; and as the base is generally shorter than it is desirable to retain the sides of the principal triangles, they should be enlarged gradually in the following manner, until they attain a length in proportion to the nature of the work and the power of the instruments employed. Fig. 157 is an illustration. A B is the base from which the several sides of the triangles ABD and ABC are computed. From B D and B C, and the contained angle, we obtain CD, as well as from A D and A C, and the contained angles. The mean of these results is taken as a new base for the triangles C D E and C D F, and in like manner E F is obtained. From EF we pro- ceed to find G H, which has now acquired a length sufficient to take a place as a side of one of the main triangles GHI. Upon HI is built I K, and so the work proceeds. It is always desirable, but of course not necessary, to take all the angles of each triangle; therefore, while the theodolite is in use at any station, all objects that can be intersected should be trigged; they will be found of infinite service in "filling in," and can never be more accurately fixed in position. Fig. 158 will represent my meaning. ABC and ABD are two triangles, and A B C D are stations, at which the theodolite will be placed for the angles of those triangles. EFGHIK and L are objects visible from two, and some of them from three, of these stations, which are readily fixed in position by arranging them in triangles and taking the angles. Where objects are thus taken from three stations, the distances obtained become a check upon each other. It frequently happens that the objects best adapted to form points in a triangle are inaccessible, and the theodolite cannot be placed over the centre of the station. It then becomes necessary 276 TRIGONOMETRICAL SURVEYING: “to reduce the angles taken to the centre." Cases of this nature are of three kinds :—First, when the nearest point at which the theo- dolite can be placed is within the triangle; secondly, when it is with- out; and thirdly, when it is on one of the sides of the triangle. Fig. 159 represents the first case. ABC is the triangle, A is the angle required, and D is the nearest point at which it can be approached by the instrument. Measure A D, and take the angle BDA, BDC, and CD A. Now the angle BDC the <BAC+ < ABD + AC D. Suppose A B, whose length is known, to be the base of the triangle ABC. Then in the triangle ABD we have the sides A B and AD and < A D B to find the remaining angles, and the side B D. Deduct the angle ABD from A B C, and we have in the triangle BCD the side B D, and the angles DBC and BDC to find the side DC. And lastly, in the triangle CDA we have the sides AD and D C, and the contained angle to find the remaining angles. From the angle BDC subtract the angle ABD, plus A CD, and the remainder is the angle B A C, which should also equal the angle B A D, plus D A C. Case 2 is illustrated by Fig. 160. ABC is again the triangle, of which AB is the base. D is the theodolite station. The angle BEC equals the angle BDC plus the angle D BA; and the angle B E C equals the angle B A C plus the angle E CA. Hence we must find the angles DB A, B E C, and E CA, and from these the angle B A C is attainable. Case 3 is when the position of the theodolite is upon one of the sides of the triangle, which is the most simple case of the three. The distance AD (fig. 161) being measured, the remaining distance of the base is known; and the angle BDC being equal to the angle B A C plus the angle A CD, we have only to find the latter angle, and subtract it from BD C, and it will give the angle B A C required. It is not always possible to ascertain A D, or the distance of the theodolite from the centre of the station by actual admeasure- ment; in such cases a short base must be measured from the theo- dolite in any direction, and the distance found by a small triangle DE A, (fig. 162.) If the triangles and the instruments made use of are very large, a correction for spherical excess becomes necessary; but in smaller instruments this correction is too minute to be noticed, in com- parison with the unavoidably greater errors of observation to which they are subject. In the conduct of a trigonometrical survey, it not unfre- TRIGONOMETRICAL SURVEYING. 277 quently becomes necessary to visit the same theodolite station a number of times, sometimes after the lapse of a consider- able interval; and although every care may have been taken to mark the station well, it may from some cause or other be lost; hence it is desirable that a ready and a certain method of finding a lost station should be known to the surveyor. Let A B C and D, (fig. 163,) be trigonometrical points, whose distances from each other have been previously determined. Let A be the lost station, and B C and D conspicuous objects. Set up the theodolite as near the point A as can be surmised. In the figure this point is represented by E, but it is necessary to observe that the distance from E to A is there much greater in pro- portion to the other sides of the triangles than it should ever be practised: it was impossible to render the figure clear and distinct without making this so. At E take the angles BEC and CE D, which being larger than the original angles B A C and C A D, it is evident the point is within the circumscribing circles of those triangles. Had our angles been smaller than the original, the point would have been without the circumscribing circles. Now, consider the angle A of the triangle A B C to be altered to the value of the angle BEC, and that the other angle diminished thereby is the angle C. With B C as a base, and these angles compute the side B F of the trian- gle BF C, subtract B F from A, produce B E, and make E G equal to F A, and at G plant a picket. Again, consider the angle A as of the value of B E C, and that the angle B is diminished in consequence, find CH and H A, produce C E to I, making E I equal to H A. In similar manner treat the angles of the other triangle CDA, and find AK and AM; produce C E to L; making EL equal A K; produce D E to N, making E N equal A M. The intersec- tion of the lines GI and L N, will be the lost station, provided all the observations and calculations have been taken with sufficient accuracy. To verify it the theodolite must now be placed on the point supposed to be the point A, and the angles between B C and CD retaken; if these read the same as the original the point is right, but if not, it must be used as a second trial station, and the opera- tion repeated. It is better, when possible, to let the operation embrace three previous triangles, because if any mistake is made in calculation, the three lines will not intersect each other at a point, but will leave a small triangle between them, the centre of which should be taken as the second trial station. On the other hand, if they do intersect each other at the same point, it affords strong proof of the accuracy of the whole work. 278 TRIGONOMETRICAL SURVEYING. If the first trial station falls without the circumscribing circle of the original triangle, the operation is precisely the same in every particular, excepting that the differences of distance between the sides found, and the original sides are set off from the trial station E towards the points B C and D, instead of producing those lines, as in the former case. It often becomes desirable to fix the position of a station by means of the angles taken at that station only. This may always be done if three objects are visible, whose distances from each other, forming three sides of a triangle, are known. Let A B C, (fig. 164,) be three objects, whose several distances from each other (A B, A C, and B C) are known. Let D be the point whose position it is required to fix. The angles ADC and C D B are taken. Now, by inspection of the diagram, it is obvious that if about the points A B D we circumscribe a circle, the angle E A B must equal the angle EDB (being in the same segment of a circle, Euclid B 3, Prop. 21), and the angle ABE equal the < ADE. Therefore in the triangle A B E we have the base A B, and all the angles to find the sides A E and B E. In the triangle ABC, the angles are either known or can be ascertained by calculation of the sides. From the angle C A B subtract the < E AB, the remainder is the < CA E, from which, and the two sides A C and A E find the < ACE - ACD. Then with the base A C, and angles A CD and AD C, find the sides AD and C D. Again, from the angle A B C, deduct the < AB E, the remainder is the < E BC, from which, and the two sides BE and B C, find the angle BCE = BCD. Then with the base B C, and angles BCD and BDC, find BD and CD. CD being common to both calculations, proves the latter part of the work. But the vertex C of the triangle A B C will sometimes be turned towards the place of observation D, as in fig. 165. Very little difference takes place in the arrangement of the cal- culation. AB, A C and B C are known, and consequently their contained angles. The angle AD C the < ADE = the the < ABE, and the < CDB = the < EDB = the angle EA B are also known. Therefore in the triangle ABE, the base AB and angles ABE and BA E are given to find the sides AE and B E. In the triangle ACE are given the sides A C and A E, and the angle C AE = EAB plus B A C to find the angle A C E. Now, the angle ACE is the external angle of the triangle TRIGONOMETRICAL SURVEYING. 279 A CD, and (Euc. B 1, Prop. 32) equal to the two internal oppo- posite angles CAD and CDA. Hence, if from the angle ACE be taken the angle CDA, the re- mainder is the <CAD, and in the triangle A CD we have the base A C, and all the angles given to find the other sides C D and AD. In like manner is found the < BCE in the triangle B CE; and the < B C E being known, <° C D B and B C D are also known; and the sides BD and CD are found from the base B C. The three known objects A B and C may possibly fall in one straight line, such as three stations of a base line. Now, the < ADC = the < And the < CDB the < = Fig. 166 represents this case. ADE the < ABE is known. EDB = the < EAB is also known. Therefore, in the triangle A B E, the base A B, and all the angles are known to find the sides A E and BE. Next, the sides AC and A E and the contained < being known, the < A CE is determined. And the < A CE being the external < of the triangle A CD, the angles of that triangle, and the base A C, are given to find the sides AD and CD. And again, BC and BE, with the contained < being known, the < BCE is obtainable; and the <B CE being the external < of the triangle B CD, we have all the angles, and base B C of that triangle given to find the sides CD and B D. But the point of observation D will sometimes fall within the triangle A B C. Let fig. 167 illustrate this case. Now, the < A D C is known, and the < ADE being the sup- plement of < ADC is also known; and the < ABE standing within the same segment, is equal to < B DE; < CD B is known; and <E DB is the supplement of < CDB, and < BDE and BAE being within the same segment, are equal. Therefore, in the triangle A B E, the base A B and all the an- gles are given, and the sides A E and B E can be thus obtained. The angles within the known triangle ABC are also given or obtainable. Next, in the triangle C A E, the sides A C and A E are known and the contained angle (equal the < C A B plus <BAE) to find the < ACE=< ACD. In the triangle A CD, the base A Cand all the angles are given to find the sides AD and CD. Again, in the triangle CBE, the sides B C and BE and the contained angle (equal the < ABC+< ABE) are given to find the < BCE = < B C D. 280 TRAVERSE SURVEYING. Lastly, in the triangle B CD, the base BC and all the angles are given to find the sides BD and CD. It is sometimes desirable to fix the positions of two new stations by means of observations, taken at those two stations with refe- rence to two old stations, whose distances from each other are known. Let A and B, (fig. 168,) represent the old stations, and C and D the new; it is required to know the distances A C, BC, A D, B D, and CD. At C take the angles A CB and B CD, and at D take the <* CD A and AD B. To compute the triangles assume CD, equal any convenient. distance G F. Then with base G F and angles AGF = ACD, and A FG = ADC, find A F and A G. In like manner find E F and E G. Then with the sides AG and the contained < A GE = < AC B, find A E. Again (as a proof) with the sides A F and E F, and < AFE = <ADB, find A E. Then, As AB: AE:: AG: A C. BC. As AB: AE:: EG: B C. As AB: AE::AF: AD. As AB: AE:: EF: BD. As AB: AE::GF: CD. Filling in. The interior details of a Trigonometrical Survey can be “filled in,” in the same manner as previously described for the filling in of a parish or estate survey, or by a traverse. The distances from one trigonometrical point to another can be chained, and between these lines other lines can be laid out and measured, as often as circumstances may require. Fig. 169 will illustrate this method. SECT. III.-Traverse Surveying Is a method of surveying by means of a chain and theodolite, or other angular instrument (according to the degree of accuracy required), which is frequently resorted to in filling in the roads on a trigonometrical survey, where it is sometimes impossible to adopt the more accurate, though less expeditious method of chain- ing between every trigged station, and filling up the interior by through lines. My survey of Guernsey is conducted in this way. TRAVERSE SURVEYING. 281 The objects chosen to form the vertices of the principal triangles (consisting of twelve windmills, seven church steeples, several martello and other towers, batteries, signal masts, &c.) occupy for the most part such inaccessible positions, and the country gene- rally is so irregular and broken as to render any attempt to chain some of the sides of the triangles ridiculously futile. The "traverse system," while it possesses the advantage noticed above, also possesses another advantage with reference to the Guernsey Survey, inasmuch as it enables the survey of the nume- rous roads with which the Island is covered to be proceeded with during the fine weather of the summer months, which would have been entirely prevented by the crops had the "right line" system of filling in been exclusively adopted. The little blocks between the roads are afterwards filled in by a system of through lines from road to road, in the same manner as though the roads bounded a right line triangle. Fig. 170 represents the mode of carrying on a traverse survey. A B C are the points of a triangle, whose positions have been computed. From A, line 1, proceeds by the nearest accessible route into the road; lines 2, 3, 4, &c., continue along the road until the end of line 9, which has arrived opposite the station B to which line 10 is directed. Lines 11, 12, 13, 14, 15, again proceed in the road; and 16 starting from station C, and crossing the end of line 15, continues the traverse along the road, and closes by line 20 falling upon the end of line 1 and beginning of line 2. Line 21 com- mences at a point on line 7, and proceeds to traverse the intersect- ing road, which is completed by line 26 falling upon line 14. The angles are now taken, and an opportunity is afforded, with- out much (if any) loss of time, for rechaining the lines without the offsets, as a proof of their accuracy. The theodolite being placed at station A, is adjusted and set to zero, and the telescope is directed to the magnetic meridian, or in other words, the entire head of the instrument is turned round until the marked end of the needle points to zero in the compass box-the other or south end pointing to 180°. The lower plate is then clamped, and the upper plate unclamped, and the telescope is directed at station B: the bearing of which is read off and entered; the upper plate is again unclamped, and the bearing of line 1 is taken and entered. The instrument is now taken to the beginning of line 2, and there set up and adjusted. The telescope is turned upon line 1, and since the upper plate has not been touched since the bearing U 282 TRAVERSE SURVEYING. of line 1 was taken, it still remains clamped at that bearing (but this should always be verified by examination, as the operation of carrying the instrument from one station to another will some- times shake it a little out of place if the clamp screws are not very securely fastened), and the screws may also be inadvertently touched in the process of levelling the instrument. It being obvious that the telescope and limb being now in a position exactly parallel to the one they occupied at the station A, excepting that they have been reversed 180°, the needle should, when set free, settle down at the same bearing as above, saving that the reading which was before at the marked or north end is now at the south end, consequent upon the reversion of the in- strument. Clamp the limb, or lower plate, and unclamp the upper one; and as this is the point at which line 20 closes the work, direct the telescope upon that line, before the bearing of line 2 is taken, so that the last reading at the station may be the bearing of the line from which the next line of the series proceeds. Here I should observe, that the compass or real bearing of the line, when the instrument follows the work in the same direction as the lines were measured, being always the bearing indicated by the marked end of the needle (as taken at the beginning of any line), it should always be written uppermost; the other or "op- posite" bearing, which differs from the real bearing exactly 180°, being placed below. Strict attention to this will serve to denote at any future time the direction of the lines; and as line 20 is now taken at the end instead of the beginning, the bearing indicated by the north end of the needle will be the "opposite" bearing of the line when the instrument is placed in true position with re- spect to it, and it must be so entered accordingly. The bearing of line 2 being taken, the instrument is moved to line 3, and in like manner the work proceeds regularly until it arrives at line 10, when the instrument being placed on station B, and directed at A, the bearing of A B should read the same (re- versed) as it read at A; if it does, the angles have all been correctly taken; if not, there is an error which must be detected before greater mischief is done. Assuming the work to be correct the bearing of A C is taken from B, and also the bearing of the station forming the end of line 11, and the beginning of 12, to which the instrument is next removed, and being adjusted and levelled, and directed at the back bearing of A B, the bearing of line 11 is taken, and then of line 12; and so we proceed until thẹ end of line 14; from whence, if visible, after taking the bearing PRISMATIC COMPASS. 283 of line 15, we take the bearing of A C, to which station we next remove the instrument, and verify the bearing of B C. We then take the bearing of C A, and after that of line 16, and proceed to close our work with line 20, the bearing of which should prove the same as at first taken from line 2. The instrument is now taken to line 21. The nonius is ad- justed to the bearing of line 7, to the most distant end of which the telescope is directed, and from it is taken the bearing of line 21; and the work proceeds in the same manner until the end of 26, where the instrument being set up, and directed from the bearing of line 26 to line 14, the bearing of this latter line should prove the same, or very nearly, as when taken in the first series; and this again proves the work. It will not be possible at all times to set the theodolite over the trigonometrical station; but it is generally practicable to place it in line between two stations, so that the bearing thereof may be taken, from which a bearing may be taken to some spot on the first line from whence the bearing of the first line may be taken. No directions that can be written will render a person an ex- pert surveyor: practice alone will effect that. Enough has been said to convey a knowledge of the theory, the practice should be acquired under the instructions of some able master. SECT. IV.-Field Instruments. THE PRISMATIC COMPASS. With this instrument horizontal angles can be observed with great rapidity, and, when used with a tripod stand, with a con- siderable degree of accuracy. It is, consequently, a very valuable instrument to the military surveyor, who can make his observa- tions with it, while holding it in his hand, with all the accuracy necessary for a military sketch. It is also a useful instrument for filling in the detail of an extensive survey,* after the principal points have been laid down by means of observations made with * The prismatic compass was used for this purpose by the gentlemen engaged in making the Ordnance Surveys. 284 PRISMATIC COMPASS. the theodolite, hereafter to be described, and for any purpose in short, in which the portability of the instrument and rapidity of execution are of more importance than extreme accuracy. C is a compass card divided usually to every 20', or third part of a degree, and having attached to its under side a magnetic needle, which turns upon an agate centre, o, fixed in the box B; n is a spring which, being touched by the finger, acts upon the card, and checks its vibrations, so as to bring it sooner to rest when making an observation; S is the sight-vane, having P C B n a fine thread stretched along its opening, by which the point to be observed with the instrument is to be bisected. The sight-vane is mounted upon a hinge-joint, so that it can be turned down flat in the box when not in use. P is the prism attached to a plate sliding in a socket, and thus admitting of being raised or lowered at pleasure, and also supplied with a hinge-joint, so that it can be turned down into the box when not in use. In the plate to which the prism is attached, and which projects beyond the prism, is a narrow slit, forming the sight through which the vision is directed when making an observation. On looking through this slit, and raising or lowering the prism in its socket, distinct vision of the divisions on the compass card immediately under the sight-vane is soon obtained, and these divisions, seen through the prism, all appear, as each is successively brought into coincidence with the thread of the sight-vane by turning the in- strument round, as continuations of the thread, which is seen directly through the part of the slit that projects beyond the prism. The method of using the instrument is as follows:-The sight- vane S, and the prism P, being turned up upon their hinge-joints, as represented in our figure, hold the instrument as nearly in an horizontal position as you can judge; or, if it be used with a tripod stand, set it as nearly as you can in a horizontal position by moving the legs of the stand, so that the card may play freely. Raise the prism in its socket till the divisions upon the card are seen distinctly through the prism, and, turning the instrument round, until the object to be observed is seen through the portion PRISMATIC COMPASS. 285 of the slit projecting beyond the prism in exact coincidence with the thread of the sight-vane, bring the card to rest by touch- ing the spring n; and then the reading at the division upon the card, which appears in coincidence with the prolongation of the thread, gives the magnetic azimuth of the object observed, or the angle which a straight line, drawn from the eye to the object, makes with the magnetic meridian.* The magnetic azimuth of a second object being obtained in the same manner, the difference between these two azimuths is the angle subtended by the objects at the place of the eye, and, which is an important point, is inde- pendent of any error in the azimuths, arising from the slit in the prism not being diametrically opposite to the thread of the sight- vane. For the purpose of taking the bearings of objects much above or below the level of the observer, a mirror, R, is supplied with the instrument, which slides on and off the sight-vane S, with sufficient friction to remain at any part of the vane that may be desired. It can be put on with its face either upwards or down- wards, so as to reflect the images of objects considerably either above or below the horizontal plane to the eye of the observer ; and, if the instrument be used for obtaining the magnetic azimuth of the sun, it must be supplied with dark glasses, D, to be inter- posed between the sun's image and the eye. There is a stop in the side of the box, not shewn in our figure, by touching which a little lever is raised, and the card thrown off its centre, as it always should be when not in use, or the constant playing of the needle would wear the fine agate point upon which it is balanced, and the sensibility of the instrument would be thereby impaired. The sight-vane and prism being turned down, a cover fits on to the box, which is about three inches in diameter, and one inch deep; and the whole, being packed in a leather case, may be carried in the pocket without inconvenience.† * The magnetic meridian now makes an angle of 24° with the true meridian at London, the north point of the compass being 24° west of the true north point. This angle is called the variation of the compass, and is different at different places, and also at the same place at different times. Since this variation will affect equally, or nearly so, all azimuths observed within a limited extent and during a limited time, the angles subtended by any two of the objects observed, being the difference of their azimuths, will not be affected by the variation, and hence the map, or plan, may be constructed with all the objects in their proper relative positions; but the true meridian must be laid down, if required, by observations made for the purpose. † For much valuable information respecting the use of the prismatic compass, espe- cially in military surveying and sketching, I can refer our readers to a Treatise on Military Surveying, &c., by Lieutenant-Colonel Basil Jackson, in which the subject is handled with great ability. 286 BOX SEXTANT. THE BOX SEXTANT. This instrument, which is equally portable with the prismatic compass, forming, when shut up, a box of about three inches in diameter, and an inch and a half deep, will measure the actual angle between any two objects to a single minute. It requires no support but the hand, is easily adjusted, and, when once adjusted, but seldom requires re-adjusting. When the sextant is to be used, the lid, E, of the box is taken off and screwed on to the bottom, where it makes a convenient handle for holding the instrument. The telescope, T, being then drawn out, the instru- ment appears as represented B a M © E T in our figure. A is an index arm, having at its extremity a vernier, of which thirty divisions coincide with twenty-nine of the divisions upon the graduated limb, 77; and the divided spaces upon the limb denoting each thirty minutes, or half a degree, the angles observed are read off by means of the vernier to a single minute. The index is moved by turning the milled head, B, which acts upon a rack and pinion within the box. To the index arm is attached a mirror, called the index glass, which moves with the index arm, and is firmly fixed upon it by the maker, so as to have its plane accurately perpendicular to the plane in which the motion of the index arm takes place, and which is called the plane of the instrument. This plane is evidently the same as the plane of the face of the instrument, or of the graduated limb, 77. In the line of sight of the telescope is placed a second glass, called the horizon glass, having only half its surface silvered, and which must be so adjusted that its plane may be perpendicular to the plane of the instrument, and parallel to the plane of the index glass when the index is at zero. The instrument is provided with two dark glasses, which can be raised or lowered by means of the little levers seen at d, so as to be interposed, when necessary, between the mirrors and any object too bright to be otherwise conveniently observed, as the sun. The eye-end of the telescope is also fur- nished with a dark glass, to be used when necessary. The principle upon which the sextant is constructed is, that the total deviation of a ray of light, after reflections succes- sively at the index glass and horizon glass, is double the inclination of the two glasses. Now the limb, 17, being di- BOX SEXTANT. 287 vided into spaces, each of 15' extent, and these spaces being figured as 30′ each, the reading of the limb gives double the angle moved over by the index arm from the position in which the reading is zero, or double the angle of inclination of the two mir- rors, if these mirrors be parallel when the reading is zero. If, then, the instrument be in perfect adjustment, and any object be viewed by it after reflection at both the mirrors, the reading of the in- strument gives the total deviation of the rays of light, by which the vision is produced, or the angle between the bearing of the object from the centre of the index mirror, and the bearing of the reflected image from the place of the eye, that is, between lines drawn respectively from the object to the centre of the index glass, and from the reflected image in the horizon glass to the eye. This angle is very nearly equal to the angle subtended by the object and its image at the place of the eye, differing from it only by the small angle subtended at the object by the place of the eye and the centre of the index glass. This small angle is called the parallax of the instrument, and is scarcely perceptible at the dis- tance of a quarter of a mile, while for distances greater than that it is so small that it may be considered to vanish. It also varies with the amount of deviation, and vanishes altogether whenever the centre of the index glass is in a direct line between the object and the eye.* To see if the instrument be in perfect adjustment, place the dark glass before the eye-end of the telescope, and looking at the sun, and moving the index backwards and forwards a little distance on either side of zero, the sun's reflected image will be seen to pass over the disc, as seen directly through the horizon glass; and if, in its passage, the reflected image completely covers the direct image, so that but one perfect orb is seen, the horizon glass is perpendicular to the plane of the instrument; but, if not, the screw at a must be turned by the key, k, till such is the case. The key, k, fits the square heads of both the screws seen at a and b, and fits into a spare part of the face of the instrument, so as to be at hand when wanted. This adjustment being perfected, bring the reflected image of the sun's lower limb in exact contact with * We have seen a method given for what is called correcting the parallax, when an observation is made at a short distance, by finding the deviation at this distance, when the angle between the object and its image is equal to zero; this deviation being given by the reading of the instrument, when the reflected image of the object observed exactly coincides with the object itself, seen through the unsilvered part of the horizon glass. This deviation, however, is not the parallax, even for a small angle between the object and its image, and, if the angle be not very small, the error introduced by the method will be greater than the parallax itself. 288 BOX SEXTANT. the direct image of his upper limb, and note the reading of the vernier; then move the index back, beyond the zero division of the limb, till the reflected image of the sun's upper limb is in exact contact with the direct image of his lower limb; and, if the zero of the vernier be now exactly as far behind the zero of the limb as it was at the former reading in front of it, so that the reading now on the part of the limb called the arc of excess, be- hind its zero division,* be the same as the former reading, the in- strument is in perfect adjustment; but, if not, half the difference of the two readings is the amount of the error, and is called the index error, being a constant error, for all angles observed by the instrument, of excess, if the first reading be the greatest, and of defect, if the second reading on the arc of excess be the greatest. In the former case, then, the true angle will be found by sub- tracting the index error from, and in the latter by adding it to, the reading of the instrument at every observation; but this error should be removed by applying the key, k, to the screw at b, and turning it gently till both readings are alike, each being made equal to half the sum of the two readings first obtained. When this adjustment is perfected, if the zeros of the vernier and limb are made exactly to coincide, the reflected and direct image of the sun will exactly coincide, so as to form but one perfect orb; and the reflected and direct image of any line, sufficiently distant not to be affected by parallax, as the distant horizon, or the top or end of a wall more than half a mile off, will coincide so as to form one unbroken line. To obtain the angle subtended by two objects situated nearly or quite in the same vertical plane, hold the instrument in the right hand, and bring down the reflected image of the upper ob- ject by turning the milled head B, till it exactly coincides with the direct image of the lower object, and the reading of the in- strument will give the angle between the two objects. To obtain the angle subtended by two objects nearly in the same horizontal plane, hold the sextant in the left hand, and bring the reflected image of the right-hand object into coincidence with the direct image of the left-hand object. * In reading an angle upon the arc of excess, the division to read on the limb is that next in front of the zero of the vernier, or between the zero of the vernier and the zero of the limb, and the divisions of the vernier itself are to be read from the end division, marked 30, and not, as usually, from the zero division: thus, if the zero division of the vernier were a little further from the zero division of the limb, then the first division on the arc of excess; and if the twenty-seventh division on the vernier, or the third from the end division, marked thirty, coincided with a division upon the limb, then the reading would be 33'. BOX SEXTANT. 289 It will be seldom that the surveyor need pay any attention to the small error arising from parallax; but, should great accuracy be desirable, and one of the objects be distant while the other is near, the parallax will be eliminated by observing the distant ob- ject by reflection, and the near one by direct vision, holding the instrument for this purpose with its face downwards if the distant object be on the left hand. If both objects be near, the reflected image of a distant object, in a direct line with one of the objects, must be brought into coincidence with the direct image of the other object, and the parallax will thus be eliminated. For the purposes of surveying, the horizontal angles between different objects are required, and the reduction of these angles from the actual oblique angles subtended by the objects, would be a troublesome and laborious process. If the angle subtended by two objects be large, and one be not much higher than the other the actual angle observed will be, however, a sufficient approxima- tion to the horizontal angle required; and, if the angle between the two objects be small, the horizontal angle will be obtained with sufficient accuracy by taking the difference of the angles observed between each of the objects, and a third object at a considerable angular distance from them. With a little practice, the eye will be able to select an object in the same direction as one of the objects, and nearly on a level with the other object, and the angle between this object and the object selected will be the horizontal angle required. S At sea the altitude of an object may be determined by observing the angle subtended by it and the verge of the horizon; but upon land a contrivance, called an artificial horizon, becomes necessary for correctly determining altitudes. The best kind of artificial horizon consists of an oblong trough, tt, filled with mercury, and protected from the wind by a roof, r r, having in either slope a plate of glass with its two sur- faces ground into perfectly pa- rallel planes. The angle SES' between the object and its re- flected image seen in the mercury is double the angle of elevation SEH, and the angle SES' being observed, its half will conse- quently be the angle of elevation required. If the angle of ele- S H 7 t E 290 THEODOLITE. A vation be greater than 60°, the angle S ES' will be greater than 120°, and cannot be observed with the sextant we have been describing. The pocket sextant is a most convenient instrument for laying off offsets or perpendicular distances from a station line; for by set- ting the index at 90°, and walking along the station line, looking through the horizon glass directly at the further station staff, or any other remarkable object upon the station line, any object off the station line will be seen by reflection when the observer arrives at the point where the perpendicular from this object upon the sta- tion line falls, and the distance from this point to the object being measured, is its perpendicular distance from the station line. For the mere purpose of measuring offsets, an instrument called an optical square is now very generally employed, which consists of the two glasses of the sextant fixed permanently at an angle of 45°, so that any two objects seen in it, the one by direct vision, and the other by reflection, subtend at the place of the observer an angle of 90. THE THEODOLITE. The theodolite is the most important instrument used by sur- veyors, and measures at the same time both the horizontal angles subtended by each two of the points observed with it, and the angles of elevation of these points from the point of observation. This instrument may be considered as consisting of three parts; the parallel plates with adjusting screws fitting on to the staff head; the horizontal limb, for measuring the horizontal angles; and the vertical limb, for measuring the vertical angles, or angles of elevation. The horizontal limb is composed of two circular plates, L and V, which fit accurately one upon the other. The lower plate projects beyond the other, and its projecting edge is sloped off, or cham- fered, as it is called, and graduated at every half degree. The upper plate is called the vernier plate, and has portions of its edge chamfered off, so as to form with the chamfered edge of the lower plate continued portions of the same conical surface. These cham- fered portions of the upper plate are graduated to form the verniers, by which the limb is subdivided to single minutes. The five-inch theodolite represented in our figure has two such verniers, 180° apart. The lower plate of the horizontal limb is attached to a conical axis passing through the upper parallel plate, and termi- nating in a ball fitting in a socket upon the lower parallel plate. THEODOLITE. 291 N (A) B P N B a A Five-inch Theodolite. be This axis is, however, hollowed to receive a similar conical axis ground accurately to fit it, so that the axes of the two cones may exactly coincident, or parallel.* To the internal axis the upper, or vernier, plate of the horizontal limb is attached; and thus, while the whole limb can be moved through any horizontal angle desired, the upper plate only can also be moved through any desired angle, when the lower plate is fixed by means of the clamping screw, C, which tightens the collar, D: T is a slow-motion screw, which moves the whole limb through a small space, to adjust it more perfectly, after tightening the collar, D, by the clamping screw, C. There is also a clamping screw, c, for fixing the upper, or vernier, plate * Upon this depends, in a great measure, the perfection of the instrument, as far as the horizontal measurements are concerned; and when we describe presently the ad- justinents of the instrument, we shall explain the method of detecting an inaccuracy in the grinding of the axes. 292 THEODOLITE. to the lower plate, and a tangent screw, t, for giving the vernier plate a slow motion upon the lower plate, when so clamped. Two spirit levels, BB, are placed upon the horizontal limb, at right an- gles to each other, and a compass, G, is also placed upon it in the centre, between the supports, FF, for the vertical limb. The vertical limb, N N is divided upon one side at every 30 minutes, each way, from 0° to 90°, and subdivided by the vernier, which is fixed to the compass box, to single minutes. Upon the other side are marked the number of links to be deducted from each chain, for various angles of inclination, in order to reduce the dis- tances, as measured along ground rising or falling at these angles, to the corresponding horizontal distances. The axis, A, of this limb must rest in a position truly parallel to the horizontal limb, upon the supports, F F, so as to be horizontal when the horizontal limb is set truly level, and the plane of the limb, N N, should be accu- rately perpendicular to its axis. To the top of the vertical limb, N N, is attached a bar which carries two Ys for supporting the telescope, which is of the same construction as the Y spirit level, and underneath the telescope is a spirit level, SS, attached to it at one end by a joint, and at the other end by a capstan-headed screw as in the Y level. The horizontal axis, A, can be fixed by a clamp- ing screw, C, and the vertical limb can then be moved through a small space by a slow-motion screw ¿. Before commencing observations with this instrument, the fol- lowing adjustments must be attended to:- 1. Adjustments of the telescope: viz., the adjustment for parallax. for collimation. 2. Adjustment of the horizontal limb: viz., to set the levels on the horizontal limb to indicate the verticality of the azimuthal axis. 3. Adjustment of the vertical limb: viz., to set the level beneath the telescope to indicate the horizontality of the line of collimation. 1. Parallax and Collimation.-These adjustments are described under the head of the Y level. 2. Adjustment of the Horizontal Limb.-Set the instrument up as accurately as you can by the eye, by moving the legs of the stand. Tighten the collar, D, by the clamping screw, C, and unclamping the vernier plate, turn it round till the telescope is over two of the parallel plate-screws. Bring the bubble, b, of the level, SS, be- neath the telescope to the centre of its run by turning the tangent THEODOLITE. 293 screw, i. Turn the vernier plate half round, bringing the telescope again over the same pair of the parallel plate screws; and if the bub- ble of the level be not still in the centre of its run, bring it back to the centre half way, by turning the parallel plate screws over which it is placed, and half way by turning the tangent screw, i. Repeat this operation till the bubble remains accurately in the centre of its run in both positions of the telescope; and then turning the vernier plate round till the telescope is over the other pair of parallel plate screws, bring the bubble again to the centre of its run by turning these screws. The bubble will now retain its posi- tion, while the vernier plate is turned completely round, shewing that the internal azimuthal axis about which it turns is truly ver- tical. The bubbles of the levels on the vernier plate being now, therefore, brought to the centres of their tubes, will be adjusted to shew the verticality of the internal azimuthal axis. Now, having clamped the vernier plate, loosen the collar, D, by turning back the screw, C, and move the whole instrument slowly round upon the external azimuthal axis; and if the bubble of the level, SS, beneath the telescope, maintains its position during a complete revolution, the external azimuthal axis is truly parallel with the internal, and both are vertical at the same time; but, if the bubble does not maintain its position, it shews that the two parts of the axis have been inaccurately ground, and the fault can only be remedied by the instrument-maker. 3. Adjustment of the Vertical Limb.-The bubble of the level, S S, being in the centre of its run, reverse the telescope end for end in the Ys, and if the bubble does not remain in the same posi- tion, correct for one-half the error by the capstan-headed adjusting screw at one end of the level, and for the other half by the vertical tangent screw, i. Repeat the operation till the result is perfectly satisfactory. Next turn the telescope round a little both to the right and to the left, and if the bubble does not still remain in the centre of its run, the level, S S, must be adjusted laterally by means of the screw at its other end. This adjustment will probably dis- turb the first, and the whole operation must then be carefully re- peated. By means of the small screw fastening the vernier of the vertical limb to the vernier plate over the compass box, the zero of this vernier may now be set to the zero of the limb, and the verti- cal limb will be in perfect adjustment. With an increase in the size of the theodolite, a second telescope is placed beneath the horizontal limb, which serves to detect any accidental derangement of the instrument during an observation, by noting whether it is directed to the same point of a distant ob- 294 THEODOLITE. ject at the end of the observation to which it has been set at the commencement of the observation. Also the vertical limb, in the larger theodolites, admits of an adjustment to make it move accu- rately in a vertical plane, when the horizontal limb has been first set in perfect adjustment. This adjustment is important, and should be examined with great care; and in the small theodolites, when the vertical limb is permanently fixed to the horizontal limb by the maker, an instrument which will not bear the test of the examina- tion which we proceed to describe must be condemned, till set in better adjustment by the maker. The azimuthal axis having been set truly vertical, direct the telescope to some well-defined angle of a building, and making the intersection of the wires exactly coin- cide with this angle near the ground, elevate the telescope by giving motion to the vertical limb; and if the adjustment be perfect, the intersection of the cross wires will move accurately along the angle of the building, still continuing in coincidence with it. A still more perfect test will be to make the intersection of the cross wires coin- cide with the reflected image of a star in an artificial horizon, and elevating the telescope, if the adjustment be perfect, the direct image of the star itself will again be bisected by the cross wires. THE USE OF THE THEODOLITE. To take an angle, whether between the magnetic meridian and a given line or object, whether between any two given lines, or at one given point between any other given points. Open the tripod stand, so that the centre is as nearly as possible over the centre of the station, which can be ascertained by a plum- met, [or what is better (inasmuch as it is always attainable when wanted, and no encumbrance when done with, because it can be thrown away), a stone tied to a string.] Level the instrument by means of the parallel plate-screws, and the levels B B; then if the angle required is one with the magnetic meridian, set the needle in motion, unclamp the upper and lower plates of the limb, and bring the zero division on the vernier to zero on the lower plate. Clamp the plates approximately by the clamp screw, and accurately ad- just them by the slow-motion screw. Unclamp the screw C, and bring the letter N, in the compass-box, to the marked end of the needle, by turning the whole body of the instrument. Clamp it approximately by the screw C, and exactly adjust it by the slow- motion screw D. The telescope and zero division of the scale is now in the magnetic meridian. Unclamp the upper and lower plates, and direct the telescope at the given object. Reclamp the limb approximately with the clamp screw, and exactly bring the THEODOLITE. 295 cross hairs of the telescope to intersect the object by means of the slow-motion screw. The angle then indicated by the instrument, is the measure of the angle required. If the measure of an angle between two lines or between two objects is required, the process is similar; excepting only, that part of it that relates to the mag- netic needle, which is in this case not required; it is simply neces- sary to place zero on the graduated arc with zero on the vernier, and direct the telescope at the left-hand object instead of in the magnetic meridian, as in the former case. Most theodolites are furnished with two verniers on the upper plate one corresponding with zero on the lower limb, and the oppo- site one with the mark denoting 180°. In taking the bearings of lines these verniers are very useful, as giving the true and apposite bearing, but in the simple process of measuring angles, one only is requisite. To read an angle taken by the theodolite, it is necessary to un- derstand the vernier scale-a very beautiful and ingenious con- trivance, by means of which the half degrees on the lower plate are accurately divided into single minutes. The 30 minutes represented by the vernier, are equal in length to 29 degrees on the graduated arc. Now, it is evident by the fig. 171, the divisions on the vernier being 30, while those on the graduated arc are 29, every division of the vernier must be one- thirtieth of a division on the graduated arc, less than such division; and, consequently, if the vernier is moved along until division 1 upon it is in contact with the first division or half degree on the graduated arc, the zero of the vernier has moved one-thirtieth part of such half degree or one minute; if 5 on the vernier is brought in contact with the fifth division, or 24 degrees on the graduated arc, then zero of the vernier must have moved five-thirtieths or five minutes, so that by this contrivance the most minute subdi- vision is accomplished.* A vertical angle, or an angle of elevation or depression, is taken with the theodolite by means of the vertical limb. Having levelled the body of the instrument as before described, bring the bubble of the telescope level into the centre of its run by means of the clamp screw c, and slow-motion screw i; observe that zero on the vernier and zero on the vertical arc are together, and then unclamp the vertical limb; raise or depress the telescope until the cross hairs intersect the object, and the angle denoted by the vernier on the * A description of the vernier in this place will explain its use in every case to which it can be applied. It often assumes various forms, but is so simple, that it must be apparent to every mathematical mind. 296 LEVELLING. vertical arc, will be the angle of elevation or depression, as the case may be, which was required. If the telescope be reversed in the Ys, and the angle taken with the other end, the mean of the two readings, if they differ, will be the nearest approach to accuracy, inasmuch as an error in the adjustment of the vernier is thereby counteracted. CHAPTER VIII. LEVELLING * Is the art of tracing a line equidistant from the earth's centre,* which shall cut the directions of gravity everywhere at right angles. The earth being a globe, it is evident that the operation of levelling does not consist in simply ascertaining the undulations of the earth above or below any given horizontal line which may be as- sumed to form its surface, as an extended plane, but in determining the relative distances of different places from the earth's centre. 1 In other words, a level line is not, as is frequently supposed, a true horizontal line, but the arc of a circle; so that if it were possible to start from London, and level round the world, the accurate level line would meet at precisely the same spot as that from which it started. I It is therefore obvious that any instrument calculated to take horizontal levels only, must, beyond a certain distance, become appreciably in error, and require correction for curvature. The horizontal line IH, in the figure, is the line which would be made by a levelling instrument standing at the point I, and for a certain distance (the relative di- ameter of the circle being considered), there would be no appreciable difference between the apparent and C G true level; but to shew my meaning, it must be palpably obvious that the point H is considerably farther from the centre * Supposing the earth a perfect sphere, which is not quite the case, but sufficiently near for our purpose, the length of the equatorial diameter being 7,924 miles, while the polar is only 7,898, the difference is only 26 miles or 3 part. H LEVELLING. 297 C than the point G is, and therefore it is not in the true level; and if any level is taken at a greater distance than ten chains, this error of curvature must be allowed for. In addition to this error, on account of curvature, is another, occasioned by refraction. It is well known that an object is never seen by us in its true position, but in the direction of the ray of light, which conveys the impression or image of the object to our senses, the most curious of all, and as yet (at all events to me) unexplained arrangement being, that the vertical position in which every reflected image is left in the eye of the observer when in- tercepted by the colouring matter that lines the back of the eye, is the reverse of reality, notwithstanding the correction of this anomaly, which takes place in the transference of the reflected image to the mind. The particles of light, in traversing the atmosphere, are always bent towards the perpendicular, and consequently describe a curved track, which to a certain extent modifies the effect of curvature in levelling, and renders it only necessary, in correcting for curvature, to do so to the extent to which the error is di- minished by refraction. Table 20, chap. I, shews the difference between the apparent and true level, both in respect of curvature and refraction. The practice of levelling requires greater care than any other operation in surveying, owing to the numerous chances of error, and the great difficulty of detecting it, without going over the whole operation again; notwithstanding which, when skilfully and circumspectly performed, the accuracy of the results may be demonstrated to a degree, exceeding if possible the proofs of a trigonometrical survey. For instance, suppose a series of levels to be taken along the principal roads of a country, and afterwards by circuitous routes, and a variety of methods, the levels of the branch roads are taken, commencing at a given point on the main line, and crossing it again and again, and finally terminating upon some other point of the main line: if at these crossings, and at the termination of the branch levelling, the reduced levels come out within a few hundredth parts of a foot of the reduced levels of the main line, there is little doubt that the levelling is correct. The most satisfactory piece of levelling, within my practice, oc- curred in the autumn of 1849. I was employed by the promoters of a public company to take about thirty-five miles of parliamen- tary levels,* commencing with a "Datum line one hundred feet * Levels from which a section is to be made for deposit in Parliament, on the 30th of November, in compliance with the Standing Orders of the House. V 298 LEVELLING. below the stone sill of the south door to Wandsworth Old Church, in the High Street, close to the middle of the door-post, on the east side of the door." I subsequently discovered that the promoters had, as a wise precaution against error, also employed another gentleman to take the same levels. When the levels were completed, myself and colleague met to compare notes. The following are a few of the results :- MY OWN. THOSE OF MY FRIEND. DIF. B. M.* At Wandsworth Church 100 100 Fork of Roads near the Printing Works 111.76 111.67 ⚫09 Branch Roads near the Plough Inn 111.65 111.63 •02 B. M. Mitcham Church 148.05 147.94 •11 A Junction near Mitcham Common 159.33 159.30 ⚫03 B. M. On a Direction Post near Hack- bridge 167.00 166.94 •06 B. M. On the front of large House. 173.75 173.65 •10 Junction of Roads 164.95 164.94 •01 At Angle of Roads 130.11 129.98 •13 Centre of Bridge near the Snuff Mills 141.58 141.47 •11 Junction of Branch 192.17 192·13 •04 Level of Water at Ford 191.28 191.27 ⚫01 At Waddon. 215.38 215.27 •11 The near side down Rail of Epsom Railway. 224.62 224.56 •06 B. M. On Croydon Church, being the close of work, on the stone sill of the principal door under the tower 228.11 228.10 •01 It will be seen that the greatest variation is 13, and that being only at an undefined point on a road, it is quite possible that a difference of a few hundredths might be made in holding the staff. * B. M. is the short way of writing Bench Mark, which signifies a firm permanent feature that can at any time be referred to. A mark on a brick or stone wall makes a good Bench Mark; they are generally cut in the form represented in fig. 172. The horizontal line A B being the level referred to. LEVELLING. 299 The curious in such matters will observe, that my results are in every instance the greater, and but that the levels of the Bench Marks also vary on the same way, I should account for it by the fact, that while my staff-holders used a tripod, those of my col- league did not. The above is inserted to shew the great accuracy with which levelling operations can be carried on. It is usual in levelling to compute all the heights from one common datum (imaginary) line, so that the relative level of any two places may be readily ascertained by the simple subtraction of one height from another. For instance, a place thirty feet above datum is ten feet higher than another that is twenty feet above datum. It is desirable that this datum line should be chosen below the lowest point to be levelled, so that all the heights may be positive quantities, which could not be the case were some above and others below datum. It does not of course follow, nor is it desirable that a datum line should coincide with any one known point, it is sufficient that it refers to it; hence it is customary to assume the datum to be 100 (or any other even number) below some known permanent point, which can always be referred to. Levelling Instruments. THE SPIRIT LEVEL. The spirit level consists of a glass tube, differing from the cylindrical form by having its diameter largest in the middle, and decreasing slightly and with great regularity from the middle to the ends. The tube is nearly but not quite filled with spirits of wine, thus leaving in it a bubble of air, bb, which rises to the highest part of the tube, so as to have its two ends equally distant from the middle, when the instrument is in adjustment, as repre- sented in the annexed figure. The tube is generally fitted into another tube of metal, and attached to a frame terminating in angular bearings, by which the level can either be suspended from, or else be stood upon, cylindrical pivots. When, however, the level forms a permanent part of any instru- ment, the manner of attaching it is modified to suit the particular form of the instrument to which it is attached. A small and accurately-divided scale is attached to the best instruments, or otherwise a scale is scratched upon the glass tube itself, as repre- sented in the figure given ante. 300 LEVELLING. The annexed figure is a repre- sentation of such a level as is used for levelling the axis of the best astronomical instruments. It is provided with a fixed scale, seen in the figure, and is suspended by means of accurately con- structed angular bearings. The following criteria of a good level are extracted from Dr. Pearson's valuable work on Practical Astronomy. Firstly, the bubble must be long enough, compared with the whole tube, to admit of quick displacement, and yet not too long to admit of its proper elonga- tion by low temperature. "Secondly, the curve must be such, that the sensibility and uniform run of the bubble will indicate quantities sufficiently minute, while those quantities cor- respond exactly to the changes of inclination, as read on the graduated limb of the instrument of which it forms a part. "Thirdly, the bubble must keep its station when the angles are moved a little round the pivots of suspension. 66 "Fourthly, the opposite ends of the bubble must vary alike in all changes of temperature, or, in other words, the ends of the bubble must elongate or con- tract alike in opposite directions, so that the middle point may always be stationary. "Fifthly, the angles of the metallic end-pieces must be so nicely adjusted that reversion on horizontal pivots that are equal will not alter the place of the bubble. "Sixthly, the distance between the two zeros of a fixed scale, when such a graduated scale is used, should be equal to the length of the bubble at the temperature of 60° of Fahrenheit's scale, and should be marked at equal dis- tances from the visible ends of the glass tube. Then, as the bubble lengthens by cold, or shortens by heat, its extreme ends may always be referred to these fixed marks, 00, on the scale, and will fall either within, upon, or beyond them, according to the existing temperature. The number of sub-divisions of the scale that each end of the bubble is standing at, counted from the fixed zero marks, at the instant of finishing an observation, must always be noted, that an allowance may be made for the value of the deviation in seconds, or as the case may require. "Seventhly, when the two ends of the bubble are not alike affected by a change of temperature, the scale should be detached, and adjustable to the new zero points, by an inversion of the level. (( Eighthly, when the scale has only one zero at its centre, which is a mode of dividing the least liable to misapprehension, the positions must be reversed at each observation, and both ends of the bubble read in each position; for in this case, if any change has taken place in the true position of this zero, the resulting error will merge in the reduction of the observation. This mode of graduating is generally practised on the continent." LEVELLING. 301 I now proceed to the description of the most accurate instru- ments for measuring the differences of level, or vertical distances, between different stations. Of spirit levels, for this purpose there are now three in use, namely, the Y level, Troughton's improved level, and Gravatt's level. THE Y LEVEL. The following figure represents this instrument. A is an achro- matic telescope, resting upon two supporters, which in shape re- semble the letter Y, and are consequently called the Ys. lower ends of these supporters are let perpendicularly into a strong The Οι EC D B a a bar, which carries a compass box, C. This compass box is con- venient for taking bearings, and has a contrivance for throwing the needle off its centre, when not in use. One of the Y sup- porters is fitted into a socket, and can be raised or lowered by the screw B. Beneath the compass box, which is generally in one piece with the bar, is a conical axis passing through the upper of two parallel plates, and terminating in a ball supported in a socket. Imme- diately above this upper parallel plate is a collar, which can be made to embrace the conical axis tightly by turning the clamping screw E, and a slow horizontal motion may then be given to the instrument by means of the tangent screw D. The two parallel plates are connected together by the ball and socket already men- tioned, and are set firm by four milled-headed screws, which turn in sockets fixed to the lower plate, while their heads press against the under side of the upper plate, and thus serve the purpose of setting the instrument up truly level. 302 LEVELLING. Beneath the lower parallel plate is a female screw, adapted to the staff-head, which is connected by brass joints with three ma- hogany legs, so constructed as, when shut together, to form one round staff, a very convenient form for portability, and, when opened out, to make a very firm stand, be the ground ever so un- even. The spirit level 77 is fixed to the telescope by a joint at one end, and a capstan-headed screw at the other, to raise or depress it for adjustment. In looking through a telescope a considerable field of view is embraced; but the measurements indicated by any instrument, of which the telescope may form a part, will only have reference to one particular point in this field of view, which particular point is considered as the centre of this field of view. We must therefore place some fixed point in the field of view, and in the focus of the eye-piece, and the point to which the measurement will have re- ference will be that point of the object viewed, which appears to be coincident with this fixed point, or which, as the technical phrase is, is bisected by the fixed point. The intersection of two fixed lines will furnish us with such a fixed point, and consequently two lines of spider's web are fixed at right angles to each other in the focus of the eye-piece. They are attached by a little gum to a brass ring of smaller dimensions than the tube of the telescope, and which is fixed to the tube by four small screws, a, b, c, d. If the screw d be eased, while at the same time c is tightened, the ring will be moved to the right; but if c be eased and d tightened, the ring will be moved to the left; and in a like manner it may be moved up or down by means of the screws a and b. When the instrument is in adjustment, the B Ա. • Da Jo axis of the tube of the telescope is set truly horizontal by means of the level beneath it, and the line of observation ought consequently to be parallel to this axis. Let A represent the proper position of the intersection of the cross wires, and OA the direction of the axis of a pencil of light passing through the object- glass and coming to its focus at A. Then, the axis of the tube of the telescope being set truly horizontal, the line AO is also truly horizontal, and every point bisected by the intersection of the cross wires will be situated on the prolongation of the horizontal line A O. LEVELLING. 303 Suppose now the position of the diaphragm carrying the cross wires to have become deranged, so that the point of intersection is moved to B, then every point bisected by the intersection of the cross wires will be on the prolongation of the line BO, and will consequently be below the true level point on the line A O. Let now the telescope be turned half round in the Ys, and let the annexed figure represent it in its new position; then, in this new position of the telescope, the pro- longation of the line BO will rise. above the prolongation of the level line A O, and at the same distance from the telescope, the point now bisected by the intersection of the cross wires will be as much above the true level point on the line AO as the point before bisected by them was below it. The true level point is therefore midway between the two points observed in the two positions of the telescope, and the diaphragm carrying the cross wires is to be moved by means of the screws a, b, c, d, till their point of intersec- tion coincides with that true level point. The telescope is then to be again turned round upon the Ys, and if the same point be still bisected by the intersection of the cross wires, they are in their proper position; but if not, the same method of adjustment must be repeated till the same point is bisected by the intersection of the cross wires in every position of the telescope. This error of derangement has a technical denomination. The line O A, or O B, from O to the point of intersection of the cross wires, is called the line of collimation, and the error arising from their derangement, the method of detecting and correcting which, I have shewn, is called the error of collimation. When the image of the object viewed, formed by the object- glass, either falls short of, or beyond the place of, the cross wires, the error arising from this cause is called parallax. The existence of parallax is determined by moving the eye about when looking through the telescope, observing whether the cross wires change their position, and are flittering and undefined. To correct this error, first adjust the eye-piece by means of the moveable eye-piece tube, till you can perceive the cross wire clearly defined, and sharply marked against any white object. Then by moving the milled-headed screw A, at the side of the telescope, the internal tube a is thrust outwards or drawn inwards, until you obtain the proper focus, according to the distance of the object, and you are enabled at once to see clearly the object, and the intersection of the wires, clearly and sharply defined, before it. The existence of parallax is very inconvenient, and where disre- 304 LEVELLING. garded, has frequently been productive of serious error. It will not always be found sufficient to set the eye-glass first, and the object-glass afterwards. The setting of the object-glass, by intro- ducing more distant rays of light, will affect the focus of the eye- glass, and produce parallax or indistinctness of the wires, when there was none before; the eye-piece must, in this case, be adjusted again. Generally, when once set for the day, there is no occasion for altering the eye-glass, but the object-glass will of course have to be altered at every change of distance of the object. In adjusting the instrument, the parallax should be first cor- rected, and then the error of collimation. The line of collimation being thus brought to coincide with the axis of the tube of the telescope, two further adjustments are necessary: the first to ad- just the bubble-tube, so that it may truly indicate when the axis of the telescope is horizontal; and the second to set the axis of the telescope perpendicular to the vertical axis round which the instru- ment turns. To adjust the Bubble-Tube.-Move the telescope till it lies in the direction of two of the parallel plate screws, and by giving motion to these screws bring the air bubble to the centre of its run. Now reverse the telescope carefully in the Ys, that is, turn it end for end; and should the bubble not settle at the same point of the tube as before, it shews that the bubble-tube is out of adjustment, and requires correcting. The end to which the bubble retires must then be noticed, and the bubble made to return one-half the dis- tance by turning the parallel plate screws, and the other half by turning the capstan-headed screw at the end of the bubble-tube. The telescope must now again be reversed, and the operation be repeated, until the bubble settles at the same point of the tube, in the centre of its run, in both positions of the instrument. The ad- justment is then perfect, and the clips which serve to confine the telescope in the Ys should be made fast. Lastly, to set the Axis of the Telescope perpendicular to the Ver- tical Axis round which the Instrument turns.—Place the telescope over two of the parallel plate screws, and move them, unscrewing one while screwing up the other, until the bubble of the level set- tles in the centre of its run; then turn the instrument half round upon the vertical axis, so that the contrary ends of the telescope may be over the same two screws, and if the bubble does not again settle at the same point as before, half the error must be corrected by turning the screw B, and the other half by turning the two pa- rallel plate screws over which the telescope is placed. Next turn LEVELLING. 305 the telescope a quarter round, that it may lie over the other two screws, and repeat the process to bring these two screws also into adjustment; and when, after a few trials, the bubble maintains ex- actly the same position in the centre of its run, while the telescope is turned all round upon the axis, this axis will be truly vertical, and the axis of the telescope. being horizontal by reason of the pre- vious adjustment of the bubble-tube, will be perpendicular to that vertical axis, and remain truly horizontal, while the telescope is turned completely round upon the staves. The adjustment is therefore perfect. The object of the above adjustments is to make the line of colli- mation move round in a horizontal plane, when the instrument is turned round its vertical axis, and the methods above explained suppose that the telescope itself is constructed with the utmost 'perfection, so that the axis of the tube carrying the object-glass is always in the same straight line with the axis of the main tube, which carries the diaphragm with the cross wires. If this perfec- tion in the construction of the instrument does not exist, the line of collimation will vary, as the tube carrying the object-glass is thrust out, and drawn in, to adjust the focus for objects of different distances. What is really required then is, that the cross wires be so adjusted that the line of collimation may be in the same straight line with the line in which the centre of the object-glass is moved, and that the bubble of the level be at the centre of its run, when this line of collimation is directed to view objects, at the same level, or at the same distance from the centre of the earth. We are indebted to Mr. Gravatt, of whose level I shall here- after speak, for a method of collimating, which satisfies the above requirements, and removes any error arising from imperfection in the slide of the telescope, while at the same time the line of colli- mation is set with the end at the object-glass, slightly depressed, instead of exactly horizontal, so as to remove, or nearly so, the errors arising from the curvature of the earth, and the horizontal refraction. To examine and correct the Collimation by Mr. Gravatt's Method.—“On a tolerably level piece of ground drive in three stakes at intervals of about four or five chains, calling the first stake a, the second b, and the third c. "Place the instrument half way between the stakes a and b, and read the staff A, placed on the stake a, and also the staff B, placed on the stake b ; call the two readings A' and B'; then, although the instrument be out of adjustment,* yet the *The axis of the instrument is to be set vertical by means of the parallel plate screws, by placing the telescope over each pair alternately, and moving them until the air bubble remains in the same position, when the instrument is turned half round upon its axis. 306 LEVELLING. points read off will be equidistant from the earth's centre, and consequently level. "Now remove the instrument to a point half way between b and c. Again, read off the staff B, and read also a staff placed on the stake c, which call staff C (the one before called A being removed into that situation.) Now, by adding the difference of the readings on B (with its proper sign) to the reading on C, we get three points, say A', B', and C', equidistant from the earth's centre, or in the same true level. "Place the instrument at any short distance, say half a chain beyond it, and using the bubble merely to see that you do not disturb the instrument, read all three staffs, or, to speak more correctly, get a reading from each of the stakes, a, b, c; call these three readings A", B", C". Now, if the stake b be half way between a and c,* then ought C"—C—(A"— A') to be equal to 2 [B" — B' —(A ' — A')]; but if not, alter the screws which adjust the diaphragm, and consequently the horizontal spider line or wire, until such be the case; and then the instru- ment will be adjusted for collimation. "To adjust the spirit bubble without removing the instrument, read the staff A, say it reads A', then adding (A" — A') with its proper sign to B' we get a value, say B'". Adjust the instrument by means of the parallel plate screws †, to read B'"' on the staff B. "Now, by the screws attached to the bubble-tube, bring the bubble into the centre of its run. "The instrument will now be in complete practical adjustment for level, cur- vature, and horizontal refraction, for any distance not exceeding ten chains, the maximum error being onlyth of a foot.” Before making observations with this instrument, the adjust- ments should be carefully examined and rectified, after which the screw B should never be touched; but at each station the parallel plate screws alone should be used for setting the axis round which the instrument turns truly vertical, when, in consequence of the adjustments previously made, the line of collimation will be truly level. For this purpose the telescope must be placed over each pair of the parallel plate screws alternately, and they must be moved till the air bubble settles in the middle of the level, and the operation being repeated till the telescope can be turned quite round upon the staff-head, without any change taking place in the position of the bubble, the instrument will be ready to read off the graduations upon the levelling staves, which we proceed to describe. In all work where great accuracy is required, the Y level above described, is preferable to either of the others; but both Trough- * Whatever be the distances between the stakes a, b, and c, the following propor- tions ought to hold, viz.: The distance from ab: the distance a to c:: B" — B′ — (A″ —A'.) : C". (A" — A'.) C' + If this adjustment be made by the screw B, instead of the parallel plate screws, the line of collimation will be brought into its proper position with respect to the vertical axis. LEVELLING. 307 ton's level and Gravatt's level are calculated, by their lightness, and by their being less liable to derangement when once properly adjusted, to get rapidly over the ground. TROUGHTON'S LEVEL. T B B In this level the telescope T, rests close down upon the hori- zontal bar, bb, the spirit level, 7 7, is permanently fixed to the top of the telescope, and does not, therefore, admit of adjustment, and the compass box, C, is supported over the level by four small pillars attached to the horizontal bar. This construction makes the in- strument very firm and compact. The staves, staff-head, and paral- lel plates by which the instrument is supported, and the vertical axis upon which it turns, are of exactly the same construction as has been already described as used for supporting the Y level. The diaphragm is furnished with three threads, two of them ver- tical, between which the levelling staff may be seen, and the third, horizontal, gives the reading of the staff by its coincidence with one of the graduations marked upon it. Sometimes a pearl micrometer scale is fixed on the diaphragm, instead of the wires. The central division on the scale, then, indicates the collimating point, and by its coincidence with a division of the levelling staff gives the re- quired reading of this staff; and the scale serves the purpose of measuring distances approximately, and of determining stations nearly equidistant from the instrument, since at such equal dis- tances the staff will subtend the same number of divisions upon the micrometer-scale. In selecting a level of Troughton's construction, and also in testing and adjusting the collimation subsequently, Mr. Gravatt's method, already described, is the best to be used; and when the line of collimation is thus brought into adjustment, if the bubble be far from the centre of its run, the fault can only be remedied by the maker; but if the bubble settle very nearly in the centre of its run, the instrument may be deemed a good one, and the divisions on the glass tube which coincide with the ends of the bubble being noted, the instrument must be set up for use with the bubble in this position. The line of collimation is set perpendicular to the vertical axis 308 LEVELLING. in the same manner as in the Y level, by means of the capstan screws B B, the bubble being made to maintain the requisite posi- tion, as above determined, while the instrument is turned com- pletely round on its axis. MR. GRAVATT'S LEVEL. This instrument is furnished with an object-glass of large aper- ture and short focal length; and sufficient light being thus obtained a B B C M to admit of a higher magnifying power in the eye-piece, the advan- tages of a much larger instrument are obtained, without the incon- venience of its length. The diaphragm is carried by the internal tube a a, which is nearly equal in length to the external tube. The external tube TT is sprung at its aperture, and gives a steady and even motion to the internal tube a a, which is thrust out, and drawn in, to adjust the focus for objects at different distances by means of the milled-headed screw A. The spirit level is placed above the telescope, and attached to it by capstan-headed screws, one at either end, by means of which the bubble can be brought to the centre of its run, as in the case of the Y level, when the line of collimation is brought to the proper level by Mr. Gravatt's method of adjust- ment, already explained. The telescope is attached to a horizontal bar, in a similar man- ner to Troughton's level, but room is just left between the teles- cope and the bar for the compass-box. A cross level, k, is placed upon the telescope at right angles to the principal level 77, by which we are enabled to set the instrument up at once with the axis nearly vertical. A mirror, m, mounted upon a hinge-joint, is placed at the end of the level, 77, so that the observer, while reading the staff, can at the same time see that the instrument retains its proper position-a precaution sometimes desirable in windy weather, or on bad springy ground. The telescope is attached to the horizontal bar by capstan- headed screws, BB, as in Troughton's level, by which the line of collimation is set perpendicular to the vertical axis ; and the instru- ment is set up upon parallel plates, as before described, for the Y level. LEVELLING. 309 The level I use, and which was specially constructed for me by the Messrs. Elliott is without either the cross level, the compass- box, or the mirror; the advantages obtained from the occasional use of which, not being equal in my estimation, to the benefits arising from the use of a light instrument, divested of every un- necessary encumbrance. Levelling Staves. One kind of staff has superiority over another only in the degree of its applicability to the purposes for which it is required—hence a folding staff is more handy for travelling, but a staff in one length is preferable for rough use, if it has not to be transported from one place to another; but of whatever description of mecha- nical arrangement the staff may partake, it is a great desideratum that it present to the observer a clear, simple, graduated face, upon which he can obtain for himself the reading of the quantities by the aid of his telescope. The old-fashioned vane staves are so far gone out of use that it is not intended to notice them here. Many levelling staves are figured by means of printed papers pasted or rather stuck on; but these are objectionable, as in wet weather the paper will, by constant use, rub off, and thus the uti- lity of the staff is at once destroyed. Levelling surveyors, who paint their own staves, have varied fancies as to the method of doing it; all first divide the staff into feet and tenths, but some subdivide those tenths into actual hun- dredths. I have tried many ways, and will give the one my experience has led me to prefer. Fig. 173 represents this staff. It will be observed, that the division of the feet is always rea- dily distinguished by the top of the large figure which numbers the feet, and the bottom of the large figure is always 85, conse- quently, the division of the 90 always crosses the large figure at 3rd of its length, and the 80 is always a little below the foot of it. •75 is marked by a red line, which differs from the 25 in this par- ticular, that one crosses the staff in a plain white space, while the other crosses through one of the black blocks. 70 is exactly at the top of the block, immediately below the distinctive mark of •75, and '60 is the mark intervening between 70 and 50, which latter is represented by the top of the letter V; 40 is the bottom of the V, and ⚫30 is next above the distinctive mark of 25, as 20 is next below it. 10 is readily distinguished as next above the preceding 310 LEVELLING. figure denoting the number of feet, and thus completes a very sim- ple, and at the same time, a very bold and distinctly marked staff, clearly legible in dull weather, and about the subdivision of which to hundredths there is no difficulty whatever to a practised eye, and no chance of error beyond a hundredth at most to an unprac- tised one. The absence of all other figures than those numbering the feet render the mistake of one figure for another impossible, and while there are doubtless many as good, it is confidently be- lieved few are better. The operation of levelling is performed in this simple way-a staff is held up at the two places between which the difference of level is required, and if the reading on one staff is more than that on the other, the difference between them is the difference of level, or the measure by which the distance of one from the earth's cen- tre exceeds that of the other. We have already seen that within a distance of 10 chains from the level there is no correction re- quired for curvature and refraction, and, consequently, no level should be taken beyond this distance from the instrument. It is hardly necessary to mention this, for very few instruments, unless too large and cumbersome for ordinary requirements, will read a staff distinctly at a greater distance. Let figure 173a represent a section of the surface between two points A and G, the difference of level between which is required. Set up the instrument at B, and read a staff at A; reverse the telescope, and read a staff at C. Remove the instrument to D; get another reading from the same staff at C, and from a fresh staff at E; again remove the instrument to F, and get readings from E and G. Now, it is evident from what has been said, that the sum of the back readings, minus the sum of the fore readings, is the difference of level required; and to avoid negative quantities, we will assume the point A is 20 feet above an imaginary level plane, which we call our Datum line. The calculation stands thus:- Height of A above datum Add reading of staff A FEET. 20 · 11.50 Deduct fore reading of staff C • 31 · 50 11 · 90 Gives the height of C above datum Add back reading of C as taken at D 19 · 60 12. 20 • 31 · 80 LEVELLING. 311 Deduct fore reading of E taken at D Height of E above datum Add back reading of E taken at F Deduct fore reading of G taken at F Height of G above datum · 31 · 80 8.46 23 · 34 7.64 30.98 7.98 23·00 A being 20 above datum, and G being 23, G is obviously 3 feet higher than A. It will however be seen, that the highest point is E, which is 23.34 above datum, and consequently, 0.34 above G; C is 19.60 feet above datum, or 0.40 feet below A. In actual practice, the adding and subtracting the back and fore readings is never (or at all events by very few surveyors) carried out in detail, in the manner which, for the sake of explicitness, it has been given above. It is obvious, that if the difference of level between two staves be added when the fore reading is the lesser, or subtracted when it is greater, it will produce the same result-for example, the difference of level between A and C is 0.40 feet, and the back sight being the lesser height if that is subtracted from the datum at A, it will give the height of C, and so on throughout the series. There are several forms of levelling books in use among sur- veyors, but they only differ as to the position and number of the vertical columns; it will be only necessary for me to describe one of these forms. Taking our preceding example then, the annexed is a specimen of the practical reduction of it in a Field Book. Levels taken from A to G. Distances. Back Fore Sights. Sights. Rise. Fall. Reduced Levels. REMARKS. Links 20. 20. 800 11.50 11.90 20. .40 19.60 Datum line 20 ft. below A Station A. C. "" 1500 12.20 8.46 3.74 23.34 E. "" 2000 7.64 7.98 .34 23. G. "" 51.34 28.34|| 23.74 .74 28.34 23. .74 23. 312 LEVELLING. Very few remarks will serve to render this form of Field Book intelligible. Distances have been inserted to shew the use of the column headed distances; but in many cases distances are not taken in levelling. The datum line is first fully described in the column of remarks. The height above datum is then placed in the column of reduced levels, as the height of station A; and it is also repeated in the columns headed "back sights," and "rise," for the purposes of the proof of the casting, as will be hereafter seen. The back sight * at A, and the fore sight at C, are now placed side by side in their respective columns, and their difference placed in the proper column of "rise or "fall," as the case may be. In like manner the back sight at C, and the fore sight at E, are entered, and so on through- out the series. The rises are now added to the preceding height above datum, and the falls deducted and the results shew the re- spective heights of each station. "" The method of keeping a Field Book admits of two proofs. First-If the sum of the fore sights is deducted from the sum of the back sights, including the first height above datum, it will give the relative height of the last station, and should conse- quently correspond with the last item of reduced levels. In like manner if the sum of the falls be deducted from the sum of the rises, including the first height above datum, it will, if correct, produce the same result. Attention to a few trifling circumstances in levelling will secure most important results. If the level is always placed perfectly central between two stations, the results will always be correct irrespective of any instrumental error. If it is sometimes neces- sary to have a long back sight and a short fore sight, it is always practicable to reverse the order within a station or two, so that the back sights and fore sights are made to balance. Never get a reading from a staff without first observing that the bubble of the spirit tube is in the centre of its run; nor ever leave a staff after the reading until it has been entered in the book, and has been again examined. If accuracy is not of less importance than expedition never use a staff as a rule, that is more than about ten feet long; it is all very well to have an extra length for excep- tional cases, but the best staff holder will not keep a long staff perpendicular. It should be borne in mind, that errors of this description are not, as is often the case in instrumental errors, capable of balancing themselves by being sometimes of a positive, * That is, the reading of the staff. LEVELLING. 313 and at others, of a negative character, and thus standing a chance of accidental adjustment. If a staff is not held perpendicular, the error must always be that the reading observed is too much, the perpendicular distance between any two points being always the shortest distance possible. Of course, if the same error exists in both back and fore read- ing it is immaterial. But the use of these long staves is only brought into action in descending or rising a hill, when one read- ing is nearly zero, while the other is perhaps fifteen feet up the staff. There is one chance of a balance with errors of this kind- and it is in cases when the ascents and descents are equal; a cir- cumstance against which the odds are very great. The staff holders should always be provided with something to stand the staff upon, to ensure the reversal of the staff between the readings from the different stations of the instrument with mathematical precision. A penny, or a small piece of tile or slate is better than nothing, but far preferable to that, is what is called a "tripod." This little instrument consists of a triangular piece of sheet iron of about an eighth of an inch thick, shod at the corners to enter the ground; and a semi-circular ball is rivetted on to the top, so that whatever the position of tripod or staff, the latter is certain to be placed on the same spot, notwithstanding any removal in the interim between the first and last reading. A small chain, with a ring or leather strap attached, enables the staff holder to lift it from the ground, and carry it from station to station without in- convenience. If any intermediate readings occur, that is, points of which it is competent to ascertain the level without moving the instrument to do it; the most simple method is to treat the fore sight of the intermediate as a fresh back sight, and re-enter it as such; but in proving the castings these need not be cast in with the others, but such as occur in both columns can of course be cancelled. I sub- join one practical example. Levels taken from Wandsworth to the Elephant and Castle. 314 Back Fore Distances. Rise. Fall. Sight. Sight. Reduced Levels. 100. 100. 100. REMARKS. Datum line 100 feet below the stone sill of the south door to Wandsworth old Church, in the High Street, close against the middle of the door-post on the east side of the door. B. M. on stone sill of gate. 3.79 * 4.05 .26 99.74 000 * 4.05 4.96 .91 98.83 Centre of High Street. 600 4.28 2.09 2.19 101.02 1000 3.33 4.05 .72 100.30 1600 5.76 3.19 2.57 102.87 2100 7.44 *0.45 6.99 B. M. on stone at corner of 109.86 North Street. * 0.45 0.23 •22 110.08 Junction of High Street and North Street. 2300 7.84 1.52 6.32 116.40 2500 8.99 1.40 7.59 123.99 2700 9.18 1.33 7.85 131.84 3000 9.84 1.55 8.29 140.13 3600 9.93 1.84 8.09 148.22 3800 6.64 * 4.46 2.18 ham Roads. 150.40 Fork of Vauxhall and Clap- 4400 * 4.46 2.69 1.77 152.17 5.77 * 4.01 1.76 4650 * 4.01 6.27 2.26 5000 2.09 5.71 153.93 151.67 3.62 148.05 B. M. on top of hanging post of gate into East Hill burying ground, from the Vauxhall Road. 6000 6.10 3.78 2.32 150.37 7000 5.32 5.84 7870 3.60 *1.00 2.60 1 mile * 1.00 7.05 750 1.66 * 6.66 1000 * 6.66 12.20 .52 149.85 152.45 6.05 146.40 5.00 141.40 B. M. on top of coping of bridge over S. W. Railway— on the south side of bridge immediately over the near side down rail (about 27.25 above rail). 5.54 135.86* *Road leads off to Tooting. 1400 1.17 12.53 11.36 124.50 1800 0.10 10.46 10.36 114.14 2100 1.86 * 7.34 5.48 108.66 2480 * 7.34 0.31 7.03 115.69 2720 9.04 0.56 8.48 124.17 2950 8.48 0.21 8.27 132.44 3300 9.24 1.58 7.66 140.10 9.24 * 6.76 2.48 142.58 | B. M. on the top of the guard 4300 * 6.76 1.46 5.30 147.88 5300 7.43 5.87 1.56 149.44 stone to western gate post at entrance to a gentleman's house, south of road. 6300 5.80 5.10 .70 150.14 7000 4.80 5.18 2 miles 4.59 4.37 .22 1000 4.67 5.54 1200 5.35 4.44 .91 1209 4.75 0.24 4.51 2000 3.10 6.02 2.92 3000 6.16 6.95 4000 5.61 2.26 3.35 .38 149.76 149.98 .87 149.11 150.02 154.53 151.61 .79 150.82 154.17 Clapham Common. B. M. on the top of mile stone marked by the Ord- nance Officers.-Five Miles from Standard, Cornhill. Junction with Dorking Road. 5000 4.05 6.53 2.48 151.69 6000 2.54 9.28 6.74 144.95 299.54 154.59 211.21 66.26 154.59 66.26 144.95 144.95 Levels between Wandsworth and the Elephant and Castle. 315' Distances Back Fore Sight. Sight. Rise. Fall. Reduced Levels. REMARKS. 144.95 144.95 6450 2.07 * 3.91 144.95 1.84 143.11 B. M on top of milestone, marked 3 miles from West- 6500 * 3.91 8.98 5.07 138.04 minster Bridge. 7000 1.80 9.30 7.50 130.54 7500 .95 7.17 6.22 124.32 3 miles 6.09 3.22 2.87 127.19 300 7.37*3.74 3.63 130.82 1000 * 3.74 8.44 4.70 126.12 0.63 1.14 2000 1.14 12.58 3000 0.82 7.97 4.52 * 0.68 3.84 4000 * 0.68 7.81 5000 6.10 6.58 .48 103.25 .51 125.61 B. M. on top of water plug, 11.44 114.17 opposite St. John's Chapel and 7.15 107.02 the Elms. 110.86 B. M. on top of milestone, marked three miles from 7.13 103.73 Blackfriars. 6000 5.13 6.95 1.82 101.43 6450 5.51 * 1.88 3.63 105.06 B. M. on top of milestone, 7000 * 1.88 5.66 3.78 101.28 marked two miles from West- minster Bridge. 7400 4.57 2.14 2.43 4 miles 2.14 6.85 4.71 99.00 103.71 B. M. on top of milestone, at corner of Albert Square. 1000 5.00 6.67 1.67 97.33 2000 6.31 5.39 .92 98.25 2500 7.90 * 5.35 2.55 3000 * 5.35 8.77 3.42 97.38 3830 4.16 * 2.65 1.51 100.80 Opposite the Griffin Inn. B. M. on top of lower hook of 98.89 T. P. Gate, next Toll House, 4000 * 2.65 5.77 3.12 95.77 on Kennington Common. 5000 4.27 6.67 2.40 93.37 6000 5.10 5.50 •40 92.97 7000 5.94 6.21 .27 92.70 5 miles 4.09 4.23 .14 92.56 1000 4.21 2.82 1.39 93.95 1300 5.87 * 3.32 2.55 96.50 2000 *3.32 6.46 3.14 3000 3.67 66.6 2.99 90.37 3600 7.33 * 3.24 4.09 * 3.24 0.45 2.79 B. M. on top of Iron Water Post, on North Side of Street 93.36 facing the Newington Registry Office for Servants. 94.46 Centre of Roads at the Ele- phant and Castle. 97.25 B. M. on the top of a mile- stone facing the Shop of Con- nelly, Stationer, &c. 257.64 160.39 177.15 79.90 160.39 79.90 97.25 97.2 NOTE.-It will be observed that the intermediate sets are cancelled and omitted in the cast up of the pages. 316 PLOTTING. CHAPTER IX. PLOTTING. THE first consideration in plotting is the choice of the paper upon which to lay down the survey that has been made. In large sur- veys it is often desirable to lay down the fundamental lines to a very small scale (twenty or thirty chains to an inch), from which to arrive at a tolerably correct notion of the size of the paper re- quired, and the most eligible position thereon for the principal line. The Officers of the Ordnance Survey have laid it down as a standing rule always to keep the north of the map towards the top of the paper; but I do not regard this as an essential feature, especially in original maps. I would at any time sacrifice it to the attainment of a more eligible position of the map upon the paper. I do not mean to say I would reverse the order of things, and place the south towards the top, but I certainly should not mind so placing the east or west. As an instance of my meaning, the survey of the parish of Horsell, hereinbefore referred to, required paper about ten feet long by five wide, the length being in the direction of east and west. To place such a map north upwards would be to render what might be comparatively a handy roll of five feet long, an unhandy one of ten feet, which few ordinary tables in private houses would accommodate. Having selected the position of the main line on the paper, the next thing is to lay it down. This must be done with a straight edge proportioned to its length, as it is a very difficult thing to produce a line by means of several splicings-a "steel straight edge" will be found desirable for this purpose. As soon as the line is down, the distances from zero at every ten chains along its course should be marked off ac- cording to the scale with which the work is to be plotted; this should be done with the point of a needle, and the figures denoting the number of chains should be very finely marked against the several dots. The number of the line should then be placed on the end at which the measurement of it commences, which answers the double purpose of being an index to the line, and the direction in which it ran. All future distances on the line laid down will be laid off from the nearest dot, without reference to the zero of the line, so that any inaccuracy arising from expansion or contrac- tion of the paper will be obviated as much as possible. It is generally less difficult to lay down the first line of a survey than it is the second and third, inasmuch as the true position of the PLOTTING. 317 latter as sides of a triangle have to be scrupulously attended to. In large surveys it is often necessary to resort to a variety of mathe- matical contrivances to get them down accurately; sometimes the use of a thread or a slip of mounted drawing paper marked the re- quired length from the main line will scribe an arc tolerably near, but it is always safer and generally more correct to adopt the best means at once, and do it mathematically. A simple process is to compute the angles accurately, and then with any convenient length as radius, say 100 chains, find the natural sine and cosine by the Table. Let fig. 174 represent this method. Suppose the triangle A D G to be a trigonometrical projection required to be plotted, whose sides are beyond the limits of all drawing tables— straight edges and scales at command. Lay off the cosine of angle A from A to B, and of angle D from D to C. Erect perpendicu- lars at B and C ; lay off the sine of angle A from B to F, and of angle D from C to E; try that AF and DE are exactly equal to the radius of 100 chains, and E and F may then be used as points from which to raise G; FG and E G having now become in all probability within manageable compass. The points E and F may be sometimes better fixed by scribing the radius and sine—much de- pends upon the angle. If a perpendicular is erected, it must be a really accurate one; and if the work is very extensive, it will be as well to calculate mathematically the length of EF. The point G obtained, the straightness of the lines A F G and D E G must be tested with the straight edge; but if the operation has been care- fully performed, there is little probability but that they will prove correct. As every line is plotted, the distances from zero should be marked off at each ten chains, as on the main line, and the line numbered as before directed. As many of the fundamental lines as possible should be laid down at one time, so that in the event of subsequent alteration of paper, which is almost certain to take place, all the work may go together, and but the minimum of inconvenience experienced. In laying down the secondary lines of the survey, such as the line R I, on the parish of Sunbury survey, having drawn the line from point to point with the straight edge, previous to marking off the furlongs, try the length on the paper, and compare it with the book, for with the most careful chaining there is at all times a lia- bility to disagreement, owing to the unevenness of the ground over, and the hedges and other places through, which the chain has to pass. This disagreement, for it is not error, should in no case ex- ceed about a link in ten chains on an average of the whole length of the line, and should be equally spread in plotting throughout 318 PLOTTING. the whole length-that is, a line entered in the Field Book a 20005 may measure on the paper 20025, and yet be practically correct; but it would be manifestly inaccurate to point off 200 chains 25 links from the end of the line. In such a case, 10 chains must be plotted as 1001; 2000 as 2002; 3000 as 3003, &c. When all the lines are down (and if expedient drawn in very finely with, carmine or lake) the offsets can be plotted. Until tolerable skill has been acquired by considerable practice, every point should be carefully pricked off with a needle upon the chain line, and the offset therefrom accurately marked off; but after a time it will be sufficient to expedite the business by any contrivance that may suggest itself, and in the absence of a better, let us suppose the following:-Lay the edge of the plotting scale A B (fig. 175) pa- rallel with the line CD, upon which the offsets are to be plotted, at such a distance that the zero division of the offset scale E may coincide with the line as it passes along it, and also that zero on scale A B may be exactly opposite the zero end of the line; then, by sliding the offset scale along the line any offset not exceeding a chain in length (which, as has been already said in another place, should be the maximum limit of the offset, and should also be the maximum space between the chain line and scale) may be ac- curately plotted on either side of the line. To Plot the Notes of a Traverse Survey by the Table of Natural Sines and Cosines. The only difference between plotting the notes of a traverse and any other survey consists in laying down the lines. In the case of our previous example (fig. 170) we will assume that the trigono- metrical points A B C are already plotted. With the aid of the Table of Natural Sines and Cosines, lay off the angle between A B and the magnetic meridian in the following manner: A and B (fig. 176) are the two stations of the survey, whose bearing is taken. Take 1, 10, or 100 in the compasses, according to the extent of the lines, and scribe the arc EF: produce A B, so that A D shall be equal to the cosine, and DF the sine of the given angle: join A F, and it will be the required meridian. In like manner, line 1 is laid down by means of the angle con- tained between it and the magnetic meridian, its length is then marked off from A, and a line drawn through the end of it parallel to the meridian from which line 2 is marked off; and so on through- out the series. PLOTTING. 319 The great objection to traverse surveying, as a means of filling in, is the opportunity afforded for error in every line. It is ob- vious, that a link too much or too little in laying down each line will prevent the work from closing at the end; hence, the great advantage of a system of right lines, which renders every one inde- pendent of another. As the method of laying down the lines of a traverse by means of their sines and cosines may be considered troublesome in a sur- vey of magnitude, a protractor, or circular instrument of brass, may be employed to facilitate the laying off the angles. THE CIRCULAR PROTRACTOR. Our engraving represents one of the best kind of protractors. 20 360 e 09 40 U z z 340 320 300 α α 140 120 И B с 270 Arny prz w 240 C 091 081 002 It is a complete circle, A A, connected with its centre by four radii, a a a a. The centre is left open, and surrounded by a concentric ring or collar, b, which carries two radial bars, c c. To the extremity of one bar is a pinion, d, working in a toothed rack quite round the outer circumference of the protractor: to the opposite extremity of the other bar, c, is fixed a vernier, which subdivides the primary divisions on the protractor to single minutes, and by estimation to 30 seconds. This vernier, as may readily be understood from the engraving, is carried round the protractor by turning the pinion d. Upon each radial bar, c c, is placed a branch e e, carrying at their extremities a fine steel pricker, whose points are kept above the surface of the paper by springs placed under their supports, which give way when the branches are pressed downwards, and allow the points to make the necessary punctures in the paper. The branches e e are at- tached to the bars cc, with a joint which admits of their being folded backwards over the instrument when not in use, and for 320 PLOTTING. packing in its case. The centre of the instrument is represented by the intersection of two lines drawn at right angles to each other on a piece of plate glass, which enables the person using it to place it, so that the centre, or intersection of the cross lines, may coincide with any given point on the plan. If the instrument is in correct order, a line connecting the fine pricking points with each other would pass through the centre of the instrument, as denoted by the before-mentioned intersection of the cross lines upon the glass, which, it may be observed, are drawn so nearly level with the under surface of the instrument, as to do away with any serious amount of parallax, when setting the instrument over a point from which any angular lines are intended to be drawn. In using this instrument, the vernier should first be set to zero (or the division marked 360) on the divided limb, and then placed on the paper, so that the two fine steel points may be on the given line (from whence other and angular lines are to be drawn), and the centre of the instrument coincides with the given angular point on such line. This done, press the protractor gently down, which will fix it in position by means of very fine points on the under side. It is now ready to lay off the given angle, or any number of angles that may be required, which is done by turning the pinion d till the opposite vernier reads the required angle. Then press downwards the branches e e, which will cause the points to make punctures in the paper at opposite sides of the circle; which being afterwards connected, the line will pass through the given angular point, if the instrument was first correctly set. In this manner, at one setting of the instrument, a great number of angles may be laid off from the same point. It is not essential that the centre be over the given point when applied to the given line, provided the pricking points exactly fall upon the line, for an imaginary line connecting the pricking points in this instrument, correspond with the diameter. Some- times, instead of a rack and pinion motion, a third radial arm is attached to the centre at right angles to the other two, upon which is fixed a clamp and tangent screw, by which the vernier is not only fixed in position upon the circular limb of the instru- ment, but by the tangent, or slow motion screw, it may be set to the required angle with the utmost precision. THE T SQUARE AND SEMI-CIRCULAR PROTRACTOR. A convenient method by which a traverse can be most expe- ditiously as well as accurately plotted, by the aid of a T square PLOTTING. 321 B A E B B and semi-circular protractor, is thus described by Mr. Howlett, chief draughtsman, Royal Ordnance Office, in vol. i. of Papers on Subjects connected with the Duties of the Royal Engineers:- or, "As, when away from home, it seldom happens that the surveyor can obtain a good drawing board, or even a table with a good straight edge, I fix a flat ruler, A, to the table BBB, by means of a pair of clamps, C D, and against this ruler I work the pattern square E, one side of which has the stock flush with the blade; if a straight-edged board be at hand, then the square may be turned over, and used against that edge instead of the ruler A. Here, then, is the most perfect kind of parallel ruler that art can produce, capable of carrying the protractor over the whole of a sheet of plotting paper of any size, and may be used upon a table of any form. It is convenient to suppose the north on the left hand, and the upper edge of the blade to represent the meridian of the station. "This protractor is held in the hand while the vernier is set, which is an immense comfort to the sight; and it will be seen that, as both sides of the arm are parallel with the zero and centre, the angle may be drawn on the paper against either side, as the light or other circumstances may render desirable." From this description and a mere glance at the engraving, it is clear that angles taken with the theodolite can be transferred to the plot as accurately as the protractor can be set, namely, to a single minute, and that, too, in a rapid and pleasant manner. My own experience in plotting traverses as the "filling in" por- tions of a survey is not favourable to the use of a metallic pro- tractor, I prefer making a protractor in the following manner:- With a radius of 10 inches describe a circle, and without altering the compasses step round the circle pointing each step; this will divide it into six parts, each being 60°. Now the chord of an arc 322 PLOTTING. being equal to twice the sine of half that arc, if from the Table of Natural Sines we take the sine of 5° and multiply it by 2, we get the chord of 10°, which being laid off, subdivides each 60° into six parts of 10° each. In like manner we continue to subdivide the circle, until we have done so as minutely as required. Divi- sions, each containing five minutes, will be found quite small enough in practice, as lesser quantities are readily estimated by the eye. The degrees should then be numbered, as in a theodo- lite, and the protractor is fit for use. The traverses of the Guernsey survey are plotted with a pro- tractor of this kind, in the following manner:-Two trigonome- trical stations that can be connected by a series of traverse lines are selected. A sheet of tracing paper is laid over the protractor, upon which the position of one of the points is marked. A straight edge is then laid across the protractor to correspond with the bear- ing of line 1, and by means of two wooden set squares or triangles a parallel line is transferred to the point from which line 1 starts, where the line is drawn to its proper length, and the station marked for the commencement of line 2. The straight edge is then laid across the paper to correspond with the bearing of line 2, which is now marked off in its proper position parallel to the bearing. In like manner all the lines are plotted until they close upon ano- ther trigonometrical station. When the tracing paper is taken up, the two trigonometrical stations thereon are laid over the corre- sponding stations on the map, and the lines are transferred from the tracing thereto. On working maps, it is customary to distinguish the dwelling- houses from other buildings, by tinting the former with carmine or lake, and the latter with neutral tint. The rivers and waters are also tinted blue, and the roads a light brown; any thing beyond this in the way of colouring amounts to a decoration which is not required. If the map is one of an estate or property, the names of the owners of the adjoining lands should be written in their re- spective positions; but if it is a parish map, the names of the ad- joining parishes are substituted, as in plate 5. The names of all gentlemen's seats, farms, hamlets, and remarkable places, should be subscribed, and the whole should be invested with as much local interest as possible. Every field or parcel of property should be distinguished by a separate reference number, by which it may be referred to from a book containing all particulars relating thereto, as well as the quantity of each field in statute measure. The following are two specimens of reference books. NUMERICAL REFERENCE. 323 Cultivation. Quantity. Remarks. NUMERICAL REFERENCE. Owner. Occupier. No. on Plan. Description. A. R. P. Phipps, George Ryde, Edward... 1 Barn Field Arable. 9 2 6 Weale, John Ryde, Edward... 2 Carthouse Field.. Arable. 6 1 30 Weale, John Ryde, Edward... Co Garson Meadow Grass. 13 1 6 Phipps, George Donaldson, John 4 Doomsday Grass 9 130 Weale, John Ryde, Edward... 5 Garson Field. Arable. 16 1 30 Weale, John Ryde, Edward. 6 High Holborn Farm Homestead 1 1 10 Phipps, George Donaldson, John . 7 The Retreat House & Garden . 1 3 20 Total Content 58 1 12 324 COLLECTED REFERENCE. Cultivation. Quantity. Remarks. COLLECTED REFERENCE. Owner. Occupier. No. on Plan. Description. A. R. P. Phipps, George Ryde, Edward... 1 Barn Field Arable 9 2 6 Phipps, George Donaldson, John • 4 Doomsday Grass 9 1 30 7 The Retreat House & Garden 1 3 20 11 1 10 Weale, John Ryde, Edward.. 2 Carthouse Field .. Arable 6 1 30 3 Garson Meadow. Grass. 13 1 6 5 Garson Field. Arable 16 1 30 6 High Holborn Farm Homestead 1 1 10 37 1 36 COLLECTED REFERENCE.-SUMMARY. 325 COLLECTED REFERENCE. SUMMARY. Owner. Occupier. Description. Quantity in each Holding. Total Quantity. Remarks. Phipps, George Land. · "" 99 Ryde, Edward... Donaldson, John. House and Land. House and Land. 11 1 10 9 2 6 20 3 16 Weale, John Ryde, Edward. High Holborn Farm 37 1 36 37 1 36 Total Quantity 58 1 12 326 COMPUTATION OF AREAS. PLOTTING SECTIONS. Plotting the notes from a level book is a very simple process. First draw the datum line an indefinite length near the bottom of the paper, then mark off all the distances along the line at which a level has been taken; at each one of which erect a perpendicular line in pencil; mark off the vertical height above datum upon each of these perpendicular lines; connect the points after the manner of plotting a fence by offsets from a chain line, and the section is complete. It is not usual to use the same scale vertically and hori- zontally; the former requiring to be much larger than the latter. Plate 11 represents a "Working Section" of a Railway. CHAPTER X. COMPUTATION OF AREAS. THE method of computing the areas of fields by arithmetical calculation, has been of late years superseded by the introduction of two very ingenious little instruments called respectively the "Pediometer," and the "Computing Scale."* These instruments obviate calculation, economise time, and diminish the liability to I will describe them both; but the "Computing Scale" is the one used by civil surveyors. error. Description of the Pediometer. The instrument consists of a square, and a graduated scale, con- structed for three chains to the inch. a-The milled head, by turning which, motion is given to the brass slider B, and the two pointers R and W. I-The index to be placed in coincidence with the ► division upon the scale. When the brass slider B is in contact with A, I coinciding with ‣ division, and R and W pointing to O upon their respective scales, the instrument is in adjustment. When deranged, restore it, by opening R and W to the proper distance, and then moving A and I, the former into contact with B, and the latter into coincidence with Required the content of the trapezium E C F D. 1st.-Place the edge A upon the point E, and open B to the point F. * By some the "Tithe Computing Scale," simply because it was first introduced for the "First Class Maps at the Tithe Office." COMPUTATION OF AREAS. 327 THE PEDIOMETER. 0 W R E F Red Scale Scale White D 2nd.-Press the square firmly down with the right hand, and with the left place the scale against the edge of it, as shewn in the figure. 3rd. Now press the scale firmly, and slide the square up, until the edge A B is upon the point C. 4th.-Press the square firmly, and slide the scale against its edge until coincides with I. Finally.-Press the scale and slide the square down until the edge A B is upon the point D, and taking out the numbers to which W and R point, subtract the latter from the former, and the contents in acres and decimal parts of an acre will at once be given. The red pointer directs to the numbers that are to be taken from the red scale, and the white one to those upon the white scale. When the pointers fall exactly upon the line engraved on the ivory edge of the scale, the folding leaf is to be doubled down to the left hand; but when the pointers fall between any two of the lines on the ivory edge, the folding leaf must then be doubled over to the right hand before the numbers are read off. For instance, when the leaf is turned to the left and the red 328 THE COMPUTING SCALE. pointer falls between the two lines which refer to 008 and 013, turn the folding leaf to the right hand, and the pointer will read 0.10. It will be found most convenient and most accurate in practice to take the shortest diagonal for the line E F. THE COMPUTING SCALE. This instrument answers the same purpose of giving mechani- cally the contents of enclosures as the Pediometer, but is more simple in its construction and principle of operation. It consists of a scale divided for its whole length from the zero point into divisions, each representing 2§ chains, and is used with a sheet of transparent tracing paper, ruled with parallel lines at equidistant intervals of one chain. 0 B 2 3 4 4 田 The slider B, which moves along the scale, has a wire drawn across its centre at right angles to its line of motion; and on each side of this wire a distance equal to one of the primary divisions of 2 chains is laid off, and divided into 40 parts. It is evident, then, that during the passage of the slider over one of the divisions of 21 chains, one rood has been measured between two of the parallel lines on the tracing paper; and that one of the smaller divisions would measure between the same parallels one perch. Four of the larger divisions giving one acre; and the scale itself generally made long enough to measure at once five acres, is thus used: Lay the transparent paper over the enclosure the content of which is re- quired, in such a position that two of the ruled lines shall touch two of the exterior points of the boundaries, as at a and b. Lay the scale, with the slider set to zero, over the tracing paper, in a direction parallel to the lines, and so placed that the portions c and d are estimated by the eye as equal to each other. Holding the scale steady, move on the sliding frame until the equality of the portions e and fare also estimated. With the slider kept at this mark, move the scale bodily down the space of one of the ruled lines (one chain), and commencing again at the left hand, estimate the equal areas of g and h, sliding the frame on to k and l. When the whole length of the scale, denoting 5 acres, is run out, com- mence at the right-hand side, and work backwards to the left, THE COMPUTING SCALE. 329 reading the lower divisions, by which the instrument is made to measure up to 10 acres. By a continuation of this process, the b C α } contents of any sized enclosures can be obtained without calcula- tion, and with a degree of accuracy proportionate to the amount of skill and care exercised on the equalization of the boundaries. Where the wire of the slider coincides with any portion of the boundary between two of the parallels no equalization is of course necessary. Explanation of the following Tables. The use of the following Tables will be obvious at first sight. If the area of a plan plotted to a scale of two chains to an inch be computed with a three-chain computing scale, seek the result or the the next smaller number thereto, in the column headed "Three Chains," and immediately adjoining, viz., in that headed "Two Chains," is the correct acreage. If the result by the three-chain scale is more than 9 acres, it must be taken at twice, that being the limit of the Tables. • The Tables have been so constructed as to exhibit the nearest relative equivalent to the results given; for instance, 7 . 1 10 on a three-chain scale is exactly equal to 3. 1. 0 on a two; but then 7.1.9 is also nearer thereto than to 3.0.39; and hence 7.1.9 is placed as the equivalent. Again, 9.0.0 (three-chain scale) is exactly equivalent to 1.0.0 (one-chain scale); but as 8.3.36 is also nearer thereto than to O. 3. 39, that is stated as the three- chain equivalent. X 330 COMPUTING TABLES. 3-Chain 2-Chain 3-Chain Scale. Scale. Scale. 2-Chain Scale. 3-Chain 2-Chain 3-Chain Scale. Scale. Scale. 2-Chain Scale. 100 A. B. P. A. 0 0 2 0 0 A. R. P. 10 R. P. A. B. P. 2 12-0 1 A. B. P. A. R. P. A. R. P. A. R. P. 1 1 0 22-0 2 11 2 32 0 3 1 0 4= 4 0 0 2 0 2 14-0 1 21 0 24 0 2 2 1 2 34 0 3 2 0 0 -0 0 30 2 16=0 1 3 1 0 26 0 2 3 1 2 36 0 3 3 0 0 8 0 0 4 0 2 18-0 1 4 1 0 28 0 2 41 238 0 3 4 0 0 11 0 0 5 0 2 21—0 1 5 1 0 31 0 2 51 3 1-0 3 5 0 0 13 0 0 60 2 23=0 1 6 1 0 33 0 2 61 3 3 0 3 6 0 0 15 0 0 70 225=0 1 7 1 0 35 0 2 71 3 5 0 3 7 0 0 17 0 0 8 0 2 27 0 1 8 || 1 0 37 0 2 81 3 7 0 3 8 0 0 20 0 0 9 0 2 30 0 1 91 1 0 0 0 2 2 91 3 10 0 3 9 0 0 22 0 0 100 2 32=0 1 10 1 1 2 0 2 10 1 3 12 0 3 10 0 0 24 0 0 11 0 2 34-0 1 11 1 1 4 0 2 111 3 14 3 14: 0 3 11 0 0 26 0 0 12 0 2 36-0 1 12 121 1 6 0 2 12||1 3 16 0 3 12 0 0 29 0 0 13 0 2 39-0 1 13 1 1 9 0 2 13|1 3 19 0 3 13 0 0 31 0 0 14 0 3 1=0 1 14 1 1 11 0 2 14 1 3 21 0 3 14 0 0 33 0 0 150 3 3=0 1 15 1 1 13 0 2 151 3 23 0 3 15 0 0 35 0 0 16 0 3 5 0 1 16|| 1 1 150 2 16||1 3 25-0 3 16 0 0 38 0 0 1 0=0 =0 0 17 0 180 0 18 0 3 10-0 3 8 0 1 17 1 1 18 0 2 171 3 28-0 3 17 1 18 1 1 20 0 2 181 3 30-0 3 18 0 1 2 0 0 19 0 3 12—0 1 19 1 1 22 0 2 191 3 32-0 3 19 0 1 4 0 0 20 0 3 14 0 1 20 || 1 1 24-0 2 20||1 3 34 0 3 20 0 1 7 0 0 21 0 3 17—0 1 21 1 1 27-0 2 211 3 37 0 3 21 0 1 9 0 0 220 3 19=0 1 22 1 1 29-0 2 221 3 39 0 3 22 0 1 11 0 0 23||0 3 21=0 1 23 1 1 31 0 2 232 0 1-0 3 23 0 1 13 0 0 24 0 3 23-0 1 24 1 1 33 0 2 24||2 0 3 0 3 24 0 1 16 0 0 250 3 26-0 3 26 0 1 25 1 1 36 0 2 25|2 0 60 3 25 0 1 18 0 0 260 3 28=0 1 26 1 26 1 1 38 0 2 26 2 0 8 0 3 26 0 1 20 0 0 1 22 0 270 3 30-0 1 27 || 1 1 2 0 0 2 27|2 0 100 3 27 0 0 280 3 32 0 1 28 || 1 2 2 0 2 28||2 0 12 0 3 28 0 1 25 0 0 290 3 35 0 1 29|| 1 2 5 0 2 292 0 15 0 3 29 0 1 27-0 0 300 3 37 0 1 30 1 2 7 0 2 30 2 0 17 0 3 30 0 1 29 0 0 310 3 39=0 1 31 1 2 9 0 2 31 2 0 19 0 3 31 0 1 31 0 0 32 1 0 1=0 1=0 1 32 321 2 11 0 2 32||2 0 210 3 32 0 134 0 0 33|1 0 4 0 1 33 1 2 14 0 2 33 2 0 24 0 3 33 0 1 36 0 0 341 0 6=0 1 34 1 2 16 0 2 34 2 0 26 0 3 34 0 138 0 0 35 1 0 8=0 1 35 1 2 18-0 2 35 2 0 28 0 3 35 0 2 0 0 0 36 1 0 10 0 1 36 || 1 2 200 2 36||2 0 30 0 3 36 0 2 3 0 0 371 0 13-0 1 37 1 2 23-0 2 37||2 0 330 3 37 0 2 5 0 0 2 7 0 0 2 9 0 0 38 1 0 391 1 0 1 0 15-0 1 38 1 2 25 0 2 382 0 350 3 38 0 17 0 1 39 || 1 2 27-0 2 27=0 2 39 2 0 37 0 3 39 0 19 0 2 0 1 2 29 0 3 0 2 0 39—1 0 0 COMPUTING TABLES. 331 3-Chain 2-Chain 3-Chain Scale. Scale. Scale. 2-Chain 3-Chain 2-Chain Scale. Scale. Scale. 3-Chain 2-Chain Scale. Scale. A. R. P. A. B. 2 1 2=1 0 P. A. 1 2 R. P. A. R. P. A. R. P. A. R. P. A. R. P. A. R. P. 3 12-1 1 1 3 1 22-1 2 13 3 32-1 3 1 2 1 4=1 0 22 3 14-1 1 2 3 1 24=1 2 2 3 3 34-1 3 2 2 1 61 0 32 3 16-1 1 3 3 1 26 1 2 33 3 36-1 3 3 3 2 1 1 81 0 42 3 18-1 1 4 3 1 28 1 2 4 3 3 38- 3 4 2 1 111 0 5 2 52 3 21=1 1 53 3 1 31 1 2 54 0 1=1 3 5 2 1 13-1 0 62 3 23=1 1 63 1 33 1 2 64 0 3=1 3 6 2 1 15 1 0 72 3 25=1 1 7 3 1 35-1 2 74 0 5-1 3 7 2 1 17 1 17=1 0 82 3 27=1 3 27=1 1 83 1 37 1 2 8 4 0 7=1 3 8 2 120 1 0 9 2 3 30—1 3 30-1 1 9 3 2 0 0-1 2 9 4 0 101 94 9 3 2 1 22=1 0 10 2 0 10 2 3 32-1 3 32 1 1 10 3 2 2 1 2 10 4 0 12-1 3 10 2 1 24 1 0 11 2 3 34=1 1 11 3 2 4 1 2 11 4 0 14=1 3 11 2 1 26 1 0 12 2 3 36 1 1 12 3 2 6= 6-1 2 12 4 0 16 1 16=1 3 12 2 1 29-1 0 13 2 3 39-1 1 13 3 2 9 1 2 13 4 0 19-1 3 13 2 131=1 0 14 3 0 1=1 1 14 3 2 11 1 2 14 4 0 21 1 3 14 2 1 33 1 0 15 3 0 31 1 15 3 2 13 1 2 15 4 0 23=1 3 15 2 1 35 1 0 16 3 0 5 1 1 16 3 2 15 1 2 16 4 0 25=1 3 16 2 1 38-1 0 173 0 81 1 17 3 2 18 1 2 17 4 0 28=1 3 17 2 2 0 1 0 18 3 0 10-1 1 18 3 2 20 1 2 18 4 0 30-1 3 18 2 2 2 1 0 19 3 0 12 1 1 19 3 2 22 1 2 19 4 0 321 3 19 2 2 4 4 1 0 20|| 3 0 14 1 1 20 3 2 24 1 2 20 4 0 34 1 3 20 2 2 7-1 -1 0 21 3 0 17-1 1 21 3 2 27-1 2 21 4 0 37=1 3 21 2 2 9 1 9-1 0 22|| 3 0 19=1 1 22 3 2 29 1 2 22 4 0 39—1 3 22 2 2 11=1 0 23 3 0 21=1 1 23 3 2 31 1 2 234 1 1=1 323 2 2 13 1 0 24 3 0 23 1 1 24 1 24 3 2 331 2 24 4 1 1 3 1 3 24 2 2 16 1 0 25 3 0 26=1 1 25 3 2 36 1 36=1 2 254 1 6-1 3 25 2 2 18 1 0 26 3 0 28—1 1 26 3 2 38=1 2 38 1 2 264 1 8-1 3 26 2 2 20 1 0 27 3 0 30=1 1 27 3 3 0-1 2 27 4 1 10-1 3 27 2 2 22 1 0 28 3 0 32 1 1 28 || 3 3 2 1 2 28 4 1 12 1 3 28 2 225-1 2 2 27=1 2 2 29 1 2 231=1 2 31 2 2 34 1 0 29 3 0 35=1 0 30 3 0 31 3 0 39-1 1 29 0 37=1 1 30 3 3 1 31 3 3 3 3 5 1 2 29 4 1 15-1 3 29 7 1 2 304 1 17=1 3 30 9 19-1 1 2 31 4 1 19 1 3 31 1 0 32 || 3 1 1=1 1 32 3 3 11=1 2 32||4 1 21=1 3 32 0 33 3 1 2 2 36=1 0 343 1 4=1 6 1 33 1 34 | 2 2 38=1 0 353 1 2 3 0 1 0 36 3 8=1 1 10=1 1 35 1 36 að að að no 3 3 14 1 2 33 4 334 1 24 1 3 33 3 3 16 1 2 344 1 26=1 1 26 1 3 34 3 3 18 1 2 35 4 1 28-1 3 35 3 3 20 1 2 36 4 1 30=1 3 36 2 3 3-1 0 373 1 13-1 1 37 3 3 23 1 2 37 4 1 33-1 3 37 2 3 5 1 0 383 1 15 1 1 38 3 3 25 1 2 38 4 1 35 1 3 38 2 3 7-1 1 2 3 9-1 0 39 3 1 17=1 1 0 3 1 39 3 3 27 1 2 39 4 1 37=1 3 39 1 19 1 2 0 3 3 29—1 3 0 4 1 39 2 0 0 332 COMPUTING TABLES. 3-Chain 2-Chain 3-Chain Scale. Scale. Scale. 2-Chain Scale. Scale. 3-Chain 2- Chain Scale. 3-Chain 2-Chain Scale. Scale. A. R. P. A. R. P. A. R. P. A. B. P. A. R. P. A. R. P. A. R. P. A. R. P. 4 2 2 2 0 0 15 0 12 2 1 1 5 2 22 2 2 1 6 0 32—2 3 1 4 2 4 2 0 2||5 0 14-2 1 2 5 2 24 2 2 26 0 342 3 2 4 2 6: -2 35 016-2 0 0 16 2 1 3 5 2 26-2 2 36 0 362 3 3 4 2 8 2 0 45 4 5 0 18-2 1 4 5 228-2 2 4 6 0 38 2 3 4 4 2 11 2 0 5 5 0 21=2 1 5 5 2 31-2 2 56 1 1 2 3 5 4 2 13 2 0 65 023=2 1 6 5 2 33=2 2 6 6 1 3 2 3 6 4 2 15-20 75 0 25-2 1 7 5 2 35-2 2 7 6 1 5 2 3 3 7 4 2 17 2 0 85 0 27 2 1 8 5 2 37-2 2 8 6 1 7= 7-2 3 8 4 2 20 2 0 95 0 30 0 30=2 2 1 9 5 3 2 2 96 1 10 2 3 9 4 2 22 2 0 10 5 0 32 2 1 10 5 3 2 2 2 2 10 6 2 10|6 1 12-2 3 10 4 2 24-2 0 11 5 0 34 2 1 11 5 3 42 2 116 1 14 2 3 11 4 226-2 0 12 5 0 36 2 1 12 5 3 6-2 2 12 6 1 162 3 12 4 2 29 2 0 13 5 0 39-2 1 13 5 3 9 2 2 13 6 1 19 2 3 13 4 2 31-2 0 14 5 1 1 1=2 1 14 5 3 11 2 2 2 14 6 2 14 6 1 212 3 14 4 2 33 2 0 15 5 1 3-2 1 15 5 3 13 2 2 15 6 1 23-2 3 15 4 2 35—2 0 16 5 1 5 2 1 16 5 3 15 2 2 166 125—2 3 16 4 2 38-2 0 17 5 1 8 2 1 17 5 3 18—2 2 17||6 1 28-2 3 17 4 3 0 2 0 185 1 10-2 1 18 5 3 20 2 2 18 6 1 30 2 3 18 4 3 2-2 0 19 5 1 12-2 1 19 5 3 22 2 2 196 1 322 3 19 4 3 4 2 0 205 1 14 2 1 20 5 3 24-2 2 206 1 342 3 20 4 3 7 2 0 21 5 1 17 2 1 21 5 3 27 2 2 21 6 1 37—2 3 21 4 3 9 2 0 225 1 19-2 1 22 5 3 29 2 2 22 6 1 39—2 3 22 4 3 11 2 0 23 5 1 21 2 1 23 5 3 31 2 2 23 6 2 1 2 3 23 4 3 13 2 0 24 5 1 23-2 1 24 5 3 33 2 2 24 6 2 3 2 3 24 4 3 16 4 3 18 2 2 0 255 1 26-2 1 25|| 5 5 3 36-2 3 36 2 2 256 2 6—2 3 25 0 265 1 28-2 1 26 5 3 38-2 2 26 6 2 8 2 3 26 4 3 20 2 0 27 5 1 30 2 1 30—2 1 27 6 0 0-2 2 27 6 2 10 2 3 27 4 3 22-2 0 285 1 322 1 28 6 0 2 2 2 28 6 2 12 2 3 28 4 3 25-2 0 295 1 35—2 1 29 6 0 5 2 2 296 2 15 2 3 29 4 3 27 2 0 30 5 1 37-2 1 30 60 7 2 2 306 2 17 2 3 30 4 3 29-2 0 31 5 1 39 2 1 31 6 0 9 2 2 316 2 19-2 3 31 4 3 31 2 0 32 5 2 1 2 1 32 6 6 0 11 2 2 32||6 2 21= 332 4 3 34 2 0 33||5 0 335 2 2 4 3 36-2 0 34 5 2 4= 4 2 6-2 1 33 6 6 0 14-2 0 14 2 2 336 2 24 2 3 33 1 34 || 6 0 16 2 2 346 2 262 3 34 4 3 38-2 5 0 0 2 0 35 5 2 8=2 0 36 5 2 10-2 1 35 6 0 18 2 2 356 2 28-2 3 35 1 36 6 0 20 2 2 36 6 2 30- -2 3 36 0 3 2 5 37||5 0 37 5 2 13-2 1 37 6 0 23-2 2 37 6 5 0 5 2 0 38 5 2 15 2 1 38 6 0 25 2 2 38||6 5 07-2 0 39 5 2 17 2 1 39 6 0 27 2 2 396 2 33 2 3 37 235=2_3 38 2 37 2 3 39 5 0 9 2 1 05 2 19-2 2 0 6 6 0 29 0 29-2 2 3 06 2 39 3 0 0 COMPUTING TABLES. 333 3-Chain 2-Chain Scale. Scale. 3-Chain Scale. 2-Chain 3-Chain 2-Chain 3-Chain Scale. Scale. Scale. Scale. 2- Chain Scale. A. B. P. A R. P. A. R. P. A. R. P. A. R. P. A. R. P. ለ. R. P. A. R. P 6 3 2 3 0 17 1 12=3 1 1 1 7 3 22-3 2 18 1 32-3 3 1 6 3 4 3 0 27 1 143 1 2 7 3 24 3 2 28 1 34 3 3 2 6 3 6 3 0 37 1 16-3 1 3 37 7 3 26=3 2 38 1 36-3 3 3 6 3 8=3 0 4|7 1 18-3 1 4 7 3 28=3 2 4 8 1 38-3 3 4 6 3 11 3 0 57 1 21=3 1 5 7 3 31-3 2 2 5 5 8 2 1 3 1-3 3 5 6 3 13-3 0 6|7 123=3 1 6 7 3 33 3 2 2 6 68 2 3 3 3 6 6 3 15 3 0 77 7 1 25-3 1 7 7 3 35-3 2 78 2 2 5-3 5 3 3 7 6 3 17 3 0 8 7 1 27=3 1 8 7 3 37=3 2 8 2 7-3 7 3 3 8 6 20-3 3 20 3 0 97 1 30-3 1 9 6 3 22-3 0 10 7 1 32-3 1 10 6 3 24 3 0 11 7 1 34 3 1 11 6 3 26-3 0 12 7 1 36=3 1 12 ∞ ∞ ∞ ∞ 8 0 0 3 2 2 98 98 2 10–3 2 10 3 3 9 8 0 2 3 2 10 8 2 12-3 2 12 3 3 10 8 0 4 3 4-3 2 2 11 8 118 2 14 3 14=3 3 11 8 0 6 3 2 128 2 16 3 3 12 6 3 29 3 0 13 7 1 39=3 1 13 8 0 9= 2 13 8 2 19–3 3 13 6 3 31=3 0 14 7 2 13 1 14 8 011 0 11-3 2 14 3 2 14 8 2 21-3 3 14 6 3 33 3 0 15 7 2 3-3 1 15 8 0 13 3 2 15 8 2 23-3 2 23 3 3 15 6 3 35 3 0 16 7 2 5 3 1 16 8 0 15 3 2 16||8 2 16 8 2 25-3 2 25 3 3 16 6 3 38=3 0 177 2 8=3 1 17 8 0 18=3 2 178 2 28-3 7 0 0-3 0 18 7 18|7 2 103 1 18 1 18 8 0 20=3 2 188 2 18 8 7 0 2 3 0 19 7 2 12=3 1 198 0 22 3 2 19 8 7 0 4 3 0 207 2 14 3 1 20 8 0 24 3 2 208 2 208 28=3 3 17 2 30-3 2 30-3 3 18 2 323 3 19 2 34-3 3 20 NNNN 7 0 7-3 0 217 2 173 1 21 8 0 27 3 27=3 2 21 8 21||8 2 37=3 2 373 3 21 7 0 9-3 0 22 7 2 19-3 1 22 8 0 29 3 2 228 2 39-3 3 22 7 0 11=3 0 237 2 21=3 1 23 8 0 31=3 2 23 238 3 1-3 3 23 7 0 13 3 0 24 7 2 23-3 1 24 8 0 33-3 2 24||8 3 3 3 3 24 7 0 16 3 7 18-3 0 25 7 2 26-3 1 25|| 8 0 36=3 2 258 3 3 6-3 6-3 3 25 0 18 3 0 26||7 0 267 2 28-3 1 26 8 0 38 3 2 268 3 8 3 8=3 3 26 7 0 20 3 0 277 2 30—3 1 27 8 1 0-3 2 27 8 278 3 10-3 3 27 7 0 22-3 0 287 2 32-3 1 28 8 1 2 3 3 2 28||8 2 288 3 12-3 3 12 3 3 28 7 0 25-3 0 29 7 2 35-3 1 29 8 1 5 3 53 2 298 3 15 3 15=3 3 29 7 0 27 3 0 307 2 37-3 1 30 8 1 7=3 2 308 3 17=3 3 30 7 0 29 3 0 31|7 2 39—3 1 31 8 1 9 3 2 318 3 19-3 3 31 7 0 31 3 0 327 3 1=3 1 32 8 1 11 3 2 328 3 21=3 3 32 7 0 34=3 7 0 36=3 7 0 38 3 0 33 7 3 43 0 347 3 6-3 0 357 3 8 3 1 33 || 8 1 14 3 2 33||8 3 24 3 3 33 1 34 || 8 1 16—3 1 16 3 2 348 3 26 3 3 34 1 358 1 18=3 2 35 3 28 3 3 35 7 1 0 3 0 367 3 10 3 1 36 8 120 3 2 368 3 303 3 36 7 1 3 3 0 377 3 133 1 37 8 1 23 3 2 37 8 3 33=3 3 37 7 1 5 3 0 387 3 15 3 1 38 8 1 25 3 2 38 8 3 35 3 3 38 7 1 7=3 0 397 3 17 3 1 39 8 1 27 3 2 398 3 37 3 37=3 3 39 7 1 9 3 1 07 3 19 3 2 0 8 1 293 3 09 0 0 0 4 0 0 334 COMPUTING TABLES. 3-Chain 1-Chain Scale. Scale. 3-Chain 1-Chain 3-Chain Scale. Scale. Scale. 1-Chain Scale. 3-Chain 1-Chain Scale. Scale. A. R. P. A. R. P. A. R. P. A. R. P. A. R. P. A. R. P. A. R. P. A. R. P. 0 0 5 0 0 12 12 1 1 5=0 1 1 4 2 5 0 2 1 6 3 5 0 3 1 0 0 14-0 0 22 1 14-0 1 2 4 2 14 0 2 2 6 3 14-0 3 3 2 0 0 23 0 0 0 32 1 23 0 23-0 1 3 4 2 23 0 2 3 6 3 23-0 3 3 0 0 32=0 0 4 2 1 32—0 1 1 4 4 232 0 2 4 6 3 32 0 3 4 0 1 1=0 0 5 2 2 10 1 5 4 3 1-0 2 57 0 10 3 5 0 1 10 0 0 62 2 100 1 6 4 3 10 0 2 6 7 0 10 0 3 6 0 1 19 0 0 72 2 19 0 1 7 4 3 190 2 77 7 0 190 3 7 0 1 28 0 0 8 2 2 28 0 1 8 4 3 28 0 2 8 7 0 28 0 3 8 0 1 37-0 0 9 2 2 370 1 9 4 3 370 2 97 0 370 3 9 0 2 6 0 0 10 2 3 6 0 1 10 5 0 6 0 2 10||7 1 6 0 3 10 0 2 15 0 0 112 3 15-0 1 11 5 0 15 0 2 117 1 15-0 115 0 3 11 0 2 24 0 0 12 2 3 24 0 1 12 5 0 240 2 12 7 1 24 0 3 12 0 2 33 0 0 13 2 3 330 1 13 5 0 33 0 2 137 1 33 0 3 13 0 3 2 0 0 143 0 2 0 1 14 5 1 20 2 14 7 2 2 0 3 14 0 3 11 0 0 15 3 0 11 0 11:0 1 15 5 1 11 0 2 15 7 2 11=0 3. 15 0 3 20 0 0 16 3 0 20 0 1 16 5 1 20 0 2 16 7 2 20 0 3 16 0 3 29 0 0 17 3 0 290 1 17 5 1 29-0 2 17 7 2 29 0 3 17 0 3 38-0 0 183 0 38=0 1 18 5 138 0 2 18 7 2 38 0 3 18 1 0 7 0 0 193 1 7 0 1 19 5 2 7 0 2 19 7 3 7 0 3 19 1 0 16 0 0 20 3 1 16-0 1 20 || 5 2 16 0 2 207 3 16 0 3 20 1 0 25 0 0 21 3 1 250 1 21 5 2 25-0 2 21 7 3 250 3 21 1 0 34 0 0 22|3 1 34 0 1 22 2 34 0 2 227 3 340 3 22 1 1 3 0 0 23 3 2 3 0 1 23 5 3 3 0 2 2 238 0 0 3 0 3 23 1 1 12 0 0 24 3 2 12 0 1 24 || 5 3 120 2 248 0 12 0 3 24 1 1 21 0 0 25 3 2 21-0 1 25 || 5 5 3 21-0 3 21 0 2 25 8 2 258 0 21 0 3 25 1 1 30-0 0 26 3 2 30-0 1 26 5 3 30 0 2 268 0 30 0 3 26 1 1 39 0 0 273 2 39-0 1 27 5 3 39 0 2 27 8 2 27 8 0 390 3 27 12 8 0 0 28 3 3 8 0 1 28 || 6 0 80 2 288 1 8 0 3 28 1 2 17 0 0 29 3 3 17 0 1 29 6 0 17 0 2 29 8 1 17 0 3 29 1 2 26 0 0 30 3 3 26 0 1 30 6 0 260 2 308 1 26 0 3 30 1 2 35 0 0 31 3 3 35 0 1 31 6 0 35 0 2 318 1 350 3 31 1 3 4 0 0 324 0 4 0 1 32 6 1 4-0 2 328 2 4 0 3 32 ATH Q 1 3 13 0 0 334 0 13-0 1 33 6 1 13 0 2 33 8 2 13 0 3 33 1 3 22 0 0 344 0 34 4 0 22 0 1 34 6 1 22 0 22-0 2 34 8 2 22=0 3 34 1 3 31-0 0 35 4 0 31-0 1 35 6 1 31-0 2 0 0 0 0 364 1 0 0 1 36 6 2 0 0 2 35 8 358 2 36 368 2 310 3 35 3 0 0 3 36 2 0 9 0 0 37 4 1 9–0 1 37 6 2 9 0 2 37||8 3 9 0 3 37 2 2 0 18 0 0 27 0 2 0 36 0 0 384 0 38 4 0 39 4 1 0 4 1 18 0 1 38 6 2 18 0 2 38 8 3 18 0 3 38 394 1 270 1 27 0 1 39 6 2 27 0 2 39 8 3 27 0 3 39 1 36 0 2 0 6 2 36 0 3 08 08 3 36=1 3 36=1 0 0 COPYING MAPS. 335 CHAPTER XI. COPYING MAPS. VARIOUS methods, according to circumstances, are resorted to for multiplying Copies of Maps; two only, which are the most usual, will be mentioned here. To copy a map by "pricking it off," lay the original over the paper intended for the copy, and with a very fine needle prick through every point at which a change takes place in the relative position of the lines of the plan; connect all these points by lines similar to those of the original, and a fair du- plicate plan will be obtained. Plans copied in this manner gene- rally answer to scale better, that is, are more nearly accurate in general features than any other duplicate maps; but the details are apt to get distorted in minute peculiarities, notwithstanding the greatest amount of care and attention. One very great disadvantage also is, the impossibility of placing the original again over the copy in the same position after it has been once removed, so as to enable any omission to be supplied. In pricking off maps there are a few things to be attended to, to secure success. The needle should always be held perfectly erect, so that the impression may be directly under the point on the ori- ginal. In narrow parallel lines, such as a river, brook, or road, a dot should not be pricked on one side without pricking one imme- diately opposite it in the line forming the other side, by which means confusion of the dots in drawing the lines of the copy is avoided. All straight lines should have a dot in the centre, as well as at either end, both as an additional precaution to ensure accu- racy, and also to afford a means of identifying the dots with the lines. Many other things will suggest themselves with practice that would occupy more space than can be appropriated here. To Copy a Map by means of" Transferring Paper."-Get a sheet of thin paper, and rub over it some powdered black lead- the palm of the hand is the best thing to rub this black lead on with; and when it has been well rubbed in, a rough cloth should be passed over it to get off as much of the superfluous lead as pos- sible, so that it may not wipe off upon the map. Place the black side towards the paper that is to receive the copy of the plan, and put the original upon the whole; then with a blunt steel point or 336 THE PENTAGRAPH. tracer go over all the lines of the original, and the pressure of the tracer will cause the black lead to come off upon the under paper, and thus delineate a fac-simile of the original. We may as well consider at once, that a tracing will first have to be taken from the original, as the paper upon which plans are plotted is in the generality of cases in practice, much too thick to admit of a transfer being made direct from it with any accuracy, or at all events without spoiling the original, which is at all times a thing worth any trouble in the avoiding. Plans may also be copied by the Pentagraph, an instrument which next claims our attention. THE PENTAGRAPH. This is an instrument but very imperfectly understood, even by those who are most frequently using it. It requires to be very ac- curately constructed and skilfully handled, and then very beautiful work will be the result. Its chief use is to reduce or enlarge plans, but it will also copy the same size. In describing the use of the Pentagraph, we may as well confine our attention to the reduction of maps, as work cannot be enlarged with any degree of satisfac- tion; small unappreciable errors are magnified into important ones, and the whole features become distorted. With reduction on the contrary, errors of all kinds are reduced in magnitude, and many entirely disappear. This instrument is represented in the annexed engraving, where it is shewn as in the act of copying a plan H, upon a reduced scale h. The Pentagraph consists of four rulers, A, B, C, and D, made of stout brass. The two longer rulers, A and B, are connected together by, and have a motion round a centre, shewn at the upper part of the engraving. The two shorter rulers are, in like manner, connected with each other, and with the longer rulers, as may be clearly understood from an inspection of the engraving. The whole instrument is supported by small pillars resting upon ivory rollers, a a a, &c., which have a motion in all directions exactly like the brass castors fixed to ordinary tables. The rulers A and C have each an equal number of similar divisions, marked †,†, &c.; and likewise a sliding index, E and F, which can be fixed to any divi- sions on the ruler by a milled-headed clamp screw shewn in the engraving. The sliding indeces, E and F, have each of them a tube adapted to slide on a pin, rising from a heavy circular weight called the fulcrum, which acts as a centre for the whole instrument to turn upon when in use, or to receive a sliding holder with a pencil, or a tracing point, as may be required. 4 THE PENTAGRAPH. 337 a E h A B F O D H Our fig. represents the instrument. The principle will at once become apparent. The bars B and C must always remain parallel to each other under every position of the instrument, as well as A and D. EFG are all in one straight line. Hence, two similar triangles are formed, whose sides are to each other as E F is to E G. By securing the point E in one spot, and by moving a tracer at G over the lines of the original, a pencil at F, left to follow the course of the instrument, will describe an exactly similar line, bearing the same proportion to the original as E F does to E G. The Pentagraph is usually constructed in brass, with steel cen- tres, and travels parallel to the paper, supported by the six ivory- mounted wheels. The pencil, in the best made instruments, is fixed in a case, something like the point of an ever-pointed Mordan pencil, by which contrivance the point is always in the centre. A small silken thread passes round the instrument from the pencil to the tracer, by means of which the pencil is caught up when it is re- 338 RAILWAY SURVEYING. quired to move the instrument across the plan in a direction that is not required to be delineated. The bars A and C are generally divided, but it is not at all necessary they should be so, as the ipse dixit of the maker should never be taken for granted, and the in- strument is easily set. Say, as the length in inches and decimals of any line upon the large map required to be reduced, is to the length of the bar B; so is the length to which the same line is re- quired to be reduced to the proper length on the bar C. Again, as the difference in length of the line upon the large and small scale is to the length of that part of the bar A, between the bars C and B, so is the length of the line on the large map to the whole length of the bar A; or on the small map to that part of the bar A, be- tween the bar C and the fulcrum. See that E F and G are in the same straight line and the instrument is set for use. While the scale of the reduced map is required to be as small as, or smaller than, one-half of the original, the position of the fulcrum will be somewhere on the bar A; but when the proportion of the small map to the original becomes such as 3 to 5, 6 to 9, 10 to 12, &c., then the fulcrum and pencil must exchange places, and the proportion is calculated as EF to F G. An inspection of the instrument, and a very little practice, will suggest all other explanation. CHAPTER XII. RAILWAY SURVEYING. SECT. I.—Exploration and Trial Levels. THE services of an engineer or surveyor, in connection with a pro- jected line of railway, commence with what is technically termed an "exploration of the country," through which it is desirable or intended that it should pass. This exploration is a general exami- nation of the district by the engineer for the purpose of making himself thoroughly acquainted with its geographical contour, and geological features. He then, by the aid of an Ordnance Map, if the line is situated in the south of England, or in Ireland, where such a map is obtainable, sketches out a line, over which he causes what are called " Trial Levels" to be taken. These Trial Levels are frequently but very rough affairs, but care should be always observed that the right point is taken at the crossing of all public RAILWAY SURVEYING. 339 roads, and B M should be frequently noted, as a check upon the levels of any future process. In taking Trial Levels, it is generally the custom, in critical localities, to level one or two alternative lines, but I would sug- gest, that one line with a number of cross sections at frequent intervals is more convenient, and affords a greater amount of useful information. The use of the "Exploration" is palpable; and the utility of the Trial Levels and Section must be obvious upon a very little consideration. By their aid the most favour- able gradients can be selected, and even the absolute practicability of the railway in the proposed direction can be determined. It not unfrequently happens, in selecting the route for a line of railway, that a slight detour from the most direct course will save a long heavy embankment, or a deep cutting, and will moreover improve the gradients to a very great extent. Practice and ex- perience will, as in most other things connected with the profes- sion of an engineer or surveyor,. be the only sure guides to success, in selecting the gradients and determining the mode of overcoming the difficulties presented by the face of the section. As a general rule, however, the cuttings should balance the em- bankments, so that the stuff taken out of the one may serve to create the other; but if it is necessary that one should predomi- nate, I would in most cases give a preference to the latter, it being generally more easy to obtain a piece of side cutting than to carry to spoil* a large amount of superabundant earth. When railways were more in their infancy easy gradients were insisted upon, and an inclination of 1 in 100 was thought as a rule sufficiently steep; but now that locomotive science and the whole subject are becoming more practically known, inclines of 1 in 80, 1 in 70, and 1 in 60, are to be frequently found on the sections of new and branch lines. All of which is of course but a question of expediency, between present economy of construction and the future expense of working the line. The following is a brief extract of some of the requirements of the Standing Orders of the two Houses of Parliament, so far as they relate to the preliminary, or, as it is technically termed, "Parliamentary Survey" for an intended railwayf. * Banks formed of surplus excavated earths are called "Spoil Banks," and the earths so treated are said to be "carried to spoil." † It is not intended to render service to the professional student, as he will find it expedient to procure a copy of the Standing Orders every successive session, in order that he may be fully acquainted with all amendments which from time to time may take place in them; but to the non-engineering enquirer this brief summary may con- tain all the information he is in search of. RAILWAY SURVEYING. 340 Plan and Sections. That a plan shall be drawn on a Scale of NOT LESS than four inches to a mile, and shall describe the line or situation of the whole work, and the lands in, or through which it is to be made, maintained, varied, extended, or enlarged, or through which every communication to or from the work shall be made. When powers to make any lateral deviation from the line of the proposed work is intended to be applied for, the limits of such deviation shall be defined upon the plan, and all lands included within such limits to be marked thereon, and in all cases, except- ing where the whole of such plan is upon a scale of not less than a quarter of an inch to every 100 feet, an additional plan of every building, yard, court-yard, or land within the curtilage of any building; or of any ground cultivated as a garden, either on the original line, or within the limits of the deviation, to be laid down on the plan, or on an additional plan to be deposited there- with, upon a scale of not less than a quarter of an inch to every 100 feet. A section shall be drawn to the same horizontal scale as the plan, and to a vertical scale of not less than one inch to every 100 feet, which shall shew the surface of the ground marked on the plan, the intended level of the proposed work, and a datum hori- zontal line, which is to be the same throughout the whole length of the work, or any branch thereof respectively, and to be referred to some fixed point stated in writing on the section, near either of the termini. The plan to exhibit thereon the distances in miles and furlongs from one of the termini, and a memorandum of the radius of every curve, not exceeding one mile in length, to be noted on the plan in furlongs and chains. The line of railway marked upon the section to correspond with the upper surface of the rails. The distances on the datum line to be marked in miles and furlongs to correspond with those on the plan, and a vertical measure from the datum line to the line of the railway to be marked in feet and inches at each change of the gradient or in- clination, and the proportion or rate of inclination between each such change must also be marked. The height of the railway over or under the surface of every turnpike road, public carriage road, navigable river, canal or RAILWAY SURVEYING. 341 railway, or junction with a railway, and the height and span of every arch of all bridges and viaducts to be marked in figures at every crossing thereof, and the extreme height over or under the surface of the ground must be marked for every embankment and cutting; and if any alteration in the present level or rate of in- clination of any turnpike road, carriage road, or railway, be in- tended, then the same to be stated on the section, and each numbered; also cross sections in reference to the same numbers on a horizontal scale of one inch to every 330 feet, and on a vertical scale of one inch to every 40 feet, to be added, to explain the nature of such alterations more clearly. Where tunnelling as a substitute for open cutting, or a viaduct as a substitute for solid embankment, be intended, the tunnelling to be marked by a dotted line on the plan, and also to be marked on the section, and the viaduct to be marked on the section. Deposit with the Clerk of the Peace. Duplicate plans and sections, with a book of reference, to be deposited for public inspection at the Office of the Clerk of the Peace, for every county, riding, or division in England or Ireland, or in the Office of the principal Sheriff Clerk of every county in Scotland, in or through which the work is proposed to be made, maintained, varied, extended, or enlarged, on or before the 30th day of November, immediately preceding the session, in which application for the bill is to be made. The Clerks of the Peace, or Sheriff Clerks, or their respective deputies, to mark in writing upon the plans, sections, and books of reference deposited with them, denoting the time at which the same are lodged in their respective offices, and at all seasonable hours of the day permit any person to view and examine one of the same, and to make copies or extracts therefrom; and one of the two plans deposited to be sealed up and retained in the pos- session of the Clerk of the Peace, or Sheriff Clerk, until called for, by order of one of the two Houses of Parliament. Deposit at Board of Trade. A copy of the Plans, Sections, and Books of Reference, to be deposited in the Office of the Railway Department of the Board of Trade, on or before the 30th of November, immediately pre- ceding the Session of Parliament, in which application is to be made; together with a published map, to a scale of not less than 342 RAILWAY SURVEYING. half an inch to a mile, with the line of railway delineated thereon, so as to shew its general course and direction. Deposit with the Railway Commissioners. That in the case of Railway Bills a copy of all Plans, Sections, and Books of Reference, required by the orders of the House to be deposited in the office of any Clerk of the Peace, or any Sheriff Clerk, on or before the 30th day of November preceding the application for the bill, together with a published map to a scale of not less than half an inch to a mile, with the line of railway delineated thereon, so as to shew its general course and direction, shall, on or before the same day, be deposited in the Office of the Commissioners of Railways. Deposits at the Private Bill Office. That on or before the 30th of November, a copy of the said Plan, Sections, and Books of Reference; and in the case of Rail- way Bills, also a copy of the said published map, with the line of railway delineated thereon, be deposited in the Private Bill Office of the House of Commons. Deposit with Parish Clerks, &c. A copy of so much of the plans and sections as relates to each parish in or through which the work is intended to be made, maintained, varied, extended, or enlarged, with a Book of Refe- rence thereto, to be deposited on or before the 30th of November with the parish clerk of each such parish in England; the school- master of each such parish in Scotland (or in the Royal Boroughs, with the Town Clerk), and the Clerk of the Union, within which such parish is included in Ireland. When any lands or houses are intended to be taken, or an ex- tension of the time granted by any former Act for that purpose, is sought, application in writing, in the form hereinafter set forth to be made to the owners, lessees, and occupiers, on or before the 15th day of December, which application must be delivered per- sonally, or left at their usual place of abode; or in the event of their being absent from the United Kingdom, be left with their respective agents; and separate lists to be made of the names of such owners, lessees, or occupiers, distinguishing which of them have assented, dissented, or are neuter in respect thereto. RAILWAY SURVEYING. 343 Lists of owners, lessees, and occupiers, to be lodged in the Private Bill Office, and the receipt thereof acknowledged on the petition before it is presented. Notice in writing of a bill, whereby any part of a work autho- rised by any former Act is intended to be relinquished, to be given to the owners and occupiers of lands in which the part of the work intended to be thereby relinguished is situate. Form of Notice to Owners, Lessees, and Occupiers. SIR,-We beg to inform you that application is intended to be made to Parliament in the ensuing session for "An Act," [Here insert the title of the Act.] and that the property mentioned in the annexed schedule, or some part thereof, in which we under- stand you are interested, as therein stated, will be required for the purposes of the said undertaking, according to the line thereof as at present laid out, or may be required to be taken under the powers of deviation, which will be applied for in the said Act, and will be passed through in the manner mentioned in such Schedule. , We also beg to inform you, that on or before the 30th day of November last a plan and section of the proposed undertaking, and also a duplicate of such Plan and Section, together with a Book of Reference thereto, and also a copy of the notice pub- lished in the London Gazette, were deposited with the Clerk of the Peace for the county of at his office in in the said county; and that on or before the said 30th day of November last a copy of so much of the said plan and sec- tion as relates to the parish or parishes in which your property is situate, together with a Book of Reference to such plan, and also a copy of the notice published in the London Gazette, was also deposited with the parish clerk of each such parish, at his place of abode, on which plans your property is designated by the numbers set forth in the annexed Schedule. As we are required to report to Parliament whether you assent to, or dissent from, the proposed undertaking, or whether you are neuter in respect thereto, you will oblige us by writing your an- swer of assent, dissent, or neutrality in the form left herewith, and returning the same to us, with your signature, on or before the day of December instant; and if there should be any error or misdescription in the annexed Schedule, we shall feel obliged by your informing us thereof at your earliest convenience, that we may correct the same without delay. We are, sir, Your most obedient servants, 344 RAILWAY SURVEYING. Property within the for. applied Limits of Deviation intended of the proposed to be at Property in the line present laid work as out Parish, Township, or No. on Descrip- tion. Owner. 194 { Arable Arable } Land ship, Extra Parochial, or other place. on Plan. No. Descrip- tion. Schedule referred to in the foregoing Notice, describing the Property therein alluded to, and the manner in which the line of the proposed work, as delineated upon the plan and section, will affect the same. extra paro- Plan. chial place. Bigwood Smallcopse 391 391 Parish, Town- {Meadow} The same. Land Description of the Section of the Line deposited, and of Occupier. the greatest height of Em- bankment & depth of Cutting. Cutting. Inches. Lessee. Embankment. Feet. Inches. Feet. The Rt. Hon. John Smith Wm. Eager. Brown, Esq. The same. Felix Gregory David Wilson 6 6 2 9 8 Owner. Lessee. Occupier. Bigwood 195 Arable} The Rt. Hon. Land Wm. Eager. Bigwood 196 Wood Land S The same John Smith Brown, Esq. The same David Wilson The same Pasture Smallcopse 392 Land S The same The same. Felix Gregory The Moors RAILWAY SURVEYING. 345 Preparation of Parliamentary Plans and Sections. The Plans and Sections required by the Standing Orders of the Houses of Parliament, to be deposited at the Private Bill Office, and other places, on or before the 30th November, preceding the Session of Parliament, in which application is intended to be made for any powers in respect of works connected with such plans and sections, are generally very simple in construction to any one ac- quainted with surveying. To describe a system which shall be best to adopt under all circumstances, would only serve to mislead, without being prac- ticable. If the country to be surveyed is tolerably open, and the landowners and occupiers favourably disposed, it may be best to range a base line in the direction of the proposed rail- way, and thereon to build such other lines as may be necessary to take up the features of the country to a sufficient width on either side, care being taken in every change of base to cross the old and new bases a sufficient length beyond the junction, to admit the admeasurement of a tie line on either side. (See fig. 177.) And in plotting the distances A B, B C, C D, D B, B E, and A E, they should be tripled or quadrupled, as circumstances may admit, to enable their more accurate delineation on the map. If the country is thick, and the landowners and occupiers not very friendly disposed, a traverse of the roads first made will much facilitate the work, as a base line cannot be ranged without cutting hedges, and nothing more exasperates a hostile farmer. A traverse of the nearest roads completed, the filling in, is a business that may be entrusted to a less experienced surveyor. In the extract of the Standing Orders given herein, it will be observed, that the scale of the plans is required to be NOT LESS than four inches to a mile, which is twenty chains to an inch; but all buildings, gardens, &c., must be drawn to a scale NOT LESS than a quarter of an inch to every hundred feet, which is six chains and about six links to an inch. Were not this latter condition necessary to a compliance with Standing Orders, most engineers would deposit plans to the smaller scale; not only because they would require less time in drawing, but also, and principally, because it would be far more difficult to detect any omission or error in them, upon which an alleged non-compliance might be founded. But the trouble of sup- plying all the requisite enlargements, and the danger of omitting some, has led to the almost universal adoption of a scale not less than six chains to an inch. Some engineers use a five-chain Y 346 RAILWAY SURVEYING. scale for their plans, principally, because curves of any given number of furlongs, or half furlongs radius, can be drawn by curve rulers of some number of inches or half inches radius; independent of which, a five-chain scale is a very pretty one; but, as I have previously observed, the larger the scale, the greater is the facility for detecting an error; and, therefore, as these plans have generally to be prepared in a very great hurry, in the bad weather and short days of the month of November, circumstances favouring as much as possible the chances of error, the scale is generally kept as small as the regulations permit, obviating the enlargements. When the plan is prepared, the course of the intended line is delineated thereon, and this is an operation requiring great care and circumspection. The trial section must be constantly con- sulted, in order that the cuttings and embankments may balance each other. Attention should also be given to the crossings of roads. If two roads fork in the vicinity of the line, so that they will each require to be crossed, an attempt should first be made to cross them at the fork, so that one bridge may serve the two; or, in the event of that being impracticable, a trial should be made to divert each road a little, so as by that means to effect the object of making one bridge serve the purpose. A crooked river will very frequently traverse the same valley as an intended railway; and there, again, a little scheming in laying down the line on the map, may save the future expenditure of large sums of money in building bridges, which might be required were the line recklessly drawn. Property possessing considerable local value, whether houses or land, should be avoided, if a slight curve will do so, without run- ning into worse ground for the section; but if this latter contin- gency presents itself in opposition to the property, it will be found more economical, as a general rule, to pay for land than works. When the line is drawn on the plan, the limits of deviation fol- low, either parallel thereto, or otherwise, as deemed expedient ; then the line must be miled consecutively from one end to the other. A memorandum must be entered under each curve of its radius in furlongs and chains. The tunnels, if any, must be dis- tinguished by a dotted line instead of a hard line; any diversion of roads or rivers must be drawn, the necessary writing and reference figures inserted, and then the plans are ready for deposit. The plans completed, a section of the line will be carefully made, in manner explained under the head of Levelling; after which the Gradients must be determined. Much diversity of opinion exists among engineers as to the ex- RAILWAY SURVEYING. 347 pediency of making the attainment of easy gradients subservient to economical considerations; but without discussing that subject in this place, it may be observed, that our most eminent engineers of the present day are constantly laying out severe gradients, as well as curving lines, to save heavy cuttings and embankments- 1 in 80 being a very common inclination, while in one case which has come under my notice in the present Session (1852-3,) 1 in 60 is laid out for a distance of upwards of six miles, with very little intermission. It has been previously remarked, that cuttings and embankments should balance each other as nearly as may be, and that if a pre- ponderancy exists, it should be of the latter rather than the former, by reason of the facility with which side cuttings can in most in- stances be resorted to. But other considerations present themselves. It is at all times desirable to affect as little as possible the ex- isting levels of public roads; an attempt should therefore be made either to cross them on a level*, or to pass 20 feet above or below them. It is decidedly advisable, if practicable, to lay out an as- cending gradient from either way of the line towards a terminus, station, or junction point. Such a gradient not only serves to check the speed of a train when approaching such a point, but it also assists it on its way when leaving. The nearer we can fulfil these conditions in practice the better. Where public roads are altered in level, a cross section is re- quired to be deposited, shewing the nature of the alteration. The level of any turnpike road must not be altered to a steeper rate of inclination than 1 in 30, or of any other public road to 1 in 20. The height of the railway over or depth under the surface of any turnpike or public carriage road, navigable river, canal, or existing railway, must be marked in figures at each crossing thereof, as well as a memorandum made of the height and span of the bridge or arches by which the crossing is proposed to be effected. If the railway passes any turnpike, or public carriage road, or railway, upon the same level, a memorandum to that effect must be made upon the section. The section must be miled to corres- pond with the plan, and a very full and explicit description of the datum line must be noted thereon. All tunnels and viaducts must be drawn upon the section, and the extreme height of every em- bankment, or depth of cutting, when the same exceeds 5 feet, must be marked. With the addition of the horizontal and vertical scale, the section is complete. Plates 8 and 9 represent a map and * Generally speaking a practice fraught with great danger to the public, saving present outlay, at the cost of annual expenditure. 348 RAILWAY SURVEYING. section, in accordance with the requirements of Standing Orders. The Parliamentary deposits involving several copies, lithography This is is usually resorted to for the purpose of supplying them. a very sore point with most engineers and surveyors; few there are who cannot call to mind some case, many there are who have experienced several, nay, are yearly experiencing them, in which very excellent drawings have been entirely botched and placed below par in their passage, through the office of the lithographer in the last days of November. Some of the most anxious hours of my professional life have been spent in these offices, alternating between hope and fear, and speculating upon the probable chances of the work being completed in time for deposit. Lithographers rarely refuse works of this description, however many of them they may have in hand; so well are they acquainted with the absolute necessity of their completion by a certain time and the safe pretext it affords for making a very heavy charge. I dare say this is fair enough as a stroke of business policy, but I think they should say when they have as much in hand as they can creditably accomplish. I do not assert that lithography and zincography are not admi- rably adapted for this very purpose of multiplying copies of plans and sections, if used as an art should be, and not abused; but speak- ing from ample experience in both methods, I advisedly say, that if time is short, and a sufficient number of assistants capable of making tracings can be secured, with a man to mount them, the deposit of mounted tracings will be found both economical and preferable. It is easy to calculate the number of tracings of any one or more sheets of drawing a clerk will make, in a given time, and it can be done under the surveyor's own superintendence; but he cannot know how long zincography will take to execute unless he knows how many other works of a similar nature the lithographer has in hand at the same time. The objection that in the case of tracings they may not be all alike, does not well apply if they are carefully made, and if they are mounted upon a preparation of white paper mounted on holland, and are neatly drawn, they look very nicely. The deposits duly made, the engineer has a rest on the 1st December sweeter than can be realised by the non-experienced reader. The work of serving the notices devolves upon the solicitors and their local agents; but the engineer must furnish the information for the notices, as to what properties are situated on the line as laid out, and what are only within the limit of deviation; with the nature of the works proposed to be constructed on such properties. The plans, sections, and book of reference being once deposited RAILWAY SURVEYING. 349 become public documents to which any one may have access at the Private Bill Office on payment of five shillings for an inspection or one pound for the privilege of copying them. At the office of the Clerk of the Peace of the County, the Documents may be inspected for one shilling, or copied at a charge of one shilling an hour for every hour during which a person is so engaged. This publicity of the Deposited Documents, is further coupled with the privilege to every person who may be specially affected by the non-compliance with any standing order to appear, and to be heard by themselves, their agents, and witnesses upon a memorial ad- dressed to the examiner complaining of such non-compliance, pro- vided the matter complained of be specifically stated in such memorial, and the party so specially affected has signed the same and shall not have withdrawn his signature thereto, and such memorial has been duly deposited in the Private Bill Office. The memorial complaining of the non-compliance with the standing orders, if the same relate to the petition for a Bill numbered in the General List of Petitions :-- From 1 to 100 101 to 200 وو 201 upwards must be deposited on or before January 17 24 وو 31 before six o'clock in the evening of any day in which the house shall sit, and before two o'clock on any day on which the house shall not sit; and two copies of such memorial for the use of the examiners must be deposited before twelve o'clock on the follow- ing day. The object of the Legislature in framing the standing orders, and in granting these privileges was manifestly a very sound and just one; affording, as they were evidently intended to do, the means by which every landowner and occupier could ascertain the exact extent and manner by which his particular interests would be affected; at the same time giving him the legitimate means of opposing the passage of the Bill through the House if he should be hostile to its preamble, or dissatisfied with its provisions or clauses. The examination of the petitions for private Bills which have been duly deposited in the Private Bill Office, commences on the 25th day of January, in such order, and in accordance with such regulations as shall be made by the Speaker. Seven days' notice is given by the Examiner in the Private Bill Office, of the day appointed for the examination of each petition and in case the promoters do not appear at the time appointed, the examiner strikes the petition out of the list, and has no power to re-insert it without the order of the House. 350 RAILWAY SURVEYING. The examiner endorses upon the petition, a certificate of com- pliance or non-compliance with the standing orders, and in the event of the latter, he reports to the House the facts upon which his decision is founded. A description of the several stages by which a Railway Bill passes through Parliament, is hardly in accordance with the in- tentions of this paper; those who wish to acquaint themselves fully upon the subject, can do so by reference to a "Treatise upon Parliamentary Proceedings," lately published by Mr. May, one of the Examiners. Sec. 2.-Proceedings subsequent to the passing of the act. The first operation after the passing of an Act of Parliament authorising the formation of a railway is the carrying out a very careful and particular survey and the preparation of an exceed- ingly accurate map, plotted to a scale of two chains to an inch, or some other large scale exhibiting faithfully every possible detail. Upon this plan all the future works can be correctly laid down, and the contents of the several lands required can be ac- curately computed. When these plans are completed the line of railway is carefully laid down thereon, either in the same course as drawn on the deposited plans, or in such an altered direction within the limits of deviation, as subsequent enquiries and a less hurried examination may have suggested. Now comes the important business of setting out the centre line. To do this with accuracy is frequently a troublesome operation, de- pending upon the nature of the ground. For, with the most accu- rate plan, it is not always possible at the first attempt in a hilly or a wooded country to range the long straight pieces of the line; if a piece of rising ground can be found intermediate, from which both ends can be seen, or any other two well defined points upon the plan which can be exactly identified upon the land, the best course to adopt will be to plant a theodolite or transit instrument upon the high ground with which the line can be ranged towards either end. Practice and experience are required to set out these straight lines with accuracy. A person accustomed to the conduct of large surveys will do this work much more readily than the constructive engineer. It is always advisable, however long the staight lines may be, to commence the ranging in the centre, and for this rea- son; a very small deviation at the commencement, although too minute to be detected on the Plan, would become clearly discern- ible, and require correction if carried on and increased throughout RAILWAY SURVEYING. 351 the whole line; but if the work commences in the centre this error can at any rate only arrive at half the magnitude, and may possibly to that extent be unimportant. It is desirable, if possible, that the straight lines forming tan- gents to curves, should be produced until they intersect each other, where a flag staff should be erected as a permanent mark of refer- ence throughout the construction of the works. This cannot often be done, but the tangents should at all times be produced to some spot beyond the works, whereon the pole may be erected, so that its continuance may not interfere with or be likely to be disturbed by the convenience of the landowners and occupiers. The methods of setting out curves, to which I purpose to direct attention here, are five in number. The three first are given by Mr. Law, in Simms' Treatise on Levelling, the fourth is described by Mr. Rankin, in a communication to the Institution of Civil Engineers, and the fifth is a method suggested by myself, in a Book of Tables, (published about five years since,) for setting out slopes and curves. Mr. Law's first method is that which has in practice, perhaps, been most extensively used, although it possesses some objections which I shall point out in the sequel. Let A B and C D, (fig. 1, plate 6) be the two straight portions of the line, which it is desired to connect by a curve; B and C being the two points at which the curve falls into the straight lines; and let B b₁, b₁ b₂, b₂ b3, &c., be the distance which it is desired that the points to be found in the curve shall be apart. Then measure upon the straight line A B produced, the distance B a₁, equal è̟, in formula IV below, and from the point a₁, set off, perpendicular to the same line, the distance a, b, equal to o₁, in formula III, which will give the first point required in the curve; then range a straight line through the points B, b₁, and upon this line lay off the distance b₁, a2, equal to d2, in formula VI, and from the point a set off perpendicular to the line B a₂, the distance a2, b2, equal to 02 in formula V, and the point b₂ will be the second point in the curve; then in a similar manner range another line through the points b₁ b₂, upon which measure the distance b₂ as equal to the distance 2 or b₁ a2, and from a, set off as before, perpendicular to the line b₁ as, the distance a, b, equal to 02, which will determine the third point in the curve; and thus proceed until the whole extent of the curve has been set out. 3 2 In order to obtain the values of 81, 82, 01 and 02, let r equal the radius and d equal the distance B b₁, or b₁ b₂, &c., which it is de- sired that the points found in the curve shall be apart, (both expressed in feet); then 352 RAILWAY SURVEYING. d² III. IV. V. VI. = 01 01 · 2 r √ d²-0² d 81 =02 d (r · 01) = 8 82. ጥ As an example of the application of this method, let the radius of the curve (r) be 15 chains or 990 feet, and the distance B b₁ (d) one chain or 66 feet; then from formula III 662 2 x 990 = 2.2 feet = 01 will be the first offset at a₁; and 2.2265·963 feet = di √ 66² — 2.22 will be the distance Ba₁, to be laid off upon the line A B produced to give the place for this offset. 66 × 65.963 990 Again, =4.397 feet = 02 will be the offset at a₂, a,, a₁, &c.; and 66 × (990-2.2) 990 = 65.85 feet 82 will be the distance b₁, a2, b₂ as, &c., to be measured from the points b₁, b₂, &c., in order to give the points a₂, ɑ3, ɑ4, &c., from which the offsets o, are to be taken. To this method there are, as has been already stated, some prac- tical objections, inasmuch as any error which may be committed in setting out only one of the points in the curve, will occasion a corresponding error in every succeeding one; and a very trifling inaccuracy in calculating either the distance 82, or the length of the offset 02, from its being frequently repeated, may ultimately cause a very considerable deviation from the true curve. Both these objections, however, may be in a great measure removed by the adoption of the following method of checking the position of about every fifth point; or which would be better, first determining the position of these points, and then filling in the intermediate ones; and as I consider this modification does away almost entirely with the above mentioned sources of error, I shall give an example of its application. 2 Suppose r and d, or the radius, and the distance the points B, b₁, b₂ &c., are apart (see fig. 2, plate 6) to be the same as in the last example, viz., 990 feet and 66 feet respectively, and let it be determined to check the position of every fourth point: then the RAILWAY SURVEYING. 353 19 values of 81, 82, 01 and 02, will be the same as before; but previous to setting out points b₁, b₂, bg, &c., we must calculate the distance BB₁, to be measured along the line A B produced, and the distance B₁, b₁, to be set off from the point B₁ to give the position of the fourth point (64) in the curve: which may be done as follows: Let the distance B B, equal A and B, b, equal 0,; and let D, be the length of the chord line connecting the two points B and b₁, and ß be the angle a, B b₁; then 1 4 1 1 and 01 rad d sin 6, 2r sin 4 ß- D₁. rad 2 2 Then, by substituting D₁, O1, and A, for d, 0, and 8, in the for- δι 1 mulæ III, IV, V, and VI, we shall obtain the values of O₁, ▷19 O2 and 2, where ▷ is the distance b₁ B₂ to be measured upon the chord line B₁ b4 produced, and O2 is the distance B₂ b, to be set off from B, in order to give the eighth point (bs) in the curve; for the values of r and d given above we shall obtain Log of o Log rad 0.342423 = 2.2 = 10·000000 Log of d Log sin of ẞ and ẞ = 1° 54′ 37″; then Log of 2 r Log sin of 4 ß || 10.342423 1·819544 = 66 8.522879 3.296665 = 1980 7° 38′ 28″ 9.123745 12.420410 Log rad = 10.000000 2·420410 = 263·27. Log of D₁ Then from formula III, 263.272 = 35 feet = O₁; 2 × 990 from formula IV, √ 263·27² — 352 = 260·92 feet = ▷ 1; from formula V, 263·27 × 260·92 990 69.4 = O2; and from formula VI, 263.27 × (990 - 35) = 253·96 =▷ 2. 990 354 RAILWAY SURVEYING. These being obtained, the position of every fourth point, b₁, bɛ, b, &c., should be first determined by the dimensions 41, O₁, 42, and O2; and then the intermediate points, b₁, b₂, bз, bы, bε, &c., by d1, 01, 2, and 02, as first described. The second method which I shall describe may be advan- tageously employed when the radius of curvature is large and the centre can be seen from every part of the curve. Let the lines (fig. 3, plate 6) A B and C D, as before, repre- sent the two straight portions of the line required to be connected by a curve having a radius of 80 chains or 1 mile. First, set up a theodolite at B and another at C (the two terminations of the straight portions of the line) and from each point range a line at right angles to the lines A B and C D respectively, and at the in- tersection of these lines (E) which will be the centre of the curve, put up a signal sufficiently conspicuous to be seen from any point between B and C: then produce the straight lines A B and CD until they intersect in the point F, and on these lines drive in stakes at equal distances, a1, a2, as, &c., commencing from the points B and C. If r equal the radius, and ♪ equal the distance between the points a, a, a,, &c., both in feet, then ✓ p² + №² r = 019 will be the distance which must be set off from the first point a1, not perpendicular to the line B F, but in the direction a, E; in like manner √ p² + 2 ô² — r r = 029 1 will be the distance to be set off from the point a, in the direction a, E; and generally √ p² + n s ² — r — On, will be the distance to be set off at the nth points from B and C. For example, let r be 5280 feet and ♪ equal 100 feet; then 528094 feet = 01 ✔ 5280² + 1002 will be the distance a₁ b₁, which must be set off from a₁ in the direc- tion a₁ E to obtain the first point b₁ in the curve, and proceeding in a similar manner with the others, the following table will exhibit the distances to be set off at the respective points a1, a2, as, &c. At a or 100 feet from B, the offset will be •94 feet 3.79 02 аз 200 300 "" 8.52 وو وو 15.13 400 "" "" 23.62 α5 500 "" وو 33.98 α6 600 "" >> RAILWAY SURVEYING. 355 At a or 700 feet from B, the offset will be 46.19 Ag 800 ag 900 " α10 1000 وو 1100 a12 1200 a13 1300 α14 1400 α15 1500 وو وو 60.26 76.16 " 93.86 113.36 "" 134.65 157.68 182.45 وو 208.93 وو وو وو وو وو وو If the extent of the curve is such that the length of the offsets before reaching the point F where the two tangent lines intersect become inconveniently long, so as to occasion a loss of time in setting them off, it will be advisable to make use of another tan- gent line as shewn at G I, fig. 4, plate 7; for determining the position of which line the following method may be made use of. Let r, as before, be the radius, & the number of degrees contained by the angle BEC, and n the number of tangent lines (as B G, G H, HI, IC) intended to be employed; then ε & r sin n COS ε n will equal the length of any one of these tangent lines. As an example, let r equal 5280 feet, & equal 60°, and n equal 4; then Log of r Log sin ε N ε Log cos 2 = 3·722634 = 5280 = 9.412996 = 15° 13.135630 = 9.984944 3.150686 = 1414.8 feet will be the length of the lines B G, GH, &c. Now having ascertained this length, nothing more remains than to set it off from B, and C towards F, and then to range a line GI from the two points thus obtained, which will be the required tan- gent line: this line must then be bisected in the point H, which may readily be done by ranging a line from F to E, which having been done, proceed as already described to set off the equal dis- tances α₁, ɑ2, ɑs, &c. from B and H towards G, and from H and C towards I; and then by setting off the distances a₁ b₁, a₂ b₂, &c. contained in the Table already given, from the several points 356 RAILWAY SURVEYING. a1, a2, &c., in directions radiating to the centre E, the course of the curve will be marked by the points b₁, b₂, b, &c. thus obtained. One advantage possessed by the above method is, that knowing exactly the direction in which to lay off the offsets, (and that by the range of a comparatively distant object,) the errors which have frequently arisen from their not having been set off perpen- dicularly, where the eye has been the only criterion, are entirely obviated; and this method is also entirely free from the objections made to the former method. When the centre point E cannot be seen from every part of the curve, so as to allow of the offsets been laid off radially, the more usual method may be adopted of laying off the offsets perpen- dicularly to the tangent B F, but in this case a cross staff should always be employed to insure accuracy, and the distances to be set off from the points a₁, a₂, as, &c. will be greater than those em- ployed in the previous method, and must be calculated from the formula 2 ✔ p² d2 01 instead of that given at page 355. The third method is most applicable where the radius of the curve is small as compared with its extent, and is deduced from the well known theorem, that all angles contained in the same seg- ment of a circle are equal to one another.* The method is as follows:-place a theodolite at B and another at C, (fig. 5, plate 7) the two terminations of the straight portions of the line, setting the telescope of the instrument at B on C, and that at C on F, the point of intersection of the lines A B and CD pro- duced; then if the former be moved through an arc of any number of degrees, towards F, and the latter the same number of degrees towards B, the point a₁, where the lines of collimation of the two telescopes intersect, will be a point in the curve; now let both theodolites be again moved the same number of degrees and in the same directions as before, and their axes produced, or lines of collimation, will again intersect at a2, another point in the curve; and in fact, to whatever extent the theodolites are moved, so long as the arc described is equal in both, the point of their intersection will always be in the required curve. Or more generally, suppose the two theodolites to be placed as first described, and then simultaneously to commence to revolve with the same uniform angular velocity, the point of intersection of their lines of col- limation will describe the circular arc C, ɑ1, ɑ2, ɑз, B; and in equal intervals of time, equal portions of the arc will be de- scribed, which will be half as great as the arc, which would have * Euclid, Book III. prop. 21. RAILWAY SURVEYING. 357 been described in the same time, by the same angular velocity, at the centre of the circle (E); from which last mentioned circum- stance, we may readily calculate the magnitude of the angle through which the theodolites at B and C must be successively moved, in order that the points a1, a2, a,, &c., at which their axes intersect, may be at the distance apart which it is desired that they should be. If r equal the radius of the curve, d the required distance, and ẞ the angle a, B C; then d rad 2 r sin ß VII. As an example of the application of this method, let r equal 20 chains, or 1320 feet, and let it be required to determine points in the curve at distances of about 100 feet; now from the above formula we shall obtain Log d Log rad Log 2 r Log sin & 2.000000 100 10.000000 12.000000 = 3.421604 2640 8.578396 2° 10' 15" As it would be inconvenient, however, in practice, to lay off so frequently as would be required an angle, with odd minutes and seconds, we may instead of the above take an angle of 2 degrees, which will make the distance d equal 92.13 feet. Having thus determined the angle, and placed the theodolites as previously de- scribed, viz., that at B in the direction of B C, and that at C in the direction CF; the former must be moved 2° towards F, and the latter 2° towards B, and a stake driven down at their point of intersection a₁, the former must then be removed 2º more towards F, and the latter 2° towards B, and another stake put down at their point of intersection a,, and so on until the theodolite at B, is brought to the direction B F, and that at C to the direction C B, when the whole of the curve will have been staked out as required the stakes being 92.13 feet apart. This method, the same as the last is not liable to the objections that the first method was, and in addition possesses the very important practical advantage, that its accuracy is entirely independent of any undulation or change of level in the surface of the ground, an advantage which is not pos- sessed by any of the other methods which I have described, the whole of which would require to have the distances and offsets cor- rected in proportion to the slope of the surface of the ground. In a hilly country-and it is in such districts that curves most fre- quently occur-this circumstance will render the last described method far superior to either of those which precede it. 358 RAILWAY SURVEYING. The next method which I shall give, is that described by Mr. Rankin, in a communication to the Institution of Civil Engineers, and depends on the theorem* that the angle, subtended by any arc of a circle at the centre of the circle, is double the angle subtended by the same arc at any point in the circumference of the circle. The method of proceeding is as follows:-first place a theodolite at B (fig. 6, plate 7) the point where the curve commences; and then lay off from the line B F, the angle B, calculated from for- mula VII, (supposing, as before, r to represent the radius of the curve, and d the distance required between the points in the curve,) and in the direction of the axis of the instrument set off the dis- tance d, which will give the first point a, in the curve; in the same manner lay off from B F the angle 26, and from a₁ set off the same distance d, and the point where it cuts the axis of the instrument produced will be the second point a2; and generally by laying off the angle n ẞ, and setting off from the proceeding point am, the distance d, the point a will be given. As an example of the application of this method, let r equal 19 chains, or 1254 feet, and d equal 100 feet; then from formula VII we obtain Log d Log rad. Log 2 r Log sin ß || || 2.000000 100 = 10.000000 12.000000 3.399328 2508 2° 17' 6" || 8.600672 then having placed the theodolite at the point B, lay off this angle 2° 17' 6" from the line B F, and upon the line B a, thus obtained set off 100 feet, which will give the first point in the curve a₁; then with an angle of 4° 34′ 12″ or 2 ẞ set off another 100 feet from a₁, which will give the second point a2, and thus proceed, until the whole extent of the curve has been set out. The last method I extract from my own Work upon the subject. "Suppose we have arrived, by a piece of straight work, at the commencement of a curve, of 80 chains radius, which for demon- stration we will call point A, (fig. 173f); the first proceeding is to produce the straight line or tangent, one chain to C; then turning to the tables (as hereafter explained) we find the single offset CD = 4.9 inches; this must be very exactly set off at right angles (in the first case only) with the tangent AC to D, which becomes a point in the curve. We now produce AD, one chain to E. Then turning again to the tables, we ascertain the double offset, * Euclid, book III, prop. 20. RAILWAY SURVEYING. 359 (as the single offset serves only to connect the tangent with the curve,) to be 9.9 inches; so with one handle of the chain held firmly at D, and one end of a tape held at E, we proceed to make DF = one chain; and E F = 9.9 inches; and F is another point in the curve. We then produce DF in the same manner as A D, and so on throughout to the end of the curve;-always bearing in mind that the tangent leaves the curve as it came on, with the single or half offset, as shewn at I. The above method requires some further test to ensure complete accuracy, as explained with reference to the first method. We will again suppose ourselves at the commencement of the curve, which we will now consider point A, fig. 173g; produce the straight line ten chains to C; there erect a perpendicular,* which, on reference to the tables, we find to be 62.7 links, and being accurately set off, we obtain D, a point in the curve. In measuring the ten chains A C, reference is required to the tables to ascertain the point B at which the next tangent inter- sects, and which is found to be 502 links from A, at which point a mark should be set up. If we produce a line formed by the points B and D, ten chains from D to F, we have a new tangent DF with which to proceed in the same manner as with A C: and so on throughout the con- tinuance of the curve. The dimensions A C and C D, D F and F G, &c., corresponding respectively with the sine and versed sine of the curve, and being of sufficient length to bear a comparison with the radius, must obviously subtend to great accuracy. The tables afford one other test, by giving the angles CBD, FEG, &c., between the intersecting tangents, in our illustra- tion, 7° 10′ 50″ Example. It is required to set out a curve of 20 chains radius: Seek in the column headed "radius" in the tables, 20 chains, then opposite the radius in 1-ft. 7.8 inches. Column 2, is the single offset CD, fig. 173ƒ, Column 3, is the double offset E F, fig. 173f, = 3-ft. 3.6 inches. Column 4, is the perpendicular CD, fig. 173g, at 10 chains on the tangent A C=267.9 links. Column 5, is the distance A B on the old tangent A C, at which the new tangent B F intersects 536 links; and in Column 6, is the angle C B D, fig. 173g, formed by the intersec- tion of the old and new tangents = 30 deg. * This perpendicular being of some length is calculated in the tables to links, as more easily measured with a chain than a tape. 360 RAILWAY SURVEYING. TABLES FOR SETTING OUT CURVES. RADIUS. SINGLE OFFSET AT 1 CHAIN ON TANGENT. DOUBLE OFFSET AT 1 CHAIN ON TANGENT. PERPENDICULAR OFFSET AT 10 CHAINS ON TAN- GENT; OR COR- RESPONDING VERSED SINE. DISTANCE ON THE OLD TAN- GENT AT WHICH THE NEW ONE INTERSECTS. ANGLE FORMED BY THE INTER- SECTION OF THE OLD AND NEW TANGENTS. Chains. Feet. Inches. Feet. Inches. Links. Links. Deg.Min. Sec. 10 3 3.6 6 7.2 1000. 1000 90 0 0 11 3 0. 6 0. 641.7 706 65 22 34 12 2 9. 5 6. 536.6 644 56 26 33 13 2 6.4 5 0.9 469.3 610 50 17 5 14 2 4.2 4 8.5 420.2 588 45 35 4 15 2 2.4 4 4.8 381.9 573 41 48 37 16 2 0.7 4 1.5 351. 562 38 40 55 17 1 11.3 3 10.6 325.2 553 36 1 54 18 1 10. 3 8. 303.3 546 33 44 56 19 1 8.8 3 5.6 284.4 540 31 45 24 20 1 7.8 3 3.6 267.9 536 30 0 0 25 1 3.8 2 7.6 208.7 522 23 34 41 30 1 1.2 2 2.4 171.5 515 19 28 16 35 0 11.3 1 10.6 145.9 511 16 36 5 40 0 9.9 1 7.8 127. 508 14 28 39 45 0 8.8 1 5.6 112.5 506 12 50 22 50 0 7.9 1 3.8 101. 505 11 32 13 55 0 7.2 1 2.4 91.6 504 10 28 32 60 0 6.6 1 1.2 83.9 503 9 35 38 65 0 6. 1 0.1 77.3 503 8 50 58 70 0 5.6 0 11.3 71.8 502 8 12 47 75 0 5.2 0 10.5 66.9 502 7 39 44 80 0 4.9 0 9.9 62.7 502 7 10 50 Miles. Fur. 1 1 0 4.4 0 8.8 55.7 502 6 22 45 1 2 0 3.9 0 7.9 50.1 501 5 44 21 1 3 0 3.6 0 7.2 45.5 501 5 12 57 1 4 0 3.3 0 6.6 41.7 501 4 46 48 1 5 0 3. 0 6. 38.8 500 4 24 42 1 6 0 2.8 0 5.6 35.7 500 4 5 45 1 7 0 2.6 0 5.2 33.3 500 3 49 21 2 0 0 2.4 0 4.9 31.2 500 3 35 35 0 2 2 0 2.2 0 4.4 27.8 500 3 11 5 2 4 0 1.9 0 3.9 25. 500 2 51 51 57 2 6 0 1.8 0 3.6 22.7 499 2 36 18 3 0 0 1.6 0 3.3 20.8 499 2 23 16 RAILWAY SURVEYING. 361 Having now given several methods by one or other of which all curves may be correctly set out, the object of my paper has been satisfied. I might have gone at some length into the absolute ne- cessity for all curves to be truly tangential to the straight work, as well as to each other; the practical tests that are required when working from an incorrect map (although as a surveyor I am bound to say the map should, in all cases, and for many reasons, be a very good one,) but I have felt that I could not do so without going still further, and perfecting, what is not at all intended, a complete trea- tise on the subject. I venture to suggest that much future eco- nomy always depends upon the manner in which the curves of a railway are originally laid out; to say nothing of the jerks and un- pleasant oscillations to which the passengers are subjected if they are untrue, or the danger by that means incurred. As soon as the line is set out, a square peg, about two and a half inches in section, and two feet long, should be driven into the ground about twenty inches, at intervals of a chain, very carefully and correctly measured from one of the termini, and between each of these pegs a triangular sod, about ten inches wide, should be cut out, and this is what is called "nicking out." I should observe, that at the tangent points of the curves a peg should be driven in, although they may not fall at an equal chain's length; and to secure the certainty of finding the exact point at a future occasion, a peg should be driven into some place where it may remain undisturbed, on either side of the line, directly at right angles with the tangent. When the line is stumped and nicked out, we prepare for making the "Working Section," by driving into the ground by the side of each of the chain stumps a peg for the levelling staff to stand upon. These pegs should be about fifteen inches long and two and a half inches square, and should be driven into the ground level with the surface. The levels are then minutely taken at each chain, or oftener if any variation in the ground between the chain pegs require it, and for the purposes of the method I am about to describe for setting out the slopes, a reading should be also obtained from the staff, held at fifty links from the centre peg on either side of the line. This extra reading furnishes the rate of inclination per chain of the cross section. What are called permanent posts, for B. Ms. of refe- rence during the execution of the works, should be fixed at înter- vals, as the levelling proceeds in situations not likely to be dis- turbed. They may be about four feet in length, should be hooped at top to prevent them from splitting, and should have an iron plate Z 362 RAILWAY SURVEYING. on the top of them for the staff to stand upon. To these B. Ms. the levels must be very accurately proved. Plate 11 is a specimen of a working section. When the working section is completed, the gradients may be carefully laid on. Two lines will be required to be drawn upon the section: the upper one representing the top surface of rails when laid, and the lower one exactly two feet below the other one, the line which is called the "Formation Level," that is the line to which the cuttings and embankments have to be constructed. Engineers generally insert upon their working sections two sets of figures—some shewing the height of the formation level at every chain above the datum line, and the depth of cutting or height of embankment; others shewing the heights of the level pegs above the datum line at the surface of the ground, and the depths of cuttings or height of embankments. In my opinion, the section should ex- hibit all three, viz., first, the height of the surface peg above the datum line; secondly, the height of the formation level above datum at every chain, arrived at by calculation; and, thirdly, the depth of cutting or height of embankment, arrived at by the sub- traction of the first and second row of figures, the one from the other. On Setting out the Widths of Ground required for the Works of a Railway or Canal, &c., &c. I shall give two methods of setting out slopes. The first will be the same as given in Simms' Levelling. The second is extracted from Tables published by myself, under the title of the Civil Engineers' and Surveyors' Assistant, in setting out Slopes, Curves, Cuttings, and Embankments. MR. SIMMS' METHOD. When the natural surface of the ground, both longitudinally and transversely, is upon the same level as that of the intended works, the process of setting and staking out the widths is very simple. Let us take, for example, the case of a railway, the base or bottom width of which, when prepared for the reception of the ballasting and permanent way, is to be 36 feet; the ratio of the inclination, or batter, of the slopes to the heights, both in the cuttings and the embankments, to be 2 to 1; beyond which, or at the outward edge, a slip of land 12 feet wide is to be taken on each side of the rail- way for the fences, &c. First, the centre line must be staked out RAILWAY SURVEYING. 363 and carefully levelled: it is customary to drive a stake about 2 feet long, and about 1½ inches square, into the ground at each chain's length, their tops to be upon the fair level of the natural surface, thus affording good stations for the levelling staves to be held upon; the relative level of each stake being then very accurately determined with respect to some given datum, they become so many zero points for reference in the subsequent operations. From each of the centre stakes a line must be set out on both sides, and at right angles to the centre line, or at right angles to a tangent to the centre line at that point, if the centre line be curved; upon these transverse lines the required widths of land must be set out. Now, if the ground at any of the centre stakes is upon the same level as the intended base of the railway, nothing more will be re- quired than to measure on each transverse line, and in both direc- tions from the centre stake, one-half the required width, which, in our supposed case, is 18 feet for the half width of the railway, and 12 feet for the fences, in all 30 feet on each side of the centre. But when, as it mostly happens, the ground is not on the proposed level of the railway, the operation is not quite so simple; and if, in addition thereto, the ground slopes sidewise or at right angles to the general direction of the line, the business is still more compli- cated, and requires some skill and care to do the work correctly. The method of doing this is our business to explain. The next most simple case to the above is when the cross sec- tion of the ground is horizontal, be the depth of cutting or height of embankment what it may. This is shewn in fig. 173h, which represents a cross section of a 20 feet cutting with slopes of two horizontal to one per- pendicular. The horizontal line at AB right angles to the centre line represents the natural surface of the ground. Under these circumstances it will readily be seen that the half width of the cutting, or the distance from the centre to the edge of the slopes C and D, equals the half width of the base (18) added to the batter of the sloping sides (40), and including the 12 feet for the fences, the total half width of land required for the purposes of such railway would be 18+ 40+12= 70 feet, and consequently the whole required width to be so appropriated and fenced in for a 20 feet cutting or embankment, when the ground does not slope sidewise, would be 140 feet. The next and more complicated, and also the most frequently occurring case, is, when the cross section of the natural surface is not horizontal, as shewn in the annexed diagram, which also represents a cutting of 20 feet. 364 RAILWAY SURVEYING. Let the line AB represent a horizontal line, passing through the centre line C of the railway, which, if it coincided with the surface of the ground would give AC and CB (each half width) 70 feet, as in the former example, the depth of cutting and the slopes being assumed the same. Let the line E H represent the natural surface of the ground upon this transverse section; it will readily be perceived that the real half width CE (on the left of the diagram) is much shorter than the horizontal or com- puted half width A C, because the ground- line is depressed on that side of the centre; likewise the half width C H on the other side of the centre is greater than the said horizon- tal or computed half width, because the ground is there elevated above the horizontal line A B passing through the centre. To de- termine exactly the distances CE and CH in actual operations in the field, would be attended with some difficulty, and consume much time; but the following method, which at the same time that it gives a sufficiently correct approximation in practice, is also a very expeditious one. H to 1 B Centre 008 ૐ A F E 2 to 1 Let us suppose that the point E or dis- tance CE be known, and that with a spirit level we determine the difference of level between the points C and E, this difference is represented by the line E F, which sup- pose to be one foot; now we have a small right angled triangle A EF, of which E F is determined, being the difference of level (one foot), and the slope or ratio of AF to E F also given, (2 to 1,) therefore the side A F is known (2 feet,) which subtracted from the computed half width A C, leaves FC approximately equal to EC, the required half width, sufficiently exact for all practical purposes, where the cross section of the ground does not differ materially from a horizontal line. We have been supposing that the point E is known, whereas that point is the object of our search; in practice, therefore, we proceed thus:—take the computed half width, and if the ground is depressed, let a levelling staff be held somewhat nearer the point C 36 > RAILWAY SURVEYING. 365 than the said computed half width, for a first approximation to the point E; then determine the difference of level between this as- sumed point and the centre point C, multiply this difference of level by the ratio of the slopes, (which doubles it when the slope is 2 to 1,) and subtract the result from the computed half width, which gives a more correct approximation to the point E; now hold the staff at this new point and find the difference of level as before; again mul- tiply by the ratio of the slopes, and deduct the result from the computed half width, which second result will in most cases be sufficiently near the real half width for a depressed line for all prac- tical purposes. Example.-Central height (or depth of cutting), 20 feet, slopes 2 to 1, base 36 feet, the computed half width was therefore 58 feet ; the ground being depressed, we estimated that the point E might fall short of the computed half width 2 feet; we therefore directed a levelling staff to be held at 56 feet from the centre line (or stake) C, at which point another staff was held, and by means of a spirit level set up at a convenient distance, we found the difference of level between these points to be 0.87 feet, which multiplied by the ratio of the slopes 2 to 1, gave 1.74 feet to be subtracted from the computed half width 58 feet, leaving 56.26 feet for a first approxi- mation to the half width CE (see last diagram.) Now, upon re- moving the staff to this new point, the difference of level was again taken, (or rather we should say that the staff was again read off as the level had not been disturbed,) and found to be 0.91 feet, which also multiplied by the ratio of the slopes (2 to 1), gave 1.82 feet to be subtracted from 58 feet, leaving 56.18 for the second approxi- mation, and which was adopted as the correct half width for the depressed side of the centre; indeed, in such a case as is above given, where the ground is so nearly horizontal, the first approxi- mation (taken by a person after a little practice) may be assumed as the correct result, for in the above example it differed but 08 from the second determination, and if it had been taken a third time, it could not have been more accurate as far as practice is con- cerned: this, however, is not the case where the inclination or slope of the ground is considerable, for then (if this method be followed) several approximations will be necessary to bring the result within admissible limits. When the ground is elevated above the horizontal line, as shewn on the right hand of the diagram, the mode of procedure will some- what differ: thus, instead of holding the staff and finding the dif- ference of level at a less distance than the computed half width, it must be held at a greater distance to obtain the point H by approxi- 366 RAILWAY SURVEYING. mation, the difference of level between that point and the centre point C being equal to H I, and multiplied by the ratio of the slopes will give the distance BI to be added to the computed half width CB, to obtain the half width C H; this may likewise be re- peated to obtain a more correct result as described for the other, or depressed side of the centre C. It will also here be obvious to a person possessing but the smallest share of mathematical know- ledge, that this result is not strictly correct, inasmuch as the line C H can never be equal to CI, but for practical purposes it is, as before observed, sufficiently correct. It may not be altogether un- necessary to observe, in this place, that the corrections B I, &c., as shewn in the foregoing diagrams, are much exaggerated, being far greater in proportion to the computed half width CB, than ever occurs in ordinary practice, but this has been done to make our explanations more distinct than otherwise. The above particulars have been confined to the case of excavations; we must now shew in what the process differs when the ground is to be covered with an embank- ment. By reversing fig. 173h, it then represents an embankment. The rule for finding the half width for an embankment where the transverse section of the ground is horizontal, remains the same as for the cuttings under like circumstances, as may be seen by an inspection of the inverted figure, but upon inverting the second diagram, it will at once be seen that some variation in the process is required. Thus :— The horizontal line is represented by that marked AB; C D and CF the computed half widths; CE the required half width on the depressed side, and CH the required half width on the elevated side, the line KL representing the natural surface of the ground. In the case of an excavation, we have shewn that the real half width is greater on the elevated side than the computed half width, and less on the depressed side; but it will be seen by the diagram that for an embankment the real half widths are less on the E 2 to 1 < 18 2 K-20 v B F ** H RAILWAY SURVEYING. 367 elevated side, and greater on the depressed side than the said com- puted half widths; therefore, in determining the approximate place of the point E on the depressed side for an embankment, the staff must be held further from the centre than the computed half width; and for the point H or the elevated side, it must be held nearer to the centre than the computed half width; and finally, for computing the real half widths from the differences of level between the points E and the centre, and H and the centre, on the depressed side the difference of level multiplied by the ratio of the slopes is to be added to the computed half widths to obtain the point E, and to be subtracted from the computed half widths to obtain the point H. The process above described may appear to the reader a very tedious one; it perhaps is so to read, but a little practice will convince him that it is a very expeditious method, for in most cases one setting up of the level will answer for several stations, and the multiplications by the ratio of the slopes upon such small numbers as mostly occur is easily performed, especially if it be an even number as 2 to 1. The columns of the Field Book may be arranged as in the following example for making the calculations in the field, or may be abridged to suit a more convenient-sized book for the pocket, at the pleasure of the surveyor; indeed, all that can be accomplished now of this kind is to give general rules which can be altered and arranged to suit the convenience of the surveyor, as experience may point out a more suitable mode of proceeding. The example is taken from an extensive field operation by the writer, and shews the work both for a cutting and an embankment; the change from one to the other, or the tailing out of the cutting, as it is called, being in- cluded therein. The slope of the cutting is calculated at 1½ to 1, and that of the embankment at 2 to 1. The width of the railway was 36 feet, consequently half the said width was 18 feet. 368 RAILWAY SURVEYING. No. of Stake. Depth of Cutting or Embankment. Computed half width. Section or Level Readings at right angles to Line. EXAMPLE. Difference of Level. + South. Centre. North. South. North. South. North. South. North. Difference of Level, ratio of Slope. X + EMBANKMENT. Feet. Feet. 285 16.97 51.94 10.90 Feet. Feet. Feet. Feet. 7.50 3.96 + 3·40 286 1.43 20.86 7.06 4.74 3.24 + 2.32 Feet. 3.54 0.07} Feet. Feet. Feet. Feet. + 6·80 - 7.08 58.74 44.86 287 2.77 23.54 8.00 5.80 4.26 + 2.20 +0.077 1.50 1.54 + 4·64 + 0.11 25.50 | 20.97 + 4·40 3.08 27.94 20.46 288 3.0624.12 8.82 6.42 5.12 + 2·40 289 2.0122.02 7.02 5.13 3.74 +1.89 - 1.30 1.39 + 4.80 - 2.60 28.92 21.52 + 3.78 2.78 25.80 19.24 290 1.22 20.44 291 1.91 21.82 6.00 4.10 2.76 7.52 6.95 5.20 +1.90 + 0.57 {+0.12}} 1.34 S 1.75 + 3·80 + 0·18 24.24 20.62 + 1·14 I CUTTING. 292 1.39 20-7812-20 11.35 10.52 -0.85 + 0.83 - 1.27 293 4.51 27.02 9.56 7.98 6.22 - 1.58 +1.76 - 2.37 + 2·64 3.50 22.96 18.32 +1.24 || 19.51 | 22-02 24.65 29.66 294 5.72 29.44 8.40 6.52 4.27 -1.88 +2.25 - 2.82 295 6.85 31.70 7.06 5.10 3.02 · 1.96 + 2·08 - 2.94 296 8.61 35.22 7.53 5.28 2.76 - 2.25 + 2.52 3.37 +++ + 3·37 26.62 | 32.81 + 3.12 28.76 | 34.82 + 3.78 31.85 39.00 Required half width for edge of Cutting or foot of Embankment. The first column contains the number of the central stakes The second column contains the depth of cutting or the height of embankment, as the case may be, at that point on the centre line. The third column, the computed half width from the centre line to the edge of the cutting, or foot of embankment, upon the sup- position that the ground is horizontal at right angles to the centre reckoned from the commencement of the work, which are conve- nient for reference. RAILWAY SURVEYING. 369 line, this half width, as before explained, is found by multiplying the central height by the ratio of the slopes, and adding to the product half the width at the base of the railway. The fourth, fifth, and sixth columns contain the readings from the levelling staves at the centre stake, and at the approximate points E and H, (see last diagram.) The seventh and eighth columns contain the differences of level between the centre stake and the above approximate points. These numbers are simply the differences of the quantities in the three preceding columns, (except at stakes 286 and 290, which we shall presently explain,) and the signs + or - denote whether they are positive or negative quantities as respects the centre, and the approximate points E and H. The ninth and tenth columns contain the differences of level (contained in columns 7 and 8) multiplied by the ratio of the slopes, and must have the same signs or as the corresponding numbers in the preceding columns. + The last two columns contain the final half widths, obtained by adding or subtracting, according to the prefixed signs + or, the numbers in the two preceding columns to the computed half width contained in column 3. After the explanations already given, the reader can find no difficulty in tracing the steps of the example, except perhaps with the stakes 286 and 290, where the difference of level on the north side is represented by two numbers bracketed tegether, one having the sign + and the other : for the stake 286 the real difference of level on the north side the centre is a rise of 150, that is, the approximate point H is 1.50 feet above the centre stake: but it happens that the height of the embankment itself at that point is to be but 1.43 feet (column 2); therefore the approximate point H is above the intended top of the embankment, and consequently will not represent the foot of an embankment, but the edge of a cutting, and therefore the calculation for the half width on the north side, must be treated as for a cutting whose depth is equal to the height of the approximate point H above the intended top of the embankment or in other words, the excess of the difference of level between the centre stake and the approximate point H, above the intended height of the embankment, is the quantity to be entered in the column (7 or 8) "difference of level," and to be computed as for a cutting instead of embankment. In the case of stake 286 this ex- cess is 0.07, to which is prefixed the sign plus; this sum multiplied by the ratio of the slope being additive (for a cutting) on the ele- vated side of the centre, as before explained. 370 RAILWAY SURVEYING. — = For the stake 290, the north side of the line (column 6) is 1.34 higher than the centre stake, and it being embankment, would have the sign - prefixed (as shewn by the lower number, column 8): but the central height of the embankment at that point is but 1-22 (column 2); therefore, 1.34 1.22 0.12, which is the depth of cutting on the elevated side, and when multiplied by the ratio of the slopes, is to be added to the computed half width to obtain the correct result. When the surface of the ground is much inclined at right angles to the centre line, the numbers to be operated upon become proportionally large. As it is a case of frequent occurrence that one side will be a cutting when the other is an embankment, we wish it to be well understood, and therefore annex the follow- ing diagram to illustrate it. The line F G represents the natural sur- face of the ground, A B the horizontal line at the centre stake, CD the intended height of the embankment, KL the width or base of the railway, 36 feet, part of which is an embankment and part in cutting; the point E, or foot of the embankment will be determined in the usual way, as explained at page 368; but the point H, which is to be the edge of the cutting, must be found by subtracting DC (the height of embankment) from HI (the difference of level,) the remainder H M, (which is the excess of the difference of level between the centre stake and the approximate point H above the intended height of embank- ment,) multiplied into the ratio of the slope, must be added to the computed half width, or in other words, treated as for a cutting, to obtain the said point H as before stated. By reversing the diagram, the corresponding case will become evident, namely, when the centre line is in cutting, and one side on em- bankment, while the other is in excavation, and the mode of proceeding will at once strike the reader after perusing what we have above written. H Κ Base of Railway, 36 feet. D Y...--- JAI! L B I E F RAILWAY SURVEYING. 371 MR. RYDE'S METHOD. It will be observed, that the preceding method is somewhat com- plex and tedious, unless to the practised surveyor. In consequence of this, some few years ago, I turned my attention to the compu- tation of a series of Tables which should obviate this and combine other advantages. The first information required under my system is, the rate of inclination per chain of the cross section. This has already been directed to be taken while levelling for the working section, when it will be found to occupy but very little time. The whole work is then done in the office, with the exception only of measuring out the widths, which can be done by a surveyor of very limited experience. I append Examples of the Tables, and of their use in Setting out Slopes, as well as a Specimen of the Field Book suited to them. It is hardly necessary to say that columns one, two, three, four, five, and six, are taken from the working section; that seven is computed; and that eight and nine are the tabulated results. And as these tabulated widths are given in links, they are more readily set out on the ground with a chain; they are easily set off on the plan by the scale with which the plan has been plotted; and the quantity of land required for the railway is simply and cor- rectly computed. On the contrary, the system in general use gives the width of the railway only on the ground, from which it has to be measured before it can be laid off on the plan. Explanation of the Tables for Setting out Slopes. Note.—In these Tables fractional parts of feet are not given in treating of the depth of cuttings or height of embankments; it is considered sufficiently accurate in practice, when those decimals do not amount to half, to reject them altogether; when they do, to add one to the integer. The columns of widths in links have been prepared by the same rule; and it may be well to observe, that these distances refer to horizontal measure. If any case should occur exceeding the greatest depth of cutting or height of embankment given in the Tables, it is easily obviated by taking the half, and doubling the result. The Tables have all been calculated by the application of loga- rithms to trigonometry, and are consequently of the most accurate solutions. 372 RAILWAY SURVEYING. Examples. Case 1.-When the surface of the land across the railway is level, and the work is a cutting or embankment. Let fig. 173b represent the cross section of a railway in a cutting; the depth A B at the centre peg A being 40 feet, the width of the permanent way DG 30 feet, and the ratio of the base to the slope 1 to 1; required the widths AE and A F on either side the centre peg A? First, find the distance B C by comparing the ratio of the slope with the half width of the permanent way B G or B D. As 1:1 BG 15 ft. BC= 10 ft. and B C being added to A B, we have a total depth of 50 feet to the point at which the slopes would intersect themselves and the vertical line A C, and form the triangles ACE and AC F. AC = 50 feet depth of cutting becomes the reference to the Tables, under which, and the slope of 1 to 1, and opposite level, we have 114 links on either side-the widths required. Case 2.--When the surface of the ground across the railway is not level, and the work a cutting or embankment : Let fig. 173c represent the cross section of a railway in a cutting; the depth A B being 40 feet, the width of way D G 28 feet, the ratio of the base to the slope 2 to 1, and the rise per chain in the cross section EAF 4.5 feet; required the widths AE and A F on either side the centre peg A? Proceed as in the last case to find B C As 2: 1 :: BG 14 ft.: BC= 7 ft. AB = 40+ BC=7= A C 47 feet. In the page of the Tables headed Depth of Cutting 47 feet, under slope 2 to 1, and opposite the rise of 4.5 feet per chain, stands the required widths, 165 and 125 links respectively. Case 3.-When the surface of the land across the railway is not level, but when the centre of the railway is neither cutting nor embankment: Let fig. 173d represent the cross section of a railway in which the width of way D G is 30 feet; the ratio of the slope 1 to 1; and the rise per chain in the cross section EAF 5 feet; required the widths A E and A F on either side the centre peg A? RAILWAY SURVEYING. 373 Find A CAB as before. As 1:1:: AD or AG = 15 feet: A C or AB = 15 feet. In the page of the Tables headed Depth of Cutting or Height of Embankment 15 feet, under slope 1 to 1, and opposite rise per chain 5 feet, is 24 links; the greater width, which is here required on both sides, being the lower side of an embankment, and the higher of a cutting. Case 4.-When the surface across the railway is not of one uni- form inclination on either side the centre peg: Let fig. 173e represent the cross section of a railway embankment, the height A B being 20 feet; D G 30 feet; ratio of the base to the slope 1 to 1; and the rise per chain in the cross section E A 4. 5 feet; and AF 7 feet; required the widths AE and A F on either side the centre peg A? Find B C as before, As 11:: B G 15 feet: B C 10 feet. AB 20 plus B C 10 AC 30 feet. In the page of the Tables representing Height of Embankment 30 feet, under slope, 1½ to 1, and opposite a rise of 4. 5 per chain, we have the lesser width A E 62 links, and farther down, opposite a rise of 7 feet per chain, we have the greater side A F 81 links. 374 SETTING OUT SLOPES. 174 SPECIMEN OF FIELD BOOK FOR SETTING OUT SLOPES. DEPTH OF DISTANCE NATURE WIDTH RATIO RISE PER ON OF CUTTING OR HEIGHT OF |COMPUTED DEPTH OR WIDTHS CHAIN OF OF HEIGHT FOR TAKEN REMARKS. IN CROSS RAILWAY. WORKS. EMBANK- MENT. WAY. SLOPES. REFER- ENCE TO FROM THE SECTION. TABLES. TABLES. Miles. Fur. Ch. Feet. Feet. Feet. Feet. Links. Links. 11 2 5 Cutting 40 30 1½ to 1 Level 50 114 114 See case 1. 15 1 8 Cutting 40 28 2 to 1 4.5 47 165 125 See case 2. 19 0 6 Level 0 30 1 to 1 5. 15 24 24 See case 3. North 4.5 19 7 4 Embankment 20 30 1 to 1 South 7. } 62 30 See case 4. 81 SETTING OUT SLOPES. 375 SPECIMEN OF TABLES FOR SETTING OUT SLOPES. DEPTH OF CUTTING OR HEIGHT OF EMBANKMENT. 15 Feet. SLOPE 1 TO 1. SLOPE 1 TO 1. SLOPE 2 TO 1. RISE Required RISE Required RISE Required per Widths, per Widths, per Widths, Chain in Chain in Chain in in Feet. Links. in Feet. Links. in Feet. Links. Level 23 23 Level 34 34 Level. 45 45 .5 23 22 .5 34 34 .5 46 45 1. 23 22 1. 35 33 1. 47 44 1.5 23 22 1.5 35 33 1.5 47 43 2. 23 22 2. 35 32 2. 48 43 2.5 3. 3.5 4. 4.5 5. 33 FFFFF 23 22 24 24 21 24 21 24 21 24 21 5.5 25 21 6. 25 21 6.5 25 7. 25 7.5 26 8.5 8.5 20 20 26 26 9. 26 9.5 26 10. 27 10.5 27 12 22222 22222 22222 9 2.5 36 32 2.5 3. 36 32 3.5 37 31 4. 37 31 4. 4.5 38 31 5. 38 88889 30 að að + Hi Lő 3. 50 3.5 4.5 5. 5.5 39 30 5.5 6. 39 30 6. 20 6.5 40 29 6.5 20 7. 40 29 7. 20 7.5 41 29 7.5 20 8. 41 29 8. 20 20 ∞ oi 8.5 42 28 ထံထံ 8.5 9. 42 28 9. 20 9.5 43 28 9.5 20 10. 44 28 10. 19 10.5 44 27 10.5 11. 27 19 11. 45 27 11. 11.5 27 19 11.5 46 27 11.5 12. 28 19 12. 47 27 12. 12.5 28 19 12.5 47 26 12.5 73 13. 28 19 13. 48 26 13. 13.5 28 19 13.5 49 26 13.5 14. 29 19 14. 50 26 14. 14.5 29 19 14.5 51 25 14.5 81 15. 29 18 15. 51 25 15. 8PIIN ZEN88 AR*2* ***** ***** * 42 42 41 40 40 39 39 55 38 38 37 37 36 36 62 35 64 35 65 35 34 68 34 70 34 33 33 75 32 32 79 32 31 83 31 376 SETTING OUT SLOPES. SPECIMEN OF TABLES FOR SETTING OUT SLOPES. DEPTH OF CUTTING OR HEIGHT OF EMBANKMENT. 30 Feet. SLOPE 1 TO 1. SLOPE 1 TO 1. SLOPE 2 TO 1. RISE Required RISE Required RISE Required per Widths, per Widths, per Widths, Chain in Chain, in Chain in in Feet. Links. in Feet. Links. in Feet. Links. Level 45 45 Level 68 68 Level 91 91 .5 46 45 1. 46 45 292 .5 69 1. 1.5 46 44 1.5 2. 47 44 2.5 47 44 ai ci 2. 2.5 72 3. 47 43 3.5 48 43 4. 48 43 4. 4.5 49 42 5. 49 42 að að ti ti zö 3. 73 3.5 4.5 5. 5.5 49 42 5.5 6. 50 42 6. 6.5 50 41 6.5 7. 51 41 7. 81 7.5 51 41 7.5 8. 52 40 8. 88REN CERCE ERI* * 67 .5 92 89 69 66 1. 94 88 70 66 1.5 95 87 71 65 2. 97 85 64 2.5 98 84 64 3. 100 83 74 63 3.5 102 82 75 62 4. 103 81 76 62 4.5 105 77 61 5. 107 77 60 79 60 as or 5.5 109 6. 111 80 59 6.5 113 59 7. 115 ཟླུ། ཟུ་ྲཆ 80 79 77 76 75 82 58 7.5 117 74 83 57 8. 120 73 8.5 52 40 ∞ 8.5 84 57 8.5 122 72 9. 52 40 9. 85 56 9. 125 71 9.5 53 40 9.5 87 56 9.5 127 70 10. 53 39 10. 88 55 10. 130 70 | 10.5 54 39 10.5 89 11. 54 39 11. 90 11.5 55 39 11.5 92 12. 55 38 12. 93 12.5 56 38 12.5 95 388 55 10.5 133 69 54 11. 136 68 54 11.5 139 67 53 12. 143 67 53 12.5 146 66 13. 56 888 38 13. 96 52 13. 150 65 13.5 57 38 13.5 98 52 13.5 154 64 14. 57 37 14. 99 52 14. 158 64 14.5 58 37 14.5 101 51 14.5 162 63 15. 59 37 15. 103 51 15. 166 62 SETTING OUT 8LOPES. 377 SPECIMEN OF TABLES FOR SETTING OUT SLOPES. DEPTH OF CUTTING OR HEIGHT OF EMBANKMENT. 47 Feet. SLOPE 1 TO 1. SLOPE 11 TO 1. SLOPE 2 TO 1. RISE Required RISE Required RISE per Widths, per Widths, per Required Widths, Chain in Chain, in in Feet. Links. in Feet. Links. Chain, in Feet. in Links. Level 71 71 Level 107 107 Level 142 142 .5 72 70 .5 108 105 .5 145 140 1. 72 70 1.5 73 69 2. 73 69 2.5 74 68 Fricici 1. 109 104 1. 147 138 1.5 110 103 1.5 149 136 2. 111 102 2. 151 134 2.5 113 101 2.5 154 132 3. 74 68 3.5 75 67 4. 76 67 + 4.5 76 66 5. 77 66 að að ti ti zồ 3. 114 100 3.5 116 99 4. 117 98 4.5 119 97 5. 120 96 að að tí ti zô 3. 157 130 3.5 159 129 4. 162 127 4.5 165 125 5. 168 124 6. 7. 20 CÓ CÒN 5.5 77 66 5.5 122 95 5.5 171 122 78 65 6. 123 94 6. 174 120 6.5 79 65 6.5 125 93 6.5 177 119 7.5 80 888 79 64 7. 127 92 7. 180 117 64 7.5 128 91 7.5 184 116 8. 81 63 8. 130 90 8. 188 114 8.5 82 63 8.5 132 89 ∞ 8.5 192 113 9. 82 62 9. 134 88 9. 196 112 9.5 83 62 9.5 136 87 9.5 200 110 10. 84 62 10. 138 87 10. 204 109 10.5 84 61 10.5 140 86 10.5 209 108 11. 85 61 11. 142 85 11. 213 107 11.5 86 61 11.5 144 84 11.5 218 105 12. 87 60 12. 146 84 12. 223 104 12.5 88 60 12.5 149 83 12.5 229 103 13. 89 59 13. 151 82 13. 235 102 13.5 89 59 13.5 153 81 13.5 241 101 14. 90 59 14. 156 81 14. 247 100 14.5 91 58 14.5 159 80 14.5 254 99 ཟ 15. 92 58 15. 161 79 15. 261 98 2 A 378 SETTING OUT SLOPES. SPECIMEN OF TABLES FOR SETTING OUT SLOPES. DEPTH OF CUTTING OR HEIGHT OF EMBANKMENT. 50 Feet. SLOPE 1 TO 1. SLOPE 1 TO 1. SLOPE 2 TO 1. RISE Required RISE Required RISE Required per Widths, Chain, in per Chain, Widths, per Widths, in Feet. Links. in Feet. in Links. Chain, in in Feet. Links. Level 76 76 Level 114 114 Level 151 151 .5 1. 1.5 ai ai 2. 2.5 að að Hi Hi Lå zo 3. 3.5 80 4. 4.5 5. CEE02 2 77 78 73 71 82 5.5 82 6. 83 6.5 84 7. 85 7.5 85 8. ∞ ∞ó oi 86 8.5 87 9. 87 *** ***88 SEENN JJ7N22 75 5. 115 112 .5 154 149 74 1. 116 111 1. 156 147 74 1.5 117 109 1.5 159 145 2. 119 108 2. 161 143 2.5 120 107 2.5 164 141 72 72 70 að að ti ti 23 121 106 3.5 123 105 4. 124 104 4. 4.5 126 103 5. 128 102 70 5.5 129 101 69 6. 131 100 að að tí ti zö 20 có 3. 167 139 3.5 169 137 172 135 4.5 175 133 5. 178 131 5.5 182 130 6. 185 128 69 6.5 133 99 6.5 189 126 68 7. 135 98 7. 192 125 68 7.5 136 97 7.5 196 123 67 8. 138 96 8. 67 8.5 140 95 ထံထံ 200 122 8.5 204 120 67 9. 142 94 9. 208 119 9.5 88 66 9.5 144 93 9.5 212 117 10. 89 66 10. 146 92 10. 217 116 10.5 90 65 11. 91 65 11.5 92 12. 92 12.5 94 13. 94 13.5 95 14. 96 14.5 97 15. 98 PUTIH CINNN 10.5 149 91 10.5 222 115 11. 151 91 11. 227 114 64 11.5 153 90 11.5 232 112 64 12. 155 89 12. 238 111 64 12.5 158 88888 12.5 244 110 63 3. 161 87 13. 250 109 63 13.5 163 87 13.5 256 107 62 14. 166 86 14. 263 106 62 14.5 169 85 14.5 270 105 62 15. 172 84 15. 277 104 RELATIVE GRADIENTS, &c. 379 TABLES OF RELATIVE GRADIENTS AND CORRESPONDING ANGLE. 1 75 50 25 ANGLE. CHAIN. LINKS. LINKS. LINKS. Feet. Feet. Feet. Feet. Deg. Min. .5 .37 .25 .12 0 25 1. .75 .5 .25 0 51 1.5 1.12 .75 .37 1 16 2. 1.5 1. .5 1 42 2.5 1.87 1.25 .62 2 8 3. að að ti ti zồ 2.25 1.5 .75 2 33 3.5 4. 4.5 5. 2.62 1.75 .87 2 59 3. 2. 1. 3 24 3.37 2.25 1.12 3 50 3.75 2.5 1.25 4 16 5.5 4.12 2.75 1.37 4 41 6. 4.5 3. 1.5 5 7 6.5 4.87 3.25 1.62 5 32 7. 5.25 3.5 1.75 5 58 7.5 5.62 3.75 1.87 6 24 8. 6. 4. ∞ 8.5 6.37 4.25 ai ai 2. 6 49 2.12 7 15 9. 6.75 4.5 2.25 7 40 9.5 7.12 4.75 2.37 8 6 10. 7.5 5. 2.5 8 32 10.5 7.87 5.25 2.62 9 17 11. 8.25 5.5 2.75 9 23 11.5 8.62 5.75 2.87 9 48 12. 9. 6. 3. 10 14 12.5 9.37 6.25 3.12 10 40 13. 9.75 6.5 3.25 11 5 13.5 10.12 6.75 3.37 11 31 14. 10.5 7. 3.5 11 56 14.5 10.87 7.25 3.62 12 22 15. 11.25 7.5 3.75 12 48 380 RAILWAY SURVEYING. • The Table of relative Gradients is inserted for use in cases wherein the cross section rises too severely, although regularly to be taken at one operation with the level. It affords an opportu- nity of determining the inclination per chain by means of an incli- nation taken at a less distance and renders results so taken at once applicable to the general Tables. The corresponding angle affords an opportunity of determining the inclination of the cross section by means of an angular instrument, if such a method pleases the surveyor. We have now arrived at the stage for the preparation of the Land Plans. The several widths required for the formation of the railway, with a sufficient addition for the bank and ditch, are laid off on the large scale plan, and the several quantities of land required out of each field are computed. These quantities admit of checking by a very simple mode at any given length of line, when the widths have been calculated by my Tables, it being only necessary to mul- tiply the average width by the length. And again, my Tables of Land Measure will obviate this multiplication. Plate 10 is a Specimen Land Plan. The contents of railway cuttings and embankments are, in most cases, found by tables, calculated for the purpose. Mr. Baker has recently gone fully into the subject, and as the author of some Tables thereon, I extract his own statement in full. He says, numerous Tables exist for this purpose, some of which are voluminous; those by M'Neill, Bidder, Huntington, Hughes, Bashforth, Sibley and Rutherford, Law and Lowe, are well adapt- ed for the purpose, assuming the surface line of the cross sections to be level, or to be reduced to that position; but none of these tables will properly apply to sectional areas, which is the most important part of their use, excepting Bashforth's; but his method of using them is erroneous, the error approximating to 50 per cent as a maximum. I would therefore recommend for this purpose, the General Earthwork Table,* in conjunction with Two Auxiliary Tables, on the same sheet, in Baker's Engineering, as being applic- able to all varieties of ratio of slopes and widths of formation level in common use; and with the help of Barlow's Tables of Square Roots, these tables will apply to sectional areas, with all the mathematical accuracy that can be attained, with very little more calculation than adding the contents between every two cross sections, as given by the General Table.-The contents in the * The numbers for the side slopes, forming the alternate lines in Bidder's Table, will supply the place of the General Table. RAILWAY SURVEYING. 381 General Table are calculated to the nearest unit, as are also those in the Auxiliary Table, No. 2, which is for the decimals of feet in the depths. The Auxiliary Table, No. 1, shows the depths of the meeting of the side slopes below the formation level, with the number of cubic yards to be subtracted from the contents of the General Table for each chain in length, for eight of the most common varieties of ratio of slope. Note 1.-These Tables, with very little additional calculation, may be extended to every variety of formation level and ratio of slopes that can occur, and even to cases where that ratio differs in the two sides of the same cutting, as shall be shown in the fol- lowing Problems. Note 2.-The investigations of the method of forming these tables and using them are given in Baker's Railway Engineering, also further investigations are given, at the end of the following Problems, respecting Mr. Bashforth's Erroneous Methods of Cal- culating Earthwork. The following explanations will further illustrate the method of taking the dimensions of railway cuttings, preparatory to using the above named tables. Let ABDC cabd, fig. 173i, be a railway cutting, of which ABDC, abde are the cross sections, AB = ab = width of for- mation level, MM', mm' the middle depths of the two cross- sections; the side-slopes A C, B D, a c, bd, when prolonged two and two, will intersect at N and n, at which points the prolonga- tions of M M', m m' will also meet, thus constituting a prism ABN nab, the content of which is to be deducted from the whole content, given by the General Table, by means of the Table, No. 1; in which the depth M'N = m'n is also given, as already stated, to several varieties of slope and bottom width. To place this subject in a more practical point of view, let figure 173k represent a longitudinal and vertical section of a cutting, passing through the middle A E of the formation level. HI, the line of the rails, and a h, the line in which the slopes, if prolonged, would meet. It will be seen that the cutting AbcdE commences and runs out on the formation level A E, and that the depth A a= Be=Cf= &c. is to be added to the several depths Bb, Cc, Dd of the cutting, the first and last depth at A and E being each = 0; or, what amounts to the same thing, the several depths must be measured from the line ah: thus, A a, be, cg, &c. are the depths to be used. And since the depth A a is given in Table, No. 1, for all the most com- mon cases, or it may be readily found by calculation for all cases, 382 RAILWAY SURVEYING. as shall hereafter be shown, the line corresponding to ah must, therefore, be ruled on the railway section, at the proper distance below A E, from which the several depths must be measured; or the vertical scale may be marked with Indian ink (which may be readily rubbed off) at the same distance, and this mark may then be applied to the formation level A E, for the purpose of measur- ing the several depths.-In the case of an embankment, the line for the several depths must be placed at a like distance above the formation-level. PROB. I.—The several depths of a railway cutting to the meeting of the side slopes, its width of formation level, and the ratio of the slopes being given, to find the content of the cutting in cubic yards, from the Tables referred to, the distances of the depths being one chain each. Rule.-Take the several quantities, corresponding to every two succeeding depths of a cutting or embankment, measured to the meeting of the side slopes, at the distance of one chain each, from the General Table in Baker's Railway Engineering and multiply their sum by the ratio of the slopes; from the product subtract the cubic yards, corresponding to the given bottom width and ratio of slopes from Table, No. 1, multiplied by the whole length of the cutting, and the remainder will be the content of the cutting in cubic yards. But when the distances of the depths are greater or less than one chain, the quantities of the General Table must be multiplied by their respective distances.-And, when the distances are given in feet, the quantities must be multiplied by those distances, and the final result divided by 66 for the content in cubic yards, as in the following examples. Examples. 1. Let the depth of the railway cutting or embankment to the meeting of the side slopes, at the end of every chain, be as in the following table, the bottom width 30 feet, and the ratio of the slopes as 2 to 1; required the content in cubic yards. Dist. in chains. Depths Qnts. per in feet. G. Table. 0 10 1.00 33 1238 2.00 39 3175 3.00 35 3350 4.00 10 1365 Note.-In the annexed table the quantity For slope 1 to 1. 9128 1238, corresponds to the depths 10 and 33 feet in the General Table; the quantity 3175 to the depths 33 and 39, and so on for Subtract the succeeding depths. By the Auxiliary Table, No. 1, it will be seen, that the depth to be added below the formation level, for 275 X 4 Content in cubic yds. 2 2 to 1. 18256 } 1100 17156 RAILWAY SURVEYING. 383 the given width and ratio of slopes, is 7·50 = 73 feet, therefore, the cutting begins and ends with a depth of 10 — 71 7금 2 feet. The corresponding number of cubic yards, to be deducted for each chain in length, is multiplied by 4 chains, the whole length of the cutting, thus giving the whole quantity to be deducted, the re- mainder being the true content in cubic yards of the cutting. 2. The several depths of a railway cutting to the meet- ing of the side slopes are as in the annexed table, the bottom width being 30 feet, and the ratio of the slopes 1 to 1; required the content of the cutting. Note. When any of the distances between two suc- ceeding depths is greater or less than 1 chain, the corres- ponding quantity from the General Table must be mul- tiplied by that particular dis- tance; as the distances be- Dist. in chains. 1.00 Depths Products for Dist. Total in feet. greater than 1 chain. quantities. 10 0 10 16 420 2.00 20 795 4.00 25 1243 x 2 2486 5.00 32 1996 7.00 39 3091 x 2 X 6182 8.00 45 4319 10.00 50 5520 × 2 11040 12.00 40 4971 × 2 9942 13.00 30 3015 14.46 10 1059 × 1.46 1546 For side slopes 1 to 1 41741 to 1 20870 1 to 1 62611 366.67 x 14.46 5302 Content in cubic yards 57309 tween the depths 20 and 25, and between 32 and 39, &c. the dis- tances being 2 chains. The last distance, viz., that between 30 and 10, is 1·46; in this case 2 figures must be cut off for decimals, after multiplying. 3. Let the depths of a rail- feet. by length. way cutting to the meeting of Dist. in Depths Quantities multiplied the side slopes, and their dis- tances in feet be as in the an- nexed table, the bottom width 30 feet, and the ratio of the slopes 1 to 1; required the content in cubic yards. Note.-When the distances are in feet, the quantities from General Table must be respec- tively multiplied by their dis- tances, the quantity from Total quantities. 0 37 90 50 4660 × 90 419400 178 61 7554 88 X 664752 278 39 6210 × 100 621000 For slopes 1 to 1 1705152 • to 1 852576 14 to 1 2557728 366-67 × 278 101933 66) 2455795 Content in cubic yards 37209 Table, No. 1, by the whole distance, and the result divided by 66, the feet in 1 chain, for the content in cubic yards, as in the an- nexed operation. 384 RAILWAY SURVEYING. PROB. II. CASE I.—The areas of two cross sections of a railway cutting to the intersection of the side slopes, its length in chains, bottom width, and ratio of the slopes are given; required the content of the cutting in cubic yards. Rule.—With Rule. With the square roots of the given areas, as depths, find the content from the General Table, as in the last Problem, from which subtract the quantity answering to the given width, and the ratio of sides slopes from Table, No. 1, and the remainder, being multiplied by the length, will be the content required. Note.-If the length be given in feet, proceed as in Example 3, last Problem. Example. 1. Let the two sectional areas of a cutting be 4761 and 1296 square feet, the bottom width 36 feet, the length 3.25 chains, and the ratio of the side slopes 2 to 1: required the content in cubic yards. √ 4761 = 69 content per General Table . . 6959 For bottom with 36 and slopes 2 to 1 per ✓ 1296 = 36 } Table, No. 1 Content for 1 chain in length 396 6563 31 19689 1641 Content for 3.25 chains 21330 cubic yards. CASE II. To find the content when the depths are given in feet and decimals of feet. α Rule.-Let a and b be the feet in any two succeeding depths, and and their respective decimal parts; find the quantity an- В swering to a and b from General Table, as in the former cases: then, 2 a + ẞ, rejecting the last figure, and a will shew the number to be added in Auxiliary Table, No. 2, and 26+a, rejecting the last figure, and 6 will shew the number to be added in the same Table. After which deduct for the quantity below the formation level, as before. Example. Let the sectional areas be 1406 and 2560 square feet, the bottom width 36 feet, length 4 chains, and ratio of slopes 1 to 1; required the content in cubic yards. RAILWAY SURVEYING. 385 Here ✔ 1406 = 37·5 and ✓ 2540 50.4. Put 37 = a, 50 = b ·5 = a•4 •5 = ß; then the depths a and b, per General Table, give 2 a + b = 124, or 12, (by rejecting last figure) and ß = ·4, per Table, No. 2 give 2 b+ a = 137, or 14 nearly, (by rejecting last figure) and a 5 give For bottom width 36 and ratio of slopes 1 to 1 deduct Content for 1 chain in length 4660 39 57 4746 528 4218 4 16872 cubic yds. Content for 4 chains in length . 0 CASE III.-In measuring contract work where great accuracy is required, the ths, of a foot, or second decimals, must be used in the calculation, by taking for them th of their respective quantities in Table, No. 2. Example The areas of seven cross sections of a railway cutting to the meeting of the side slopes, and their distances are as in the annexed table; the bottom width is 30 feet, and the ratio of the slopes 11 to 1; required the cubic yards in the cutting. Dist. in Chains. Areas in 8q. feet. 0 2727 2.00 3136 6.00 4221 9.60 4100 14.00 5141 3759 2161 16.00 18.00 Ans. The content, per General Table, and Table, No. 2, is 172318 cubic yards from which the quantity corresponding to the given bottom width and ratio of slopes × by the whole length, viz. 275 x 18 = 4950 cubic yards, must be deducted, which leaves 167568 cubic yards, the content required. Note 1.-When the distances of the sectional areas are given in feet, the quantities of the General Table must be multiplied by their respective distances, and the final result divided by 66, as in Example 3. Prob. I. Note 2.-When the surface lines of the sectional areas are either level or are readily reducible to that position, the decimals, if any, in depths must be taken into the calculation, as in Cases II and III. PROB. III. To adapt the General Table to such widths of the formation level and ratios of slope as are not found in Table, No. 1. Put width of formation level, and r: 1 the ratio of slope. Then =feet to be added to the depth of cutting below ω r formation level. 386 RAILWAY SURVEYING. 22 w2 = cubic yards to be subtracted for each chain in And 9 r length. Example. = 10·4 ft. = distance Let the width of formation level be 26 feet, and the ratio of slopes 1 to 1; then r = 13 ÷ 14 w below formation level to meeting of slopes. And 22 × 13º ÷ 9 × 14 = 330.5 cubic yards to be deducted for each chain in length from the contents of the General Table. PROB. IV. To find the content of a cutting when each of the sides have two different ratios of slope. Rule.-When the cutting A B C D (fig. 1737) has two different slopes, as A a or B b and a C or b D; it must be divided into two parts by the line a b, and the quantities of the parts A B b a, a b D C of the cutting must be found separately by Prob. I. If the surface line C D be sloping or curved, Prob. II. will also be required; and, if the depths m'n' m N and their corresponding quantities of cubic yards are not found in Table, No. 1, they must be found by Prob. III, the sum of the contents of the two parts being the required content of the cutting. Note.-Cuttings of this kind are often advantageously adopted, where their upper parts are of loose or springy earth, and their lower parts strong clay or rocky. PROB. V. To find the content of a cutting when the ratio of the slopes of the two sides are different. CASE I.—When the surface is level. RULE.-Find the central depths to the meeting of each of the side slopes, and take their corresponding contents by Problem I for the whole length of the cutting, in the same manner as if it were for two cuttings, and, from the sum subtract the sum of the cubic yards corresponding to the given bottom width and ratios of slope multiplied by the whole length of the cutting, and half the difference will be the content required. CASE II.-When sectional areas are given. RULE.-Find the contents corresponding to the sectional areas to the meeting of the side slopes by Prob. II, and from their sum RAILWAY SURVEYING. 387 deduct W = 44 w² 7 W g(r+r') cubic yards for the content. In this formula bottom width, 7 = whole length of cutting, and r and r' the first terms of the ratios of the side slopes. Note.-Cuttings with slopes of this kind are frequently adopted in practice, where the ground is springy on one side of them, the greater ratio of slope being on the springy side. PROB. VI.-To find the quantity of the cutting of a tunnel. RULE.-Multiply continually together the width, mean height and length; divide the product by 9, if the length be given in yards, but if the length be given in chains, multiply the product by 22 and divide by 9, the width and height, in both cases, being given in feet. Note.-Examples are not given in the three last Problems, the methods of solving which being sufficiently obvious from the Rules and the first three Problems. THE FOLLOWING EXAMPLES SHOW THE ERRORS OF METHODS PUT FORTH BY MR. BASHFORTH AND OTHERS, TO FIND THE CONTENT OF CUTTINGS. Examples. 1. The areas of two cross sections of a cutting to the meeting of the intersection of the side slopes, are 1296 and 361 square feet, their distance one chain, the bottom width 36 feet, and the ratio of the slopes 1 to 1; required the content of the cutting by the true and the erroneous methods practically used. (1.) By the true method:- ✓ 1296 = 36 361 19 content by General Table 1907 Deduction from Table, No. 1. True content for 1 chain in length (2.) By Mr. Bashforth's method :— 792 1115 cubic yards. By Table, No. 1, the depth of the meeting of the side slopes below formation level is 18 feet; hence the area of the triangle below it is 36 × 9 = 324 square feet, which, being taken from the given sectional areas, will give 972 and 37 square feet for the areas used by Mr. Bashforth; whence, 388 RAILWAY SURVEYING. ✓ 976 = 31·18 ✓ 37 37 = 6.08) } content by General Table, &c., 975 cubic yards. This content taken from the true content, given above, leaves 140 error in defect. Whence 975: 140:: 100: 14:36, or above 141 per cent, the error in defect by Mr. Bashforth's method. 2. Let the areas of the two cross sections to the intersection of the slopes be 324 and 2916, and the other things as in the last ex- ample, required the content of the cutting by the correct and er roneous methods. (1.) By the true method. √ 219654 content by General Table . ✓ 324 = 18 Deduction from Table, No. 1. True content for 1 chain in length 3432 792 2640 cubic yds. (2.) By Mr. Bashforth's method :— Here the sectional arcs used are 2592 and 0, whence 2592 = 0 50.91 0 content by General Table 2112 nearly, which taken from the true content leaves 528 error in defect. Whence 2112: 528 :: 100: 25 per cent., the error in defect in this case. By taking a mean of the areas in Example 1. 22 (972 + 37) × 9 = 12233 cubic yards, which exceeds the true content 1183 cubic yards, being about 93 per cent. in excess. By taking a mean of the areas in example 2. 22 9 1 (2592 + 0) × = 3168 cubic content by 528 cubic yards, being 16 yards, which exceeds the true per cent. in excess. Note.-By taking a mean depth the error in defect is just half the preceding one, or 83 per cent. These methods only give a near approximation to the true content, when the sectional areas of a cutting are nearly equal. See the results of the following for- mula and remarks. The above examples show with sufficient clearness the inaccur- acy of Mr. Bashforth's method; but since it has been defended, as sufficiently correct for practical purposes, the following formula RAILWAY SURVEYING. 389 will more rigidly prove its failure. Let A' and B' be the sectional areas of a cutting, as used by Mr. Bashforth, and a the area be- tween the formation level and the meeting of the slopes; then by Baker's Railway Engineering, page 55, §1 (√ A' + a × B' + a ✓ A' B' A′ × B′ — a) = his error in defect, the content by his method being (A' + B' × √ A′ + B′), the length being unity; whence 81 100 (√ A' + a × B' + a−√ A′ × B′ A' + B' +√ A' × B' Mr. Bashforth's method. 81 a) = error per cent. by Examples. 1. When A' = a and B' = 9 a, the above formula gives 100 (✓ 3º × 10 −√ 3 × 9 1, a (3 × 9 + √ ‡ × 9,) a 10 1-2 1200 10/1/ 91 131 per cent. error in defect. 2. When A' = 0 and B' = 3 a, the above formula gives, 100 (2 — 0 — 1) 3 = 333 per cent. the error in defect. 3. When A' = 0 and B = a, the error in defect is 41 per cent. Errors of this kind will repeatedly occur in practice, where cut- tings and embankments are made, as in the following figure; wherein A B is the formation level, and the corresponding curved line is a section of the earth's surface; the small figures below being cross sections taken to the intersection of the slopes, in which M N, m n, represent the formation level, the sectional areas, used by Mr. Bashforth, being those above the lines M N, m n, the cross section cdmn may either be very small, as in Example 1, or 0, as in Examples 2 and 3; in which latter cases the surface c' d' of the section cuts m n. C N m B From the above figure it will at once be seen that more than one- 390 RAILWAY SURVEYING. half of the sectional parts of the cuttings and embankments will be affected by errors in defect of an average of the above-named per- centages, which are most decidedly prominent; and sufficient, in many cases that occur in practice, to take away more than the whole of a contractor's profits.-The error of Mr. Bashforth's method at- tains its maximum, which is 50 per cent., when both the sectional areas A' B' vanish, which, however, is a case that can never occur in practice. I have given Mr. Baker's comparisons at length, because he complains in his Rudimentary Treatise on Land and Engineering Surveying, that notwithstanding the errors he has proved to exist in the method given by Mr. Bashforth, for finding the contents of cuttings, that gentleman accuses him of copying. Now, had this been the case, Mr. Baker observes, he must also have copied the errors, that is, he ought to have adopted Mr. Bashforth's me- thod of finding the contents of cuttings, from sectional areas, where the surface of the ground is laterally sloping or curved, in which method the prism below the formation level is left out of the question, whereas Mr. Baker has included it in his calculations. Moreover, Mr. Baker asserts that his method was communicated to several gentlemen long before the publication of Mr. Bashforth's method, among whom was Professor Tate, of the Training Insti- tution, near Twickenham, who is a competent judge of such mat- ters, and who has himself published on the same subject in his Geometry. As for the General Table, Mr. Baker defends it by saying it is calculated from one of the same formulæ, used by Sir John McNiell, Mr. Bidder, and others, as the basis of their Tables, and must, therefore, be common property. Tunnelling is generally adopted on a railway when the cutting would require to be more than about 60 feet. It is desirable that the gradient in a tunnel should have a fall in one direction, for the purpose of allowing the water generated therein to be discharged by the natural force of gravitation. If the tunnel is very long, a fall may be given to the gradient from the centre towards either end. A tunnel on a curve requires to be very accurately set out, as well as levelled, or very great embarrassments may arise in its construction. The mining operations in a tunnel are directed by a miner's compass. The direct bearing of the line, if straight, or of the tan- gent of the curve, if in a curve, being taken at the top of a shaft, and laid out in the same direction at the bottom. Experience in the use of instruments is required in these operations, to detect any concealed attraction of the needle, or other instrumental errors that may so easily occur. It must be borne in mind, that the forma- RAILWAY SURVEYING. 391 tion line in a tunnel is much below an ordinary cutting, inas- much as there is generally an inverted arch to be turned beneath the ballasting, except indeed in those strata that are of themselves sufficient to maintain the shape of the tunnel. The following notes on the construction of tunnels, are extracted from Dempsey's Practical Railway Engineering. NOTE 1. Like mining and all other subterranean operations, the construction of a tunnel can be but little aided by mechanical appliances; it chiefly requires hard manual labour, exercised under circumstances which do not admit of that thorough superintendance which promotes economy, and, moreover, liable to un- foreseen interruptions, of surmounting which neither the manner nor the expense can be predetermined. Thus the Kilsby tunnel, on the North Western Railway, was estimated to cost £40 per yard lineal; whereas the actual cost was £130 per yard, owing to its intersecting a quicksand that had escaped the trial borings. Thus a vast expense was incurred in setting up and working pumping machinery to dry the sand. The Box tunnel on the Great Western Railway, excavated through oolite rock, and lined with masonry only through a portion of its length, cost up- wards of £100 per lineal yard. The length of this tunnel is 3123 yards, or upwards of 1 miles; it has eleven principal shafts, and four intermediate ones. The Blet- chingley and Saltwood tunnels, on the South Eastern Railway, cost respectively £72 and £118 per lineal yard, the greater cost of the latter work arising from the great body of water in the sand which it intersects.-The method of proceeding with tunnelling depends mainly upon the kind of material to be excavated. This having been generally ascertained by boring and trial shafts, which must be suffi- ciently capacious to admit readily of lowering men and materials, raising materials excavated, fixing pumps, and also for starting the head way of the intended tunnel when the required depth is reached. NOTE 2. The working shafts are made from 8 to 10 feet internal diameter. They are of brick work, usually 9 inches thick, and carried up 8 or 10 feet above the sur- face of the ground. These, and all other shafts, rest upon curbs of cast iron, fitted into the crown of the tunnel, and forming a level base for the shaft. The air shafts are of a smaller thickness and diameter, the latter of which is usually about 3 feet. -The number of working shafts will depend chiefly on the rate of speed with which the work is required to be accomplished. With plenty of men, horses, material, and plant, the work is much facilitated by sinking extra shafts, which will usually well repay their cost. NOTE 3. The Watford tunnel, 75 chains in length, on the North Western Railway, was worked with six shafts, about 8 feet internal diameter; the brick work was moulded to fit the circumference of the shafts, and laid in two half-brick rings. Air shafts were sunk at about 2 chains distance on each side of each working shaft. The arch and side of the tunnel were chiefly made two bricks thick, and the invert, one and a half brick, except where the stratum passed through seemed to suggest an increased or diminished thickness. The form of the top of the tunnel is nearly semi-circular, supported by curved side walls stand- ing on side footings, or skew backs, which rest on the invert. 392 RAILWAY SPECIFICATION. SPECIFICATION. SPECIFICATION to be observed by the Contractor for the works to be executed upon the railway, com- mencing at a peg numbered 1901 on the plans of the said railway, and terminating at a point where the said new railway forms a junction with the main line in the parish of being a distance of three miles and sixteen chains, or thereabouts. It includes the formation of the railway, with all the excavations and embankments complete; the drains, fences, gates, and other works connected therewith; and the erection of the following bridges, [here set forth fully a description of the bridges,] together with the formation and completion of the several approaches thereto, and roads over them. The building of the culverts, in the position shown in the plan and section, and of the dimensions there given, together with all the necessary diver- sions of the streams and drains to lead the water into and from the culverts; the laying and ballast- ing of the permanent way; the providing of all timber, bricks, lime, stone, or other materials ne- cessary for the completion of the works in a sound, substantial and workmanlike manner; the excava- tions of the occupation bridges, occupation roads, and diversions, marked upon the plan and section, and of all other works mentioned and described in the accompanying drawings and specifications, and the keeping of the whole of the works in a perfect state of repair for twelve months after completion. [Here must follow a full and minute description of all the drawings.] The preceding enumerated works, and the mode of execution are described at length in the specification of each particular work, and their forms and dimensions described in the ac- companying drawings, which are referred to in RAILWAY SPECIFICATION. 393 Written di- mensions to be taken. All minor parts to be inclnded, though not described. Contractor to nick out cavations and ments. - each specification; but should any discrepancies exist between the measurement by the scale attached, and the written dimensions, the latter are to be taken as correct, any thing contained in the drawings or specification shall be considered as contained in both. The written dimensions are those by which it is in- tended the contractor shall make his estimate. And wherever neither the drawings nor the specifica- tion contain any notice of minor parts, the intention to include which is nevertheless clearly to be inferred, and which parts are obviously necessary for the completion and stability of the work, all such additional parts are to be provided by the contractor, and are supposed to be included in the sum at which he contracts for the works, and wherever any thing is directed to be done, or to be pro- vided, if required, or words of similar import, it must be understood that every thing so referred to will be consi dered as included in the contractor's tender. The centre line of railway is staked out on the ground, slopes of ex but the contractor must at his own expense nick out the embank- slopes of the excavations and embankments, as also the exterior of the ditches previously to the commencement of any of the works, and provide the engineer with all necessary assistance in setting out and measuring off work during the continuance of this contract. Contractor to adhere to liament. The contractor will in all cases be required to strictly provisions of adhere to the provisions contained in the Act of Parlia- Act of Par-ment, for making this railway, as he will be held respon- sible for all claims which may be brought against the Company in consequence of any infringement of the stipu- lations therein contained. Trees that are felled on line to be barked. Fencing of two kinds. All trees that are in the line of the railway, and which require to be felled, must, if the season permit, be carefully barked, and the bark properly stacked. FENCING AND DITCHING. The fencing and ditching described in the following specification is of two kinds, the first, temporary, for the protection of lands adjoining the railway, during the pro- gress and until the completion of the works; the second the permanent for the enclosure of the railway when finished. 2 B 394 RAILWAY SPECIFICATION. Temporary Fencing. Slip Rails to afford con- venient ac- cess to lands. TEMPORARY FENCING. Immediately after the delivery of any portion of the site of the intended railway into the possession of the contractor, and previous to the commencement of the other works, the temporary fencing shall be completed, and shall include the whole area of land belonging to the company, as also all land occupied by any of the works Gates and contained in this contract; and gates and slip rails shall be placed to be so placed as to afford a convenient occupation of the adjacent lands, for the convenience of cartage of mate- rials, and a general passage along the line; openings shall be made in the cross fences and gates or slip rails erected for more effectual prevention of trespass, and the con- tractor shall be held liable for all damage done to the adjoining lands by cartage of materials, or by the stray- ing of horses, cattle, or other beasts that may happen by his neglect, or by that of his agents or workmen, in not maintaining the fences or gates, or otherwise; and the contractor shall, without delay, when required, make good any fence, or gate, or railway, that may have been destroyed or injured, from whatever cause, and shall pre- serve the most effectual security to the cattle grazing in the land adjoining, in neglect of which the engineer shall have full power to pay all claims for trespass to the pro- per parties, and to deduct the same from the account due to the contractor at the next or any subsequent payment. Temporary fencing de- scribed. Permanent fencing. Ditch. The temporary fencing shall consist of split oak posts placed nine feet apart, and three and a half feet high above the ground, morticed for the reception of three horizontal oak or larch rails, which are to be supported by an intermediate stay or prick post, firmly nailed to each of the rails. PERMANENT FENCING. Drawing, No. 16. The permanent fencing will consist of post and rail fencing, ditches and quicksets, and must be placed within the limits of the slip of land allowed for this purpose, beyond the termination of the slopes. A ditch of three feet wide at the top and one foot wide at the bottom, and twelve inches deep, shall be made RAILWAY SPECIFICATION. 395 Company's property. Drains. Mound or Cop. Quicks, Posts. upon the higher side of the ground occupied by the rail- way, and a ditch three feet wide at the top, one foot wide at the bottom, and one foot six inches deep on the lower side of the ground. These dimensions shall be increased or diminished, as in the opinion of the engineer the circumstances may require, so as to produce an effectual drainage and keep the water out of the excavations, and carry it away from the foot of the embankments, and where necessary, the existing drains and ditches must be deepened to obtain a sufficient fall. The outer slopes of the ditch must, in all cases, cor- respond with the boundary of the company's property. All drains, or alterations, or deviations in existing drains, or water courses necessary for the exclusion of the water from the cuttings, or for the prevention of drainage to the adjoining property, or any other property whatsoever, shall be made by the contractor at his own expense. The material excavated from the ditch shall be used to form a mound on the space between the edge of the ditch and the railway slope, and the side adjoining the ditch shall be neatly ramparted with turf sods, which shall not exceed four inches in thickness, to be ten inches wide, and eighteen inches long. When the material excavated from the ditch shall be more in quantity than sufficient to form the mound, the surplus must be conveyed to the nearest embankment. The best portion of the vegetable soil excavated from the ditch shall be placed in the middle of the mound, on which a row of three years old good quicksets shall be planted, and not less than nine quicksets shall be con- tained in one lineal yard; on the inner edge of the ditch, oak posts and rails must be set to protect the quicksets. The posts are to be of split oak or good larch, six feet six inches in length, and equal to at least five inches by three and a half in sectional area; they are to be placed at a distance of nine feet, from centre to centre, and to stand four feet above the surface of the land. Each post is to have three mortices for the reception of the ends of the rails, which are to be made of split oak or larch, and to be as straight and nearly of an uniform size as possible. 396 RAILWAY SPECIFICATION. Rails. Prick Posts. Hoops. Fencing to be made with ings as pos- sible. The horizontal rails, three in number, between each pair of posts, are to be of oak or larch, not less than four inches in sectional area at the small end, and ten feet in length, and the ends are to be scarfed so as to fill the mortices of the posts. Midway between the posts an oak or larch stay five feet six inches long, and two and a half inches square, being driven into the ground, at least eighteen inches is to be firmly nailed to each of the three horizontal rails with good tenpenny nails. The posts must be firmly fixed, by being set in the ground without being sharpened, the ends of the rails properly fitted into the mortices of the posts, and a piece of new iron hoop one inch and a quarter wide, and one sixteenth of an inch in thickness, shall be nailed round the top of every post to prevent its splitting. The fencing shall be made with as few bendings as the as few bend- nature of the ground will permit of, and the ditch along- side the mound shall descend as uniformly as possible to the nearest main drain, or watercourse, by which the draining of the adjacent land is at present effected. Draining tiles through mound. Fencing to be kept in order. Quicks to be cleaned, and The permanent fencing shall proceed as rapidly as the progress of the works and the nature of the season will admit of. At the bottom of the embankments small draining tiles shall be laid through the quick mounds at intervals of not more than ten yards, to convey the water draining from the slopes into the fence ditches. Such parts of the permanent fencing as shall have been completed, before the finishing of the other parts of the work, shall be kept in complete order by the contractor. The quicksets shall be cleaned or weeded twice at least broken rails in a year, and any broken rails, or posts, or stays replaced by new ones, equal in quality to those originally used. replaced. Dead quicks to be pulled up. Cross fences to be joined up. All quicksets which may not take root and grow must be pulled up, and three years old living quicksets planted in their stead. The railway fencing must be effectually joined to the cross fences by posts, rails, and quicks, and the mound for the cross fence must be carried over the ditch of the railway by means of a short culvert, of a sufficient size to preserve a free and uninterrupted water-way along the railway ditch. RAILWAY SPECIFICATION. 397 Fencing to be substantial. Temporary fences dis- in particular cases. The whole of the fencing, both temporary and perma- nent, must be firmly and substantially fixed, so as to exclude sheep, pigs, and all other cattle from the excava- tions and other works, and effectually prevent the adjoin- ing lands from trespass during the progress of the works. Should the contractor be prepared to erect the per- pensed with manent fencing on any part of his contract, previous to any interference with the existing fences of the fields, he will be permitted to do so, in which case the temporary fencing may be dispensed with altogether, on that parti- cular part of his contract. Temporary fencing may be used in Such part of the temporary fencing as can be made available shall be permitted to be used in the permanent nent fencing. fencing, provided the material be of the requisite strength and quality, and uninjured in other respects by its previ- the perma- Fence wall- ing described. Gate Posts, &c. ous use. When stone walls are made use. of for permanent fencing they are to be built of good sound red sandstone rock, in block, and course work set in lime of the form and dimensions shown in Drawing, No. The stones to be firmly bedded and break joint properly. The The gates and posts, &c., are represented in Drawing No. The heads and heels are to be made of sound oak or ash morticed to receive the horizontal bars, which together with the diagonal stays and uprights may be of memel timber, sawn or dressed, or of oak, ash, or larch; the hanging and clapping posts must be of oak or stone, if of oak the lower ends are to be charred. iron work to be of the best quality, neatly fitted up and riveted to the woodwork; the diagonal and upright pieces are likewise to be riveted to the horizontal bars. The whole of the wood to be well seasoned and of sound quality, and to be put together and fixed in a workman- like manner, and to receive two coats of good oil paint. The contract includes gates, with their posts, covered drains, &c., complete, and comprises about lineal yards of single post, rails, and quickset fencing. If stone gate posts are used the dimensions must not be less than nine feet in length, with a sectional area of 1½ square feet or fifteen inches square. 398 RAILWAY SPECIFICATION. Width of slopes. Slopes to be dressed sown. and Slopes to be altered if engineer. EXCAVATIONS AND EMBANKMENTS. The excavations and embankments throughout this con- tract shall be thirty feet wide at the level of the red line, on the section, neither more nor less, and shall extend at that level to an equal distance on each side of the outside rails when they are finished and laid in their proper line as hereinafter described under the head of permanent way. The excavations are to be made with the slopes marked upon the section, where it is stated" 13 to 1," it is under- stood that where the base of the slope is one foot and a half, the height shall be one foot only, and when "2 to 1,” that for the base of the slope two feet, the height shall be one foot only. As the cuttings and embankments advance and the latter become consolidated, the slopes shall be carefully dressed or trimmed to the specified inclinations, and as near to the face of the work as possible, and covered with turf or soil, which shall be carefully obtained from the surface of the ground to be occupied by the railway. The soil must be uniformly laid on of the thickness of six inches, and sown with rye grass and clover seeds, as soon as the proper season will admit of its being done; and not less than one pound and a half of rye grass and one pound and a half of clover seed to be sown on each acre. When the engineer shall require it, the slopes must be neatly faced with the turf, not less than eight inches in thickness, and laid with the green sward outwards. In the formation of the excavations and embankments, in this contract, the contractor shall not remove the turf or soil from the ground for a greater distance than half a statute chain in advance of the face of the excavation or embankment, and that which has been cut must be re- moved back to a point where the slope is ready for receiv- ing it, and laid down as directed with as little delay as possible. Should the contractor be required by the engineer to required by alter the rate of the inclination of the slopes, he shall do so, and a proportionate addition or reduction (as the case may be) shall be made to or from the contract sum, at the average price per cubic yard stated in the schedule. Borings. Shafts have been sunk and borings made on the line in RAILWAY SPECIFICATION. 399 Contractor to find all mate- gons, bar- rows, &c. various situations with the view of ascertaining the nature of the material. The contractor may see the account, but must satisfy himself of its accuracy, as no allowance will be made should the material differ from that account. Their situations are marked in the general section. In the formation of the excavations and embankments, rials, as wag- the contractor must provide all necessary rails, chairs, keys, pins, blocks, and sleepers, as well as waggons, barrows, planks, and other machinery, materials or utensils, which stipulation is however modified to a certain extent by the following conditions. Delivery of permanent It is not intended to deliver to the contractor any of the rails, &c. &c. permanent rails, chairs, keys, or pins, until, at least, one continuous mile of railway, together with three hundred yards in continuation of each extremity of such mile, shall have been completed and certified by the engineer as being ready for the reception of the permanent ballasting, as in this contract is hereinafter mentioned: on which certifi- cate, a sufficient number of rails, chairs, keys and pins, shall be delivered to the contractor by the company, and he shall be permitted to use them in such manner only as is hereinafter described in the specification of the laying and ballasting of the permanent way. Provided, however, that such permanent rails shall, in no case whatever, be laid down and employed within three hundred yards of the face of any excavation, or at the end of any embankment then in progress. Surplus ma- terial to be Spoil Banks. The surplus material beyond that required for the for- deposited in mation of embankments, approach roads, and other em- banking, is to be deposited in spoil banks, in such places immediately contiguous to the line of railway as the en- gineer may direct, the company giving the contractor temporary possession of the land; the foot of the slopes of the spoil bank in no case being placed nearer than five yards to the top of the slope of the railway excavation ; the height of the spoil bank shall in no place exceed fifteen feet above the natural surface of the ground. The sides of the spoil banks are to be sloped at the rate of six hori- zontal to one perpendicular. Previous to laying out any spoil bank, the contractor shall give to the engineer notice in writing, together with 400 RAILWAY SPECIFICATION. Soil to be re- moved and laid upon Spoil Banks, and the slopes of cut- bankments. a plan, describing the quantity and situation of the land he requires for that purpose. If so directed by the engineer, the contractor must con- vey the material to any greater or less distance, according to which, if the cost be thereby increased, he is to receive a greater or less price as specified in the schedule. The whole of the soil upon the surface of the ground through which any excavation extends, or over which there is any embankment or spoil bank, is to be removed, tings and em- and afterwards laid upon the slopes of the cuttings and em- bankments and the surface of the spoil banks, so as to leave the spoil banks in a state fit for agricultural purposes, and the slopes of the cuttings and embankments in a state fit for the growth of grass, or shrubs, either on the line of rail- way, or on the side of diverted roads or bridge approaches, or in any situation. The thickness of soil and sodding over the whole surface and slopes of the spoil banks must be not less than twelve inches, nor less than eight inches on the slopes of the embankments, and the contractor is to sow the slopes of the embankments and the spoil banks with grass or any other seed which the engineer may direct. The period at which the soil is laid on and the seed sown is to be determined by the engineer. Slips in Ex- cavations. All slips which may take place in the excavations, and which are not attributable to the improper mode in which the contractor may have conducted the work, are to be removed by him at the price stated in his schedule: such as are attributable, in the opinion of the engineer, to any improper mode of conducting the work, are to be removed at his own expense, and will be considered as included in the tender. Embank ments. EMBANKMENTS. The embankments are to be made with the slopes stated upon the section, to which the foregoing explana- tions under the head of excavations will apply. The embankments are to be formed of the materials obtained from the excavations, and when finished and con- solidated they are to be of the height represented by the red line on the longitudinal section, and of the width Width and shown on the cross section, viz., thirty feet, being made of such extra height and width in the first instance, as to Height. RAILWAY SPECIFICATION. 401 Embank- ments to be kept dry. Deficiency of material to allow for the subsidence of the embankment and they are to be made at the full height and width at once in a single battery. The surface of the embankment at the height of the red line is to be made slightly convex. Every part of the embankment must be kept dry, and no water must be allowed to remain either at the base or upon the surface. Should there be a deficiency of materials in the adjoin- be supplied. ing cutting to make up any of the embankments, the con- tractor must make up the deficiency, either by side cutting near the spot, or by increasing the width or slopes of the adjoining cuttings, uniformly, throughout their entire length, as the engineer may determine. The company will provide the contractor with land for this purpose, in such a situation as the engineer may approve, the contractor bringing the surface of the ground to an uni- form slope of 6 to 1, and covering it with a layer of sods and soil not less than twelve inches in thickness. Pitching sides. Slips in Em- bankments, Earth to be trimmed to slopes and widths at In the schedule a price must be named for paving or pitching the sides of the embankment with red sandstone, nine inches thick, the price per cubic yard for the em- bankments remaining the same. In case of slips taking place in the embankments, the contractor will be required to make them up at his own cost. Whenever the material teemed over the end of the em- bankment shall not form the proper slope, it shall be care- once, and no fully trimmed to its required slope, and this operation made after- must proceed at the same time with the end of the em- bankment, so as to obviate the necessity of any further addition of material to the sides of the embankments. additions wards. Large lumps to be broken. When the material brought to the embankment consists of large lumps, they shall be broken into pieces of not more than six inches in diameter, unless they consist of rock. A cross section of an embankment is shown in Drawing, No. DISPOSAL OF MATERIAL. Throughout the whole of this contract, the material from the excavations is to form the next adjoining em- bankment as well as the approaches to the bridges, and 402 RAILWAY SPECIFICATION. Bricks. No broken bricks al- lowed. Grouting. Brick on edge. Stone to be of hard sound quality. paved crossings of every description, and whenever and wherever any excavation shall not be sufficient in quan- tity to complete the next adjoining embankment and approaches to bridges, or sloped roads, the quantity so deficient must be brought from the nearest excavation which shall have a surplus or otherwise obtained by side cutting at the contractor's own cost, and according to the conditions contained under the head of general stipu- lations hereinafter given. BRIDGES, CULVERTS, &C. General Stipulations Which are to apply to the whole of the bridges, cul- verts, and other works, wherein the workmanship or ma- terials here described may be used excepting to such work as may be directed otherwise. BRICKWORK. The Bricks made use of thoughout the work shall be hard, sound, well shapen, thoroughly burnt and of uni- form size and those used in the face of the work shall be of uniform colour and unless made a year before they are used, every brick shall be well saturated with water before being set. No broken bricks will be permitted to be used either externally or internally unless absolutely necessary as closers, except in case of backing when no course shall contain a greater number of bats than whole bricks. No difference of workmanship will be allowed in the inside and outside work, every course shall be well grouted, the whole of the joints shall be flushed up solid with mortar, and the outside joints to be neatly pointed and drawn. No joint of mortar shall exceed one quarter of an inch in thickness, and the work shall be laid in English or Flemish bond, as the engineer may direct. In all cases where brick on edge is used as coping, the bricks are to be laid as headers in Roman cement. STONE. All the stone used for bridges, culverts, or other masonry throughout the contract, shall be of a sound and hard quality, and approved by the engineer and free from spots and flaws of every description. RAILWAY SPECIFICATION. 403 Beds to be dressed. Cramps to be used if di- rected. Block in course work. ASHLAR WORK. The Ashlar work shall be laid in courses at least nine inches in thickness, all the beds and joints being chisel dressed throughout. The whole to be square jointed and made to fit close. The courses to be laid in such propor- tion that there shall be at least one header to every stretcher. No stone shall be less in area of bed than five feet, nor shall the width of any stone be less than one and a half times its thickness, and all the joints to overlap at the least twelve inches. The greatest care will be required to have all the beds dressed to accurate planes, and no pinning of any kind will be permitted in any part of the work, the faces shall be fair tooled or left rough with rustic champhered joints as may be directed in the description of each particular work. The beds of the stones in all arches consisting of ashlar shall be carefully dressed to fit the summering of the arch. The whole to be laid in mortar and grouted at every course. When the engineer shall deem it necessary the work shall be cramped together with iron cramps run with lead; but in this case, the contractor shall be paid extra for the iron work according to the schedule of prices. BLOCK IN COURSE WORK. The block in course shall consist of stones in courses at least six inches in the thickness and as nearly of an uniform thickness as practicable. No stone shall be less on the bed than ten inches by fourteen inches, and where rubble or brickwork backing is employed there shall be a through at every six feet in each course so as to bond the whole effectually together. The face beds and ends of each stone shall be carefully hammer dressed to accurate planes, and no pinning of any kind will be allowed. In all cases where block in course work with rubble backing is employed, the area in any cross section of the work shall contain as much block in course as rubble. The whole of the block in course work shall be neatly pointed. 404 RAILWAY SPECIFICATION. Rubble Stones not of a foot. RUBBLE. The rubble shall be constructed of stones, each con- less than 1-6 taining not less than one-sixth of a cubic foot, to be care- fully laid so as to make the closest possible work; when employed as backing, each stone to be bedded in mortar when laid, and the upper surface of the work brought to an uniform level at the height of every course of the face work, and the whole to be well grouted at this level. Squared up at 18 inches. A good bond with Ashlar When the rubble is not used for backing to the block in course work, the whole may be brought to a level at every eighteen inches in height and then grouted. In all cases great care must be taken to make close work and effect a good bond with the face, whether it be block Brickwork. in course work, ashlar, or brickwork. and Mortar of Welsh Lime and Sand. dry state. MORTAR. The mortar shall consist of fresh burnt Welsh lime, or other lime approved of by the engineer, and clean sharp sand in the proportion of two measures of sand to one of unslacked lime. Mixed in a They shall be intimately mixed in a dry state, and well tempered with a proper quantity of water, and only mixed as required for use; the mortar that has previously set or become hard upon the ground shall not be permitted to be used in any part of the work. Water Lime. Roman Cement. Gravel to 1 of Lime. If in any situation water lime is ordered to be used, the contractor shall do so without any extra charge; and where the engineer shall deem it necessary, the mortar shall be tempered in a pug mill. ROMAN CEMENT. The Roman cement is to be of the best quality, and shall be mixed with an equal quantity of clean sharp sand. None shall be used which has set or become hard. CONCRETE. Concrete 6 of All concrete must be composed of gravel perfectly clean and mixed with fresh well burnt quick lime, in the pro- portion of six parts of gravel to one of lime. The proportions are to be accurately guaged and mixed in the dry state, it is then to be moistened and well beaten RAILWAY SPECIFICATION. 405 To be Levelled at every 18 inches Arches to be laid with Mallet. Ashlar Quoins. Any imper- removed. until a thorough admixture of all the parts is effected and brought to a tough consistency, when it is immediately to be filled into barrows and teemed from a height never less than eight feet, as near as may be to the place required, so as to need as little levelling as possible, the runs being shifted for that purpose. It is to be brought up in layers not exceeding eighteen inches in thickness, each layer to be completed and brought to a level surface before another layer is commenced; the lime to be fresh burnt, well mixed, and carefully preserved from moisture until actually used. ARCHES AND COUNTERFORTS. The arches, when of brick, shall be laid carefully with a mallet, and built either in concentric half-brick rings, or in such other manner as the engineer may direct; and where counterforts are built upon any part of the arch, they shall be worked into the body of the arch, and their courses shall run in the direction of the radii of the said arch. In all cases where ashlar stone quoins are used in the face of the arch, the greatest care will be required to pre- vent an unequal settlement. Great care must be taken in the proper summering of fections to be the bricks or stones in each course, and any irregularity of form created by imperfections in the laggings, work- manship, centring, or any other cause, shall be removed and amended by the contractor. Askew Bridges, laid in spiral When the arches are askew, the contractor shall lay the courses to be courses in spiral lines, at right angles to the face, when- lines. ever he shall be so directed by the engineer; and the beds of the stones forming the arches shall be carefully dressed to the proper twist; also, in all elliptical brick arches, six feet in width measured on each side of the crown shall be laid in Roman cement. Soffits Pointed. The soffits of all the brick arches shall be well and neatly pointed. BACKING TO ARCHES. The Backing shall consist of rubble work, laid in mortar, as before described. 406 RAILWAY SPECIFICATION. Abutments of Brick or Stone as drawings de- scribe. Bricks in Spandrills to be dressed. Openings to be left in wings. Parapet. Imposts. Skewbacks. String Courses and Coping. ABUTMENTS, WINGS, AND SPANDRILS. The abutments, wings, and spandrils will consist either of brickwork or stonework laid in mortar, as before de- scribed, and they will be built battering or plumb, as shown on the drawings. The bricks in the spandrils must be neatly cut, or the stone work neatly dressed, so as to fit the extrados of the arch; where the work is battering on the face, the courses shall be laid at right angles to the batter. Small openings shall be left in the lower parts of the abutments and wing walls for the effective drainage of water which might otherwise lodge behind them. PARAPET WALLS. The parapets to be built plumb on each of the sides, the straight part to be perfectly true, and the curvature of that portion upon the wing walls uniform and regular. The courses to be made parallel to the string course and coping. STONE IMPOSTS. Where stone impost or springing courses are used, the stone shall always be equal to the full thickness of the arch, and no stone shall be less than two feet six inches in length, and when required they shall be dowelled and cramped together. In cases of skew arches, the skewbacks must be worked so as to suit the oblique directions of the springing of the courses, and in every course the stones shall be fair tooled all over, excepting at the back which may be left rough. STRING COURSES AND COPING. These must be of the form and dimensions shown upon the drawings. No stone must be less than two feet six inches in length, and the whole to be throated under- neath. Each stone in the coping must be dowelled and leaded to the adjoining one. All the surface must be fair tooled or chisel dressed, and the joints made square and to fit close. RAILWAY SPECIFICATION. 407 Cast Iron from Cupola. IRONWORK. Wherever cast iron is required to be used, it shall be cast from the cupola, and be of the toughest grey iron, free from air bubbles or pin holes, or any other defect. All the abutting faces must be filed and accurately fitted. All wrought iron work to be of the best hammered scrap iron. Iron Work to All iron work to be subjected to whatever test the engi- be tested. neer may think it expedient to prescribe, and any defect which may be detected, is to be rectified at the expense of the contractor, and likewise the cost of testing defrayed by him; but the contractor is not exempted by the above provision from the obligation to uphold the work when erected. Wood to be Kyanized. Drains under Bridges. Wall 9 inches WOODWORK. All woodwork in gates, sleepers, &c., and all other wood- work to be subjected to Kyan's patent process, to be of sound memel timber or American pitch pine, free from knots and other imperfections, and to be well seasoned before subjected to Kyan's process, to receive three coats of good oil paint. All bolt holes to be well charged with thick white paint. All arrisses to be champhered. DRAINS UNDER Bridges. Drains must be constructed under all the bridges which are in the excavations on each side of the railway, fifteen inches wide at the top, and twelve inches at the bottom, to be sunk as low as the drain at the outside of the bal- lasting. They will be formed by a wall of brick or of block in course stone work to support the ballasting, nine inches deep and three feet deep parallel with the abutments, and the length will be equal to the width of the bridge, and as much more as shall be necessary to conduct the water easily in the common side drains. The whole to be laid in mortar in the same manner as described for the bridges. 408 RAILWAY SPECIFICATION. Contractor to excavate EXCAVATONS OF FOUNDATION, PROVIDING CENTRING, FILLING IN OVER BRIDGES, AND OTHER GENERAL REGULATIONS. The contractor is to excavate for the foundations of all foundation of bridges, culverts, and all other works, to keep out the Bridges. water by coffer dams, if necessary; form drains, do all necessary pumping, and provide all centring, planks, and tools of every description necessary to the perfect execu- tion of the works at his own expense, and they are to be included in the amount of this tender. If founda- tions carried price as per Schedule. In case the foundation of any of the works require in lower, extra the opinion of the engineer to be carried lower than is shown upon the drawing, the contractor is to make such extra excavations, provide extra coffer dams, and to do all extra pumping or other contingent works incident thereto, being paid only for the increased quantity of brickwork or masonry, concrete, or other material according to the prices set forth in the schedule for such description of work. Foundations. puddled over. The foundations must be cut out as nearly to the size of the brickwork or masonry as possible, and the vacant spaces must be carefully punned up to the surface of the ground. Arches to be The arches of all bridges are to be carefully puddled over their entire surface with a layer of puddle not less than nine inches in thickness; and the space between the wing walls of all the bridges shall be filled in with hard dry material well rammed down where it can be obtained, but when it is necessary to use clay for that purpose, it shall be firmly punned in layers of not more than nine inches in thickness. Bridges to be balanced. Stays if ne- cessary to be used. In bringing an embankment up to a bridge the con- tractor shall load the bridge equally on both sides, by wheel- ing the material from the embankment or elsewhere, or by teeming from off the bridge so as to allow of its laying against the abutment, with a slope outward from it, and punning it as previously described, so as to ensure its per- fect form and safety. He shall also take such additional precaution as the en- gineer may consider necessary, by setting up temporary or permanent stays or shores without making any extra charge. RAILWAY SPECIFICATION. 409 Water from Bridges to be through In all bridges where there is more than one arch, the carried spandrills shall be completely drained by means of iron Abutments. pipes, or the openings cased with brick, in cement, through the centre of the piers and abutments. Piers and String course and parapet on till di. The string course, parapet walls, and coping shall not not to be put be put on until after the centres are withdrawn; and in no case shall the centring be struck before permission of the engineer is obtained. rected. Centring. Rails to be laid equi-dis- tant from side walls. Embanked Approaches. Surplus ma- terial to be approaches to All the centring shall be such as shall be approved of by the engineer. Great care must be taken that each bridge is so placed that the outside rails, when laid in their uniform and pro- per line, are equidistant from, and parallel with, the faces of the abutments or parapet walls, according as the bridge is over or under the railway. It is to be understood, that whenever in the drawings, or in any part of the particular specification, the dimen- sion of parts, or the nature of materials, may be directed differently from the above general stipulations, the parti- cular directions are to be complied with. APPROACHES TO BRIDGES AND PAVED Crossings. Drawings, No.-. These excavations and embankments are to be made in the same manner as before described for the main line of railway, and with such slopes as may be directed by the engineer. The contents of the excavation shall be conveyed to the nearest embankment or spoil bank. The embankments are to be made from the surplus ma- terial in the excavation. When no surplus exists, then the material shall be pro- cured from side cutting in the nearest excavation, and the contractor to be paid for it at the rate specified in the sche- dule of prices attached to his tender. But wherever there is a surplus material, the contractor used to form shall employ it to form approaches to bridges or sloped Bridges, &c. roads, and the cost of so employing it shall be considered a part of his contract, to which the stipulations and prices for extra work do not apply. Excavated approaches. The same regulations shall be applicable (where side cutting is required) to the excavation of these approaches. 2 C 410 RAILWAY SPECIFICATION. Approaches to be of height All the approaches shall be made of the height, depth, in the Draw- and inclination shewn upon the section of the approaches to each bridge. ings. Metalling. Length. The metalling shall in all cases be the width of the bridge between the abutments and parapet walls, as the case may be, and the width of the cutting or embank- ment shall be five feet more than this at the level of the top of the metalling. The length shall be equal to the whole distance of the altered surface as shown in the section of approaches. Slopes 11 to 1 All the slopes of both excavation and embankment of bridge approaches being made at the rate of 18 inches horizontal to 1 foot in height. Embank- ment to be beaten. 2 Coatings of Broken Stones. Ruts to be filled up. To be fenced. Rails to be painted. Two Lines of Posts and Rails. The surface of the embankment when formed, shall be made regular and even, and well beaten with heavy beaters. First, a cover of brushwood or heath, and then a coating of good gravel or broken stone must be laid over the whole surface eight inches in thickness, and as soon as it shall have become hard by the carriages passing over it, another covering of material, of equal quality with that upon the road at present, shall be laid on seven inches thick in the middle, and four inches thick on each side. The ruts must be filled up from time to time, and the surface kept smooth and even. The whole of the approaches which are embanked from either termination of the earthwork to the parapet walls of the bridges must be protected on both sides by wood posts and rails, as shown in Drawing, No. -. The wood railing must be made of good oak, free from sap, and straight grained. The rails, and so much of the posts as are shown above the ground, shall be sawn out square, neatly planed, and painted with two coats of stone-coloured paint; all the joints must be made with white lead, and all the wood beneath the surface of the ground well charred. Those approaches where the line of road and not the level is altered, and also those that are formed by exca- vating, must be protected on each side and throughout the whole of the extent of the alteration by quickset fencing and ditching, similar to that described for the railway, but having an additional line of posts and rails, namely, one on each side of the quicksets. RAILWAY SPECIFICATION. 411 Temporary Roads to be fenced during alterations to public Roads. Previous to the works connected with any bridges, provided and approaches to bridges, approaches to paved crossings, or diversions of roads, which may in any way affect existing roads, being commenced, a good and well-made tempo- rary road shall be provided and maintained for the free and uninterrupted passage of carriages of every descrip- tion. Every precaution shall be taken by the contractor during the alteration of any road to erect proper fencing, and fix and maintain lights for the protection of travellers, as the company will not be held responsible for any injury which may arise from the neglect of these precautions. The whole of these observations shall be considered to apply, unless in any particular case they may be directed otherwise. Paving Stones. Rails to be protected by Iron Bars. PAVED CROSSINGS. Drawing, No. —. All the roads crossing the railway without bridges, are to be paved at the intersection with the railway, in the same manner as shown in Drawing, No. with good six-inch paving stones of Penmaen Mawr, Dublin, or other granite equally good. The paving must be laid on a bed of fine clean gravel of six inches in thickness, in a solid and substantial manner. The paving stones must be cubes as near as possible. Each rail must be protected by two iron bars, as shewn in Drawing, No.-; they will be considered part of the rails, and provided by the company. The present con- tract is to comprise six of these, and any additional number that may be required shall be executed at a price to be named in the schedule. Culverts. CULVERTS. Drawing, No. The culverts throughout this contract are to be built in the situations marked upon the general section, of the form and dimensions shown in Drawing, No.-. The size being selected to suit the particular situation. 412 RAILWAY SPECIFICATION. Directions of Drain to be altered. Soft Ground to be taken out. Cover of dry material to Culverts. Wherever the direction or position of the culvert does not correspond with that of the stream, either in line or level, the stream shall be altered so that the water may be conducted to or from each end of the culverts in the manner best fitted for facilitating the drainage. Where the foundations are insecure, the soft ground is to be taken out, and the space filled in with solid dry material, such as the engineer shall approve of, without any extra charge. All culverts exceeding three feet diameter, shall be be laid over covered with dry or hard material two feet above the top, and ten feet on each side; and the part adjoining the cul- vert, extending to a distance of four feet from the brick- work or masonry, to be well punned in layers of one foot in thickness, before the embankment shall be allowed to come upon it. Culverts to extend under Fences. Alterations in Roads. Soil to be taken off. Metalling. Where no Fencing or quired. Culverts, under three feet in diameter, are to extend in length under the fence of the railway; each culvert must be built in a direction which may, in the opinion of the engineer, afford a free and uninterrupted passage for the water. The general stipulations for masonry and brickwork, hereinbefore given, are applicable to these culverts. DIVERSION OF ROADS. The alteration necessary to be made in the direction of the existing roads for this contract, exclusive of those which are required in approaching bridges, are shown upon the general plan (Drawing, No. —). Where the level of the new roadway is near the sur- face, the top soil must be removed from the space to be occupied by the road, and the surface made uniform and regular for receiving the metalling. The material and manner of laying it on to be the same as described for the approaches to bridges, the thickness being twelve inches when a public road, and eight inches when an occupation road. In cases where, in the opinion of the engineer, no me- Metalling re-talling or fencing is required, a deduction will be made of the cost of such metalling or fencing, according to the schedule of prices. Excavations or Embank- ments. Any excavation or embankment that may be necessary, RAILWAY SPECIFICATION. 413 Fencing. Planes. Curves. Laying and Ballasting. shall be done by the contractor in the same manner as directed for similar works upon the line of the railway. The fencing shall be similar to that described for the railway, but having an additional line of posts and railing, viz., one on each side of the quicksets. BALLASTING AND LAYING THE PERMAnent Way. The railway is intended to form a double way, composed of four single lines of rails. The several level and inclined planes are shown by the blue line on the Section Drawing, No. —, which repre- sents the surface of the rails, and the directions on the general plan, (Drawing, No. —). The greatest care will be required that the portions shown upon the plan as straight be made strictly so upon the ground, and that the curves are all uniform and neatly brought into the straight lines. The laying and ballasting the permanent way is in- tended to be completed in such portions and at such times as will suit the convenience of the contractor in executing the works. Previous to the delivery of the materials of the perma- nent way to the contractor, the surface of the embank- ments and bottoms of the excavations shall have been made of the proper line, height, and depth, and uniform Embank- in width, level, and inclination. They shall be completely Excavations drained from all water, and certified by the engineer as &c. being in a fit state to receive the permanent ballasting. Materials. The materials to be delivered to the contractor will con- ments and to be drained, Delivery of Materials. Lengths. sist of sleepers or blocks, rails, chairs, and fastenings; and he will be held responsible for the replacement in case of loss or injury to the materials thus delivered to him from the time of their delivery till the expiration of this contract. They will be delivered by the company at some conve- nient wharf, whence they must be conveyed by the con- tractor to the works at his own expense. The company will provide the necessary sleepers, a particular description of which is hereinafter given. The rails will be in lengths from 12 to 18 feet; they will be supported at every yard by a cast-iron chair or pedestal, which will be accompanied by wrought-iron keys for fixing 414 RAILWAY SPECIFICATION. Broken Stone Bal- last. Inches thick. Top Layer of Broken Stone. Ballast to be beaten. Bed of Sleep- ers to be beaten, If too low to be raised. Rails to be laid level. the rails on the chair, and with two pins or spikes for fixing the chair on the sleeper. The dimensions of each part, and the construction of the whole, are shown on Drawing, No.-. The material for ballasting shall be composed of broken stone, cinders, or clean gravel, entirely free from any ad- mixture of clay or material retentive of moisture; if broken stone be used, none shall be larger than will pass through a ring two inches in diameter. The ballasting shall be spread over the whole surface of the tops of the embankments or bottoms of the excavations between the drains, of an uniform thickness of twelve inches. And as soon as the sleepers have been carefully laid, the intervals between them, and between the outer ends and the edge of the embankment, or the drain at the bottom of the cuttings, are to be filled in to the level of the top of the sleeper with broken stones, equal in quality to those in the bottom bed, and to a height of two and a half inches below the surface of the rail, and the interstices to be filled in with smaller stones, they being beaten down to render the entire width a consolidated mass. This stratum of ballast shall be beaten into a firm and solid mass by heavy beaters, worked by at least two men; and the thickness before mentioned shall be considered to ap- ply only after this operation has been effectually performed. Upon this surface the sleepers are to be laid in their proper situations for receiving the rails. The ballasting intended for the bed of the sleepers shall be beaten by heavy beaters, and each sleeper also forcibly beaten when it has been placed in its position until it has become firmly and uniformly bedded throughout its whole length and reached its proper level. If it should be found lower than required, it shall be re- moved, and additional material to be placed in its bed; the same process as before must then be renewed until it has reached its proper level. The rails must be laid at the proper level and inclina- tion, and at the proper bevil to fit the cone of the wheels, to be perfectly parallel, and at the same height at any one point; the joints must be made perfectly even, whether square, half-lapped, or scarfed, and be firmly secured in the chairs. RAILWAY SPECIFICATION. 415 feet apart. Lines to be 6 The two lines of way are to be six feet apart, and the width between the insides of the rails of each way four feet eight inches and a half. Sleepers to be chaired, Rails to be straightened. Contractor may use Excavations, casion defi- The wood sleepers must be cut on the upper surface to the proper level for the reception of the chair, which must be firmly fixed on the exact guage, to be furnished by the engineer. The pins shall not on any account be driven into the sleepers without the hole having been previously bored with a proper sized auger. The rails must be securely fixed in each chair by keys; the chair shall be firmly fixed on the sleeper. Any of the rails which may be twisted or bent in the least degree, to be made perfectly straight with proper hammers and anvils, previous to their being laid down. The contractor may use any rock, gravel, or other Gravel out of suitable material for ballasting which may occur in any of but not oc- the excavations included in this contract; but if in so doing ciency. he shall cause any deficiency in the material for the for- mation of the embankments, he shall make up the deficiency by a side cutting in such of the excavations as the engineer may point out, and at his own expense. Stone taken from Cut- tings not to occasion de- ficiency. No material to be taken from Em. bankments. Tile drains. To be laid without mor- tar part in water lime. The contractor is also at liberty to obtain stone for bridges, culverts, drains, or other masonry, provided it is of a quality approved by the engineer; but if in so doing he shall cause any deficiency in the material for the forma- tion of the embankments, he shall make up the deficiency by a side cutting, at his own expense, in such of the exca- vations as the engineer may point out; and if such side cutting shall require an additional quantity of land, the contractor shall indemnify the company for the purchase of the same. The contractor shall in no case remove any material from the intended sites of any of the embankments unless permitted by the engineer. Tile drains, throughout all the excavations, are to be laid in the ballasting, as shown in Drawing, No.-; one shall be laid in the centre of the ballasting throughout the whole extent of the excavation, and shall have cross drains at intervals of every five yards, communicating with the drains on either side alternately; they must be properly and securely laid, without mortar, excepting 18 inches in length at the open ends, which shall be laid with water lime. 416 RAILWAY SPECIFICATION. Receipt for Rails. Contractor may make Sidings. Limit to weight car- porary wag- gons. The contractor shall give the assistant engineer a receipt stating the number of rails or other materials in each par- cel delivered to him and placed in his possession; he shall be accountable for the loss of any part of them; he shall also replace any rails, chairs, pins, blocks, trenails, or sleepers which may have been broken, or otherwise ren- dered unfit for use while in his possession, or during the progress of the works. The contractor shall be at liberty to make sidings or crossings from one line of the permanent road to the other, for his own convenience during the progress of the work, provided he does not injure the rails in so doing, and re- moves them when the works are complete. No waggons, carriages, or engines employed by the con- ried on tem- tractor on the permanent road, shall have a greater weight placed on any one axle than three tons, unless the engine or carriages are placed on good and sufficient springs; and when they are so mounted, the weight on any one axle shall not exceed four tons. Permanent way to be Such portions of the permanent road as are used by the maintained. contractor in conveyance of material from the excavations (according to the stipulations already described under that head,) or for any other purpose, shall be carefully attended to, and kept well drained, and in good repair, and ad- justment. No Sleeper to be used if injured. Sleeper to be No sleeper which has been used in any temporary road during the progress of the work shall be made use of in the permanent road, unless such shall have been inspected and pronounced sufficient by the engineer. WOODEN SLEEPERS. The sleepers to be of larch, oak, pitchpine, or teak. Larch sleepers to be cut from sound trees, slowly grown; 9 feet long. each sleeper to be nine feet long by 10 inches wide and five inches thick, at the centre of the smaller end, being a pole of larch ten inches in diameter (exclusive of bark,) at the smaller end, and nine feet long, sawn up the middle. Oak, Larch, or Teak. When sleepers are cut from oak trees not larger than those above specified for larch, they shall be sound, and of the same dimensions and thickness, but these dimensions are only to include half an inch of sap. When the sleepers are made from large timber, whether RAILWAY SPECIFICATION. 417 To be Kyanized. Sidings to be as drawn and directed. Rails to be Cut. Contractor to find Bal- last. Time of Completion. Measure- ments. Contractor to be present on works. Contractor oak, pitchpine, or teak, they shall be sound, free from sap or decay, and not shaken, to be squared up to the dimen- sions of nine inches by four and a half inches at the smallest part and nine feet long. All the wooden sleepers above described are to be subjected to Kyan's Patent Process. LAYING AND BALLASTING THE PERMANENT SIDINGS. The sidings are to be laid in such positions and in such lengths as may be directed by the engineer; they must be laid in the manner and form shown in the Drawing. The contractor will be required to take up any part of the rails already laid down that may be found necessary to cut them into their proper lengths for the reception of the other iron work, to relay them, and fix all the necessary crossing plates, check rails, moveable points, or sliding rails, with the requisite machinery for moving them. The whole must be made equally as firm and substantial as the other parts of the permanent way. The specifica- tion of the permanent ballasting, already described, must be considered applicable in all respects to the construction and ballasting of the sidings. The iron rails, chairs, keys, pins, points, crossings, switches, check rails, moveable points, or siding rails, and sleepers, being found by the company. TIME OF COMPLETION, MEASUREMENTS, PAYMENTS, &c. The contractor shall, on or before the complete the whole of the works herein specified, and such additional works as the engineer may direct to be executed, so as to render the line of railway along the whole distance in every respect fit for the safe and conve- nient transit of locomotive engines and other carriages. All measurements of works shall be according to the actual dimensions, notwithstanding any general or local custom to the contrary. The contractor shall at all times be present on the works, or in his absence he shall provide a competent representa- tive, fully authorized to act in his behalf in all matters re- lating to this contract. The contractor shall at all times, by day and by night, 418 RAILWAY SPECIFICATION. and materials and to proceed as Engineer directs. to find labour provide and use, at his own cost, all overlookers, labour, and materials of every description whatever that may be required for proceeding with and completing the works in a workmanlike manner, and shall proceed therein at the rate of progress that may be from time to time required by the engineer. Descriptions and stipu- lations, It is to be understood, that though certain descriptions and stipulations are not repeated or implied in different repeated, to parts of this specification, and in the contract to be entered though not be under- stood. Contractor to furnish every two months. be made. into for the fulfilment of the same, it shall not be thence inferred that the remaining directions, descriptions, and stipulations, of which there shall be no repetition or ampli- fication, are in anywise invalidated. The contractor shall at intervals of every two months statements furnish to the engineer a statement of all contract work done by him during that period; the value of which work shall be estimated according to the schedule of prices at- tached to the contract, and the amount of such account, Payments to after being certified by the engineer, shall be paid to the contractor after deducting 10 per cent. off the amount; one half of such deducted sum for the preceding six months shall, at the discretion of the company, be paid over to the contractor at the termination of every interval of six months, if the contractor is proceeding with the works to the satisfaction of the engineer, and he shall certify to that effect, and the remaining half shall remain in the hands of the company during the progress and till the completion of the works, and for twelve months after their completion, when the amount, together with interest at the rate of 4 per cent., calculated from the period of completing the work, shall be paid to the contractor upon the certifi- cate of the engineer of the whole of the work being in a satisfactory and proper state. Advances to the Con- tractor. Contractor to furnish previous to advances In intervals between the periods of payments above- named, viz., every two months, the company will, if re- quired, advance to the contractor payments on account of work and materials; the amount of such payments being dependent upon the certificate of the engineer. The contractor shall furnish to the engineer a statement statements of work done, and in respect of which he requires inter- mediate advances; but the certificate of the engineer shall only be for such amount as he may think proper to certify. And should the engineer be at any time dissatisfied with being made. RAILWAY SPECIFICATION. 419 do not proceed satisfactorily, If the works the nature or mode of proceeding in or at the rate of pro- gress of the work, or any part thereof, he shall have full Engineer has power to procure and make use of all labour and materials procure any which he may deem necessary, deducting the cost of such assistance he labour and materials from the money that may be due or power to labour or may deem necessary, and charge cost to Contractor. Alterations in additions tions from, any of the works. become due to the contractor. But it is hereby expressly declared, that the possession of this power by the engineer shall not in any degree relieve the contractor of his obli- gation to proceed in the execution of, and to complete the works with the required expedition. Should the con- tractor fail to proceed with the works in the manner and at the rate of progress required by the engineer, this con- tract shall be (at the option of the company but not other- wise) considered void, so far as relates to the work remain- ing to be done; and all sums of money that may be due to the contractor, together with the materials and implements in his possession, and all sums of money named as penalties for the non-fulfilment of the contract, shall be forfeited to the company, and the amount shall be considered as ascer- tained damages for breach of contract. It is to be distinctly understood that the engineer may to, or deduc- at all times direct that there shall be made any alterations in, additions to, or deductions from, any of the works hereinbefore described or referred to; and which alter- ations in, additions to, or deductions from, the amount of work contracted for, shall be valued or estimated according to the schedule of prices, filled up by the contractor, and at- tached to his tender, and that the prices inserted in the schedule shall be considered including all labourage, mate- rials, and all contingent expenses connected with the work to which such prices apply, and the contractor is required to fill up the whole of the schedule, whether the same appears applicable to the present contract or not. 420 RAILWAY TENDER. of I FORM OF TENDER. do hereby propose to make and complete the railway, with all the excavations, em- bankments, bridges, culverts, drains, fences, and other works con- nected therewith, including the laying and ballasting the permanent way throughout the entire length, from to being a and to keep the same distance of in repair for one year after completion, and to find and provide all the requisite materials (except the iron rails, sleepers, chairs, and fastenings) according to the plans and specifications, and within the periods, and upon the terms and conditions mentioned and contained in the draft contract, exhibited to me, for the sum of And I have in the SCHEDULE hereto annexed, set forth the price of the different descriptions of work at which the aggregate amount of this tender is computed, and according to which the value of all additions to, or deductions from, the work specified, is to be estimated; and hereby undertake to execute a contract accord- ing to the draft before referred to within a fortnight from this date. And I propose and of of as sureties day of for the due performance of such contract. WITNESS my hand this SCHEDULE referred to, containing a list of the prices at which the foregoing tender of is computed, and according to which the value of all additions to, or deductions from, the work specified, is to be estimated. Average price of earthwork deposited in embank- ments, per cubic yard Earthwork deposited in embankments when the length of lead does not exceed one quarter of a mile, at per cubic yard Not exceeding half a mile £ s. d. at per cubic yard Not exceeding three-quarters of a mile do. Not exceeding one mile. do. Not exceeding one mile and a quarter do. Not exceeding one mile and a half do. Not exceeding one mile and three-quarters do. Not exceeding two miles do. For every additional quarter of a mile do. RAILWAY TENDER. 421 Average price of earthwork in spoil banks per cub. yd. Earthwork in spoil bank excavated to the depth of 10 ft. below the surface of the ground, at per cubic yard Earthwork for every succeeding 10 ft. in depth, at per cubic yard Earthwork barrowed a distance not exceeding 25 yards, at per cubic yard Ditto for every additional 25 yards, ditto Soiling and sodding embankments, &c., including sowing with hay seeds, per sup. yard Soiling and sodding cuttings, per do. Dry pitching with sand stone, 9 in. thick, per do Ashlar stone in foundations and in bond courses, pick dressed, and set in mortar, at per cubic yard Ashlar stone in walls from quarry, per cub. foot £ s. d. Tool dressed and set Hammer dressed and laid in mortar. in mortar. Do. Do. Do. Do. Do. وو وو وو وو do. do. do. do. do. Block in course stone work from quarry, per cub. yard Do. Do. Do. Do. Do. Do. وو from وو وو دو وو do. do. do. do. do. do. Coursed rubble backing with mortar, per cubic yard Random rubble backing Do. do. do. laid dry Well-burnt hard bricks, per thousand do. do. Brickwork of do. set in mortar, at per cubic yard Brickwork of blue Staffordshire or Bulkley mountain bricks, at per cubic yard Extra price of masonry in askew arches, at do. Extra price of setting masonry or brickwork in Ro- man cement, at do. Do. of setting masonry or brickwork in water lime, at do. Concrete (6 of gravel to 1 of lime) with common lime, at do. 422 RAILWAY TENDER. Concrete with water lime, at per cubic yard Puddle of clay, well tempered, at do. • Do. laid in 9 in. courses, and well punned, at do. Common rubble walls for feuces, including coping set in mortar, per Drawing, No.-, at per sup. yard • Larch sleepers, Kyanized, at per sleeper Do. do. chaired and laid, at do. Oak sleepers do., at do. Do. do. chaired and laid, at do. Common draining tiles laid in drains, at per thousand Bulkley mountain drain tiles, at do. Post and rail fencing, including ditch and quicksets, at per lineal yard A field gate, with posts, &c., complete Larch posts for fencing, 6 ft. 6 in. long, at per post Oak posts Larch rails do. do. do. do. 10 ft. 6 in. long, at per rail Post and rail fence for approaches to bridges, as per Drawing, per lineal yard, single fence Laying and ballasting permanent way, including tile or brick drain, per lineal yard Laying permanent way, exclusive of ballast and drains, per lineal yard Ballasting only, per cubic yard Furnace slags, broken or spread, per ton Common cinders, do. do. A paved crossing, complete, (see Fig.—, Drawing, No.—). Leading rails, and other materials, including loading and unloading, at per ton per mile Pitch pine timber in balks, or large scantlings, de- livered, at per cubic foot American red pine, do. Do. yellow pine, do. Baltic or Memel do. Subjecting timber to Kyan's patent process, do. Cast-iron in girders or heavy work, fit and fixed, at per ton Do. in columns or piles, Do. small and ornamental, do. do. do. do. Wrought-iron, upwards of 7lbs. in a piece, such as plates, bolts, &c., fit and fixed, at per cwt. £ 8. d. RAILWAY TENDER. 423 Wrought-iron, less than 7 lbs., and more highly finished, fit and fixed, at per cwt. Paving roads or streets with Welsh boulders, 6 inches thick, per sup. yard Ditto square sets, do. do. Metalling roads with hard stone, broken and spread, at per cubic yard An occupation bridge over the railway Do. do. Culverts of 6 ft. diam. without fronts, per cub. yd. £ s. d. According to general Drawing. under Do. 5 do. do. do. Do. 4 do. do. do. Do. 3 do. do. do. Do. 2 do. do. do. Do. 1-6 do. do. do. Culvert fronts do. The price of sheet piling of Dantzic or Memel tim- ber from 4 to 8 inches in thickness, shod with iron, hooped, and driven to any depth not exceeding 15 feet, and the tops cut off level and bolted to the walling, at per cubic foot Do. driven to a greater depth than 15 feet, but not exceeding 20 feet, at per cubic foot Do. 25 feet, at per do. The price of memel or beech sleepers (" Waling tim- ber") bolted to the pile heads, complete, at do. The price of larch, beech, or memel bearing piles, from 10 to 16 inches diameter, hooped, shod, and driven, with their tops cut off and levelled, ready to receive the planking- For any length not exceeding 15 ft., at per cubic foot Do. Do. 20 ft., 25 ft., do. do. The price of memel or beech planking, 2 to 4 inches thick, spiked to the pile heads, and prepared for the masonry, at per cubic foot The price of maintaining or keeping in good order the double line of permanent way and fences for the period of one year after the completion of the whole works, at per mile N.B. It is to be understood that only the exact quantity or net measurement of any material or work is to be taken in all cases, notwithstanding any custom to the contrary. 424 COLONIAL SURVEYING. CHAPTER XIII. COLONIAL SURVEYING. THE first operations required in a perfectly new settlement, are, the division of the land upon which settlers are to be located into sections of such size as may be considered best adapted to their wants,—and the marking out the plan of the first town or towns, the sizes and positions of which will of course be regulated by local circumstances and advantages; whilst the first rural sections will naturally be required either in their immediate vicinity, or conti- guous to the main lines of communication leading to the different portions of the province, whose local importance is the earliest developed. In the case of a small settlement established upon the coast of any country for the immediate reception of settlers who require to be put in possession, directly upon their arrival, of a certain stipu- lated amount of land for agricultural or other purposes, the simplest form of survey must necessarily be adopted; that de- scribed in Capt. Dawson's Report upon the Survey of New Zealand for instance,-which consists simply in marking methodi- cally upon the ground the angles of a continued series of square or rectangular figures, leaving even the roads which are intended to surround each block of sections, to be laid off at some future period,―would answer the purpose of putting impatient emigrants in possession of a homestead containing about the number of acres to which they might be entitled. But this system could not be carried out extensively with any degree of accuracy, even in a comparatively level country, and not at all in a mountainous or irregular one. In fact, it is not a survey; and though perhaps it may sometimes be necessary to adopt what Mr. F. Wakefield, in his recently-published pamphlet upon Colonial Surveying, terms this "make-shift process," the sooner a regular survey takes its place the better for the colony, even on the score of the ultimate saving that would be effected by getting rid of the necessity of incessant alterations and corrections; to say. nothing of the amount * For an explanation of the details of this species of surveying, see Mr. Kingston's Statements, page 33, Third Report of the South Australian Commissioners, 1838; and Captain Dawson's Report on the Survey of New Zealand, 1840. COLONIAL SURVEYING. 425 of litigation laid up in store by persevering in a system necessarily entailing an incorrect division of property, upon which there is no check during the progress of the survey, and for which there is no remedy afterwards. Excepting in some isolated instances such as described above, where every thing is required to give way to the imperative necessity of at once locating the first settlers upon land for which payment has been received, (for, by the present system of colo- nization, no land is alienated from the Crown otherwise than by purchase, the greater portion of the proceeds of the sale being devoted to the purpose of further emigration,) the first step to be undertaken at the commencement of the survey of a new country, is a careful and laborious exploration within the limits over which its operations are to extend; during which would be collected for subsequent use a vast amount of practical information as to the number and physical condition of the aboriginal natives (if any); the geological character of the soil; its resources of all kinds; sources and directions of rivers; inland lakes and springs; the pro- bable sites of secondary towns; the most apparent, practicable, and necessary main lines of communication; prominent sites for trigo- nometrical stations, &c., &c. A sketch of the country examined, rough and inaccurate doubtless, but still sufficient for future guidance, is at the same time obtained; the positions of many of the most important points for reference being determined by astro- nomical observation, and the altitudes of some of them by the mountain-barometer or aneroid. The next step should be, if this question has not been already determined by strongly-marked local advantages, or previous settlement, the position of the site of the first principal township; a nucleus being immediately required where fresh arrivals may be concentrated, prior to their dispersion over the country. The size* and figure of the town will of course vary according to circum- stances; and the principal general requirements that should suggest themselves to any one charged with a decision of this nature, are,— facilities of drainage; plentiful supply of good water; easy access both to the interior of the country, and, if not situated on the coast, to the adjacent port; the apparent salubrity of the site; facility of procuring timber and other building materials, such as sand, lime, * The size of the lots into which the township is to be divided may vary from a quarter of an acre to one acre; half an acre would be found generally sufficient. It is customary to give to the first purchasers of rural sections one town lot in addition for every such section, the remaining lots to be sold either by auction, or at some fixed price. 2 D 426 COLONIAL SURVEYING. brick-earth, stone, &c.; security from predatory attacks, and vici- nity to sufficient tracts of land suited to agricultural and pastoral purposes. The site of the town, with its figure and extent, being decided upon after a careful investigation of the above and a variety of other minor considerations, the best main lines of road diverging from it in all the palpably-required directions should be marked out; and upon these main lines should abut the sections to be first laid out for selection. Errors of judgment will doubtless be sub- sequently found to have been made in the directions of some of these roads; but this is certainly productive of less injury to the colony than the plan of systematically marking out the land without providing for any main lines of communication at all, leaving them to be afterwards forced through private property under the authority of separate acts of the colonial legislature; a system entailing discontent, litigation, delay, and expense. The marked natural features of the ground, such as the lines of the coast, or the banks of lakes or rivers of sufficient importance to constitute the division of property, and the main lines of roads alluded to, will, where practicable, guide the disposition of the lines forming the boundaries of the sections to be now marked out. Where no such natural or artificial frontages exist, the best directions in which these rectangular figures can be laid out are perhaps those of the cardinal lines, excepting in cases where the nature, inclination, and general form of the ground evidently point out the advantage of a deviation from this rule. The size of these sections is a question to be determined by that of the minimum average number of acres which it is supposed is best adapted to the means and wants of the settler; the latter being in a great measure regulated by the apparent capabilities of the soil. Land divided into very large farms is placed beyond the reach of settlers of moderate capital; and if subdivided into very small portions, the expense of the survey is enormously increased, and labourers are tempted to become at once proprietors of land, very much to their own real disadvantage, as well as that of the colony. In South Australia, 80 acres has been adopted as the average content. In parts of New Zealand and elsewhere, 100 acres. In Canada†, generally more than double that quantity. * In the Canterbury Settlement, on the Middle Island, New Zealand, 50 acres has been fixed as the minimum size; the maximum is unlimited. As in South Australia, no reservation is made of coal and other minerals, the purchaser being put in possession of all that is on and under the surface. †The rude and inaccurate mode in which land has been marked out in Canada by COLONIAL SURVEYING. 427 Whatever size may be determined upon, it is advisable to adhere to it as nearly as possible, in all general cases; though, where special application is made for rather larger blocks, there has been found no mischief in departing from the average size, provided this devia- tion is not so extreme as to prevent fair competition for any pecu- liarly valuable locality. In such cases, it is however always necessary to guard particularly against the monopoly of surface water within the area of the section, or of any extended valuable frontage; as well as against any impediment that might be placed in the way of forming roads through the property. Where the main lines of communication have not been previously laid out, it is requisite, especially in large blocks of land, to reserve to the government, at all events for a limited number of years, a right of forming such roads as are evidently for the public benefit, making of course compensation for any damage that may be thereby done, though this can generally be met by a previous allowance of a cer- tain number of acres in excess of the proper content of the block*. Indeed, if proper precautions could be taken to prevent its being abused, it would be advisable to reserve this power of making such general roads as are clearly advantageous to the community, through all sections of land of whatever size; with the right of taking stone and timber for making and repairing these roads and the bridges erected along their line; though all such interference with private rights should as much as possible be obviated by previous careful examination of the country. The rapid settlement of a newly-formed colony being an object always to be fostered, the sections marked out for sale should be so arranged as to conduce as much as possible to this desideratum; to attain which end, the surveys should, at all events at first, be kept well in advance of the demand for land, for the purpose of giving the most ample choice of selection to intended purchasers. By the opposite system of selling land in advance of the survey, an unfor- tunate emigrant not unfrequently finds the greater part of his sec- tion occupied by the bed of a salt lagoon or swamp, and experiences no slight dismay in discovering that he is not even in possession of the number of acres for which he has paid, and to which perhaps he has no access with any sort of wheeled vehicle, in consequence of the occupation roads being marked down upon the ground the chain and compass, and the little value that has been set upon waste land which used to be alienated from the Crown in grants of extensive size, render the survey of that country not a fair point of comparison with that of more modern colonies. * Two or three per cent. upon the average, is proved amply sufficient in small or moderate-sized sections. In very large blocks, one per cent. would perhaps be as much as could be required. 428 COLONIAL SURVEYING. to correspond with straight lines previously drawn upon paper; so that they lead, without any controlling power in the surveyor to alter their course, up and down almost inaccessible ravines, or probably for several hundred yards at a stretch along the bed of a stream. In marking out these sections, the following remarks* will direct attention to the different local peculiarities which require a deviation from established rules, and to the general system of con- ducting the work in the field; the mechanical practice of surveying being of course supposed to be already known. Sections laid out with frontages upon main lines of road,— rivers, or wherever increased value is thereby conferred upon the land, should have their frontage reduced to one-half, or even one- third of the depth of the section, so as to distribute this advantage among as many as can participate in it, without rendering the dif- ferent sections too elongated in figure to be advantageously cul- tivated as a farm. In addition to this contraction of frontage, easy access by roads must be provided from the country in the rear leading to this water, or main road; without which precaution the owners of the front lots would, by blocking up the land behind them, virtually obtain possession of it, for at least pastoral purposes, without pay- ment. These roads should occur at intervals proportioned to their requirement, generally between every third or fourth section. Every section should have an available road on one of the four sides forming its boundaries, by which the proprietor has access to the main lines of communication; its breadth may vary from half a chain to one chain, according to circumstances. In square or rectangular sections of 80 or 100 acres each, roads surrounding each block of six or eight sections have been found amply sufficient; but in a country at all broken or irregular, some of the roads so laid out would often be found quite impracticable; in such cases, it is necessary either to trace and mark on the ground along the ridges of the secondary features, or wherever the ground may offer fewest impediments, cross roads leading into the main lines, and to lay off the sections fronting upon them; or to make these by-roads run through the sections; which is to be avoided as much as pos- sible on account of their cutting up small properties, and entailing a very considerable expense in the increased quantity of fencing required. In parts of the country where water is scarce, the greatest care should be taken to prevent its monopoly by individuals. Springs * Partly extracted from the instructions issued to surveyors employed in South Australia. COLONIAL SURVEYING. 429 and permanent water-holes should in such localities be enclosed within a small block of land (one or two acres), and reserved for the use of the neighbouring flock-owners and the public generally; and practicable roads must be arranged leading to these reserves, without which, excellent and extensive tracts of land would often be comparatively valueless. As it would evidently very much increase the cost of laying out sections having broken and irregular frontages, if they were re- quired each to contain exactly the same number of acres; the nearest approximation that can be made to the established size by the judgment of the surveyor should be adopted, and the section afterwards sold according to the quantity of land it is found to measure. For the purpose of giving to settlers seeking for land upon which to locate, every facility for acquiring information respecting its capabilities, and the positions of the different surveyed portions, the freest access to the statistical reports of the surveyors, and to the plans of the different districts deposited in the Survey Office, should be given. In addition to which, the sections themselves should be marked so distinctly upon the ground by short pickets, driven at intervals, regulated by the comparatively open and level character of the country, as to enable any person to follow up their boundary lines without difficulty. The angular pickets should be much larger, and squared at the head, on which the number of the section, and of all the contiguous sections, should be marked. Ad- jacent roads should also be designated by the letter R. Inde- pendent of the corners of sections being pointed out by these pickets, they should be deeply trenched with a small spade or pick, showing not only the angle formed by contiguous sections, but also the directions of their boundary lines. Road. Such marks remain easily recognised for years, and are not injured either by bush fires or by the constant pas- of herds of cattle, by both of which means many sage the wooden pickets are soon destroyed. 120 121 of It has been generally considered expedient, that roads should be reserved, if not actually marked on the ground, (excepting in cases where they would interfere with the erection of wharves, mills, &c.,) along the banks of all navigable rivers, the borders of lakes, and along the lines of a coast. This regulation, if stringently applied, without reference to peculiar circumstances in different localities, would often be found oppressive and mischievous. Very frequently, roads laid out with judgment to the various points on the margins of these waters which are best adapted for the pur- poses of fisheries, watering flocks, establishment of ferries, building 430 COLONIAL SURVEYING. or launching boats, &c., with a sufficient space reserved for the use of the public at these spots, would prove of more general utility. As a general rule, as many sections as possible should be laid out in the same locality, if the land is of a nature to be soon brought into cultivation. Whilst greater choice of selection is thus given, the comparative cost per acre of the survey is diminished; of course, this remark applies only to situations the rapid settlement of which is anticipated. In marking the boundaries of sections on the ground, all natural features crossed by the chain should be invariably noted in the Field Book, on the outlines plotted from which are drawn the general character of the contours of the hills, the different lines proposed for roads, directions of native paths, wells, springs, and every other object tending to mark the nature and resources of the country. Copies of these plans* should always be transmitted to the principal Survey Office, accompanied by a rough diagram, showing for future reference, the construction lines of the work, and the contents and length of the sides of all sections, also the measure of the angles, when not right angles; and by an expla- natory report, describing the nature of the soil, description of timber, &c., upon each section, and the facilities for making and repairing roads and bridges, and peculiar geological formations of the different districts. A collection of botanical and mineralogical specimens from all parts of the province will also contribute mate- rially to the early development of its natural resources; and sur- veyors should not be deterred from giving their attention to this subject by ignorance of these sciences, as the specimens can be afterwards weeded and arranged, and afford invaluable statistical information. At the head Survey Office, a meteorological register is of course supposed to be kept. It is also very desirable that each of the surveyors employed in any large district should be furnished with a good thermometer, rain-guage, and a mountain-barometer, or aneroid, for the purpose of registering daily observations to be forwarded periodically to the general office for comparison with those obtained from different parts of the province, between which the difference of peculiarities of climate will be thus arrived at. Surveyors working on a line of coast should be particular in noting all phenomena connected with the rise and fall of the tides; and obtain soundings, laid down with reference to established and easily-recognised marks on shore, of all creeks and harbours, when- *Two inches to one mile is found a very convenient scale for plans of these sec- tions, intended for the information of the public. COLONIAL SURVEYING. 431 ever this may be in their power. The depths and velocities of all rivers should also be noted at different points in their course, as well as the periods of floods, and their observed influence upon the volume of water in the river. In laying out sections up narrow rocky ravines, or in situations where creeks or any other natural features present obstacles to the continuance of the methodical rectangular form adopted as the standard figure, a deviation from this form becomes of course neces- sary, and the contents of some of the sections thus often unavoidably differ from the established average. Care should however be taken in such cases, to make the outline of these irregular figures as simple as the ground will admit of, both on account of the addi- tional trouble and time lost in their survey, and the increased cost of subsequent fencing by the purchaser. Attention has already been drawn in page 428 to the necessity of guarding against the monopoly of road or water frontage. The same sort of precaution is also required in marking out land in rich narrow valleys, or in spots valuable on account of minerals. As a general rule, from which no deviation whatever should be allowed, it may be laid down that no section should ever be per- mitted to enclose an undue proportion of land, unusually valuable from whatever cause, by extending its length in the direction in which that valuable portion of land runs; whether it be a rich agricultural valley, a mineral lode, a stream, or water-course. As regards the actual marking out of the sections upon the ground, when the figure is of a square or rectangular form, the pro- cess is a very simple one; whether the true meridian, or the direct line of some main road, or a line forming any angle with the meri- dian that may be found better adapted to the local peculiarities of the district, be adopted as the guiding line of direction. A spot being fixed upon for the starting point, represented by A in the accompany- ing figure*, the normal line AB is carefully marked out by a good theodolite in the re- quired direction; if intended to correspond, or to form any fixed angle, with the meri- dian, this must be previously determined by one of the methods usually practised. The right angle B A C is then set off, which angle should be observed on both sides of A B (produced on purpose to D), and the chain measurement along these lines A B IB A D C * This figure represents rectangular sections of 80 acres, as laid out in South Australia, 432 COLONIAL SURVEYING. and A C, and afterwards along the parallels to A C, may, if two parties are employed together, which can generally be managed under the charge of one efficient surveyor with an intelligent assistant, be carried on simultaneously, the points of junction at the angles of the blocks forming in some measure checks upon the accuracy of the work as it proceeds. The size of these sections, and the intervals between the parallel sectional roads, will depend of course upon local regulations. The operation would evidently be simplified by running all the measured lines in the middle of these roads, leaving half their breadth to be afterwards set off on each side by the proprietors of the land, but the palpable objections to this are too serious to be compensated by the trifling saving thereby effected. In fact, the real boundaries of no one section are by this plan marked on the ground by the surveyor; and con- stant disputes and encroachments would be the consequence of adopting it. It must be obvious to every practical surveyor, that it would be impossible for him to continue this mechanical system of marking a series of rectangular figures on the ground to any great extent, without being liable to constantly-increasing errors, which could not be guarded against by any degree of care in the operation, and of the amount of which he could never be aware, without estab- lishing some check altogether independent of the chain measure- ment of the sections themselves: this is only to be accomplished by combining with it a triangulation of the country, more or less ac- curate, according to the nature of the survey. Whilst, then, this methodical division of the land is in progress, it is advisable, if any thing like accuracy is required, and if the detached portions of settled country are to be laid down upon a general map, that the sites of the trigonometrical stations should be decided upon, and the stations themselves (however roughly they may be constructed) erected, in order that they may throughout be made use of as guides and checks upon the measurements. The triangulation indeed would be found of the greatest service, if carried on rather in advance of the detail, as in the survey of old countries. Any great accumulation of error could be then easily guarded against, by the angles observed at different parts of the chain survey, sub- tended by three or more of the trigonometrical stations; and in very many instances these stations could be actually measured up to, which should be done wherever practicable; by which means the length of which bore to their breadth the proportion of 2 to 1-occupation roads one mile apart, enclosing eight sections. They were, however, frequently laid out square, according to the nature of the ground. COLONIAL SURVEYING. 433 the marking out of the sections answers the same purpose that is obtained in ordinary surveys by the measurement of check lines, and traversing along the roads, by which the interior detail is mostly filled in. Angles of depression and elevation should also be taken to these trigonometrical points (whose altitudes are all ob- tained by the triangulation), from various parts of the chain survey, the heights of which positions, above the level of the sea, are thus obtained with tolerable accuracy. As to the mode of conducting this triangulation, all necessary instructions have already been previously given. The degree of accuracy with which the base is measured, and the angles observed, will depend evidently upon various contingencies; for instance- the extent over which the triangulation is to be carried; the time and expense that can be bestowed upon it; the degree of minutiæ required in the maps, &c., &c. On the survey of South Australia the base was measured upon a nearly level plain very little ele- vated above the sea, with a standard chain, the operation being repeated several times, to obtain a more correct mean value: the angles were observed with a very excellent 7-inch theodolite; and the result was found sufficiently accurate for the purpose of con- necting all the detached blocks of surveyed land, and laying down the work to the scale of 2 inches to 1 mile. In addition to the above use of the triangulation, it is found, in the survey of a wild country, peculiarly serviceable in enabling the Government to define, with the aid of marked natural features, the boundaries of the extensive tracts of land leased to different individuals for pasturage, until, with the increase of population and civilization, more convenient and better-defined demarcations are substituted. Some of the principal natural landmarks of a country also, such as chains of mountains and rivers, traverse the wildest parts of the land, where chain surveying would never penetrate. Many of these landmarks are made the boundaries of counties, and other internal territorial divisions; and their positions in differ- ent parts of their course are often only to be determined by refer- ence to the trigonometrical stations, which likewise serve as guides for ascertaining and laying down upon paper the direc- tions of roads through extensive, barren, and uninhabited tracts of country. Most of the foregoing remarks have been made under the sup- position that a number of detached surveying parties are distri- buted over different parts of the country, all working under the directions of, and reporting to, a central Survey Establishment. As the population becomes distributed over a wider extent, and 434 COLONIAL SURVEYING. applications are constantly made for the survey of small, irregular blocks of land to complete and consolidate properties, some altera- tions will be required in the method of carrying on the measure- ment of land, to meet these new demands*. It could evidently be only by an increased expenditure of time and money that sur- veying parties could be kept constantly moving from one distant spot to another, to lay out perhaps, only a very limited number of acres at each; and the division of the country into Districts, for the purposes of the survey, becomes almost imperative. Copies of the plans of sections open for selection, and other information of a similar character, would be thus placed more within reach of dis- tant settlers, and their wants could more readily and rapidly be met without augmented expense. Portions of the work might also at this advanced stage of pro- gress be filled in by contract, subject to careful and rigid examina- tion; the triangulation, and the previous chain measurement con- nected with it, affording sufficient checks for this purpose; without which, surveying by contract should be most carefully avoided, especially in new communities where but little competition can be expected, and where it would be unreasonable to expect to find competent surveyors distributed over the remote parts of the colony. The rate of progress and cost per acre of a sectional survey, such as has been described, must vary considerably, according to the nature of the country, the prices of labour and provisions, and the minuteness of the divisions. If the size of the sections is small, 80 or 100 acres for instance, the number of lineal miles to be mea- sured is of course very much greater in proportion than would be the case with blocks of a larger area, and the progress must bear an inverse ratio to the increased expense. The facility of trans- port is another item that materially influences both these questions, as also the system of marking out patches of land in whatever loca- lity they may be applied for, instead of carrying the survey regu- larly forward, embracing all the available land in its progress. The expense of the surveys in all new colonies is now defrayed out of the proceeds of the sales of land; and proof of the recogni- tion of the advantages of the accurate delineation of the boundaries * These subsequent wants and demands do not affect the first stage of the survey in a new country; it is only as it becomes gradually settled that they are felt. The first survey evidently cannot be a complete one, unless it could embrace every acre of land that might by possibility be required; it is constantly demanding extension in every direction, therefore the more imperatively necessary it is, that the first land sur- veyed and laid down on the maps should be based upon a triangulation sufficiently accurate to allow of this extension, without the certainty of accumulating error. COLONIAL SURVEYING. 435 of property, features of the ground, and main lines of roads, &c., is given by the system adopted by the New Zealand Association, in the establishment of the "Canterbury Settlement," of charging for all land the uniform price of £3 per acre*, (instead of the £1 fixed as the lowest upset price in the other Australian colonies, where the plan of selling land by auction is in force), to provide funds for a superior nature of survey, and a variety of works of a public character; the proportions being 10s. per acre as the price of waste land; 10s. per acre for the cost of the surveys, formation of roads, and other miscellaneous expenditure; 20s. per acre to be devoted to the purposes of emigration; and another 20s. per acre to eccle- siastical and educational purposes. The boundaries of what in the Australian colonies are termed Runs," for depasturing sheep and cattle, are not generally marked out during the survey, but are described by reference to the trigonometrical stations, and other known fixed points; the approximate distances and bearings of the lines being stated. As portions of this land are at all times liable to be purchased by in- dividuals after a due stipulated notice to the occupier of the run, who pays yearly a trifling sum for his licence, it would of course be a waste of labour to mark out such temporary divisions; but the settlers themselves very frequently define their respective limits, either by blazing the trees in a wooded country, or by running a plough line across it in an open one. As regards the interior division of a colony into counties, &c., the following general regulations, established many years since, are still in use:- Counties are to contain, as nearly as may be, 40 miles square; hundreds, 100 square miles; and parishes, 25 square miles. Natural divisions, such as rivers, streams, highlands, &c., to con- stitute as much as possible these boundaries; and, for the purpose of obtaining a well-defined natural boundary, a smaller or greater quantity than the above averages is permitted; but not to exceed or fall short of such established areas by more than one-third of each. Reserves are allowed to be made for all necessary public roads and other internal communications, either by land or water; also * Formerly land used to be sold in South Australia at the uniform fixed price of 17. per acre. The system of selling by auction was introduced by the Australian Waste Land's Act in the year 1843. There are various opinions as to the comparative merits of these opposite systems, the first of which was introduced by Mr. E. G. Wakefield; and its advantages are strongly set forth in the pamphlet upon Colonial Surveying, recently published by his brother, Mr. F. Wakefield. 436 COLONIAL SURVEYING. for the sites of towns, villages, school-houses, churches, and other purposes of public utility and convenience. When the division between Provinces or Counties, or other lines of territorial demarcation, is represented, either altogether or in part, by a meridian line; or a line having any fixed angle with the meridian; or by a portion of the arc of a parallel (as is the case in many of the Australian provinces), it is of course necessary to be able to determine and mark upon the ground with accuracy such meridian or parallel. Most useful practical information upon this subject will be found in the narrative of the survey and marking of the boundary between the British possessions in North America and the United States of America, in 1842, published by Major Robinson, Royal Engineers, in the second and third volumes of the "Corps Papers." Operations of this nature, if conducted with the very great care and precision that were bestowed upon the boundary alluded to, involve the perfect knowledge of the manner of using and adjusting the transit, and altitude and azimuth instruments; and also the management of chronometers. The boundary line between South Australia and what now constitutes the province of Victoria, (the 141st degree of east longitude) was however determined (and since marked on the ground for a considerable distance,) under the New South Wales Government, by one of their surveyors*, with only a sextant, a pocket chronometer, and a small 3-inch theodolite; but though the work was performed with the greatest care and attention, and with probably as great a degree of accuracy as could be obtained with these imperfect instruments, the result can of course only be looked upon as an approximation far too vague for the determination of a division of importance. The North American boundary, on the other hand, may perhaps have been defined with more precision than was absolutely necessary in a line of demarcation running for its whole length through a wild uncleared country. Having now gone through the method of dividing the land into minute sections for occupation, and its further division for terri- torial purposes; we will conclude with a short reference to the objects to be held in view in conducting exploring expeditions be- yond the bounds of the settled districts, for the purpose of adding to the geographical knowledge of the country and developing its resources; which objects are very similar in character to those already alluded to, when treating of the preliminary operations of a survey in a newly-formed colony. * Mr. Tyers. COLONIAL SURVEYING. 437 The nature of the country to be traversed will, as far as this is known, indicate the method of travelling that must of necessity be adopted. Extensive inland water communication, as in the Cana- das, points to the canoe as the readiest mode of transport; com- paratively open and generally grassy land, as in Australia and Southern Africa, requires the use of horses and oxen; whilst in many other countries the thick underwood can, in parts, be tra- versed only on foot, and barren deserts by the aid of camels. These different modes of locomotion evidently all require different pre- liminary arrangements. The objects in view, however, are much the same in all cases*; viz., a knowledge of the climate, soil, native population, geological formation, botanical character, of the country, and its resources of all kinds; as well as the delineation (as perfect as the time and means that are available will admit) of the natural features of the ground. All points known as portions of the settled country being soon left behind, the explorer has to trust to his own judgment as to the best directions in which to conduct his party; to his own energy in overcoming the natural obstacles that he will be certain to en- counter; and his own practical skill in fixing at proper intervals. his different positions by means of astronomical observations, and mastering rapidly the general massive features of the ground for the purpose of making a rough sketch of the country passed over, showing more particularly the directions of the principal ranges of hills, and of rivers, and water-courses. In a large party these labours may often be subdivided advan- tageously; but the leader must remember that the entire respon- sibility still rests with him; and if he does not actually participate in every portion of the work, he must nevertheless exert a general influence over the whole. As regards the fixing, with as much accuracy as may be attain- able, the various positions of encampments, the directions and sources of rivers, and all marked prominent features; much assist- ance is to be obtained by carrying on, as far as it can be done, a species of rough triangulation (with a sextant or other portable instrument), from the extreme trigonometrical stations, or any prominent landmarks the positions of which are known and repre- sented on the plans. This may however very soon become imprac- ticable from the nature of the country or other causes, and the traveller then finds himself much in the same predicament as at sea, having little beyond his dead-reckoning to trust to for the de- * Expeditions for one single definite object, such as tracing the sources of a river, &c., are not intended to be here referred to. 438 COLONIAL SURVEYING. lineation on paper of his day's work. In this position he must look to the heavens for his guide: and hence the necessity for his becoming himself, or having with him, a good and rapid observer. At sea, the latitude is always obtained at noon by a meridian altitude of the sun (when visible); "sights," as they term obser- vations of single altitude for time, having been taken three or four hours before. The latitude obtained at noon is then reduced by dead-reckoning to what it would have been at the time and place of the morning observation, (using the traverse table ;) and with this deduced latitude the hour angle is computed, and the equation of time, plus or minus, applied for the mean local time, which, when compared with the Greenwich time, shown by the chronometer, (allowing for its rate and error), gives the longitude east or west of Greenwich at the time of the morning observation. By applying, by dead-reckoning, the change in longitude between that time and noon, the longitude of the ship at noon is obtained,— the latitude has already been found by direct observation,-and the two determinations afford the means of recording upon the chart the position of the ship at noon on that day. Somewhat similar to the above proceeding, must be that of the explorer in a wild unknown tract of country. He would not probably find it convenient always to obtain his latitude at noon; but he can generally do so, and more correctly, at night, by the meridian altitude of one or more of the stars of the first or second magnitude, whose right ascension and declination are given in the Nautical Almanac. His local time can, immediately before or after, be ascertained by a single altitude of any other star out of the meridian (the nearer to the prime vertical the better); and if he carries a pocket chronometer upon which any dependance can be placed, he has thus the means, by comparison with his local time, of obtaining his approximate longitude, and of laying down his position upon paper. In travelling, the rate of the chronometer will probably be found to vary; but as frequent halts of two or three days are likely to occur, these opportunities should never be lost of ascertaining its change of rate.. The longitude should also be obtained occasionally by lunar observations on both sides of the meridian; or by some of the other methods given in the works on Practical Astro- nomy. The results deduced from such observations must not be relied upon within ten or twelve miles, but a careful observer should rarely exceed these limits; and his latitude ought always to be within half a mile, or under the most unfavourable circumstances, one mile, of the truth. COLONIAL SURVEYING. 439 With these all-important data, enabling him to fix with approxi- mate accuracy point after point* in his onward course, the explorer can have no difficulty in interpolating by angles, taken with a sextant or with an azimuth compass, all strongly-marked promi- nent features, or in laying down his route upon paper correctly enough for the purposes of identifying particular spots, and giving a faithful general representation of the features of the ground he has travelled over. The value of this sketch will be much enhanced by its having recorded on it, as nearly as they can be ascertained by the mountain barometer or aneroid, or by the temperature at which water is found to boil, the altitudes of the most important positions, as the summits of hills, the levels of plains, and sources of springs and rivers. Daily meteorological observations, even of the most simple cha- racter; such as merely recording the readings of the thermometer and barometer at stated times, will also prove of essential service as illustrative of the climate; and these will be of additional value if accompanied by a record of the quantity of rain fallen on different days, should any portion of the party be stationary for sufficient length of time at any one spot, to make these observa- tions. If not provided with a rain guage of a better description, a tin pipe with a large funnel, the area of the top of which bears a certain proportion to that of the tube, will answer perfectly to measure the quantity of water fallen. A light graduated wooden rod is fixed in a cork float, and indicates, above the level of the top of the funnel, the number of inches; the graduations of the rod of course being proportioned to the ratio between the areas of the surface of the funnel and that of the tube. Thus, if the proportion is 10 to 1, the measuring rod will be lifted 10 inches for every inch of rain. * The distance between positions, the latitudes and longitudes of which have been determined, can be easily obtained by calculation; by which means they can be laid down with more accuracy, provided the extent of ground travelled over is not very great. 440 HYDRAULICS. CHAPTER XIV. HYDRAULICS, IN CONNECTION WITH DRAINAGE, SEWERAGE, AND WATER SUPPLY. THE first principle to be understood and to be ever borne in mind in hydraulic or hydrostatical calculations is that, unlike "solids," whose pressure is always downwards in the direction of gravity, "fluids" press equally in every possible direction, even upwards; consequently, if any portion of the upper part of a fluid be replaced by a part of the vessel containing it, the pressure against this from below will be the same which before supported the weight of the fluid removed, and every part remaining in equilibrium, the pressure on the bottom of the vessel will be the same as it would be if the vessel were a cylinder or a prism. It is usual to calculate the pressure of fluids with reference to a square inch of the surface of the vessels containing them, or in contact with them; but, whatever may be the modicum of surface assumed, the pressure is equal to the weight of a column of the fluid whose base is equal to that modicum, and whose height is equal to its depth below the apex or top surface of the fluid. Hence what is called "head," or the height of a fluid, is of the utmost possible importance, for, if there is but a sufficiency of head, a column of fluid of the smallest possible diameter, may be made to balance another quantity, or any weight as large as you please. This principle has been denominated the Hydrostatic Paradox, but as I believe, inappropriately, for I do not think there is anything paradoxical about it. I H C The figure represents a machine called the hydrostatic bellows, which is sometimes used to illustrate this principle. The bellows con- sists of two thick boards CD and E F, con- nected with leather, or other expansive material; & a pipe of very small diameter, but of considerable length, communicates with the bellows a little above the point F. Now if water be allowed to run into the pipe at the point A—either by connecting it with a cistern, or, if the experiment be made in a room, with an ordinary water-can B F E HYDRAULICS. 441 suspended from the ceiling, it will fall down the pipe into the bellows, and will gradually separate the bellows boards raising and sustaining a weight that may be placed thereon, bearing the same proportion to the weight of water in the pipe above the level of D C as the area of the bellows board bears to the sectional area of the pipe, and this is evident from what has been said as to the equilibrium of the pressure of fluids; since whatever may be the downward pressure of water in the pipe, there is an upward pressure in the bellows upon every fractional part of its surface that corresponds with the sectional area of the pipe, equal to the weight of a column of water, whose diameter is the diameter of the pipe, and whose height is the height of the pipe diminished by the height of the water in the bellows. It is a well known principle of hydraulic science that “water will always find its level," hence water poured into a bent tube at one end will rise to the same level at the other end before it becomes quiescent: thus are we able to supply water to the inhabitants of a town from a reservoir on a hill, to any height in their dwellings that shall not exceed the level of the water in the reservoir, notwithstanding the pipes conveying the water may in their passage from the reservoir to the town, have passed through valleys and hollows of great depth. Fluids of different specific gravities that do not mix will counterbalance each other in a bent tube when their heights above the surface of junction, are inversely as their specific gravities. In common-place matters of business, the most useful, although perhaps, the most difficult, and until lately the least advanced branch of hydraulic science, is that which relates to the motion of fluids, and the part which friction plays upon them in their passage through confined channels and (especially at the present day) conduit pipes. There is little doubt that some simple fixed mathematical law, prevails throughout all nature's works, and that such is the case with regard to fluids in motion has been demonstrated by frequent experiments. Perhaps the most able exposition of this law in hydraulics, is to be found in a work called "Prac- tical and Experimental Researches in Hydraulics," by R. A. Peacocke, C.E. extracted from Weale's Quarterly Papers on Engineering. I have already explained that the pressure of fluids is alike in all directions, consequently in considering the question of 2 E 442 HYDRAULICS. discharge of water through pipes, we must make no difference between a pipe laid level but having a constant head behind it, and another pipe whose gradual fall amounts in the aggregate to that constant head. As an illustration, let B C, fig. 179, be a constant head of water, and A B a horizontal pipe; then the same quantity of water will be discharged at the point A, in the same time, by the horizontal pipe, as would be discharged by a pipe laid hypothe- nusally, as in fig. 180, provided that the top surface of the water be kept at the same height at C, above the point A in each case, and that the point A, is at the same horizontal distance from C. If any be inclined to doubt the correctness of this principle, they may find a strong confirmation of it, in the results of some very valuable experiments communicated to the Institution of Civil Engineers by Mr. W. A. Provis, M.I.C.E., and contained in the "Account of the Transactions of that Society," vol. ii, p. 201. But for the existence of friction, water would fall a given height in the same space of time whether the points of supply and discharge were situated vertically above each other or whether a considerable horizontal space intervened, but inas- much as the discharge of water must be vertical unless con- ducted otherwise by some artificial medium, the resistance offered by friction is greater or less according to the rate of inclination at which the conducting medium is brought in contact with the water. At a time then when sanitary questions are occupying a very great share of public attention, and every town in the kingdom is establishing its waterworks and carrying out works of drainage, it becomes more than ever important that the quantity of water discharged from pipes under all the varied circumstances of greater or less diameter, head and pressure, should be distinctly understood. Among the several rules for calculating the discharge of water through pipes, may be mentioned that of the Chevalier Dubuat, in his Principes d'Hydraulique, an abridged account of which is given by Professor Robison in his article on rivers and water works in the Encyclopædia Britannica; the formula of M. Eytelwein, a German mathematician, who devoted much time to enquiries of this nature, and published at Berlin in 1801 a valuable compendium of hydraulics, entitled Handbuch der Mechanik und der Hydraulik. The formula and table of Mr. HYDRAULICS. 443 Smeaton; the formula of M. Prony; Dr. Young's deductions from experiments and comparisons; the conclusions of M. Genieys contained in a quarto work, published in Paris in 1829, entitled Essai sur les Moyens de conduire, d'élever et de distribuer les Eaux, par M. Genieys, Ingénieur au Corps Royal des Ponts et Chaussées, attaché au service de la Distribution des Eaux dans Paris; the experiments of the Abbé Bossuts; and the experiments of M. Couplet; the results of the very valuable experiments by Mr. Provis, M.I.C.E.; the researches of Mr. Peacocke, C.E.; and the formula of Mr. Hawkesley. The rules and formula of most of the early authors are expressed in such different terms, and produce such conflicting results, that they are of little value for the practical requirements of the present day. Two or three years ago, I turned my attention to this subject; collected and investigated the several formula, in connection with the recorded experiments, and tabulated the results. A second and very extended edition* of these Tables has been for several months in progress, and will probably be ready for the press by the time this work leaves the hands of the printer. * Synopsis of the Second Edition of "RYDE's Hydraulic Tables.” Table 1. Relative inclinations, especially applicable to Table 8. "" 2. Relative inclinations, especially applicable to Table 10. "" 3. Relative values of the properties of a circle, (very complete). "" 4. Square roots of numbers, from 1 to 1000. "" 5. Cube roots of numbers, from 1 to 1000. "" 6. Logarithms of numbers. 7. Hyperbolic logarithms. "" "" وو "" "" "" "" "" "> 8. Discharge and velocity of water and sewage passing through pipes. 9. Loss of head, occasioned by the friction of bends and angles, whether in pipes, rivers, canals, or other arterial cuts. 10. The mean velocity of water flowing through rivers, canals, drains, or other arterial cuts, according to depth and fall. 11. Surface, mean and bottom velocities of rivers. 12. Approximate swell occasioned by the piers of a bridge or other con- traction of the water way. 13. Weight and thickness of cast iron pipes, required to sustain the pressure of different heads. 14. Velocity of water discharged from reservoirs, sluices, bridges, and ver- tical pipes. 15. Discharge of weirs and overfalls. 16. Quantity of water in cubic feet due to rain-fall, on any number of acres. 17. Relative quantities of rain-fall for different measures of time. 444 SPECIMEN OF HYDRAULIC TABLES. DIAMETER OF PIPE. INCLINATION 1 IN 15. DISCHARGE PER MINUTE. Inches. Gallons. VELOCITY PER MINUTE. Feet. Feet. 1 8. 1.2 228. 1/1/10 21. 3.4 278.5 2 43. 6.9 318. 2/1/18 76. 12.2 358. 3 120. 19.2 392.5 4 245. 39.3 451.5 5 429. 68.9 505.5 6 677. 108.7 554. 7 996. 159.8 598. 8 1390. 223.2 639.5 9 1867. 299.6 678.5 10 2429. 389.9 715. 11 3082. 494.8 750. 12 3832. 615.1 783. 13 4678. 750.8 814.5 14 5626. 903. 845. 15 6694. 1075. 875.5 16 7862. 1262. 904. 17 9143. 1468. 931. 18 10560. 1695. 959. HYDRAULICS. 445 The Tables (of which a specimen is given on page 444) show the discharge and velocity of water and sewage flowing through pipes of any diameter from 1 inch to 18 inches, and at any rate of inclination from 1 in 10 to 1 in 1000. They are equally applicable to the passage of sewage through drains, or pure water through water pipes; because in the case of the former, every additional junction throughout the entire course of the drain increases the pressure, and consequently the velocity; while in the case of the latter, the effect produced by each branch of a water service, in- creases the friction, and therefore diminishes the flow. The arrangement of the Tables is so simple as to need but little explanation. If it be required to ascertain the size of pipe that will discharge a certain amount of sewage, or supply a given amount of water at a known fall, it is simply to turn to the page headed with the given rate of inclination, and take out the dia- meter, which stands opposite the number most nearly representing the given discharge. It is not at all times understood why a small pipe drain shall effectually perform the functions for which it is intended, when a larger pipe has been previously deputed to the same task and failed. In a large drain the run of water is spread over a broad surface in a thin sheet, by which means the friction is considerably increased, indeed exerted to the utmost-the flow is greatly retarded thereby, and the heavier matters at first held in suspension are by the natural law of gravity eventually deposited. In the small pipe on the contrary the water is concentrated, friction is reduced-the flow is greatly accelerated in consequence and all matters are held in suspension and carried away. Thus if anything not intended to be received by the drain, should accidentally find its way thither, the shallow stream with little velocity or power to float a heavy body, and having moreover plenty of room to pass it by, adopts the opportunity afforded by the unnecessary size of the large drain, and leaves the foreign substance where it found it; there to accumulate other matters and become the nucleus to what may eventually choke the drain. In the small drain on the contrary, if a foreign substance enter, or an impediment of any kind is presented to the ready flow of the water--the hydraulic pressure is immediately increased and brought to bear upon the resisting medium, which cannot long resist, and it is carried head- long down the channel by means of the superior force itself has created, and never stops again until it is precipitated at the outlet of the sewer. Fig. 181 represents a 15-inch drain in which the height of water is supposed to be as there shown-and 446 HYDRAULICS. the impeding substance is also drawn. But if this were a 4-inch pipe as shown in fig. 182, the same quantity of water would have assumed a very different relation towards the impediment, and its power to remove it will be readily comprehended on examination of the sketch. Having referred to my tables as simple expositors of the capacities of pipes for the purposes of drainage, sewerage, and water supply, according to the inclination at which they are laid, I now propose to treat briefly the practical operation of draining a town and supplying it with pure water. Undoubtedly the first desideratum in considering the question, is to secure the best possible outfall for the drainage, sufficiently removed from the town to prevent inconvenience or nuisance from noxious effluvia, and yet in a position if possible to enable the sewage to be intercepted and used as an agricultural manure, if the agriculturists in the neighbourhood are willing and can make it answer their purpose to co-operate with the town's people for its purchase. Upon this question of application of sewage to agricultural purposes, much diversity of opinion exists; personally I am inclined to believe, that if the landowners and farmers in the vicinity of every town in which proper works of drainage have been executed be invited to make propositions for the right of using the sewage, it will be found that in most cases, after a sufficient trial has been allowed to enable them to discover the proper mode of using it, and most economical manner of applying it, that a revenue of 5s. per annum for each inhabitant, at the very minimum, may be realised from that which is at present not only thrown away, but what is far worse, is suffered to injure to a large and unknown extent the health and physical condition of our town populations. Having determined upon the outfall, the next question is to lay out judiciously the main sewers, so that each street may have at least one drain, laid at such a depth as shall drain the foundations of the houses; into which surface grates, at properly regulated intervals, will open by means of trapped side drains, as well as the secondary drains from houses, courts, &c. There are few towns, excepting only the very largest, that may not be efficiently drained by means of glazed stone ware pipes, without resorting to more expensive, and less serviceable sewers. The main drains should be laid out, so as to reach by as direct a course as possible the point of outfall, for to decrease the length of a drain is the same as to increase the fall; they should also be } HYDRAULICS. 447 as free as possible of sharp angles and bends, and should maintain throughout, as nearly as can be accomplished, a regular rate of inclination. The greatest internal diameter of drain pipe recommended to be used, is 15 inches; beyond this size they are rarely true in form, and are very difficult to lay down properly. I have had laid down under my supervision pipes 18 inches in diameter, but the work is not nearly so satisfactory as the smaller sizes, although it has now worked very efficiently for more than four years. In all future operations, I shall consider the propriety of making two drains in all cases in which a 15-inch pipe will not meet the requirements. In digressing a little from my subject to describe the kind of map upon which the drains must be marked out, I feel I cannot do better than refer to the valuable suggestions of the General Board of Health on this particular question, bearing as they do the high stamp of official authority, and being exempt, as they neces- sarily must be, from every imputation of interested motives, which generally attaches to a professional man, when suggesting works tending to benefit himself or his order. Having issued to engineers and surveyors specimen plans on a prescribed scale showing every possible detail relating to sewerage, drainage, and water supply, the General Board in their Minutes of the 26th July 1850, remark:— “There appears to be generally an imperfect acquaintance with the actual necessity and value of proper surveys upon which required works of improvement have to be founded. It seems to be very frequently supposed that if any sort of plan exists of a town or neighbourhood it will answer the purpose and that further expenditure upon the survey of a district would be both unnecessary and wasteful. It may be safely asserted however that so far from these surveys being either valueless or costly, that works of sanitary improvement cannot be satis- factorily or economically carried out without trustworthy plans prepared from these surveys. "In respect to the principal works of improvement, namely, drainage works, one chief source of waste from inefficiency, arising from the want of a complete system of levels, has been the laying down of lines of sewers at insufficient or wrong inclinations, which combined with errors as to forms and modes of con- struction have made drains and sewers, instead of serving for the rapid discharge of all matters intended to be conveyed away, mere reservoirs of deposit, increasing the amount of noxious evaporating surface beneath the site of the town. "It has been moreover the usual custom hitherto to lay out the lines of drainage upon street plans merely, without regard to the disposition of properties, or other facilities for the work which would present themselves upon good and complete plans. Thus a line of sewer is necessarily marked down every street into which the drainage of each house has to be separately led. "It has appeared also upon recent investigations, that there has been great extravagance, not only from this want of complete general surveys as the founda- 448 HYDRAULICS. tion of drainage works, but from the insufficiency of any district surveys for the laying out of the main works, those of house drainage. "Various comparisons have been recently made of different districts of the metropolis, with the view of exhibiting the immense economy of the proposed detailed plans on a large scale as affording the opportunity of laying out lines of drainage in the most judicious directions; and looking at the question as one of mere economy, without reference to the advantages of better drainage by greater falls and quicker flows, it has invariably been found that the saving of public sewer alone rendered practicable by the detailed survey, amounted to many times the actual cost of the survey, and that one half of the cost of private house drains might be economised by aid of the same guide.” With reference to the new survey of the metropolis undertaken by the Ordnance Survey Department at the recommendation of the Metropolitan Sanitary Commission, and now in course of com- pletion, the General Board of Health remark in their report on the water supply:- in "By the aid of this survey, combined works may now be executed with certainty. Under the present method, according to which water works are laid down piecemeal, and in disorganised portions, the mains are separated from the other and most important part, the apparatus for the delivery of water into houses, and under this system an accurate system of levels is not apparent. But by means of the accurate levels set forth on the survey, the inclines and directions of the branches may be determined, with the effect of saving considerable lengths, and of securing the greatest amount of flow and the readiest supply of water at the least cost. By the system of levels, the relation of every minute portion of the work to the whole system, the degree of pressure and strength of the apparatus required any room, the height and force of the jets; and the quantity of water delivered for any purpose on any spot and the average pressure of the water supply in any district; may be known and regulated at any period; whilst, every workman engaged in the execution of combined works in the dark and densely crowded districts, may be guided by the survey in laying down house and branch drains for the discharge of soil water at the proper inclinations, and in directions having correct relation to works often at several miles distant. By the levels taken for this survey, the waste in laying out extensive lines of sewers with no fall, or with falls the wrong way, waste such as that of laying out a table of drainage, in- cluding an entire district in such imperfect relation to other districts as would involve in the opinion of the chief surveyor, an expense of upwards of £250,000, to set the levels right, may be prevented; and the whole of the public works of the metropolis, including roads may now be placed in correct relation to other works. A "The General Board desire to lay stress, at the present time, upon the im- portance of this view of the subject alone; but, surveys sufficient for sanitary purposes, will be permanently available for all others, and will prove of great value for the complete map delineation of many classes of information. In the general consideration of the necessity of such plans for the purposes of the Public Health Act, the General Board have not overlooked these several other uses to which they may be applied, tending in various ways to much ultimate improve- ment and advantage. "Besides the more immediate uses of plans, therefore, for the complete delinea- HYDRAULICS. 449 1 tion of main and house drainage, water works, gas works, and pavements, specimen plans have been prepared, exhibiting among other things, the value of such surveys in the registration of property, in street and building improvements, in valuations and assessments, in rate collections, and in the records of public officers, the District Surveyor, the Officer of Health, the Registrar, the Relieving Officer, and the Police. Plans adapted to these additional uses might be made to present in time a complete historical record of the progressive improvement of town populations of greater national value than any registration in books. In order to lay out with completeness and efficiency works of improvement under the Public Health Act, two plans will be required to be prepared from the survey, one a general plan to a small scale, affording a complete view of the entire district, and the other a detailed plan of the town portion of the area. "The scales proposed by the General Board of Health are for the general plan two feet to the mile, and for the detail plan 10 feet to the mile. “In fixing the scale of the general plan it appeared to be desirable that it should be so small as to afford a complete view at once of the entire district under con- sideration but at the same time large enough to admit of the accurate measurement of areas of land and other general uses. For the first consideration a smaller scale than that proposed would have been equally serviceable, but the experience of the Tithe Office has found that areas cannot be determined with the required accuracy upon a less scale than three chains to an inch. A scale of two feet to the mile has been adopted as the nearest approach to the tithe scale that would form an aliquot division of the scale of the detailed plan. "A complete system of levels should form one most essential feature of the general plan. In the practical carrying out of proposed works the general board have every reason to believe that a great number of fixed points of level, which can at any time be found and referred to on the ground, will be of infinitely greater service than any system of contour lines, which, after they have been levelled, have no existence but on the plans. The comparatively small value of a system of contour lines does not appear to warrant the very large expense of their execution, more particularly as with an extensive system of fixed points of level for guidance, the general configuration of the ground may be lined out by the surveyor on a small scale plan with sufficient accuracy for all the purposes for which contour lines are generally serviceable. "The scale of the detailed plan has been determined mainly by the experience of what is required for the complete exhibition of all the particulars of main and house drainage; for it has been found that any scale large enough for this purpose would be sufficient also for any other service for which a complete and detailed map would be required. "Prior to any decision on this important point, considerable trial was made of various scales, and all available experience sought upon the subject. The scale adopted is an inch to 44 feet, or 10 feet to the mile. "The Ordnance Town Scale is only one half of this, or five feet to the mile, but in some towns in which recent surveys have been made, considerably larger scales than now proposed have been adopted. The Town Council of Liverpool have had a plan executed to a scale of 22 feet to the mile, notwithstanding that the ordnance had already made a survey of that town to the scale of 5 feet to the mile; but the trials which have been made by the General Board, and the experience on the subject obtained in the metropolis, have clearly shown that while, on the one hand, so large a scale is inconvenient and unnecessary, the Ordnance Scale for Town Surveys first 450 HYDRAULICS. adopted in Ireland is, on the other, quite inadequate to the puposes for which the plans are now required. "Provided that the scale is sufficiently large for the proper exhibition of the most crowded subject matter of information-the house drainage, it appears to be far more desirable, for the clear exhibition of the various particulars required, that the separate classes of work should be shown on separate copies or tracings of the plan, than that the scale should be enlarged for the purpose, for no practicable enlargement avoids the confusion which arises from crowding these different classes of work, however imperfectly, upon the same plan. "There is one essential feature in the specimen plan, which has not hitherto re- ceived attention, and without which no attempt should be made to lay out works of drainage, that is, the level of the basement or lowest floor of every house. In the absence of this information, it continually occurs that sewers are laid down some feet higher than the places they are intended to drain, and the sewers drain into them instead. The great object of the deep drainage of towns is effectually to carry off the refuse from habitations, and yet works are constantly executed without any certainty of accomplishing this special object. The General Board have already had presented to them, under the Public Health Act, plans for ap- proval, in which no information whatever has been obtained on this point, and in which there was not the least security that the sewers would not be laid above the level of the basement." It To resume my subject, the main drains having been marked out on the map, the next consideration is, the size they will require to be constructed, to fulfil all the uses for which they are in- tended; at the same time it should be forcibly borne in mind that the less the diameter of the sewer is in excess of its actual require- ments, the easier it is to be constructed, the cheaper will be the present cost and future repairs, and the easier and more effectively will it cleanse itself with the aid of the ordinary sewer water. is a very common error to assume that a sewer to a reasonable size cannot be too large; and it is the most certain course for the inha- bitants of a town to take, upon the first mention of improvements of this nature, to set about framing extravagant estimates of the cost of a sewer large enough to drain five times the amount of their population, as though there were no medium between the absence of drains in their town, and the existence of sewers that would require the full force of a large river to keep them clean. It has been found in many instances, upon opening large sewers that have become stopped up from a supposed inability to carry off all the water they have been required to do, that the sole rea- son has been the deposit of cesspool matter, accumulated beyond the power of water to remove it, and leaving but a mere fractional part of the sectional area of the sewer for the passage of the water. HYDRAULICS. 451 Fig. 183 represents a large sewer in the metropolis, and the condition in which it was found by the officers of the Sewers Commission. The space occupied by the ordinary run of the sewage in the form to which it had worn itself, is shown near the crown of the arch. Figs. 184 and 185 represent two instances in large sewers in which the actual requirements of the run of the sewage is depicted in a smaller amount of deposit. It will be seen by these examples that a pipe sewer would have carried off all the ordinary sewage water, and, as has been previously advanced, would, in its passage, have carried off all the matters which formed the deposit in the larger one. The notion that large sewers must be used to carry away an oc- casional excess of storm water is at once refuted by these examples, for since accumulations of this kind will continually take place under ordinary circumstances, these extraordinary occasions find no greater accommodation in the larger sewer than in the smaller one. The proper functions of sewers are obviously to convey away from a town the whole of the sewage refuse of every house in the district, the accumulations of foul matter in courts, lanes, and alleys; and so much of the rain-fall of the district as may fall upon the surface of the roads, streets, courts, &c., the roofs of buildings, and of yards, or other spaces attached to them; but to attempt to provide for the subsoil drainage of the site of the town by any other than the natural means, or an independent system, totally separated and distinct from the sewers, is expensive and futile. If the whole of the rain or storm waters falling upon the streets and buildings of the town is conducted away in the sewers within a reasonable space of time after it falls, and the whole of the house drainage is provided for in the same way, what can be the amount of dampness or moisture from below that it may be necessary to be careful for? In determining the capacity of sewers, we therefore have to as- certain, the amount of house drainage to be provided for, by estimating the number of houses we intend to drain into the sewers, and by assuming that each house will, in a given time, discharge a certain quantity of sewage. This calculation is of ne- cessity only an approximation, but it will be found to be a useful one. an For its basis, we may consider that each house contains on average five individuals, and that for every individual 452 HYDRAULICS. twenty gallons of sewage matter, including waste water from all household sources, will pass into the drain in the course of the day. The maximum rain-fall may be taken as two inches in any one day, and may be computed on the total area of site occupied by streets, houses, buildings, yards, and gardens, according to circum- stances, and the probability of the whole or chief part of the bulk being discharged without evaporation into the sewer. We have taken the house drainage and rain-fall of one entire day of twenty-four hours; but inasmuch as the drainage is exceed- ingly irregular and uncertain, and not at all likely to be spread equally throughout the whole time, and a July storm may cause a large accumulation of surface water in a very little while, it has been deemed advisable by very able and experienced practitioners to allow for the possibility of the combined quantity being dis- charged in two hours. It frequently happens that a few straggling houses stand in grounds of considerable extent, but it must not be understood that the calculation for rain-fall is to be computed on such sites; it has already been explained that for the drainage of such properties the natural drainage out-fall of the district must be resorted to, as it would hardly be sanctioned by the loudest economists to build a sewer sufficiently large to provide against inconvenience such as this, which may not arise twice in the year. Having arrived at the approximate quantity of sewage matter to be conveyed away by the sewers in two hours, and having al- lowed some additional quantity for the probable increase of the neighbourhood, if we divide the sum in the aggregate, reduced into cubic feet by 120, we get the quantity per minute, which at once identifies us with our Tables. But the quantity we have now ob- tained is the total quantity at the outfall, and the sewer will not be required to accommodate so large a supply throughout the entire length of its course; it will be expedient, therefore, in the first place, to consider such a length of it only, commencing from the outfall, as partakes of no very great diminution, and by taking the rate of inclination from the section, ascertain from the Tables the size of pipe that will be necessary to fulfil the requirements. Other portions may then be taken, and the sewer may be gradually dimi- nished in size, as the purposes for which it is intended may become lessened in extent. It may, however, be well to limit the minimum size of a main or principal sewer to nine inches of clear internal diameter, thence increasing to twelve, and reaching its maximum at fifteen. HYDRAULICS. 453 If it becomes necessary to exceed the diameter of fifteen inches, it will be desirable to resort to the old description of brick sewers; consequently, a few words with reference to the most approved form of such drains, will be in consonance with the object of the present work. The form of a sewer should be conducive to strength, at a mini- mum cost; hence the adoption of the circle, as a form offering to all the exterior parts of the surface a uniform resistance to pressure from without. But the top, sides, and bottom of a sewer are not required to sustain a uniform pressure, being acted upon in very different directions, the greatest amount of pressure being verti- cally, and consequently the greatest ability to resist pressure should be above and below, the sides being more or less tried, according to the nature of the surrounding soil, and its ability to support itself by its own tenacity. As fluids flow with greater velocity the less they are exposed to friction, the best description of sewer must be that which offers under all circumstances of more or less supply, the least amount of surface in contact with the fluid. It will, therefore, be seen, that what is called the "Egg-shaped Sewer," which is illustrated in fig. 186, affords in the greatest de- gree the two considerations we have been discussing, viz., "strength vertically," with the advantage of a confined channel, and a "mini- mum amount of surface exposed to friction," under all circum- stances, of much or little matter in the sewer. This form of sewer is simply constructed by observing the fol- lowing proportions:-Let the diameter of the lower arc be 1; the diameter of the upper arc 2; the height of the sewer 3; and the radius of the side arcs 3. In computing the capacities of brick sewers, the values given in the Tables must not be depended upon, as they are based upon the discharges of pipes having a glazed internal surface, through which the sewage matter passes more freely than the surface of the brick sewers will allow it to do. The discharge will, therefore, be considerably less, more or less varied, according to circumstances, but probably 30 or 40 per cent; the pipes being altogether better suited to the purpose. It is interesting to investigate the varied powers possessed by water in motion under different circumstances. A stream of water 4 feet wide and an inch deep, with a fall of 1 in 150 is sluggish, while the same water running through a 12-inch drain pipe, laid at the same rate of inclination, flows at a considerable velocity. 454 HYDRAULICS. The former would deposit silt or sand, the latter would certainly remove it. One very great objection to large drains is the necessity of cleansing them by manual labour. The legislature has very properly prohibited the sweeping of chimnies by boys as an occupation degrading to human nature, eminently cruel, and belonging to a low state of art; but that oc- cupation was a princely one as compared with the employment of cleansing sewers by hand. Instances have occurred of the death of men who have been sent to crawl up sewers charged with foul gases, while many have had their health irreparably injured in this disgusting labour for their daily bread. The following are extracts from some of the reports of the sur- veyors employed upon the subterranean survey of the metropolis, recently conducted for the Metropolitan Sewers Commission:- 66 '69 miles of sewers have been surveyed in the Surrey and Kent district. The surveyors find great difficulty in levelling the sewers of this district; for, in the first place, the deposit is usually about 2 feet in depth, and in some cases it amounts to nearly 5 feet of putrid matter. The smell is usually of the most horrible description, the air being so foul that explosion and choke damp are very frequent. On the 12th January, 1849, the surveyors were very nearly losing a whole party by choke damp, the last man being dragged out on his back (through 2 feet of black fœtid deposit) in a state of insensibility. Another ex- plosion took place on the 12th February, in the Peckham and Camberwell Road sewer, and one on the 21st February, in the Kennington Road sewer; in both cases the surveyors had the skin peeled off their faces, and their hair singed. Two men of one party had also a narrow escape from drowning in the Alscot Road sewer, Rotherhithe, on the 24th instant; but fortunately none of the foregoing cases were attended with serious damage. "The sewers on the Surrey side are very irregular; even where they are in- verted they frequently have a number of steps and inclinations the reverse way, causing the deposit to accumulate in elongated cesspools. It must be considered fortunate that the subterranean parties did not first commence on the Surrey side, for if such had been the case, they would most undoubtedly have broken down." These surveyors report that in the modern district of Belgrave and Eaton Squares, although the brickwork of the sewers is gene- rally sound and good, they contain several faulty places, and abound with noxious matter, in many cases stopping up the house drains, and smelling horribly. In the neighbourhood of Hyde-park Gardens, and the costly squares and streets adjacent, the sewers abound with the foulest deposit, from which the most disgusting effluvia arises. It has been estimated by professional men that the whole eva- porating surface of stagnant and pestilential matter beneath the HYDRAULICS. 455 houses and streets of the metropolis is equal to a canal 50 feet wide, 10 miles long, and 6 feet deep, and that it would form a putrid swamp nearly 800 acres in extent, or nearly tiree times as large a surface as the whole population could lie down upon. Without any reference to the injury to heath that must inevi- tably result, even to the strongest constitutions exposed to such emanations, or how insensibly yet fatally they prove when concen- trated upon the weakly, and without any reference also to the very great cost of such large sewers, I submit, tha: on the question of efficiency alone, I have shown ample reason for their abandonment, excepting under the most urgent contingencies. The main sewers having been laid out and their sizes determined, the arrangement of the house drainage next denands our attention. Perhaps no branch of the constructive art has received greater improvements from science, than the formatim of house drains. Prior to the year 1846, it was the custom in the metropolis to construct house drains, either square or circuar, 12 or 9 inches in width or diameter, the latter being the minimum size permitted by the regulations. These drains were constructed either of brick or stone, emptying into large brick sewers 5 feet to 5 feet 6 inches in height, 2 feet 6 to 3 feet in width, vith curved top and bottom and straight sides. The expense of this method amounted to about ten guineas per house. In 1846 this system was modified, under the direction of the Westminster District Sewer Commission, a sx inch pipe was sub- stituted for the former house drains, dischargig into an egg shaped sewer 3 feet 3 inches by 1 foot 9 inches in courts from 300 to 400 feet in length, 2 feet 9 inches by 1 foot 6 incies, in places varying from 150 to 300 feet in length, and 2 feet 3 inches by 1 foot 3 inches, in places less than 150 feet in length. The expense of this improved system averaged about five guineas per house. About the year 1849 a system of back drinage was introduced into London by the surveyors of the Metropolitan Commission of Sewers, which, for economy and efficiency, surpassed every thing of the kind that had preceded it to an astonising degree. A great number of house drains were laid down, conposed of glazed stone ware impermeable pipes four inches in diameter, and instead of the previous system of leading the drainage (the most deleterious por- tions of which are generated chiefly in the back premises) through the house, into the main sewer in the midde of the street, favor- ing to the utmost the emission of effluvia n the passage through the house, and having, moreover, to pass over a considerable space, 456 HYDRAULICS. with the least possible declivity and proportionate velocity, the new system concentrated the sewage in smaller drains at the farthest possible disance from the houses, and conveyed it away from them with far greater velocity produced by the increased inclination consequent upon the shortened length of drain. The junctions too were formed so as to interfere, as little as possible, with the flow of the sewage being made curvilinear, instead of the right angled construction of the old system. In addition to all which advantages, he expense of construction is reduced to its minimum. Plates 13 and 14 are two plans of the same block of 40 houses, and will illustrate tle old and defective system, as well as the im- proved one now recommended. In this block, the total length of drains by the old separate system is 2,956 fed, by the improved system of back drainage 1,300 feet; while the cost is considerably less by the latter than by the former arrangement. The sizes of house drains will, of course, become the subject of calculation, in the same manner as the larger drains. Three inch pipes are recommended to be the minimum, and six inches will be found sufficiently large for the maximum. Besides the advanages of diminished friction, economy in con- struction and improvement in form, obtained by the use of pipes for house drains, a positive gain in fall is obtained, without alter- ing the relative position of the drain. The height of a nine inch barrel drain with a 4 inch rim is 13 inches above the level of the outfall, while the heght of a 4 inch pipe is but about 5 inches. So that, if a drain feet long would require, if constructed in brickwork to be laid level, the pipe might have a fall of more than 8 inches, equal to an inclination of 1 in 90, and this gain would be considerably more important and apparent, if the length of drain were shorter, such, for instance, as the case of a drain in a court yard 10 feet long, towhich the gain of 8 inches in the fall would impart an inclinationof 1 in 15, and a capacity to discharge 245 gallons of water per ninute, while the old brick drain would not discharge 30 gallons in the same time. I will now add a few words relative to the new theory of back drainage, in addition to what has been previously advanced. Be- sides diminishing the ength of the drains in the aggregate, and so increasing the velocity and reducing the expense, great improve- ment is effected in eachseparate drain. Water is chiefly used in and about the back offices of houses; closets are generally situated there, and thence the lischarge of waste water will principally be. HYDRAULICS. 457 I have already noticed the common practice of placing sewers for the reception of house drains, so as to compel the necessity of passing the drain across the court yard, underneath the basement rooms of the house, under the foot paving and into the middle of the carriage way; while by the new system, the drain is not re- quired to be nearly so long, and hence the rate of inclination is considerably greater. Figs. 189 and 191 are plans, and figs. 188 and 190 are sections of a house, which will illustrate this more fully. The plan, Fig. 191, shows the old system: C is the sewer in the centre of the street: A is the closet in the yard and B in the house. The plan from A and B to C displays the proportion of noxious evaporating surface formed by the house drains. The lines from A and B to C, in the section, fig. 190, show the proportion of the capacity of the drains and so much of the sewer as are unoccupied by deposit, to act as reservoirs of foul gases. The plan, fig. 189, is illustrative of the improved system. The diminished extent of evaporating surface obtained by the pipes, supposing them to be proportionately occupied by ordure, will be apparent, but when the pipes are properly laid, they will keep them- selves perfectly clear of all deposit. The section, fig. 188, of these improved drains exhibits a rapid fall, in place of the slight inclination under the old system. One other great desideratum of improvement possessed by the new system over the old, must not be omitted a notice. When a stoppage takes place in one of the old description of drains, it fre- quently can only be rectified by taking up, first the carriage way, next the foot paving, then the flooring of the front and back room, and, finally, perhaps the paving of the yard. Under the new sys- tem, this latter operation is all that can possibly be required. The rats, too, had the means of conducting the noxious effluvia from the old defective brick drains into the house; but the glazed stone ware pipes prevent them the exercise of this mischievous pastime. Before I take leave of this part of my subject, I must state, that all the improvements I have suggested and explained will be en- tirely futile, unless works are skilfully and properly executed; and I am firmly of opinion, that so far from the professional man's fee being thrown away for advice in matters of this nature, it will very frequently save double its amount in present outlay, besides rendering the expenditure serviceable to the purposes for which it is intended. I never yet knew a case of failure of pipe drainage 2 F 458 HYDRAULICS. that did not result from some accountable cause that should have been avoided at the commencement; and so rapid is the flow of the sewage in some of the well-constructed pipe drains, at good in- clinations, that pieces of paper in a perfect state have been observed to pass the outlet of the sewer. A word on the subject of junctions for house drains will but oc- cupy an appropriate place in a paper of this kind. The general custom with engineers and surveyors was to make the junctions of house drains at right angles. Experiments have proved that while a given quantity of water running direct in a drain was discharged in 90 seconds, it required 140 seconds to discharge the same amount of water from a drain of equal size and fall which turned at a right angle, but 100 seconds only was required with a drain laid in a true curve. A house drain at right angles, whether hori- zontal or vertical, is vicious in principle; the sewage will never flow so freely as in one properly constructed, and accumulations will constantly take place. The right-angled junction for horizontal drains is pretty generally abandoned at the present time, but it is still erroneously continued by some for vertical drops. Exactness of workmanship, both in the make of the pipes, and in the method of laying them is equally as essential as the skilful arrangement of the drains throughout the house; for, from what has been said, it must be evident, that in a proper system of drain- age, water is not required to clear away accumulations, but to pre- vent their ever forming. Cases will frequently occur in which a junction of a four-inch branch with a four-inch main will require no additional capacity in the main to receive the sewage of the branch, the additional hydraulic pressure counteracting the effect of the additional quan- tity; and the same may be said of other sized branches and mains; but in all cases when such is not the fact, the main should be in- creased by a tapering pipe. When drains are left to the management of bricklayers without professional supervision, it is not at all an uncommon circumstance, indeed, I dare say, I may call it a "common one," to increase or diminish the size of a drain by pushing the end of the smaller pipe into the larger one. I have also seen a man very busily engaged cutting a hole in a pipe into which to insert another, and thus form a rude junction; the result of these practices is a speedy failure of the drain, a wholesale condemnation of the system, and an increased additional expenditure on some more favoured but far less scientific substitute. In passing in review the works of house drainage, as recom- HYDRAULICS. 459 mended under the new system of back drains, we find that we must provide to every closet, sink, court yard stone, and roof or stack pipe, a 3 or 4 inch drain, communicating by proper curvi- linear junctions with the main sewers, and these must be properly trapped. With reference to the mode of trapping house drains and of pre- venting the egress of foul gases into habitations, the best form, because the most economical, simple, and least liable to derange- ment, is the common syphon trap, which being made of the same material, and of the same guage and length as the drain pipes, is readily adapted to its purpose, and may be inserted at any interval or in any position along the drain. It is a very popular error, that the new system of drainage requires better traps than the old. Nothing is more common than for an engineer to be told-"Ah! now that we have these new drains, we must take care that they are well trapped, or we shall be in a fine state." Why the best protection we can have against inconvenience of this nature is, the removal of all masses of decomposing matter from beneath or near habitations before decomposition can have advanced, and before any part of it can get into those ultimate stages of decay which in the present, or perhaps I ought to say, old methods of town drain- age, it usually reaches before removal. It has been found by an experience of three years, that house sewage, drained through im- permeable pipes into a water-tight tank, may be stored even for four or five days without becoming offensive. It should be borne in mind that such sewage, so stored in an im- permeable receiver, differs very strangely indeed in its degree of fluidity and other qualities from the noxious contents of an ordinary cesspool, from which the more fluid portions are constantly oozing. I might, perhaps, advance a few observations on the construc- tion of the chief apparatus for the decent and efficient sanitary ar- rangement of every house-I mean the water-closet. It is a room to which but very slight attention is paid by too many of our popu- lation, with the machinery of which too many are wholly unac- quainted, and of the importance of attention to the perfectness of all its parts, more especially the apparatus for preventing the effluvia from returning into the house, so few are sufficiently alive. But my chapter has already extended far beyond the limits within which I originally intended to confine it. I will, therefore, simply suggest, that the chief points to be sought in the construction of the apparatus appear to be:- 1. A sufficient spread of the water to effect a complete scour for the removal of the soil; 460 HYDRAULICS. 2. Economy of water to effect the scour and replenish the trap; 3. The best trap to prevent the ingress of the effluvia from the general system of drainage, with which the apparatus must be in connection, and also to prevent the return of any effluvia from the soil of the closet itself; 4. Freedom from stoppages; 5. Non-liability to derangement; 6. Facility for repair; and 7. Economy in price. The effectual removal of rain and storm water from the surface of the public highways, will require a grating at properly regulated intervals, on either side of the street, according to the nature of the road and the rate of inclination. These grat- ings must be made to communicate with the main sewer through a properly constructed trap and pipe drain. If the road be a Mac Adamized one, some contrivance will be necessary to intercept the detritus that will pass the grating from entering the sewer, to which it is very injurious by reason of the short time in which it concretes, and forms an impediment to the flow of the sewage. Fig. 192 is the plan, and fig. 193 the section, of a trap and cesspit, which has been advantageously used in many cases, and of which favourable reports have been made. Fig. 194 is a plan, and fig. 195 a section, of an extension of the same principle by means of a double cesspit; but in either case, periodical cleansing with water is required. The surveyor to the Preston Local Board of Health has adopted an extra grating placed within the cesspool in a vertical position over the mouth of the shoot, the advantage of which is, that the street grating may be made of such a width as not to be liable to become choked. A perforated plate would be preferable to long bars, through which substances of considerable length although narrow can easily pass. The manufacture of earthenware pipes for drainage purposes dates only since the year 1842, when the sanitary enquiry gave rise to their adoption, and since that time the demand has been so great, that manufacturers have given very little attention to im- provements which, under a less extensive demand, and with greater competition, must have been inevitable. As much as 35 per cent. upon the prices advertized was offered to me by a manufacturer if I could procure him the order for about £1000 worth of pipes required in the drainage of a provincial town to which I was acting as engineer. Such an offer is quite sufficient to convey an idea of the large profits which have arisen in the HYDRAULICS. 461 trade; and I only notice it here, to justify any person purchasing drain pipes, in insisting upon perfect symmetry and workmanship in the articles that are supplied him. The first joint that was suggested to these stoneware drain pipes was, the “butt joint," which simply consisted in pushing one pipe against another, and joining them as well as might be practicable. This was soon improved by the introduction of the socket joints The objection to these pipes principally consists in the difficulty of opening the drain in case of necessity, as it will be evident that if the flanges or sockets are sufficiently long, a pipe must be broken to accomplish an entrance to the drain. To obviate this, pipes with half sockets have been used, the socket extending only on the under side of the pipe; and it has been suggested, that one moiety of the pipes to be used should have one of these half sockets on either end, while the other moiety should be without sockets, so that every alternate pipe, as it were, drops into its place upon the half sockets of the pipes before and after it, and could of course be removed with equal facility. Another suggestion gave rise to the adoption of a pipe to be laid at intervals along the drain, the upper half of which could be removed, and thus afford the means of more readily ascertaining the point at which a drain might have become choked, or for the insertion of a junction. This pipe, however, will not efficiently answer the purpose of such pipes, it cannot be impermeable, and consequently should not be used. An objection to any socket at all on the pipes arises from the fact of its interfering with the proper laying of the pipe, which generally acquires a bearing upon the flange without being bedded in the centre, and consequently its liability to be broken is much increased. As an improvement upon this, the rabbeted cone junc- tion pipes have been introduced. The drainage of Croydon has been (I believe) entirely carried out by pipes of this make. Upon the question of laying the drain pipes, making the exca- vations, joints, junctions, traps, and such like, I omit a description here, as full particulars will be found contained in one or other of the specifications appended to this chapter. WATER SUPPLY. We next come to the question of Water Supply, and unlike the drainage question, in which our first concern was to look out for a place of deposit, we now have to do exactly the reverse, and to find the purest and best source from whence we may obtain a supply. According to the highest authorities, the qualities for the water 462 HYDRAULICS. supply of a town population range themselves in the following order :- 1. Freedom from all animal and vegetable matter especially matter in a state of decomposition. 2. 3. 4. Pure aeration. Softness. Freedom from earthy or mineral, or other foreign matters. 5. Coolness in delivery, at a medium temperature, neither warm in summer, nor excessively cold in winter. 6. Limpidity or clearness. If the slightest taste or smell is perceptible in water, some foreign matter is present which should be expelled if possible, the smell either denoting organic matter in a state of decomposition, or some insalubrious mineral property. If water is tinged with colour, it is caused by earthy or vegetable matters which require to be removed by filtration. In seeking a supply of water for all the uses of a town popu- lation, it is doubtless desirable, if possible, to avoid the adoption of a river source in which the water may possess many degrees of hardness; but if the natural physical features and the geological stratum of the surrounding country, do not present that facility for obtaining a supply of soft water from gathering grounds, it certainly becomes a question of expediency whether the waters of the river source cannot be so far purified from animal and vegetable matter as to render them eligible for the purposes required. Those towns that are without the presence of a neighbouring river are generally well situated for obtaining an abundant supply from gathering grounds and storage reservoirs. Water obtained from such a source will undoubtedly be more or less superior in quality according to the soil and subsoil of the lands upon which it is collected. The less the interval during which rain water remains upon the surface, the smaller must necessarily be the im- purities it will take up during that time. And again, the smaller the surface over which it is driven before it can percolate into the land, the smaller will be the amount of organic matter with which it will become impregnated. If the town to be supplied has in its vicinity a sufficient area of hill lands at an elevation to enable the collection of the required quantity of water, and its storage in a reservoir situated above the level of the top floors of the highest houses in the town, that is of all others the most desirable site for gathering ground be- cause all lifting of the water by pumping will be entirely obviated, HYDRAULICS. 463 and every house, indeed every room in the town, may be supplied by the natural power of gravitation. The method of catching the rain fall of an elevated area must be varied according to circumstances. For manufacturing pur- poses in the North of England the practice has been to cut a cer- tain number of catch water ditches around the apex of the hill, in the form of contour lines, varied of course according to the extent of the gathering ground and other physical features; and below these catch water contrivances, to construct a reservoir, regard being had to the relative elevation of the reservoir and the place at which the water is required for use. Large pasture lands on a sharp sandy or gravelly porous soil incumbent in a clay subsoil, offer the most geological advantages for gathering grounds; and the modern method of land drainage by permeable pipes is probably the best mode of collecting the water. The impurities held in suspension by the water are dis- turbed in its passage through the sand, and the organic and other matters held in solution are seized upon by the growing herbage, so that water so collected will flow from the pipes in a state superior, generally speaking, to water from all other sources. If no gather- ing grounds can be found of sufficient altitude to supply the town by natural gravitation, the water must be lifted to a reservoir on a site that is high enough for that purpose. It will be found far more convenient to lift the water previous to storage than after- wards, because if the water is supplied to the inhabitants by gra- vitation, the pipes will always keep themselves full and a constant service may result. The pumps will then only be required to work as water from the collecting pipes requires to be lifted to the reservoir. Water from deep wells may be sometimes found free from animal, vegetable, and mineral impurities, and in such cases it only becomes a question of pecuniary expediency as to its use. In estimating the quantity of water that may be collected by means of gathering grounds, the first information must be, the average rain fall of the district, and in estimating the proportion of that fall which may be reasonably expected to be collected and stored, considerable attention must be given to the absorptive pro- perties of the surface soil, and also to the nature of the subsoil. The first should allow the water to soak into the land as fast as it falls, and the latter, if impervious, will allow little to pass the pipes and be lost. If water can be collected by means of land drainage, such as we have hinted at above, and from a bed of vegetation, such as pasture grasses, on sandy or gravelly soils, it will require no filtration 464 HYDRAULICS. if properly stored in a well constructed reservoir, a better filter than this natural one being beyond the power of science to suggest. It will take about an inch and a half of rain-fall on an acre to sup- ply a house with the quantity of water we have herein assumed to be the proper supply, viz., 100 gallons per day, (always bearing in mind we are speaking of an average; a house with six inhabi- tants having 120 gallons, while one with four inhabitants has but 80 gallons), so that if we can save nine inches of the annual depth of fall, every acre of gathering ground will supply six houses; and for a town of 6000 inhabitants, or (at our average) 1200 houses, 200 acres of gathering ground will be sufficient. In computing the expense of this mode of collection, much will again depend upon circumstances, the price of pipes, and skilled labour in the neighbourhood, but £6 per acre may be pretty safely taken as the maximum, against which a considerable set-off may be generally calculated on from the owner of the soil, whose land would be benefited by the execution of the works. But if we take the full cost as a first outlay it amounts to £1200, or £1 per house on the houses benefited, which may be said to be placed in the same position as they would be by the sinking of a well on every premises, with this advantage, that the water in the former case is ample in quantity and pure in quality; while in the latter it is often scarce, or else so hard as to be unfit for many domestic purposes, and so contaminated with the percolation of the neigh- bouring cesspools as to be injurious to health and unpleasant to taste. It may be useful to bear in mind that the quantity of water here allotted to each individual, is a very bountiful allowance. Some engineers, I am aware, estimate one inch of rain-fall per acre as sufficient to supply each house, the allowance being about 62 gallons per day, or assuming the average of five occupants, 12 gallons to each person. It is no doubt as essential to have quan- tity as quality, but still, if instead of finding that a town of 1200 houses possesses an eligible gathering ground of 200 acres, we find only 130 or 140 acres; we may nevertheless consider that with an occasional auxiliary supply for those purposes in which quality is not a consideration, such a town to be well supplied. The next question that will demand attention, whether we adopt the gathering ground as a source of supply, or whether we obtain our water from a river or a well, is the storage reservoir. In elevation we have already said this should be sufficient to serve the highest houses in the district, in their upper floors, by the simple HYDRAULICS. 465 power of gravitation. In size it will be guided by the source of supply; if this is from a river or a well, a capacity to contain enough for six days' use will be ample, because the pumps may be worked at any time, the six days' being only provided as a provision in case of accident; but if the supply is from gathering grounds, calculated upon a basis which assumes that none of the water falling thereon shall be wasted, our reservoir must be sufficient to hold the excess of the supply above the demand in wet seasons, to provide for the deficiency of supply in seasons of long draught. If we assume that a reservoir should contain a four months' supply, we shall appear to make ample provision for this irregularity. If our reservoir is within reasonable dimensions, it should be certainly covered over, and the light should be excluded. A reservoir in- tended to contain the four months' supply just spoken of could hardly be so treated. In all cases, the reservoir should be con- structed as deep as possible; but this is of less importance in a covered reservoir than in an open one, the great desideratum being to prevent as much as possible the rays of light from exercising any objectionable influence upon the purity of the water. Having determined the site of the reservoir and the size, we come next to the consideration of the course and direction of the service mains. The same desiderata should now occupy attention as influenced the laying out of the main sewers. Friction should be avoided as much as possible, and a regular inclination will in- sure a more steady pressure upon the pipes. In calculating the sizes of the mains, a distinction will become apparent between a constant and an intermittent system. In the former we may with tolerable security assume that the whole of one day's supply will not be required in a less space of time than four hours; while in the latter, the cisterns of the inhabitants will be filled in a time, limited only by the capacity of the machinery adopted for the purpose. A few words on the comparative merits of the two sources of supply may not be out of place. The expense of erecting cisterns, and the necessary apparatus for the intermittent system in new houses of the first class in the fashionable districts of the metropolis, rarely comes under £100 per house; and in one block of building, the details of which have come under my observation, the expense of cisterns, ball-cocks, and extra pipes amounted to £900, of which £500 was for the cisterns alone; whereas £200, or, at the most extravagant estimate, £300 would have furnished the means of a better supply by the constant system. In all towns that are supplied with water under 466 HYDRAULICS. the constant system, the advantages are apparent in the immense saving of water, and the general comfort and cleanliness of the inhabitants, without reference to the pecuniary advantage above alluded to. Independent of other advantages, the quality of water suffers less deterioration under the constant than the inter- mittent system; and beyond doubt, the strain upon the mains and submains is not so severe, inasmuch as all hydraulic shocks common to the intermittent system have not to be resisted under a constant supply. It is in accordance with common sense, that water exposed in a cistern out of doors, in a smoky neighbourhood, must soon become impregnated with the impurities that are floating about in the at- mosphere in every possible direction; and if the cistern is within doors, the water soon loses its freshness, and acquires a slimy cha- racter. Under the constant system of supply, if all the pipes are made to communicate, a free circulation is kept up by the constant drawing from one pipe or another, and as nearly as may be the same quality of water is maintained throughout the town; the water always flowing towards the point of draught. From what has been stated, it is evident that no town can be said to have a proper supply of water that does not give to every house a tap, from which an unlimited draught can be taken at any hour of the day and night. That the establishment of apparatus to carry out the constant supply is less expensive, and that the water so supplied is better in quality than by any other method of distribution. The basis of a calculation for the sizes of the mains being a given quantity of water required to be conveyed a certain distance in a certain time with a known head, the Hydraulic Tables will speedily determine the requisite diameters. It should be added, that in all cases where practicable, the water pipe and the drain pipe should be laid in the same trench, by which means a great saving is effected in the excavation and replacement of the ground in laying down the pipes. But in every case, the water main should be above the drain, so that all chance is avoided of any escape from the drain polluting the water service. The sub mains and house services, stand pipes for street watering, fire plugs, stop-cocks, and other minutiae of detail, will be laid out at the discretion of the engineer. The method of carrying out the works on the ground we will endeavour to illustrate in the specifications annexed. As much misconception exists with reference to artesian wells and springs, a word or two thereon may be appropriately advanced HYDRAULICS. 467 under this branch of our subject. Some assert that an artesian well ceases to become so directly it ceases to throw up water, but such an argument is not tenable for a minute. An artesian well, so called from the province of Artois, in France, (at which place the practice of boring used in the construction of an artesian well was chiefly carried on,) is nothing more than an illustration of the old and well known hydraulic fact, that "water will always find its level." The theory of these artesian wells is very simple. Let the points A A, fig. represent the exposed surface of a porous strata, perfectly absorptive of water, and on the contrary, let the points B B be the surface of a strata of tenacious clay, wholly im- permeable; now if it be desired to create an artesian well at the point C, we shall have to bore through the impermeable clay, and while so doing, no discharge of water will take place; but as soon as we tap the porous strata at D, the water therein will rise to the surface C, and (if confined by a stand pipe) to such a height above C as shall correspond with the level of the water in the porous strata. Inasmuch as it is possible to exhaust the supply, so will the working capacity of this well depend upon the extent of surface area of the collecting porous strata, as it must be evident that in a dry season the longer the well is worked the lower must the alti- tude of the water in the strata become, and the less efficient will be the discharge, and if rain does not replenish before the water in the earth is drawn to the level line E, the well can no longer dis- charge water above the surface, the hydrostatic pressure being all removed from it. But this by no means deprives the well of its character or right to its name, since no sooner is the water in the porous strata replenished by a fall of rain on the surface, than the well resumes its operations with a vigour proportionate to the fall of rain. Some porous strata stretch out so wide and offer so vast an area of exposed surface, that the water contained in them can hardly ever become exhausted. What has been said with reference to artesian wells, will also serve to explain the properties of springs, which are only so many additional examples of hydrostatic pressure acting upon water con- tained in porous strata, which freely finds vent at the first place at which such strata becomes exposed to the surface of the earth at a low level. In Mr. Weale's Rudimentary Treatises will be found a little work, entitled, Well Digging, Boring, and Pump Work, by John Geo. Swindell, R.I.B.A., which will be found to be a most able though brief elementary description of this question. Before finally closing this subject, I will observe, that the re- 468 SPECIFICATION. gulations of good drainage can hardly tolerate the existence of old cesspools, and positively prohibits the creation of new ones within the vicinity of, or in proximity to, any collection of dwellings, of whatever description, as well as an untrapped connection with any drain or sewer. Interpreta- tion. Extent of Contract. Quality of Iron. Casting of Pipes. SPECIFICATIONS, &c. BIRCH END LOCAL BOARD OF HEALTH. 1853. Contract, No. I. IRON PIPES AND CASTINGS. Specification to be observed by the contractor for making and delivering at the railway station at Birch End, certain iron socket pipes and castings, required for purposes of water supply by the Local Board of Health, Birch End. In this specification the words " Local Board of Health," shall be understood to mean the Local Board of Health, for the time being, duly elected and acting in and for, the district of Birch End. The word "Engineer" shall mean, Edward Ryde of 14 Upper Belgrave Place, Eaton Square, London, Civil Engineer and Surveyor, or other, the duly appointed Engineer, or Surveyor, to the said Local Board of Health for the time being; and the word Contractor shall mean one or more Contractor or Con- tractors, and shall include his or their heirs, executors, and administrators. This contract includes the manufacture and supply of all the pipes, cocks, and special castings that are required, to construct and completely finish the water works about to be carried out by the Local Board of Health. The iron shall be remelted in the cupola or air furnace; and shall be of the best description without admixture of cinder, or other matter, to render it inferior in quality. It shall be strong, close grained, and tough, and shall be as hard as can be conveniently drilled and clipped. All the pipes shall be cast vertically in dry sand, and shall be of the kind, or description, usually denominated "socket pipes:" they shall be of the forms, thicknesses and dimensions shown in the drawings, and in case of any Pipes must be sound and free from Defects. Pipes shall be proved. Engineer may attend dry. IRON PIPES AND CASTINGS. 469 discrepancy between the scaling and figured dimensions, the latter are in all cases to be observed. The pipes are to be cast perfectly sound, free from cold shuts, honey comb holes, or other defects, and shall be truly cylindrical in the bore, straight in the axis, and internally of the full specified diameter. They shall be thoroughly cleaned, internally and externally, and great care shall be taken in cutting off the runners to preserve a square angle on the inner edge of the socket against which the lead joint is made. At the junction of the branch pipes the inside diameter of the outlet pipe is to be made half an inch larger than the other portions; and the thickness of the sockets shall be in all cases a quarter of an inch more than the body of the pipe. To insure that in all cases the beads will enter the sockets, a circular iron template shall be passed to the bottom of every socket, and a circular iron ring shall be passed over every bead. The socket shall not be larger than is absolutely required, and stated in the drawings, otherwise the expense of jointing will be unnecessarily augmented. The pipes are to be each proved before leaving the foundry under a pressure equal to a column of water 600 feet in height, and such pressure shall be maintained for at least three minutes, whilst the pipe is being sufficiently and repeatedly struck in every part with a hammer of weight suitable to the size of the pipe. The engineer is to be at liberty to attend at the foundry at the Foun- during the casting of the pipes or any of the special cast- ings referred to in this specification, or he may depute a competent person to attend on his behalf, for the purpose of ascertaining that his instructions and the provisions of this specification are complied with; and the contractor shall at all times afford him every facility he may require, and pay immediate attention to any directions he may give. Length of Pipes. Pipes. The two-inch pipes shall be cast in lengths of six feet; the larger sizes in lengths of nine feet; exclusive of the socket in either case, and shall be of the weights contained in the schedule hereto annexed. Quantities of The probable quantities of the various pipes and castings required are set forth in the schedule hereto annexed; but it is to be distinctly understood that the engineer shall have the power at any time to make alterations in, additions 470 SPECIFICATION. Pipes, &c., to be coated with Dr. Smith's pre- paration. Contractor responsible in pipes. to, or deductions from, any part of this contract, which alterations in, additions to, or deductions from, shall not annul the contract, but an equivalent shall be given or taken as the case shall require. The whole of the pipes and pieces, as soon as they are cast and cleaned, and before any rust shall have been produced upon them, are to be submitted to Dr. Angus Smith's patent process, in such a manner as to receive, while at the proper temperature, a complete and thorough coating of the preparation over the whole of the internal and external surface. Should the iron be of inferior quality, or the pipes too for all flaws light, or any flaw or other defect appear in any of them after they have been delivered, the contractor is to be responsible for that defect, and is to replace the defective pipes with good ones to the satisfaction of the engineer. Delivery of pipes. Contractor responsible within twelve months. Cocks. Engineer to have same The pipes and pieces are to be delivered by the con- tractor, at the railway station, Birch End, in such quantities and at such times, as the engineer may from time to time direct, the whole quantity to be sent in on or before the 31st December next. In the event of the failure of any of the pipes within twelve months of their delivery, and the failure should arise from any defect in their construction, of which the engineer shall be sole judge, the contractor shall be held responsible for the damage, and shall on demand, refund to the Local Board of Health, any expense to which they may have been subjected by reason of such failure. The cocks required are of the description commonly called, "double faced screw cocks." The shell of each cock is to be cast in one piece, and to be a sound clean casting, made from the best description of iron, and fitted up with bored and turned stuffing boxes, faced joints, and all the necessary bolts and nuts for the same. The spin- dles are to be of gun metal, with square thread, and each to be provided with a wrought iron box key head, cottered in. The valves of the cocks from two inches, to four inches in diameter, are to be of gun metal; above that diameter iron castings will be allowed, but with gun metal facings. Each cock must be perfectly tight, and of the best workmanship. All the powers conferred upon the engineer with power, and reference to the pipes, in this specification, and all the re- IRON PIPES AND CASTINGS. 471 ity with cocks as same liabil- sponsibility of the contractor shall equally relate to the cocks and other special castings, so long as the same is not repugnant to, or inconsistent with, any acknowledged engineering practice. pipes. Special castings to be made as soon as possi- ble after ordered. Sureties. Payment. All branches, bends, taper pipes, fire plug pipes, and special castings of every description shall be made and delivered as soon as possible after the receipt of the orders by the contractor. The contractor shall, if so required, find two good and sufficient sureties, in a penal sum as nearly as may be equal to one quarter of the amount of the accepted tender, for the due performance of his contract. And the said contractor shall be entitled to payment for his work, in manner following, that is to say, 50 per cent. of the value of pipes and castings from time to time made and delivered, within one month of such delivery; forty per cent of the value of the whole of the pipes and castings delivered, within two months of the final comple- tion and delivery of the whole contract; and the remaining 10 per cent. at the expiration of six months from the final delivery of the pipes, provided the said pipes have proved sound, or the balance of such 10 per cent., if any, as may remain due to the Contractor, after deducting any costs and expenses the Local Board may have been obliged to incur, by reason of any unsoundness, or failure of the pipes. Always premising that the certificate of the En- gineer will be required, in all cases, before any payment will be made by the Local Board. Inside Diameter of Pipe in Inches. Schedule hereinbefore referred to. Length of each Pipe in Feet. Weight of each Pipe. Probable number of each kind required. Cwt. Qrs. lbs. 2 ∞∞29 C I WON 6 0 1 20 3 9 4 9 5 9 6 9 7 9 8 9 9 10 9 11 9 12 9 12230 + + 20 co 0 3 20 1 1 7 1 3 0 1 U 3 0 3 1 20 4 0 0 4 2 0 12 6 1 14 15 472 TENDER. Contract, No. I. TENDER FOR PIPES AND CASTINGS. We the undersigned Contractors will undertake to make and deliver, according to the specification annexed, the several probable quantities of pipes and special castings therein referred to at the prices stated below. Straight pipes not exceeding 2 inches in diameter, at per Cwt. £ s. d. Curved pipes Taper pieces Branch pieces Straight pipes, exceeding 2 and not exceeding 4 inches in diameter Curved pipes Taper pieces Branch pieces Straight pipes, exceeding 4 and not exceeding 6 Curved pipes Taper pieces Branch pipes inches in diameter Straight pipes exceeding 6 and not exceeding 9 Curved pipes Taper pieces Branch pipes inches in diameter Straight pipes exceeding 9 and not exceeding 12 Curved pipes inches in diameter Taper pieces Branch pipes Cock and plug castings and other hollow castings not exceeding 3 inches in diameter Exceeding 3 inches and not exceeding 6 inches Exceeding 6 inches and not exceeding 9 inches Exceeding 9 inches and not exceeding 12 inches And we will undertake to execute an agreement (to be prepared by, and at the expense of, the Local Board) for the due and complete fulfilment of all the conditions expressed, and implied in and by, the specification hereto annexed. Gentlemen, Your most obedient servants, CONTRACTORS. SPECIFICATION. 473 Interpreta- tion. Extent of Contract. Quality and description of pipes. BIRCH END LOCAL BOARD OF HEALTH. 1853. Contract, No. II. STONE WARE DRAIN PIPES. Specification to be observed by the Contractor for making and delivering at the Railway Station, at Birch End, certain glazed stone ware tubular socket pipes, half socket pipes, bends, curves, junctions, traps, soil pans, &c., required by the local Board of Health, Birch End, for the purposes of drainage. In this specification, the words, "Local Board of Health," shall be understood to mean the Local Board of Health for the time being, duly elected and acting in and for the district of Birch End. The word "Engineer," shall mean Edward Ryde, of No. 14, Upper Belgrave Place, Eaton Square, London, Civil Engineer and Surveyor, or other the duly appointed Engineer or Surveyor to the said Local Board of Health, for the time being; and the word Con- tractor shall mean one or more Contractors, and shall include his or their heirs, executors, and administrators. This contract includes the manufacture and supply of all the straight and curved drain pipes, curve, bend, taper, and junction pieces, traps, soil pans, &c., required to con- struct and entirely complete the drainage of the town of Birch End, as the same are particularly delineated, and described upon the plans and drawings deposited in the offices of the Engineer, in London, and of the Clerk to the said Local Board of Health, at Birch End, and accord- ing to this specification. The ordinary pipes and pieces shall be of the descrip- tion usually denominated "socket pipes," sound, well burnt, glazed stone ware, free from cracks, flaws, and all other imperfections, perfectly impermeable, truly cylindrical in the bore, straight in the axis, internally of their full specified diameter, with their inner and outer surfaces as nearly as possible concentric, and especial care must be taken that the sockets, which in the larger sizes of pipes exceeding nine inches internal diameter, shall be at least three inches in depth, will receive the smaller ends of the pipes. The engineer shall be at liberty so often, and for so 2 G 474 SPECIFICATION. power attend at Manufactory &c. Engineer has long as he may think fit to attend at the manufactory, either by himself or his duly authorised clerk, for the pur- to inspect, pose of inspecting the processes of the manufacture, and of ascertaining if his own instructions and this specification are properly attended to; and the contractor shall pay im- mediate attention to any directions he may think proper Length and dimensions to make. All pipes not exceeding six inches in diameter shall be of pipes, &c. made in lengths of two feet exclusive of the socket; Soil Pans. Times of delivery. Engineer has power to tests, and to fect pipes. beyond that diameter the length shall be three feet. The dimensions of the several pieces of bend pipe, curves, junctions, traps, and soil pans, are mentioned and described in the drawings, and should any discrepancy exist between the figured or written dimensions and the admeasurements by scale, the former are in all cases to be taken as the correct dimensions. The soil pans must be of the shape delineated in the drawings, and the spreaders must be so adjusted as to keep the pans entirely clear of soil. The whole of the pipes, bends, junctions, curves, traps, and soil pans, must be delivered at the railway station, Birch End, in such quantities and at such times as the engineer may from time to time direct; the whole of the contract to be finally completed and delivered on or before the 31st December next. The engineer shall be fully at liberty to make a further make further test of the pipes after their delivery, either as to their reject imper- impermeability or strength or any other quality he may think fit, and if from any cause whatever he shall consider the pipes or other contrivances and things contained in this specification are not in his judgment of the best quality both in material and workmanship, according to the true intent and meaning of this specification, he shall be at liberty to reject the whole, or any part thereof, and the contractor shall immediately remove, at his own cost and charges, the pipes or pieces so rejected. Samples of pipes, &c. Contractor to find sureties. The contractor shall submit with his tender, samples of each description of pipes and pieces he intends to supply. The contractor shall, if required, find two good and competent sureties, who are willing to become bound in a penal sum equal in amount to one-fourth of the tender, for the due and complete performance of the contract. The quantities of the several descriptions of pipes and TENDER. 475 pipes, etc., required. Quantities of pieces, so far as it is possible to ascertain, are stated in the schedule hereto annexed, and they are believed to be close approximations, but it is to be distinctly understood, that the engineer shall at all times have power to make any alterations in, additions to, or deductions from, the quan- tities so stated, which alterations in, additions to, or de- ductions from, shall not annul the contract, but an allow- ance shall be given or taken as the case may require; for the calculations of which allowance the schedule of prices. shall be the basis. Engineer shall deter- In the event of any doubt arising after the execution mine doubts. of the contract, as to the true intent or meaning of this specification, the said drawings therein referred to, or the said contract, the same shall be referred to the engineer, and his decision shall be conclusive and binding; any order or rule of court of law or equity to the contrary notwithstanding. Times of payment. And the said contractor shall be entitled to payment for his work, in manner following, viz., i.e., 50 per cent. of the value of the pipes and pieces delivered from time to time, within one month of such delivery, and the re- mainder within two months of the final completion of the contract; the certificate of the engineer to the effect that the contractor is entitled to payment, being required in either case, before any money will be paid by the local board. Tender for impermeable glazed stoneware, tubular socket, sewerage, and drain pipes, soil pans, &c. 1853. To the Birch End Local Board of Health. agree We, the undersigned contractors, hereby offer and to make and deliver at the railway station, at Birch End, impermeable glazed stoneware tubular socket pipes, half socket pipes, bends, curves, junctions, traps, soil pans, &c., in accordance with the terms and conditions of the an- nexed specification, and of the following schedule. 476 TENDER. Description. Straight Pipes SCHEDULE. Internal Diameter Probable of each Pipe and Piece. quantities required. Length of each Pipe exclusive of Socket. Price per Foot. (Whole Sockets.)) 00 + 20 Co 3 500 4 650 1000 6 1150 9 2300 12 3800 15 1261 NNNN ∞ ∞ ∞ɔ 2 2 2 2 3 3 Curved Pieces and Bends . OOH LO 3 12 2 4 16 2 5 23 2 6 25 2 9 40 3 12 60 3 15 10 3 Straight Pipes (Half Sockets.) 6 22 2 9 46 3 12 76 3 15 30 3 Taper Pieces.. 4 :당 3 to 4 10 5 20 5 6 30 "" 6 9 30 9,, 12 30 12.15 15 NAN∞ ∞ að 2 2 2 3 3 Single Junction Pieces } "" Diameter of straight Piece. 3 20 5 4 10 5 20 6 20 9 30 12 30 15 30 NNNN ∞ ∞ ∞ 2 2 2 2 3 3 3 Double Junction Pieces 3 4 10 6 10 9 10 12 10 15 10 4-99999 5 7 CO CO CO NNNN 2 3 3 3 SPECIFICATION. 477 Description. Bore. Number required. Length. Price each. Inches. ននននន នននន 50 50 NNNN M 2 2 Patent Syphon Traps 6 23 + CO 4 50 50 9 50 Patent Yard Syphons, 4 with detached Grating, by which means they can be easily cleansed. 6 9 12 50 Common Syphon Pans. 50 Patent Syphon Pans. 50 Hopper Pans and Syphon Traps.. S 50 Gully Sinks, 12 with Traps for Street Gratings 15 22 18 នន 50 50 50 And we will undertake to execute an agreement (to be prepared by and at the expense of the local board) for the due and complete fulfilment of all the conditions ex- pressed and implied in and by the specification hereto annexed. We are, Gentlemen, Your obedient servants, CONTRACTORS. Interpreta- tion. BIRCH END LOCAL BOARD OF HEALTH. 1853. Contract, No. III. PIPE LAYING. Specification to be observed by the Contractor for laying and. jointing water and drain pipes, for the Local Board of Health, Birch End, according to the instructions of Mr. Edward Ryde, the Engineer to the Local Board. In this Specification the words "Local Board of Health" shall be understood to mean, the Local Board of Health duly elected, and acting in and for the district of Birch 47.8 SPECIFICATION. Extent of Contract. End, and shall include themselves and their successors. The word "Engineer" shall mean Edward Ryde, of No. 14, Upper Belgrave Place, Eaton Square, London, Civil Engi- neer and Surveyor, or other, the duly appointed Engineer or Surveyor to the said Local Board of Health for the time being. The word "Contractor" shall mean one or more Con- tractors, and shall include his or their heirs, executors, or administrators. This contract includes the excavating for, and the laying and jointing of, all the water and drain pipes and other contrivances connected therewith, required to construct and completely finish the several sewers, drains, water mains, sub mains, &c., described and delineated upon the drawings prepared by the engineer; the taking up and sub- sequent replacement of the pavement, roadway, or surface soil, of whatever description; filling in and punning up the trenches; carting away the surplus earth; carting the pipes and pieces from the railway station at Birch End to the situations in which they will be required; lead and gasket for joints of water pipes, and clay or cement for joints of drain pipes; watching day and night to guard the public from accidents; the finding and providing of all and all manner of labour, and tools and materials (excepting only the pipes and pieces which will be delivered at the railway station by other contractors), necessary to the com- pletion of the works to the entire satisfaction of the engineer. Directions of The directions of the several sewers, drains, water mains, and sub mains, are respectively marked and delineated upon the plan, and the depths of cutting, and rates of inclination, are severally drawn upon the section, and marked in figures thereon. No deviation whatever from these drawings will be allowed, except by the express direction of the engineer, and should any descrepancies exist between the figured di- mensions and the admeasurement by scale, the former are, in all cases, to be taken as the correct dimensions. The engineer will, at all times, set out and mark the several works upon the ground, and the contractor shall provide proper assistants, implements, and materials for that pur- pose, when called upon, from time to time, to do so. Works and depths of cuttings. Contractor to give notice of Highways Before commencing to break up any public road, footway, to Surveyors or street, for the purposes of this contract, the contractor before break shall give all necessary notices to the surveyors of high ways, or other proper authorities, and shall pay any ing up roads. PIPE LAYING. 479 Excavations. Laying the fees that may be legally payable in respect of the same. The excavations of the specified depths shall be made in such lengths as the engineer may direct, and of sufficient widths, as shall, in the judgment of the engineer, enable the pipes to be properly laid and backed up. The bottom of the trench, for the larger sizes of drain pipes, shall be moulded to the shape of the pipe, and a notch shall be cut for the socket, so that the pipes may take a firm bearing and be securely bedded upon the foundation. The trench is, in all cases, to be an open cutting, as no tunnelling or bench- ing will be allowed, excepting in cases of special emer- gency by express permission of the engineer. The sides of the cuttings are to be securely shored up where requisite, to prevent the adjacent earth from slipping or colting in, to protect the adjacent buildings, or to ensure the proper con- struction of the sewer. Where the foundations shall be unfit for the bedding of the pipes, the soft ground is to be taken out, and a proper and sound bedding, or foundation, substituted. If clay is met with in the excavations, so much of it is to be preserved as will be sufficient to make a layer of nine inches, at least, in thickness round all the sewers, so as to form an impermeable clay collar or casing to the same. The excavations are to be kept perfectly free from water during the progress of the work, the contractor providing all necessary apparatus for that purpose. The excavated earth is not to be thrown about in any direction most convenient to the navvies, but it is to be so placed as to cause as little interruption as possible with the free passage of the public, or annoyance to the adjacent inhabitants. When the line of sewer crosses through private property, none but unavoidable injury shall be done to the same, or the contractor shall be responsible. The pipes shall be carted from the railway station, at drain pipes. the cost and expense of the contractor, and shall be stacked as conveniently as possible for use, without unnecessarily impeding the public highway. The trench being opened to the satisfaction of the engi- gineer or his clerk of works, the pipes are to be properly and carefully fitted and matched, before they are taken into the trench. The pipe layer shall then be furnished with a bag stuffed with shavings or hay, of a size to fit the 480 SPECIFICATION. Filling in. Water pipes. Pipe laying. Hydrants and Screw Cocks. pipe rather tightly, with a rope about ten yards in length, fastened at one end to the mouth of the bag. The bag must be placed in the first pipe at the outfall, and the rope passed through each pipe as it is laid down, until the rope is served out; the joints are then to be made with clay of approved quality, and properly tem- pered, and left perfectly water tight. The bag is then to be drawn forward through all the pipes into the last pipe laid down, when other pipes are laid down until the rope from the bag has been again served out, when the joints are made as before. Curved, half socket, junction, and taper pieces are to be laid where directed. Neither the pipe layer, nor any other person, shall be allowed to walk over the pipes until they are covered over to an extent of at least nine inches. The pipes being laid, and the joints made to the satis- faction of the engineer, a layer of clay of nine inches thick is to be well punned in around the pipes, so as to form an impermeable casing of clay. The trench may be then filled in with the excavated earth up to the level of the bed for the water pipes, two men being constantly kept in the trench ramming to every man filling in. The contractor to cart, at his own expense and cost, all the iron pipes and castings delivered at the railway station by another contractor to the respective positions in which they will be required, there to be stacked in places that may be least objectionable to the general public. Before the pipes are lowered into the trench, they are to be thoroughly cleaned out, so that no earth or rubbish may be contained in them. The joints are to be made sound, of lead and gaskett of approved quality; the depth of lead in the sockets to average two inches. No split or defective pipes or castings are on any account to be laid down, nor any screw cocks or hydrants to be fixed which leak or allow the water to pass by them; and should it be found that any such have been laid down or fixed, the con- tractor will have to take them out and substitute others at his own expense. The contractor is to fix screw cocks and hydrants where indicated by the drawings or directed by the engineer; the hydrants to be connected with the main by two inch pipes. All branch pipes and dead ends are to be properly capped and left secure. PIPE LAYING. 481 Gully Gra- tings, &c. Remaining earth to be filled in. Pavements, Roads, etc. good. The contractor shall securely fix in brickwork set in hydraulic mortar, such gully gratings, sinks, fire plugs, and other contrivances as may be marked on the drawings, or directed by the engineer. The engineer being satisfied with the works that have been constructed, the remaining excavated earth, or so much thereof as may be required, shall be filled in in re- gular layers, not exceeding six inches in thickness, two men being kept ramming to every man filling in. If in the opinion of the engineer, the shoring and strutting timber cannot be removed from the deeper trenches with safety to the adjoining buildings, the same shall be left in the ground, and the contractor shall not be entitled to any extra payment on that account. Care is to be taken that all materials for re-forming the road are to be retained until the last, or until it becomes necessary to use them. The pavement, roadway, or surface soil is to be made to be made good, and left in as perfect a state as it was found to be previous to the commencement of the works, or as near thereto as may be, to the satisfaction of the engineer, his clerks, and assistants, and the surveyor of the highways, or other proper authorities. Surplus earth. Commence- ment and of works. The contractor is to cart away all surplus earth at his own expense, the same to be emptied into such open ditches or other places as the engineer may direct. GENERAL CONDITIONS. The contractor is to commence the several portions of completion the work immediately on an order being given by the en- gineer to that effect, and shall, on or before the 31st December next, complete the whole of the works herein specified, and such additional works as the engineer may direct to be executed. Contractor to works. The contractor shall at all times be present on the works, be present on or in his absence he shall provide a competent representa- tive, fully authorized to act in his behalf in all matters relating to this contract. provide la- terials, and to Contractor to The contractor shall at all times, by day and by night, bour and ma- provide and use at his own cost all overlookers, labour, and prevent acci- materials of every description whatever, that may be re- quired for proceeding with and completing the works con- tained in this contract in a workmanlike manner, or for preventing accidents, or affording accommodation to the dents. 482 SPECIFICATION. Minor parts included in contract. Descriptions not repeated validated. public during the progress of the said works, and shall in all cases immediately attend to the reasonable requirements of the engineer. Wherever neither the drawings nor specification contain any special notice of minor parts, the intention to include which is nevertheless to be inferred, and which parts are necessary for the completion and stability of the said works, all such additional parts are to be provided and performed by the contractor, and are supposed to be included in the sum at which he contracts for the works; and where any thing is directed to be done, or to "be provided if required," or words of similar import, it must be understood that every thing so referred to will be considered as included in the contractor's tender. It is to be distinctly understood, that though certain de- are not in- scriptions and stipulations are not repeated or implied in different parts of this specification, and in the contract to be entered into for the fulfilment of the same, it shall not be thence inferred that the remaining directions, descrip- tions, and stipulations, of which there shall be no repetition or amplification, are in anywise invalidated. Contractor to proceed with works to satisfaction The contractor shall at all times proceed with the works at the rate of progress required by the engineer; and should of engineer. the engineer be at any time dissatisfied with the nature or mode of proceeding in, or at the rate of progress of the work, or any part thereof, he shall have full power to pro- cure and make use of all labour and materials which he may deem necessary, deducting the cost of such labour and materials from the money that may be due or become due to the contractor. But it is hereby expressly specified and declared, that the possession of this power by the engineer shall not in any degree relieve the contractor of his obli- gation to proceed in the execution of, and to complete the works with the required expedition. Contract to be void if con- to proceed Should the contractor fail to proceed with the works in tractor fails the manner and at the rate of progress required by the su- with works perintending engineer, this contract shall be (at the option of engineer. of the Local Board of Health, not otherwise) considered to satisfaction void, so far as relates to the work remaining to be done; and all sums of money that may be due to the contractor, together with the materials and implements in his pos- session, and all sums of money named as penalties for the non-fulfilment of the contract, shall be forfeited to the PIPE LAYING. 483. Engineer may direct Local Board, and the amount shall be considered as ascer- tained damages for breach of contract. It is to be distinctly understood, that the engineer may alterations. at all times direct that there shall be made any alterations in, additions to, or deductions from, any of the works here- inbefore described or referred to; and which alterations in, additions to, or deductions from, shall not annul the contract, but the same shall be valued according to the schedule of prices, filled up by the contractor, and attached to his tender, and that the prices inserted in the schedule shall be considered as inclusive of all labourage, materials, and expenses connected with the work to which such prices apply. Sureties. Payments. Contractor responsible The contractor shall (if so required) find two good and sufficient sureties in a penal sum, as nearly as may be equal to one-fourth the amount of the accepted tender, for the due performance of his contract. Payments to the extent of two-thirds of the value of the work executed will be made to the contractor upon the certificate of the engineer that the works have been exe- cuted in accordance with this specification, and to his satis- faction; one moiety of the remaining one-third will be paid to the contractor on the completion of the whole of the works contained in his contract, and the balance upon the expiration of six months, upon the certificate of the engi- neer that the whole of the work is in a satisfactory and proper state, and that no penalty under this specification has been incurred. The contractor shall guarantee and hold harmless the for damage. Local Board of Health from any damage that may arise by reason of the negligence of his workpeople, or from any other cause, during the execution of this contract. And Engineer to should there be any doubt as to the meaning of any portion determine doubts. of this specification, the contractor tendering is requested to set forth the particulars of such doubt or obscurity in writing, and submit the same with his tender before the contract is signed; the question shall be discussed by the engineer and contractor, and if necessary, shall be formally settled in writing. After the execution of the contract, the decision of the engineer shall be conclusive and binding. The Local Board do not bind themselves to accept the lowest or any tender. 484 TENDER. BIRCH END LOCAL BOARD OF HEALTH. Contract, No. III. TENDER FOR PIPE LAYING. 1853. To the Local Board of Health, Birch End. Gentlemen, I hereby propose, undertake, and agree to exe- cute, perform, and do, the several works described in the foregoing specification, and in the drawings, according to the true, intent, and meaning thereof for the sum of pounds; and I also agree that the prices mentioned in the following schedule shall form the basis of a calculation for ascertaining the equivalent to be given or taken, in respect of any alterations in, additions to, or deductions from, the said works, that may be made from time to time, by order of the engineer. I am, Gentlemen, Your obedient servant, CONTRACTOR. Schedule of Prices before referred to. For laying stoneware drain pipes and pieces, including excavating, laying, jointing and filling in, punning ground, making good surface, cart- ing away surplus earth, and every other expense in conformity with the specification. 3 inches to 6 inches diameter 2 feet deep Price per foot lineal. £ 3. d. 4 "" 6 8 وو 10 9 inches to 15 inches diameter 2 وو 4 وو 6 وو 8 وو 10 " 12 "" For fixing gully shoots and traps sink and yard gratings 59 each وو SPECIFICATION. 485 For laying water pipes and pieces, including excavating, laying, jointing, filling in, and pun- ning ground, and every other expense in confor- mity with the specification. 3 inches diameter per lineal yard £ s. 4 "" 5 وو 99 6 "9 "" 7 وو 8 وو 9 "" 39 10 وو 11 12 99 وو وو "" For fixing stop cocks, including fixing and jointing, providing and fixing elm box over cock, and making good paving up to box. 4 inches diameter each 5 95 6 دو 7 "" 8 رو 9 دو 10 11 12 وو وو For fixing hydrants, including excavating, laying connecting pipes, and uniting the same to the mains, jointing, filling in and punning ground, and making good paving each d. BIRCH END LOCAL BOARD OF HEALTH. Contract, No. IV. RESERVOIR. Specification to be observed by the Contractor for the works set forth therein, required to be executed by con- tract, for the Local Board of Health, Birch End, according to the designs, drawings, and instructions of Mr. Edward Ryde, Civil Engineer and Surveyor. 486 SPECIFICATION. Excavator. Embanking top of reser- voir. 1 to 1. Extent of Contract.—The works comprised in this con- tract, include the excavating for, and embanking and con- structing a covered reservoir; the finding of all and all manner of materials, labour, tools, carriage, tra- velling expenses, and all other things of whatsoever description that may be required to carry on, erect, con- struct and completely finish such reservoir, as the same is particularly delineated and described in the several draw- ings, and in this specification. Plate DRAWINGS. Plan and Section of Reservoir. To excavate for the proposed reservoir to such depths as shown in the drawings, care being taken that the whole of the top soil or turf is to be removed and placed in a heap by itself, and to be used again in covering over the embankment and slopes of the said reservoir, when the same is constructed, and also that those soils which may be most retentive of water, may be placed as much as pos- sible by themselves, to be used again on the embankment of the reservoir. To embank the reservoir when constructed, with such of the excavated earths as the engineer may direct to be used for that purpose; the same to be executed in regular layers not exceeding six inches in thickness, and well punned, the proportion of punners, being such as the engi- neer may from time to time approve, but never less than three to one barrow load. Capping the To cap the top of the reservoir with the remaining excavated earths, regularly laid on in thin layers, well and solidly rammed over the arches before the removal of the cen- tering. It is proposed to slope the embankments at an incli- Slopes to be nation of 1 to 1, that is the base, being one foot and a half to every foot of height. But if, during the execu- tion of the work, the contractor should have reason to suppose that such rate of inclination will not ensure the stability of the embankment, the engineer is to be imme- diately apprised of his misgivings, and the contractor will be held responsible for all damage arising from slipping or any other cause. Slopes to be trimmed and As the embankments advance and become consolidated, covered with the slopes shall be carefully dressed or trimmed to the turf. specified inclinations, and covered with the turf that was RESERVOIR. 487 Lining of puddle. Puddle: Foundation of concrete. removed from the site of the reservoir. This shall be done in the manner pasture lands are sometimes grafted; that is, the turf shall be laid on in slips, with an interval of uncovered ground between each slip, so that the turf taken off the horizontal surface, before the excavation for the reservoir, may by this means be made sufficient to cover with sward the increased surface of the reservoir and slopes, which shall then be sown with good and proper grass seeds. To line with a coating of puddle at least nine inches in thickness the bottom of the reservoir; to line with a similar coating of puddle the space between the sides of the ex- cavation and the brickwork, from the foundation upward, to about 1 foot 6 inches above the top water line, so that such lining may be about 9 inches thick at the top, 12 inches thick at the springing of the arches, and gradually in- creasing in width to the foundations, as shown on the draw- ings; to line thoroughly, with a similar coating of puddle, the whole of the excavations for the main and other pipes passing into and out of the reservoir, and extend the same a sufficient distance beyond the outside of the brickwork, the object being to seat the reservoir in an impermeable puddle basin. The puddle is to be made of pounded clay, of approved quality, well worked with water, cut, and rammed solid, and free from stones and rubbish. Great care is to be taken after it is placed, to preserve it from the effects of sun, air, wind cracks, or other flaws; and the contractor shall repair, at his own cost, all damage resulting from such causes. To form a foundation for the brickwork of the reser- voir by spreading a layer of concrete, three inches in thick- ness on the top of the puddle, all over the bottom of the excavations forming the site of the intended reservoir. Fill in span - To fill in the spandrel of the arches to a height of 18 drel of arches inches above the top water line, with concrete, before the centering is removed from the arches. Clay. Concrete. If sufficient clay for the puddle, should not be found in the excavations, concrete must be substituted in lieu of the puddle. The concrete must be compounded of gravel, perfectly clean and mixed with fresh well-burnt hydraulic lime of 488 SPECIFICATION. Gravel, Proportions of lime, sand in con- crete. approved quality, in the proportion of six parts of gravel to one of lime. The gravel to be perfectly clean and free from marl or loam, being a nice admixture of about two parts gravel to one part coarse sand. All stones in the gravel larger than about an inch and a half in diameter are to be broken. The proportions of lime, gravel, and sand are to be gravel, and accurately gauged. The lime is to be brought upon the ground fresh from the kiln, laid on a bed of gravel and sand not less than twelve inches thick, and spread over this to a depth of about 18 inches; and, while spreading, is to be slowly but continually sprinkled with clean water, from a rose headed watering pot, until the steaming has commenced, when the lime is to be covered up with gravel and sand so that no steam can escape, and to be left in that state until it is completely slaked and turns out an impalpable powder; the gravel and lime are then to be mixed in a dry state, to ensure their thorough incor- poration, after which on a clean platform a proper pro- portion of clean water is to be added, the whole is to be turned over and well beaten, until a thorough admixture of all the parts is effected and brought to a tough consistency, when it is to be immediately filled into barrows, and teemed from a height of at least ten feet on to the place required, when it must be levelled at once to its proper thickness before it has time to set. Barrow road. Bricks. Bats. Workman- ship. Mortar. The contractor shall erect a proper barrow road or scaffold, from which the concrete can in all cases be teemed on to the place at which it is required. BRICKLAYER. The bricks made use of throughout the work shall be hard, sound, well shapen, thoroughly burnt, and of uniform size, and shall be well saturated with water before being set. No broken bats will be allowed to be used either externally or internally, unless absolutely necessary as closers. The workmanship shall be of the best description. No joint of mortar shall exceed one quarter of an inch in thickness, and the work shall be laid in English bond. The mortar shall consist of fresh burnt lias lime of RESERVOIR. 489 Lime. Concrete foundations. Brickwork. Skewbacks. Arches over Reservoir. Soffits of Arches. Groined Arch. Centring. approved quality and clean sharp sand, in the proportion of two parts sand, to one of unslacked Lime. They shall be intimately mixed in a dry state and well tempered with a proper quantity of water, and only mixed as required for use, the mortar that has previously set or become hard upon the ground shall not be permitted to be used in any part of the work. When the lime is required to be slacked it shall be done with clean water, and covered up with sand so that no air slacked lime shall be used for any purpose whatever. No brickwork is to be commenced on the concrete foundations until they have become hard and solid. To build the pier, side, and end walls of reservoir in English bond, the whole of the joints to be flushed up solid with mortar, and in all walls of 18 inches thick and upwards, every third course shall be well grouted; the internal bricks of that course being properly floated in, and driven up one against another in the grouting so as to fill up all the interstices, and render the whole of the work a compact solid mass. The longitudinal pier and cross walls are to be well and properly bonded together, and the side and end walls must be battered and have piers, offsets, and step buttresses as shown in the drawings. The skewbacks of walls to be correctly worked to tem- plates, and to be built with feather edge bricks made to shape, as no filling in with bits or pieces will be allowed. The arches over the reservoir are to be composed of two four and a half inch rings; the whole of them are to be proceeded with at one time, and carried on as regularly as possible. The side and end arches must spring from the brickwork on a line forming a right angle with the batter face of the centre of the arch. To set close, and well flush up with mortar, the soffits of all the arches; and after the centring has been drawn, point the under side. To turn a groined arch in side wall for entrance into reservoir. All centring, as may be requisite to turn all the arches of the reservoir, as well as all struts, close planking, and ribs necessary for carrying on the whole of the arches together in one breast, shall be found by the contractor. And no centring shall be removed until the whole of that set of arches has been properly keyed and backed with 2 H 490 SPECIFICATION. Other Brickwork. Masonry. Carpenter's Work. Painter's Work. Smith's Work. Commence- ment and of Works. Contractor to find materi- the concrete spandrels, and the capping brought up as close as the work will permit. To do all other brick work that may be required to complete the construction of the reservoir, according to the directions expressed or implied in the specification and drawings and to the satisfaction of the engineer. Cover the entrance to reservoir with three inch York flagging, and provide and fix tooled and rounded York stone treads and brick risers. Perform any other masonry, necessary and requisite, for the completion of the work. Fit up the doorway at entrance with 13 inch four paneled door; hang the same with a pair of 4 inch butts to 4 by 3 inch rebated frame; and provide and fix a suitable lock and key. Perform any other carpentry necessary to complete the works. Knot, stop, pumice, paint in four oils, grain oak and varnish the door, and door frame. Provide and fix a wrought iron step ladder as shown in drawing, and a wrought iron grating in York flagging over entrance. TIME OF COMMENCEMENT AND COMPLETION. The works are to be commenced immediately on an order being given by the engineer and to be proceeded with at a rate of progress satisfactory to him-and to be finally completed within four months of the date of such order to commence, or the contractor shall forfeit £10 for every day that the work is delayed beyond the time specified, unless the engineer shall certify that the delay arises from any unavoidable or excusable cause. The contractor is to provide all materials of every als to be re- description and labour of every kind, that may be neces- sponsible for damage; and six months. to keep work sary to construct, and properly complete the work. He in repair for is to be responsible for all damage and accidents of every kind that may occur during the execution of the work and he is to keep the works in repair for six months, from the date of their completion. Minor parts to be in- cluded, al- though not And wherever neither the drawings nor this specifica- tion contain any special notice of minor parts, the intention noticed in to include which is, nevertheless, to be inferred, and which parts are necessary for the completion and stability of the Specification. TIMBER MEASURING. 491 Works to be executed to of Engineer. works, all such additional parts are to be provided and performed by the contractor, and are supposed to be in- cluded in the sum at which he contracts for the works, and wherever any thing is directed to be done, or to be provided, if required, "or words of similar import,” it must be understood that every thing so referred to will be considered as included in the contractor's tender. The whole of the works herein described, both as regards satisfaction quality of materials and workmanship, shall be executed to the entire satisfaction of the engineer according to the true intent and meaning of the specification of which the engineer shall be the sole judge. Engineer may direct alterations. Payments. It is to be distinctly understood that the engineer may at all times direct, that there shall be made alterations in, additions to, or deductions from the works herein described or referred to; which said alterations in, additions to, or deductions from, shall not annul the contract, but an equivalent based upon the schedule of prices annexed to the contractor's tender shall be given or taken as the case may require. Payments to the extent of ninety per cent will be made monthly upon the value of the work executed provided the engineer shall certify that the work is proceeding to his satisfaction. In one or other of the preceding specifications will be found the general stipulations usually contained in such documents. CHAPTER XV. TIMBER MEASURING. TIMBER is computed at its solid contents, whether standing, rough, or hewn. Boards and planks are measured superficially. 40 feet of rough timber or 50 feet of hewn properly make a load, but in practice it is usual to consider 50 feet of timber, of any description, as a load. The reason assigned for the establishment of the different sizes of the load of rough and hewn timber is, that the former being measured in a round state (as will be presently shown) by taking one-fourth of the circumference as the side of equal square produces a result one-fifth short of the actual solid 492 TIMBER MEASURING. content, while squared or hewn timber is measured upon more accurate mathematical principles. In treating the subject of measuring solid timber, it is necessary to premise that the rules about to be given are such as have be- come customary in practice, and not those which a mathematician would apply to the operation. The true mathematical solid con- tent of any piece of timber may be found by the application of one or more of the rules contained in the mensuration of solids in a former part of this work, but such a content would not be in ac- cordance with customary usages, and consequently but of little value to the practical man, while the mode of its attainment would also be tedious and complex. In measuring standing timber, the first thing to be estimated approximately is the height of the tree. This is done by holding a 20-feet rod as high up the tree as a man can reach, and by guess- ing the remainder, which may generally be very nicely done; for supposing the bottom of the rod to be held 6 feet from the ground, 26 feet up the tree is actually measured, and the proportion which the unmeasured height bears to the measured will become tolerably apparent to the eye. I have heard of a ladder being carried about with which to measure the heights of the trees, but never saw it done. What is called the lop and top of the tree is measured or estimated separately, as it generally carries a less price. Up to 24 inches circumference or 6 inches quarter girt is generally taken as timber, and all below that size goes as "lop and top;" but the ex- act minimum of the timber and maximum of "lop and top " is made the subject of agreement between the "surveyors for buyer and seller" before they commence their work. CC The method of taking the "girt" of a tree and allowing for bark is also (in many cases) the subject of agreement between the surveyors." It is in some localities (but we will hope very few) customary for the purchaser's surveyor to insist that the girting line be first divided into three parts, and that one-third of the cir- cumference be entirely thrown out as an allowance for bark, the re- maining two-thirds only to be divided into four for the "quarter girt." Another custom allows the "purchasing surveyor" to girt the tree where he pleases between the middle and bottom part. A third insists that, let the tree taper however irregularly, the girt shall be taken exactly half-way up the tree. But these and all similar customs are so obviously uncertain in the results they produce, that no surveyor of common ability or in- tegrity will agree to adopt them. The simple business-like way is to ascertain as nearly as possible the fair average quarter girt, TIMBER MEASURING. 493 or one-fourth part of the circumference, and to make therein such an allowance as may be fairly estimated to reduce it to what it would have been had the tree been without bark. This allowance in the quarter girt for bark may be very fairly reduced to an agreed standard. Up to a given figure in quarter girt, the allow- ance to be one inch; beyond that, and up to some other size, an inch and a half; and so on. The description of tree will of course have great weight in arranging this standard. Oak trees, in which the quarter girt is 12 inches, may require 1 inch allowance there- out for bark, while in the case of ash, elm, and beech, half an inch may in some cases be sufficient. A mathematically educated surveyor will of course readily as- certain the correct allowance to be made for bark by guaging its approximate thickness, and deducting twice that thickness from the calculated diameter of the tree, including bark, and he will then have the actual diameter without the bark. This being re- duced to circumference and divided by 4, the actual quarter girt of the timber may be placed in comparison with the quarter girt of the tree, and the true allowance for bark will be their difference. A calculation of this kind applied to about three sizes of trees will form the basis of an arrangement which may be fairly adopted in the manner I have previously suggested. The average quarter girt of a standing tree that tapers with tolerable regularity may be ascertained by girting it at the bot- tom, and taking the mean between the quarter girt there and the six inches, or whatever may be agreed on as the minimum quarter girt at which the timber of the first quality is to cease, and the "lop and top” to commence. The point at which the tree will girt 24 inches in circumference is of no importance in taking the quarter girts, but it requires the exercise of the surveyor's judg- ment in ascertaining the heights. It is well for the sake of accuracy that it is not so, as an error in the girt would enter into the whole calculation of the tree, while an error in length is confined to the extent of the error itself. Where the tree does not taper regularly, various expediences must be adopted to ascertain the average girt. It is impossible to lay down rules that may produce approximate results in every case; the exercise of a very little ingenuity will overcome most of them. When a tree continues up to a certain height, nearly the same size, and then tapers, it will be best to measure the two parts separately. The girt of these two parts may be very often obtained in this way, suppose the lower part to be 14 feet high, take the quarter girt at 7 feet, which suppose to be 30 inches, this will be the mean of 494 TIMBER MEASURING. the lower part; take the quarter girt at the bottom of the tree, which suppose 35 inches, which being 5 inches greater than the quarter girt at 7 feet high, we may consider the quarter girt at that point is 5 inches greater than at 14 feet high; hence we have 25 inches, to average with 6 inches, for the mean quarter girt of the upper part of the tree. To In measuring round timber that has been felled, the length can be accurately taken, and the girt as often as required to obtain a correct average, bearing in mind, that when the girt is taken several times, it should always be at equidistant points. illustrate this, let fig. 196 be the section of a piece of timber 25 feet long, and of the respective quarter girts as figured. Incom- petent measurers would take the girt at about three places, namely at B which they would suppose to represent the girt of the length A B C; at D, and at F, and would average them in this way: Quarter girt at B 20 at D 14 وو وو وو at F 10 3) 44 141 Mean quarter girt Now let us see the correct result of averaging the quarter girts, taken at equidistant points. Quarter girt at A 220 at B "" 99 "" "" at C 20 at D 14 وو وو at E 15 "" at F 10 6) 99 16 36 ft. 6 in. Correct average quarter girt The content of a piece of timber 25 feet long by 14 inches quarter girt is. The same length, but 16 inches quarter, girt is. Loss by the incorrect method of taking the dimensions 47 3 وو وو 10 ft. 9 in. Practical timber surveyors generally have a tape or strap for taking the girt of trees, marked to inches, but numbered only at every fourth division; that is, at 4 inches it is numbered 1; at 8, 2; at 12, 3, and so on; by which simple arrangement, the quarter girt in inches and quarters is shown at once. Squared timber is measured by taking the length, breadth, and TIMBER MEASURING. 495 thickness. The length and breadth are reduced to the side of equal square, which is then treated as the quarter girt. It is very cus- tomary to add the breadth to the thickness, and take half for the side of equal square, but such a custom is very erroneous, and a Table has been added to obviate it. The superficial content of planks is found, by multiplying the length, in feet and inches, by the widths; attention is required in taking the widths of irregular planks, to do so at equidistant points, as explained in the girting of irregular timber. EXPLANATION OF TABLE No. 1. Table of solid measure. Each page of this table is divided into two parts, and each part into five columns. At the head of each part, is set forth the length in feet; and in the first column of each part is the quarter girt or side of equal square in inches. In the second column of each part is the solid content in feet and inches, of the piece of timber (or any cube) whose length is equal to the length set forth at the head of the table; and whose quarter girt, or side of square, is equal to the one expressed in column 1, opposite to the cubic content in column 2. In columns 3, 4, and 5, are contained the contents of solids, corresponding to the same length; but whose respective quarter girts are increased by the fractional parts of an inch, which are severally denoted at the heads of such columns. Ex. 1.-What is the content of the standing tree (according to the customary method of treating one-fourth of the circumference, or quarter girt, as the side of equal square), whose height is 39 feet, and average quarter girt 40 inches. In the section of the table headed 39 feet, and in column 2, opposite 40 inches in column 1, stands 433 ft. 4 in., the required content of the tree. Ex. 2-Required the content of the piece of timber whose length is 20 feet and quarter girt 164 inches. In the section of the table headed 20 feet long, opposite 16 inches quarter girt, and in the column headed inch, stands 36 feet 8 inches, the required content. Ex. 3.-Required the content of the tree, 15 feet long and 201 inches quarter girt. In the table headed 15 feet long, opposite 20 inches quarter girt, and in the column headed inch, stands 43 feet 9 inches, cubic content. 496 TIMBER TABLES.-No. 1. Quarter Girt. inches ft. in. 1 foot long. Quarter Girt. 2 feet long. 14 11 11/8 3 4 ft. in, ft. in. ft. in. inches ft in. ft. in. 11 34 ના ft. in. ft. in. 1 Q3 0 0 0 1 0 0 0 0 2 0 0 1 1 1 1 1 1 1 1 3 1 2 1 1 2 2 3 3 4 5 2 2 3 4 5 5 6 3 3 3 4 6 6 4 4 5 5 8 9 10 8 6 6 6 8 11 11 1 0 1 1 9 10 78 7 7 8 9 1 1 1 2 1 3 1 4 9 9 10 10 11 10 10 11 11 12 1 0 1 0 1 1 1 1 13 1 2 1 3 1 3 1 4 13 IEEE 8 1 5 1 5 1 6 1 7 1 8 1 9 1 10 1 11 12 20 2 1 2 2 2 3 4 2 5 2 6 2 7 14 1 4 1 5 1 5 1 6 14 2 9 2 10 2 11 3 0 15 1 7 1 7 1 8 1 9 15 3 1 3 3 34 3 5 16 1 9 1 10 1 11 1 11 16 3 3 8 3 9 3 11 17 2 0 2 1 2 1 18 2 3 2 4 2 4 19 2 6 2 77 28 20 2 9 2 10 2 11 2223 2 17 4 0 4 2 4 3 4 4 5 18 4 6 4 4 9 4 10 8 19 5 2 5 3 5 5 0 20 5 7 5 8 5 10 60 22*******. 7******88* 3 1 3 2 3 2 3 4 3 5 3 6 3 8 3 9 3 10 co co co 3 3 21 6 1 63 3 7 22 6 9 6 10 3 11 23 7 7 6 677 6 5 6 7 0 7 2 8 7 10 24 0 4 1 4 2 4 3 24 8 0 8 2 8 4 86 25 4 4 4 5 4 6 4 7 25 88 8 10 90 9 2 26 27 4 8 4 10 0 26 9 5 9 7 9 9 9 11 5 1 5 2 5 3 5 4 27 10 1 10 4 10 6 10 8 5 5 5 6 5 8 9 28 10 11 11 1 11 3 11 6 5 10 5 11 60 6 2 29 11 8 11 11 12 1 12 3 30 6 3 6 4 6 5 6 7 30 12 6 12 8 12 11 13 13 2 86 32 33 34 35 6 8 69 0 677∞ ∞ 817 67780 6 11 3 7 4 7 9 8 3 7777 0 31 13 4 13 7 13 9 14 O 0 51 32 14 3 14 5 14 8 14 11 7 11 33 15 1 15 4 15 7 15 10 8 4 34 16 1 16 3 16 6 16 9 8 8 9 8 10 35 17 0 17 3 17 6 17 6 17 9 36 9 0 9 1 9 3 9 4 36 18 0 18 3 18 6 18 18 9 9 6 9 8 9 9 9 11 37 19 0 19 3 19 6 19 9 10 0 10 2 10 3 10 5 38 20 1 20 4 20 7 20 10 39 10 7 10 8 10 10 11 0 39 21 121 5 21 8 21 11 40 11 1 11 3 11 3 11 5 11 6 40 22 3 22 6 22 9 23 23 1 41 11 8 11 10 11 11 12 42 12 3 12 5 12 6 12 1 41 842 23 4 23 8 23 11 24 2 24 6 24 9 25 1 25 5 43 12 10 13 0 44 13 5 13 7 13 2 13 3 43 25 8 8 26 0 26 3 26 7 13 9 13 11 44 26 11 27 2 27 6 27 10 45 14 1 14 3 14 3 14 14 4 14 6 6 45 28 1 28 5 28 9 29 1 46 14 8 14 10 15 0 15 2 46 29 5 29 8 30 0 30 4 47 15 4 48 16 0 16 2 15 6 15 15 8 15 10 47 30 8 31 0 31 31 4 31 164 16 16 6 48 32 0 32 32 4 4 32 8 33 50 49 16 8 17 4 16 10 17 0 17 17 2 2 49 33 4 33 8 34 0 34 4 4 17 6 17 8 17 11 50 34 9 35 35 1 35 5 35 35 9 SOLID MEASURE. 497 Quarter Girt. inches 3 feet long. Quarter Girt. 4 feet long. 1 4 1 143 3 ft. in. ft. in. ft. in. ft. in. inches ft. in. ft. in. ft. in. 3 14/0 ft. in. 2 3 12 1 1 2 3 3 3 4 4 5 6 QB4 1 2 3 3 3 4 6 77 267 5 6 7 8 5 9 10 6 10 10 11 6 7 1 0 1 1 1 2 1 3 8 1 4 1 5 1 6 1 7 9 1 8 1 9 1 10 20 9 10 2 1 2 2 23 2 5 10 HIIQQ 1 0 1 1 1 1 4 1 5 27 1 7 1 1 9 1 11 2 0 3 2 4 2 6 2 9 2 11 3 1 TIQQM 11 1 3 8 2 3 2 ∞ ∞ 1∞ Q 11 26 2 8 2 9 2 10 11 3 4 3 6 3 8 3 10 12 3 0 3 1 3 3 3 5 12 13 3 6 38 3 9 3 11 13 ++ 4 0 4 2 4 4 4 6 8 4 10 0 5 3 14 4 1 4 3 4 4 4 6 14 5 5 58 5 10 6 0 15 4 8 4 10 5 0 5 2 15 63 6 5 68 6 10 16 5 4 5 6 5 8 5 10 16 1 7 4 7 7 77 9 17 6 0 6 2 6 4 6 7 17 8 0 8 3 8 6 8 9 18 6 9 6 11 7 1 7 4 18 9 0 9 3 9 6 9 9 21 222 223* 19 7 6 7 9 7 11 8 1 19 10 0 10 3 10 7 10 10 20 84 86 8 9 9 0 20 11 111 1 11 5 11 8 11 11 9 2 9 5 9 8 9 10 21 12 3 12 6 12 10 13 2 10 1 10 4 4 10 10 6 10 9 22 13 5 13 9 14 1 14 4 11 0 11 3 11 6 11 9 23 14 8 15 0 15 4 15 8 24 12 0 12 3 12 6 12 9 24 16 0 16 4 16 17 0 25 13 0 0 13 3 13 13 6 13 10 25 17 4 4 17 17 8 18 1 18 5 26 14 1 14 4 14 7 14 11 26 18 9 19 2 2 19 6 19 10 27 15 2 215 6 15 6 15 9 16 0 27 20 3 20 7 7 21 0 21 5 33 322 788 28 16 4 16 7 16 11 17 3 28 21 9 22 22 222 22 7 7 22 11 29 17 6 17 10 18 1 18 5 29 23 4 23 9 24 2 24 30 18 9 19 1 19 19 4 19 8 30 25 0 0 25 25 5 25 10 26 3 20 0 20 4 20 8 21 0 31 32 22 8 21 4 21 8 22 0 23 0 0 23 4 22 4 32 23 9 34 24 1 24 5 24 9 25 2 34 35 25 6 25 11 26 26 3 26 7 35 36 27 0 27 4 27 4 27 27 9 28 2 36 288*88 26 8 27 1 27 7 28 0 28 5 28 11 29 4 29 9 33 30 3 30 8 312 31 231 8 32 1 32 7 33 1 33 6 34 0 0 34 34 6 35 0 35 6 36 0 36 6 6 37 0 37 37 6 37 28 6 28 11 29 3 29 8 37 38 0 38 6 39 1 39 7 38 30 1 30 6 6 30 10 31 3 38 40 1 40 7 7 41 2 2 41 41 8 39 31 8 32 1 32 6 32 11 39 42 3 42 9 9 43 43 4 43 11 40 33 4 4 33 9 34 34 2 34 7 40 44 5 45 0 45 7 46 1 41 35 0 35 5 5 35 10 36 4 41 46 8 47 3 47 10 48 5 42 36 9 37 237 37 7 38 1 42 49 O 49 7 50 2 50 9 43 38 6 6 38 11 39 5 39 10 43 51 4 51 11 52 7 53 2 44 40 4 45 40 9 42 2 2 42 8 43 41 3 41 9 44 53 9 43 143 7 45 56 3 56 10 46 44 44 7 45 0 45 6 46 58 9 59 5 5 54 54 5 55 0 55 7 57 6 58 2 60 60 1 1 60 8 47 46 0 46 6 47 47 0 47 6 47 61 4 62 0 62 8 63 4 48 48 0 48 6 49 0 49 6 48 64 0 64 8 65 466 4 66 6 49 50 0 0 50 6 51 0 51 7 49 66 8 67 4 68 068 9 50 52 1 52 7 53 53 1 53 8 50 69 5 70 5 70 2 70 10 71 6 498 TIMBER TABLES.—No. 1. Quarter Girt. inches ft. in. 5 feet long. 1 111 ft. in. 914 ~~3/+ Quarter Girt. 6 feet long. 1 1/3/1/18 3 4 ft. in. ft. In. ft. in. ft. in. inches ft. in. ft. in. Q34 2 247 2 3 3 4 5 6 7 9 233 240 10 11 1 1 1 2 1 0 1 2 6 1 3 1 4 1 6 1 7 1 6 1 7 4867 6 2 3 4 6 7 9 0 11 1 3 1 4 9 1 11 1 8 1 10 1 11 2 1 0 2 2 2 4 2 6 2 3 2 4 2 6 2 8 8 28 2 10 3 0 3 2 9 2.10 3 0 3 2 3 4 9 4 3 7 3 9 3 11 10 36 3 8 3 10 4 0 10 4 2 4 4 4 7 4 10 11 4 2 4 5 4 7 4 9 11 5 0 5 3 5 6 59 12 5 0 5 2 5 5 58 12 0 6 3 6 6 69 13 5 10 6 1 6 4 6 7 13 7 0 7 4 77 7 7 10 14 6 10 7 0 7 3 7 6 14 8 2 8 5 8 9 9 1 15 7 10 8 1 8 4 8 77 715 9 4 9 8 10 0 10 4 16 8 11 9 2 9 5 9 9 16 10 8 11 0 11 4 11 8 17 10 0 10 4 10 8 10 11 17 12 0 12 5 12 9 13 1 18 20 122 72***ANA.. 11 3 11 77 11 11 12 2 18 13 6 13 10 14 3 14 8 12 6 6 12 10 13 2 13 6 19 15 0 15 5 15 10 16 3 13 11 14 3 14 7 14 11 20 16 8 17 1 17 6 17 11 21 15 4 15 8 16 1 16 5 21 18 4 18 10 19 3 19 8 22 16 10 17 2 17 7 18 O 0 22 20 2 20 7 21 1 21 7 18 4 18 9 19 2 19 7 23 22 0 22 6 23 0 23 6 24 20 0 20 5 20 10 21 3 24 24 0 24 61 25 0 25 21 8 22 2 22 7 23 0 0 25 26 0 26 7 27 25 6 127 by 7 23 6 23 11 24 5 24 10 26 28 2 28 8 29 3 29 10 25 4 25 25 9 26 3 26 9 27 30 4 30 11 31 6 32 1 27 3 27 8 28 2 28 8 28 32 8 33 3 33 10 34 5 33 10 29 2 29 8 30 3 30 9 29 35 0 35 8 36 3 36 10 30 31 3 31 9 32 4 32 10 30 37 6 38 1 38 9 39 5 31 33 4 33 10 34 5 35 0 31 40 0 40 8 41 4 42 0 32 35 7 7 36 36 1 36 8 37 3 32 42 8 43 4 44 0 44 8 33 37 10 38 5 39 0 39 7 33 45 4 46 1 46 9 47 5 34 40 2 40 9 41 4 41 11 34 48 2 48 10 49 7 50 4 35 42 6 43 2 43 9 44 4 4 35 51 0 51 9 52 6 53 3 36 45 0 45 7 46 3 46 10 36 54 0 54 9 55 6 56 3 37 47 6 648 48 2 48 10 49 6 37 57 0 57 10 58 7 59 4 38 50 2 50 10 51 5 52 2 38 60 2 60 11 61 9 9 62 7 39 52 10 53 6 54 2 54 10 39 63 4 64 2 65 0 65 10 40 55 7 56 3 56 11 57 8 40 66 8 67 6 68 4 69 2 41 58 4 59 1 59 10 60 6 41 70 0 42 61 3 61 11 62 62 9 63 5 42 73 6 45 43 64 2 44 67 3 70 4 46 73 6 64 11 65 8 68 0 68 9 66 5 43 77 0 69 6 44 80 8 71 1 71 11 72 8 8 45 84 4 85 74 3 75 1 75 11 46 47 76 8 77 678 4 48 80 0 0 80 10 81 8 49 83 4 84 3 85 1 79 2 47 92 0 93 82 6 48 96 0 97 70 11 74 4 75 3 76 2 71 9 72 7 77 11 78 10 79 9 81 7 82 6 82 6 83 5 4 86 3 87 2 88 2 89 1 90 1 91 0 094 095 98 0 99 0 0 85 11 49 100 0 101 1102 1103 1 50 86 10 87 8 88 7 89 5 50 50 104 2105 2106 3 107 4 SOLID MEASURE. 499 Quarter Girt. inches ft. in. 7 feet long. 1 114 1 음 3 4 ft. in. ft. in. Quarter Girt. ft. in.inches 8 feet long. 1 1247 catat 44 ft. in. ft. in. ft. in. ft. in. 234567∞ a 2 3 4 4 2 6 7 8 9 10 1 0 1 1 1 3 1 4 1 6 1 7 1 9 1 11 2 1 2 2 2 5 2 7 29 2 11 8 3 1 3 4 3 6 3 9 9 3 11 2 4 7 Q345 6 7 ∞ ∞ 3 3 4 5 6 7 8 9 11 1 0 1 1 1 5 1 6 18 2 0 2 2 2 4 2 6 2 9 2 11 3 1 3 7 3 9 4 0 4 6 4 9 5 0 10 4 10 5 1 4 5 7 10 5 7 5 10 6 1 1HQ CO HILO co 3 1 10 3 4 4 3 5 3 6 5 11 5 10 12 7 0 67 6 2 6 5 6 8 11 6 9 7 0 7 3 7 7 7 11 12 0 8 4 4∞ 7 8 8 8 9 0 13 8 3 8 6 810 9 2 13 9 5 9 9 10 1 10 6 14 9 6 9 10 10 2 10 7 14 10 11 11 3 11 8 12 1 15 10 11 11 4 11 8 12 1 15 12 6 12 11 13 4 13 9 16 12 5 12 10 12 10 13 3 13 8 16 14 2 14 8 15 1 15 7 17 14 1 14 5 14 11 15 4 17 16 1 16 6 17 0 17 6 18 15 9 16 2 16 8 17 1 18 18 O 18 6 19 619 0 19 6 19 17 7 18 0 18 6 18 11 20 19 5 19 11 19 11 20 5 20 11 20 21 21 5 21 11 22 5 23 0 22 23 6 6 24 24 1 24 7 25 2 23 25 9 9 26 3 26 10 27 5 23 22 72* 20 1 20 7 21 1 21 8 22 3 22 9 23 4 23 11 24 6 25 1 25 8 26 5 22 26 11 27 6 28 1 28 9 29 5 30 30 0 30 8 31 4 24 28 0 28 7 29 2 29 9 24 32 0 32 8 33 4 34 0 25 30 5 31 31 0 0 31 7 32 3 25 34 9 35 5 5 36 1 36 10 26 32 10 33 6 34 6 34 2 34 9 34 9 26 37 7 38 3 39 0 39 9 27 35 5 5 36 36 1 36 36 9 37 5 27 40 6 41 3 42 0 42 9 28 38 1 38 9 39 6 40 2 28 43 7 44 4 4 45 1 45 11 29 40 11 41 7 42 4 43 0 29 46 9 47 6 48 4 49 2 30 43 9 44 6 45 3 45 11 30 50 0 50 10 51 8 52 6 31 46 9 9 47 47 6 48 3 49 0 0 31 53 5 54 3 55 2 56 0 32 49 9 9 50 7 51 4 52 2 32 56 11 57 9 58 9 59 59 7 33 52 11 53 9 54 7 55 55 4 33 60 6 61 5 62 4 63 3 34 56 2 57 0 57 10 58 58 8 34 64 3 65 2 66 1 67 35 59 7 7 60 5 61 3 62 1 35 68 1 69 0 0 70 0 71 0 36 63 0 63 10 64 9 64 9 65 65 8 36 72 0 37 66 7 7 67 67 5 5 68 4 69 3 37 76 1 73 0 74 0 75 77 1 78 1 79 2 38 70 2 71 1 72 0 73 0 38 80 2 39 73 11 74 10 75 10 76 10 39 40 куку 9 9 78 9 79 9 80 9 40 81 3 84 6 85 88 10 90 82 4 83 5 7 86 8 87 0 91 192 3 7310025a m 9 41 81 9 9 82 9 83 9 42 85 9 9 86 9 9 87 10 43 89 11 90 11 92 0 44 94 1 95 2 2 96 96 84 9 41 88 10 42 93 93 0 43 3 97 4 44 9 103 11105 93 5 94 6 695 8 96 10 98 0 99 1100 4 101 6 102 1106 4 107 7 108 9110 0111 3 45 98 5 5 99 6 100 8 101 9 45 112 6 113 9 115 0116 3 46 102 10 104 0105 1106 3 46 117 7118 10120 1121 5 47 107 5 108 6109 8 110 10 47 122 9 124 9 124 0 125 4126 8 48 112 0113 2114 49 116 9 117 11119 4115 6 48 128 0129 4 130 8 132 0 1120 4 49 133 5134 9136 9136 1137 6 50 121 6 122 9 124 0 125 2 50 138 11 140 3 141 8 143 1 500 TIMBER TABLES.-No. 1. Quarter Girt. inches ft. in. 9 feet long. 12 तम 1 ft. in. ft. in. Go44 ft. Quarter Girt. in. inches ft. in. 10 feet long. 14 1/1/143 3 4 ft. in. ft in. ft. in. QB + 2 3 3 7 48 5 6 2 3 4 5 6 9 10 3 7 9 10 1 0 1 0 1 1 1 2 1 5 4 5 1 7 1 9 1 11 2 1 5 6 2 3 2 5 28 2 10 6 3 1 3 3 3 6 3 9 7 8 4 0 4 3 4 6 4 9 5 1 5 4 5 8 5 11 9 10 6 3 6 7 6 11 7 3 10 1AQ∞ CO 1 1 3 1 5 1 7 19 1 11 2 1 2 3 2 6 28 2 11 3 2 3 5 3 8 3 11 4 2 4 5 4 9 5 0 5 5 7 5 11 6 3 6 6 11 7 3 7 8 8 0 11 7 7 7 11 8 3 8 7 11 8 5 8 9 9 2 9 7 12 9 0 9 4 9 9 10 2 12 10 0 10 5 10 10 11 3 13 10 7 11 0 11 5 11 10 13 11 9 12 2 12 8 13 1 14 12 3 12 8 13 2 13 7 14 13 7 14 1 14 7 15 1 15 14 1 14 6 6 15 0 15 0 15 6 15 15 7 16 2 16 8 16 8 17 3 16 16 O 16 6 17 0 17 6 16 17 9 18 4 18 11 19 6 17 18 1 18 7 19 2 19 8 17 20 1 20 8 21 321 10 18 20 3 20 10 21 5 22 0 18 22 6 23 1 23 9 24 5 19 22 7 23 2 23 9 24 4 19 25 1 25 9 26 5 27 1 20 25 0 25 7 26 3 26 11 20 27 9 28 6 29 2 29 11 228 21 27 7 28 3 28 11 29 7 21 30 7 31 4 32 1 32 10 30 3 30 11 31 8 32 4 22 33 7 34 4 35 2 35 11 23 33 1 33 934 6 35 3 23 36 9 37 6 38 4 39 2 24 36 0 36 9 37 6 38 3 24 40 0 40 10 41 8 42 6 25 39 1 39 10 40 8 41 5 25 43 5 44 3 45 2 46 0 26 42 3 43 1 43 11 44 9 26 46 11 47 10 47 10 48 9 48 9 49 8 27 45 7 46 5 47 3 48 1 27 50 7 51 7 52 6 53 6 28 49 0 49 10 49 10 50 9 51 8 28 54 5 55 5 56 5 57 5 29 52 7 53 6 54 5 55 4 29 58 5 59 5 5 60 5 61 5 30 56 3 57 258 259 1 30 62 6 63 6 64 7 65 8 31 60 1 61 0 62 0 63 0 31 66 9 67 10 68 11 70 0 32 64 0 65 066 0 67 0 32 71 33 68 1 69 1 70 271 2 33 75 34 72 373 73 4 74 5 75 6 34 1 72 3 776 9 80 3 81 5 73 474 6 77 11 79 1 82 8 83 10 35 76 777 8 8 78 9 78 9 79 10 35 85 186 1 86 3 87 6 88 9 39 95 1 96 3 40 100 0 101 3 102 6 103 36 81 0 82 1 37 85 7 86 9 87 11 38 90 3 91 5 97 6 98 9 83 3 84 5 36 90 0 0 91 3 92 6 93 9 89 1 37 95 1 96 4 97 8 98 11 92 8 93 10 38 100 39 9 105 40 111 41 105 42 110 1 106 4 107 8 108 11 3111 6 112 11 114 3 41 116 9 118 2119 3 101 7 102 11 104 3 7 106 11 108 4 109 9 1112 6 113 11 115 4 7 121 0 42 122 6 123 11 125 5 126 11 46 132 3 133 47 138 1139 48 144 0145 43 115 7 116 11 118 3119 44 121 0122 4 123 9 125 2 45126 7 128 0 129 5 130 10 8135 2136 6 141 0142 6 6 147 0148 6 49 150 1 151 7153 2 154 8 50 156 3 157 10 159 5 161 0 7 43 128 5 129 11 131 5 132 11 44 134 5 136 0137 45 140 7 142 2 143 7 46 146 11 148 6 150 47 153 5 155 0156 48 160 0161 8 163 49 166 9 168 5 170 6139 1 9 145 4 2 151 9 8 158 4 4165 0 2171 10 50 173 7 175 4 177 1 178 10 鲁 SOLID MEASURE. 501 Quarter Girt. 11 feet long. 1 inches in. ft. ft. in. Quarter Girt. 12 feet long. 914 114 11/1 31 4 ft. in. ft. in. inches ft. in. ft. in. ft. in. ft. in. 23 45O 1 488 5 6 7 10 11 1 1 3 1 4 1 6 9 234+ 4 5 6 7 9 10 1 0 1 2 1 4 1 6 1 8 1 10 1 11 2 1 2 4 6 5 2 1 23 2 6 2 9 6 2 9 3 0 3 3 3 6 6 3 0 3 3 36 3 9 7 3 9 4 0 4 3 4 7 7 1 4 4 8 5 0 4 11 5 2 5 6 5 10 8 5 4 8 6 0 6 4 50 9 6 2 66 6 11 7 3 9 6 9 7 1 7 6 7 11 10 17 8 8 0 8 5 8 10 10 8 4 8 9 9 2 9 7 11 9 3 98 10 1 10 6 11 10 1 10 6 11 0 11 6 12 11 0 11 5 11 11 12 5 12 12 0 12 6 13 O 13 6 13 12 11 13 5 13 11 14 5 13 14 1 14 7 15 2 15 9 14 15 0 15 6 16 1 16 7 14 16 4 16 11 17 6 18 18 1 15 17 2 17 9 18 4 18 4 18 11 15 18 9 19 4 20 0 20 8 16 19 7 20 2 20 9 21 5 16 21 4 22 0 22 8 23 4 17 22 1 22 9 23 5 24 1 17 24 1 24 9 25 6 26 3 18 24 9 25 5 26 2 26 10 18 27 0 0 27 27 9 28 6 29 3 19 27 7 28 4 29 29 0 29 9 19 20 30 7 31 4 32 1 32 1 32 11 20 888333 30 1 30 10 30 10 31 8 32 32 6 33 4 34 2 35 0 35 10 21 33 8 34 6 35 4 36 21 21 36 9 9 37 37 7 38 6 39 5 22 37 0 37 10 23 40 5 38 8 39 39 6 22 40 4 41 3 42 2 43 1 41 3 42 2 43 11 23 44 1 45 0 46 0 47 0 24 44 O 0 44 11 45 10 46 9|24 48 0 49 O 25 47 9 48 8 49 8 49 8 50 8 25 52 153 50 051 0 154 2 55 3 26 51 8 52 8 53 8 54 54 8 26 56 4 57 57 5 58 6 6 59 7 27 55 8 8 56 9 57 9 58 10 27 60 9 61 10 63 0 64 2 28 59 11 60 11 62 0 063 2 28 65 4 66 667 67 8 68 10 29 64 3 65 4 66 6 67 7 7 29 70 1 71 3 72 6 73 9 30 68 9 69 11 71 1 71 172 3 30 75 0 76 3 77 6 78 9 31 73 5 74 7 75 9 77 0 31 80 1 81 4 82 8 84 0 32 78 3 79 5 80 8 81 11 32 85 4 86 8 88 O 89 4 33 83 2 84 5 85 9 87 0 33 34 88 4 89 7 90 11 92 3 34 90 9 92 1 96 4 97 97 93 6 94 11 9 99 2100 7 35 36 93 7 94 11 96 99 0 100 4101 37 104 7 106 0107 38 110 4 111 9113 39 116 2117 2117 8119 40 122 3 123 9 125 5 108 10 37 3114 838 2120 8 39 3 126 10 40 41 128 5 130 0131 42 134 9 136 3 138 43 141 3 142 11 144 44 147 11 149 7 151 45 154 8 156 5 158 46 161 8163 5165 47 168 9170 6172 48 176 0177 10179 49 183 5 185 3187 2189 1 49 50191 0 192 11 194 10 196 9 50 7133 2 41 0139 7 42 140 3 97 7 35102 1 103 6 105 9103 236 0 106 6 112 6 2118 9 6 125 1 8 0131 8 138 4 6 145 3 108 0 109 6 111 114 1115 7117 120 4 121 11 123 126 9 128 133 4 135 4130 0 136 1 141 9143 147 0 148 8 150 6 152 3 6 146 2 43 154 1155 10 157 8159 6 3153 0 44 161 4163 2165 0166 10 2 159 11 45 168 9 170 7 172 6 174 5 2166 11 46 176 4 178 4 178 3 180 2182 1 4 174 2 47 184 1186 0188 0190 0 8181 6 48 192 0194 200 1202 208 4 210 0196 1 204 2 206 3 5 212 6 214 7 0198 0 502 -No. 1. TIMBER TABLES. Quarter Girt. inches ft. 121414 13 feet long. 1 Ha 2 من احد 3 4 Quarter Girt. 14 feet long. 1 1242 용 3 4 in. ft. in. ft. in. fit. in. inches ft. in. ft. in. ft. in. ft. in. 2345 C 4 5 7 8 10 11 1 1 1 3 1 5 1 7 1 10 20 G1 M → 2 5 6 7 9 3 10 1 0 1 2 1 4 4 1 7 1 9 2 0 2 23 2 6 29 3 0 5 2 5 2 8 2 11 3 2 3 3 3 6 3 10 4 1 36 3 9 4 1 4 5 4 5 1 5 5 4 9 5 1 5 5 5 10 8 5 9 6 2 6 6 6 11 8 6 3 6 7 7 0 7 5 9 7 4 77 8 2 8 7 9 7 10 8 4 8 9 9 3 10 90 9 6 9 11 10 5 10 9 9 10 2 10 9 11 3 11 10 11 11 5 11 11 12 5 11 11 9 12 12 4 4 12 10 13 5 12 13 0 13 6 14 1 14 8 12 14 O 14 7 15 2 15 10 13 15 3 15 10 16 5 17 1 13 16 5 17 1 17 9 18 4 14 17 8 18 4 19 0 19 8 14 19 1 19 9 20 5 5 21 2 15 20 4 21 0 21 8 22 5 15 21 10 22 7 23 4 24 1 16 23 1 23 10 24 7 25 4 16 24 11 25 8 26 6 27 3 17 26 1 26 10 27 8 28 5 17 28 1 28 11 29 9 30 7 18 29 3 30 1 30 11 31 9 18 31 6 32 4 33 3 34 2 20 22 7******888 19 32 7 33 33 5 34 3 35 2 19 35 1 36 0 37 0 37 11 36 1 37 0 37 11 38 10 20 38 11 39 10 40 10 41 10 39 10 40 9 41 9 42 8 21 42 10 43 11 44 11 46 0 22 43 8 44 8 45 8 46 9 22 47 1 48 1 49 3 50 3 23 47 9 48 10 49 10 50 11 23 51 5 52 7 53 8 54 10 52 0 53 1 54 2 55 4 24 56 0 57 2 58 4 59 7 25 56 5 57 7 58 8 59 10 25 60 9 62 0 63 3 64 5 26 61 0 62 2 63 5 64 7 26 65 9 67 0 68 3 69 7 65 10 67 0 68 3 69 6 27 70 10 72 2 73 73 6 74 10 70 9 72 0 73 4 74 7 28 76 3 77 7 79 0 80 4 75 11 77 3 3 78 7 79 11 29 81 9 83 2 84 7 86 0 30 81 3 82 7 84 0 85 4 30 87 6 88 11 90 5 91 11 31 86 9 88 2 89 7 91 0 31 93 5 94 11 96 5 98 0 32 92 5 33 35 110 7 112 93 11 95 4 96 101 32 98 4 99 9101 4102 10 33 34 104 4 105 11 107 5 109 0 34 2113 9 115 4 35 99 7 101 1102 105 10 107 6 109 8104 3 1110 9 112 5 114 0115 9117 5 119 1120 10 122 6 124 3 36 117 0118 7 120 3 121 11 36 126 0127 9 129 6131 4 37 123 7 125 3 126 11 128 8 37 133 1134 10 136 8138 6 38 130 4 132 1133 10 135 7 38 140 5 142 3 144 1145 11 39 137 4 139 40 144 5 146 1140 10 142 8 3 148 1 149 11 39 40 147 10 149 9 151 155 7 157 8153 7 6 159 6 161 5 41 151 9153 6157 4 41 42 159 3 161 1 163 1165 0 42 43 166 11 168 10 170 10 172 9 43 44 174 9 176 9 178 9180 9 44 45 182 10 184 10 186 11 188 11 45 46 191 0 193 1 195 2 197 4 7155 46 48 208 49 216 47 199 5 201 7 203 8 205 10 0210 2 212 4 214 9218 11 221 2223 50 225 8 227 11 230 3 232 47 163 5165 2167 5169 5 171 6173 5 175 7 177 8 179 9 181 10 183 11 186 1 188 3 190 4192 6194 8 196 10 199 1201 3 203 6 205 9 207 11 210 214 9 217 1219 3 212 6 4 221 8 7 48 224 0 226 4 228 8 231 0 5 49 6 50 233 5 235 10 238 3 240 7 243 1 245 6 247 11 250 5 SOLID MEASURE. 503 Quarter Girt. inches 15 feet long. Quarter Girt. 16 feet long, 144 1-140 goo 1 1-24 مداح ft. in. ft. in. ft. in. ft. in. inches ft. in. ft. in. ft. in. ft. in. Q34567 2 เล 5 6 9 2 5 7 8 10 11 1 1 1 3 1 5 3 1 0 1 2 1 4 1 7 1 8 1 10 2 1 2 4 4 1 9 2 0 2 3 2 6 27 2 10 3 2 3 5 5 29 3 1 3 4 38 3 9 4 1 4 5 4 9 6 4 0 4 4 4 5 1 1 5 6 5 10 6 3 8 68 1 7 6 8 0 9 8 5 8 11 9 5 9 11 9 684 5 5 5 10 6 6 8 7 1 7 7 8 0 8 6 9 0 9 6 10 0 10 7 10 10 5 10 11 11 11 6 6 12 0 10 11 1 11 8 12 3 12 10 11 12 7 13 12 15 0 15 13 17 7 18 273 13 9 14 4 11 13 5 14 1 14 8 15 4 16 3 16 11 12 16 0 16 8 17 4 18 1 19 O 19 8 13 18 9 19 6 20 3 21 0 14 20 5 21 2 21 11 22 8 14 21 9 22 7 23 4 24 2 15 23 5 24 3 25 0 25 10 15 25 0 25 10 26 8 27 7 16 26 8 27 6 28 4 29 3 16 28 5 29 4 30 3 31 2 17 30 1 31 0 31 11 32 10 17 32 133 1 34 0 35 35 0 18 33 9 34 8 35 8 36 7 18 19 37 7 38 7 39 7 40 7 2 22***ANKA. 20 41 8 42 8 43 9 44 10 20 21 45 11 47 0 48 2 49 3 21 50 5 51 7 52 9 53 11 222 22 36 0 37 0 38 0 39 1 40 1 41 2 42 3 43 43 4 44 5 45 7 46 8 47 10 49 0 50 2 51 4 52 7 22 53 9 55 0 56 3 57 6 23 55 1 56 4 57 6 58 9 23 58 9 60 1 61 4 62 8 24 60 0 61 3 62 6 63 10 24 64 0 65 4 66 8 68 1 25 65 1 66 5 67 9 69 0 25 69 5 70 9 72 373 8 26 70 5 71 9 73 2 74 6 26 75 1 76 7 78 78 0 79 079 6 27 75 11 77 4 78 9 80 2 27 81 0 82 6 84 0 85 7 28 81 8 83 1 84 7 86 1 28 87 1 88 8 90 3 91 10 29 87 7 89 1 90 8 92 2 29 93 5 95 1 96 8 98 98 4 30 93 9 95 4 96 11 98 6 30 100 0 101 8 103 4 105 1 100 1101 88 31 32 106 8 108 33 113 5 115 34 120 35 127 36 135 37 142 38 150 5122 7 129 0136 10138 7 144 5152 9103 4 105 0 31 106 9 108 6 110 4 110 0111 9 32 113 9 115 7 117 2116 11 118 2124 5 131 8 33 121 0122 10124 0125 3133 1 35 9 34 128 5 130 4 132 136 1 138 1140 3112 0 4 119 2 8126 7 3 134 2 0142 0 9 140 8 36 144 0146 0148 0 150 1 6 146 6148 5 37 152 1154 2 156 3158 4 5154 5 156 5 38 160 5162 6 164 8166 10 39 158 5 160 5 162 6164 7 39 169 0171 2 173 4 175 7 40 166 8 168 9 170 10 173 0 40 177 9 180 0182 3 184 6 41 175 1 177 3179 42 183 9 185 10 188 43 192 7 194 10197 44 201 8 203 11 206 45 210 11 213 3 215 46 220 5 222 10 225 47 230 1 232 7 235 48 240 0 242 6|245 49 250 0 252 8 255 8 255 50 260 5 263 0 265 5 181 7 41 186 9189 1191 4 193 2 190 4 42 196 0 198 3 200 8203 1 1199 4 4 43 3 208 7 44 7 218 2 227 8 0 237 6 0 247 6 2257 10 49 8 268 3 50 0 45 46 47 48 205 5 207 10 210 215 1 217 7 220 225 0 227 6 230 235 1 237 245 5 248 256 0 258 3212 0222 6 0 232 7 ∞ ∞ ∞ 8 8 8 240 3 242 10 1 250 8 253 4 8 261 4 264 0 266 9 269 6 272 3 275 0 277 9 280 7 283 4 286 2 504 TIMBER TABLES.No. 1. Quarter Girt. inches ft. in. 17 feet long. 11/14 ft. in. 1-2/4 ft. in. ft. 09/+ Quarter Girt. in. inches ft. in. 18 feet long. 1 11/ 3 4 ft. in. ft. in. ft. in. 23 4 6 7 11 2 6 1 1 1 3 1 5 1 8 1 1 1 11 2 2 2 5 28 4 2 0 2 11 3 3 3 *7 3 11 3 1 3 ∞ 4 M LO 123 8 9 11 1 6 1 9 3 2 6 2 10 5 3 9 4 2 6 4 3 7 5 0 5 4 4 6 4 11 5 3 5 8 5 9 6 2 68 7 1 6 1 6 7 7 0 7 6 8 7 8 0 8 6 9 0 8 8 0 8 6 9 0 9 7 9 9 10 7 1 10 8 11 3 9 10 1 10 8 11 3 11 11 10 11 10 12 5 13 0 13 8 10 12 6 13 2 13 9 14 5 11 14 3 14 11 15 7 16 4 11 15 1 15 10 16 6 17 3 12 17 0 17 9 18 5 19 2 12 18 0 18 9 19 6 20 4 13 19 11 20 9 21 6 22 4 4 13 21 1 21 11 22 9 23 8 14 23 2 24 24 O 24 10 25 8 14 24 6 25 5 26 3 27 2 15 26 27 5 28 4 29 3 15 28 1 29 1 30 031 0 16 30 3 31 232 2 33 1 16 32 0 33 0 34 0 35 1 17 34 1 35 1 36 237 37 2 17 36 1 1 37 2 38 3 39 5 18 38 3 39 4 40 5 41 6 18 40 6 41 8 42 9 43 11 19 42 7 43 9 44 11 46 1 19 45 1 46 4 47 6 48 9 20 47 3 48 5 49 7 50 10 20 50 0 51 3 52 6 53 10 21 52 53 4 54 7 55 10 21 55 1 56 5 57 9 59 2 22 57 2 58 5 59 9 61 1 22 60 6 61 11 63 3 64 8 23 62 63 10 65 2 66 7 7 23 66 1 67 7 69 0 70 6 24 68 69 5 70 10 72 41 24 72 0 73 6 75 0 76 7 25 73 9 75 3 76 9 78 3 25 78 1 79 8 81 3 82 11 26 79 10 81 4 82 11 84 6 26 84 6 86 2 87 9 89 89 5 27 86 1 87 8 89 3 90 11 27 91 1 92 10 94 6 96 3 28 92 7 94 3 95 11 97 7 28 98 0 99 9101 6103 4 40 28 78******** 29 99 3 101 0102 9104 6 6 29 105 1106 11108 9110 8 30106 3 108 0 109 10 111 7 30112 6 114 5 116 3 118 2 113 5115 3117 2119 0 31 120 1 122 32 120 11 122 9 124 8126 7 32 128 0 130 1124 0132 0126 0 0134 1 33 34 128 7130 6132 6134 6 33 136 1138 2140 3 142 5 136 6 138 6140 6142 7 34 144 6 146 8 148 9150 11 35144 144 7 146 8 148 9 150 11 35 35 153 1 155 4 157 36 153 0155 2157 3159 5 36 162 0164 3166 161 7163 10 166 0168 0 37 171 1173 5 175 38 170 6 172 9 175 39 179 7181 10184 0177 0177 3 38 2186 6 39 190 180 6182 11185 188 11 191 3 193 8 196 0 40200 1192 7 195 0202 6 205 6 159 9 6 168 10 9178 2 3 187 8 0197 6 0207 7y 41 42 43 198 5 200 10 203 208 3 210 71213 3 215 218 3 220 10 223 5 226 4 205 9 9 44 228 7 231 210 1 212 8 215 42 220 6 223 0 225 231 0 43 1 233 10 236 7 231 2 233 9 236 5 44 242 0 244 9 247 41 3 217 11 9228 5 6 239 3 6 250 4 45 239 46 239 1 241 9244 5 247 249 10 252 6 253 3 258 0 46 1 1 45 45 253 1 255 11 258 9 261 8 264 6 267 5 270 47 48 260 272 0 274 10 277 8 280 7 9 263 7 266 4 269 2 47 276 1 279 1282 48 288 0 291 49 283 5 286 4 289 3 292 2 50 295 295 2 298 1 301 1304 2 49 300 7 50 312 1303 6 315 0 294 2 0285 0 0 297 1 2 306 3 309 5 8 318 9 321 11 3 273 SOLID MEASURE. 505 Quarter Girt. inches ft. in. 19 feet long. 1-44 ft. in. ft. in. 3318 4 Quarter Girt. ft. in, inches ft. in. 20 feet long. 1 142 3 4 ft. in. ft. in. ft. in. 2 3 4 5 6 8 10 1 0 1 2 1 5 1 7 1 10 23 7 8 10 1 1 1 3 1 6 1 8 1 11 2 1 2 5 28 3 0 4 2 3 2 6 2 10 3 2 3 4 38 4 0 4 4 5 36 3 10 4 2 4 7 6 4 9 5 2 5 7 6 0 5 0 5 5 5 10 6 4 7 6 6 6 11 7 5 7 11 6 10 7 4 7 10 8 4 8 5 9 0 9 6 10 1 8 11 9 5 10 0 10 8 9 10 8 11 3 11 11 12 6 9 11 3 11 11 12 6 13 2 10 13 2 13 10 14 6 15 3 10 13 11 14 7 7 15 4 15 4 16 1 11 16 0 16 8 17. 5 18 3 11 16 10 10 17 7 18 4 19 2 12 19 0 19 10 20 7 21 5 12 20 0 20 10 21 8 22 7 13 22 4 23 2 24 0 24 0 24 11 13 23 6 24 5 25 4 26 3 14 25 10 26 9 27 9 28 8 14 27 3 28 2 29 2 2 30 3 15 29 8 30 8 30 8 31 31 8 32 9 9 15 31 3 32 4 33 4 34 5 16 33 9 34 10 35 11 37 0 16 35 7 36 8 37 9 39 0 17 38 2 39 3 40 5 41 7 17 40 2 41 4 42 6 43 9 18 42 9 43 11 45 246 5 18 45 0 46 3 47 47 6 48 10 19 47 8 48 11 50 2 51 6 19 50 2 51 6 52 10 54 2 20 52 9 54 1 55 5 56 10 20 55 7 56 11 58 4 59 10 2283 21 58 259 59 7 61 062 62 5 21 61 3 62 9 64 2 65 8 63 10 65 4 66 9 68 3 22 67 3 68 9 70 70 4 71 11 23 69 9 71 4 72 10 74 5 23 73 6 75 1 76 8 78 4 24 76 0 77 7 79 2 80 10 24 80 0 81 8 83 4 85 1 25 82 6 84 1 85 9 87 6 25 86 10 88 7 90 4 92 1 26 89 2 90 11 92 8 94 94 5 26 93 11 95 8 97 6 6 99 5 2828 27 96 2 98 0 99 9101 17 27 101 3103 2105 0106 11 103 29 5105 4 107 2109 1 111 0 112 11114 10 116 9 30118 9 120 9 122 9 124 28 108 11 110 10 112 10 114 10 29 9 30 125 0 127 31 126 10 128 10 130 11 133 32 135 1137 3 139 4 141 6 33 143 8 145 10 148 34 152 6 154 9 157 0 31 133 116 10 118 10 120 10 122 11 0 127 1 129 2131 4 6135 8137 10140 0 32 142 3 144 5 146 8149 0 1150 3 33 151 3153 7 155 10158 2 0159 4 34 160 7 162 11 165 39 200 8 203 35 161 8 163 11 166 36 171 0173 5 175 37 180 8 183 1185 6188 0 37 38 190 6 193 0195 7198 1 3 205 10 208 6 3 168 8 35 170 2 172 7 175 4167 9 0177 6 9178 2 36 180 0182 6 185 190 2 192 38 39 211 40 211 1 213 9 216 5 219 1 40 222 200 7 203 3 214 3 225 0187 7 9195 4 197 11 2 205 10 208 7 0216 8 219 5 0 227 10 230 8 41 221 10 224 6 227 3 230 42 232 9 235 5 238 4 241 2 0 41 42 43 244 0 246 10 249 8 252 7 43 44 255 5 258 4 261 3 264 45 267 2 270 2 273 2 276 3 44 233 6 236 4 239 2 242 1 245 0 247 9 250 10 253 10 256 10 259 10 262 10 265 10 268 11 271 11 275 0 278 2 2 45 281 3 284 5 287 6 290 8 46 279 2 282 3 285 3 288 4 46 293 11 297 1300 4303 7 47 291 6 294 7 297 8 300 10 47 306 10 310 1313 4 316 8 48 304 0 307 2310 4 313 7 48 320 0 323 4 326 8330 1 49 316 10 320 0 323 50329 10 333 2 336 3 326 7 49 333 6336 11 340 4343 9 6 339 10 50 347 3 350 8 354 2 357 9 2 I 506 -No. 1. TIMBER TABLES. Quarter Girt. inches ft. 21 feet long. 1 1--14 من الحر 3 Quarter Girt. 22 feet long. 1 4 11/18 3 in. ft. in. ft. in. ft. in.inches ft. in. ft. in. ft. in. ft. in. 23 4 9 11 1 1 1 4 1 6 1 9 2 1 2 4 2 8 2 11 3 3 5 38 4 0 4 5 4 10 Q MTH LO 7 9 11 1 3 1 4 4 2 5 5 3 10 124 7 1 10 2 2 ૭૭ 2 9 3 1 3 5 4 77 5 1 6 5 3 5 8 6 2 6 8 5 6 6 6 5 6 11 7 7 2 7 8 8 2 8 9 7 6 8 0 8 7 9 2 8 9 4 9 11 10 6 11 2 9 9 10 5 11 0 0 11 11 8 9 11 10 12 6 13 2 13 10 12 4 13 1 13 9 14 6 10 14 7 15 4 16 1 16 10 10 15 3 16 1 16 10 17 8 11 17 8 18 5 19 3 20 2 11 18 6 19 4 20 2 21 1 12 21 0 22 11 22 9 23 8 12 22 0 22 11 23 10 24 10 13 24 8 25 7 7 26 7 27 7 13 25 10 26 10 27 10 28 11 14 28 7 29 7 30 8 31 9 14 29 11 31 0 32 1 33 3 15 32 10 33 11 35 0 36 2 15 34 4 35 6 36 8 37 11 16 37 4 4 38 38 6 39 39 8 40 11 16 39 1 40 4 41 41 7 42 10 17 42 2 43 5 44 8 45 11 17 44 2 45 5 46 9 48 48 2 18 47 3 48 7 49 11 51 3 18 49 6 50 11 52 3 53 8 19 52 8 54 0 55 5 56 11 19 55 2 56 56 7 58 1 59 7 20 58 4 59 10 61 3 62 9 20 61 1 62 8 64 2 65 9 21 64 4 65 10 67 5 69 0 21 22 70 7 72 2 73 10 75 6 283 67 4 69 0 70 7 72 3 22 73 11 75 8 77 4 79 1 23 77 2 78 10 80 6 82 3 23 80 10 82 7 84 4 86 86 2 24 84 0 85 85 987 9 87 6 89 4 24 88 0 89 10 91 8 93 7 25 91 2 93 0 94 10 96 8 25 95 6 97 5 99 4 101 4 26 98 7100 6 102 5 104 26 103 3105 3107 3 109 4 27 106 4 108 4 108 3 110 3 112 4 4 27 111 4113 5 115 6117 8 4116 28 114 29 122 8 124 9 126 11 129 1 30 131 3 133 4 116 5 118 5 120 6 28 119 9 121 11 124 1126 3 29 5 135 8 137 11 30 128 6 130 8 132 11 135 3 137 6 139 10 142 1 144 5 31 140 2 142 32 149 4151 33 158 9 161 34 168 7171 35 178 8 181 36 189 0191 37 199 8 202 38 210 7 213 39 221 10 224 8 227 40 233 4 236 3 239 5 144 8 147 0 8 154 0156 5 3 163 8 166 1 1173 7 176 1 2 183 9 186 5 31 32 33 34 35 8 194 3 196 11 36 4 205 1 207 10 37 146 10 149 2151 156 5 158 11 161 4 163 10 166 4168 11 171 5 174 0 176 7 179 3 181 10 184 6 187 2 189 10 192 6 195 3 198 0 200 9 203 6 206 4 209 2 212 0 214 10 217 9 7154 0 4 216 2 219 0 38 220 7 223 6 230 5 39 232 4235 6 226 5 229 5 4 238 4241 5 2 242 2 40 244 5 247 6 250 7 253 8 43 41 245 2 248 2 251 42 257 3 260 3 260 269 8 272 9 275 11 279 2 254 2 41 256 10 259 11 263 1266 4 2 263 5 266 6 42 269 6 272 7 275 11 279 2 2 43 44 282 4 285 7 288 9 292 0 44 45295 45 295 4 298 7 301 11 305 3 45 282 6 285 295 9 299 2 302 309 4 312 10 316 9 289 1 292 5 6 305 11 3 319 9 47 48 322 2 325 336 0339 49 350 2 353 46 308 7 311 11 315 4 318 9 46 7 329 323 3 326 10 330 4333 11 0 332 6 47 337 6 343 0346 7 48 9 357 9 357 4 360 11 49 352 6341 0355 1344 8 359 8 348 4 4363 1 366 10 370 7374 4378 2 50 364 7 368 3 371 11 375 7 50 381 11 385 9389 7 393 6 SOLID MEASURE. 507 Quarter Girt. 23 feet long. 11414 1 2 4 2010 Quarter Girt. inches ft. in. ft. in. ft. in. ft. in. inches 24 feet long. 1 1-1-18 ft. in. ft. in. ft. in. 3 / 4 ft. in. 2 3 4 5 CO 8 10 1 0 1 2 2 10 1 0 1 3 1 5 1 8 1 11 2 3 3 1 6 2 7 2 11 3 3 3 7 4 2 8 13 9 2 0 2 4 0 3 4 3 9 4 0 4 5 4 10 5 3 4 2 4 5 0 5 6 5 9 6 3 69 7 3 6 0 6 6 7 0 7 7 7 10 8 5 9 0 9 7 8 2 8 9 9 4 10 0 8 10 3 10 10 11 6 12 3 8 10 8 11 4 12 0 12 9 9 12 11 13 8 14 5 15 2 9 13 6 14 3 15 0 15 10 10 16 0 16 9 17 7 18 5 10 16 8 17 6 18 4 19 3 11 19 4 20 2 21 1 22 1 11 20 2 2 21 1 22 0 23 0 12 23 0 24 0 24 11 25 11 12 24 0 25 0 26 0 27 1 13 27 0 28 0 0 29 1 30 2 13 28 2 29 3 30 4 31 6 14 31 4 32 5 33 7 34 9 14 32 8 33 10 35 0 36 3 15 35 11 37 2 38 4 39 7 15 37 6 38 9 40 9 40 0 41 4 16 40 11 42 2 43 6 44 10 16 42 8 44 0 45 4 46 9 17 46 2 47 6 48 11 50 4 17 48 2 49 7 51 0 52 6 18 51 9 53 2 54 8 56 2 18 54 0 0 55 6 57 0 58 19 57 8 59 2 60 9 62 4 19 60 2 61 9 63 4 65 0 20 63 11 65 6 67 67 1 1 68 9 20 66 8 68 4 70 0 71 9 2223 21 70 5 72 1 73 10 75 7 21 73 6 75 3 77 0 78 10 77 4 79 1 80 10 82 8 22 80 8 82 6 84 4 86 3 23 84 6 86 4 88 2 90 1 23 88 2 90 1 92 0 94 O 24 92 0 93 11 95 10 97 10 $135 24 96 0 98 0100 0102 1 25 99 10 101 10 103 10 105 11 26 108 0 110 1112 2114 3 27 116 5118 25 104 2 106 3 108 4 110 6 26 112 8 114 10 117 0 119 3 7 120 9 123 0 27 121 28 125 3 127 6 129 9 132 0 28 130 8 133 0135 29 134 4136 8139 0141 4 29 140 2 142 7 145 30 143 9 146 2 148 7 151 0 30 150 0 152 6 155 31 153 6156 0158 6161 0 31 160 2162 2162 9165 32 163 7166 1168 8 171 4 32 170 8 173 4 176 33 173 11 176 7179 3181 11 33 181 6 184 3 187 6 123 9 126 0 128 4 137 4 9 0147 6 0 157 7 4168 0 0 178 9 0189 10 36 37 38 34 35 195 8 198 5 201 207 0 209 11 212 218 8 221 7 224 230 8 233 8 233 39 242 11 246 40 255 7 258 184 8 187 4 191 1192 10 34 192 8195 8195 6 198 4 201 3 3 204 1 35 204 2 207 1 210 0 213 0 9 215 8 36 216 0219 0 222 0 225 1 7 227 7 8 236 9 239 10 37 228 2 231 3 234 4 237 6 38 240 8 243 10 247 0 250 3 0 249 0 249 2 252 4 39 253 6 256 6 256 9 260 0 263 4 9 262 0 265 3 40 266 8 270 0 273 4 276 9 41 268 6 271 9 275 42 281 9 284 11 288 43 295 4 298 9 302 44 309 3312 1 278 5 41 280 2 283 7 287 0 290 6 6 291 11 42 294 0 297 4 301 0 304 7 3 305 9 43 308 2311 9 315 4 319 0 9 316 3 319 10 44 322 8 326 4 330 0 333 9 45 323 5 327 0 330 8 334 4 45 337 6 341 3 345 0 348 10 46 338 0341 8 345 4 349 1 46 352 8 356 6 360 4 364 3 47 48 352 10 356 7 360 4 364 368 0 371 10 375 8 379 49 383 6 387 5 391 50 399 4 403 4 407 2 47 368 2 372 1376 0 380 0 7 48 384 0 388 0 392 0 396 1 4 395 4 4 411 4 50 49 400 2404 3408 4 412 6 416 8 420 10 425 0 429 3 508 TIMBER TABLES.-No. 1. Quarter Girt. inches ft. 25 feet long. Quarter Girt. 26 feet long. 1 1 18 2 3334 1/4 1-1/48 3 4 in. ft. ft. in. in. ft. in. inches ft. in. ft. in. ft. in. ft. in. 2 3 4 1 2 9 878 10 1 10 12 1 1 4 2 1 2 5 3 2 36 3 11 234 9 11 1 1 1 4 1 7 1 11 2 2 2 6 2 11 3 3 3 8 1 5 4 4 4 9 5 3 59 5 4 6 5 0 5 5 60 6 6 3 69 7 4 7 11 66 8 3 7 8 6 9 1 9 9 10 5 8 10 9 6 10 2 10 10 8 11 1 11 10 12 6 13 3 8 11 7 12 3 13 0 13 10 857EIGASSE 5. 14 1 14 10 15 8 16 6 9 14 7 15 5 16 3 17 2 10 17 4 18 3 19 1 20 1 10 18 1 19 0 19 11 20 10 21 0 22 0 22 11 24 0 11 21 10 22 10 23 10 24 11 12 25 0 26 1 27 1 28 3 12 26 0 27 1 28 2 29 4 29 4 30 6 31 8 32 10 13 30 6 31 8 32 10 34 2 14 34 0 35 3 36 6 36 6 37 10 14 35 5 36 8 37 11 39 3 15 39 1 40 4 41 8 43 1 15 40 7 42 0 43 4 44 9 44 5 45 10 47 3 48 8 16 46 3 47 8 49 2 50 8 50 2 51 51 8 53 2 54 8 17 52 2 53 9 55 3 56 11 56 3 57 10 59 5 61 0 18 58 6 60 2 2 61 9 63 6 62 8 64 4 66 0 67 9 19 65 2 66 11 68 8 70 5 20 69 5 71 2 72 11 74 9 20 72 3 74 0 75 10 77y 223 21 76 7 7 78 78 5 80 3 82 1 21 79 8 81 6 83 5 10 85 5 22 84 0 85 11 87 11 89 10 22 87 5 89 5 91 5 93 5 23 91 10 93 10 95 10 95 10 97 11 23 95 6 97 7 99 8101 10 24 100 0 102 0 102 1104 2106 41 24 104 0106 2 108 2 108 4 110 7 25108 6 110 8 112 11 115 1 25 25112 112 10 115 1 117 5 119 9 26 117 4 119 7 121 11|124 3 26 122 1124 5 126 9 129 2 27 126 7 128 11 131 3 133 8 27 131 7134 1136 6139 0 888888 28 136 1 138 7 141 29 146 0148 6151 30156 3 158 10 161 0143 6 28 141 7144 1146 8149 3 1153 8 29 151 10154 10 157 1159 10 6 164 2 30 162 6 165 3 167 11 170 9 31 166 10 169 6 172 3 175 0 31 2 32 32 177 9180 7 183 4186 33 189 0 191 11 194 10 197 9 9 33 34 200 8 203 8 206 8 209 8 34 35 212 8 215 8 218 9 221 11 35 36 225 0 228 2 231 3 234 6 36 237 8 240 11 244 2 247 5 37 173 6 176 184 11 187 196 7 199 208 9 211 2 224 221 234 0237 37 247 2 250 38 250 8 254 0 257 4 260 8 38 260 9 264 39 264 0 267 0 267 5 270 10 274 40 277 9 281 3 284 9 289 4 39 3 274 7 278 40288 11 292 41 0302 741 291 10 295 5 299 42 306 3 309 9 313 7 317 3 42 43 321 0 324 9 328 6 332 4 43 44 336 1 339 11 343 9 347 8 44 45 351 7 355 6 359 5 363 4 45 46 367 4 371 4 375 5 379 5 46 47 383 6 387 7 391 8 395 10 47 48 400 0 404 2408 4 412 7 48 49 416 10 421 1 425 5 429 8 49 50 434 0 438 4 442 9 447 2 50 4 179 2 182 0 9190 8 193 8 7 202 7 205 8 10 214 11 218 0 4 227 6 230 9 3 240 6 243 10 6 253 11 257 4 2 267 7 271 1 2 281 8 285 3 6 296 2 299 10 303 6 307 318 6 322 333 10 337 349 7353 365 7 369 382 1386 3 390 5 394 7 398 101403 1 407 4 411 8 416 0 420 4 424 8 429 1 433 6 437 11 442 5 446 11 451 5 455 11 460 5 465 0 3 310 11 314 9 1 326 1330 0 9 341 8 345 7 6 357 6 361 7 8 373 9 377 11 SOLID MEASURE. 509 27 feet long. Quarter Girt. 28 feet long. 11 101 34 Quarter Girt. 4 1 ㅎ 3 2 3 4 inches ft. in. ft. in. ft. in. ft. in. inches ft. in. ft. in. ft. in. ft. in. 6 QM TO CO 2 3 9 1 8 11 3 2 0 3 4 8 5 2 5 Q 3 - 1Q35O 2 2 3 9 124 ∞ ∞ cr 5 8 6 2 2345 9 1 9 3 1 4 10 6 9 7 4 8 0 8 6 7 0 1 2 3 N 1 0 1 3 1. 6 1 2 5 2 9 6 3 11 4 5 5 4 5 10 6 5 7 7 8 3 8 10 7 9 2 9 10 10 6 11 3 9 6 10 10 3 10 11 11 8 8 12 0 12 9 13 6 14 4 12 5 13 3 14 1 14 11 9 15 2 16 16 0 16 11 17 10 9 15 9 16 8 17 7 18 6 10 18 9 19 19 8 20 8 21 8 10 19 5 20 5 21 5 22 6 11 22 8 23 23 9 24 9 25 11 11 23 6 24 7 25 9 26 10 12 27 0 28 2 29 3 30 61 12 28 0 29 0 29 2 30 5 31 7 13 31 8 32 11 34 2 35 2 13 32 10 34 2 35 35 5 36 9 14 36 9 38 1 39 5 40 9 14 38 1 39 6 40 11 42 4 15 42 2 43 43 7 7 45 45 0 46 6 15 43 9 45 3 46 9 48 3 16 48 0 49 6 51 0 52 52 7 16 49 9 51 4 52 11 54 7 17 54 2 55 55 9 9 57 57 5 59 1 17 56 2 57 10 59 59 7 61 3 18 60 9 62 64 2 65 11 18 63 064 9 9 66 7 68 4 19 67 8 8 69 6 71 3 73 2 19 20 75 0 76 11 76 11- 78 78 9 80 9 20 70 2 72 777 9 79 9 81 73 11 75 10 9 83 9 21 82 8 84 8 27 24 108 25 117 2119 26 126 9 129 9129 136 8 139 86 8 88 8 21 22 90 9 92 10 94 11 97 0 22 23 99 2101 4 103 6 105 9 23 0110 3 112 6114 10 24 85 9 87 10 94 1 96 3 89 11 91 11 102 10 105 112 0114 6 121 11 6 121 11 124 4 25 2131 8 134 2 26 121 6 124 0126 131 5 134 3 141 9144 5 27 141 9 144 28 147 0 149 8 152 3 154 11 28 152 5 155 98 1107 4 116 9 119 1 0 126 5 128 11 0136 9 144 5 147 1149 5 155 2 157 11 160 9 5100 8 5109 8 7 139 2 9 29 8160 5163 5163 2 165 11 29 7 174 5 177 3 0189 0 31 0 201 1 32 5 213 7 33 2226 5 3 239 9 253 8 3 6 157 30168 9 171 31 180 2183 1186 32 192 0195 0198 33 204 2 207 3 210 34 216 9 219 11 223 35 229 8 232 11 236 36 243 0 246 5 249 37 256 8 260 2 263 8 267 38 270 9 274 4 277 11 281 39 285 2 288 10 292 6 296 40 300 0 303 9 307 6 311 祐市 41 315 42 43 2 319 0322 11 326 10 41 $30 9 334 6 338 8 342 8 42 346 8 350 8 354 9 358 1 43 44 363 0367 2371 3 375 6 44 45 379 8 383 11 388 2 392 46 396 5 401 1405 47 414 2418 7423 10 273 6 288 7 303 7 303 5 307 3 0 318 11 322 11 3 292 0 326 10 330 10 334 11 338 11 343 0 346 11 351 3 355 4 359 6 363 9 367 11 372 11 376 5 380 5 380 9 385 1389 5 393 9 398 2 402 7 407 0 411 5 415 11 420 429 6 434 1 438 448 0 452 8457 8 476 5 45 45 5 409 9 46 0427 6 47 48 432 0 436 6 441 0445 7 48 49 450 2 454 9 459 5 464 1 49 50 468 9 473 5 478 2 482 11 50 50 466 10 471 486 1 491 5 425 0 9443 4 5 462 1 5481 3 0 495 11500 10 163 6 166 4 169 3 172 1 338 175 0 177 11 180 11 183 10 186 10 189 11 192 11 196 0 199 1 202 211 9 215 34 224 9 228 1 231 35 35 238 2 241 7 245 36 252 0 255 6 259 2 205 5 208 7 0 218 0 218 3 221 6 5 234 10 1 248 6 1262 7 2 37 266 2 269 5 277 1 6 38 3 280 9 284 3 39 4 40 295 9 299 311 1 315 510 TIMBER TABLES.-No. 1. Quarter Girt. 29 feet long. 1 4 -~ Quarter Girt. } 3 4 inches ft. in. ft. in. ft. in. ft in. inches ft. in. 30 feet long. 14 3 cokk ft. in. ft. in. ft. in. 2 3 M 10 1 10 1Q 0 1 3 1 6 2 1 2 6 2.10 3 3 3 8 4 1 4 6 234 10 1 1 1 4 1 7 1 10 2 2 2 7 2 11 3 4 3 9 4 3 4 8 5 0 5 7 6 1 6 8 5 5 2 5 9 6 4 6 11 7 3 710 8 6 9 2 6 7 6 8 2 8 10 9 6 7 9 10 10 7 11 4 12 1 10 3 10 11 11 9 12 6 8 12 11 13 8 14 7 15 5 16 4 17 3 18 2 19 2 ∞ a 8 13 4 14 2 15 1 15 11 16 10 17 10 18 10 19 10 10 20 2 21 21 2 2 22 2 23 3 3 10 20 10 21 11 23 0 24 1 11 24 4 25 6 26 8 27 10 11 25 2 26 4 27 7 28 9 12 29 0 30 3 31 6 32 32 8 12 30 0 31 3 32 7 33 10 13 34 0 35 4 36 8 38 1 13 35 2 36 7 36 7 38 38 0 39 5 14 39 6 40 11 42 4 43 10 14 40 10 42 4 43 10 45 4 15 45 4 46 10 48 5 49 11 15 46 10 48 5 50 1 51 8 16 51 77 53 2 54 10 56 6 16 53 4 55 0 56 9 58 58 5 17 58 2 59 11 61 8 63 5 17 60 2 62 0 63 10 65 8 18 65 3 67 1 68 11 70 10 18 67 6 69 5 71 71 4 73 3 19 72 8 20 8888 74 7 76 7 78 7 19 75 2 77 2 79 79 3 81 3 80 7 82 7 84 8 86 8 20 83 4 85 5 87 7 89 8 21 88 10 90 11 93 1 95 3 21 91 10 94 10 96 4 98 7 22 97 6 99 8 101 11 104 23 106 6 108 10 111 3113 24 116 0118 5 120 11123 25 125 10 128 26 136 2138 27 146 10 149 28 157 11 160 29 169 4 172 30 181 3 184 6196 3 22 100 10 103 10103 2105 6 107 10 7 23 110 2112 7115 1117 6 4 24 120 0122 6 125 1127 7 5 130 11 133 6 25 130 2 132 10 135 6 138 2 9 141 5 144 1 26 140 10 143 7 146 4 149 1 7 152 4155 1 27 9163 4 175 7166 5 3 178 3 3 187 4 190 5 206 3 209 31 193 32 33 219 4 222 34 232 10 236 3 239 8 243 35 246 8 250 3 253 1 257 5 36 261 0 264 8 268 37 275 8 279 5 283 38 290 10 294 8 298 6 302 39 306 4 310 3 314 3 318 40 322 3 326 3 330 4 334 8 199 10 203 0 31 200 2 203 5 212 9 216 0 32 213 4 216 8 226 0 229 5 33 226 10 230 2 34 240 10 244 151 10 154 8 157 28 163 4166 29 175 2 178 30187 6 190 3 172 4184 5 8 193 10 197 0 5 206 9 210 0 8 220 1223 5 4 233 10 237 4 5 248 0 251 7 7 160 5 3 169 3 181 2 5 35 255 2 258 10 262 7 266 3 4 272 0 36 270 0 273 9 277 9 277 7 281 7 281 4 2 287 0 37 285 2 289 1 293 0 296 11 5 38 300 10 304 10 308 10 312 10 2 39 5 40 40 333 4 337 6 341 316 10 320 11 325 9 345 11 1329 2 43 44 41 338 6 342 8 346 10 351 42 355 3 359 3 363 9 368 372 4 376 8 381 1385 389 11 394 4 398 10403 0 41 350 1 42 6 43 3 44 2354 6 358 367 6 371 8 376 4 380 385 2 389 8 394 403 4 407 11 412 10 363 2 3 398 9 7 417 2 45 407 10 412 4 416 11 421 6 6 45 421 10 426 7 431 4 436 1 46 426 2 430 9 435 5 440 2 46 440 10 445 8 450 6 455 4 47 444 10 449 7 454 5 459 2 47 460 2 465 1470 1475 0 48 464 0 468 10 473 8 478 49 483 6 488 6 493 7 48 480 0 485 0 490 1495 1 5 498 5 49 500 2505 4510 6 515 8 50 503 6 508 6 513 7 518 8 8 50 50520 10 526 1 531 4 536 7 SOLID MEASURE. 511 Quarter Girt. inches ft. in. 31 feet long. 1 1/2 Quarter Girt. 32 feet long. *400 3 114 1124 3 4 ft. in. ft. in. ft. in. inches ft. in. ft. in. ft. in. ft. in. 2 3 4 10 1 1 1 4 1 11 2 3 2 8 180 7 2 11 1 2 1 5 10 1 8 3 0 3 2 0 2 4 2 9 3 2 3 5 3 11 4 4 4 10 3 7 4 0 4 6 5 5 5 5 11 6 6 7 1 5 7 62 69 7 4 6 9 8 5 9 1 9 10 6 0 8 8 9 5 10 2 10 7 11 4 12 1 12 11 7 11 11 11 8 12 6 13 8 13 9 14 8 15 7 10 6 8 14 3 15 2 16 1 17 9 17 5 18 5 19 5 20 20 6 9 18 0 19 0 20 1 21 10 21 6 22 22 7 7 23 23 9 24 11 10 22 3 23 4 24 6 25 8 4028 11 26 1 25 3 28 6 29 9 11 26 11 28 2 29 5 30 8 12 31 0 32 4 33 8 35 0 12 32 0 33 4 34 9 36 2 13 36 5 37 10 39 3 40 8 13 37 7 39 0 40 6 42 0 14 42 2 43 9 45 3 46 10 14 43 5 45 2 46 9 48 4 15 48 5 50 151 50 1 51 9 53 5 15 50 0 51 51 8 8 55 55 5 55 2 16 55 1 56 10 58 7 60 5 16 56 11 58 8 60 6 62 4 17 62 3 64 1 65 11 67 10 17 64 3 66 2 68 1 70 0 18 69 9 71 8 73 8 75 8 18 72 0 74 O 76 1 78 2 19 77 9 79 9 81 10 84 0 19 80 3 82 4 84 6 86 9 20 86 1 88 3 90 6 92 92 8 20 88 11 91 2 93 5 95 8 21 94 11 97 2 99 6101 10 21 98 0 100 4102 9 105 2 22 104 2 106 7 109 23 113 11 116 4 118 24 124 0126 25 134 7 137 0 111 5 22 107 7 110 0112 6 115 0 11 121 5 23 117 7 120 2129 9 125 4 7 129 3131 10 24 128 0130 8133 3 140 0 142 9 25 138 11 141 9 144 26 145 6148 6 148 4151 2154 0 26 150 3153 1156 156 11 159 10 162 10 165 27 28 168 9171 10 174 10 177 11 29 181 1184 2 187 4190 6 30 193 9 197 0 200 3 203 7 30 9 27 162 0165 0168 28 174 3 177 4 180 5136 2 6 147 4 1158 11 1171 2 6183 8 29 186 11 192 2 193 5 196 200 0 203 4 206 9 210 2 31 206 11 210 3 213 32 220 5 223 11 227 33 234 5 238 0 241 34 249 10 252 6 256 35 263 9 267 6 271 4 275 36 279 0 282 11 289 10 290 37 294 9 298 9 302 38 310 10 315 0 319 7 217 0 0 31 213 7 217 0 220 6 224 0 5 230 11 32 227 7 231 2 234 9 238 4 7 245 3 33 242 0 245 8 249 5 253 2 3 260 0 34 256 11 260 8 264 6 268 4 2 35 35 272 3 276 2 280 1284 0 9 36 288 0 292 0 292 0 296 0 296 1 300 2 9 306 9 37 304 3 308 4 312 6 316 8 1323 3 38 39 327 5 331 8 335 11340 40 344 5 348 9 353 1 357 2 39 6 40 355 320 11 325 2 329 338 0 342 4 346 7360 5 333 9 351 2 0 364 6 369 0 1402 1402 41 361 11 366 4 370 9 375 42 379 9 384 1 388 10 393 5 43 398 8407 4 412 1 43 44 416 9 421 45 435 11 440 46 455 6460 6 460 47 475 7 480 3 41 373 7 378 7 378 2 382 9 387 4 42 392 0 396 6 401 5 406 2 6 426 4 431 1 44 410 11 415 8 420 430 3 435 6 425 4 2 440 9 445 8 450 7 45 450 0 455 0 460 6465 6 470 6 46 470 3 475 4 480 • 1445 0 1 465 2 6 485 6485 8 7485 48 496 0 501 49 516 11 522 50 538 2 543 2 506 2527 9490 10 47 5 511 7 6 532 10 49 48 7 549 0 554 6 50 50 490 11 496 512 0 517 4 522 533 7 539 0 544 555 7561 2 566 2 501 5 506 8 9 528 1 0 550 0 9 572 4 512 TIMBER TABLES.-No. 1. Quarter Girt. inches ft. in. 33 feet long. 118 Ho Alw Quarter Girt. 34 feet long. 1 114 3 12/0 ft. in. ft. in. ft. in. inches ft. in. ft. in. ft. in. ft. in. 2 Q345 CO 11 1 2 1 5 19 2 1 2 5 2 10 3 3 23 11 1 2 1 6 1 9 2 2 2 6 2 11 3 4 3 8 4 2 4 8 5 2 3 9 4 3 4 9 5 4 5 9 6 4 6 11 7 7 5 11 6 6 7 2 7 10 8 3 8 11 98 10 5 6 6 9 3 10 0 10 9 7 11 3 12 1 12 11 13 9 7 11 7 12 5 13 3 14 2 8 14 8 15 7 16 7 17 7 8 15 1 16 1 17 1.18 1 9 18 7 19 19 7 20 8 21 9 9 19 2 20 2 21 21 4 4 22 5 10 22 11 24 1 25 3 26 6 10 23 7 24 10 26 0 27 3 11 27 9 29 29 0 0 30 4 31 8 11 28 7 29 11 31 3 32 7 12 33 0 34 5 35 10 37 4 12 34 0 35 5 36 11 38 5 13 38 9 40 3 41 41 9 43 4 13 39 11 41 5 43 0 44 8 14 44 11 46 6 48 2 49 10 14 46 3 47 11 49 8 51 4 15 51 7 53 4 55 1 56 10 15 53 2 54 11 56 9 58 7 16 58 8 60 6 62 5 64 4 16 60 5 62 4 64 3 66 3 17 66 3 68 2 70 2 72 2 17 68 3 70 3 72 4 74 5 18 74 3 76 4 78 5 80 7 19 82 9 84 11 87 2 89 4 20 91 8 94 0 96 4 98 8 20 252 18 76 6 78 8 80 10 80 10 83 0 19 85 3 87 6 89 9 92 2 94 5 96 10 99 3 101 8 21 101 1103 6 105 11 108 5 21 104 2106 7109 2111 8 22 110 11113 5 116 0118 71 22 114 3 116 11119 6122 2 23 121 3123 11 126 7 129 3 23 124 11 127 8 130 5 133 2 24 132 0134 9 137 7 140 5 24 136 0138 10 141 25 143 3 146 1 149 0 151 11 25 147 7 150 6 153 9144 8 6 156 7 26 154 11 157 11 160 11 163 11 26 159 7162 8165 10 168 10 27 167 1 170 2 173 4 176 6 27 172 2175 4 178 7 181 10 28 179 8 182 11 186 29 192 9 196 1 199 30 206 3 209 8 213 2189 5 28 185 1188 5191 9 195 2 5 202 10 29 2216 8 30 198 7 202 0205 6 209 0 212 6 216 1 219 8 223 3 40 31 220 3 223 10 227 32 234 8 238 4 242 1 245 10 32 33 249 7 253 4 257 2 261 0 33 0 34 264 11 268 10 272 9 276 9 35 280 9 284 9 288 10 292 11 36 297 0 301 2 305 4 309 6 37 313 9 318 38 330 11 335 8344 1 38 39 348 7 353 1 357 7 362 1 39 366 8 371 3 375 11 380 40 5 231 0 31 226 11 230 241 9 245 257 2 261 34 272 11 277 7234 3 238 0 7 249 7 249 5 253 3 0 265 0 268 11 0281 0 285 1 35 289 3 293 289 3 293 5 297 7 301 9 36 306 0 310 3 314 7 318 11 0 322 3 326 7 3 339 37 323 3 327 7 332 0 336 6 340 11 345 5 350 0 354 6 359 2 363 9 368 5 373 1 7 40 377 9 382 6 387 3 392 1 41 385 3 389 11 394 8 399 5 41 396 11401 9 406 8 411 7 42 404 3408 10 413 11 418 10 43 423 9 428 42 416 6421 6421 8 433 8 438 8 43 436 7 441 44 443 45 464 1 469 46 484 11 490 47 506 3 511 48 528 0 533 8448 9 453 10458 11 3 474 5 479 8 2495 6 500 10 8 517 1522 6 44 457 1 462 45 478 2 483 46 499 7 505 47 3 426 6 431 6 8446 9 451 11 4 467 7 472 10 5 488 10 494 2 1510 6 516 0 49 50 6 539 1 544 550 3 555 10 561 6 567 2 49 572 11 578 8 584 5 590 3 50 8 521 7 527 48 544 01549 2 532 9 538 4 8 555 5 561 2 566 11 572 8 578 578 6 584 5 590 3 596 2 602 2 608 1 SOLID MEASURE. 513 Quarter Girt. inches 35 feet long. 1 14 937 Quarter Girt. 36 feet long. 114 13/13 4 00/+ 3 ft. in. ft. in. ft. in. ft. in.inches ft. in. ft. in. ft. in. ft. in. QEHLO CO 2 1 0 1 3 1 6 1 10 2 3 2 2 2 7 3 0 3 5 3 11 4 5 4 11 5 6 6 1 6 8 7 4 8 0 6 8 9 9 6 10 3 11 1 7 11 11 12 9 13 8 14 77 8 15 7 16 7 17 7 18 7 9 19 8 20 10 21 11 23 1 10 24 4 25 6 26 10 28 1 10 11 29 5 30 9 32 233 7 11 12 35 0 36 6 38 0 39 6 12 13 41 1 42 8 44 4 45 11 13 Q 34E CO ** R* 1 0 1 3 1 7 1 11 2 3 28 3 1 3 6 4 0 4 6 5 1 5 8 63 6 11 ry my 8 3 6 0 9 9 10 7 11 5 12 3 13 2 14 1 15 O 16 0 17 0 18 1 19 2 20 321 21 5 22 7 23 9 25 0 26 3 27 7 28 11 30 3 31 8 33 33 1 34 6 36 0 37 6 39 1 40 8 42 3 43 11 45 7 47 3 14 47 8 49 4 51 1 52 11 14 49 0 50 50 9 52 7 54 5 15 54 8 56 6 58 5 60 4 15 56 3 58 2 60 1 62 62 0 16 61 3 64 2 66 2 68 2 16 64 0 66 0 68 1 70 2 17 70 3 72 4 74 5 76 1 17 72 3 74 5 76 7 78 9 18 78 9 80 11 83 2 85 5 18 81 083 3 85 7 87 11 19 87 9 90 0 92 5 94 10 19 90 3 92 8 95 1 1 97 6 20 97 3 99 8 102 2104 8 20 20 100 0 102 6 105 1107 8 21 107 2109 9 112 4 115 0 21 110 3 112 22 117 8120 4123 1125 10 22 121 0123 23 128 24 7131 140 0142 11 145 5134 3137 1 23 132 3135 11148 11 24 144 0147 11115 9 126 2138 0 150 7 118 3 7 129 5 1141 0 1153 2 25 151 11 155 0 158 26 164 4 167 6 170 8 173 10 26 1161 2 25 25 156 159 5 162 7 165 9 169 0172 3175 7 178 11 27 177 2180 5 183 10 187 10187 2 28 190 27 182 3 185 8189 1192 6 7194 0197 5 200 11 28 29 204 5 207 11 211 30 218 9 222 5 226 196 0199 6 203 1206 8 6 215 1 29 210 3 213 11 217 7 221 3 1 229 10 30 30 225 0 228 9 232 7 236 5 31 233 7 237 4 241 32 248 11 252 10 256 33 264 9 268 9 272 34 281 0 285 35 297 9 302 2 245 0 31 240 3 244 2 248 1|252 0 9 260 8 32 256 0 260 0 264 1268 2 9 276 10 33 272 3276 5 280 7284 9 1 289 4 293 6 34 289 0 293 3 297 7 301 11 0306 4 310 8 35 35 306 3 310 8 315 1 319 6 36 315 37 332 0319 9 337 5 323 10 328 3 36 324 3341 10 346 4 37 342 0 328 6 333 3 346 11 351 1337 8 7 356 3 38 351 0355 7360 0 39 369 8 374 8 374 5379 5 379 40388 11 393 9398 3365 3384 1 39 380 8403 7 40 40400 0 405 38 361 0 365 9 370 7 375 5 3 385 2 390 1 395 0 0 410 1415 2 41 408 7 413 7 418 42 428 9 433 8 439 43 449 5 454 8459 44 470 7475 11481 45 492 2 497 8 503 46 514 4 519 11 525 47 536 11 542 8 548 7423 8 41 420 0444 2 42 441 3 425 5 430 7 435 9 0 446 0451 7 456 11 11 465 2 43 462 3 467 8 473 4 486 9 9 44 484 0 489 6 495 2 508 9 45 506 3 511 11 517 1478 1500 6 8 7 523 3 7 531 3 46 529 0 534 9 540 7 546 5 5 554 2 47 552 3 558 1564 1570 0 48 560 0 565 10 571 49 583 7 589 7595 7 601 7 9 577 8 48 576 0 582 0588 1594 2 49 600 3 606 5 612 7618 9 50 607 8 613 9 619 10 626 0 50 50 625 0 631 3 637 7 643 11 514 TIMBER TABLES.-No. 1. Quarter Girt. inches 37 feet long. 11-4 ft. in. ft. 12 19/20 Quarter Girt. in. ft. in. ft. in. inches ft. 38 feet long. 114 1-2/14 03/1 4 in. ft. in. ft. in. ft. in. 234 1 0 1 4 2 4 2 9 4 1 4 8 5 6 5 7 1 1357 79 7229 1 11 3 7 Q2 00 1 1 1 4 1 8 1 11 3 2 5 2 9 3 3 3 9 5 10 4 4 3 4 9 5 4 5 11 86 6 7 7 3 8 0 8 9 6 9 3 10 0 10 10 11 8 6 9 6 10 4 11 2 12 0 12 7 13 6 14 5 15 5 12 11 13 10 14 10 15 10 8 16 5 17 6 18 7 19 8 16 11 18 O 0 19 1 20 2 9 20 10 22 0 23 2 24 5 9 21 5 22 7 23 10 25 1 10 25 8 27 0 28 4 29 8 10 26 5 27 9 29 1 30 6 11 31 1 32 6 34 0 35 6 11 31 11 33 5 34 11 36 5 12 37 0 38 7 40 2 41 9 12 38 0 39 7 41 3 3 42 11 13 43 5 45 1 47 0 48 7 13 44 7 46 4 48 1 49 11 14 50 4 52 2 54 0 55 11 14 51 9 53 7 55 6 57 5 15 57 10 59 9 61 59 9 61 9 63 9 15 59 5 61 4 63 5 65 6 16 65 9 67 10 69 11 72 1 16 67 7 69 8 8 71 10 74 74 O 17 74 3 76 5 78 8 80 11 17 76 3 78 6 6 80 10 83 2 18 83 3 85 7 87 11 90 4 18 85 6 87 11 90 3 92 9 19 92 9 95 3 97 3 97 8 100 2 19 95 3 97 9 100 4 102 11 20 102 9 105 4 108 0 110 0 110 8 8 20 20 105 7 108 105 7 108 3 110 11 113 7 21 113 4 116 30 0 118 22 124 4 127 2 130 2130 1133 0 22 23 135 11138 11 141 11 144 11 23 24 148 0151 1154 3157 5 24 25 160 7 163 10 167 1 170 4 25 26 173 8 177 1180 5183 10 27 187 4 190 10 194 4|197 10 28 201 5 205 0 208 0 208 8 212 5 29 216 1 219 10 223 0227 5 231 3 235 1 239 0 118 9121 7 21 116 5119 2 122 0 124 10 9130 8 133 26 27 28 127 139 7142 8145 152 0155 0 155 2 158 164 11 168 164 11 168 3 171 178 5 181 10 185 192 5 195 11 199 206 11 210 7 214 5161 8 7 175 0 7 136 7 9 148 10 4 188 10 7 203 3 4 218 1 29 221 11 225 9 229 0 242 11 30 237 6 241 237 6 241 6 245 8233 6 249 7 6 31 246 11 250 11 254 11 259 0 32 263 1 267 3 271 5 275 7 31 253 7 257 8 261 10 266 0 32 270 33 279 10 284 1 288 4 292 8 33 287 5 291 34 297 0 301 5 305 10 310 3 34 3 274 6 278 5 291 9 296 305 1309 7314 9 283 0 2 300 7 35 314 9 319 3 323 10 328 5 35 323 3 327 11 332 1318 8 7 337 3 36 333 0 337 8 342 4 347 0 0 36 342 0 346 9 351 7 356 5 37 351 9 356 6 361 4 366 2 37 361 3 366 2 371 38 371 0 375 11 380 10 385 10 39 390 10 395 10 400 11 405 12 40 411 1 416 3 421 5 426 8 38 381 1386 39 401 5 406 1 391 6 411 6411 1376 1 2 396 3 9 417 0 40 422 3 427 6 432 10 438 2 41 431 11 437 42 453 3458 2 442 6 445 10 41 443 7 449 0 454 6 460 0 5 464 1 469 7 42 465 6 470 10 476 8 482 3 43 44 475 1480 497 5 503 8 486 2 491 10 43 487 11 493 7499 4 501 1 45 520 4 526 46 543 8 549 1 508 10514 7 1 531 11 537 10 537 10 7 555 7 561 7 44 510 11 516 9 522 7 528 5 45 45 534 5 540 534 5 540 4 546 4 552 4 46 558 5 564 6 570 7 576 9 47 567 7573 48 592 0 598 8 579 9 585 10 47 582 11 589 2 595 5 601 8 2 604 2 604 5610 8 48 608 0 614 4 620 9 627 2 49 3 629 7 635 11 49 50 616 11 623 3 629 642 4 648 10 655 3 661 9 50 659 9 666 633 7 640 1646 7 653 659 9 666 4 673 0 679 8 SOLID MEASURE. 515 Quarter Girt. inches ft. in. 39 feet long. 1 3 Quarter Girt. 40 feet long. 4 14 11. 324 ft. in. ft. in. ft. in. inches ft. in. ft. in. ft. in. ft. in. 2 3 2 15 1Q 1 4 1 8 2 1 2 1 1 1 5 1 9 2 1 2 10 3 4 3 10 3 2 6 2 11 3 5 3 11 4 4 4 11 5 6 6 1 4 5 5 0 5 7 6 3 5 69 76 8 2 8 11 5 6 11 7 8 8 5 9 2 6 9 9 10 7 11 5 12 4 10 0 10 10 11 9 12 8 7 13 3 14 3 15 3 16 3 13 7 14 7 15 7 16 8 8 17 4 18 5 19 7 20 9 8 17 9 18 11 20 1 21 3 21 11 23 2 24 5 25 9 22 6 23 9 25 1 26 5 10 27 1 28 5 29 10 31 4 10 27 9 29 29 2 2 30 7 32 1 11 12 13 FREE 32 9 34 3 35 10 37 5 11 33 7 35 2 36 9 38 4 39 0 40 8 42 4 44 0 12 40 0 41 8 43 5 45 2 45 9 47 7 49 4 51 2 13 46 11 48 9 50 7 52 6 14 53 1 55 0 57 0 58 11 14 54 5 56 5 58 5 60 5 15 60 11 63 0 65 1 67 2 15 62 6 64 7 66 9 68 11 16 69 4 71 6 73 9 76 0 16 71 1 73 4 75 7 77 11 17 78 3 80 7 82 11 85 4 17 80 382 8 85 1 87 6 18 87 9 90 2 90 2 92 8 95 3 18 90 0 92 6 95 1 97 8 19 97 9100 20 108 4 111 21 119 4103 0105 8 19 100 3102 11105 7108 4 1113 10 116 7 20 111 22 131 5 122 1134 23 143 24 156 3 146 0159 3 162 25 169 3 172 8 176 26 183 1 186 27 197 5 201 7190 4 125 2128 1 21 1137 1140 2 22 5 149 7 152 9 91 23 7 165 11 24 1 179 7 25 2193 10 26 122 134 5137 146 11 150 160 0163 173 7 177 1 180 187 9191 1204 10 208 7 27 202 6 206 28 212 4 216 29 2 220 0 223 10 227 9 231 9 235 8 239 8 29 30 243 9 247 10 251 11 256 1 30 28 217 9 221 8 225 1113 11 116 6 125 5 128 6140 2153 4 166 5 195 3210 9 119 7 5 131 5 7143 9 5 156 8 9170 2 7 184 2 1 198 9 1213 11 7 229 7 233 7 237 250 8 241 9 245 10 0 254 2 258 5 262 8 283 31 33 260 3 264 6 268 9 273 0 31 32 277 4 281 8 286 1 290 61 32 294 11 299 5 303 11 308 6 33 34 313 1317 8 322 4 327 0 34 35 331 9 336 6 341 4 346 2 35 36 351 0 355 11 360 10 365 9 37 370 9 375 10 380 10 385 11 266 11 271 3 275 7280 0 284 302 5288 11 293 6307 1 311 5 297 11 9 316 5 321 1325 10 330 340 3 345 36 360 0 365 2 350 0370 7335 5 1 355 0 1375 2 37 380 3 385 5 390 7395 10 38 391 1 396 3401 406 8 38 401 1 406 5 411 9 417 1 39 40 411 11 417 3 422 7 427 11 433 4 438 9 444 3 449 39 9 422 40444 6427 11 433 5 438 11 5 450 0 455 7 461 3 44 45 0 630 6 637 3 656 11 663 677 1 683 10 690 41 455 3 460 10 466 5 472 1 41 42 477 9 483 2 489 2 495 0142 43 500 9 506 7 512 6 518 5 43 524 4 530 4 536 4 542 4 44 548 5 554 6 560 8 566 10 45 46 573 1 579 4 585 47 598 3 604 8 611 48 624 49 650 50 466 11 472 8 478 490 0 495 7 501 5484 9 507 8 2 513 7 519 7 525 7 531 8 537 9 543 11 550 1556 3 562 6 568 9 575 1 581 5 7 591 11 46 587 9 594 9 594 2 600 2 600 7607 1 1617 6 47 613 7 620 2 626 9 633 4 1 643 81 48 640 0 646 0 646 8 653 5 660 2 7 670 4 49 8 697 6 50 694 5 701 666 11 673 9 680 7 687 6 5 708 5 715 5 516 TIMBER TABLES.-No. 2. TIMBER TABLES, No. II. Tables of unequal sided Timber, and side of equal square. Each page of these Tables contains twelve columns. In the outer column on either side is set down the greater side in inches, and in the remaining columns are contained the side of equal square corresponding to the unequal sides. USE OF THE TABLE. Ex. 1.-A piece of timber 27 inches broad, and 40 inches deep, what is the side of equal square? In the column headed 27 inches lesser side, and opposite 40 inches greater side, stands 334 inches side of equal square. Ex. 2.-A piece of timber 25 feet long, 23 inches broad, and 37 inches thick, what is its solid content? In Table, No. 2, under 23 inches lesser side, and opposite 37½ inches greater side, is 292 inches side of equal square. In Table, No 1, in the portion headed 25 feet long, opposite 29 inches quarter girt, and in the column headed inches, is 153 ft. 8 in. solid content. It is not unfrequent in practice for measurers to add together the unequal sides and consider half their sum as the side of equal square. When there is not much difference in the dimensions of the two sides, this is not productive of great error; but the two preceding examples will show, that when the sides are very dis- proportioned the error is considerable. In Ex. 1, 27 401 2) 68 sum of two sides 34 mean 334 True side of equal square. 3 difference. UNEQUAL SIDED TIMBER. 517 In Ex. 2, 2) 61 30 mean 29 231/ 37/1/2 sum of two sides True side of equal square error. ft. in. Content of a tree 25 feet long, 30 inches quarter girt, 161, 6 Content of a tree 25 feet long, 29 inches quarter girt, 153, 8 Error due to the incorrect method of determining the side of equal square 7, 10 518 —No. 2. TIMBER TABLESTABLES.. Lesser side, Lesser Greater 2 side, Lesser side. in. 21 side, in. 3 Lesser side, in. 3/1/20 in. Side of Lesser equal Side of side, square. equal square. Side of 4 Lesser side, Lesser equal Side of in. 4/1/1 side, Lesser square. inches. inches. equal in. 5 side, square. inches. in. 51 inches Side of in. Lesser inches. equal Side of side, 2334 NNNN HE -2 Mj mle 238 23 or cr h 41 3 İQ co na ma m Bid Bid 6778 3/3/20 6 6/1/1 8 3/2/20 7/12/20 4 08/12/20 4 4/1/20 9 9/1/20 10 10/1/ 4/12/2 11 111 12 121/ 5 4329290 4 20 5/1/ 51 500 44 Old Col Col 41 2/1/12 21 3/12/20 2112 29 2 OFF 31/12 31/ 31 31 3 39 0 3/1/2 33 110 39 90 3 OFF 39 0 4 41 41 49 F 5 51 3 4 41 411 4292909 41 4/1/20 51 5/1/ 51 5/1/ 444 14 12 BE BE HAHN LO LO LO CO LO LO LO LO HT HE HA - M< < 4445 CO 10 10 HK 4 LO LO LO LO HE HE HA F BE B 4445 5 51 51 IN BEBE 5/1/ 5 5 6 6 6 61 61 6 61 61 520 6 61 64/12 61 6/1/1 61 69210 7N77 HITHE HO∞ld 69/ 7211 71 K 6777 IQ BT Bl< 6/1/10 CO CO 63210 HE HE HQ ME 81 8/1/ ∞ ∞ ∞ ∞ FRE 7788 71 7 7 NN7 HATA MIE 67727 Hea old co}< < 6/ 69/1/ 7 7 61 630 7/1 77 13 13 51 5 20 61 14 51 6 730 8777 IN BİQ BİER square. equal square. Side of equal 6 Lesser side, inches. square. Side of equal in. 6/1/ in. square. inches. inches. Side of inches. equal Side of 4& H HQ + cold 44 HAHN square. equal square. Greater 5 51 51 5/1/2 HAHA inches. side. 5 inches. 5 5/1 H2 HQ B LO LO LO CO 10 HA HA H 5/1/ 5/1/ 5320 6 61 6 61 61 6 7 6 61 << 778 7/11 7931 I BE BE 730 8 81 8/1/20 8/3/10 ∞ ∞ ∞ ∞ H4 Hle ole osle 9 9/1/20 10 101/20 11 11/1/0 12 8 1/1/0 ∞ ∞ ∞ ∞ 81 81 ∞ ∞ ∞ ∞ 8/1/10 8 20 9 12 989 1990 941 13 921 13/1/20 91 9/14 HIQ BE B{E 7778 HE HE HA 7 7፤ 7፤ 141 15 15/1/ 51 16 5元 10 10 10 LO HAHA HAI Old cold cal LO LO COCO 16/1/20 52 17 17 18 5 / 6 6 61 61 61 6 6/1/ 7 6 71 7/1 HD HQ H< HOME BIE 71 ~~ 73 ∞ ∞ ∞ 6 6 HOME MICH 9 91/1 9/14/20 9 91/ 10 15 941 992 10 15/1/1/0 קט 9 9/12 99 10 16 91 91 9/11 9/21/20 HD HD HQ HIN 91/20 10 101 161/20 921 10 101 17 99 101/ 10 10 10/10 10 17 18 8/1/12 81/1 HH HH HO 8 ∞ ∞ ∞ ∞ 1/2 + 01+ ∞ ∞ ∞❤ 83 9 UNEQUAL SIDED TIMBER. 519 Lesser Lesser side, Greater 7 side. side. in. 7/1/20 Lesser side, in. 8 Lesser side, in. 8/1/ Side of equal square. in. Lesser Side of side, Lesser equal inches. inches. square. inches. inches. inches. Side of equal square. 9 side, Side of in. 9/1/ Lesser side. equal square. in. 10 Lesser side, in. 10/1/ Side of in. Lesser equal Side of side, Lesser 9/1/20 10 10/1/ 8/1 8/1 8/1/20 11 89100 111 9 HA HOME 12 7778 7∞∞ HA ∞ ∞ ∞ ∞ HI HA HA MK square. 788 732 equal square. equal Side of 11 side, Side of in. 11/ 8/1/ ∞ ∞ 8/1 8/1/10 1412 square. inches. ∞ 08900 equal square. in. inches. inches. inches. СО СО СО 00 8 cold 9 9/11 Side of equal square. Side of equal 9/1/12 9/1/20 92910 square. Greater 9/1/1 9/2 10 101 inches. side. 9/1/20 993/9 10 10 10 10 inches. CO 9/21/2 9/1/20 10 101 10/1/20 12 9/1/20 91 929/200 10 10/1/20 1032 HQ ME 102/2 11 11 111 12/1/ 91 10 10/1/ 10/1/10 11 111 11/1/ 13 9/1/10 9300 101 101 10 11 11 112 Ha col 111 11/1/20 1121 12 122 HHA BH 112 223 12/1/ 13/ 93/1 10 10/1/ 14 10 1011 10/1/20 141 10 10/1 103/ 12 12 BH 102 11 114 11 111 11 1/2/ 11 11 119/2 HAHAB 111 129 12 124 12 11/2/20 12 12/ 12/1/20 15 101 101 11 111 12 121 123/ 111 12 121 121 12 123/ PH HIS CO 13 131 14 14/1/ 13 15 15 ט 10/1/2 16 10/1/ 16 1/1/20 10%/ HI HIQ B}< 102 11 11 114 11 111 112 12 11/3/20 121 121 11 17 11 11 112 112/20 11 12 121 12/1/ 121 122 HHHHHIN COE 12/ 123/ 13 131 15 123/ 13 131 13/31/20 16 123 13 131 13 13 131/1 132 16/ 14 17 17/ 11 11/1/ 11 18 111 111/ 12 121 121 19 18/1/ 111 11A 112 12 12 12 124 12 12/1/20 13 131 123/20 13 13/ 13 131 131 13 131/ 13/9/1 HHN HINI ME 13 1321 1234 133 141 17 14 14/1/0 18 14 19 14 141 14 18 141 1423/20 13/1/20 14 141 14/3/20 15 191 139/ 14 141 14/ 143/2 15 20 141 143 15 15 14 14 14 151 15 HK HK HK¥ OD/F# 1431 15 20 21 151 15 21 14 15 15 16 22 15 151 151 152 16 22 161 23 151 15 16 21 12 12/1/20 191 131 11/9/ 12 12 12 20 119 121 1280 13 13 20/1/1 12 12/ 122 131 HE HN HN Col 13/ 13 131 13 HN 21 22 12/1/ 22/1/10 123 23 12 ૭ ૭ ૭ 121 H HIS Hoa coleg 1291 13 131 14 141 1231 131 13 14 14 13 131 132 141 14 13 13 14 14 14 520 TIMBER TABLES.—No. 2. Greater Lesser side. side, Lesser 16 153 161 16 16/1/ 16 4 161 20 163/ 162 16/ 16 17 in. 12 side, Lesser 121 side, Lesser in. 13 side, in. 131 Side of equal in. Lesser Side of side, Lesser square. equal Side of 14 side, square. equal Lesser Side of in. 141 side, inches. inches. square. equal Lesser in. 15 side, inches. square. in. 15 inches. Side of in. Lesser inches. equal Side of side, 13/ 14 HTHA BH 223 HE HC BD ca 121 13 121 12/1/20 123 13 14/1/ 15 131 13/12/ 15/1/20 139 16 161/1 14 17 141 171 141 18 142 #IWDT PL 1234 18 15 15 15/0 19 15 151 15/1/ 19/ 151 15/1/20 153/ 151 152 16 HQ HQ M}< square mky col 129/00 13 13 131 132 131/ 1323/ 14 139/ 139/10 14 14 14/ 141 141 132 141 14 14/12 141 14/1/1 143 15 equal square. Side of 16 Lesser side, equal Side of in. 161 square. inches. equal in. square. inches. inches. Side of inches. 44 HIT HIN COCH Hit Hky cl➡ square 1432 equal Side of equal square. 15 151 151 15 15 inches. Greater inches. side. 141 14/1/ 14312 143 15 151 10 10 151 15/1/ 15/ 1521 HE MIGH 14232 15 151 152/2 16 15 151 15 16 161 16 16 152 16 161 16 161 161 16/1/20 HAHA + 16/1/0 163/ 17 1632 17 171/ 17 17 18 4 -ka Hla colet 163 17 17 171 17 17/ 171 17 HTHIN HIN 171 17/1/20 17 18 17 3/4 19 1732 18 19/1 18 18 20 20/1/ 159/ 16 161 162 21 152 161 16/ 163/1 Colt Calst 17 171 17/1 223 21/ 16 16/1/20 162 17 171 16 161 17 171 171 HAHA IN 17/ 173 17 HAHAHH 17/ 173 18 18/201 173 18 181 181 21 18 181 181 18 21/ 181 181 18 19 22 2*** 221/1 161 999 HOME MEH 169/1 17 17 17 17 23 163 23/1/20 16232 24 17 24/1/1 171 25 171 251 26 HAHAHN ©}< 17/1/20 17 171 172 18 17/ 17/ 181 18 171 17 17/1/10 173 Hka Hika cakH 172/ 181 18/1/20 18/ 18/3/2 183 19 19/ 18 18 19 191 19 26/1/1 17939 27 17 18 181 18 181 181 19 1911 19/1/20 193/20 18/1/20 189/9 19 19/1/ 19 20 181 183 1234 19 19 1914 19/1/20 20 201 201 202 26 19 193 201201 202/1 21 27 19 20 201 202 21 21 27 19 20 201 202 20 211 21 28 18 181 183/2 27/ 181 18/1/ 19 191 28 181 18 19 19 HK HA 18 181 18 181 183 19 19 191 19 22 23 19 23 19 20 24 ∞ ∞ 18/ 18/3/ 183 19 191 191 19/1/20 4 198 HION COLCH COLCH 20 19232 20 24/1/ 201 25 201 20 HK HA 20 25 20 26 UNEQUAL SIDED TIMBER. 521 Greater 17 Lesser side, Lesser side. Lesser side. in. 17 side, Lesser in. 18 side, in. 18/1/1 in. Side of equal Lesser Side of side, Lesser square. equal Side of 19 side, Lesser square. equal Side of in. 19 side. Lesser inches. inches. square. equal square. in. 20 side, inches. in. 20/ inches. in. 17/1/ 17/1 18 17/ 173/ Side of inches. equal equal square. square. equal Lesser Side of side, Lesser equal Side of 21 side, Side of in. 21/1 19 18 18/1/ 17/3/1 18 181 181 1811 square. inches. equal in. 18% square. inches. inches. Side of inches. equal Side of square. 19/1/ 181 20 18 1/1 20/1/ 183 FEHN COLEH 18/1/20 18/3/20 19 191 equal square. 183/ 19 191 19 191 19/1/20 21 19 191 19 193 19/1/20 193 ·193 20 20/41/ 20 2014 201 inches. Greater side. 20/21 inches. 211/2 19 22 191 191 192 20 1932 2220 20/1 20/1/1 22/1/1 23 19/1 193/ 24 201 241/ 201/20 25 201/2 201 20/0 203/ 199 20 201 202/1 21 23/12/20 20 Ha Ha H 201 2011 2223 20/1/ 220 IN MA 20-3/1 20/31/ 211 211 21 aaa HOME HV COE 211 2013/ 21 214 21 211 21 21 251/ 203/10 21 212 22 211 HN HOME 21/ 2272 Ale mlb cakes 2272 20/1/1 21 203/2 20/31/ 21 21 214 aaa 211 211 21 21/ 21 211 212 213 21/ HQ ME M< 21/3/1 21/1/1 22 219319 221 2222 - Ha Bl< 22/1/2 2222 23 23 221 26 21 21/1/ 22 221 221 26/1/ 214 27 211/ 14-2 212 21 221 221 223/1 - Ha cslett 221/1 223/1 231 23/1/20 223/10 23 231 233 23 231 23/1/20 23 21 221 22 23 231 23 233 24 27 27/1/0 28 21 21 ~~~~ 223 221 22 223 231 23/1/20 221 22 223 23 2341 233/14 28/1/20 22 221 22 23 231 231 233/1 - clodH 233/20 24 24 27 24 241 24/1/20 28 241 24 243/28/ 29 221 22 221 231 333 233 24 241 24 25 29 291/10 22/ 223 23 231/1 233/ 4 30 221/ 231 301/ 22$ 23 231/ 31 23 231 23 23 23/1/20 233/1 311 231 32 23/ 23/31/ 241 24 231 23-3/1 24 241 243 32 1/1/0 231 233 241 24 243 DKO PEORGH 22 24 24/1/10 22 241 241/ 2391 24 24/1/1 24 241 24 25 IT IN MI 243 24時 1234 25 25 243/2 25 25291 25/1/ 30 251 25 30 2223 2228 IKH HON ME 222 213/1 22 22/1/10 22 23 221231 24 223/ 24/1/20 231 25 Hi coles coleti 25/1/ 26 26/1/ 25 25 25 31 22 242 25 25/1/ 25 251 251 25/ 25/1/ HA HOM 25 25 35 253 26 31 /1/20 ~~ 26 261 32 26 261/2 321/10 26 26 33 33 233 24 24 24 25 2 K 522 TIMBER TABLES.-No. 2. Greater Lesser side. side, Lesser 22 side, Lesser in. 22/1/2 side, in. 23 Lesser side, in. 23 Side of equal square. in. Lesser Side of side, Lesser equal square. Side of 24 side, Lesser equal Side of in. 24/1/ side, square. Lesser inches. inches. equal in. 25 side, square. inches. in. 25/1/ inches. Side of in. Lesser inches. equal Side of side, 2*** 22/1/1 221 23 22/1/ 23/1/10 24 23 223/1 P/CO 29/- *- square. Lesser equal Side of 26 side, 22/3/ square. equal Side of in. 26 23 231/1 inches. square. equal in. 231 231 23 square. inches. inches. Side of inches. equal Side of 241 25 راحة 231 23/1/ 233/1 24 241 23/1/ 233140 наколя 24 24/1/1 241/ 25/1/ 233 24 241 241 242 24¥ 141234 26 24 241 24 24 25 26 24 27 244 22 24/1/ 242 25 243210 25 251 10 10 24210 equal square. 25 251 inches. Greater side. 25 25 25% inches. 251 25 25/12/ 25/ 25310 26 26 261 2641 261 HIT HA MI< 261 26/1 26/3/20 27 26-3/10 27 27/ square. 27/ 24 243 251 251 259 26 28 249190 25 251 252 26 261 261 26 28/1/20 25 2511 29 251 25 8228 HD kame 29/1/ 25/ 2531 30 25 26 25910 25 25 261 26 261 261/1 26/ 26 261 26/1/0 27 mica coleti 26/1 27 27 27 28 27/ 27 28 27 271 27/ 273/ 29 271 27! 27/3/20 28 29/1/20 261 262 26 27 271 27 28 28 30 2223 30/1/1 26 261 261 262 27 271 31 26 26/1/0 26/3/ 27 27 31 261 261/ 27 271 27/1/20 HAFIQ B 27 27 22888 POOL PL 27/ 27/ 28 HQ H 70 32/1/20 262 27 33 27 27/1/ 331/1 271 34 27 271 27 HAHN BA 22 288 26 26 271 271 2792108 271 27/1/0 27 28/1/0 888888 27/ 28 281 28/1/20 28/1/20 30/1/ 283 31 28/1/ 28/1/20 282 31 1/ H4 HQ H 27/1 28 281 28/1/20 283/ ко 273/ 281/1 28 1/1/0 28/31/0 28 28/14/ 289/90 281 28 28% 291 29 29 291 29/1/ 291 292 28 28 29 32 29 291 321 291/1 29/1/ 33 29 33 30 34 341 35 27/ 27 281/ 28/1/20 283/1 29 35 28 36 888888 281 28 888888 273/ 28 28/1/1 28/9/10 29 281 29 28/1/20 291 291 2921 30 30/1/20 341/ 29/1/0 293/ 301 30/1/20 35 88888 28 29 2833 291 29/1/ 293/ 30 30 303/ 35/1/20 29 29 30 30 30 31 36 37 361/1 281/1/ 2891 28/1/20 283/ 29 3888888 37/ 28/9/1 29 2222 29/1/1 29/1/2 30 291 3041 30 30 31 361/1 29/1/20 293 30 301 303/1 31 2941 293/ 30 301/1 301 31 311 29 29 29 29 30 30 30 31 311 311 31 1/1/0 HEIN BE 37 37/ 31 38 UNEQUAL SIDED TIMBER. 523 Greater Lesser side. side, Lesser 27} 271 28 27/1/1 28/12 273 29 28 27 side, Lesser in. 27 in. 28 side, Lesser side, in. 28/1/2 Side of in. Lesser equal Side of side, square. Lesser equal Side of 29 square. side, Lesser equal Side of in. 29/1/ side, square. Lesser inches. inches equal in. 30 side, inches. square. in. 30/1 inches. Side of in. Lesser inches. 2282 TH-IN CO equal square. Side of equal Side of side, 31 2888888 square. equal Side of in. 281 281 282 inches. square. equal square. inches. inches. inches. Lesser side, 31 in. 29/1/ 281 28 30 28/ 283/20 28/21 29 29 29- 301/20 289190 29 291 31 29 29/1/1 2223 29/1/20 29/1/20 29/ 293/ HE HQ ME 29 29 30 293 30 301 inches. Greater 30 30 30% 4 inches. side. Side of equal square. square Side of equal 311 32 291 29/1 29/1 293 29/9/ 30 30/1/20 30 301 33 32/1/2 29/ 29 30 293 301 30/1/20 30 30% HEIN BE 301 30/2 303 HE HABEH 30/1/20 303/20 302 31 4 31 34 311 31 314 31/1/1 1412 313 HEIN M 31 311 31/1/2 HE HIN Mer 331/ 34 34/1/20 30 30/1 3034 31 311 301 301 303/1 311 31/1/20 30/1/ 303/1 31 314 31 3/4 35 30 31 31 31 31 HITHIN MICH COLCH 31 313 312 32 3211 4 311 31 1/1/0 313/ 32 32 321 32 32 4 32 32/1/20 323 32 33 33/1/20 34 313/ 32 : 32 321 32 32 14 12 321/10 323/10 33 34/ 32 33 33 35 351 36 361/1 37 مرات 12 HE HADO 8888888 Ha 37 38 31 314 311 31 313/ 32 321 32/1/20 38 321 323 321/20 39 325 32 33 331/ 391/10 323 33 331 40 3230 331 401 33 331 311 31/1/20 313 ww 31/ 313 32 3123 32 321/1 321/ 32314 331 33/1 32 3211 32/ 323/ 33 331 321 323100 33 331 33/1/20 33 31/0 35/1/0 36 333/20 34 361/ 32 32 32 323 33 33 33 333 الايم 341 37 32 321/10 12 12 3ojen 323/1 33 33 331 3311 33/ 33 1/1/0 331/20 333/ 34 34 37 34 341 34/ 38 33 33 33/3/2 34 341 34 343 38 3311 33 34 34/1/1 34 341 35 39 33320 41 331 331/10 34 - FİQ Odje 33 34 333 34 341 345/ 343 341 34 343 35 411/20 331/1 33330 34 34 343/2 35 42 33 34 421 33 3/10 341 43 34 34 لمواتير سرت 344/ 34 35 351 343 342 35 351/1 343 35 1 -2 -2 351/ 351 353 36 411 36 361 42 ACP p | pat 35/ 353/1 353 36 361 36/1 421/1 36/1/0 36 43 35 35 36 361 33 34 341/20 341 343210 218885 HQ MİTH ME 343 35 35 39 35 351 35/1/20 40 35 3512 35% 40 352 36 41 524 TIMBER TABLES.No. 2. Lesser side, Greater 32 Lesser side, side Lesser in, 321 side, Lesser in. 33 side, in. 331/ Side of in. Lesser equal Side of side, square Lesser equal Side of 34 square. equal Side of side, in. 341/1 Lesser side, inches. inches. square. equal Lesser in. 35 side. inches. square. in. 35/1/ inches. Side of in. inches. Lesser equal Side of side. 3232 square. equal Lesser Side of 36 side, 33 321/1 331/1 323/20 HBE 323/1 square. equal Side of in. 36 33 331 inches. 34 33 331 332 33 inches. inches. 34 33 33/1/ 33 3/1 colet 34 341 square. equal square. Side of inches. equal Side of square. equal in. 35 331/1 332/2 34 341 34 3432 square. 35 333/1 34 341 342 343 35 36 34 341 342 34 35 351 335 351 inches. Greater size. 35 H 352/1 inches. 36 341 37 37 ཚཚ 34/ ကက 34 343/20 35 351 351 35232 36 361 34232 35 35 35 353 36 361 36 36 37 342 35 351 352 35 36 361 361 362 37 38 343 35 35 35 35 35 35 35 4 36 36 36 37 37 55888 371/ 38 38 35 351 352/ 36 36 361 39 351 35 35 36 361 362 1234 39 35 352/ 36 36 36 37 40 35 36 36 36 36 36 371 co co 37 371 371 37 37 37 HHH CH 38 40/ 36 361 361 362 37 37/1/1/0 37/3/1 38 363/1 37 37 37 38 371/ 3732/4 39 373/ 38 391/1 38 40 3840 381 41 361 361/ 36212 37 371 37/1/0 38 381 41 N 42 36 36/ 363 37 371 37 37 37 H 37 37 38 381 37 8888 421 37 43 37 43/1/ 371/ www 371 37/ 37/ 373 373 38 44 37 37 38 Ika ole 88 777 HI HA HAa colet 3723/1 38 381 38 38 381 381/1 382/20 39 38 38 38/ 38/3/20 39 HAHAHA 38/1/ 383 383/1 41 39 411 39 39 42 391/ 3942 391 381 381 3893/42 39 391 391/ 38 38 39 39 39 4 39 PWNH PH 391/ 421/ 43 393/ 43/1/ 40 44 44 373 38 381 381/ 383 391 45 38 381 45 38 381 381 46 3811 38 38 39 38 383/20 39 391/ 39 4 391 39 39 39 HK HK HKI CH 391/ 3932 40 401 441 3931 40 401 40 45 40 401 402 403 45½ 40 401 402 41 46 46 381 382 47 3832 39 471 39 391 48 39 39 39 4 8888 39 392 393 40 401 40/1/ 41 391 39232 40 401 39/ 40 40 40/1/ 4 cole 40 401 40 HHQ Bler 40/1/ 43/3/20 411 402/20 41 411 41 411 41 واطر ماهر و 41 46 41/1/20 47 412 47 412 48 UNEQUAL SIDED TIMBER. 525 Lesser side, Lesser Greater 37 side, size. Lesser in. 37/1/20 side, Side of equal in. 38 Lesser side, in. 381/ in. Lesser Side of side, square. Lesser equal square. Side of 39 side, Lesser inches. inches. equal square. Side of in. 391/1 side, equal in. 40 Lesser side, inches. square. in. 40/1/ inches. Side of in. Lesser inches. equal Side of side. Lesser 37/1/ 371 square. equal Side of 41 side, 38 37 373/ square. equal Side of in. 411/ 38/1/ 37 38 381/1 inches. square equal in. 39 38 381 38 38 square. inches. inches. Side of inches. 391 سراحه 40 381 381/20 40/1/ 38 HI HA MCH 381/ 3831 39 391 equal square. Side of equal 383/ 39 391 39 391 39/ 41 39 39 39 39 HHH MICH 391/ 393/1 PAGIP 393/1 square. 40 401 inches. Greater side. 40 401 402 40 inches. 41 391 391/ 3932 40 401 402 403 41 411 40 42 391/1 393/ 42 393 40 401 43 40 40 401 402 41 411 41/ 401 40/1/ 40/1/ 402/2 41 411 411/ 402 41 41 4 411 41 IPKO KOI MP HE HOME 413/2 42 413 42 423 42 424 43 44 45 431/1 40 401 442/ 401/1 40 090 401 Het mica col-H PPPON- 451 41 46 411 461/ 41/ 47 419 47 42 421 421 48 48/1/ 421 49 42 49/1/2 423/1 43 50 43 431 HHHHK 42/ 423/ 423 HH HCG CG evaluati PW NH HP HIGH HOT COK 42 403- 402 41 411 41 411 41 412 412 42 411 412 42 413/2 42 424 42 421 421/ 421 42 421 402/2 41 411 41 41 41 41 411 HAHAHAI HH Hea Col 41 412 413/2 42 42 421 421 42 42 421 421 42 42 423 HAHN CH 42 43 422 432 42210 44 43 442 431 45 HH HON COK 422 423 43 4231 43 431 431 43 45 431 432 46 423 431 431/ 432 44 46 43 431 431 44 44 47 421 422 43 50/1/ 431 432 51 431/10 43 51 43/3/20 52 4321 COLER COLEH 52/1/1 44 53 441 مراه مراح تتهم 421/1 43 431 43/1/20 4332 431 431 432 44 43/ 432/2 44 441 423 431 43 43 43 431 432 44 431 432 441 433 44 444 44 441 44 ور سرحد ساوه 44 441 44 442/2 441 44/ 441 4432/2 44 44 mika coleri ester 44 441 441 441 443 44 48 44 48 44 45 49 441 44 443/4 45 4549 441 442 45 451 45 50 443/ 45 451 45/ 45 50 45 451 45 45 46 51 45 452 46 46 51 45 453 46 46 46 52 46 461 46 47 53 45 44232 45 451 45 451 45/2 45 45/1/ 45 H mdagi mica coleg 46 46 46 52 441 | 44 | 47½ 526 TIMBER TABLES. NO. 2. Greater Lesser side. side, Lesser 42 side, Lesser in. 421/ side, in. 43 Lesser side, in. 431/1 Side of in. Lesser equal Side of side, Lesser square. equal Side of 44 side, Lesser square. equal Side of in. 44/1/ side, inches. inches. square. equal Lesser in. 45 side, inches. square. in. 451 inches. Side of in. Lesser inches. equal Side of side, 42/1/20 421 square. Lesser equal Side of 46 side, 43 42 422/1 square. equal Side of in. 461/ 431/ 423/1 43 44 43 431 434 43 43 inches. square. inches. equal square. in. inches. Side of inches. equal | Side of 44/1/ 431 431/1 433 44 441 45 431/ 433 44 441 44/2 46 451 432/2 44 44 44 44 441 442 44 443/2 HE HA MJEH square. 44232 equal square. 45 Greater 451 inches. side. 45 45 45 45 inches. 46/1/ 441 47 442 47/1/ 44/9/20 HAHABE 441/ 442/2 45 443 45 451 48 45 45 45 45 451 45 45 HAHA MH 9999 HE HOCH 451 451/ 45 46 461 451 453/20 452 46 461 462 4632 47 46 461 461/ 463/2 47 47/ 46 46 46 46 47 471 48 48/1/1 451 45/1/2 453 46 49 451 451 46 49/1/2 45/1/ 452/2 461 50 45 46 46 46 47 471 471 9999 461 461/1 463 47 471 471/ 48/1/20 461 461 461/ 46232 463 47 471 47 473/1 49 47 471 473 47 48 491/ 47 48 48 50 4 47/2 473/ 47& HQ MEHME 473/4 48 481 48 481 482 48 48 கக 4814 48/1/ 483/2 سرار مروة تتهم 489/90 49 48 50 483 51 49 511 4914 52 483/1 49 HS Hica col 48 483/2 49 4952 子 483/1 49 491 493 53 4 49 491 491/ 49 53 491 49 49 50 54 50/1/ 46 46/14/ 461 462 471 51 461 51 461/ 52 46 461/ 469/ 47 462/2 47 471 47 471 47/ 47 47 47 HA HA HQ ME 52 47 471 53 471 53 47 54 471 HAININ 47/1 473/ THE MI< 2 BH 48 47/1/ 472/ 48 481 481 4732/ 48 48 481 489 HD HQ Col< 481 481 48 48/1/20 UNEQUAL SIDED TIMBER. 527 Greater Lesser side. side, Lesser 47 side, Lesser in. 471/10 side, Lesser in. 48 side, in. 48/1/1 Side of in. Lesser equal Side of side, Lesser square. equal square. Side of 49 side. Lesser equal equal Side of in. 491/ side, Lesser inches. inches. square. equal in. 50 side, square. inches. in. 50 inches. Side of in. inches. equal Side of Lesser 471/ 471 square. equal side, Lesser 48 481/1 473/ 48 47 473/20 Side of 51 side, square. equal Side of in. 511 481 inches. square. equal in. 49 48 481 48 483 inches. square. inches. Side of inches. 491 481 481 482 49 491 equal Side of square. equal 50 50/ 483/2 49 491 481 483/ 49 491 49 4932 square. 491 493/20 50 501 inches. Greater side. 51 49 491 49 49 50 50 50 50 inches. 51 491 49/1/ 4932 50 501 4 50/ 52 49/1/20 4932 50 50 50 5032 Flea colet 521 493 50 501 50 50% 51 502 51 51 514 511 51 511 53 50 50 50 50 | 51 51 51 51 HEINWE 531/1 501 50 503 54 50 50 51 51 511 51 51 511 512/ 34 51 52 521/ 53 52 521 521 531 521 52 52 54 51 5132 52 51 52 52 52 Greater Lesser side. side, Lesser 52 side, Lesser in. 521 side, Lesser Lesser in. 53 side, side, in. 531 54 Side of in. in. equal Side of square. equal Side of square. equal Side of Side of inches. inches. square. equal equal inches. square. square. inches. inches. inches. 5252 53 53 بياسر 54 53 521 5232 522 53 531 53 53 53 54 528 TIMBER TABLES.-No. 3. 1 TIMBER TABLES, No. III. Tables of Superficial or Flat Measure. These Tables commence with 1 inch in width, and extend by the progressive addition of an inch up to 2 feet, and from thence by the addition of 2 inches up to 10 feet. The first and fifth columns contain the lengths from 1 inch to 30 feet. The remaining columns contain the superficial contents due to any given length and width, the columns of which intersect each other in the positions in which such quantities severally stand. The use of the Tables is too obvious to require comment. Ex. 1.-Required the superficial content of a board 19 feet long and 16 inches broad. In page 531, opposite 19 feet long, and under 1 foot 4 inches broad, stands 25 feet 4 inches, the content required. Ex. 2. The side of a room 9 feet 10 inches high, is 26 feet 7 inches, what is its superficial content? In page 540, under 9 ft. 10 in. broad and opposite Ft. In. Ft. In. 26 0 is 255 8 0 7 is 5 8 26 7 261 261 4 Required content. SUPERFICIAL MEASURE. 529 Lengths. 1 inch wide. 2 inches 3 inches wide. wide. Lengths. ft. in. ft. in. ft. in. ft. in. ft. in. 4 inches 5 inches 6 inches wide. wide. wide. ft. in. ft. in. ft. in. 0 1 0 0 2 0 00 0 0 0 3 0 0 4 0 5 0 6 بار بار مراه براد -H HK 2/5 yj 0 0 7 08 09 0 0 10 0 11 HAHN ocker celer 0 0 - Ha colt AIA 0 0 2 0 3 1 0 4 1 0 1 1 0 5 0 1 0 1 0 6 0 2 0 2 HDF 22 0 2 0 0 3 ANTIQ QI OD 2 1 0 1 0 1 0 2 0 0 0 1 0 2 0 1 0 IQQQN 0 7 0 2 0 2 0 3 08 0 2 0 3 0 4 2 09 0 3 0 3 4 0 10 0 3 0 4 0 2 0 11 0 3 04 0 5 1 0 0 1 0 2 03 1 0 0 4 0 5 0 6 2 0 2 0 4 0 6 2 0 08 0 10 1 0 3 0 3 0 09 3 0 1 0 1 3 1 6 4 04 0 1 0 4 0 4 1 8 2 0 5 0 0 5 0 10 1 3 5 0 2 8 2 1 2 6 60 0 6 1 0 1 6 6 0 2 0 26 3 0 7 0 0 7 1 2 I 9 7 0 2 4 2 11 3 6 8 0 08 1 4 2 0 2 8 3 4 4 0 9 0 0 9 1 6 2 3 9 3 0 3 9 4 6 10 0 0 10 1.8 2 6 10 0 3 4 4 2 5 0 11 O 0 11 1 10 2 9 11 0 38 4 7 5 6 12 0 1 0 2 0 3 0 12 0 4 0 5 0 6 0 13 0 1 1 2 2 3 3 13 0 4 4 5 5 66 14 O 1 2 2 4 3 6 14 0 4 8 5 10 7 0 15 0 1 3 2 6 3 9 15 0 50 6 3 7 6 16 O ] 17 O 0 1 5 18 O 1 19 0 20 0 1 8 1 45678 O Q M M ca 2 8 4 0 16 O 5 4 68 8 0 2 10 4 3 17 0 5 8 7 1 8 6 3 0 4 6 18 O 0 6 0 7 6 9 0 3 2 4 9 19 0 6 4 7 11 9 6 3 4 5 0 21 0 1 9 3 6 22 0 1 10 3 8 10 10 5 3 23 0 1 11 3 10 5 9 24 0 2 0 4 0 5 6 22 0 23 0 6 0 24 0 2 288* 20 0 68 8 4 10 0 21 0 25 0 2 1 4 2 6 3 25 0 777 ∞ ∞ 7 0 8 9 10 6 4 9 2 11 0 8 9 7 11 6 8 0 10 0 12 0 8 4 10 5 12 6 26 0 27 0 28 0 29 30 0 20 10 10 10 10 4 4 6 6 26 0 10 10 13 0 4 6 6 9 27 0 9 0 11 3 13 6 4 8 7 0 28 0 9 11 8 14 O 5 4.10 7 3 29 0 9 8 12 1 14 6 2 6 5 0 77 6 30 0 10 0 12 6 15 0 530 TIMBER TABLES. -No. 3. Lengths. wide. 7 inches 8 inches 9 inches wide. wide. Lengths. ft. in. ft. in. ft. in. ft. in. ft. in. 10 inches 11 inches 12 inches wide. wide. wide. ft. in. ft. in. ft. in. 0 1 0 0 2 0 0 3 0 1 0 2 0 0 4 0 2 0 2 0 0 5 0 0 3 0 0 6 0 3 04 0 * Q * CO ◄ 3 0 1 0 0 0 2 2 0 3 0 2 0 3 0 4 0 0 3 0 0 4 0 4 4 0 6 0 5 0 5 * Q * 45 0 1 1 0 2 2 0 3 0 4 0 5 0 6 0 7 0 4 04 0 5 0 7 0 5 0 8 0 4 0 5 0 6 0 8 0 0 9 0 5 0 6 0 6 0 9 0 0 10 0 5 0 6 0 7 0 10 0 8 0 11 0 6 07 08 0 11 09 667∞ ∞ 06 0 7 077 08 08 0 9 09 0 10 0 10 0 11 1 0 2 0 7 1 3 1 9 2 729+ 08 1 4 2 0 4 2 8 5 2 11 3 4 ☺ present Q? ∞ ∞ 0 9 1 6 2 3 3 0 1234 0 0 10 0 11 1 0 0 1 8 1 10 20 0 2 6 2 9 3 0 4 0 3 4 3 8 4 0 39 5 0 4 2 4 7 5 0 6 0 3 6 4 0 4 6 6 0 5 0 5 6. 60 7 0 4 1 4 8 5 3 7 0 5 10 6 5 7 0 8 0 4 8 5 4 6 0 8 0 6 8 7 4 8 0 9 0 5 3 6 0 6 9 9 0 7 6 8 3 9 0 10 0 5 10 6 8 7 6 10 0 8 4 9 2 10 0 11 0 6 5 7 4 8 3 11 0 9 2 10 1 11 O 12 O 7 0 8 0 9 0 12 0 10 0 11 0 12 0 13 0 7 7 8 9 9 13 0 10 10 11 11 13 0 14 0 8 2 9 4 10 6 14 0 11 8 12 10 14 O 15 0 8 9 10 0 11 3 15 O 12 6 13 9 15 0 16 0 9 4 10 8 12 0 16 0 13 4 14 8 16 0 17 0 9 11 11 4 12 9 17 0 14 2 15 7 17 0 18 20 228 78*** 2**28 0 10 6 12 0 13 6 18 0 15 O 0 16 6 18 0 19 0 11 1 12 8 14 3 19 0 15 10 17 5 19 0 0 11 8 13 4 15 0 20 0 16 8 18 4 20 0 21 0 12 3 14 O 15 9 21 O 17 6 19 3 21 0 22 0 12 10 14 8 16 6 22 0 18 4 20 2 22 0 23 0 13 5 15 4 17 3 23 0 19 2 21 1 23 0 24 14 0 16 0 18 0 24 0 20 0 22 0 24 0 25 0 14 7 16 8 18 9 25 0 20 10 22 11 25 0 26 0 15 2 17 4 19 6 26 0 21 8 23 10 26 0 27 0 15 9 18 O 20 3 27 0 22 6 24 9 27 0 0 16 4 18 8 21 0 28 0 23 4 25 8 28 0 29 0 16 11 19 4 21 9 29 24 2 26 7 29 0 30 0 17 6 20 0 22 6 30 0 25 0 27 6 30 0 SUPERFICIAL MEASURE. 531 Lengths. wide. 1ft. lin. 1ft. 2in. 1ft. 3in. wide. wide. Lengths. 1ft. 4in. 1ft. 5in. 1ft. 6in. wide. wide. wide. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. 0 1 1 0 1 0 1 0 0 0 2 0 2 0 2 0 0 3 0 3 0 3 03 0 0 4 0 4 0 4 0 4 0 0 5 0 5 0 0 5 0 0 6 06 07 0 7 0 6 1 2 3 4 5 6 1 0 1 0 1 0 1 2 0 2 0 2 0 3 0 4 0 4 0 4 0 5 0 5 0 6 0 6 0 7 0 08 08 0 9 pand CO79 0 ་ 0 7 0 8 08 0 7 09 09 0 10 08 08 0 9 0 9 08 0 10 0 11 1 0 0 9 09 0 10 0 11 0 9 1 0 1 0 1 1 0 10 0 10 0 11 1 0 0 10 1 1 1 2 1 3 0 11 0 11 1 0 1 1 0 11 1 2 1 3 1 4 1 0 1 2 0 2 2 3 0 3 4 0 4 070-0 5 0 5 5 6 0 1 2 3 4 5 1 2 1 3 1 0 1 4 2 4 2 6 20 28 3 6 3 9 3 0 4 0 4 8 5 0 4 0 5 5 10 6 3 5 0 6 8 12 457 20 5 210 13 6 3 0 4 3 4 6 6 0 1 7 6 66 ~ ཌ 0 7 6 60 8 0 8 6 9 0 0 7 7 8 2 8 9 7 0 9 4 9 11 10 6 8 0 8 8 9 4 10 O 10 8 11 4 12 0 9 0 9 9 10 6 11 3 9 0 12 0 12 9 13 6 10 0 10 10 11 8 12 6 10 0 13 4 14 2 15 0 11 0 11 11 12 10 13 9 11 0 14 8 15 7 16 6 12 0 13 0 14 O 15 0 12 0 16 0 17 0 18 0 13 0 14 1 15 2 16 3 13 0 17 4 18 5 19 6 14 0 15 2 16 4 17 6 14 O 18 8 19 10 21 15 0 16 3 17 6 18 9 15 0 20 0 21 3 2233 0 6 16 0 17 4 18 8 20 0 16 O 0 21 4 22 8 24 0 17 O 18 5 19 10 21 3 17 O 0 22 8 24 1 25 6 18 O 19 6 21 0 22 6 18 0 24 0 25 6 27 0 19 O 20 7 22 2 23 9 19 O 25 4 26 11 28 6 20 0 21 8 23 4 25 0 20 0 26 8 28 4 30 0 21 0 22 9 24 6 26 3 21 0 28 0 29 9 31 6 22 0 23 10 25 8 27 6 22 0 29 4 31 2 33 0 23 0 24 11 26 10 28 9 23 0 30 8 32 7 34 6 24 0 26 0 28 0 30 0 24 0 32 0 34 0 36 0 25 0 27 1 29 2 31 3 25 0 33 4 35 5 37 6 26 0 28 2 30 4 32 6 26 0 34 8 36 10 39 0 27 0 29 3 31 6 33 9 27 0 36 O 38 3 40 6 28 0 30 4 32 8 35 0 28 0 37 4 39 8 42 0 29 0 31 5 33 10 36 3 29 0 38 8 41 1 43 6 30 0 32 6 35 0 37 6 30 0 40 0 42 6 45 0 532 TIMBER TABLES.-No. 3. Lengths. wide. 1ft. 7in. 1ft. 8in. 1ft. 9in. wide. wide. Lengths. 1ft. 10in. 1ft. 11in. 2ft. Oin. wide. wide. wide. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. 0 0 0 123 0 1 0 1 0 1 0 1 0 1 0 1 0 2 0 3 0 3 0 3 0 2 0 3 0 3 0 4 0 4 0 5 0 5 0 3 0 0 6 0 4 0 6 0 6 0 7 0 0 77 0 77 08 0 5 06 7 08 0 8 0 5 0 9 0 9 0 10 09 0 10 0 10 0 6 0 11 0 11 1 0 0 7 0 11 0 11 1 0 8 1 0 1 1 1 0 9 1 2 1 3 1 0 10 1 3 1 4 1 5 0 11 1 5 1 6 1 7 O QIM L7 0 0 7 1 0 1 2 0 8 1 2 1 3 9 9 1 4 1 0 10 1 6 1 0 11 1 8 19 13579 1 2 1 4 1 6 1 8 1 10 12345 0 I S 1 7 1 8 1 9 3 2 3 4 3 6 4 9 5 0 5 3 4 0 6 4 68 7 0 5 0 7 11 8 4 8 9 1∞∞ + LOO 0 1 10 1 11 20 2 0 3 8 3 10 4 0 3 0 5 6 5 9 4 0 7 4 77 8 8 0 50 9 2 9 7 10 0 6 0 9 6 10 0 10 6 7 11 1 11 8 12 3 8 0 12 8 13 4 14 0 9 0 14 3 15 0 15 9 6789 6 0 11 0 11 6 12 0 0 12 10 13 5 14 O 0 14 8 15 4 16 0 0 16 6 17 3 18 0 10 0 15 10 16 8 17 6 10 0 18 4 19 2 20 0 11 0 17 5 18 4 19 3 11 0 20 2 21 1 22 0 12 0 19 0 20 0 21 0 12 0 22 0 23 0 24 O 13 0 20 7 21 8 22 9 13 0 23 10 24 11 26 0 14 0 22 2 23 4 24 6 14 0 25 8 26 10 28 0 15 0 23 9 25 0 26 3 15 0 27 6 28 9 30 0 16 O 25 4 26 8 28 0 16 0 29 4 30 8 32 0 17 0 26 11 28 4 29 9 17 0 31 2 32 7 34 0 18 0 28 6 30 0 31 6 18 0 33 0 34 6 36 0 19 0 30 1 31 8 33 3 20 0 31 8 33 4 35 0 21 0 33 3 35 0 36 9 21 0 22 0 34 10 36 8 38 6 22 23 0 36 5 38 4 40 3 24 0 38 0 40 0 42 0 25 0 39 7 41 8 26 0 41 2 43 4 45 6 27 0 42 9 45 0 47 3 28 0 44 4 46 8 49 0 3280 29 0 45 11 48 4 50 9 30 0 47 6 50 0 52 6 30 0 23 78324 27828 19 34 10 36 5 38 0 20 0 36 8 38 4 40 0 38 6 40 3 42 0 0 40 42 0 44 43 9 25 0 45 10 +200 33 4 42 2 44 0 44 1 46 0 46 0 48 0 47 11 50 0 26 0 47 8 49 10 52 0 27 0 49 6 51 9 54 0 28 0 51 4 53 8 56 0 29 53 0 55 0 2 55 7 58 0 57 6 60 0 SUPERFICIAL MEASURE. 533 Lengths 2ft. 2in. 2ft. 4in. 2ft. 6in. wide. wide. wide. Lengths. 2ft. 8in. 2ft. 10in. 3ft. Oin. wide. wide. wide. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. 0 1 02 2 0 2 0 1 0 2 02 0 3 02 0 4 0 0 5 0 2 0 5 0 5 06 0 3 0 6 0 7 0 7 0 3 0 08 09 0 4 08 0 9 0 10 0 4 0 10 0 11 1 0 0 5 0 10 0 11 1 0 0 5 1 1 1 2 1 3 0 6 1 1 1 2 1 3 0 6 1 4 1 5 1 6 0 7 1 3 1 4 1 5 0 7 1 6 1 7 1 9 08 1 5 1 6 1 8 08 9 1 10 2 0 09 1 7 1 9 1 10 09 2 0 2 1 2 3 0 10 1 9 1 11 2 1 0 10 2 2 2 4 2 6 0 11 1 11 2 1 23 0 11 2 5 2 7 2 9 1 0 2 2 2 4 2 0 4 4 4 8 3 0 66 7 0 257 2 6 0 6 4 0 88 9 4 10 0 5 0 10 10 11 8 12 6 12345 0 2 8 2.10 3 0 2 0 5 4 58 6 0 0 8 0 86 9 0 0 10 8 11 4 12 0 5 0 13 4 14 2 15 0 60 13 0 14 0 15 0 6 0 16 O 17 0 18 0 7 0 15 2 16 4 17 6 7 0 18 8 19 10 21 0 8 0 17 4 18 8 20 0 8 0 21 4 22 8 24 0 9 0 19 6 21 0 22 6 9 0 24 0 25 6 27 0 10 0 21 8 23 4 25 0 10 0 26 8 28 4 30 0 11 0 23 10 25 8 27 6 11 O 29 4 31 2 33 0 12 0 26 0 23 0 30 0 12 0 32 0 34 0 36 0 13 0 28 2 30 4 32 6 13 0 34 8 36 10 39 0 14 0 30 4 32 8 35 0 14 0 37 4 39 8 42 0 15 0 32 6 35 0 37 6 15 0 40 0 42 6 45 0 16 0 34 8 37 4 40 0 16 0 42 8 45 4 48 0 17 0 36 10 39 8 42 6 17 0 45 4 48 2 51 0 18 0 39 0 42 0 45 0 18 48 0 51 0 54 0 19 O 41 2 44 4 47 6 19 0 50 8 53 10 57 0 20 0 43 4 46 8 50 0 20 0 53 4 56 8 60 0 21 0 45 6 49 0 52 6 21 0 56 0 59 6 63 0 22 0 47 8 51 4 55 0 22 0 58 8 62 4 66 0 23 0 49 10 53 8 57 6 23 0 61 4 65 2 69 0 24 0 52 0 56 0 0 60 0 24 0 64 0 68 0 72 0 25 0 54 2 58 4 62 6 25 0 66 8 70 10 75 0 26 0 56 4 60 8 65 0 26 0 69 4 73 8 78 0 27 0 58 6 63 0 67 6 27 0 72 0 76 6 81 0 28 0 60 8 65 4 70 0 28 0 74 8 79 4 84 0 29 0 62 10 67 8 72 6 29 0 77 4 82 2 87 0 30 0 65 0 70 0 75 0 30 0 80 0 85 0 90 0 534 TIMBER TABLES.-No. 3. Lengths. 3ft. 2in. 3ft. 4in. 3ft. 6in. wide. wide. wide. Lengths. 3ft. 8in. 3ft. 10in. 4ft. Oin. wide. wide. wide. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. 0 1 0 3 03 0 3 0 1 0 3 03 0 4 0 2 0 6 0 6 0 7 0 2 0 7 0 7 0 8 0 3 0 9 0 10 0 10 0 3 0 11 0 11 1 0 0 4 1 0 1 1 1 2 0 4 1 2 1 3 1 4 0 5 1 3 1 4 1 5 0 1 6 1 7 1 8 06 1 7 1 8 1 9 0 6 1 10 1 11 20 0 7 1 10 1 11 2 0 0 7 2 1 2 2 2 4 08 2 1 2 2 2 4 0 8 2 5 2 6 2 8 0 9 2 4 2 6 2 7 0 9 29 2.10 3 0 0 10 2 7 2 9 2 11 0 10 3 0 3 2 3 4 0 11 2 10 30 3 2 0 11 3 4 3 6 38 1 0 3 2 3 4 20 6 4 6 8 37 3 6 0 3 0 9 6 10 0 10 6 4 0 12 8 13 4 14 0 5 0 15 10 16 8 17 6 12345 0 3 8 3 10 4 0 0 7 4 7 8 8 0 0 11 0 11 6 12 0 0 14 8 15 4 16 O 5 0 18 4 19 2 20 0 60 19 O 20 0 21 0 6 0 22 0 23 0 24 0 7 0 22 2 23 4 24 6 7 0 25 8 26 10 28 0 8 0 25 4 26 8 28 0 29 4 30 8 32 0 9 0 28 6 30 0 31 6 9 0 33 0 34 6 36 0 10 0 31 8 33 4 35 0 0 10 0 36 8 38 4 40 0 11 0 34 10 36 8 38 6 11 0 40 4 42 2 44 0 12 0 38 0 40 0 42 0 12 44 0 46 0 48 0 13 0 41 2 43 4 45 6 13 0 47 8 49 10 52 0 14 0 44 4 46 8 49 0 14 0 51 4 53 8 56 0 15 O 0 47 6 50 0 52 6 15 0 55 0 57 6 60 0 16 0 50 8 53 4 56 0 16 58 61 4 64 0 17 0 53 10 56 8 59 6 17 0 62 4 65 2 68 0 0 57 0 60 0 63 0 18 0 66 0 69 0 72 0 21 22 72*** ***88 0 60 2 63 4 66 6 19 0 69 8 72 10 76 0 20 0 63 4 66 8 70 0 20 0 73 4 76 8 80 0 0 66 6 70 0 73 6 21 0 77 0 80 6 84 0 22 0 69 8 73 4 77 0 22 0 80 8 84 4 88 0 23 0 72 10 76 8 80 6 23 0 84 4 88 2 92 0 24 0 76 0 80 0 84 0 24 0 88 0 92 0 96 0 25 0 79 2 83 4 87 6 25 0 91 8 95 10 100 0 0 82 4 86 8 91 0 26 0 95 4 99 8 104 O 0 85 6 90 0 94 6 27 0 99 0 103 6 108 O 28 0 88 8 93 4 98 0 28 0 102 8 107 4 112 0 0 91 10 96 8 101 6 29 0 106 4 111 2 116 O 30 0 95 0 100 0 105 0 30 0 110 O 115 0 120 0 SUPERFICIAL MEASURE. 535 Lengths. 4ft. 2in. 4ft. 4in. 4ft. 6in. wide. wide. wide. Lengths. 4ft. 8in. 4ft. 10in. 5ft. Oin. wide. wide. wide. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. 0 1 0 4 0 4 0 4 0 1 0 4 0 4 0 5 0 2 08 08 0 9 0 2 09 09 0 10 0 3 1 0 1 1 1 1 0 3 1 2 1 2 1 3 0 4 1 4 1 5 1 6 0 4 1 6 0 5 1 8 06 2 1 12 1 9 1 10 0 5 1 11 2 2 3 06 2 4 705 122 8 2 1 2 5 2 6 0 7 2 5 2 6 2 7 07 2 8 2 9 2 11 0 8 2 9 2 10 3 0 0 8 3 1 3 2 3 4 09 3 1 3 3 3 4 0 9 36 3 7 3 9 0 10 3 3 7 3 9 0 10 3 10 4 0 4 2 0 11 3 9 3 11 4 1 0 11 4 3 4 5 4 by 12345 0 4 2 4 4 4 6 1 0 4 8 4 10 5 0 20 8 4 8 8 9 0 2 0 9 4 9 8 10 0 0 12 6 13 O 0 13 6 3 0 14 0 14 6 15 0 0 16 8 17 4 18 0 4 0 18 8 19 4 5 0 20 10 21 8 22 6 5 0 23 4 24 2 223 20 0 25 0 6 0 25 0 26 O 27 0 85ZEL CERSE 50.0 A 0 29 2 30 4 31 6 67 60 28 0 29 0 30 0 32 8 33 10 35 0 0 33 4 34 8 36 0 8 0 37 4 38 8 40 0 0 37 6 39 0 40 6 9 0 42 0 43 6 45 0 10 0 41 8 43 4 45 0 10 0 46 8 48 4 50 0 0 45 10 47 8 49 6 11 0 51 4 53 2 55 0 0 50 0 52 0 54 0 12 0 56 0 58 0 60 0 0 54 2 56 4 58 6 13 0 60 8 62 10 65 0 14 0 58 4 60 8 63 0 14 0 65 4 67 8 70 0 15 0 62 6 65 0 67 6 15 0 70 0 72 6 75 0 0 66 8 69 4 72 0 16 O 74 8 77 4 80 0 70 10 73 8 76 6 17 0 79 4 82 2 85 0 0 75 0 78 0 81 O 18 0 84 0 87 0 90 0 19 0 79 2 82 4 85 6 19 0 88 8 91 10 95 0 20 0 83 4 86 8 CO 0 O 200 93 4 96 8 100 0 21 0 87 6 91 0 94 6 21 0 98 0 101 6 105 0 22 0 91 8 95 4 99 0 22 0 102 8 106 4 110 0 23 95 10 99 8 103 6 23 0 107 4 111 2 115 24 0 100 O 0 104 O 108 0 24 0 112 0 116 0 120 25 0 104 2 108 4 112 6 25 0 116 8 120 10 125 0 28 0 29 0 30 0 26 0 27 0 112 6 117 0 116 8 121 4 120 10 125 8 125 0 130 0 130 0 108 4 112 8 117 121 6 27 0 126 0 28 0 130 6 29 0 135 0 30 0 0 26 0 121 4 125 8 126 0 130 6 130 0 135 0 130 8 135 4 140 0 135 4 140 2 145 0 140 0 145 0 150 0 536 TIMBER TABLES.-No. 3. Lengths. 5ft. 2in. 5ft. 4in. 5ft. 6 in. wide. wide. wide. Lengths. 5ft. 8in. 5ft. 10in. 6ft. Oin. wide. wide. wide. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. 0 1 0 5 0 5 0 5 0 1 0 5 0 5 0 6 0 2 0 10 0 10 0 11 02 0 11 0 11 1 0 3 1 3 1 4 1 4 0 3 1 5 1 5 1 6 0 4 1 8 1 9 1 10 0 4 1 10 1 11 2 0 0 5 2 1 2. 2 2 3 0 5 2 4 2 5 2 6 0 6 2 7 28 29 0 6 2 10 2 11 3 0 0 7 3 0 3 1 3 2 0 7 3 3 3 4 3 6 08 3 5 3 6 38 08 3 9 3 10 4 0 0 9 3 10 4 0 4 1 0 9 4 3 4 4 4 6 0 10 4 3 4 5 4 7 0 10 4 8 4 10 5 0 11 4 8 4 10 5 0 0 11 5 2 5 4 5 6 1 0 5 2 5 4 5 6 1 0 5 8 5 10 6 0 2 0 10 4 10 8 11 0 2 0 11 4 11 8 12 O 3 0 15 6 16 O 16 6 3 0 17 O 17 6 18 0 4 0 20 8 21 4 22 0 4 0 22 8 23 4 24 0 5 0 25 10 26 8 27 6 5 0 28 4 29 2 30 0 60 31 0 32 33 0 6 0 34 0 35 0 36 0 36 2 37 4 38 6 7 0 39 8 40 10 42 0 8 0 41 4 42 8 44 0 8 0 45 4 46 8 48 0 9 0 46 6 48 0 49 6 9 0 51 0 52 6 54 0 10 0 51 8 53 4 55 0 0 10 0 56 8 58 4 60 0 11 0 56 10 58 8 60 6 11 0 62 4 64 2 66 0 12 0 62 0 64 0 66 0 12 0 68 0 70 0 72 0 13 0 67 2 69 4 71 6 13 0 73 8 75 10 78 0 14 0 72 4 74 8 77 0 14 O 79 4 81 8 84 0 15 0 77 6 80 0 82 6 15 0 85 0 87 6 90 0 16 0 82 8 85 4 88 0 16 O 90 8 93 4 96 0 17 0 87 10 90 8 93 6 17 0 96 4 99 2 102 0 18 0 93 0 96 0 99 0 18 O 102 0 105 0 108 0 19 0 98 2 101 4 104 6 19 0 107 8 110 10 114 0 20 0 103 4 106 8 110 0 0 20 0 113 4 116 8 120 120 0 21 0 108 6 112 0 115 6 21 0 119 0 122 6 126 22 0 113 8 117 4 121 0 22 0 124 8 128 4 132 0 23 0 118 10 122 8 126 6 23 0 130 4 134 2 138 0 24 0 124 0 128 0 132 0 24 0 136 0 140 0 144 25 0 129 2 133 4 137 6 25 0 141 8 145 10 150 0 26 0 134 4 138 8 27 0 139 6 28 0 144 8 29 0 149 10 143 0 144 0 148 6 149 4 154 0 154 8 159 26 0 147 4 151 8 156 0 27 0 153 0 157 6 162 0 28 0 158 8 163 4 168 0 6 29 0 164 4 169 2 174 O 30 0 155 0 160 0 165 0 030 0 170 0 175 0 180 0 SUPERFICIAL MEASURE. 537 Lengths. wide. 6ft. 2in. 6ft. 4in. 6ft. 6in. wide. Lengths. wide. 6ft. 8in. 6ft. 10in. 7ft. Oin. wide. wide. wide. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. 0 1 06 0 6 0 6 0 1 0 6 06 0 7 2 1 0 1 0 1 1 0 2 1 1 1 1 1 2 0 3 1 6 1 7 1 7 0 3 1 8 1 8 1 9 0 4 2 0 2 1 2 2 0 4 2 2 2 3 2 4 0 5 26 2 7 2 8 0 5 2 9 2 10 2 11 0 6 3 1 32 3 3 0 6 3 4 3 5 36 0 7 3 7 3 8 3 9 0 7 3 10 3 11 4 1 08 4 1 4 2 4 4 0 8 4 5 4 6 4 8 0 9 4 7 4 9 4 10 0 9 5 0 5 1 5 3 0 10 5 1 5 3 5 5 0 10 5 6 5 8 5 10 0 11 5 7 5 9 5 11 0 11 6 1 63 6 5 1 0 62 6 4 6 6 1 0 68 6 10 7 0 2 0 12 4 12 8 13 0 2 0 13 4 13 8 14 0 3 0 18 6 19 0 19 6 3 0 20 0 20 6 21 0 4 0 24 8 25 4 26 0 4 0 26 8 27 4 28 0 5 0 • 30 10 31 8 32 6 5 0 33 4 34 2 35 0 6 0 37 0 38 0 39 0 60 40 0 41 0 42 0 7 0 43 2 44 4 45 6 7 0 46 8 47 10 49 0 8 0 49 4 50 8 52 0 8 0 53 4 54 8 56 0 9 0 55 6 57 0 58 6 9 0 60 0 61 6 63 0 10 0 61 8 63 4 65 0 0 10 0 66 8 68 4 70 0 11 0 67 10 69 8 71 6 11 O 73 4 75 2 77 0 12 0 74 0 76 0 78 0 12 0 80 0 82 0 84 0 13 0 80 2 82 4 84 6 13 O 86 8 88 10 91 0 14 0 86 4 88 8 91 0 14 O 93 4 95 8 98 0 15 0 92 6 95 0 97 6 6 15 0 100 0 102 6 105 0 16 0 98 8 101 4 104 0 16 O 106 8 109 4 112 0 17 0 104 10 107 8 110 6 17 O 113 4 116 2 119 0 18 0 111 0 114 0 117 O 18 0 120 0 123 0 126 0 19 0 117 2 120 4 123 6 19 O 126 8 129 10 133 0 20 0 123 4 126 8 130 0 20 0 133 4 136 8 140 0 21 0 129 6 133 0 136 6 21 0 140 0 143 6 147 0 22 0 135 8 139 4 143 0 22 0 146 8 150 4 154 0 23 0 141 10 145 145 8 149 6 23 0 153 4 157 2 161 0 24 0 148 0 152 0 156 O 24 0 160 0 164 0 168 0 25 0 154 2 158 4 162 6 25 0 166 8 170 10 175 0 26 0 160 4 164 8 169 0 26 0 173 4 177 8 182 0 27 0 166 6 171 0 175 6 27 0 180 0 184 6 189 0 28 172 8 177 4 182 0 28 0 186 8 191 4 196 0 29 0 178 10 183 8 188 6 29 0 193 4 198 2 203 0 30 0 185 0 190 0 195 0 30 0 200 0 205 0 210 0 2 L 538 TIMBER TABLES.-No. 3. Lengths wide. 7ft. 2in. 7ft. 4in. 7ft. 6in. wide. wide. Lengths. 7ft. 8in. 7ft. 10in. 8ft. Oin. wide. wide. wide. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. 0 1 0 7 0 7 0 7 0 1 0 7 07 08 0 2 1 2 1 2 1 3 0 2 1 3 1 3 1 4 0 3 1 9 1 10 1 10 0 3 1 11 1 11 2 0 0 4 2 4 2 5 2 6 0 4 2 6 2 7 2 8 0 5 2 11 3 0 3 1 0 5 3 2 3 3 3 0 6 3 7 38 3 9 06 3 10 3 11 4 0 0 7 4 2 4 3 4 4 0 7 4 5 4 6 4 8 08 4 9 4 10 5 0 0 8 5 1 5 2 5 4 0 9 5 4 5 6 5 7 0 9 59 5 10 6 0 0 10 5 11 6 1 63 0 10 6 4 6 6 6 8 0 11 66 68 6 10 0 11 7 0 7 2 77 4 1 0 7 2 7 4 7 6 1 0 7 8 7 10 8 0 2 0 14 4 14 8 15 0 2 0 15 4 15 8 16 0 3 0 21 6 22 0 22 6 3 0 23 0 23 6 24 0 4 0 28 8 29 4 30 0 4 0 30 8 31 4 32 0 5 0 35 10 36 8 37 6 5 0 38 4 39 2 40 0 6 0 43 0 44 0 45 0 6 0 46 0 47 0 48 0 7 0 50 2 51 4 52 6 17 0 53 8 54 10 56 0 8 0 57 4 58 8 60 0 8 0 61 4 62 8 64 0 9 0 64 6 66 0 67 6 9 0 69 0 70 6 72 0 10 0 71 8 73 4 75 0 10 0 76 8 78 4 80 0 11 0 78 10 80 8 82 6 11 0 84 4 86 2 88 0 12 0 86 0 88 0 90 0 12 0 92 0 94 0 96 0 13 0 93 2 95 4 97 6 13 0 99 8 101 10 104 O 14 0 100 4 102 8 105 0 14 107 4 109 8 112 0 15 0 107 6 6 110 0 112 6 15 0 115 0 117 6 120 120 0 16 0 114 8 117 4 120 0 16 O 122 8 125 4 128 0 17 O 121 10 124 8 127 6 17 0 130 4 133 2 136 0 18 0 129 0 132 0 135 0 18 0 138 0 141 0 144 0 19 0 136 2 139 4 142 6 19 0 145 8 148 10 152 0 20 0 143 4 146 8 150 0 20 0 153 4 156 8 160 160 0 21 0 150 6 154 0 22 0 157 8 157 161 4 165 621 0 161 0 164 6 168 0 0 22 0 168 8 172 4 176 0 23 0 164 10 168 8 172 6 23 0 176 4 180 2 184 0 24 0 172 0 176 O 180 0 24 0 184 0 188 0 192 0 25 0 179 2 183 4 187 6 25 0 191 8 195 10 200 200 0 26 0 186 4 190 8 195 0 26 0 199 4 203 8 208 0 27 0 193 6 198 O 202 6 27 0 207 0 211 6 216 0 28 0 200 8 205 4 210 O 28 0 214 8 219 4 224 0 29 0 207 10 212 8 217 6 29 0 222 4 227 2 232 0 30 0 215 0 220 0 225 0 30 0 230 0 235 0 240 240 0 SUPERFICIAL MEASURE. 539 8ft. 2in. 8ft. 4in. 8 ft. 6in. Lengths. wide. wide. wide. Lengths. 8ft. 8in. 8ft. 10in. 9ft. Oin. wide. wide. wide. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. 0 1 08 08 0 8 0 1 08 08 0 9 0 2 1 4 1 4 1 5 0 2 1 5 5 1 6 0 3 2 0 2 1 2 1 0 3 2 2 2 2 2 3 0 4 2 8 2 9 2 10 0 4 2 10 2 11 3 0 0 5 3 4 3 5 3 6 0 5 3 7 38 3 9 0 6 4 1 4 2 4 3 06 4 4 4 5 4 6 0 7 4 9 4 10 4 11 0 7 5 0 5 1 5 3 08 5 5 5 6 5 8 08 5 9 5 10 6 0 0 9 1 6 3 6 4 09 6 6 6 7 6 9 0 10 6 9 6 11 7 1 0 10 7 2 7 4 7 6 0 11 7 5 7 7 7 9 0 11 7 11 8 1 8 3 1 0 8 2 8 4 8 6 1 0 88 8 10 9 0 2 0 16 4 16 8 17 0 20 17 4 17 8 18 O 3 0 24 6 25 0 25 6 3 0 26 0 26 6 27 0 4 32 8 33 4 34 0 4 0 34 8 35 4 36 0 5 0 40 10 41 8 42 6 5 0 43 4 44 2 45 0 60 49 0 50 0 51 0 60 52 0 53 0 54 0 7 0 57 2 58 4 59 6 7 0 60 8 61 10 63 0 8 0 65 4 66 8 68 0 8 0 69 4 70 8 72 0 9 0 73 6 75 76 6 9 0 78 0 79 6 81 0 10 0 81 8 83 4 85 0 10 0 86 8 88 4 90 0 11 0 89 10 91 8 93 6 11 O 95 4 97 2 99 0 12 0 98 0 0 100 0 102 0 12 0 104 0 106 0 108 0 13 0 106 2 108 4 110 110 6 13 0 112 8 114 10 117 0 14 O 114 4 116 8 119 O 14 O 121 4 123 8 126 0 15 0 122 6 125 0 127 6 15 0 130 0 132 6 135 0 16 O 130 8 133 4 136 0 16 0 138 8 141 4 144 0 17 0 138 10 141 8 144 6 17 0 147 4 150 2 153 153 0 18 0 147 0 150 0 153 0 18 0 156 0 159 0 162 0 19 0 155 2 158 4 161 6 19 0 164 8 167 10 171 0 20 0 163 4 166 8 170 0 20 0 173 4 176 8 180 0 21 O 171 6 175 0 178 6 21 0 182 0 185 6 189 0 22 0 179 8 183 4 187 0 22 0 190 8 194 4 198 0 23 0 187 10 191 8 195 6 23 0 199 4 203 2207 0 24 0 196 0 200 0 204 0 24 0 208 0 25 0 204 2 208 4 212 6 25 0 216 8 212 0 216 0 220 10 225 0 26 0 212 4 216 8 221 0 26 0 225 4 27 0 220 6 6 225 0 229 6 27 0 234 0 229 8 238 234 0 6 243 0 28 0 228 8 233 4 238 0 28 0 242 8 247 4 252 0 29 0 236 10 241 8 246 6 29 0 251 4 256 2 2 261 30 0 245 0 250 0 255 0 30 0 260 0 265 0 270 0 540 TIMBER TABLES.—No. 3. Lengths. 9ft. 2in. 9ft. 4in. 9ft. 6in. Lengths. 9ft. 8in. 9ft. 10in. 10ft. Oin. wide. wide. wide. wide. wide. wide. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. ft. in. 0 1 09 0 9 09 0 1 09 09 0 10 0 2 1 6 1 6 1 7 0 2 1 7 1 7 1 8 0 3 2 3 2 4 2 4 0 3 2 5 2 5 2 6 0 3 0 3 1 3 2 0 4 3 2 3 3 3 4 3 9 3 10 3 11 0 5 4 0 4 1 4 2 0 6 4 7 4 8 4 9 0 6 4 10 4 11 5 0 0 7 5 4 5 5 5 6 0 7 5 7 5 8 5 10 0 8 6 1 62 6 4 0 8 6 5 6 6 68 0 9 6 10 7 0 7 1 0 9 7 3 7 4 7 6 0 10 7 7 7 9 7 11 0 10 8 0 8 2 8 4 0 11 8 4 86 88 0 11 8 10 90 9 2 1 0 9 2 9 4 96 1 0 9 8 9 10 10 0 2 0 18 4 18 8 19 0 2 0 19 4 19 8 20 0 3 0 27 6 28 0 28 6 3 0 29 29 6 30 0 4 0 36 8 37 4 38 0 4 0 38 8 39 4 40 O 5 0 45 10 46 8 47 6 5 0 48 4 49 2 50 0 6 0 55 0 56 0 57 0 6 0 58 0 59 0 60 0 7 64 2 65 4 66 6 77 0 67 8 68 10 70 0 8 0 73 4 74 8 76 0 8 0 77 4 78 8 80 0 9 0 82 6 84 0 85 6 9 0 87 0 88 6 90 0 10 0 91 8 93 4 95 0 10 0 96 8 98 4 100 0 13 HRRAD 11 0 100 10 102 8 104 6 11 0 106 4 108 2 110 0 12 0 110 0 112 O 114 0 12 0 116 0 118 O 120 0 0 119 2 121 4 123 6 13 0 125 8 127 10 130 0 14 0 128 4 130 8 133 0 14 0 135 4 137 8 140 O 15 0 137 6 140 0 142 6 15 0 145 0 147 6 150 0 16 O 146 8 149 4 152 0 16 O 154 8 157 4 160 0 17 0 155 10 158 8 161 6 17 0 164 4 167 2 170 0 18 0 165 0 168 O 171 0 18 0 174 0 177 O 180 0 19 0 174 2 177 4 180 6 19 0 183 8 186 10 190 0 20 0 183 4 186 8 190 0 20 0 193 4 196 8 200 0 21 0 192 6 196 O 199 6 21 21 0 203 0 206 6 210 O 22 0 201 8 205 4 209 0 22 0 212 8 216 4 220 0 23 0 210 10 214 8 218 6 23 0 222 4 226 2 230 0 24 0 220 0 224 0 228 0 24 0 232 0 236 0 240 0 25 0 229 2 233 4 237 6 25 25 0 241 8 245 10 250 0 26 0 238 4 242 8 247 0 26 0 251 4 255 8 260 0 27 247 6 252 0 256 6 27 0 261 0 | 265 6 270 0 28 0 256 8 261 4 266 0 28 0 270 8 275 4 280 0 29 0 265 10 270 8 275 6 29 0 280 4 285 285 2 290 0 30 0 275 0 280 0 285 0 30 0 290 0 295 0 300 0 ARTIFICERS' WORK. 541 CHAPTER XVI. ARTIFICERS' WORK. SECT. I.-Bricklayer and Excavator's Work. THE standard measure for Brickwork in London is the rod of 16 ft. 6 in. square, which dimension being multiplied into itself produces 272 ft. 3 in., but the odd 3 inches are never taken into account. It is therefore always considered as 272 superficial feet, at 1 brick, or 13 inches thick, or 306 feet cube, viz., 272 ft. by 1 ft. 1 in. All the other thicknesses are reduced to this standard, as shown hereafter in the manner of taking the dimensions and ab- stracting the work. In measuring bricklayers' work, it is usual to begin by taking the excavations; first, for the basement story, if any, which is stated as digging and throwing out or wheeling away; the ground for sunk stories, according to circumstances; next the excavations for footings to walls. It is customary in taking the digging to footings of walls, to allow about six inches on each side, over and above the thickness of the walls, for room to work them; but if they are deep, and the ground bad and loose, allow nine inches on each side on account of its falling in. But in sunk stories only allow to the extent of the footings, except in very loose ground. In taking the dimensions, the length, depth, and width must be measured as before described, and reduced to the yard cube of 27 feet, viz., 3 ft. by 3 ft. by 3 ft. Claying of Vaults, by the yard square of 9 feet, describing the thickness, 3 ft. by 3 ft. In measuring digging in sideling ground, where the areas of the two ends of the excavation are unequal, the cubic content must be found by the following rule:- Multiply the sum of the extreme areas, plus four times the mid- dle area, by one-sixth of the length, and the product will be the answer required. Ex.-To find the cubic content of the excavation A B C D E F 542 ARTIFICERS' WORK. for the sunk stories of a house, to be built on the side of a hill:- 6.0 84.0 8.0 120.0 112.0 B 140 x 10 2 700 84 × 6 2 252 112 x 8 2 140.0 G H 952 sum of extreme areas = 1792 four times middle area 2744 120 length 54880 2744 6)329280 27) 54880 ( 2032 yards 16 feet 54 88 81 70 54 | 16 As an illustration of the correctness of the rule, let us take the same example on a different principle of measurement. The solid BRICKLAYER. 543 ABCDEF may be divided into the two prisms GHIBED, and EFCIHD and the pyramid DA HG. Taking each of these separately, we have— Prism G H IBED= 84 x 4 x 120 20160 2 Prism EF CIHD 120 × 6 × 84 2 = 30240 56 × 4 120 Pyramid DA HG = X 4480 2 3 or 2032 yards 16 feet, as before. Total. 54880 cubic ft. In measuring brickwork, always begin with the foundations, then proceed with measuring each story separately (or as high as the wall continues of the same thickness), as solid work, according to its respective thickness; then add for all projections, as breasts of chimneys, &c., deducting the openings, but not the flues, as the extra trouble and the pargetting is deemed equivalent to the defi- ciency of materials; but deduct the openings of doors, windows, &c. If the house or building be rectangular, measure two walls the whole length of the external face, and the other two internally, so as to get the true cubical contents. But in measuring for labour only, the external face of the work is girt, and multiplied into the height and thickness, to pay for the extra labour of plumbing the angles, andworking the returns fair. In measuring walls that are faced with superior bricks, the walls are first measured as common work, and then the superficial quan- tity of facing is taken, as hereafter shown, and is valued by con- sidering the facing as two-thirds of a brick thick, and deducting the common brickwork from the price thereof, the same thickness, viz., two-thirds of a brick; by which the value per foot superfi- cial is ascertained. In measuring circles, or semicircles, they are marked accordingly in the measuring-book, thus: with the diameters figured. 3.4 or 3.4 To measure angle chimneys, draw lines on the floor, parallel to the two sides of the room, cutting the parts intersected by the chim- ney; take either side by the height of the floor, and half the other (the work forming a triangle) for the thickness, either as the number of bricks, or as cube work, which, by the directions before 544 ARTIFICERS' WORK. given, prove it to be exactly the same: consequently, if the pro- jection should not amount to any certain number of half-bricks, it would be best to take it as a cube dimension. In all cases it is supposed that the walls are measured before the projecting chim- neys are taken, which is the usual custom. In taking the dimensions of vaults, measure the abutments, or side walls, to the springing of the arch, then bend your rods round the soffit of the arch; and add once and a half the thickness there- of, by which you obtain the average girt of the arch; then take the length clear of the walls; but if the arch is turned over one or both walls, add the thickness thereof to the length of the arch. But in taking the height of the walls, measure to the crown of the arch, without making any deduction for the declivity of the arches, on account of the additional trouble and waste of bricks, in cutting and fitting them to the curved soffit of the arch. Likewise, in deducting openings with circular heads, the dimensions should only be taken to the springing of the arches, on account of the trouble and waste of bricks in fitting them to the arches. Drains to be taken and reduced as common brickwork if built with mortar. Shafts of chimneys are measured as solid work. * Ovens and coppers are measured as solid cube brickwork, de- ducting the ash-holes only. Tiles, Welsh lumps, and fire bricks are to be allowed as extras. In these, or any other brickwork that it is considered best or most convenient to measure by the cubic foot, multiply the solidity by 8, the number of 1 inches in a foot, and divide it by 9, the number of 1½ inches in 13 inches, which will reduce it to the standard of 1½ brick or 13 inches in thickness. In measuring brickwork no allowance is to be made in quantity for small or difficult works. Timbers inserted in the walls are not to be deducted. When plates are bedded in the walls, two inches to be allowed for ditto where no brickwork is over them. All sills and stone strings are measured in. All cuttings to be measured superficial; as outside splays, cut and rubbed to show fair, or inside ditto rough cut for battens, &c. Birds' mouths at per foot run, being notched to fit. Facings of all descriptions to be measured extra by the foot superficial; in which case the reveals are also measured, except where intended to be stuccoed. * This method is in common use amongst surveyors; but it would be far more con- sistent to measure the actual quantity of brickwork, allowing for the extra labour in price. BRICKLAYER. 545 Gauged arches to doors, windows, &c., are also measured by the foot superficial. Groins are measured as common work, only taking the run of cut groins at per foot. Bricknogging, by the yard square of nine feet, including the timbers. Brick paving, ditto, ditto. Facias, beads, and quirks, dentil or plain cornices, &c., measured and valued by the foot run. TILING. Plane and pan tiling are measured by the square of 100 feet. In measuring plane tiling— Allow for the eaves 4 inches extra. Ditto for dripping do. 6 inches extra. Ditto for all cuttings, hips, &c., 3 inches extra. Ditto for valleys, 12 inches extra. In measuring pan tiling― Allow for the barge per foot run. Ditto for heading to barge per foot run. Ditto for cutting to hips and splays per foot run. Ditto for hips and ridges per foot run. Number the hip hooks, which should be painted three times in oil. Ditto T nails, ditto. Deduct for chimneys, and deduct and add for dormers. If the roofs are hipped, take the length at the bottom of the sides, and not measure the end; the two side triangles being equal to the hipped end one. VALUATION OF BRICKLAYERS' WORK. CALCULATION OF MATERIALS. Digger.—27 cubic feet, or one cubic yard, is called a single load, and contains 21 striked bushels. Two cubic yards = one double load. In estimating the cubic content of excavation required to form a given amount of embankment, due regard must be paid to the nature of the soil of which the embankment is to be formed. The following may be safely taken as average rates of the alter- ation in bulk of various soils when excavated and carried into embankment. 546 ARTIFICERS' WORK. Clays.—Compression about one-tenth of the original bulk in excavation. Gravels.-Compression about one-twelfth of the original bulk in excavation. Sand occupies the same space in bank as in excavation. Chalk.-Slight increase of the original bulk in excavation, pro- portionate to the size and hardness of the fragments. Rock.-Increase about one-half of the original bulk in excava- tion, according to the size of the fragments. 234 cubic feet of sand weigh one ton. 213 do. gravel do. 17 do. clay do. 13 do. chalk do. 18 do. night-soil do. Concrete is made of ground stone lime and sharp gravel, with a proper proportion of sand, mixed in the proportion of five or six parts of gravel to one of lime, according to the nature of the lime and the proportion of sand mixed with the gravel. Its quality is much improved by the addition of smith's ashes, or any material containing iron; and for this reason ferruginous gravel is to be preferred whenever it can be obtained. A cubic yard of concrete, containing 27 cubic feet when mixed, requires 34 cubic feet of gravel, sand, and lime. Therefore, at the proportion of six of gravel to one of lime, a cubic yard of concrete will require 1.1 cubic yard of gravel and sand and three bushels of lime. Concrete expands slightly in slaking; but this expansion is too trifling to be taken into account in framing an estimate. Size and Weight of various Articles. Length. Breadth. Thickness. Weight. ft. in. ft. in. 10-inch Stock bricks Paving do. Dutch Clinkers 12-inch paving tiles Pan tiles Plain tiles do. Pan tile laths, per 10 ft. bundle Ditto, per 12 ft. bundle • each do. 0 • 832343 0 41 ft. in. 0 21 lbs. OZ. 5 0 0 9 0 4 0 12 4 0 • do. 0 61 0 3 0 13 1 8 do. • do. • do. do. 흡흡흡흡 0 112 0 112 0 13 0 0 93 0 0 1 8 9 1 14 0 0 0 101 0 ager*- 5 4 2 5 120 0 1 0 1 4 6 144 0 0 1 5 0 A bundle contains 12 laths. Plain tile laths, per bundle 500 0 0 1 0 01 3 0 Thirty bundles of laths make a load BRICKLAYER. 547 A bricklayer's hod measures 1 ft. 4 in. x 9 in x 9 in., and will hold 20 bricks. A single load of sand is 27 cubic feet, or one cubic yard. A double load of sand is 54 cubic feet, or two cubic yards. A measure of lime is 27 cubic feet, or one cubic yard, and con- tains from 16 to 18 bushels. QUANTITIES, ETC. A rod of brickwork measures 16 ft. 6 in. x 16 ft. 6 in., or 272 ft. 3 in. superf., 1 brick or 13 inches thick, called the standard thickness, or 306 cubic feet, or 11 cubic yards. A rod of brickwork laid to a 12-inch gauge, i.e., four courses to measure one foot in height requires 4353 stock bricks. Ditto, laid to 11-inch gauge, requires 4533 stock bricks. A foot of reduced brickwork requires 16 bricks. These calculations are made without allowance for waste; and indeed there is very little, as nearly every part is worked in, and much space is occupied by timbers, flues, &c., for which no deduc- tion is made in measurement; and therefore in the erection of dwelling-houses containing flues and bond timbers, 4300 stocks is quite sufficient, and this is the usual number allowed for a rod of brickwork. 5370 stocks to the rod, if laid dry. 4900 do. in wells and circular cesspools. A rod of brickwork, laid four courses to gauge 12 inches, con- tains 235 ft. cube of bricks, and 71 ft. cube of mortar; and the average weight is about 15 tons. A rod of brickwork requires 1 cubic yard of chalk lime and three loads of sand; or one cubic yard of stone lime, and 3 loads of sand; or 36 bushels of cement, and 36 bushels of sharp sand. A cubic yard or load of mortar requires nine bushels of lime and one load of sand. The proportion of mortar or cement, when made up, to the ma- terials in their mixed state, is as two to three. Facing requires 7 bricks per foot superficial. Gauged arches 10 do. do. Bricknogging per yard superficial, requires 30 bricks on edge, or 45 laid flat. Description. Stock bricks, laid flat Do. PAVING. Number required. per yard 36 on edge. 52 وو 548 ARTIFICERS' WORK. Description. Paving bricks, laid flat Do. Dutch clinkers 12-inch paving tiles . 10-inch do. on edge • وو TILING. Number required. per yard 36 82 99 140 وو وو وو 9 13 • Number Gauge. required. inches. Pan tiles, per square 12 150 Ditto ditto 11 164 Ditto ditto 10 180 A square of pan tiling requires one bundle of laths and 14 hundred of 6d. nails. Plain tiles, per square 1 4 600 Ditto ditto 3 3/1/20 700 Ditto ditto 3 800 Ditto ditto laid flat 210 A square of plain tiling requires one bundle of laths and nails, one peck of tile pins, and three hods of mortar. CALCULATION OF LABOUR. Digger. The amount of digging which a man can perform in a day depends so much on the nature of the soil on which he has to operate, that it is almost impossible to fix a constant for this de- scription of labour: the following data may, however, serve as a slight guide. In loose ground a man will throw up about ten cubic yards per day; but in hard or gravelly soils, where hacking is necessary, from three to five cubic yards, according to the hardness of the ground, will be a fair day's work. Wheeling is estimated by the run of 20 yards. A gang of three men, two for filling and one for wheeling, will remove about 30 yards per day to this distance; and the labour of removing earth may be calculated according to distance, allowing three men to the first run, and an additional man for every twenty yards of distance. The following table, although far from complete, contains con- stants for all the principal descriptions of bricklayer's work. SLATER. 549 Concrete.-Labour in mixing, wheeling, throwing in from a stage, and puddling (where required to be done), including erection of scaffolding, per yard cube Brickwork, per rod Extra labour to malm facings Paving. Brick paving laid flat in sand . Do. laid on edge in sand Do. laid flat in mortar Do. laid on edge in mortar per yard وو وو وو Constant. To be multiplied by the rate of wages for a labourer per day. .335 To be multiplied by the rate of wages for a bricklayer and la- bourer per day. 4.941 To be multiplied by the rate of wages for a bricklayer per day. .014 To be multiplied by the rate of wages for a bricklayer and la- bourer per day. .046 .075 .056 • .084 Paving-brick paving laid flat in sand. .046 29 Paving-brick paving laid on edge in sand, per yard .106 Do. laid flat in mortar .075 "" Do. on edge in mortar .121 Clinker paving on edge in sand 10 or 12 inch tile paving وو وو وو .132 .010 Tiling. Pan tiling laid dry per square .422 Do. pointed outside .685 وو Do. pointed inside and outside .790 وو Plain tiling laid to a 4-inch gauge .739 Do. Do. to a 34-inch gauge to a 3-inch gauge .764 وو .790 SECT. II.-Slater's Work. Slating is measured superficially, and charged per square of 100 feet. In measuring, allow for the eaves whatever the bottom course measures, and for the hips and valleys measure their length by 12 inches, viz., six inches on each side; also the length of all irregular angles, as chimneys, dormers, &c., by six inches wide, as a fair allowance for cutting and waste. For circular slating allow one-third extra. 550 ARTIFICERS' WORK. VALUATION OF SLATER'S WORK. Table of Materials and Labour. Average 1200 will Average sizes of Slates. gauge when laid. cover squares. Weight per thousand of 1200 in tons. Number required to cover one square. Nails required to a square. Iron, cast or wrought, at per hundred. Constant. To be multi- plied by the Copper, at per lb. rate of wages for a slater per diem. ft. in. ft. in. in. lbs. Doubles 1 1 by 0 6 5/1/2 21 480 480 5 Ladies 1 3 08 7 "" Countesses 1 8 0 10 "" 10 7호 Duchesses 2 0 1 0 11 10 122 11 280 280 160 320 33 "" 3 127 254 22 коко Tavistock 31/2 A ton will cover. Imperials 2 6 2 0 "" Rags and Queens 3 0 2 0 "" Westmorelands, various 21 to 21 21 .173 .155 .137 .119 CARPENTER AND JOINER. 551 Example.-To find the value of a square of duchess slating copper nailed. No. 127. Duchesses, at per thousand. 2 lbs. of copper nails, at per lb. £ s. d. per cent. profit Labour on above, at per day. Value per square £ SECT. III.—On Carpenters' and Joiners' Work. MEASURING. There are two methods of measuring carpenters' work: one by taking the superficial contents of roofs, floors, partitions, &c., at per square of 100 feet for the labour and nails, and then the cube contents of the timber without labour; the other, by mea- suring the cube contents of the timber as cube fir and labour, framed, &c. &c. If the scantlings of the timber are small or light, it will pay the carpenter best to measure the roofs, floors, &c. as labour and nails, and the timber as no labour; but if the scantlings of the timber are large and heavy, then it will be more to his advantage to measure the work as timber, with the particular labour thereon, as follows:- If the work is measured as timber and labour, the scantling of each piece is taken as cube fir or oak and labour, and entered accordingly; as Cube fir, or oak, in ground joists, bonds, lintels, plates, &c., labour and nails, included. Do. framed in roofs, partitions, naked floors, &c., labour and nails included. Do. do. Do. wrought and framed Do. wrought, framed, and rebated truss framed do. do. do. Do. wrought, framed, rebated, and beaded, labour and nails included. Do. in door-cases. Oak trusses put into girders, per foot run, stating their size, as 4 inch square, &c. In measuring for labour and nails to roofs, naked framed floors, ceiling floors, quarter partitions, or any other rough framed work, 552 ARTIFICERS' WORK. the dimensions should be taken from the exteme ends of the timber each way, to ascertain the superficial contents thereof, as labour and nails at per square of 100 superficial feet. The openings to chimneys, staircases, &c. are not to be deducted, as the trouble of framing the trimmers and the joists into those openings is fully equivalent to running the joists through them. The same rule must be observed in taking the labour and nails in quarter partitions, as doors, &c., which must be entered in the measuring-book and valued according to the description of the work, as follows :— For Roofs. Labour and nails to common shed roofing. Do. do. with purlins. Do. do. with purlins and struts. Do. do. rafters. Do. do. common span or valley with purlins and span with collars, dovetailed into sides of rafters notched to receive purlins, filled in with common rafters. do. framed with principals, king posts, two struts Do. and purlins, filled in with common rafters. Do. Do. do. do. with king and queen posts. do. For Floors. common kerb roof. Labour and nails to fir ground joists, bedded and not framed. Do. do. Do. do. stairs. Do. do. Do. do. and ceiling joists. Do. do. and ceiling joists. pinned down on plates and framed to chimneys. single framed floors, trimmed to chimneys and with girders and cased bays. framed floors, with girders, binding, bridging, to common framed ceiling floors, with binding Quarter Partitions. Labour and nails to common 4 in. quarter partitions. Do. do. Do. do. 5 in. 6 in. do. do. Do. do. truss framed with king posts. Do. do. do. with king and queen posts. If oak is used, describe it. Having taken the labour and nails, you must then proceed to take the timber therein, which must be entered as cube fir, or oak without labour. CARPENTER AND JOINER. 553 In roofs, it is customary to take the highest timbers first, as the ridge piece, hips, &c., next the rafters, and so proceed downwards to the ceiling floor. In partitions, floors, &c., begin with the timbers of the largest scantlings. Wherever a tenon is made, the length must be taken from the ends of the tenon, and not from the shoulders. Likewise the length of joists, including the part in the wall. In measuring king and queen posts, take the whole length by the scantling of the shoulders. The parallel pieces sawed out for the abutment of the principal rafters must be deducted, should they exceed 2 feet in length and 2 inches in thickness; but taken 5 or 6 inches short of the length between the shoulders, as the saw cannot enter with much less waste. But if the pieces are less than 2 inches thick, no deduction must be made, they not being worth more than the labour of cutting them out. ROOFS. Hips and valley to be taken at per foot run, for cutting and waste. All plates, lintels, discharging pieces, to be taken as bond timber. Gutter plates, diagonal ties, dragging pieces or braces, struts, and tie-beams, as fir framed. Deduct half the length of bond timbers running through openings. Allow the length of dovetails or scarf in bond timber, but only taken as bond timber. Fixing iron straps, screw bolts, hanging ditto, and all iron-work, to be taken and allowed extra. FLOORS. Oak trusses, let into breastsummers, to be taken at per foot run. at Oak king or queen posts, let into brestsummers, each Girders sawed down, reversed and bolted, per foot run extra. Letting in screw-bolts, plates, &c., each extra. Common or herring-bone strutting between the joists, per foot run extra. Furrings to ceilings, quarter partitions, battenings to walls, &c., are measured by the square, including labour and nails, and valued according to the thickness of the deals, used from 2 to 3 inches 2 M 554 ARTIFICERS' WORK. thick. Describe the battening either as framed or nailed only, or if plugged, or if with horizontal backings. All wall-hooks and holdfasts to be allowed extra. Centring to groins, vaults, recesses, &c.-Take the depth by the circumference for the superficial dimensions, which is valued at per square for use and waste, materials and time. If taken in this way, the whole of the vaults or recesses must be taken, although the same centring might have been used. But where there are a number of vaults or recesses of the same size, the fairest way is to allow the whole of the materials and time, or if any trifling alteration only is wanted, to allow the time expended in doing it. Bracketing to cornices, to be measured at per foot superf., according to the girt, viz., 24 inches by the length, as whole or 1½ inch deal, according to the thick- ness of deals used. Some allow the bracketing the same girt as the cornice. inches. 6 11/1 9 64 11/1 244 Cradling for entablatures, measured and charged per foot superf., according to their thickness. All circular bracketing, cradlings, &c., to be charged double those of straight work. Ashlering at per foot superf., according to the thickness of the deals used. Gutters and bearers.-Measure the length, then the breadth of the bottom and half the eaves-board. Gutters between the roofs having two eaves-boards, one on each side, take for the width of gutter one of them. Arris or fillet gutters per foot superf. Water trunks per foot run; describe size, and allow for laps and half the length of shoe. Sound boarding.-Measure the dimensions between the joists at per foot superf.; observe if single or double fillets. Chimney grounds, per foot superf. If the side grounds are very narrow, framed only for small mouldings, take them by the foot run, and enter them as narrow framed grounds. Hinges to be numbered and described. Skirtings, either plain or raking, taken at per foot superf. If on narrow grounds, take them per foot run. If plugged to the walls, allow extra for plugging. Moulded plinths.-Measure the square part by the length and width, and enter it. Whole deal, wrought one side, rebated and backed plinth. Girt the moulding, and allow half an inch behind the plinth. CARPENTER AND JOINER. 555 Flooring.—In measuring boarded flooring, the dimensions must be taken, allowing the thickness of the skirting, and valued at per square. Enter them according to their thickness, and if yellow or white deal, if common or second best or clean deal, if laid folding, straight joint or dowelled. The slabs are not generally deducted if they have mitred bor- ders; if they have not mitred borders, deduct the opening or slab from the flooring. If the deduction is made when there are bor- ders, the borders must be taken at per foot run, which will amount to as much as the deduction made on the floor. Moulding, such as architraves, round doors, windows, &c., base, surbase, &c., &c., are to be measured round the mitres and girt with a fine tape, and entered as moulded architrave, base, &c., as the case may be. But in the abstract, they must be all classed under the same head as mouldings. Single mouldings, as Q O G and bead, or Q* ovolo and bead, &c., may be taken at per foot run, but their girt must be described, as they will be valued accordingly. Doorcases, linings, &c., &c.-Doors are measured and valued at per foot superficial, according to their description. Solid doorcases are taken at per foot cube. Door linings, grounds, &c, at per foot superficial. If there is a sill, take it the same as the head, viz., by making an allowance for its passing under and beyond the jambs, as may be; and also allow the additional length of jambs for framing into ditto. If a stone sill, iron shoes should be secured to the bottom of jambs, which must be numbered. Sashes and frames, shutters, and fitting up to windows. Take the dimensions from the beads of sashes on the inside, and allow seven inches additional height for head and sill, and eight inches in width for frames in common sashes; but nine inches for large sashes. French sashes, hung on hinges, or sashes hung on centres in solid frames.-Take the sashes separate, and the frames as directed for doorcases. If Venetian frames, describe them as such. If mouldings up munten, take them per foot run. If circular heads, take the sash by itself, and the frames as run of circular frames, as per description, viz., with beads, parting slips, &c., &c., as may be. Window shutters are taken per foot superficial, allowing for the rebates. Number the sash fastenings, locking bars, spring latches, hinges, &c., &c. 556 ARTIFICERS' WORK. The framed grounds, rebated and beaded boxings, linings, moulded architraves, &c., are taken per foot superficial, similar to the doors. Staircases are taken per foot superficial, by girting the riser and tread by the length of the step, allowing extra for the thickness of the skirting, which is entered in the measuring book, according to their thickness and description, viz., inch deal common steps, risers, and carriage. 14 inch deal second best, steps, risers, and carriage, with moulded nosings, close or cut string; or, 14 inch deal second best, S R & C M nosings, mitred to receive brackets or string boards and return nosings, and dovetailed to re- ceive balusters. 14 inch clean deal, do. do. 14 inch clean deal, S R & C, to geometrical stairs on a circular plan, the risers mitred to the string board. VALUATION OF CARPENTERS' AND JOINERS' WORK. Memoranda. 50 cubic feet of timber equal one load. 100 feet superficial equal one square. 120 deals are called one hundred. A reduced deal is 1 inch thick, 11 inches wide, and 12 feet long. 120 12 ft. 3 in. deals equal 5% loads of timber. 400 feet superficial of 1½ inch plank or deals equal one load. Planks are 11 inches wide, deals 9 inches, and battens 7 inches. A square of flooring requires- Laid rough Do edges shot Wrought and laid folding Do. straight joint Do. do. and ploughed and tongued • One square of wrought folding floor requires Do. straight joint Number of 12 ft. boards. 121 121 13 131 14 Number of 12 ft. battens. 17 18 WEIGHT OF TIMBER. 39 cubic feet of oak equal 1 ton. 65 fir do. وو وو 66 39 deals. do. وو CARPENTER AND JOINER. 557 60 cubic feet of elm 51 beech وو 45 ash دو 34 وو mahogany. equal to 1 ton do. وو do. وو وو do. CALCULATION, showing the method of ascertaining the VALUE of a CUBE FOOT of FIR or other timber from the prime cost prices:- Fir timber at per load, say Carriage (according to distance) Sawing on an average Waste in converting, fo 20 per cent profit £ s. d. 5 0 0 050 0 10 0 5 15 0 . 0 11 6 6 6 6 1 5 3/1/2 £ s. d. 7 11 91 7 11 9/1/2 = 3s. 04d. per foot cube. 50 The constants in the following tables are to be multiplied by the rate of wages for a carpenter per day. LABOUR AND NAILS TO ROOFS. At per square of 100 superficial feet. If two stories, add Labour. Nails. Days. 8. d. To common shed roofs, one story high Do. do. with purlins .650 2 0 .800 2 0 . .084 .169 . 1.000 .084 20 If three do. add Common span or valley, with purlins and rafters two stories high. If three stories, add. Framed roofs, with collars dovetailed into sides of rafters, notched to receive pur- lins, and filled in with common rafters Roofs framed with principals, king posts, purlins, braces, and common rafters Do. do. with king and queen posts, Common kerb roofs on one side If two sides, add If three sides, add If above two stories, add . 1.906 2.940 . 3.170 3 6 4 0 4 0 1.125 2 0 .084 .169 .100 558 ARTIFICERS' WORK. LABOUR AND NAILS TO NAKED FLOORS. At per square of 100 superficial feet. Labour Nails. days. 8. d. Ceiling floors, joists only Do. framed with tie-beams Do. with binding and ceiling joists .584 1 6 .834 1 9 . 1.000 1 11 Ground joists, bedded but not framed Do. pinned down on plates and framed to chimneys .836 Single framed floors trimmed to chimneys and stairs If above 9 in. deep, add • .500 1 6 1 6 1.050 1 9 • .169 Framed with girders and cased bays . 1.700 3 0 Framed with girders, binding, bridging, and ceiling joists . 2.500 4 0 LABOUR AND NAILS TO QUARTER PARTITIONS. At per square of 100 superficial feet. Common 4 in. partitions .900 1 3 Do. 5 in. do. 1.050 1 6 • Do. 6 in. do. . 1.100 1 6 Truss framed with king posts Do. with king and queen posts . 1.736 2.000 1 6 If oak, extra one-third. LABOUR ON FIR TIMBER. At per foot cube. Cube fir bond Do. framed Do. truss framed Do. framed and chamfered Do. wrought and framed Do. do. and rebated Do. W, F, R, and beaded Do W, F, R, and D beaded. Do. proper doorcases Planing fir per foot superf. Days. .063 .126 .168 .168 .210 .252 .294 .336 .378 .014 Bond timbers, wall plates, wood bricks, pole and kerb, &c., are all to be under the head of bond. CARPENTER AND JOINER. 559 CALCULATION, showing the method of finding the VALUE of DEALS or BATTENS from the prime cost prices. Prime cost per hundred of 12 ft. 3 in. deals, say Carriage according to distance 20 per cent profit £ s. d. * 42 12 0 = 7s. 1d. to be allowed in day-bills 120 for each 3 in. deal In measured work, allow for waste, o £ 8. d. 35 0 0 0 10 0 35 10 0 7 2 0 £ 42 12 0 07 1 008/1/2 0793 In calculating the value of deals in thicknesses, add the value of the sawing, according to the number of cuts. Every rise and fall of 97. per hundred, will increase or diminish the price of deals as near as possible, per foot superficial, 1d. per inch in thickness. This rule will be found sufficiently correct for practice where the quantities are not large; where they are, the exact calculation should be made. LABOUR ON DEALS, AT PER FOOT SUPERFICIAL. In order to facilitate the fixing of proper prices for the labour on deals, at per foot superficial, the different descriptions of work which have always been considered of equal value, are classed to- gether, by which the system adopted for valuing the various sorts of labour on deals, will be rendered more simple and easy; over the column in which is inserted each kind of work of equal value, is placed the decimal which, multiplied by the rate per day allowed for a carpenter at the time and place where the work is performed, will show the fair and equitable price to be allowed. 560 ARTIFICERS' WORK. No. 1. No. 2. No. 3. No. 4. For deals from to 1 .009 .019 .027 ⚫037 ín. thick • For deals from 2 to 3) in, thick .013 .027 .037 .049 Edges shot. Labour and Cut circular. Cut standards Plugged. nails. Sunk Shelves. Jacked, Planing on Scolloped. Rounded. each side. Ledged. Dovetailed. Grooved. Rebated. Ploughed & tongued. Framed. Battened. Mitred. Scribed. Backed. Throated. Clamped. Beaded. BATTENING, PER SQUARE. Labour. Nails. Days. 8. d. ₫ in. to 14 in. 12 in. from centre to centre If plugged to walls, add .590 2 0 .170 1 0 Extra for wall hooks. WEATHER BOARDING, PER SQUARE. Rough .420 2 6 Ditto splayed edges .680 3 0 Wrought 1.000 3 3 Ditto and beaded 1.255 3 6 ROUGH BOARDING, PER SQUARE. 2 in. deal, rough .500 2 6 Do. edges shot .667 3 0 Do. ploughed and tongued .750 3 0 Inch deal, rough .542 2 9 Do. edges shot .709 3 0 Do. ploughed and tongued .918 4 0 Whole deal, rough .584 3 0 Do. edges shot .750 3 6 Do. ploughed and tongued 1.042 4 0 1 in deal, rough .667 3 0 Do. edges shot .862 3 6 Do. ploughed and tongued 1.167 4 0 DEAL FLOORS, PER SQUARE. Inch, rough edges shot .765 2 6 A CARPENTER AND JOINER. 561 Labour. Days. Nails. 8. d. Do. wrought folding 1.180 2 6 Inch, wrought folding straight joint 1.500 3 6 Whole deal, rough edges shot .840 3 0 Do. wrought folding 1.255 4 0 Whole deal, wrought straight joint, splayed headings 1.760 4 6 Do. do. dowelled € 3.170 8 0 1½ in. deal, rough edges shot .920 3 0 Do. wrought folding 1.340 4 0 Do. do. straight joint, splayed heading 2.000 4 6 If ploughed and tongued headings, add .295 If ploughed and tongued edges, add .510 For tongues to edges of boards, add .840 BATTEN FLOORS, PER SQUARE. Inch, wrought folding 1.500 4 6 Do. straight joint, splayed headings . 1.792 4 9 14 in. wrought folding 1.667 6 0 dowelled Do. straight joint, splayed headings Do. 2.167 6 3 4.167 10 O If ploughed and tongued headings, add If ploughed and tongued edges, add .431 .750 For tongues to edges of boards, add If battens less than 5 in., add 1.250 .334 FRAMED GROUNDS, PER FOOT SUPERFICIAL. Common framed grounds 1 in. do. ploughed for plastering 1 in. do. do. do. 1 in. do. do. do. SKIRTINGS, PER FOOT SUPERFICIAL. Labour and Nails. .063 .070 .076 .083 Plain skirting .037 Do. raking cut to steps .070 Torus skirting .065 Do. raking cut to steps .085 GUTTERS AND BEARERS, PER FOOT SUPERFICIAL. Inch or whole deal .076 562 ARTIFICERS' WORK. DOOR LININGS, PER FOOT SUPERFICIAL. Labour and Nails. Plain single rebated .056 Do. and beaded .063 Do. double rebated .070 Do. do. do. and double beaded .077 Square framed jambs, each in 2 panels and soffit in 1 panel .105 If bead butt, or moulded, add .013 Bead flush, or quirk moulded .027 Raised panel and moulded .042 For every extra panel if square .021 Do. flush or moulded .027 If double rebated .021 If double beaded .013 LEDGED DOORS, PER FOOT SUPERFICIAL. 14 in. rough edges shot .065 Add, If ploughed and tongued .013 If ploughed and beaded .021 If wrought each side .013 If braced .027 If hung folding .021. If 1 in. thick .013 FRAMED PARTITIONS, PER FOOT SUPERFICIAL. 1½ in. square framed .065 2 in. do. .076 Add, If BB or moulded .027 If BF or quirk moulded .042 DEAL MOULDINGS, FIXED COMPLETE. Common mouldings .128 .028 Add, if quirked The materials for mouldings in deal will be found as near as possible of the same value as the labour. Small mouldings may be measured at per foot run, and valued according to the girt and form. DOORS HUNG COMPLETE, PER FOOT SUPERFICIAL. Two panel square framed .070 Add, for every additional two panels ; CARPENTER AND JOINER. 563 If framed square, For 1½ in. deal 2 in. do. 21 in. do. If framed BB and square, For 14 in. deal 2 in. do. 21 in. do. If framed BF and square, For 1 in deal 2 in. do. 2 in. do. If framed Q. O G and Bd. and square, or Q O. and Bª. and square, For 1 in. deals 2 in. do. 23 in. do. If double margins 4 in. wide Do. Hung folding 5 or 6 in. do. WINDOW LININGS, PER FOOT SUPERFICIAL. Inch deal two panel square framed back linings If B B or moulded, add BF or quirk moulded, add For each panel above two, if square Do. do. If splayed if moulded Labour and Nails. .019 .021 .027 .021 .024 .027 .027 .037 .042 .021 .024 .027 .021 .042 .013 .101 .013 .021 .021 .027 .007 WINDOW BACKS, ELBOWS, AND SOFFITS, PER FOOT SUPERFICIAL. Inch deal, plain keyed or two panel square backs Do. two panel square backs, elbows and soffits Add for each panel above three, If splayed If bead butt or moulded BF or quirk moulded BOXINGS TO WINDOWS, PER FOOT SUPERFICIAL. Framed, rebated, and beaded boxings Splayed FR and beaded boxings .085 .098 .010 .013 .021 .101 .120 564 ARTIFICERS' WORK. INSIDE WINDOW SHUTTERS, PER FOOT SUPERFICIAL. Labour and Nails. in. deal clamped flaps in one height .120 Inch do. two panel square in one height .125 For every panel above two add, If framed square If B B or moulded .022 .022 BF or Q. moulded QOG & b, or QO & b & square For every extra height add .026 .026 .013 SASHES AND FRAMES HUNG COMPLETE, PER FOOT SUPERFICIAL. Sashes- 1 in. deal ovolo sashes Do. wainscot or mahogany If 2 in. or 2 in. sashes deal, add If do. wainscot or mahogany, add .049 .070 . .021 . .028 If astragal and hollow in deal, add .013 If do. in wainscot or mahogany, add .021 Frames- Deal cased frames O S sills, DPPB & PS, S hung .070 If prepared for 2 or 2țin. sashes, add. .013 If prepared with wainscot or mahogany PP Bds. & P slips add .085 If for 2 or 2 in. sashes add 1 .019 If double hung, add .013 To find the value of sashes and frames, add to the above for labour and nails only, the amount of materials expended. STAIRCASES, PER FOOT SUPERFICIAL. Common steps and risers and two fir carriages Do. moulded nosings and close strings .070 .098 Do. do. mitred to cut string-boards and dove-tailed to balusters .127 Add, If winders circular one end .042 Do. circular two ends .085 Do. geometrical with wrought and blocked carriages .056 Riser tongued to step bottom edge .021 Do. do. both edges .042 Feather tongue joints Add for each- .021 Quarter curtail glued upright .667 CARPENTER AND JOINER. 565 Do. blocked and veneered Proper curtail step and riser Returned moulded nosing Do. circular Plain cut bracket Do. circular Housing to step and riser Do. to winders Do. to moulded nosings Do. to do. circular ends Labour and Nails. OUTSIDE STRINGS TO STAIRS, PER FOOT SUPERFICIAL. Whole deal, plain Do. sunk Do. sunk and moulded Do. do. cut Do. do. mitred to risers If wreathed,-four times the above. If ramped,—once and half do. WALL STRINGS, PER FOOT SUPERFICIAL. Plain and plugging If moulded, add If rebated for plastering, add DADOS, PER FOOT SUPERFICIAL. Proper dado, with dovetailed keys, joints secured with slips, and dovetails hung to grounds by keys grooved into do. and dado Add, If raking scribed to steps Do. to moulded nosings If base grooved into floor For each external mitre beyond two in the room If circular on the plan,-double the above. If wreathed do, treble do. 1.167 3.334 .250 .417 .250 .417 .098 .125 .167 .459 .084 . .098 .112 .127 .140 .080 .021 .028 .070 .019 .021 .009 .228 566 ARTIFICERS' WORK. COLUMNS AND PILASTERS PER FOOT SUPERFICIAL.: Labour and Nails. 14 in. deal plain pilasters, properly glued and blocked Do. do. diminished 14 in. deal diminished columns, properly glued and blocked, . .112 .153 under 14 inches diameter .420 Do. do. above do. .350 Add for Arris or deep fluting to pilasters, one inch wide .021 Do. two inches wide .028 Do. three inches wide .042 Arris or deep fluting to columns, one inch wide .027 Do. two inches wide .042 Do. three inches wide .056 Straight grooves to columns .021 Headings to flutes to do.. .070 .013 .042 Straight grooves to pilasters Headings to flutes to do. SECTION IV.-Sawyers' Work. The charges for sawyers' work are often very inconsistent, and differ widely in various parts of the country. The proper mode of valuing the labour on sawing fir or any other kind of timber is by the square of 100 superficial feet, the price depending on the usual rate of wages and the hardness of the timber: Sawing to old timber is usually charged double, on account of the extra labour occasioned by nails, &c: Small scantlings may be charged by the foot run. Planks, deals, battens, and flat cuts, according to their length, at per dozen cuts. And all other descriptions of sawyers' work may be valued in a similar manner, according to the circumstances of the case. SECTION V.-Stone-Masons' Work. There is a variety of opinions respecting the manner of mea- suring stone-masons' work, both in taking the dimensions for the stone, and also for the labour. It certainly requires more practi- cal knowledge of the operative or working part of the business STONE MASON. 567 than any other trade, to determine correctly between these con- flicting opinions. The following rules may be considered suffi- ciently explanatory of the principle on which the practice is governed or founded. In measuring cube Portland or other stone; all stones that are worked square should be taken accurately as they come from the saw to the banker, of course including the parts laid on or pinned into the walls. But as bevelled or irregularly formed stones can- not be converted without more waste than square ones, the dimen- sions should be taken so as to make a fair allowance for such additional waste, particularly as the solid contents of all the dif- ferent descriptions of Portland stone, whatever shape the stones may be worked to, are abstracted under the same head, (viz., cube Portland,) and therefore should be of the same value; but which cannot be the case, unless the extra waste in the bevelled stone, &c., is allowed for in taking the dimensions. When this is done, it is only requisite, in estimating the prime cost, to calculate for the waste as if all the stones in the building were cut and worked square. If this method were not adopted, it would be requisite, in ascertaining its real value, to make so many different heads in the abstract for cube Portland, as there are different shaped or bevelled stones, accurately describing each; when the calculations for waste, and of course the price, must vary according to each particular form, the trouble of which would be endless, and without any advantage; indeed, it would come to the same thing, viz., making the necessary allowances for waste, according to the form of the stone. Bevelled or arch stones should be taken about one- sixth above the mean dimension to allow for waste. In measuring the cubic contents of spandrel steps, some diffe- rence of opinion exists as to the best method of taking the re- quisite dimensions. The following three methods are in common use, viz.:- 1st. Take the length of the step by its extreme width, and by the whole height of the riser measured from tread to tread. 2nd. Take the length of the step by the extreme width from the nosing of the tread to the acute angle, and by half the height of the riser taken from the top of the tread to the acute angle downwards. 3rd. Take the length of the step by its extreme width, and by three-fifths of the depth of the riser taken from the top of the tread to the acute angle downward. A better way than either of the above methods is to take the 568 ARTIFICERS' WORK. length of the step by a dimension found as follows, allowing half an inch on each step for waste. 18 116 1 3 width of step. 6 2 base of rectangle. 1.3 4 half do. of triangle. 6 12// This gives 5 0 1 3 6 3 1 6 as before. In measuring winders, the content may be found in the same way, taking the extreme length of the step by the mean sectional area, making due allowance for waste. The labour on the under side to be taken as circular sunk work. All stones exceeding three inches thick should be taken as cube measure, with the labour, &c., on do. All stone, three inches thick and under, should be taken as slab, at per foot superficial. The usual custom has been to measure in such edges as are worked and show fair. Objections have been made to this prac- tice, and with some degree of justice; but it will make very little difference, if the edges of thin slabs are measured separate, and a fair price allowed for the labour; and for cutting into narrow pieces for mantles, jambs, &c., it would be nearly equal to the value of the stone; but in thick slabs the same argument will not hold good; and, therefore, as the object in measuring work should be to ascer- tain its real value, and allow only a fair remunerating price, it appears more correct to measure the labour on the edges at per foot run, offering a fair price, according to their thickness, instead of entering it as stone. An extra price should be allowed for very large scantlings, also for hoisting stones on exceedingly high build- ings, according to circumstances. MASON. 569 LABOUR ON PORTLAND OR OTHER STONE. In measuring the labour of working Portland stone, the principal difference of opinion arises in determining what faces or beds. should be taken as plain work. In superior work, a plain face must be taken previous to measuring the sunk, moulded, or other work, when the mould could not be applied without first making that plain face. There cannot be much difference of opinion in taking the other labour, such as sunk work, moulded work, circular-sunk or circular-moulded work, &c., which must be girt as it appears when the work is finished, but which is not always the case with the plain work; and therefore it is requisite to know the manner in which the work is executed, to form an accurate conclusion, and to do justice to the workman in its measurement. WEIGHT OF STONE. 14 cubic feet weigh one ton. Purbeck stone Portland Bath Yorkshire Granite Marble 16 17 99 15 99 131 13 وو وو وو وو Purbeck paving 50 feet superf. Do. step 13 by 61 25 feet run do. 99 do. وو do. do. do. do. do. VALUATION OF LABOUR. Table of Constants for the different descriptions of Mason's, Work. N.B.-The factor to be applied is the rate of wages for a mason per day. Days. Labour, squaring and laying new York or Purbeck paving per foot superficial .021 If in courses, add .010 Labour on Portland or similar stone per foot superficial. Sawing to be taken as half plain work. Plain work to bond stones per foot superf. .140 Do. to beds and joints do. .181 Do. rubbed face do. .209 Do. do. circular do. .291 Sunk work rubbed do. .250 Do. do. circular do. .313 Moulded work rubbed do. .292 Do. do. circular do. .417 2 N 570 ARTIFICERS' WORK. Days. Circular work to shafts of columns having the neck moulding or part of the base worked in the same stone per foot superf. .334 Circular circular or spherical work to domes or balls do. .500 If rubbed, add extra do. .049 Taking up, squaring, and relaying old paving do. .042 Add, if in courses do. .015 LABOUR ON STATUARY OR VEIN MARBLE, Including Sawing, Working, and Polishing. Plain work per foot superf. . .875 Circular work do. 1.250 • Sunk work do. 1.667 • Moulded work do. . 2.334 Circular sunk work do. 2.334 Circular moulded work do. 3.000 ON OLD WORK. Old vein marble chimney reset Do. do. squared and reset per foot superf. do. .125 .167 Do. do. sanded, grounded, and squared do. .209 Do. do. and reset do. .250 Do. do. cleaned and reset do. .250 Do. do. sanded, polished, and reset do. .375 Do. do. sawed, sanded, polished, squared, and reset do. .626 In the west of England, and all the counties in which stone is abundant, it is usual and customary to build with the rough stone of the country, and the practice generally is to measure the walls by the perch of 18 superficial feet, supposing them 24 inches thick; to which thickness all the walls, whether more or less, are reduced by multiplying the superficial contents by the thickness in inches, and dividing them by 24; or they may be reduced to the cube perch of 36 feet: but some regulate the prices per perch, according to the thickness of the walls. In measuring the work, some contend to girt the quoins and all projections, as they say, to pay them for the extra trouble in work- ing and setting the stones; but this should not be allowed, except for labour only; and even then it is much fairer to measure the quantity of walling as it is, and make a proper allowance for the extra labour, either in quoins, chimney breasts, flues, reveals, &c. PLASTERER. 571 SECT. VI.-On Measuring Plasterers' Work. Plasterers' work is taken superficially, and valued by the square yard of 9 feet. If cornices are round the room, take the ceiling only to half the projection of the cornice, or one projection in and one out; or mea- sure the ceilings clear of the cornices, and take the whole of their projection as lathing and pricking up. If the cornices are bracketed, measure the ceilings clear of the cornice. The sides of the room should be taken from the ground, through the bed-mould, or half the height of the cornice. 1 If on brick, or bracketed, take them only to the bottom of cornice. In taking the length of cornices, measure the size of the room, taking one projection in and one out, and girt them from the mould, or from the ceiling to the wall line. Number all the angles in the room above four, as extra.* In taking cornices where there are coves, take the coves as su- perficial of cove to cornices, and allow 1 inch extra on the girt of the cornice for the return of the mould on the cove. All enrichments to be taken separately. Friezes, under the cornice, must be taken as superficial of plain floated frieze. A floated ground must be taken under all enriched friezes. If cornices are run to old ceilings, a screed must be allowed. Enriched friezes, ceilings, or soffits must be measured first as plain work, and then the enrichments taken separately at per foot run, and a price fixed, according to their description and value. All circular mouldings and enrichments to be taken one face in and one out. Take first the ceiling through the reeds. Second, length of cove above the cornice by 2 ft. Third, do. of moulded cornice by 1 ft. 2 in., being 1 in. extra for top on cove. Fourth, do. of plain floated frieze by 6 in. Fifth, do. of moulded architrave by 8 in. * The present practice, however, of making four additional mitres to carry the cornice round a projecting chimney, is as absurd a deformity as it is an extravagant waste. Even the architects of the last generation had the wit to keep their ceiling a simple rectangle, by arching in brick the recesses on each side of the chimney. 572 ARTIFICERS' WORK. Sixth, length of moulded reeds by 9 in. Reveals to windows taken at per foot run, price according to width. VALUATION OF PLASTERERS' WORK. Calculation of Materials. 1 hundred of lime = 25 strike bushels (old measure). Materials. 100 yards of render ( 14 hd. of lime. set require 130 yards of lath, plaster, and set require 1 double load of sand. 4 bushels of hair. 1 load of laths. 10,000 nails. 23 hd. of lime. 1 dble. Ids. of sand. 7 bushels of hair. LATHING. Labour. Plasterer, labourer and boy, three days each. Plasterer, labourer and boy, six days each. 1 bundle of laths and 384 nails will cover 5 yards. RENDER ONLY. 1 hd. of lime. 1874 yards require 2 double loads of sand. 5 bushels of hair. Floating requires more labour, but not more than half the quantity of stuff as rendering. SETTING ONLY. 11 hd. of lime. 375 yards require 5 bushels of hair. 20 per cent. is always allowed on the prime cost of the materials. Calculation of Labour. The decimal is to be multiplied by the rate of wages for plas- terer, labourer, and boy, per day. Days. Rough render .019 Floating do. .021 Setting .016 Lathing .019 If circular work, add on the lathing and also on each coat of plastering .008 If to groins, add as above .010 L IRONMONGER. 573 SECT. VII.-Ironmongery. Nails are sold by weight, and charged by the hundred. Screws at per dozen. Iron bolts and screws at so much each. Brass flush bolts at per inch. Pulleys each, according to diameter. and screws at per pair. Locks at so much each. Hinges Twenty per cent. profit is allowed on the prime cost of all ironmongery. MEASUREMENT OF IRON-WORK. Cast iron in girders, story-posts, columns, &c., is charged by the ton or the cwt. Moulds are generally charged extra, if out of the common run. Articles in common demand, as cast-iron water pipes, gutters, &c., are sold by the yard, according to diameter. Cast-iron in railings, gratings, casements, brackets, &c., is charged by the pound, according to the nature of the work. Wrought-iron in chimney-bars, railings, hand-rails, shoes to piles, &c., is charged by the pound. SECT. VIII.—Painter's Work. In measuring painters' work, all work not cut in on both edges, must be taken, including edges and projections, at per yard square of 9 feet. Work cut in on both edges, as skirtings, cornices, shelves, &c., are measured at per foot run. Ornamental work first taken as common, and then superf. of labour to ornaments at per foot superf. or run. Sash frames, window lights, casements, bars, dormers, frontis- pieces, chimney-pieces, &c., numbered and valued at each. Sash squares at per doz. Iron or wood railings, balusters to stairs, &c., are measured on both sides as solid work, to allow for the extra trouble of painting round the bars, rails, &c., at per yard. If ornamented, add extra one face in the width of such ornamental parts. If ornamented turned balusters, also add one extra face as far as the turned work goes. Handrails, &c., grained mahogany, first measure them in with the balusters, and then per foot run for graining. Soffits to windows per foot run. Letters or figures numbered and valued at per inch in height. 574 ARTIFICERS' WORK. Windows and doors are measured thus:- WINDOWS. ft. in. ft. in.} 11 O Window front. 5 5 ft. in. ft. in. 7 6 4 6 0 4 edges. 1 6 boxings and edges. 7 10 Shutters 6 0 710 6 0 7 6 If the backs 10 61 ft. in. viz.26 3 7 6 are cut away 10 65 linings 1 2 0 9 the linings 4 6 soffit 20 3 Linings must be 4 6 0 9 elbows 1 2 measured to the floor 20 3 thus: 26 3 7 6 39 22 6 Beads varnished, supposing them to be mahogany or 11 3 wainscoat sashes and beads 11 3 22 6 12 squares varnished. 1 locking bar. Some only allow the shutters to be taken thus: • The outside of window would be taken as . 1 6 boxings. 0 6 edges. 20 3 9 shutters. 5 9 instead of 6 feet. N 1 frames. 1 dozen of squares. 1 sill, if the stone still is painted. Doors. 2)7 0 4 4 Door fronts for both sides 40 projection of archi- 0 4 f traves. 4 4 6 6 6 6 16 0 08 Linings 3 0 0 6 f edges of door and 0 21 rebates. 08 16 O PAINTER. 575 VALUATION OF PAINTER'S WORK. Calculation of Materials. 45 yards of work, 1st coat, including knotting, stopping, and every pre- paration requisite for the second coat, will require Second and following coats 5 lbs. of white lead. 5 lbs. of putty, litharge, &c. 1 quart of oil. 5 lbs. of white lead. 1 quart of oil. 20 per cent. profit is always allowed on the prime cost of the materials. Calculation of Labour. The decimal to be multiplied by the rate of wages for a painter per day: First coat, including stopping, &c. Second and following coats .027 .019 The above data will suffice for the valuation of common work, for which alone it is possible to lay down any rules, as the value of decorative work, as graining, imitations, &c., depends upon the ability of the artist, and the manner in which the work is executed. SECT. IX.-Glaziers' Work. In measuring glaziers' work, the dimensions must be taken between the rebates, and all irregular panes the extreme size each way. The price per foot must be calculated from the prime cost per crate, allowing for carriage and 20 per cent. profit. The larger the panes are, the more difficulty, risk, and waste; consequently the price should increase in the following proportions :— Panes whose superficial con- tents are Do. do. do. ft. in. ft. in. under 2 0 at per foot. from 2 0 to 2 6 add 2d. Do. do. do. do 2 6 to 3 0 add 4d. Above the squares whose Do. do. do. do 3 0 to 3 6 add 6d. contents under 2 feet. are A CRATE OF CROWN GLASS Contains 12 tables of the best, at per crate وو وو وو 15 18 18 وو وو seconds thirds fourths 33 وو Each table is from 4 ft. to 4 ft. 6 in. diameter: some tables 576 ARTIFICERS' WORK. may be cut to within 2 in. of the centre, others not nearer than 4 inches. Supposing a crate to be 4 ft. 6 in. diameter, and that it may be cut to 2 in. from the centre, the quantity of glass that may be cut from it, including the triangular pieces, will be ft. in. 14 2 If only 4 ft. diameter, and cannot be cut nearer that 4 in. of the centre 10 10 25 0 And deducting the triangular pieces, which are of very little value 2 6 We have as the available contents of the two tables The average contents per table 22 6 11 3 Taking the sizes of squares that will cut to the most advantage: but as squares of all sizes must be cut from the tables as they are wanted, the average produce per table is not more than 10 ft. superficial. Labour and putty per foot may be found by multiplying the rate of wages for a glazier per day by the decimal .110. Ex.-To find the value per foot of glazing, with best Newcastle crown glass, or any other kind of glass:- Prime cost of crate (12 tables) Carriage, &c. 20 per cent. profit £ S. d. 0 0 0 0 0 0 0 0 0 0 0 0 120) 0 0 0 Divide by No. of feet the crate will pro- duce, for best glass 0 0 0 per foot: Labour and putty 0 0 0 Total per foot £0 0 0 SECT. X.-Paper-Hanger. A piece of paper is 12 yards long, and when hung, 20 inches wide. Twelve yards running measure is equal to 6 square yards, or 60 feet superficial; therefore divide the superficial feet by 5, which will give the number of yards, and these divided by 12 will give the number of pieces of paper. It is usual to allow one piece in seven for waste. VALUATION OF ESTATES. 577 CONSTANTS OF LABOUR. These constants represent the time requisite to perform a given quantity of work, of the kind specified, in days and decimal parts of a day; the factor to be applied, being the rate of wages per diem for one or more men, according to the nature of the work. These decimals are calculated, in all the trades, for the price per day allowed the master in his day bills, consequently, with his profit thereon, being the only rate that can be ascertained, the master, of course, paying each man per week, according to his abilities and industry; therefore the full value of the labour, including the master's profit, will be found by multiplying the decimal by the rate of wages, as shown in their respective tables. Likewise, in all cases it must be understood that the prices stated in the tables for labour and nails include fixing; and when added to the price of deals, will give the value of the work fixed complete, including labour, nails, and materials, according to the prime cost of materials and rate of wages allowed. CHAPTER XVII. THE VALUATION OF ESTATES. UNLIKE all the other subjects that have been treated of in this book, this one cannot be demonstrated. The theory may indeed be enun- ciated, but in the event of a difference of opinion arising, there is no mode of reconciling the variance in a manner that shall place it be- yond doubt. The profession of a land valuer is very often confounded with, and designated by, the title of that of the land surveyor. I do not mean to say a land valuer cannot by possibility be also a land sur- veyor; on the contrary, I am personally acquainted with several bril- liant examples of the practice-the successful practice-of both pro- fessions; but, as a general rule, the land valuer, most efficient in his calling, is a man who has spent the greater portion of his early life upon land, in the study and practice of agriculture; who has by experience gained such a knowledge of the several treatments which may be most successfully applied to those particular soils that chiefly abound in the vicinity of his agricultural operations, or in the adjoining counties; who is thoroughly acquainted with 578 VALUATION OF ESTATES. No the cost of labour and tillages upon these lands, and of the seasons and periods of which advantage must be taken in due course. one can doubt for a moment that such a man, particularly if he be more intelligent than the generality of his order, is the most fitting person to exercise a profession requiring a practical knowledge of all these things as its chief ground work. But then to call such a man a land surveyor is a libel upon a very different profession-a profession moreover which requires quite as long practice as the other to make its possessor thoroughly efficient; and, therefore, the two are not likely to be perfectly acquired by the same person in very early life. I said I knew of one or two brilliant examples of the exercise successfully of the two professions by the same persons. These gentlemen, whom I have in my mind, are men of excellent abilities; were originally educated as land surveyors, at which, as it is their great pride to boast, they for several years earned a maintenance. During that time each kept his attention steadily riveted on the different kinds of agriculture practised in the varied localities and counties over which his legitimate profession called him; observed with interest every variation of treatment to which land, apparently of the same nature, but in different counties, was treated by different farmers; investigated the reasons of such ap- parent anomalies by all possible references to climate, soil, and pecuniary consideration, until, I have no hesitation in saying, he gradually and contemporaneously with the exercise—the profitable exercise—of the profession of land surveying for a sufficient number years to be thoroughly experienced and grounded therein, en- tirely qualified himself to conduct the profession of land valuing. of Such is the prospect and such the possibility of a land surveyor acquiring in time a competent knowledge to act as a land valuer. Another way of effecting this object has been adopted, though not, as I believe, successfully, nor without considerable pecuniary sacri- fice. The land surveyor has taken a farm whereon he of course has gained knowledge by experience, but then the knowledge thus acquired has been of necessity limited, and too often the harass and worry of the farm must have distracted his attention from the proper exercise of land surveying, or the duties of the latter call- ing must have been located in a quarter many miles from home, at the same time that the business of the farm required the presence of the master. Now let us take a view of our experience among the several in- stances of persons who are legitimately land valuers, but who also practice as land surveyors. I do not hesitate for myself to state, that I am unacquainted with any single instance in which a land VALUATION OF ESTATES. 579 valuer, qualified either by his experience as a farmer, or by early education as a valuer, has subsequently adopted land surveying with any pretensions to the title of a land surveyor, or with the smallest atom of success. He may, as I am aware by an example I have in my mind, acquire a rudimental knowledge that may enable him to map a field, a farm, or a small estate. But while as a valuer he would, the moment he entered a field, detect a gravelly brow subject to burn, or slovenly farming, and the presence of couch, a glaring error in a plan, that would at once rivet the attention of the experienced surveyor, would entirely escape his notice. Thus he might be able to define within a shilling an acre the value of the land, but by attempting the exercise of both professions, the emi- nent knowledge in the one would be entirely nullified by some error of two or three acres in the quantity, which an acquaintance with the other would have corrected. I knew an instance of a man who was brought up as a tradesman in London, and who, much to his credit, so industriously pursued an honest calling, that at the age of 40 he had saved a sufficient sum of money to retire from his business into the country, where he took a farm. Being somewhat intelligent, he announced him- self as a land valuer, and very shortly afterwards a land surveyor. Some ten years after, a gentleman, who knew nothing of the qua- lifications of a land surveyor, had occasion to employ a number of surveyors as witnesses in a law suit; among them came this one. Of course the opposing counsel was duly instructed as to the qua- lifications of the witnesses, and in cross-examination endeavoured to furnish the jury with the information he himself possessed. In vain our witness appealed to his age, and his ten years' residence on his farm. The counsel was perfectly willing to accord to him the benefit of his experience in his London calling, and on his farm; but unless said he, he were a heaven-born surveyor, or could point to some work which he had performed, he could not allow a jury to attach importance to his evidence as a surveyor. The very age upon which he relied but aggravated his insufficiency; since three years spent in the acquirement of correct first principles in any science are better than ten years bungling in erroneous ones. Notwithstanding this little check our friend continued his career, his greatest ignorance being apparent in his want of information that his own works were at all below par. The tendency of my remarks has been to show that land survey- ing can only be learned in youth, and thorougly acquired by con- siderable subsequent experience. That a land valuer cannot take it up at pleasure and exercise it any more than a lawyer can prac- 580 VALUATION OF ESTATES. tise medicine, or the surgeon carry on the law. But that a clever land surveyor may by a long course of industry become a qualified land valuer. And the object I have had in view in making these observations has been to promulgate correct ideas upon the subject, affording employers the means of forming an opinion of the quali- fications of men to whom they entrust their interest, and furnishing a hint to those who may select these professions for their sons, as to the proper course to pursue to conduce to future advantage. The greatest amount of success is attained in matters of valua- tion by the joint co-operation of two professional men; the one being a competent valuer, the other a qualified surveyor; the practical knowledge of the one is considerably assisted by the science of the other, and appreciable advantages ensue. It is much to be pitied that so much jealousy exists between the two profes- sions, which militates to the injury of both. The practice adopted by most valuers is to assume that they are aware on inspection, without any enquiry, of the worth of an acre of land per annum. Now this is in many instances an erroneous and in all cases a vicious theory. I will endeavour to illustrate my meaning by an example: Assume a valuer to have a farm for which he pays, he believes, from experience, of its pro- ductiveness, and we will consider equitably 20s. an acre as rent; therefore, directly he comes to similar land in making a valuation, he says, this is worth 20s. an acre. But now just as- sume his own land to be situated in a parish where the local bur- dens amount, on an average, to 3s. in the pound, while the land he is valuing is situated in a parish where those burdens are 6s. in the pound. The calculation then stands thus, his own land which he has taken as his standard of value is worth in the aggregate of rent and rates 23s. per acre, which, when reduced by the amount of rates, exhibits 20s. as its net value. Now reduce the aggregate value of the land he is valuing by the amount of the rates, and we shall get but 17s. as the net value. The two lands being similar in every respect as to quality, tenacity, and eligibility of situation, but the one being subject to 3s. excess of taxation over the other, is to that extent depreciated in value for rental. The difference is doubly apparent if we assume the standard to be worth 46s. per acre, rent and rates, or reduced by the amount of the latter at 3s. in the pound to 40s. Our compared acre of equal fertility upon which the rates are 6s. in the pound, would be reduced in value to 34s., so that land otherwise equal in value, but affected by a cause which the generality of valuers entirely disregard, is, when properly adjusted, equitably worth in one parish 40s., in the other only 34s. VALUATION OF ESTATES. 581 This comparison is sufficiently accurate for practice, but in reality it is not the actual equity of the case. For the rates of 3s. and 6s. in the pound are levied on the rental, and therefore the calculation stands as under:— £ s. d. • Rent at 40s. per acre Rates at 3s. in the pound 2 0 0 06 0 26 0 Rent at 34s. per acre Rates at 6s. in the pound 1 14 0 • 0 10 41 2 4 4/1/ The correct adjustment of the latter example would be— Rent at 35s. 4d. per acre Rate at 6s. in the pound £ s. d. 1 15 4 0 10 8 2 6 0 In some counties (Surrey to wit,) the acts of husbandry per- formed on the fallows of the last year are paid for at valuation by the incoming tenant. This is a matter which again affects the rental of land. These valuations of tillages, and what is called tenant right, will be treated of bye and bye; my present purpose is to show how they influence the rent. I have mentioned Surrey-in that county the valuation of fallows frequently amounts to four pounds per acre, and the dressings to other four pounds. Now, if we take the fallow lands to be one- fourth of the whole farm, we have a sum amounting to 27. per acre all round, to be paid down by the tenant on entering, and there locked up for the whole term, without any advantage or benefit to him, except indeed it is taken into consideration in fixing the rent. Even if it is so, the capital thus expended would be far more useful and remunerative to the tenant than such a reduction of rent. Therefore we must once more suppose that the land which we assumed to be worth 40s. an acre in one parish is not subject to this valuation, but that of equal quality which the excess of local bur- dens reduced to 35s. in the other parish is. And we shall again see how this charge tends to a still farther reduction. I think no man would take a farm and risk capital in it if he did not expect to get 10 per cent. for the use of his money, so that we 582 VALUATION OF ESTATES. have 4s. to deduct from the already reduced estimate of 35s. 4d. per acre to arrive at the fair rental. Thus Original value £ s. d. 200 Reduced by excess of local burdens to 1 15 4 Further reduced by interest on money paid for valuation to 1 11 4 The cost of production materially influences the value of land. Lands of equal fertility but of different tenacity are of very dif- ferent values. Indeed if we seek an example among the poorer soils, we shall find that in some cases the cost of labour entirely consumes the value of the produce, leaving nothing for rent, while on a lighter soil, less expensive to cultivate, but of the same fer- tility, a small rent is deducible. I think I have said enough to show that the system of valuing lands by "experience only," as it is called, is erroneous; it is indeed comparing the net rent of land and not the gross, for after all, taxes and outgoings of a similar nature are but rent, expressed by ano- ther word. And this leads me to the consideration of what is rent? It is undoubtedly the surplus that remains for the landlord after all the expenses of cultivation, tithe, taxes, outgoings of every description, tenant's profit, interest for his capital, and provision for wear and tear, and for renewals, have been satisfied out of the value of the produce; and land which leaves no such surplus, is worth no rent for the purposes of agriculture. The first thing, therefore, which has to be done in entering fairly on the valuation of an estate is to estimate the yearly value of the produce it is capable of yielding under skilful management, and with a liberal but judicious expenditure of capital. Next to appraise the cost of the labour and other outlays neces- sary to ensure in the ordinary chances of the seasons the estimated amount of produce. Then the amount of tithe rent charge, and tenant's rates and taxes are matters to be ascertained by enquiry. The tenant's profit should be such an amount of remuneration as a person should receive at the current rate of skilled labour for such an amount of supervision and attention as the farm may require, without any reference to the style in which he lives, whether he dines at one o'clock or five, keeps hunters, or walks to market. The tastes and habits of a tenantry on a large estate may vary im- mensely, but their rights are identical and equal. VALUATION OF ESTATES. 583 Allowance for wear and tear of live and dead farming stock must also be made. This involves an estimate of the value of the whole stock, and when this is arrived at, a calculation must be made of the probable average length of time within which the whole will be required to be renewed, and the proper proportion thereof for the one year must be placed among the deductions from the value of the produce. The interest on capital must be a fair liberal al- lowance, according to the current rate of money, subject to risks and casualties; and when all these deductions have been made, the landlord has for the first time an interest in the residue (if any,) as rent. Our theory, when illustrated, stands thus- Assume the value of produce the cost of cultivation 100 53 Tithe 10 Tenant's rates and taxes Tenant's profit 7 Interest on capital 5 Wear and tear 5 Residue rent 20 100 دو وو وو وو وو It was formerly the custom to say that the produce of a farmı should carry three rents-one of which was to be apportioned to the landlord, a second to the tenant, and the third to pay expenses. It is hardly necessary to observe that such an apportionment must be very impracticable and ridiculous. Take for example the case of our illustration, where the landlord gets one-fifth only; the tenant rather less than that; and more than three-fifths are absorbed for expenses. I may also observe, that in framing that illustration, the farm I had in my mind was a light land farm; had it been a tenacious clay, the expenses might have been so swollen as to in- trench considerably on the surplus rent. The method of including farm homesteads (by which I mean both farm houses and buildings,) in the valuation, has been a much vexed question among valuators. Some omit to consider the homestead at all, alleging that a discretion is exercised in fixing the value of the land: others add so much to their valua- tion for every 50 acres of land possessing a homestead, omitting to make the addition where no buildings exist. Others, and this is I believe the more common way, profess to value the house and each separate building at its intrinsic value, and add the amount to their valuation of the land. 584 VALUATION OF ESTATES. In my opinion none of these are worthy of imitation. To con- vert the produce of land a certain number of buildings are requi- site, as well as a house for the farmer, and lodging for his cattle. Without these accommodations the farm would not be tenantable, and the value of it would be entirely problematical, as it might be difficult to hire suitable buildings elsewhere; or if they were to be had, the rent might be so excessive as to consume a large portion of the value of the produce. Therefore it appears to me that the only correct way to adopt in practice, is to assume when valuing land, that all requisite building accommodation exists in a conve- nient position upon the farm, the value of which is included in the estimate of the land. If upon examination the buildings are too small or are inconvenient, a proportionate reduction must be made from the valuation: but if, on the other hand, a surplus number of buildings are situate on the estate, no addition should be made, as the farmer is not benefited thereby; on the contrary, all beyond his actual requirements are so many additional expenses to him in keeping them in repair; unless indeed he can rent some land ad- joining the farm that is without a homestead, in which case it would be only fair to charge him with the excess. If lands that have been so valued are found to be without a homestead, then the damage occasioned thereby must be deducted. When I first promulgated this system of valuing farm buildings among my professional friends, I recommended that the farm houses should be subject to the same arrangement, but a practical difficulty arose with respect to them. The requirements of a farm- stead with reference to farm buildings may be defined, and as I have shown, any excess is valueless to the tenant, except under an unlikely or a rare contingency. But it is not so with the house. If a farm has a good house upon it, pleasantly situated, that farm will more readily let than one affording merely accommodation to the farmer; and excess of room in a farm house may be very fre- quently profitably let. Moreover, a farmer has no right to expect that the profits of his business are to be estimated differently to those of other people, who pay the rent of their houses out of their profits: so that it appears reasonable that while all other build- ings are included in the arrangement, and treated as I have sug- gested, the house should be made the subject of separate and additional valuation. I have described the mode of valuing adopted in general practice, which assumes the valuator to be possessed of the capability of at once determining the value of a piece of land while he is upon the field without reference to particular circumstances VALUATION OF ESTATES. 585 that may specially affect it. To that practice I take an exception, and say that it is not a correct one. I am fully aware of all the imputations to which I shall be subjected for promulgating ideas contrary to generally accepted customs. I shall be dignified with the title of "Theorist," and many similar appellations. But "theory with practice " has ever been a favorite motto with me, and I have sufficiently considered the matter to know that a sound theory is as requisite in land valuing as in any other art or science. The only thing that requires to be estimated on the ground is the produce the land is capable of yielding, which may be expressed in bushels of wheat or barley, according to the nature of the soil, which should be noted. I would then advise every valuer to reduce to the same mea- sure (bushels of wheat or barley,) all other items that enter into the computation of the cost of production, out-goings, &c., and to tabu- late the results according to his notions of expense and profit, and he will find the arrangement conducing to convenience and advantage. To illustrate what I mean and what the Tables should be, take the figures in my previous example to represent the produce in bushels of wheat on three acres of land. We will discuss four cases and tabulate the results. The first shall be in every respect as it stands originally, and shall be sup- posed to be on light land: the second is supposed to be land of the same density and fertility, but subject to 5 bushels of taxation instead of 10. The third case is heavy land, and the cost of culti- vation becomes 70 instead of 53; other charges remaining the same. The fourth and last case is on heavy land, with the same charge of 70 bushels for cost of cultivation, but taxes reduced to 5. The Table would be thus- PRODUCE 100 BUSHELS. LIGHT ARABLE LAND. HEAVY ARABLE Land. Local Burthens, in- Rent in cluding Tithe Rent Bushels of Charge, Rates, and Tenant's Taxes. Wheat. Local Burthens, in- cluding Tithe Rent Charge, Rates, and Tenant's Taxes. Rent in Bushels of Wheat. When amounting to 10 Bushels p. acre 20 When amounting to 10 Bushels p. acre 5 25 5 ∞ 00 3 8 "" 20 586 VALUATION OF ESTATES. It will be obvious that a system of Tables of this nature ex- tended to every variety of soil that differs in its cost of cultiva- tion and in fertility, and to all the variations of taxation, would be the most equitable mode of valuing land that could be well devised. The Tables once made would be permanent, as the results show the rent in bushels of wheat, and whether that grain were worth in the market 5, 6, or 7s. per bushel, would be equally applicable. When time permits, it is my intention to calculate, for publication, a series of tables of this nature. Cottages on a farm should form the subject of an additional item in the valuation, affording as they do the convenience of locating the permanent labourers in desirable proximity to their several occupations. Cottages, therefore, if judiciously situated quite enhance the value of a farm, to the extent of their fair annual value. It is not intended in this paper to treat of the geological knowledge necessary to the proper practice of land valuing, but simply to elucidate correct principles therein. Consequently we now approach the consideration of those special circumstances which affect the value of land in particular localities, and raise it above its ordinary value to an extent only limited by the nature of the particular causes which operate upon it. This is what is properly called accommodation land. Land in the neighbourhood of a large town, desirable in small quantities to the inhabitants, for the acquirement of which great competition usually exists, partakes of this character; as does also land adjoining, but not belonging to a gentleman's residence, the renting of which will afford him pleasureable amusement, or the means of removing or preventing a nuisance; and many other cases, too numerous to mention, but which will at once suggest themselves to every man of business. It will be obvious that the value of this description of land, depends upon circumstances wholly beyond the rules which regulate the worth of ordinary estates. And it will be equally manifest that no defined directions can be given for estimating this extra value, which can be alone arrived at by a full consideration of all the attendant circumstances. Wood Lands occasionally perplex the valuation of an estate. If the tenant has the liberty of using the lands in his occupation as may be most conducive to his own interest, the value of mere coppice lands, by which I mean lands growing underwood, is manifestly in accordance with the agricultural character of the soil VALUATION OF ESTATES. 587 and subsoil; and for this reason-a valuation should always re- present the worth of an estate at the time it is made according to its natural capabilities under liberal and judicious treatment; there- fore, it should be assumed, that whatever the mode of cultivation might be, it is such as has been found by experience to conduce most largely in conjunction with local circumstances to the advantage of the occupier. On the other hand, if a valuer is exercising his profession for the purpose of estimating the rent of a farm upon which the tenant is bound to maintain all existing coppices and underwoods, either as preserves for game, or for other purposes over which he has no control, then, although the intrinsic value of the land remains the same, and should be so reported, still a greater rent cannot be charged the tenant than he can be enabled to pay out of the pro- ceeds of the sale of the underwood, after defraying the whole of the expenses attending its cultivation and conversion, a proper interest for the use of his capital, and a fair remuneration to himself for his superintendence; and if the worth of the underwood when con- verted is not sufficient to meet these demands, then a sufficient sum must be deducted from the rent of the remaining lands to make up the deficiency, as it is manifestly in strict accordance with justice and equity that the landlord should alone suffer from a cause which he only is instrumental in perpetuating. Wood lands, properly speaking, that is to say, lands growing timber trees, can only be estimated by the value of the timber they are capable of producing after a certain number of years' growth. A very small annual value sometimes attaches to wood lands offering pasture to cattle, but no general rule can be laid down for its computation. Before I conclude this portion of my subject, it will be proper to observe, with reference to the cost of labour upon a farm, that the interest of an agricultural peasant in the land he cultivates must al- ways be such as will afford him a maintenance, to whatever fluctua- tions the landlord's and tenant's interests therein may be nevertheless subjected. Both the proprietor and the occupier may be possessed of means that will enable them to speculate upon the future pros- pects of their respective positions, and to agree upon some arrange- ment that may exist between them throughout the continuance of a long lease; but the labourer of necessity can become no party to such a contract. The daily wants of himself and family are the same continually, partaking only of a pecuniary character, inas- much as his requirements consist of a sufficiency of the necessities of life to enable him to conduct and carry on his humble avoca- 588 VALUATION OF ESTATES. tions with comfort to himself and satisfaction to those for whose advantage he is toiling, and who are in consequence equally in- terested in his prosperity. Therefore, in considering the cost of labour, the rate of wages is a primary consideration, and no method seems better calculated to ensure the proper fulfilment of this desideratum, than the method of valuing I have endeavoured to explain, that takes for its basis an estimate of all the items in bushels of wheat, inasmuch as it affords to the labourer a uniform amount of bread-stuff for the sus- tenance of his family irrespective of fluctuations in price. THE PURCHASE VALUE OF ESTATES. Having arrived at the annual rent which land is fairly worth to a tenant, if we deduct the amount of landlord's out-goings and bur- thens to which it is subject, we obtain a clear income or net an- nuity in perpetuity to the possessor, the value of which in fee simple it is very easy to determine. It is customary to assume that freehold land is worth 30 years' purchase, but its exact value must of course depend upon the worth of other good securities at the same time. The following Tables will be found to contain all the information and assistance that can be required in reducing the net annual rental of an estate to its purchase value, whether it be freehold (equal to an annuity in perpetuity,) or leasehold of any denomination. VALUATION OF ESTATES. 589 A Table 1. Showing the NUMBER OF YEARS' PURCHASE upon the Net Rental required to return a given Rate of Interest. Rate of Interest per Centum per Annum. Number of Years' Purchase on the net Rental. 2 50 44.4 40 23030 36.3 3 33.3 31 30.7 31/1 28.5 26.6 4 25 44 23.25 22.2 21 5 6 LO LO LO LO CO CÓ CONT778 20 19 51 18.1 52 17.4 6 16.6 16 15.4 14.8 14.2 71 13.7 13.3 12.9 12.5 EXAMPLE. 1. An Estate required to pay 4 per cent. interest must be purchased at 22.2 years. EXAMPLE 2. An Estate purchased at 30.7 years' purchase pays 31 per cent interest. 590 VALUATION OF ESTATES. Table 2. Showing the PRESENT WORTH of an ESTATE, LEASE, or ANNUITY, for any number of years certain and in perpetuity, a t the several rates of Interest which a purchaser may thereby make o f his money. Note.-The rate of Interest shown in this Table is that which a purchaser may make of his money, and get back his Capital, provided he can re-invest his money at the same rate of Interest. Years Purchase at Years Purchase at 3 4 5 Term of 6 Years. per cent. per cent. per cent. per cent. 8 9 ↑ 10 per cent. per cent. per cent. per cent. .5 .5 .5 .5 1. 1. 1. .9 1 .9 is ir .5 .5 .5 .5 .9 .9 .9 1.4 1.4 1.4 1.4 11 1.4 1.4 1.3 1.3 1.9 1.9 $1.9 1.8 1.8 1.8 1.8 1.7 2.4 2.3 2.3 2.3 23/ 2.2 2.2 2.2 2.1 2.8 2.8 2.7 2.7 2.6 3.3 3.2 3.1 3.1 3호 3. ai ai 2.6 2.5 2.5 3. 2.9 2.8 3.7 3.6 3.5 3.5 4 3.4 3.3 3.2 3.2 4.2 4. 3.9 3.8 3.7 3.7 3.6 3.5 4.6 4.5 4.3 4.2 cr 4.1 4. 3.9 3.8 5. 4.9 4.7 4.6 5-1/2 4.4 4.3 4.2 4.1 5.4 5.2 5.1 5. 6 CO 4.8 4.6 4.5 4.4 5.8 5.6 5.4 5.3 61/1 5.1 4.9 4.8 4.6 6.2 6. 5.8 5.6 6.6 6.4 6.1 5.9 7. 6.7 6.5 6.2 778 5.4 5.2 5. 4.9 7호 5.7 5.5 5.3 5.1 6. 5.7 5.5 5.3 7.4 7.1 6.8 6.5 8호 6.2 6. 5.8 5.6 7.8 7.4 7.1 6.8 9 6.5 6.2 6. 5.8 8.2 7.8 7.4 7.1 91 6.8 6.5 6.2 6. 8.5 8.1 7.7 7.4 10 7. 6.7 6.4 6.1 8.9 8.4 8. 7.6 101 7.3 6.9 6.6 6.3 9.2 8.8 8.3 7.9 11 7.5 7.1 6.8 6.5 9.6 9.1 8.6 8.1 111 7.7 7.3 7. 6.7 9.9 9.4 8.9 8.4 12 7.9 7.5 7.2 6.8 10.3 9.7 9.1 8.6 121 8.2 7.7 7.3 7. 10.6 10. 9.4 8.9 13 8.4 7.9 7.5 7.1 11. 10.3 9.6 9.1 131/1 8.6 8.1 7.6 7.2 11.3 10.6 9.9 9.3 14 8.7 8.2 7.8 7.4 11.6 10.8 10.1 9.5 14 8.9 8.4 7.9 7.5 11.9 11.1 10.4 9.7 15 9.1 8.6 8.1 7.6 12.2 11.4 10.6 9.9 151 9.3 8.7 8.2 7.7 12.6 11.7 10.8 10.1 16 9.4 8.9 8.3 7.8 12.9 11.9 11.1 10.3 13.2 12.2 11.3 10.5 13.5 12.4 11.5 10.7 13.7 12.7 11.7 10.8 161 9.6 9. 8.4 7.9 17 9.8 9.1 8.5 8. 171 9.9 9.2 8.7 8.1 18 10.1 9.4 8.8 8.2 EXAMPLE. A Lease for seven years to make 5 per cent. is worth in present money 5.8 years' purchase. If it is required to make 6 per cent. it will only be worth 5.6 years' purchase. Again, a Lease for fourteen years that can be purchased for 8.2 years' purchase will pay 8 per cent. and get back the principal. VALUATION OF ESTATES. 591 Table 2. Showing the PRESENT WORTH of an ESTATE, LEASE, or ANNUITY, for any number of years certain and in perpetuity, at the several rates of Interest which a purchaser may thereby make of his money. Note. The rate of Interest shown in this Table is that which a purchaser may make of his money, and get back his Capital, provided he can re-invest his money at the same rate of Interest. 3 Years Purchase at 4 5 per cent. per cent. per cent. per cent. Years Purchase at Term of 6 7 Years. 8 9 per cent. per cent. per cent. per cent. 10 14. 12.9 11.9 14.3 13.1 12.1 11. 18/1/ 10.2 9.5 8.9 8.3 11.2 19 10.3 9.6 8.9 8.4 14.6 13.4 12.3 11.3 193 10.5 9.7 9. 8.4 14.9 13.6 12.5 11.5 20 10.6 9.8 9.1 8.5 15.1 13.8 12.6 11.6 201 10.7 9.9 9.2 8.6 15.4 14. 12.8 11.8 21 10.8 10. 9.3 8.6 15.7 14.2 13. 11.9 211 10.9 10.1 9.4 8.7 15.9 14.5 13.2 12. 22 11.1 10.2 9.4 8.8 16.2 14.7 13.3 12.2 221/ 11.2 10.3 9.5 8.8 16.4 14.9 13.5 12.3 23 11.3 10.4 9.6 8.9 16.7 15.1 13.6 12.4 231 11.4 10.5 9.6 8.9 16.9 15.2 13.8 12.5 24 11.5 10.5 9.7 9. 17.2 15.4 13.9 12.7 243 11.6 10.6 9.8 9. 17.4 15.6 14.1 12.8 25 11.7 10.7 9.8 9.1 17.6 15.8 14.2 12.9 253 11.7 10.7 9.9 9.1 17.9 16. 14.4 13. 26 11.8 10.8 9.9 9.2 18.1 16.2 14.5 13.1 261 11.9 10.9 10. 9.2 18.3 16.3 14.6 13.2 27 12. 10.9 10. 9.2 18.5 16.5 14.8 13.3 271 12.1 11. 10.1 9.3 18.8 19. 16.8 15. 19.2 17. 15.1 13.6 19.4 17.1 15.3 19.6 19.8 17.4 15.5 16.7 14.9 13.4 28 12.1 11.1 10.1 9.3 13.5 281 12.2 11.1 10.2 9.3 29 12.3 11.2 10.2 9.4 13.7 291 12.3 11.2 10.2 9.4 17.3 15.4 13.8 30 12.4 11.3 10.3 9.4 13.8 30 12.5 11.3 10.3 9.5 20. 17.6 15.6 13.9 31 12.5 11.3 10.3 9.5 20.2 17.7 15.7 14. 311 12.6 11.4 10.4 9.5 20.4 17.9 15.8 14.1 32 12.6 11.4 10.4 9.5 20.6 18. 15.9 14.2 321 12.7 11.5 20.8 18.1 16. 14.2 33 12.8 20.9 18.3 16.1 14.3 331 10.4 9.5 11.5 10.5 9.6 12.8 11.6 10.5 9.6 21.1 18.4 16.2 14.4 34 12.9 11.6 10.5 9.6 21.3 18.5 16.3 14.4 341 12.9 11.6 10.5 9.6 21.5 18.7 16.4 14.5 35 12.9 11.7 10.6 9.6 21.7 18.8 16.5 14.6 21.8 18.9 16.5 14.6 351 13. 11.7 10.6 9.7 36 13. 11.7 10.6 9.7 EXAMPLE.—A Lease for 21 years to pay 4 per cent and get back the principal is worth in present money 14 years' purchase. To pay 5 per cent. the same Lease is worth 12.8 years' purchase. To pay 7 per cent. 10.8 years' purchase, &c. 592 VALUATION OF ESTATES. Table 2. Showing the PRESENT WORTH of an ESTATE, LEASE, or ANNUITY, for any number of years certain and in perpetuity, at the several rates of Interest which a purchaser may thereby make of his money. Note.-The rate of Interest shown in this Table is that which a purchaser may make of his money, and get back his Capital, provided he can re-invest at the same rate. Years Purchase at Years Purchase at 3 4 5 6 Term of Years. 7 8 9 10 per cent. per cent. per cent. per cent. cent.per per cent. per cent. per cent. per cent. 22.2 19.1 16.7 14.7 37 13.1 11.8 10.7 9.7 22.5 19.4 16.9 22.8 19.6 23.1 19.8 14.8 38 13.2 11.8 10.7 9.7 17. 14.9 39 13.3 11.9 10.7 9.8 17.2 15. 40 13.3 11.9 10.8 9.8 23.4 20. 17.3 15.1 41 13.4 12. 10.8 9.8 23.7 20.2 17.4 15.2 42 13.5 12. 10.8 9.8 24. 20.4 17.5 15.3 43 13.5 12. 10.8 9.8 24.3 20.5 17.7 15.4 44 13.6 12.1 10.9 9.8 24.5 20.7 17.8 15.5 45 13.6 12.1 10.9 9.9 24.8 20.9 17.9 15.5 46 13.6 12.1 10.9 9.9 25. 21. 18. 15.6 47 13.7 12.2 10.9 9.9 25.3 21.2 18.1 15.6 48 13.7 12.2 10.9 9.9 25.5 21.3 18.2 15.7 49 13.8 12.2 10.9 9.9 25.7 26. 21.6 18.3 21.5 18.3 15.8 50 13.8 12.2 11. 9.9 15.8 51 13.8 12.3 11. 9.9 26.2 21.7 18.4 15.9 52 13.9 12.3 11. 9.9 26.4 21.9 18.5 15.9 53 13.9 12.3 11. 9.9 26.6 22. 18.6 15.9 54 13.9 12.3 11. 9.9 26.8 22.1 18.6 16. 55 13.9 12.3 11. 9.9 27. 22.2 18.7 16. 56 14. 12.3 11. 10. 27.2 22.3 18.8 16. 57 14. 12.3 11. 10. 27.3 22.4 18.8 16.1 58 14. 12.4 11. 10. 27.5 22.5 18.9 16.1 59 14. 12.4 11. 10. 27.7 22.6 18.9 16.1 60 14. 12.4 11. 10. 27.8 22.7 19.1 16.2 61 14. 12.4 11. 10. 28. 22.8 19. 16.2 62 14.1 12.4 11.1 10. 28.1 22.9 19.1 16.2 63 14.1 12.4 11.1 10. 28.3 23. 19.1 16.3 64 28.5 23. 19.2 16.3 65 14.1 12.4 11.1 10. 14.1 12.4 11.1 10. 28.6 28.7 23.1 19.2 23.2 16.3 66 14.1 12.4 11.1 10. 19.2 16.3 67 28.9 23.3 19.3 16.3 68 14.1 12.4 11.1 10. 14.1 12.4 11.1 10. 29. 23.3 19.3 16.4 69 14.1 29.1 23.4 19.3 16.4 70 12.4 11.1 10 14.2 12.4 11.1 10 29.2 23.4 19.4 16.4 29.3 23.5 19.4 16.4 2223 71 14.2 12.4 11.1 10 72 14.2 12.4 11.1 10. EXAMPLE.—An Estate held for sixty years to get back principal and interest is. worth in present money: If 3 per Cent. Interest is required • 27.7 years' purchase 4 22.€ " 10 5 18.9 "" 35 16.1 VALUATION OF ESTATES. 593 Table 2. Showing the PRESENT WORTH of an ESTATE, LEASE, or ANNUITY, for any number of years certain and in perpetuity, at the several rates of Interest which a purchaser may thereby make of his money. Note.-The rate of Interest shown in this Table is that which a purchaser may make of his money, and get back his Capital, provided he can re-invest at the same rate. 3 Years Purchase at 4 5 6 Term of Years. Years Purchase at 8 9 10 per cent. per cent. per cent. per cent. 29.5 23.6 19.4 16.4 29.6 23.6 19.5 16.4 29.7 23.7 19.5 16.4 29.8 23.7 19.5 16.5 29.9 23.8 19.5 16.5 30. 30.1 23.9 23.8 19.5 16.5 19.6 16.5 30.2 23.9 19.6 16.5 8IILIAFI per cent. per cent. per cent. per cent. 14.2 12.4 11.1 10. 14.2 12.5 11.1 10. 75 14.2 76 14.2 12.5 12.5 11.1 10. 10. 11.1 77 14.2 12.5 11.1 10. 14.2 12.5 11.1 10. 14.2 12.5 11.1 10. 80 14.2 12.5 11.1 10. 30.3 24. 19.6 16.5 81 14.2 12.5 11.1 10. 30.4 24. 19.6 16.5 82 14.2 12.5 11.1 10. 30.5 24. 19.6 16.5 83 14.2 12.5 11.1 10. 30.6 24.1 19.7 16.5 84 14.2 12.5 11.1 10. 30.6 24.1 19.7 16.5 85 14.2 12.5 11.1 10. 30.7 24.1 19.7 16.5 86 14.2 12.5 11.1 10. 30.8 24.2 19.7 16.6 87 14.2 12.5 11.1 10. 30.9 24.2 19.7 16.6 88 14.2 12.5 11.1 10. 30.9 24.2 19.7 16.6 89 14.2 12.5 11.1 10. 31. 24.3 19.7 16.6 90 14.2 12.5 11.1 10. 31.1 24.3 19.8 16.6 91 14.2 12.5 11.1 10. 31.1 24.3 19.8 16.6 92 14.3 12.5 11.1 10. 31.2 24.3 19.8 16.6 93 14.3 12.5 11.1 10. 31.3 24.4 19.8 16.6 94 14.3 12.5 11.1 10. 31.3 24.4 19.8 16.6 95 14.3 12.5 11.1 10. 31.4 24.4 19.8 16.6 96 14.3 12.5 11.1 10. 31.4 24.4 19.8 16.6 97 14.3 12.5 11.1 10. 31.5 24.5 19.8 16.6 98 14.3 12.5 11.1 10. 31.5 24.5 19.8 16.6 31.6 24.5 19.8 16.6 99 14.3 12.5 11.1 10. 100 14.3 12.5 11.1 10. 33.3 25. 20. 16.7 Perpetuity 14.3 12.5 11.1 10. EXAMPLE.—A Lease for ninety-nine years to pay 7 per cent., and get back the principal, is worth 14.3 years' purchase. The Fee Simple of a Freehold Estate to pay 5 per cent. is worth 20 years' pur- chase or to pay 3 per cent., 33.3 years' purchase. 594 VALUATION OF ESTATES. Table 3. PRESENT WORTH of Property held on a single life, as of a person in possession of a LIVING or BENEFICE, or the holder of a LEÃSE, ESTATE, or ANNUITY, according to the Northampton Table of Mortality. * Note. The rate of Interest shown in this Table is that which a purchaser can make of his money, and get back his Capital, provided he can re-invest at the same rate. Years Purchase at Years Purchase at Age of 3 4 5 6 7 8 the Life. per cent. per cent. per cent. per cent. per cent. per cent. 16. 13.5 11.6 1 10.1 9. 8. 18.6 15.6 13.4 2 11.7 10.4 9.3 19.6 16.5 14.1 3 12.3 10.9 9.8 20.2 17.0 14.6 4 12.8 11.3 10.1 20.5 17.2 14.8 5 13. 11.5 10.3 20.7 17.5 15. 6 13.2 11.7 10.5 20.9 17.6 15.2 7 13.3 11.8 10.6 20.9 17.7 15.2 8 13.3 11.8 10.6 20.8 17.6 15.2 9 13.3 11.8 10.6 20.7 17.5 15.1 10 13.3 11.8 10.6 20.5 17.4 15. 11 13.2 11.8 10.6 20.3 17.3 14.9 12 13.1 11.7 10.5 20.1 17.1 14.8 13 13. 11.6 10.5 19.9 16.9 14.7 14 13. 11.5 10.4 19.7 16.8 14.6 15 12.9 11.5 10.3 19.4 16.6 14.5 16 12.8 11.4 10.3 19.2 16.5 14.3 17 12.7 11.3 10.2 19. 16.3 14.2 18 12.6 11.2 10.1 18.8 16.2 14.1 19 12.5 11.2 10.1 18.6 16. 14. 20 12.4 11.1 10. 18.5 15.9 13.9 21 12.3 11. 10. 18.3 15.8 13.8 22 12.3 11. 9.9 18.1 15.7 13.7 23 12.2 10.9 9.9 18. 15.6 13.7 24 12.1 10.9 9.9 17.8 15.4 13.6 25 12.1 10.8 9.8 17.6 15.3 13.5 26 12. 10.8 9.8 17.5 15.2 13.4 27 11.9 10.7 9.7 17.3 15.1 13.3 28 11.8 10.7 9.7 17.1 14.9 13.2 29 11.8 10.6 9.6 16.9 14.8 13.1 30 11.7 10.5 9.6 16.7 14.6 13. 31 11.6 10.5 9.5 16.5 14.5 12.9 32 11.5 10.4 9.5 16.3 14.3 12.7 33 11.4 10.3 9.4 16.1 14.2 12.6 34 11.3 10.3 9.4 15.9 14. 12.5 35 11.2 10.2 9.3 15.7 13.9 12.4 36 11.1 10.1 9.2 EXAMPLE. An Estate, Annuity, or a Lease, held on a single life aged 29, to make 4 per cent, and to get back the Principal, is worth 14.9 years purchase. To make 5 per cent. it would be 13.2 years' Purchase The Carlisle Tables of Mortality are the most favorable to the seller of Lifehold Estates, and the London the most favorable to the purchaser. The Northampton Tables as the mean may perhaps be considered the most equitable. VALUATION OF ESTATES. 595 Table 3 continued. PRESENT WORTH of PROPERTY held on a single life, as of a person in possession of a LIVING or BENEFICE, or the holder of a LEASE, ESTATE, or ANNUITY, according to the Northampton Table of Mortality. Note.-The rate of Interest shown in this Table is that which a purchaser may make of his money, and get back the Principal, provided he can re-invest at the same rate. Years Purchase at Years Purchase at Age of 3 4 5 6 17 8 the Life. per cent. per cent. per cent. per cent. per cent. per cent. 15.5 13.7 12.2 37 11. 10. 9.2 15.3 13.5 12.1 38 10.9 9.9 9.1 15.1 13.4 12. 39 10.8 9.8 9. 14.8 13.2 11.8 40 10.7 9.8 8.9 14.6 13. 11.7 41 10.6 9.7 8.9 14.4 12.8 11.6 42 10.5 9.6 8.8 14.2 12.7 11.4 43 10.4 9.5 8.7 13.9 12.5 11.3 44 10.2 9.4 8.6 13.7 12.3 11.1 45 10.1 9.3 8.5 13.4 12.1 10.9 46 10. 9.2 8.4 13.2 11.9 10.8 47 9.8 9. 8.3 13. 11.7 10.6 48 9.7 8.9 8.2 12.7 11.5 10.4 49 9.6 8.8 8.1 12.4 11.3 10.3 50 9.4 8.7 8. 12.2 11.1 10.1 51 9.3 8.6 7.9 11.9 10.8 9.9 52 9.1 8.4 7.8 11.7 10.6 9.7 53 9. 8.3 7.7 11.4 10.4 9.6 54 8.8 8.2 7.6 10.9 10. 9.2 56 8.5 7.9 7.4 10.3 9.5 8.8 58 8.2 7.6 7.1 9.8 9. 8.4 60 7.8 7.3 6.9 9.2 8.5 8. 62 7.4 7. 6.6 8.6 8. 7.5 64 7.1 6.6 6.3 8. 77.5 7.4 6.9 6.7 6.4 6.1 5.8 5.5 5.2 4.9 4.7 4.4 4.2 3.8 3.6 3.2 3.1 2.8 2.7 ZÓW ti ti að aɔ ci 7. 66 6.6 6.3 5.9 6.5 68 6.2 5.9 5.6 6. 70 5.7 5.4 5.2 5.5 72 5.2 5. 4.8 5. 74 4.8 4.6 4.4 4.5 76 4.3 4.2 4.0 4. 78 3.9 3.7 3.6 3.5 80 3.4 3.3 3.2 3. 82 2.9 2.8 2.8 2.6 84 2.6 2.5 2.4 2.5 2.4 2.3 86 2.3 2.2 2.2 2.2 2.1 2.1 88 2. 2. 1.9 1.8 1.8 1.7 90 1.7 1.7 1.6 EXAMPLE. An Estate, Annuity, or a Lease, held on a single life aged 50, to make 3 per cent. and to get back the Principal, is worth 12.4, years' purchase. To make 4 per cent. it would be 11.3 years' purchase. The next presentation to a living being vacant is to be considered as a Lifehold at 5 per cent. All annual charges, of whatever kind (including that of a Curate,) must be deducted from the gross income to find the net annual income. 596 VALUATION OF ESTATES. Table 4. PRESENT WORTH of Property held on a single life, as of a person in possession of a LIVING or BENEFICE, or the holder of a LEASE, ESTATE, or ANNUITY, according to the Carlisle Table of Mortality. Note.-The rate of Interest shown in this Table is that which a Purchaser may make of his money, and get back his Principal, provided he can re-invest at the same rate. Years Purchase at Years Purchase at 3 4 5 Age of the Life. 6 7 8 per cent. per cent. per cent. per cent. per cent. per cent. 20.1 16.6 14. 21.5 17.7 15. 22.7 18.7 15.8 23.3 19.2 16.3 23.7 19.6 16.6 23.8 19.7 16.7 23.9 19.8 16.8 123 LO CON 12.1 10.6 9.4 12.9 11.3 10.1 13.7 12. 10.7 4 14. 12.3 11. 5 14.3 12.6 11.2 6 14.5 12.7 11.3 7 14.5 12.8 11.4 23.8 19.8 16.8 8 14.5 12.8 11.4 23.7 19.7 16.7 9 14.5 12.8 11.4 23.5 19.6 16.7 10 14.4 12.7 11.3 23.3 19.5 16.6 11 14.4 12.7 11.3 23.1 19.3 16.5 12 14.3 12.6 11.3 23. 19.2 16.4 13 14.3 12.6 11.2 22.8 19.1 16.3 14 14.2 12.5 11.2 22.6 19. 16.2 15 14.1 12.5 11.1 22.4 18.8 16.1 16 14.1 12.4 11.1 22.2 18.7 16.1 17 14. 12.4 11.1 22.1 18.6 16. 18 14. 12.3 11.1 21.9 18.5 15.9 19 13.9 12.3 11. 21.7 18.4 15.8 20 13.8 12.3 11. 21.5 18.2 15.7 21 13.8 12.2 10.9 21.3 18.1 15.6 22 13.7 12.2 10.9 21.1 18. 15.5 23 13.6 12.1 10.9 20.9 17.8 15.4 24 13.5 12. 10.8 20.7 17.6 15.3 25 13.5 12. 10.8 20.4 17.5 15.2 26 13.4 11.9 10.7 20.2 17.3 15.1 27 13.3 11.8 10.7 20. 17.2 14.9 28 13.2 11.8 10.6 19.8 17. 14.8 29 13.1 11.7 10.5 19.6 16.9 14.7 30 13. 11.6 10.5 19.3 16.7 14.6 19.1 16.6 14.5 32 18.9 16.4 14.4 33 18.7 16.2 14.3 18.4 16. 14.1 18.2 15.9 14. 22828 12.9 11.6 10.5 12.9 11.5 10.4 12.8 11.4 10.4 34 12.7 11.4 10.3 35 12.6 11.3 10.2 36 12.5 11.2 10.2 EXAMPLE. An Estate, Annuity, or a Lease held on a single life aged 29, to make 4 per cent. and get back the Principal, is worth 17 years' purchase. To make 5 per cent., 14.8 years' purchase. VALUATION OF ESTATES. 597 Table 4 continued. PRESENT WORTH of Property held on a single life, as of a person in possession of a LIVING or BENEFICE, or the holder of a LEASE, ESTATE, or ANNUITY, according to the Carlisle Table of Mortality. Note.-The rate of Interest shown in this Table is that which a Purchaser can make of his money, and get back his Capital, provided he can re-invest at the same rate. Years Purchase at Years Purchase at 3 4 5 Age of the Life. 6 17 8 per cent. per cent. per cent. per cent. per cent. per cent. 17.9 15.7 13.8 37 12.4 11.1 10.1 17.7 15.5 13.7 38 12.2 11. 10. 17.4 15.3 13.5 39 12.1 10.9 9.9 17.1 15.1 13.4 40 12. 10.8 9.9 16.9 14.9 13.2 41 11.9 10.8 9.8 16.6 14.7 13.1 42 11.8 10.7 9.7 16.4 14.5 13. 43 11.7 10.6 9.7 16.1 14.3 12.8 44 11.6 10.5 9.6 15.9 14.1 12.6 45 11.4 10.4 9.5 15.6 13.9 12.5 46 11.3 10.3 9.4 15.3 13.7 12.3 47 11.2 10.2 9.3 15. 13.4 12.1 48 11. 10.1 9.2 14.7 13.2 11.9 49 10.8 9.9 9.1 14.3 12.9 11.7 50 10.6 9.7 9. 13.9 12.6 11.4 51 10.4 9.6 8.8 13.6 12.3 11.2 52 10.2 9.4 13.2 11.9 10.9 53 10. 9.2 12.8 11.6 10.6 54 9.8 9. 12. 11. 10.1 56 9.3 8.6 ∞ ∞ ∞ ∞Ó 8.7 8.5 8.4 75+ 8. 11.2 10.3 9.5 58 8.8 8.2 7.6 10.5 9.7 8.9 60 8.3 7.7 7.2 9.9 9.1 8.5 62 7.9 7.4 6.9 9.2 8.6 8. 64 7.5 7. 6.6 8.6 8. 7.5 66 7. 6.6 6.3 7.9 7.4 6.9 68 6.5 6.2 5.9 7.1 6.7 6.3 70 6. 5.7 5.4 6.4 6. 5.7 72 5.4 5.2 4.9 5.8 5.5 5.2 74 4.9 4.7 4.5 5.3 5. 4.8 76 4.6 4.4 4.2 4.8 4.6 4.4 78 4.2 4.1 3.9 4.4 4.2 4. 80 3.9 3.7 3.6 3.9 3.7 3.6 82 3.5 3.3 3.2 84 mai ai 3. 2.9 2.8 86 2.8 2.5 - ∞ 2.7 2.6 88 2.4 2.3 90 ∞ ∞ ai ci ai 3.5 3.4 3.2 3.1 3. 2.9 2.7 2.7 2.6 2.5 2.4 2.4 2.3 2.2 2.1 EXAMPLE. An Estate, Annuity, or a Lease held on a single life aged 50, to make 3 per cent. and get back the Principal, is worth 14.3 years' purchase. To make 4 per cent., 12.9 years' purchase. Note.-It will be observed that the Carlisle Table of Mortality is more favor- able than the Northampton, and may be used accordingly on healthy lives. 598 VALUATION OF ESTATES. Table 5. PRESENT WORTH of an ESTATE, ANNUITY, or a LEASE held on Two Joint Lives, according to the Northampton Table of Mortality. Note.-The Rate of Interest shown in this Table is that which a purchaser may make of his money, and get back his Principal, provided he can re-invest at the same rate. Years Purchase at Years Purchase at 3 4 Ages. 5 6 per cent. per cent. per cent. per cent. 16.34 14.28 10 10 12.66 11.34 15.15 13.36 10 20 11.91 10.72 14.15 12.59 10 30 11.30 10.24 12.79 11.51 10 40 10.44 9.54 11.04 10.08 10 50 9.26 8.55 8.95 8.31 10 60 7.75 7.25 6.35 6.01 10 70 5.70 5.42 3.65 3.52 10 80 3.39 3.28 14.13 12.53 20 20 11.23 10.16 13.29 11.87 20 30 10.71 9.73 12.10 10.92 20 40 9.94 9.10 20.52 9.63 20 50 8.86 8.19 8.60 8.00 20 60 7.46 6.99 6.15 5.83 20 70 5.53 5.26 3.57 3.44 20 80 3.32 3.21 12.59 11.31 30 30 10.25 9.36 11.57 10.49 30 40 9.58 8.79 10.16 9.32 30 50 8.60 7.97 8.38 7.80 30 60 7.29 6.84 6.04 5.73 30 70 5.44 5.18 3.53 3.41 30 80 3.29 3.18 10.76 9.82 40 40 9.02 8.32 9.59 8.83 40 50 8.18 7.60 8.02 7.49 40 60 7.01 6.59 5.87 5.57 40 3.47 3.35 40 8.71 8.08 50 7.46 6.99 50 5.58 5.30 50 3.36 3.25 50 6.61 6.23 60 5.14 4.90 60 3.20 3.09 60 4.26 4.09 70 | | | | | | | | | | 70 5.30 5.05 80 3.24 3.13 50 7.52 7.03 60 6.57 6.19 70 5.05 4.82 80 3.14 3.04 8282 60 5.89 5.58 70 4.68 4.48 80 2.99 2.90 70 3.93 3.78 EXAMPLE.-An Estate, Annuity, or a Lease held on Two Joint Lives, aged 40 and 50 years, which is to be determined on the death of either, to make 3 per cent. and get back the Principal, is worth 9.59 years' purchase. To make 4 per cent. it is worth 8.83 years' purchase. Ages of the Lives. 5 5 10 5 5 25.3 20.9 5 15 24.7 20.6 5 25 24.0 20.0 5 35 23.3 19.6| 45|| 22.6 19.0 5 55 21.9 18.5 65|| 21.3 18.0 -75 20.9 17.7 10 25.0 20.8 10 20 24.1 20.2| 10 30 23.4 19.7 10 40 22.7 19.2 10 50 22.1 18.7| 10 60 21.5 18.2 10 70 21.0 17.9 15.5 10 80 20.8 17.6| 15.3| 13.4|40 VALUATION OF ESTATES. 599 Table 6. Showing the PRESENT VALUE of an ESTATE, AN- NUITY, or a LEASE, held on the longest of Two Lives, calculated according to the Northampton Table of Mortality. Note. The rate of interest shewn in this Table is that which a purchaser may make of his money, and get back his Capital, provided he can re-invest at the same rate. 10 40 or er er Years Purchase at 5 3 4 6 p. cent. p. cent. p. cent. p. cent. Ages of the Lives. Years Purchase at 4 5 6 3 p. cent. p. cent. p. cent. p. cent. 15.3 13.6 13.1 12.7 17.7 15.3 25 65|| 18.7 16.3| 14.3| 12.7 17.5 15.1 25 — 75|| 18.2 15.8 75 18.2 15.8 13.9 | 12.4 17.1| 14.9|30-30|| 20.3| 18.2 30 20.3 18.2 15.9 14.0 16.8| 14.6|30-40|| 20.2 | 17.5 40 20.2 17.5 16.4| 14.3 30 50 19.2 16.7 14.7 16.0 13.9 30. 60 18.3 16.0 14.2 15.6| 13.6|30 70 17.6 15.4 13.7 12.2 15.2 13.3 30 17.6| 15-2| 35 80 17.2 15.0| 13.3| 11.9 35 20.1 17.5 15.3 13.6 17.2| 15.0 | 35 45 19.0 16.6 14.7 13.1 16.9 14.7 35 55 18.0 15.8 14.0 12.5 16.5 14.5 35 65 17.1 17.1 15.0 13.4 12.0 16.1| 14.2 | 35 75 16.4 14.5 12.9 11.6 15.8 13.9 40 40 18.9 16.6 14.7 13.1 13.4 40 J 50 17.7 15.6 13.9 12.5 15.3 13.4 40 15 15| 24.0 20.2| 17.2 14.9 40 60 16.6 14.7 13.2 70 15.7 14.0 12.6 11.4 11.9 15 25|| 23.2 19.6 16.8 14.7 | 40 · 80 15.2 13.5 12.1 11.0 15 35|| 22.4| 19.0 16.4 14.4|45 45 17.6 15.6 13.9 12.5 15 45 21.7 18.5 16.0 15 55 21.0 17.9 15.6 15 65 20.4 17.4 15.2 13.3 45 15 75 19.9 17.1 14.8 13.1 50 20 20 23.1 19.5 16.8 14.6 50 20 30 22.3 18.9 16.4 14.3 50 20 40 21.4 18.3| 15.9 | 14.0|50 20 50 20.6 17.7 15.4 13.6 55 20 60 19.8 17.1 14.9 13.2 55 20 70|| 19.2 16.6| 14.5| 12.91 55 20 80 18.8 16.2 14.2 12.6 60 25 25 22.2 18.9 16.4 14.4 60 25 35 21.3 18.3 15.9 14.0 60 25 45 20.3 17.6| 15.4 13.6 65 25 55 19.5 16.9 14.8 13.170 14.0 45 55 16.3 16.3 14.5 13.1 11.8 13.7 45 65 15.1 13.6 12.3 11.3 75 14.3 12.9 11.6 10.6 55 50 16.2 14.4 13.0 11.8 60 14.8 13.3 12.1 11.0 70 13.6 12.3 11.2 10.3 80 12.9 11.7 10.6 9.8 14.6 13.2 12.0 11.0 65 13.1 12.0 11.0 10.1 75 12.0 11.0 10.1 9.3 710 - 60 12.9 11.9 10.9 10.1 70 11.4 10.5 9.7 9.1 80 10.4 9.6 8.9 8.3 75 9.5 8.9 9.2 8.6 8.4 8.1 7.6 7.8 EXAMPLE. An Estate, Annuity, or a Lease, to be determined at the death of the longest of Two Lives, whose ages are 25 and 35 years; to make 3 per cent. and get back the Principal, is worth 21.3 years' purchase; to make 4 per cent. it is worth 18.3 years' purchase. 600 VALUATION OF ESTATES. Table 77. PRESENT WORTH of an ESTATE, ANNUITY, or a LEASE, held on the longest of Three Lives, according to the Northampton Table of Mortality. Note.-The rate of Interest shewn in this Table is that which a purchaser may make of his money, and get back the Principal, provided he can re-invest at the same rate. Years Purchase at Years Purchase at Ages of the Lives. 3 4 5 6 Ages of the Lives. 3 4 5 6 p. cent.p.cent.p.cent.p.cent. p.cent.p.cent. p. cent. p. cent. 10 10 10 26.6 || 10 10 20 || 26.2| 21.9 18.3 15.7 10 40 40 23.7 19.9 17.1 14.9 21.7| 18.3 15.7 10 40 50 23.1 19.6 16.8 14.7 10 10 30 25.8 10 10 40|| 25.4 21.4 18.0 15.6 10 40 60 22.9 19.4 16.7 14.6 21.1 17.9 15.5 10 40 70 22.7 19.1 19.1 16.5 14.4 10 10 50 25.3 20.8 17.7 15.3 10 45 45|| 23.3 19.5 16.8 14.7 10 10 60 10 10 70 25.0 20.8 17.6| 15.2 10 45 55 22.6 19.2 16.6 14.6 25.0 25.0 20.8 17.6 20.8 17.6 15.2 15.2 10 45 65 10 45 65|| 22.5 19.0 16.4 14.5 10 20 20 25.7 | 21.3 | 18.1 15.510 45 75 22.2 18.8 16.2 14.2 10 20 30 25.1 21.0 17.8 15.4 10 50 50 22.6 19.2 16.6| 14.5 10 20 40 24.6 20.6 17.6 15.2 10 50 60 22.2 18.9 16.3 14.3 10 20 50 24.5 20.4 17.4 15.1 10 50 70 22.0 18.7 16.1 14.1 10 20 60 24.3 20.3| 17.4 15.1 10 55 55 22.3 19.0 16.4 14.2 10 20 70 24.1 20.1 17.2 14.9 10 55 65 21.8 18.5 16.0 14.1 10 25 25 25.1 20.9 17.8 15.5 10 55 75 15.5 10 55 75 21.8 18.5 16.0 14.1 10 25 35 24.6 20.6 17.6 15.2 10 60 60 22.0 18.7 15.9 14.0 10 25 45 24.4 20.5 17.4 15.1 10 60 70 21.6 18.4 15.9 14.0 10 25 55 24.1| 20.3 17.2 | 14.9 10 65 65 21.5 18.2 15.8 14.2 10 25 65 23.9 20.1| 17.2 17.2 14.9 10 65 75|| 21.2 18.0 15.6 13.7 10 25 75 23.7 23.7 19.8| 17.0 19.8 17.0 14.7 10 70 70 14.7 10 70 70 || 21.3| 18.1 15.7 13.8 10 30 30 24.8 20.6 17.6 15.3 15 25 25 24.8 20.8 17.7 15.4 10 30 40 24.3 20.3| 17.4 15.1 15 25 35 24.2 20.3 17.4 15.2 10 30 50 23.8 20.0 17.2 15.0 15 25 45 23.9 20.2 17.2 15.0 10 30 60 23.6 19.8 17.0 14.8 10 30 70 23.5 19.7| 16.9 14.8 15 25 55 15 25 65 23.6 19.9 17.1 14.8 23.4 19.7 16.9 14.7 10 35 35 24.2 20.4 17.5 15.1 15 25 75 10 35 45 23.8 19.9 17.1 10 35 55 23.3 19.6 16.9 10 35 65 23.1 19.5 16.8 10 35 75 23.0 19.4 16.7 14.9 15 35 35 14.715 35 45 14.6 15 35 55 14.6 15 35 65 23.1 19.5 16.7 14.6 23.7 20.1 17.1| 15.0 23.3 19.7 16.9 14.8 22.7 19.3 | 16.6 | 14.6 22.5 19.1 16.5 14.5 EXAMPLE. An Estate, Annuity, or a Lease, to determine on the death of the longest of Three Lives, aged 10, 35, and 55 years, to pay 3 per cent. and get back the Principal, is worth 23.3 years' purchase. To make 4 per cent. it is worth 19.6 years' purchase: VALUATION OF ESTATES. 601 Table 7 continued. PRESENT WORTH of an ESTATE, AN- NUITY, or a LEASE, held on the longest of Three Lives, according to the Northampton Table of Mortality. Note. The rate of interest shown in this Table is that which a purchaser may make of his money, and get back the Principal, provided he can re-invest at the same rate. Years Purchase at Years Purchase at Ages of the Lives. 3 4 5 6 p.cent.p.cent.p.cent.p.cent. Ages of the Lives. 3 4 5 6 p.cent.p.cent.p.cent.p.cent. 15 35 75 15 45 45 15 45 55 15 45 65 15 45 75 22.4 19.0 16.4 22.7 19.1 16.5 22.0 18.8 16.3 21.8 18.6 16.1 21.5 18.3 15.9 15 55 55 15 55 65 15 55 75 15 65 65 13.9 20 40 70 13.8 20 45 45 15 65 75 20 20 20 21.6 18.5 16.1 21.6 18.5 16.1 21.1 21.1 18.0 15.6 18.0 15.6 21.0 18.0 15.6 20.8 17.8 15.5 20.8 17.8 15.5 20.3 17.4 15.1 25.2 20.8 17.8 25.2 20.8 17.8 19.3 16.7 14.6 22.1 18.9 16.4| 14.4 14.0 20 40 60|| 21.7 18.6| 16.2| 14.2 14.4 20 35 55|| 22.1 14.6 20 35 65|| 21.9 14.3 20 35 75 21.8 21.8 14.2 20 40 40 || 22.8 | 22.8 14.0 20 40 50|| 18.9 16.4| 14.4 18.7 16.2 14.3 18.6 18.6 16.1 14.2 19.3 21.4| 18.3 15.9 14. 22. 18.7 16.3 14.5 13.9 20 45 55|| 21.4 13.4 20 45 65|| 21.1 15.4 20 45 75| 20.8 18.4 16. 14.2 18.1 15.8| 14.1 17.9 15.5 13.8 20 20 30 24.5 20.6 17.6 15.2 20 50 50 || 21.4 18.4| 16. 14.1 20 20 40 23.9 20.2 17.3 23.9 20.2 17.3 15.120 50 60|| 20.9 18. 15.7 13.9 20 20 50 23.7 19.8 17.1 14.9 20 50 70 20.6 20.6 17.7 15.4 13.6 17.7 20 20 60 23.4 19.7 17.0 23.4 19.7 17.0 14.8 20 55 55 20.9 | 18. 15.6 13.8 20 20 70 23.2 19.5 16.8 14.6 20 55 65 20.3| 17.5 20.3 17.5 15.2 13.6 20 25 25 24.4 20.6 17.6 24.4 20.6 17.6 15.3 20 55 75 20.3| 17.3 20.3 17.3 15.2 13.5 20 25 35 23.8 20.1 17.3 15.1 20 60 60|| 20.5 17.7 15.2 | 13.5 20 25 45 23.5 19.9 23.5 19.9 17.0 17.0 14.9 20 60 70 || 20. 17.3 15.1 13.4 20 25 55 23.119.6 23.1 19.6 16.9 16.9 14.7 20 65 65|| 20. 17.2 15.1 13.6 20 25 65 22.9 19.4 22.9 19.4 16.7 16.7 14.6 20 65 75 19.5 16.8 14.7 13.1 20 25 75 22.6 19.1 16.5 14.4 20 70 70 19.6 16.9 14.8 13.1 20 30 30 24.4 20.1 17.3 24.4 20.1 17.3 15.1 30 30 30 || 23.3 | 19.6 17. 14.9 20 30 40 23.8 23.8 19.7 17.0 19.7 17.0 14.9 30 30 40 22.6 20 30 50 22.8 22.8 19.4 16.8 19.4 16.8 14.7 30 30 50 19.2 21.9 18.8 16.4 14.4 16.6 14.6 20 30 60 22.5 22.5 19.1 16.5 19.1 16.5 14.5 30 30 60 21.5 18.5 16.1 14.2 20 30 70 22.4 19.0 16.5 22.4 19.0 16.5 14.4 30 30 70 21.4 18.4 16. 14.1 20 35 35 23.3 19.8 16.9 23.3 19.8 16.9 14.8 30 35 35 22.5 19.3 16.6 14.7 2035 45 22.7 19.4 16.8 14.7 30 35 45 21.8 18.6| 16.2 14.4 EXAMPLE. An Estate, Annuity, or a Lease, to determine on the death of the longest of Three Lives, aged 20, 25, and 55 years; to pay 3 per cent. and get back the Principal, is worth 23.1 years' purchase. To make 4 per cent. it is worth 19.6 years' purchase. 2 P 602 VALUATION OF ESTATES. Table 7 continued. PRESENT WORTH of an ESTATE, AN- NUITY, or a LEASE, held on the longest of Three Lives, according to the Northampton Table of Mortality. Note.-The Rate of Interest shown in this Table is that which a purchaser may make of his money, and get back the Principal, provided he can re-invest at the same rate. Ages of the Lives. Years Purchase at 4 5 3 p. cent. p. cent. p. cent. p. cent. 6 Ages of the Lives. 3 4 p. cent. p. cent. p. cent. p. cent. Years Purchase at 5 6 30 35 55 21.1 18.2 15.9 14.1 40 45 75 18.2 16. 30 35 65 20.9 18. 15.7 14. 40 50 50 19. 14.2 12.8 16.7 14.9 13.3 30 35 75 20.7 17.9 15.6 13.8 40 50 60 || 18.3 16.2 14.4 12.9 30 40 40 21.8 18.6 16.3 14.3 40 50 70 || 17.8 17.8 15.7 14. 12.6 30 40 50 21. 18.2 15.9 14.1 40 55 55 18.3 16.2 14.2 12.8 30 40 60 20.6 17.8 15.6 13.9 40 55 65 17.5 15.5 13.8 12.6 30 40 70 20.2 17.5 15.4 13.6 40 55 75 17.3 15.3 13.7 12.4 30 45 45 21.1 18.2 16. 14.2 40 60 60 17.6 15.6 13.7 12.4 30 45 55 20.2 17.6 15.5 13.7 40 60 70 16.9 15.0 13.5 12.2 30 45 65 19.9 17.3 15.2 13.5 40 65 65 16.6 14.7 13.2 12.4 30 45 75 19.6 17. 14.9 13.3 40 65 75 16.2 14.4 12:9 11.8 30 50 50 20.2 17.6 15.5 13.8 40 70 70 16.2 14.5 13. 11.8 30 50 60 19.6 17.1 15.1 13.4 50 50 50 17.9 15.9 14.2 12.8 30 50 70 19.3 16.8 14.8 13.2 50 50 60 17. 15.2 13.6 12.3 30 55 55 19.7 17.2 14.9 13.4 50 50 70|| 16.4 14.6 13.2 12. 30 55 65 18.8 16.4 14.5 13.2 50 55 55 17. 15.2 13.6 12.3 30 55 75 18.7 16.3 14.3 13. 50 55 65 15.9 14.3 12.9 11.9 30 60 60 30 60 70 19.1| 16.7 | 14.6| 13. 18.6| 16.3 14.4 50 55 75 15.6 15.6 14. 12.7 11.6 12.9 50 60 60 16. 14.4 12.8 11.7 30 65 65 18.3 16. 14.1 13. 50 60 70 15.2 13.7 12.4 11.4 30 65 75 17.9 15.7 13.9 12.5 50 65 65 14.8 13.4 12.2 11.5 30 70 70 40 40 40 18. 15.8 14. 12.5 50 65 75 14.3 12.9 11.8 10.9 20.9 18. 15.8 20. 40 40 50 40 40 60 19.4 40 40 70 19. 40 45 45 20. 40 45 55 19.1 16.7 14.9 40 45 65 18.6 16.4 14.5 17.4 15.4 14. 13.7160 60 60|| 50 70 70 14.3 14.3 12.9 11.8 10.8 14.6 13.2 12.0 11.0 17. 15. 13.4 60 60 70 13.5 12.4 11.4 10.5 16.6 14.7 13.1 60 65 65 13.2 12.1 11.1 | 10.7 17.5 15.5 13.8 60 65 75 12.4 11.4 10.5 9.8 13.3 60 70 70 || 12.3 12.3 13. 11.3 10.5 9.7 70 70 70 10.5 9.8 9.2 8.6 EXAMPLE. An Estate, Annuity, or a Lease, to determine on the death of the longest of Three Lives, aged 30, 45, and 65 years, to pay 3 per cent. and get back the Principal, is worth 19.9 years' purchase. To make 4 per cent. it is worth 17.3 years' purchase. VALUATION OF ESTATES. 603 Table 8. AMOUNT of FINE to be paid for RENEWING any num- ber of years lapsed IN A LEASE originally granted for 10 years. Note.-The rate of Interest shown in this Table is that which a Purchaser may make of his money, provided he can re-invest the surplus at the same rate, so as to replace the Fine at the end of his Lease. 3 Years Purchase at 4 5 6 Years. Years Purchase at 8 10 17.950 per cent. per cent. per cent. per cent. per cent. per cent. per cent. per cent. .7 .7 .6 .6 1 .5 .5 .4 1.5 1.4 1.3 1.1 2 1.1 1. .8 2.3 2.1 1.9 1.8 3 1.6 1.5 1.3 247 +∞ .2 .4 .7 3.1 2.9 2.6 2.4 4 2.3 2.1 1.8 1. 3.9 3.7 3.4 3.1 2.9 2.7 2.4 1.4 4.8 4.5 4.2 3.9 6 3.6 3.4 3. 1.8 5.7 5.3 5.0 4.7 7 4.4 4.1 3.7 2.3 6.6 6.2 5.9 5.5 8 5.2 4.9 4.4 2.9 7.6 7.1 6.8 6.4 9 6.1 5.8 5.2 3.7 8.5 8.1 7.7 7.4 10 7.0 6.7 6.1 4.5 EXAMPLE.-The Fine which a Tenant should pay for the renewal of 5 years lapsed in his Lease of 10 years, in order that he may make 4 per cent. for the money he advances, is 3.7 years' purchase of the Net Annual Income. 604 VALUATION OF ESTATES. Table 9. AMOUNT OF FINE to be paid for RENEWING any number of years lapsed in a LEASE originally granted for Twenty Years. Note.-This Table shows the rate of Interest which a person may make of his money, provided he can re-invest the surplus at the same rate of Interest, so as to re-place the Fine at the end of the Lease. Years Purchase at 3 4 5 6 Years. Years Purchase at 7 8 10 £12 6 1 per cent. per cent. per cent. per cent. per cent. per cent. per cent. per cent. .6 .5 .4 .3 1.1 .9 .8 is co .6 1.7 1.4 1.2 1. 2.3 1.9 1.6 1.4 2.9 2.5 2.1 1.8 3.6 4.2 4.9 að að + 3. 2.6 2.2 3.6 3.1 2.6 123LO CON .3 .5 .8 ∞O 2000 247 4 1.1 1. & cr co i .1 .2 .5 .3 .5 1.5 1.3 .9 .6 6 1.8 1.6 1.1 .8 7 4.2 3.6 3.1 8 5.6 4.8 4.2 3.6 9 6.3 5.5 4.7 4.1 10 7.1 6.2 5.4 4.7 11 ai aż að að + 2.2 1.9 1.4 1. 2.7 2.3 1.7 1.2 3.1 2.7 2. 1.5 3.6 3.1 2.4 1.7 4.1 3.6 2.8 2.1 7.9 6.9 6. 5.3 12 4.6 4. 3.2 2.4 8.6 7.6 6.7 5.9 13 5.2 4.6 3.6 2.8 9.5 8.3 7.4 6.6 14 5.8 5.2 4.2 3.3 10.3 9.1 8.1 7.3 15 6.5 5.8 4.7 3.8 11.2 10. 8.9 8. 16 7.2 6.5 5.3 4.3 12. 10.8 9.7 8.8 17 8. 7.2 6. 4.9 13. 11.7 10.6 9.7 18 8.8 8. 6.8 5.6 13.9 12.6 11.5 10.5 19 9.7 8.9 7.6 6.4 14.9 13.6 12.5 11.5 20 10.6 9.8 8.5 7.3 EXAMPLE. The Fine a Tenant should pay for the Renewal of 12 years lapsed in a Lease originally granted for 20 years, to make 4 per cent. of the money he advances, is 6.9 years' purchase of the net Income. VALUATION OF ESTATES. 605 Table 10. AMOUNT OF FINE to be paid for RENEWING any number of years lapsed in a LEASE originally granted for Twenty- one Years. Note. This Table shows the rate of Interest which a person may make of his money, provided he can re-invest the surplus at the same rate of Interest, so as to replace the Fine at the end of the Lease. Years Purchase at Years Purchase at 3 4 5 6 7 Years. 816 11.564 10 OR £11 11 3 per cent. per cent. per cent. per cent. per cent. per cent. per cent. per cent. .5 .4 .4 1.1 .9 .7 47 .3 .6 1.7 1.4 1.1 .9 2.2 1.9 1.5 1.3 2.9 2.4 2. 1.7 3.5 2.9 2.4 2.1 1234 LO CO .2 .8 ∞o ir is .2 .5 24 .1 .1 .4 .3 .2 .6 .4 .3 1.1 .9 .6 .5 1.4 1.2 .8 .6 6 1.7 1.5 1. .8 1935∞∞ 4.1 3.5 2.9 2.5 2.1 1.8 1.3 1.0 4.8 4. 3.4 2.9 8 2.5 2.1 1.5 1.2 5.5 4.6 4. 3.4 9 2.9 2.5 1.8 1.5 6.2 5.3 4.5 3.9 10 3.3 2.9 2.2 1.7 6.9 5.9 5.1 4.4. 11 3.8 3.3 2.5 7.6 6.6 5.7 5. 12 4.3 3.8 2.9 ai ai 2. 2.4 8.4 7.3 6.4 5.6 13 4.9 4.3 3.3 2.7 9.2 8. 7. 6.2 14 5.4 4.8 3.8 3.2 10. 8.8 7.7 6.8 15 6.1 5.3 4.3 3.6 10.8 9.6 8.5 7.6 16 6.7 6.0 4.9 4.1 11.7 10.4 9.3 8.3 17 7.4 6.7 5.5 4.7 12.6 11.3 10.1 9.1 18 8.2 7.4 6.2 5.4 13.5 12.1 11. 9.9 19 9. 8.2 6.9 6.1 14.4 13.1 11.9 10.8 20 9.9 9.1 7.7 6.9 15.4 14. 12.8 11.8 21 10.8 10. 8.6 7.8 EXAMPLE. The amount of Fine which a Tenant should pay for the Renewal of 12 years lapsed in a Lease originally granted for 21 years, to make 4 per cent. of the money he advances, is 6.6 years purchase of the Net Annual Income. 606 VALUATION OF ESTATES. Table 11. AMOUNT OF FINE to be paid for RENEWING any number of years lapsed in a LEASE originally granted for 40 years. Note.-This Table shows the rate of Interest which a person may make of his money provided he can re-invest the surplus, beyond the available interest, at the same rate, so as to replace the Fine at the end of the Lease. 3 Years Purchase at 4 5 6 Years. Years Purchase at 7 8 9 10 per cent. per cent. per cent. per cent. per cent. per cent. per cent. per cent. .3 .2 .1 .6 .4 .3 .9 .6 1.3 .9 1.6 1.1 .8 ∞ ∞ is ¿o i .1 .2 .4 .3 .6 2. 1.4 1. 2.3 1.6 1.2 .8 ∞ 2 år in co io ind .4 .5 .7 2.7 1.9 1.4 1. 12342 OZ∞ .1 .1 .2 .1 .3 .4 6 .5 7 .6 8 77 .5 3.1 2.2 1.6 1.1 9 .8 .6 3.5 2:5 1.8 1.3 10 .9 3.9 2.8 2. 1.5 11 1.1 4.4 3.1 2.3 1.6 12 1.2 ∞ ∞ 2 6 år iA co čo ¿o in jimat Ö .0 .1 .1 .2 .3 .3 .4 .7 .8 .9 4.8 3.5 2.5 1.8 13 1.3 1. 5.2 3.8 2.8 2. 14 1.5 1.1 .8 5.7 4.2 3.1 2.3 15 1.7 1.2 .9 ∞ ∞ & à à ER IA ID ∞ DDHHHÖ .0 .0 .1 .0 .1 .1 .1 .1 .2 .2 .3 .4 .4 .3 .5 .4 .6 .6 .5 .7 .5 .6 .7 6.2 4.5 3.4 2.5 16 1.9 1.4 1.1 .8 6.7 4.9 7.2 5.3 4. 7.7 5.8 ढाई मं 3.7 4.3 ai as as 2.7 17 2.1 1.6 1.2 .9 12233 TL 20 C7B9 .2 .3 .4 3. 18 2.3 1.7 1.3 1. 3.3 19 2.5 1.9 1.5 1.1 8.2 6.2 4.7 3.6 20 aż 2.7 2.1 1.6 1.3 8.8 6.7 5.1 3.9 21 3. 2.3 1.8 1.4 9.4 7.1 5.5 4.2 22 3.3 2.6 2. 1.6 9.9 7.6 5.9 4.6 23 3.6 2.8 2.2 1.8 10.6 8.1 6.3 4.9 24 3.9 3.1 2.4 11.2 8.7 6.8 5.3 25 4.2 3.4 ai 2.7 11.8 9.2 7.3 5.8 26 4.6 3.7 3. 12.5 9.8 7.8 6.2 27 5. 4. 3.3 13.2 10.4 8.3 6.7 28 5.4 4.4 3.6 13.9 11. 8.9 7.2 29 5.8 4.8 4. 14.6 11.7 9.4 7.7 30 6.3 5.2 4.3 15.3 12.4 10.1 8.2 31 6.8 5.7 4.8 qi ci si ci si að að + 2. 2.2 2.4 2.7 3. 3.3 3.6 4. 16.1 13.1 10.7 8.8 32 7.4 6.2 5.2 4.4 16.9 13.8 11.4 9.5 33 7.9 .6.7 5.7 4.9 17.7 14.6 12.1 10.1 34 8.6 7.3 6.3 5.4 18.5 15.3 12.8 10.8 35 9.2 7.9 6.9 6. 19.4 16.2 13.6 11.6 36 9.9 8.6 7.5 6.6 20.3 17. 14.4 12.4 37 10.7 9.3 8.2 7.3 21.2 17.9 15.3 13.2 38 11.5 10.1 9. 8. 22.1 18.8 16.2 14.1 23.1 19.8 17.2 15. 39 12.4 11. 9.8 8.9 40 13.3 11.9 10.8 9.8 EXAMPLE. The amount of Fine which a Tenant should pay for the renewal of 20 years lapsed in a Lease originally granted for 40 years, to make 4 per cent. of the money he advances is 6.2 years' purchase of the net annual Income. VALUATION OF ESTATES. 607 Table 12. AMOUNT of FINE to be paid for RENEWING with ONE LIFE the LEASE of an ESTATE originally granted on THREE LIVES. Note.-This Table shows the rate of Interest which a Purchaser may make of his money, provided he can re-invest the Surplus Income, beyond the Interest on the Purchase Money outstanding, at the same rate of Interest. Years Purchase. 3 4 per cent. per cent. Life put in. Ages of Years Purchase. Years Purchase. Lives in posses- 5 6 3 4 sion. per cent. per cent. per cent. per cent. Life put in. Ages of Years Purchase. Years Purchase. Lives in posses- · 5 6 3 4 sion. per cent. per cent. per cent. per cent. Life put in. Ages of Years Purchase. Lives in posses- sion. 5 6 per cent. per cent. 2.8 3.3 ai ai 2. 25-25 1.5 1.1 2.5 1.8 25-25 1.4 1. 2.2 1.6 25-25 1.2 .9 2.3 25-35 1.7 1.2 2.9 2.1 25-35 1.5 1.2 2.5 1.8 25-35 1.4 1.1 4.1 2.9 25-45 2. 1.5 3.6 2.6 25-45 1.8 1.4 3.1 2.3 25-45 1.6 1.3 4.6 3.4 25-55 2.4 1.8 4.1 3. 25-55 2.3 1.7 3.6 2.7 25-55 2.1 5.2 3.8 25-65 2.8 2.2 4.6 3.4 25-65 2.6 2.1 4.1 3.1 25-65 ல்ல் 1.5 2.4 1.9 5.5 4.1 25-75 3.1 2.4 4.9 3.7 25-75 2.8 2.2 4.4 3.3 25-75 2.6 2. मं 4.1 2.9 35-35 2.1 1.5 3.6 2.6 35-35 1.8 1.4 3.1 2.3 35-35 1.6 1.3 4.8 3.3 35-45 2.4 1.9 4.3 3.1 35-45 2.2 1.8 3.7 2.8 35-45 2.1 1.6 5.3 3.8 35-55 2.8 2.2 4.7 3.5 35--55 2.6 2. 4.2 3.1 35-55 6. 4.4 35-65 3.3 2.6 20 5.4 4. 35-65 3.1 2.5 4.9 3.7 35-65 ai ai 2.4 1.9 2.8 2.3 6.6 4.9 10 35-75 3.8 3. 6. 4.5 15 35-75 3.5 2.8 5.4 4.1 20 35-75 3.2 2.6 5.7 3.9 45-45 2.9 2.3 5.1 3.5 45-45 2.6 2.2 4.4 3.2 45-45 2.4 2. 6.4 4.7 45-55 3.5 2.7 5.7 4.2 45-55 3.2 2.5 5.1 3.8 45-55 2.9 2.3 7.3 5.4 45-65 4.1 3.2 6.6 5. 45-65 3.8 7.9 5.9 45-75 17.7 5.8 55-55 मंमं 4.6 3.6 7.2 5.5 45-75 4.2 4.4 3.3 7.0 5.3 55-55 4.1 8.7 6.5 55-65 5. 4. 7.9 6. 55-65 4.7 có có có có 3.1 6. 4.5 45-65 3.5 2.9 3.4 6.5 5. 45-75 3.9 3.2 3.1 6.3 4.8 55-55 3.5 2.8 3.8 7.2 5.5 55-65 4.2 3.5 9.8 7.5 10.3 7.9 11.6 55-75 5.9 4.7 9. 7. 55--75 5.5 4.5 8.3 6.5 55-75 5.1 4.2 9.1 65-65 6.2 5. 65-75 7.2 5.9 9.6 7.5 10.8 8.5 65-65 5.9 4.7 65-75 6.8 5.6 8.8 6.9 65-65 5.5 4.4 9.9 7.9 65-75 6.3 5.2 EXAMPLE. The amount of Fine which a Tenant should pay for putting in a new life, aged 15, in a Lease originally granted on three lives, one of which has dropped, the ages of the lives in possession being 45 and 75, to make 4 per cent. of his money, is 5.5 years' purchase of the Net Annual Income 608 VALUATION OF ESTATES. Table 13. PRESENT VALUE of the PERPETUITY of one year's Rent or Fine, payable at every interval of years stated below. Years Purchase at Years Purchase at 3 4 5 Interval of Years. 6 8 10 per cent. per cent. per cent. per cent. per cent. per cent. 16.4 12.3 9.8 2 8.1 6. 4.8 10.8 8. 6.3 3 8. 5.9 4.6 4 6.3 4.6 3.6 5 5.2 3.8 2.9 6 4.3 3.2 2.5 7 ~~~ 2.9 2.1 1.6 10 2ð að að ai ai – 5.2 3.9 3. 3.8 2.8 2.2 3. 2.1 1.6 2.4 1.7 1.3 2. 1.4 1.1 1.3 .9 .6 2. 1.4 1. 14 .8 .5 1.2 1.2 .4 ∞o oo oo .8 .8 .6 .3 .2 669 20 .5 .3 .2 21 .4 .2 .2 40 .1 .0 .0 64220 .4 EXAMPLE.-The present* worth of the perpetuity of one year's Rent or Fine, payable every 10 years, is at 4 per cent. 2.1 years' purchase. * That is to say, immediately after a Fine has been paid for renewal. VALUATION OF ESTATES. 609 Table 14. PRESENT VALUE of the REVERSION to a FREE- HOLD ESTATE, or a PERPETUITY, after any given number of years not exceeding sixty. Years Purchase at Years Purchase at After these 3 4 5 6 77 8 Years. per cent. per cent. per cent. per cent. 10 per cent. per cent. per cent. per cent. 9 32.4 24. 19. 15.7 1 13.4 11.6 10.2 9.1 31.4 23.1 18.1 14.8 2 12.5 10.7 9.4 8.3 30.5 22.2 17.3 14. 3 11.7 9.9 8.6 7.5 29.6 21.4 16.5 13.2 10.9 9.2 7.9 6.8 28.8 20.5 15.7 12.5 10.2 8.5 7.2 6.2 27.9 19.8 14.9 11.7 6 9.5 7.9 6.6 5.6 27.1 19. 14.2 11.1 7 8.9 7.3 6.1 5.1 26.3 18.3 13.5 10.5 8 8.3 6.8 5.6 4.7 25.5 17.6 12.9 9.9 9 7.8 6.3 5.1 4.2 24.8 16.9 12.3 9.3 10 7.3 5.8 24.1 16.2 11.7 8.8 11 6.8 5.4 23.4 15.6 11.1 8.3 12 6.3 5. 22.7 15. 10.6 7.8 13 5.9 ti 4.6 22. 14.4 10.1 7.4 14 5.5 4.3 Hi Hi Hi að as 4.7 3.9 4.3 3.5 4. 3.2 3.6 2.9 3.3 2.6 21.4 13.9 9.6 7. 15 5.2 3.9 3.1 2.4 20.8 13.3 9.2 6.6 16 4.8 3.6 2.8 2.2 20.2 12.8 8.7 6.2 17 4.5 3.4 2.6 19.6 12.3 8.3 5.8 18 4.2 3.1 2.4 19. 11.9 7.9 5.5 19 3.9 2.9 2.2 6+2 2. 1.8 1.6 18.5 11.4 7.5 5.2 20 3.7 2.7 2. 1.5 17.9 11. 7.2 4.9 21 3.4 2.5 1.8 1.4 17.4 10.5 6.8 4.6 22 3.2 16.9 10.1 6.5 4.4 23 3.0 16.4 9.8 6.2 4.1 24 2.8 ai ai ai 2.3 1.7 1.2 2.1 1.5 1.1 2. 1.4 1. 15.9 9.4 5.9 3.9 25 2.6 1.8 1.3 .9 15.5 9. 5.6 3.7 26 2.5 1.7 1.2 .8 15. 8.7 5.4 3.5 27 2.3 1.6 1.1 .8 14.6 8.3 5.1 3.3 28 2.1 1.4 1. .7 14.1 8. 4.9 3.1 29 2. 1.3 .9 .6 13.7 7.7 4.6 2.9 30 1.9 1.2 .8 .6 EXAMPLE. The present worth of the Reversion to a Freehold Estate after 25 years, to make 4 per cent. interest is 9.4 years' purchase of the net annual rent. 610 VALUATION OF ESTATES. Table 14 continued. PRESENT VALUE of the REVERSION to a FREEHOLD ESTATE, or a PERPETUITY, after any given number of years not exceeding sixty. Years Purchase at After these 3 4 5 6 Years Purchase at 8 9 10 Years. per cent. per cent. per cent. per cent. per cent. per cent. per cent. per cent. 13.3 7.4 4.4 12.9 7.1 मं 4.2 si si 2.7 31 1.8 1.1 2.6 32 1.6 1.1 12.6 6.8 4. 2.4 33 1.5 1. .6 12.2 6.6 3.8 2.3 34 1.4 .9 .6 11.8 6.3 3.6 2.2 35 1.3 .8 .5 11.5 6.1 3.5 2. 36 1.2 .8 11.2 5.9 3.3 1.9 37 1.2 .7 .5 10.8 5.6 3.1 1.8 38 1.1 .7 10.5 5.4 3. 1.7 39 1. .6 10.2 5.2 2.8 1.6 40 1. .6 9.9 5. 2.7 1.5 41 .9 .5 9.6 4.8 2.6 1.4 42 .8 .5 9.4 4.6 2.5 1.4 43 .8 .5 9.1 4.5 2.3 1.3 44 .7 .4 8.8 4.3 2.2 1.2 45 7 .4 8.6 मं 4.1 2.1 1.1 46 .6 .4 .2 8.3 4. 2. 1.1 47 .6 .3 8.1 3.8 1.9 1. 48 .6 .3 7.8 3.7 1.8 1. 49 .5 .3 NNNNNWo čo čo čo ip it if år år år å is 2 ∞ .8 .5 .7 .5 .4 .4 .4 .3 .3 .4 .3 .4 .3 .2 .3 .2 .2 .2 .2 .1 .1 .1 .1 .1 7.6 3.5 1.7 .9 50 .5 .3 .1 .1 7.4 3.4 1.7 .9 51 .5 .2 .1 .1 7.2 3.3 16 7. 3.1 1.5 6.8 6.6 as ai 3. 1.4 2.9 1.4 6.4 2.8 1.3 .6 6.2 2.7 1.2 .6 6. 2.6 1.2 5.8 2.5 1.1 5.7 2.4 1.1 .5 ·∞∞776 CO CO LO LO .8 52 .4 .2 .1 .1 .8 53 .4 .2 .1 .1 .7 54 .4 .2 .1 .1 55 .3 .2 .1 ·.1 56 .3 .2 .1 57 .3 .2 .1 .0 58 .3 .1 .1 .5 59 .3 .1 .1 60 .2 .1 .1 CHOOOOO .0 EXAMPLE. The present worth of the Reversion to a Freehold Estate after 60 years, to make 4 per cent. interest, is 2.4 years' purchase of the net annual rent. VALUATION OF ESTATES. 611 Table 15. PRESENT VALUE of a REVERSIONARY ESTATE in FEE after the Life of a person of a given age, at the several rates of 3, 4, 5, 6, 7, and 8 per cent. Interest. Years Purchase at Years Purchase at Age in 3 per cent. 4 per cent. 5 per cent. 6 7 8 Possession. per cent. per cent. per cent. 12.9 7.8 5.2 or 5 3.7 2.8 2.2 12.7 7.5 4.9 10 3.4 2.5 1.9 13.7 8.2 5.4 15 3.8 2.8 2.2 14.7 9. 6. 20 4.3 3.2 2.5 15.5 9.6 6.4 25 4.6 3.4 16.4 10.2 6.9 30 17.4 11. 7.5 35 18.5 11.8 8.2 19.6 12.7 8.9 20.9 13.7 9.7 22.2 14.8 10.6 23.6 16. 11.6 25. 17.2 12.7 26.6 18.6 14. 28.1 20. 15.3 29.6 21.4 16.5 80 30.7 22.5 17.5 31.5 23.2 18.3 33.1 24.8 19.8 KURONJACAJAS 40 6. 20 20 có 5. 3.7 ai ai 2.7 2.9 5.4 4.1 3.2. 4.5 3.6 45 6.6 5. 4. 50 7.2 5.6 4.5 55 8. 6.2 5. 60 8.8 7. 5.6 65 9.8 7.8 6.4 11. 8.9 7.3 75 12.1 9.9 8.3 13.3 11. 9.3 85 14.3 11.9 10.2 15. 12.6 10.9 95 16.4 14. 12.3 EXAMPLE. The present value of a Freehold Reversionary Estate or of an Ad- vowson subject to the life of a person aged 60, at 4 per cent., is 16 years' purchase. At 5 per cent., it is worth 11.6 years' purchase. ། 7 612 VALUATION OF ESTATES. Table 16. Showing the PRESENT VALUE of a REVERSIONARY ESTATE in FEE after the longest of Two Lives of given ages at the several rates of 3, 4, 5, and 6 per cent. Interest. Years Purchase at Years Purchase at 3 4 Ages. 5 6 per cent. per cent. per cent. per cent. 8.3 4.2 10 9.2 4.8 10 9.9 5.3 10 9280 10 2.4 1.4 20 2.8 1.7 30 3.1 1.9 10.6 5.8 10 40 3.5 2.2 11.3 6.3 10 50 3.9 2.5 11.8 6.8 10 60 4.2 2.8 12.3 7.1 10 70 4.5 3.1 12.5 7.4 10 80 4.7 3.3 10.2 5.5 20 20 3.2 2. 11. 6.1 20 30 3.6 2.3 11.9 6.7 20 40 4.1 2.7 12.8 7.3 20 50 4.6 3. 13.5 7.9 20 60 5.1 3.4 14.1 8.4 20 70 5.5 3.8 14.5 8.8 20 80 5.8 4.1 12.1 6.8 30 30 4.1 2.7 13.1 7.5 30 40 4.7 3.1 14.1 8.3 30 50 5.3 3.5 15. 9. 30 60 5.9 4. 15.7 9.6 30 70 6.3 4.4 16.2 10. 30 80 6.7 4.8 14.4 8.4 40 40 5.3 3.6 15.6 9.4 40 50 6.1 4.1 16.7 10.3 40 60 6.8 4.7 17.6 11. 40 70 7.4 5.3 18.2 11.5 40 80 7.9 5.7 17.2 10.6 50 50 7. 4.9 18.6 11.7 50 60 7.9 5.6 19.7 12.7 50 70 8.8 6.4 20.5 13.3 50 80 9.4 6.9 20.4 13.1 60 60 9.1 6.6 22. 14.5 60 70 10.3 7.6 23. 15.4 60 80 11.1 8.4 24.1 16.4 70 70 11.9 9. EXAMPLE. A Reversionary Freehold Estate, after the longest of two lives aged 30 and 50, at 3 per cent., is worth 14.1 years' purchase. At 4 per cent., it is worth 8.3 years' purchase. VALUATION OF ESTATES. 613 Table 17. PRESENT VALUE of a REVERSIONARY ESTATE or ANNUITY on a single Life, after any other single Life now in Possession, at the several rates of 3, 4, 5, and 6 per cent. Interest. Years Purchase at Years Purchase at 3 per cent. 4 per cent. Age of Life in Reversion. Age of Life in Possession. 5 6 per cent. per cent. 6.5 4.9 30 3.8 3.0 7.9 6. 40 4.7 3.7 9.6 7.4 50 5.9 4.7 11.7 9.2 10 60 7.4 6. 14.3 11.5 70 9.4 7.9 17. 14. 80 11.7 10. 5.4 4.2 30 3.3 2.7 6.5 5.1 40 4.1 3.3 8.1 6.4 50 5.1 4.2 10. 8. 20 60 6.5 5.4 12.5 10.2 70 8.5 7.1 15.1 12.6 80 10.7 9.2 4.3 3.5 30 2.8 2.3 5.4 4.3 40 3.5 2.9 6.8 5.5 50 4.5 3.7 8.5 7. 30 60 5.8 4.8 10.9 9.1 70 7.6 6.5 13.4 11.4 80 9.8 8.5 3.3 2.7 30 2.3 1.9 4.1 3.4 40 2.8 2.4 5.3 4.4 50 3.7 3.1 6.8 40 5.7 60 4.8 4.1 9.0 7.6 70 6.5 5.7 11.4 9.9 80 8.6 7.6 2.3 1.9 30 1.7 1.5 2.8 2.4 40 2.1 1.8 3.7 3.2 50 2.7 2.4 50 5. 6.9 9.1 8. ti có cơ 4.3 60 3.7 3.2 6. 70 5.2 4.6 80 7.1 6.4 1.4 1.2 30 1.1 1.0 1.8 1.5 40 1.4 1.2 2.3 2.0 50 1.8 1.6 60 3.2 2.8 4.6 4.1 6.6 5.9 80 928 60 2.5 2.2 70 3.7 3.3 5.4 4.9 EXAMPLE. A Reversionary Estate on a single life aged 30, after a single life in possession aged 60, at 3 per cent., is worth in present money, 8.5 years' purchase of the net Annual Income. 614 VALUATION OF ESTATES. Table 18. PRESENT VALUE of a REVERSIONARY AN- NUITY on a Single Life, to be nominated at the death of a person now in Possession, at the several rates of 3, 4, 5, and 6 per cent. Interest. Years Purchase at Years Purchase at 3 4 per cent. per cent. Ages of Life in Reversion. Ages of Life in Possession. 5 6 per cent. per cent. 8.8 6.3 30 4.7 3.6 9.9 7.3 40 5.5 4.3 11.2 8.5 50 6.6 5.3 25 12.6 9.9 60 7.9 6.4 14.2 11.5 70 9.5 7.9 15.8 13.2 80 11.2 9.6 8.3 6. 30 4.5 3.5 9.4 7. 40 5.3 4.2 10.6 8.1 50 6.4 5.1 12. 9.4 30 60 7.6 6.2 13.5 11. 70 9.1 7.7 15. 12.6 80 10.8 9.3 7.8 5.7 30 4.3 3.4 8.8 6.6 40 5.1 4. 10. 7.7 50 6.1 मं 4.9 35 11.3 9. 60 7.3 6. 12.8 10.5 70 8.7 7.4 14.1 12. 80 10.3 8.9 7.3 5.4 30 4.1 3.2 8.2 6.2 40 4.8 3.8 9.3 7.3 50 5.8 4.7 10.5 8.4 40 60 6.9 5.7 11.8 9.8 70 8.3 7. 13.2 11.3 80 9.8 8.5 6.7 5. 30 3.8 3. 7.6 5.8 40 4.5 3.6 8.6 6.7 50 5.4 4.4 9.7 7.8 45 60 6.4 5.4 10.9 9.2 70 7.8 6.6 12.1 10.5 80 9.2 8.1 6.1 4.6 30 3.6 2.8 6.9 5.3 40 7.8 6.2 50 5. đó 4.2 3.4 4.1 8.8 7.2 50 60 6. 5. 9.9 8.4 70 7.2 6.2 11. 9.6 80 8.5 7.5 EXAMPLE. The present value of a Reversionary Annuity on a Single Life aged 30, to be nominated at the death of a person, now in possession aged 50, to pay 3 per cent., is worth in present money, 10.6 years' purchase of the net annual income. At 4 per cent. it would be 8.1 years' purchase. VALUATION OF ESTATES. 615 Table 19. PRESENT VALUE of £1, payable at the death of a person of a given age. 3 PER CENT. By the 4 PER CENT. 5 PER CENT. By the By the Age. Northampton Carlisle Age. Northampton By the Carlisle Age. Tables of Tables of Tables of Tables of Mortality. Mortality. Mortality. Mortality. By the Northampton Tables of Mortality. By the Carlisle Tables of Mortality. 10 .369 .286 10 .287 .208 10 .232 .159 15 .398 .313 15 .315 .232 15 .258 .180 20 .428 .339 20 .345 .255 20 .285 .199 25 .452 .369 25 .368 .283 25 .306 .224 30 .478 .401 30 .393 .313 30 .330 .251 35 .507 .434 35 .422 .345 35 .357 .280 40 .538 .472 40 .454 .382 40 .389 .315 45 .572 .508 45 .489 .419 45 .424 .350 50 .609 .554 50 .528 .466 50 .463 .409 55 .646 .609 55 .569 .527 55 .506 .460 60 .686 .665 65 .729 .711 70 .775 .763 75 .819 .810 80 .861 .843 85 .895 .877 90 .919 .898 CRONIRI 60 .614 .590 60 .553 .527 .663 .642 65 .606 .583 .717 .703 70 .666 .651 75 .771 .760 75 .726 .715 80 .821 .800 80 .785 .761 85 .864 .842 85 .835 .809 90 .894 .869 90 .870 .841 EXAMPLE. £1 payable at the death of a person aged 55 years is worth, in present money at 5 per cent., according to the Northampton Tables of Mortality .506, or by the Carlisle Tables .460. E. G. £100 is worth £50.6 or £46. £1000 is worth £506 or £460. 616 VALUATION OF ESTATES. MEMORANDA As Facts to assist the Memory in matters of Calculations and Valuations*. In respect to the value of freehold land, it is generally considered 30 to 33 years' purchase Freehold ground-rent, 25 to 30 years' purchase Freehold houses and buildings, 1st and 2nd class, 18 to 20 years' purchase Ditto, 3rd and 4th ditto, 16 years' purchase For leasehold property refer to the Table for the term of years unexpired for long terms, 1st and 2nd class houses and buildings, 15 to 16 years' purchase For do. 2nd and 3rd do. For do. 3rd and 4th do. For do. 4th and 5th do. For do. 5th and 6th do. 14 to 15 years' purchase 12 to 13 years' purchase 11 to 12 years' purchase 10 years' purchase 3 per cent. • 4 per cent. 5 per cent. 6 per cent. 6 per cent. 7 per cent. 8 per cent. 9 per cent. 10 per cent. Renewing Leases held under Deans and Chapters. The Dean and Chapter of Westminster renew their leases, originally granted for FORTY YEARS, under the 8 per cent. Tables; the renewing fine of one year's rent payable by the tenant every fourteen years;-except for very superior houses at the West-end of the town, which are renewed under the 7 per cent. Tables. The renewing fine of 1 years being payable by the tenant every fourteen years. The Bishop of Winchester's Estates. 11 Years renewing fine for 14 years lapsed in a lease originally granted for 40 years, 7 per cent. Tables if next the river; or, 11 year's fine in land 8 per cent. * Chiefly extracted from the 13th Edition of Inwood's Tables. VALUATION OF ESTATES. 617 City of London Leases, Scale of Ground Rents. situations} Per foot frontage S. d. d. 5 0 Per foot deep 3 2nd do. ditto 3rd do. ditto 4th do. ditto 5th do. ditto 4 0 ditto 2 3 0 ditto 1/1/ 2 0 ditto 1 1 0 ditto Renewing fine, 7 years' ground rent every 14 years, for a term of 41 or 61 years. Lessee to insure, repair, &c. Purchase of Good Will in Retail Trade, &c. If retail trade is carried on, giving credit, say, 1 year's purchase. Ditto, as a ready money concern, say, 1½ year's purchase. Ditto, trade subject to be annihilated, as public houses, say 2 to 3 years' purchase. Calculating rent for fixtures, say 12 per cent., or §, being 2s. 6d. in the pound. Allowance to Tenants for Repairs. 8 per cent. allow for amount of repairs for 21 years. 7 do. Or, generally, say, allow— 12 per cent. 10 do. 9 do. 8 do. 7 do. 6 do. 31 do. for 12 years. 15 do. 18 do. 23 do. 33 do. above do. Purchase of Land Tax. To be made under the Land Tax Act at the price of the 3 per cent. consols, and to which add one-tenth to the amount, the income tax being now taken off. Memorandum relative to the Valuation of Land. 43.560 feet superficial, an acre, at— d. per foot do. do. 1 do. 14 do. 14 do. • £ S. d. 45 7 6 per acre. 90 15 0 do. 136 2 0 do. . 181 10 0 do. 226 17 6 do. . 272 5 0 do. 2 Q 618 VALUATION OF ESTATES. Crown Lands. The mode adopted in respect to the valuation for renewal of the crown leases, allowance for repairs as under- Houses £25 per annum, and under,. 10 per cent. £25 to £50 . £50 to £100 £100 and upwards 6 per cent. 7 per cent. 5 per cent. The rack rent not an overstrained rent on account of crown property, and to encourage improvements, viz., Calculation. Rack rent Deductions Present repair, £200 £63 per annum. £ S. d. . 14 0 0 Ordinary repairs, 3 3 0 3 3 0 Insurance, £700 . 1 4 0 Outgoings 480 Land tax 25 18 0 £37 2 0 Say, £40 per annum clear rent. Or, in another case, Rack rent Deductions Present repairs, £250 £150 per annum. £ S. d. 17 10 0 Ordinary repairs 7 10 0. Land tax 5 12 0 Insurance, £1500 3 7 6 Contingencies 7 10 0 41 9 6 42 £108 Crown leases, their custom under act of parliament, is to renew leases when within 20 years of being expired, not earlier, a new rent is then assessed taking fine, and more effectually the rent so reserved. rent, in order to secure Increase of Population. 810) 15 per cent. First 10 years of the century-1800 to 1810 Increase in England and Wales 1810 to 1820 17 per cent. 1820 to 1830 15 per cent. VALUATION OF ESTATES. 619 Increase in population in England and Wales, 9 millions. Population of London. Ditto, including environs 1810 10 millions. 1821 12 millions. 1 millions. 12 millions. Out of 1000 persons there die annually about 30; and that the number of inhabitants of every city and county is renewed every thirty years, or nearly so. Calculations have been made tending to show that the propor tion of mortality is diminishing; which fact is confirmed by the returns in several great cities, proving incontestably the material amelioration which has taken place in great cities. Mortality. 100 years since, 1 died in 30. 50 do. 30 do. 20 do. وو وو 1 1 1 وو وو وو in 40. in 48. in 52. in 60. Present time, 1 وو For Surveys and Valuations Made in respect to the extensive improvements which have taken place in London,-Regent-street,-Strand, the Commis- sioners of Improvements of Westminster, the City and New London Bridge, St. Katharine's Docks, and other improvements -the charges have been at the rate of per cent., and 3 guineas for each surveyor attending to give evidence before a judge and jury. It is usual to charge 1 per cent. for the first thousand pounds, and the remainder per cent. Her Majesty's Commissioners for Building Churches, for tra- velling expenses, allow 1s. 6d. per mile out, and the same back, but no expenses; and four journeys, not more, allowed to each church. 620 VALUATION OF ESTATES. Rule for determining the Value of a Beneficial Lease for Years, so that the Purchaser may be able to make a given Interest on the Price paid, and replace his Capital at the expiration of the Lease. In every question of this kind, it is evident that two circumstances may vary considerably: first, the interest which a purchaser may be considered entitled to make of his money, which in some de- scriptions of leasehold property, would be as low as 5, and in others as high as 8 or 9 per cent.; and, secondly, the rate of compound interest at which he may reckon with certainty upon employing the money annually laid by to replace his capital at the expiration of his lease, and which may be considered to range at about 3 or 4 per cent. Any formula, therefore, to be useful, must require the following data:- 1. The amount of the clear improved rent. 2. The rate of interest required on the purchase-money. 3. The rate of compound interest at which the money annually laid by to replace capital may be expected to be employed. 4. The length of the lease. N.B. The two last data being given, tables of compound interest will give the amount of £1 per annum at the given rate of com- pound interest for the given number of years. Now let a = amount of clear improved rent ; b = C = com- amount of £1 per annum at ʼn per cent. pound interest for r years (n standing for the rate of interest at which money may be expected to be employed; r standing for the number of years in the lease); rate of interest per cent. required on purchase- money; x = amount of purchase money; sum to be annually laid by at n per cent. com- y=pound interest, to replace capital at expiration of lease. by Then, from this statement, we shall have— =X These two are the unknown quantities. These three may, of course, be considered as known quantities. (for the amount of £1 per annum for the number of years of the lease at the given rate of compound interest multi- plied by the number of pounds annually laid by, must equal the purchase-money; VALUATION OF ESTATES. 621 CX 100 +y=a for сх 100 annual interest on purchase-money, since the annual interest on any sum = that sum multiplied by the rate of interest, and divided by 100; and the annual interest on the purchase- money added to the sum annually laid by to replace capital, must = clear improved rent. X From the first of these equations, y, = which, substituted in the second, gives с х 100 x = + X b α 100 a b 100+ b c X 100 a 100+ b c and y = b From the foregoing formula, it follows that the value of any beneficial lease the product of 100 multiplied into the amount of clear improved rent, multiplied again into the amount of £1 per annum for whatever number of years the lease may be, at the given rate of compound interest; the product of this continued multiplication being divided by 100, added to the product of the rate per cent. of interest required on purchase-money, multiplied by the aforesaid amount of £1 per annum, &c.,, &c. Therefore, if a = £500 وو b = 28.6765 (supposing n = 3 per cent., rate of comp. interest; r = 21 years, length of lease; c=7, rate per cent. of interest required on purchase-money; we shall have x= y 100+ 7 × 28.6765 100 × 500 × 28.6765 = £4769 15 91; £166 6 71; 100 × 500 100+ 7 × 28.6765 and £500–166 6 7 = £333 13 4, which is the yearly interest at 7 per cent. on £4769 15 94, the amount of the purchase-money; and £166 6 7 annually laid by for 21 years, at 3 per cent. compound interest, will amount to £4769 15 91; thereby replacing the principal at the end of the lease. Where the question is as to the proper sum to be given for renewing any number of years lapsed in a lease, it is clear that the party wishing to renew gives up whatever may be the number of years remaining in his old lease, together with a certain sum 622 VALUATION OF ESTATES. of money in consideration of receiving a new lease for the time agreed upon; and the value of the remainder of the old lease must be therefore deducted from the value of the new lease; and the remainder will be the proper sum to be given for the renewal. Thus, supposing it is wished to renew 14 years lapsed in a 21 years' lease, here the value of the remaining part of the lease = value of a lease for 7 years, and supposing, as before, that a = £500; Sn being = 3 per cent. of compound interest; b = 7·6625 { c = 7 X r 99 = 7 years, length of lease; 100 × 500 × 7·6625 100 + 7 x 7.6625 = £2493 13 10; which is the value of the remaining 7 years of the old lease. Now, the value of a new lease of 21 years, we shall find thus : a = £500; n being 3 per cent. compound interest; Sn b = 28·6765 {7 c = 7 x دو = = 21 years. 100 × 500 × 28.6765 100 + 7 × 28.6765 we deduct value of remaining} 7 years of old lease we shall have. £4769 15 91; from which, if 2493 13 101, £2276 1 103 as the proper sum to be paid for the renewal of the 14 years lapsed. What Amount of Increased Rent should be given instead of Premium for the Renewal of any Number of Years lapsed in a Beneficial lease for Years ? The same data will suffice for solving this question which were required for determining the amount of premium to be paid for a renewal. In the first place, the value of the tenant's remaining interest in the old lease must be calculated by the first formula; and this value must be considered as the premium he pays for renewal; and the increased rent to be paid by him must therefore be such a sum as, if deducted from the amount of the clear annual improved rent, will leave a sufficient remainder to afford the tenant the given rate of interest upon the value of his remainder of lease, considered as capital, and also enable him to lay by a certain sum annually, which, at the given rate of compound interest, will replace this capital at the expiration of the new lease. VALUATION OF ESTATES. 623 Supposing... a = clear improved rent; b = amount of £1 per annum for r years at n rate of com- pound interest, where r = number of years of new lease, n = rate of compound interest at which money can be safely employed; c = rate per cent. required on capital; d = value of present interest in old lease; x= increased annual rent to be paid instead of premium; sum to be annually laid by to replace capital, (i.e. y=value of the remainder of old lease) at the expiration of new lease; then will by = d x=α c {od being the Known quantities. Unknown quantities. being the interest at the given rate upon 100 the capital sum. c d -y 100 d .. y b cd d x = α a 100 b From this formula it follows, that the proper increase of rent to be paid instead of a premium, for the renewal of any number of years lapsed in a beneficial lease the amount of the clear improved rent, after deducting the quotient of the value of re- mainder of old lease, multiplied by the rate per cent. required on capital, and divided by 100; further deducting, also, the quotient of the value of remainder of old lease, divided by the amount of £1 per annum for the number of years in the new lease, at the given rate of compound interest; if.. a = £500 amount of clear improved rent; b = 28-6765 { n being = 3 per cent., rate of comp. interest = 21 21 years length of new lease γ c = 7 rate per cent. required on capital; This is on the supposition that 7 years = £2493 13 10 remain unexpired of the old lease; the value being found by the first formula. d x = £500 7 × 2493 13 101_2493 13 101 100 28.6765 x = £500 — 174 11 1-86 19 8 = £500 — 261 10 92; .. x = 238 9 24; which is the proper amount of increased rent to be paid instead of premium, for the renewal of 14 years lapsed in a lease of which 7 years remain unexpired, of a property, the clear improved rent of which is £500 a-year. 624 VALUATION OF ESTATES. There is only one more way in which renewals may be pur- chased, and that is, by paying for them partly by premium, and partly by increased rent; and the foregoing formula will solve any question of this kind. The amount, however, of one of these two quantities (i.e. the amount of the premium, or of the increased rent expected,) must of course be given, as they evidently vary in- versely to each other. If the amount of premium expected be given, that amount must be added to the value of remaining part of old lease; and the last formula will find the additional rent to be paid. Ex. gr., if, in the last case, a premium of £500 had been de- manded, then- a = £500 clear annual rent; b = 28.6765, amount of £1, &c.; C = 7, rate per cent. required on capital ; d = £2493 13 10+ £500 (amount of prem.) = 2993 13 101; 7 × 2993 13 10 2993 13 101 x = £500 100 28.6765 ; 104 7 102 £500 — 313 19 0 = x = £500 — 209 + 11 1 11 — 104 £186 1 0. .. if £500 premium is demanded for a renewal of 14 years in a lease, of which 7 years remain unexpired, of a property, the clear annual rent of which is £500, the amount of increased rent to be paid for such renewal (in addition to such premium of £500,) is £186 1 0 annually. If the amount of increased rent expected is given, such amount must, of course, be deducted from the amount of the clear im- proved rent, and the premium to be paid for the renewal may be calculated by the formula before given for that purpose; the clear improved rent being stated at its reduced amount. VALUATION OF TILLAGES. 625 CHAPTER XVIII. VALUATIONS OF TILLAGES AND TENANT RIGHT. THIS branch of practice attains its greatest importance in Surrey and parts of the adjacent counties, by reason of the number of items which the "custom of the country" (as it is technically termed,) in that neighbourhood, renders subject to the dealings of the valuator at a change of occupancy. The following is a list of the various customs prevailing in the several counties of England, so far as I am acquainted with them, or they have in any way come under my observation. Bedfordshire. In this county an outgoing tenant generally has the option of sowing the wheat crop, if it be a Michaelmas holding, or of allowing the incoming tenant to enter upon the land suffi- ciently early to do it himself. And the same with respect to the spring corn, if the entry be at Lady-day. But in either case, the corn must be sown by Michaelmas or Lady-day, as may be. The valuation then takes place upon the labour, seed, and sowing. If the outgoing tenant exercises this option of sowing the corn against the wishes of an incoming tenant, the latter may exercise an option as to taking the crop. The dung upon the premises at the expiration of the tenancy has to be left for the use of the incoming tenant without forming any item in the valuation. Seed, sowing, and labour upon the grass seeds are valued, and labour upon the fallows, as well as the labour upon the lands pre- pared for spring corn not sown by an outgoing tenant at a Lady- day entry. Berkshire.—The incoming tenant generally enters upon the land at Lady-day, to make his fallows and prepare the wheat lands for the ensuing crop. He pays for hay at a fodder price, and for seed, labour, and sowing of grass seeds, but not for rent and taxes on the fallows, which are all paid in full by the outgoing tenant to the end of his term. Buckinghamshire.—The incoming tenant pays for labour, seed, and sowing, but not for dung. Cambridgeshire. The incoming tenant pays for all kind of 626 VALUATION OF TILLAGES. labour, seed, and sowing, but not for dung. He also takes to straw and chaff at a fodder price. There is however a custom by which the incoming tenant thrashes and draws to market the corn of the last year's growth, receiving in return the straw and chaff as remuneration. Cheshire.—The incoming tenant pays for seed, labour, and sow- ing, but not for dung. Cornwall. The incoming tenant pays rent and taxes for the fallow land, as in Surrey, but generally has the option of pre-entry. The dung upon the premises is not paid for. Cumberland.—The incoming tenant at Candlemas-day pays for seed, sowing, and labour of every description, as well as a propor- tionate sum of the year's rent and rates on the fallows. Derbyshire.—The incoming tenant to a farm in this county pays for very much the same tillages as in Surrey; viz., for full fallows and full dressings, the value of the labour and manure expended for seed and sowing, and a year's rent and rates. For half fallows and half dressings on those lands from which only one crop has been taken subsequently to the fallow, at the value of half the labour on such fallows, half the value of the manure, and a half-year's rent and rates. But with reference to seeds that may have been sown on the half fallow and failed, the custom of Derbyshire differs from that of Surrey, inasmuch as the outgoing and incoming tenant are made to share the loss in equal moieties. Where the seeds do not fail, seed and sowing is valued in full. Hay and straw is taken at market price. Devonshire.—The incoming tenant has a right of pre-entry to prepare the wheat lands on a Michaelmas tenancy, and the lands for spring crops of a Lady-day tenancy. In the latter tenancy, he pays for the wheat crop at valuation. Nothing is paid for manure, hay, and straw. Dorsetshire.—The very simple custom of quitting a farm in the same manner as the tenant entered appears to be the most general. Durham.-The incoming tenant generally has the right of pre- entry to fallows, and the use of the unexpended manure arising out of the last year's crop. Pays for seeds and sowing, and for the after feed. Essex. The incoming tenant pays for labour and manure upon the fallows, seeds, and sowing, and for dung in the yards. Gloucestershire.—The incoming tenant has generally a right of pre-entry, and is entitled to the dung arising from the last year's crop. Herefordshire.—The incoming tenant has a right of pre-entry, VALUATION OF TILLAGES. 627 and to the manure from the last year's crop, but pays for seeds sown. Hertfordshire. The right of pre-entry to work fallows exists pretty generally. The incoming tenant is entitled to one-fifth of the land for fallow, and one-fifth upon which he can sow grass seeds. Hampshire.—The incoming tenant pays for labour upon the fal- lows, and for carting and spreading dung; but is entitled to the dung without payment. Huntingdonshire. The incoming tenant pays for labour upon the fallows, but is entitled to the dung free of cost. Kent.-The incoming tenant pays for fallows and half fallows, dressings and half dressings, seed and sowing, clover leys, under- wood down to the stub, manure upon the premises, and hay and straw of the last year's growth at a fodder price. Lancashire.—The outgoing tenant is paid (usually speaking) for wheat sowing, and is bound generally to leave the farm in the same state as he found it. Leicestershire.-The incoming tenant pays for labour, and the year's rent and rates upon the fallows. For seed, sowing, and full dressings. Lincolnshire. The incoming tenant has the right of pre-entry; pays for clover and grass seeds, and for carting manure, but is en- titled to the dung free of cost. Middlesex.—In this county there is a great breadth of land under culture as market gardens and meadows, to which special agree- ments generally apply. On the arable lands the incoming tenant at Michaelmas generally pays for fallows, half fallows, dressings, half dressings, clover leys, hay, straw, and dung. There are very few woods and coppices, but where one is met with the underwood is taken to according to its growth. Norfolk. The incoming tenant pays for the crop of seeds and turnips, and for clover leys, but not for dung. He has to draw to market within reasonable distance the outgoing tenant's corn from the last year's crop, in return for which he gets the straw and chaff. Northamptonshire.—The incoming tenant pays for fallows, seeds sown, and labour, but not for manure. Northumberland.-The right of pre-entry allows an incoming tenant to make his fallows, sow clover and grass seeds, and cart out the dung of the last year's crop, to which he is entitled. The hold- ings generally expire at Lady-day, but the outgoing tenant is en- titled to the crops of the last year; the carting and stacking of 628 VALUATION OF TILLAGES. which is done by the incoming tenant, who in return is entitled to the straw when thrashed. Nottinghamshire.-The incoming tenant pays for fallows, labour, seed, and sowing, and to a limited extent for unexhausted im- provements. Oxfordshire.—The incoming tenant pays for labour on fallows, seeds, and sowing, and for hay of the last year at a fodder price, but not for dung. Rutlandshire.—The incoming tenant pays for labour on the fal- lows, and for carting the dung. If a Lady-day tenancy, he also pays for wheat crop, turnips, and seeds, for winter ploughing; and if the spring corn, is sown for seeds, sowing, and labour. Shropshire. The incoming tenant pre-enters on the farm. Pays for the wheat crop and clover seeds upon the land, if they have not been previously fed off, and for the dung and unconsumed hay and straw of the last year's growth. (This custom assumes a Lady- day entry.) Somersetshire.—The tenancy generally commences at Christmas or Lady Day. The incoming tenant pays for the crop of wheat, or for labour, seed, and sowing, for clover seeds and sowing, some- times for dung, and generally for hay and straw at fodder price. Staffordshire. The incoming tenant at Lady-day pays for what in this county is called pin-following, but what in Surrey would be termed a bastard fallow, and for hay and straw at fodder price, which here is two-thirds of the market price of the former, and one- third of the latter. The custom leaves the dung on the farm for the use of the incoming tenant, but it is equally the custom of this county that what a tenant pays for when he enters, he is to be paid for when he leaves. The custom as to the wheat crop is very undefined. Suffolk.-The incoming tenant at Michaelmas pays for all the labour on the fallows, the seeds sown, and labour attending them, and for the dung and hay. He is required to draw out the out- going tenant's corn, and in return gets all the straw and chaff of the last year's crop free. Surrey.—The county of Surrey is notorious for its high valua- tions. The tenancies, although frequently entered upon at other times, are generally computed as from Michaelmas. The valuation comprises fallows, half fallows, dressings, half dressings, grass seeds, underwood, clover leys, hay, straw, and manure upon the premises. Under the heading of " Fallows" are included all the ploughings, harrowings, rollings, and couchings, whether judicious or unneces- VALUATION OF TILLAGES. 629 sary, that the fallow can be shown to have received at the hands of the outgoing tenant, a year's rent and rates, and if sown with turnips, the seed and sowing. Half fallows are generally charged at an agreed sum by the valuators, without going into the details of the previous fallow. They are said to arise, as has been pre- viously explained, on lands that have only borne one straw crop since the full fallow. Dressings are charged at the full value of the dung, in addition to the cost of carting and spreading. Half dressings arise in the same way as half fallows, and are generally treated similarly by the valuers. Clover seeds are charged at the cost of seed and la- bour. Clover leys at their estimated value. Underwoods accord- ing to their growth. Hay and straw sometimes at a fodder price, and sometimes at a market price; and dung at its measured value. In those cases that the occupancy commences at a period of winter or spring, the incoming tenant is charged with the costs of all the labour, seed and sowing, rates and taxes, that have been expended upon the farm since the previous Michaelmas (from which date his rent commences,) in addition to the valuation to which he would have been subject had he entered at Michaelmas. When the occupation commences in summer, the incoming tenant generally takes to the standing crops at a valuation, and the out- going clears up the rent to the following Michaelmas, excepting such parts thereof as are taken into account in the valuation of the fallows. It is an essential feature in the custom of Surrey that a tenant is entitled to be paid on leaving for all such things as he paid for when he entered. The general tenure of Surrey may be said to be leases of 7, 14, or 21 years, the middle term prevailing. The rentals are almost without exception half-yearly payments in money. The landlord generally finds timber rough upon the stem, and bricks, tiles, and lime at a kiln within seven miles, for the repairs, the tenant finding cartage and labour. In most cases the restrictions as to cultiva- tion direct that one-fourth of the arable lands must be in wheat or beans; one-fourth fallow and turnips; one-fourth barley or oats; and one-fourth seeds. I have gone more fully into the customs of this county because they are familiar to me, and because it will in some measure tend to illustrate my interpretation of certain technical expressions made use of by me which bear a different meaning in different counties. To take but one instance, I understand a "Dressing to be a quantity of manure bestowed on the land; whereas I believe in many parts of England the word "dressing" is applied to one course "" 630 VALUATION OF TILLAGES. of ploughing, harrowing, &c., and it is very common to say that a fallow has five dressings. Sussex. Those portions of the county that adjoin Kent and Surrey have very similar customs to those of the adjoining counties. In other parts the labour upon the fallows is charged, but not the rent and rates. The dung arising out of the crop of the last two years of the tenancy belongs to the incoming tenant, the only charge upon it being for carting, casting into heaps, turning, and spreading. The incoming tenant sometimes carts to market the corn of the last year's growth belonging to his predecessor, taking in return the straw and chaff. When this carting is not done, the straw and chaff is paid for at fodder price. Warwickshire.—The incoming tenant at Lady-day generally pays for seed, sowing, rent, and rates on the wheat crop from Michael- mas; but a custom prevails allowing the outgoing tenant to retain possession of the wheat lands that are after fallow, not otherwise, until the following Michaelmas, to get in his wheat crop, in which case he pays the new occupier the half-year's rent and rates. The custom as to spring crops allows no right of pre-entry to the in- coming tenant; if the outgoing occupier prepares and sows the land, he is paid for so doing at valuation. No fallows are paid for in this county; but if the turnip crop fails on fallowed land, the out- goer is allowed one half-year's rent and rates thereon in considera- tion of the labour he has expended. The dung is not paid for. Westmoreland.—The incoming tenant pays for seed, sowing, and labour, previously expended, and a portion of the rent and rates of fallows. (The expressions waygoing and oncoming are substituted in the North for outgoing and incoming in the South.) Wiltshire. The incoming tenant has the right of pre-entry, to make his fallows and sow his wheat, turnips, and grass seeds. He is entitled to the dung arising from the crops of the last two years, and the outgoing tenant consumes the fodder. Worcestershire.-The chief feature in the custom appears to be, that a tenant leaves a farm on the same conditions as he entered upon it. Yorkshire, East Riding of.-The incoming tenant at Lady-day is entitled to pre-entry at Candlemas to plough lands for fallow. He has to pay for clover seeds and sowing, and for the manure arising from the last year's crop. He also pays for the growing crops of corn at a valuation, made at suitable times near harvest. The pay- ments for the amount of the growing crops are (in some cases I am aware, but whether generally so I am not fully informed) allowed to be made by instalments, as the corn is thrashed, so that a VALUATION OF TILLAGES. 631 smaller capital is required to take to a farm under this custom than is at first sight apparent. Yorkshire, North Riding of.-The same right of pre-entry exists as in the East Riding from Candlemas-day, the tenancy com- mencing at Lady-day. The incoming tenant pays for clover seed and sowing of the preceding year, and for the manure from the last year's crop. He also pays for the wheat crop at valuation at harvest, or allows the outgoing tenant to harvest the crop. Yorkshire, West Riding of. The tenancy commences at Lady- day, the tenant having a right of pre-entry at Candlemas. Fallows and half fallows, dressings and half dressings, are valued in this Riding in some instances. The wheat crop is sometimes har- vested by the outgoing tenant; sometimes the incoming occupier pays for it at valuation; and clover leys are paid for. I have now gone through the whole of the customs in force in the several counties of England, so far as they relate to, or form the subject of, valuations of tenant-right, and as well as I have been enabled to gather information. It will be obvious to every practical man that the customs of many counties are exceedingly difficult to define, varying as they frequently do in different parishes of the same county, and especially is this the case with reference to the periods of entry. My endeavour has been to place together such an amount of information as will convey a general idea of the whole question; the information is of necessity imperfect, but at the same time it affords a key to the principal features. The following specimen of a Surrey Valuation will sufficiently elucidate the principle of making them, and writing out the in- ventory. Before commencing a valuation, the valuators should always appoint in writing an umpire, to whom matters of difference may be referred. If this is not attended to, difficulties sometimes arise at a subsequent stage in the choice of an umpire, causing great delay and trouble. 632 VALUATION OF TILLAGES. SPECIMEN OF FIELD BOOK. Quantity in each Field. Name of Field. Quantity Price in each Course. Items of Valuation. per Acre. Value of Labour and Tillages. Value of Dressings. A mount of Rent and Total Value. Rates. Value of each Field. A. R. P. 42 20 Garson. A. R. P. 40 0 0 5 times Ploughed.@10/ £. s. d. 100 0 0 £. s. d. £. s. d. £. s. d. £. s. d. Fallow. 2 tine Dragged ,, 1/4 568 Once Rolled Fallow Rotation of Crops, 1849 Wheat Fallow 1850 Tares fed 1851 Wheat 1852 Fallow (with 4 horses) », 1/6 300 108 6 8 20 0 0 Dunged 12 Cart Loads per Acre Carting and ,, 80/ 80 0 0 80 0 0 Spreading 40 0 0 Rent and Rates ,, 35/ 70 0 0 70 0 0 258 6 8 20 0 0 Barn Field. 20 0 0 5 times Ploughed.,, 11/ Fallow. 2 tine Dragged » 1/6 Once Rolled Rotation of Crops, 55 0 0 300 1 10 0 1849 Wheat 1850 Tares fed Fallow 1851 Wheat 1852 Fallow (with 4 horses) Dunged 12 Cart Loads per Acre Carting and Spreading Rent and Rates 1/6 ", 80/ ,, 351 80 0 0 .. 59 100 80 0 0 35 00 35 0 0 174 100 VALUATION OF TILLAGES. 633 34 1 6 Guildford Field. Seeds Rotation of Crops, 1849 Wheat 1850 Beans 1851 Fallow, Swedes 1852 Wheat, Oats. Seeds. 33 0 0 7 lbs. of Clover Seed, per acre 7 lbs. of Trefoil per acre 2 tine small Harrowing. Once Rolling @ 6d. 5 156 4d. 3 170 6d. 1 130 ,, 6d. 0 16 6 Half Fallow. 40s. 66 00 "" 78 2 0 18 0 0 Half Dressing. 40s. 36 0 0 "" 36 0 0 114 2 0 20 316 Twenty Acres. 20 0 0 Twice Ploughed. 12s. 24 0 0 24 0 0 "" 24 0 0 Rotation of Crops, 1849 Wheat 1850 Clover 1851 Oats 1852 Peas. 20 216 Long Field. Clover Ley Rotation of Crops, 1849 Tares and Swedes 20 0 0 The Ley 458. 45 00 "" Half Dressing. 35s. 35 0 0 45 0 0 35 0 0 "" 80 0 0 8 030 Common Field. 8 00 Half Fallow. 40s. 16 0 0 16 0 0 16 0 0 1850 Peas 1851 Wheat 1852 Clover. Rotation of Crops, 1849 Clover Ley 1850 Oats 1851 Tares fed Fallow 1852 Wheat. 2 R 634 VALUATION OF TILLAGES. 29 1 6 Pond Field. Rotation of Cropping, 1849 Clover Ley 1850 Wheat 1851 Peas Fallow 1852 Wheat. 28 0 0 Half Dressing. @ 40s. 56 0 0 56 0 0 || 56 0 0 0 29 3 10 Carthouse Field. 28 0 0 Two tine small 6d. 1 8 0 Seeds Harrowing. >> Rotation of Cropping, 1849 Beans 1850 Wheat 1851 Swedes, Mangold, Tares 1852 Wheat Seeds. Once Rolling 200lbs of Clover Seed 6d. 140 "" 6d. 5 0 0 "" 10 Bushels of Rye Grass S 6s. 3 00 "" 10 2 0 20 0 0 Half Dressings 40s. 40 0 0 40 0 0 .... 20 0 0 Half Fallow 40s. 40 0 0 40 0 0 "" 90 2 0 35 2 8 Cross Path Field. 34 0 0 Rotation of Cropping, 16 0 0 Twice Ploughed * Rent and Rates. 13s. 44 4 0 44 4 0 "" 30s. 24 0 0 24 0 0 1849 Peas "" 68 4 0 Fallow 1850 Wheat 1851 Winter Beans 1852 Tares Tares fed, cut, Fallow. * The Rent and Rates is allowed on that portion of the Field from which the Tares were fed. This has been decided by very com- petent judges as being the Surrey custom. I cannot discover the equity of it. The Tenant should surely pay the Rent of Land upon which he has kept a flock of Sheep VALUATION OF TILLAGES. 635 SUMMARY. Quantity in each Field. Name of Field. Quantity in each Course. Items of Valuation. Value of Price. Labour and Tillages. Value of Dressings. Amount of Rent and Rates. Value of Total Value. each Field. A. R. P. A. R. P. L. S. D. L. S. D. 42 2 0 Garson 4000 Fallow 108 68 80 0 0 200 0 Barn Field 2000 Fallow. 59 10 0 8000 I.. S. D. 70 0 0 3500 L. 8. D. 341 6 Guildford Field 3300 Seeds 78 20 36 3600 20 3 16 Twenty Acres 2000 Ploughed after Peas 24 L. S. D. 258 68 17410 0 114 20 24 00 20|2|16|| Long Field 2000 Clover Ley. 45 010 350 0 80 00 • 8030 Common Field. 80 Wheat Ersh 16 ΟΙ Ο 291 6 Pond Field 28 0 0 Wheat Ersh 56 1010 29 3 10 Carthouse Field. 28 0 0 35 2 8 Crosspath Field. 3400 Seeds Fallow 50 20 40 40 00 44 40 24 010 241 0 12 23100 425 48327 0 0 129 16 O 56 0 90 2 68 40 881 48 A Hill of Dung, 33 yards by 10 yards, and 2 feet high, at 5s. per yard A Rick of Clover Hay, 10 yards by 6 yards, and 4 yards high, at £4 10s. per load Three Years' growth in about 3 acres of Underwood Amount of the Valuation 55 00 162 00 660 1104108 £1104 108 EDWARD RYDE, JAMES SMITH, } Valuators. 636 VALUATION OF TILLAGES. With reference to the preceding form of Field Book, little need be said. It will be found convenient in general use, although perhaps few valuers will adopt it, simply because it appears to cause extra trouble; such, however, is not the case, and the information it affords is very interesting. The first column sets forth the actual quantity of the field, including waste and hedge and ditch: the outside measure thereof, properly speaking. The second column contains the name of the field, under which is written the cultivation, and in the same column there is always room to make a memorandum of the rotation of cropping, which should be enquired into. The third column sets forth the inside measure of the field, or the different quantities included in one course of husbandry. The fourth column contains the different items of the valuation. The fifth is set apart for the price. The sixth, seventh, and eighth contain respectively the amounts of different charges, distinguishing those for dressings and half dressings, and the allowance for rent and rates from the valuation of the tillages and labour. The ninth is a column for the totals of the three preceding columns and for any extraneous matters that cannot be ranged under either of the other heads. The tenth and last column contains the total amount of valuation in each field in a convenient form for casting. In writing out the inventory the prices are not given. The following is the manner in which this is done:— An INVENTORY and VALUATION of tillages and tenant- right upon a farm in Surrey, as made between Mr. Daniel Long- staff and Mr. Richard Smith, this 25th day of October, 1852, by Edward Ryde, on the part of the said Daniel Longstaff, and James Smith, on the part of the said Richard Smith. A. R. P. 42 2 0 Garson-Fallow 40 0 0-5 times ploughing 2 tine dragging 20 0 0 40 0 0 Once rolling Dunging, carting & spreading Rent and rates. 20 0 0 Barn Field-Fallow 5 times ploughing 2 tine dragging Once rolling Dunging, carting & spreading Rent and rates. VALUATION OF TILLAGES. 637 A. R. P. 34 1 6 Guildford Field-Seeds 33 0 0 Clover seed and sowing 2 tine small harrowing Once rolling Half fallow 18 0 0 Half dressing. 20 3 16 The Twenty Acres 20 0 0 Twice ploughing. 20 2 16 Long Field-Clover Ley 20 0 0 The ley Half dressing. 8 0 30 Common Field-Wheat Ersh 8 0 0 Half fallow. 29 1 6 Pond Field— Wheat Ersh 29 3 10 28 0 0 Half dressing. Carthouse Field-Seeds 28 0 0-2 tine small harrowing Once rolling Clover seed and sowing 20 0 0 Half dressing Half fallow. 35 2 8 Cross Path Field-Fallow 34 0 0 16 0 0 Twice ploughed Rent and rates A hill of dung A rick of clover hay 3 0 0 Wood-3 Years' growth of underwood. The tillages, and other acts of husbandry, matters and things mentioned in the foregoing inventory, are valued at the sum of one thousand, one hundred and four pounds, ten shillings and eight pence, by us, EDWARD RYDE, JAMES SMITH. In connection with this subject the following directions and Tables for Measuring Hay Ricks will be useful. Let fig. 173" represent a hay stack, the content of which is required :- It will be obvious that the mean length, width, and height, taken at the places indicated on this fig., are the correct dimen- sions for ascertaining the proper cubic content of the stack. The density of the stack must then be estimated, and the remaining operations are supplied by the tables. 638 TABLES FOR MEASURING HAY RICKS. Table 1. To be used when the Hay is very close. Feet 6 77 8 9 10 11 12 13 14 Feet feet feet feet feet feet feet feet feet feet wide. high. high. high. high. high. high. high. high. high. wide. 67 72 7 84 B88 84 96 108 120 132 144 156 168 98 112 126 140 154 168 182 196 67 7. 96 112 128 144 160 176 192 208 224 9 108 126 144 162 180 198 216 234 252 10 120 140 160 180 200 220 240 260 280 11 132 154 176 198 220 242 264 286 308 13 15 16 17 19 20 21 224 B CO 2 222 12 144 168 192 216 240 264 288 312 336 12 156 182 208 234 260 286 312 338 364 13 14 168 196 224 252 280 308 336 364 392 180 210 240 270 300 330 360 390 420 192 224 256 204 238 272 288 320 306 352 384 416 448 340 374 408 442 476 17 216 252 288 324 360 396 432 468 504 18 228 266 304 342 380 418 456 494 532 19 240 280 320 360 400 440 480 520 560 20 252 294 336 378 420 462 504 546 588 21 264 308 352 396 440 484 23 276 322 368 414 27 24 288 336 384 25 300 350 26 312 364 324 378 400 416 460 506 432 480 528 450 500 550 468 520 432 486 540 528 572 552 598 576 624 672 600 650 700 572 624 676 728 594 648 702 756 616 644 23 24 25 26 27 ∞∞ = 22± 2 CFD - 222 * *&& 9 10 11 14 15 16 EXAMPLE. Required the Content of a Hay Stack 23 feet long, 16 feet wide, and 10 feet high; the Hay being very close. In Table 1, opposite 16 feet wide, and under 10 feet high, stands the number 320, which is carried to Table 4, to complete the calculation. Note. A very little practice will show which of the Tables, 1, 2, or 3, should be made use of for different description of Ricks, as, for example, suppose a person were to measure a Rick and estimate the content by Table 2, which when cut out proved to contain more Hay than the Tables gave him, he would know in future, that that description of Rick must be measured by Table 1, or if it contained less, then would he know that Table 3 must in future be used; and, having acquainted himself with the kind of Rick adapted for the two extremes, the mean, or Table 2, will of course follow. TABLES FOR MEASURING HAY RICKS. 639 Table 2. To be used when the Hay is of a mean density. Feet 6 7 8 9 10 11 12 13 14 Feet feet feet feet feet feet feet feet feet feet wide. high. high. high. high. high. high. high. high. high. wide. 67 8 9 90 105 88888 220 82 88 70 90 100 110 120 130 140 81 93 105 116 128 140 151 163 67 93 106 120 133 146 160 173 186 8 120 135 150 165 180 195 210 9 10 100 116 133 150 166 183 200 216 233 10 11 110 128 146 165 183 201 220 238 256 11 231 12 120 140 160 180 200 220 240 260 280 13 130 151 173 195 216 238 260 281 303 14 140 163 186 210 233 256 280 303 326 221 12 13 14 15 150 175 200 225 250 275 300 325 350 15 210 2 222 3 238 A 16 160 186 213 240 266 293 320 346 373 17 170 198 226 255 283 311 340 368 396 18 180 210 240 270 300 330 360 390 420 19 190 221 253 285 316 348 380 411 443 20 200 233 266 300 333 366 400 433 466 20 21 210 245 280 315 350 385 420 455 490 21 220 256 293 330 366 403 440 476 513 23 230 268 306 345 383 421 460 498 536 23 24 240 280 320 360 400 440 480 520 560 24 25 250 291 333 375 26 260 303 346 416 390 433 458 500 541 583 476 520 563 606 27 270 315 360 405 450 495 540 585 630 9702 222 * *** * 17 18 19 25 26 EXAMPLE Suppose a Hay Stack, 33 feet long. 18 feet wide, and 12 feet high, and the Hay of a mean density, what does it contain? In Table 2, under 12 feet high, and opposite 18 feet wide, stands the Number 360, which must be carried to Table 4, to complete the calculation. 640 TABLES FOR MEASURING HAY RICKS. Table 3. To be used when the Hay is very loose. Feet 6 8 9 10 11 12 13 14 Feet Feet Feet Feet Feet Feet Feet Feet Feet Feet wide. high. high. high. high. high. high. high. high. high. wide. 6 51 7 10 11 ∞ DOE & B 8 9 DO 8 N* 60 68 77 85 100 94 110 ༄ཧྨ ཙ 828 889 77 85 94 102 111 120 6 90 100 110 120 130 140 7 102 114 125 137 148 160 102 115 128 141 154 167 180 114 128 142 157 171 185 200 10 125 141 157 172 188 204 220 12 102 120 137 154 171 188 205 222 240 12 13 111 130 148 167 185 204 222 241 260 14 120 140 160 180 200 220 240 260 280 15 128 150 171 192 214 235 257 278 300 15 16 137 160 182 205 228 251 274 297 320 16 18 19 *** & ***3 * 285 145 170 194 218 242 267 291 315 340 154 180 205 231 257 282 308 334 360 18 162 190 217 244 271 298 325 352 380 19 171 200 228 257 285 314 342 371 400 180 210 240 270 300 330 360 390 420 21 22 188 220 251 282 314 345 377 408 440 23 197 230 262 295 328 361 394 427 460 24 205 240 274 308 342 377 411 445 480 214 250 285 321 357 392 428 464 500 25 26 222 260 297 334 371 408 445 482 520 27 231 270 308 347 385 424 462 501 540 27 ∞ DOE 2 BED FOR 2 723 * Q&A 13 14 17 20 24 26 EXAMPLE.-Suppose a Hay Rick 40 feet long, 18 feet wide, and 12 feet high, the Hay very loose, what are its contents? In Table 3, under 12 feet high, and opposite 18 feet wide, stands the number 308, which carried to Table 4, will complete the calculation. TABLES FOR MEASURING HAY RICKS. 641 21 22 23 24 25 26 ft. long. | ft. long. | ft. long. | ft. long. | ft. long. | ft. long. Trusses. Trusses. Trusses. Trusses. Trusses. Trusses. Numbers. 15 16 17 18 19 20 ft. long. ft. long. ft. long. ft. long. ft. long. ft. long. Trusses. Trusses. Trusses. Trusses. Trusses. Trusses. Numbers. Table 4. Completing the Calculations and showing the Content of Ricks, in Trusses. 123 1 3 13 1 2 1 3 3 3 4 2 24 2 2 2 4 Q 4 2 4 6 3 7 7 7 6 7 8 9 9 10 10 7 8 8 9 9 10 10 11 11 12 12 13 9 9 10 10 11 12 6 12 13 13 14 15 15 10 11 11 12 13 14 7 14 15 16 16 17 18 12 12 13 14 15 16 16 17 18 19 20 20 9 13 14 15 16 17 18 9 18 19 20 21 22 23 10 15 16 17 18 19 20 10 21 22 20 30 32 34 36 38 40 20 42 44 30 45 48 51 54 57 60 30 63 66 40 60 64 68 72 76 80 40 84 88 9:2 2988 24 25 26 48 50 52 72 75 78 96 100 104 50 75 80 85 90 95 100 50 105 110 115 120 125 130 60 90 96 102 108 114 120 60 126 132 138 144 150 156 70 105 112 119 126 133 140 70 147 154 161 168 175 182 80 120 128 136 144 152 160 80 168 176 184 192 200 208 90 135 144 153 162 171 180 90 189 198 207 216 225 234 100 200 150 160 170 180 190 200 100 210 220 230 240 250 260 300 320 340 360 380 400 200 420 440 460 480 500 520 300 450 480 510 540 400 600 640 680 720 500 750 800 850 900 600 900 960 1020 | 1080 700 1050 1120 1190 1260 570 600 300 630 660 1140 760 800 400 950 1000 500 1200 600 840 1050 1260 690 720 750 880 920 960 1000 1040 1100 1150 1200 1250 | 1300 780 1320 1380 1440 1500 1560 1330 1400 700 1470 1540 1610 1680 1750 1820 EXAMPLE, In Example to Table 1 our calculation was held in abeyance after finding the number 320. Now by this Table, under 23 feet long, opposite 300 stands 690 Trusses. 20 46 "" "" "" 320 content. 736 1 642 TABLES FOR MEASURING HAY RICKS. 27 28 29 30 31 32 ft. long. ft. long. ft. long. | ft. long. | ft. long. ft. long. Numbers. 33 34 35 36 37 ft. long. ft. long. ft. long. ft. long. ft. long 38 ft, long Trusses. Trusses. Trusses. Trusses. Trusses. Trusses. Numbers. Table 4 continued. Showing the Content of Ricks, in Trusses. Trusses. Trusses. Trusses Trusses. Trusses. Trusses. 12 9 & 3 Q7 20 00 3 3 6 6 6 9 123 3 3 3 3 3 6 6 7 7 7 7 9 10 10 10 11 11 4 10 11 11 12 12 12 4 13 13 14 14 14 15 13 14 14 15 15 16 16 17 17 18 18 19 6 16 16 17 18 18 19 6 19 20 21 21 22 22 18 19 20 21 21 22 23 23 24 25 25 26 8 21 22 23 24 24 25 26 27 28 28 9 24 25 26 27 27 28 9 29 30 31 32 8883838 30 34 10 27 28 29 30 31 32 10 33 34 35 36 37 38 20 54 56 58 60 62 64 20 66 68 70 72 74 76 30 81 84 87 90 93 96 30 99 102 105 108 111 114 40 108 112 116 120 124 128 40 132 136 140 144 148 152 50 135 140 145 150 155 160 50 165 170 175 180 185 190 60 162 168 174 180 186 192 60 198 204 210 216 222 228 70 189 196 203 210 217 224 70 231 238 245 252 259 266 232 80 216 224 90 243 252 261 100 270 280 290 300 310 200 540 560 580 600 620 300 810 840 870 900 930 960 300 990 400 1080 1120 1160 1200 1240 1280 400 1320 | | 500 1350 1400 1450 1500 1550 1600 500 1650 600 1620 1680 1740 1800 1860 1920 600 1980 700 1890 1960 2030 2100 2170 2240 700 2310 240 248 256 80 264 272 280 288 296 304 270 279 288 90 297 306 315 324 333 342 320❘ 100 330 340 350 360 370 380 640 200 660 680 700 720 740 760 1020❘ 1050 1360 1400 1440 1480 1700 1750 1800 1850 2040 2100 2160 2380 2450 2520 2590 1080 1110 1140 1520 1900 2220 2280 2660 number 360. In Table 4, under 33 feet long, opposite 300 stands 990 Trusses. EXAMPLE. In Table 2 our calculation was held in abeyance after finding the 27 60 360 content. 1188 198 79 effort. have been taken from the Table, and cast together mentally, without the slightest troublesome at first sight, but on inspection, it will be obvious that the figures might Note.—This calculation, containing two lines of figures, may appear unnecessarily TABLES FOR MEASURING HAY RICKS. 643 in others. Table 4 continued. Showing the Content of Ricks, in Trusses. 45 46 47 48 49 50 ft. long. ft. long. | ft. long. ft. long. | ft. long. | ft. long. Trusses. Trusses. Trusses. Trusses. Trusses. Trusses. Numbers. 39 40 42 41 ft. long. ft. long. ft. long. | ft. long. 43 44 ft. long. ft. long. Trusses. Trusses. Trusses. Trusses, Trusses. Trusses. Numbers. 1 2 IQ 3 3 7 11 12 4 15 16 19 6 23 24 +0202*8 4 12 16 +020 4 4 4 4 8 8 8 12 12 13 1Q3 4 4 4 4 4 5 2 9 9 9 9 9 10 13 13 14 14 14 15 16 17 17 18 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 24 25 25 26 6 27 27 28 28 29 30 7 27 28 28 29 30 30 31 32 32 33 34 35 8 31 32 32 33 34 35 36 $6 37 38 39 40 9 35 36 36 37 38 39 9 40 41 42 43 44 45 10 39 40 41 42 43 44 10 45 46 47 48 49 50 20 78 80 82 84 86 88 20 90 92 94 96 98 100 30 117 120 123 126 129 132 30 135 138 141 144 147 150 40 50 156 160 164 195 200 205 210 215 60 234 240 246 252 70 273 280 287 294 80 312 320 328 336 90 351 360 369 378 387 430 168 172 176 40 180 184 188 192 196 200 220 50 225 230 235 240 245 250 258 264 60 270 276 282 288 294 300 301 308 70 315 322 329 336 343 350 344 352 80 360 368 376 384 392 400 396 90 405 414 423 432 441 450 300 400 1560 700 500 1950 600 | 2340 2730 100 390 400 410 420 200 780 800 820 840 860 920 940 960 980 1170 1200 1230 1260 1290 1320 300 1350 1380 1410 1440 1470 1600 1640 1680 1720 1760 400 1800 1840 1880 1920 1960 2000 2050 2100 2150 2200 500 2250 2300 2350 2400 2450 2400 2460 2520 2580 2640 600 2700 2760 2820 2880 2940 2800 2870 2940 3010 3080 700 3150 3220 3290 3360 3430 440 100 450 460 470 480 490 500 880 200 900 1000 1500 2000 2500 3000 3500 EXAMPLE number 308. In Table 4, under 40 feet long, opposite 300 stands 1200 Trusses. By Table 3 our calculation remained in abeyance after finding the 32 8 "" calculating by the Load of 36 Trusses in some counties, and by the Ton of 40 Trusses Note.-The Contents are given in Trusses on account of the different custom of 308 content. 1232 644 TABLES FOR MEASURING HAY RICKS. Trusses. Table 5. Showing the number of loads and tons which are contained in any number of trusses. Trusses. 36 1 0 40 1 4 0 36 1 0 270 280 7 18 6 30 504|| 14 0 7 28 7 0 510 14 6 12 24 12 30 760 756 21 21 0 18 36 4 19 0 50 1 14 1 10 288 8 0 7 8 520 14 16 13 0 792 22 0 19 32 60 1 24 1 20 290 290 8 8 2 7 10 530 14 26 13 10 800 22 8 20 0 820 70 1 34 1 30 300 8 12 7 20 540 15 0 13 20 828 23 0 20 28 72 2 0 1 32 310 8 22 7 30 550 15 10 13 30 840 23 12 21 0 80 2 8 2 0 320 8 32 8 0 560 90 2 18 2 10 324 90 8 100 2 28 2.20 330 9 6 15 20 14 0 864 15 30 14 10 880 16 0 14 16 900 108 3 0 2 28 340 9 16 110 3 2 2 30 350 9 26 120 3 12 130 3 22 3 0 3 10 360 10 0 370 10 10 140 3 32 3 20 380 10 20 8 30 590 9 0 600 9 10 610 9 20 612 144 4 0 3 24 150 4 6 3 30 160 4 16 4 0 390 10 30 396 11 0 396 11 0 400 11 4 9 30 620 16 8 4 570 10 576 8 20 580 9 36 630 9 36 630 10 0 640 16 4 14 20 920 16 14 14 30 936 16 24 15 0 960 16 34 15 10 972 17 0 15 12 1000|| 17 8 15 20 1100 17 18 17 28 15 30 1200 24 0 21 24 24 16 22 0 25 0 22 20 25 20 23 0 26 0 23 16 26 24 24 0 27 27 0 24 12 27 28 25 0 30 20 27 20 33 12 30 0 01300 36 36 4 32 20 170 4 26 4 10 410 11 14 10 10 648 18 0 16 81400 81400 38 32 35 0 180 5 0 4 20 190 5 10 4 30 200 5 20 5 0 420 11 24 430 11 34 432 12 0 10 20 650 10 30 660 10 32 670 18 2 16 10 1500 41 24 37 20 18 12 16 201600 44 16 40 0 18 22 16 30 1700 30|1700 47 210 5 30 5 10 440 12 8 11 0 680 18 32 17 216 6 0 5 16 450 12 18 220 6 4 230 6 14 5 20 5 30 460 12 28 468 13 0 240 6 24 6 0 470 13 2 250 6 34 252 7 0 490 6 10 480 13 12 6 12 260 7 8 8 6 20 500 11 10 684 11 20 690 11 28 700 11 30 710 12 0 720 13 22 12 10 730 13 32 12 20 740 19 0 17 0 1800 41900 47 8 42 20 50 0 45 0 52 28 47 20 6 17 10 2000 17 20 2500 17 30 3000 19 19 16 19 26 20 0 18 03500 97 8 87 20 20 10 18 10 4000 111 4100 0 20 20 18 20 5000 138 32125 0 55 20 50 0 69 16 62 20 83 12 75 0 EXAMPLE 1. In 1800 trusses, how many loads or tons? Opposite 1800 trusses stands 50 loads or 45 tons. EXAMPLE 2. In 736 trusses, how many loads ? Opposite 730 stands 20 loads, 10 trusses, to which if we mentally add 6 trusses, we get the required answer. EXAMPLE 3. In 736 trusses, how many tons ? Opposite 730 stands 18 tons 10 trusses, to which if we mentally add the remaining 6 trusses, we get the required answer. VALUATION OF HAY RICKS. 645 2s. 4d. Trusses. Per Truss, £4 4s. Od. Per Load, £4 138. 4d. Per Ton. £ s. d. £ s. d. £ s. d. £ s. d. 30 40 20050 0 10 0 0 10 5 0 10 10 5 0 11 3 0 11 10 1 0 0 1 0 10 1 1 8 10 1 2 1 3 28. Table 6. Showing the Value of any Number of Trusses at various prices per Truss, Load, or Ton. Per Truss, £3 12s. Od. Per Load, £4 0s. Od. Per Ton. 2s. id. Per Truss, £3 15s. Od. Per Load, £4 3s. 4d. Per Ton. 2s 2d. Per Truss, £3 18s. Od. Per Load, £4 68. 8d. Per Ton. 28. 3d. Per Truss, £4 ls. Od. Per Load, £4 10s. Od. Per Ton. 28. 5d. Per Truss, £4 78. Od. Per Load, £4 168. 8d. Per Ton. 28. 6d. Per Truss, £4 10s. Od. Per Load, £5 0s. Od. Per Ton. 28. 7d. Per Truss, £4 138. Od. Per Load, £5 38. 4d. Per Ton. 28. 8d. Per Truss, £4 16s. Od. Per Load, £5 68. 8d. Per Ton. £ s. d. 0 13 4 48 £ s. d. £ s. d. £ s. d. £ s. d. 8 0 12 1 5 0 12 6 0 12 11 4 1 4 2 10 1 5 5 0 1 5 10 1 6 8 200 2 1 8 2 3 4 20 2 5 0 2 6 8 2 8 4 20 2 10 0 2 11 8 2 13 4 3 0 0 3 26 3 5 0 30 3 7 6 3 10 0 3 12 6 30 3 15 0 3 17 6 4 0 0 0 4 0 0 0 4 3 4 4 6 8 40 4 10 0 4 13 4 4 16 8 40 500 5 3 4 568 50 5 0 0 0 5 4 2 5 8 4 50 5 12 6 5 16 8 6 0 10 50 6 5 0 69 2 6 13 4 60 6 0 0 0 6 5 0 6 10 0 60 6 15 0 7 0 0 7 5 5 0 60 7 10 0 7 15 0 8 0 0 70 7 0 0 7 5 10 7 11 8 70 7 17 8 3 4 8 9 2 70 8 15 0 9 0 10 9 6 8 80 8 0 8 6 8 8 13 4 80 9 0 0 9 6 6 8 9 13 4 80 10 0 0 10 6 10 13 4 90 9 0 0 9 7 6 9 15 0 90 10 2 6 10 10 0 10 17 6 90 11 5 0 11 12 6 12 0 0 100 10 0 0 10 8 4 10 16 8 100 11 5 0 11 13 4 12 1 8 100 12 10 0 12 18 4 13 6 8 200 20 0 0 20 16 8 21 13 4 200 22 10 0 23 6 6 8 24 3 4 200 25 0 0 25 16 8 26 13 4 300 30 0 0 31 5 0 32 10 0 300 33 15 0 35 0 0 36 5 0 300 37 10 0 38 15 0 40 0 0 400 40 0 0 41 13 4 43 6 8 400 45 0 0 46 13 4 48 6 8 400 50 0 0 51 13 4 53 6 8 500 50 0 0 52 1 8 54 3 4 500 56 5 0 58 6 8 60 8 4 500 62 10 0 64 11 8 66 13 4 600 60 0 0 62 10 0 65 0 0 600 67 10 0 70 0 0 72 10 0 600 75 0 0 77 10 0 80 0 0 0 700 70 0 0 72 18 4 75 16 8 700 78 15 0 81 13 4 84 11 8 700 87 10 0 90 8 4 93 6 8 800 80 0 83.6 0 8 86 13 4 800 90 0 93 6 8 96 13 4 800 100 0 0 103 6 6 8 106 13 4 900 90 0 0 93 15 0 97 10 0 900 101 5 0 105 0 0 108 15 0 900 112 10 112 10 0 116 5 0 120 0 0 1000 100 0 200 0 0 2000 3000 300 0 0 4000 400 0 0 104 3 208 6 4 8 312 10 0 416 13 4 EXAMPLE. What is the value of 666 Trusses of Hay at four guineas per Load? Under £4 4s. per Load, opposite 600 stands £70 0 0 108 6 8 216 13 4❘ 2000 325 0 0 3000 433 6 8 4000 1000 112 10 0 116 13 4 120 16 8 1000 125 0 0 129 3 4 133 6 8 225 0 0 233 6 6 8 8 241 13 4 2000 250 0 0 258 6 8 266 13 4 337 10 0 450 0 0 350 0 0 362 10 0 3000 375 0 0 387 10 0 400 0 0 466 13 4 483 6 6 8 4000 500 500 0 0 516 13 4 533 6 8 60 7 0 0 "9 5 and 1 is 18 666 0 11 8 024 £77 14 0 Note.-Here again Trusses have been used as the measure of quantity given, that it might serve equally whether Tons or Loads are the custo- mary measure. Most of the calculations may be made mentally, or at all events with very little addition. -646 VALUATION OF HAY RICKS. Trusses. 3s. 1d. Per Truss. £5 118. Od. Per Load, £6 3s. 4d. Per Ton. £ s. d. £ s. d. £ s. 202UNU. 5 0 14 2 0 14 7 5 0 15 0 1 8 4 1 9 2 10 1 10 0 2 16 0 2 18 4 20 3 0 0 4 5 4 7 6 30 4 10 0 5 10 0 5 13 4 5 16 8 40 600 50 6 17 6 7 1 8 7 5 10 50 7 10 0 8 5 0 8 10 0 8 15 0 60 9 0 0 70 9 12 6 9 18 4 10 4 2 70 10 10 0 80 11 0 0 11 6 8 11 13 4 80 12 0 0 90 12 7 6 12 15 0 13 2 6 90 13 10 0 Table 6 continued.-Showing the Value of any Number of Trusses at various prices per Truss, Load, or Ton. 2s. 9d, Per Truss, £4 19s. Od. Per Load, £5 10s. Od. Per Ton. £ s. d. 0 13 9 1 7 6 2 15 0 4 2 6 28. 10d. Per Truss, £5 2s. Od. Per Load, £5 13s. 4d. Per Ton. £ s. d. 28. 11d. Per Truss, £5 58. Od. Per Load, £5 16s. 8d. Per Ton. 3s. Per Truss, £5 88. Od. Per Load, £6 0s. od. Per Ton. 3s. 2d. Per Truss, 3s. 4d. Per Truss, £6 0s. od. Per Load, £6 138. 4d. Per Ton. 3s. 6d. Per Truss. £6 68 Od. Per Load, £7 08. Od. Per Ton. 3 10 0 5 5 700 8 15 0 10 10 0 12 5 0 14 0 0 15 15 0 £5 14s. Od. Per Load, £6 6s. 8d. Per Ton. 3s. 3d. Per Truss, £5 17s. Od. Per Load, £6 108. od. Per Ton. d. £ s. d. £ s. d. £ s. d. £ s. d. 0 15 5 0 15 10 5 0 16 3 0 16 8 0 17 6 1 10 10 1 11 8 10 1 12 6 1 13 4 1 15 0 3 1 8 3 3 4 20 3 5 0 3 6 8 4 12 6 4 15 0 30 4 17 6 5 0 0 6 3 4 668 40 6 10 0 6 13 4 7 14 2 7 18 4 50 8 2 6 8 6 8 9 50 9 10 0 60 9 15 0 10 0 0 10 15 10 11 1 8 70 11 7 6 11 13 4 12 6 8 12 13 4 80 13 0 0 13 6 8 13 17 6 14 5 0 90 14 12 6 15 0 0 100 13 15 0 14 13 4 14 11 8 100 15 0 0 15 8 4 15 16 8 100 16 5 0 16 13 4 17 10 0 200 27 10 0 28 6 8 29 3 4 200 30 0 0 30 16 8 31 13 4 200 32 10 0 33 6 8 35 0 0 300 41 5 42 10 0 43 15 0 300 45 0 0 46 5 0 47 10 0 300 48 15 0 50 0 0 52 10 0 400 55 0 0 56 13 4 58 6 8 400 60 0 0 61 13 4 63 6 6 8 400 65 0 0 66 13 4 70 0 0 500 68 15 0 70 16 8 72 18 4 500 75 0 0 77 1 8 79 3 4 500 81 5 0 83 6 8 87 10 0 600 82 10 0 85 0 0 87 10 0 600 90 0 92 10 0 95 0 0 600 97 10 0 100 0 0 105 0 0 700 96 5 0 99 3 4 102 1 8 700 105 0 0 107 18 4 110 16 8 700 113 15 0 116 13 4 122 10 0 800 110 0 0 113 6 8 6 8 116 13 4 800 120 0 0 123 6 8 126 13 4 800 130 0 0 133 68 140 0 0 900 123 15 0 127 10 0 131 5 0 900 135 0 0 138 15 0 142 10 0 900 146 5 0 150 0 0 157 10 0 1000 137 10 0 141 13 4 145 16 8 1000 150 0 0 154 3 4 158 6 8 1000 162 10 0 166 13 4 175 0 0 2000 275 0 0 283 6 6 8 291 13 4 2000 300 0 0 308 6 8 316 13 4 2000 325 0 0 333 6 8 350 0 0 3000 412 10 0 425 0 0 437 10 0 3000 450 0 0 462 10 0 475 0 0 3000 4000 550 0 0 566 13 4 583 6 8 4000 600 0 0 616 13 4 633 6 8 4000 487 10 0 650 0 0 500 0 0 666 13 4 0 525 0 0 0 700 0 0 EXAMPLE. What is the value of 3660 Trusses at £5 10s. per Ton? Opposite 3000 trusses is 600 "" 60 3660 £412 10 0 82 10 0 8 5 0 £503 5 0 VALUATION OF PARISHES. 647 CHAPTER XIX. VALUATION OF PARISHES. In addition to what has been adduced in previous chapters, a very brief description of the principles that govern Parish Valuations, made for the purposes of Poor Law Assessment, will be sufficient. The words of the "Parochial Assessment, Act" are-that no rate for the relief of the poor in England and Wales shall be al- lowed by any justices, or be of any force, which shall not be made upon an estimate of the net annual value of the several heredita- ments rated thereto, that is to say, the rent at which the same might be reasonably expected to let from year to year, free of all usual rates and taxes, and tithe commutation rent charge, (if any,) and deducting therefrom the probable average annual cost of re- pairs, insurance, and other expences (if any,) necessary to maintain them in a state to command such rent. The instructions issued by the Poor-Law Commissioners with reference to this particular clause in the Act, run as follow:- The column headed "Gross Estimated Rental," must be filled up with the estimated value of the holding, calculated on an esti- mate of what would be a reasonable rent to pay from year to year, if there were no tenant's rates and taxes, no tithe, or commutation rent charge, no repairs to be done by the tenant, nor insurance, nor other expences to be incurred by him as necessary to keep the pro- perty in its present condition. The column headed" Rateable Value," must be filled up thus:- From the gross rental, ascertained as above, must be deducted the estimate amount of tenant rates and taxes, of tithe commutation rent charge, (if any,) of repairs and insurance, and of any other expences necessary to keep the property in its present condition. The residue will be the "Rateable Value," or "Net Annual Value," according to the first section of the "Parochial Assessment Act." Now, with reference to the words of the Act, it is quite obvious that the rent alluded to is not intended to be the rent actually paid by the tenant, but the rent the property is fairly worth, in compari- son with other properties in the same parish, and comprised in the same assessment. The correct basis of all parish valuations must evidently be equality and fairness; therefore, it is not possible to make the 648 VALUATION OF PARISHES. amount of rent that any individual tenant may chance to pay for his holding the foundation of any calculation for the assessment of that holding. Yet this is by no means an unusual manner of view- ing the matter. Men say a thing is worth what it will fetch. If a farm or a house is not worth the money that is given for it, how has the tenant been found who will undertake to pay that which he cannot afford. They urge it is strong presumptive evidence of the value of the properties, and therefore, as such, the rent so paid, should be the amount at which the property should be assessed. A landed proprietor, of considerable intelligence, in a parish I once surveyed, told me he should have made a better valuation than I did, for he could have access to the returns of the rentals made for the Income Tax, at which amounts he would have as- sessed all properties that were tenanted, and would have valued those only that were in hand. I will not go beyond this very parish to refute the arguments thus adduced. Take the case of one of the farms, which we will call A. The land is in a high state of cultivation, and is good in quality. The homestead and residence are above the average cha- racter. Previous to the present tenancy it was farmed by the proprietor, who let it without a great portion of the incoming valuation, that is to say, there were so many acres of fallow upon the farm, for which the tenant did not pay; he is to leave the same number on quitting the same, with half fallows, dressings, and half dressings. The dung arising out of the last year's crops was left upon the premises for the use of the tenant, and is to be left in like manner when he quits. Now a farm so taken to, is in a posi- tion to, and did, command a high rent. Take an opposite case. A farm we will call B. The incoming present tenant found no stable nor cow-house upon the premises, and the landlord too poor to build one. The tenant undertook to do it, and it cost him £400. He also paid £800 for the incoming valuation. Now this tenant of course has a lease for 21 years, but then look what deduction must be made in his rent on account of his outlay. year. To take the valuation sum of £800, first: I have already shown in the proper place that a tenant should get something like 10 per cent. for capital thus locked up, so that £800 amounts to £80 a We must next assume that he puts by about £15 per an- num to a sinking fund, to accumulate at compound interest at 5 per cent., to replace at the end of the term the capital expended upon the buildings, upon which he is also entitled to 10 per cent. interest, so that a further sum of £40 arises under this head. VALUATION OF PARISHES. 649 To review the question, suppose each farm to be worth £600 per annum, while the tenant of farm A pays this rent to his landlord, the tenant of B deducts the three sums of £80, £15, and £40, and pays his landlord £465. The following is a tabular view of the case. Amount of Assessment as Yearly Rent paid by estimated at the fair yearly Tenant. value of each Farm. £ Farm A. 600 B. 465 £ 600 600 If these farms were assessed on their rental, A would pay to- wards a rate, at 1s. in the pound, £30; while B would pay but £23 5s., notwithstanding the two farms are of equal value. Such is the comparison with respect to farms and lands; now take one as to houses. Take a row of three houses, all of equal value but belonging to separate proprietors. A takes No. 1, which the landlord has placed in good repair, and undertakes so to maintain it. The rent under these circum- stances is £50 per annum. B takes No. 2, which the landlord has also placed in good repair, but the tenant is to do future repairs and to insure. The rent under such circumstances is £44 a-year. C takes No. 3, which is sadly out of repair, and the landlord too poor to do what is necessary. The tenant undertakes to do the repairs, and to maintain them afterwards, as well as to pay the in- surance. The rent under such circumstances is £37. According to the principle of assessing properties at the rent paid for them- £ s. d. A would pay for No. 1, to a rate at 1s. in the pound 2 10 0 B for No. 2, 2 4 0 وو وو وو وو C for No. 3, 1 17 0 99 وو وو وو an arrangement manifestly unfair, unequal, and incorrect. I am aware it may be objected to what I have said, that tenants do not get sufficient allowance made in their rent, under circum- stances such as I have enumerated; but to this I would reply, that it is quite a matter of personal moment to themselves only. If they are not sufficiently acquainted with business of this nature to 2 s 650 VALUATION OF PARISHES. make an equitable arrangement, there are at all times plenty of competent professional men, who, for a very small fee, would fur- nish all the information that is required. I therefore submit, that in construing the Parochial Assessment Act, the word rent must always be understood to imply such a yearly sum as a property may be fairly estimated to be worth in comparison with other property in the same parish. To pass to the instructions of the Poor Law Commissioners, as to filling up the column headed Gross Estimated Rental, and I must repeat the instructions. "The column headed Gross Estimated Rental must be filled up with the gross estimated value of the holding, calculated on an estimate of what would be a reasonable rent to pay from year to year, if there were no tenant's rates and taxes, no tithe or commu- tation rent charge, no repairs to be done by the tenant, nor insur- ance, nor other expenses to be incurred by him as necessary to keep the property in its present condition.' "" It will be obvious, that to fill up the column in this way, the fair rental of a farm must first be computed in the manner shown in a previous chapter, to which must be added the amount of the poor rates, church, highway, and other rates, now paid by the tenant, because if there were none of these imposts, all tenants would be able to pay a higher rent than they now pay by just the amount of these outgoings. These instructions were adopted by many valuers, myself among others, in about one instance to each valuer; but it was never re- peated. The gross value so obtained represented such entirely fictitious sums, that the greatest dissatisfaction among the rate- payers resulted; and notwithstanding the additions were all taken off again before the rateable value was entered, the thing appeared so grossly inconsistent, that the poor valuer was assumed to know very little of his profession, if his motives were not characterized by a harder term. The practice is, to place in the column of Gross Rental, the sum at which the property has been valued, and to deduct therefrom an amount for repairs, insurance on the buildings, and the tithe or commutation rent charge (if any) for the net rental. It has been suggested that an allowance should be made for the repairs of the gates, roads, and fences on a farm; but the practical difficulties that arise, render futile any attempt to do so. To adopt the principle fairly, a greater allowance must be made on small fields than on large ones; and it could never be a per centage de- duction from the amount of the valuation, inasmuch as a gate costs VALUATION OF PARISHES. 651 as much to repair, if it belongs to land not worth 10s. an acre, as one that belongs to land of four times the value. Moreover, in the valuation of single fields, it would become necessary to ascertain exactly the length of fence belonging to each field, (for some fields are bounded entirely by fences belonging to the adjoining fields,) and whether there is a gate or not. In entering upon the valuation of a parish, considerable care is necessary in arriving at a proper standard of value, which should not be too high; but having determined upon the standard, all the remainder is easily accomplished by comparison. The principles enunciated in the chapter on the Valuation of Estates, will apply in the Valuation of Parishes; so that they need not be again referred to; but a few brief remarks upon the rating of railways, gas and water companies, will not be out of place. If we take the case of a railway, it will serve for the water or gas companies without further illustration. A railway, like a farm, cannot be valued on its cost of construc- tion, since cost is not the measure of value. It is the yearly sum it is worth to a tenant by way of rent that can alone form the sub- ject of calculation as to its value. The first amount to be ascertained is the sum of the annual earnings, which will answer to the item of produce on a farm. From this has to be deducted, first, the cost of working the line, including all outgoings, which is the same thing as the cost of cul- tivation on a farm; secondly, the sum for renewing the rolling stock or plant; thirdly, the interest due to the tenant on the value of his rolling stock; fourthly, a sum for superintendence and manage- ment; and the remainder is rent, at which the railway should be assessed. The cost of construction clearly having nothing to do with the yearly value of the railway, nor the sum at which it should be assessed. There is one item which should possibly be considered in the case of a railway; an extra allowance for casualties, over which a tenant may not be able to exercise control; but great caution must be used in admitting to what extent railway accidents are beyond control. It is exceedingly likely that if the great lines of railway were in the occupation of tenants to whom respon- sibility individually attached, some of the accidents that have occurred would have been avoided, even if we suppose the present managers to be the tenants. For there are, doubtless, many things now sanctioned by managers and boards of directors, of which they cannot approve, but to which they are partly coerced by their 652 VALUATION OF PARISHES. desire to retain the satisfaction of the shareholders, who care very little about anything beyond a large dividend. It is not at all likely that a railway will be situated entirely in one parish, hence comes the necessity of dividing the rate, and fairly apportioning it among the several parishes. Some valuators have argued that this should be done by an equal mileage rate, because say they, inasmuch as no money is taken in some parishes, while large sums are taken in others, an average is all that can be arrived at. Others there are who say that those parishes in which no money is taken, cannot possibly lay claim to any rate, as the earnings there are nothing; or at any rate, they say, you must either assess them on an estimate of the cost of con- structing the line, or of the original value of the land. This is all very fallacious, which there is small difficulty in proving. We must never lose sight of the fact that the railway is liable to be rated at what it is worth to rent. Now, to estimate this rent suppose the portion of the line that is situate in each parish to be held by a separate tenant; of course in such a case all the expenses must be borne by a pro-rata mileage charge, and all the tenants must equitably divide the allowance for superin- tendence and management. To look at the case of the tenant in the parish in which no station is situate; what is his position? He cannot take any money of the public; but would not he take care that if the other tenants took money of the public in other parishes, for travelling over his portion of the line, they should, if he allowed them so to travel, pay him his share of such earnings; and therefore his portion of the line would become as well worth a rent as any of the others, upon which rent he should be assessed, and thus explode the erroneous principles to which I have alluded. The method of apportioning the rent of a railway among the several parishes for the purposes of assessment has been much discussed, and is, as I believe, very little understood. Notwith- standing it is very simple and clearly demonstrable. The working expenses I am prepared to admit may be spread equally over the whole railway according to the earnings, (except in cases of long lines that are worked in distinct sections, and in such cases each section may be considered as a separate line,) the allowance for wear and tear or renewal of the rolling stock may also be so; the interest on tenants' capital should be made to follow the same proportion as the allowance for the renewal of the rolling stock; and the allowance for superintendence should be evidently greater on those parts of the line where the earnings are large, than where they are small. VALUATION OF PARISHES. 653 It is with the division of the earnings or value of the produce of the railway among the several parishes, I have mostly to deal in this place. To illustrate this clearly we must draw a Plan. Fig. 173 m. Without any reference to scale we will assume, that, from the terminus at A, there is in the parish No. 1, 5 miles; and that from terminus A to station B is seven miles, so that two miles of that length is in parish No. 2. From B to C we will take to be 5 miles, of which 1 mile is in parish No. 2, 3 miles in parish No. 3, and 1 mile in parish No. 4. From C to D we have 2 miles-1 mile in parish No. 4, and 1 mile in parish No. 5. From D to E is 6 miles, of which 1 mile is in parish No. 5, and 5 miles in parish No. 6. The most convenient mode will be to tabulate the details, and the results will become apparent. 654 VALUATION OF PARISHES. Names of Stations. Whole Length. Total Length of Line. Earnings. Parish No. 1. Parish No. 2. Parish No. 3. Parish No. 4. Parish No. 5. Parish No. 6. Total Length of Apportioned of Apportioned Line. Earnings. Line. Earnings. Length Length Length of of Apportioned Apportioned Line. Earnings. Line. Earnings. Line. Length of Length Apportioned Earnings. of Line. Apportioned Earnings. Miles. £ Miles. £ Miles. £ Miles. 43 Miles. બ £ Miles. £ Miles. વર £ A to B B to A Ꭰ MODE AODE ABDE 7 21.000 C 12 42000 14 56000 20 80000 or or or cr 15000 2 17500 20000 20000 ☺ ☺ ☺ N 6000 3 10500 3 10500 3 12000 3 12000 3 12000 3 12000 21000 5 15000 2 6000 C 5 15000 1 3000 7 14000 2000 13 32500 1 2500 co co co 9000 6000 7500 122 122 3500 8000 107 8000 2 4000 8000 6 20000 3000 4000 5000 12 10 2000 5000 5 12500 C to A 12 36000 5 LO 15000 5 5000 1 BI 9000 3 9000 1 3000 1000 3 3000 1 1000 3000 1500 16000 11 2000 12 1500 4000 or 10000 ABCE D to A 14 49000 5 17500 3 7 14000 1 10500 3 2000 10500 3 6000 2 3000 221 7000 1 3500 4000 1 2000 1500 1 1500 6 12000 1 2000 20 10000 E to A D ABCA 20 70000 LO 13 26000 5 17500 3 10500 10500 1 2000 3 6000 ww 8 12000 221 7000 4000 1500 6 12000 1 222T 7000 5 17500 4000 10000 3000 2000 or cr 539500 5 137500 89000 102000 64000 49500 7500 10000 97500 VALUATION OF PARISHES. 655 The preceding Table clearly shows the earnings between each separate station and also in each parish. The following table shows the fallacy of taking a general average of the receipts to guide the valuation of a separate parish; it being quite evident that, if the length of line in each of these parishes were let to a separate tenant, the length in parish No. 3, would be worth infinitely more rent than that in parish No. 6:- Parish. No. 1 "" 99 وو 99 وو No. of Miles. Gross Earnings. Earnings per Mile. £ 5 137,500 27,500 3 89,000 29,666.6 3 LO MM 225 123 5 6 Total 20 102,000 | 34,000 64,000 32,000 49,500 24,750 97,500 19,500 539,500 26,975 General Average. Union valuations have been spoken of for the purpose of equalising assessments. The real fact is that there should be one universal assessment throughout England and Wales entrusted to the central authority of one competent surveyor, who should select some 500 or 1000 acres of arable and meadow land, and in the most careful manner estimate its value according to its productiveness. The average price of corn upon which this estimate is based should be preserved, as a standard for regulating the valuation at any future time when higher or lower prices might prevail. The object of valuing these 1000 acres would be to afford a test to the ideas of the several valuators who might be engaged in the work, and as a means whereby uniformity might be attained. Every valuer, upon com- pleting the valuation of a parish or district, should proceed to the valuation of the 1000 acres. If his value of it is in excess of the standard estimate, the valuation he has previously made must be reduced accordingly. This will be found (it is suggested), a very sound way of securing equality of rating, far preferable to any other. Most valuers have impressed upon their minds a certain scale of prices for all kinds of lands, and it is of little use to show them any other standard whether higher or lower: for if the doing so influences them at all, it only has the effect of causing them to commit irregularities of which they would not otherwise have been guilty by causing them to put some fields higher or lower as the case may be, while others they assess at their own standard. SPECIMEN of the Mode of WRITING OUT the VALUATION 1 2 3 4 5 6 7 Name or Situation of each Field or Parcel of Property. Descrip- tion or Mode of No. on Cultivation Map (if of each there Field or be any.) Parcel of Property. Quantity of each Field or Parcel of Property. Gross Total Quan- Estimated tity in each Holding which is separately Rated. Rental of each Hold- Rateable Value of each Hold- ing which is ing whichis separately separately Rated. Rated. Barn Field .... Arable. 16 A. R. P. 9216 A R. P. £ s. d. £\s. d. Long Field . . . . . Arable. 1910 2 1 Little Mead..... Grass.. 25 13 11 Great Mead.... Grass.. 26 19 2 10 Garson. Arable. 27313 1 Oxted Field Arable. 28 29 0 6 Barn and Yard .. 29 0030 Cottage and Garden 30 01 0 102 2 || 35 ||150 0 | 0 ||140|0|0 Lane End Field .. Arable. 3153 2 16 Upper Down. . . . . Arable. 32 19 110 Middle Down. Arable. 3322310 Lower Down Arable. 34 23 110 Drove Lane 35 1 112 Barn and Yard ... 36 0 120 120 2 38 1800 0175 00 Stable Mead... Orchard ... Lawn Pasture. Grass.. 131 5110 Grass.. 132 1120 House and Garden. Grass.. 133 3110 134 03 20 10 3 20 7000 5500 8 11 9 10 in the Form Prescribed by the Poor Law Commissioners. Name or Situation of Description of each each Holding which is separately Rated. Holding which is separately Rated. Name of Occupier of each Holding which is separately Rated. No. in Rate Book. Name of Owner of each Holding which is separately Rated. Bunker's Hill Farm and Lands Smith, John Carlow, Earl of Down Farm Down Land Smith, John Derry, William Manor House House and Land Smith, John Himself SPECIMEN OF FIELD BOOK, Occupier, Higgins, James No. on Plan. Name of Field. State of Cultivation. Price per Quantity. Acre. A. 16 Barn Field... Arable. 5 200 20 R. P. 3 30 30s. 17 Furze Brook. Grass.. 2 3 19 12s. 6d, 18 Long Mead ... Grass.. 5 2 0 30s. 23 Hazle Field.. Arable.. 4 2 6 25s. 24 Pond Field... Arable. 21 16 18s. 25 Loampit Field Arable.. 5 1 30 25s. 26 Common Field ... Arable.. 52 10 27s. 6d. 27 Quarry Field . Arable... 9 1 16 25s. 28 Station Field .. Arable.. 10 2 13 22s. 6d. 29 Windmill Hill .. Grass. 5 3 30 25s. 30 Garson. Arable... 9 2 18 22s. 6d. 36 Length Furlong. Arable... 10 1 13 27s. 6d. 38 First Home Mead ..... Grass.. 2 3 16 40s. 39 Second Home Mead..... Grass.. 51 13 40s. 40 Large Home Mead Grass. 11 2 15 42s. 6d. 41 The Vineyard Grass.. 15 3 3042s. 6d. 42 Cherry Orchard ... Grass.. 10 2 9 45s. 44 Oxford.. Grass.. 15 3 1 40s. 45 Lock's Farm... (Homestead. . . House & Garden 1 3 10 0 1 10 Allotment Field ... Arable. 48 1 1 10 32s. 6d. 190 2 5 Deduct for Tithe, Insurance, and With reference to the form of Valuation, it is necessary to observe that the three owners, three valuations are required to be stated. recommended for a PARISH VALUATION. Owner, Long, John 48 Value. Gross Rental. Rateable Value. Remarks. S. 818 d. 1 1 15 10 8 20 48 5 0 5 13 6 2 2 6 616 0 7 13 0 1113 9 11 18 0 7 8 10 16 20 5 3 Co 14 4 0 S. d. 514 0 10 13 3 24 12 9 3317 4 23 17 10 31 10 3 48 S. d. Rushy and poor. Unhandy; wet. Gravelly on brow. 25 0 78 10 1 330 19 10 331 0 0 280 0 0 Repairs. 51 00 Burns. 35/; 32/6; 30/ value of each separate holding must be given. So that, if one occupier hold of 660 BUILDERS' PRICES. CHAPTER XX. BUILDERS' PRICES. SECT. I-Carpenters' and Joiners' Prices. ROOFS, At per square of 100 feet superficial. Common shed roofs, one story high The same, with purlins If two stories, add If three stories, add Common span or valley, with purlins and rafters, two stories high If three stories, add Framed roofs, with collars, dove-tailed into sides of rafters, notched to receive purlins, and filled in with common rafters Roofs framed, with principals, king posts, purlins, braces, and common rafters The same, with kings and queens Common curb roofs on one side If two sides, add If three sides, add If above two stories, add Labour. Nails. S. d. S. d. 3 3 1 0 4 0 1 6 0 6 0 0 1 0 0 0 5 0 2 0 0 6 0 0 9 6 3 6 13 5 4 0 • . 15 9 4 0 5 7 2 6 0 6 0 0 1 0 0 0 0 6 0 0 The timber to be measured and taken at per foot cube. NAKED FLOORS, At per square. Labour. Nails. Ceiling floors, joists only 2 11 1 6 The same, framed with tie beams 4 2 1 9 The same, with binding and ceiling joists. 5 0 1 11 Ground joists bedded, but not framed The same, pinned down on plates, and framed to chimnies Single-framed floors, trimmed to chimnies and stairs If above 9 inches deep Framed with girders and cased bays Framed with girders, binding, bridging, and ceiling joists . 12 6 6 40 2 6 1 6 4 2 1 6 5 3 1 9 7 10 0 0 8 6 3 0 BUILDERS' PRICES. 661 QUARTER PARTITIONS, At per square. Common 4 inch braced partitions Labour. Nails. 4 Do. 5 inch do. 5 Do. 6 inch do. 5 or or + as S. d. S. d. 6 1 3 3 1 6 6 1 6 Truss-framed with king posts 8 8 1 6 Do. with king and queen posts 10 0 0 0 If oak, extra one-third. Cube fir bond* Do. framed Do. LABOUR ON FIR TIMBER, At per foot cube. truss framed Do. framed and chamfered Do. wrought and framed Do. wrought, framed, and rebated Do. wrought, framed, rebated, and beaded Do. Do. proper door cases wrought, framed, rebated, and double beaded Planing fir per foot superficial. LABOUR ON DEALS, 0 4 0 8 0 10 0 10 1 1 1 3 1 6 8 1 11 0 1 "" "" "" "" plugged At per foot superficial. For deals from in. to 12 in. thick— 0 0 edges shot "" 414 ༤ jacked rounded "" "" HN HN HN HN "" "" planing on each side 0 1 "" "" grooved 0 1 rebated 0 1 "" 35 ploughed and tongued 0 1 framed 0 1 "" "" battened 0 1 "" mitred 0 1 "" "" scribed 0 1 "" "" backed 0 1 "" ་ "" throated 0 1 "" "" "" "" clamped 0 1 beaded 0 1 "" "" ✦ Bond timbers, wall plates, wood bricks, pole and curb, &c., are all to be under the head of bond. 662 BUILDERS' PRICES. Nails. d. Labour. For deals from in. to 1½ in. thick- S. d. S. cut circular 0 11 "" cut standards 0 21 "" sunk shelves 0 21 "" "" "" "" "" 35 scolloped 0 21 "" "" "" "" ledged dovetailed For deals from 2 to 3 in. thick— edges shot plugged 0 21 0 21 0 1 0 1 "" "" jacked 0 1 rounded 0 1 "" "" "" planing on each side 0 11 grooved 0 11/ "" rebated 0 11/ "" "" ploughed and tongued. 0 11 "" framed 0 12 "" battened 0 11/ "" "" mitred 0 11 "" "" scribed 0 11/ "" backed 0 11 "" throated 0 11 >> "" "" clamped 0 11/2 beaded 0 12/ "" "" cut circular 0 21 "" cut standards 0 3 "" >> sunk shelves 0 3 "" >> "" "" scolloped 0 3 "" "" ledged 0 3 dovetailed . 0 3 "" པ "" BATTENING TO WALLS, ₫ in. to 14 in., 12 in. from If plugged to walls, add Wall hooks add extra At per square. centre to centre 3 0 2 0 0 10 1 0 0 0 0 0 0 0 WEATHER BOARDING, At per square. Rough "" Wrought Wrought and beaded 2 1 2 0 splayed edges 3 5 2 0 5 0 2 0 6 3 2 0 BUILDERS' PRICES. 663 At per square. ROUGH BOARDING, Labour. Nails. S. d. S. d. inch deal, rough • 2 CO 6 1 6 "" "" Inch deal, edges shot . 3 4 1 6 ploughed and tongued 3 9 1 6 rough 2 9 2 0 "" edges shot 3 6 2 0 "" ploughed and tongued 4 7 2 0 Whole deal, rough 2 11 3 0 edges shot. 3 9 3 0 "" ploughed and tongued 5 2 3 0 1½ in. deal, rough 3 4 3 6 edges shot 4 4 3 6 "" "" ploughed and tongued. 5 10 3 6 DEAL FLOORS, At per square. Inch deal, rough edges shot 3 10 1 6 "" wrought, folding 5 11 1 6 "" Whole deal, straight joint 7 6 1 6 rough edges shot 4 3 2 0 "" wrought folding 6 3 2 0 "" "" "" wrought straight joint, splayed} do. do. dowelled 1½ inch deal, rough edges shot wrought folding 8 10 3 0 15 10 4 0 • 4 7 2 6 6 8 2 6 "" "" "" wrought straight joint, splayed heading 10 if ploughed and tongued headings, add if ploughed and tongued edges, add for tongues to edges of boards, add . 0 3 0 1 6 0 0 2 7 0 0 4 2 0 BATTEN FLOORS, At per square. Inch wrought folding Inch wrought, straight joint, splayed headings Inch and quarter wrought folding Inch and quarter straight joint, splayed headings The same dowelled If ploughed and tongued headings, add . 10 10 2 6 2 6 6 3 6 20 10 5 0 7 6 9 0 8 4 ~ ~ ~ ~ 2 If ploughed and tongued edges, add For tongues to edges of battens, add If battens less than 5 inch, add 2 2 0 0 3 9 0 0 6 3 0 0 1 8 0 0 664 BUILDERS' PRICES. Common framed grounds 11 inch do. do. do. 1 inch do. do. do. FRAMED GROUNDS, Labour and Nails. At per foot super. S. d. 0 4 1 inch do., ploughed for plastering 0 4 0 5 0 5 SKIRTINGS, At per foot super. Plain skirtings 0 2 Do. do. raking cut to steps 0 4 Torus skirtings 04 Do. do. raking cut to steps 0 5 GUTTERS AND BEARERS, At per foot super. Inch or whole deal DOOR LININGS, At per foot super. Plain, single rebated Plain, single rebated, and beaded Plain, double rebated Plain, double rebated, and double beaded Square framed jambs, each in 2 panels, and soffit in 1 panel If bead, butt, or moulded, add Bead, flush, or quirk moulded, add Raised panel and moulded, add For every extra panel, if square Do. flush or moulded If double rebated If double beaded • 14 rough edges shot LEDGED DOORS, At per foot super. Add, if ploughed and tongued if ploughed and beaded if wrought each side if braced · if hung folding. if 1 inch thicker 0 41 0315 0 32 0 4 0 5 06 0 2/ 0 11 0 21 0 11 0 11/ 0 11 0 3 COLE 0 4 0 222 0 11 0 0 11/ 0 11/ 0 3 BUILDERS' PRICES. 665 FRAMED PARTITIONS Labour & Nails. S. d. 04 At per foot super. 1½ inch square framed 2 inch do. do. Add, if bead, butt, or moulded if bead, flush, or quirk moulded DEAL MOULDINGS, Common mouldings Add, if quirked Fixed complete, at per foot super. Small mouldings can be measured at per foot run. DOORS HUNG COMPLETE, At per foot super. Two panel square framed 0 41 • 0 11 0 21/ 08 2 0 4 Add for every additional 2 panels- If framed square, For 1½ inch deal 2 inch do. 21 inch do. If framed bead, butt, and square, For 1 inch deal 2 inch do. If framed bead, flush, and square, 0 1 0 1 0 11 0 11 0 11 1금 For 1 inch deal 0 12/2 2 inch do. 0 2 21 inch do. 0 21 · If framed quirk O. G. and bead, and square, or quirk Ov., and bead and square, For 1 inch deal 0 11 2 inch do. 0 11 If double marquis, 4 inch wide 0 14 "" "" 5 or 6 inch wide Hung folding 0 21 0 WINDOW LININGS, At per foot super. Inch deal, two panel square, framed back linings "" "" if bead, butt, or moulded, add if bead, flush, or quirk moulding, add For each panel above two, if square if moulded "" "" >> if splayed 0 6 0 28 0 11 0 11 0 11 2 T 666 BUILDERS' PRICES. Do. WINDOW BACKS, ELBOWS, AND SOFFITS, At per foot super. Inch deal, plain keyed, or two panel square backs two panel square backs, elbows, and soffits Add, for each panel above three, "" if splayed. "" if bead, butt, or moulded if bead, flush, or quirk moulded BOXINGS TO WINDOWS, At per foot super. Framed, rebated, and beaded boxings Labour & Nails. S. d. 05 06 H COLE KI 220 0 0 11 06 0 7 Splayed, flush, rebated, and beaded boxings INSIDE WINDOW SHUTTERS, At per foot super. inch deal clamped flaps in one height Inch deal two panel square in one height For every panel above two, If framed square If bead, butt, or moulded If bead, flush, or quirk moulded Quirk O. G. and bead, or quirk ov., and bead and square For every extra height, add Sashes- SASHES AND FRAMES HUNG COMPLETE, 1 inch deal ovolo sashes At per foot super. Do. wainscot or mahogany If 2 or 21 inch sashes deal, add If do. wainscot or mahogany, add If astragal and hollow in deal, add If do. in wainscot and mahogany, add Frames- Deal cased frames, oak sunk sills, double pulley, P. B. and P. S., single hung If prepared for 2 or 2 sashes, add If prepared with wainscot or mahogany P. P.Bds. and P. slips If for 2 or 2 inch sashes, add If double hung, add 0 7 0 71 0 11/1 0 1/1/0 0 11 0 11 0 2 3 0 3 04 0 11/10 0 11/ 0 2018 10 11 04 0 CORH 2 0 5 0 1 0 32 BUILDERS' PRICES. 667 STAIRCASES, At per foot super. Labour & Nails. s. d. Common steps and risers, and two fir carriages Do. moulded nosings and close strings Do. do. mitred to cut string boards, and dovetailed to balustres Add, 0 4 0 6 07 If winders, circular one end Do. do. circular two ends carriages Do. do. both edges Feather-tongued joints Add, Quarter curtail, glued upright, each 0 21/20 0 5 Do. do. geometrical, with wrought and blocked Riser-tongued to step bottom edge 0 31 0 11 0 21 0 11 3 4 Do. blocked and veneered, each 5 10 Proper curtail, step and riser, each 11 O Return moulded nosing, each Return circular, each Plain cut bracket, each Circular cut bracket, each Housing to step and riser, each 1 3 2 1 1 3 2 1 0 6 "" to winders, each "" to moulded nosings, each "" to circular ends, each 0 7 0 10 2 31 • Whole deal plain Whole deal sunk OUTSIDE STRINGS TO STAIRS, At per foot super. Whole deal sunk and moulded Whole deal sunk, moulded, and cut Whole deal sunk, moulded, cut, and mitred to risers If wreathed, four times the above. If ramped, once and a half. 0 5 06 0 623 08 0 81 WALL STRINGS, At per foot super. Plain and plugging 0 5 If moulded, add. If rebated for plastering, add 0 1 0 12 • 668 BUILDERS' PRICES. DADOS, At per foot super. Proper dado, with dovetailed keys, joints secured with slips, and dovetails hung to grounds by grooves keyed into do., and dado Add, If raking, scribed to steps If raking, scribed to moulded nosings If base, grooved into floor Labour & Nails. s. d. 0 4 0 11 0 11 0 1 For each external mitre beyond two in a room 1 12 If circular on the plan, double the above. If wreathed, treble the above. COLUMNS AND PILASTERS, At per foot super. 14 inch deal plain pilasters, properly glued and blocked Do. do. diminished • 14 inch deal diminished columns, properly glued and blocked, under 14 inches diameter Do. do. above 14 inches diameter Add, for- 062 09 2 1 1 9 0 11 two inches wide 0 11 three inches wide 0 22 "" 01/2 two inches wide "" three inches wide 0 23 031 "" Arris or deep fluting to pilasters, one inch wide "" "" "" "" Arris or deep fluting to columns, one inch wide "" "" "" "" Straight grooves to columns Headings to flutes to columns. Straight grooves to pilasters. Headings to flutes to pilasters. 0 11 0 4 0 424 0 22 In the foregoing list of Carpenters' and Joiners' Prices, all calculations in respect of materials have been omitted, owing to the very unsettled state of the market at the present time, (March, 1853,) and the fluctu- ations to which it is subject. The charges for labour being less affected by fluctuations of a similar nature, can be more satisfactorily relied on as permanent approximations to reasonable remuneration to the tradesman, and may consequently be taken as a basis for estimates for some years to come. The timber must be added at its measured value, according to market price at the time being. The method of ascertaining the value of a cube foot of timber from the prime cost prices is given in the Chapter on Arti- ficers' Work, and the following Tables will be found useful. BUILDERS' PRICES. 669 £. s. d. £. s. d. £. s. d. £. s. s. d. £. s. d. 2 10 0 2 18 4 3 6 8 3 15 0 4 3 4 £. 8. d. £. s. 4 11 8 5 0 0 d. £ s. d. £ s. d. 5 8 4 5 16 8 Table showing the price to be charged per foot cube for Fir, or other Timber, used in measured work, calculated at the various rates of prime cost, standing at the head of the several columns, allowing 5s. for cartage, 10s. for sawing, 10s. for waste, and £1 5s. for profit, per load. PRIME COST PER LOAD. Fir Timber, no labour Fir Timber, in bond, Plates, Curb, &c., labour included. Fir Timber, framed Fir Timber, truss framed. Fir Timber, framed and chamfered Fir Timber, wrought and framed Fir Timber, wrought, framed, and rebated 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 2 10 0 3 0 0 3 20 3 4 0 2 40 2 40 260 2 8 0 2 10 0 3 0 0 3 2 0 3 4 0 3 603 8 0 2 80 2 10 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 3 10 0 4 0 0 2 10 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 3 10 0 4 0 0 4 2 0 2 10 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 3 10 0 4 0 0 4 2 0 3 10 3 3 0 3 5 0 3 70 3 9 0 3 110 4 10 4 30 4 5 0 3 3 0 3 5 0 3 70 3 9 0 3 11 0 4 10 4 3 0 4 50 47 Fir Timber, wrought, framed, rebated, and beaded 0 3 6 0 3 8 0 3 10 0 4 0 0 4 2 0 4 4 0 4 60 4 8 0 4 10 Fir Timber, wrought, framed, rebated and double beaded Fir Timber, in proper door cases • 0 3 8 0 3 10 0 4 0 0 4 20 4 4 0 4 60 4 8 0 4 10 0 5 0 0 3 11 0 4 10 4 3 0 4 5 0 4 7 0 4 90 4 11 0 5 10 5 3 670 BUILDERS' PRICES. PRIME COST PER LOAD. Table showing the price to be charged per foot cube for Fir, or other Timber, used in measured work, calculated at the various rates of prime cost, standing at the head of the several columns, allowing 5s. for cartage, 10s. for sawing, 10s. for waste, and £1 5s. for profit per load. £ 8. d. £ s. d. £ s. d. £ s. d. s. d £ s. d. £ s. d. £ s. d. £ s. d. 6 5 0 6 13 4 7 1 8 7 10 0 7 18 4 8 6 8 8 15 0 9 3 4 10 0 0 Fir Timber, no labour Fir Timber, in bond, Plates, Curb, &c., labour included. Fir Timber, framed Fir Timber, truss framed Fir Timber, framed and chamfered Fir Timber, wrought and framed Fir Timber, wrought, framed, and rebated 0 3 6 0 3 8 0 3 10 0 4 0 0 4 2 0 4 4 0 4 60 480 5 0 0 3 10 0 4 0 0 4 2 0 4 4 0 4 60 4 8 0 4 10 0 5 0 0 5 4 60 0 4 20 4 4 0 4 6 0 4 8 0 4 100 5 4 10 0 5 0 0 5 20 5 40 5 8 0 4 4 0 4 60 4 8 0 4 10 0 5 0 0 5 2 0 5 4 0 5 6 0 5 10 0 4 4 0 4 60 4 8 0 4 10 0 5 0 0 5 205 40 5 6 0 5 10 0 470 4 9 0 4 11 0 5 1 0 5 3 0 5 5 0 570 590 6 1 0 4 9 0 4 11 0 5 10 5 3 0 5 5 0 5 7 0 5 9 0 5 11 0 6 3 Fir Timber, wrought, framed, rebated, and beaded 0 5 0 0 5 20 5 4 0 5 6 0 5 8 0 5 10 0 6 0 0 6 20 6 6 Fir Timber, wrought, framed, rebated, and double beaded Fir Timber, in proper door cases 0 5 2 0 5 40 5 6 0 580 5 10 0 6 0 0 6 2 0 6 4 0 6 8 0 5 5 0 570 5 9 0 5 11 0 6 10 6 30 650 670 6 11 BUILDERS' PRICES. 671 Table showing the Length of Timber of any Scantling contained in a foot cube. Scantling. Length. Scantling. Length. Scantling. Length. in. in. 2 - 2 .ମୁଁ ସେ ବବି ବଡ ft. in. in. in. ft. in. in. in. ft. in. 36 0 4 — 4 9 0 6-10/1 2 3 28 9 4/1/20 8 11 2 2 24 0 5 7 11/1/0 2 31 20 7 5/1/ 6 12 2 4 18 0 6 6 0 my _ my 4/ 16 0 6/12/ 5 6 7/1/20 5 14 5 5/1/20 13 1 6 12 0 6/1/20 11 1 7 10 3 77∞ ∞ ∞ 1 8 4 9 8312 8 4 6 9 81/1 4 3 9/1/ 9 4 0 10 NNNNNNNNN 1 0 2 11 2 9 2 6 2 5 2 2 321 7 1/1/0 9 7 91/2 3 9 10/1/ 1 8 0 10 3 7 11 11 1 10 8/1/1 6 10/1/20 3 9 8 0 11 3 10 00 5 11/1/ 1 9 3 12 91/2 7 7 11/1/ 3 2 8 — 8 10 7 3 12 3 0 HK 10/1/1 6 10 5 - 5 5 9 9 11 6 6 5/1/ 5 3 9/1/2 111/ 6 4 6 4 10 10 I Q Q QAT 1 8 3 2 1 2 0 1 10 1 9 12 6 0 6/1/2 4 5 10/1 1 8 3 - 3 16 0 3/1/20 13 8 4 12 778 HK 4/ 10 8 8/12/2 5 9 7 9 5/ 9 0 9/1/2 6 8 0 10 6/1/20 7 4 7 6 10 10/1/20 11 7/1/ 6 4 8 6 0 11/1/ 12 5 8 6 - 6 9 4 6 9/1/2 5 0 7 10 4 10 7/ 101 4 6 11 4 4 8/1/ 11/1/ 4 2 12 4 0 9/12/20 10 +∞ ∞ ∞ 0 0 N NNNNTH 03 03 03 M N N NN HK 4 1 11 1 7 3 10 11/1/20 1 7 3 7 12 1 6 3 5 9 - 9 1 9 3 2 931/ 1 8 3 0 10 1 7 2 10 10/1 6 2 9 11 1 5 2 8 111 1 4 2 6 12 1 4 2 4 10 - 10 1 5 4 0 1011 1 4 8 11 1 4 5 11/1/ 1 3 2 12 1 2 3 0 11 11 1 2 2 10 8 11/1/2 12 1 2 2 6 12 12 1 1 1 0 2 5 672 BUILDERS' PRICES. Table showing the Price to be charged per foot run for Scantling of Fir, or other Timber, calculated at various Prices per foot cube. Scantling. 2-2 2s. 6d. 3s. Od. per ft. cube. per ft. cube. per ft. cube. 3s. 6d Scantling. 2s. 6d. 3s. Od. 3s. 6d. per ft. cube. per ft. cube. per ft. cube. 0 1 0 1 0 11 5 7 0 7/1/2 0 8/2 0 101 4 21/ H 0 11 0 11 0 12 73 08 0 91/2 0 111 3 0 31/1 1층 4 0 12 4/2 0 2 5 0 5/1/ 0 61 0 0 MH 0 0 3 31 0 9 0 0 10/1/10 0 11 0 11/1/ 0 12 0 3-3 0 2 31/ 0 9/1/20 0 4 10 0 3 77∞ ∞ …. 8 9 0 HK HK HÊa calen PH Ha CalCH COLCH HD HQ M IIIQNNN Q ∞ ∞ ∞ ∞ ∞ EEE 10 62 ∞ ∞ ∞ ∞ HH HQ CS — Hk col DEH TC+ HILO LO LO CO 0 1 1/ 0 12 8 08/3/2 0 10 1 0 12 21 81/1 09 0 1022 1 03/2 0 2 0 2/ 9 091/ 0 111 1 11 0 21 0 0 HIHIGA COLCH 0 23 9/2 0 101 1 0 24/ 0 3 10 0 10/ 1 031 1 31 0 31 10/1 0 11110 1 11 1 32 0 3 031 11 0 11 1 1/2/ 1 4 0 31/1 0 4 11/13/ 1 0 1 2 1 42 0 31/ 0 41 12 1 03/2 1 3 1 5/20 0 3 0 4/1/2 6–6 0 7 09 0 10/ 0 4 0 6/1/ 081 0 92 0 11 0 41 5 0 83 0 10/1/20 1 01 0 0 51 0 0 144 71/ 0 9 0 111 1 11 8 0 93 1 0 2 0 5 0 6 8/1/2 0 10 1 02 4/1/2 0 51 0 61 9 0 111 1 1/ 1 32 0 6 9/1/2 1 0 1 21 1 0 0 6 0 0 21 0 29/ 0 2/3/1 0 31 31 3/1/2 10 11 4 0 21/0 0 3 41/2 5 0 5/1/ 0 6 7호 0 0 0 5 8/ 0 9/2/2 0 5 6 0 61 51 0 52 0 6 0 ง 10/12/ 0 632 08 11/1/ 0 71 0 51 3호 0 31 4 0 332 0 COLH 0 0 731 0 CHHICH HA H 6723 ∞ ++ LO HIT CHAT COLER 667 7 ∞ ∞ ∞ 10 10/1/20 1 3 15 OT A CO C~ 3 4328 101/ 1 11 1 32 1 62 11 1 12 1 1 7 111 1 2 1 51 1 81 12 1 3 1 6 1 9 7_7 0 101 1 01 1 2/1/20 7 0 11 1 11 1 3 со 0 112 1 2 1 4/1/2 1 02/ 1 3 15 1 11 1 32 16/ 9/1/20 1 2 1 432 1 7 10 1 23 15/0 1 81 101/ 1 3 1 61 1 9 11 1 4 1 101 11 1/2 1 42 1 81 1 11 12 1 5 1 91 201 8-8 1 1/1/20 1 4 1 7 0 8/1/1 1 21 1 56 1 8 0 0 93 9 1 3 1 1 9 0 HCOLH 0 101 9/12/ 1 4 1 7 1 101 12 0 7 0 9 0 10/1/20 10 1 5 1 8 1 1111 4-4 0 3/1/20 0 4 0 43 10/1/ 1 6 1 9 2 03 4/1 0 5 5 0 0 5 4445 4 0 4/1/2 0 51 11 1 7 1 10 2 12 41 0 5 0 6 11/ 1 71 1 11 2 3 424 0 5/1/20 0 12 1 8 2 0 2 4 0 6 0 9-9 1 5 1 81 1 11½ 6/1/10 5 06/12/20 0 73 91 1 6 1 91 2 1 0 6 0 7 0 81 10 1 7 1 10 2 21 7호 0 6 0 Ha 0 9 101/20 1 8 1 112 2 330 8 0 632 08 0 9 0 81 09 09/21/2 0 10 11 1 83 2 03/ 2 5 11/1/0 1 92 93/4 2 2 2 63 0 10/2/20 12 1 10 2 3 2 7 9/1/ 0 091/ 0 111 10-10 1 10 1 2 7 10 0 8/12/20 0 10 0 112 10/1/20 1 101/20 21 2 7/1/20 101 09 11 0 9 0 101 0 11 1 010 11 1 11 2 3/1/20 2 8 1 1 11 1/ 2 0 251 2 9/1/2 11 1 0 92 12 0 10 5-5 5/1/ 0 5/1/ 0 6 0 11/12/20 1 0 06/0 1 1/ 12 2 1 2 6 2 11 1 2 11-11 2 11 6 2 111 0 73 11/1/1 2 2 21/ 0 7 0 12 2 3/ 2 9 3 2 321/20 6 0 6/1 0 73/2 0 82 12-12 61 0 7 081 0 93 BUILDERS' PRICES. 673 Scantling. Table showing the Price to be charged per foot run for Scantling of Fir, or other Timber, calculated at various Prices per foot cube. 5s. Od. 4s. Od. 4s. 6d. per ft. cube. per ft. cube. per ft. cube. Scantling. 4s. Od. 4s. 6d. 58. Od. per ft. cube. per ft. cube. per ft. cube 2-2 0 1/1/20 1글 21 3 0 4 0 412 0 5 51 6/1/ 7 711 8 112 0 0 0 4 05 0 52 0 9 0 1122 N M ∞ M 44 LO LO 0 1/1/0 0 12 0 2 0 21/1 2층 21 0 3 3 31/ 0 4 33/2 0 41 0 051 5 0 532 4 10 10/1/ 11 9/1/ 063/1 0 63 0 7 11/1 0 72 06/1/20 62 0 71 0 0 7 71 0 8/1/0 0 HCH ODCH 1222 m ∞ * TH10 LO LO CO Hic eslat Hlas me calet mla cola 0 12/20 3 5-7 1 0 1 1/1/0 1 3 71 1 03/ 1 3 1 4 0 21/0 0 3 20 1 1/1/20 1 41 1 5 1 21 1 42 1 6 0 31/12 9 1 3 1 5 1 63 0 332 9/1/ 1 41 1 62 1 7 0 41 10 15 7232351 1 9 0 42 10/1/ 1 6 1 811 1 93 0 5 11 1 61 1 82 1 10% 05/2 1 1 1/ 1 7 1 9 2 112/2 06 12 1 8 1 10/ 2 1 061 6-6 1 0 1 1/1/20 1 3 0 622 6 1 1 1 23/ 1 41 0 71 1 2 1 3/1 1 5 0 7/1/0 7/10 1 3 1 5 1 62 08 8 1 4 1 6 1 8 08/1 1 5 1 71 1 91 0 9 1 6 1 81 1 10 0 91 91/2 1 7 1 9/2 1 112 12 0 8 0 9 0 93 0 10 10 1 8 1 10/ 2 1 10/1/20 1 9 1 112 2 21 3-3 0 3 C++ LO LO CO 12 445 0 31 4 4/2 5 5글 61 0 0 51 0 6 0 51 0 52 061 0 63 0 7 6/1/ 0 7/ 0 7 8 0 3/1/20 0 4 0 3/2/ 11 1 10 2 02/2 2 3/ 0 4/1/20 11/1/2 1 11 2 2 2 42 04/ 0 5 12 20 2 3 26 0 52 7___7 1 41 1 6 18/10 0 61 0 0 0 KIN 0 71 0 0 77∞∞ ∞ HK HABER 7∞ 71 1 52 1 8 1 10 8 1 7 1 91 1 111 8/1/20 1 81 1 101 2 2、 1 91 1 112 2 21 91/ 1 101 2 11 2 331 931 10 1 11/1/20 2 2/1/20 25 8 8/3/2 0 8 0 81 0 9 0 10 10 2 02/ 2 3/2/20 26 0 93 0 102 11 2 12 2 5 2 8 4 9 09 0 101 0 11/1/20 11/1/ 2 3 26/2 29/ 9/1/2 09/1 0 102/20 1 0 12 2 4 2 7/1/1 2 11 10 0 10 0 111 1 0/21/20 8-8 19 20 23 10/1/ 0 101 1 0 1 11 14 8/1/15 1 102 2 1/1/0 2 4 11 0 11 1 03/ 1 12 2 0 2 3 2 6 11/1/2 0 11/1/20 1 1 1 2 2호 91/1 مرادی 2 1/ 24/ 2 7 12 1 0 1 1/ 1 3 10 2 23/1 2 6 29 4-4 0 5/1/ 06 0 6 10/1 2 4 2 7/ 2 11 41 0 61 0 632 0 73/ 11 2051 29 3 09/ 5 0 63/ 0 7፤ 08/1/ 0 71 081 0 91 111/ 12 2 10/ 3 21 3 0 3 4 08 09 0 10 9-9 2 2 26 2 9 61 0 832 0 921 0 11 9/1/ 24/ 2 8 2111 0 91 0 10 0 112 10 2 2 10 3 1/2 71 0 10/1/20 0 111 1 02/ 10 2 7 2 11/21/ 3 3 8 0 102 1 0 1 1/ 11 2 9 31 351 0 1111 1 01 1 21 111/1 2101/2 3 3 3 7 1 0 1 11 1 3 12 3 0 3 4 3 9 91 1 1 21 1 4 10-10 2 11 3 3/1/20 38 10 1 1/1/20 1 3 1 42 10/1/ 3 0 3 4/1/20 3 9 10/1/ 1 21 1 3 3/1/ 15 11 3 03 3 5 3 93 11 1 2/9/ 1 4 1 61 111/ 3 24 3 7 4 0 11 1 1 31 1 5 12 5-5 1 4 1 6 1 710 1 8 12 3 4 3 9 4 2 11-11 3 412 39/1/0 4 23 08/ 0 10 0 11 51 0 9/1/20 0 102 0 1121 111/ 12 3 61 3 11/2 4 43 3 8 4 1 4 7 6 0 10 0 11 1 1 0 12 12 6/1/2 0 11 1 01/0 1 13/14 674 BUILDERS' PRICES. SECT. II.-Mason's Prices. s. d. Labour, squaring and laying New York or Purbeck pav- ing per foot super. 0 11 If in courses, add 0 13/14 LABOUR ON PORTLAND OR SIMILAR STONE. N.B. Sawing to be taken as half plain work. Plain work to bond stones per foot super. 081 "" "" to beds and joints "" "" rubbed face circular "" "" Sunk work "" "" "" زو Moulded work rubbed "" "" "" circular 0 11 "" "; 1 1 01/2 51 1 3 "} 1 7 "" 1 51 "" 2 1 "" Circular work to shafts of columns having the neck moulding, or part of the base worked in the same stone Circular circular or spherical work to domes or balls If rubbed, add Taking up, squaring, and relaying old paving Add, if in courses 1 8 "" 2 6 "" 0 3 "" 0 "" 21/ 0 1 "" LABOUR ON STATUARY OR VEIN MARBLE, INCLUDING SAWING, WORKING, AND POLISHING. Plain work Circular work Sunk work Moulded work Circular sunk work • per foot super. 4 4호 6 3 "" 8 4 "" 11 11 "" 11 11 "" 15 0 39 Circular moulded work ON OLD WORK. Old vein marble chimney, reset 0 71/2 "" "" "" squared and reset 0 10 sanded, grounded & squared 1 01/ "" sanded, grounded, squared and reset 1 3 cleaned and reset, sanded 1 3 >> "" polished and reset 1 101 >> "" "" sawed, sanded, polished, squared, & reset 3 1 The above prices are confined to labour only. The prime cost of stone and marble varying considerably in different localities, according to the expense of carriage and other circumstances, it would answer no useful purpose in a book intended for general circulation, to include any calculation for materials; especially as price lists of the various kinds can at all times be obtained of the merchants and dealers. BUILDERS' PRICES. 675 As an illustration of this difference, the annexed extract from the price list of Messrs. Randell and Saunders, for Bath stone, is annexed. It will be seen that the same description of goods varies more than cent. per cent. at different stations. PRICES. At Bristol. Paddington. Liverpool. Combe Down, ditto at Bath BLOCK. Corsham Down, delivered into trucks, at Corsham Box ground stone, ditto at Box S. d. s. d. s. d. s. d. • per foot cube 0 7 0 9 1 4 1 6 0 80 911 5 "" or Corsham Farley Down, ditto at Box Corn Grit, ditto at Corsham 70 914 0 8 0 91 5 "" 0 50 71 2 "" Selected Blocks, 1d. per foot extra. Blocks, of large dimensions, or cut to order, supplied at a moderate cost. LANDING. Four inch, under 24 feet • per foot super.0 310 410 61071 Ditto, above 24 feet 0 410 "" 510 710 81 51071081 Six inch, under 24 feet 0 410 420 910 101 "" Ditto above 24 feet 33 0 510 610 1010 111 PAVING. Three inch, corn grit Ditto ditto, Corsham Down ASHLAR. Corsham Down ashlar, 4 inch "" 10 3 со до 2 0 5 0 6 "" Ditto, 5 inch Ditto, 6 inch Ditto, 7 inch Ditto, 8 inch "" "" "" "" "" This Stone is cut to range in courses, 10, 12, or 14 inches deep; a small allowance being made in each case for dressing. 0 210 220 50 6 0 210 310 6 0 30 330 70 9 3207109 0 310 410 83 0 40 50 101 0 RANGE STONE. Sawn range stone per yard 1 3 1 93 6 This Stone is cut to range in courses, 4, 5, 6, 7, and 8 inches deep, and varies from 3 to 7 inches wide; 5 yards make a ton. QUOINS. Random sizes per foot super.0 3 WALL STONES. per ton 1 0 676 BUILDERS' PRICES. SECT. III-Bricklayer's Prices. Concrete-Labour in mixing, wheeling, throwing in from a stage, and puddling, (where required to be done), including erection of scaffolding Brickwork. Extra labour to maim facings Labour. S. d. per yard cube per rod 0 10 37 1 0 1 PAVING. Brick paving laid flat in sand per yard 0 4 "" laid on edge in sand laid flat in mortar "" "" laid on edge in mortar 0 7 "" 0 5 >> 0 8 "" Paving brick paving laid flat in sand 0 4 "" "" laid on edge in ditto "" 091/2 laid flat in mortar 0 7 "" "" laid on edge in mortar 0 11 "" Clinker paving on edge in sand 10 to 12 inch tile paving 1 0 "" 0 1 "" Pan tiling laid dry TILING. per square 3 2 5 2 "" 5 11 "" 5 7 "" 5 9 "" 5 11 "" Pan tiling pointed outside "" inside and out Plain tiling laid to a 4 inch guage laid to a 3½ inch ditto laid to a 3 inch ditto "" The prices of bricks, slates, and tiles, vary in price in different locali- ties, at the present time, (March, 1853), they are very dear, so that any calculation on account of materials would not be useful in this place. Rough render Floating ditto Setting Lathing SECT. IV-Plasterer's Prices. If circular work, add on the lathing, and also on each coat of plastering If to groins, add as above 0 2 0 21 0 12 0 2 0 1 0 1 BUILDERS' PRICES. 677 SECT. V-Ironmonger's Prices. AIR BRICKS. Per Doz. Per Doz. S. d. s. d. Hollow sides 6 0 Half bricks 4 0 Hollow sides, heavy 70 Half bricks, heavy 4 6 Full sides 9 0 Half bricks 5 0 Full sides, heavy 12 O Full sides, heavy 5 6 BRASS BOLTS. inch flush brass bolts. 2 inches 23 3 4 "" "" 33 ∞ ∞ + 20 CO E ∞ · inch sunk slide. per doz. per doz. § inch sunk slide. per doz. S. d. 1 10 4 inches 5 "" 5 6 "" 7 8 "" 9 10 11 12 "" 2 3 4 9 6 5 6 6 4 10 7 3 11 8 2 12 9 0 "" 10 0 10 10 "" "" "" "" ∞ ∞ ∞ H2O CO 2 3 20 5 6 "" 6 "" 8 789 8 ∞ ∞ or es S. d. S. d. 0 4 inches 5 4 3 7 6 9 "" 10 0 11 3 12 610 5 ∞ ∞ a as cr 6 8 "" 8 0 "" 9 4 "" 8 35 10 8 9 12 0 "" 13 4 • "" 13 "" 15 911 0 12 14 "" • 8 16 0 2 inch sunk slide. per doz. S. d. 4 inches 6 0 4 inches 7 inch sunk slide. per doz. S. d. 1 inch sunk slide. 7 0 4 inches per doz. S. d. 8 0 5 7 6 5 8 9 "" "" 6 9 0 6 10 6 6 39 "" 7 10 6 33 8 9 12 0 13 6 789 "" • 12 3 7 18 14 0 15 9 ∞ COL ∞ ∞ 5 10 0 • "" 12 0 29 14 0 "" 8 16 0 "" 9 18 0 "" "" "" 10 15 010 17 610 20 0 "" "" "" 11 16 6 11 19 311 22 0 "" "" "" 12 18 0 12 21 0 12 24 0 "" "" "" NIGHT BOLTS. 6 inch 3s. each. 7 inch 4s. each. 678 BUILDERS' PRICES. BRASS SOCKET BOLTS, With iron bolts and back plates. All brass. per doz. per doz. S. d. S. d. TH 20 CO← ∞ – 3 inches 4 18 0 3 inches 16 O 24 04 20 0 5 6 7 8 "" "" "" 30 05 24 O "" 36 06 28 0 "" • ະ "" 42 07 33 0 "" "" 50 08 40 O "" 9 33 60 0 9 48 O "" STRONG BRASS SOCKET BOLTS, All brass. With iron bolts and back plates. per doz. per doz. S. d. S. d. 6 7 ∞ COD ∞ ∞ 3 inches 4 5 "" "" 23 0 28 0 16 0 3 inches 12 6 19 04 5 15 6 "" LO CO 33 19 O 6 23 0 "" "" 34 07 28 0 "" "" 8 42 0 8 33 0 "" 9 50 0 9 38 0 "" "" 3 inches 4 "" 20 5 33 3 inches 4 "" 5 20 "" SOLID BRASS SHIP BOLTS. S. per doz. d 26 66 inches 32 0 7 "" 40 0 SHIP BOLTS, ALL BRASS, SMOOTH SANDED. per doz. S. d. 12 0 6 inches 13 18 68 0 per doz. S. d. 45 6 55 O per doz. S. d. 22 0 40 O RACK AND SPRING BRASS BOLTS. 1 inch wide, 12 inches long, 4s. 3d. each. RACK AND SPRING IMPROVED ESPAGNIOLETTE BRASS BOLTS. 180 § 3s. 23s. 6d. BRASS BOLTS FOR BLINDS. 폼 48. From 2s. to 3s. per dozen. BUILDERS' PRICES. 679 6 inches 7 " 5 inches 6 7 "" "" 8 "" IRON NIGHT BOLTS. per doz. S. d. 15 0 8 inches 17 O DOOR CHAIN BOLTS. per doz. d. per doz. S. d. 20 0 per doz. S. s. d. 8 6 9 inches 15 O 9 6 10 18 O "" 10 6 11 22 0 "" 12 0 12 26 0 COTTAGE OR PORTABLE IRON OVENS. Inside Measure. 9 inches long, 7 inches wide, 64 deep, 11s. 3d. each. 11 "" 81 6/1/ 14s. "" "" CASEMENT AND FRENCH WINDOW BRASS FASTENERS. From 5s. 6d. to 50s. per dozen. HINGES, BRASS BUTTS. s. d. per doz. s. d. per doz. s. d. s. d. inch, from 0 10 to 1 0 2 inch, from 29 to 5 9 0 11 1 1 21 3 6 7 6 1 1급 >> "" 1 1 1 3 2 4 6 90 "" 1 3 1 6 6 23/20 5 6 12 0 "" 11 1 4 1 9 3 7 3 16 O "" "" 13 1 7 2 0 "" 31 90 20 0 "" 11/ 1 9 3 4 3 11 O 28 0 "" 15 20 "" 3 932 14 O 34 0 12 2 3 4 3 4 17 6 42 0 " "" 17 2 6 4 9 "" STRONG PROJECTING BRASS BUTTS, WITH POLISHED AND LACQUERED BACKS. per doz. S. d. per doz. 8. d. 12 inches 2 NNN "" 21 23 21 2g HHHI MKO TO LOKO "" 5 9 3 inches 20 0 7 031 31 0 "" 8 9 3 34 0 "" 10 6 32 39 0 "" 35 12 6 4 45 0 "" >> 15 O 33 680 BUILDERS' PRICES. PROJECTING BRASS BUTTS, WITH POLISHED BACKS AND FRONTS. per pair. per pair. s. d. s. d. 2 inches 1 0 34 inches 2 6 21 "" 1 3 31 3 0 "" "7 21/ 2朵 "" 1 6 6 32 3 6 "" 1 10 4 4 3 "" 3 "" 2 2 SKEW BRASS BUTTS, WITH STEEL JOINTS. From 7s. 9d. to 15s. per pair. STRONG BROAD PROJECTING BRASS BUTTS, WITH POLISHED BACKS AND FRONTS, per doz. 2 inch 21 "" per doz. s. d. s. d. 1 4 2 inch 2 2 . 1 7 22 "" 2 9 3 inch 31 "" 31/12 "" WITH HOLLOW JOINTS. per doz. s. d. per doz. s. d. 3 0 3 6 4 4 0 32 inch 4 6 "" 5 6 3 inch 31 "" BRASS RISING HINGES ON STEEL SCREWS. per pair. S. d. per pair. S. d. 11 6 4 inch 15 0 13 6 41 17 6 "" BUILDERS' PRICES. 681 BEST CAST IRON HINGES. Pew Hinges, Egg joint, per doz. Japanned, Japanned, Parliament per doz. per doz. Strong loose joint Strong Knee'd Butts, per doz. Loose Pew Loose Butts Turned ends Butts, per doz. per doz. Loose Butts per doz. New Skew Butts, Turned ends per doz. Back Flaps Skew Butts per doz. Pew Butts, per doz. Japanned, per doz. Square Butts, per doz. Edge Butts, Sizes. per doz. s. d. S. d. S. d. 8. d. S. d. S. d. S. d. S. d. s. d. S. d. S. d. S. d. S. d. inches. 3 0 2 8 1 8 1 5 4 6 3 0 1 10 1 9 ♡ cr 1 6 0 10 1 1 8 1 0 11 4 6 4 4 0 5 3 6 0 69 6 20 20 CO CT 5 0 5 6 5 6 6 0 TH LO LO Co 9 1 8 3 3 2 0 2 4 2 0 1 3 5 0 2 2 3 9 2 6 3 3 4 0 3 0 1 7 6 2 8 4 6 3 0 3 9 5 0 4 0 2 0 3 3 5 3 3 6 4 6 7 9 5 6 4 6 2 4 21 0 9 0 4 0 5 4 0 10 6 6 6 8 6 6 0 2 8 6 6 8 0 6 6 9 9 3 6 9 8 0 3 2 # 7 0 8 9 11 0 56 7 3 5 6 12 6 10 0 4 2 9 6 8 6 4 11 3 9 3 12 6 7 3 9 0 7 3 16 O 12 6 5 3 10 6 14 0 6 0 18 0 8 9 10 6 89 200 15 6 6 6 11 6 20 0 8 0 12 6 22 0 12 0 13 9 12 0 24 0 19 0 9 6 15 0 16 9 15 0 28 0 24 0 12 0 LO 13 6 13 6 14 6 14 6 35 0 30 0 17 O 20 0 61 23 0 30 0 7호 36 0 42 0 8/3/2 2 U 682 BUILDERS' PRICES. size. BROAD CAST IRON BUTTS. per doz. s. d. size. per doz. s. d. 2 by 2 open 2 94 4 by 3 open 8 6 HQ 21 21/2 "" "" "" གྲགས་ཡུས་ ཐུས་པ 239 35 33 2 3 3 31 8 9 >> "" 36 9 0 21 3 9 "" 35 4 0 "" 32 4 "" 96 "" 10 O 21 "" "" 23 "" པ 22 239 сон 33 " HKHTY COKH "" "" "" "} "" 21/2 "" 3 "" "" "" 2호 2232 3 31 2호 232 3 "" "" 3 9 3 6 "" "" "" 10 6 23 4 4호 11 O "> 4 11 9 "" >> 4 9 19 5 341 "" 4 6 4 23 5 0 5 6 "" 5 0 5 ༢。ིལ--。 12 6 " 32 10 6 "" 11 0 "" 11 6 4호 12 6 "" 13 6 33 "" 25 23 5 6 41 "" 29 3 1/2 12 O "" 25 39 23 56 "" 31 "" "" "" "" "" "" "" 3 31 320 4 22 31 3호 32 3 31/12 31/2 3232 4 "" "" 6 0 "" 6 6 "" 322 12 6 4 13 0 14 7 0 "" 39 41 13 6 "" COLH 7 6 56 "" 4/1/2 14 O "" 7 9 60 "" 42 14 6 >: 5 15 O ་ 14 "" "" 6 6 7 0 7 6 "" 80 8 6 "" 7 0 7 6 "" 25 >> 51 15 9 5/1/2 16 6 "" 5 20 31 15 O "" "" 4 16 O 353 "" 41 17 0 35 33 "" 5 18 O 23 5/1/2 19 O "" >" 8 0 86 6 5 8 9 "" 6 21 0 "" 4 17 O "" >> "" 34 4/1/2 18 O "" 41 9 3 20 5 19 6 "" "" "" 41 9 6 51 21 6 "" "" >> 330 COKH 39 16 "" "" "" 3 31 3 1/2 3/201 4 7 6 6 "" ♡ HKH TO COL 8 0 "" 8 66 "" "" 9 0 5 "" 9 6 "" >> "" 4/1 10 3 6 ༩ 。EN CO 24 0 "" 6/1/2 27 0 "" 4호 20 0 "" 21 6 "" 23 6 "" 26 0 "" "" "" 3:35 41 11 0 61 29 0 "" >> 22 BUILDERS' PRICES. 683 No. mai as 1. 10 inch 2. 12 "" 3. 14 "" CROSS GARNET AND T HINGES. per pair. No. s. d. 0 5 4. 16 inch per pair. s. d. 09 0 6 5. 18 1 0 "" 08 6. 20 1 3 "" Strong Cross Garnets, 5d. per lb. HOOK AND EYE HINGES same price. CAST IRON PARLIAMENT HINGES. per doz. Joint. Open. s. d. Joint. 11 by 21 4 9 2 by Open. 3 per doz. s. d. 11/ " 12 2 5 3 "> 3 5 6 "" 39 33 3/1/201 7 0 7 3 "" 4 "" CORN 2 "" 2 ༄༦: 54 33 "" "" "" 21 3 33 13 THICY HIN HA 6 6 6 69 7 0 3 21 +++ 7 6 4 8 6 "" "" 4/1/2 "" 21/ "" >> "" 6 3 567 9 6 10 6 12 0 16 0 "" "" 2 14 6 6 "" "" 5/1/2 12 6 33 21/1 6 9 3 6 15 0 CAST IRON LATCHES, WITH WROUGHT FURNITURE. Gate latch, with screws and nuts s. d. s. d. 19 0 per dozen. Common thumb latches from 2 3 to 4 6 "" New thumb latches 4 6 11 0 "" "" "" Norfolk latches 4 8 14 6 "" "" A "" Flush latches 5 0 "" Strong fluted Norfolk latches from 5 6 12 0 "" "" Flush stable latches 9 0 15 0 "" "" "" Jointed handle stable latches 13 6 "" Secret latches, with moving plate 17 6 with drawback bolt "" "" for gates 20 0 "" 10 0 33 § inch 2 oka w okr 33 39 1 11 1호 12 "" 34 34 · SCREWS, NAILS, &c. BRASS HEADED NAILS. per doz. s. d. per doz s. d. 1 2 2 inch 2 9 1 3 21 3 3 "" • 1 4 2 "" 1 1 6 8 22 "" 3 "" 1 2 2 9 93 31 4 "" "" 9 4 3 5 0 7 0 86 3 684 BUILDERS' PRICES. LOTO COLEH NOO § inch 226 >> ་ "" 1 11 1/1/20 35 པོ "" § inch 20/00 coRH 100 "" 1 11 11 17/2 ICT CORH 12 "" >> "" " BRASS PLATED HEAD COUNTER-SUNK NAILS. per doz. s. d. 1 0 12 inch 1 12 "" 1 3 3 21 "" 1 3 2 "" 1 6 22 per doz. s. d. 2 0 2 3 2 9 3 0 . 3 6 4 0 1 9 Co "" BRASS TAPER-HEADED NAILS. per doz. s. d. 1 7 2 inch per doz. s. d. 3 3 1 8 8 21 3 9 " 1 9 9 · 2 4 6 33 1 10 22 53 "" 2 03 6 0 2 3 3 3 7 0 "" 2 94 8 6 "" BRASS SASH SCREWS. From 2s. to 3s. 3d. per dozen. WROUGHT NAILS. s. d. Threepenny per 1000 1 6 | Threepenny CUT NAILS. s. d. per 1000 0 8 Fourpenny "" 1 9 Fourpenny 0 10 " Sixpenny 2 2 Sixpenny 1 0 "" Tenpenny 3 0 " Tenpenny 2 0 Twentypenny "" 4 0 Twentypenny 3 0 "" Twentyfourpenny 3d. per lb. Larger sizes 24d. per lb. Spikes 3d. per lb. JOINER'S CUT BRADS. s. d. s. d. inch per 1000 0 2 1 inch per 1000 0 5 228 1 "" "" 0 3 11 "" 0 42 0 6 1 0 "" CUT FLOOR BRADS. 2, 2, and 3 inches, 2d. per lb. Cut lath nails, 24s. per cwt. I SASH LINE, at per gross of yards. Cast lath nails, 16s. per cwt. s. d. s. d. No. 1. 2. 3. 4. 5 0 No. 5. 10 O 5 6 6. 14 O 6 6 7. 18 O 8 0 8. 26 0 Common ditto 8d. per lb. BUILDERS' PRICES. 685 LOCKS. Drawback for Street Doors. Rim Locks with Brass Knobs, complete. 6 inch s. d. s. d. each 2 6 8 inch each 4 6 36 9 6 0 "" "" "" 5 0 10 10 0 "" "" "" 7 " 8, MORTICE LOCKS. Without furniture, from 3s. 6d. to 6s. each. Brass furniture to ditto, 2s. per set. China "" from 2s. upwards. Cupboard Locks, from 6d. to 2s. 6d. each. GARDEN ROLLERS, MOUNTED. s. d. s. d. 14 inches wide each 23 0 23 0 22 inches wide each 64 0 16 18 20 " " 29 0 24 78 0 "" "" " 36 0 26 "" "" 39 99 O " 50 0 "" Octagon HAY RACKS, from 7s. to 9s. each. PILLARS FOR CORN STACKS. s. d. each 10 6 Feathered Circular, 6s. each. PIPES, GUTTERING, &c. 2 s. d. each 9 6 23 31/ 4 4 5 5/1/ inches inches inches inches inches inches inches inches Pipes for Rain Water s. d. s. d. s. d. s. d. s. d. 1 3 1 6 1 10 2 3 2 31 2 32 s. d. s. d. s. d. 6 2 9 3 3 per yard. Flat Heads. 2 0 2 3 2 6 2 9 3 0 3 6 4 3 each. Angle Heads 2 32 6 2 9 3 03 3 4 0 4 6 Angle Shoes 1 01 31 31 6 1 9 2 6 3 0 3 6 Angle Boots 1 6 2 0 2 2 6 3 03 6 4 0 4 6 Guttering, half round 1 01 11 21 4 1 6 Guttering,long angles 1 3 1 6 1 Guttering, O.G. . Guttering, O.G. angles Guttering, Lion Head Clips.. Ditto, plain ditto . Flange pipes for pumps Pumps, various 3 0 3 6 4 35 045 3 055 0 9 2 0 2 3 1 7 71 8 2 2 1 10 2 3 2 6 0 10 0 8 1 9 per yard. 2 6 each. 2 6 per yard. 30 each. each. per yard. each. 686 BUILDERS' PRICES. SECT. VI.-Prices of Materials for Drainage and Water Supply. GLAZED STONE WARE DRAIN PIPES. 3 inches internal diameter 4 "" "" "" 18 "" 6 9 12 15 18 "" "" " "" "" "" "" "" 3 inches internal diameter 4 6 9 12 15 18 "" >" "" "" "" "" "" "" "" 3 inch bore of main tube 4 6 9 12 15 "" "" دو "" "" "" "" BENDS. • s. d. per foot run 0 5 0 6 "" 08 "" • 1 >> 11/ 1호 1 10 "" 3 0 4 0 "" each 1 3 1 9 >> 2 3 "" 13 39 36 5 6 8 0 པ 10 6 "" JUNCTIONS. each 1 3 1 6 235 2 0 • >" 3 6 "} 5 6 33 8 0 "" 10 6 >> DOUBLE JUNCTIONS. 3 inch bore of main tube each 1 8 "" 9 3 inch bore 4 6 9 "" 4 6 "" "" "" 2 0 "" 33 25 2 8 • 34 4 6 TRAPS FOR IRON FLAP. each 1 3 1 6 "" 2 0 "" 56 3 3 SYPHON TRAPS. 3 inch bore each 2 6 4 3 6 • "" "" 6 5 0 "" 9 7 6 "" "" Water Closet Pans, with Syphon Traps, from 7s. 6d. each. NOTE. Very large discounts are given by the pipe manufacturers for cash payments. BUILDERS' PRICES. 687 The Prices, Numbers, Sizes, and Weights, in Cast Iron, of Lowe's Patent Effluvia Trap Sewer Gratings, or Stench Trap Grids, are as follow, viz. :- In. In. In. Weight. No. 1 Size 30 by 18-16 deep, about 5 cwt. No. 2 Size 20 by 12-13 deep, about 2 cwt. No. 3 Size 14 by No. 4 Size 11 by No. 5 Size 9 by No. 6 Size 6 by 9 9 deep, about 1 cwt. 7— 7 deep, 56lbs. 53-53 deep, 25lbs. 4- 4 deep, 10lbs. No. 7 Size for Sink Stones, in white metal, square pattern. No. 7 Size for Sink Stones, in iron, square pattern, with brass Ditto ditto Ditto ditto Ditto ditto Ditto ditto grating and screw plug in iron, round pattern, with brass grating and screw plug all brass, square pattern, with screw plug all brass, round pattern, with ditto brass top and grating and lead body, with screw plug £ s. d. 1 18 0 0 16 O 090 0 6 9 040 0 3 0 0 2 6 0 19 020 0 3 6 0 3 9 03 0 Glazed or unglazed draining bricks patented by Messrs. RANDELL and SAUNDERS, can be supplied at the following prices, in any locality where clay of good quality can be obtained. BRICKS 12 inches long, 4 inches wide, and 2 inches thick, 1d. each. 12 >> "" 4/1/2 "" 31/2 1글이 "" The Cost of Bricks to make Drains of various dimensions will be as follows:- No. of Bricks Thickness of Diameter of Drain. per foot. Brick. Cost per foot. ft. 0 in. 6 in. 8. d. 4 12321 0 4 0 9 6 2 1 0 8 21 1 3 10 21/1 1 6 12 2321 1 9 14 2 0 16 2 2 2 Y 3 18 3호 6 20 9 22 3 0 24 4 42/2/2 N N N N Y N N N N ∞ ∞ ∞ ∞ + 0 6 0 8 0 10 1 . 0 1 9 2 0 2 3 2 6 2 9 3 0 688 BUILDERS' PRICES. IRON SINK TRAPS. ROUND JAPANNED TRAPS. per doz. per doz. s. d. s. d. 4 0 6 inch 12 0 4 6 61 13 6 "" 7 15 0 44 73 16 6 "" 7 6 8 18 0 "" 9 6 9 21 0 "" 11 0 10 26 0 "" 21 inch 3 31 4 4/ LO 5 5/1/2 "" "" "" "" "" "" 5 6 6 6 4 inch 5 CO 6 "" SQUARE JAPANNED TRAPS, WITH BARS OR ROUND HOLES. per doz. s. d. 9 07 inch 11 08 "" "" 14 09 STABLE DRAINS, JAPANNED. per doz. s. d. . 18 0 23 0 28 0 S. d. s. d. 6 inch square each 0 10 10 inch square each 2 3 8 1 612 3 6 " "" >> "" STRONG GRATES AND FRAMES FOR GRAVEL WALKS, 7 inch square at top, 3s. SOUGH GRATES, JAPANNED. per doz. s. d. per doz. 4 inch square s. d. 20 8 inch square 8 6 5 6 "" 3 0 9 "" 12 0 "" 7 " 4 6 10 6 6 "" O 15 O STRONG SOUGH GRATES WITH BARS, JAPANNED. per doz. per doz. s. d. s. d. 4 inch square 3 0 8 inch square 9 6 5 4 0 9 13 0 " "" 6 5 6 "" 10 16 O 7 7 6 22 BUILDERS' PRICES. 689 SECT. VII.-Plumber's Prices. Milled lead in sheet, per cwt. Cut to dimensions Window lead £ s. d. 1 8 0 1 9 0 1 17 0 0 1 15 0 0 18 0 Laying Milled lead in gutters, flats, hips, or ridges 1 13 Do. in step or other flashings DS or P traps, each Strong service boxes, each Safes for closets and straps Solder, per lb. Plumber, per day Labourer, Do. Wall hooks, each 0 10 0 080 0 0 10 0 6 0 04 0 0 0 11 Lead-headed nails 0 0 1 Large do. 0 0 2 Allow for old lead in exchange, 4lbs. to be deducted for waste, per cwt. 060 DRAWN WATER PIPES. Middling. Strong. s. d. s. d. HOY COKH inch per foot 0 5 0 6 0 7 08 "" "" 39 1 11 1 1/2 2 21 "" "" "" "" "" 09 0 10 0 11 1 1 1 31 1 7 "" 1 10 2 3 2 3 28 35 FUNNEL PIPES. 6 lbs. 7 lbs. 4 inch per foot 2 4 2 9 41 2 9 3 0 20 41 5 51 6 "" "" "" 4 inch joints "" "" "" 3 0 3 4 3 4 38 "" 38 4 0 "" each 4 3 4 6 "" 20 5 0 "" 51 5 6 "" 6 " "" 61 "" 39 60 6 6 2 inch 21 3 3 1/2 "" SOCKET PIPES FOR SINKS. per foot "" "" >> 23 1 5 1 7 1 7 1 9 20 2 3 2 3 2 6 690 BUILDERS' PRICES. RAIN WATER PIPES, INCLUDING FLAPS AND COLLARS. 3 inch 31 "" 4 "" inch 1 oo 1/ 11 2 21/2 "" "" "" "" "" "" 21 inch 3 H 312 4 "" per foot. "" "" s. d. s. d. 2 0 2 3 2 3 2 6 • 2 6 2 9 JOINTS, INCLUDING SOLDER AND LABOUR. each "" "" པོ "" • COMMON LEAD PUMPS. complete "" " "" "" 22 2 inch 3 31/12 4 "" FORCE LEAD PUMPS. complete "" "" "" "" 2135 2 inch complete £ s. d. 0 26 0 29 0 3 0 0 3 3 0 3 9 0 4 3 049 1 12 0 • 250 2 15 0 3 50 • 3 0 0 4 0 0 4 15 0 5 15 0 HYDRAULIC PUMPS. "" 4 15 0 5 10 0 700 8 0 0 2-1/2"> 3 22 31/2" 4 "" "" 9 10 0 23 inch PUMPS FOR DEEP WELLS. complete 4 15 0 3 5 15 0 "" "2 3 1/2 6 15 0 "" "> 4. 7 15 0 "" "" • BUILDERS' PRICES. 691 WATER CLOSETS. Best pan closet with valve, complete Do. with sunk ivory handle Do. with shoe valve, extra Blue painted basin, extra Bramah's valve closet, complete Ship Closet with copper basin, complete Square way inch STOP COCKS. 1 cold 2 11 11 "" "" "" "" Large cocks, per lb. BIB AND BALL COCKS. Screw ferrules inch CO "" 1 11 11/ "" "" £ s. d. 2 5 0 2 15 0 040 04 0 5 10 0 4 10 0 0 3 0 040 076 0 10 6 0 15 6 020 0 3 6 043 08 0 0 11 6 0 18 0 BOSSES, EACH. inch 0 0 10 1 "" 0 1 0 020 COPPER WATER BALLS. Wrought Rods. For inch cock "" "" 1 CONH 11 11/ "" "" "" " "" "" 1 2 11 inch "" Cobourgs DRIVING FERRULES. 020 0 2 4 0 4 3 070 . 0 9 0 0 1 1 0 14 0 2 3 0 3 6 + 0 36 692 BUILDERS' PRICES. LEAD AIR TRAPS, With Brass Bell Grates. £ 8. 8. d. 21 inch. 0 2 3 3 31 4 "" "" 0 2 9 0 3 6 0 4 6 13 inch 2 21/ 3 31 4 41 "" " ,, "" "" 20 "" BRASS GRATES. 1 11 11 2 21 3 inch "" "" "" "" "" WASHERS AND WASTES, Or plugs. 1 11 11 2 2 3 3 inch "" " "" "" 33 SHORT SPINDLE VALVES. LONG SPINDLE VALVES. 1½ inch 2 21/ 3 39 92 35 Plain pan closet basin Hopper Blue painted basin "" • SUNDRIES. 004 0 0 5 0 0 6 008 0 0 10 0 1 0 0 1 2 0 16 • 0 19 0 29 0 3 9 • 0 49 07 0 0 12 0 0 18 O 020 0 29 0 3 3 040 0 6 0 0 13 0 060 0 8 0 • 0 12 0 0 16 0 09 0 0 11 0 0 14 0 BUILDERS' PRICES. 693 Fan and mounting basin Wash-hand basin with brass washer and chain Blue printed do. Copper tinned basins Round cistern valves Shoe do. Spring do. Spring board and spring £ s. d. 0 3 0 066 0 8 6 046 059 0 10 6 0 10 6, 066 0 1 0 Cranks each Stool cocks with plates and handle Copper wire, per lb. inch 1 11/ 11 "" "" 1 24 inch "" "" 0 7 6 0 18 BOILER SCREWS. 0 1 3 018 0 2 6 0 3 6 0 4 3 COCKS FOR SLATE CISTERNS. 0 4 3 0 5 6 0 10 0 inch SCREWS WITH NUTS AND UNIONS FOR SLATE CISTERNS. "" 1 "" 0 3 4 049 0 6 6 WASHERS AND WASTES FOR SLATE CISTERNS WITH UNIONS. inch 是 "" 1 "" 0 2 9 0 5 6 0 7 6 SPINDLE VALVES FOR SLATE CISTERNS WITH UNIONS. inch 0 5 9 1 0 7 6 694 BUILDERS' PRICES. SECT. VIII.-Painter's Prices. COMMON COLOURS, INCLUDING KNOTTING AND STOPPING. Once in oil Twice in "" Three times in "" Four times in "" per yard Add to every extra coat If flatted "" If finished in party colours, add If sanded do. "> "" "" "" "" EXTRA COLOURS. s. d. 0 31 0 6 08 0 10 0 2 031/2 0 11/ 0 6 French grey, fawn, salmon, peach, or like tints Light green, or olive green. Patent greens, French greens, yellows or blues Chinese Vermilion or Lakes "" twice done on scarlet ground Imitation granite or splashed work Mouldings cut in, per foot run, common colours "" if grained in imitation of woods Broad lines to form panels add 0 1 0 3 "" 06 "" 1 9 2 9 "" 0 6 "" 0 0212 per foot 0 2 0 11 "" Light and shadowed lines 0 2 "" Cross banded margins • "" 0 31/12 PLAIN SKIRTINGS, NOT EXCEEDING EIGHT INCHES WIDE. Once in Twice oil per foot run 0 032 "> "" 0 11 Three times 0 12 "" "" Four times 0 21 "" If flatted, add 0 01/ >" MOULDED SKIRTINGS, EXCEEDING EIGHT INCHES WIDE. Once in Twice oil • per foot run 0 1 0 11 "" Three times 0 2 "" "" Four times "" 0 21/1 "" If flatted, add 0 1-194 "" PLAIN CORNICES, NOT EXCEEDING TWELVE INCHES GIRT. Once in oil • per foot run 0 11 Twice "" "" 0 12 Three times 0 21 "" Four times 0 3 "" If flatted, add 123 0 1 BUILDERS' PRICES. ENRICHED CORNICES, FRIEZES, OR OTHER ENRICHMENTS. Once in Twice oil "" 695 S. d. per foot super. 0 11/ 0 21 "" 031/20 Three times, Four times "" "" If flatted, add "" "" "" If picked in party colours add one half. REVEALS TO WINDOWS AND DOORS. 0 5 06 Once in oil • per foot run 0 12 Twice 0 12 وو Three times 0 21 "" "" Four times 0.3 "" "" WINDOW SILLS, STRINGINGS, COPING EDGES, PLINTHS, &c. Once in oil . • per foot run Twice 0 21/0 0 31 "" Three times 0 5 "" "" Four times 0 6 "" RAIN WATER PIPES AND GUTTERS. Once in Twice oil per foot run 0 12 "" 0 21/20 "" Three times Four times 0 3 "" "" "" 0 31/12 SASH FRAMES AND SQUARES. Frames once in oil, not exceeding 25 feet super. Do. twice "" Do. three times "" 08 1 0 >> 1 4 "" "" Sash squares Do. four times For large Venetian frames, add one-third once 1 8 per dozen 08 Do. twice 1 0 "" Do. three times 1 4 "" Do. four times 1 8 "" If the squares exceed 30 inches, add per doz. each coat 0 3 If different colour from the frames, add 0 1 If flatted, add 0 4 SASH FRAMES AND SQUARES, GRAINED. Wainscot oak or mahogany frames, each 1 6 Do. squares per doz. 1 6 696 BUILDERS' PRICES. squares per doz. Rosewood, satinwood, maple, &c. Varnishing squares per doz. or frames each, in copal Cleaning old work, rubbing down, or bringing forward, &c., to be charged day work, ladder work to be charged extra, according to trouble and labour. The term, party colours, is applied where the framing is one colour and the panels another. DAY ACCOUNT. Painter, per day Common colour per lb. Putty "" Hard stopping "" Brushes each Tools "" Pots "" Small do. "" IMITATIONS OF WOODS AND MARBLES*. s. d. 20 0 6 6 0 0 6 0 3 0 6 36 1 4 0 6 0 4 Wainscot oak per yard 1 6 Mahogany, maple, or sycamore 1 9 "" Rosewood or Coromandel-wood, and satinwood 2 0 "" Bird's-eye maple or pollard oak 2 6 For enrichments and carved work, add one-fourth Hand-rail, grained mahogany and varnished per foot run 0 4 Veined marble, including white ground per foot super. 0 3 Dove, bardilla, or black and gold 0 5 Sienna, brocatella, Venetian, French, Devonshire 0 6 "" Green verd, or porphyry Verd antique, oriental, jasper, giolla antico. Lapis lazuli If to columns, add 06 08 "" 1 0 "" 03 "" If to fluted do., add 0 4 Spirit varnish, each coat Varnishing once in best copal Do. Do. twice do. "" three times do. "" "" Cleaning and sizing old work Hand polishing, per foot super Do. on columns VARNISHING. per yard 06 0 7 1 0 1 4 08 0 6 10 "" Do. do. fluted 1 6 22 French polishing 0 6 "" Do. hand-rails and small articles, per foot run 04 * The prices here given are for work of the very best quality. BUILDERS' PRICES. 697 £ s. d. WRITING. Plain letters per inch 0 0 012 Do. from 3 to 6 inches girt "" 0 0 21 Sunk or Egyptian 0 0 1 "" Gold plain, under 3 inches girt 0 " 0 1/1/2 Gold sunk or Egyptian do. 0 "" Gold plain, from 3 to 6 inches girt 0 2 0 0 2 "" Gold plain, from 6 to 9 do. 0 "" 0 21/ Gold plain, from 9 to 12 do. 0 0 3 "" Gold Egyptian, from 6 to 9 inches girt 0 0 3 "" Gold do. from 9 to 12 do. 004 If shadowed, add "" 0 0 03/2 If do. double or indented, add 0 0 03 If shaded to appear as projecting letter, add for the double shadow Letters enamelled in gold on glass, per inch Antique or ornamental letters, once and a half the above prices. 0 0 1 0 0 3 GILDING. Gilding in oil gold, including preparation, per foot super. "9 Do. in burnished gold Carved work, from once and a half to double the above prices, according to the depth of the enrichment. Gilding inch mouldings, per foot run Do. & do. وو 0 3 6 046 Do. 1 do. "" "" Gilder per day 002 0 0 3 004 0 7 0 Gold leaf Oil gold size do. Pumicing, sizing, and preparing walls, Lining paper Do. stout Canvas lining per book Parchment size per lb. SECT. IX.-Paperhanger and Decorator's Prices. per piece 0 0 6 0 0 9 01 0 0 3 6 0 20 008 030 Hanging do., including tacks and slipping 0 1 6 22 Do. common papers do. 4 do. Hanging lining paper Do. satin do. Do. flock or embossed, marbles or granites in blocks Common papers, 3 colours, or two blocks, per piece 0 Do. For every extra colour, add 0 0 9 "" 0 10 "" 0 1 2 "" 0 16 " 1 0 to 0 2 0 0 2 0 "" If in rich colours, add 0 2 6 0 0 2 01 0 "" 2 V 698 BUILDERS' PRICES. £ s. d. £ s. d. Imitation marble per piece 0 1 6 to 0 2 6 Do. do. done by hand in a superior manner 0 4 6 08 0 "" Do. granite posted 0 2 0 040 "" "" Do. wainscot 0 1 0 "2 Do. do. overgrained Satin papers, 3 blocks 0 2 6 0 16 0 3 6 22 "" 0 4 0,, 0 6 0 "" Do. do. 5 do. 0 6 0 0 10 0 "" Embossed satin 080 0 10 0 "" "" Do. do. bronzed 0 12 0 0 15 0 "" "" Rich crimson flock 0 14 0 0 18 0 "" Do. do. bronzed 0 18 0 "" Panelled decoration 090 29 "" Do. do. including hanging 0 11 0 "" Gothic Common borders, per dozen yards Corners to do., each as one yard of border. Hanging borders, per dozen yards 0 1 0 1 5 0 1 16 0 200 0 3 0 "" do. 0 6 0,, 080 0 0 6,, 0 1 0 Sizing two coats, and varnishing papers per piece 0 2 6 0 3 6 Do. do. and do. two coats 0 4 0,, 0 6 0 BORDERS AND MOULDINGS, INCLUDING Half-inch wide, HANGING AND PAPER FIXING. per yard run Five-eighths wide, "" Three-quarters wide, "" Inch wide, "" Inch and quarter wide, "" Inch and half wide, "" Inch and three-quarters wide, Two inches wide, Rich flock borders, 2 inches wide, Do. 31/1 do. Old mouldings, up to one inch girt, taken down regilt and refixed, per yard For every inch extra width, add . Ebon lines, drawn out in panels, per foot Light and shadowed lines, "" Do. with shaded margin, 3 inches wide MOULDING. Black Gold. Black polished gold. s. d. s. d. s. d. s. d. 0 30 60 9 0 30 70 10 00031091 0 0010 410111 2 0 0 0 6 1 11 6 0 10 71 21 9 0 10 8 1 42 0 0 1010 1 8 2 4 03 04 1 0 0 2 0 01/ 0 1 0 2 SCAGLIOLA. Gray Granite or Porphyry, on slate, per foot 5 6 Statuary, black and gold 6 0 "" Sienna, Verana, Giallo antico, or Rondara "" 7 0 Brocadilla, or Egyptian green Verd Antique, or Lapis Lazuli Columns, including skeleton, extra 7 6 "" 80 "" 10 "" BUILDERS' PRICES. 699 DISTEMPERING. Once. Twice. s. d. 8. d. Washing, stopping, and whitening per yard 0 31 0 5 "" cream tint 0 4 0 6 "" "" drab, fawn, grey green, lilac, or peach blossom 0 5 08 08 0 10 "" pea green or light blue with verditer 1 0 1 4 "" "" clouded ceilings 2 0 "" in turps If one coat of oil color add Ditto Plain cornices per foot super., half the above prices. Enriched ditto, two-thirds. 0 2 "" 0 3 "" SECT. X.-Glazier's Prices. CROWN GLASS IN NEW SASHES. At per foot super. Best Best. Seconds. Thirds. Fourths. Ground. S. d. s. d. s. d. s. d. s. d. Squares from 3 ft. 0 in. to 3 ft. 6 in. 1 4 1 2 1 1 0 9 20 2 6 3 0 1 2 1 1 "" 0 11 08 1 10 "" 2 0 "" 2 6 10 0 11 0 90 7 1 8 1 6 2 0 0 11 "" "" 0 10 0 8 0 61 6 "" 0 90 80 7 under the above 0513 For flatted glass add one third, and for bent two thirds to the above. PATENT PLATE GLASS IN SQUARES FOR GLAZING. At per foot super. BEST. No. 1. No. 2. No. 3. No. 4. s. d. s. d. s. d. s. d. 6 by 4 and under 9 by 7 1 2 1 3 1 4 1 5 9 by 7 and not above 10 by 8 . 1 3 1 4 1 5 1 6 10 by 8 1 ft. 1 8 1 10 2 0 2 2 "" 1 ft. "" 11 ft. 1 11 2 0 2 2 2 4 1½ ft. 2 ft. 2 2 2 4 2 6 2 9 "" 2 ft. 3 ft. 2 4 2 7 2 9 2 11 "" 3 ft. 4 ft. 2 62 9 2 11 3 1 "" 4 ft. 8 ft. 3 0 3 3 3 0 3 0 8 ft. 10 ft. 3 3 3 6 3 9 4 0 "" 10 ft. 12 ft.. 3 6 3 9 4 0 4 3 "" 700 BUILDERS' PRICES. For seconds up to 1 foot 6 inches deduct 1d. and for all above that size 3d. No. 1 averages 1-16th of an inch, in thickness and 13 oz. weight to the foot. No. 2 >> "" No. 3 1-12th 1-10th 17 22 21 "" "" No. 4 1-9th 24 "" COLOURED GLASS. Yellow and lemon, Orange, blue, purple and red per foot super. "" Green, flashed ruby, and blue Embossed glass from Rosettes per inch 34 36 Best. Seconds. 8. d. s. d. 2 6 1 9 3 3 2 3 3 9 3 0 • 2 6 08 CROWN GLASS STOPPED IN OLD SASHES. Best. Seconds. Thirds. s. d. s. d. s. d. In squares 3 ft. 0 in. to 3 ft. 6 in. per foot super. 2 01 8 1 3 Ditto 2 6 3 0 1 8 1 5 1 2 "" "" Ditto Ditto 2 0 under 23 2 6 1 5 1 3 1 1 "" 2 0 1 3 1 1 "" 1 0 HORTICULTURAL GLASS, IN LIGHTS, GLAZED. 13 16 21 OZ. Oz. oz. s. d. s. Do. Not above 12 in. long, and 10 in. wide, per foot super. 0 40 3 ft. super., and not above 40 in. long 0 50 • d. s. d. 50 7 60 71 FLUTED GLASS, GLAZED. 10 in. by 8 in., and not above 1 ft. per ft. super. 1 0 1 11 5 11 ft. do. 2 1 11 31 7 2 do. 2 ft. 6 in. 1 41 61 11 "" "" 2호 do. 3 1 5 1 723 "" "" "" Best flattened crown glass, per foot super., extra 10 4 BUILDERS' PRICES. 701 POLISHED PLATE FOR GLAZING PURPOSES. £. s. d. per foot 0 1 9 Under 1 superficial foot 1 ft. and under 2 feet. 0 2 3 2 ft. 3 ft. 026 "" "" 3 ft. 4 ft. 02 9 "" "" 4 ft. 6 ft. 0 3 0 "" "" 6 ft. 8 ft. 0 3 3 "" 8 ft. 10 ft. 0 3 6 "" 10 ft. 12 ft. 038 "" "" 12 ft. 14 ft. 0 3 10 "" "" 14 ft. 16 ft. 0 4 0 "" 16 ft. 18 ft. 04 2 "" 18 ft. 20 ft. 0 4 4 "" "" 20 ft. 25 ft. 0 4 6 "" 25 ft. 30 ft. 0 49 "" 30 ft. 35 ft. 0 4 11 "" "" 35 ft. 40 ft. 0 5 2 "" 40 ft. 45 ft. 0 5 5 "" 45 ft. 50 ft. 0 58 "" 50 ft. 55 ft. 0 5 10 "" 55 ft. "" 60 ft. 060 " 60 ft. 65 ft. 06 3 "" "" 65 ft. 70 ft. " 35 0 6 6 Glazing 4d. per foot extra. Ground edges 6d. per foot run. ROUGH PLATE GLASS. At per foot super. 1 子 34. 1 11 11 2 inch. inch. inch. inch. inch. inch. inches. s. d. s. d. s. d. s. d. s. d. s. d. s. d. Not above 15 in. long 0 11 1 5 3 0 4 6 5 3 6 0 8 6 Above 15 in. and not above 35 1 01 63 45 06 07 010 0 35 75 1 3 2 04 06 07 7 08 0 8 0 11 0 22 "" 75 100 1 52 5 2 14 67 0 "" "" "" 100 and upwards. 1 62 65 0 If ground on one side add 6d. per foot. If smooth on one side and polished the other 2s. Bending rough plate 28. per foot. Do. polished plate 3s. For silvering plate glass add one fifth and for embossing do. 5s. per foot super. on squares not exceeding 6 feet. 702 BUILDERS' PRICES. HARTLEY'S PATENT ROUGH PLATE GLASS, INCLUDING GLAZING. At per foot super. THICKNESS. 3 444 14 Under 3 ft. superficial s. d. s. d. s. d. s. 0 8 0 10 0 111 d. s. d. 11 2 "" 4 0 90 11 1 01 21 4 دو 5 6 0 10 0 111 11 31 5 "" 6 " 011 1 0 1 2 1 41 6 "" 010 1 01 11 31 51 7 "" 12 1 01 11 41 61 8 ཝ "" "" 15 ་ "" 1 01 21 51 71 9 20 "" • 1 11 31 61 8 1 10 25 1 41 71 91 11 " "" 30 1 8 1 10 2 0 "" "" Quarries, 0 10 0 11 "" SUNDRIES. Quarries stopped in old lead lights each Squares under 7 by 5 7 by 5 and under 8 by 6 New lead lights with squares 6 in. by 4 in., per ft. super. Do. do. to 10 by 8 If with quarries add one fourth. "" "" £ s. d. . 0 0 11 0 11 002 003 0 0 5 "" "" 9 by 7 and under 10 by 8 008 "" New leading old lights, per foot super. 0 0 10 "" Repairing and part leading do. 0 0 6 "" Do. "" Casements pinned in each Puttying windows or skylights, each side, per doz. squares Cleaning windows per dozen squares common size Moore's moveable glass louvre ventilators, zinc frames and levers, brass rivets, 16 oz. sheet glass, rough edges, per foot 008 0 0 2 0 0 6 large 0 1 0 0 8 0 Do. 21 oz. sheet glass, rough edges per foot 0 10 0 Do. patent plate, ground edges 0 16 0 "" Brass frames and levers, British plate, ground and polished edges 1 3 0 BUILDERS' PRICES. 703 THICKNESS. 1 To $ 114 inch. inch. inch. inch. | inch. s. d. s. d. s. d. s. d. s. d. Glass tiles, each 0 81 01 62 02 6 Do. slates, each 24 in. by 2 in. •1 10 2 03 104 65 6 Do. do. 20 10 1 01 52 93 33 10 "" "" Do. do. 16 8,, 0 10 1 32 32 02 2 42 9 SECT. XI.-Zinc Worker's Prices. Malleable zinc laid with rolls, including labour to laying, complete. GAUGE. No. 10 11 12 13 14 15 16 14 16 18 21 24 26 30 Weight per foot superficial · OZ. Oz. OZ. Oz. Oz. Oz. Oz. Flats, Verandahs, Gutters, "" s. d. s. d. s. d. s. 0 50 50 60 70 80 9 0 60 70 70 80 8100101 0 510 60 60 70 71081091 d. s. 60 d. s. d. s. d. GUTTERS AND RAIN WATER PIPES. At per foot run. DIAMETER. O. G. Gutters. Square O. G. Octagon Octagon Shoes Gutter. Pipes. Heads, Heads, Heads, each. each. each. each. s. d. s. d. s. d. S. d. s. d. s. d. s. d. 2 inches 0 3 2 0 2 9 3 8 1 4 21 0 4 2 6 3 6 4 8 1 7 99 3 "" 31 "" 4 "" 41 "" cr "" 0 30 5 0 5 2 9 040 510 5 3 3 0 40 610 6 3 10 0 50 70 7 4 2 0 510 710 7 4 10 4 3 5 4 2 0 4 9 5 9 2 4 5 3 6 3 2 8 6 0 6 9 210 6 6 7 3 3 2 704 BUILDERS' PRICES. Chimney pipes, per foot Malthouse cowls, each Lobster back cowls, each Smoke dispersers 10 DIAMETER. 11 12 inch. inch. inch. s. d. s. d. s. d. 2 6 2 93 0 4 65 66 6 6 67 68 6 7 68 09 0 SUNDRIES. 48 s. d. Perforated plates Do. fitted into squares. Metal skylights and fan lights Do. large stout made • Ventilating tops according to size up to Bell tubing, verandah caps and roles Fan light and skylight bar Zinc nails for slates Do. tacks Soft solder Zinc worker Labourer Plumbic zinc, · per foot super. 0 0 41 "" "" • 0 0 6 026 030 1 5 0 per lb. 0 0 6 "" "" 0 0 7 0 0 7 01 0 0 0 10 per day 06 0 040 per cwt. 1 14 0 GALVANIZED TINNED IRON, Per Square. Plain galvanized tinned iron for roofs or flats laid complete with No. 28 gauge Do. 24 200 2 8 0 "" Do. 22 2 16 0 "" Straight corrugated . 24 2 12 0 "" Do. 22 "" 2 18 0 "" Do. 20 3 5 0 "" Do. 18 " 3 18 0 Curved 24 "" 2 15 0 " Do. 22 "" 3 3 0 "" Do. "" 20 3 15 0 "" Do. 18 "" "" Do. 16 4 0 0 4 18 0 BUILDERS' PRICES. 705 STEAM AND GAS FITTINGS EXCLUSIVE OF FIXING. 2 1호 inch. inch. 11 20 1 inch. inch. inch. inch. inch. inch. inch. 1 1 Patent wrought iron welded tubing, per ft. S Ditto galvanized "" Bends and springs, wrought, Bends and elbows, T's equal & diminish- ing outlets, s. d. s. d. s. d. s. d. s. d. s. d. s. d. s. d. s. d. 0 110 8 0 6 0 5 0 420 4 0 31 1 2 0 100 80 7 1 101 1 0 110 9 19 11 2 1 3 10 24 14 each "" 3 6 20 19 1 0 0 9 0 8 3 6 each 20 1910 0 9 0 7 "" 4 3 1 4 10 38 Crosses, equal outlets, Diminishing sockets or nipples,caps or plugs, & hexagon nuts, each) Plain sockets, "" Connecting pipes or long screws, each S 0 6 0 510 5 0 8 07 06 0 60 50 4 0 60 50 4 2 9 2 6 1 9 1 6 1 2 1 0 0 9 0 9 0 10 09 07 06 05 04 03 03 0 80 70 0 7 0 6 0 5 0 4 0 3 0 210 2 2 4 2 2 1 8 1 2 0 100 9 0 8 0 7 Iron cocks screwed to 18 0 11 0 fit Brass main cocks, Flanges, وو 5 0 3 0 2 6 2 0 0 10 0 9 0 7 0 6 0 5 1 4 0 100 8 0 7 9 0 5 6 4 6 3 0 2 6 2 0 1 9 each "" 144 0 18 0 13 0 8 0 1 10 17 29 20 1 3 1 0 1 4 1 0 each J "" 10 0 6 0 60 49 3 3 2 3 1 8 1 4 Stout tin pipe, per foot Union joints for metal pipes, Strong do. for iron 3 light gas meters 5 do. do. 10 do. do. SECT.-XII. Coppersmith's Prices. Copper pipes for main water, with rings and tacks com- plete, per foot run :— 48 s. d. 200 2 10 0 300 21 inch 3 "" 31 . 0 1 2 018 0 19 8 "" 4 27 Copper gutters semicircular, arwired, complete : 6 inches girt, per foot run "" 0 1 11 0 1 0 0 1 3 10 0 16 "" "" 12 0 19 "" "" Tinned do., 2d. to 3d. extra. Fixing extra. 706 BUILDERS' PRICES. £ s. d. Spike and screw prepared with copper ties, 1s. to 1s. 6d. each. Copper cistern heads, from 7s. 6d. to 12s. 6d. 12 oz. copper for flats and gutters, including seams, labour, ties, and nails, per ft. super. 16 oz. "" 0 1 3 0 1 8 020 "" 20 oz. "" "" "" For verandahs, add per foot 0 0 2 COPPER PIPES. Joints Weight. Price. each. lbs. Washing copper 2 inch 21/ 3 31 4 4/7/ 5 "" "" "" "" 22 "" Sheet copper per foot run s. d. s. d. 1 2 8 6 0 12 3 86 8 24 07 0 "" 21 4 67 6 3 5 490 "" 3/2 6 411 0 7 9 13 0 per lb. "" 1 0 1 8 SECT. XIII.-Wire Worker's Prices. Iron wire for skylight Strong ditto, inch mesh Fly wire for safes Copper do. Brass trellis wire for bookcases Octagon do. £ s. d. per foot super. 0 1 1 01 4 "" 0 20 "" 0 39 "" 0 3 3 "" 0 3 3 0 5 6 Strong brass trellis for window guard frames Fine wove wire for blinds "" Do. in mahogany frames, French polished, and painted Do. with lines and ornamental corners Extra for copper wire 0 1 6 028 0 3 6 0 1 2 DILAPIDATIONS AND NUISANCES. 707 CHAPTER XXI. ON DILAPIDATIONS AND NUISANCES. SECT. I.-General Definitions. THE rights of parties with respect to immoveable property so closely border on each other, and the line of demarca- tion between them is so indistinct, that one man, in the fancied exercise of his right, is continually liable to en- croach upon or disregard the right of another. No person, however absolute his property in land, can put it to any use he pleases; his right to use is restrained by the rights of his neighbour; he is bound to take care that his man- ner of using does not interfere with the inoffensive and profitable occupation by his neighbour of his land. Ques- tions as to the mode in which lands should be used may arise, either between parties who have different rights to the same land, and between whom there is a privity or connection of interest as between landlord and tenant, tenant for life and remainderman, or incumbent of a bene- fice and his patron or successor, or between parties who are strangers to each other in respect of the land used, as the occupiers of two adjoining tenements. In cases where Distinction there is a privity in respect of the land, every defect in lapidations & the condition of the land or house is termed a dilapidation, and the act or default of the tenant causing or permitting such defect is termed waste: in cases where tenements, from misuser or defect of repair, become injurious to a stranger, the act or default of the party is termed a nuisance. If a landlord complain that his tenant has dilapidated the premises leased, he must prove that the dilapidations in question are such as either the general nature of the tenure or the particular stipulations of the lease oblige the tenant to repair; but if the possessor of a house complain that his neighbour has obstructed his lights or in- jured his foundation, he must establish his right to the lights or foundation injured, and by so doing he proves the obliga- tion of the neighbour not to infringe those rights. The between Di- Nuisances. 708 DILAPIDATIONS AND NUISANCES. Waste de- fined. Nuisances defined, Obligation to repair; to party complaining of a dilapidation must show an original inherent qualification of the presumed absolute right of the party possessed; the party complaining of a nuisance has to prove either that the party complained of has ex- ceeded his presumed absolute right, or has granted a por- tion of it to him, and has derogated from that grant. Waste may be defined as the act or default of one party, having a right to use a tenement to the injury of another, having a right to the same tenement.-Nuisances compre- hend all nuisances which are the acts or defaults of the possessors of tenements to the injury of strangers, or of parties interested in the neighbouring tenements. It is only where the right to use is limited in point of what Estates duration, and the right of the successor certain to take attached. effect, that there can be any obligation to repair; thus tenant in fee simple and tenant in tail are under no obli- gation in this respect. It is not essential that the right of succession should be vested in any certain person, if there be a right of succession which is certain to take effect; thus, in the case of an ecclesiastical benefice, though the successor be not known until after the incumbent's estate is determined, he is under an obligation to repair, which the successor may enforce against him or his represen- tatives. Nature of Obligation to repair. The obligation to preserve from dilapidations, resulting from the right to use, varies with the nature and extent of that right; different tenants being bound to different re- pairs, according to the nature of their estates, and the covenants and conditions to which they agree. To suffer Distinction dilapidations, is called Permissive Waste; and to do any missive and act which will cause dilapidations, is, in legal language, to Voluntary commit voluntary waste. between Per- Waste. Alteration of Tenement. Division of Waste. The rule against Voluntary Waste includes an alteration in the tenement, although it be not thereby rendered less valuable, or even though the effect of the alteration be to increase the value. Hence there are three species of waste,-permissive, voluntary, and malicious. Permissive waste is of five sorts: first, the neglect to repair the necessary effects of time and use; second, the neglect to repair the consequences of in- evitable accident; third, the neglect to repair the external or internal coverings of a building; fourth, the omission to protect the fabric of the building from the consequences DILAPIDATIONS AND NUISANCES. 709 Of gation to re- of dilapidations in the coverings; and, fifth, the omission to prevent the wrongful act of a stranger. The obliga- of the Obli- tions of parties with respect to dilapidations may be pair. ranged into three classes. Ecclesiastics. Of the first class, are the obligation to repair, of the Obligation of incumbent, of an ecclesiastical benefice, the obligation of the public to repair churches, highways, bridges, and sewers. The incumbent of a benefice receives the whole profits of the tenements of which the benefice is endowed, and is bound to supply the necessary effects of time and use, and the consequences of inevitable accidents, upon the buildings attached to the benefice. repair Highways, The public have the sole right to use churches, high- of Public to ways, bridges, and sewers, and they are all interested in Churches, having them kept in perfect repair. They must, at all &c. events, keep them in such a state of repair as is necessary for the purposes for which they are required. > Churches and highways are repairable by the inhabit- ants of the parish in which they are situate. The obliga- tion is an obligation of the parishioners towards the public generally, who all have an interest in the support of churches and maintenance of highways; and there is also an obligation of each individual parishioner towards the general body, to contribute his proportion of the expense. Bridges being maintained at a greater expense than Bridges. ordinary highways, and not being situate in every parish, it tends more to the equality of the burden that the charge of repairing them should be borne by a larger district: for this reason, the law has imposed the obliga- tion of repairing bridges upon the inhabitants of the county. Sewers, which include sea walls, and every other erec- Sewers. tion or device for the protection of lands from the inunda- tions of the sea or rivers, or for draining off land-waters, are not, like churches, highways, and bridges, beneficial to the public generally, but only the proprietors of parti- cular levels, liable to be damaged by inundations, or requiring drainage. The inhabitants and proprietors of a level alone are bound to repair the walls and banks by which they are protected from floods, and the sewers by which they are drained; and this is, in its nature, an obligation of one proprietor towards the other proprietors, who are subject to a common danger or inconvenience, 710 DILAPIDATIONS AND NUISANCES. } Obligation of Tenants for Life and Years. and rather private than public, though common to many individuals. Although the obligations to repair churches, highways, bridges, and sewers, are equally well ascertained, there is an observable difference as to the manner in which they are sanctioned. It is the duty of churchwardens to see that the church is repaired: but it is left to the parishioners themselves to determine what repairs shall be done, and the amount that shall be expended; if they deny their obligation, the votes of the majority denying the obligation to repair are considered as thrown away, and the votes of the minority who admit the obligation, pre- vail; and if they suffer the church to become dilapidated, they may be proceeded against by ecclesiastical censures. At common law, the repairs to be done to highways and bridges, and the amount to be expended, were equally under the control of the inhabitants of the parish or county; though, if they neglected to do sufficient repairs, they were and still are liable to an indictment. By statute, the repairs of highways are subject to the control of a surveyor, and those of bridges to the justices of the peace. The maintenance of sewers and sea walls was never voluntary, but was under the direction of commis- sioners of the Crown. The second class includes the obligation on all particular tenants, whose estate is less than an estate of inheritance, except ecclesiastical incumbents. The law relating to the general obligation of these tenants to repair is called the Law of Waste; the law relating to the obligation of eccle- siastics is called the Law of Dilapidations. At common law only those tenants whose estates were created by law were liable for permissive waste in the absence of express stipulation. If the estate was created by the party, and there was no condition against waste, or covenant to repair, it was considered that it was not intended to place the tenant under any obligation to repair, and the case was presumed to be of the third class. The statute of Marlbridge has altered this presumption, and now tenants for life and for years, whether their estates are created by act of law or act of the party, are equally liable for waste, as well permissive as voluntary, unless it is expressly provided that they shall be without impeachment of waste. : DILAPIDATIONS AND NUISANCES. 711 In these cases, it being presumed that an equivalent for the occupation is given to the grantor, the tenants are not bound to repair the necessary and inevitable effects of time and use. Their obligation is to preserve the tene- ments from premature decay by reason of exposure to the weather, and for this purpose to repair the external and internal coverings of the fabric of the buildings. They are liable for permissive waste of the fourth sort. Mortgagees, who, although they have at law an absolute Mortgagees. estate in the tenements mortgaged, are in equity deemed to hold them as a pledge merely, are in equity under a similar obligation to the mortgagors. Of course they are entitled to be allowed the sums expended in necessary repairs out of the profits of the premises. by Covenant. The obligation of a tenant for life or years may be ex- Obligation tended by express covenant. Such covenant is construed with reference to the common law obligation, and unless an intention to the contrary is manifest, does not render the tenant liable to repair the necessary effect of time and use, or the inevitable decay of the fabric of the building. In ordinary cases the obligation is against permissive waste of the third sort. They are also liable to repair dilapidations caused by inevitable accident. Strangers. All tenants who are liable for permissive waste are re- Waste by sponsible for waste committed by strangers, which it is presumed they are able to withstand, and against whom they have a remedy. If the strangers are the Queen's enemies, or felons, their acts of waste are in the nature of inevitable accidents, for which tenants for life and years, not under covenant to repair, are not liable. without Im- Waste, and Will. In the third class may be ranged-tenants without im- Tenants peachment of waste and tenants at will. Neither of these peachment of are liable for permissive waste,—the tenant without im- Tenants at peachment by reason of the expressed intention of the grantor of the estate; and the tenant at will by reason of the infirmity of his estate. An estate at will is, in contem- plation of law, of no value; and therefore whatever services such tenant renders to his landlord, and it may be presumed that he renders some, must be more than an equivalent for his estate. All tenants, except tenants without impeachment of waste are liable for voluntary waste; and tenants without impeachment of waste are liable in equity, but not at law, 712 DILAPIDATIONS AND NUISANCES. Malicious Waste. Tenants in Common. Subjects of Dilapidations Gardens. Lands. for malicious waste. Malicious waste consists in pulling down the mansion house, or felling timber planted for the ornament or protection of the mansion-house. The Court of Chancery considers that it was not the intention of the grantor to confer the power of destroying such things. From this waste being solely cognizable in Courts of Equity, it is called Equitable Waste. Questions respecting dilapidations occasionally arise between persons interested jointly or in common in tene- ments. In such cases there is no obligation by one to the other to repair any particular dilapidations. One tenant has a remedy against his co-tenant if he commit voluntary waste, and may compel him to contribute towards the necessary repairs of houses and mills. The general obligation of neighbours as to party walls and fences dividing their premises is the same as that of tenants in common, if they are tenants in common of the wall or fence. One may be, by prescription or contract, bound to repair a fence so as to prevent cattle in his land from straying into his neighbour's. The subjects of dilapidations are houses and other arti- ficial erections and ways, gardens, land, and trees. Things made by art demand the exercise of art to preserve them from decay. It is only as to such things that the law of permissive waste is applicable. With respect to gardens, lands, and trees, tenants are by the general law merely prohibited from committing voluntary waste. But where lands are let for the purpose of cultivation, as they are almost universally to tenants for years, they are bound to cultivate them in a husbandlike manner, and according to the custom of the country; that is, in the manner in which farm-lands are usually cultivated in the part of the country in which the lands leased are situate. It is voluntary waste in gardens to cut down the fruit trees, or destroy or remove the shrubs and plants growing there, except for the purpose of culti- vation. It is voluntary waste in land to alter its nature so as to diminish its value or affect the evidence of title; an altera- tion in the course of good husbandry, which does not either diminish the value of the land, or impair the evidence of title, is not waste. It is also waste to take the substance of the land, as clay or minerals, except where open DILAPIDATIONS AND NUISANCES. 713 mines or quarries are leased, in which case there is an implied authority to continue working them. Waste as to trees consists in felling timber trees, that Timber. is, trees which contain, or when mature will contain, wood useful for building purposes. The property in such trees belongs to the owner of the inheritance, and in the case of ecclesiastical property to the Church. No particular tenant can do any act to destroy or injure their growth, or fell them, except for the benefit of the inheritance, as to repair buildings and fences standing on the land demised. It is not waste to cut down trees not timber, in such a manner that they will grow again, unless they have been planted for some particular purpose implying permanence, such as for the ornament or shelter of a house, or for the support of a bank or hedge, or in a field for the shade of cattle. But it is waste to grub up or destroy any trees, whether timber or not. There is an important exception to the law against Fixtures. voluntary waste in the instance of fixtures. By this ex- ception a particular tenant, who has made erections or fixed machinery to premises for the purposes of a manu- facture or trade, or has added to a house any particular article of ornament or domestic convenience, which may be removed without injuring the house, is entitled to re- move the things so fixed. From the occasion and purpose of the annexation, an authority from the owner of the in- heritance to fix and remove is inferred, and an intention of the particular tenant to abandon his property in the fixture, which would in ordinary cases be presumed, is negatived. Neighbour's A nuisance is an act or neglect of a man on his own Nuisances to land, the consequences of which extend beyond his pos- Land; sessions, and encroach upon the possessions or rights of his neighbour. The general law as to the limits of possessions is, that he to whom the soil belongs has a right to all the space perpendicularly above and below; and therefore, so long as the effects of an act or neglect are confined within those limits, there is, generally speaking, no nuisance. But if, in using our land, we encroach upon or disturb our neighbour in the enjoyment of any part of the space above or below his land, such act is a nuisance; as if we build so as to overhang our neighbour's land, and cause the water from the eaves of our building to fall upon his 2 W 714 DILAPIDATIONS BY To Easement Public Nuisance. Parties liable for Waste; land, or if we carry on a noisome and offensive trade, so as to corrupt the air over the adjoining land with noxious effluvia, or disturb it with deafening noises, or dig under the foundation of a house standing thereon. It would manifestly interfere with the conveniences of society, if every noise, or every smell, which the deli- cate perceptions of a neighbour considered disagreeable, amounted to a nuisance; the law, therefore, modifies itself to the exigencies of mankind, and determines that the noise or stench must be so considerable in degree, and so long continued, as to destroy the comfort of a person of ordinary sensibility in the occupation of his property. Our neighbour may by grant, or by long enjoyment, which causes a grant to be presumed, acquire an easement over our land, for the more convenient or profitable occu- pation of his own, by which his rights spread themselves into our possessions, and become, as it were, interfused with ours, and operate to control us in the use of our land; in such case it is a nuisance to obstruct his enjoyment of such easement, though we do not encroach upon his terri- tory: thus, if we give him permission to build upon the verge of his land, and to open windows looking over our land, he acquires right to our land for the support of his house, and to the air over our land for light to his house, which rights are called easements; and we cannot dig into our land so as to weaken the foundation of his house, or build so as to darken his windows, though, if he had ac- quired no right to those easements, either by grant or prescription, we might. If the tenement be used so as to prejudice the whole neighbourhood, or to injure a public right of way, it is a public nuisance; and the parties causing it are punishable by indictment, at the suit of the Queen, and not by action at the suit of an individual, unless he has sustained some particular injury over and above that inconvenience which he has suffered in common with the rest of the public. SECT. II.—Dilapidations by Tenants for Life and Years. By the common law, only tenant in dower, tenant Tenant by by the curtesy, and guardian, were punishable for waste, because their estates being created by the law, the law annexed to them the condition that they should neither do the curtesy, &c. TENANTS FOR LIFE AND YEARS. 715 Marlbridge. nor permit waste; but a tenant for life or for years, whose estate was created by act of the party, was not liable for waste, (that is, for permissive waste,) unless the grantor so stipulated; the parties being at liberty to contract as to the manner in which the tenements should be used: the law did not imply a condition against waste in cases where they did not so provide. This was remedied by the statute Statute of of Marlbridge, which provides "that farmers during their terms shall not make waste or exile of houses, woods, or men, or of any thing belonging to the tenements that they have to farm, without special license had by writing of covenant, making mention that they may do it, which thing if they do and thereof be convict, they shall yield full damage, and be punished by amerciament grievously." The statute of Glocester further enacts, "that a man from of Glocester henceforth shall have a writ of waste in the Chancery against him that holdeth by law of England or otherwise for term of life or for term of years, or a woman in dower; and he who shall be attainted of waste shall lose the thing that he hath wasted, and moreover shall recompense thrice so much as the waste shall be taxed at.' "" Life and These statutes extend to every description of tenant for Tenant for life or years, whether created by grant or devise, to a party Years. to whom lands are granted for an uncertain period to a tenant from year to year, for a year, or half a year. Although a tenant in tail after possibility of issue extinct is not punishable for waste, yet if he grant over his estate, his assignee is but tenant for life, and liable therefore. Every person in whom the estate for life or years becomes vested as assignee, executor, or occupant of an estate per auter vie, takes it subject to the condition against waste. Soccage. Will. A guardian in soccage is liable for waste, voluntary Guardian in or permissive, but not for waste done by a stranger. Tenants at will (that is, those who hold merely at Tenant at the will of the lessor, and whose estate may be determined at any time, not those who hold under yearly tenancies determinable by notice, and who are sometimes improperly termed tenants at will,) are not included in the statute of Marlbridge or Glocester, and are not bound to do any repairs; but still they cannot lawfully commit voluntary waste. The estate of tenant at will is so infirm, that it is 716 DILAPIDATIONS BY Liability of Tenants for Waste. reasonable that he should not be bound to do any repairs, since, if he expend money upon the tenements, his lessor may immediately determine his interest, and prevent him from deriving any advantage from such outlay; and if the tenements are falling into decay, it is always in the power of the lessor to enter and take measures for their vation. preser- Waste is of two sorts, voluntary and permissive. permissive According to the old cases, every tenant for life or years within the statute of Glocester is liable for waste in the same degree; but in modern times doubts have been en- tertained, though it would seem without any sufficient foundation, whether a tenant from year to year, or a tenant for years, not under covenant, is liable for permis- sive waste. No distinction can in reason be made between a tenant for life and a tenant for a year, or for a part of year. Each is a farmer within the statute of Marlbridge and a tenant within the statute of Glocester, and each is made liable by the same words; and there is no provision that one shall be liable for one sort of waste and one for another. Waste in Buildings. The statute of Marlbridge prohibits waste or exile Houses and of houses, woods, or men, or any thing belonging to the tenements had to farm. These words are large enough to include every thing that is part of the tenements demised. The books enumerate buildings, gardens, lands, and woods, as the subjects of waste. It is proposed to state the law applicable to each of these subjects separately. First, And first, of waste in houses and buildings. It has Voluntary. been expressly decided that the law of waste extends not only to dwelling-houses, but to every description of build- ing, such as outhouses and barns, The word houses in the statute includes every description of building: but an incomplete building, such as a pale, a post, or an uncov- ered wall (which probably means erections not forming part of a building or a fence), are not subject to the law of waste. Voluntary waste is a wilful act committed by the tenant or by his orders, by which the tenements are de- stroyed, injured, or altered: it is voluntary waste in a house to prostrate it, or to destroy or remove any part of it, as a post, a door, a window, a furnace, a bench, or TENANTS. FOR LIFE AND YEARS. 717 wainscot fixed to the house. The rule against voluntary waste extends to additions made to the house by the tenant himself: thus it has been decided that " glass annexed to the windows by nails or in any other manner by the lessor or the lessee cannot be removed by the lessee, for without glass it is no perfect house. Peradventure great part of the costs of the house consists of glass, which if it be open to tempests and rain, waste and putre- faction of the timber would follow. Wainscot also is parcel of the house, and it makes no difference whether fixed by great nails or little nails, or by screws or irons put through posts or walls (as have been invented of late time); for if wainscot is by any of the said ways, or by any other, fastened to the posts or walls of the house the lessee cannot remove it." Things merely placed by the tenant on the premises, but not fixed, however bulky such things may be, are not within the rule as to voluntary waste: thus a barn placed upon pattens and blocks of timber lying upon the ground, but not fixed in or to the ground, may be removed; so if it rest upon blocks of stone which are fixed in the ground, but not fastened to the blocks by mortar or otherwise. A mill removable at pleasure, which was an octagonal wooden building, raised on a casement of brickwork and anchored to the ground by shores and land-ties, part of the shores and the whole of the land ties being one foot under the surface of the earth, was found by the jury not to be a fixture. So distillers' vats supported upon brickwork, but not fastened to the ground, are goods and chattels, and no part of the premises on which they are placed. And where certain caps and steps of timber were fixed by a tenant to a building, and he placed in these caps and steps, jibs which he fastened there by pins above and below, the jibs might be taken out of the caps or steps without in- juring either them or the building; the jibs were held to be the personal property of the tenant, and no part of the building, so that he did not lose his right to them by leaving them there after the expiration of his term. the rule voluntary The right to remove fixtures is an exception to the Exception to rule against voluntary waste. By this exception a tenant against for life or years, who during his tenancy has fixed certain waste. chattels to the premises for the purposes of his trade or as matters of ornament or furniture, and which can be re- 718 DILAPIDATIONS BY # Fixtures. Tenant may remove Buildings moved without injury to the premises, is entitled to remove them, and is not guilty of waste in so doing. Although the cases of tenant for life and of tenant for years are separately treated of in the books on this subject, there is no authority for saying that they are not equally entitled to fixtures. And, as they are made liable for waste without distinction by the statutes of Marlbridge and Glocester, it may be inferred that the exception extends in the same degree to both. There is distinction between chattels which are substan- tially of the same character before they are fixed, when fixed, and after removal, such as engines, pumps, and grates, which are engines, pumps, and grates, whether chattels or fixtures; and things the character of which is altered by their annexation to the land, such as buildings which, when fixed, exist as buildings, and before and after severance exist merely as materials, bricks and mortar. Things of the first class may be removed, whether fixed for the purpose of trade or of ornament, or domestic con- venience. Buildings, it seems, may be removed if erected for the purpose of trade, but agricultural buildings are not within the same rule as trade buildings. and Fixtures cc erected by him on Farms, lord elect to take to them. The law as to farm buildings has been recently modified by the act of the 14th & 15th Vic., c. 25, s. 3, whereby it is enacted “That if any tenant of a Farm or Lands shall "after the passing of this Act, with the Consent in Writing of the Landlord for the Time being, at his own "Cost and Expense, erect any Farm-building, either de- unless Land-tached or otherwise, or put up any other Building, Engine, or Machinery, either for Agricultural Purposes "or for the Purposes of Trade and Agriculture, (which “shall not have been erected or put up in pursuance of "some Obligation in that Behalf,) then all such Buildings, Engines, and Machinery, shall be the Property of the "Tenant, and shall be removable by him, notwithstanding "the same may consist of separate Buildings, or that the same or any Part thereof may be built in or perma- nently fixed to the Soil, so as the Tenant making any "such Removal do not in anywise injure the Land or Buildings belonging to the Landlord, or otherwise do "put the same in like Plight and Condition, or as good Plight and Condition, as the same were in before the "Erection of any thing so removed: Provided, neverthe- 66 66 TENANTS FOR LIFE AND YEARS. 719 66 "less, that no Tenant shall, under the Provision last aforesaid, be entitled to remove any such Matter or Thing as aforesaid without first giving to the Landlord "or his Agent One Month's previous Notice in Writing "of his Intention so to do; and thereupon it shall be law- "ful for the Landlord, or his Agent on his Authority, to "elect to purchase the Matters and Things so proposed to “be removed, or any of them, and the Right to remove "the same shall thereby cease, and the same shall belong “to the Landlord; and the Value thereof shall be ascer- "tained and determined by Two Referees, One to be "chosen by each Party, or by an Umpire to be named by "such Referees, and shall be paid or allowed in account "by the Landlord who shall have so elected to purchase "the same. Things coming within the building class which are an- nexed for the purpose of ornament or convenience, it may be concluded, cannot be removed, such as an out-house. The right of nurserymen to remove green-houses and Nursery- hot-houses as trade buildings is left in doubt, it being af Fixtures. firmed by Lord Kenyon, and doubted, if not denied, by Lord Ellenborough. On the one hand, it may be said, that their case resembles those relating to mining fixtures. It is at least a mixed case between occupying land and carrying on a trade. If any distinction can be made, it is in favour of the gardener, green-houses and hot-houses being erected for rearing of exotics, which are raised by the gardener's skill, and have not necessarily any connec- tion with the land demised. On the other hand, it must be borne in mind that the mining cases were not cases of simple buildings, but of machinery and of buildings merely necessary to the machinery, and that green-houses and hot-houses have a peculiar adaption to the nursery ground demised; and it may be presumed were intended to form part of the freehold, unless otherwise agreed. In consequence of the exception as to fixtures, they have become a peculiar description of property, and there are many rules of law relating to them as such, which are not within the scope of this treatise. It should be noted, however, that the tenant must remove them during his term, and that if he omit to do so, they become the pro- perty of the landlord. An alteration of the buildings demised is wilful waste Alterations. 720 DILAPIDATIONS BY Improve- ments. Permissive Waste in if it be injurious to the inheritance, either by diminishing the value of the estate, increasing the burden upon it, or impairing the evidence of title. There are conflicting authorities as to whether it is waste to build a new house where none was before. The conflict is as to the application of the rule of law, not as to the rule itself. It is not waste simply to alter, but it is waste to alter to the injury of the inheritance. Some think that to build a new house is necessarily a benefit to the lessor, others that it is not. The latter seems to be the better and prevailing opinion. the burdens of the lessor by the charge of its repair; and the act of building a house may be used as evidence that the builder is the absolute owner of the land. A new house may increase Although a landlord may complain of a new erection as voluntary waste, he may waive this right, and insist upon the tenant keeping it in repair. But if the lessor, without the consent of the lessee, build a cottage on the premises during the lease, the lessee is not liable for waste, either voluntary or permissive, to such cottage. If a tenant for life or years choose to alter or im- prove tenements by erecting buildings, or rebuilding, or doing extensive repairs to those already erected, whereby their value is increased, he has no claim at law or in equity against the remainderman or landlord for the value of the improvements. Permissive waste in buildings is the injury happen- Buildings. ing to them during the term by the permission or neglect of the tenant; that is, an injury which the tenant might have prevented, by taking care of the building, and doing precautionary repairs. Roof. The obligation to preserve the tenements from waste compels the tenant to keep the walls and timbers of the house from exposure, and renders him liable for any injury the fabric or skeleton of the house sustains for want of such repairs as were necessary to preserve it from exposure. The tenant is bound to keep the external coverings, the roof, and other outworks, of the building in repair, and to renew them when they decay, so as to preserve the tim- bers, walls, and skeleton from premature decay. obligation to do such repairs is not absolute, but relative, with reference to the condition of the main timbers and walls of the house in consequence of his neglect to do His TENANTS FOR LIFE AND YEARS. 721 them. Thus, suffering houses to be uncovered, whereby the spars, rafters, planchers, or other timbers become rot- ten, is waste; but barely suffering them to be uncovered without rotting the timber is not waste. Where a tenant permitted the standings before the door of his house to be uncovered and out of repair, whereby the principal timbers became decayed and in danger of falling, it was held to be waste. Glass is an external covering which the tenant is bound Glass. to keep entire; and if in consequence of the windows being broken, the interior of the house is injured, he is liable for waste. Outer doors must for the same reason be kept in repair Outer Doors. and entire. Coverings. It is also permissive waste if the fabric of the house is Internal injured by reason of the tenant not keeping in repair the internal coverings of the walls. Plastering. He is also bound to keep filth and water out of the In Drains, house by repairing the groundsills and drains. and not Cleansing. Repairs. The repairs which a tenant for life or years is bound to Tenantable do are usually called tenantable repairs. They extend only to the finishing, and not to any part of the skeleton of the house; they include the work of the joiner, plas- terer, and glazier, but not that of the bricklayer and car- penter. Stopping out wind and weather, as mending tiles and chimneys, are included in tenantable repairs, because such repairs tend to preserve the fabric of the house from premature decay. They are, therefore, intermediate be- tween substantial and ornamental repairs; bricklayers' and carpenters' work being, generally speaking, substantial repairs; and painting, papering, and whitewashing, orna- mental repairs. the House If the house is ruinous at the time of the lease, that is, Condition of if the timbers and walls are decayed so that it falls by when leased. reason of its age and bad condition, and not by the default of the lessee, it is not waste. If the timbers are standing, but the rafters are gone, and it falls during the lease, the tenant is not liable, because he cannot cover the house without rafters, and he is not bound to find them. On the point whether if a house is simply uncovered at the time of the lease, the tenant is bound to cover it, so as to be responsible for any dilapidations that may ensue by reason of the want of covering, the authorities are conflicting. 722 DILAPIDATIONS BY Waste by Fire. Waste by Strangers. By Under- Tenant. Inevitable Accidents. Waste by fire, when the fire was caused by the negli- gence of the tenant, and perhaps when the fire happened accidentally and without negligence, was accounted per- missive waste under the statutes; and, according to a recent decision, waste by fire, occasioned by negligence, is permissive waste, but the law on this point is not in a satisfactory state. If a tenant suffer a stranger to do waste, he shall be answerable; for it is presumed in law that the tenant may withstand it, et qui non obstat quod obstare potest, facere videtur. Another reason given for making the tenant liable for waste done by a stranger is, that he has a remedy against the stranger. Being liable for waste by a stranger, of course the tenant is liable for waste by his under-lessee, to whom he has given the opportunity of committing such waste; and a guardian is liable for waste, by those with whom he is connected by privity of estate, as where an abbot was guardian, and one of his monks committed waste; and where joint tenants are guardians, and one of them does waste, both are liable. For dilapidations occurring by inevitable accident a tenant is not answerable, as where a house is destroyed by the king's enemies, who are not amenable to the law, or by superhuman agency, as by lightning or tempest. And where a house has been blown down by tempest, it is not waste for the lessee to sell the materials, because they have become chattels. But if a part of the house which the tenant is bound to repair is destroyed or injured by tempest, he is bound to restore it; as if a house is un- covered by tempest, but the timber is left standing, and it afterwards fall for want of covering, the tenant is liable for waste and if a tempest take away a small part of the thatch, the tenant is bound to repair it; and if he neglect to do so, and in consequence the house is thrown down by tempest, he is liable for waste. Where lands are flooded in consequence of the decay of a wall of the sea, or the banks of rivers, it is waste in the tenant; but if the lands be damaged by the sudden rage and violence of the sea, or by a sudden flood of the river, it is not waste; and it has been held, that if the banks of the Trent be unrepaired, it is waste, because the Trent is TENANTS FOR LIFE AND YEARS. 723 not so violent, but that the lessee, by his policy and in- dustry, may well enough preserve the banks. repair; A covenant to repair is negative as well as positive in Covenant to its obligation; and the tenant is thereby bound as well not Alterations. to do an act amounting to voluntary waste as to repair dilapidations. Thus an alteration of the demised premises is a breach of a covenant to repair: for example, breaking a doorway through the house demised into the adjoining house. So the act of pulling down a brick wall, which divided one part of the demised premises from another, was held to be a breach of a covenant to repair and uphold the brick walls belonging to the demised premises. But where the covenant was, that the tenant should leave the premises in as good plight as he found them, and he pulled down houses, the lessor it was held could have no action until the end of the term, for the covenant had relation thereunto; but that if he had wasted the woods, covenant would have lien, because it would be impossible to repair such waste. And if from the language of the lease it appears that the parties contemplated alterations being made, an al- teration is no breach of the covenant to repair. Thus, where the covenant was to repair the demised premises, together with such buildings, improvements, and additions, as at any time during the term should be erected, set up, or made by the tenant, it was decided that the tenant had not broken the covenant by converting the windows on the ground floor into shop windows, and stopping up an inter- nal door in one place, and opening one in another. Tear. A covenant to repair obliges the lessee at all events to Wear and repair and restore those parts of the building which fall away, wear out, or are destroyed during the term. He is not bound to repair parts which are merely in progress of decay. His covenant is to repair all accidents, and to take all reasonable precautions against the fabric of the building being exposed to the weather, or becoming more depre- ciated than it necessarily would from time and ordinary use. The covenant must be construed with reference to the age and general condition of the building at the commence- ment of the term. The covenant to repair is not a cove- nant to improve, or to keep and yield up the building demised in as perfect a state as when demised, but to keep it, as nearly as possible, in the same state as when demised, DILAPIDATIONS BY 724 } and to do such repairs as are adapted to the nature of the building. The obligation imposed by the covenant to repair differs from the common law obligation against permissive waste in this. The common law obligation is merely to guard the fabric of the building from decay, and is not infringed by an external dilapidation unless the fabric is injured in consequence. By the covenant the tenant is uncondi- tionally bound to repair all dilapidations, whether the fabric of the building is injured or not. Injuries to the building caused by inevitable accident are excepted from the common law obligation, but not from the obligation of a general covenant. The obligation of a covenant differs from the obligation of an ecclesiastic in this. The ecclesiastic is bound to re- pair buildings and parts of buildings about to fall away (proximo casuras)—those parts which are nearly but not quite worn out. The covenantor is only bound to repair those parts which are actually fallen away and worn out. If the house falls merely from natural decay, and with- House falls out default of the tenant, it would seem that he is not from Decay. bound to rebuild it under an ordinary covenant to repair. Under a general covenant to repair, the tenant is bound to keep in repair the inside painting, and this, although he expressly covenants to paint the outside. Obligation to rebuild when Painting. Materials. Accidents. Where any part has fallen away, the tenant is not bound to replace it with new materials, but only with materials of the same value and in the same condition as those defi- cient ought to have been, had they only been subject to ordinary decay and wear, except from accident or exposure to the weather. In determining this, reference must be had to the age of the building at the time of the lease granted, and to the duration of the lease; and so much ought to be deducted from the cost of new materials as it may be supposed they would be depreciated in value by ordinary wear during the period the materials to be sup- plied have formed part of the building. Mr. Woods thinks, that in hardly any case could the landlord require more than three-fourths of the new value, and none would occur in which one-fourth ought not fairly to be demanded. On a covenant to repair, the covenantor is bound to repair at all events, and is not excused from repairing de- fects caused by inevitable accident. An inevitable acci- TENANTS FOR LIFE. AND YEARS. 725 dent does not render it impossible to perform the covenant. The covenant is performed by repairing the consequences of the accident. Where the law infers from circumstances such obligation as is reasonable, there it limits the obliga- tion with those qualifications and exceptions, which under the circumstances are reasonable. It presumes that con- tract to have been entered into which is just and equal to both parties. But where the parties have themselves ex- pressed the contract which they conceive to be just, there all the law has to do is to apply it to their acts and enforce its performance; for although it may, with much probability, be conjectured that a certain contingency was not foreseen, yet it might have been foreseen, and nothing said about it, because not intended to be excepted from the generality of the obligation. For these reasons, where there is a gene- ral covenant to repair, and the buildings are destroyed by accidental fire, the lessee is bound to rebuild. It is no answer to a covenant to repair a bridge, that it was de- stroyed by an extrordinary flood, such as the covenantor could not resist, and without default on his part. But when a house is destroyed by inevitable accident, the lessee performs his covenant to repair if he rebuild it within a reasonable time; the covenant to repair not meaning that the house shall never be out of repair, but that the lessee will restore all dilapidations which happen during the term. dence of repair and The general obligation of the covenant to repair is not Indepen- limited by a covenant to insure in a specific sum. If such Covenants to sum be insufficient to rebuild the premises, he must supply insure. the deficiency. Performance If the dilapidations are caused by the act or neglect of Excuse from the landlord himself, or if he renders it impossible for the by Act of tenant to perform the covenant, the breach of covenant is excused. But an act of the lessor which merely impedes but does not wholly prevent the lessee from performing his cove- nant, cannot be alleged by him as an excuse for a breach. And so it is no answer to an action on a covenant for not repairing and cultivating, that the plaintiff entered on parcel of the demised premises, and ejected the defendant therefrom. Lessor. And a covenant cannot be discharged by a parol license By License of the covenantee. If the landlord, by word of mouth, or of Lessor. 726 DILAPIDATIONS BY Indepen- dence of Covenants to pay Rent. pay Rent ses are burned. writing (not being a deed), authorize the lessee to do an act which is a breach of covenant, the lessee is liable to an action of covenant notwithstanding. And the tenant is not excused from the performance of repair and to a covenant to pay rent by the premises becoming unten- antable by inevitable accident, as if the house demised is Obligation to burned down, or land is surrounded by water, or the when Premi-tenant is evicted by a foreign enemy. And where the lease contains covenants to pay rent and to repair, and in the covenant to repair the case of the premises being de- stroyed by fire is excepted, the tenant must pay the rent accruing after the premises have been destroyed by fire, and before they are rebuilt; and he must do so although it be assumed that it is the duty of the lessor to rebuild, the covenants being distinct, and he having a sufficient remedy by action against the lessor for not rebuilding. It has since been decided that such an exception does not bind the landlord to rebuild. Obligation to pay Rent ses untenant- able in Tenancies And when premises demised by verbal or written agree- when Premi- ment, from year to year, or for a shorter time, are destroyed by fire, in which case the tenant is not bound to rebuild, without the destruction of the building does not determine the tenancy, and the tenant still continues liable for the rent. Covenant. Covenant to improve. It is now settled, notwithstanding some decisions to the contrary, that the tenant has no right to quit the premises because they are at the commencement of the tenancy un- tenantable from dilapidations, which ought to have been repaired by the landlord, or become so during its conti- nuance, unless such power is expressly reserved, and ex- cept, perhaps, in the case of a furnished house, or furnished apartments, which are taken merely for the purpose of temporary occupation. It is not a condition implied on the demise of real property, that it shall be fit for the purpose for which it is demised, or shall continue fit for such pur- pose. In this respect the modern and the ancient autho- rities agree. Sometimes leases contain covenants to alter and im- prove: where they do, such covenants must be strictly performed, and they are not satisfied by substantial and thorough repairs. Again, a covenant to make a shop front is not performed by merely enlarging windows, though such enlargement be sufficient for the purposes of the tenant's trade; and in TENANTS FOR LIFE AND YEARS. 727 matters of taste, as to the style and manner in which a house is covenanted to be rebuilt, equity will enforce a specific performance; for instance, a covenant to make the elevation of a house correspond with the elevation of the adjoining houses. insure. Another covenant relating to dilapidations is the cove- Covenant to nant to insure. The object of this covenant is to compel the tenant to procure a Joint Stock Insurance Company to become responsible for the repair of dilapidations by fire. The covenant to insure binds the tenant to effect an in- surance directly the covenant is made. The insurance must be regularly continued without in- termission, and must be strictly according to the covenant. By the Building Act of 14 Geo. III., Insurance Offices are required, on the request of any persons interested in houses or buildings destroyed or damaged by fire, to lay out the insurance money in rebuilding or repairing the premises. The Act is confined to London and West- minster, and the Bills of Mortality. In ejectment on the ground that the lease has been for- feited by not insuring, it lies upon the landlord to prove that the premises were not insured. The tenant refusing the landlord information as to insurance, or refusing to show a policy upon demand, is no evidence of non-insur- ance. In an action on the covenant it seems that the tenant would have to prove performance. In an action for breach of this covenant the damages are not necessarily nominal. Where the landlord has effected an insurance on the tenant's default, though such act is not the necessary consequence of such default, and therefore the landlord is not as a matter of law entitled to recover the premiums paid, the jury may, if they please, award the amount of such premiums, by way of damages, as a sum reasonably expended to relieve himself from the anxiety incident to the premises being uninsured. But where the landlord was a leaseholder under a covenant to insure, and he demised to the tenant under a similar covenant, the tenant failed to insure, and the superior landlord brought ejectment, and recovered, it was held by the Court of Common Pleas that the sub-landlord was only entitled to nominal damages in an action against his tenant for breach of his covenant. He was not entitled to the value of his estate in the premises, because that had been forfeited by 728 DILAPIDATIONS BY Extent of Covenants to repair. As to Things. Persons. the breach of his own covenant, and not by the breach of the tenant's. Besides the degree of care which the covenant to repair imposes, there are three other points to be attended to in the construction of such covenants: On the first point, a general covenant to keep and leave in repair the premises demised will extend to every part thereof, and every thing attached thereto, which can be considered as part of the freehold, and not removable by the lessee as a tenant's fixture. The tenant is bound to leave a building erected by him- self in substantial repair, although the erection was origi- nally of defective construction. Extension to On the second point, all covenants relating to the man- ner of using the premises during the term, as to repair houses, to cultivate lands, run with the land, and are bind- ing not only on the lessee, but also on the assignee of his interest, though he be not expressly named. And such covenants affect all and each part of the land demised; and therefore, if the lessee assign his interest in part of the land, the assignee is bound by the covenants to repair and to cultivate, so far as they are applicable to the part of the land which he holds. And they may be taken advantage of, as well by the assignee of the reversion as by the lessor himself. And the assignee of the reversion of part of the premises may sue on a covenant relating to such part. The assignee of the lessee is liable by the common law to perform the covenant. The right of the assignee of the reversion to enforce performance is founded on the stat. 32 Hen. VIII., c. 4, which only applies where the lease is by indenture; and therefore when a house is let by verbal or written agreement, and the tenant agrees to repair, and the landlord assigns his interest, the assignee cannot sue the tenant for not repairing; and as there is an express agreement to repair with the original landlord, an agree- ment with the assignee to use the premises in a tenant-like manner cannot be implied. The original landlord, of course, may sue on the agreement, notwithstanding the assignment of his reversion. But in such case, if the tenancy is merely from year to year, and the tenant or his assignee continue as tenant from year to year of the lessor or his assignee, an agreement between the new parties will TENANTS FOR LIFE AND YEARS. 729 be implied that such renewed tenancy shall be on the old terms. Notwithstanding some decisions to the contrary, it is now decided that an assignee in equity of a lease, for in- stance, a party who has had it deposited with him by way of equitable mortgage, is not liable on the covenants as assignee, and that the Court of Chancery will not compel him to take an assignment. A covenant to do any thing upon the land, as to build a wall or a house, or which in any way affects the land, as in a lease of mines, a covenant to build a smelting mill, is a covenant which runs with the land, and the benefit there- of will pass to the assignee of the reversion. But such a covenant being to do a specific act, and not continually to be performed during the term, does not bind the assignee, if not named. Thus, if B covenant for himself, his execu- tors and administrators, to build a wall, the assignee is not bound, because the intention appears to be that the wall shall be built by the lessee before assignment; but if the covenant be that the lessee or his assigns shall build a wall, the assignee is bound. If the lessee covenant for himself and his assigns to build a house within a certain time, and assign after the expiration of the time, the assignee is not bound; but if he assign before the covenant is broken, the assignee is. The assignee of the reversion cannot sue for a breach of covenant before the conveyance to himself. A covenant not to build is at all events, in equity, binding on the assignee, and the Court will restrain the assignee, who has notice of such covenant, from violating it. In considering the third point, the time during which Duration of the obligation of a covenant to repair continues, it is to be seen, first, when it begins; and, secondly, when it ends. The obligation to repair usually commences at the date of the lease, or at the commencement of the term when the term commences subsequent to the date of the lease. But when the habendum is from a day prior to the date of the lease, the covenant binds from the date of the lease. A covenant to leave in repair at the end, or other sooner determination of the term, applies when the term is determined by notice, according to a power reserved to the lessee. When a lease is conditioned, that if the lessee does not repair within six months after notice, the lessor may re- Covenant. 2 x 730 DILAPIDATIONS BY Form of Co- venant. Waste in Gardens. Waste in Lands; Al- teration. enter, the notice to repair must be given to the lessee or his assignee. A notice to repair given to an under-lessee will not suffice. A general covenant to repair is not only obligatory during the continuance of the lease, but also, where the lessee continues tenant after its determination, it will be presumed that he holds under the same terms. Those covenants alone are implied as continuing in force which regulate the manner in which the tenements shall continue to be used. There are no particular formalities requisite to give validity to an agreement to repair, as that it should be contained in a valid lease of the premises. Waste may be committed in a garden or orchard. Thus it is waste to cut down apple-trees, or pear trees growing in a garden or orchard; but not if they grow scatteringly on divers places of the land. When apple trees are blown down, the tenant may take them; but where such trees were abated by a great wind, and fell upon the crops, and several of the boughs fell into the ground, and the trees bore fruit two years afterwards, it was held waste for the lessee to grub them up. A gardener who cultivates trees for their fruit has no right to remove them; but a nurseryman who rears them to sell and transplant has a right to remove. Nor can the tenant of a pleasure garden remove trees, ornamental hedges, or shrubs, or a border of box, although planted by himself, such things being intended to be per- manent; nor can he plough up a strawberry-bed before it is exhausted. There is no authority for saying that a tenant is under any positive obligation to cultivate a garden or orchard; the cases only establish a negative obligation against voluntary waste. The tenant is entitled to cultivate and to remove or transplant any plants in the fair course of cultivation, but not to remove things merely for his own benefit, unless the purpose for which the garden was let authorizes him to do so, as in the case of a nurseryman; nor can he alter the character of the garden, or any part of it, as by ploughing up a strawberry bed and sowing turnips. It is waste permanently to alter the character of land, though its value may be increased, such as to convert TENANTS FOR LIFE AND YEARS. 731 meadow into arable land by ploughing it up, or arable land into wood, or a meadow into an orchard, because it not only changes the course of husbandry, but affects the proof of title. But it seems that if a meadow is ploughed for the purpose of improving it as a meadow, and not of permanently altering its character, as where by the custom of the country it is good husbandry to do so, it is not waste to plough it: and so it seems the tenant may root up bushes, furze, and thorns growing on the land, for me- lioration: for that is good husbandry, and he is entitled to such things for fuel. The rule appears to be, that a per- manent alteration of land, which necessarily affects the evidence of title, or any alterations which diminish the value of the land, is waste; but a mere temporary altera- tion in the ordinary and reasonable course of husbandry is not: and by reason of the injury to the evidence of title, it is waste to enclose and cultivate waste land. It is waste if the tenant take away the substance of the land, as if he dig and take away clay, because the soil is impoverished for want of clay; and he cannot open mines, Mines. quarries, or clay-pits: but if mines, quarries, or clay-pits are open, and in work, when the estate for life or years is created, the tenant may continue to work them; because an intention that he may do so may be presumed; but it seems that a tenant for life has no right to re-open and work clay-pits which the grantor had ceased to work be- fore the creation of the estate. A tenant has no right to minerals deposited on the land by mountain streams. As a tenant is entitled to work mines open at the time the lease is granted, so he may use all means necessary for working them, and therefore may open new shafts and pits to follow the same vein of coal. "Otherwise," said Lord Chancellor King, "working in the same mine would be impracticable, because the miners would be choked for want of air, if new holes were not continually opened to let the air into them; and the same vein of coal frequently runs a great way, and is very knowable, and easy to be discerned. The Court of Chancery will restrain a tenant for life or years from sowing woad or mustard, they being poisonous and exhausting plants, by which the vegetative power of the land is destroyed. A tenant is bound to keep the fences in repair, and he Fences, 732 DILAPIDATIONS BY Obligation to cultivate Lands. may cut timber for this purpose; but he has no right to make fences where none were before. And it would ap- pear that he is not liable if the fences become dilapidated from natural decay, and there is no wood on the premises with which he can repair them. By the general law a tenant for life or for years is under no obligation to cultivate lands. Thus it is not waste to suffer arable land to lie fresh and not manured, so that it grows full of thorns; it is merely ill-husbandry. To oblige a tenant to farm according to good husbandry, there must either be an express contract or a custom of the country. In most, if not all cases in which lands have been usually let to farmers, there is a custom of the country regulating the manner in which the lands are to be cultivated. A custom of the country need not have existed from time immemorial, as must a custom properly so called. It is the approved habits of good husbandry practised in that part of the country in which the lands are situate, and is a means of ascertaining the course of cultivation adapted to the nature of the lands. It may be proved by cove- nants usually inserted in farming leases, and need not be definite and precise. The obligation to expend manure, and right to remove must in every case, where there is no express contract, be governed by the custom of the country. There is no rule of law on the subject, irrespective of such custom: farm- ers are more fit than lawyers to decide such a question. The obligation to cultivate lands according to the cus- tom of the country does not apply to a garden or to a meadow let with a gentleman's residence. • Where there is a special agreement as to the manner in which the lands shall be cultivated, the obligation to culti- vate according to the custom of the country is superseded, as where the tenant agreed to farm the land in a good and husbandlike manner, to be kept constantly in grass; and where the landlord recovers damages for the conversion of a meadow into arable land, he cannot also recover for re- moving the straw grown on such land, as contrary to the custom of the country as to the cultivation of arable land. If tenant of a park, vivary, warren, or dove-house, de- Doves, &c. stroy so many of the deer, game, rabbits, or doves, that sufficient be not left for store, having regard to the num- Obligation as to Live Stock, TENANTS FOR LIFE AND YEARS. 733 ber at the time his estate was created, it is waste. To stop the holes of a pigeon-house so as to prevent the pigeons building there, is waste. If the tenant of a park permit the pales to decay, so that the deer escape, he is liable for waste. Breaking a wear or suffering the banks of a fish-pond to decay, so that the water and fish run out, are respectively acts of waste. But the subversion of coney-burrows has been held not to be waste. Emblements are the products of the earth, which a Emblements. tenant, the determination of whose estate is sudden and fortuitous, is allowed to take after his interest in the land has expired, in consideration of his labour and manurance employed upon the land: "lest the ground should be unma- nured, which would be hurtful to the commonwealth, he shall reap the crop which he sowed in peace." The doc- trine of Emblements has been entirely changed by the act of the 14 and 15 Vic., c. 25, sec. 1, whereby it is enacted: 66 nation of Tenancies for Life, &c., Emblements hold until current Year, "That where the Lease or Tenancy of any farm or on determi- "Lands held by a Tenant at Rackrent shall determine by Leases or "the Death or Cesser of the Estate of any Landlord en- under Tenant "titled for his Life, or for any other uncertain Interest, instead of "instead of claims to Emblements, the Tenant shall con- Tenant to "tinue to hold and occupy such Farm or Lands until the Expiration of Expiration of the then current Year of his Tenancy, &c. "and shall then quit, upon the Terms of his Lease or Holding, in the same Manner as if such Lease or "Tenancy were then determined by Effluxion of Time or "other lawful Means during the Continuance of his "Landlord's Estate; and the succeeding Landlord or "Owner shall be entitled to recover and receive of the "Tenant, in the same manner as his Predecessor or "such Tenant's Lessor could have done if he had been CC living or had continued the Landlord or Lessor, a fair "Proportion of the Rent for the Period which may have "elapsed from the Day of the Death or Cesser of the "Estate of such Predecessor or Lessor to the Time of the "Tenant so quitting, and the succeeding Landlord or "Owner and the Tenant respectively shall, as between "themselves and as against each other, be entitled to all "the Benefits and Advantages, and he subject to the Terms, Conditions, and Restrictions, to which the pre- ceding Landlord or Lessor and such Tenant respectively CC 66 734 DILAPIDATIONS BY Waste as to Timber. "would have been entitled and subject in case the Lease 66 or Tenancy had determined in manner aforesaid at the "Expiration of such current Year: Provided always, "that no notice to quit shall be necessary or required by "or from either Party to determine any such Holding and "Occupation as aforesaid." Timber trees are parcel of the inheritance, and a tenant for life or years has only a right to their shade and fruit during the term. It is waste if he cuts them down, or does any act to cause them to decay, as if he lops or tops them. Timber trees are such as are useful for the purpose of building. Oaks, ashes, and elms are timber in all places. Thorn-trees, which have stood for sixty or a hundred years, have been accounted timber. In some countries where timber is scant, beeches and white-thorns are used for building, and therefore accounted timber: in such case it is waste to fell or injure them. In the Countess of Cumberland's case, birches of a hundred years' growth, which were serviceable for timber, for sheep-houses, cot- tages, and other mean buildings, were held to be timber, which a tenant for life had no right to cut. If by custom oaks and ashes are seasonable wood, and cut at stated times, the tenant may cut them at such times; thus, if it is customary to cut ashes every ten years, the tenant may cut them. It is also waste to cut down any trees, though not tim- ber, such as beeches, maples, willows, &c., which are planted for the defence or ornament of the house, or in a pasture-field for the shade of cattle, or on a bank to sus- tain it, or which form part of a hedge, it being the appa- rent intention of the landlord or grantor of the estate that such trees shall continue. It is not waste to cut down trees which are not timber, either by law or custom, and are not planted for any of the above special purposes, in such a manner that they will grow again. Thus a tenant for years may lawfully cut down willows, leaving the stools or butts from which they will shoot afresh. Whitethorns, blackthorns, and hazels may in like manner be cut down. Nor is it waste to cut the underwood of hazels, willows, or thorns, maple or oak. But if the tenant dig up such trees, or underwood, or suffer the germins to be bitten by cattle after they are felled, so that they will not grow TENANTS FOR LIFE AND YEARS. 735 again, or mow the stocks with a wood scythe, it is waste. Against such waste the Court of Chancery will grant an injunction. It is not waste for the tenant to fell timber trees which are completely dead, and bear neither fruit nor leaves, and have not sufficient timber in them for build- ings or posts. If timber trees are blown down by tempest, or severed from the land by other means, they become the property of the tenant who takes the first estate of inheritance. But if dotards, or old trees which have no timber in them, are blown down, they become the property of the tenant. And if the landlord fells such trees during the term, the tenant may take them. As the tenant is entitled to cut hedges and bushes, the cuttings belong to him; and if a stranger cut them, the landlord cannot maintain an action. The trimmings of fir trees under twenty years old belong to the tenant for life, and not to the remainderman. The tenant being entitled, during his term, to the shade and fruit of timber trees, if the landlord fell them, he may maintain trespass. An equitable tenant for life has no right to cut timber without the consent of the trustees; if he does, he is bound to account for the timber and its proceeds to the trustees. cayed Tim- When timber is in a state of decay, and will not improve Felling de- by standing, but is likely to do damage to other trees, and ber. when the felling of it will be a benefit to all parties con- cerned, the Court of Chancery will order it to be cut down, either on the application of the tenant for life or of the remainderman. When the application is by the re- mainderman, care will be taken that the tenant for life is not prejudiced by those trees being taken which are necessary for repairs. The Court will not order generally that those trees be cut down which are fit to be cut, and which a provident owner might think fit for felling. Tim- ber will on like conditions be ordered to be cut when the tenant entitled to it is an infant. When trees are thus felled by order of the Court of Chancery, the produce of the sale is invested, and the tenant for life has the interest for his life, such being equivalent to the fruit and shade of the trees. The first person entitled to cut timber is entitled to the capital in- 736 DILAPIDATIONS BY Right to cut Timber for vested. Thus, when lands are conveyed in trust for A., for life remainder to B., for life without impeachment for waste, the proceeds arising from the sale of timber belong to B., on the death of A. Ornamental timber and trees planted for the defence and safety of the house will not be allowed to be cut down, though decaying. A tenant for life or years may cut timber for the repairs Repairs, &c. of his house, barns, or fences, for the necessary purposes. of husbandry, or to be consumed as firewood.. He may fell timber to repair houses which he is not strictly bound to repair; for instance, those which were ruinous at the time of the lease, or those which the lessor covenants to repair, because the law favours the supportation of houses of habitation for mankind. But he cannot take timber for improvements, such as to make fences where none ex- isted before; or to repair houses which he has wasted, or suffered to be wasted, nor can he cut timber for the pur- poses of working mines, such being no benefit to the land. The right to cut timber for firewood is qualified, and the lessee can only justify cutting timber trees for that pur- pose when there is no underwood or deadwood upon the land. Covenant as to Trees. Timber can only be cut down for the express purpose of being used in the repairs of buildings, &c. It cannot law- fully be sold to raise money for the purchase of other timber; nor can it be exchanged for other timber better adapted for the repairs in question. If the timber be cut down bonâ fide for the purpose of being used in reparations, the tenant is justified, though he may have over-calculated the quantity required; but he cannot cut down timber by way of anticipation, to be used in dilapidations which may hap- pen at some future time. Where, by the lease, the lessor is to assign trees to the lessee for requisite repairs, and a particular tree is assigned to the lessee by the lessor's bailiff, such assignment operates as a delivery, and vests the property of the tree in the lessee, who may fell at any time afterwards. Where the tenant covenants to deliver up all the trees standing in an orchard at the time of the demise, reason- able use and wear only excepted, he is not precluded from removing trees decayed and past bearing from a part of the orchard which is too crowded. Where there is a cove- MORTGAGEE OR MORTGAGOR. 737 nant not to remove or grub up trees, the tenant cannot remove trees from one part of the premises to another, unless they are dead, even although he plant more trees than he removes. are excepted Sometimes trees are excepted out of the lease; they are where Trees then considered as in the possession of the lessor, and are out of Lease. not subject to dilapidations or waste; but if the tenant cut or fell them, the landlord may have an action of trespass against him. Where trees generally are excepted out of a lease, such exception is construed to relate to timber trees only, and not to apple or other fruit trees, or the like; since, if it did, the tenant would not be entitled to the fruit of such trees. And where the exception was of timber and other trees, but not the annual fruit thereof, it was held that apple-trees were not within it, because it was to be construed strictly against the lessor. SECT. III.-Dilapidations by Mortgagee or Mortgagor. Mortgagee to A mortgagee, who in equity is considered as holding the Obligation on land as a pledge for the payment of his debt, is bound to repair. preserve the premises from extraordinary dilapidations ; but for that depreciation which is caused by gradual de- cay, the mortgagee is not responsible. or rebuild. Although, generally speaking, a mortgagee has no right Right to alter to alter the mortgaged tenements, yet he may pull down ruinous houses, and build better ones, to prevent a for- feiture. ment of Ex- He is entitled to be allowed for repairs necessary for the Reimburse- support of the property, and for the expenses of doing that pense. which is essential to the maintenance of the mortgagee's title. But he will not be allowed monies expended in in- creasing the value of the property, unless the mortgagor has consented or acquiesced. If he has improved the pro- perty with the consent of the mortgagor, he is entitled to be reimbursed the monies expended, with interest, in the same manner as if it was a new loan. Mortgagee to Minerals. The mortgagee in possession has no right to cut down Right of timber, except the land is an insufficient security, when it Timber and seems that the mortgagee may sell the timber. He cannot open and work mines, or take brick earth; if he does, he is chargeable with the gross receipts, and not allowed any of the expenses. 738 DILAPIDATIONS OF } Right of Mortgagor to Timber. Property in Party Walls. The mortgagor cannot cut down timber to the prejudice of the security; and therefore if it appear that the security is scanty, equity will restrain him from felling timber, but not unless it be clearly shown that the security is deficient, the presumption being that it is not. If he have cut down timber to the prejudice of the security, and sold it, he will be ordered to pay the amount into Court, in trust for the mortgagee. Underwood, which is in the nature of a crop, the mortgagor will not be restrained from cutting at sea- sonable times, and this though the underwood be expressly mentioned in the mortgage. But where the mortgagor becomes bankrupt, his assignees will be enjoined from taking even underwood, because the mortgagee is entitled to the land in exactly the same plight as it is at the date of the bankruptcy, and to prove for the residue of his debt. SECT. IV.-Dilapidations of Party Walls and Fences. Where a party wall exists between two buildings or gar- dens, which is used by the occupiers of both buildings indiscriminately, and it does not appear on whose land it was built, the presumption is that the parties are tenants in common of the wall. The presumption of property arising from acts of ownership must correspond with those acts; and, as in the case of a party wall, each party equally makes use of the whole wall, the inference is that they are equally entitled to the whole wall. It follows that if one party build against the wall on his side, no action can be maintained by the other. And if one pull down the wall for the purpose of rebuilding it, or heighten it, it is not a trespass against his neighbour; but the neighbour may have an action on the case for the temporary loss of the protec- tion of the wall, or for any injury he may sustain from the increased height, or he may pull down any additional erec- tion upon the wall. And one tenant in common of a hedge may have trespass against his co-tenant if he grub it up, but not if he merely clip it. Whether a party wall stand- ing between two houses belong half to the owner of one house and half to the other, or is the common property of both owners, one has no right to underpin any part of the wall, unless he can do it without injury to the house of the other. The rebuilding and repairs of party walls within London PARTY WALLS AND FENCES. 739 and a limited district around, are regulated by the Metro- politan Buildings Act, by which the owner of one of the houses separated by the party wall may, under the super- intendence of a district surveyor and official referees, re- build or repair the party wall when necessary, either with or without the consent of the owner of the other house, and recover contribution from other parties benefited by the works. As this statute is of itself a book, and there have been as yet no legal decisions on its provisions, this general reference to it must suffice. In the case of a party wall out of the limits of the Building Act, the rights and liabilities of parties with re- spect to the repairing or rebuilding it will be the same as those of tenants in common, if they are tenants in common of the party wall. If half the wall belongs to each party, then each may repair or rebuild his part. Fences. In the case of a fence between two fields, which has a Property in ditch at its base, the presumption is that the fence belongs to the party on whose side the ditch is not. It is reasonable to suppose that, in making the fence by the party who made it, the ditch was dug on the verge of his own land, and the earth thrown up on his land, so as to form a bank on which to plant the fence. And thus, the outer edge or side of the ditch furthest from the hedge is presumed to be the boundary of the lands; and if the party to whom the fence belongs proceeds to widen the ditch, it is prima facie a trespass on the neighbour's land. Where there are ditches on both sides the hedge, or where there is no ditch at all, the proprietorship of the hedge may be proved by acts of ownership; and if both parties have equally exer- cised acts of ownership, the right of property will, I appre- hend, be presumed to be common. repair Fences A tenancy in common in a party wall or fence does not obligation to imply any obligation in one tenant towards his companion to repair such wall or fence, nor does the existence of a fence on a man's land impose on him any obligation to re- pair it as against his neighbour. to repair. Though the obligation to repair a fence be annexed to who bound the fee simple of the land, yet the party bound to do the repairs is the actual occupier, he being the person whose immediate duty it is to prevent cattle from straying from one close into the other; and having the exclusive posses- sion of the fence, he is the only person who can lawfully 740 DILAPIDATIONS OF Who to com- plain of Dila- pidations. Inhabitants of Parish. repair it, or who can be presumed to know of the defects. The obligation to repair is only towards the occupier of the adjoining close, and not general, as against the public; and therefore a party seeking to take advantage of that obligation, either as excusing a trespass, or charging the obligor for injuries happening to his cattle, must show an interest in the adjoining close, or a right to have his cattle there. SECT. V.-Dilapidations of Highways and Bridges. Obligation of By the general rule of the common law, the parish that is, the occupiers of land within the parish—are bound to repair all the highways therein. Sometimes, by special prescription, the inhabitants of a township are bound to repair highways within the township, and sometimes one parish is bound to repair highways situate in another. A corporation or individual may be bound to repair highways by reason of the tenure of some particular lands; an indi- vidual may also be bound to repair highways by reason of enclosure. These are exceptions: the general rule is, that parishioners shall repair the highways; and where the parties bound by prescription become insolvent and unable to repair, the charge falls upon the parish. Where the inhabitants of a township had immemorially repaired high- ways within the township, and a new road was made by Act of Parliament, which expressly exempted the inhabi- tants of the township from the charge of repairing it, it was held, that, ex necessitate, the rest of the parish were liable. And where a turnpike road is made by an Act of Parliament, and placed under the management of trustees, who are to repair out of the tolls, the parish may be in- dicted if the road be out of repair, because they are liable by the general rule of the common law; and the tolls, &c., in the hands of the trustees, are only an auxiliary fund; and if such fund fail, recourse can only be had to the parish. But where such road is made in a township which, by pre- scription, is bound to repair the roads within it, the inha- bitants of the township must repair, because, by the prescription, the township stands in the place of a parish as to the repair of highways. It is obvious that the pa- rishioners cannot discharge themselves from their liability HIGHWAYS AND BRIDGES. 741 to repair a highway by agreement or otherwise, since such an agreement would affect the rights and security of the public, to whom the parish is bound. Where highways are situate within an extra-parochial hamlet, it has been doubted whether the inhabitants of such hamlet are, with- out a special custom, liable to repair; but it would seem, upon principle, that they are liable to repair, because other- wise the roads would not be repaired at all; and in the case of a turnpike road, there could be no persons ulti- mately liable to keep it in repair, in the event of the tolls, &c., proving inadequate, because to such road no prescrip- tion or custom would apply. Every thoroughfare which is used by the public is a highway, whether it be a carriage-way, a horse-way, or a foot-way a navigable river is a highway. In one case parishioners were indicted for not repairing stairs leading to the Thames. A way merely leading to a church, a village, or a private house, and therefore not useful to the public generally, is not a highway. A highway may be created by Act of Parliament; and when it has been recognized in an Act of Parliament as public, it is a highway, and repairable as such. Where a highway is created by a temporary Act, it ceases to be such when the Act expires, and statute duty done upon it in obedience to the Act is no adoption of it by the public. When, by Act of Parliament, trustees are empowered to make a road or roads, no part of them becomes a highway until the whole are made. But when several roads are authorized to be made, and it is provided that they shall not become public until two justices have certified that the said roads respectively are fit to be travelled on, each road becomes public so soon as the justices have certified; and it is not a condition that they shall all be made before any are public highways. What is a Highway. Highway. Formerly, wherever a party made a way over his land, Dedication of and dedicated it to the public, and the public used the way, it became a public highway, and repairable by the parish. Now, by the Highway Act, (which came into operation on the 30th of March, 1836,) "No road or occupation-way made, or hereafter to be made, by and at the expense of any individual or private person, body politic or corporate, nor any roads already set out, or to be hereafter set out, as a private driftway or horse-path, in any award of Com- 742 DILAPIDATIONS OF Limited Dedication. missioners under an Enclosure Act, shall be deemed or taken to be a highway, which the inhabitants of any parish shall be liable to repair, unless the person proposing to de- dicate such highway to the use of the public shall give three calendar months' previous notice, in writing, to the surveyor of the parish, of his intention to dedicate such highway to the use of the public, describing its situation and extent, and shall have made, and shall make, the same in a substantial manner, and of the width required by the Act, and to the satisfaction of the surveyor and two jus- tices of the peace, of the division in which such highway is situate, in petty sessions assembled." A way may be dedicated for a limited time; it may also be dedicated for particular periods, as where it appeared that a bridge was used by the public at all times, on foot and with horses, but only occasionally with carriages, in times of flood and frost, when it was unsafe to pass through the river. In ordinary times the carriages went through the ford, and the bridge was sometimes barred against car- riages by a chain, locked to posts. Lord Ellenborough held that this was a public right of way, limited as to time. It has been doubted, however, whether there can be a par- tial dedication of a way, that is, of a right of way for some carriages and not for others. The argument against such a dedication is, that it is unjust for the public generally to be obliged to repair a road which a portion of the public only are allowed to use. There cannot be a dedication to a particular part of the public, as to the inhabitants of a parish; such a dedication is simply void. Where lands chargeable with the repair of a highway are conveyed to several, they are all liable to do the repairs in proportion to the quantity of land they hold; though if the way be dilapidated, any one of the proprietors may be indicted separately, and compelled to pay the whole fine. He may proceed against those who are jointly liable with him for contribution. If lands so chargeable come into the hands of the Crown, they are not discharged. It is the occupier and not the freeholder of the lands chargeable with repairs of a highway against whom the indictment should be preferred. But the occupier is en- titled to be reimbursed by his landlord the sum expended in repairs. HIGHWAYS AND BRIDGES. 743 The surveyor is to make every cart-way leading to any Width. market-town twenty feet wide at the least, every horse- way eight feet wide, and every foot-way at the side of any cart-way, &c., three feet wide, if the space between the fences will admit thereof. Gateways across any carriage-way must be ten feet width of wide, and across any horse-way five feet wide, clear be- Gateways. tween the posts; and if the owner of any narrower gate omit to enlarge or remove it after twenty-one days' notice from the surveyor, he is liable to a penalty not exceeding 10s. per day for so long time as he so neglects. Snow. The surveyor is bound to remove any accumulation of Removal of snow within twenty-four hours after notice from a justice of the peace. He is empowered to make, scour, cleanse, and keep open all ditches, gutters, drains, or water-courses, Cleansing and to make and lay such trunks, tunnels, plats, and Ditches, &c. bridges, as he may deem necessary, in and through any lands, adjoining the highway, making the owner or occu- pier compensation if the lands are not waste or common; the amount to be settled in the same manner as the amount of damages for getting materials from enclosed lands. If any person alter or obstruct the ditches, &c., after they have been taken under the charge of the surveyor, he is bound to reimburse the surveyor the expense of re- instating them, and to forfeit a sum not exceeding three times such expense. Posts, &c. The surveyors of parishes more than three miles from Direction- the post office are also required, with the consent of the vestry, or by the direction of the justices at special sessions, to set up direction-posts or stones in places where two ways meet, and boundary stones; and on such parts of highways as are subject to floods, to erect graduated stones to guide travellers the safest track through the floods, and to secure horse causeways and foot causeways from being passed over by waggons, by banks of earth, posts, and stones. ments. No tree, bush, or shrub can be planted on any carriage- Encroach- way within fifteen feet of the centre. And if the owner do not remove it within twenty-one days after notice from the surveyor, he forfeits 10s. for every neglect. Highway. The highway is that portion of ground which has been Centre of maintained and repaired by the surveyor for six months next preceding, and the fifteen feet are to be measured from the centre of that. 744 DILAPIDATIONS OF I Cutting Hedges. Materials for Repairs of If the surveyor think that a highway is prejudiced by any hedges or trees (except trees planted for the ornament or shelter of any hop-ground, house, building, or court- yard,) he may summon the owner of the land before a justice, who may determine whether the trees, &c., shall be cut, pruned, or plashed. If the owner fail to obey the order of the justice, the surveyor may cut the hedge, and the owner must reimburse him the expense incurred. No person can be ordered to cut any hedges between the last day of September and the last day of March, nor to fell any timber tree, unless the highway is ordered to be widened, and then he can only be compelled to grub up oak-trees in April, May, and June, and ash, elm, or other trees in December, January, February, and March. The surveyor may, with the consent of the vestry, con- Highways. tract for the purchase of materials required for the repair of highways. He is not to have any interest in such con- tract without the license of two justices at special sessions, under a penalty not exceeding £10, and incapacity of being employed as a surveyor with a salary. Where lands belonging to parishes, or to the surveyor of highways for the purpose of obtaining materials, become exhausted, the surveyor may, with the consent of justices at special sessions, sell the land to the owner of adjoin- ing land, or, if he refuse, to any other person, for such price as the justices think reasonable, and apply the money, with like consent, in the purchase of other lands. The surveyor may search for, dig, and carry away gravel, sand, stone, or other materials, in any waste, common, river, or brook, within the parish; or, if sufficient cannot be ob- tained in his parish, he may take them from any other parish, leaving sufficient for the repairs of the highways in such parish. Where sufficient materials cannot be had in the waste, commons, rivers, and brooks, the surveyor may, with the license of two justices at special sessions, dig and carry away materials from the enclosed land of any person within the parish (such land not being a garden, yard, avenue to a house, lawn, park, paddock, or enclosed plantation, or en- closed wood not exceeding one hundred acres), or within any parish adjoining the highway, if sufficient materials cannot be had within the parish or in the wastes, &c., of the adjacent parish, and so that sufficient materials be left HIGHWAYS AND BRIDGES. 745 for the repairs of the highway in the parish where the lands lie. These questions to be determined by the justices. The surveyor is to make satisfaction for the materials taken, and also for the damage done to the lands in taking and carrying away the same. Public bridges, if not within a city or town corporate, of Bridges. are repairable by the inhabitants of the county; if within a city or town corporate, by the inhabitants of such city or town. If part in one shire, city, or town, and part in ano- ther, the inhabitants of the shire, city, or town, are bound to repair so much of the bridge as lies within their limits. A bridge may, by custom, be repairable by the hundred or parish in which it is situate; or an individual may by pre- scription be bound to repair, by reason of the tenure of lands. paired. Those who are bound to repair bridges, must make them How re- of such height and strength as shall be answerable to the course of the water; and if it take a new channel, they must erect a bridge there. But they are not bound to widen the bridge, however convenient or necessary it may be to the public. Counties are also bound to repair the highways at the Causeways to ends of bridges for 300 feet. lic Bridge. Every bridge which is of public utility is a public bridge, What a pub- and prima facie repairable by the inhabitants of the county. Although the bridge is erected by a private individual for his own private advantage, yet, if it becomes of public be- nefit, it is a public bridge. By 43 Geo. III., c. 59, s. 5, no bridge built by an indi- vidual shall be deemed a county bridge, unless erected in a substantial and commodious manner, under the direction, and to the satisfaction, of the county surveyor, or person appointed by the justices at quarter sessions, or, in Lan- caster, by the justices at the annual sessions; which sur- veyor, or person appointed, is to attend and superintend the erection of the bridge, when required by the party erecting the same; and if the builder be dissatisfied, the matter is to be determined at the quarter or annual sessions. The justices of the peace are to appoint two surveyors, with salaries, to see bridges amended. 2 Y 746 NUISANCES. a Nuisance. SECT. VI.-Nuisances. Definition of A nuisance may be defined to be a wrongful act or neg- lect of one man, in the use or management of his land, which occasions damage to the possession or easement of his neighbour, or to a public easement. Acts injuri- ous to pri- Any act done by one man on his land which is the cause vate Posses- of an encroachment on that of another, to his damage, is an actionable nuisance. sions, Offensive Trades. If, in consequence of an act done in one colliery, damage is caused to another, though at some distance, an action lies by the owner of the colliery injured. In determining what acts are nuisances, it is necessary to ascertain the legal extent of the possessions of an occu- pier of land. He to whom the soil belongs is entitled to all the space of air above to the sky, and of the earth below to the centre. His rights extend perpendicularly above and below his own land, and not laterally, so as to claim any use from the earth beneath or the air above the adjoin- ing land. It is therefore not only a nuisance to cause an encroachment or injury to the soil of a neighbour, as if a house is built overhanging the land of another; but also if the air over his land is corrupted or disturbed by noisome smells or deafening noises, it is a nuisance. Not every disagreeable smell or noise which spreads from one man's land to his neighbour's is actionable. The smell or noise must arise from some permanent cause, and occasion continual annoyance and discomfort, to a degree sufficient to depreciate the value of a dwelling-house, and render it less eligible in consequence of the neighbourhood. A man is not restricted in the fair and reasonable use of his land by any delicacy of sense or peculiarity of habit of his neighbour. A pig-sty, lime-kiln, privy, smith's forge, tobacco mill, tallow furnace, and glass-house, set up near a private residence, are nuisances. And so a mill for steeping sheep-skins, by which the air is corrupted; a building for manufacturing acid spirit of sulphur, which occasions noisome and offensive smells; a place for slaugh- tering horses. It is not essential that the stench raised should be unwholesome; it is sufficient if it renders the enjoyment of life and property uncomfortable. NUISANCES. 747 of occupation Any wilful and mischievous act of one man which dis- Disturbance turbs another in the enjoyment of the reasonable profits of of Lands. his land is a nuisance, though without the inalicious motive of the agent the act is innocent. Water. It is also a nuisance to the occupier of the land over Diversion of which it flows to obstruct or divert a stream of water. By this act a natural profit is prevented from coming to the land. "The proprietor of land on each bank of a stream is prima facie entitled to half the land covered by the stream, but there is no property in the water. Every pro- prietor has an equal right to use the water which flows in the stream, and, consequently, no proprietor can have the right to use the water to the prejudice of any other pro- prietor. No proprietor can either diminish the supply of water, which would otherwise descend to the proprietor below, or throw it back upon the proprietor above." By grant, or by prescription, a proprietor may acquire a right to take the water, to the prejudice of the other proprietors of land on the banks of the stream; but by merely appro- priating to himself water which is not at the time useful to the other proprietors, he acquires no such right. Thus, a person who first builds a mill on the banks of a stream has no right to pen back or divert the water for the supply of his mill, so as to diminish the quantity of water which would come to the proprietors below, on the ground that they have not applied the stream to any particular use. In public navigable rivers no right can be gained, even by prescription, to divert or obstruct the stream, to the prejudice of the public. All that the proprietor of the land on the banks (and to whom the soil belongs, to the middle of the river) can do, is to take so much water as may be necessary for his private purposes by pipes, or otherwise, so as not sensibly to diminish the quantity, to the prejudice of the navigation. Lands from Where the ancient course of water is to flood certain Protection of lands at certain seasons, the owners of those lands cannot Inundation. justify fencing it off their lands, to the prejudice of other property; though, if such be not the ancient course of the waters, they may. Thus if a river periodically inun- dates the surrounding country at certain places, the parties whose lands are thus periodically subject to floods have no right to protect their lands against the river, if they there- by cause the waters to flood the lands of their neighbours, 748 NUISANCES. Nuisances to Foundations. Easements. By Prescrip- tion. Dangerous Nuisance. Nuisances: because by such act they improve and increase the value of their property at the expense of their neighbours. A man who builds a house on the verge of his own land, has no right to the support of his neighbour's land for the foundation of his house; nor if he build against the wall of his neighbour's house, has he any right to the support of such wall; and if he place windows looking to- wards his neighbour's land, he cannot complain if his neighbour build so as to obstruct the light. If the occupier of a house suffers it to be dilapidated so as to injure the adjoining house, he is liable to an action. If one has conduit pipes passing by the foundations of the house, and he neglects to repair them, whereby the house is injured, it is a nuisance. So a party having a water course in his land is bound to cleanse it, at all events so as to prevent its becoming in- jurious to his neighbour; and is liable for an obstruction, although he has no notice of it. The cases as to nuisances caused by fire have already been stated. An easement is a right which one man has to use the land of his neighbour for a special purpose. A prescriptive right to the easement of light is acquired by twenty years uninterrupted enjoyment, unless it appears that such enjoyment was had by some consent or agreement expressly given for that purpose by deed or writing. The enjoyment must be by a window or opening in a building, by which the claimant visibly appropriates the light flowing through such window to himself. If a person suffers his tenement to become dangerous to the public, or exercises an occupation dangerous to health or life in a public situation, he is guilty of a nuisance. Thus, if the occupier of a house near a highway suffer it to become so dilapidated that it is likely to fall on the passengers, he is indictable. Remedies for A private nuisance may be abated by the party injured Abatement. by it, provided he commits no riot in the abatement; but a public nuisance cannot be abated by an individual, unless he is specially inconvenienced thereby. LAW RELATING TO APPRAISEMENTS. 749 CHAPTER XXII. THE LAW RELATING TO APPRAISERS AND AUCTIONEERS. SECT. I.-The Law relating to Appraisements. duly quali- can act as By the Laws regulating Attorneys, no person who is None but not admitted and enrolled, and otherwise duly qualified to fied persons act as Attorney or Solicitor, can sue out any writ or pro- Attorneys. cess, or commence, carry on, or solicit any action, suit, or other proceeding, in any Court of Equity, or Law, Civil or Criminal. (6 & 7 Vic., c. 73, s. 2.) alty of £50. By 44 Geo. 3, c. 98, s. 14, Every person, who, for, or Under pen- in expectation of fee, gain, or reward, draws or prepares any Conveyance or Deed relating to any real or personal estate, or any proceedings in Law or in Equity, other than and except a Serjeant-at-Law, Barrister, Solicitor, Attor- ney, Notary, or Proctor, having obtained a regular certi- ficate; Special Pleader, Draftsman in Equity, or Convey- ancer, being a Member of one of the four Inns of Court, and having taken out a certificate; or a person employed to engross any Deed, Instrument, or other proceeding, not drawn or engrossed by himself, as a public officer pre- paring a public document, in the course of his duty, is liable to a penalty of £50. The act does not extend to prevent any person from preparing a will, an agreement not under seal, or a letter of attorney. must obtain By 46, Geo. 3, c. 46, Appraisers are required to obtain Appraiser licenses from the Inland Revenue Office, for the purpose License. of carrying on their business; and appraisements are re- quired to be stamped. an Appraiser. Every person who values or appraises any estate or Definition of property, real or personal, or any interest in possession or reversion, or any goods, merchandise, or effects, for, or in expectation of hire, fee, gain, or reward, is an Appraiser within the act. (s. 4.) No person No person can exercise the calling or occupation of an can act as 750 LAW RELATING TO APPRAISEMENTS. Appraiser without License. Licenses, when dated. Penalty of £50 for act- ing as Appraiser without Li- cense. An Auction- Appraiser without taking out a license, which is granted by the Commissioners of Inland Revenue. (s. 5.) Licenses issued between 5th July and 5th August, are dated 6th July; those issued at other times are dated on the day of issue. Every license continues in force until the 5th of July following its issue. Any person who appraises or values any estate or pro- perty, &c. for, or in expectation of hire or reward, without being licensed, is liable to a penalty of £50. (s. 6.) An Auctioneer duly licensed as such, may act as an eer can act as Appraiser without an Appraiser's license. (s. 7.) Appraiser. Appraiser must deliver within four- stamped pa- per. Every Appraiser must set down in words or figures Valuation every valuation made by him, and the full amount thereof, teen days on and within fourteen days deliver the same, duly stamped, to his employer, under a penalty of £50. (s. 8.) Employer If the employer of an Appraiser receives, or pays, or an unstamp. makes compensation for making an appraisement, and the same is not set down on paper duly stamped, he forfeits £20. (s. 9.) who receives ed Valuation liable to Pen- alty. One Sheet of Paper only need be stamped. License sub- ject to £2 Stamp. License to be taken out yearly. Amount of Stamp Duty ments. If more than one sheet or piece of paper is used in writing an appraisement, that only which contains the ag- gregate amount of the valuation need be stamped. (s. 10.) The license to use and exercise the calling or occupation of an Appraiser in the United Kingdom, is (by 8 & 9 Vic., c. 76,) subject to a stamp duty of £2. It must be taken out yearly by every person (except a licensed auctioneer) who exercises the calling or occupa- tion of an appraiser, or who for, or in expectation, of any gain, fee, or reward, makes any appraisement or valuation chargeable by law with any stamp duty. The stamp duty on Appraisements is imposed by 55 on Appraise Geo. 3, c. 184, on an Appraisement or valuation of any estate or effects, real or personal, heritable or moveable, or of any interest therein, or of the annual value thereof, or of any dilapidations, or of any repairs wanted, or of the materials and labour used, or to be used in any buildings, or of any artificer's work whatsoever. Where the amount of such appraisement or valuation exceeds not Where it exceeds £50, and exceeds not 100 100 "" 200 " 500 "" وو £. s. d. £50 . 0 2 6 0 5 0 200 10 10 0 500 0 15 0 100 LAW RELATING TO APPRAISEMENTS. 751 The exemptions from duty are Appraisements or valuations made in pursuance of the order of any Court of Admiralty or Vice-Admiralty, or of any Court of Appeal, from any sentence, adjudication, or judgment of any Court of Admiralty or Vice-Admiralty. Appraisements or valuations of any property made for the purpose of ascertaining the legacy duty payable in respect thereof. Exemptions. how recover- It should be noted that the above penalties can only be Penalties, sued for in the name of the Attorney-General, or of the able. Solicitor of Stamps, or some other officer of the Stamps. (44. Geo. 3, c. 98.) cover his If a person acts as an Appraiser without being licensed, Unlicense or if an Appraiser omits to write his appraisement on a cannot re- stamp, his conduct is illegal, and he cannot recover for his Charges. services. (Palk v. Force, 17, Law Jour., G. B. 299, 12 par. 797.) do not apply made for pri- mation only. The Stamp Acts do not apply to appraisements made Stamp Acts merely for private information, but to such only as are to Valuations intended to be binding between two parties with opposing vate infor- interests. Thus, a valuation of parish lands made by a farmer and a basket-maker for the sidesmen of the parish, with a view to the equalisation of the poor-rate, has been held not to require an appraisement stamp, and the farmer and basket-maker recovered compensation for their ser- vices, although they were not licensed as Appraisers. (Atkinson v. Fell, 5 Maule & Sel. 240.) And so, where two partners in a coal mine directed a third person to balance the profit and loss of the concern, and to value the materials and utensils, and each party was to take an article alternately at his valuation, until the whole was divided, it was held that the valuation so made was for the mutual information of the partners; and although it was afterwards adopted as the terms of their agreement, it was not an appraisement within the stamp laws. (Jackson v. Stophurd, 4 Tyr. 330.) ment does Award An appraisement or valuation although it is agreed to Appraise- be and is binding upon the parties as an award, does not not require require an award stamp. Thus a valuation of the amount Stamp. due to a builder for building a house was held to be suf- ficiently stamped with an appraisement stamp. (Perkins v. Potts, 2 Chit. 399.) So an appraisement of the amount to be paid by an incoming to an outgoing tenant for stock 752 LAW OF AUCTION. £10 Stamp on Auction- and implements, and of the amount to be allowed by the outgoing tenant for repairs, is sufficiently stamped with an appraisement stamp. (Leas v. Burroughs, 12 East. 1.) SECT. II.—The Law of Auction. By 8 & 9 Vic., c. 15. The Auction Duty is repealed, eer's License. and an Excise Duty of £10 is imposed upon every License to be taken out annually by every person exercising or carrying on the trade of an Auctioneer, in any part of the United Kingdom. Every Auc- tioneer is re- quired to take out Li- cense. Every person who exercises or carries on the trade or business of an Auctioneer, or who acts in such capacity at any sale or roup, and every person who sells, or offers for sale, any goods or chattels, lands, tenements, or heredita- ments, or any interest therein, at any sale, or roup, when any person or persons become the purchaser of the same, by competition, and being the highest bidder, either by being the single bidder, or increasing upon the biddings made by others, or decreasing on sums named by the Auctioneer, or person acting as Auctioneer, or other per- son, at such sale, by any other mode of sale, by competi- Which must tion, is required to take out the license. The license annually. should be renewed annually, ten days at least, before the expiration thereof, on the 5th day of July, in each year. Every Auctioneer having had such license, who continues to carry on the business of an Auctioneer in the year next ensuing the expiration thereof, and omits to renew his license as aforesaid, and every person who carries on the Without Li- business of an Auctioneer as aforesaid, without taking out such license, forfeits £100. be renewed Auctioneer conducting business cense, forfeits £100. Persons exempt from License. Auctioneer can sell any Persons selling goods or chattels by auction under a distress, for non-payment of rent or tithes, to a less amount than £20, or under the authority of any act or acts of par- liament, in force on 8th May, 1845, in which an exemption is given to the officer of a court to sell effects seized under the process of the court, by auction, without taking out or having any license as an Auctioneer, if the sum for which the process is enforced, is under £20, need not be licensed as Auctioneers. A licensed Auctioneer may sell any description of goods kind of goods. without having an excise license to authorise him to sell such goods by retail; and may sell by auction gold and LAW OF AUCTION. 753 silver plate, patent medicines, and other articles, without a special license for the sale of such things. Must post his The Auctioneer before beginning the auction must affix or Name in Sale suspend, or cause to be affixed or suspended, a ticket or Room. board containing his true and full christian and surname, and residence, painted, printed, or written in large letters, pub- licly visible or legible in some conspicuous part of the room or place where the auction is held, so that all persons may easily read the same, and must keep such ticket or board so affixed or suspended during the whole time of such auction being held, under a penalty of £20. his License or deposit The Auctioneer must at the time of any sale by auction Must show on demand of any officer of excise, customs, stamps, or on demand, taxes, produce and show to such officer a proper license £10. granted under the act and then in force, or deposit with the officer £10. If he fails, he may be arrested and detained by any officer of the peace. Any officer of the peace, at the request of the excise officer, &c., may at the termina- tion of the sale, or sooner, if convenient, arrest and convey the person acting as Auctioneer, before a Justice of the Peace, of the county, or place, where the sale has been held, and the Justice may examine into the fact or facts charged, and upon proof either by confession of the party offending, or by the oath of one or more credible witness or witnesses, (which oath the Justice is empowered to ad- minister), that the person brought before him did act as an Auctioneer as aforesaid, and did not produce such license, or deposit such sum of money, may by warrant made under his hand commit the offender to the common goal or house of correction, for the county or place where the sale has been held, for any time not exceeding one calendar month from the day of the commitment. Neither the imprison- ment nor the deposit prejudices or affects any proceedings afterwards instituted for the recovery of the penalty in- curred for acting as an Auctioneer, without the license by the act directed. If the Auctioneer deposits the £10, and before the expiration of a week from the date of the sale produces to the officer a proper license to him granted and in force before and at such sale, the officer must imme- diately repay the deposit; otherwise, he must, at the expi- ration of the week, account for it to the Commissioners of Inland Revenue, or such persons as they may appoint to receive it. 754 LAW OF AUCTION. Each Partner If must be Licensed. Auctioneer's duty to make productive Sale. Conditions of Sale, Auc- for omissions. persons carry on the business of Auctioneers in part- nership, each partner must take out a separate license. (6 Geo 4, c. 81, s. 7.) With respect to the duty of an Auctioneer, he should, before the sale, take all proper and usual precautions by advertising, &c., to make the sale as productive as possible to his client. If he takes upon himself to frame the conditions of sale, tioneer liable which, if a solicitor is employed, are usually drawn out by him, he should insert all usual and proper conditions which the subject of sale requires. If, in consequence of his omission to insert proper and usual conditions, the sale proves ineffectual, he is not entitled to recover anything from his employer for his services. Dunew was employed by Daverell to sell a leasehold estate; he omitted to insert in the particulars of sale a condition that the purchaser should not inquire into the lessor's title. The purchaser, as he was entitled to do in the absence of express stipula- tion to that effect, called for the lessor's title, which Da- verell being unable to furnish, could not make out his title. An action having been brought by Dunew for the money which he supposed to be due to him for endeavouring to sell the property, Lord Ellenborough held that he was entitled to recover no compensation for his services be- cause they had been found to be wholly abortive by reason of his own neglect. (Dunew v. Daverell, 3 Campb. 451.) Description of Property stantially correct, or the sale is void. He should describe the property to be sold correctly in must be sub- the particulars. Any material misdescription will render the sale voidable by the purchaser, as if a house is de- scribed to be a free public-house, when the lease contains a covenant binding the tenant to take beer of a particular brewer. (Jones v. Edney, 3 Campb., 294.) So if a right of way is omitted or misdescribed in the particulars and plan, (Dykes v. Blake, 4 Bing, Q.C., 463,) or if an objec- tionable projection is omitted, (Pope v. Garland, 4 Y & Z., 403.) Any extraordinary condition to which the property is subject, should be described. An annuity payable out of the tolls of Waterloo-bridge was put up for sale, but was not described as redeemable, which it was, the pur- chaser was allowed to repudiate his contract. (Coverley v. Burrell, Sugden on Vend., 211.) On a sale of lease- hold property, it was omitted to be mentioned that an Act LAW OF AUCTION. 755 of Parliament empowered a company to purchase it, the result was the same. So on the sale of a wood, an incor- rect description of the average size of the trees prevented the seller from enforcing the contract. (Lord Brooke, v. Rownthwaite, 5 Hare, 298.) that misde- shall not an- does not ap- ulent mis- Even if there is a condition that misdescriptions shall A Condition not annul the sale, but that compensation shall be given scription for the difference in value, it will not apply to a fraudulent nul Sale, misstatement or a misdescription, so far affecting the sub-ply to fraud- ject matter of the contract, that it may be reasonably sup- statements. posed that but for such misdescription the purchaser might never have entered into the contract. (Flight v. Booth, 1 Bing, Q. C., 377.) Thus, where before the reform in parliament an estate was described as situate about one mile from Horsham, (a parliamentary borough,) when it was between three and four miles from that place, the error was held fatal. (Duke of Norfolk v. Northy, 1 Campb., 337.) And so where a lease at a rack rent was described as held at a ground rent. (Stewart v. Alliston, 1 Mer., 26.) So where a house which was built partly of brick and partly of timber—parts of the exterior of which were built of only lath and plaster, and had no party wall, was described as a brick-built dwelling-house. (Powell v. Double, Sugden 21.) So where the particulars described a house as No. 4 instead of No. 2, although the name of the occupier was correctly stated, and the houses No. 2 and 4 were of the same description, and the latter was rather in better repair than the former, the purchaser was not bound. (Leach v. Mullett, 3 C. & P., 115.) So where a house was held under a lease, and a small yard, which was an essential part thereof, was held under a yearly tenancy, and the particulars omitted to notice the difference of tenure. (Dobell v. Hutchinson, 3 Ad. & E., 355.) Fixtures, are at Valuation, lars must so If the purchaser is to take timber or fixtures at a valua- If Timber, or tion it should be so expressed in the particulars or condi- to be taken tions; if not, he will be entitled to them as part of his the Particu- purchase without additional payment. (Higginson v. state it. Clowes, 15 Ves. junr., 516; Colegrave v. Dias Santos, 2 P. & C., 76.) tion of Goods spection, is In the case of goods, which the purchaser sees at the Misdescrip- time of bidding for them, and buys from inspection, a mis- bought by in- description is not fatal to the contract, but it may in some not fatal. cases be considered as amounting to a warranty that the 756 LAW OF AUCTION. Auctioneer not liable for mistakes arising out of of opinion. goods are of the description specified; if they are not, the auctioneer may be liable to an action for breach of warranty. But if from the nature of the subject of sale the descrip- tion can only be fairly considered as matter of opinion, a mere matter mistake there being no fraud, does not render the auctioneer liable. Thus, on a sale of pictures by auction, one was described in the catalogue as by Claude Loraine, and ano- ther by Teniers, Lord Kenyon held that the description was a mere statement of the seller's opinion, and not bind- ing. (Lendwine v. Slade, 2 Esp. 572.) A different de- cision was arrived at by a jury, where some pictures were described in an invoice as the work of Canaletti. The court refused to disturb the verdict, remarking that he was a very old painter, (he died in 1798,) and that it was for the jury to say, under all the circumstances, whether the words in the invoice implied a warranty of genuineness, or conveyed only a description or an expression of opinion. Littledale, J., observed, that all the auctioneers in London would be alarmed if they thought that words such as those used were to be understood as a warranty. (Power v. Barham, 4 A. & R., 470.) Puffing at Sales. Statute of Frauds ex- It is illegal to employ puffers, or even one person to screw up the price, unless the fact is publicly adver- tised and known. Such conduct is a fraud upon the bid- ders, and inconsistent with the usual condition that the highest bidder shall be purchaser; but it seems to be the better opinion that one bidder may be employed to pre- vent the property from being sold at an under-value. (Sugden on Vendors, 8.) As the Statute of Frauds, 29 Car. 2, c. 3, extends to tends to Sales sales by auction, it is necessary for the auctioneer to attend to its provisions. by Auction. Contract of Sale, or must be in The 4th section enacts "That no action shall be brought Agreement, whereby to charge any person upon any contract or sale of Writing. any lands, tenements, or hereditaments, or any interest in or concerning them, unless the agreement upon which such action shall be brought, or some memorandum or note thereof shall be in writing, and signed by the party to be charged therewith, or some other person thereunto by him lawfully authorised." What cir- cumstances binding. The 17th section is, "That no contract for the sale of any goods, wares, or merchandize for the price of £10 ster- LAW OF AUCTION. 757 ling, or upwards, shall be allowed to be good, except the buyer shall accept part of the goods so sold, and actually receive the same, or give something in earnest to bind the bargain, or in part of payment, or that some note or memo- randum of the said bargain be made and signed by the parties to be charged by such contract, or their agents, thereunto lawfully authorised." Lands. On a sale of lands by auction, there must be a writing Sale of signed by the party to be charged, specifying the names of the vendor and purchaser, and all the particulars and con- ditions of the contract. Goods. On a sale of goods of the price of £10 or upwards, there Sale of must either be such a writing, or a part payment, or ear- nest, or acceptance of the goods, or part of them. is generally both parties. The auctioneer is in most cases considered to be agent Auctioneer of both parties to sign the contract. His employment by Agent of the vendor to sell gives him authority to sign for him, and the purchaser by bidding confers on him an authority to sign for him, unless he otherwise expresses himself. (Ken- worthy v. Schofield, 2 B. & R., 945; Bartlett v. Parnell, 4 A. & R., 792.) So that if he signs a sufficient memo- randum in writing, either party may enforce the contract against the other. But the signature of the auctioneer will not make him to sue the purchaser on the contract, because if he appears as principal he is not allowed to say that he was the agent of the other party. (Farebro- ther v. Simmons, 5 B. & Ald. 333.) Clerk Agent The auctioneer's clerk is the agent of the purchaser, to Auctioneer's sign the contract, if he signs it in his presence without ob- for purchaser jection. The auctioneer may sue on a contract so signed. (Bird v. Boulter, 4 B. & Ad., 443.) Lot is a tract. On a sale by auction, the sale of each lot is a distinct Sale of each contract, and therefore in the case of goods, if the price of separate con- each lot is under £10, the Statute of Frauds does not apply. And the acceptance of or part payment on one lot does not establish the contract as to the other. (Roots v. Lord Dormer, 4 B. & Ad. 77.) of Goods. amounts to it. Nice questions sometimes arise as to what amounts Acceptance to an acceptance of goods within the statute. Some ear- what rings were put up to auction upon a condition that the purchaser should pay a deposit of 30 per cent. Bristolli was the highest bidder, at 88 guineas; the ear-rings were thereupon handed to him, and he received them without 758 LAW OF AUCTION. Auctioneer holds deposit as a Stake- holder. If vendor fail to perform Contract, Auctioneer deposit to the pur- chaser. objection; after they had been in his hands three or four minutes he returned them to the auctioneer, saying, that he had been mistaken as to the price at which they had been knocked down. The auctioneer refused to receive them: he did not pay the deposit. Lord Tenterden at the trial ruled, that there had been an acceptance. The court granted a new trial, remarking that it was improbable that the auctioneer intended to part with the property before payment of the deposit, and that there was very slight evi- dence of acceptance, which was a question for the jury. (Phillips v. Bristolli, 2 B. & C., 911.) If a deposit is paid to the auctioneer, he holds it as a stakeholder between the parties, and is bound to pay to the vendor immediately the contract is completed, or to the purchaser, if the purchase goes off, immediately the vendor has made default. As he may be called upon to pay the deposit at any moment, he is not liable for interest, al- though he may have invested the money and made interest thereby, (Harrington v. Hoggart, 1 B. & Ad., 577,) nor is he liable to any expenses which the purchaser has been put to. But if he has put up the property for sale without authority, he is liable both to interest and ex- penses. (Noratt v. Ellis, Sugden, 30.) He is not entitled to any notice of the purchase being completed or going off, but must inform himself of the circumstances, and pay over to the party entitled at his peril. He impliedly un- dertakes to do so when he receives the deposit. (Duncan v. Cafe, 2 M. & W., 244.) If the vendor is not ready to perform his contract at the stipulated time, the auctioneer is bound at law to return must return the deposit to the purchaser; and this, although the pur- chaser is not prepared, and although if the case is within the Statute of Frauds, negotiations and steps towards com- pletion have been taken after the time, unless the time has been enlarged by an agreement, signed by the purchaser or his agent. (Stowell v. Robinson, 3 Bing, N. C., 928; Clarke v. King, Ry. & Mood, 394.) He may not be so bound if proceedings in equity have been taken by either party. If sued for the deposit, the auctioneer has no right to compel the vendor and purchaser to interplead. He can- not be relieved from the performance of his contract which is to pay the deposit to the party entitled. (Deller v. Prickett, 15 Ins., 168.) LAW OF AUCTION. 759 cannot pur- An auctioneer being employed to sell and obtain the Auctioneer best price from a third person cannot purchase the pro- chase him- perty himself. (Esp. Hughes, 6 Ves., 617.) self. Purchaser. As he has an interest in the contract of sale for his May sue'a commission, he may sue on the contract in his own name. (Williams v. Millington, 1 H. Br. 81.) He is also personally liable as principal to the if he does not disclose the name of his principal. v. Roberdraw, Peake, 120.) purchaser (Hanson he does not Is liable if disclose the name of his principal. to purchaser Goods he to do, if he faith. on the pre- If he bona fide sells goods which he has no right to Is not liable sell, he is not liable to the purchaser, as upon a sale by for selling auction or other sale of goods there is no warranty of the has no right title to the goods sold. (Morley v. Attenborough, 3 Ex., acts in good 500.) But he is liable to the real owner of the goods. Although he is employed by the owner of premises As to selling to sell on them, he has no right to remain on the premises mises. if the owner revokes his authority and requires him to quit even though his remaining there is necessary to complete his contract with the purchasers of the goods. He must quit the premises directly he is requested by the owner, and if he sustains any damage in consequence, must sue the owner. (Taplin v. Florence, 15 Ins., 402.) And if entitled to tion when completed. An auctioneer, as well as every other agent, when Auctioneer he has performed the stipulated service, is entitled to the remunera- remuneration agreed to be paid him, or if there is no ex- service is press agreement to the customary remuneration. there is an agreement as to the rate of payment, it will be construed with reference to the custom of the business, if such custom be so notorious as to render it probable that the employer knew of it. Commission, Sale is not him. It is the custom of auctioneers employed to sell estates Entitled to to claim their commission upon a sale being completed, al- although the though the sale has not been effected by them, and this effected by custom has been considered to be incorporated into agree- ments with their employers, if not expressly excluded. In Driver v. Cholmondeley (9 C. & P., 559) tried before Lord Denman and a special jury, in 1835, the plaintiffs claimed a commission of 1 per cent. on £128,500, the price of an estate which one of the defendants had sold by pri- vate contract after the plaintiffs had been employed to sell it under an agreement, by which they were to have 1 per cent. on the purchase-money; the defendants contended that as the plaintiffs had not effected the sale, they were 760 LAW OF AUCTION. & not entitled to the commission, but the jury gave them a verdict. In Rainy v. Vernon, (9 C. & P., 599,) the plaintiff was employed to sell ground rents by auction, on the terms of receiving a commission of 1 per cent. on sale. After he had advertised the property, the defendants sold it by private contract. Mr. Winstanley proved the cus- tom to be that if an auctioneer is employed, and a sale ad- vertised, and before sale the property is sold by the owner himself, the auctioneer is to be paid his commission. If the particulars are prepared before the employment of the auctioneer it makes no difference. If the auctioneer inserts advertisements and calls the attention of the public to the property, and brings forward a person who eventually be- comes the purchaser, he is always paid his commission. Mr. Shuttleworth confirmed Mr. Winstanley. Mr. Hoggart said, the usage is for the auctioneer to receive his commis- sion after he is employed, however the property may be sold. The amount of commission does not depend upon whether the auctioneer does much or little. Lord Denman directed the jury that if they thought that a usage so no- torious that the defendants must have known it, had been proved, it was part of the contract. But if the custom was not so notorious, it was not engrafted on the contract, and the fair value of the plaintiff's services only ought to be given. The verdict was for the amount of the commission. (See Maltby v. Christie, 1 Esp., 340, and see Lawrence, 3, in Tomkins v. White, 3, Smith, 440.) In Murray v. Currie, (7 C. & P., 584,) it was proved to be the custom of land-agents, that where several were employed to sell an estate, the agent who found a pur- chaser was entitled to a commission of 2 per cent., whether he did anything more towards the completion of the pur- chase or not. It appeared that the purchaser was first informed that the estate was in the market by the plaintiff, but he negotiated the terms of the purchase through the agent employed by the defendant. Lord Denman left it to the jury to say whether the plaintiff had found the pur- chaser, in which case he said they were to find for him, otherwise not; but he told them that they were not bound to give him all the commission that he claimed. They found for the plaintiff for part of the commission claimed. If by the terms of the agreement, commission is to be mission is to paid on the sum obtained, nothing is due until the contract If by agree- ment, Com- LAW OF AUCTION. 761 obtained, due until the completed, paid. is completed, and the purchase-money paid to the vendor. on the sum (Bull v. Price, 7 Bing., 237.) On a negotiation for an ex- nothing is change of livings the employer agreed to pay the agent his Contract is commission when the abstract of the conveyance was drawn and money out. The court held that he was not entitled to be paid when an abstract of title on one side only had been de- livered, no abstract having been delivered by the other party. (Alder v. Boyle, 4 C. B., 635.) But if the em- ployer, having the opportunity to complete the contract, wilfully refuses to do so, the agent is entitled to his com- mission. (Horford v. Wilson, 1 Taunt., 12 W. Tindal, C. J.; Bull v. Price, 7 Bing., 241.) By agreement, an auctioneer was to have a commission of 1 per cent. if the estate was sold by auction, or within two months afterwards, or per cent. if it was not sold within two months. The estate was not sold by auction, but was sold more than two lunar months, but within two calendar months, afterwards. The court held that it was not a mercantile contract, in which the term month always means a calendar month, and that prima facie month meant lunar month, but that it was for a jury to say whether there was any usage of trade for month in such cases to mean calendar month. (Simpson v. Margisson, 11 Q.B., 23.) Conditions of Sale-On the Sale of Freehold Property. 1. That the highest bidder shall be the buyer: and if any dispute arise as to the last or best bidder, the lot in dispute shall be put up at a former bidding. 2. That no person shall advance less at any bidding than £ or retract his or her bidding. 3. That every purchaser shall immediately pay down a deposit, in the proportion of £for every £100, of his or her purchase-money into the hands of the Auctioneer, and sign an agreement for payment of the remainder to the proprietor, on the day of at next, at which time and place the purchases are to be completed, and the respective purchasers are then to have the actual possession of their respective lots; all outgoings to that time being cleared by the vendor. 4. That within from the day of the sale, the vendor shall at his own expense, prepare 2 Z 762 LAW OF AUCTION. and deliver an abstract of his title to each purchaser, or his or her solicitor; and shall deduce a good title to the lots sold, commencing with a deed bearing date the and that no earlier title A.D. day of shall be enquired into or required. 5. That if from any cause the purchase shall not be completed at the time mentioned in the 2nd condition, the purchaser shall pay interest on his purchase money at the rate of 5 per cent., per annum, in addition thereto. 6. That the purchaser of each lot shall pay for all tenant's fixtures and timber on his lot, at a valuation to be made by two valuers or their umpire, one valuer to be named by the vendor and one by the purchaser, within days after the sale, and if either party shall neglect to appoint a valuer, the valuation shall be made by the valuer appointed by the other, and shall be final. That the amount of such valuation shall be paid at the time and place mentioned in the 2nd condition in addition to the purchase-money, or in default of payment, interest shall be paid thereon according to the 5th condition. 7. That upon payment of the remainder of the pur- chase-money, the amount of the valuation and interest as aforesaid, the vendor shall convey the lots to the respective purchasers: each purchaser, at his or her own expense, to prepare the conveyance to him or her, and to tender or leave the same at for execution by the vendor. 8. That if any of the purchasers shall neglect or fail to comply with the above conditions, his or her deposit- money shall be actually forfeited to the vendor, who shall be at full liberty to re-sell the lot or lots, bought by him or her, either by public auction or private contract, and the deficiency (if any) occasioned by such second sale, shall immediately after the same sale, be made good to the vendor by the defaulter at this present sale: and in case of the non-payment of the same, the whole thereof shall be recoverable by the vendor, as liquidated damages, and it shall not be necessary to previously tender a con- veyance to the purchaser. Lastly. That if any mistake be made in the descrip- tion of the premises, or any other error whatever, shall appear in the particulars of the estate, such mistake or error shall not annul the sale, but a compensation or equi- LAW OF AUCTION. 763 valent shall be given or taken as the case may require. Such compensation or equivalent to be settled by two referees, or their umpire; each party within ten days after the discovery of the error, and notice thereof given to the other party, to appoint one referee by writing; and in case either party shall neglect to nominate a referee within the time appointed, the referee of the other party alone may make a final decision. If two referees are ap- pointed, they are to nominate an umpire before they enter upon business, and the decision of such referees or umpire (as the case may be) shall be final. Conditions to be inserted where the title deeds cannot be delivered up. That as the title deeds which concern this estate relate to other estates of greater value, the vendor shall retain the same in his custody, and enter into the usual cove- nants (to be prepared by his solicitor and at his ex- pense) for the production of them to the respective pur- chasers; but all attested copies which may be required of such deeds shall be had and made at the expense of the person requiring the same. Where an estate is intended to be sold in lots, and the title deeds are to be delivered up, the following condition may be inserted: That as the aforesaid lots are holden under the same title, the purchaser of the greater part in value of the said estate shall have the custody of the title-deeds, upon his entering into the usual covenants for the production thereof to the purchaser or purchasers of the remaining or other lots: if the largest portion in value of the estate shall remain unsold, the seller shall be entitled to retain the deeds upon entering into such covenants as aforesaid; all such covenants to be prepared by and at the expense of the person or persons requiring the same, who may have attested copies of such deeds, at his, her, or their own expense. 764 LAW OF AUCTION. Condition to be inserted instead of the fourth-if the property to be sold is leasehold. That within from the day of sale, the vendor shall, at his own expense, prepare and deliver to the purchaser, or his solicitor, an abstract of his title to the property sold, commencing with a lease bearing date the ; but he shall not be required to produce the lessor's title, nor shall any en- quiry be made into the lessor's title. day A.D. Agreement to be signed by the purchaser and to be printed or written on the conditions and particulars. I have this day purchased of [name of vendor] by public auction, lot mentioned in the above-written particulars, for the sum of £, and have paid into the hands of the sum of £ as a deposit and in part payment of the said purchase-money; and I do hereby agree to pay the remaining sum of £ -, at , on or before the unto day of ; and in all other respects, on my part, to fulfil the above-written conditions of sale. As witness my hand, this day of 185- Purchase-money Deposit-money £ Remainder unpaid £ Witness, Conditions of Sale on Sale of Goods. 1. That the highest bidder shall be the buyer, and if any dispute shall arise, between two or more bidders, the lot shall be put up again and resold. 2. That no person shall advance less at a bidding than -, or retract his bidding. 3. That every purchaser shall immediately pay to the auctioneer a deposit, at the rate of per cent. on the amount of his bidding and in part payment. 4. That the remainder of the purchase-money shall be paid and each lot cleared with all faults at the expense within days from the day of sale. AGREEMENTS AND LEASES. 765 5. That no error of description shall annul the sale, nor shall any allowance be made for such error. 6. That if the purchaser shall make default either in payment of remainder of the purchase-money, or in clear- ing the lot or lots purchased by him, according to the above conditions, his deposit-money and all his right and interest in the goods purchased shall be forfeited, and the lot or lots may be re-sold, either by public auction or private contract, at any time within and if any loss shall arise on such re-sale, the party so in default shall make good the same. CHAPTER XXIII. LANDLORD AND TENANT. SECT. I.-Agreements and Leases. Lawyers only may "Deed." sional men an Agree- ment." must be by Tenancy 1. Ir has been seen, that by 44 Geo. III., c. 98, none prepare a but the lawyers therein specified, can prepare a deed for Non-profes- gain, fee, or reward, but that any person not a lawyer, may prepare may prepare an agreement not under seal. By the conjoint operation of the Statute of Frauds, what Lease (29 Car. 2, c. 3, s. 1 and 2,) and the statute 8 & 9 Vict., C. Deed. 106, s. 3, all leases for more than three years from the making thereof, must be by deed. By the same statute, the assignment, or surrender in writing of a decree, must be by deed. A lease for three years or less, from the making thereof, need not be by deed. An agreement for a Nature of lease for any term is good without deed; and if a tenant is under an let into possession under such an agreement, he is at first for a Lease.” a mere tenant-at-will, and may be turned out upon a demand of possession, or may quit without notice. If he occupies and pays rent for an aliquot portion of a year under such agreement, he becomes tenant from year to year, upon the terms of the agreement, and can only quit or be expelled from possession, by giving or receiving a half year's notice to quit, expiring at the period of his year when his tenancy commenced. If he remains in possession during the whole term mentioned in the agree- "Agreement 766 AGREEMENTS AND LEASES. Obligation of the party re- fusing to give or take ment he may quit, or be turned out without notice to quit. An agreement for a lease renders the party who neglects or refuses to give or take a lease according to its pro- a Lease ac- visions liable to an action at law for compensation in Agreement. damages or to a bill in equity for a specific performance. It should provide that the intruding lessees shall not call for the lessor's title. cording to What Agree- ments are Leases. Stamps upon Any agreement which provides for the tenant having possession of the land for three years or less from its date, does not contemplate another instrument being executed before possession is given, is a lease, and must be stamped as such. Agreements. 2. The stamp upon an agreement for a lease is Or if it contains 2160 words, then for every 1080 above the first 1080, a progressive duty of The stamp upon a lease of lands at a yearly rent without premium is— Stamps upon Leases. If the yearly rent does not exceed £5 s. d. 2 6 2 6 06 If it exceeds £5 and not £10 1 0 10 15 1 6 وو وو 15 20 2 0 دو وو 20 25 2 6 99 وو 25 50 5 0 "" وو 50 75 7 6 وو "" 75 100 10 0 وو وو 50 5 0 100 then for each 50 and also for every fractional part of Leases, on which premiums are paid, and leases of mines on which Royalties are reserved, are subject to other duties, for which see the Stamp Act, 13 and 14 Vic., c. 97. There is a progressive duty of 10s. for every 1080 words beyond the first 1080, if the lease contains 2160 words or upwards. If the duty on the lease is 5s., or less, the duty on the counterpart is the same as on the lease. But if the duty on the lease exceeds 5s., the counter- part may be stamped with a 5s. stamp, and a progressive duty of 2s. 6d. for every 1080 words beyond the first 1080, if it contains 2160 words. But this counterpart must have a denoting stamp, and can only be so stamped, on production of both instruments, duly executed and duly stamped. AGREEMENTS AND LEASES. 767 Tenancy year. 3. The ordinary tenancy of lands, houses, &c., is a Ordinary tenancy from year to year. This tenancy is implied by from year to law: 1st, where lands, &c., are let at annual rent, and it is not expressed how long the tenancy is to last. 2nd. Where a tenant holds over, after the expiration of a lease, or other tenancy, for a definite term, and pays rent for a year, or an aliquot part of a year, as a quarter. 3rd. Where a tenant enters into possession under an agreement to purchase, as an agreement for a lease, and pays rent in like manner. In the two last cases, the payment and acceptance of rent raises an inference that the tenancy is to last for a definite period, and when no other period is defined, the presumed term is from year to year. tion of Ten- If the tenancy is for a year, or other prescribed Determina- period, the tenant is bound to quit at the end of the ancy. the term without notice; but if the tenancy is from year to year, it can only be determined by a notice to quit expiring at the period of the year when the tenancy com- menced, unless it is otherwise expressed in the agreement, If a tenant holds as tenant from year to year under an agreement for a lease for a certain term of years, his tenancy may be determined at the expiration of any year during the term by a six months' notice to quit ; but at the end of the term mentioned in the agreement, he is bound to quit without notice. If the tenancy is for a year, and so on from year to year so long as the parties please, it is a tenancy for two years at the least (Doe d. Chadborn v. Green, 9 A. R., 658; Reg. v. Chawton, 1 G. B., 247). But a tenancy from year to year so long as both parties please, may be put an end to at the end of the first year. (Doe d. Clarke v. Smaridge, 7 G. B., 957; Doe d. Plumer v. Mainby, 10 G. B., 473.) 4. In agreements for leases, the term, the rent, the Covenants of times of payment, and all the covenants upon which the ment for a tenant is to hold, should be mentioned. It should also be stated at whose expense the lease and counterpart is to be prepared, and that the intended lessees shall not enquire into the lessor's title. an "Agree- Lease." Leases. 5. In agreements for tenancies, which in law are leases, Covenants of the latter stipulations as to preparation of a lease, and the landlord's title, are unnecessary. 6. A lease should specify the time from which the term 768 AGREEMENTS AND LEASES. ment and Commence- is to commence, and the term during which the tenant is to hold the premises; if this is mentioned, the tenant is bound to quit at the end of the term without notice to quit. length of term. Rent and times of pay- ment. Rates and Taxes. Repairs. Agreement to cultivate Lands. 7. The rent payable and the times of payment. If an annual rent is reserved, and no time of payment mentioned, it is not payable until the end of the year: therefore, if the intention is that the rent should be payable quarterly or half yearly, it is necessary expressly to mention it. 8. The property tax, land tax, and sewers rate imposed on the rent, are taxes on the rent; and the tenant is entitled to deduct so much of such taxes as are rated on the rent from it. But if the premises are rated at a higher value than the rent, he cannot deduct the whole of such taxes. An agreement that the tenant shall pay the landlord's property tax, is not binding; but it is lawful for the tenant to agree to pay the land tax and sewers rate. The property tax and land tax must be deducted from the rent, which is paid next after such taxes have been paid. If the deduction is not then claimed, the landlord is not bound to allow such taxes out of a subsequent arrear of Other taxes and rates, such as the house tax and parish rates, are payable by the tenant. If the tenant agrees to pay all rates and taxes or to pay rent clear of all rates and taxes he is bound to pay the land tax and sewers rate. rent. 9. There should also be an agreement to repair. If the agreement to repair is absolute, the tenant is found to rebuild if the premises are destroyed by fire or other acci- dent. (Gibbons on Dilapidations, 165.) If this is not the intention an exception should be introduced into the agree- ment. He is also to pay rent if the premises are destroyed by fire, unless the event is provided for in the agreement. (ib. 168.) A landlord is under no obligation to repair, except by the custom of the city of London, Norfolk, and the Isle of Ely, in which places the landlord is bound to repair in the absence of express agreement binding the tenant to do so. The Landlord is not understood as war- ranting that the premises are or will continue tenantable during the term; and if they become unsafe or uninhabit- able, the tenant cannot claim compensation from the land- lord, nor if he quits them in consequence, is he excused from the payment of rent. (ib. 171.) 10. In a lease of lands an agreement to cultivate should be inserted. In the absence of express agreement on a AGREEMENTS AND LEASES. 769 letting of farm lands, an agreement to cultivate according to the custom of the country is implied. (ib. 201.) ment and the particular 11. If it is intended to restrain the tenant from assign- As to Assign- ing his interest either absolutely or without license, or carrying on from carrying on any particular trades on the premises, Trades. an agreement to such an effect should be inserted in the lease. This is especially necessary if the landlord holds under a lease by which certain trades are prohibited. ment of Rent 12. There should also be a proviso of forfeiture, in the Non-pay. event of non-payment of rent or breach of covenant. or breach of This will enable the landlord, in the events provided for, to put an end to the tenancy, and recover possession. Lease for three years, or less, of a House. Lease made the Covenant. day of of of lets, and the said of the other part. 18 و between of the one part, and The said premises numbered -, in parish of takes the messuage or tenement, and in the county of street, in the with the appurtenances, for the term of three years from the day and year above-mentioned*. The rent to be £ a year, payable quarterly, with- out deduction or abatement, on any account whatever, on the usual quarter days : the first quarterly payment to become due and be made on the next. day of Should the premises be burnt down or rendered unin- habitable by accidental fire, the rent to be suspended until they are repaired by the landlord so as to be habitable, and the tenant on the quarter-day subsequent to the fire, to pay a proportion of the rent calculated up to the day of the fire; and on the quarter-day subsequent to the repair of the premises, to pay a proportion of the rent, calculated from the day of such repair, up to next subse- quent quarter-day. * Or some day before. If it is to hold for three years from the day sub- sequent to the making the lease must be by deed. 770 AGREEMENTS AND LEASES. The tenant to keep and leave the premises in as good repair and condition as the same now are in, reasonable wear and tear, and accidents by tempest or fire only excepted. The tenant to pay all rates and taxes assessed or imposed on the premises during his tenancy, or on the landlord or tenant in respect thereof, including land tax, sewers rate, and water and gas rate, but excepting the landlord's pro- perty tax. The tenant not to assign or underlet without the license in writing of the landlord, nor to carry on any of the fol- lowing trades * * * * * * * If the tenant shall neglect to pay the rent within twenty-one days after it shall become due, although it be not demanded, or if he shall desert the same, and leave the same, without a sufficient distress for a quarter's rent, whether any rent shall be in arrear or not; and if he shall make breach of, or fail to perform any of the above agree- ments, this demise shall be void, and it shall be lawful for the landlord, his heirs, executors, administrators, or assigns, to re-enter and re-take possession of the premises. The tenant has paid to the landlord £ for the fixtures mentioned in the schedule; and the landlord agrees to re-purchase the said fixtures at the end of the tenancy, at their value, not exceeding the said sum of £ such value to be ascertained, in case of disagreement, by two brokers, one to be named by each party or their umpire. Should the tenancy continue beyond the term herein mentioned, it may be determined by a quarter's notice, expiring at any quarter day. Schedule of Fixtures. [The Schedule should be written on the same paper, or annexed to the lease. If not, it requires a schedule stamp.] Agreement for a Farm. Agreement between of in the parish of of > of and for letting a farm in the county the particulars whereof are mentioned in the schedule hereunder written. 1. Term to be -years, to be computed from the AGREEMENTS AND LEASES. 771 day of continues beyond that time, the same to be determined on the day of- , and if the tenancy in any year, by six calendar months' notice in writing, to be given by either party to the other. the 2. Rent to be £ day of per annum, to commence from next, and be paid quarterly on the usual quarter days. 3. The landlord reserves to himself all timber and timber-like trees. He also reserves to himself and any person authorised by him the right of sporting over the premises. 4. The tenant to pay and discharge all land-tax, rates, taxes, tithes, and rent-charges in lieu of tithes, and other outgoings of every description, except the landlord's pro- perty tax. 5. The tenant not to plough or convert to tillage any part of the premises described in the said schedule to be meadow or pasture, without the consent in writing of the landlord, or his agent; nor sow or plant flax, rape, hemp, or teasels, upon any part of the said premises, under an additional sum, at the rate of £20 per acre, per annum, to be payable quarterly, on the days aforesaid, and to be con- sidered as rent, and payment thereof to be enforceable accordingly. 6. The tenant not at any time between the 1st day of November, and the 1st day of April, to depasture or feed more than two horses, mares, or geldings, in any one close, at any one time, after giving or receiving notice to quit the same. 7. The landlord to keep in repair the roofs, walls, beams, and stanchions of the dwelling-house and out-houses, be- longing to the said premises. 8. The tenant not to sell or part with any dung or compost to be made on the premises, nor any hay, straw, halm, or stubble, or the fodder that shall arise therefrom, but to spend and consume the same on the premises. 9. The tenant not to let or in any manner otherwise dispose of or permit to be occupied by any other person, any part of the premises, without the landlord's consent in writing. 10. The tenant to keep in repair the glass of the win- dows of the dwelling house, and to do all internal repairs UorM 772 AGREEMENTS AND LEASES. and painting; and also to repair all gates, posts, stiles, rails, pales, and backings; and the hedges, walls, and other fences, and to cleanse the ditches, watercourses, and drains. 11. The tenant not to mow any part of the meadow lands more than once in any year, or after the 10th day of August, in every year; and in all respects to manage and cultivate all the premises in a husbandlike manner. 12. The landlord to have and take immediate possession of the premises, in case the tenant shall be adjudged bank- rupt, or in case he shall take the benefit of any act for the relief of insolvent debtors, or shall permit any writ of execution to be levied on his effects; or if the rent shall be in arrear for twenty-one days after any quarter-day, and there shall not be sufficient distress on the premises, or if the tenant shall make a breach of, or neglect to per- form any of the above stipulations. In witness whereof the said parties to these presents have hereunto set their hands, the day of Witness, 185 The Schedule by the foregoing terms referred to. No. on Map. Description of Premises. Culture. Quantity. Observations. A. B. P. Maou NOTICE TO QUIT. 773 SECT. II. -Notice to Quit. sary. 1. A Notice to Quit is necessary in all cases when the When neces- tenant holds as tenant from year to year, or from month to month, or from week to week, or for a continuing term not precisely defined; but not if he holds for a precise term or at will. Notice. 2. If the holding is from year to year, the notice must Length of expire at the end of the current year. It may either be given 182 days before the end of the current year, or prior to, or on the corresponding feast, which happens two quarters before the feast on which the current year ends, as on Michaelmas-day, to quit on Lady-day. (Doe d. Harrop v. Green, 4 Esp., 199.) If the tenancy is quarterly, or monthly, or weekly, it may be determined by a quarter's, a month's, or a week's notice expiring at the end of any quarter, month, or week, of the tenancy. ancy is con- commencing. 3. In general the tenancy is understood as commencing When Ten- from the time of the tenant's entering, and the notice to sidered as quit must expire at that period of the year; but if his quarterly or yearly rent is calculated from the quarter- day preceding or succeeding his entry, his tenancy will be taken to commence on such quarter-day. (Doe d. Hol- comb v. Johnson, 6 Esp., 10.) If the yearly tenancy arises from a holding over, after the expiration of a lease, it dates from the time when the lease ended. If different parts of the premises are held from different times as is often the case in farms, it is sufficient if the notice is given a half year before the day on which the first year's rent is payable, or on which the tenancy of the principal part of the premises commenced. (Dugget v. Snowden, 2 Black., 1224; Doe d. Ld. Bradford v. Watkins, 7 East., 551.) 4. A notice to quit may be given by an agent, but he By whom must have authority at the time he gives the notice. An be given. agent to let and receive rents has authority to give a notice to quit; but a mere agent to receive rents has not. One of several joint tenants may give a notice to quit. But the notice of one of several co-partners or tenants in com- mon, without authority from the others, only determines the tenancy of his share. Notice is to be given, and 5. It should be given to the tenant himself or to his To whom to assignee, not to a sub-tenant. If served on the person in Service. Uor M 774 NOTICE TO QUIT. Form of Notice. Waiver of Notice. Holding over after the Landlord's Notice. possession of the premises, it will be presumed that he is assignee of the original tenant in the absence of proof to the contrary. It may be served on the wife or servant of the tenant on the premises. 6. The notice should be explicit, and not give the tenant the option of entering into a new contract. But a notice to quit, or "I shall insist on double rent," is not bad on this ground, as it merely intimates the legal consequence of the tenant holding over. It should also be precise as to the time of quitting. A notice to quit at "the end of the current year of your tenancy," when the current year ends within a half year from the notice, is bad; but a notice to quit "at the end of the current year of your tenancy, which will expire next after a half year from the service of this notice," is good, and the proper form to adopt in all cases where the time of the commencement of the tenancy is not known or cannot be proved. 7. A notice to quit is waived by receiving or distraining for rent accruing due after the expiration of the notice. 8. If a tenant wilfully holds over after the termina- tion of his term, and after demand made and notice in writing given for delivering possession by the landlord or his agent, he is liable to pay to the person kept out of possession for the time he holds over, at the rate of double the yearly value of the lands detained. (4. Geo. 2., c. 28.) This provision applies to a tenant holding over after notice to quit given by the landlord, and such notice is a suffi- cient notice and demand of possession under the statute. Holding over 9. If the tenant holds over after a notice to quit given by himself, he is liable to pay double rent, which may be distrained for. (11 Geo. 2, c. 19, s. 18.) after the Tenant's Notice. Form of Notice to Quit. Mr. [Tenant's name.] day of I hereby give you notice, to quit and deliver up on the* the dwelling-house [or next, the possession of ]with the appurtenances which you now hold of mef, situate in the parish of 2 in the county of > provided your tenancy originally commenced at that time of the * Day on which tenancy expires. + If notice is signed by an agent, here insert landlord's name. Maou DISTRESS. 775 year, or otherwise, that you quit and deliver up the posses- sion of the said dwelling-house, &c. at the end of the year of your tenancy, which shall expire next after the end of one- half-year from the time of your being served with this notice; and further take notice, that unless you quit at the expiration of this notice, you will be liable to pay double the yearly value of the premises held over, for so long as you shall hold over the same. Dated this day of Yours, &c. 185-. " SECT. III.-Distress. Distress, and it may be 1. A Distress is a right to seize goods to enforce pay- Nature of ment of rent. The landlord distraining must have a in what cases reversion, that is an interest and right to possess the premi- made. ses after the determination of the tenancy to which the rent is incident. There must also be a tenancy for a term certain, at a rent certain. A person let into possession under a mere agreement for a lease, who is only tenant at will and may be ejected at his landlord's pleasure, or may quit at his own, cannot be distrained on until he has become tenant from year to year, by payment of rent. time. 2. A distress must be made during the term, or within At what six calendar months after its determination, during the landlord's interest and the tenant's possession (8th Ann, c. 14, s. 6 & 7.) It must be made in the day-time between sunrise and sunset. It cannot be made until the day after that on which the rent is payable. place. 3. The goods distrained must be taken on the premises At what from which the rent issues. If the goods of the tenant are fraudulently removed from the premises after the rent has become due, the landlord may follow and distrain them within thirty days after the removal, provided they have not, before seizure, been bonâ fide sold for a valuable con- sideration. The tenant and all persons wilfully assisting him in removing or concealing the goods, are liable to a penalty in double the value of the goods, and if the value of the goods does not exceed £50, the penalty may be reco- vered before two justices. If the goods removed are locked up in any house or other place, the landlord or his bailiff may, in the day-time, break open and enter the house or place, first calling to his assistance the constable of the 776 DISTRESS. What Goods are Distrain- able. Goods abso- lutely privi- leged from Goods in the Custody of the Law. Distress. Fixtures. Things part of the De- mise. Things not the subject place, and in the case of a dwelling house, making oath of a reasonable ground to suspect that the goods are in such dwelling-house (11 Geo. II., c. 19, s. 1 to 7.) 4. All goods on the premises, with certain exceptions, may be distrained for rent, also cattle and stock on a com- mon, appendant appurtenant, or in any ways belonging to the premises-growing corn, grass, hops, fruits, pulse, and other produce, may also be distrained and may be cut when ripe, and laid up in barns on the premises, and in convenient time may be appraised and sold. Notice of the place where the crops are lodged must be given to the tenant within one week after they are lodged. If the tenant pays or tenders the rent and expenses before the crops are ripe and cut, cured, or gathered, the distress is to cease (11 Geo. II., c. 19, s. 8 & 9.) 5. Goods privileged from distress are 1st, goods in the custody of the law, that is, goods already under distress or under execution. In this latter case, the execution creditor is bound to pay the landlord the rent due at the time of the seizure, not exceeding one year's rent, before the goods can be removed under the execution (8th Ann, c. 14.) 6. 2ndly, Fixtures or things fixed to the freehold, such as grates, doors, windows, and the like: a temporary dis- union of a fixture does not render liable to a distress, as if a mill-stone is removed for the purpose of being picked. 7. 3rdly, Things which are part of the demise as the furniture of a furnished lodging. 8. 4thly, Things which are not the subject of property, of Property. as wild animals, but tame animals such as cattle, dogs, tame deer, or deer in an inclosure kept for profit, may be distrained. (Davies v. Powell Willes, 50.) Perishable Things, and which cannot 9. 5thly, Things which cannot certainly be identified Things and cannot be returned in the same state, such as loose be identified. money, meal, or the like, and things which quickly perish, such as meat and milk, are not distrainable, because they cannot be returned in the same state. But by W. & M., c. 5, s. 3, sheaves of corn, or corn loose or in the straw, or hay in any barn or granary, or in any hovel, stack, or rick or otherwise, upon any part of the land may be dis- trained, and locked up and detained in the place where found, until replevied or sold. Goods deli- 10. 9thly, things delivered to a person exercising a vered for pur- DISTRESS. 777 public trade to be carried, wrought, or managed in the way of his trade: under this head, a horse sent to a farrier to be shoed, goods sent to an auctioneer to be sold, or an ox sent to a butcher to be slaughtered, are exempt from being distrained, so the horses and carriages of a guest standing at an inn are privileged; but horses and carriages at a livery stables are not. (Parsons v. Gingell, 4 C. B., 545.) poses of Trade. 7thly, Things in actual use are privileged, because Goods in use. to take such things may provoke a breach of the peace, for instance, an axe in a man's hand, a horse on which he is riding, a cart in which he is standing, a loom at which he is working. their way to 8thly, Cattle on their way to market, put on the land Cattle on for their necessary refreshment, with the privity of the Market." lessor or the lessee, are privileged. So cattle which es- cape into the land because there are not sufficient fences, unless the owner of the cattle is bound to keep up the fences, are privileged, until they have been levant and couchant on the tenant's land (which means until they have been there a whole night). If the landlord or tenant of the land into which the cattle escape is bound to keep up the fences, they are not distrainable unless notice has been given to the owner of his cattle having strayed, and he has neglected to remove them for a reasonable time after such notice. In no case can stray cattle be dis- trained for rent, if the owner has made fresh pursuit and endeavoured to bring them back. leged condi- Implements of husbandry, and beasts of the plough, Things privi- saddle horses, poultry, implements of trade, wearing apparel tionally. and jewels, should not be distrained if there is other suffi- cient distress. In making a distress no outer door or window can be broken, nor can the door of a barn or stable. Manner of Distraining, not to break outer door. and tender of The goods must be seized and impounded; they may Impounding be, and usually are, impounded and sold on the pre- Rent. mises (11 Geo. II, c. 19, s. 10,) where this is done, they are considered as impounded as soon as seized. They can- not be impounded out of the county in which they are taken, (stat. Marlbridge, 52, Hen. III, c. 4), nor out of the hundred except in a pound in the same county, and not above three miles from the place of the distress, under a penalty of £5 and treble damages. If the rent is tendered before the distress is impounded, either to the 3 A 778 DISTRESS. Sale. Notice of Distress and ment. landlord or to the bailiff making the distress (Hatch v. Hale, 15 G. B., c. 10,) it must be accepted. But after the distress is impounded, the landlord is bound to accept the rent and costs if tendered. A distress cannot be sued by stat. 2, W. & M., sess. 1, c. 5, if the tenant does not replevy within five days next after distress taken, and notice thereof left at the chief mansion house or other most notorious place on the pre- mises, the person distraining may, with the sheriff or under-sheriff of the county, or the constable of the hun- dred, parish or place, where the distress has been taken, cause the goods distrained to be appraised by two sworn appraisers (whom such sheriff, under-sheriff, or constable must swear to appraise the same truly according to the best of their understanding,) and after such appraisement, may sell the same for the best price that can be gotten for them, for satisfaction of the rent and charges of the dis- tress, appraisement, and sale, leaving the overplus, if any, with the sheriff, under sheriff, or constable, for the owner's use. The notice must be in writing (Wilson v. Nightin- Appraise gale, 8 G. B., 1034.) It must specify the goods distrained. It is sufficient to say that all goods on the premises are dis- trained (Wakeman v. Lindsay, 19 L. J. G. B., 166), but not sufficient to say all goods on the premises that may be required to satisfy the rent and expenses, (Kirby v. Harding, 6 Ex., 234.) Five clear days must elapse after the day of the distress and notice given, before the goods can be appraised or sold. (Robinson v. Waddington, 13 Q. B., 753.) The appraisers must be two persons having no interest in the matter, the distraining broker cannot be one. (Westwood v. Cowne, 1 Stush., 172.) There must be two appraisers, although the rent is under £20. (Allen v. Flicker, 10 A. V. E., 640.) in Distress. Irregularities The distress should not be excessive. The mere cir- cumstance of the distress being for more rent than due, does not render the landlord liable to the tenant unless some special damage has been sustained by him. (Tancred v. Leyland, 16 G. B., 669.) There cannot be a second distress for the same rent, unless the value of the first distress, is found insufficient. (17th Jas. II, c. 7, s. 4; Dawson v. Cropp, 1 C. B., 961.) Costs of Dis- tress. By 57 Geo. III, c. 93, no person making a distress DISTRESS. 779 for rent, when the sum demanded and due does not exceed £20, can take, either from the tenant or the landlord, any other or more charges for any matter or thing done in the distress, than are mentioned in the schedule to the act, or can make any charge for any act mentioned in the schedule, unless the act has been really done. If he violates the act, a justice of the peace may order him to pay treble damages and costs to the party grieved, which may be levied by distress warrant; in case of no sufficient distress, he may be committed to gaol, until he pays or satisfies the order; if the complaint is unfounded, the complainant may be ordered to pay costs. The landlord is not liable under this statute, unless he personally levies the distress. Every broker who makes a distress must give a copy of his charges, although the rent demanded exceeds £20. The schedule of charges are:- Levying Distress Man in possession, per day Appraisement 6d. in the pound on the value of the goods Stamp, the lawful amount thereof All expense of advertisements if any such Catalogues, sale and commission, and delivery of goods ls. in the pound on the net produce of sale 0 3 0 026 . 0 10 0 The provisions of this statute are extended to distresses for land tax, assessed taxes, poors rates, church rates, tithes, highway rates, sewer rates, or any other rates or taxes, if the sum demanded and due does not exceed £20, and to all cases in which the whole of several sums sought to be levied by distresses, taken for different purposes at the same time, do not exceed the sum of £20. (7 & 8 Geo. IV., c. 17.) tress on or Insolven- In the event of the bankruptcy or insolvency of the Right of Dis- tenant, the landlord's remedy by distress is limited to Bankruptcy one year's rent due at the time of the bankruptcy or in- cy of Terant. solvency, if more is due he must come in as a creditor. (12 & 13 Vict., c. 106, s. 129; Bankrupt act, 1 & 2 Vict., c. 110, s. 58; Insolvent debtor's act, persons in prison for debt who petition for their discharge, 7 & 8 Vict., c. 96, s. 18; Protection act, insolvents who petition for protection from process.) 780 DISTRESS. Warrant of Distress. To Mr. goods and chattels of -, my bailiff. Distrain the 2 (the tenant,) in the house he now dwells in, (or on the premises in his possession,) situate in county of for in the pounds, being one year's rent due to me for the same at day last, and for your so doing this shall be your sufficient warrant and authority; and in consideration of your so doing, I hereby undertake to indemnify against loss, costs, charges, damages, or expenses which you may thereby incur or sustain, and against any action or proceeding, lawful or unlawful, which may be brought against you for acting in obedience to this warrant. Dated this day of Mr. -185-. Notice of Distress. Take notice, that I have this day distrained (or that as bailiff to , your landlord, I have this day dis- trained) on the premises above-mentioned, the several goods and chattels specified in the inventory hereunder written, for the sum of year's rent due to me (or to the said - at being one -₂) day last, for the said premises, and that unless you pay the said rent, with the charges of distrain- ing for the same, or replevy the said goods and chattels within five days from the date hereof, they will be ap- praised and sold according to law. Given under my hand the day of -, in the year 18—. Consent by Tenant to hold over. Memorandum. That I, do hereby consent and agree that my landlord, who hath distrained my goods and chattels for the rent in a dwelling-house, situate at , in the county of shall continue in the possession of my said goods and chat- tels, in the said dwelling-house, space of for the days from the date hereof, the said having agreed to forbear the sale of the said goods and chattels for the said space of time, to DISTRESS. 781 enable me to discharge the said rent; and I, the said do hereby agree to pay the expenses of keeping the said possession. As witness my hand the in the year of our Lord, 18—. Witness, day of- Notice of Distress of Standing Corn. Take notice, that I have this day, as bailiff of , your landlord, taken and distrained on the premises undermentioned, the several growing crops spe- cified in the inventory underwritten, for the sum of -, being one year's rent due to the said £ - at day last, for the said premises, and unless you previously pay the said rent, with the costs of dis- training the same, I shall proceed to cut, gather, make, cure, carry, and lay up the crops, when ripe, in the barn, or other proper place on the said premises, and in conve- nient time sell and dispose of the same, towards satisfac- faction of the said rent, and of the costs of the distress, appraisement, and sale, according to the form of the sta- tute in that case made and provided. Given under my hand this day of Appraiser's Oath. 18-. You and each of you shall well and truly appraise the goods and chattels mentioned in this inventory (holding it up in his hand) according to the best of your judgment. So help you God. Appraisement. We, the above-named, and Evangelists, by being sworn upon the Holy the constable , above-named, well and truly to appraise the goods and chattels mentioned in this inventory, according to the best of our judgment, and having viewed the said goods and chattels, do appraise the same at the sum of pounds. As witness our hands the -, in the year of our Lord 18—. day of Sworn Appraisers. 782 RECOVERY OF POSSESSION. Right of Entry. If Premises are Deserted. SECT. IV. Recovery of Possession. In all cases where the interest of the tenant has ex- pired, the landlord has a right by law to enter and take possession, and may do so without resorting to any legal proceeding, if he can, without disturbing the public peace. But if the tenant is in possession, and is likely to resist the landlord's entry, it is advisable to proceed at law, as al- though the tenant can maintain no action, the landlord may render himself liable to an indictment for a forceable entry. (See Davison v. Wilson, 11 G. B., 890.) If a tenant holding lands, &c., at a rack rent, or a rent which is full three-fourths of the yearly value of the demised premises is in arrear for a half-year's rent, and deserts the premises, and leaves them uncultivated, or un- occupied, so as no sufficient distress can be had to counter- vail the arrears of rent, two or more justices of the peace of the county, riding, division, or place having no interest in the demised premises, at the request of the landlord, his bailiff or receiver may go upon and view the same, and affix, or cause to be affixed, on the most notorious part of the premises, notice in writing, stating what day, (at the distance of fourteen days at the least,) they will return to take a second view thereof, and if upon such second view, the tenant, or some person on his or her behalf, does not appear and pay the rent in arrear, or there is not a suffi- cient distress on the premises, the justices may put the landlord into possession of the demised premises, and the lease thereof, as to any demise therein contained, only be- comes void. This proceeding may be taken, although there is no right or power of re-entry reserved in the lease to the landlord upon non-payment of rent. The tenant may appeal to the next justice or justices of assize of the county in which the lands lie, or if in London or Middle- sex, to the judges of the Queen's Bench or Common Pleas, or if in a County Palatine, before the judges thereof (11 Geo. 2, c. 19, s. 16 & 17; 57 Geo. 3, c. 52.) If the premises are within the Metropolitan Police Dis- trict, a police magistrate, at the request of the landlord, his bailiff, or receiver, made in open court, and upon proof given to the satisfaction of the magistrate of the arrear of rent and desertion of the premises, may issue his warrant RECOVERY OF POSSESSION. 783 Magistrate, if more than directed to the police constable, requiring him to go upon and view the premises, and affix the notices, and upon re- turn of the warrant and proof that it has been duly executed, and that neither the tenant nor any person on his behalf has appeared and paid the rent, and that there is not sufficient distress on the premises, the magistrate may issue his warrant to a police constable, requiring him to put the landlord into possession. (3 & 4 Vict., c. 84, s. 13.) If the interest of a tenant holding at will, or for any term not exceeding seven years, either without rent, Before a or at a rent not exceeding £20, and upon which no fine Rent not has been reserved or made payable, has ended or been £20. duly determined by a legal notice to quit, or otherwise, and the tenant, or any person by whom the premises or any part is occupied, neglects or refuses to quit and de- liver up possession, the landlord or his agent may cause the person so neglecting or refusing to be served with a written notice, in form set forth in the schedule; and if the tenant or occupier does not appear at the time and place appointed, and show to the satisfaction of the justices reasonable cause why possession should not be given, and still neglects or refuses to deliver possession, the landlord or his agent may give the justices proof of the holding and of the end or determination of the tenancy, with the time or manner thereof, and if the title of the landlord has ac- crued since the letting, the right by which he claims pos- session, and upon proof of the service notice, and the neglect or refusal of the tenant or occupier, the justices acting for the district, division, or place within which the premises or any part thereof are situate, in petty sessions assembled, or any two of them may issue a warrant under their hands and seals to the constables and peace officers of the district, division, or place, within which the premises, or any part thereof, are situate, commanding them within a period therein named, not less than twenty-one nor more than thirty clear days from the date of the warrant, to enter by force if needful and give possession thereof to the landlord or agent. The warrant must be executed be- tween nine in the morning, and four in the afternoon, and not upon Sunday, Good Friday or Christmas-day, an action of trespass may be brought against the party apply- ing for the warrant, if there is no right of entry. Any rights which the tenant may be entitled to, as outgoing 784 RECOVERY OF POSSESSION. In County Court, if Rent not more than £50. tenant by custom of the country, or otherwise, are not affected by the proceeding. The notice of application may be served either personally or by leaving the same with some person, being in, and apparently residing at, the place of abode of the person holding over. The person serving the notice must read it over to the person served, and explain the purport and intent. If the person holding over cannot be found, and his place of abode is not known, or admission thereto cannot be obtained for serving the summons, the posting it up on some conspicuous part of the premises held over is good service. If the party to whom the warrant is granted has not at the time a lawful right to enter, the obtaining of the warrant is an act of trespass. The execution of the warrant is to be stayed if the tenant, with two sureties to be approved of by the justices, enters into a bond to try an action of trespass and pay the costs if unsuccessful. If he succeeds in the action, the warrant is suspended. The bond is to be given to the landlord or his agent, and to be prepared at his (the landlord's or agent's) costs, and is to be deemed forfeited, unless the judge at the trial, indorses on the record that the condition has been fulfilled. The Court in which the action is brought may relieve the parties from the bond. No action can be brought against the justices for granting, or the constables for executing the warrant (1 & 2Vict. c. 74). The County Courts have jurisdiction to give posses- sion to a landlord in all cases when the term or interest of the tenant of premises the value or the rent payable in respect of which does not exceed £50 by the year, and upon which no fine has been paid, has ended or been duly determined by a legal notice to quit if the tenant or person in occupation neglects or refuses to quit and deliver up possession of the premises or any part thereof. The proceeding in the County Court is by plaint, upon which a summons issues; and if the tenant or occupier does not appear and show cause to the contrary upon similar proof, as is required by 1 & 2 Vict., c. 72, the County Court may grant a warrant to the bailiff, to the same effect as the warrant to the constable under the former statute, which has the same effect and must be executed, or may be suspended in the same manner as the magistrates' warrant, (9 & 10 Vict., c. 95, s. 122, 3, 4, 5, 6, 7.) RECOVERY OF POSSESSION. 785 Form of Notice of Owner's Intention to apply to Justices to recover Possession, under 1 & 2 Vict. c. 74. I owner (or agent to the owner as the case may be), do hereby give you notice, that, unless peaceable possession of the tenement, (shortly describing it,) situate which was held of me (or of the said as the case may be,) under a tenancy from year to year or (as the case may be) which expired (or was determined) by notice to quit from the said (or otherwise as the case may be,j day of on the و , and which tenement is now held over and detained from the said. be given to (the owner or agent) on or before the expiration of seven clear days from the service of this notice, I, the day of 2 shall, on at next, of the clock the same day, apply to Her Majesty's Justices of the Peace, acting for the district of (being the district, division, or place, in which the said tenement, or any part thereof, is situate,) in Petty Sessions assembled, to issue their warrant directing the constables of the said district, to enter and take possession of the said tenement, and to eject any person therefrom. Dated this To Mr. (Signed)- (Owner or Agent.) Complaint before two Justices. The complaint of (owner or agent, &c., as the case may be) made before us two of her Majesty's Justices of the peace acting for the district of of did let to for- > in Petty Sessions assembled, who saith that the said at enement consisting under the rent of and that the said tenancy expired (or was determined by notice to quit given by the said as the case may be), on the of the said " day did serve on (the tenant overholding) a notice in writing of his intention 786 RECOVERY OF POSSESSION. to apply to recover possession of the said tenement (a duplicate of which notice is hereto annexed) by giving, &c., (describing the mode in which the service was effected,) and that notwithstanding the said notice, the said refused (or neglected) to deliver up possession of the said tenement and still detains the same. Taken the (Signed) day of (Signed) before us. [A duplicate of the notice of intention to apply is to be annexed to this complaint.] Warrant to Peace Officers to take and give Possession. Whereas, (set forth the complaint,) we, two of Her Majesty's Justices of the Peace, in Petty Sessions as- sembled acting for the of do authorize and command you on any day within days from the date hereof, (except on Sunday, Christmas Day, and Good Friday, to be added if necessary,) between the hours of nine in the forenoon and four in the afternoon, to enter (by force if needful and with or without the aid of the owner or agent, (as the case may be,) or any other person or persons whom you mày think requisite to call to your assistance, into and upon the said tenement, and to eject thereout any person, and of the said tenement full and peaceable possession to deliver to the said (the owner or agent). To Given under our hands and seals this and all other constables and peace officers acting for the district of day of CHAPTER XXIV. TABLES OF NATURAL SINES AND COSINES; AND ADDITIONAL USEFUL TABLES. 788 NATURAL SINES & COSIN ES.. 0° 1º 2° N. sin N. cos N. sin N. cos N. sin N. cos 0 00000 1.00000 01745 99985 03490 99939 60 1 00029 1.00000 01774 99984 03519 99938 59 2 00058 1.00000 01803 99984 03548 99937 58 3 00087 1.00000 01832 99983 03577 99936 57 00116 1.00000 01862 99983 03606 99935 56 00145 1.00000 01891 99982 03635 99934 55 6 00175 1.00000 01920 99982 03664 99933 54 7 00204 1.00000 01949 99981 03693 99932 53 8 00233 1.00000 01978 99980 03723 99931 52 9 00262 1.00000 02007 99980 03752 99930 51 10 00291 1.00000 02036 99979 03781 99929 50 11 00320 .99999 02065 99979 03810 99927 49 12 00349 .99999 02094 99978 03839 99926 48 13 00378 .99999 02123 99977 03868 99925 47 14 00407 .99999 02152 99977 03897 99924 46 15 00436 .99999 02181 99976 03926 99923 45 16 00465 .99999 02211 99976 03955 99922 44 17 00495 .99999 02240 99975 03984 99921 43 18 00524 .99999 02269 99974 04013 99919 42 19 00553 .99998 02298 99974 04042 99918 41 20 00582 .99998 02327 99973 04071 99917 40 21 00611 .99998 02356 99972 04100 99916 39 22 00640 .99998 02385 99972 04129 99915 38 23 00669 .99998 02414 99971 04159 99913 37 24 00698 .99998 02443 99970 04188 99912 36 25 00727 .99997 02472 99969 04217 99911 35 26 00756 .99997 02501 99969 04246 99910 34 27 00785 .99997 02530 99968 04275 99909 33 28 00814 .99997 02560 99967 04304 99907 32 29 00844 .99996 02589 99966 04333 99906 31 30 00873 .99996 02618 99966 04362 99905 30 31 00902 .99996 02647 99965 04391 99904 29 32 00931 .99996 02676 99964 04420 99902 28 33 00960 .99995 02705 99963 04449 99901 27 34 00989 .99995 02734 99963 04478 99900 26 35 01018 .99995 02763 99962 04507 99898 25 36 01047 .99995 02792 99961 04536 99897 24 37 01076 .99994 02821 99960 04565 99896 23 38 01105 .99994 02850 99959 04594 99894 22 39 01134 .99994 02879 99959 04623 99893 21 40 01164 .99993 02908 99958 04653 99892 20 41 01193 .99993 02938 99957 04682 99890 19 42 01222 .99993 02967 99956 04711 99889 18 43 01251 .99992 02996 99955 04740 99888 17 44 01280 .99992 03025 99954 04769 99886 16 45 01309 .99991 03054 99953 04798 99885 15 46 01338 .99991 03083 99952 04827 99883 14 47 01367 .99991 03112 99952 04856 99882 13 48 01396 .99990 03141 99951 04885 99881 12 49 01425 .99990 03170 99950 04914 99879 11 50 01454 .99989 03199 99949 04943 99878 10 51 01483 .99989 03228 99948 04972 99876 9 52 01513 .99989 03257 99947 05001 99875 8 53 01542 .99988 03286 99946 05030 99873 7 54 01571 .99988 03316 99945 05059 99872 55 01600 .99987 03345 99944 05088 99870 56 01629 .99987 03374 99943 05117 99869 57 01658 .99986 03403 99942 05146 99867 58 01687 .99986 03432 99941 05175 99866 59 01716 .99985 03461 99940 05205 99864 60 01745 .99985 03490 99939 05234 99863 210 1 N. cos N. sin N. cos N. sin N. cos 89° 88° 87° N. sin NATURAL SINES & COSINES. 789 30 40 50 N. sin N. cos N. sin N. cos N. sin N. cos 1 0 05234 99863 06976 99756 08716 99619 60 123 + 05263 99861 07005 99754 08745 99617 59 05292 99860 07034 99752 08774 99614 58 05321 99858 07063 99750 08803 99612 57 4 05350 99857 07092 99748 08831 99609 56 5 05379 99855 07121 99746 08860 99607 55 6 05408 99854 07150 99744 08889 99604 54 7 05437 99852 07179 99742 08918 99602 53 8 05466 99851 07208 99740 08947 99599 52 9 05495 99849 07237 99738 08976 99596 51 10 05524 99847 07266 99736 09005 99594 50 11 05553 99846 07295 99734 09034 99591 49 12 05582 99844 07324 99731 09063 99588 48 13 05611 99842 07353 99729 09092 99586 47 14 05640 99841 07382 99727 09121 99583 46 15 05669 99839 07411 99725 09150 99580 45 16 05698 99838 07440 99723 09179 99578 44 17 05727 99836 07469 99721 09208 99575 43 18 05756 99834 07498 99719 09237 99572 42 19 05785 99833 07527 99716 09266 99570 41 20 05814 99831 07556 99714 09295 99567 40 21 05844 99829 07585 99712 09324 99564 39 22 05873 99827 07614 99710 09353 99562 38 23 05902 99826 07643 99708 09382 99559 37 24 05931 99824 07672 99705 09411 99556 36 25 05960 99822 07701 99703 09440 99553 35 26 05989 99821 07730 99701 09469 99551 34 27 06018 99819 07759 99699 09498 99548 33 28 06047 99817 07788 99696 09527 99545 32 29 06076 99815 07817 99694 09556 99542 31 30 06105 -99813 07846 99692 09585 99540 30 31 06134 99812 07875 99689 09614 99537 29 32 06163 99810 07904 99687 09642 99534 28 33 06192 99808 07933 99685 09671 99531 27 34 06221 99806 07962 99683 09700 99528 26 35 06250 99804 07991 99680 09729 99526 25 36 06279 99803 08020 99678 09758 99523 24 37 06308 99801 08049 99676 09787 99520 23 38 06337 99799 08078 99673 09816 99517 22 39 06366 99797 08107 99671 09845 99514 21 40 06395 99795 08136 99668 09874 99511 20 41 06424 99793 08165 99666 09903 99508 19 42 06453 99792 08194 99664 09932 99506 18 43 06482 99790 08223 99661 09961 99503 17 44 06511 99788 08252 99659 09990 99500 16 45 06540 99786 08281 99657 10019 99497 15 46 06569 99784 08310 99654 10048 99494 14 47 06598 99782 08339 99652 10077 99491 13 48 06627 99780 08368 99649 10106 99488 12 49 06656 99778 08397 99647 10135 99485 11 50 06685 99776 08426 99644 10164 99482 10 51 06714 99774 08455 99642 10192 99479 9 52 06743 99772 08484 99639 10221 99476 8 53 06773 99770 08513 99637 10250 99473 7 54 06802 99768 08542 99635 10279 99470 6 55 06831 99766 08571 99632 10308 99467 5 56 06860 99764 08600 99630 10337 99464 4 57 06889 99762 08629 99627 10366 99461 3 58 888888 06918 99760 08658 99625 10395 99458 2 59 06947 99758 08687 99622 10424 99455 1 60 06976 99756 08716 99619 10453 99452 0 N. cos N. sin N. cos 86° N. sin 85° N. cos N. sin 84° 790 NATURAL SINES & COSINES. 6° mo 8° N. sin N. cos N. sin N. cos N. sin N. cos 0 10453 99452 12187 99255 13917 99027 60 1 10482 99449 12216 99251 13946 99023 59 10511 99446 12245 99248 13975 99019 58 3 10540 99443 12274 99244 14004 99015 57 4 10569 99440 12302 99240 14033 99011 56 5 10597 99437 12331 99237 14061 99006 55 6 10626 99434 12360 99233 14090 99002 54 7 10655 99431 12389 99230 14119 98998 53 8 10684 99428 12418 99226 14148 98994 52 9 10713 99424 12447 99222 14177 98990 51 10 10742 99421 12476 99219 14205 98986 50 11 10771 99418 12504 99215 14234 98982 49 12 10800 99415 12533 99211 14263 98978 48 13 10829 99412 12562 99208 14292 98973 47 14 10858 99409 12591 99204 14320 98969 46 15 10887 99406 12620 99200 14349 98965 45 16 10916 99402 12649 99197 14378 98961 44 17 10945 99399 12678 99193 14407 98957 43 18 10973 99396 12706 99189 14436 98953 42 19 11002 99393 12735 99186 14464 98948 41 20 11031 99390 12764 99182 14493 98944 40 21 11060 99386 12793 99178 14522 98940 39 22 11089 99383 12822 99175 14551 98936 38 23 11118 99380 12851 99171 14580 98931 37 24 11147 99377 12880 99167 14608 98927 36 25 11176 99374 12908 99163 14637 98923 35 26 11205 99370 12937 99160 14666 98919 34 27 11234 99367 12966 99156 14695 98914 33 28 11263 99364 12995 99152 14723 98910 32 29 11291 99360 13024 99148 14752 98906 31 30 11320 99357 13053 99144 14781 98902 30 31 11349 99354 13081 99141 14810 98897 29 32 11378 99351 13110 99137 14838 98893 28 33 11407 99347 13139 99133 14867 98889 27 34 11436 99344 13168 99129 14896 98884 26 35 11465 99341 13197 99125 14925 98880 25 36 11494 99337 13226 99122 14954 98876 24 37 11523 99334 13254 99118 14982 98871 23 38 11552 99331 13283 99114 15011 98867 22 39 11580 99327 13312 99110 15040 98863 21 40 11609 99324 13341 99106 15069 98858 20 41 11638 99320 13370 99102 15097 98854 19 42 11667 99317 13399 99098 15126 98849 18 43 11696 99314 13427 99094 15155 98845 17 44 11725 99310 13456 99091 15184 98841 16 45 11754 99307 13485 99087 15212 98836 15 46 11783 99303 13514 99083 15241 98832 14 1 47 11812 99300 13543 99079 15270 98827 13 48 11840 99297 13572 99075 15299 98823 12 49 11869 99293 13600 99071 15327 98818 11 50 11898 99290 13629 99067 15356 98814 10 51 11927 99286 13658 99063 15385 98809 9 52 11956 99283 13687 99059 15414 98805 8 53 11985 99279 13716 99055 15442 98800 54 12014 99276 13744 99051 15471 98796 6 55 12043 99272 13773 99047 15500 98791 5 56 12071 99269 13802 99043 15529 98787 4 57 12100 99265 13831 99039 15557 98782 3 58 12129 99262 13860 99035 15586 98778 2 59 12158 99258 13889 99031 15615 98773 1 60 12187 99255 13917 99027 15643 98769 0 N. cos N. sin N. cos N. sin N. cos 83° 82° N. sin 81° 1 NATURAL SINES & COSINES. 791 g⁰ 10° 11° ! N. sin N. cos N. sin N. cos N. sin N. cos 0 15643 98769 17365 98481 19081 98163 60 1 2 3 4 15672 98764 17393 98476 19109 98157 59 15701 98760 17422 98471 19138 98152 58 15730 98755 17451 98466 19167 98146 57 15758 98751 17479 98461 19195 98140 56 5 15787 98746 17508 98455 19224 98135 55 15816 98741 17537 98450 19252 98129 54 15845 98737 17565 98445 19281 98124 53 8 15873 98732 17594 98440 19309 98118 52 9 15902 98728 17623 98435 19338 98112 51 10 15931 98723 17651 98430 19366 98107 50 11 15959 98718 17680 98425 19395 98101 49 12 15988 98714 17708 98420 19423 98096 48 13 16017 98709 17737 98414 19452 98090 47 14 16046 98704 17766 98409 19481 98084 46 15 16074 98700 17794 98404 19509 98079 45 16 16103 98695 17823 98399 19538 98073 44 17 16132 98690 17852 98394 19566 98067 43 18 16160 98686 17880 98389 19595 98061 42 19 16189 98681 17909 98383 19623 98056 41 20 16218 98676 17937 98378 19652 98050 40 21 16246 98671 17966 98373 19680 98044 39 22 16275 98667 17995 98368 19709 98039 38 23 16304 98662 18023 98362 19737 98033 37 24 16333 98657 18052 98357 19766 98027 36 25 16361 98652 18081 98352 19794 98021 35 26 16390 98648 18109 98347 19823 98016 34 27 16419 98643 18138 98341 19851 98010 33 28 16447 98638 18166 98336 19880 98004 32 29 16476 98633 18195 98331 19908 97998 31 30 16505 98629 18224 98325 19937 97992 30 31 16533 98624 18252 98320 19965 97987 29 32 16562 98619 18281 98315 19994 97981 28 33 16591 98614 18309 98310 20022 97975 27 34 16620 98609 18338 98304 20051 97969 26 35 16648 98604 18367 98299 20079 97963 25 36 16677 98600 18395 98294 20108 97958 24 37 16706 98595 18424 98288 20136 97952 23 38 16734 98590 18452 98283 20165 97946 22 39 16763 98585 18481 98277 20193 97940 21 40 16792 98580 18509 98272 20222 97934 20 41 16820 98575 18538 98267 20250 97928 19 42 16849 98570 18567 98261 20279 97922 18 43 16878 98565 18595 98256 20307 97916 17 44 16906 98561 18624 98250 20336 97910 16 45 16935 98556 18652 98245 20364 97905 15 46 16964 98551 18681 98240 20393 97899 14 47 16992 98546 18710 98234 20421 97893 13 48 17021 98541 18738 98229 20450 97887 12 49 17050 98536 18767 98223 50 17078 98531 18795 98218 20478 20507 97875 97881 11 10 51 17107 98526 18824 98212 20535 97869 9 52 17136 98521 18852 98207 20563 97863 8 53 17164 98516 18881 98201 20592 97857 54 17193 98511 18910 98196 20620 97851 55 17222 98506 18938 98190 20649 97845 56 17250 98501 18967 98185 20677 97839 57 17279 98496 18995 98179 20706 97833 8888 58 17308 98491 19024 98174 20734 97827 59 17336 98486 19052 98168 20763 97821 60 17365 98481 19081 98163 20791 97815 3210 0 N. cos N. sin N. cos N. sin N. cos N. sin 80° *790 78° 792 NATURAL SINES & COSINES. 12° 1 13° 14° 1 N. sin N. cos N. sin N. cos N. sin❘ N. N. cos 0 20791 97815 22495 97437 24192 97030 60 1 20820 97809 22523 97430 24220 97023 59 2 20848 97803 22552 97424 24249 97015 58 3 20877 97797 22580 97417 24277 97008 57. 4 20905 97791 22608 97411 24305 97001 56 5 20933 97784 22637 97404 24333 96994 55 6 20962 97778 22665 97398 24362 96987 54 7 20990 97772 22693 97391 24390 96980 53. 8 21019 97766 22722 97384 24418 96973 52 9 21047 97760 22750 97378 24446 96966 51 10 21076 97754 22778 97371 24474 96959 50 11 21104 97748 22807 97365 24503 96952 49 12 21132 97742 22835 97358 24531 96945 48 13 21161 97735 22863 97351 24559 96937 47 14 21189 97729 22892 97345 24587 96930 46 15 21218 97723 22920 97338 24615 96923 45 16 21246 97717 22948 97331 24644 96916 44 17 21275 97711 22977 97325 24672 96909 18 21303 97705 23005 97318 24700 96902 21 22723*3 21331 97698 23033 97311 24728 96894 20 21360 97692 23062 97304 24756 96887 43 42 41 40 21388 97686 23090 97298 24784 96880 39 21417 97680 23118 97291 24813 96873 38 21445 97673 23146 97284 24841 96866 37 24 21474 97667 23175 97278 24869 96858 36 25 21502 97661 23203 97271 24897 96851 35 26 21530 97655 23231 97264 24925 96844 34 27 21559 97648 23260 97257 24953 96837 33 28 21587 97642 23288 97251 24982 96829 32 29 21616 97636 23316 97244 25010 96822 31 30 21644 97630 23345 97237 25038 96815 30 31 21672 97623 23373 97230 25066 96807 29 32 21701 97617 23401 97223 25094 96800 28 33 21729 97611 23429 97217 25122 96793 27 34 21758 97604 23458 97210 25151 96786 26 35 21786 97598 23486 97203 25179 96778 25 36 21814 97592 23514 97196 25207 96771 24 37 21843 97585 23542 97189 25235 96764 23 38 21871 97579 23571 97182 25263 96756 22 39 21899 97573 23599 97176 25291 96749 21 40 21928 97566 23627 97169 25320 96742 20 41 21956 97560 23656 97162 25348 96734 19 42 21985 97553 23684 97155 25376 96727 18 43 22013 97547 23712 97148 25404 96719 17 44 22041 97541 23740 97141 25432 96712 16 45 22070 97534 23769 97134 25460 96705 15 46 22098 97528 23797 97127 25488 96697 14 47 22126 97521 23825 97120 25516 96690 13 48 22155 97515 23853 97113 25545 96682 12 49 22183 97508 23882 97106 25573 96675 11 50 22212 97502 23910 97100 25601 96667 10 51 22240 97496 23938 97093 25629 96660 9 52 22268 97489 23966 97086 25657 96653 8 53 22297 97483 23995 97079 25685 96645 7 54 22325 97476 24023 97072 25713 96638 6 55 22353 97470 24051 97065 25741 96630 5 56 22382 97463 24079 97058 25769 96623 4 57 22410 97457 24108 97051 25798 96615 58 22438 97450 24136 97044 25826 96608 59 22467 97444 24164 97037 25854 60 22495 97437 24192 97030 25882 96600 96593 ~210 3 N. cos N. sin N. cos N. sin N. cos N. sin ryngo 76° 75° NATURAL SINES & COSINES. 793 15° 16° N. sin N. cos N. sin N. cos N. sin 170 N. cos 1 0123 4 25882 96593 27564 96126 29237 95630 60 25910 96585 27592 96118 29265 95622 59 25938 96578 27620 96110 29293 95613 58 25966 96570 27648 96102 29321 95605 57 25994 96562 27676 96094 29348 95596 56 5 26022 96555 27704 96086 29376 95588 55 6 26050 96547 27731 96078 29404 95579 54 789 26079 96540 27759 96070 29432 95571 53 26107 96532 27787 96062 29460 95562 52 26135 96524 27815 96054 29487 95554 51 10 26163 96517 27843 96046 29515 95545 50 11 26191 96509 27871 96037 29543 95536 49 12 26219 96502 27899 96029 29571 95528 48 13 26247 96494 27927 96021 29599 95519 47 14 26275 96486 27955 96013 29626 95511 46 15 26303 96479 27983 96005 29654 95502 45 16 26331 96471 28011 95997 29682 95493 44 17 26359 96463 28039 95989 29710 95485 43 18 26387 96456 28067 95981 29737 95476 42 19 26415 96448 28095 95972 29765 95467 41 20 26443 96440 28123 95964 29793 95459 40 21 26471 96433 28150 95956 29821 95450 39 22 26500 96425 28178 95948 29849 95441 38 23 26528 96417 28206 95940 29876 95433 37 24 26556 96410 28234 95931 29904 95424 36 25 26584 96402 28262 95923 29932 95415 35 26 26612 96394 28290 95915 29960 95407 34 27 26640 96386 28318 95907 29987 95398 33 28 26668 96379 28346 95898 30015 95389 32 29 26696 96371 28374 95890 30043 95380 31 30 26724 96363 28402 95882 30071 95372 30 31 26752 96355 28429 95874 30098 95363 29 32 26780 96347 28457 95865 30126 95354 28 33 26808 96340 28485 95857 30154 95345 27 34 26836 96332 28513 95849 30182 95337 26 35 26864 96324 28541 95841 30209 95328 25 36 26892 96316 28569 95832 30237 95319 24 37 26920 96308 28597 95824 30265 95310 23 38 26948 96301 28625 95816 30292 95301 22 39 26976 96293 28652 95807 30320 95293 21 40 27004 96285 28680 95799 30348 95284 20 41 27032 96277 28708 95791 30376 95275 19 42 27060 96269 28736 95782 30403 95266 18 43 27088 96261 28764 95774 30431 95257 17 44 27116 96253 28792 95766 30459 95248 16 45 27144 96246 28820 95757 30486 95240 15 46 27172 96238 28847 95749 30514 95231 14 47 27200 96230 28875 95740 30542 95222 13 48 27228 96222 28903 95732 30570 95213 12 49 27256 96214 28931 95724 30597 95204 11 50 27284 96206 28959 95715 30625 95195 10 51 27312 96198 28987 95707 30653 95186 9 52 27340 96190 29015 95698 30680 95177 8 53 27368 96182 29042 95690 30708 95168 7 54 27396 96174 29070 95681 30736 95159 6 55 27424 96166 29098 95673 30763 95150 5 56 27452 96158 29126 95664 30791 95142 4 57 27480 96150 29154 95656 30819 95133 3 8888 58 27508 96142 29182 95647 30846 95124 2 27536 96134 29209 95639 30874 95115 1 60 27564 96126 29237 95630 30902 95106 0 N. cos N. sin N. cos N. sin N. cos N. sin 74° 73° 72° 3 B 794 NATURAL SINES & COSINES. 18° 19° 20° N. sin N. cos N. sin N. cos N. sin N. cos OIQ3 4O7∞☹ 0 30902 95106 32557 94552 34202 93969 60 1 30929 95097 32584 94542 34229 93959 889 59 2 30957 95088 32612 94533 34257 93949 58 30985 95079 32639 94523 34284 93939 57 31012 95070 32667 94514 34311 93929 56 5 31040 95061 32694 94504 34339 93919 55 6 31068 95052 32722 94495 34366 93909 54 31095 95043 32749 94485 34393 93899 53 8 31123 95033 32777 94476 34421 93889 52 9 31151 95024 32804 94466 34448 93879 51 10 31178 95015 32832 94457 34475 93869 50 11 H23: 31206 95006 32859 94447 34503 93859 89 49 12 31233 94997 32887 94438 34530 93849 48 13 31261 94988 32914 94428 34557 93839 47 14 31289 94979 32942 94418 34584 93829 46 15 31316 94970 32969 94409 34612 93819 45 16 31344 94961 32997 94399 34639 93809 44 17 31372 94952 33024 94390 34666 93799 43 18 31399 94943 33051 94380 34694 93789 42 19 31427 94933 33079 94370 34721 93779 41 20 31454 94924 33106 94361 34748 93769 40 21 31482 94915 33134 94351 34775 93759 39 22 31510 94906 33161 94342 34803 93748 38 23 31537 94897 33189 94332 34830 93738 37 24 31565 94888 33216 94322 34857 93728 36 25 31593 94878 33244 94313 34884 93718 35 26 31620 94869 33271 94303 34912 93708 34 27 31648 94860 33298 94293 34939 93698 33 28 31675 94851 33326 94284 34966 93688 32 29 31703 94842 33353 94274 34993 93677 31 30 31730 94832 33381 94264 35021 93667 30 31 31758 94823 33408 94254 35048 93657 29 32 31786 94814 33436 94245 35075 93647 28 33 31813 94805 33463 94235 35102 93637 27 34 31841 94795 33490 94225 35130 93626 26 35 31868 94786 33518 94216 35157 93616 25 36 31896 94777 33545 94206 35184 93606 24 37 31923 94768 33573 94196 35211 93596 23 38 31951 94758 33600 94186 35239 93585 22 39 31979 94749 33627 94176 35266 93575 21 40 32006 94740 33655 94167 35293 93565 20 41 32034 94730 33682 94157 35320 93555 19 42 32061 94721 33710 94147 35347 93544 18 43 32089 94712 33737 94137 35375 93534 17 44 32116 94702 33764 94127 35402 93524 16 45 32144 94693 33792 94118 35429 93514 15 46 32171 94684 33819 94108 35456 93503 14 47 32199 94674 33846 94098 35484 93493 13 48 32227 94665 33874 94088 35511 93483 12 49 32254 94656 33901 94078 35538 93472 11 50 32282 94646 33929 94068 35565 93462 10 51 32309 94637 33956 94058 35592 93452 9 52 32337 94627 33983 94049 35619 93441 8 53 32364 94618 34011 94039 35647 93431 7 54 32392 94609 34038 94029 35674 93420 6 55 32419 94599 34065 94019 35701 93410 5 56 32447 94590 34093 94009 35728 93400 4 57 32474 94580 34120 93999 35755 93389 3 58 32502 94571 34147 93989 35782 93379 2 59 32529 94561 34175 93979 35810 93368 60 32557 94552 34202 93969 35837 93358 0 N. cos N. sin N. cos 71° N. sin 70° N. cos N. sin 69° NATURAL SINES & COSINES. 795 21° 22° 23° 1 N. sin N. cos N. sin N. cos N. sin N. cos 0123 + 35837 93358 37461 92718 39073 92050 60 35864 93348 37488 92707 39100 92039 59 35891 93337 37515 92697 39127 92028 58 35918 93327 37542 92686 39153 92016 57 35945 93316 37569 92675 39180 92005 56 5 35973 93306 37595 92664 39207 91994 55 6 36000 93295 37622 92653 39234 91982 54 7 36027 93285 37649 92642 39260 91971 53 8 36054 93274 37676 92631 39287 91959 52 9 36081 93264 37703 92620 39314 91948 51 10 36108 93253 37730 92609 39341 91936 50 11 36135 93243 37757 92598 39367 91925 49 12 36162 93232 37784 92587 39394 91914 48 13 36190 93222 37811 92576 39421 91902 47 14 36217 93211 37838 92565 39448 91891 46 15 36244 93201 37865 92554 39474 91879 45 16 36271 93190 37892 92543 39501 91868 44 17 36298 93180 37919 92532 39528 91856 43 18 36325 93169 37946 92521 39555 91845 42 19 36352 93159 37973 92510 39581 91833 41 20 36379 93148 37999 92499 39608 91822 40 21 36406 93137 38026 92488 39635 91810 39 22 36434 93127 38053 92477 39661 91799 38 23 36461 93116 38080 92466 39688 91787 37 24 36488 93106 38107 92455 39715 91775 36 25 36515 93095 38134 92444 39741 91764 35 26 36542 93084 38161 92432 39768 91752 34 27 36569 93074 38188 92421 39795 91741 33 28 36596 93063 38215 92410 39822 91729 32 29 36623 93052 38241 92399 39848 91718 31 30 36650 93042 38268 92388 39875 91706 30 31 36677 93031 38295 92377 · · 39902 91694 29 32 36704 93020 38322 92366 39928 91683 28 33 36731 93010 38349 92355 39955 91671 27 34 36758 92999 38376 92343 39982 91660 26 35 36785 92988 38403 92332 40008 91648 25 36 36812 92978 38430 92321 40035 91636 24 37 36839 92967 38456 92310 40062 91625 23 38 36867 92956 38483 92299 40088 91613 22 39 36894 92945 38510 92287 40115 91601 21 40 36921 92935 38537 92276 40141 91590 20 41 36948 92924 38564 92265 40168 91578 19 42 36975 92913 38591 92254 40195 91566 18 43 37002 92902 44 37029 92892 45 37056 92881 46 37083 92870 38617 92243 38644 92231 38671 92220 38698 92209 40221 91555 17 40248 91543 16 40275 91531 15 40301 91519 14 47 37110 92859 38725 92198 40328 91508 13 48 37137 92849 38752 49 37164 92838 38778 92186 92175 40381 40355 91496 91484 12 11 50 37191 92827 38805 92164 40408 91472 10 51 37218 92816 38832 92152 40434 91461 9 52 37245 92805 38859 92141 40461 91449 8 53 37272 92794 38886 92130 40488 91437 7 54 37299 92784 38912 92119 40514 91425 6 55 37326 92773 38939 92107 40541 91414 5 56 37353 92762 38966 92096 40567 91402 4 57 37380 92751 38993 92085 40594 91390 3 58 37407 92740 39020 92073 40621 91378 888 59 37434 92729 39046 92062 40647 91366 60 37461 92718 39073 92050 40674 91355 210 N. cos N. sin N. cos N. sin N. cos N. sin 68° 67° 66° 796 NATURAL SINES & COSINES. 24° 25° 26° N. sin N. cos N. sin N. cos N. sin N. cos 012345 40674 91355 42262 90631 43837 89879 60 40700 91343 42288 90618 43863 89867 59 40727 91331 42315 90606 43889 89854 58 40753 91319 42341 90594 43916 89841 57 40780 91307 42367 90582 43942 89828 56 40806 91295 42394 90569 43968 89816 55 6 40833 91283 42420 90557 43994 89803 54 40860 91272 42446 90545 44020 89790 53 8 40886 91260 42473 90532 44046 89777 52 9 40913 91248 42499 90520 44072 89764 51 10 40939 91236 42525 90507 44098 89752 50 11 40966 91224 42552 90495 44124 89739 49 12 40992 91212 42578 90483 44151 89726 48 13 41019 91200 42604 90470 44177 89713 47 14 41045 91188 42631 90458 44203 89700 46 15 41072 91176 42657 90446 44229 89687 45 16 41098 91164 42683 90433 44255 89674 44 17 41125 91152 42709 90421 44281 89662 43 18 41151 91140 42736 90408 44307 89649 42 19 41178 91128 42762 90396 44333 89636 41 20 41204 91116 42788 90383 44359 89623 40 21 41231 91104 42815 90371 44385 89610 39 22 41257 91092 42841 90358 44411 89597 38 23 41284 91080 42867 90346 44437 89584 37 24 41310 91068 42894 90334 44464 89571 36 25 41337 91056 42920 90321 44490 89558 35 26 41363 91044 42946 90309 44516 89545 34 27 41390 91032 42972 90296 44542 89532 33 28 41416 91020 42999 90284 44568 89519 32 29 41443 91008 43025 90271 44594 89506 31 30 41469 90996 43051 90259 44620 89493 30 31 41496 90984 * 43077 90246 44646 89480 29 32 41522 90972 43104 90233 44672 89467 28 33 41549 90960 43130 90221 44698 89454 27 34 41575 90948 43156 90208 44724 89441 26 35 41602 90936 43182 90196 44750 89428 25 36 41628 90924 43209 90183 44776 89415 24 37 41655 90911 43235 90171 44802 89402 23 38 41681 90899 43261 90158 44828 89389 22 39 41707 90887 43287 90146 44854 89376 21 40 41734 90875 43313 90133 44880 89363 20 41 41760 90863 43340 90120 44906 89350 19 42 41787 90851 43366 90108 44932 89337 18 43 41813 90839 43392 90095 44958 89324 17 44 41840 90826 43418 90082 44984 89311 16 45 41866 90814 43445 90070 45010 89298 15 46 41892 90802 43471 90057 45036 89285 14 47 41919 90790 43497 90045 45062 89272 13 48 41945 90778 43523 90032 45088 89259 12 49 41972 90766 43549 90019 45114 89245 11 50 41998 90753 43575 90007 45140 89232 10 51 42024 90741 43602 89994 45166 89219 52 42051 90729 43628 89981 45192 89206 8 53 42077 90717 43654 89968 45218 89193 7 54 42104 90704 43680 89956 45243 89180 6 55 42130 90692 43706 89943 45269 89167 5 56 42156 90680 43733 89930 45295 89153 4 57 42183 90668 43759 89918 45321 89140 3 58 42209 90655 43785 89905 45347 89127 59 42235 90643 43811 89892 45373 89114 60 42262 90631 43837 89879 45399 89101 210 0 N. cos N. sin N. cos N. sin N. cos N. sin 65° 64° 63° NATURAL SINES & COSINES. 797 27° 28° 29° N. sin N. cos N. sin N. cos N. sin N. cos 0 45399 89101 46947 88295 48481 87462 60 123 45425 89087 46973 88281 48506 87448 59 45451 89074 46999 88267 48532 87434 58 45477 89061 47024 88254 48557 87420 57 4 45503 89048 47050 88240 48583 87406 56 45529 89035 47076 88226 48608 87391 55 6 45554 89021 47101 88213 48634 87377 54 7 45580 89008 47127 88199 48659 87363 53 8 45606 88995 47153 88185 48684 87349 52 9 45632 88981 47178 88172 48710 87335 51 10 45658 88968 47204 88158 48735 87321 50 11 45684 88955 47229 88144 48761 87306 49 12 45710 88942 47255 88130 48786 87292 48 13 45736 88928 47281 88117 48811 87278 47 14 45762 88915 47306 88103 48837 87264 46 15 45787 88902 47332 88089 48862 87250 45 16 45813 88888 47358 88075 48888 87235 44 17 45839 88875 47383 88062 48913 87221 43 18 45865 88862 47409 88048 48938 87207 42 19 45891 88848 47434 88034 48964 87193 41 20 45917 88835 47460 88020 48989 87178 40 21 45942 88822 47486 88006 49014 87164 39 22 45968 88808 47511 87993 49040 87150 38 23 45994 88795 47537 87979 49065 87136 37 24 46020 88782 47562 87965 49090 87121 36 25 46046 88768 47588 87951 49116 87107 35 26 46072 88755 47614 87937 49141 87093 34 27 46097 88741 47639 87923 49166 87079 33 28 46123 88728 47665 87909 49192 87064 32 29 46149 88715 47690 87896 49217 87050 31 30 46175 88701 47716 87882 49242 87036 30 31 46201 88688 47741 87868 49268 87021 29 32 46226 88674 47767 87854 49293 87007 28 33 46252 88661 47793 87840 49318 86993 27 34 46278 88647 47818 87826 49344 86978 26 35 46304 88634 47844 87812 49369 86964 25 36 46330 88620 47869 87798 49394 86949 24 37 46355 88607 47895 87784 49419 86935 23 38 46381 88593 47920 87770 49445 86921 22 39 46407 88580 47946 87756 49470 86906 21 40 46433 88566 47971 87743 49495 86892 20 41 46458 88553 47997 87729 49521 86878 19 42 46484 88539 48022 87715 49546 86863 18 43 46510 88526 48048 87701 49571 86849 17 44 46536 88512 48073 87687 49596 86834 16 45 46561 88499 48099 87673 49622 86820 15 46 46587 88485 48124 87659 49647 86805 14 47 46613 88472 48150 87645 49672 86791 13 48 46639 88458 48175 87631 49 46664 88445 48201 87617 50 46690 88431 48226 87603 49697 86777 49723 86762 49748 86748 10 12 11 51 46716 88417 48252 87589 49773 86733 9 52 46742 88404 48277 87575 49798 86719 8 53 46767 88390 48303 87561 49824 86704 7 54 46793 88377 48328 87546 49849 86690 6 55 46819 88363 48354 87532 49874 86675 5 56 46844 88349 48379 87518 49899 86661 4 57 46870 88336 48405 87504 49924 86646 3 8888888 58 46896 88322 48430 87490 49950 86632 59 46921 88308 48456 87476 49975 60 46947 88295 48481 87462 50000 86617 86603 210 N. cos N. sin N. cos N. sin N. cos N. sin 62° 61° 60° 798 NATURAL SINES & COSINES. 30° 31° 32° 1 N. sin N. cos N. sin N. cos N. sin N. cos 0 50000 86603 51504 85717 52992 84805 60 1 50025 86588 51529 85702 53017 84789 59 2 50050 86573 51554 85687 53041 84774 58 3 50076 86559 51579 85672 53066 84759 57 4 50101 86544 51604 85657 53091 84743 56 5 50126 86530 51628 85642 53115 84728 55 6 50151 86515 51653 85627 53140 84712 54 7 50176 86501 51678 85612 53164 84697 53 8 50201 86486 51703 85597 53189 84681 52 9 50227 86471 51728 85582 53214 84666 51 10 50252 86457 51753 85567 53238 84650 50 11 50277 86442 51778 85551 53263 84635 49 12 50302 86427 51803 85536 53288 84619 48 13 50327 86413 51828 85521 53312 84604 47 14 50352 86398 51852 85506 53337 84588 46 15 50377 86384 51877 85491 53361 84573 45 16 50403 86369 51902 85476 53386 84557 44 17 50428 86354 51927 85461 53411 84542 43 18 50453 86340 51952 85446 53435 84526 42 19 50478 86325 51977 85431 53460 84511 41 20 50503 86310 52002 85416 53484 84495 40 21 50528 86295 52026 85401 53509 84480 39 22 50553 86281 52051 85385 53534 84464 38 23 50578 86266 52076 85370 53558 84448 37 24 50603 86251 52101 85355 53583 84433 36 25 50628 86237 52126 85340 53607 84417 35 26 50654 86222 52151 85325 53632 84402 34 27 50679 86207 52175 85310 53656 84386 38 28 50704 86192 52200 85294 53681 84370 32 29 50729 86178 52225 85279 53705 84355 31 30 50754 86163 52250 85264 53730 84339 30 31 50779 86148 52275 85249 53754 84324 29 32 50804 86133 52299 85234 53779 84308 28 33 50829 86119 52324 85218 53804 84292 27 34 50854 86104 52349 85203 53828 84277 26 35 50879 86089 52374 85188 53853 84261 25 36 50904 86074 52399 85173 53877 84245 24 37 50929 86059 52423 85157 53902 84230 23 38 50954 86045 52448 85142 53926 84214 22 39 50979 86030 52473 85127 53951 84198 21 40 51004 86015 52498 85112 53975 84182 20 41 51029 86000 52522 85096 54000 84167 19 42 51054 85985 52547 85081 54024 84151 18 43 51079 85970 52572 85066 54049 84135 17 44 51104 85956 52597 85051 54073 84120 16 45 51129 85941 52621 85035 54097 84104 15 46 51154 85926 52646 85020 54122 84088 14 47 51179 85911 52671 85005 54146 84072 13 48 51204 85896 52696 84989 54171 84057 12 49 51229 85881 52720 84974 54195 84041 11 50 51254 85866 52745 84959 54220 84025 10 51 51279 85851 52770 84943 54244 84009 9 52 51304 85836 52794 84928 54269 83994 8 53 51329 85821 52819 84913 54293 83978 17 54 51354 · 85806 52844 84897 54317 83962 55 51379 85792 52869 84882 54342 83946 5 56 51404 85777 52893 84866 54366 83930 4 57 51429 85762 52918 84851 54391 83915 58 888 51454 85747 52943 84836 54415 83899 59 51479 85732 52967 84820 54440 83883 60 51504 85717 52992 84805 54464 N. cos N. sin N. cos N. sin N. cos 83867 N. sin 3210 59° 58° 57° NATURAL SINES & COSINES. 799 33° 34° 35° N. sin N. cos N. sin N. cos N. sin N. cos 0 54464 83867 55919 82904 57358 81915 60 54488 83851 55943 82887 57381 81899 59 2 54513 83835 55968 82871 57405 81882 58 3 54537 83819 55992 82855 57429 81865 57 4 54561 83804 56016 82839 57453 81848 56 54586 83788 56040 82822 57477 81832 55 1 6 54610 83772 56064 82806 57501 81815 54 7 54635 83756 56088 82790 57524 81798 53 8 54659 83740 56112 82773 57548 81782 52 9 54683 83724 56136 82757 57572 81765 51 10 54708 83708 56160 82741 57596 81748 50 11 54732 83692 56184 82724 57619 81731 49 12 54756 83676 56208 82708 57643 81714 48 13 54781 83660 56232 82692 57667 81698 47 14 54805 83645 56256 82675 57691 81681 46 15 54829 83629 56280 82659 57715 81664 45 16 54854 83613 56305 82643 57738 81647 44 17 54878 83597 56329 82626 57762 81631 43 18 54902 83581 56353 82610 57786 81614 42 19 54927 83565 56377 82593 57810 81597 41 20 54951 83549 56401 82577 57833 81580 40 21 54975 83533 56425 82561 57857 81563 39 22 54999 83517 56449 82544 57881 81546 38 23 55024 83501 56473 82528 57904 81530 37 24 55048 83485 56497 82511 57928 81513 36 25 55072 83469 56521 82495 57952 81496 35 26 55097 83453 56545 82478 57976 81479 34 27 55121 83437 56569 82462 57999 81462 33 28 55145 83421 56593 82446 58023 81445 32 29 55169 83405 56617 82429 58047 81428 31 30 55194 83389 56641 82413 58070 81412 30 31 55218 83373 56665 82396 58094 81395 29 32 55242 83356 56689 82380 58118 81378 28 33 55266 83340 56713 82363 58141 81361 27 34 55291 83324 56736 82347 58165 81344 26 35 55315 83308 56760 82330 58189 81327 25 36 55339 83292 56784 82314 58212 81310 24 37 55363 83276 56808 82297 58236 81293 23 38 55388 83260 56832 82281 58260 81276 22 39 55412 83244 56856 82264 58283 81259 21 40 55436 83228 56880 82248 58307 81242 20 41 55460 83212 56904 82231 58330 81225 19 42 55484 83195 56928 82214 58354 81208 18 43 55509 83179 56952 82198 58378 81191 17 44 55533 83163 56976 82181 58401 81174 16 45 55557 83147 57000 82165 58425 81157 15 46 55581 83131 57024 82148 58449 81140 14 47 55605 83115 57047 82132 58472 81123 13 48 55630 83098 57071 82115 58496 81106 12 49 55654 83082 57095 82098 58519 81089 11 50 55678 83066 57119 82082 58543 81072 10 51 55702 83050 57143 82065 58567 81055 9 52 55726 83034 57167 82048 58590 81038 8 53 55750 83017 57191 82032 58614 81021 7 54 55775 83001 57215 82015 58637 81004 6 55 55799 82985 57238 81999 58661 80987 56 55823 82969 57262 81982 58684 80970 4 57 55847 82953 57286 81965 58708 80953 58 55871 82936 57310 81949 58731 80936 59 55895 82920 57334 81932 58755 80919 60 55919 82904 57358 81915 58779 N. cos N. sin N. cos 56° N. sin 55° N. cos 54° 80902 N. sin 3Q10 2 800 NATURAL SINES & COSINES. 36° 37° 38° N. sin N. cos N. sin N. cos N. sin N. cos 0 58779 80902 60182 79864 61.566 78801 60 1 58802 80885 60205 79846 61589 78783 59 2 58826 80867 60228 79829 61612 78765 58 3 58849 80850 60251 79811 61635 78747 57 58873 80833 60274 79793 61658 78729 56 5 58896 80816 60298 79776 61681 78711 55 6 58920 80799 60321 79758 61704 78694 54 58943 80782 60344 79741 61726 78676 53 8 58967 80765 60367 79723 61749 78658 52 9 58990 80748 60390 79706 61772 78640 51 10 59014 80730 60414 79688 61795 78622 50 11 59037 80713 60437 79671 61818 78604 49 12 59061 80696 60460 79653 61841 78586 48 13 59084 80679 60483 79635 61864 78568 47 14 59108 80662 60506 79618 61887 78550 46 15 59131 80644 60529 79600 61909 78532 45 16 59154 80627 60553 79583 61932 78514 44 17 59178 80610 60576 79565 61955 78496 43 18 59201 80593 60599 79547 61978 78478 42 19 59225 80576 60622 79530 62001 78460 41 20 59248 80558 60645 79512 62024 78442 40 21 59272 80541 60668 79494 62046 78424 39 *** 22 59295 80524 60691 79477 62069 78405 38 23 59318 80507 60714 79459 62092 78387 37 24 59342 80489 60738 79441 62115 78369 36 25 59365 80472 60761 79424 62138 78351 35 26 59389 80455 60784 79406 62160 78333 34 27 59412 80438 60807 79388 62183 78315 33 28 59436 80420 60830 79371 62206 78297 32 29 59459 80403 60853 79353 62229 78279 31 30 59482 80386 60876 79335 62251 78261 30 31 59506 80368 60899 79318 62274 78243 29 32 59529 80351 60922 79300 62297 78225 28 33 59552 80334 60945 79282 62320 78206 27 34 59576 80316 60968 79264 62342 78188 26 35 59599 80299 60991 79247 62365 78170 25 36 59622 80282 61015 79229 62388 78152 24 37 59646 80264 61038 79211 62411 78134 23 38 59669 80247 61061 79193 62433 78116 22 39 .59693 80230 61084 79176 62456 78098 21 40 59716 80212 61107 79158 62479 78079 20 41 59739 80195 61130 79140 62502 78061 19 42 59763 80178 61153 79122 62524 78043 18 43 59786 80160 61176 79105 62547 78025 17 44 59809 80143 61199 79087 62570 78007 16 45 59832 80125 61222 79069 62592 77988 15 46 59856 80108 61245 79051 62615 77970 14 47 59879 80091 61268 79033 62638 77952 13 48 59902 80073 61291 79016 62660 77934 12 49 59926 80056 61314 78998 62683 77916 11 50 59949 80038 61337 78980 62706 77897 10 51 59972 80021 61360 78962 62728 77879 9 52 59995 80003 61383 78944 62751 77861 8 53 60019 79986 61406 78926 62774 77843 54 60042 79968 61429 78908 62796 77824 6 55 60065 79951 61451 78891 62819 77806 5 56 60089 79934 61474 78873 62842 77788 4 5888 57 60112 79916 61497 78855 62864 77769 3 60135 79899 61520 78837 62887 77751 2 59 60158 79881 61543 78819 62909 77733 1 60 60182 79864 61566 78801 62932 77715 N. cos N. sin N. cos N. sin N. cos N. sin 53° 52° 51° NATURAL SINES & COSINES. 801 39° 40° 41° N. sin N. cos N. sin N. cos N. sin N. cos 0 62932 77715 64279 76604 65606 75471 60 1234 62955 77696 64301 76586 65628 75452 59 62977 77678 64323 76567 65650 75433 58 63000 77660 64346 76548 65672 75414 57 63022 77641 64368 76530 65694 75395 56 5 63045 77623 64390 76511 65716 75375 55 6 63068 77605 64412 76492 65738 75356 54 7 63090 77586 64435 76473 65759 75337 53 8 63113 77568 64457 76455 65781 75318 52 9 63135 77550 64479 76436 65803 75299 51 10 63158 77531 64501 76417 65825 75280 50 11 63180 77513 64524 76398 65847 75261 49 12 63203 77494 64546 76380 65869 75241 48 13 63225 77476 64568 76361 65891 75222 47 14 63248 77458 64590 76342 65913 75203 46 15 63271 77439 64612 76323 65935 75184 45 16 63293 77421 64635 76304 65956 75165 44 17 63316 77402 64657 76286 65978 75146 43 18 63338 77384 64679 76267 66000 75126 42 19 63361 77366 64701 76248 66022 75107 41 20 63383 77347 64723 76229 66044 75088 40 21 63406 77329 64746 76210 66066 75069 39 22 63428 77310 64768 76192 66088 75050 38 23 63451 77292 64790 76173 66109 75030 37 24 63473 77273 64812 76154 66131 75011 36 25 63496 77255 64834 76135 66153 74992 35 26 63518 77236 64856 76116 66175 74973 34 27 63540 77218 64878 76097 66197 74953 33 28 63563 77199 64901 76078 66218 74934 32 29 63585 77181 64923 76059 66240 74915 31 30 63608 77162 64945 76041 66262 74896 30 31 63630 77144 64967 76022 66284 74876 29 32 63653 77125 64989 76003 66306 74857 28 33 63675 77107 65011 75984 66327 74838 27 34 63698 77088 65033 75965 66349 74818 26 35 63720 77070 65055 75946 66371 74799 25 36 63742 77051 65077 75927 66393 74780 24 37 63765 77033 65100 75908 66414 74760 23 38 63787 77014 65122 75889 66436 74741 22 39 63810 76996 65144 75870 66458 74722 21 40 63832 76977 65166 75851 66480 74703 20 41 63854 76959 65188 75832 66501 74683 19 42 63877 76940 65210 75813 66523 74664 18 43 63899 76921 65232 75794 66545 74644 17 44 63922 76903 65254 75775 66566 74625 16 45 63944 76884 65276 75756 66588 74606 15 46 63966 76866 65298 75738 66610 74586 14 47 63989 76847 65320 75719 66632 74567 13 48 64011 76828 65342 75700 66653 74548 12 49 64033 76810 65364 75680 66675 74528 11 50 64056 76791 65386 75661 66697 74509 10 51 64078 76772 65408 75642 66718 74489 9 52 64100 76754 65430 75623 66740 74470 8 53 64123 76735 65452 75604 66762 74451 7 54 64145 76717 65474 75585 66783 74431 6 55 64167 76698 65496 75566 66805 74412 5 56 64190 76679 65518 75547 66827 74392 4 57 64212 76661 65540 75528 66848 74373 3 58 64234 76642 65562 75509 66870 74353 59 64256 76623 65584 75490 66891 74334 60 64279 76604 65606 75471 66913 74314 210 N. cos N. sin N. cos 50° N. sin 49° N. cos N. sin 48° 802 NATURAL SINES & COSINES. 42° 43° 44° / N. sin N. cos N. sin N. cos N. cos❘ N. sin N. cos 0 66913 74314 68200 73135 69466 71934 60 12345 66935 74295 68221 73116 69487 71914 899 59 66956 74276 68242 73096 69508 71894 58 66978 74256 68264 73076 69529 71873 57 66999 74237 68285 73056 69549 71853 56 67021 74217 68306 73036 69570 71833 55 67043 74198 68327 73016 69591 71813 54 7 67064 74178 68349 72996 69612 71792 53 8 67086 74159 68370 72976 69633 71772 52 9 67107 74139 68391 72957 69654 71752 51 10 67129 74120 68412 72937 69675 71732 50 11 67151 74100 68434 72917 69696 71711 49 12 67172 74080 68455 72897 69717 71691 48 13 67194 74061 68476 72877 69737 71671 47 14 67215 74041 68497 72857 69758 71650 46 15 67237 74022 68518 *72837 69779 71630 45 16 67258 74002 68539 72817 69800 71610 44 17 67280 73983 68561 72797 69821 71590 43 18 67301 73963 68582 72777 69842 71569 42 19 67323 73944 68603 72757 69862 71549 41 20 67344 73924 68624 72737 69883 71529 40 21 67366 73904 68645 72717 69904 71508 39 22 67387 73885 68666 72697 69925 71488 38 23 67409 73865 68688 72677 69946 71468 37 24 67430 73846 68709 72657 69966 71447 36 25 67452 73826 68730 72637 69987 71427 35 26 67473 73806 68751 72617 70008 71407 34 27 67495 73787 68772 72597 70029 71386 33 28 67516 73767 68793 72577 70049 71366 32 29 67538 73747 68814 72557 70070 71345 31 30 67559 73728 68835 72537 70091 71325 30 31 67580 73708 68857 72517 70112 71305 29 32 67602 73688 68878 72497 70132 71284 28 33 67623 73669 68899 72477 70153 71264 27 34 67645 73649 68920 72457 70174 71243 26 35 67666 73629 68941 72437 70195 71223 25 36 67688 73610 68962 72417 70215 71203 24 37 67709 73590 68983 72397 70236 71182 23 38 67730 73570 69004 72377 70257 71162 22 39 67752 73551 69025 72357 70277 71141 21 40 67773 73531 69046 72337 *70298 *71121 20 41 67795 73511 69067 72317 70319 71100 19 42 67816 73491 69088 72297 70339 71080 18 43 67837 73472 69109 72277 70360 71059 17 44 67859 73452 69130 72257 70381 71039 16 45 67880 73432 69151 72236 70401 71019 15 46 67901 73413 69172 72216 70422 70998 14 47 67923 73393 69193 72196 70443 70978 13 48 67944 73373 69214 72176 70463 70957 12 49 67965 73353 69235 72156 70484 70937 11 50 67987 73333 69256 72136 70505 70916 10 51 68008 73314 69277 72116 70525 70896 9 52 68029 73294 69298 72095 70546 70875 53 68051 73274 69319 72075 70567 70855 54 68072 73254 69340 72055 70587 70834 55 68093 73234 69361 72035 70608 70813 56 68115 73215 69382 72015 70628 70793 4 57 68136 73195 69403 71995 70649 70772 3 58 68157 73175 69424 71974 70670 70752 2 59 68179 73155 69445 71954 70690 70731 1 60 68200 73135 69466 71934 70711 70711 0 / N. cos N. sin N. cos N. sin N. cos N. sin 47° 46° 45° TABLES FOR REDUCING LINKS INTO FEET. 803 Links. Feet. Links. Feet. Links. Feet. Links. Feet. 1234 •66 61 40.26 121 79.86 181 119.46 1.32 62 40.92 122 80.52 182 120.12 1.98 63 41.58 123 81.18 183 120.78 2.64 64 42.24 124 81.84 184 121.44 5 3.30 65 42.90 125 82.50 185 122.10 6 3.96 66 43.56 126 83.16 186 122.76 7 4.62 67 44.22 127 83.82 187 123.42 5.28 68 44.88 128 84.48 188 124.08 9 5.94 69 45.54 129 85.14 189 124.74 10 6.60 70 46.20 130 85.80 190 125.40 11 7.26 71 46.86 131 86.46 191 126.06 12 7.92 72 47.52 132 87.12 192 126.72 13 8.58 73 48.18 133 87.78 193 127.38 14 9.24 74 48.84 134 88.44 194 128.04 15 9.90 75 49.50 135 89.10 195 128.70 16 10.56 76 50.16 136 89.76 196 129.36 17 11.22 77 50.82 137 90.42 197 130-02 18 11.88 78 51.48 138 91.08 198 130.68 19 12.54 79 52.14 139 91.74 199 131.34 20 13.20 80 52.80 140 92.40 200 132.00 21 13.86 81 53.46 141 93.06 201 132.66 22 14.52 82 54.12 142 93.72 202 133.32 23 15.18 83 54.78 143 94.38 203 133.98 24 15.84 84 55.44 144 95.04 204 134.64 25 16.50 85 56.10 145 95.70 205 135.30 26 17.16 86 56.76 146 96.36 206 135.96 27 17.82 87 57.42 147 97.02 207 136.62 28 18.48 88 58.08 148 97.68 208 137.28 29 19.14 89 58.74 149 98.34 209 137.94 30 19.80 90 59.40 150 99.00 210 138.60 31 20.46 91 60.06 151 99.66 211 139.26 32 21.12 92 33 21.78 93 34 22.44 94 60.72 152 61.38 153 62.04 154 100.32 212 139.92 100.98 213 140.58 101.64 214 141.24 35 23.10 95 62.70 155 102.30 215 141.90 36 23.76 96 63.36 156 102.96 216 142.56 37 24.42 97 64.02 157 103.62 217 143.22 38 25.08 98 64.68 158 104.28 218 143.88 39 25.74 99 65.34 159 104.94 219 144.54 40 26.40 100 66.00 160 105.60 220 145.20 41 27.06 101 66.66 161 106.26 221 145.86 42 27.72 102 67.32 162 106.92 222 146.52 43 28.38 103 67.98 163 107.58 223 147.18 44 29.04 104 68.64 164 108.24 224 147.84 45 29.70 105 69.30 165 108.90 225 148.50 46 30.36 106 69.96 166 109.56 226 149.16 47 31.02 107 70.62 167 110.22 227 149.82 48 31.68 108 71-28 168 110.88 228 150.48 49 32.34 109 71.94 50 33.00 110 72.60 169 170 111.54 229 151.14 112.20 230 151.80 51 33.66 111 73.26 171 112.86 231 152.46 52 34.32 112 73.92 172 113.52 232 153.12 53 34.98 113 74.58 173 114.18 233 153.78 54 35.64 114 75.24 174 114.84 234 154.44 55 36.30 115 75.90 175 115.50 235 155.10 56 36.96 116 76.56 176 116.16 236 155.76 57 37.62 117 77.22 177 116.82 237 156.42 58 38.28 118 77.88 178 117.48 238 157.08 59 38.94 119 78.54 179 118·14 239 157.74 60 39.60 120 79.20 180 118.80 240 158.40 804 TABLES FOR REDUCING LINKS INTO FEET. Links. Feet. Links. Feet. Links. Feet. Links. Feet. 241 159.06 301 198.66 361 238.26 421 277.86 242 159.72 302 199-32 362 238.92 422 278-52 243 160.38 303 199-98 363 239.58 423 279.18 244 161.04 304 200.64 364 240.24 424 279.84 245 161.70 305 201.30 365 240.90 425 280-50 246 162.36 306 201.96 366 241.56 426 281.16 247 163.02 307 202.62 367 242.22 427 281.82 248 163.68 308 203.28 368 242.88 428 282.48 249 164.34 309 203.94 369 243.54 429 283.14 250 165.00 310 204.60 370 244.20 430 283.80 251 165.66 311 205.26 371 244.86 431 284.46 252 166.32 312 205.92 372 245.52 432 285.12 253 166.98 313 206.58 373 246.18 433 285.78 254 167.64 314 207.24 374 246.84 434 286.44 255 168.30 315 207.90 375 247.50 435 287.10 256 168.96 316 208.56 376 248.16 436 287.76 257 169.62 317 209.22 377 248.82 437 288.42 258 170.28 318 209.88 378 249.48 438 289.08 259 170.94 319 210.54 379 250.14 439 289.74 260 171.60 320 211.20 380 250-80 440 290-40 261 172.26 321 211.86 381 251.46 441 291.06 262 263 266 172.92 322 212.54 173.58 323 264 174.24 324 265 174.90 325 175.56 326 382 252.12 442 291.72 213.18 383 252.78 443 292.38 213.84 384 253.44 444 293.04 214.50 385 254.10 445 293-70 215.16 386 254.76 446 294.36 267 176.22 327 215.82 387 255.42 447 295.02 268 176.88 328 216.48 388 256.08 448 295.68 269 177.54 329 217.14 389 256.74 449 296.34 270 178.20 330 217.80 390 257.40 450 297.00 271 178.86 331 218.46 391 258.06 451 297.66 272 179-52 332 219.12 392 258.72 452 298-32 273 180.18 333 219.78 393 259.38 453 298.98 274 180.84 334 220.44 394 260.04 4.54 299.64 275 181.50 335 221.10 395 260.70 455 300-30 276 182.16 336 221.76 396 261.36 456 300-96 277 182.82 337 222.42 397 262.02 457 301.62 278 183.48 338 223.08 398 262-68 458 302.28 279 184.14 339 223.74 399 263.34 459 302.94 280 184.80 340 224-40 400 264.00 460 303.60 281 185.46 341 225.06 401 264.66 461 304.26 282 186.12 342 283 186.78 343 284 187.44 344 285 188.10 345 225.72 402 265.32 462 304.92 226.38 403 265.98 463 305.58 227.04 404 266.64 464 306.24 227.70 405 267.30 465 306.90 286 188-76 346 228.36 406 267.96 466 307.56 287 189.42 347 229.02 407 268.62 467 308-22 288 190.08 348 229.68 408 269.28 468 308-88 289 190.74 349 230.34 409 269.94 469 309.54 290 191.40 350 291 192.06 351 292 192.72 352 293 193.38 353 294 194.04 354 295 194.70 355 296 195.36 356 297 196.02 357 298 196.68 358 231.00 410 231.66 411 271.26 232.32 412 271.92 232.98 413 233.64 414 270-60 470 310-20 471 310-86 472 311.52 272.58 473 312.18 273.24 474 312.84 234.30 415 273.90 475 313.50 234.96 416 274.56 476 314.16 235.62 417 275.22 477 314.82 236.28 418 275.88 478 315.48 299 197.34 359 300 236.94 419 276.54 479 316.14 198.00 360 237.60 420 277-20 480 316.80 TABLES FOR REDUCING LINKS INTO FEET. 805 Links. Feet. Links. Feet. Links. Feet. Links. Feet. 481 317.46 541 357.06 601 396.66 661 436.26 482 318.12 542 357.72 602 397.32 662 436.92 483 318-78 543 358-38 603 397.98 663 437.58 484 319.44 544 359.04 604 398.64 664 438.24 485 320.10 545 359-70 605 399.30 665 438.90 486 320.76 546 360.36 606 399.96 666 439.56 487 321.42 547 361.02 607 400.62 667 440.22 488 322.08 548 361.68 608 401.28 668 440.88 489 322.74 549 362.34 609 401.94 669 441.54 490 323.40 550 363.00 610 402.60 670 442.20 491 324.06 551 363.66 611 403.26 671 442.86 492 324.72 552 364.32 612 403.92 672 443.52 493 325.38 553 364.98 613 404.58 673 444.18 494 326.04 554 365.64 614 405.24 674 444.84 495 326.70 555 366.30 615 405.90 675 445.50 496 327.36 556 366.96 616 406.56 676 446.16 497 328.02 557 367.62 617 407.22 677 446.82 498 328.68 558 368-28 618 407.88 678 447.48 499 329-34 559 368.94 619 408.54 679 448.14 500 330.00 560 369-60 620 409.20 680 448.80 501 330-66 561 370.26 621 409.86 681 449.46 502 331-32 562 370.92 622 410.52 682 450-12 504 503 331.98 563 332.64 564 371.58 623 411.18 683 450.78 372.24 624 411.84 684 451.44 505 333.30 565 372.90 625 412.50 685 452.10 506 333.96 566 373.56 626 413.16 686 452.76 507 334.62 567 374.22 627 413.82 687 453.42 508 335.28 568 374.88 628 414.48 688 454.08 509 335.94 569 375.54 629 415.14 689 454.74 510 336-60 570 376-20 630 415.80 690 455.40 511 337.26 571 376.86 631 512 337.92 572 377-52 513 338.58 573 378.18 416.46 691 456.06 632 417.12 692 456.72 633 417.78 693 457.38 514 339.24 574 515 339.90 575 379.50 516 340.56 576 378.84 634 418.44 694 458.04 635 419.10 695 458.70 380.16 636 419.76 696 459.36 517 341.22 577 380.82 637 420.42 697 460.02 518 341.88 578 381.48 638 421.08 698 460.68 519 342.54 579 520 343.20 580 382.80 640 521 343.86 581 383.46 641 522 344.52 582 384.12 642 523 345.18 583 384-78 643 524 345.84 584 385.44 644 525 346-50 585 386.10 526 347.16 586 386-76 646 527 347.82 587 528 348-48 588 388-08 529 349-14 589 388.74 530 349.80 590 389.40 650 531 350.46 591 390.06 651 429.66 711 532 351.12 592 390.72 652 430.32 533 351.78 593 391.38 653 430.98 534 352.44 594 392.04 654 535 353.10 595 392.70 655 536 353.76 596 393.36 656 537 354.42 597 538 355.08 598 539 355.74 599 540 356.40 600 382.14 639 421.74 699 461.34 422.40 700 462-00 423.06 701 462.66 423.72 702 463.32 424.38 703 463.98 425.04 704 464.64 645 425.70 705 465-30 426.36 706 465.96 387.42 647 427.02 707 466.62 648 427.68 708 467-28 649 428.34 709 467.94 429.00 710 468.60 469.26 712 469.92 713 470.58 431.64 714 471.24 432.30 715 471.90 432.96 716 472.56 394.02 657 394.68 658 395.34 659 433.62 717 473.22 434.28 718 473.88 434.94 719 474.54 396.00 660 435.60 720 475.20 806 TABLES FOR REDUCING LINKS INTO FEET. Links. Feet. Links. Feet. Links. Feet. Links. Feet. 721 475.86 781 515.46 841 555.06 901 594.66 722 476.52 782 516.12 842 555.72 902 595.32 723 477-18 783 516.78 843 556.38 903 595.98 724 477.84 784 725 478-50 517.44 844 557.04 904 596.64 785 518.10 845 557.70 905 597-30 726 479.16 786 518.76 846 558.36 906 597.96 727 479.82 787 519.42 847 559.02 907 598.62 728 480.48 788 520.08 848 559.68 908 599.28 729' 481.14 789 520.74 849 560.34 909 599.94 730 481.80 790 521.40 850 561.00 910 600-60 731 482.46 791 522.06 851 561.66 911 601.26 732 483.12 792 522.72 852 562.32 912 601.92 733 483-78 793 523.38 853 562.98 913 602.58 734 484.44 794 735 485.10 795 524.04 524.70 855 854 563.64 914 603.24 564.30 915 603.90 736 485.76 796 525.36 856 564.96 916 604.56 737 486.42 797 526.02 857 565.62 917 605.22 738 487.08 798 526.68 858 566.28 918 605.88 739 487.74 799 527.34 859 566-94 919 606.54 740 488.40 800 528.00 860 567.60 920 607.20 741 489.06 801 528.66 861 568-26 921 607.86 742 489.72 802 529.32 862 568.92 922 608.52 743 490.38 803 529.98 863 569.58 923 609.18 744 491.04 804 530.64 864 570-24 924 609.84 745 491.70 805 531.30 865 570-90 925 610.50 746 492.36 806 531.96 866 571.56 926 611.16 747 493.02 807 532.62 867 572.22 927 611.82 748 493.68 808 533.28 868 572-88 928 612.48 749 494.34 809 533.94 869 573.54 929 613.14 750 495.00 810 534.60 870 574-20 930 613.80 751 495.66 811 535.26 871 574-86 931 614.46 752 496.32 812 535.92 872 575.52 932 615.12 753 496.98 813 536.58 873 576-18 933 615.78 759 760 754 497.64 755 498.30 815 756 498.96 816 538.56 757 499.62 817 539.22 877 758 500-28 818 539.88 878 500.94 819 540.54 879 501.60 820 541.20 880 814 537.24 874 576.84 934 616.44 537.90 875 577.50 935 617-10 876 578.16 936 617.76 578.82 937 618.42 579.48 938 619.08 580.14 939 619.74 580.80 940 620.40 761 502.26 821 762 502.92 822 763 503-58 823 541.86 881 542.52 882 543.18 883 581.46 941 621.06 582.12 942 621.72 582.78 943 622.38 764 504.24 824 543.84 884 583.44 944 623.04 765 504.90 825 544.50 885 584.10 945 623.70 766 505.56 826 545.16 886 584.76 946 624.36 767 506.22 827 545.82 887 585.42 947 625.02 768 506.88 828 546.48 888 586.08 948 625.68 769 507-54 829 770 508.20 830 547.14 889 586.74 949 626.34 547.80 890 587-40 950 627.00 771 508.86 831 548.46 891 588.06 951 627.66 772 509.52 832 549.12 892 588.72 952 628.32 773 510.18 833 549.78 893 589.38 953 628.98 774 510.84 834 550.44 894 590-04 954 629.64 775 511.50 835 551.10 895 590-70 955 630.30 776 512.16 836 551.76 896 591.36 956 630.96 777 512.82 837 552.42 897 592.02 957 631.62 778 513-48 838 553.08 898 779 514.14 839 553.74 899 780 514.80 840 554.40 900 592.68 958 632.28 593.34 959 632.94 594.00 960 633.60 DECIMALS OF A POUND STERLING. 807 1/3 062 2/6 125 3/9 187 5/0 25 D 1·001 ⚫002 2003 6/3 312 7/6 375 1.064 065 2.066 1.126 127 2.128 1.189 1.251 •19 3.191 4.252 2.253 1 .004 4 067 7129 10 192 • 1 .254 1.005 1.006 3.007 ساهر من انت اهر 1.068 3.069 1.13 193 1.255 1.314 315 2.316 4 317 1.318 4.376 8/9 437 1.439 ·377 •44 378 2·441 • 7 379 10 ·442 1.38 1.443 •131 3.194 •256 ·319 1.381 444 3.07 •132 2.195 3.257 2.32 3.382 445 HEINKE 2 .008 5 071 1.009 3.01 3.011 3 ⚫012 8 ·133 11 196 2 .258 5 .321 8 .383 11 446 1.072 1.134 •134 197 1.259 1.322 •384 1.447 073 135 198 26 ·323 2.385 •448 2.074 2.136 199 261 3.324 .386 449 6 .075 9 137 4/0 2 3 .262 6 325 9 387 1.014 Ha 3·015 3.016 1.076 1.077 3.078 9/0 45 1.139 201 1.264 1.326 1.389 1.451 3.14 2.202 -265 -327 •39 .452 2.141 2.203 3.266 ·328 2.391 4 017 2.453 7 079 10 ·142 1 .204 4 +267 7329 10 ·392 1 •454 2018 1.08 •143 1.205 1.268 1.33 1.393 019 1.081 •144 206 .269 331 .394 3.02 2.082 3.145 2.207 2.27 2.332 2395 1.455 456 3.457 5 021 8 .083 11 146 2 .208 5 271 8 .333 11 396 141分24 1.022 1.023 3.024 6 ·025 2 .458 1.084 1·147 1.209 1.272 1.334 1.397 1.459 1.085 ∙148 3.21 1.273 3.086 3.149 3.211 3.274 •335 2.336 .398 2.399 46 2.461 9 087 3/0 ·15 3 .212 6 275 9 337 8/0 •4 3 -462 1.026 1.089 151 1.214 1.276 1.339 ·027 ·09 152 215 •277 $.028 3.091 ·153 77-029 10 092 1 154 2.216 4 ·217 3.278 1.34 2.341 नमनाला 1.401 1.464 402 •465 •403 2.466 7 279 10 ·342 1 404 4 .467 1.03 1.093 1.155 +218 1.28 1.343 ·031 094 •156 219 1.281 3.344 3.032 2.095 2.157 3.22 3.282 3.345 1.405 406 2·407 -468 -469 •47 8 033 11 096 2 158 5 -221 8 283 11 346 2 .408 5 -471 1.034 1.097 1.159 1.222 1.284 1.347 1.409 1·035 ·098 1.16 .223 -285 3.036 099 161 3.224 3.286 2/0 1 HH|GKAH 9 037 1.039 ·04 $.041 10 ·042 1 104 4 167 3 .162 6 .225 9 287 348 2.349 7/0 35 41 2.411 3 ·412 4.101 1.164 1.226 1.289 1.351 1.414 1.472 •473 2.474 6 .475 2.476 1.102 165 227 1.29 352 3.103 166 228 1.291 2.353 415 2.416 7 .229 10 ·292 1 .354 4 ·417 ··477 2.478 7479 1.043 1.105 2.168 1.23 1.044 •106 •169 231 3.045 2.107 3.17 232 IPWNUPH 1.293 1.355 • •294 356 295 -357 1.418 •419 $.42 1.48 •481 .482 11 046 1.047 1.048 $.049 2 108 1.109 ∙110 2.111 5 171 8 233 11 296 2 .358 5 421 8 483 1.172 173 2.174 4.234 1.297 1.359 1.422 1.484 •235 .298 •36 423 236 3.299 •361 •424 1/0 -05 •485 2.486 3 112 6 175 9 237 6/03 3 .362 6 .425 9 .487 1.051 1.114 1.176 1.239 4.301 1.364 1.052 1.426 1.489 •115 177 .24 •302 ·365 427 053 1 •054 2.116 4 117 3178 7179 2.241 10 242 303 2.366 3.428 1 •304 4 .367 7429 PKNUPL 1·055 118 49 2.491 10 -492 2.18 1.243 1.056 119 181 ·057 •12 2.182 ·244 2.245 1.305 ·306 368 1.43 1.493 369 2.307 2.37 •431 3.432 1.494 2 .058 5 121 8. 183 11 246 2 '308 5 .371 8 •433 2.059 2.495 11 496 4.122 184 1.247 1.309 1.372 3.06 1.123 185 1.248 31 2.061 2.124 ·186 3.249 4.311 373 4.374 1.434 435 2.436 1.497 498 3.499 808 DECIMALS OF A POUND STERLING. • 10/0.5 11/3 11/3 562 12/6 625|13/9 687 15/0 75 16/3 812 17/6 875 18/9 937 1.501 · 1.502 503 1.564 565 2.566 +626 •627 1.689 •69 1.751 1.752 814 1.815 1.876 877 1.939 94 2.628 691 3.753 1 -504 4 567 816 2.878 77629 941 10 ·692 1 754 1.505 4 817 7879 568 4.63 10 942 1.693 1.506 1.755 .569 1.818 631 694 1.756 • 3.507 2.57 819 1.88 1·881 1.943 .632 · 944 695 2.757 3.82 < ⚫882 2.945 2 .508 5 .571 8 .633 11 -696 2 758 5 .821 509 4.572 1.634 4.697 1.759 3.51 1.822 573 635 ·698 3.76 823 2.511 8. 883 11 ·946 1.884 885 1.947 2.574 3.636 .948 ⚫699 1.761 3 512 6 .575 4.824 .886 9 637 14/07 3.9.9 3 .762 1.514 6 .825 1.576 639 1.701 9 887 19/0 95 515 1.764 1.826 2.577 1.889 951 ·64 1.702 .765 2.516 827 89 2.578 952 2.641 2.703 2.766 2.828 891 953 4 .517 7.579 10 ·642 1 704 4 .767 7-829 1.518 1.58 10 ·892 1.643 1 .954 1.705 •519 1.768 581 2.644 1.83 1.893 1.955 1.706 •706 .769 •831 .52 894 2.582 2.645 .956 $707 2-77 ⚫832 5 .521 8 .583 2.895 11 646 957 2 708 5 771 522 8 .833 11 -896 1.584 1.647 2 ·958 1.709 1.772 523 2585 1.834 1.897 •648 1.71 773 2.524 2.586 •649 711 774 835 2.836 1.898 1.959 .96 899 3.961 6 .525 9 587 13/0 65 3 712 6 775 4.526 1.589 1.651 9 837 18/0 .9 3 .962 4.714 1.527 1.776 1.839 1.59 1.901 .652 1.964 •964 715 3.528 * ·529 2.591 2·653 2.716 -777 2.778 2.84 1.902 .965 10 ·592 2.841 3.903 1 654 2.966 4 717 1.53 1.593 1.655 718 7 779 1.78 10 ⚫842 1 904 4 ·967 531 1.843 1.905 •594 •656 1.968 719 1.781 532 1.844 .906 -595 969 .657 2.72 782 .845 2.907 2.97 8. 533 11 ·596 2 ·658 5 721 8 783 1.534 11 ⚫846 1.597 2 .908 5 .971 659 722 .535 1.784 •598 1.847 66 723 .785 2.536 2.599 1.848 1.909 .91 4.972 2.661 .724 9 537 12/0 6 2.786 849 3.911 3 662 973 2.974 6 725 1.539 1.601 9 787 17/0·85 3 .912 6 .975 3.54 .602 2.541 603 1.664 665 4.666 726 789 1.851 1.914 .976 1.727 •727 1.79 1.852 .915 977 1.728 4.791 3.853 .916 .978 10 ·542 1 .604 4 .667 1.543 1.605 •668 •544 7 -729 1.73 10 ·792 1 ·854 4 917 7.979 •606 1.793 1.855 1.918 669 1.98 731 2.545 3.794 .856 919 607 981 2.67 11 546 2 ·608 5 -671 4.732 8 733 3.795 2.857 .92 3.982 1.547 1.609 11 -796 2 .858 5 921 3.548 ·61 .549 -611 नमनोबलम 1.672 8 .983 1.734 1.797 1.859 1.922 673 1.984 ·735 3.798 86 .923 •674 -985 2.736 2.799 861 924 .986 11/0 •55 1.551 1.552 2.553 3 .612 1.614 •615 2.616 6 ·675 1.676 ⚫677 9 737 16/08 3 .862 6 .925 9 ·987 1.739 1.801 1.864 3.74 802 865 1.926 .927 989 2.678 1 -554 2.741 4 •617 2.803 2.866 77 679 2.928 10 742 1.555 1.618 1 ·804 4 .867 -929 68 -99 2.991 10 -992 1.743 556 .619 1.805 1.868 681 1.93 •993 4.744 2.557 62 *682 2.745 2 -558 5 -621 806 2.807 1.869 931 2.87 932 8 .683 ⚫994 2.995 11 746 2.559 1.622 2 .808 5 871 8 .933 11 -996 1.684 1.747 3.56 1.623 1.809 1.685 748 2.561 .81 1.872 873 1.934 ·935 624 $.686 2.749 3.811 .874 $.936 1.997 • 998 2.999 STAMP DUTIES. 809 CHAPTER XXIV. STAMP LAWS RECENTLY PASSED In relation to the Duties for the several purposes of Trade, and for the Con- veyance and Disposal of Property, together with the Duties on Imports. AN ACT TO AMEND THE LAWS RELATING TO STAMP DUTIES. FROM and after the tenth day of October one thousand eight hundred and fifty-three the several stamp duties now payable in Great Britain and Ireland respectively, under or by virtue of any Act or Acts of Parliament for or in respect of the several instruments, matters, and things men- tioned or described (otherwise than by way of exception) in the schedule to this act annexed, and whereon other duties are by this act granted, shall respectively cease and determine, and shall be and the same are hereby repealed; and in lieu and instead thereof there shall be granted, raised, levied, collected, and paid in and throughout the United Kingdom of Great Britain and Ireland, for and in respect of things described in the said schedule, or for or in respect of the vellum, parchment, or paper upon which any of them respectively shall be written, the several duties or sums of money set down in figures against the same respectively, or otherwise specified and set forth in the said schedule, which said schedule, and the several provisions, regulations, directions and exemptions therein con- tained with respect to the said duties, and the instruments, matters, and things charged therewith or exempted therefrom shall be deemed and taken to be part of this act, and shall be applied, observed, and put in exe- cution accordingly: Provided always, that nothing herein contained shall extend to repeal or alter any of the said stamp duties now payable in re- lation to any deed or instrument which shall have been signed or executed by any party thereto, or which shall bear date before or upon the tenth day of October one thousand eight hundred and fifty-three. Stamps for drafts. The duties of one penny by this act granted on receipts and on drafts or orders for the payment of money respectively may receipts and be denoted either by a stamp impressed upon the paper whereon. any such instrument is written or by an adhesive stamp affixed thereto, and the Commissioners of Inland Revenue shall provide stamps of both descrip- tions for the purpose of denoting the said duties. In any case where an adhesive stamp shall be used for the purpose aforesaid on any receipt or upon any draft or order respectively charge- able with the duty of, one penny by this act, the person by whom such receipt shall be given or such draft or order signed or made shall, before the instrument shall be delivered out of his hands, custody, or power, can- cel or obliterate the stamp so used, by writing thereon his name or the initial letters of his name so and in such a manner as to show clearly and distinctly that such stamp has been made use of, and so that the same may not be again used; and if any person who shall write or give any such receipt or discharge or make or sign any such draft or order with any 3 C 810 STAMP DUTIES. Penalty for adhesive stamp thereon, shall not bonâ fide in manner aforesaid effectually cancel or obliterate such stamp, he shall forfeit the sum of ten pounds. If any person shall fraudulently get off or remove, or cause or committing procure to be gotten off or removed, from any paper whereon frauds. any receipt or any draft or order shall be written, any adhesive stamp, or if any person shall affix or use any such stamp which shall have been gotten off or removed from any paper whereon any receipt or any draft or order shall have been written, to or for any receipt, draft, or order, or any paper whereon any such receipt, draft, or order shall be or be intended to be written; or if any person shall do or practise, or be con- cerned in any fraudulent act, contrivance, or device whatever, not specially provided for by this or some other Act of Parliament, with intent or de- sign to defraud Her Majesty of any duty by this act granted upon receipts or upon drafts or orders, every person so offending in any of the said several cases shall forfeit the sum of twenty pounds. For better securing the stamp duties by law chargeable on policies of insurance upon lives, and for preventing frauds in respect of any such insurances : Stamps for policy of insurances. Every person who shall make or agree to make, or shall re- ceive any premium or valuable consideration for making, any assurance or insurance upon any life or lives, or upon any event or contingency relating to or depending upon any life or lives, shall, within one calendar month after the payment or giving of any such premium or consideration, make out and sign or execute, or cause and procure to be made out and signed or executed upon vellum, parchment, or paper, duly stamped, a policy of such assurance or insurance, and have the same ready to be delivered to the party entitled thereto, and shall upon demand made by any such party, or any agent in that behalf duly authorized, deliver the same to him, or in default in any of the cases aforesaid shall forfeit the sum of fifty pounds: Articles of Every person who at the time of the payment or giving of any such premium or consideration shall be a managing director of or the secretary to or other principal officer of any society or company receiving any such premium or consideration, shall be deemed to be a person making or agreeing to make such assurance or insurance, and shall be subject and liable to the penalty by this act imposed for any such default as aforesaid. Whereas by an act passed in the fifty-fifth year of the reign clerkship to of King George the Third, chapter one hundred and eighty-four attorneys. certain stamp duties are imposed on any articles of clerkship or contract whereby any person shall first become bound to serve as a clerk in order to his admission as an attorney or solicitor in any court; that is to say, in order to admission in any of the Courts at Westminster, the stamp duty of one hundred and twenty pounds, and in order to admission in any of the Courts of the Counties Palatine, the stamp duty of sixty pounds: And whereas where any person has become bound and has served as a clerk under any such articles or contract stamped with the said duty of sixty pounds in order to his admission as an attorney or solicitor in any of STAMP DUTIES. 811 the Courts of the Counties Palatine, he is capable of being admitted in any of Her Majesty's Courts at Westminster, but only upon the payment of the further stamp duty of one hundred and twenty pounds; and it is expedient to afford relief in such cases : Where any person shall have become bound as a clerk in order to his admission as an attorney or solicitor in any of the Courts of the Counties Palatine by articles or contract stamped with the said duty of sixty pounds, then upon payment of such further sum of money as with the said duty of sixty pounds will make up the full stamp duty which, at the date of such articles or contract, was payable by law on articles of clerkship in order to admission in any of the Courts at Westminster, it shall be lawful for the Commissioners of Inland Revenue and they are hereby required to stamp the said articles or contract with a stamp or stamps to denote such further duty, and thereupon such articles or contract shall be as valid and effectual for entitling such person to admission in any of the Courts at Westminster as if the same had been duly stamped with such full duty in the first instance. And whereas by an act passed in the forty-eighth year of the reign of King George the Third, chapter one hundred and forty-nine, section thirty- eight, persons intromitting with or entering upon the possession or manage- ment of any personal or moveable estate or effects in Scotland of any person dying, are required to exhibit a full and true inventory, duly stamped, to be recorded as in the said act is provided, of all the personal or moveable estate and effects of the deceased already recovered or known to be existing; and if at any subsequent period a discovery shall be made of any other effects belonging to the deceased, an additional inventory of the same is in like manner to be exhibited and recorded; and every such additional inventory is chargeable by law with the full ad valorem stamp duty payable in respect of the total amount or value of the estate and effects specified therein, and in any such former inventory; and thereupon the party exhibiting the same is entitled to receive back the amount of the stamp duty paid on such former inventory; and it is expedient to prevent the inconvenience attending the over-payment of the stamp duty in such cases by charging on any such additional inventory the deficient stamp duty only. For inven- Scotland. Every such additional inventory to be made and recorded as aforesaid shall be chargeable only with such amount of stamp tories in duty as, together with the stamp duty charged upon any for- mer duly stamped inventory of the estate and effects of the same deceased person already exhibited and recorded, shall make up the full amount of stamp duty chargeable by law in respect of the total amount or value of all the estate and effects of the said deceased specified in the said additional and any such former inventory. No license granted to any spiritual person to perform divine service in any building approved by the bishop in lieu of any church or chapel whilst the same is under repair or is rebuilding, or in any building so approved for the convenience of the inhabitants of a parish resident at a distance 812 STAMP DUTIES. from the church or consecrated chapel, shall be chargeable with any stamp duty. And whereas by the said act passed in the fifty-fifth year of the reign of King George the Third, it is provided that where any property is sold and conveyed subject to any debt or sum of money to be afterwards paid by the purchaser, the same shall be deemed to be purchase or consideration money in respect whereof the said ad valorem duty charged upon the sale and conveyance of property is to be paid: And whereas it has been held and determined that the said ad valorem duty is payable in respect of any such sum or debt only where the purchaser is personally liable or bound, or undertakes or agrees to pay the same or to indemnify the vendor against the same; and it is expedient to alter and amend the law in this respect : Where any lands or other property shall be sold and conveyed conveyance subject to any mortgage, wadset, or bond or other debt, or to any gross or entire sum of money, such sum of money or debt shall be deemed the purchase or consideration money, or part of the pur- chase or consideration money, as the case may be, in respect whereof the said ad valorem duty shall be paid, notwithstanding the purchaser shall not be or become personally liable or shall not undertake or agree to pay the same or to indemnify the vendor or any person against the same, any- thing in any act or otherwise to the contrary notwithstanding. Sale and of land, &c. And whereas it has been adjudged and determined by law that upon the sale of property, where the consideration expressed in the conveyance is a rent charge or an annuity, made subject to redemption or repurchase, ad valorem stamp duty is chargeable under the act passed in the Session of Parliament held in the thirteenth and fourteenth years of Her Majesty, chapter ninety-seven, only where such redemption or repurchase may be enforced at the option of the vendor, and it is expedient that such duty should be chargeable in all cases where such rentcharge or annuity is made redeemable. In any case where property shall be sold and conveyed in consideration of any rentcharge or annuity, or any annual or periodical payment to be made permanently or for any indefinite period, so that the total amount of the money to be paid for such property cannot be previously ascertained, which rentcharge, annuity, or other payment shall be made subject to redemption or purchase upon terms and conditions specified in the deed or instrument whereby the property sold shall be conveyed to or vested in the purchaser, or any person by his direction, the money or the considera- tion mentioned in the said deed or instrument as that on payment or trans- fer, delivery or satisfaction, of which the said rentcharge, annuity, or other payment shall be redeemed or purchased or repurchased, or shall cease to be payable, shall be deemed to be the purchase money or con- sideration on the sale of the said property so sold and conveyed, and in respect of which last-mentioned purchase money or consideration the ad valorem duty shall be chargeable; and where any such last-mentioned consideration shall consist wholly or in part of any stock or security men- tioned in the said act, the value thereof shall be ascertained as in such act STAMP DUTIES. 813 is in that behalf provided; and where any such annuity, rentcharge, or other payment aforesaid shall be made subject to redemption or purchase or repurchase or discontinuance upon payment or satisfaction of any money or value to be ascertained or calculated in manner provided in the said deed or instrument, the amount of such money or value shall, for the pur- pose of charging the said ad valorem duty, be ascertained or calculated as in such deed or instrument shall be so provided. And whereas by the said act of the thirteenth and fourteenth years of Her Majesty, chapter ninety-seven, a stamp duty of five shillings was granted and imposed upon the duplicate or counterpart of any deed or instrument chargeable with stamp duty (exclusive of progressive duty) to the amount of five shillings or upwards; and it is provided that in such case the duplicate or counterpart shall not be available unless stamped with a particular stamp for denoting or testifying the payment of the full and proper stamp duty on the original deed or instrument; and it is ex- pedient to dispense with the said particular stamp on counterparts of leases : Notwithstanding anything contained in the said act, the counterpart of any lease of lands, tenements, or hereditaments, being duly stamped with the said stamp duty of five shillings, or any higher stamp duty (exclusive of progressive duty), and not being executed or signed by or on the be- half of any lessor or grantor, shall be available as a counterpart without being stamped with a particular stamp for denoting or testifying the pay- ment of the stamp duty chargeable on the original lease. And whereas by the said act of the thirteenth and fourteenth years of Her Majesty, when any deed or instrument shall be presented to the Commissioners of Inland Revenue, and the fee of ten shillings shall be paid to them for their opinion as to the stamp duty with which such deed. or instrument in their judgment is chargeable, the said commissioners are required to assess and charge the stamp duty on such deed or instrument, and, on the same being duly stamped, to impress thereon a particular stamp to signify and denote that the full amount of stamp duty with which such deed or instrument is by law chargeable has been paid: And whereas the said Commissioners are not authorized to impress a particular stamp upon any deed or instrument not chargeable with any stamp duty in order to denote that the same is not so chargeable; and it is expedient that provision should be made for that purpose. It shall be lawful for any person to present to the said commissioners any deed or instrument, and upon payment of the fee of ten shillings, as in the said act is mentioned, to require their opinion whether or not the same is chargeable with any stamp duty, and if the said commissioners shall be of opinion that such deed or instrument is not chargeable with any stamp duty, it shall be lawful for them and they are hereby required to impress thereon a particular stamp, to be provided by them for that purpose, with such word or words, or device or symbol thereon as they shall think pro- per in that behalf, which shall signify and denote that such deed is not chargeable with any stamp duty; and every such deed or instrument upon 814 STAMP DUTIES. which the said stamp shall be impressed shall be deemed to be not so chargeable, and shall be receivable in evidence in all courts of law and equity, notwithstanding any objection made to the same as being chargeable with stamp duty, and not stamped to denote the same : Pro- vided always, that if the said commissioners shall assess and charge any stamp duty upon or in respect of any such deed or instrument, and the party presenting the same and paying such duty shall declare himself dissatisfied with their determination, it shall be lawful for him to appeal against the same to Her Majesty's Court of Exchequer, on the terms and in the manner in the said act provided; and the said court shall hear and determine the appeal, and decide whether the said deed or instrument is chargeable with any, and if any, what stamp duty; and if the court shall be of opinion that the same is not so chargeable, or is chargeable with a less amount of duty than shall have been assessed and charged thereon, then the amount of such duty or of the excess (as the case may be) shall be returned to the appellant, together with the sum deposited as in the said act mentioned; and if the court shall be of opinion that any further duty is chargeable on the said deed or instrument, such further duty shall be paid to the said commissioners, and the court shall order and enforce the payment thereof accordingly. And whereas it would facilitate the transfer of the bonds and mortgages given by public companies under the provisions of Acts of Parliament as securities for money which such companies are by the said acts expressly empowered or authorized to borrow, if the transfers or assignments of such-bonds or mortgages were endorsed thereon, and were exempted from stamp duty, and it is expedient to grant such exemption in consideration of a composition stamp duty being paid on such bonds and mortgages on the original making and issuing thereof, in lieu of the stamp duty with which such transfers or assignments would otherwise be chargeable : Transfers of mortgages. Where on the original making and issuing of any such bond bonds and or mortgage as aforesaid, and before any transfer or assignment thereof, the same shall be stamped with an amount of stamp duty equal to three times the amount of the ad valorem stamp duty chargeable thereon by law, and over and above the said ad valorem duty, then every transfer or assignment thereafter made of such bond or mort- gage by endorsement thereon shall be deemed to be exempt from the stamp duty which would otherwise be payable in respect of such transfer or as- signment: Provided always, that nothing herein contained shall extend to exempt any such transfer or assignment from any stamp duty to which it may be liable as a settlement of the money or stock secured by such bond or mortgage, or any portion thereof. And whereas it is desirable to facilitate the purchase of stamped paper, covers, or envelopes, and of other stamps for expressing or denoting the rates or duties of postage (all of which are hereinafter designated as post- age stamps), and for that purpose to enable certain persons in the service of the Post Office to sell postage stamps without having any such license STAMP DUTIES. 815 as the laws now in force require in that behalf, and without being subject or liable to any penalty for carrying about postage stamps for sale: It shall be lawful for the Postmaster General by writing under Persons au- Postmaster General may sell postage stamps. his hand to authorize and appoint any person in the service or thorized by employment of the Post Office to sell postage stamps at any par- ticular house or place to be specified for that purpose, and also any messenger or other person employed in the delivery of letters sent by post to carry about for sale and to sell at any place postage stamps, and all such persons shall, during the period that such authority and appointment shall remain in force and unrevoked, without any license or any authority other than last aforesaid, be at liberty to sell at any house or place to be specified as aforesaid, or if so authorized, to carry about for sale and sell at any place, any postage stamps, and such persons respectively shall not be subject or liable to any penalty or forfeiture for so doing, any- thing in any act or acts to the contrary notwithstanding. sion of the duties on playing cards And whereas by an act passed in the ninth year of the reign For prevent- of King George the Fourth, chapter eighteen, granting stamp ing the eva- duties upon playing cards made fit for sale or use in the United Kingdom, such duties to be denoted on the ace of spades of each pack of cards, it is enacted that no playing cards shall be sold as waste cards unless a corner of each card shall be cut off at least half an inch in depth, and other provisions are therein contained for securing the said duties: And whereas packs or parcels of cards fit and intended for use and play, but not containing an ace of spades duly stamped, are commonly sold under the pretence of being waste cards, each of such cards having a corner cut off, whereby the said duties are evaded; and it is expedient to prevent such practice: No playing cards, except such as shall be bonâ fide spoiled and rendered unfit for use as playing cards in the process of manufacture, and which shall have a corner cut off as in the said last-mentioned act is provided, nor any cards commonly called or known as picture cards or court cards, shall be deemed to be waste cards; and no playing cards, except waste cards, shall be sold otherwise than in packs each pack containing fifty-two cards of the four usual suits of thirteen cards each, including an ace of spades duly stamped for denoting the duty by the said act granted on a pack of cards, and tied up together in manner directed by the said act; and if any person shall sell or expose or keep for sale any playing cards, not being a pack of cards as aforesaid, and the same not being bonâ fide waste cards within the meaning of this act, he shall for every pack, parcel, or separate quantity of cards so sold or exposed or kept for sale forfeit, if he shall not be a licensed maker of playing cards, the sum of ten pounds, and if he shall be such licensed maker the sum of twenty pounds; and all cards so sold or exposed or kept for sale shall be forfeited, and may be seized and taken by any Officer of Inland Revenue, and be disposed of as the Commissioners of Inland Revenue shall direct; provided that if in any proceeding any question shall arise whether any cards are or were bonâ 816 STAMP DUTIES. fide waste cards or not, proof of the affirmative thereof shall lie on the party selling the same or having or keeping the same for sale. And whereas by an act passed in the session held in the seventh and eighth years of the reign of King George the Fourth, chapter fifty-three, Officers of Excise and persons employed in the collection or management of or accounting for the revenue of excise are exempted from serving as mayor or sheriff, or in any corporate or parochial or other public office or employment, or on any jury or inquest, or in the Militia; and it is expe- dient to extend the same to all other officers appointed by or under the Commissioners of Inland Revenue. No officer or person appointed by the Commissioners of Inland Revenue, or employed by them or under their authority or direction in any way re- lating to any of the duties under their care or management shall, so long as he shall continue in and exercise such last-mentioned office or employ- ment, be compelled to serve as mayor or sheriff, or in any of the offices, employments, or capacities in the said act and herein before in that behalf mentioned. Allowance for receipt stamps on hand. Where any person shall be possessed of any stamps rendered useless by this act, it shall be lawful for the Commissioners of Inland Revenue, on application to them or to their proper officer in that behalf, at any time within six calendar months after the commencement of this act to cancel and make allowance for the same, as in the case of spoiled stamps, after deducting the discount by law granted on the purchase of receipt stamps. Drafts on bankers. Provided always, that any draft or order drawn upon a banker for a sum of money payable to order on demand which shall, when presented for payment, purport to be endorsed by the person to whom the same shall be drawn payable, shall be a sufficient authority to such banker to pay the amount of such draft or order to the bearer thereof; and it shall not be incumbent on such banker to prove that such endorsement, or any subsequent endorsement, was made by or under the direction or authority of the person to whom the said draft or order was or is made payable either by the drawer or any endorser thereof. And whereas by an act passed in the Session of Parliament held in the fifth and sixth years of Her Majesty's reign, chapter eighty-two, certain rates and duties denominated stamp duties were granted and made payable in Ireland for a limited term; and by four several acts passed respectively in the eighth, eleventh, fourteenth, and fifteenth years of Her Majesty's reign the same rates and duties were continued for four other several and successive terms, the last of which will expire on the tenth day of October one thousand eight hundred and fifty-three; and it is expedient to make the said rates and duties perpetual: Stamp duties in Ireland. All the several sums of money and duties and composition for duties granted and made payable in Ireland by the said act of the fifth and sixth years of Her Majesty, chapter eighty-two, and not repealed by any subsequent act, and also all duties now payable in lieu or instead of any of the said duties which may have been so repealed, STAMP DUTIES. 817 shall be and the same are hereby continued and made perpetual, and shall be charged, raised, levied, collected, and paid unto and for the use of Her Majesty, her heirs and successors for ever: The said act of the fifth and sixth years of Her Majesty, and all and every other act, and acts now in force in relation to the duties and composition for duties which are con- tinued by this act, shall severally be continued and remain in full force in all respects in relation to the said duties and composition for duties hereby continued and granted, and all and every the powers and authorities, rules, regulations, directions, penalties, forfeitures, clauses, matters, and things contained in the said acts or any of them, and in force as aforesaid, shall severally and respectively be duly observed, practised, applied, and put in execution in relation to the said duties and composition for duties hereby continued and granted, for the charging, raising, levying, paying, account- ing for, and securing of the said duties and composition for duties, and all arrears thereof, and for the preventing, detecting, and punishing of all frauds, forgeries, and other offences relating thereto, as fully and effectually to all intents and purposes as if the same powers, authorities, rules, regu- lations, directions, penalties, forfeitures, clauses, matters, and things were particularly repeated and re-enacted in the body of this act with reference to the said duties and composition for duties hereby granted. The Schedule referred to by this Act. Apprenticeship and Clerkship.-Indenture or other instrument or writing containing the covenants, articles, or agreements for or relating to the service of any apprentice, clerk, or servant who shall be put or placed to or with any master or mistress, or to or with any new master or mistress, either by assignment, transfer, or turn-over, or upon the death, absence, or incapacity of the former master or mistress, or other- wise, to learn any profession, trade, or employment whatsoever (ex- cept articles of clerkship or apprenticeship to any attorney, solicitor, or other person in order to admission in any court, or in any office in any court), or any writing whatever (except as aforesaid) whereby any such assignment, transfer, or turn-over may be effectuated or fas- certained; Where no sum of money or other matter or thing shall be paid, given, assigned, or conveyed, or be secured to be paid, given, assigned, or conveyed to or for the use or benefit of the master or mistress, with or in respect of any apprentice, clerk, or servant Debenture or certificate for entitling any person to receive any drawback of any duty or duties, or part of any duty or duties of customs or ex- cise, or any bounty payable out of the revenue of customs or excise, for or in respect of any goods, wares, or merchandise exported or shipped to be exported from any part of the United Kingdom to any part beyond the sea; Where the drawback or bounty to be received shall not exceed ten pounds Where the same shall exceed ten pounds and not exceed fifty pounds • • And where the same shall exceed fifty pounds Duty. £ s. d. 026 0 1 0 026 050 818 STAMP DUTIES. Draft or order for the payment of any sum of money to the bearer or to order, on demand And the following instruments shall be deemed and taken to be drafts or orders for the payment of money within the intent and meaning of this act, and of any act or acts relating to the stamp duties on bills of exchange, drafts, or orders, and shall be chargeable accordingly with the stamp duties imposed by this act or any such act or acts; viz. All documents or writings usually termed Letters of Credit, or whereby any person to whom any such document or writing is or is intended to be delivered or sent shall be en- titled, or be intended to be entitled to have credit with, or in account with, or to draw upon any other person for, or to receive from such other person any sum of money therein mentioned. Exemptions from the Duties on Drafts or Orders. All drafts or orders for the payment of money to the bearer on demand, drawn upon any banker or bankers, now by law exempt from stamp duty. All letters of credit, whether in sets or not, sent by persons in the United Kingdom to persons abroad authorizing drafts on the United Kingdom. Policy of assurance or insurance, or other instrument, by whatever name the same shall be called, whereby any insurance shall be made upon any life or lives, or upon any event or contingency relating to or de- pending upon any life or lives; Where the sum insured shall not exceed five hundred pounds; Then for every fifty pounds, and any fractional part of fifty pounds Duty. £ s. d. • 0 0 1 of one hundred pounds • 006 And where it shall exceed five hundred pounds, and shall not exceed one thousand pounds; Then for every one hundred pounds, and any fractional part 0 1 0 Then for every one thousand pounds, and any fractional part of one thousand pounds 0 10 0 0 0 1 And where it shall exceed one thousand pounds; Receipt or discharge given for or upon the payment of money amounting to two pounds or upwards Exemption. Receipts given for money deposited in any Bank, or in the hands of any banker, to be accounted for, whether with interest or not; provided the same be not expressed to be received of or by the hands of any other than the person to whom the same is to be ac- counted for: Provided always, that this exemption shall not extend to receipts or acknowledgments for sums paid or deposited for or upon letters of allotment or shares or in respect of calls upon any scrip or shares of or in any Joint Stock or other Company or proposed or intended company, which said last-mentioned receipts or ac- knowledgments, by whomsoever given, shall be liable to the duty by this act charged on receipts. STAMP DUTIES. 819 Repeal of certain Stamp Duties, and to grant others in lieu thereof, to give relief with respect to the Stamp Duties on Newspapers and Sup- plements thereto, to repeal the Duty on Advertisements, and otherwise to amend the Laws relating to Stamp Duties. on instru- nexed re- others grant- thereof. Whereas it is expedient to repeal the stamp duties now payable in respect of the several instruments, matters and things mentioned or described in the schedule to this act annexed, and to impose other stamp duties in lieu thereof, and also to give relief with respect to the stamp duties on newspapers and supplements thereto, and otherwise to amend the laws relating to stamp duties, and to repeal the duty charged on advertisements: Be it therefore enacted by the Queen's most Excellent Majesty, by and with the advice and consent of the lords spiritual and temporal, and commons, in this present parliament assembled, and by the authority of the same, as follows: From and after the passing of this act the several stamp Stamp duties duties now payable in Great Britain and Ireland respectively, ments in the under or by virtue of any Act or Acts of Parliament for or in schedule an- respect of the several instruments, matters and things mentioned pealed, and or described in the schedule to this act annexed, and whereon ed in lieu other duties are by this act granted, shall respectively cease and determine, and shall be and the same are hereby repealed; and in lieu and instead thereof there shall be granted, raised, levied, collected, and paid in and throughout the United Kingdom of Great Britain and Ireland, to and to the use of Her Majesty, her heirs and successors, for and in respect of the several instruments, matters, and things described or mentioned in the said schedule, or for or in respect of the vellum, parchment, or paper upon which any of them respectively shall be written, the several duties or sums of money set down in figures against the same respectively, or otherwise specified and set forth in the said schedule, which said schedule, and the several provisions, regulations, and directions therein contained with respect to the said duties, and the instruments, matters, and things charged therewith, shall be deemed and taken to be part of this act, and shall be applied, observed, and put in execution accordingly: provided always, that nothing herein contained shall extend to repeal or alter any of the said stamp duties now payable in relation to any deed or instru- ment which shall have been signed or executed by any party thereto, or which shall bear date before or upon the passing of this act. The new duties to be denominated stamp duties, &c. The said duties by this act granted shall be denominated and deemed to be stamp duties, and shall be under the care and management of the Commissioners of Inland Revenue for the time being; and all the powers, provisions, clauses, regulations, directions, allowances, and exemptions, fines, forfeitures, pains, and penal- ties contained in or imposed by any act or acts, or any schedule thereto, relating to any duties of the same kind or description heretofore payable in Great Britain and Ireland respectively, and in force at the time of the passing of this act, shall respectively be in full force and effect with respect to the duties by this act granted, and to the vellum, parchment, and paper, 820 STAMP DUTIES. instruments, matters, and things charged and chargeable therewith, and to the persons liable to the payment of the said duties, so far as the same are or shall be applicable in all cases not hereby expressly provided for, and shall be observed, applied, allowed, enforced, and put in execution for and in the raising, levying, collecting, and securing of the said duties hereby granted, and otherwise in relation thereto, so far as the same shall not be superseded by, and shall be consistent with the express provisions of this act, as fully and effectually to all intents and purposes as if the same had been herein repeated and specially enacted, mutatis mutandis, with reference to the said duties by this act granted. on newspa- As to duties No higher stamp duty than one penny shall be chargeable on pers and sup- any newspaper printed on one sheet of paper containing a su- perficies not exceeding two thousand two hundred and ninety- plements. five inches: A supplement published with any newspaper duly stamped with the duty of one penny, such supplement being printed on one sheet of paper only, and together with such newspaper containing in the aggregate a superficies not exceeding two thousand two hundred and ninety-five inches, shall be free from stamp duty: Any other supplement to any such duly stamped newspaper shall not be chargeable with any higher stamp duty than one halfpenny, provided it does not contain a superficies exceeding one thousand one hundred and forty-eight inches: And any two supplements to any such duly stamped newspaper shall not be chargeable with any higher stamp duty than one halfpenny on each, provided each of such supplements be printed and published on one sheet. of paper only, and that they contain together a superficies not exceeding in the aggregate two thousand two hundred and ninety-five inches : The superficies in all the cases aforesaid to be one side only of the sheet of paper, and exclusive of the margin of the letter press. Allowance per stamps on hand. Where any person shall be possessed of any stamps for news- for newspa- papers rendered useless by this act, it shall be lawful for the Commissioners of Inland Revenue, on application to them or to their proper officer in that behalf, at any time within six calendar months after the commencement of this act, to cancel and make allowance for the same, as in the case of spoiled stamps After passing duties on ad- And whereas it is expedient to repeal the duties now pay- of this act all able on advertisements: From and after the passing of this act the vertisements duties now payable under any act or acts in force for or in respect to cease. of any advertisement contained in or published with any gazette or other newspaper, or contained in or published with any other periodical paper, or in or with any pamphlet or literary work, and all enactments, clauses, provisions, and regulations for levying, collecting, and securing the said duties; but so far only as they relate to such duties, shall respec- tively cease and determine, and shall be and the same are hereby repealed, save and except as to any of the said duties, which shall have been charged or incurred on or before the day of the passing of this act, and any arrear STAMP DUTIES. 821 thereof, and as to all fines and penalties incurred or which may be in- curred in respect of the said duties or arrears, all which said duties and arrears, fines and penalties, so excepted as aforesaid, shall respectively be sued for, recovered, levied, paid, and applied in the same manner as if this act had not been passed. signments of Ireland, and knowledg- ment in Scotland. Whereas it is expedient to remove doubts which have arisen Duties on as- as to the stamp duties upon assignments of Judgment in Ire- Judgment in land; and it is also expedient to reduce the stamp duties now writs of ac- chargeable in Scotland upon writs of acknowledgment by per- sons infeft of lands in favour of the heirs or disponees of cre- ditors: In lieu of the stamp duties now payable upon the instruments hereinafter mentioned there shall be chargeable (besides any progressive duties to which the same respectively may be liable by reference to the head of progressive duty in the schedule to the act of the thirteenth and fourteenth years of her present Majesty, chapter ninety-seven,) the respec- tive stamp duties following; (that is to say,) For and upon every assignment of any judgment in Ireland, one pound fifteen shillings: And for and upon any writ of acknowledgment by any person infeft of lands in Scotland in favour of the heir or disponee of a creditor fully vested in right of an heritable security constituted by infeftment, ten shillings. And whereas under and by virtue of certain Acts of Parliament now in force the governor and company of the bank of Scotland, and the royal bank of Scotland and the British linen company in Scotland are respec- tively authorized and empowered to make an issue and re-issue their promissory notes payable to bearer on demand on unstamped paper, giving security, and keeping and producing true accounts of all the notes so issued by them respectively, and accounting for and paying the stamp duties payable in respect of such notes: And whereas it is expedient to authorize and empower the commissioners of Her Majesty's Treasury to compound with the said banks, as well as all bankers in Scotland, for the stamp duties on their promissory notes payable to bearer on demand, as well as for stamps payable on their bills of exchange: It shall be lawful for the Commissioners of Her Majesty's Treasury for the time being, power to or any three of them, and they are hereby authorized and em- powered to compound and agree with the said governor and company of the bank of Scotland, and the royal bank of Scot- land, and the British linen company in Scotland, and all or any other bankers in Scotland, or elsewhere, respectively, for a composition in lieu of the stamp duties payable on the promissory notes of the said banks and bankers respectively payable to the bearer on de- mand, as well for stamps payable on their bills of exchange; and such composition shall be made on such terms and conditions, and with such security for the payment of the same, and for keeping, producing, and rendering of such accounts, as the said last-mentioned commissioners may deem to be proper in that behalf; and upon such composition being entered into by such banks and bankers respectively it shall be lawful for them to Treasury to with bankers for the stamp their promis- compound in Scotland duties on sory notes. 822 STAMP DUTIES. issue and re-issue all notes and to draw all such bills for which such com- position shall have been made on unstamped paper, anything in any act contained to the contrary notwithstanding. Stamp duty on scrip cer- From and after the passing of this act the following stamp tificates duty shall be chargeable and paid; (that is to say,) On any scrip certificate, that is to say, any document denoting or in- tended to denote the right or title of the holder thereof or any person to any share or shares in any joint stock or other company, or proposed or intended company, or any certificate declaring or entitling the holder thereof or any person to be or become the proprietor of any share or shares of or in any such company, where such certificate or the right or title to such share or shares shall be or be intended to be transferable by the delivery of such cer- tificate, or otherwise than by deed or instrument in writing Receipts for land or as- sessed taxes or Income £ s. d. 0 0 1 No receipt given for any sum or sums of money received for or on account of land tax, or the duties of assessed taxes, or the duties on profits arising from property, professions, trades, and offices, by any collecter or receiver of such taxes or duties, or by any person having authority to collect or receive the same, shall be subject or liable to any stamp duty. Tax exempt from stamp duty. Stamps de- noting the cies of life assurance The duties granted by an act of the present Session of Parlia- duty on poli- ment on policies of assurance may be denoted either by a stamp impressed upon the paper whereon any such instrument is written, or by an adhesive stamp affixed thereto, and the Com- missioners of Inland Revenue shall provide stamps of both descriptions for the purpose of denoting the said duties. may be im- pressed or affixed. Certain par- written on adhesive stamps for policies. The adhesive stamps to be so provided for the purpose afore- ticulars to be said shall be adapted for the writing of the following particu- lars thereon; (that is to say,) the date and number of the policy, and the names of the person insured and of one of the direc- tors of the assurance company, or other person by whom the same shall be signed; and where an adhesive stamp shall be used or intended to be used for or upon any such policy, such stamp shall be firmly and securely affixed and made to adhere to such policy, and all the several particulars aforesaid shall be fairly and distinctly written upon such stamp at or before the time of the signing thereof by such director or other person aforesaid, or in default thereof such director or other person signing such policy shall forfeit the sum of Fifty Pounds. The Schedule referred to by this Act. Duty. Articles of Clerkship or contract, whereby any person shall first become £ S. d. bound to serve as a clerk in order to his admission as an attorney or solicitor in any of Her Majesty's Courts at Westminster or in Ireland, or in order to his admission as a proctor in the High Court of Admi- ralty in England, or the Court of Admiralty in Ireland, or in any of the Ecclesiastical Courts in Doctors Commons or in Ireland Certificate to be taken out yearly by every person admitted as an attorney or solicitor in any of Her Majesty's Courts at Westminster or in Ire- land, or in any other court in England holding pleas where the debt 80 0 0 AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. 823 ? or damage amounts to forty shillings; and by every person admitted as a writer to the signet, or as a solicitor, agent, attorney, or procu- rator in any of the courts in Scotland; and by every person admitted or enrolled as a notary public in England, Scotland, or Ireland, who in his own name or in the name of any other person shall commence, prosecute, carry on, or defend any action, suit, prosecution, or other proceeding in any of the courts aforesaid, or do any notarial act what- ever, for or in expectation of any fee, gain, or reward, as an attorney, solicitor, agent, proctor, procurator, or notary public, although not admitted or enrolled as such; If he shall reside within the distance of ten miles from the Gene- ral Post Office in the city of London, or within the city or shire of Edinburgh, or in the city of Dublin, or within three miles thereof; And if he shall have been admitted for the space of three years or upwards . Or if he shall not have been admitted so long If he shall reside elsewhere, and if he shall have been ad- mitted for the space of three years and upwards • Or if he shall not have been admitted so long Certificate to be taken out yearly by every person being a member of one of the Four Inns of Court in England, and by every person in Ireland who in the character of conveyancer, special pleader, draftsman in equity or otherwise, shall, for or in expectation of any fee, gain, or reward, draw or prepare any conveyance of or deed or instrument relating to any estate or property, real or personal, or any other deed or contract whatever, or any pleadings or proceedings in any court of law or equity; If he shall reside within the distance of ten miles from the Ge- neral Post Office in the city of London, or in the city of Dublin, or within three miles thereof • And if he shall reside elsewhere Conveyance of any kind or description whatsoever, in England or Ireland, and charter disposition or contract containing the first original consti- tution of Feu and Ground Annual Rights in Scotland (not being a lease or tack for years), in consideration of any annual sum payable in perpetuity, or for any indefinite period, whether fee farm or other rent, feu duty, ground annual, or otherwise: Where the annual sum thereby reserved, secured, or made pay- able shall not exceed 20s. And where the same shall exceed 20s. and shall not exceed 127. then for every 20s. or any fractional part of 20s. of such annual sum And where the same shall exceed 127. and shall not exceed 241., then for every 40s. and for any fractional part of 40s. of such annual sum And where the same shall exceed 247. then for every 47. and for any fractional part of 47. of such annual sum AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. Duty. £ s. d. 900 4 10 0 600 3 0 0 900 600 0 2 6 0 26 050 0 10 0 Duties now on under- Articles to chargeable mentioned The Duties of Customs now chargeable on the articles under- mentioned imported into Scotland and Ireland shall cease and determine, and in lieu thereof the following duties shall be charged from and after the twenty-first day of April One following thousand eight hundred and fifty-three; viz. cease, and duties to be charged. 824 AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. Duties Spirits or strong waters, for every gallon of such spirits or strong waters, £ s. d. of any strength not exceeding the strength of proof by Sykes's Hydrometer, and so in proportion for any greater or less strength than the strength of proof and for any greater or less quantity than a gallon, viz. chargeable hereafter mentioned Spirits or strong waters, the produce of any British possession in America, not being sweetened spirits or spirits mixed with any article, so that the degree of strength thereof cannot be exactly ascertained by such hydrometer: If imported into Scotland Ireland • the gallon 0 5 0 the gallon 0 3 8 Rum, the produce of any British possession within the limits of the East India Company's charter, not being sweetened spirits or spirits so mixed as aforesaid, in regard to which the conditions of the Act 4 Victoria, Chapter 8, have or shall have been fulfilled: If imported into Scotland Ireland • the gallon 0 5 0 the gallon 0 3 8 Rum shrub, however sweeted, the produce of and imported from such possessions, in regard to which the conditions of the Act 4 Victoria, chapter 8, have or shall have been fulfilled, or the produce of and imported from any British possession in America: If imported into Scotland Ireland • the gallon 0 5 0 the gallon 0 3 8 The duties of customs chargeable upon the goods, wares, and on goods, &c. merchandise hereafter mentioned imported into the united king- dom shall cease and determine on and after the first day of June imported into united king- one thousand eight hundred and fifty-three; viz. dom to cease on June 1, 1853. Agates or cornelians, cut or manufactured; albumen; amber, manu- factures of, not enumerated; anchovies; aquafortis; bandstring twist ; barytes, sulphate of, ground; bast ropes, twines, and strands; blacking; books being of editions printed prior to the year 1801, bound or un- bound; bran; brass, powder of; bricks and clinkers, Dutch and other sorts; bronze powder; brushes, paint; buttons of metal and other sorts; cameos, not set; camphor, refined; cantharides; carmine; carriages of all sorts; casks, empty; catlings; chalk, prepared or manufactured, and not otherwise enumerated; cider; citron, preserved in salt; cobalt, oxide of; corks, fishermen's; crayons; crystals, cut or manufactured; cucumbers preserved in salt; elder flower water; extract of chesnut bark and wood; quercitron bark; logwood; safflower. Fish, viz.: eels, turbots, of foreign taking, oysters, salmon, soles, turtle, fresh, not otherwise enumerated; cured, not otherwise enumerated; frames for pictures, prints, drawings, or mirrors; furniture woods, excepting ash, beech, birch, elm, oak, wainscot; gauze of thread; gold, leaves of; gunpowder; hair, manufactures of hair or goat's wool, or of hair or goat's wool, and any other material not particularly enumerated or otherwise charged with duty; hams of all kinds; harp strings or lute strings, silverved; honey; ink, Indian; iron wire; rough castings; isinglass; latten wire; mead or metheglin; meat, preserved in any other manner than salted; mercury, prepared; metal, leaf metal; naptha; oil of resin; olives; orange flower water; orsedew; painters colours, manu- factured; pencils, of slate and not of slate; perry; phosphorus; pickles, and vegetables preserved in salt; pollard; pomegranates; pots, viz: melting pots for goldsmiths, of stone; rose water; saccharum Saturni; sausages or 1 AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. 825 puddings; seed, viz.: canary, carrot, clover, grass of all sorts, leek, lucern, mustard, onion, trefoil; all other sorts, not particularly enumerated, or other- wise charged with duty; silkworm gut; skins; articles manufactured of skins or furs; smalts; spectacles; spelter or zinc, viz.: rods and oxide of; stone and slate, hewn; marble sawn into slabs, or otherwise manufactured; tamarinds; tiles; tobacco pipes, of clay; tongues; turpentine, of a greater value than 15s. per cwt.; oil or spirit of; twine; vanelloes; varnish, not otherwise described; verdigris; wafers, wax, sealing; whipcord; waste wood, viz. billet wood or brush wood, used for the purpose of stowage; yarn of silk and worsted, spun together and not dyed; raw worsted yarn not dyed, or only partially dyed, and not being fit or proper for embroidering, or other fancy purposes. : In lieu of the Duties of Customs now chargeable on tea imported into the United Kingdom, the following duties shall be charged on and after the first day of June one thousand eight hundred and fifty-three : 5th April 1855 inclusive. To 5th April 1854 inclusive. From and after 5th April 1854 to From and after 5th April 1855 to 5th April 1856 inclusive. From and after 5th April 1856 £ s. d. £ s. d. 0 1 10 per Pound. 0 1 3 per Pound. £ s. d. 0 1 6 per Pound £ s. d 010 per Pound. The Duties of Customs chargeable upon the goods, wares, and merchan- dise hereafter mentioned imported into the United Kingdom, shall cease and determine on and after the fourth day of June one thousand eight hundred and fifty-three; viz. Cables, not of iron, new and old, tarred and untarred; coir rope, twine, and strands; copper, ore of; regulus of; and brass, old, fit only to be re-manu- factured; unwrought, viz.: in bricks or pigs, rose copper, and all cast copper; part wrought, viz.: in bars, rods, or ingots, hammered or raised; in plates and copper coin; or brass wire; cordage, tarred or untarred, including stand- ing or running rigging; glass; all plate glass, cast or rolled, of whatever thickness, however small each pane, plate, or sheet, whether silvered, polished, or rough, painted or otherwise ornamented, all white flint glass bottles, not cut, engraved, or otherwise ornamented, and beads and bugles of glass; wine glasses, tumblers, and all other white flint glass goods, not cut, engraved, or otherwise ornamented; bottles of glass covered with wicker (not being cut glass), or of green or common glass; articles of green or common glass, manufactures, not otherwise enumerated or described, and old broken glass, fit only to be re-manufactured; lead, pig and sheet; linen, or linen and cotton, viz.: cambrics and lawns, commonly called French lawns, whether plain or bordered; lawns of any sort, not French; damasks and damask diaper; sails of all sorts; mats and matting; pictures; poultry and game, alive or dead; tin, viz. in blocks, ingots, bars, or slabs; truffles; verjuice; wire, viz.: gilt, plated, silver and brass; yarn, cable yarn. In lieu of the Duties of Customs now chargeable on the articles under- mentioned imported into the United Kingdom, the following duties shall be charged on and after the fourth day of June one thousand eight hun- dred and fifty-three; viz. Apples, raw (not of British Possessions). dried Butter (not of British Possessions) £ s. d. the bushel 0 0 3 the bushel 0 1 0 the cwt. 0 5 0 3 D 826 AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. Cheese (not of British Possessions) to be charged on the landing £ weight s. d. the cwt. 0 2 6 Cocoa the lb. 0 0 1 Husks and shells the lb. 0 0 0 paste and chocolate Nuts, small walnuts Raisins Almonds, Jordan not Jordan, nor bitter paste of Arrow root Barley, pearled Baskets, viz.: the lb. 0 0 2 the bushel 0 1 1 0 the bushel 0 1 0 the cwt. 0 10 0 the cwt. 0 10 0 the cwt. 0 10 0 the lb. 0 0 2 the cwt. 0 0 4 the cwt. 0 0 0 0 43 Baskets corresponding with the description commonly called Berlin the cubic foot 0 0 7 all others the cubic foot 0 0 2 Beads, coral the lb. 0 1 6 arango, crystal, jet, and other sorts not enumerated or de- scribed the lb. the cwt. 0 0 2 0 10 0 Brocade of gold or silver • the lb. 0 5 0 the cwt. 0 10 0 Brass, manufactures of, not otherwise enumerated Bronze, manufactures of, not otherwise enumerated Candles, viz.: spermaceti the cwt. 0 2 4 stearine, till the 5th of April 1858, unless the duty upon tallow shall be repealed at an earlier time, in which case this duty shall be reduced to the same rate as tallow candles tallow wax Canes, viz.: the cwt. 0 3 6 the cwt. 0 2 4 the cwt. 0 2 4 walking canes or sticks, mounted, painted, or otherwise orna- mented umbrella or parasol sticks Capers, including the pickle the 100 0 6 0 the 100 0 3 0 the lb. 0 0 1½ Cards, viz., playing cards · Cassava powder Cassia lignea ་ the dozen packs 0 15 0 the cwt. 0 0·42 the lb. 0 0 1 Chicory, or other vegetable matter applicable to the uses of chicory or coffee, viz. : raw or kiln-dried, until 10th October 1854 inclusive, the cwt. 0 4 0 from and after 10th October 1854 roasted or ground the lb. the lb. Free. 0 0 4 0 10 0 0 2 China ware, or porcelain, painted or plain, gilt or ornamented, the cwt. Cinnamon Clocks, viz. : Cloves not exceeding the value of 5s. each the dozen 040 exceeding the value of 5s. and not exceeding the value of 12s. 6d, each the dozen 080 exceeding the value of 12s. 6d. and not exceeding the value of 31. each each 0 2 0 exceeding the value of 37. and not exceeding the value of 107. each exceeding the value of 107. each Coculus Indicus Coffee, roasted or ground each 0 4 0 each 0 10 0 the lb. 0 0 2 the cwt. 0 5 0 • the lb. 0 0 4 AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. 827 Comfits, dry, until 5th July 1854 inclusive from and after 5th July 1854 Confectionery, until 5th July 1854 inclusive from and after 5th July 1854 • £ s. d. the lb. 0 0 2 0 0 11 the lb. the lb. 0 0 2 the lb. 0 0 1 Copper, manufactures of, not otherwise enumerated or described, and copper plates, engraved Corks, ready made squared for rounding Dates Dice • Earthenware not otherwise enumerated or described Feathers, dressed, viz. : ostrich paddy bird not otherwise enumerated or described the cwt. 0 10 0 the lb. 0 0 6 the cwt. 0 8 0 the cwt. 0 10 0 the pair 1 1 0 the cwt. 0 10 0 the lb. 0 3 0 the lb. 0 3 0 the lb. 0 3 0 the cubic foot the cubic foot 0 12 0 0 12 0 the bushel 0 0 2 the lb. 0 0 2 the lb. 0 0 1 Flowers, artificial, not made of silk, per cubic foot as packed, no allowance for vacant spaces wholly or in part made of silk Fruit, raw, not otherwise enumerated • Ginger, preserved, until 5th July 1354 inclusive Glass, viz. : Grapes from and after 5th July 1854 any kind of window glass, white or stained of one colour only, (except plate or rolled glass,) and shades and cylinders, until 5th April 1855 inclusive the cwt. from & after 5th April 1855 until 5th April 1857 inclusive the cwt. from and after 5th April 1857 all flint cut glass, flint coloured glass, and fancy ornamental glass, of whatever kind • 026 0 1 6 Free. the cwt. the bushel 0 0 2 of hair or 0 10 0 Hair articles; manufactures of hair or goat's wool, or goat's wool and any other material, wholly or in part made up, not particularly enumerated or otherwise charged with duty Hats or bonnets, viz.: of chip of bast, cane, or horse-hair of straw for every 1007. value 5 0 0 the lb. 0 2 6 the lb. 0 2 6 of felt, hair, wool, or beaver the lb. 0 2 6 each 0 1 0 Hats of silk or silk shag laid upon felt, linen, or other material, each 0 1 0 Iron and steel, wrought or manufactured, viz. : machinery, wrought castings, tools, cutlery, and other manu- factures of iron and steel, not enumerated fancy ornamental articles of iron of steel • the cwt. 0 2 6 the cwt. 0 15 0 the cwt. 0 15 0 Jewels, emeralds, and all other precious stones, set, for every 1007. value 10 0 0 Lead, manufactures of, not otherwise enumerated Leather, viz.: boot backs cut into shapes Liquorice paste (not of British Possessions) Maccaroni Mace powder (not of British Possessions) root, until 5th April 1857 inclusive from and after 5th April 1857 Marmalade, until 5th July 1854 inclusive • the cwt. 0 2 0 the dozen pairs 0 1 6 0 the cwt. 0 10 the cwt. 1 0 0 the cwt. 1 0 0 the cwt. 0 5 0 Free. the cwt. 0 1 0 the lb. 0 1 0 the lb. 0 0 2 from and after 5th July 1854 Medlars • the lb. 0 0 1 the bushel 0 0 2 828 AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. Musical instruments, viz.: boxes, small, not exceeding four inches in length, the air 0 £ s. d. 0 3 large the air 0 0 8 overtures, or extra accompaniments piano fortes, horizontal grand the air 0 2 6 each 3 0 0 upright or square each 2 0 0 harmoniums or seraphines, not exceeding three stops, each 0 12 0 four stops, and not exceeding seven stops each 1 4 0 eight stops, and not exceeding eleven stops each 1 10 0 exceeding eleven stops each 2 0 0 the 100 notes 0 1 0 accordions, commonly called Chinese other sorts, including flutinas and common German square concertinas, the 100 notes 0 5 0 concertina of octagon form, not common German, each 0 4 0 brass instruments, all sorts instruments, not otherwise enumerated or described, for Mustard flour Nutmegs, except those commonly called wild Nux vomica Oil, viz.: the lb. 0 0 9 every 1007. value 10 0 0 the cwt. 0 1 6 the lb. 0 the cwt. 0 1 0 2 0 the lb. 0 0 1 ålmond bays essential oil of cloves Onions Pears, raw dried the lb. 0 0 1 the lb. 0 1 0 the bushel 0 0' 1 the bushel 0 0 3 the bushel 0 1 0 the 1,000 00 1 Percussion caps Perfumery, not otherwise enumerated, and scented or fancy soap the lb. Pewter, manufactures of, not otherwise enumerated Pickles preserved in vinegar Pimento Plate of gold of silver, gilt or ungilt 0 0 2 020 the cwt. the gallon 0 0 1 • the cwt. 0 5 0 the oz. troy 1 the oz. troy 1 0 0 1 8 Platting, or other manufactures of straw, chip, or other materials to be used in or proper for making or ornamenting hats or bonnets, not otherwise enumerated or charged with duty cordonet, single, and twist of straw, or of other materials, the lb. willow squares Plums, commonly called French plums and prunellos dried or preserved (except in sugar), not otherwise preserved in sugar, until 5th July 1854 inclusive, from and after 5th July 1854 Pomatum Potato flour Powder, viz.: hair powder perfumed the dozen the lb. 0 2 0 0 0 6 00 1 0 15 0 0 15 0 0 0 2 0 0 1 002 the cwt. described, the cwt. · the lb. the lb. the lb. the cwt. 0 0 41 the lb. 0 0 2 the lb. 0 0 2 not otherwise enumerated or described, that will serve the same purpose as starch Prints and drawings, plain or coloured, single bound or sewn · the cwt. 0 0 41 the lb. 0 0 3 the lb. 0 0 3 admitted under treaties of international copy- right, single bound or sewn the lb. 0 0 11 the lb. 0 0 1 AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. 829 Quassia Quinces Rice, not rough, nor in the husk £ the cwt. 8. d. 010 the bushel 0 0 3 the cwt. 0 0 42 rough, and in the husk Sago Scaleboard Semolina the quarter 0 0 9 the cwt. 0 0 41/2 the cwt. 01 0 the cwt. 0 0 43 for every 1007. value for every 100%. value the cubic foot 500 5 0 0 0 0 6 Ships, foreign ships, to be broken up, with their tackle, apparel and furniture (except sails), broken up Spa ware Spelter or Zinc, manufactures of, not otherwise enumerated, the cwt. Spirits, cordials, or strong waters, not being the produce of any British Possession in America, nor of any British Possession within the limits of the East India Company's Charter, in regard to which the conditions of the Act 4 Vict. cap. 8 have or shall been ful- filled, sweetened or mixed with any article so that the degree of strength cannot be exactly ascertained by Sykes's hydrometer, and perfumed spirits to be used as perfumery only, the gallon Starch the cwt. Gum of, torrified or calcined Succades, including all fruits and vegetables preserved in sugar, until the 5th July 1854 inclusive From and after the 5th July 1854 • Tapioca Tin foil 0 20 1 0 0 0 0 43 the cwt. 0 0 41 the lb. 0 0 2 the lb. 0 0 1 the cwt. 0 0 41 the cwt. 0 10 0 the cwt. 0 10 0 the cwt. 0 1 0 Manufactures of tin, and not otherwise enumerated, Toys, viz.: marbles all other toys Turnery, not otherwise described Varnish, containing any quantity of alcohol or spirit Vermicelli Vinegar Washing balls the cubic foot 0 0 4 the cubic foot 0 0 4 the gallon 0 12 0 the cwt. 0 1 0 the gallon 0 0 3 the lb. 0 0 2 Water, Cologne water, the flask (thirty of such flasks containing not more than one gallon) when not in flasks (as perfumed spirits) each 008 the gallon 1 0 0 In lieu of the present ad valorem rates of duties of customs charged upon the importation into the United Kingdom of the undermentioned articles as not being enumerated in the Tariff, the following duties of customs shall be charged thereon on and after the fourth day of June one thousand eight hundred and fifty-three; viz. Biscuit and bread Caoutchouc or Indian rubber, manufactures of Coral negligées Daguerreotype plates Fig cake the cwt. 0 0 41 the lb. 0 0 4 the lb. 0 1 0 the lb. 0 0 3 the cwt. 0 15 0 the cwt. the lb. 0 5 0 002 Gutta percha, manufactures of, not moulded, such as bands, sheets, soles, tubing articles moulded Lucifers of wood in boxes containing not more than 100 matches, the gross of boxes in boxes containing more than 100 matches, the gross of boxes vesta of wax, in boxes not exceeding 1,000 matches, the 0 0 2 0 0 3 dozen boxes 0 0 6 830 AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. £ 8. d. Lucifers in boxes exceeding 1000 matches the 1000 matches 0 0 0 Mandioca flour the cwt. 0 0 4 Salacine Manna croup Oil cloth, for table covers Sauces, not otherwise enumerated the cwt. 0 0 41 Mustard, mixed or manufactured, except flour the cwt. 0 5 0 • the square yard the oz. 0 0 1 0 0 3 the lb. 0 0 1 Soy the gallon 0 0 6 Sterine, till the 5th April 1858, unless the duty upon tallow shall be repealed at an earlier time, in which case this duty shall then cease, After the 5th April 1858 Veneers the cwt. 0 3 6 Free. the cwt. 0 1 0 In lieu of the duties of customs now chargeable on the article under- mentioned imported into the United Kingdom, the following duties shall be charged on and after the eighth day of June one thousand eight hun- dred and fifty-three; viz. Eggs not of British Possessions the 120 0 0 4 In lieu of the duties of customs now chargeable on the articles under- mentioned imported into the United Kingdom, the following duties shall be charged on and after the twelfth day of July one thousand eight hun- dred and fifty-three; viz. Soap, not being scented or fancy, viz.: hard soft Naples the cwt. 0 0 8 the cwt. 7 08 the cwt. 0 0 8 In lieu of the duties of customs now chargeable on the articles under- mentioned imported into the United Kingdom, the following duties shall be charged on and after the eleventh day of June one thousand eight hun- dred and fifty-three; viz. Oranges and lemons the bushel 0 0 8 Books, being bound in editions printed in or since the year 1801, bound or unbound the cwt. 1 10 0 admited under treaties of international copyright, or if of and from a British Possession. Cherries, raw dried, until 5th July 1854 inclusive ditto, from and after 5th July 1854 Cotton manufactures, viz.: fringe gloves, of cotton or thread stockings, of cotton or thread socks, or half hose, of cotton or thread, the cwt. 0 15 0 the bushel 0 0 2 the lb. 0 0 2 the lb. 0 0 11 the lb. 0 0 2 the dozen pairs 0 0 3 the dozen pairs 0 0 6 the dozen pairs 0 0 articles or manufactures of cotton, wholly or in part made up, not otherwise charged with duty, for every 1007. value 5 0 0 Embroidery and needlework, viz. : silk net, figured with the needle, being imitation lace, and ar- ticles thereof the lb. 0 10 0 cotton net, figured with the needle, being imitation lace, and articles thereof the lb. 0 8 0 curtains, commonly called Swiss, embroidered on muslin or net, all other embroidery not enumerated, of and from British Possessions the lb. 0 1 0 for every 1001. value 10 0 0 for every 1001. value 5 0 0 AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. 831 Lace and articles thereof, viz. : mohair or worsted • £ 8. d. the lb. 0 1 0 the lb. 1 0 0 thread or cotton pillow lace (not being Brussels point or Saxon bone lace), not exceeding one inch in width thread or cotton pillow lace (not being Brussels point or Saxon bone lace), exceeding one inch in width the lb. 2 0 0 silk lace, pillow and application, not being Saxon wire ground lace the lb. 1 10 0 silk Saxon wire ground lace, and all lace known as Maltese, the lb. 0 8 0 Brussels point, and other lace made by the hand, not other- wise charged with duty for every 100l. value 10 0 0 Linen, or linen and cotton manufactures, viz.: cambric handkerchiefs, hemmed or hemstitched, not trimmed, the dozen stays the dozen pairs articles, manufactures of linen, or of linen mixed with cotton or with wool, wholly or in part made up, not particularly enumerated or otherwise chargeable with duty, for every Mill boards Paper, viz.: 026 0 4 0 1007. value 5 00 the lb. 0 0 2 brown paper made of old rope or cordage only, without sepa- rating or extracting the pitch or tar therefrom, and without any mixture of other materials therewith the lb. 0 0 21 printed, painted, or stained paper or paper-hangings, or flock paper the square yard 0 0 1 Paper, waste paper, or paper of any other sort not particularly enume- rated or described, not otherwise charged with duty, the lb. Pasteboard Silk manufactures, being 11 velvet, the produce of Europe, plain or figured: broad stuffs. 0 0 2 the lb. 0 0 21 the foundation of which is wholly composed of cotton or other materials than silk the lb. 0 9 0 the lb. 0 3 0 0 10 0 6 ribbons of velvet, or silk embossed with velvet, the lb. the foundation of which is wholly composed of cotton, or other materials than silk the lb. 0 3 manufactures of silk, or of silk mixed with any other mate- rials, the produce of Europe, called plush black plush, commonly used for making hats, parasols and umbrellas the lb. 0 3 0 the lb. 0 1 0 each 0 1 0 damask of silk and wool or other materials, for furniture China the lb. 0 0 10 the running yard 0 0 8 corahs, choppahs, Bandannas, and Tussore cloths, viz.: in pieces not exceeding 54 yards in length, the piece 0 0 4 exceeding 5 and not exceeding 64 yards, the piece 0 0 6 6 and not exceeding 7 74 and not exceeding 8 yards, the piece 0 0 8 yards, the piece 0 0 9 81 and not exceeding 94 yards, the piece 0 0 10 and for every additional yard in length China crape shawls, plain and damask embroidered the yard 0 0 1 the lb. 0 3 0 the lb. 0 5 0 Pongees, in pieces not exceeding 15 yards in length, the piece 0 20 exceeding 15 yards and not exceeding 21 yards in length, the piece 0 3 0 exceeding 21 yards and not exceeding 31 yards in length, the piece 0 5 0 832 AN ACT TO ALTER CERTAIN DUTIES OF CUSTOMS. 9 yards in length Silk handkerchiefs, plain and figured, in pieces not exceeding £ s. d. the piece 0 1 6 exceeding 9 yards and not exceeding 18 yards in length, the piece 0 3 0 Watches, of gold, silver, or other metal, exceeding the value of 107. each each 1 0 0 other watches, viz. : gold, open faces each 0 5 0 hunters each 0 7 6 repeaters silver, or any other metal not gold: open faces hunters repeaters Woollens, articles or manufactures of wool (not being goat's wool) or each 0 15 0 each 0 2 6 each 0 3 6 each 0 8 0 of wool mixed with cotton, viz.: carpets and rugs the square yard 0 0 6 shawls, scarfs, and handkerchiefs, plain and not printed, the lb. the lb. 0 0 the dozen pairs 0 0 0 0 4 8 printed gloves articles or manufactures of wool mixed with cotton, wholly or in part made up, not otherwise charged with duty, for every 100%. value 5 0 0 In lieu of the present ad valorem rates of duties of customs charged upon the importation into the United Kingdom of the undermentioned articles as not being enumerated in the tariff, the following duties of cus- toms shall be charged thereon on and after the eleventh day of June one thousand eight hundred and fifty-three; viz. Paper, gilt, stained, coloured, embossed, and all fancy kinds, not being paper-hangings the lb. 0 0 2 The duties of customs chargeable upon the goods hereafter mentioned, im- ported into the United Kingdom, shall cease and determine on and after the twenty-third day of June one thousand eight hundred and fifty-three; viz. Flock for paper stainers. On and after the fifth day of July one thousand eight hundred and fifty-three so much of an act passed in Session of Parliament holden in the third and fourth years of the reign of His late Majesty King William the Fourth, chapter one hundred and one, section three, as provides that the allowance commonly called draft, then made by the Commissioners of Excise in the weighing of tea, should be made by the Commissioners of Customs under the authority of the said act, shall be and the same is hereby repealed; and the allowance of one pound for draft on each chest of tea exceeding twenty-eight pounds in weight now made by the Com- missioners of Customs under the authority of the said act shall cease and determine upon all tea which shall arrive and be reported at the custom house of any port in the United Kingdom on and after the fifth day of July one thousand eight hundred and fifty-three. The duties imposed by this act shall be under the management of the Commissioners of Her Majesty's Customs, and shall be ascertained, raised, levied, collected, paid, recovered, and allowed, and applied or appropriated, under the provisions of any act or acts now in force or hereafter to be made relating to the customs. 833 HARWICH, DOVERCOURT NEW TOWN. 2ND CLASS. END ELEVATION. ELEVATION NEXT GARDEN. 16 by 14 [O] 28 by 16 6 ONE PAIR. ESTIMATED COST £450. 16 by 14 28 by 16 6 GROUND FLOOR. 3 D 835 VILLAS, CARLTON ROAD, KILBURN PARK. ROAD,KILBURN ELEVATION, 10 by 8 6 17 6 by 15 6 14 6 by 12 6 11 by 9 6 10 by 8 6 17 6 by 15 6 22 6 by 146 『 10 by 86 1 20 by 16 20 by 16 17 by 15 6 196 bym 7 17 by 156 ONE PAIR. GROUND FLOOR. ESTIMATED COST £850 THE PAIR. 837 WESTBOURN PARK, PADDINGTON. FULL-SIZED 3RD CLASS. ELEVATION. 74 FEET. 14 6 by 12 12 by 10 6 14 6 by 12 18 by 13 12 6 by 8 9 12 6 by 8 9 18 by 13 GROUND PLAN. CHAMBER PLAN. ESTIMATED COST £800 THE THREE. ONE PAIR. [over. PLAN VARIED. 14 6 by 12 12 by 10 6 14 6 by 12 18 by 13 12 6 by 8 9 18 by 18 839 HILL, ST. JOHN'S WOOD. No. 2, CARLTON HILL, ELEVATION. 20 by 16 16 by 13 20 by 16 27 by 16 12 by 12 16 by 13 12 by 12 ONE PAIR. ESTIMATED COST £475. GROUND PLAN. 841 33 PADDINGTON ESTATE. 2ND CLASS. ELEVATION. H 14 by 13 14 by 13 20 by 18 20 by 18 白宫 GROUND PLAN. ONE PAIR PLAN. Cost £1000 THE PAIR. [over. : GROUND PLAN. 14 by 13 20 by 18 843 TORIANO AVENUE, KENTISH TOWN. SMALL 3RD CLASS. Conser- vatory. MRUMIMILA ELEVATION. 39 FT. 6 IN. 18 by 13 18 by 13 10 2 by 8 9 13 by 8 9 10 2 by 13 by 8 9 8 9 14 by 12 14 by 12 14 by 12 14 by 12 BASEMENT AND GROUND PLAN. COST £500 THE PAIR. ONE PAIR PLAN. [over. O rezzak 18 by 13 14 by 12 Conser- vatory. BASEMENT AND GROUND PLAN. 845 SAXON VILLA, CLIFTON TERRACE, BRIGHTON. SA PERSPECTIVE SKETCH. 16 6 by 17 by 14 17 by 14 16 16 6 by 16 13 by 12 18 by 15 14 by 10 ONE PAIR. ESTIMATED COST £200. 13 by 12 18 by 15 GROUND PLAN. [over. 17 by 14 13 by 12 GROUND PLAN. 18 by 15 847 HARWICH, VILLAS AT DOVERCOURT NEW TOWN. 3RD CLASS. TAVA NAVA VAYA ELEVATION. 21 by 12 21 by 12 18 by 12 18 by 12 BASEMENT AND GROUND PLAN. COST £750 THE PAIR. 849 VILLAS, CARLTON ROAD, KILBURN PARK. ELEVATION. 14 6 by 11 by 10 11 by 10 12 6 17 by 14 6 lo T 14 9 by 14 6 14 9 by 14 6 88 17 by 146 17 by 14 6 116 | 11 by 10 10 by 14 9 by 14 6 96 14 9 by 14 6 10 by 96 BASEMENT AND GROUND FLOOR. ONE PAIR. TWO PAIR. ESTIMATED COST £650 THE PAIR. 3 F 851 DOVERCOURT NEW TOWN, NEAR HARWICH. GARDEN FRONT. 1 ܢܶܐ. 20 0 ELEVATION. PRINCIPAL FRONT. 13 by 12 16 6 by 12 18 10 by 14 14 by 9 3 14 by 95 GROUND PLAN. CHAMBER PLAN. COST £650. [over. GROUND PLAN. I 1 I 16 6 by 12 18 10 by 14 853 DALSTON, NEAR LONDON. FI 1 190 10 8 8 12 13 12 13 10 15 15 20 10 feet Cost £340 THE PAIR. LET AT £23 PER ANNUM. CONTAINING SIX ROOMS AND CONVENIENCIES. Thos. Tatlock, Archt., Dalston.] 855 Ο 1 Thos. Tatlock, Archt., Dalston.] VILLAS IN REGENT'S PARK. PANE 19 2452049 9310. clost Area. Tardr Store Room Passage Coals C Kitchen Scullery 12 by 10 6 1 LI 6 2 14 12 11 77 6 6 11 61 8 39 4 20 10 feet. CONTRACT PRICE £1500. EACH CONTAINS TEN ROOMS, PANTRY, CELLARS, AND CONVENIENCIES. RENTAL £75 EACH. 13 3 857 ON LANDED PROPERTY. CHAPTER I. LANDLORD AND TENANT-THEIR POSITION AND CONNECTIONS. THE landlord is the owner of the soil, whose proprietorship Right of oc- has been derived chiefly from priority of occupation, and from cupancy the act of labour subsequently bestowed. To these rights of occupancy a tacit acknowledgment and virtual acquiescence have been yielded by the general consent of the human race. Jurists have entangled themselves in very lengthened disputations and much subtlety of argument in trying to determine whether the act of labour was necessary to support the right acquired by priority of occupation; and also, if the public assent be essen- tial to confirm the two privileges, when joined, in constituting the owner- ship of property. The question has been long since settled by general opinion conferring on land the same rights as any other articles confirmed by which a man can call his own; the same vested interests, and law. the same inalienable adjuncts. The law of civilized nations, or morality armed with power, has sanctioned the conferment, and upholds the continuance. land. 4 Land has been appropriated in order to make it more generally useful, and to create a general interest in its favour. An enlightened barbarism made the first appropriations in large grants of land as the plunder of conquest, and the reward of services, to be held in tenure for future per- formances and attendance. The inconvenient superintendence soon induced the dismemberment of the extensive grants; the uncertain and Grants and short-lived reigns which prevailed, caused many confiscations; alienations of and the constant wars and intestine broils of unsettled times, produced large changes in the possession of the separated portions of the grants. The no less quarrelsome leisure of peace had a large effect in leading to fines and confiscations, which still further augmented the distri- bution of the land as private property. When trade became flourishing, and money became abundant, land was bought and sold as any other marketable commodity, the divisions being varied chiefly by chance and accident; a large part generally remaining with the name of the Rest on ap- original holder, and still giving the title and rank which accompa- nied the gift. In this way land has become the property of the present pos- sessors, who hold by purchase, which rests on the original appropriation. For a very long period of time the property of land constituted almost the only form of wealth and power, and carried along with it the sole dis- propriation. 3 G 858 ON LANDED PROPERTY. Land the dis- tinction of society, and its power tinctions of society. The nobles and proprietors formed one part of the community; and retainers, dependents, and slaves, were the other portion, which was almost wholly bereft of personal liberty, and lived on the charity and pleasure of the higher grade. There was no nobility without property in land—no power, no respect, nor even the natural gift of personal freedom. Every idea was based upon the soil: all settlements and associations, isolated or collective, were founded upon the country, by which the mode of life was regulated, and the social institutions conformed. In every country where land has been appropriated, in every form of government, and under every dynasty which has ruled on earth, in every change and revolution that has happened, and under every different phase which society has assumed, the land-owning body has ever had a preponderance in the legis- lation, and has directed the machinery of government. A certain pres- tige of independence and patriotism has always in some kind and degree been found attaching to the owners of the soil, which has not a little con- tributed to the essential qualification in a member of the legislature, and of the open recognition of landed property conferring a title to the dis- tinction in that respect. The early preponderance of the owners of the soil has not been lost, and little if at all impaired by the upheaving of the other classes of society-an influence still clings to it, as compared with other kinds of property, and an earnest desire for the possession of it is evinced by all persons who can command the means of purchase. and avidity The durable nature of its essence forms the primary considera- its influence of purchase, tion, the current value may fluctuate as that of other commo- dities, but a total loss never can be sustained by its possession, as no evanescence takes place of the original matter. This quality confers the superiority of property in land over other inheritances, and has raised the estimation both of the article and the possessor. The detached and iso- lated position of the property confers a power that is of a very useful and agreeable exercise, and it affords a relaxation not enjoyed by other employ- ments of capital and time. This leisure gives opportunity for the dis- charge of public duties, which interfere least with the absence from business of the habits of life which those duties occasioned and required. The business of legislation gradually fell into the hands of the party which had most leisure for the purpose, and inclination for the object. The and changes from the social effect. gradual increase of numbers soon acquired a preponderating force, which materially changed the original idea and constitu- tion of the British House of Commons. Under the gifts of feudal tenure, the possession of land was conferred on the condition of military service, and of furnishing a fixed quota of armed followers, bearing the same relation to the landlord as he did to the sove- reign. Land under its feudal relations was regarded as a thing out of com- merce altogether, and no idea was entertained of its being a certain amount of property appreciable at a money value. It was estimated to be an in- alienable "entirety" held under the crown, and the gift and the condition ON LANDED PROPERTY. 859 holding. of tenure, with the concomitant obligations, passed exclusively Original to the eldest son, whose prior right in every affair has been re- cognized from the first dawn of civilization and of social arrangements. This “backbone" of feudalism has been copied into the laws of real pro- perty, as the land is termed, along with its immoveable subordinations, in contradistinction; or of personal property, which consists of moveable goods of every kind that are evanescent in quality and perishable in the nature. When the growth of towns, and the influx of money, along with other cir- cumstances, compelled land to be an article of ordinary bargain and sale, and of conversion into money and reconversion, the custom primogeni- was continued of devolving on the eldest son, the inheritance of ture, the landed property: it was ultimately restricted by law to cases of intes- tacy only. This law of primogeniture has been much reviled, as “to enrich one it beggars all the rest of the children," and as making distinctions, which tend to disarrange and disunite the frame-work of society. But in the main it has been productive of much good: the landed property has been preserved in fair and suitable divisions, which uphold the influence and support the respectability: it has been kept from being use and abuse partitioned in minute sub-divisions, which derange the general of it; utility and take away the power of its own improvement by the total want of means. Feudalism saw that its purposes required the grants of land to be large rather than small, and civilization finds that to be improved and its resources developed, land must be in the hands of wealth of an amount that is able to furnish the sufficient means for that purpose, and also to make the suitable family provisions that attend the relations of human nature. In Britain, primogeniture applies in cases of intestacy only, and most completely differs from the arbitrary laws of continental Europe, which divide the land among the children, without or with the differs from parent's consent. This compulsory partition, though seemingly the continent founded on justice and equity, has been found very injurious to of Europe, the general interest, and not very profitable to the parties themselves, who obtain shares of insufficient amount, and which must be assisted by other pursuits. The evil has been produced by an extreme of the application, which in a well-meant intenseness overlooks the contingencies that are near, and the consequences that are remote. It has been much and less more hurtful than the use of primogeniture, even in the hurtful. opinion of its warmest admirers. the law of Land-ownership is thus privileged with the application of a law, which in cases of intestacy conveys the property intact to the eldest son, or heir- at-law, who receives the patrimony in exclusion of all other claims. It meets our approbation in so far as it preserves the land in portions suffi- cient to support its respect and maintain its dignity, and by which the general utility is developed, and the efficiency remains unimpaired. When divided estates of land are held in one possession, the parental judgment must exercise its discretion in devising, by will, the due bequeathments of the adequate value and amount. And if by intestacy the whole landed 860 ON LANDED PROPERTY. property goes to primogeniture, the next revolution in the family of pos- session may correct the discrepancy, and modify the standard of in- heritance. Entail of land. Stretch of ture; A stretch of primogeniture has produced the entail, by which landed property is devised by one possessor to pass for ever in one line of possession, as may be defined in the deed of settlement. It also passed free of all debts, which were obliterated on the successor re- ceiving the property. This regulation has proved a complete snare to the commercial dealer, who was debarred from touching the property itself, and who found his claims wholly extinguished by the exchange of pro- prietors. The entail of lands of a proper and moderate extent in a direct line of succession constituted no evil of itself, it was only pri- primogeni- mogeniture secured by a regulated assignment, which set aside any other intentions on that point. But very questionable was annulling of the extinction of debts of all kinds at every change of ownership, debts hurtful the iniquity was palpable, and the damage to society needed not any demonstration. The remedy was simple, in leaving the property to pass intact, and in the law allowing the creditor a fixed annuity till paid his claim from every successor in the property. As the entail stood, a barrier was raised against any movement on the property, no improvements could be done, nor any liability contracted. The hands of the landlord were fastened, and his willing energies rendered useless. In many cases, the difficulty of improvement lies far less in the unwillingness or ignorance restricts im- of the landowner, than in the irrelevance of the proposed advan- provements. tage to his personal interests in his parental or other capacity, or in his pecuniary inability to undertake it. The landlord may be the father of a large family, all unprovided for, except the eldest son, upon whom the estate devolves, and every outlay on the land only adds to the settled in- heritance, to the loss of the unportioned part of his family, or he may be a young proprietor just come into a possession burdened with jointures, mortgages, and the unpaid portions of younger brothers and sisters charged upon his estate. Debts, mortgages, and incumbrances will be incurred in the course of human transactions, and whenever a landed security can be got, an encouragement is held out to advance money upon it. It is certain that not more than one-half the income derived from land truly belongs to its nominal owners, and the proportion has by many well-informed persons been estimated at not more than one-third. The remainder belongs chiefly to others, to mortgagees, rent-charge owners, jointresses, annuitants, and the like; while the nominal owners bear all the costs of management, and all the accidental or occasional losses which are necessarily incident to landed property, whether held beneficially or other- wise. Such cases, and others of a similar nature, form the large majority: absolute and independent ownership is a rare occurrence. Burdens by it. Disruptions These impediments have been somewhat removed by the par- and power tial disruption of large entails, and by a recent act to lay out money. capital upon the settled estates in such a manner as to constitute to lay out ON LANDED PROPERTY. 861 a separate investment, devolving as rent-charge upon the heir-at-law, or next in the settlement. It remains to be seen whether these measures shall prove only momentarily advantageous or permanently of the benefits that have been expected. The borrowing of capital to carry on business of any kind is not generally to be approved, and it is preferred to reduce the business to the capital. Loans of money contracted upon the Loans of provision of the principal and interest being repaid together in money not a fixed number of years, seem to double the evil which are in- geous, tended to be modified, by encouraging a course of investment which will call for artificial aid to support it, and by strengthening and indirectly sub- sidising a system of family entail, as against purchasers, and thus prevent- ing the application of free capital to the soil, which should be facilitated by every wise government. advanta- unless due exercised. But if there be not a sad deficiency of judgment in the application of capital in the improvement of landed property, such incumbrances and an- nual charges as are incurred by the government loans of money are very trifling in comparison with the quick and lasting benefits that are derived from the drainage of arable lands that are fitted to repay the cost, from the erection of suitable and well-designed farm buildings, and from the plant- ing of waste grounds that are naturally removed beyond any spe- cies of cultivation. The two latter purposes are only in prospect, judgment is but must soon be included in the act; and though the profit of plantations be of a distant nature, it must be reckoned an application of a most suitable kind as a permanent investment. The raising of embank- ments and the cutting of water-courses may also be included in the provi- sions of the act, and thus comprehend the most obvious and tangible im- provements that can be effected on land. The charge must be reckoned trifling in respect of the benefits derived, and as the tenant will assist with the draining of land and the erection of farm buildings, the charge is in these two points very much lightened to the proprietor of the land. And the benefit remains with him, for the tenant cannot carry away or undo the labour he has expended in assisting the drainage of land, or in the erection of farm buildings. The policy has been questioned of for younger. securing by the act the outlay of money on settled estates sepa- rate from the inheritance in investments for younger children, as being a fresh edition of ostensible ownership, the next heir being a mere rent-payer for his predecessor's improvements, the rent-charge of which will belong beneficially to others. children. Holders of and at will. The position of the landlord who is tenant for life, and of the farmer who is tenant at will, is strictly analogous. In both cases the land for life outlay of private capital is discouraged, in both cases the natural policy of reducing the extent of land to the means that are at command, is preferable to the expediency of the artificial and temporary aid of loans. The improvement effected by drainage has been allowed an exception to two rules of policy-one public and the other private; the first against the loaning of government funds to individuals, and the other against entering upon investments with borrowed capital. This compliment has been seen 862 ON LANDED PROPERTY. to be well deserved by the operations of the Drainage Act. It has been ob- jected that it goes to keep lands beyond the reach of commerce, which every policy of law should discourage. But in transfers of land very both hurtful. much uncertainty prevails-the new comer may have different views from the old possessor, who may be supposed to have better local knowledge and more solid views of the wants and capabilities of the land. In many cases, loans may be much more beneficial when judiciously ap- plied than an influx of capital, which must seek its way for use, and its vents for application. Government money. Draining, The government loans of money can be applied only to the loans of purposes of improving the land, which enables the proprietor to provide for his younger family with the rental of the property. Nor can any heir of land with any reason object to a charge being paid annually for improvements of which he derives both the immediate and lasting benefits. Drained lands are of large value over wet buildings,and grounds, commodious and substantial farm buildings offer a planting strong enticement to a spirited tenant, and rising plantations are an encouragement in sheltering cultivated lands for the use of stock. Such provisions justify the incurring of a rent-charge, which differs wholly from common debts that have been contracted for other purposes, and ex- haust instead of renewing the sources of the property. No charge claims the name of debt, which pays itself by its own action, as in the case of landed improvements. The peculiar position of many landowners is very much promoted by the government advances of money, the negotiation of which is simple and firmly regulated, and admits no jarring or most useful. tendency to litigation. Much good has been done, and very comprehensive benefits will accrue from the inevitable enlargement of its provisions, as has been already suggested in the application to farm build- ings, plantations, embankments, roads, water-courses, and permanent pur- poses of every kind. Encumbered When an estate of land has got encumbered with debts and estates, burdens that are absolutely beyond the power of recovery, and the property is incapable of supporting itself, or of affording a maintenance to the owners, a power ought to be lodged in the law court of the last re- sort, by which to sell the property, extinguish the burdens, apply the residue, and convert the land to the free course of the legitimate purposes. The want of this remedy has been long felt, and is now applied how freed. in Ireland, where the just expectations are being realized. Such a course is essentially necessary for public purposes, and to relieve the pro- prietors from a burden intolerable to themselves, and most obnoxious to the future inheritance. The landowner has been gradually relieved of the encumbrances which were placed on landed property in order to secure the successive inheri- tance at a time when the appropriation of it had not discovered the just purposes of its use, and the true development had not appeared. As Altered policy. population increased, the social organization was enlarged, new wants arose, and fresh demands clamoured for satisfaction. The ON LANDED PROPERTY. 863 trammels of feudal policy, and the fetters of selfish monopoly, were com- pelled to succomb before the rise and growth of free ideas and liberal in- stitutions; and the changes that were compelled to be adopted contributed most powerfully to the benefit and aggrandizement of the owners of the soil. The relaxations have been slow and very gradual, and have been forced by circumstances, rather than adopted from conviction, of justice and utility. and of leases. Experience soon showed that the owner of a large tract of land, even when he has the requisite capital or knowledge, could not successfully be- come the great farming merchant of his own acres, or employ Origin of them so advantageously in any way as by letting them in sub- farms, divided portions to others. This very obvious conclusion soon led to the giving to other persons the use of the lands in definite portions on paying to the superior a fixed quota yearly: first, of personal services; next, of the different kinds of produce; and lastly, of money only. The land was long held by the payment of services and of produce, and the feudal dominion existed over the goods of the tenant in liability for the debts of the pos- sessor of the soil. The holding existed only for the life of the grantor, and for one year during his pleasure. This uncertainty was not removed till near the end of the fifteenth century, when the goods of the tenant were declared not liable for the debts of the landlord, and a tenure for a specified number of years was held good against the successors in the property, These two acts fixed the basis of the position of the tenant, and consequently, of the success of British agriculture. The tenant of land is the holder of a certain extent of ground, for the use of which, in cultivation, he pays to the owner of it a fixed amount of money, which is commonly called the yearly rent of the farm, or of the land that is used. On this quantity of land the farmer employs a capital that is at first floating, and gradually becomes fixed, by means of being invested in the soil, by increasing its productiveness, from operations more or less permanent in their nature. Every operation requires the means of performance, and results can only come from causes that are adequate to produce them. The tenant of land who employs. these means, most naturally expects to enjoy the results, and to reap the benefit of his operations. He looks to the landlord to grant him the security of enjoying the reward of his labours, and of reap- ing the harvest of the seeds which he has sown. The position of the tenant is based on this primary foundation, which the landlord can- not with any justice refuse to grant, for he will not himself build a house, make a road, or plant a tree, till the rights of property are securely granted him, and he cannot with any reason expect others to do what he will not do himself under exactly similar circumstances. Capital recoils with instinctive abhorrence from the want of security; and next to the preservation of human life, the safety of property constitutes the leading feature of civilized society. Without this safeguard, capital re- Great value mains in a useless condition, labour is unemployed, and the of them. population is deprived of the legitimate enjoyments of their vested inheri- Policy and security. 864 ON LANDED PROPERTY. Length of most essen- sary. "" tance. It is found to be most essentially necessary in every case of rear- ing a durable superstructure, to find a firm foundation on which to lay the rests of the construction; if it be unstable and shifting, the aversion will quickly appear of refusing to expend capital and time in an undertaking of that precarious and fluctuating constitution. The security must be ex- tended over a time that is sufficient for the development of the intended purpose, which must be calculated in strict relation with the elements on which the action will be exerted. The nature of the productions of land requires a much longer time than many other employments in which to repay the cost of cultivation, years are required for each kind of tenure, produce to contribute a share of the outlay that has been made. Hence, a short tenure is nothing better than a yearly holding, if there is more time to expend, there is a very insufficient opportunity to reap the fruits that are grown. "Give a man the secure possession of a bleak rock," says Arthur Young, "and he will turn it into a garden—give him a nine years' lease of a garden, and he will convert it into a desert. It is not possible to banish from the mind of the tenant-at-will the very pal- pable truth, that every improvement he makes on the land is producing a value to others, and in all probability raising the rent against himself. Besides, the annual expenditure that is necessary to carry for- tially neces- ward the current operations, many contingencies occur that are unavoidable, and which trench upon the capital of the tenant. It is impossible to cultivate land in any profitable way without incurring an expenditure more or less beyond the bare necessities of a pinched utility of the ground. The tenant may have a well-grounded and unbounded confidence in the owner of the property, that he will not be disturbed by him, nor denied the fruits of his labours, but he has no knowledge of the successor—a widow in straitened circumstances, who may be compelled to use every means to raise money—a minor under unscrupulous guardians, Danger from who will stickle at no point in order to accumulate the wealth of want of it, their charge, or some prodigal hunter or lover of the turf, who, in order to gratify his passions, cares not for to-morrow, nor even for the afternoon of the present day. These, and many other changes of a similar kind, stare in the face the tenant who depends on the faith that is not beyond chance and accident, and convince him of the inconvenience of his situation, and the irksome apathy to which he is reduced. The conse- quences never fail to re-act upon the landowner himself, who finds a dimi- nution of his rental to happen yearly, in order to supply the necessary demands, of which the situation of the tenant prevents the performance. He soon finds that it is much easier to uphold than to restore, and that fer- tility when once abandoned, requires much time and cost to be repaired. The tenant finds a constant diminution of his sup- plies, and fears to use the means of increase, as others may obtain the aug- mentation. Habit and custom may accommodate the minds of men to such a mode of tenure, as by it the natural indolence is cherished, and exertion is not required. A rent is raised by certain means which have been long practised, and are well understood; no prejudices require to be removed and its evils ON LANDED PROPERTY. 865 nor any entertainment made of troublesome innovations. Exertion and in- dependence, which are the life and soul of industry and exertion, are wholly lost. Not only all great improvements, but even the most common works of the season will be imperfectly performed, and little can be hazarded beyond the expenses which the returns of the year will defray, when the farmer cannot look to the future with security. Capital will be spa- upon every ringly expended on another man's property when that security kind of pro- of possession is denied, which is essential to the safe and pro- fitable application of money; the agriculture of the country will never ar- rive at the advanced condition of which it is susceptible; and the persons employed in the occupation will lag behind the other productive classes in their means of improving their art and acquiring knowledge. ceedings. Not only the landlord but the country suffers by the less improved condition of the public territory, from the want of just and fitting tenures on his estate. Much land remains uncultivated, or is kept in a very inferior condition of growing grass, which renders security of comparatively less value, as the land requires little expenditure, that cannot be re- placed within the year, and a long possession is not absolutely Cultivation necessary to enable the rearing and feeding of cattle and sheep. is lessened. This state of things incurs a large diminution of the general production, in which every individual of the community is interested, from the pea- sant at the plough to the peer who legislates for universal satisfaction. It has been urged against leases of land, that the farmers themselves set no value upon them; but this argument leads to a very different con- clusion than the intended contradiction. The absence of security has engendered an utter ignorance in the cultivation of the soil, of the means of employing their own capital with advantage, has indisposed them to the exertion which improvements demand, and has produced a better contentment, with an easy rent and dependent condition, than with the prospect of an independence to be earned by an increased labour Ignorance both of body and mind. The rent is lower and requires less and indo- exertion, and the eye having been accustomed to behold one produced. state of things, no other condition can be entertained. This tenancy having become the habit of the country, not only re-acts upon the condi- tion of the occupiers of farms, and the means of perfecting their own art, but it affects, essentially and directly, the interests of the landowner and the country. lence are The only fitting security for a man who has capital to employ in the cultivation and improvement of land, is a written covenant subsisting for a definite and adequate period. The term must be defined, in order that the property may not seem to be alienated, and the period of time must be adequate, to draw back by periodical returns, in the lapse of years, the capi- tal that has been expended. It is the peculiar nature of the returns from land to be extended over a number of years, and to be obtained in a succession of crops that are allowed by the sea- son; and not only is a period required to effect the operation, but a time likewise to recover the funds expended. The employment completely Written co- venant the best security. 866 Land differs ON LANDED PROPERTY. differs from manufactures of perishable articles; the results of one opera- tion are generally sufficient to reimburse the outlay, and the capital is restored with recompense. The changes of summer and winter do not interfere with the proceedings, nor does the want of security affect the use of the means that are necessary to promote the advancement. The machine is the property of the person who erects it for the purposes of trade, and the more perfect it is made, the more profit will be derived by the owner. But no such assurance rests with the cultivator of the soil, from Manu- who tills the great machine on which his all depends. It is factures. the property of another, who will in the end profit by the im- provements which are made by the temporary possessor. The manufac- turer receives directly the profits of his stock in trade; the farmer must share the profits with another, who risks neither money nor labour. The farmer is fettered by conditions imposed upon no other class of traders, and the inconvenience of obtaining returns for the current expenditure more slowly than in any other occupation, are frequently attended with the uncer- tainty, if the capital advanced can ever be recovered. The employment of capital on the property of another, must ever be attended with certain drawbacks that are not easy of adjustment with relation to the value of the returns: but the insecurity with respect to the future, and where the possessor cannot employ his funds in the man- ner which his interest requires, will greatly increase the inconvenience and perplex the equitable adjustment in an affair where just concessions are essential to any legitimate compromise. Longer secu- rity neces- sary. Security the base of farming, The security of possession being the basis of the position of the farmer, constitutes the foundation on which all the other relations depend: without it, the very best arrangements, and the most favourable subordi- nations are impotent and wholly useless. Not that other points of posi- tion do not bear a part in forming the proper place in which the cultivator of the soil must be located. The sequel of this chapter will show the value and necessity of the accompaniments; but unless they are based on freedom of action and security of possession, no corresponding benefits accrue from the attendance of the isolated at- tachments. The action of the whole possessions is paralysed and ren- dered of none avail, by reason of the want of the lever power to raise the joint operations. With every propriety and the utmost justice, the security of tenure in land for an adequate period of time, is made propriety to occupy the first place in every arrangement of relations between the owner and occupier of the soil. No sane person will involve himself in any undertaking without that essential provision. The capital of the farmer being expended on security of tenure, comes next to be used upon the capital of the landlord, which is sunk in the permanent provisions which are required to make the land advantageous to the occupier. These provisions constitute the furniture of the farm, Furniture of without which the occupation cannot be converted into the be- the farm pro- neficial purposes. The nature of the utensils is durable, as being fixed upon and growing in the soil, and continue for years with every and justice, vided by landlord, ON LANDED PROPERTY. 867 to fulfil the intentions of the formation, consequently they become exclu- sively the province of the landlord, and are entirely of his concern in the cultivation of the soil. The outlay of the necessary fixed capital must be regarded as that which falls peculiarly and primarily upon the owner of the land, and which cannot be devolved on the temporary occupier without a more than corresponding sacrifice of the permanent interests of an estate. The capital being expended by the landlord, who receives in- terest on the outlay, in the form of the greater rent which the land is rendered capable of yielding. The two interests involved in the profitable occupation of the soil, are the permanent and the temporary, or the owner who holds in perpetuity, and the farmer who uses the soil for a specified duration. Hence the provisions that are durable in nature, and which fulfil the purposes of use for a length of time, are very naturally assigned to the cost of the land- owner, whose interest in the land accords with the services of the pro- visions. To the tenant who holds for a fixed period of time, upheld by there is naturally assigned the temporary upholding of the fur- the tenant. niture which he uses, on his receiving the raw material of which the fur- niture is made. This arrangement well coincides with the temporary interest of the tenant. He uses, but does not afford; he repairs the wear of application, but not the decays of nature; and maintains the fixed ap- pendages in the current going order. Farm, The first object of attention and necessity in the cultivation of land, is the adequacy of the houses, or buildings, for the use of the farmer: and of these erections, the chief attention is the dwelling-house to be inhabited by the family of the farmer. The comforts and elegancies of life have descended in Britain to the degrees of capital which have been estab- lished among the different grades of society, each class challenging Dwelling- and expecting that their vocation shall afford equal accom- house on the modation with similar grades of employment. The reasonable- ness of this expectation cannot be disputed; the manufacturing classes have shown the way, and the agricultural employment must necessarily follow. Scarcely any provision will form a stronger inducement for the occupation of land than a dwelling of suitable accommodations, at least to the respectability, which it must ever be a leading object with the land-owner to induce, to settle upon his property. Several wants and in- conveniences will be overlooked, and even very necessary demands will be relinquished in cases where this primary provision is fully complete, and when attended with a well-stocked garden and orchard, the Garden and owner of land cannot devise any more alluring objects to the orchard. eye of inspection. Vegetables and fruits are now indispensable articles of almost daily consumption, and a rural dwelling loses the name without them. The farmer having seen on a farm a suitable accommodation for his family and domestics, next proceeds to examine the buildings that are intended for the protection of animals, and the manufacture of produce. These erections must exist in the corresponding degree of convenience 868 ON LANDED PROPERTY. ment. General buildings and usefulness, and in the number requisite to the amount of business to be performed. The inspecting tenant, if he be of the enlightened sort, will speedily ascertain if the number and arrangement of the buildings will suit the purposes of cultivation which he intends to adopt, and will point, at the same time, to the wants that appear, and suggest the amend- That the greater part of the farm buildings of the present day are sadly deficient, no person offers to deny; but it is pretended that no substitution has yet appeared to warrant the removal, or that no complete form has yet been devised beyond which no advance can be made. But from deficiency to a completeness of no further pro- gression, many steps intervene, and very much usefulness is contained; neither nature or art advances by such extended leaps, but by gradual steps of progressive ascent. Improved designs of farm buildings are known which will command five per cent. on the outlay for the lease of twenty years, separately considered as an item, or will add very consider- ably to the general rent of the farm. Without the proper accommoda- tions, the live stock cannot be bred and reared, with the known advantages, nor can the grain produce be manufactured with the economy that is requisite in the detailed business of farming. It is idle to pretend that ideas are undetermined on the subject of farm buildings, the progression in that point is equal to the general advancement, and the adoption is only prevented by the general aversion to change. To wait for a "ne plus ultra" perfection on any point, would delay all human progress. are most necessary. Labourers' cottages The cottage dwellings of the labourers that are required on a farm, claim a most especial attention both from the landlord and the farmer. Till of late years, this department found no notice in the general esti- mate of the furniture of landed property; the old hovels, resembling pin- folds, were considered sufficiently good, and the horses and dogs. had more consideration than the labourer, who is the life and soul of every act and operation. Some considerate landlords have led the way in erecting very much improved dwellings for the accommodation of labour; and philanthropy has appealed to the feelings of human nature in behalf of the hitherto neglected portion of the community. The far- mer must see that he has got accommodation for the labour he may require, afforded in the necessary quantity, and placed in the proper convenience. Any want on that head, will form a very great determent to the embark- ing of a floating capital to be productive of mutual benefits. Immorality and disease have been widely propagated from the confinements sable. in which cleanliness cannot be adopted, nor the decencies of life maintained. The civilization of the present age demands a wider step being made at once on this point than on almost any other provision of the social system. When a moderate exaction in the shape of rent has been arranged with the farmer, and the land has been amply provided. with the fixed capital that is necessary for the development of the float- ing funds of the tenant, the attention of the landlord should descend to the condition of the labourer, by the employment of whom both his own are indispen- ON LANDED PROPERTY. 869 Accommoda- wages. station and that of the cultivator of the soil is raised and upheld. Capi- tal is merely an accumulation of labour, and it is just and reasonable, morally binding, and religiously imperative, that its attention be directed to, and its care be bestowed upon, the comfort and maintenance of the source whence it originates, and by which it is sustained. The owner of the soil has wholly in his own hands the power and the means of providing comfort for labour in suitable cottages, garden grounds, bakeries, pig-styes, and the supply of water: but he is unable to fix the tion and wages of labour, as it is a marketable article, and liable to the fluctuations of supply and demand. But it is more stationary, and much less evanescent than those articles that are strictly perishable in their nature, and it is capable, if not of a permanent adjustment, at least of a temporary understanding, as to the amount of the remuneration. With this view of the matter, the farmer may be understood by the landlord to pay labour in the highest rate that is known to be given in the district, and if that amount be low, an advance may be led in a small progression. The state of society does not yet admit a binding clause to this effect in an agreement of demise and use, but it is quite possible to introduce a tacit understanding of the performance, which may soon lead to a public avowal of the arrangement, than which nothing will more powerfully conduce to the strength of society. It will rivet fast in affection the con- tiguous planes of the social organization, and solder the jarring elements of discord, it will multiply the strength of every chain, and link together in a firm union all the junctions of the mixed connections. Of all the plans that have been designed, or that may be intended for the ameliora- tion of the labouring classes, none is so simple and so effectual as the increase of the commodity by which are obtained the essential necessaries of life; and in the case of farm labourers, the landlord must lead the way in the provision of the fixed articles in dwellings and their appurtenances. An example must be shown from the highest quarter, and then the next lowest can be used by treaty to confirm and uphold the arrangement. Though the figure of the numerical amount of wages be not named, the sum can, nevertheless, be entertained in a tangible estimate. Roads, affording a convenient and ready access from the farmery to the different parts of the farm, are a very essential part of the provi- sions that are required by an extent of cultivated land. Most farms adjoin a public road, or are intersected by it, and the private roads will be much guided by the public line, both in the direction they are made to take, and in the number of the paths they afford. The roads Roads and must be durably made by the cost of the landlord, and the keep- gates must ing in repair devolves on the tenant. The farmer must see that provided. the quantity of land which he intends to rent is suitably provided with the necessary intersections of access, or the animal labour will be much harassed, and the wheel carriages be unnecessarily worn. amply If any rivers or large brooks of water run through the farm, or form the boundary of it on any side, the overflowings of the swollen state must be prevented by suitable embankments, and the courses assisted by being 870 ON LANDED PROPERTY. straightened and thrown at the turnings into the proper channel. The farmer must observe that no damage will happen from overflowings of sluggish streams, nor from alluvial flats being torn and wasted by impe- tuous torrents, rushing against the banks and wasting the soft materials. If neglect has allowed these devastations, the loss must be estimated, and the recurrence prevented. Fences a Fences and gates constitute a part of the fixed capital or furniture of a farm, that demands a very ample fulfilment on the part of the owner of the soil. Fences enable the farmer to guard his crops from damage, to separate the different kinds of beasts, to divide into suitable lots special care. the grazing animals, and to use the fields of land in the due ro- tations of cropping. Without divisions, these purposes could not be at- tained, nor the value of the land realized. Gates are no less necessary to open and shut on the gaps in the fences that are left for a road into the fields, and which afford an ingress and egress to the animals, and to the wheeled carriages and other implements when the fields are cultivated. The fences must be complete for the purpose of confining the lots of ani- mals, and the gates must be ready in the action, and strong in the form. The provision of water for some special fields of the farm may be men- tioned as an appendage to the necessary furniture of the possession. A Provision of field or fields may be required for cows' pasture, one for horses water. or young cattle, to which water may be brought by boring, or in pipes from a distance. This provision is not general, but may be very properly hinted in this place. must Equitable rents must occupy a large consideration in fixing the position of the cultivator of the soil. Rent is the surplus of the value of the pro- duce of the land that remains after every labour is paid, and the farmer's family maintained. This original and very just definition of rent has been Rents much encroached upon, and almost wholly overturned by the be equitable, revolutions of society, which have brought the word to mean the market price of the soil as an article of commerce for the specified time, from which the other considerations are wholly excluded. Two elements in the present day, which cannot be separated in practice, con- stitute the payment made by the farmer to the owner of the soil, the sim- ple price paid for the use of the land, and the interest on the fixed capital in the buildings, enclosures, and other improvements which have added permanently to the productiveness of the soil. It is not necessary for our present practical purpose to make any illustration of the theory of these separate elements, or to pursue the paths of investigation that have been followed by political writers, in order to explain the nature and causes of rent. All land in this country capable of cultivation, justed. yields a rent; and also if it produces the grasses in sufficient quantity that feed the domesticated animals, the rent will bear a pro- portion to the fertile or barren quality of the soil, the favourable position of the farm, and the advantages of occupying it by buildings and other necessary adjuncts. and practi- cally ad- . No rules can be established in respect of the proportion of the value of ON LANDED PROPERTY. 871 the produce that shall be paid in any case as rent. The mode of agricul- ture that is pursued, and the habits and condition of the tenantry possess a large degree of influence, the nature of the returns, whether it be corn or animal produce, the labour that may be required, both in quantity and quality, and the natural constitution of the land; these are chief objects of consideration in making an estimate of the probable amount of rent. Highest un- A larger produce is raised by the same labour when der improved used under an improved system of tillage, and higher rents can tillage. always be paid where agriculture is most improved. The general varia- tion of rent is from one-fourth to one-half of the value of the gross pro- duce, the portion of one-third yet prevails chiefly in the case of perma- nent grass land. The rent depends on elements that vary with the nature of the soil, the kinds of produce, and the skill of the farmer. Per centage The actual profit to be derived by the farmer must bear a ratio to the capital employed by him. The best regulated calculations award him fifteen and even twenty per cent. with which to support himself, and bear the risks of his trade. The fixed capital which must allowed the be advanced, should form the first calculation with the farmer who rents land for use. The landlord's rent and the expenses are left after allowing fifteen per cent. for interest, the profits of stock, maintenance, and the risks of trade to the farmer. farmer. Rents might be fairly adjusted if the prices of produce remained the same or nearly the same; but the greater or less supply causes fluctuations, and also causes that could not be foreseen or provided against at the time of contract. Fair assumptions with respect to prices and produce form the safest ground for those who let as well as for those who take land, and founded on their knowledge of the past, joined with reasonable analogies with respect of the future: these data will lead to safe conclusions about rent. Fewer mis- takes would be committed both by landlords and tenants, if more care was bestowed on the above assumptions. There is a constant to rise rather tendency in Britain for rents to rise rather than fall, from the difficulty and necessity of finding employment for capital, and the limited supply of farms in the market. There is ever a greater hazard that the landlord shall receive or obtain the promise of too high a rent from the eagerness of competition, than that he will suffer loss from the land being underlet. Rents tend than fall. This tendency in the rent of land to rise, and the causes which produce it, claim an important attention in the management of landed property; it should be partially checked, rather than keenly encouraged. A land- owner or any other proprietor never can be able to take an impartial view of the value of that in which he has so great an interest in render- ing available as a source of income; but in every view of the Must be mo- subject, the farmer, must be allowed, such a profit as will ena- derate to al ble him to cultivate the land, meet the contingencies of trade, tency. and maintain his family comfortably and respectably. A deficiency of profit hazards the trenching upon the capital of the farmer, which dimin- ishes and dries up the source whence is derived the rent and revenue of al- low compe- 872 ON LANDED PROPERTY. the landlord. The loss of the requisite funds is the greatest of all evils that can afflict the farmer, and the recovery from it is the most difficult. A retrogression once begun on this point is gradually quickened in speed, till it ends in total ruin. Sound policy directs, fair dealing justifies, and good practice supports the rule, that a fair and lenient exaction shall be made on the industry of the farmer. The most certain and steadiest revenue is ever derived where fair and moderate rents are exacted, and not from the sources of improvident demands and severe treatment. No landlord ever must be leni- profits by a system of exorbitant rents that is rigidly enforced. A few years suffice to exhaust the capital stock of the tenants : the stoppage of improvements, the failure of tenants to fulfil their obli- gations, and the general deterioration of the property, both in condition and character, are the certain results of the continuance of rack rents. Exactions ent. Adjustment of rents, Acts of great liberality are published in returns of rent being made to the farmers at the audit days, of ten, fifteen, and twenty per cent. In special cases of a sudden contingency, such acts are necessary and proper, but as a general system, the management must be bad that calls for the constant repetition. The fair adjustment of rents needs no temporary bounties, it must be able to bear the pressure of low prices and of deficient crops; and it must allow every tenant the means of meeting the contingencies of trade that arise from the fluctuations in the amount and price of his commodities. The rent should be at once re- duced, when land is seen to be overlet, and the tenant's condition consti- tuted to meet the demands and engagements. A rack rent, and the relief or charity of an audit day, create a dependence not to be endured. The quarter of a century of years that followed the termination of the late European struggle, has left a lesson to succeeding generations, and one which may never be equalled, and far less exceeded. Prices of all articles fell in an unprecedented degree, the landlords clung to the rents as en- gaged for, the tenants could not pay them, temporary expedients were adopted, capital was swept away, and more efficient remedies were com- pelled to be adopted. The necessities of the case being promptly met, and new arrangements being made with the tenants and suited to the altered circumstances, no damage ensued to landlord or tenant, the interests were preserved from the ruin that attended the denial of justice. A prosperous tenantry, and the improvement of an estate, will not proceed from the feudal fashion bounty of an audit day, but from the condition of the tenants, enabling them under a fair and well-considered covenant to fulfil all obligations, and meet and surmount every demand that is made upon them. to suit al- tered cir- cumstances. Local know- Much local knowledge and correct enquiry are necessary to enable the forming of an estimate of rent of land. Each district has its peculiar ad- vantages and drawbacks, which are known to, and can only be ledge neces- estimated by, enlightened practical men who have resided in the country, and have learned the calculations. A professional stranger with a long array of figures and calculations, only leads the land- sary ON LANDED PROPERTY. 873 lord into mistakes, anent the real value of the estate, and the means of entering into equitable contracts with his tenants: he must draw infor- mation from persons who are better informed than himself, regarding the letting of land in the district, and the current value of the soil. But local surveyors are always found of some experience and observation; and if they have a character of integrity, they can furnish the best local know- lege of the value of land. These persons being joined with the country agents of the land-owners, and if both parties are left undisturbed by the proprietor himself, who is generally the least qualified of any one to form an impartial judgment, will produce the most correct and best arranged estimate of the value of the cultivable soil. The improvements that may be effected, will probably come from a more comprehensive view and more adventurous judgment and spirit of action. Even in duct im- that case, an especial attention is ever due to the observations of local knowledge, and to the practices that have been established by the experience of ages. The most enlightened judgment will never despise to hear any truths that relate to its occupation. even to con- provements. Beneficial terms for the management of a farm, constitute a most im- portant condition in the relations between landlord and tenant. The temporary occupier of land is necessarily entrusted with the management of the farm during the period of his possession; and if he consults his own interests truly, he will conduct the cultivation of the soil Terms of ma- in the manner best calculated to maintain or increase its produc- nagement, tiveness. But knowledge may be wanting to adopt the proper means, and his interest, real or apparent, and even his necessities, may lead and com- pel him to attempt to take more from the farm than is compatible with the preservation or increase of its productiveness, and especially towards the end of the lease, when his interests and those of the landlord begin to diverge. The written contract is devised to guard against these results, and to allow the one party the privileges that are necessary to carry on his business, and to the other, a legal security that these rights shall be em- ployed only in the purposes contemplated by the parties to the contract. The essential conditions must be few in number, easily understood, and as easily complied with. No questions need occur in a well-considered contract, which must not be made up of a multiplication of con- simple and ditions, penalties, and restrictions, which only serve to perplex, pointed. and afford the fruitful source of litigation. The expressions must be so pointedly obvious in the meaning, that no doubt can arise in the construc- tion. Two faults are usually committed, a mass of cumbersome and use- less restrictions fetter the judgment of the farmer, and cramp his energies, prevent the exercise of judgment, and the powers of adapting the practice to the circumstances that may arise: the other omission consists in leav- ing to the farmer an unrestricted power of proceeding to a Two faults degree of management very hurtful to the landlord, and on every change of tenants, tending to a deterioration of the farm. The midland and western counties of England are oppressed with clauses and enactments that have descended from the practice of olden times, and common. 3 H 874 ON LANDED PROPERTY. which either remain a dead letter, or kill the freedom of action that is demanded by an improving condition of the tenant. In Scotland, where the lease of land has wrought miracles of the kind, a remarkable degree of laxity prevails, and whole estates are managed on a simple letter or a memorandum with constant reference to the custom of the country. The details so essential to the interest of both parties, are wholly neglected; towards the end of the lease, land is scourged, buildings are dilapidated; and in cases where a removal is inevitable on the part of the tenant, stipulations and restrictions are essentially necessary, though they must be few: an excess of caution and of laxity, is equally to be avoided, in order that the interests of both parties may be secured, the landlord protected, and the tenant disencumbered of useless verbiage and unmeaning phraseology. Restrictions. Not only individual interests are damaged by the neglect of the neces- sary regulations in the ownership and temporary possession of land, but the general interests of agriculture do suffer in a very high degree. The progress of the tenant is retarded by an adherence to obsolete customs and antiquated practices; the very worst rules are often enforced, and often all directions are wholly merged in the weighty consideration of the amount of rent, and the times of payment, not forgetting a penalty in case of neglect. If good farming cannot be introduced by the stipula- Bad farming may be omit- tions of a lease, it may, at least, prevent much that is bad, and by wholly omitting the notice of exploded practices, room is left to mention the better rules, and to render them compulsory when time has fully sanctioned the superiority. The practice of agriculture clings so very tenaciously to old customs, that every possible means must be used to unfetter the bonds and loosen the grasp, and many very useful notices may be made in the small compass of a lease. A mass of stipu- lations and restrictions, and the total want of conditions, are equally ob- jectionable: a number may be refused, but some are necessary. ted. The condi- The essential conditions of using land in cultivation, may be recapitu- lated: 1. Security of possession for a proper length of time. 2. An ade- quate provision of fixed capital on which to employ the floating tions that are funds of the farmer, in farm buildings, enclosures, and other ne- cessary appendages of the land. 3. Equitable rents. 4. Suitable conditions in respect of the treatment of the land and general manage- ment. essential. All experience has shown that the means of advancing and perfecting the agriculture of Britain as a branch of public industry, depend essen- tially upon the relationship which is established between the land-owner and the farmer. No attainments on the part of the tenant, no varied and comprehensive professional learning, and no eager willingness to exert these advantages, are able to compensate for the want of the not be com- foundation on which the edifice must rest: the structure must pensated. be firmly based, or no elevation can be raised. Even the pos- session of a large capital by the farmer, will not avail for giving to agri- culture the means of successful cultivation and improvement, the owner and that can- ON LANDED PROPERTY. 875 must be given the means of employing it with advantage, by security of possession, by the privileges required for the proper management of the business, and by that fair and lenient exactions upon his industry, which will enable him to employ his capital with a remuneration. Benefits of granted. If these conditions are withheld, the capital employed in the cultiva- tion of land is exposed to drawbacks in the application of it to the proper ends, which diminish the possible returns and also the means of improving the national source of wealth to the degree which is admitted by the case of adaptation. The improvement of the country, their being and of its agriculture, follow as a sure consequence, whenever along with the power of acquiring capital, the means are afforded of apply- ing it with effect to the legitimate purposes. And wherever these con- ditions are supplied, agriculture improves, education and intelligence are extended amongst the large body of the farmers, and each succeeding generation excels the preceding one in the knowledge acquired, and the means of employing it for private advantage, and the general wel- fare. To these benefits must be added the tendency to advance the wages of labour, and the improvement of the dwellings of the lower grade of society, which sustains the upper in every stage of elevation. The utmost freedom un- derlies obli- gations. “To do as he likes with his own" is a definition of human privileges that sounds most agreeable to the love of power which so very strongly actuates on the will of man. But the sound will be found to contain the whole boast and extravagance of the often quoted phrase. A thousand obligations and influences surround the will and conduct even of the most apparently irresponsible and unfettered owner, con- supposed trolling him by an operation far better and less easily evaded than legal compulsion, to consult his own interest by consider- ing that of others. In the capacity of landlord, nothing is wanted but a knowledge of his own true interest to render this principle effective to a degree unsurpassed, if indeed equalled, in any other relation which one man can bear to another. One axiom comprehends nearly the whole that has been, or which may be said on the relations between landlord and tenant, that of all of the encouragements to the tenant occupier The grand that exist, of all the stimulants to individual improvements that axiom of ten- can be devised, the surest, the most legitimate, and in truth, the easiest and most permanent in effect, is to make every tenant feel to the utmost possible degree that the farm to which he devotes his labour and capital is his "own." If it be true that the best tenant is he who treats a farm of land as if it was his own, it can scarcely require proof that_the best landlord is he whose tenant is least made sensible that he is not his own landlord. Paradox as this has appeared, and may still seem to be, it is the only statement that approaches the whole truth of the case. The relation is one of that class which, like the functions of animal life, are most healthily discharged when they are not felt. ancy. The rents and profits of the land are the owner's, and his only: with re- gard to the soil, in every thing he does with it, and in every thing he 876 ON LANDED PROPERTY. The rents "only are. the owners ;" abstains from doing, he is bound to make his interest and pleasure con- sistent with public good. The community still retains of its original claim to the soil of the planet it inhabits, as much as is compatible with the purposes for which it has parted with the remainder. The land-owner inherits or has purchased the superior interests of the soil and by that possession he takes upon himself the duties which God and nature have placed upon it. The development of the resources of the land rests upon the arrangements that are made for the use of capital in its cultivation, and labour expects employment and maintenance from the vested interest of its inheritance. The moral condition of the people is vastly promoted by the ownership of the soil, which affords to the public use the means and materials of promoting its respective undertakings. A liberal policy on this point has promoted the cause of humanity beyond many other seemingly more urgent causes of impulse. The most selfish and shrewdest utilitarian that ever sought out the shortest road to his own interest, may take an advice in the shape of a moral recipe to the owner of land, to realize the feelings of the tenant, to put himself imaginarily in "his" position, so as to be able to enter into his wants from "his own" points of view, and never to discard the just idea, that the well-being of every creature is not only compatible with, but essentially necessary to, his own. The owner of land is morally bound and socially obliged, by the performance of many duties, and the bearing of many charges, which do not fall on other classes, and are not attached to property of other sorts and constitutions. Though no class of the people are now held to be " adscriptæ glebæ" or to form part and parcel of any landed property, yet on the soil, their education and main- tenance is devolved, and becomes the duty of every land-owner to have performed. By granting to the farmer the essential conditions rights in the that have been mentioned, and by refusing no reasonable demand, by which is acquired a fixed interest in the soil by the cultivation of it, the land-owner has the power of intro- ducing into agriculture as great improvements in point of production, as the invention of the spinning-jenny or the steam engine. To these must be added the adoption of every new principle that tends in practice to economise labour, and cheapen the price of articles by which to extend the sphere of their use. While a population exists, the earth must be cultivated; and the very first responsibility rests with the virtual owner who has both the means and the power that are required for that purpose. No individual in private life possesses the same wide scope of moral ca- pability with the resident land-owner, in the most variously inviting field of practical studies and duties. The leizure it affords is a land owner- high priviledge, and leads to the pursuit of important and humanizing objects, which lie open in the same degree to no other condition in life. The pursuit of gain is sufficiently attractive with- out any over-exactions, and which is allied with and not arrayed against the enjoyment of natural pleasures, while the love of distinction so natural to most minds, is indulged by a prominence almost inseparable from the the other soil. The scope of ship. ON LANDED PROPERTY. 877 position it confers. Example, almost the effect of law, invests it with a commission both wider and higher than the magisterial authority which generally forms one of its leading duties, while the daily recurring sphere of rural economy in many problems that required solution, and the wide field of practical and scientific knowledge involved in them, legal and demand a breadth of varied education, in the fullest sense of social. the word that is not exceeded by the learning of any other branch of pro- fessional life. Till the general education happens of the whole body of the people, the extensive influence of the owner of the soil, and the commonly great early advantages, form a source of very powerful central force, from which will emanate a wide dissemination of the most useful knowledge, and of the accompanying moral and physical blessings to the human race. The last to be mentioned-relation of the landlord and tenant-consists in the case of the non-fulfilment of the terms of the contract. The landlord pursues for the rent by entering a distress on the goods of the farmer, or waiving his right of distraint he can proceed by action at law. Landlord's The tenant can proceed by action against the landlord in default means of re- of the performance of his part of the contract. But the equit- able adjustments that should prevail will wholly prevent these disagreeable resorts. covery. Fixtures. The much agitated uncertainty about fixtures on the soil has been set- tled by a late act, which directs the farmer to give a month's notice to the landlord of his intention to remove a fixture that has been erected by himself with the consent of the landlord, within which time a negotiation of purchase by the owner of the soil can be effected. But in all such cases a special agreement settles every point, and on the simple principle that "conventio vincit legem," all disputes are completely removed. In making agreements of any kind, the chief point of attention is the simple plainness of expression, by which all am- simple agree- biguity is extinguished, and every doubt dispelled. Validity of ments. CHAPTER II. LEASE OF LAND, CONDITIONS, AND RESTRICTIONS; CHOICE OF TENANT & ASSIGNATION OF THE DEED. fined. A LEASE of land, is the demise, transfer, or letting of the Lease de- ground by the owner of the soil, by which he grants for a specified time, the use of its productiveness to another person, on condition of receiving a fixed amount of money as the consideration due to him for the value of the temporary occupation. It is a written agreement between two parties, who engage to perform certain stipulations and restrictions by mutual consent, and it contains the specified conditions on which the 878 ON LANDED PROPERTY. agreement is founded, and the times at which they must be fulfilled. The conditions are obligatory, and even compulsory, and contain the grounds of proceedings to enforce the observance. It possesses the power of making itself respected, and of commanding the obedience of the parties that constitute the formation of the agreement. Form to be cise. From having contained much useless phraseology and unmeaning and irrelevant verbiage, the lease of land has been reduced into a neat and con- neat form concisely worded, and pointedly expressed, calculated to lead rather than hinder, and to improve rather than deter. It has been cleared of the feudal tendency to enervate the mind and fetter the energies of man, and has been converted into an instrument by which to serve the purposes of the human race in the different grades of which the mixed society is composed. Necessity compelled very early the assigning of land for the temporary use of employment, but the advantages never became extensively beneficial till the goods of the vassal were freed of re- sponsibility for the debts of the landlord, and a lease from one proprietor for a specified time, was held good against the successors in the property. From that time, the lease of land has become the basis of agricultural improvement, and a very great source of national wealth. To govern and use landed property without the security of tenure, and of capital, and without some general stipulations, is the same thing as if kings and deputies would rule "arbitrarily " without any laws or written customs, which is wholly repugnant to all just ideas of modern civilization, and the privileges of natural right. Landed property is loaded with the burdens which God and nature have imposed upon it in employing, maintaining, andeducating the people, and in every properly constituted social system, there must be no dependence of any class of per- sons upon another, except in the simple affair of exchanging value for value, or as the Latins expressed it, the "quid pro quo." The love of dominion, and the inclination to be under masters, are equally to be dissipated and abolished. the best tenure. The most eligible duration of a lease of land has now been fixed Twenty years by the best experience in the term of twenty years. Twenty years length of is a very unusual term in the home counties-7, 14, or 21 has the preference. This period has been reckoned a long term during which to part with the control of property, and lose the advantages that may happen of an increased value—but it has been proved to be in a fair accordance with the interests of both parties to allow the possessor to adopt and use a pro- fitable system of management, and the landlord to derive an adequate rent. Prospective view. All the operations on a farm, except those required for the cultiva- tion of the ground from season to season, have a reference to future years for the returns to be obtained, and periodical returns after the lapse of a certain period are required to regain the capital that has been expended, beyond the funds of the ordinary routine. Unless the farmer can look forward with a certainty of future recompense for the expenditure that may be made, no farm can be cultivated in a suitable manner in this country. The most common executions need a time to be performed, and ON LANDED PROPERTY. 879 Time for out- farmer. the farmer requires a further time to get back his capital with a profit. The space of eight or ten years is required for the development of long known applications to land; and more expensive and lengthened processes, are daily being pushed forward, by the ingenuity of lay by the science, and the researches of enlightened practice. In many cases the erection has been done by the tenant of thrashing machines, driven by steam, which cost a very considerable sum of money, and which never could have happened unless an adequate time was secured in order to derive the ex- pected benefits. Owners of land require every security which can be given to permanent property in order to induce them to improve their lands; and they must consider that where a lease is denied, no reasonable expectations can be formed of the tenant deviating from the path adopted by themselves. No proprietor of land should ever think of withholding some Equitable equitable share of the privileges he has claimed, and has ob- to be with- tained, or rather has taken to himself. The general benefit of held. society and the individual good of his fellow-creature, most earnestly and justly demand this privilege through his hands. A more liberal policy is loudly called for in order to second the exertions of genius, and of acces- sory science, which attempts to promote the advancement of an art on which national prosperity so very much depends; for without it, societies may meet, the chemist may analyse, and the philosopher will lecture in vain. General success in any business depends as much on the Social policy social policy as on individual exertion, which must be free and necessary. unfettered, and in every way encouraged. The period of twenty years cannot be regarded as an extension beyond the nature of the pursuit, nor in any way unconnected with the interests of both parties. Very rich lands will sometimes occur, which require little or no expenditure beyond the ordinary expenses of tillage; and on these soils, a long Shorter ten- tenure seems less necessary than on improving grounds of more ure for rich or less extent. But these exceptions are not very general, and even there the landlord will derive but little benefit from abridging the lease unduly he will excite the attention of the tenant in closely crop- ping the land in order to have a guard on his outlay, and to be ready for a removal with as little as possible lagging behind. Short leases are worse than none-they provoke an inclination to expend, but afford no foundation of action-they afford a time to lay out money, but none in which to recover the amount : so that no advantage is conferred except that the tenant is not liable to be ousted for the number of years men- tioned on the rent being duly paid. But in point of inducing improve- ments by the outlay of capital, a yearly tenancy is just as effectual as short terms of tenure. Time and experience, the most convincing of all teachers, and the most despotic of all governors, have long since most satisfactorily settled the irrefragable truth of the above observations. The lease of land settles, 1, the time of entry to the farm, the duration, and the issue of the tenure; 2, the amount, and kind made by the of rent, and the terms of payment; 3, the stipulations re- garding the erection and keeping in repair the buildings, fences, and other lands. Settlements lease. 880 ON LANDED PROPERTY. fixed appertainments of the farm; 4, the rules and conditions of manage- ment; 5, the reservations made by the landlord; 6, the rights of the respective parties who contract the agreement. entry. The period of entry to farms of land are various, in March, in May, in September, and in November. The custom of the district generally establishes the time of entering into the possession of land, and not being founded on any uniform principle, much embarassment has accrued Times of in the management of landed property. In March, there remains much produce unconsumed of the crops of the former year; and too much interference is occasioned between the outgoing and incoming tenants, by the former having to use the farmery in manufacturing the remaining goods of his possession. In September and in November, the whole crops of the year have been produced by the expense of the out- going tenant, and they must be manufactured during the winter, by his own arrangements in the farmery, or sold by auction, or to the incoming tenant by valuation. The Michaelmas entry prevails much in South Britain, and is found to be attended with great inconvenience. The green crops are on the ground, and the whole expense of raising them must be repaid to the outgoing tenant: the tillages of the former year are not exhausted by one crop, and a value is owing: manures otherwise used for one crop, must be appraised in the forthcoming use: copse woods that are cut for fuel and sale, are valued in the standing growth, and thus a large amount of valuations comes against the incoming tenant, and must be paid in ready money before he enters upon the ground: the grain crops are lodged in the barns, or built in ricks, and are converted into money during winter by the outgoing tenant, who may be removed to a distance the connection is thus continued which should be ended when the possession is quitted, and a large amount of money is required at the entry, for which no return is made for some time. This time very incon- of entry, with all its customs and dues, will be found amply de- tailed in "Bayldon, on Rents and Tillages," (Longman,) and in the former part of this work, edited by Mr. Ryde, where valuations are given as examples, and accurate comparisons are made. The alteration of the term of entry to the spring, would require a sacrifice on the part of the landlord of the whole appraisements due to the outgoing tenant, and thus set clear the entry to the new possessor. The sacrifice would be very considerable, and the advantages may in some respects seem distant-but it would prevent the large demand that is made on the in- coming tenant, and leave the money thus expended, to be used in making other improvements. The inconveniences of the present system are very frankly acknowledged, and the benefits of a change largely changed. anticipated, but custom has got a very firm hold, and habit exerts its prerogative. An additional evil consists in creating too long a connection with the farm in the case of the outgoing tenant using the barns for thrashing the grain crops during the winter, after quitting the occupation of the land. This is a very fatal objection, as the chief object in the entry to possession of lands and the quitting of farms, is to sever Michaelmas venient. Must be ON LANDED PROPERTY. 881 every connection as quickly as possible betwixt the outgoer A stir is now and the incomer, and to make the change so easy and simple as being made. to be scarcely perceptible. The autumn entry is worse than that of the spring, as in the former case, the whole crops of the year are on the ground for conversion and manufacture, while, at the latter term, only a part remains to be consumed of the crops of the former year. On these grounds, both periods of the year are inconvenient for the purpose of taking and quitting the occupation of lands. entry. The most enlightened judgment and the best practical experience, universally prefer the first of May as the most eligible period May the best of the year, for the purpose of exchanging an old tenancy for a period of new possession of the soil in the temporary use. At that time, the whole crops of the previous year have been manufactured by the out- going tenant, and the new crops are only just sown. The labour of the year are also best divided at the beginning of May—the preparation of the ground for the fallow crops of the year is commenced, and the grain crops have been sown by the outgoing tenant on the fallows of the previous season. In this arrangement, the whole manure on the farm that has been made from the straws and root crops of the previous season, belongs to the landlord as the owner of the soil, and through him to the incoming tenant, wholly free of any charge whatever. And the condition is most equitable, that the manures that are produced by any grounds shall be used for their benefit and charged only with the application. The incoming tenant has had the accom- modation since 1st of January of the year of entry, of two teams of horses in the stables of the farmery, for the purpose of carrying the dung from the yards to heaps in the fields, where to be used for green crops, and to give the second and third tilths to the lands of the fallow crops of the ensuing year. The outgoing tenant performs the "first" ploughing during the winter, of all the lands to be fallowed in the following year, for which he is paid by the incoming tenant according to the rates of labour in the district. This essential clause in the lease is devised for the purpose of securing to the land the benefit of the pulverization it. done on the surface of the exposed ground by the winter's frosts and rains, of which no subsequent working of the soil ever can compensate the want. The incoming tenant pays to his predecessor, the amount of Winter the bill of grass seeds which were sown the previous year, and ploughing also the expense of sowing them, as he will derive the whole benefit in a crop of hay during the first summer of his occupation. The seeds of the year of his entry, are sown by the teams which are accom- modated on the farm previous to his arrival. The grain crops of the year of expiry, are sown by the outgoing tenant, and some two weeks before full maturity, the standing grains are valued by referees, and the sum is paid by the incoming tenant to his predecessor, in ready money, or by a credit accommodation of mutual agreement, when the residences are not very distantly removed. This enactment prevents the crops Grain crops being parcelled by auction, and carried to distances by much purchased. labour, and also the incoming tenant from going to similar occasions, and bringing what quantity he may require at some considerable cost and trouble. Conditions of paid for. 882 ON LANDED PROPERTY. By the above simple arrangement at this period of the year, the quitting connection is the easiest and most thoroughly severed, and the incoming possession is the readiest obtained. On being paid by the new possessor the value of ploughing the fallow lands in the winter furrow, and for the grass seeds of the previous year, the quitting tenant leaves the whole concern without any lag in connection, except the simple operation of having the grain crops valued, and receiving the money, shortly before the full maturity. The incoming tenant on fulfillng these few and simple conditions, obtained at once the free and unfettered possession and use of Quitting and the houses and lands. There is no mixture of the employ- entry easy and uncon- nected. ments as when the thrashing of crops is one person's, and the cattle in the yards are another's; there are no grounds for brawl- ings or collisions, in cases of work being done by one man for the benefit of another, when the entry is in the spring or autumn. The connection is cut by an absolute removal of all property on the day of separation, and every settlement is made except in the case of the growing crops of grain, which must wait the period of attained value. This general arrangement that has now been detailed, is very generally used in the North of England, and in much of the South of Scotland. The clauses anent the winter ploughing of the fallow lands by the outgoing tenant, and the purchase of the standing grain crops by the new occupier of the farm, have hardly advanced beyond a bare and scarcely pronounced notice. Yet both enactments have been introduced and are now used on the extensive landed estates in Northumberland belonging to the Green- Mr. Grey's practice. wich Hospital, which are under the enlightened management of John Grey, Esq., Dilston, a gentleman of a very liberal mind, and judicious understanding, and equally eminent in the practice of agricul- ture, as in the policy of every connection of the art. It is gratifying that our recommendation of both provisions is justified by Mr. Grey's opinion, and sanctioned by his practice. The arrangements that have been detailed form the prevailing custom over the whole of Scotland, and two-thirds of the extent of England, being adopted and used in the widest meaning by the most extensive landed noblemen of the midland and leading counties. Leases of fourteen years and even of seven years are most prevalent over the southern counties, where the arrangements of entry and quitting of farms are not different in the chief points, and only in the minor details that are occasioned by the locality and established usages. These lesser points are easily gathered from local information, and while the primary regulations are maintained. The very general tendency to adopt on every opportunity the system that has been recommended is the best proof of the superior utility; and the wish that is now expressed to introduce the arrangement where not yet used, shows that the value is appreciated, and that the benefits are known. Having fixed the term of entry, the lease next mentions the length of its duration in the number of years from the determined period of occu- pation. The most proper and advantageous length of a lease has been ON LANDED PROPERTY. long. 883 shown to be twenty years, both for the interest of the landlord Twenty and tenant; the former by granting an adequate length of years not too security, gets his property improved, and prosperously managed, and the tenant obtains a period of years, in which to employ his capital and his time, with pleasure and advantage. The time is not at all too long for parting with the control of property, as another person is induced to take an interest in it, which cannot be accomplished by keeping the possession, in perpetually moving from hand to hand, and changing occu- piers who have different views, and practise diverging modes of manage- ment. A longer period than twenty years has been thought to tend to an alienation of the property, and consequently objectionable; but "issues" by mutual consent could be introduced into long leases, and A lease must thus shorten the duration; and the consent of both parties being have an issue required to effect a termination, no damage can happen to either party on account of unrepaid expenditure on lands or buildings. But a determined issue of the lease is generally preferred which dates from the time of entry, which are both mentioned in the agreement by the years of the respective periods. It is essential that a lease have the time of issue expressly specified, or it may seem a conveyance of property. It is ex- pedient that the year of expiry be written in the words or figures of the year in which the lease falls, reckoning twenty from the date of entry. Though computation can easily ascertain the term of issue, it is better that the precise time be written, which at once shows the period that is sought. The amount of the yearly rent is expressed in one sum, Rent defined. and is most satisfactory in a fixed quantity of money. Corn rents have been adopted, and partially used; but, a very great objection consists in the case of deficient crops imposing a heavy rent on the tenant, when he is least able to pay it, the prices being high and the quantity of grain being small: hence the necessity has arisen, of fixing a “maximum,” beyond which the rent shall not rise; as in one single year, of a very deficient crop, the tenant may be irretrievably ruined, unless he have a large capital to support him. On the other hand, the rent to the land- lord may be very low, owing to very fruitful seasons, and a "minimum" of the amount becomes necessary to be fixed, below which the rent shall not fall. Two points are thus to be ascertained and fixed, a maximum of rent, and a minimum; and there is just as much sum of difficulty and chance of error, in fixing these two points as extremes, as in fixing a point of medium, or in fixing a certain rent in money. In some few cases of very rich corn-growing districts, this mode of paying rents in a certain quantity of grain valued in money by the average prices of the year, may answer a good end—but grain is not the true measure of rent, which depends very largely upon animal produce of various kinds. The fairness of the above transaction should have neither "maximum" nor "minimum ;" and the rent must be regulated, not according to the prices of a single year, but by the average of a certain number of years, in five or seven, so that the fluctuations of rent may not be sudden, but spread over a sufficient period. But even then the Fixed in a money. 884 ON LANDED PROPERTY. Grain rents useful. objection is not removed, of an increase of rent in deficient seasons; for the high prices of that year being included in making the not generally average, raise the sum to be paid by the farmer beyond the general amount of the common returns; and the quantity of grain on which the rent is calculated, cuts heavily into the diminished stock of the farmer, which may be lessened by one third of the usual produce. A fixed payment in money is the most suitable and satisfactory kind of rent, which is regulated to afford the necessary profits to the farmer, and to bear the occasional deficiencies of produce and the variations of price, which are inseparable from the nature of his business. Every in- telligent tenant of land will prefer this calculation of rent to any other system, even of rack rents, which ought never to exist. Rack rents never to exist. Payments in kind abolished. Payments in kind, as in grain, meals, fowls, and in the labour of men and animals, are now nearly abandoned, and should be forthwith exploded. They are the remnants of feudal vassalage and former connection between landlord and tenant, which cannot exist in any emancipated country. The public markets of commodities are free to all classes of society, where sales and purchases are made by fair pay- ments. To these general resorts all parties must go and sell to meet the demand, and purchase by the amount of supply. A bare mention is sufficient as the custom scarcely exists. Times of pay- The times of paying rent vary much in different parts of the ing rents. kingdom: but every where the yearly amount is divided into equal halves, and paid at half-yearly periods of time. The most common practice begins the payments at the end of six months after entry, the second payment after the lapse of a similar interval, so that a year's rent is paid during the first year of possession. In North Britain, it is very common to demand no rent till after eighteen months' possession of the farm, and after the farmer has reaped a crop to enable him to meet the de- mand. In the last way, a smaller capital is required to take a farm of land, as the year's crop pays the year's rent; but at the expiry of the lease, a long connection is maintained between the outgoing tenant, the Long dates landlord, and the farm which, as formerly observed, should avoided. cease as promptly as possible at one time. The first method requires the first year's rent to be paid from the capital of the tenant, lessened by the proceeds of the animal produce, which has been obtained during the year. This amount may reach the half-year's rent, so that the capital of the farmer has to bear only the rent of the other half-year. the expiry of the lease, the rent is paid when the farmer quits posses- sion, and the connection wholly ceases. It is the best regulation of paying rents in the due periods of time-the postponement for one year brings into the market an host of speculators, who, at less capital, raise the rents of farms, and ultimately defeat the special purpose. Long usage having established these two periods of payments of rent, and the general capitals of farmers having become suited to the conditions, it matters not much at entry to be At ON LANDED PROPERTY. 885 which system is adopted, and the disturbance of either method is not desired to answer any purpose that is seen to be very beneficial. delay When the entry to the farm is made in May, the mode of One year's delaying the rent for one year, and the usual credit of six months, fix the first half-yearly payment of rent, at the expiry of eighteen months after the tenant has taken possession of the farm. In this time, he has obtained the year's production of the animal department, and the profits for one and a half years of the grazing stock, which will, no doubt, largely contribute to the payment of the current going expenses of cultivation, and of the domestic establishment. But it makes little provision for the rent of the year—the crop of grain sown by the farmer has been reaped but not manufactured in the month of November, when the first half-year's rent is due in eighteen months after the entry. It is true, that the produce of these crops provides well for the rent of the next half-year, and the proceeds will repay the deficiency of the animal pro- ducts in meeting the rent of the first half-year, and thus the rent of the whole is drawn from the farm, without at all trenching on makes a long year the capital of the farmer, whose funds are thus replenished, but calculation. must still make an advance of money as required during the currency of the year; low prices and dull markets may prevent the timeous disposal of the produce, and a deficient crop of grains may demand a store whence to supply any want that is caused by the failure. The farmer may calculate on a some- what less capital to take a farm by this mode of paying the rent, but not in the full amount of the year's rent, by reason of the accidents that may happen. The Novem- similar ber entry is When the entry takes place in November, a period of twelve months has elapsed when the first half-year's rent is demanded, in the same month of the following year. The farmer has obtained the proceeds of the animal department for a year, and has reaped "only" the spring crops of grain, as the autumnal wheats are his predecessor's, being sown before he quits possession of the farm. In this point of view little difference is found between the entries of May and November. The pos- session of the land during the previous summer, enables a better perform- ance of some parts of the cultivation, and is freed of heavy valuations, while it is liable to the greater bustle and inconvenience that is attached to the commencement, than to the fall of the year. As has been observed, the autumn entry is very objectionable, as it brings the whole crops of the year to be arranged and manufactured, after the possession of the farm has passed from the owner of the crops. The Michaelmas entry accumu- lates a heavy expense on the incoming tenant, the valuation of the and the unexhausted tillages, the purchase of the outgoing grain crops, Michelmas if he is bound to do so, and the rent of the year, in half-yearly payments, before any crop has been reaped of his own property, raise an expense that is very unsuitable to the extents of possession and the con- stitutional value of the lands, and very justly condemn that period of the year as an entry to a farm. The expense is much too great in the first year to be met by ordinary circumstances, and no adequate result attends the arrangement, that cannot be obtained by an easier mode of dealing. one. 886 ON LANDED PROPERTY. The May The entry on the 1st of May, to which the best preference is entry is least given, is by much the least expensive, and by far the most con- expensive. venient. The first half-year's rent is paid in November of the year of entry, being six months from that date, and gives the summer produce of the animal department to the farmer, wherewith to meet the current expenses, and the first rent, if any surplus remains for that purpose. The amount of the first year's rent enters into the capital necessary to manage the farm, but the payment of the rent regularly as the time pro- gresses, is in keeping with correct business, and at the expiry of the lease the possession of the farm and the payment of rent cease convenient together. This method accords with compact movements and agreeable separations. But an accommodation having been formed for the postponement of the rent till a crop has been reaped, the objections have been much reconciled; but, still giving the preference to the entry in May, rather than in November, on account of the whole crops of the year being at the latter period on the hands of transfer, which causes much unnecessary business and commotion. and most when the lease ex- pires. Stipulations The stipulations of the lease condescend to the upholding and of the lease. preservation of the buildings on the farm, and of the fences and roads, and any other fixed appendages that may be on the lands of occupa- tion. The outgoing tenant is usually bound to keep and leave in good repair, all the fixed utensils of the farm, and the incoming tenant accepts them in that condition, and comes under the same obligation as his prede- cessor. If the latter party has failed in this part of the contract, the duty falls upon the landlord, that the neglect be repaired by the party who is liable, or that the utensils be put into the proper order, at his own cost, in which the incoming tenant can receive them. The landlord can have the necessary repairs, that have been neglected, to be estimated, and charge the outgoing tenant with the amount. The necessary repairs must always be done by the possessing tenant when seen to be required, and it is the duty of the agent on the estate to inspect the condition of every appen- dage, examine the stability, and direct the effective maintenance. When new buildings are to be erected, or extensive alterations to be made, a separate clause in the lease is required for the special case; and when the occurrence happens during the lease, a new agreement is made to suit the business, which is appended to the original document. In these specialties, the performances and obligations of both parties are clearly defined, and distinctly expressed. The tenant receives of the landlord, the raw materials of the repairs. Support of buildings. It is a very equitable condition which requires the tenant to uphold the buildings in the same good condition in which he found them, as his fair interest in the use of the houses imposes upon him the very just demand. The extensive and irreparable decays of nature are always excepted-the roof of a house, the doors, walls, and gates, may have lasted beyond the possibility of repair, and no dispute can happen anent the complete restitution. The tenant is frequently held liable for ON LANDED PROPERTY. 887 damage to the buildings by fire-but as the houses are the property of the landowner, equity would direct that the insurance of the buildings be done by the proprietor's cost, and the farmer pays for the security of his own property, which is lodged or manufactured in the erections. A clause in the lease stipulates this arrangement. fences. The roads, fences, and watercourses are managed on the same condi- tions. The incoming tenant examines the state of these appendages, and accepts them, and is bound to uphold the suitable condition, and to exhibit it when he quits the farm. If any extensive alteration be ar- Roads and ranged, it is specially expressed in the lease, and when a wholly new execution is determined, it is made the subject of a mutual contract, which is singly entertained and expressed. All these arrangements be- tween the contracting parties must, and very easily can, be so pointedly expressed, and easily understood, as never to afford occasion to disagreeable and unseemly disputes. The watercourses here mentioned are the beds of small streams that in- tersect the grounds of the farm, and which at occasional periods will cause damage to the lands by pulling down and carrying away the alluvial banks of the stream. The courses of rivers and of all large water- bodies of water which rise to the name of brooks, and form the courses. boundaries of estates, or of farms, are the province of the landlord, and are kept in the proper order by his administration. The means that are to be adopted, and the execution of the guards against depredations by unruly bodies of water, will form the matter of a subsequent chapter. The farmer has only to do with occasional torrents of water which intersect his lands, tear the soil, and make a waste of ground. The bed may receive the covered drains of wet grounds, and require a clear discharge at all times, or it may run alongside a fence, and endanger the stability of it, when the outrageous torrent is not securely confined. In these cases the duty of preservation is evidently that of the farmer, but subjected to such assist- ance from the landlord as will seem to be required from his permanent and future interests in all such matters. In case of any violent Landlord's and extraordinary accident, the landowner will not refuse the aid, liability of part of the restoration, and sometimes materials rather than labour will be required, and the former may be readily at his command. Strong stakes to be driven into the soft bottom of the torrent, and branches of trees to be woven among the stakes, with the growing end favouring the direction of the water, are very useful materials in the cases of small brooks of water, or slender courses that are liable to be much swollen by heavy rains or sudden thaws, and to become unmanageable by the ordinary confinements. These articles may well be afforded by the landlord, as the strong work that is done will add to the future permanence. The under- standings had better be expressed in the lease which relate to such and similar points, and also the exemptions, which are expressly and in em- the duty of the landlord, who must be equally bound with the bankments. tenant in the mutual obligations. Roads, fences, watercourses, and em- bankments will undergo a subsequent discussion, and the propriety will 888 ON LANDED PROPERTY. be considered of almost wholly relieving the farmer of the charge of any fixed appendages on the farm. A temporary interest ever leads to neg- lect, which it is the right of the landlord to have redressed, the latter must have an oversight of the former, which might probably be commuted into a beneficial charge, when some necessary arrangements are made to suit the alteration. The hint is merely given here, the adoption remains for the future expediency. Rules of must be spe- cified The rules and conditions of management are a very essential branch of the subject of a lease, and have been generally treated at greater length than any of the others, from a belief of its vast importance, and being far- thest removed from the knowledge of those persons who pretend to draw the stipulations of the lease of land. In the infancy of improved agri- culture, directions and restrictions were not only justifiable, but management. very imperatively required; but now that agriculture is every- where known, much less occasion prevails for the use of conditions in the management of land. An extreme liberality has pronounced against any restrictions being imposed upon the exertions of an engagement which promises to do a certain thing upon enjoying a specified privilege, and that upon that thing being done, it matters not how or in what way the privilege be used. To confine the farmer in the sphere of his operations, or to dictate to him a certain course of proceeding in the cultivation of the soil in which he has invested a usu-fructuary interest, resembles pre- scribing to a maltster how many quarters of barley he must steep in a week, and to a cotton manufacturer how often the spindles must revolve in a day. But the analogy between the two pur- poses does not hold, as the circumstances of application are wholly dif- ferent, the farmer and the manufacturer pay rent to the landlord for the use of articles that are very different in nature and constitution, variously adapted, and liable to very opposite susceptibilities. The walls, doors, windows, and roof of the house which covers the manufacturing operations. suffer no damage, even from the perpetual motion of the whole machinery that is employed, accidents being excepted, there is no connection between the two parties that can impair the value or constitution by the one prey- ing upon the other. The operations are done by matter working upon matter by means of an intellectual superiority over brute force, there is no vitality employed which requires a sustenation from the powers of another article, and which is damaged by the subtraction of its essence. The employment of the farmer is engaged upon different ele- ments, the produce which he acquires is manufactured by the active powers of life, which are contained and operated in the land for which the rent is paid, and are there excited by artificial processes and applications. A very continued use of the soil in certain purposes is found to deteriorate the quality, and very much to impair the value, and conse- quently restrictions have been imposed to preserve the value of the original article which forms the property of the landowner. It is, therefore, still necessary, that some rules and restrictions be mentioned in the lease for the purpose of guarding property from spoliation. are not analogical. ON LANDED PROPERTY. 889 ordering. Any directions given to the farmer should relate rather to Forbidding what he is not to do than to what he is to perform. The end rather than proposed must not be to fetter and control the tenant in the necessary details of his business, but to lay down a few general rules as will lead to some benefit and prevent what is prejudicial. No particular directions are to be given of the labours of the farm, as these duties belong wholly to the farmer himself, but only general stipulations are to be used, which are seen to be of ready observance, and which do not require to be enforced by a useless and injurious interference with the legiti- mate concerns of the tenant. An imperfectly cultivated country may be much assisted by the directions of a lease, which may be made a powerful instrument for that purpose; but even in that case, general principles and rules of management must show the interest to be pursued, rather than vexatiously disturb and annoy the existing forms of practice. Suggesting rather than annoying. General The enlightened knowledge of the present period of agricultural prac- tice renders unnecessary the insertion of details for the use of the farmer, and even the general principles must be few, and which appear to be im- peratively necessary and altogether indispensable. In the case of farms that are near to a town, and within the convenient distance of one journey in a day, or of two journeys in the twelve hours of summer, the under- standing may be expressed in the lease that the land be cultivated in the course of four years, viz.:-1, fallow or root crops; 2, grain crops; 3, grasses; 4, grains; and then the hay and straw are allowed to be exchanged for half-rotted manure brought from the town in scheme; return. This rotation may be continued in the very favoured situations of the best lands, where is an extraneous source of obtaining manures. On the best qualities of soils that are placed beyond the advantages of manure above the quantity made from the yearly crops, the rotation of five years is mentioned in-1, fallow or fallow crops; 2, grain crops; 3, clovers; 4, pasture; 5, grains. With some very few exceptions, this course of cropping may be pronounced to be the most generally suitable for the British isles. On the most inferior cultivated lands, the course of six years becomes very appropriate, as—1, fallow or fallow crops; 2, grain crops; 3 clovers; 4, pasture; 5, pasture; 6, grains. It may be mentioned, that in preparing the grounds for the fallow crops, the land shall receive at least three clean earths, exclusive of the winter ploughing and the drilling of the ground for sowing the seeds of the crops. These clauses may but not com- be inserted or omitted, as the circumstances of each special case pulsory : may seem to require. The farmer must agree not to take two crops of grain in succession from the same ground, and not to mow any grass land for hay twice in the same year. Any fields of grass land that are of very superior quality, must be designated by name to be kept in that condition of use, and to be mown or pastured, as circumstances may require, and without any provision in the lease for that purpose; but no restrictions must be imposed on the tenant breaking up and using as arable grounds all inferior grass lands, which at present yield chiefly very scanty crops of weeds and mosses. It may be 3 I 890 ON LANDED PROPERTY. varied by cir- mentioned, that all hays and straws are to be consumed on the cumstances. farm, except in the vicinity of towns, when a special arrange- ment provides for the alienation by an express clause in the lease. Hay is in some cases allowed to be sold, and straw is prohibited; potatoes are sold everywhere, but turnips must be consumed on the farm. These varia- tions are guided by the peculiar circumstances in which the location of the land exists. "Good hus- bandry de- fined." These and similar rules of general adaptation are as few in number as possible, in order that the farmer may not be converted into a mere ma- chine, the action of which is altogether directed by an external application. The much criticised words, "by the rules of good husbandry," are appropriate enough, and sufficiently intelligible, and mean that all the performances of cultivation shall be done in the best and most approved methods. These operations are well understood in the present day of practical farming. In the courses of cropping that have been mentioned, one-fourth, one-fifth, and one-sixth part of the arable lands will be yearly fallowed, as shown by the number of years in the rotation. In the end of the lease the tenant must not depart from the course of cultivation that has prevailed during the currency of the lease, and a clause is made to contain this enactment, in order that the land is not scourged by severe cropping to fill the pockets of the outgoing tenant. The interests of the landlord and farmer are certainly the same in reality, but they do somewhat differ in the latter years of the lease when the farm is to be quitted; and fair dealing requires that no interest shall abuse Last years of the other; and there can be no hardship in binding the tenant to continue to the end of the lease the system which he has reck- oned to be the best for his own interest. A sufficient guarantee of good management does not invariably lodge in the interest of the tenant, the circumstances of his position may be widely changed during an extended term of years, and the landlord must not be injured by the casualties or contingencies that may happen to the private means of the tenant. Public property should not suffer from private accidents. tenure. The root crops and the hay of the previous year will be wholly con- sumed by the first of May, or the time of entry; but part of the straw will be remaining in a thrashed state, and all the dung made in the cattle yards during winter will be on the ground, and best carried out to heaps near to the fields to which it will be applied. These unapplied productions belong to the farm, and are used by the incoming tenant free of any charge; but a tenant right of three years is given for the unexpired value of artificial Dung and manures, as bones and guano, which are extraneous to the farm, straw go free. and require a separate consideration. The remaining benefit in one or two years is valued by referees, and paid by the incoming tenant. Artificial When three crops have been got since the application of the have a right manure, the right of compensation ceases. This enactment has been introduced on the extensive estates of the Greenwich Hos- pital, in Northumberland, under the direction of John Grey, Esq., Dilston, whom we have before mentioned, as the agent on that property. It is a manures of 3 years. ON LANDED PROPERTY. 891 most equitable stipulation, as it does not hinder the tenant from making useful applications, even when he knows he quits the farm from the dread of losing the full value by the removal. By getting no value Mr. Grey's for the farm-yard dung, he does not lose any thing, as he gets practices. the same conditions on the farm to which he removes; but there may not be any artificial manures in use, and no benefit can be derived from them. Hence the extra application of artificial manures requires a separate con- sideration, and are justly entitled to the above recompense. Even under a lease, the liability does not cease, as it has an issue, just as tenancy at will expires on a due notice being given. The landlord reserves for his own use, and witholds from the woods and occupier of the surface, the workable minerals, as metals, coals Minerals. and limestone: clay may be added, when the quality of it suit the use in making bricks and tiles. The farmer is paid for any surface damage that may be done, by the award of arbitrators, as it cannot be known at the time of negotiating the lease. Growing wood of all kinds belong to the landlord, with the provisions of felling and pruning the trees, and car- rying away the produce. All woodlands enclosed or unenclosed, are the landlord's reservation, which is not abandoned by the pasturage being used by the farmer. But the lease must expressly mention the special rights in these cases. A power is sometimes reserved of taking, to be planted with trees during the lease, any quantity of ground, on the tenant being abated in the rent for the estimated value. The rent of one and a half years is generally deducted, as a set-off for the inconvenience of losing probably an undue quantity of land, or at least an unexpected choice of the bereavement. It is best when the landlord reserves at once from the lease, some fixed quantity of lands to be resumed at any time, and merely defers his power to do so to a convenient time. Uncertain reservations often lead to misun- derstandings and disputes. Hunting and The right of the landlord to shoot, hunt, fish, and fowl, on the lands let to the farmer, is generally understood to be of common Fishing; law, but is best expressly mentioned in the lease. The keeping of ex- tensive and thickly stocked preserves of game animals, is quite a different subject from walking over grounds in search of the stray birds that alight upon the surface from hunger, or from being wearied on the wing: the former case requires that the cultivated lands which surround the pre- serves, be used by the landowners themselves, the damage done to the crops by the animals will fall upon the proper quarter, and complaints and bickerings will be removed. In common cases of the open farms at a distance from the seats of landowners, the right to shoot the four-footed animals might be given to the farmer, reserving to the landlord the privilege of murder- ing the winged tenants of the air. Some such arrangement might lead to a settlement or a lull of the vexatious question of game, and damage shooting to growing crops. The right is not likely to be relinquished by accommo- the owner of the soil, and therefore should be accommodated. dated. The insertion of a clause is quite harmless that the landlord or his agents have a power, at any time, to enter the grounds and see that the 892 ON LANDED PROPERTY. conditions are complied with. Such a power must evidently be under- stood; but a clause to that effect is generally inserted. Lease is heritable. The rights of the contracting parties are capable of being determined by common law, but are generally fixed and explained by the terms of the agreement. The farmer and his heirs hold the lease during the stipu- lated time, on the conditions being fulfilled which were laid down in the contract. A lease of land is an heritable subject, and in case of intestacy, goes to the heir-at-law and in England the deed ex- cludes subtenants, but is directed to heirs and assigns, without any moles- tation from the landlord. In Scotland, not only are subtenants excluded, but likewise assignees, legal or voluntary, inferring that the lease shall go to the heir-at-law alone. This rigid destination of the lease, does not answer any purpose of utility: it is intended to give to the landlord the choice of a tenant on the death of the original occupier. Should not be strictly applied: During the currency of the lease, the farm may pass into the hands of distant heirs, of whom the landlord can know nothing, or into the hands of guardians or other legal managers, that are altogether unknown to him. The "electus personæ," or the choice of the person who shall occupy his property, has been much insisted upon, as the privi- lege of the landowner; and it has led to the nomination in the lease of the parties who shall inherit the farm in the case of changes occurring in the natural lives of the occupiers. But even with these pro- visions, the landlord does not obtain the certainty that the heir of the lease, who may be then unborn, shall choose the farming profession, and be qualified to conduct the cultivation of land; nor does he know that the specified members of the family will undertake the conditions of the lease, with the willingness and ardour that are requisite to ensure success in any undertaking. The heir-at-law, or the eldest son, may be prevented by circumstances from becoming a farmer, he may be the least qualified mem- ber of the family, and various causes may render him unfit for vised by the the intended occupation. The farmer has no power to rectify tenant. the evil, by making any other assignation; but there may be some advantage in getting the eldest son trained to agriculture as a pro- fession from childhood, from being regarded as the heir of the lease. Though not many practical inconveniences result from the established custom, the tenant may, without any damage on the opposite side, have the power of devising his lease as any other part of property. might be de- Choice of a tenant. The choice of a tenant or temporary occupier of land, in- volves several points of very grave consideration. The cus- tomary acuteness of the Roman people did not overlook the qualifications that should attend the amenable cultivator of the soil--for Columella in the book "De Re Rustica," expressly says, that the occupier should be a person "qui sciet, qui poterit, et volet," or one who knows how to do the busi- ness, who has the means of doing it, and who has the willing ardour to per- form the duties of the undertaking. The professional knowledge of the offer- ing person must be very strictly regarded, and a satisfaction on this point must be obtained before any advances are made to the other points of ad- ON LANDED PROPERTY. 893 known. justment. Ample recommendations must be got of his capability on this head, from quarters that set aside any expressed doubts. Ignorance will ruin any property, and render of no avail all the safeguards which a lease can contain. It may appear a very inquisitorial sort of business, but there seems to be a necessity, that the landowner shall know the means Means that are possessed by the offering tenant, to enable him to culti- should be vate the land in the most approved practice of agriculture. Ex- tensive damages have accrued to the owners of the soil, and heavy losses and large inconveniences have attached to the cultivators themselves, from the perpetual desire of grasping more in the hands than can be firmly held, and of extending the sphere of operations much beyond the means of the proper accomplishment. Expansion will ever be much weaker than compression, and combination of force, of any kind, has ever been attended with magical results, when directed by the legitimate com- prehension of its value. The owner of the soil is entitled to have some understanding on this head—a correct statement of means need not be re- quested—but a gross estimate may be offered, and confirmed by the proper marks of validity. The capital required will vary from £6 to Capital £10 per acre, according to the circumstances of the price of required. commodities, and the condition of the farm as arable or grazing grounds. Of the whole amount of capital, at least one-fourth part must be Reserved reserved in store as a fund at interest for the purpose of meet- capital. ing the demands of accidents, and unexpected contingencies. Casualties of every kind must be supplied by the reserves, which must be ready at command when wanted, promptly administered, and of sufficient power to fill the gap and repair the disaster. No prudent director of a consider- able amount of power of any kind, ever expends the whole amount in the first effort-a part is always reserved to assist the points that may fail from unexpected resistance, and to supply the wants that may occur, and the accidents that may happen. Many enterprises miscarry from want of this reserve-and farming being exposed to many contingencies, requires such a provision as much as any undertaking of action. Of all the evils that can affect the farmer, none is more to be dreaded, or more pernicious, than the want of the requisite funds, and of a reserved capital: without a sufficient amount of means, every effort is vain and delusive—the absence of the prime mover sinks every knowledge, and destroys all the attempts of an eager progression. The landlord is damaged in his property, and the public are despoiled the legitimate inheritance in the production of the necessaries of life. Labour is robbed of its patrimony, in not being employed to the due extent, and the formation and accumulation of capital are stopped at the very fountain head. There is also required in a farmer, the wish and the willing- Necessary ness, to do the business in the proper manner; the ardour which willingness. creates the zealous emulation, and the enthusiasm which renders success to be certain in any undertaking. A sluggish, mindless plodding, must if possible be avoided, which neglects the opportunities that may be lib- erally offered in the due security of tenure, the very full and adequate 894 ON LANDED PROPERTY. provision of fixed capital, on which the floating funds of the farmer are used in the permanent appendages that have been before mentioned, and the compliance, on the part of the landlord, with every reasonable demand that is made by the tenant, on his means and his liberal consideration. The farmer should possess an eager desire to enter into these views, and to advantage himself, by the use of the endowments which are seen to exist, and which may in future be granted. The landlord has a right to be satisfied on these points, as far as enquiry can lead to an opinion. Expired When land is out of lease, the general rule should be to treat leases. with the tenant in possession. He is acquainted with the farm, and attached to it by habit, and some one of his family or relations may look on the farm and the lease as their descending patrimony. The feel- ings of old age and of infancy are torn asunder, by the dispossession of the old tenant, and doubts and fears may darken the later years of life. Violence is required to break the long association which even the respect of place winds round the heart, and the pangs of separation are many and acute. Cases will arise which forbid the treating with the old tenant— he may be superannuated, or has been a slovenly cultivator, and has ne- glected the opportunities that have been offered. Then another person must be sought by private acquaintance, or by advertising. When to be The treaty with the tenant in possession, when circumstances renewed. are suitable, should be ended two or three years before the old lease expires, as it removes any inducement to scourge the land by cropping, the ordinary management is uninterrupted, and the land is bet- ter treated than if the lease had expired. The old tenant is generally preferred to give the full value of the land, which his experience will warrant. He will be easier treated with than a stranger on matters of new outlay, and any requirements that are made, will be more speedily adjusted with him, than in the case of a new possessor, who will see more wants, and require more accommodation. The troublesome conditions will be avoided which attend all changes, even when done under the easiest and least intrusive conditions. This fact carries with it some very considerable weight, on the subject of letting farms that are out of lease. Advertising When any farm is wholly voided by the late possession, an of farms. advertisement may be made of the opportunity of negotiation, for its use, but no auction should ever be allowed to the highest bidder. Not the promise of a rent is to be regarded; but the skill, capital, and character of the tenant, are the chief considerations, and must be found in existence, or very serious losses will happen to the owners of the soil, as have already been witnessed in a large abundance. The promise of a very high rent argues an ignorance of the business, or that no loss can be sustained; and no evils that can attach to landed property, have inflicted more serious and lasting damage, than the want of skill and funds by the tenant. By treating with private offers, the landlord secures the choice of a tenant, and deserving persons have the means afforded them of procuring farms. The character and circumstances of the offerers can be privately ascertained, and a general comparison effected-and it will be learned · ON LANDED PROPERTY. 895 if the most likely person that offers is known to exert his professional skill and his means with an enthusiastic discretion, and if in his private capacity and social relationship as a man, he maintains the dignity of human nature, as a responsible moral agent. These observations do not at all Extraneous tend to introduce any political or religious distinctions-those avoidances. views are wholly beyond the subject—but the special duties that devolve on landed property along with its rights, render it imperative that there be upheld by its station, a careful and nicely scrutinized selection from the broad phase of human nature, of the agents that are to perform every im- portant subordinate part in the large operation of fulfilling the mighty scheme of nature's grand intent. The general course of human nature demands the provision of the above-mentioned qualities in the station that, is occupied by the farmer, of capital and intelligence. in the lease: The persons are generally mentioned in a lease of land, who Succession are agreed by the landlord and tenant, to succeed in the occupa- tion of the farm, in case of the lapse of one or more lives, during the currency of the period of tenure. These provisions very frequently give the lease to some person, who may think it a very troublesome incum- brance, being bred to, and occupied in, a wholly different branch of business, and he has no power to assign it or give it to another person. He is compelled to perform the occupation, and whether he succeeds or fails, he must implement the conditions of the lease. The eldest son, or some younger member of the family, may be bred to farming, with the express view of inheriting the lease; and in that case, the lease may pro- vide, that the farm be transferred to a specially educated son of the farmer, and in default of his life to a similarly qualified member of the relations of the family. The farmer, no doubt, should have the power of devising the lease as any other property-but though the lease be heritable, the pro- perty in it is not absolute, but fettered with conditions, that relate to other interests, which must be taken into account, and legitimately considered. It is most equitable and just, that an assignation of the lease assignation have the consent of the landlord, and that he be consulted in any intention of changing the temporary proprietorship of the land. His own interests will not, or should. not, compel an unwilling occupation by an incompetent person, and no damage can result to the family of the farmer, from the friendly interference of the landlord in settling the affairs of a decease. The words of the lease may allow the farmer to demise the property to the most qualified son or member of the family—and in case of another vacancy, it shall go to the next heir who may appear the most eligible, the heir-at-law being always in reserve, to step in and settle any interminable disputes. If these directions are thought too vague, and not sufficiently precise, the lease may be held to be devisable, as any other property in case of the death of the first holder, and to be assignable by any living possessor of it with the consent of the proprietor of the land. The bankruptcy of the tenant must be held as an "ipso facto" Bankruptcy irritancy of the lease, which will expire the first of May that voids the follows the event, and the same obligations must be done on of it. tenure. 896 ON LANDED PROPERTY, both sides as are prescribed for the last year of the natural termination of the agreement. No creditors must be allowed to enter upon the farm, in any way, for the purpose of reimbursing themselves by a lease of the property—the moveable goods only are liable for debts, the heritable are beyond the power of seizure. The farm is vacant, and to be relet, or granted in possession to the family of the farmer, as circumstances may direct. The landlord in that case must see a suitable person to continue A new tenant the farm, and be satisfied that sufficient means exist for that purpose otherwise a new tenant must be found. found. Sketch of a lease. The following sketch of a lease is drawn from the principles that have been stated, and contains the chief points of agreement, to which may be added the additional clauses which may be rendered necessary by local and adventitious causes. A. B. lets, and C. D. accepts, in lease for the period of twenty years, from 1st of May 18 the farm of land known by the name of and situated in the parish of and consisting of acres, or thereby, partly in grass, and mostly in arable grounds. A. B. warrants to C. D., the free and unmolested possession and use of the lands for the time specified, against all intrusion whatsomever. A. B. reserves as his own property, all the standing timbers on said farm, whe- ther contained in the enclosed plantations, or standing by the sides of roads or growing in hedge-rows, with liberty to approach, cut, fell, sell, and de- liver, the said trees or timber at the proper season of the year. All work- able minerals below ground, as lime, coals, clay, and metals, are the property of A. B., and may be used by him at any time on allowing to C. D. the valued arbitration of the damage done to the surface by the operations of mining. A. B. has the liberty of shooting and fishing over the grounds thus let (in the proper seasons,) and by other persons to whom he may give the permission. A. B. restricts the quantity of game as not to visibly damage the farmer's crops. A. B. engages to uphold and maintain in proper condition, all the fences of plantations which are now formed, or may be afterwards made, and also to give to C. D. at the place of manufacture, the raw materials, as felled timber, lime, bricks, and stones, that may be required during the currency of the lease for the purpose of repairing the partial decays of the farm buildings, gates, and fences. Obligations. On the other hand, C. D. binds and obliges himself, his heirs, and assignees, to give for the use of said lands, the yearly amount of £ in money; and to be paid to A. B., in equal halves of half-yearly payments, the first being at the expiry of six months after the term of entry, and to continue at the end of every six months for the term of the lease; C. D. agrees to pay to the outgoing tenant the value of ploughing in the winter. furrow the lands intended to be fallowed during summer, which will be fixed by referees, according to the price of labour in the district. He also agrees to buy from the outgoing tenant, the whole standing crops of grain in the beginning of maturity, which will be valued by two persons mutually chosen, with an umpire whose decision shall be final. He also pays to the outgoing tenant the price of the grass seeds Perform- ances. ON LANDED PROPERTY. 897 that were sown the spring before his entry, and of the attendant labour. He pays the unexpired value of auxiliary manures, as bones and guano, but nothing for farm-yard dung. C. D. engages that during the currency of the lease, the arable lands shall be cultivated by the most approved rules of husbandry, with the ob- servance of the following special conditions. Two crops of grain shall not be grown on the same lands in two successive years, and no grass lands shall be mown twice for hay in the same year; one fourth, one fifth, or one sixth part of the lands shall be in fallow preparation yearly, according as the course of four, five, or six years, be adopted as the rotation of crop- ping, and the same quantity will be left in the last year of the lease. C. D. accepts the present condition of the farm buildings, fences, gates, and roads, and engages to uphold them all in proper order throughout the lease, and to leave the same condition of these appendages at the termination of his tenure: he engages not to fell any timber, or growing trees, and not to shoot or destroy any game animals, except by the express permission of the landlord. In the case of draining wet lands, C. D. agrees to perform all carriage work that may be required, and to pay 5s. an acre for the drained grounds, along with the rent in half-yearly payments. And also the carriage work for any new buildings that may be agreed to have erected during the lease by a special agreement: C. D. engages not to sublet any part of the lands that are in his temporary occupation, and designates as his successor in the lease, the eldest son [or any other son,] who may be trained to the business; and in case of accident or non-acceptance in any case, the lease to be assignable with the consent of the landlord. Observances. If C. D. quits the farm at the specified termination on 1st of May, 18-, he engages to quit the possession at that date without any legal notice or warning whatever. He leaves, as he received at the entry, the remaining straw and dung in the yards during winter, to the Quit duties. incoming tenant free of any charge-he will be paid for unexpired value of manures as he did on entry; for winter ploughing the fallow lands, and for the grass seeds of the foregoing spring. His grain crops will be valued before maturity, and the amount paid to him by the in- coming tenant. He gives stable room to two pair of horses, after 1st of January, as he received on entering. Signed this Witnesses, { A. B. C. D. day of " 18-. The chief attention in the form of a lease, is simplicity and conciseness, avoiding all multiplicity and complexity of detail, and making the con- ception of it to be ready to any understanding, and the performance easy to every knowledge of execution. The above mode of entry and arrange- ments renders almost imperceptible any change in the tenancy of the land, and approaches to the much desired perpetuity of occupation. Such a holding, or the nearest possible similarity to it, is required for Specialties the benefit of the property, and of all parties concerned. The of a lease. granting of such a thing becomes a pleasure, and the acceptance of it, a tribute of willing respect. 898 ON LANDED PROPERTY. CHAPTER III. CULTIVATION OF LAND, AND ROTATION OF CROPS. Cultivation CULTIVATION is the art of tilling, preparing, and improving the defined. soil by means of labour and manure, so as to render it in a fit condition for affording plentiful crops, according to the nature of the cli- mate, situation, and other circumstances in which it is placed. It includes tillage, in all its branches, in the cultivation of arable lands; the application of manures on the prepared grounds; the use, sowing, and reaping of particular crops; and the management of grass lands. But it is more par- ticularly applied to the preparation of the soil by the implements of culture, which fits the ground to receive the seeds, and produce the respective crops. The working of land by the implements and manual labour, along with the kinds and order of plants which are used for crops, will sufficiently Notices to be comprehend the sphere of cultivation, accompanied by a notice of the mode of applying the special manures for the different made. plants that are used. ploughing. In the present state of agricultural practice, the operations of cultivation begin after the harvest of the year has been finished, with the view of the next year's preparations. In Britain, the crops are secured in the months of August and September, and protracted into October in the nor- thern parts of the kingdom. The change of season, and the autumnal rains will have softened the land into a ploughable condition by the month Winter of November, when the stubble grounds, for the fallows of next year, are ploughed with furrow of seven or eight inches in depth. The power of two horses will suffice for the light lands of all kinds; three will be necessary for heavy stiff loams, and four are required to plough the obdurate clays, as the plastic and London formations. The three horses are yoked on the principle of the steelyard; two animals walk in the furrow in tandem, the foremost drawing from the back shoul- der of the hind one, by the common chains, lengthened by the stretcher chains of the two-horse cart; the third horse walks on the unploughed land, and is made equal to the two in the furrow, by being yoked to the long end of the main-tree of draught, which gives an advantage of the power of an animal by means of the point of centre being one foot removed to the end by which the two horses are attached. A lad is required to drive the animals, which form a very strong team for ploughing. Four horses in a plough are yoked as the two in the furrow, as above-mentioned, and are driven by a lad, or stout boy. It is essential that the winter ploughing of land be deeply done, in order to afford abundance of loose soil for the operations of the next summer and spring. An early and deep ON LANDED PROPERTY. 899 winter ploughing produces a tilth, and imparts a mellowness to the soil, which late ploughed lands never acquire, and is never to be obtained by any subsequent workings of the ground. The condition remains cloddy, rough, and clammy; and the soil never falls from the implements, till the approach of autumn weakens the adhesion of the particles by diminishing the contraction of the clayey constituents. With sands and light loams, the matter is not so very great, but all lands are better in being early ploughed, in November, December, and not extending far into January. Turnip lands are ploughed in breadths of many yards, as the Modes of soil is dry, and no attention is required to the direction of the ploughing: surface water. But clay lands that are summer fallowed for wheat, are laid into ridges of four to eight yards, and the furrows are cleanly opened that the water may freely escape. The ridges may be cleaved by the ploughing, or cast in two or four together; in either way the furrows are kept open and cleaned out by the plough. This method retains the furrows in the present position and form, and is called casting to the gore furrow; two ridges are gathered, and two are cleaved, and makes a work of much neat- ness. When the ridges are high in the middle, each single one may be cleaved out in the winter ploughing-the accumulation of soil in the centre is exposed to the atmosphere, and the gathering of the ridge is facilitated. for being sown with the seeds in antumn. Where the whole field is ploughed, the headlands must be cleared; and the inside furrow, which receives the water from the longitudinal furrows of the field, must be deeply and cleanly drawn by the plough, in order that the water may quickly escape, which requires a cut made by the spade from the ends of the fur- row into the side ditch of the field. Headlands should not be under six yards in width, in order to give ample room to the ploughs in turning, and to avoid the land being trampled by the horses after it is ploughed, a most unpardonable blunder in the art of ploughing, besides the damage. done to the land by the prints of the feet of the animals holding water during winter, and starving the roots of the wheat plants. It is a rule in the management of clay-lands, that no hollow or stoppage must be neat be allowed in which water can lodge, but that the furrows are and honest. clean of earths or clods, and that the corners of the fields have open cuts made by the spade from the furrows into the land ditches. In the plough- ing of all lands, and more especially of clay soils, honest work must be done, or the furrows must be cleanly moved from below, laid at the same height, and be of a uniform width and depth. No unmoved land, or "rafters,” must remain between the furrows, nor any flat position, nor the standing on edge of the slices from the plough. The edge of the furrow that is cut by the coulter and share must be placed quite perpendicular, and the same position must be preserved throughout the whole work. The average of spring seasons will mostly permit the second Spring tilth of winter ploughed lands to be done in the end of March, ploughing. or during the month of April. The ploughing is performed at right angles to the first furrow, or straight across the field; in some cases the ridges are singly cloven by the spring ploughing, but it is inferior to a cross plough- 900 ON LANDED PROPERTY. Best cross- wise. ing in effecting the required purpose. In cross ploughing clay soils, it is essentially necessary that narrow furrows be used, in order that the land be completely stirred, and none be left unmoved between the furrows. The furrow must be to the depth, or even deeper than the winter plough- ing, that abundance of soil be raised for the future operations. If the land be very wet, the furrows must be opened by the longitudinal operation of the common plough, after the cross ploughing is finished. In some places the cross ploughing of wet clays is never done, but the lands are wholly tilled by ploughing longitudinally, from dread of heavy deluges of rain, inundating the land when all the furrows for the discharge of the water are choked up. The working of the land is not so complete as by cross ploughing, but the alternative is preferred. Previous to the cross-ploughing being commenced, a skilful ploughman is sent on a day or two previous, for the purpose of drawing straight fur- rows across the field at the distance of twenty to thirty yards from the continuous divisions. These furrows serve as marks to the ploughs when the work is begun, and no time is lost by looking for directions to the pro- cess. The marking plough goes and returns in the same furrow, and throws out an open space in which the ploughing begins, and maintains a level work on the surface of the ground. The two furrows of the commence- ment of cross ploughing are laid together as a turnip drill, which is readily done in the widely opened mark by the plough—a narrow comb thrown up at the commencement of any ploughing, forms a blot on any pretensions to skill in the art. The open furrows made in the spaces of cross ploughing by the termination of the work, are to be filled up by ploughing in reverse for three or four turns of the plough. This reversal prevents any opening to remain after the land is harrowed and rolled. Harrowing The state of the land and of the weather will direct the and rolling. application of the harrows or of the roll, in the first use of the implements. In dry seasons, and on hard viscous clays, the harrows will be unable to make any impression, and the roll must be used, even if four horses are required to draw it. But the cost must not prevent the most important purpose of reducing to dust, during dry weather, the hardened clods of clay, and the masses of soil that are often produced by cross ploughing. On soft clays, and in moist seasons, the harrows may be immediately applied, when, with the intervening assistance of the roll, the land will be reduced and pulverized, and weeds will be extracted. The weeds and stones that this first operation is capable of operation. eradicating must be without delay gathered by hand, and carried away from the field. Little delay must occur in performing these operations. In mild showery seasons, the weeds will quickly revive and show a green appearance, of which no vestige must be allowed during the process of the arable cultivation of land. The last harrowing of the land and the picking of the weeds may go on simultaneously, and be nearly finished together. The farm should possess a suf- ficient quantity of strength to enable the furtherance in conjunction of the processes of action that are nearly allied in the performance; The first ON LANDED PROPERTY. 901 the close connection must be studied, and the regulations correspond- ingly adapted. In the end of May, or in the first part of the month of June, Subsequent the land is again ploughed, and done longitudinally, in casting operations. together two or four ridges, and keeping open the furrows as the ploughing is performed. The surface is immediately harrowed, rolled, and harrowed again, and the weeds and stones are gathered by hand and removed from the field. This operation constitutes the second cleansing process, and puts the land into a good cultivated state. When the soil is a friable clay, and not excessively hard and stubborn, the above ploughing may be deferred for a time, in order to make the next furrow be the bed of the dung and lime. But where weeds abound, or the land is very stiff and viscous, another ploughing is given in the end of July, when the ground is harrowed, rolled, and harrowed, and cleaned of stones and weeds as before. This furrow reverses the last ploughing by throwing the ridges in the contrary direction. The land will now be ready to re- Use of lime ceive the lime, if any be applied, which is carried to the field in one way; in hot cinders, and laid on the ground in heaps of one to two bushels on a square perch, or a space of six yards by five. The quantity used on an acre will regulate the size of the heaps, but one to two bushels is the common average. A man with a shovel must be employed to lay the heaps in a neat form, and cover them with earth, the moisture of which will gradually reduce the cinders to powder. When this reduction is effected, the whole of the heaps must be regularly and evenly spread over the surface of the land, and immediately covered by a double tine of harrowing. The process of spreading and of harrowing the lime must go on together, by a combined arrangement, as a high wind will blow away the lime if left spread and uncovered. by burying cinders. Another method lays the cinders of lime in a longitudinal in another heap on the headland of the field where it is slowly turned way; over, and at the same time dissolved into powder by the application of water; in this powdered state it is carried to the field, and spread from the carts with shovels, in the space of one ridge, with the cart moving along the centre. The quantity applied must be regulated by the eye of the master in the thickness of the strewing on the ground. A new method directs the hot cinders to be scattered over the ground, and covered by the ploughing, when the moisture in the soil the hot will dissolve the shells, and the land will derive much benefit by the damp exhalations of heat that are evolved during the dissolution of the cinders. As the powder will lie underground in lumps, a future working of the land must be understood in order to spread abroad the lime that is dissolved, and in at least two operations done lengthwise and across the field. This necessity demands an earlier application of the lime during the second stirring of the land in the month of June. When the application is properly done at this period of the year, and the subse- quent workings of the land are seen to spread the powdered lime in the soil, this mode of applying calcareous manure must be very superior 902 ON LANDED PROPERTY. to any other, as the caloric evolved by the hot cinders during the disso- lution will penetrate the body of clay, sunder the particles, break the texture, and pulverize the whole mass. It will also impart to the ground a higher degree of temperature than it before enjoyed, which is the mode by which lime communicates any benefit to the land. Dung applied in broad cast: So soon as the process of liming is performed, the dunging of the land may commence. The heap of dung may be in the field, having been carted to it during winter, or it may be at the homestead, having been turned over in the yards. The dung is laid from carts in small heaps on the ground, and in a row along the single ridges of land; it is immediately spread evenly over the surface, and covered by the ploughing of the ground. The dung must be well broken from lumps, and scattered in small pieces over the surface, and must lie uncovered for as short time as possible. Farmers who entertain nice ideas on the subject of evaporation and loss by exposing dung on the ground to atmospheric influence, appoint a woman or lad to follow each plough, and with a light fork to throw into the furrow any lumps or clods of dung that are pushed before the plough, and lie uncovered. This simple precaution prevents any rough dung being exposed to view, renders the work more complete, and is fairly worth the expense, though the principle of loss by exposure yet remains to be proved. A method has lately been adopted by drilling the land with one furrow of the common plough, and laying the dung in the furrows. The plough makes a drill by one furrow or rut in going the length of the field; the dung is laid and spread along the hollows, the plough in returning covers a drill of dung with one furrow, and the land presents the appearance of being ridged with green crops. This method is superior to the broad cast plan in covering the dung; and drilling the land is less work than ploughing across. Harrowing will be required to level the drills before the land is ploughed for being sown. by drilling. In ploughing the land this time, some attention is required that the fur- rows are neatly ploughed out as the season is advancing, and floods of rain may be expected; the two last furrows on each side of the closing being always done by a plough drawn by two horses walking in "tandem,” in order that the horses may not walk upon and damage the ploughed land. It should be managed by a skilful ploughman, and the closing water fur- row should be deep and narrow to suit the plough that draws the furrow afresh after the land is seeded. A wide, open, gaping furrow with flat sides is a great deformity in finished work: it is often seen, but is not the less reprehensible on that account. The headlands being neatly gathered up by the plough, the cuts at the ends and corners must be opened into the ditches, and in this state the land waits the seed furrowing after harvest. Sowing of wheat. The month of October is the general season of sowing wheat in Britain, when the land is neatly ploughed by one furrow and the ridges gathered. The seed is sown by broad cast or by drill machine, the water furrows are drawn by the plough, and the cuts made by the spade ON LANDED PROPERTY. 903 when the process of cultivation is finished, which was begun about the same period of the previous year. straight. A very considerable part of the clay lands in England are lying in ridges of a crooked serpentine form, of unequal widths at the ends, and often terminate in a point in the middle of the field. The working of the land in consequence becomes very awkward; and many attempts have been made to straighten the ridges, and in some cases successfully, from the ridges not being very high nor very crooked, but in many attempts with very great damage, from the contrary circumstances of height and shape. By reason of the long continued gathering of the ridges in the olden mode of cultivation, the subsoil has become convex as well as the upper soil, and when a newly made ridge took a slanting or crossing direction over these convexities, the water lodged in the hollows, and reduced the full half of the land to a state of mortar: much loss was in many cases sus- Crooked tained, and the failures had the usual effect of deterring other ridges made attempts where the same obstacles did not exist. It has been recommended to make a complete alteration at once by a levelling with the spade, removing the too high subsoil to the lower places and then re- placing the top soil; but this expense would in many cases exceed the value of the land, and has been little used. When the ridges are not very high nor very crooked, the alteration is easily effected by the plough, and the harrows filling up the hollow places; and in extreme cases a very safe method consists in making with the plough a narrow ridge of four or six feet in width in the old deep furrows, and increasing it in breadth every following course of fallowing till it rises and fills the hollows, and levels the high ridges, when the new ridges may be drawn as nearly as possible in the direction of the old ones, and then the water will obtain a gradual flow. This method may be reckoned slow, but it is the safest and most convenient yet practised, being wholly done by the common plough. Turnips may be raised on any clay soils in the following way. Turnips on The land may be wrought in the usual method into July by clay lands. three ploughings and harrowings, when the dung is applied in broad cast, and the ridges are gathered by the ploughing. The surface is harrowed to the utmost possible fineness of tilth, when the turnip seed is sown in broadcast, or by a drill with long coulters which make ruts in the ground, and form the crop into rows. The hoeing of the turnips is done in the usual way. It is supposed that clay lands will produce turnips by this treatment, or some similar cultivation. The turnips grown on lands pared and burned without being ploughed, show that the root of the plant does not require a finely reduced body of soil, provided the surface is pulverized to the degree that induces the early vegetation and growth of the tender plant. The encouragement that is given on the surface of the ground seems to secure the growth of the plant. Green crop lands require the same early ploughing in winter as clay soils, in the months of November, December, and January. The furrow must be round in form and square in the cut, and to the depth Turnip of seven or eight inches where the soil will possibly allow. Stiff lands. 904 ON LANDED PROPERTY. loams may require the power of three horses to move the required depth of soil. The average of seasons usually allows the second ploughing or the cross furrow to be done in the end of March, or early in April, when the furrow slices must be narrow, so as to leave no unmoved ground be- twixt the motions of the plough, and that the earth turned over may not lie in very large masses. A day or two previous to the ploughing being commenced, a skilful ploughman is sent with poles to mark out the field into spaces of twenty to thirty yards, which are made by a furrow of the common plough, moving twice in the mark that is made. This provision Working of affords a ready beginning of work, when a number of ploughs the soils. are sent to the field. When the spaces of ground are finished in the ploughing, the open furrows are filled to the level of the surface by the furrows being reversed on each side in the extent of two or three yards. The harrowing is immediately done and repeated till the clods of land pass between the teeth of the harrows without being broken, the roll follows in one application, and the harrows are again used to tear the weeds and pulverize the squeezed clods. The three processes in the first harrowing, the rolling, and the second harrowing, may proceed together; and the hand-picking of stones and weeds can also accompany the opera- tions. These nuisances are removed from the fields by carts very soon after being gathered into heaps. The next ploughing is done lengthwise, and in breadths of about thirty yards as before, and will be finished by the end of April. The same rolling and harrowing, and picking of stones and weeds are done as before, when the state of the land will show if the soil be fitted to be planted with potatoes; if not, another ploughing must be given without delay. The potato ground should be ready in the third week of April, when the land is opened into drills of thirty inches apart by one deep furrow of the common plough. The half- rotted dung of the farm yards is placed in the intervals, and evenly spread along by light forks in the hands of women and lads, who are super- intended by a trustworthy man of the farm. The sets of potatoes fresh cut are carefully placed by hand over the dung at the distance of eight or nine inches apart, and pressed into the position by the foot of the person that deposits the sets of the plant. The plough follows and splits the drills, throwing a heavy furrow to the right hand over the dung, and in returning along the opposite side throws another furrow of fresh earth over the last mentioned, by which the dung is deeply covered with the loose soil of the ground. A light roll passes along the finished drills and levels the narrow tops, by which a uniform appearance is secured of the young plants, and it ends the planting of potatoes. Potatoes. Beet-root. In the second week of May, the land intended to be sown with beet-root is raised into drills of twenty-eight inches apart; the half-rotted farm yard dung is spread evenly along the furrows, the drills are split and reversed by the plough, the seeds are inserted by dibble on the tops at the distances of four to six inches, and a light rolling finishes the process. Double drill machines are now fitted with large cups and proper barrels to deposit the seeds of beet-root along the drills, and in both ON LANDED PROPERTY. 905 ways a rolling of the tops must follow. It excludes drought and retains moisture. The sowing of Swedish turnips follows the planting of beet-root, and is done in the ways that have been described, the seed being sown along the tops of the drills by a machine of two rows, drawn by a horse and directed by a man. The land to be sown with common turnips in June, Swedish receives the last ploughing after the potatoes, and beet-root are turnips. planted, being deferred till these operations have been finished. During that month the turnips are sown with farm yard dung, as has been de- scribed, and with bones and guano, and other auxiliary manures by the drop drill, which deposits at fixed distances the manure and seed in mix- ture. The seed is sown over the farm yard dung by the two drill implements. Drilling of In all these operations of forming and reversing drills with the common plough, the main tree of draught is five feet in length, which stretches over the breadth of two drills, and allows the horses to walk widely, and gives the ploughman a necessary sight of the forward objects. In reversing the drills to cover the dung, the left-hand horse walks in the furrow of the last split drill, and the horse on the right hand travels on the top of the unmoved ridgelet, while the plough splits the intervening drill, and throws a furrow of earth over the dung. By this method, the dung in the drills is not disturbed by the feet of the horses as when the all green animals walk in the intervals, and the advantage is very useful in not treading on the sets of potatoes which are placed upon the dung. The common plough is more beneficial in making drills than the imple- ment with two mould boards. The narrow-pointed share penetrates deeper and raises more fresh earth than the feathered share of the latter tool, of which the bottom part of the two mould boards constantly heaves the plough upwards, and dispossesses the hold of the ground. crops. When lime is applied on the green crop fallows, the pulverized material is spread over the ground before the land is drilled, in the way as de- scribed for wheat fallows, or the hot cinders are ploughed into the land, which undergoes one or two subsequent workings in order to mix and dis- seminate the reduced calcareous substance in the ground. In Lime used. either way, the lime must come into contact with the soil, when the former is in the hottest state that is possible. Turnip soils are very effectually and economically brought to readiness by the workings of Finlayson's harrow, or a similar grubber. The first ploughing of the land is done in early winter to the depth of seven or eight inches, which affords plenty of loose soil for the future operations of the grubber. The spring working is done across the plough furrow, and repeated in contrary directions till the proper tilth is produced. In the intervals between the operations of the grubber, the weeds and stones are removed by means of the action of the harrow and the roll. The circular tines of the grubber drag the weeds to the surface, and does not expose the land to drought as by the ploughing of the ground. working. The soil is stirred and pulverized by the repeated action of the imple- Grubber 3 K 906 ON LANDED PROPERTY. ments, and the moisture is preserved by reason of the land not being turned up. It promises to be a very great improvement in the working of turnip lands. Art of ploughing It may not be improper to conclude the notice of cultivation of land with a few observations on the art of ploughing. The first and most important thing to be attended to by the ploughman, is the pro- per adjustment of the implement by means of the coulter and share. If these parts of the plough be not properly set with a due inclination to the land sideways, and to the earth downwards, the implement will never move sweetly nor easily, it will be ever inclining to one side or the other, go too deep or too light, increase the friction, and distress the animals, and perform the work in a rough and unsightly manner. This nicety of adjustment shows the skill of the ploughman; for, if well managed, the implement should proceed with a very slight touch of the hand. The plough must be held flat on the bottom, and not obliquely, and leave no ridges or rafters, or land unmoved between the furrows. The furrow slices must be all cut of the same width, and be laid at the same height; if laid too flat backwards, or if the furrow itself and not the edge be per- pendicular, the harrows cannot raise so much fine mould to cover described. the seed. The cut made by the coulter in the side of the un- ploughed land must be as perpendicular as possible, and neat and clean. The reins extending from the bridle of the horse through an iron ring fastened on the leather backband, are held on the rounded extremities of the handles of the plough by means of a plaited groove on the end of the rope, just before the hands of the ploughman; and with well-trained horses a plough properly adjusted, and a tolerably skilful ploughman, the use of the reins will seldom be required, except in turning the horses at the ends of the field. The headlands must not be under twenty feet in width, so as to allow room for the horses to turn without treading on the ploughed ground and leaving footmarks-a most unpardonable blunder in the art of plough- ing. The ploughman must walk with both feet in the furrow, and with his body at ease and erect, speak seldom to the horses, and make no blus- tering noise. Many very good ploughmen walk with one foot in the furrow and the other on the unploughed land, but it rather spoils the appearance, and seems intended to guard against any lateral movement of the implement, which should be wholly prevented by the adjustment. The horses must be trained to walk at a certain distance of space from each other, in order that the ploughman may see clearly forwards to rectify any mistake committed in the preceding furrow. The horses must be yoked to move freely and easily, and as near to the plough as not to impede the freedom of step, with a check rope extending from the inside bridle of each horse to the harness or backband of the other, in order to keep them fairly opposite to each other. It is better when a single connection rope from mouth to mouth is only used; but this mode requires animals of a very uniform temper, and much attention on the part of the ploughman in training the animals to one rate of pace. Practical directions. It is a very common opinion that any person may be a ploughman, and ON LANDED PROPERTY. 907 Attention required. that the performance of the art requires neither pains nor trouble; but ex- perience does not enforce the belief that the operations of any art whatever can be properly performed without attention and trouble. No doubt some processes are easier performed than others, and some persons acquire the mode of performing them easier and more quickly than others; but that aptitude is very far from being a general rule, and forms no exception to the labour and attention that are universally found to be necessary to eminence in any branch of business. The subject of fallowing lands, either for grain or root crops, must not be dismissed without reminding the cultivator that the proper performance of fallowing constitutes the basis of all good and profitable husbandry; and that if it be neglected, not only the crop immediately sown will suffer, but the damage will extend to all the crops of the rotation. Cultivation means that nothing grows on land except what is sown; and though this degree of eminence may never be attained, as there ever may remain a wide dif- ference between possible and ideal excellence, yet the nearer we approach to it, the nearer we approach to perfection. The constant and vigilant at- tention of the cultivator must be incessantly exercised to see that all and every part of the operations be duly and strictly performed in the proper season, and to the fullest extent that is required. He must not only give orders that they should be done, but he must see that they are done; and if negligently performed, have the process repeated, till satisfaction itself be satisfied. True economy consists, not in getting things cheaply done, as many persons erroneously suppose, but in getting them portance of well done; and the effects of minute care are very great in in- creasing the produce of land. The goodwill, activity, and energy of the labourers must be secured and incited by good treatment, which is seldom or never repaid with carelessness or neglect: exceptions do happen, but they are few. The implements must be all of the first order, and kept in full completion, ready when wanted, and never out of repair. The horses must be spirited and active, well fed, and fierce as lions. The very best ploughmen may be wholly lost with starved and useless animals; care is misapplied, and wages are lost in the value. The mind that directs must attract obedience, and not compel submission-lead his fellow-creatures in the most noble of arts, from which he and they reap the same fruits, and experience the same benefits. Great im- fallowing, and of rota- Rotation of crops, or the order in which the several plants that are used as crops are made to succeed each other, forms a branch tion of crops. of the profession of agriculture, than which no other part requires more judgment, or more conspicuously shows the skill of the farmer; nor is there any portion of the art on which the profits of the cultivator more certainly depend. The effects of plants on the soil are very various; some have a tendency to impoverish it much more than others; some bind and others loosen it: hence it is necessary to attend to the peculiar nature of each plant, and to examine in what manner its culture affects the soil. By this means we shall be enabled to determine in what order we ought to ar- range the crops one after another, so as to keep the ground always in 908 ON LANDED PROPERTY. heart, and yet to make it yield the greatest possible produce, which two par- ticulars form the grand object of a correct and systematic rotation of crops. Alternation of plants. Culmiferous crops are such as have a smooth jointed stalk, and mostly contain the seeds in chaffy husks. These, especially when they are approaching the ripe state, draw their nourishment chiefly from the soil, and derive but very little from the air; therefore, when they are cultivated for seed, which is most generally the case, the ground cannot fail to be impoverished by them. On the contrary, the same plants, when young and clothed with verdure, will derive a considerable portion of their nourishment from the atmosphere; and, therefore, a culmiferous crop when cut green, or consumed in that state by animals, does little or no injury to the land. A crop of hay, cut before the seed is ripe, as it should be, does not much rob the ground. Leguminous plants, as beans, peas, and vet- ches, extract, by means of the broad spreading leaves, most of the nourish- ment from the air, and none of these plants when cut young injure the ground, but if leguminous plants be allowed to ripen the seed, their effects Seeded crops. Leguminous plants. on the ground are still much less severe than of culmiferous crops in a similar condition. Other remarkable circumstances distinguish those plants. All the seeds of culmiferous plants ripen at the same time. As soon as they begin to form, the plant becomes stationary, the leaves wither, the roots cease to push, and the plant when cut down is blanched and sapless. The seeds of a leguminous plant are formed suc- cessively; flowers and fruits appear at the same time in different parts of the plant. This plant is, therefore, continually growing and pushing its roots; hence the value of pea and bean straw over that of wheat or oats; the latter is withered and dry when the crop is cut, the former is green and succulent. The difference, therefore, with respect to the soil, between a culmiferous and leguminous crop is very great; the latter growing till cut down, keeps the ground in constant motion, and leaves it to the plough in a loose and mellow state; the former ceases growing long before being reaped, and the ground from a want of motion be- comes hard and compact. And also dew falling on a culmiferous crop after the ground begins to harden rests on the surface, and is wholly evaporated by the next sun. Dews that fall on a leguminous crop are shaded from the sun by the broad leaves of the plants, and sink at leisure into the ground. Accordingly, the ground after a culmiferous crop is dry and hard; after a leguminous crop it is loose, soft, unctuous, and mellow. Bulbous rooted plants, as turnips, and especially potatoes, are superior to any other in loosening, dividing, and pulverizing the soil: potato roots grow generally eight or ten inches below the surface; and by their number and size they divide and pulverize the ground better than can be done by the plough; and whatever be the natural colour of the soil, it is black when the potato crop is dug up. But carrots and parsnips are superior even to potatoes in this valuable property; for the tap roots penetrate to a depth of eighteen inches and more, and divide the soil in their course. Turnips are rather inferior as the bulb grows above the ground; but it is still much superior to a culmiferous, or a fibrous Root crops. ON LANDED PROPERTY. 909 rooted plant. Red clover is similar to the turnip in that respect. From the properties now mentioned which the plants inherit, culmiferous crops in a continued succession would render the soil too hard, and leguminous crops would effect the contrary in making the land too loose; and hence the necessity of making the one succeed the other in alternation, so as to keep the land in a proper state, and at the same time produce the greatest possible quantity of each crop. ment of crops In arranging any system of rotations of crops, no invariable rules can be given which will prove adapted to all cases, because very much depends on soil, situation, climate, and other circumstances. In the very variable state of British soil and climate, no very fixed rotations can be prescribed; but there are some material points to be regarded which no circumstances must overlook. The crops must be suited to the nature and Arrange- state of the lands, and the culmiferous and leguminous crops must be interposed betwixt each other-and this method constitutes what is called the "alternate husbandry;" but it has been found that the lighter soils, are not suited even for alternate husbandry, and that they require a rest in a state of herbage or grass in order to recruit the fertility. Another general rule may be mentioned, that the same kind of crop or plant must not be repeated at too short intervals, or both the produce and the quality will be diminished. And this experience holds as well in green crops as with the cereal plants. The basis of every rotation must be held to be the summer fallows, and the fallows on which the drilled and manured crops are cultivated; and the conclusion of the course to be with the crop taken in the year preceding a return of the fallow on the drilled crops when the rotation ceases, and a new one commences. cannot be universal : In mentioning rotations of crops as a most vital part of the science of agriculture it is by no means intended to convey an impression of the necessity that every farmer should and must bind himself to a slavish routine, but only to direct attention to the study and con- sideration of that branch of the art from which so many great and lasting benefits have been found to proceed. A cultivator proceeding without a cor- rect knowledge, or some knowledge of rotations, is not unlike a ship at sea without a helm; but even with this knowledge, the real value of every rotation depends, in a very great measure, upon the fidelity shown in executing the several processes of labour that belong to it; though, in the variable climate of Britain, no fixed rotation can be prescribed, yet some rotations must be viewed as more valuable than others, because the crops therein included may be most suitable to the particular soils on which they are cultivated, or the produce may be better adapted to the market demand of the country, which must ultimately regulate the kinds of pro- duce that are most deserving of cultivation. Holding these points in view, alternate husbandry, or the system of having leguminous and culmiferous crops to follow each other, must be reckoned most judicious and deserving of commendation, and with some modifications it may be practised on any soil and in any situation. According to its rules, the some are general. 910 ON LANDED PROPERTY. land would rarely get into a foul or exhausted state; at least, if foul and exhausted under alternate husbandry, matters would be much worse if any other system was followed. The rotation may be long or short, as is consistent with the richness of the soil on which it is executed and other local circumstances. The crops cultivated may be of any of the varieties that compose the two tribes, according to the nature of the soil and the climate of the district where the rotation is used; and where circumstances render ploughing not so advantageous as pasturage, the land may remain in grass till these circumstances are obviated, care being always taken where it is broken up, to follow alternate husbandry during the time it is under tillage. In this way, it is perfectly practicable to follow the alternate system in every situation-nor is the cir- cumstance of the land being in grass for two, three, or four years, any departure from that system, as it is usually rendered necessary by the scarcity of manure, poverty of the soil, the want or the distance of markets for corn or other accidental circumstances. The basis of every rotation, as before observed, is the bare summer fallow on clay soils, and the fal- lows on which drilled and manured crops are cultivated; and the conclusion of the rotation is with the crop taken in the year preceding a return of the fallow or green crops, when of course a new rotation commences. We e now proceed to state the most approved rotations, on strong clays, loams, on the lighter loams, and on sands and peaty soils. Alternate system. The clay soils which have been found incapable of being reduced in texture to suit the cultivation of green crops, may be divided into two kinds the superior class, that produces very abundant crops, and con- stitute the greater part of the arable lands in some districts; while the inferior kinds, which much abound in this kindgdom, yield very scanty and precarious returns. On clays of the best quality, and in situations where manure is plentiful, a very favourite rotation has been first year, fallow; second year, wheat; third year, clover; fourth year, oats; fifth year, beans drilled and hoed; sixth year, wheat. Manure may be applied on the oat stubble, or in the spring with the beans, if the nature of the land will admit. In the most favoured Rotation on best clay lands: six years: situations, this rotation is well adapted for alternation, and for keeping the land clean, and in proper tilth. The four years course of 1, fallow; 2, wheat; 3, clover, peas, beans or tares; 4, oats, is much esteemed by many eminent cultivators, and may suit very well on lands of good quality, but the recurrence of the same crop is too frequent on land of any quality, and it is gradually giving way to a more extended rotation. Where the land is loamy, and sufficiently mellow to admit the growth of barley, rotations of six and eight years have been followed, and they include a larger change of plants from that circumstance: 1, fallow; 2, wheat; 3, beans, or peas; 4, barley; 5, clover; 6, wheat or oats: or, 1, fallow; 2, wheat; 3, pease; 4, barley; 5, clover; 6, oats. Here the clover crop is too far removed from the fallowing process, which supposes the land in the best state of preparation for the reception of the small and tender seeds of grasses. eight years. A ON LANDED PROPERTY. 911 Barley used. shorter course is sometimes used: 1, fallow; 2, barley; 3, clover; 4, beans, pease, or tares; 5, wheat and also: 1, fallow; 2, barley; 3, pease, beans, or tares; 4, wheat: or, 1, fallow; 2, wheat; 3, pease; 4, oats. These courses may be varied alternately with clover in the third year. The longer courses most approved, are: 1, fallow; 2, barley; 3, beans; 4, wheat; 5, tares; 6, barley, dunged on the stubbles; 7, clover; 8, beans; 9, wheat: and, 1, fallow; 2, wheat; 3, beans; 4, barley; 5, clover, dunged; 6, oats; 7, beans; 8, wheat. This course may be reduced to six years, by not dunging the clover ley, and by making oats the last crop and also 1, fallow; 2, barley; 3, clover; 4, beans, dunged; 5, wheat; 6, tares; 7, wheat; the two wheat crops are here too near to each other, and the fifth crop may very well take the place of the second. Another course has been used as: 1, fallow; 2, wheat; 3, beans; 4, barley; 5, clover, dunged; 6, oats; 7, beans, drilled; 8, wheat. If the land be clean and in tilth for clovers, this rotation claims much merit, and may be improved by exchanging the fourth and second crops for each other. The following course possesses much merit, and joins the very valu- bean and pasturage farming, a circumstance that is never met able course: with, and which would rarely be allowed, by the common ideas of crop- ping: 1st year, fallow, dunged; 2, barley; 3, clovers; 4, grass; 5, oats; 6, beans, drilled and hoed; 7, wheat. The crops are well varied, and the land derives the advantage of a rest in pasturage, which refreshes the ground more effectually and durably than any manuring. Lime may be applied on the bean stubbles, and the winter ploughing of the fallow will secure a pulverized surface for the barley tilth, if due advan- tage be taken of a dry state of the land for sowing. The action of the lime might be better developed if applied on the barley or bean tilth, in the spring; but if the climate and soil be precarious, they might prevent the application. A better course can scarcely be devised; but it supposes a loaminess in the clay to admit the growth of barley, which is wholly denied by the viscous marine formations of South Britain. The rotation originated with Mr. Grey, of Dilston, in Northumberland, whose name has been already mentioned in the chapter on "Lease." The land on which it is used is an alluvial clay on the southern bank of Tweed, near Berwick, and consequently a fresh water formation. The idea arose from the very frequent failure of the grass seeds when sown on the stale surface of the winter wheats, and along with the exchange of barley with the wheat on the fallow. Mr. Grey very judiciously combined the grass from Mr. of two years, a system wherever adopted and perseveringly con- tinued in the due performance, is always attended with the same results of a very superior efficacy. Grey. In many places, the land is much too hard and stiff for barley, and then the course of four and five years with beans and oats may be adopted. On inferior soils of this description, the following course may be usefully employed: 1, fallow; 2, wheat; 3, clovers, trefoils, seeds, or cinque 912 ON LANDED PROPERTY. foils; 4, ditto; 5, wheat, or oats, beans, pease, or tares. The grass crops may be prolonged if thought fit, and form a course of six years. Another rotation for inferior clays has been recommended in, 1, fallow; 2, oats; 3, grass; 4, ditto; 5, ditto; 6, beans, drilled; 7, wheat. And also: 1, fallow; 2, barley, wheat, or oats; 3, clovers; 4, ditto; 5, oats. A crop of winter tares sometimes precedes the fallowing process, and are eaten on the ground; but the mode is generally imperfect, as a Legumes used. very effectual part of the process is usually performed by the time the first furrow is given to the land, and the state of cultivation is always much inferior to the fallows that are effected by winter ploughings, which have derived the benefits of atmospheric action. The custom is not unfrequent on turnip soils; but even on these lands, the fallowing tilth will be inferior, except in some few particular cases. Inferior These courses of cropping suppose lands of good quality, and a capa- bility in the soil of being drilled with leguminous crops, for the purpose of preserving the land in a clean and pulverized condition. But on the inferior clay lands of this kingdom, there is no possibility of drilling any green plants; the dung may be applied on the autumnal stubble, and a leguminous crop may be sown in the spring, but it will be lands. a broad-cast crop, and confers no benefits on the land, and has no tendency to defer the fallowing process. As it has been found im- possible to assist the benefits of fallowing to the land by any inter- mediate operation of dunging and pulverizing the soil, the rotations of cropping on these lands are more curtailed, as the entire processes of the rotation depend on the benefits of fallowing; and the quality of the land will not endure the constancy of cropping that is practised on soils of richer constituent quality. On all wheat lands, the operation of fallow- ing constitutes the foundation of the whole course: if that be neglected, the future produce will in every case be diminished. If the rotation be formed of alternate cropping, the land is speedily exhausted, and the too frequent recurrence of the operations of ploughing are known to tine lands that are weak in texture and composition. These soils are generally of two kinds,—one of a brick-like nature, and red or black in colour; the other of a much softer texture; and both rest on a wet clay bottom, and more or less retentive, and not unfrequently mixed with sands Sterile clays. and gravels. Of all soils they are the most precarious to manage, and yield the smallest returns. They are mostly, but not always, found in inland situations, and distant from the sources of manure, and are unable in themselves to maintain the animals that are necessary to afford the requisite materials of that indispensable article. A farm wholly, or mostly, composed of these sterile clays, is a very heartless concern; but they are generally interspersed with portions of turnip fields, which very much im- proves the management, on such soils. Wheat has been proved, in most cases to be the most profitable crop, though many high-lying situations will occur where oats may succeed better, from the climate being too late for an early plant. The rotation of four years: 1, fallow; 2, wheat; ON LANDED PROPERTY. 913 Four years judicious. 3, grass seeds, mown or pastured; 4, oats, has been, and is yet very injudiciously followed on these lands, for the farmer does not possess manure sufficient to support constant cropping, and con- course in- sequently a rest in pasturage must be substituted to recruit and refresh the land. It has been proposed to sow pease, beans, and tares during the third year in the field alternately; so that clovers may occur only once in eight years. The following course has been very profitably employed: 1, fallow; 2, wheat; 3, grass seeds, mown or pastured; 4, pasture; 5, pease, beans, or tares; 6, oats. A course of five years may be adopted by sowing any of these plants after pasture, and would become : 1, fallow; 2, wheat, or oats; 3, grass seeds mown or pastured; 4, pease, beans, and tares; 5, oats: or, 1, fallow; 2, wheat, or oats; 3, grass seeds; 4, pasture; 5, oats, or pease, beans, and tares. In high latitudes that are unfavourable to leguminous plants, the following course may be useful: 1, fallow; 2, oats or barley; 3, grass seeds; 4 and 5, pasture; 6, oats. Many or most of the soils are physically inappropriate for barley, and also for leguminous plants; and a Legumes and failure of the latter crop invariably produces an abundance of grasses used. weeds, and renders the land very foul. If the tare crop be eaten on the ground by sheep, it would very much assist the following grain crop; but the nature of the land is adverse to such a system, unless in some few cases of soils and of seasons, that are of rare and unfrequent occurrence. Pasture will preserve the land in a cleaner state, and adds to the vegetable freshness, that will supply the place of manure, which the farmer does not possess; and if leguminous crops cannot be obtained in fair quantities, they had better not be attempted, and the poor quality of the soil prevents the use of tares and clovers by being consumed on the ground, for the crops themselves cannot be got in sufficient abundance to confer any benefit on the land by that mode of manuring, the crop of hay being in many instances too light to be cut, and must consequently be used in pasture. A very general opinion prevails that grasses will not grow on these lands, and certainly for the best of all reasons, because the seeds are never But experience has proved that a close sward may be produced, and sheep grazed and fattened without any danger from rot and other diseases that are so much apprehended on wet lands of that description. The fresh herbage of the sown grasses afford a wholesome bite, which is renewed by a fresh sowing of the seeds, before a contagious deterioration of the herbage takes place. It may not be improper to mention List of here some plants that have been found to produce the pasturage grass seeds. that is so very desirable on such lands : sown. bushel of rye grass, bushel of cocksfoot, 6 lbs. of dogstail, 4 lbs. of catstail, Per Acre, 4 lbs. of meadow fescue, 6 lbs. of red clover, 4 lbs. of white clover. If the soil be damp and soft, and does not rank among the hard brick- like clays, the quantity of dogstail may be diminished, and that of the 914 ON LANDED PROPERTY. clays. catstail and the meadow fescue increased. A mixture of rare and expen- sive grasses would be altogether misapplied on such lands; and in case of soils of any quality, it will be found more profitable to sow a quantity of the seeds that are known to be best suited to answer the purpose, than a mixture of plants that may never grow in any sufficient quantity, and many of which are of doubtful value when obtained. The harder kinds For barren of these soils should be reduced and pulverized, in the early season, by the mechanical action of the plough and the roll, harrowing will be of little use till the later season soften the very adhe- sive composition of the clay. Lands of any description cannot be too much reduced and pulverized, but they may be rendered too spongy and vacant between the particles, which shows the necessity of consolidation after a complete reduction had been effected. The black and softer kinds will require less labour, as they will crumble spontaneously by the effects of the late rains; and if power was applied to reduce the texture in the early season, the soil would become too fine for wheat, and be apt to throw out the plants during winter. On some lands, the early reduction would be very difficult, if at all possible, but it would be attended with the advantage of consolidating and acquiring a consistency by October for the seed furrow. On this latter sort of clay lands, leguminous plants have a better chance of success than on the bricky kinds, and a crop of peas and tares may be very profitably used in the rotation. A variation in the kind of plants that are sown is thus obtained, and a benefit is conferred on the lands by Legumes the smothering shade of the leguminous crops; but they ought barely of use. not to be used unless a crop can be produced to cover the ground closely and evenly, for a thin straggling crop of such plants is the most pernicious to clean lands that is known. The grass seeds should be sown on a surface that is pulverized by harrowing and rolling, and then covered by a lighter application of the same implements. Draining Any improvements that may be contemplated to be executed necessary. on clay lands, must be preceded by complete draining at the distance of twelve to twenty feet, according to the extreme or partial wetness of the soil; and may be effected by drains running straight, oblique, or across the lands, as may suit the inclination of the locality. Many of the better clay lands are at present in a high state of cultivation in the neighbourhood of towns, and in favorable districts; but the greater part is yet susceptible of very much improvement, and probably of more profitable improvement, than any other kind of land in the kingdom. The draining should be executed as a permanent improvement chiefly by the landowner, with a corresponding assistance from the farmer, or it may be done by the single expense of the farmer, on the proper security of a lengthened tenure. The circumstance of all wet lands not being drained, after the obvious and profitable results which have been obtained by that improvement have been made known to every possessor of the the soil, reflects a disgrace on those concerned, and who have both the means and the power, hardly to be wiped away by the future tardy per- ON LANDED PROPERTY. 915 water- action of formance. In the midst of the greatest rage and outward anxiety for improvements, the most obvious, the most necessary, and the most certain of any in the result, is much neglected, and without which operations in that class of soils, all other improvements are in a great measure lost in effect. The cutting and clearing the courses of brooks and General rivulets must precede or accompany draining, and also the clearance of opening of the receiving ditches round the field; and, after courses. the complete drainage has been effected, the modern improvement of ploughing the subsoil may be introduced, and followed by an application of calcareous earths, limes, and chalks, in quantities of 300 to 600 bushels an acre, in order permanently to alter and improve the texture as the nature of it may require. Any general benefit that might be derived from the use of calcareous matters on such soils is lost by reason of the want of quantity, and from the land not being prepared for the mixture. It remains to be seen what ultimate effect the complete drainage All neces- will operate on these stubborn clays, if they will be converted sary for the in any instance into a fit state for green crops, or only rendered cultivation. more accessible at the different seasons, and easier of management by the present mode of cultivation, in addition to the increased productiveness. Some soils, from an original near alliance, may be rendered fit for green crops, but the most truly clay lands are probably placed beyond that possibility. When such improvements are required to be performed, they should be done at once, promptly and effectually, for not only is more time gained for reaping the benefits, but the frittering policy is avoided which squanders the means of action on many points, and effects no object completely, and by which the produce of each is lessened from want of concentration to produce any satisfactory results. In no active business of life has this policy, absurd and puerile as it must appear, been attended with more mischievous consequences than in agriculture, for with some very few meritorious exceptions, it pervades every arrangement and detail of operations, and fetters and prohibits any very great advances in the improvement of the art. When a quantity of means is allowed to effect any object, it is very usually exerted on multiplied points of resistance, and none of which is overcome by reason of the force being too small that is applied to each, and consequently none of the objects are productive of the expected results. Covering of land. The general mode of reducing and working clay lands by exposure during the heats of summer and the vicissitudes of the weather is well known, and, in most cases, is performed in tolerable perfection; but observation has shown that the covering of land produces a fertilizing effect, and kills weeds; and it is probable that, at some future time, there may proceed from this hint an important and valuable altera- tion in practice, which may be ascertained by a few decisive trials made on fair and tangible grounds, which do not in the smallest degree affect the usual results of cultivation, and at the same time are fitted to justify the conclusion. The covering that would be afforded by a crop of tares, or a similar substance, to rot on the ground, might lead to some means of 916 ON LANDED PROPERTY. accomplishing the purpose. Straw has been applied one inch thick as a covering to wheat seeds pressed into the soil on untilled lands, and the crop yielded a very large return of sound and healthy grain. The straw would afford protection against both cold and drought, and also nutritious matters by its decomposition, and the weeds will be effectually destroyed. One good crop of any plant may be got from a single process, and yet be inadmissible into a system; the means that are required for the purpose May be of of protection must be carefully considered, and also the bearings future use. on the future crops, and also on the other parts of the pre- vailing mode of cultivation, as it may operate more damage in some quarters than the advantages that are derived in another. Such suggestions tend to confirm the seemingly very just opinion that all manures are best applied on the surface, and that plants derive the chief part of their nourishment from the atmosphere, and that the earth performs only a secondary part in the process of vegetation. Dung covered in the soil encourages an exuberance of roots and fibres, whereas all healthy and soundly productive plants have the roots sharp, hard, and crisp, like the claws of a bird. Wheat covered with straw on a plate of glass grew well, which further confirms the theory. The present modes of production are very laborious and expensive, and our investigations may probably soon discover much easier and shorter roads, for in the progress of obser- vation and of science, the necessity is daily felt of surrendering opinions and maxims which have long been trusted and received on authority; and we must not suppose that our observation and experience have explored all the paths, or exhausted all the stores of nature. Grasses for cropping. The grasses may be given which are suitable to be sown, with the different rotations of cropping. For a hay crop of one year, Sow per acre, bushel of ray grass, bushel of cocksfoot, 4 lbs. of meadow fescue, 4 lbs. of catstail, 10 lbs. of red clover. For hay of one crop and one year in pasture, Sow per acre, 8 lbs. of red clover, 4 lbs. of white clover, bushel of ray grass, bushel of cocksfoot, 4 lbs. of meadow fescue, 4 lbs. of catstail. The grass plants have been already mentioned that are proper to dry arid clays in permanent pasture of two and three years. On the subject of clay lands, and the proper rotations, the reader is referred to "Clay Lands and Loamy Soils," price 1s., published by Weale, and written by the author of this work. In that treatise, the various kinds of clay are investigated and described, geologically, chemi- cally, naturally, and practically, in a very systematic and detailed order ; the proper cultivation of each kind of land is stated from the best experience; the rotations of cropping that are suitable to each soil, and ON LANDED PROPERTY. 917 the grasses adapted to the nature of the grounds. The comprehensiveness of the little work very much enhances the value. Turnip land Best soils. The second class of soils that was mentioned contains the better turnip lands and the loamy clays, that are capable of rotations. being cultivated and planted with green crops. These soils constitute the most valuable class, and are capable of producing in abundance all the plants that are held in the highest estimation for the purposes of hus- bandry. The fallowing crops are: swedish turnips, potatoes, and mangel- wurzel, being the most valuable plants that are known, and all of them capable of being raised on these lands with due preparation and encouragement. On many loamy clays, draining will be required, and must be performed, before any other expense be incurred. These crops can be removed to admit wheat being sown at the proper season, and hence the high value of the land in producing the two crops of the greatest value in succession. A course of six years is much ap- proved on these soils: 1, green crops; 2, wheat; 3, clover cut for hay, or used for soiling, or consumed by live stock on the ground; 4, oats or leguminous plants; 5, winter tares or late turnips consumed on the ground; 6, wheat. On the four years' course: 1, green crops; 2, wheat; 3, clover; 4, oats. Beans, horse and hand hoed, may be used along with the winter tares, in portions and alternately, as the rotation goes on, and the land will then obtain a change of plants, and the green crops may be varied to suit a similar mode of cultivation. The four years' course: 1, turnips; 2, barley; 3, clover; 4, wheat is too short, and the same plants recur too frequently; and it has been proposed to double the course, and to extend it to eight years, thus: 5, cabbages or mangel- wurzel; 6, oats; 7, tares or pease; 8, barley: and, for two years more, 9, beans; 10, wheat: and also, 1, turnips or cabbages; 2, barley; 3, clover or tares; 4, wheat; 5, potatoes or beet; 6, barley; 7, clover; 8, oats or wheat and also, 1, beet or potatoes; 2, oats; 3, clover; 4, wheat; 5, turnips and cabbages; 6, barley; 7, beans, pease, and tares; 8, wheat. The rotation of eight or more years is a repetition of that of four years, with the object of changing the plants raised as green crops, and substituting a leguminous and clover crop alternately, so that each occurs only once in the course of the rotation. But this object may be attained by varying the four years' course in the fields, as they occur for cropping in succession; and if the soil be not all alike suitable for similar cropping, a change in the plants will be necessary. A course of five or six years is most generally to be preferred, and is found the most commodious, as it affords a full opportunity of cultivating the most valuable plants, and also of profitable alternation. A course of six years has been very usefully employed-1, turnips and other esculents; 2, wheat; 3, beans, pease, or tares; 4, barley; 5, clover; 6, oats; unless the land is very clean and in high condition, the clover crop is too far removed from the clearing and manuring process, otherwise the crops are well arranged. It is desirable that one crop is 918 ON LANDED PROPERTY. Legumes used. eaten on the ground, as an auxiliary manure to support constant cropping as a leguminous crop is proposed in a similar course on clay fallows, and then the rotation would stand thus: 1, green crops; 2, barley or wheat; 3, clover; 4, oats; 5, vetches consumed on the ground; 6, wheat and in five years thus: 1, turnips; 2, barley; 3, seeds; 4, pease, or tares consumed in the ground; 5, wheat or oats. Good lands, when well cultivated, will produce two crops of wheat in six years, and will not require the fallow manuring oftener than once, as it will have the benefit of a crop consumed on the ground. In some cases of very favourable situations, the auxiliary manuring may be withdrawn ; and if the fallowing for green crops occurs twice in six years, it is evident that the rotation ceases. It is more pleasing to see a field under a crop of one plant, than of many kinds-and if a farm be suitably divided, alter- nation may be accomplished without much subdivision in that respect. Inferior These rotations apply to clayey loams of the very first quality. lands. On those of an inferior description, and on the best turnip lands, rotations somewhat different are used, including grass for two years, where there are no grass or meadow lands for producing hay and pasturage for the live stock. A course of six years includes the following crops: 1, turnips, or other green plants; 2, barley or wheat; 3, clover; 4, grass; 5, beans, pease, or tares; 6, wheat or oats alternately on the fields. A course of five years is followed by omitting the pease and beans, and sowing oats as the fifth crop-or pease and beans may be sown in the fourth year, and followed by oats. A course of eight years has been recommended: 1, turnips; 2, wheat or barley; 3, clover; 4 and 5, pasture; 6, oats; 7, tares; 8, wheat: or it may be limited to seven years' by omitting one year of the pasture. These courses of cropping are adapted to loamy lands, and it may be very safely affirmed, that no bet- ter are yet known. Grass seeds. The proper grasses are, for hay for one year, Sow per acre, bushel of ray grass, bushel of cocksfoot, 6 lbs. of meadow fescue, 12 lbs of red clover, 8 lbs of white clover, bushel of ray grass, 6 lbs of catstail, 12 lbs of red clover. For two years' grass, Sow per acre, bushel of cocksfoot, 6 lbs. of meadow fescue, 6 lbs. of catstail. These soils produce large crops of hay, with a luxuriant pasturage, and should be very liberally seeded. Lightest lands. The third division of soils that was mentioned, consists of inferior loams, sands, chalks, and gravels. These lands are chiefly adapted for green crops, and for sheep feeding, and the quality in many instances not permitting the production of an average weight of the heavier roots, herbaceous and leguminous plants have been employed, which yield a maintenance for sheep, and consequently a manuring to the ON LANDED PROPERTY. 919 land. On the inferior turnip lands, the following rotations have, for a long time, constituted a very successful practice: 1, turnips; 2, barley; 3 clover; 4, pasture; 5, oats; and on the lighter qualities of land: 5, pasture; 6, oats and pease and tares may be sown on the grass turf, to supply the demands of the farm. The great advantages that are here derived, consist in the vegetable remains that are accumulated for decom- position, and it has been found that land cultivated in this manner, yields greater returns both in grain and in animals, than when used in constant cropping of more than a usual proportion of the ameliorating crops, and supplied with all the manures that the crop afforded. For hay and 2 or 3 years in pasture, Sow per acre on sands and gravels, 8 lbs. of red clover, 4 lbs of white clover, bushel of ray grass, bushel of cocksfoot, 2 lbs. of hard fescue, bushel of ray grass, bushel of cocksfoot, 8 lbs. of red clover, 4 lbs. of white clover, 6 lbs. of crested dogstail, 2 lbs of barley-like fescue, 2 lbs. of yellow oat grass, 2 lb. of upright brome grass. On inferior loams, Sow per acre, 4 lbs. of meadow fescue, 4 lbs. of crested dogstail, 4 lbs. of hard fescue, 4 lbs. of meadow catstail, 2 lbs. of yellow clover, 2 lbs of rib grass. The land acquires a freshness and a consolidation from the rest it enjoys under pasture-but it supposes a dampness in the soil and climate to induce and favour the growth of grass seeds that are sown for pasture. In many cases of the very hot and dry soils in South Britain, Scorching it is wholly impossible, to procure by any means, a sward of soils. grass—and hence the necessity of using the green crops for sheep feeding, and of sowing very few grain crops, and in a very diminished proportion. On hot burning sands of the iron description, and on some chalks and gravels, a grain crop very seldom succeeds; if the early months of the year be dry and hot, a total failure very often ensues, where autumn sown rye would yield a much greater produce both from its nature, and from attaining a tall growth, and forming a shade to the land before the scorching heats commence. The most inferior sorts of these lands will be most profitably cultivated by a succession of three or four feeding crops to one of grain for seed: rye, winter tares, and sum- mer sown rape, may be succeeded alternately by turnips, rape, and spring vetches, and relieved occasionally by a crop of clover and corn. On chalks, gravels and sands of the better quality, a course may be adopted thus: 1, turnips; 2, barley; 3, winter tares, consumed on the ground; 4, rape, also eaten on the ground; 5, spring vetches, also consumed on the ground; 6, rye for a seed crop, being four feeding crops to two of grain: or, 1, turnips; 2, spring vetches; 3, rye for a seed crop; 4, winter tares; 5, rape; 6, barley—each grain Rotations: 920 ON LANDED PROPERTY. crop having thus the benefit of two crops eaten on the ground. A crop of clover sown at the rate of 30 lbs. an acre, may succeed the barley crop, and may be cut or consumed on the ground as may be required. The very inferior soils and burning sands may be well used in a similar manner, with one crop of seed rye to four of the feeding plants-as, 1, turnips; 2, barley or oats; 3, clover; 4, tares; 5, cole. Thus rye, winter vetches, turnips, spring vetches, and rye for feed, may be followed at pleasure by turnips, barley, and clovers-and the lands may be then suc- cessively cropped with those plants, and kept in good condition. Peaty soils. Peaty soils and lands that have been pared and burned may be cropped in a similar manner, according to quality, and always with a large and full proportion of the feeding plants. On clayey soils, pared and burned: 1, turnips or cole; 2, oats or wheat; 3, grasses or tares; 4, pease or beans; 5, oats; 6, fallow, followed by wheat and grasses for several years. On thin clays: 1, cole; 2, oats; 3, pease, beans, and tares, oats or wheat, followed by cole, oats, and grasses, for several years. On chalks, sands, and peats: 1, turnips or cole; 2, barley or oats; 3, grasses; 4, grasses; 5, grasses; 6, oats; 7, tares or pease; 8, turnips; followed by barley and grasses for a time: or, 1, turnips; 2, barley; 3, grasses or trefoils; 4, ditto; 5, pease; 6, rye; 7, turnips, followed by barley and grasses. For a more detailed, and separately arranged enumeration of the ro- tations of crops, on loamy soils, the reader is referred to “Clay Lands and Loamy Soils," price 1s., published by Weale, and written by the author of this work. The various kinds and modifications of loams, are very fully described, and the use and improvement specified and suggested. The division of the different soils as above-mentioned, will comprehend every possible variety-and it is presumed that the above rotations will be applicable in most cases, with the variations that particular circumstances and opinions are known to require. Experience Experience has now fully established the fact, that in a proper of rotations. rotation of crops, a plant with a naked stem, and a farinaceous seed should follow one with a branched stem and a fleshy root, which has been taken from the ground without bearing seed-and if all these con- ditions cannot be obtained, that some one of them, at least, must be com- plied with. Wheat sown after clover, which is allowed to be the best succession on light soils, fulfils all these conditions when it is sown after beans, the condition of the preceding crop not ripening the seed is given up, and consequently this succession is inferior to the other. It is not possible, however judiciously the land may be manured, to raise the same crops in regular succession, without loss and detriment both to the land and in the quantity of the crops. Wheat and clovers answer well in alternation, but not singly; and this shows that the same effect is not produced in the soil by these two crops. Experiments have been made by very eminent chemists, particularly by Macaire of Geneva, at the request of Decandolle, the celebrated botanist, which lead us to sup- pose, that in the formation of the seed, or other nutritious parts of plants, ON LANDED PROPERTY. 921 the sap is digested, and that it takes up certain elements and deposits others, which are the residue of the process-and these being Exudation of plants. no longer necessary for the formation of the seed, are rejected by the vital action of the plant, and exude by the roots. Thus certain inferior animals, which in many respects have some analogy with the vegetables in their growth, as the "polypes," take in nourishment by the same openings or pores by which the excrements are voided after diges- tion; and the different constitutions of different animals enables one class to feed on the excrements of another-whereas, no animal in a healthy state, can derive nourishment from that which has already been digested and voided. Our ignorance of the functions of Not fully vegetable life prevents us from seeing the effects produced recognised. on the sap, by the expansion of the blossom, or the ripening of the seed; but experience leads us to perceive, that certain plants thrive best after certain others—and that in this case, they are always of distinct and different natures, and of different natural botanic families. Macaire, and some other scientific men, observed the change that took place in the water, in which wheat had been made to grow. They found a deposit in the water of the nature of bitter extract, and this they considered to be excrementitious. Beans grew well in this water; and on the other hand, wheat throve in the water in which beans had grown. The effect of fallowing land is explained on the same principle-the ex- crement is washed out by the rains, or it is decomposed by the light and air to which it is exposed by repeated ploughings thus the land is "sweetened," -an expression very common among the farmers engaged in fallowing. However interesting it may be to the curious en- quirer, to ascertain the real causes, it is sufficient for the practical the best farmer to learn by experience, what crops do succeed best after each other, and how soon the same kind of seed may be sown again in the same ground, with a reasonable prospect of its producing a good crop-and this, after all, can only be learned from actual experiment and observation. Experience guide. CHAPTER IV. BUILDINGS NECESSARY ON CULTIVATED LANDS,- DWELLING HOUSES, FARMERIES, AND COTTAGES FOR LABOURERS. THE farmer of land having obtained a security for the outlay Farm of his capital in a lease of the proper duration, and being provi- buildings. ded with a sufficient quantity of the means for the necessary operations of cultivation, the attention is next directed to the provisions of the fixed appendages of the farm, on which his capital is to be used, and his occupa- tion has to be employed. The tenant uses a number and variety of tools 3 L 922 ON LANDED PROPERTY. in the cultivation of the soil, some of which are possessed of life, and others are inanimate, while many are fragile and evanescent, and require a frequent renovation. All these articles, of whatever denomination, demand a pro- vision for their use, and done in such a way as will lead to the utmost fruition of the development. And the first implement to be considered is the farmer himself. Dwelling house. The increasing opulence, and gradual refinement of the age, demand a provision of personal comforts, which are suited to the station in society that is held by the individual representative. The accommodation of the "Farm House" must be suited to the value of the farm, and the habits and condition of the occupier. The opulent and exten- sive farmer will require a very different kind of house from the humble tenant of a small farm. He will expect personal conveniences suited to his condition; and a man of good capital, accustomed to the conveniences of society, will hardly consent to hire a farm which does not possess them, The uniform progress of things leads to this natural condition, and the state of the dwelling houses in any country is a very sure indication of an improving, a stationary, or a non-progressive tenantry. The tenant who is little superior to the condition of a labourer, will be satisfied with a com- paratively humble dwelling, and his physical comforts would not be any way increased by furnishing him with a house superior to his habits and ideas. Hence the dwelling houses of farmers are to be varied, and uni- formity is as little admissible in that department of social life, as in any other branch of occupational business. Its accom- Assuming the medium size of farms at 300 acres, the possessor of that extent must have a capital of £2000 to £3000, and the deriveable annuity from this sum entitles the receiver to a genteel and comfortable residence. The accommodation of the house must be respectable, and afford modation. the proper conveniences to the tenant and his family. In the present social ideas, a division is required between the master and his ser- vants; and the sitting and sleeping apartments of both grades must be separated. This arrangement requires the dwelling house to be two stories in height, and the ground floor to consist of apartments in which Apartments. the inmates are separated in employments, and in the places of abode. The master's family requires a sitting room, in which to live pro- miscuously, and where the sittings and the conversations are done-and another room for the purpose of assembling at meals, and which is kept for that sole use. The farmer will need a room for his business of accounts, and for the visits of his employés-another room is very useful as a nur- sery for the children; and where no family is, it may be used as a spare or lumber room. The accommodation may extend to five rooms, and must not be under four, in order to meet the extent of capital employed, and which demands some comfort for its use. There must be a kitchen of suitable dimensions, and a scullery or back kitchen adjoining, and also a pantry and dairy. These apartments are most conveniently placed in the back part of the dwelling house, and to open into the area behind, which contains the fuel and the ashes, and other minor conveniences. The second floor is di- ON LANDED PROPERTY. 923 vided into four or more bed rooms and closets, which will accommodate the family of the farmer, and the occasional visits of a stranger. The sleep- ing apartments of the servants are reached by a different stair from that by which the family ascend. Our limited purpose does not allow a very large advance into General the subject of farm buildings—a general description and exhi- description. bition can only be given; but at the end of this chapter, references will be given to special publications on the subject, which contain a large variety for selection, and an utility that ever must accompany all such devices. Two designs are here given of dwelling houses, which will show the intent of our purpose, and point to the accommodation that is thought to be required. K J E L H E D G F Га M O 0 C NMIZ B N A ס! سانس 10 20 2- 0 0 80 40 3-30 50 FI A Sitting Room. B Best Room. C Kitchen. D Scullery. E Lumber. F Ashes. G Yard. H Fuel. J Wash-house, K Privy. I Dog. L Dairy. M Closet. N Stairs. O Bed Rooms. Plan, No. 1, contains two rooms in the length, and is entered by a cen- tral front door, and by turning to the right and left. The fire-places are in the gables, and each room has a window in the front. The lobby leads to the back apartments, and from it the stair springs to the second floor. The second floor is divided into three bed rooms and a closet, for the family of the farmer, and a sleeping apartment for the female domestics. The rooms are all specially marked in the plan. Extra buildings. It is absolutely essential to every habitation of civilized nature, that there be some back buildings for the performance of dirty operations, and for keeping articles out of sight that never should be seen. The position of these accommodations is best right behind the dwelling houses, in the length of the dwelling, and joining it at the ends. The dairy occupies the east side, as being a cool exposure; and there are placed in the small square, as seen in the plan, a wash-house, lumber room, a house for fuel, ashes, and a privy, and an apartment for a dog. These erections are low, and stand as lean-tos on a wall that surrounds the en- closed area. This house is suited for farms of 200, and to 300 acres, and presents a 924 ON LANDED PROPERTY. very snug accommodation. The garden may be in front, or on the west side, as will be afterwards discussed, when mention is made of the general position of farm buildings in the useful connection. N M • L J K G ரு E F P I H F D C D Q Q E B R R A R R 10 20 20 30 40 50 F: M Privy. N Wash-house. A Sitting Room. E Stair Closet. I Kitchen. B Parlour. F Stairs. J Yard. C Passage. G Larder. K Fuel. O Lumber. D Rooms. H Scullery. L Dog. P Dairy. House end for front. Q Servants' Rooms. R Bed Rooms. Plan, No. 2, is calculated for extents of land in 300 and 400 acres. The end of the house stands for the front, which is entered by a porch. The house is of double width, and contains two longitudinal ranges of apartments. which are covered by two tiers of roofing, that meet in a central valley, along which the water flows to the back end of the dwelling. The central passage of the house leads to the kitchens, which stand across the dwelling, and have a side door opening into the back area, of small accommodations, as in the last design. The sleeping apartments are arranged and divided for the family and the servants, according to the ideas already expressed, and the former plan. The houses are built with mortar, stones or bricks, as the mate- Materials. rials may abound in the locality. The rooms are floored with deal, and the kitchens are paved with flags or flooring bricks. The side walls and ceilings are plastered in the usual way, and in the better rooms are covered with paper. The second floor is joisted and laid with deal in the common method of finishing such work. The roofs are covered with tiles or slates, as the locality may direct. A good sized garden for growing fruits and vegetables is a most useful, and, in fact, a most essential appendage to any extent of land that is intended to be let for cultivation. It must be made into shape, and very amply provided with fruit trees and shrubs, by the expense of the proprietor; and when suitably accommodated, it constitutes ON LANDED PROPERTY. 925 a very great inducement to the occupation of the farm by wealth and re- spectability: when joined with a commodious and neatly furnished dwel- ling house, a very large portion has been accomplished in these two appendages, of the fixed provisions which constitute the necessary furniture of a farm. The farmer himself must be first accommodated, and then will look to the maintenance, in comfort and safety, of the live and dead stock of his employment. The landowner sadly neglects his own interest, who omits the above-mentioned provisions, on a scale that is rather above than below the standard which the occupation may seem to require. Farmeries. Description. Farmeries constitute the mass of houses which are grouped to- gether for the special purposes of the tenant of land, and are a very important part of the fixed provisions of the farm. The houses are designed to enable the farmer to thrash, prepare for use, and lay in store, the produce of the ground to lodge and feed the horses, and other labouring cattle, and to separate, shelter, and fatten the oxen, and other live stock; to preserve the implements and machines; to collect manures; and generally to carry on the works that are required to be performed under the shelter of roofs and buildings. The principal parts of the farm houses are the barns, the stables, the feeding houses, the yards or courts, and the shed for containing the implements and machines of the farm. The barn consists in a ground floor, on which the thrashed grain falls from the upper floor, where the machinery is at work, and where it is dressed by fanners and made ready for use. The straw is thrown by the machinery into an adjoining house, called the straw barn, in which the straw is lodged, and whence it is carried as wanted for the different purposes of use. buildings are required to be two stories high, to lodge the thrashing ma- chinery on a second floor, and to afford room in the straw barn, for the accumulation upwards of the thrashed culmy materials. A central position must be given to the barns, as a very frequent access is required. shed for implements demands a northern exposure, in order to preserve the tools from the heats of the sun, and being vacant below on the ground floor, it affords the best store room over it for the lodging of thrashed grain. Two stories in height afford a shed, and a granary over it; and the building most conveniently adjoins the thrashing barn, in which an inside stair leads to the granary floor. A house for holding small tools, under lock and key, adjoins the cart shed, and is floored over with it. These The Sheds and Stables. The stables are contrived to lodge the work horses of the farm; and the house may be only of one story in height, but open to the top of the roof, and no floor over it. Each animal stands in a trevise of six feet in width, and is provided with a rack in front, and a manger by which to be fed with hay and grains. The width of a stable within walls may be eighteen feet, and the ventilators placed at the ridge of the roof. A hay house adjoins the stable, and in it the corn chest is placed, into which the grain descends by a spout from the granary above. Young horses are kept in yards during winter, and are introduced to the stable as they are broken to work. The riding stable is fitted for, at least, three horses, in the same way as the working stable. . 926 ON LANDED PROPERTY. Cow shed. The cows, which breed the fattened animals of beef demand a very suitable accommodation; and as some part of the milk will be required for domestic purposes, the position of the cow shed is most commodious on the west side of the farmery, where it will be near to the dwelling of the farmer. The animals enter most conveniently by an end door, and stand in double trevises of two together, and are tied by chains round the neck. The house for lodging the calves adjoins the cow shed, where the young animals are confined in single pens of about ten by four feet, divided by wooden partitions, and on a boarded floor, thickly pierced with auger holes, in order to convey the moisture into the vacuum under- neath. If suckled, the calves are led by halter to the cows: if fed by pail, the door of each apartment is provided with an opening in the centre, through which the calf puts its head, and drinks the milk. houses, the riding stable, hay house, and gig house, are one story in height, and form the west wing of the farmery, which adjoins the dwelling of the farmer, and are convenient to the special purposes. Feeding Yards. These Experience not having yet decided the single superiority of the two modes of fattening cattle, tied in stalls, and loose in yards, both ways may be adopted; and accordingly a feeding house is placed in the farmery, in which any backward animals may be forwarded, and any choice beasts placed for the first selection. The animals stand in double trevises, and are supplied with roots and hay from houses that adjoin each end of the feeding apartment. The yards are divided into large and small extents for young cattle and feeding beasts. Each yard has a shelter shed, in which the animals repose from colds and heats. Swine and poultry are so wholly distinct from horses and cattle, that they are much best kept in separate apartments, of which designs and ex- planations will be given. Liquid draining. The liquid excrements of the farmery are most beneficially absorbed by the straws and litter of the yards; but if the quantity of these articles be deficient for that purpose, oozings may be led and conducted to a central point, in front of the farmery, and fall through an iron grate into a covered drain, which conveys the urine to a tank, in which a mixture is made with earths and vegetable matters. But on farms that are systematically arranged and conducted, the straws will be in abun- dance to absorb the urinary feces of the proper quantity of animals. In very rainy countries, the rain water from the roofs of the houses is inter- cepted by spouts at the eaves, and conducted from deluging the yards with moisture. Water is supplied to every part of the farmery, by conducting water from higher ground to an elevated cistern, where pipes lead it to troughs, and supply it to them by means of ball cocks or a force-pump raises water to the cistern, which supplies it as above. Remarks. All enlightened practical men have agreed for a long time past in the opinion, that there is not a wider field to be seen at present in any branch of rural economy, than appears in the arrangement and construction of farm buildings. Very great and beneficial alterations have certainly been made within the last half century, and which are in some degree corresponding with the extensive improvements in other bran- ON LANDED PROPERTY. 927 ches of the rural art; but in many parts of the kingdom, it may be said that any advances on that point have not yet commenced; and even where a considerable progress has been made, or at least attempted, a suitable effect has not been produced, from want of the necessary knowledge and judg- ment in adapting the extent of the accommodation to the purposes required, and in combining and adjusting the utility of the whole concern with the proper expenditure. From looking at the present state of farm Bad arrange- buildings over a great part of the United Kingdom, it would ment. appear that ingenuity had been employed to devise and erect the most awkward and useless forms imaginable. Declivities are chosen for the sites of farmeries in order, it is said, to keep the yards dry, and, at the same time, to discharge the whole quantity of moisture into ponds and ditches, or into the ruts of a public road; the straw lies dry and unreduced, and becomes very unfit for the purposes of manure. The houses are scattered and disjoined, and require a useless quantity of fencing to connect them— the yards are large, open, and exposed, and afford a very insufficient ac- commodation and shelter to the animals, and no proper means of preparing manure in the most approved and economical manner. The useless expen- diture in building large timber barns has been long condemned by every practice of enlightened knowledge-being an expense fully double of what is required to be used on that point alone. The same latent bar- barisms of the mind that retard improvements on other points in use. operate with full force in this respect-an aversion to make the necessary outlay, and a general and very strong inclination to continue the old usages and erections at the least possible expense, and to repair and patch up so long as any possibility exists, and the want of security in the case of any person, except the landowner, expending capital even for such a necessary and essential purpose. An improper expenditure, might, no doubt, be in- curred, by making a number of extensive alterations at one time; but by gradually introducing the best plans, as occasion may require, and oppor- tunity offers, either piece-meal or altogether, an important and valuable change would soon be made, which would show a very different result from the frittering policy generally pursued, of expending money on many points, which only serve a temporary purpose, and which, if combined, and directed to one or more chief objects would introduce some positive bene- fit in one place, and then in others, as it may be successively applied. Continued In consequence of the general aversion to make the necessary New designs outlay, and the adoption of a temporary system of management, necessary. few opportunities occur of showing a suitable and economical erection of buildings on any farm; but few farmers will refuse, and offers are made to pay the usual interest on the cost of an improved farmery for the lease of twenty years; and such an erection will always be an inducement to pay a higher rent, and will become itself a capital in money, paying the usual revenue of profit. A certain class of cultivators will deny that any im- provements can be made-and another class, more irrational still, will acknowledge that the suggested improvements are all very good, but that they are not required, and are unnecessary-reasons that cannot for a moment be admitted by any intelligent mind. In many places, where large 928 ON LANDED PROPERTY. > Proper expenditure. sums of money have been expended in erecting farm buildings, very glaring blunders have been committed, and much ignorance has been displayed, even of the most simple and evident details of prac- tice, arising from the incompetency and conceit of the persons employed who have never practised the art they pretend to assist, and therefore do not know the wants they attempt to supply. The land-owner very gener- ally makes an unprofitable expenditure upon unnecessary erections, and in useless decorations; or is led away by the plans of architects, who, however well qualified to plan and build dwelling houses, gothic windows, and spiral columns, experience has shown to be most miserably deficient in contriving and placing the accommodations that are required on a quantity of land in Judgment required. cultivation. The economy of labour that is derived from the juxtaposition of articles that are required to act or to be used in combination, has been wholly disregarded, if the advantages were fully known-barns and rick-yards have been placed at opposite sides of a large farmery-stables and cart sheds in a similar manner, and the granary placed at a distance from the barn, for the evident purpose of creating useless labour in carrying the grain from one place to the other. Farm horses are often allowed to enter through a cattle yard, and, in many cases, must travel round the farmery in order to reach the cart shed. Pigs are huddled into some cold damp corner, and the poultry are similarly treated, and the door of the house is often found opening to the north, which is the coldest exposure of any quarter of the heavens. These two kinds of live stock require much warmth, and a sunny exposure, and their common treatment is just the reverse. Many similar blunders might be pointed out which must be obvious to any experienced person, and which abound in the best Experience publications on the subject. However simple the matter may necessary. appear, no person is capable of devising plans of convenient farmeries, without the most intimate knowledge, from long and extensive experience, of the most minute details of practice; and the first requisite is to ascertain the number and size of buildings that may be required on any lands under a certain system of cultivation, without too much curtail- ment to create inconvenience, and without any useless appendages that require an unnecessary expense-and then how to connect them, so as to afford the greatest possible convenience with the least possible labour. General mistakes In planning farmeries, two mistakes are very apt to be committed-to extend the buildings too much, and make the yards cold and uncomfortable; or to make them too confined, and consequently deficient in ventilation and fresh air. It is no easy matter to steer midway of the two extremes : situation and exposure will claim much of the direction of the arrangement, which local experience only can know and estimate. Hence arises in a very great degree, the frequent occurrence of a wrong exposure and of insufficient accommodation-of one thing very good, and another very bad, placed side by side-all showing the paucity of ideas on the subject, and the niggardliness of execution. With the present accom- modation, as it is most generally found, the farmer cannot use the winter crops so as to derive the full value; he is consequently discouraged, and has not the proper inducement to expend his capital on the legitimate object, ON LANDED PROPERTY. 929 Best forms. or the cultivation of the soil, and the increase of the quantity of produce. In the best shapes of farmeries, the form of a parallelogram is preferred, with the front open to the south, so as to admit the beneficial effects of the rays of the sun, and without any houses being placed in front, which would exclude that enjoyment. The building consequently consists of three sides or wings, with interior accommoda- tions. For the purpose of illustration, we are able to give three designs of farmeries for extents of land from 200 to 500 acres, which may be in- creased or diminished so as to suit any intermediate size of a farm. K G Q 囲 I J A R B C H ЈЈЈЈЈЈ L P S P 0 - T T T T T M S S D E H p F N A Barn. B Straw Barn. C Cart-shed. D Tool-house. 10 10. E Stable. F Box. G Gig-house. H Hay-house. 20 I 40 Store-house. J Gangway. K Riding-stable. L Calf Pens. 60 80 M Cow-shed. N Feeding-house O Root-house. P Road. 100 FT Q Engine. R Machinery. S Sheds. T Yards. 930 ON LANDED PROPERTY. Farmery No. 1. Plan No. 1 exhibits the accommodations ranged in the order that has been mentioned, and with an interior road between the build- ings and the yards. The room thus occupied has been made an objection, but it yet remains for decision if it be not the readiest access to every situation, and the most convenient arrangement yet devised. The dwelling-house of the farmer is supposed to stand on the west side of the farmery, and, with the garden behind it, will equal the extent of the range of conjoined buildings. The west wing is occupied with a cow shed, calf pens, hay house, riding stable, and gig house: these appendages will be convenient to the pur- poses of the farmer's domestic use. The walls are 10 feet high, and made with mortar, stones, or bricks. The cow shed and stable are pitched with stones; the other houses have earthen floors. The north wing is formed of houses of the height of two stories, and are a spare house, gang-way, thrashing barn, straw barn, cart shed, and tool house. The walls are 24 feet high, and the whole range of buildings is floored with joists and boards, at the height of 14 or 16 feet from the ground. The floor of the barn is of boards; the other houses have the floors of earth. The east wing of the farmery contains a stable for the work horses, a hay house, a feeding house, and a house for holding roots. The walls are 10 feet high; and every house, and also of the west wing, are open to the top in the in- side, and have no floors over the tops of the walls. The horses enter and leave the stable by an end door, which does not disturb any yard where cattle are confined. Arrange- ments. The interior room of the farmery that is contained between the three wings, is diminished by the road, which is 20 feet in width, and the remainder is divided into yards for store and for feeding cattle, as shown in the plan. The road is pitched with stones, and the yards are dug in the bottom to the hard concretion that is beneath the soft soil. The shelter sheds are twelve feet in width, and low in the roof. The ricks of grain stand on the north side of the farmery, and are carted to be thrashed into the gangway, whence the sheaves are thrown on the second floor of the barn, where the machinery is at work: they are immediately handed to the person who feeds the scutchers. The piggery and poultry yards are made separate designs, and are placed as shown in the plan: the piggery on the east side of the farmery, and level with the front of it; and the poultry yard in the centre of the farmery, and in front of the whole erections. The walls being low will not intercept the sun from shining on the yards of the farmery. The piggery breeds and feeds swine on a large scale, as every extent Piggery. of land in use ought to be held as a manufactory of raw and finished produce. The boar and brood sows are separately and singly ac- commodated, and the store pigs have a large yard well littered, with shelter sheds, and a pond of water in which to roll and wallow. The feeding hogs are two in a sty, and are there fed with steamed potatoes mixed with meals, which are prepared in the cooking house, as shown in the plan. A light iron waggon on four wheels conveys the food along the ON LANDED PROPERTY. 931 passages, which are laid with flags. The store pigs are fed in the yard during summer with clovers and vetches, and in winter with potatoes, turnips, and beet-root, raw or steamed, or in both conditions. The poultry yard shows a house for each kind of animals, and a hatching house for all sorts. The young broods are conveyed to small cribs, and there confined till grown strong to go abroad. A fire-house cooks the food in steamed or boiled potatoes, which are given to the poultry along with dry grains, in troughs, in the shelter sheds, which protect Poultry yard. the animals from rains, storms, and suns. A pond of water in the centre floats the ducks and geese. Poultry in turkeys and hens are natives of hot countries, and require much warmth; and hence, the great fecundity of poultry that roost in labourers' cottages, and enjoy the heat of the dwelling. In the plan now given, the houses are heated by pipes from the boiler of the cooking house, that convey heat to stones in cast- iron pots below the floor, which retain heat for a long time, and impart warmth to the whole apartment. Arch. Pigeon- house. An arch may be raised over the south-end of the roadway, on which a pigeon-house may be placed, and the top surmounted by a clock. This latter appendage is very useful for maintaining order and regularity in the operations of business. The floor of the pigeon-house may be of boards, and hung upon hinges, which will let fall the floor when necessary and discharge the excrements on the ground beneath. This provision will save the inconvenience of intruding on the pigeons, and the trouble of collecting and heaving the quantity of excrements. Farmery, No. 2. Plan, No. 2, shows the buildings arranged, as in the last design, but a very wide difference in the interior of the farmery. The road of access is placed outside the two wings of the buildings, and the feeding yards are in consequence advanced close to the walls of the houses. The shelter sheds are placed in two central rows, between which a railway runs from the stores of roots in the rick-yard through the straw barn, and conveys potatoes to the cooking house of the piggery and poul- try yard, and turnips to the cattle in the sheds, which receive the roots through holes in the wall. This facility of conveyance saves much labour in cartage and manual work. Straws for litter and hay for pro- vender are conveyed on the same passage. The piggery and poultry yard are joined in this plan by which one cooking house serves both departments with the steamed roots for being mixed with meals. The buildings being low in the walls, will not much obstruct the rays of the sun from shining on the yards of the farmery. Ricks of grain. The ricks of grain stand in two rows, which extend the width of the farmery, and between the rows a railway conveys on a light waggon of four wheels the unthrashed grain to the machinery, and is turned into the gangway by a turn-table on the main line of rail. The ricks may not be thatched, but are covered by a roof of corrugated iron, which extends over both rows, and rests on cast-iron pillars, which stand on each side of the rows of ricks. The introduction Railway. 932 ON LANDED PROPERTY. of railways is a great improvement, as it strengthens power and dispatches business. This design of a farmery possesses much merit. G H J L E H J G F E B M A K 12 N Р mimi R T S T S T C D T 8 p J m n N S Z a O S 10 20 40 S d T f h મ T + • I I P U T E 9-3 60 80 100 FT A Straw Barn. B Barn. C Cart-shed. D Tool-house. E Root-house. F Spare-house. G Ricks. H Store-shed. I Stable. J Railway. K Gangway. L Engine. O Riding-stable. Poultry Yard and f P Hay-house. Calf-pens. R Cow-shed. S Sheds. M Machinery. T Yards. Piggery. g a Yard. b Shed. Sties. m Roost. Feeding sties. n Hatch. h Store-yard. i Pond. C Food-house. j Cribs. d Vats. N Gig-house. U Feeding-house e Fire. k Ducks. L Geese. o Turkeys. p Pipes. ON LANDED PROPERTY. 933 P N X • K Y F B A Υ D E⚫ W G L T T 2 K G T R G 20 G b n a T Ꮓ L H X M G T T b K G ប G V a F e k F A Barn. d B Engine. C Machinery. D Straw Barn. E Cart shed. F Spare-house. G Sheds. H Box. го I Stable. تسلس J Tool-house. K Hay-house L Yard for young horses. M Yard for store Pigs. FFFFFF k h 2- 20 40 60 80 100 FT O House for pro- V Root-house. vender. b Fire. j W Stairs. C Vats Turkeys. k Geese. P Gig-house. R Calf-pens. X Railway. d Ponds. e Sheds. 1 Ducks. m Roost. Z Roads. Piggery. h Store-yard. Q Riding-stable. Y Ricks. f Feeding-shed. n Hatch. S Cow-shed. Poultry Yard and g Sties. T Yards. N House for bull U Feeding-house a Food-house. i Cribs. and stallion. o Pipes. Plan, No. 3, exhibits all the houses of the farmery ranged in two rows, having separate roofs, with a longitudinal valley over the central wall. 934 ON LANDED PROPERTY. No. 3. The shelter sheds form the inside row of buildings, and the north wing of Farmery, the farmery is composed of the houses in two rows that usually occupy that position. A central road leads to the straw barn, and along it, by cart or railway, roots are conveyed to the yards and pig- gery, and straws for litter from the straw barn. This house occupies the width of the two rows of buildings, and is large and roomy: it receives the straw from the thrashing barn, which stands at right angles with it, and this position gives opportunity in the straw barn of making any divi- sions of the kind of straw. The ricks of grain stand in two rows, as in last plan; the unthrashed grain is conveyed along the railway to the end of the barn, and is pitched from the waggon to the second floor, on which the machinery is at work. This arrangement of the rick-yard and barns is much the most convenient of the designs now given, or probably of any that may be devised. Ricks on a It is proposed that each rick of grain stands on a square plat- platform. form of four wheels, which rests on a short branch railway at a sharp angle of divergence, along which the entire rick runs to the barn when it is wanted to be thrashed. Any rick may be thrashed that is wanted, as the way to the barn is wholly unobstructed, and the platform, after its load is disburdened, is sent back to the position on the branch railway, where it receives in the end of harvest another rick of grain from the fields. This plan might deserve a fair trial. Thrashing The thrashing of grain is in every case performed by machinery, machinery. which is best impelled by the power of steam. The absurd prejudice is here discarded that the use of machinery diminishes labour, and the latent barbarism of the mind is expelled which continues the thrashing of grain by means of two sticks tied together, and employs labour on a non-productive point. Machinery increases labour, and performs the brutifying parts of the operations, so far as the application is possible. The thrashing machinery of every farm is provided by the landlord as part of the fixed furniture of the farm, and upheld in use by the tenant. No fixed utensil should be removed by the change of occupiers, as when the machinery belongs to the farmer. covered as a It has been proposed to cover a farmery wholly under one roof, like the terminus of a railway. The dung would be thus protected from rains and scorching suns, and the animals will live under a uniform temperature. The roof of corrugated iron would rest on cast-iron pillars, and be extended in separate tiers along the greatest length of the farmery. In Farmery exposed situations, hollow cylinders may be formed in the con- railway ter- cavity of the roof, which will convey the wind harmlessly over the buildings. It is doubted if it would be beneficial to ex- clude the influence of the sun altogether from the farmery; the warming effects may not be compensated in the absence by the exclusion of heavy rains. Colds and currents of wind are generated under lofty roofs, but which may be removed in this case by a close walling round the farmery. minus. Slates form the best covering that is yet known for roofs of houses; tiles are the next best article; asphaltum-paper, and some other substi- tutes have not come into reputation. ON LANDED PROPERTY. 935 The coarsest glass yet made is too dear for the purpose of roofing; but as there is a general tendency to cheapen the prices of articles, and extend the sphere of their use, the time may not be distant when roofs are wholly made with that article. A most notable specimen is just now exhibited in the circular roofs of glass resting on rounded rafters of bended deals, like the springs of a carriage, which stretch the railways at the terminus of the lines. Those mighty exertions of capital and intellect offer to view very many lessons to be learned, and performances to be adopted, when pride will allow imitation, and conceit perceive its ignorance. Aspect and exposure. site: as The aspect and exposure of farm buildings deserve some con- sideration. The position of the farmery should evidently be central, but many hindrances will prevent that selection of the proximity to a public road, a convenience to water; and shelter will, in many places, very much influence the choice of the position. The situation should be dry, or can be easily made so; the approach not difficult, or can be made convenient without any heavy expense. The exposure should be low rather than high, and have an open front, whence there come enliven- ing heats and currents of refreshening air. The aspect may be fixed to the south, as being the most benign quarter of the heavens in the British isles; the west is boisterous and wet; and the east, though cold and dry, is favoured with the rising sun; and on that account be- South-east comes preferable as a deviation from the south. The subjoined preferable. quotation will show that, even in the benign climate of Italy, the proper aspect of the farmeries did not escape the notice of the Roman people :- "Edificium meridianam partem respiciat, in primo angulo excipiens ortum solis hyberni, et paululum ab occidente avertatur hybernali. Ita proveniet, ut per hyemen sole illustretur, et calores ejus æstate non sen- tiat." Palladius de Re Rustica. Lib. I., cap. viii. The front of the buildings being low in the walls and turned to the east, the low suns of winter will shine upon the yards; and during the fierce and scorching heats of summer, the meridian blaze will have lost its power over the extent of the farmery by reason of the averted position. The best aspect ranges from west to east, and the intermediate points will accom- modate almost any situations in Britain. Cottages or dwelling-houses for labourers, are an object of Cottages. very great importance, and form a point of much consideration. Labour is the source of every gain; and it is most just and equitable that wealth, which is the accumulation of labour, be used in providing comfort and competence to the springs of its existence. But the very slow and gradual upward progress of the social system has not yet brought labour and the actors of it into the proper degree of the very just estimation ; and the condition of labour yet rests almost wholly dependent on the benevo- lence of the wealth of the upper grades of society; and that power never can be more beneficially or agreeably employed than in affording comfort to its fellow-creatures. The present accommodation of the agricultural labourers forms a very great blot on the rapidly improving social economy of the present day. Till of late years the hovels of the working class never attracted any 936 ON LANDED PROPERTY. of them. notice, large families being confined in a single apartment of sixteen feet square, where the common decencies of life cannot be preserved. The pro- miscuous intercourse of age and sex at all times and on every occasion violates the feelings of propriety and decorum, and engenders immorality that is seldom forgotten during the after-life. Filth and stench abound Deficiencies where cooking and sleeping are done in conjunction, and the roofs being low, a foul air is constantly respired, and the very healthy enjoyment is denied of breathing in a large volume of the sur- rounding atmosphere. Such dwellings resemble the stalls of a stable, where the animal performs all the functions of life in one apartment. A house with one door for ingress and egress of every article never can be clean, and will be very deficient in ventilation from the want of a current of air that is produced by openings in the opposite sides of a house. These very glaring deficiencies are now being noticed, and the remedies suggested and applied. The decent separation of age and sex is the first step in the arrangements of civilization among human beings that are located in permanent dwellings. This very obvious truth requires that any human dwelling consists of at least two apartments on the ground floor. The same necessity of separation demands that the sitting and sleeping apartments be distinct; and experience has shown that bedrooms are much more dry and comfortable when placed on a second floor from the ground: hence, every cottage must have a second floor. Improve- ments gradual. It would be a very useless undertaking to make dwellings be- yond the means of being supported, or to raise expectations beyond the power of being realized. The present ideas must only lead a step in the progress, and point the way to a further advance- ment; the conditions of the social arrangement must always be considered, and the upward progress must be ahead rather than behind the state of the system. The present state of things will sufficiently warrant the essential requisites of a labourer's cottage, that every habitation have two apart- ments on the ground, of which one serves for the sitting and cooking de- partment, and the other for better purposes and occasions, that the bedrooms are placed on a second floor of joists and boards, and that there be some small back buildings as minor accommodations for the purpose of works that would incommode the dwelling, and also to conceal articles that never should be seen. These principles, in three requisites, form the basis of the following details, in which are implied the cottage having a door in front, and another opening backwards, and a height of wall that admits a large volume of air to traverse the habitation. Stated. Subjoined are the plans of three cottage dwellings that are arranged on the above principles, and which are not attended with any unsuitable decorations or a lavish expenditure. Plan, No. 1. Plan of cottage, No. 1, is a single dwelling for one family, with the proposed accommodations. The ground floor contains two rooms with opposite fire-places, and the stair rises from the kitchen to the second floor. A porch in front breaks the uniformity of bare walls, and affords some little inside room. The walls of the cottage are 14 feet high, leaving 10 feet for the height of the ground floor, and 4 feet to the ON LANDED PROPERTY. 937 E Р bakililim (NAIADA יך. F G Η K C D K 10 5 0 A N B 10 M I 2- 20 30 40F? L A Room. B Kitchen. C Yard. E Pig. F Poultry. G Wash-house. I Privy. K Garden. L Road. M Porch. N Fires. O Stairs. P Bed Rooms. D Dog. H Ashes. The second floor is divided The back area contains small sleeping floor, which is placed in the roof in the remaining height to make apartments. The windows are in the roof. into three bed rooms, as shown in the plan. buildings as lean-tos on a surrounding wall of 8 feet high, in a privy, ash-house, wash-house, fuel-house, poultry-house, and pig-sty. The con- tents of the privy and wash-house pass into the ash-pit, and form a good mixed manure for the surrounding garden, which contains or parts of an acre. This appendage is most necessary to the cottage for growing vegetables, and to afford an agreeable recreation to the cares and toils of life. 3 M 938 ON LANDED PROPERTY. A B AA 自康 A Garden. B Road. M Tx C 10 A L K K Ι Ι H H F F E G G E G D H D G ......... E Kitchen: F Stairs. M N B A 10 20 90 40 H Fuel. I Wash-house. K Ashes. L Privy. M Poultry. N Pig. No. 2. C Porch, D Room. G Fires. Plan, No. 2, shows two cottages that are joined longitudinally, and have the ends for front. The porch is in the side of the house, and enters through the garden. The accommodation and arrange- ment are the same as in last design, and the back area has the same small buildings. The garden surrounds the cottages, and a road leads to each dwelling through the garden. ON LANDED PROPERTY. 939 H ID 10 田 P I 10 E D Р 20 3,0 40F3 F M L K E T N A F D G B H 20 30 40 FT A Room. E Yard. I Fowl. B Kitchen. F Wash-house. K Dog. C Poultry. G Road. L Pig. D Stairs. H Garden. M Ashes. N Privy. O Bed Closet. P Bed Rooms. No. 3. Plan, No. 3, shows the design of a single cottage, with the poultry-house placed under the roof of the dwelling, and be- twixt the fires, of which the heat will convey a very agreeable warmth to the animals. This provision will largely contribute to the laying of eggs and the hatching of chickens throughout the year. The other accommo- dations are similar to the last plans. The entire site of the cottages is excavated to the depth of two feet, which is filled with stones of the convenient size and flatness to form the foundation of the building; and below the brick floor of each apartment there is one foot in depth of broken stones, which will render the cottage very dry underneath. 940 ON LANDED PROPERTY. Expense. The cost of the single cottages in each dwelling will vary from £80 to £100, according to circumstances, and the two that are joined will cost about £180. Groups of cottages. Groups of cottages have been devised-square, circular, and polygonal, and containing six to twelve dwellings in one con- gregation, with a garden attached to each habitation, and having a pump of water and a bakery to serve the whole of the families that dwell in the house. But lazy assemblages are created, and much idle gossiping is en- couraged; and it is preferred to have not more than two cottages in con- nexion, and the fronts averted from any close communication of business. The gardens are best when closely joined to the dwellings, both for plea- sure and usefulness. Books of For a variety of choice and selection on the subject of farmeries and cottages, the reader is referred to "Donaldson's Improved Farm Build- ings," and "Designs of Cottages," by the same author. This reference. work may be had of the publisher of this book. farmeries contains designs for farms of 50 to 1000 acres and polygonal, and embracing much variety of design. accompany the farmeries, and also a number of cottages. designs of cottages comprehends these habitations only, and and useful variety of design and invention. The book of square, circular, Farmer's houses The book of 40 exhibits a large The cost of the erection of farm buildings varies from two to five years' rent of the land; the calculation being liable to the usual variations by cir- cumstances that affect all such arrangements. Employers very much neg- lect their own interest who omit the provision of affording the labourer pleasure after pain, and of giving some little solace to the cares of poverty and toil. A commodious lodging is equally required with the Necessity of comfortable payment of the wages of labour, as without it the value does dwellings. not appear, nor is the desire properly excited to the future de- velopment. The spirit sinks when the relish is withheld of enjoying the hard-earned rewards of toil, however small they may be, and no earnest- ness can be reasonably expected, nor can any anxiety be manifested, when the small indulgence is denied the labourer of having a comfortable fireside and a warm bed in which to recruit the body and refresh the spirits for the coming exertions. Negligence and inconvenience aggravate the filth of poverty, and put to flight every idea of living in the vicinity. Land-owners lose the value of their property by not pro- by the want viding the ample fixed appendages of the farm on which the tenant uses his floating capital, and the labourer exerts his share in the bodily performances. In the former case he loses the present value, and in the latter he fails to obtain the attachment and esteem of the ground-work of society, on which the whole superstructure leans for sup- port. It is only to be got by just rewards and kind treatment, and must not be neglected if the higher grade of existence be contemplated to endure. Value is lost of them. ON LANDED PROPERTY. 941 CHAPTER V. LAYING OUT FARMS, ROADS, FENCES, AND GATES. farms. IN old inhabited, thickly peopled, and highly improved countries as Great Britain now presents in the cultivable surface, no opportunities occur, except in the few cases of enclosing large commons, of making an original formation of farms. The form should be as compact as possible from the attending circumstances, for time is saved in the til- Position of lage, the expenses are lessened in several ways, and the super- intendence is rendered more easy; the boundaries should be as straight as can be obtained, and curved only to suit the bends and sinuosities of the surface of the ground. The courses of rivers and of large brooks of water, the line of roads that are drawn for public use, the access to water, and the provision of shelter, will all be entitled to due considera- tion, and must have much weight in determining the division of land into fields, the size of the enclosures, and the exposure of the grounds. A va- riety of soils will also happen to disturb a regular uniformity; it is very highly eligible to join with clay lands a portion of turnip soils, Much varied. and these again must be divided by the fences of the farm in order that the same field may not undergo two processes of cultivation, nor produce crops of different kinds. It is convenient, when a public road intersects or runs along some part of a farm of land, when the access is convenient to the business of the occupation, and the road may very beneficially form the boundary of two contiguous farms. Rivers, roads, plantations, and stripes of trees constitute the divisions of lands in culti- vation, as the passage is generally troublesome, and the distance inconve- nient. High and low grounds are often required to be joined in the occupation, in order to attach grazing grounds with arable lands, and to afford the shelter of the valley to the exposure of the hills. Many variations must have attention, and much consideration and weighing of circumstances are deserved by the very important purpose of allotting grounds for the convenient and effectual cultivation. Few or no general rules can be laid down with respect to the size of farms. In practice the size of farms must be made to suit the demand, the condition of the tenantry, and other circum- stances. Size very various. In the vicinity of towns, the quantity of lands will tend to be small in the single occupations. The cultivation is market-gardening rather than farming, and the demand is for articles, in the raising, transport, and dis- posal of which a minute care is necessary. The rent is high, which 942 ON LANDED PROPERTY. Nearer towns represses the size of the extents of land, as the articles sell dearly, the sale is ready, manure is at command, the produce is quick in succession, and a smaller capital is required. But when land is removed from a convenient distance from towns or marts of small quantities of produce, which are sold in retail, the rent will be very much less, and the management will be conducted under very different circum- stances; the produce will be chiefly in grain and live stock, which will be more cheaply produced, and sold in considerable quantity. One very general rule may be stated, that no farm of lands shall be less than employs one plough with two horses to perform the yearly labour. This quantity will be forty or fifty acres, as the soil may be clay or turnip land. Below that extent the condition of a tenant of land descends to the common labourer, and even that quantity does not raise the occupier above the servile employment of bodily labour, as the quantity of capi- tal that is used cannot command a profit that is sufficient to maintain an idleness. The quality of the soil, the opulence of the district, and the benignity of climate, and the geographical position, will very much deter- mine the size of farms; and while no doubt can exist, of the General rule. general superiority of farms of sufficient magnitude, it is not by any means advocated, that the size of farms must be increased and in- definitely, either for the individual interest of the land-owner, or for the public benefit. It is quite certain, that the example of beneficial improve- ments has always been set by extensive farmers, who are persons of capi- tal and education, and enjoy a station that places them above vulgar pre- judices and local conceit. But a variety in the extent of farms is suited to the variety of demand, which is generally greatest for small possessions ; and landlords often do not much heed these regulations, provided a good rent is conveniently obtained. The spirit and enterprize of the larger farmer are often outweighed by the greater frugality and attentive detail of the smaller tenant; and the compensation is often surprising when the disadvantages are considered under which the smaller tenant labours. The dimensions of farms are frequently increased from large extents requiring less expenditure for buildings and enclosures than small pos- sessions; but there is danger by so doing in placing the lands beyond the reach of the farmers around. A continued exten- sion of this kind may place particular farms beyond the reach of the common capital of farmers, and the demand may be very much lessened when they are brought into the public market. Large farms. Pastoral or hill grazing farms must be extensive because a large sur- face is necessary to yield a good return, and different animals require to be kept on the grounds, which cannot be done without sufficient space. The expense is less in managing these large congregations; a greater number of animals can be bought and sold at a time, and few or many shepherds are equally capable of being managed, and of bestowing their superintendence. The tendency of farms to increase in size, shows the improving con- dition of a tenantry and a sub-division of lands implies a declining ON LANDED PROPERTY. 943 tends to in- crease the size of farms. condition, or a defective connexion between them and the land-owners ; capital is shown to be wanting for the purposes of cultivation, Condition of and the tenantry to descend into a worse condition. A regularly tenantry continued progress of sub-division of lands will ruin any coun- try, as is seen in the case of France, on the score of ownership; and in tenancy, in a great part of Scotland, in many remote districts of England and Wales, and over the whole kingdom of Ireland. Such a state of things is most peculiarly unfavourable to the progress of agricul- ture; and the increase of the farms in size will be the first symptom of revival, for it will show that funds have begun to be acquired, and that a superior class of tenantry will be established. Every progress Minute sub- of agriculture has increased the extent of the holdings of land, division al- and if ever the tenantry of Ireland rise above their present condition of starved and ill-requited labourers, the existing possessions of land must be formed into extents that can be cultivated with effect. Such changes are gradual, and require much time; the evil has been extending for generations, and as many more may pass away before a suitable allot- ment is seen of the land for cultivation, and the substitution of a class of spirited and independent yeomanry for the present unfortunate occupants of the cabin and the bog. ways hurtful. Roads. Materials. Roads are artificial pathways formed on the surface of the earth for the transport of heavy bodies, and as the natural ground is soft and yielding, it becomes necessary to protect the tracks from pres- sure and attrition by a covering of some harder matter, as pavement, small stones, or gravel. The first article is costly, and not to be found in many places; gravels are worn round by the action of water, and the small peb- bles never bind together to form a compact bed of road, and consequently stones broken small by the hand-hammer, which are got from a quarry or from surface stones, are the most useful materials in the making of roads. The disunited fragments present many angular points, which when acted upon by pressure, are fitted into the alternate shapes, and become almost a solid mass of small particles possessing a broken continuity. These angular points are wanting in gravels, which require to be broken by hammer, and even then the remaining round side prevents the junction so well as in quarried materials. Hence stones of any hard kind have been long established as the most suitable materials for making roads, and broken to the size of passing through a ring of two inches in diameter. The direction of roads is an object of very great importance, whether the line be a public thoroughfare, or a cross-road of communication, or a private farm outlet. The inclination of the surface, and the hardness, smoothness, and durability of the covering, constitute the chief properties of a road, the highest of which is a plane with a surface resist- ing the pressure of bodies, and opposing the least resistance to their motion. Steep acclivities must be avoided in the direction of roads, when high grounds cannot be ascended by a rise of one foot of slope to thirty-five of base, and from that figure to fifty, the line of road must be Direction. 944 ON LANDED PROPERTY. Cross mences. Roads. Grass turf tom. diverted round the hill, and to skirt the base of the high ground, rising or descending in its course, according as the object to which it leads is situated above or below the level whence the road com- A circuitous line is certainly produced in this way, but it is unavoidable, as the hills cannot be climbed, nor deep vallies crossed with- out an overwhelming inconvenience. The vallies that intersect a country are to be crossed by roads at the narrowest point which can be approached, when a bridge will be generally necessary. The cutting of the upper side of a road that skirts the side of high grounds, very conveniently affords the materials for embanking the lower side, and the expense is less than when a road is made on a level plain, where the whole formation is made of raised materials. This line of a road affords a drier bed generally than when the direction lies along low grounds, which may be wet and swampy, and exposed to inundations. A ditch along the high side of the road intercepts the waters from the high grounds, and conveys it to stone culverts which cross the road at the proper places for discharge. In every case where the advantage can be obtained, the hard materials that compose a road, should be laid upon the grass turf, as it presents a tough and matted surface which resists the pressure, and pre- the best bot-vents the broken stones from sinking into soft ground. But when excavations are made, and embankments formed for the passage of a road, that advantage is not got, and the materials are com- pelled to be laid on the newly-formed bed of fresh earths, which are mostly soft, and yield to the pressure. In that case, the hardest and driest materials that can be got, are selected and laid in an even surface below the track of the road and broken to a small size. Over it is laid a body of broken stones, which were before mentioned, in the depth of twelve inches, and width of twenty feet; and this space is bounded on each side by a sloping ground of twelve to fifteen feet reaching to the side ditches which run along the front of the boundary fence. This width of sixty feet is not beyond the use of a public thoroughfare; and the hard materials of twenty feet in width, allow the car- riages to change the tracks, and not to follow, as in narrow roads, the same path of wheels, which is a most pernicious accompaniment of a con- fined space, and very soon destroys the consistency of the road. Convex roads, or having a high centre with sloping sides, are discontinued from an excess of the method of formation, but as much convexity is eligible as will throw the water to the side ditches. Roads must be kept dry, and Draining of where wet grounds must be passed, drains are necessary to be placed below the road in three longitudinal cavities filled with broken stones, one in the centre of the road, and the others at the division of the hard materials with the sloping sides of earth. Cross drains are necessary in the hollow places, to convey the water to the side ditches. Width. Roads. The most public roads are turnpike trusts, with which the land-owner has only a small joint concern, and over which his property control does not extend; but the private roads are his jurisdiction, jointly or singly; and the roads on his farms are exclusively his undivided patrimony and ON LANDED PROPERTY. 945 Surveyor- ship. employment, and deserve an especial attention. When money is collected from the farmers by a rateage, and applied in the making and repairs of roads of a general use, some competent person must be appointed as the permanent overseer, who shall employ labour and collect materials, at the times and places, which shall appear to be most eligible and generally beneficial. The custom is not yet abandoned of the farmers serving in the yearly rotation as overseers of parish roads, and of bestowing so low a minimum of attention as scarcely ever to see the object of their care. The tenure of office is far too short to allow any ideas on the subject, and as it must occupy some time, less or more, an utter carelessness is evinced towards an object of the most primary attention. These district and parish roads are the first divergence from the main trunks, or parliamentary trusts; they are the arteries, and the farm or private roads form the veins of the ramified intersection of a country by the means of communication. The parish roads may be one-third below the width of the turnpike lines, and the farm roads may be one-fourth narrower than the district tracks, making the breadths to be forty feet and thirty feet respectively. The first extent will be divided into sixteen. feet of hard materials in the centre, with twelve feet of sloping ground on each side, and the farm road will be fourteen feet in the centre of bro- ken stones, and eight feet in the sides of sloping surface. These widths will be sufficient for all ordinary purposes. Private roads. All roads must join each other at right angles, with an arc or circular sweep on each side of the junction, in order to indulge the constant ten- dency of animals and carriages to turn in the intended direction before the whole equipment has reached the road that has been Junction of approached. Ample room is better than pillars or railings roads. placed at these points, as the carriages run against the securities in a con- fined passage, and break the outposts of safety. A strong railing recommended on the extreme edge of the circular sweep, after a very ample ground has been allowed to render the use of it very seldom required. Parish and district roads have the same object in view as the main trunks, to reach the point of attention in the most convenient and eligible manner : the location of farm roads is directed by the position of the farmery, the formation of the intervening grounds, and to afford access to the adjoining fields of land. The square or parallelogram form of fields must be preserved, if at all possible; if beyond the reach, then a bended or curvilinear shape must be preferred to a polygonal cir- cumference of corners and abutments. In other cases, two sides, or one side, of a field, may possibly be got in a straight—and the others will be directed by the adjoining lines of road, or formations of the ground. It is best when each field of land opens into a hard road, and which prevents the travelling over the soft surface of any field in order to reach the other beyond it, which is often very inconvenient. For this purpose, the breadth of two fields must intervene between two roads, and when this arrangement cannot be obtained, the headlands of the field that adjoins the road, must be made into a road, and kept for that use. There Between every two fields. 946 ON LANDED PROPERTY. is a greater necessity that straight lines be preserved in the placing of farm roads than in the direction of the main trunks; the latter have only one object in view, while the private purposes have several contemplations. Still the roads may be located in places such as are found to be low grounds, and at such distances as will shape the fields in the oblong direction, along the line of the private road, or stretching across between the two roads. The equal size of fields of land is also to be pre- served as much as possible; and the best experience has fixed the size of twenty acres, or varying from fifteen to thirty, as the most suitable extent of divided lands, for the purposes of arable or grazing husbandry. Small enclosures create too many fences and gates, and incur an expense in the upholding and repair; and large fields are in many instances much exposed from want of shelter, and require too large a number Ready access. of animals for the pasturage, and small flocks of beasts always thrive best. The access to water will have much influence in determining the extent and position of fields, and the most essential article may be procured by forming a pond in the lowest ground, by boring as a well, or by bringing the water from one place to another in a rill, in a covered drain, or in metallic pipes. In the latter case, a trough being placed across a subdivision fence, will supply two fields, and when the grounds are very high in the position, the pasture must be used by sheep, which require little or none of the element of water for the organized develop- The shape of fields must not depart far from the square form, or the grounds will become formed into a number of longitudinal slips, that Corners to are both unsightly and inconvenient. Corners are in all cases be planted. to be avoided; but when the situations are unavoidable, the nar- row angle must be planted with trees, and thus make a straight fence of the field. The junction of roads, as was before mentioned, must be at right angles which will direct the joining of the fields to be in the same position in all cases of a contiguity. ment. Roads a provement. It may be very safely affirmed that the making of roads as primary im- convenient lines of communication are the first improvements to be done in any country, and the keeping of the tracks in a sufficient repair, is a point of little less importance than the original for- mation. When roads are in bad repair, the wheel carriages are broken, the animals of draught are distressed, and small loads are transported; cir- cumstances which operate against the prosperity of agricultural under- takings. The landowner has the power of enforcing the proper condition of the parish roads, and the tracks for farm purposes are wholly and absolutely his own performance. No fixed appendage of the farm possesses a higher useful value than an ample sufficiency of well-made roads, nor will any enlightened practical man neglect to examine and estimate the con- venience which his floating capital will enjoy in that respect: he will use his judgment in comparing the advantages which are presented by different great value situations, and make his choice by the greatest number of to any farm. facilities that are offered for the employment of his money and his time. The approach to the main trunks of communication is the first ON LANDED PROPERTY. 947 noticed. attention, and then the access to each field from the farmery, which is the focus of the whole movements. The finest farmery that can be devised and erected, may be rendered of small utility when the application of its merits is withheld by the want of the ways of traffic; when the loads must be restricted in weight, and the frequency of the transits is limited. Practical men know full well the drawback of these prohibitions, and will not fail to place them on the proper side of the account in reckoning the sum of the intended offer for land to be used in cultivation. It becomes the interest, and also the duty of the landowner, to have the Always farms of land unobjectionably provided with convenient and well-made roads, as well as with buildings for habitations. The means of transit must be very ample and ready, and no want must appear that can hinder the full per centage being given to the owner of the soil for the interest be has purchased in it, from allowing the floating capital of the tenant the beneficial and prosperous opportunity of use, and from employ- ing and maintaining labour, which is the paramount and overruling con- sideration of every object and design. Any neglect on these points baffles the fulfilment of the intended purpose, and destroys the arrangement of the joint performances. The maintenance of farm roads in the proper repair devolves on the farmer, who must support the bed of hard materials, and keep Good repair the side ditches clear as currents for water. This charge is indispensable seldom expensive; the field stones that are periodically gathered, serve as broken materials, and the earthy scourings of the side ditches are generally useful in compost with lime for making a manure of very considerable value. The farmer's own interest must ever induce him to perform these operations. The smoothness of roads for his carts and horses, and soaked earths for manure, are worth the attention of every cultivator that deserves the appellation. Enclosed Fences are barriers raised betwixt the fields of land for the purpose of protecting the crops that are growing in an enclosure from injury done by the animals which are grazing in the adjoining division. They also serve the purpose of separating the flocks of animals, and enable the production of different plants and crops in the required divisions without any mixture or confusion. Lowland arable farms require to be closely and permanently subdivided by lasting boundaries, while upland grounds. farms and hill grazings are only provided with a general fence which surrounds the whole farm, so as to protect the grounds, and save the sheep and other animals from disturbance. Large flocks of mountain sheep do not require any minute subdivision, but are spread over an extensive range of surface. Lower pastures that have some tillage lands, are divided in the crops from the grazing grounds; and near to the homestead, there will be two or three paddocks or small enclosures for the rams of the flock, for weak ewes, and similar purposes. The comparative small value of the surface ground prevents the extension of enclosures in a practical view; Open farms. but where the ground increases in value, a greater use of en- closures is required, and will be admissible on the score of profit. Sometimes 948 ON LANDED PROPERTY. the quantity of arable lands in these possessions is so large that another farm is constituted distinct from the grazing ranges, and then the enclosing of the cultivated parts is similar to lowland farms. Stone walls. Fences are made with stones from the quarry of rocks, or with the gatherings of the field in boulders and slaty fragments. These stone walls stand either wholly above ground in the entire height, or are sunk in an excavation, and form a fence in the front having the top level with the ground behind the slope that has been dug. This last is called a sunk fence. Mortar walls are erected on the sides of highways in the vicinity of towns and other situations that are much ex- posed to trespass and injury. They are the most complete and durable of all fences; but the cost is beyond a very extended application. The foundation is made with broad flat stones in a firm subsoil-the width of eighteen inches at the base slopes to one foot at the top, which is covered with rough stones set on edge, and projecting over the wall on both sides. The height is from four and a half to five feet. walls. Dry stone Dry stone walls, admit a much larger application than the erections with mortar as a common masonry. But even that provision of fences is confined to certain districts which contain suitable rocky formations that are near to the surface of the ground, and easy of access. Schistoze formations are the most eligible, as the laminar fracture produces a form of the fragments that is adapted to the purpose of build- ing walls in which no mortar is used as a cement. The foundation is dug to a firm depth on which flat sided stones are laid in the width of nearly four feet; the wall to be raised is laid on these stones in the width of three feet; the top at the height of five feet from the ground is narrowed to eighteen inches, over which is laid a tier of long narrow rough stones placed on edge, and projecting over the wall on both sides. The sides of the wall are built with the best shaped stones in the manner of the common walling, and the small lumps are firmly packed in the centre. A cope of stones is much preferable to turf which soon moulders away; and it adds to the solidity of the fences in the weight of the stones that are laid on the top of the wall. Boulders. Boulders or field stones are very abundant in many parts of North Britain, and very good fences are formed with these materials, the shape is rounded, and seem to be a large formation of primitive gravel, and are difficult to be built into walls. The hand-ham- mer is applied to break the lumps into at least one square side, which is placed outwards in the wall, and the centre is very closely filled with the smaller boulders. There being no large stones to form a coping, the top is rounded with the unbroken stones into a narrow apex, which is ter- minated with one row of the largest lumps that are found. The sunk fence of these stones consists of only one facing of boulders, as the back rests against the solid bank of earth, which has been excavated in the depth of the fence. Plantations are well fenced in this way, and the top of the fence is level with the surface of the cultivated land and of the planted ground. The top of the wall is covered with turf, as part of the surface of the plantation. Sunk fences. ON LANDED PROPERTY. 949 useful. Stone walls are called dead fences, and under peculiar circumstances the preference is justly due to these erections as the boundaries of lands, and for the separation of grounds. Less space is occupied by the stone wall than by the live fences; it does not harbour vermin of any kind, and less expense is required in keeping up the dilapidations. But the appearance is dull, and wants the enlivening and cheerful aspect of the blossoming hawthorn, and less shelter is afforded to animals by the wall than by the hedge. Dry grounds which do not require ditches as outlets for water, are best adapted for stone walls, and always with the understanding Walls when that the rocks are adjacent to the grounds that are to be fenced; that the access is easy, the rock conveniently dug, and the whole operation capable of being done at a moderate expense. On high exposed grounds, where the climate is outrageous and the soil unfavourable, no care or at- tention is able to raise live fences, and then walls of some kind are the necessity of the case. Turf walls will last for a very considerable time, when well built at first, and where the climate is moist, and the grassy ve- getation ample and strong. But they form no obstacle to the trespass of sheep over the soft materials; cattle rub upon them, and hot suns induce the mouldering and dilapidation. Thorn fences Live fences are the most common boundaries of fields over the greater part of the British isles; and for the purpose of raising the fence of growing shrubs, the most approved plant is the common haw- thorn of white blossom. It is a perennial plant, of much durability, and has a large adaptation of growth in different soils and situations. This last quality constitutes a very large recommendation to the use of its application, and where a varied utility is required, the last importance is attached to that property of the article that is selected. Experience has long ago shown most incontrovertibly that the common white thorn is the most generally useful plant for forming hedges: it grows quickly, and on a great variety of soils, and the prickles or spines are very annoying to stragglers that trespass from field to field. The plant is raised in nur- series to the age of three or four years from the haws or ripened fruit of the aged plants, which are sown in beds of fine earths that are prepared for the purpose. The sets are raised for use, and cut to the length of six to twelve inches, as new shoots from the cut end are ever more vigorous than the continuation of the stem produced in the nursery. The Erection. line of new fence being determined and marked with planted stakes, a turf is cast by the spade along the line and inverted upon the ground, with one side touching the cord, and the other sloped by the spade from the middle of the turf to the surface of the ground. On this sloped earth of turf, the cut thorn sets are very carefully placed by hand at the distance of four inches from each other, the upper end being even with the high end of the slope. A ditch, in the case of wet grounds, is dug at the width of three feet, and the depth of two feet; and the earth that is excavated is thrown backwards to form a mound. The best earth on the surface of the ditch is placed over the roots of the thorns, the upper ends being left in sight, whence the shoots will proceed. On dry lands no ditch is required, and the sets are placed deep in order to enjoy the benefits 950 ON LANDED PROPERTY. Care when young. of moisture. The mound of loose earth is raised to a height be- hind the row of thorn sets, and upon it is placed a fence of strong dead thorns, or better in a paling of three bars of sawn timber, which will last for many years. The front of the young hedge is pro- tected by a similar fence, which is placed in a slanting manner along the side of the ditch, and in this way defends the young shoots from injury. These fences must be upheld and repaired with a very vigilant and con- stant care, in order that the young thorns are securely protected during the years of tender growth. Weeds re- During the first two or three years of the growth of young thorns, so many weeds must be pulled away by the hand as will afford room for the young plants, and no more need to be destroyed, as the covering of weeds defends the bank of earth from drought, retains moisture, shel- moved. ters the plants, and is beneficial to the growth of the thorns. On no account are spades to be applied, as is usually done, to pare away the bank of earth by gradual operations, and expose the roots and stems of the thorns to the influence of sun and drought. After three years, or in less time, the thorn shoots will overtop the weeds, and then no more care is necessary on that point. Some shoots of the thorns will rise much above the other growths, both in height and sideways; these overgrowths are lopped by the pruning knife, but no other cutting or slashing is done; as wherever an incision is made in any vegetable growth, a bundle of feeble shoots are protruded, which divert the juice from the main purpose, Training of and enfeeble the special growth. Hedges must be allowed to the hedge. grow in the wild luxuriance of nature to the height of full five feet, when the form may be fashioned into any shape that may be wished; and generally, in the period of eight years, the fence will be complete, and need no protection from accessory aid. A sufficient regularity of height and straightness of sides can be obtained by lopping the overgrowths that appear; and with this small application hedges are best allowed to remain without any cutting or plashing; and the luxuriant blossom of nature's forms is much more pleasing than the dull uniform sameness that is pro- duced by the shears of the clipper. Gaps are to be very carefully filled up from the first year of the growth by planting young sets in the open space, or better by pulling across the gap the young shoots on each side of it, which are fixed in that position by means of hooked pegs of wood driven into the ground. This precaution is necessary in order to procure a close hedge, and unless it be thick in stems and foliage, passages will be made at the weak places, which destroy the utility and impair the value of No cutting of the performance. Hedges never should be cut in any stage of the growth. growth in a young state, the progress is retarded by it, and in the advanced condition an expense is incurred which is wholly useless and unnecessary. It only remains to raise a hedge to the required height, and then to keep it in that condition of existence. Furze. Furze forms a very good fence in some places, but the plant flourishes only on dry banks, under warm early climates. When the growth rises high, it is apt to become open below, which objection is ON LANDED PROPERTY. 951 partly remedied by having the hedge in two parallel rows, and by cutting the rows alternately, so that one row forms the fence while the other is growing after being cut. Beech. Beeches grow well on some damp cold soils, and form a good fence, but the plant is of slow growth, and it wants the formidable prickles of the thorn, which constitute the weapons of defence against the trespass of animals. The hornbean tree is of a similar nature and value. The sloe thorn, or black thorn, from its very sharp and nu- merous prickles, forms a strong and durable fence, but the plant is both slow and shy of growth. Sloe. Thorn hedges never grow well at gateways, and it is very advantageous to raise a piece of stone wall on each side of the passage, and to insert the thorn roots between the stones, with the shoot end projecting outwards, and from the young shoots growing upwards, very strong fences are often obtained from this mode of inserting the thorns. All fences raised by the land owner, and upheld by the farmer Fences of every kind must be first raised by the proprietor of the land, and subsequently kept in repair by the farmer; and nothing more clearly shows a farmer in every sense of the word than a range of fences in a thorough and complete condition of use and efficiency, without any gaps or weak places. Good husbandry never understands a carelessness to be evinced in any one single depart- ment on the farm; the most attentive vigilance is to be adopted even in the most minute articles of utility, and the habitual custom must be exercised of keeping all things in use and every thing in order. New fences of thorns are to be placed, if possible, on the grassy surface of turfy ground, in which the roots of the thorns spread in search of sus- tenance. The length of the thorn-set fits the sloped side of the inverted turf that was laid to form the base of the fence; one end sends Sets laid on upwards the shoots which form the hedge, and the under end grass turf. which is covered with earth, projects the roots which nourish the plants. The operations of life are on the surface of the ground, and these processes are engendered by the life and decomposition of the animal and vegetable existences that are in being on the surface of the earth. The roots of the thorns spreading among the decomposition of these minute portions of life, receive a food that is of all others the most favourable to life of any kind, for no manure yet known can be compared with decaying vegetables when in connection with the quicker elements of animal bodies. No ploughing or digging of the ground is required on which a new fence is to be placed. A number of trees growing in a hedge-row is no doubt very Hedge-row objectionable, but a few 'standards in scattered distances enliven the scenery and improve the landscape, and the damage to the hedge is inconsiderable. The distance of 50 or 60 yards seems a proper distribu- tion. It has been proposed to make a plantation in the sharp corners of the fields, and to round the inner fence, so that the ploughs in ploughing the headlands do not turn, but go round the field and lay the headland in one direction. These clumps of trees will add to the scenery, and in some places be a useful shelter. trees. 952 ON LANDED PROPERTY. Gates. (( Gates are a part of the fence or boundary which is raised for the purpose of dividing land into portions that are convenient for its use, in the state of arable or pasturing applications. The judicious arrangement and proper maintenance of these boundaries form a very im- portant department of modern agriculture; and, consequently, a value is attached to the consideration of the best materials and the fabrication that are adapted to the special purpose. The fences are stationary and fixed, and as the use of the enclosed portion of land requires the ingress and egress of the tools that cultivate and convert the produce into value, an entry is necessarily selected, which shall be opened for admission and closed for prohibition. A bar or hindrance in this entry was very early con- trived, and has been long used, called a Gate," which is formed of bars of timber fastened together, and being hung or suspended on a fixed post or pillar by means of turning appliances of iron, which join together the parts of the timber frame, the gate moves on either side of the entry, and opens the road, or it remains across the way and shuts the passage. In every case two timber posts are required: one on which the gate is hung or suspended, and another on which it shuts, and to which it is fastened to remain across the road. The entry to the field or the gateway admits only one form of gate in an oblong square, as some objects in nature are limited to certain forms and applications. But the interior parts of this square form admit a great variety of ap- plications with which to fill the vacant space, and it is chiefly this portion of the article that constitutes the differences of which the implement is sus- ceptible. An adherence to practical utility must be rigidly attended to, and at the same time a neatness must be produced, which denotes a simi- larity with other refined objects. Every article of use must bear a cor- responding degree of refinement: strong without being clumsy, and neat but not gaudy, or fancifully ostentatious. Can only be square in form. Two gates to every field. Every field of land should be provided with at least two gate- ways on the opposite sides, so as to make it approachable from each side of the ground. The width of the gateway should not be below 12 feet, nor the gate itself under 9 feet in length, so as to afford a free passage to the loaded vehicles. Gateways should be placed on dry grounds, and are most convenient when opposite to the headlands of the field, at either or both ends. The carts, empty or loaded, travel to the ends of the field, and find a straight road along the headland to the gateway, and pass to the road outside the field. The gate posts of oak, or some durable timber, should not be under nine feet in length, three feet below ground, and six feet above the earth. The part under ground should have a thick butt end, and be well fixed by means of closely rammed moist clay; the hole must be filled in that manner from the bottom to the top, with the post upright in the centre, and a turf of grass laid over the surface. The utility and stability of the gate wholly depends on the secure fixation of the hanging post; if it is unable to carry the weight of the gate, or if it yields to the frequency of the opening and shutting by the traffic, the fore end will soon fall to the ground, and the implement is Posts to be firm. ON LANDED PROPERTY. 953 rendered useless. Some little labour and attention is required to make secure the foundation of the gate, which is best done in the first perform- ance, and not to require a repetition, which is never so effectual. Gates are formed of five longitudinal bars about four inches wide and one inch thick; the wood may be larch, ash, willow or the durable firs, and dressed by the plane to receive the covering of paint. The bars are mortised at the ends into upright small square posts of hard timber, and fastened by a wooden pin. The back end post of the gate is heavier than the fore end, as it is next to the hanging post, and is fitted to receive the iron work by which the gate is suspended. The gate is best hung by crooks and thimbles of iron; the former being driven into the Clap gates hanging post, and the latter being clasped on the upper and most lasting. lower bars of the gate. It is best attached to the catch post by means of a small iron catch driven into the post, and a small chain attached to the hand-bar of the gate. This fastening never can be opened, except by the hand of man. Swing gates that pass to either side are ever liable to fall too deep or rise too shallow in the iron latch that is sunk in the catch post, and spring fastenings are very liable to be undone by the animals rubbing against them. The gate must be of a height sufficient to prevent any animals getting their heads over it, and pushing with the animal's their breast against the upper bar, otherwise it is quickly broken. The posts of a gate look well when they are octagonal shaped and rounded to a top. All gateways should be deeply laid with small broken stones, as animals always congregate at the gates and convert soft ground into a pud- dle. No better sign need be required of a good farmer than having every gate in proper order, and every gateway affording a dry and firm passage at any season of the year. High above reach. The reader is referred to "Designs of Gates for the Park, the Policy, and the Farm," by the author of this work, and to be had of the publisher, where a large variety of gates is delineated, with a strict regard to economy and the useful convenience. CHAPTER VI. PLANTATIONS-YOUNG AND OLD TIMBER. A PLANTATION is formed of trees that are placed in the ground at such distances as allow room of the full growth being attained. The object is to raise timber for artificial purposes; to convert into a profitable use the barren grounds, and irregularly formed lands; to adorn the surface, beautify the landscape, and enliven the scenery, and in unpro- pitious climates, to afford shelter to the cultivated portions of the earth. A tree seems to have been among the earliest productions of Woods: 3 N 954 ON LANDED PROPERTY. nature destined for the purpose of clothing the ground with vegetation; tall, shrubby, or fruticose, the stem is seldom absent in any latitude that permits the existence of any degree of organized life. The bulk is regu- lated by the quality of the soil and climate, and the foliage undergoes the same modifications. In most parts of Britain, a very equable medium is established; the bulk attains a useful standard, and the growth is gene- rally ready, and sufficiently progressive. ren lands, The rearing of timber is an object of much value to the owner of the soil, and of a very considerable interest to the national community, in relation to only on bar- the vested right which is enjoyed anent the purposes to which the surface of the earth is appropriated. In arranging these distribu- tions of use, the rule may be held as absolute, that all lands be planted with trees, which are inaccessible to the plough by reason of elevation, declivity, or other insuperable establishment of nature. And where a grassy surface on a kindly subsoil yields a grateful herbage to animals, the position of plantations must be so arranged as to afford shelter to the grounds that produce the value in pasturage. The profit of the grazing will determine if the use continues for animals, or may be better converted into a plan- tation. Very high elevations deny the growth of any vegeta- nient to cul- tion; grasses will grow where trees cannot live, and conse- or inconve- tivation. quently such a value must come from these situations as nature is pleased to allow. Plantations are best made on moderate elevations, on sloping grounds that deny cultivation, and on low situations where for special reasons a congregation of trees may be eligible. Use and orna- ment will always determine the establishment of plantations, and regu- lated and modified by the contingent circumstances that ever attend the purposes of active intention. Trees of use are naturally divided into two large assortments of hard and soft timber, the former bearing the seeds in imbricated cones, and the latter in shells, nuts, and drupes, which form coverings of a greater or less hardened consistence. At the periods of full ripeness, the seeds are gathered, and safely reserved for being sown in the proper seasons on finely prepared grounds, that are fenced round, and duly cultivated for the pur- Young plants. pose of nursing the young vegetations. The seedling plants are moved from the bed of one year, and placed in rows, where the weeds are killed by hoeing the intervals, and only the moderate growth of the plant is encouraged. At the end of two years, the trees are ready for the use of the plantation, or to be placed in wider rows in the nur- sery, there to wait the demands of sale. Grounds intended to be planted with trees, must be completely fenced during the year previous to the planting, and thoroughly laid dry by open drains, if the nature of the land requires the removal of water. These ditches are placed in the lowest grounds, and follow the sinuosities of the surface in every direction, however crooked or awkward the appearance may become. The general discharge must lead to a large ditch, brook, or rivulet, into which the water escapes. The conveyance must be clear and uninterrupted to the outside of the plantation, if at all possible to be ON LANDED PROPERTY. 955 got. If a flat surface occur, an artificial level must be sought and made for the special use. Two methods are adopted in planting trees: one way opens circular pits in the ground, three to four feet apart, about one foot deep, and one foot and a half in diameter. The tree is placed upright in the centre of the hole, with the rootlets carefully spread abroad by the hand; Planting of the excavated earth is turned into the pit, and trodden firmly trees in pits; round the trees by the foot, and then the grassy turf is placed as before over the pit, and cut in two parts with the tree in the incision. The earth being trodden firmly by the foot, and the turf being compressed by the back of the spade, finishes the planting of the tree. This mode is adopted for plants of the largest size, which are placed at the widest distances on the ground. The second way of planting trees, makes two incisions with the common spade, centrally crossing each other at right angles; the tree is placed in the ground at the point of intersection, the spade holding up the turf till the plant is fixed, and then depressing it to secure the position. The roots of the plant are neatly dressed by knife, and the feathers are arranged in the new position before the fixture is accomplished. This method is cheap and expeditious, and leaves the roots among the best soil on the surface of the ground, among which to spread horizontally, and establish its abode; whereas in pits, by the first way, the roots are placed in the subsoil, which is often very pernicious and inimical to by incisions vegetation; the growth is stopped, till new roots emerge from in the ground. the stem, and draw subsistence from the upper soil. Trees are fibrous rooted plants, and spread horizontally along the surface of the earth; no tap root descends to require a depth of humified earths, and consequently the insertion may be more shallow, and the labour less costly. The last mentioned method is therefore the preferable way of planting young trees in the ground. The distance between the plants and the number of trees that are required to cover an acre of ground, are very much varied both in opinion and practice. Hard timber trees, as oak, ash, and elm, are usually planted at four feet apart, on the calculation that the one-half of the trees are taken out when risen to one-third of the full growth, in order to make room for the standing crop, and that these remaining trees need Trees on an the space of eight feet between them. But experience has acre of ground shown that a full crop of timber trees can stand in four feet apart, and consequently the first planting must be thicker on the ground. The larch and Scotch fir are found the most suitable plants on the highest exposures, and even on the sheltered slopes of these elevations, these trees maintain the greatest worth: on the lowest declivities, and upon the best grounds, the oak, ash, and elm, usurp the preference: and on low flooded lands which cannot be amended, the willow and alder will be the chosen plants. The beech on chalks, the hazel on rocky banks, and the birch on barren gravels, will be useful introductions; and in some situations, the Spanish chesnut will equal in value the most esteemed tree in Britain. In every case of planting trees on high or low grounds, and of firs or hard tim- varied by situation. 956 ON LANDED PROPERTY. ber, the distance between the plants will be two feet, and the number on an acre will vary from eight to ten thousand. The plants of hard timber may stand at two feet and a half apart, and in certain expo- sures, the firs may be so close as eighteen inches. These close distances are required to create a mutual warmth, and to promote the upright shoot- ing of the plants by preventing the lateral expansion. Time of planting. The planting of trees is best done in the months of November, Decem- ber, and January, and during the mild fresh weather that occurs betwixt the frosts and snows of these wintry divisions of the year. So soon as the setting of the plants is accomplished, the gates are shut, and as the fencing has been previously done, the performance is wholly completed. Roads of twenty feet in width are left in the conve- nient directions over the planted grounds, and so arranged as to afford a ready and convenient access to the working requirements, and to the ve- hicles of export when the felled timber is removed. This con- venience is never to be omitted being made in all cases of plantations of trees. Open ditches are to be dug along the sides of the road in all places where water may overflow the passages, and are di- rected to discharge the contents into some one of the main outlets. wet lands only these drains are necessary. Roads in woods. On Our system of close planting allows the trees to grow altogether unmo- lested, save the insertion during two years of fresh sets in the places where a failure of the growth is seen to happen. The most vigorous and thriving trees take the lead, and carry the pre-eminence, and strive to reach the benefit of sunshine, which is necessary to a prosperous vegetation. A cer- Thick planting tain number of plants attain that station, and form an umbra- geous canopy of leaves and branches that join in the contact; beneath this covering, all vegetation is killed, and almost every life ex- tinguished, at least that rises upwards in any considerable height. The trees that cannot rise upwards into the sunshine, are killed, and when seen to be fairly mastered, are usefully removed for fencing purposes; the lateral branches of the trees that succeed in obtaining the permanent elevation, die away, from a beginning at the bottom of the stem, and are killed pro- gressively upwards, according as the tree rises in height. The decay fol- lows closely on the ascent of the stem, and there is left on the top of the tree "only" a round canopy of green branches and leaves, of a small ver- tical extent, and so far laterally as the contiguous formations will allow. The stem of the tree becomes a straight bole without any knots or blem- ishes; the upward struggle of growth prevents any bendings or lateral inclinations, and the efforts of nature are directed to one chief point. By this method, nature exhibits the finest timber in the world; pruning not in the wilds of America, in the straths of Scotland, and on the necessary. Alpine cliffs of Norway, the seeds are sown by the wind, and the roots are struck into the uppermost stratum of decayed vegetable earth -a lesson which forbids the pruning or lopping of branches, and the inser- tion of the young plants deeply into the ground. renders The pruning of trees, or the cutting away of the branches, by a saw ON LANDED PROPERTY. 957 Expense avoided. or chisel, is a mangling process, which very much damages the timber of the stem. Sap flows to an incision, and very often protrudes a number of young shoots; or a struggle is made to cover the wound, which forms a large blemish when the timber is sawn for use. When the tree prunes itself by means of a killing confinement of the lower parts, as by thick planting, no such accident happens; the decay is gradual and progressive, and the sap flowing upwards by the attraction of heat, leaves the branches to a complete annihilation: there is no wound to be covered with bark, the branch drops off, and the junction with the stem is soon imperceptible: the expense of pruning is avoided, and also the labour and cost of thinning, which is seldom repaid by the value of the clearances. The trees grow to a full maturity, and have no attention, ex- cept in keeping the fences good against trespass, and in removing the stems that are undergrown, before rottenness destroys the use for fencing. About one-fourth of the number of trees planted will remain for crop, and will average about two thousand on an acre, standing at four to six feet apart. The other portion of the original plants is sacrificed to the purpose of .raising the standing crop into a prosperous condition. Quality of timber im- proved. The observant eye that looks into a congregation of trees which have been grown from nature's care, or that have escaped the havoc of the thin- ning and pruning performances, cannot fail to discover the truth of all the above statements, and that the system is also supported by the most rigid adherence to established laws. In these places are seen the stems of trees, tall and straight, without branch, knot, or excrescence of any kind, and the bark slippery and smooth without any interruptions. Wherever the sun and light are allowed to pe- netrate the branches of trees will seek it laterally as well as vertically, and the number of shoots will be proportioned to the free access that is given to these necessary elements of growth. The vegetation is thus directed to many points, the tree becomes a bush, and fails to reach the height of a timber provision; the stem is knotty and rifty, and worthless in the hands of the workman; and the wider standing of the trees reduces the number on an acre of ground. On low grounds which approach the residence of demesne, a luxuriant foliage may be wished, and then the trees are thinned to the distances that may be required. An undergrowth of bushes may be wished to shelter the beasts of game, when the openings betwixt the trees must be wide to admit the sun and light to nourish the evergreens that form the cover. In such cases, a distance of ten to twenty feet may intervene betwixt the trees, and the first planting may be in the half or a third of that distance, and the supernumerary quantity of plants are re- moved at different stages of the growth, leaving the number to stand for crop. trees. The fir tribe of trees generally reach maturity in about thirty years, and the hard timbers in forty to sixty. Fellings and sales are then Maturity of made according to the wants of the locality, and the purposes that require to be supplied. In every case the trees are felled, topped, and lopped by the owner's expense, and drawn outside the plantation, and 958 ON LANDED PROPERTY. Sales. laid in convenient lots for sale, whence the removal is made by the pur- chaser. Every tree must be cut down, save some few choice standards that are left in the outside to adorn the scenery, and the empty ground is immediately filled with the suitable plants, as before directed. No trees are to be left standing in the interior of the wood; the ground must be clear, as young trees never thrive under the shade and drip of the full grown forerunners. The custom is most pernicious that mixes growing trees of different ages; the younger always clean cut and suffer from the older, and the general appearance is never thriv- ing or satisfactory. In this way the cutting and planting of trees go on in an uninterrupted succession, and the ground is never empty of production. Woods to be none left. Neglected woods to be wholly re- newed. When plantations have been neglected, and allowed to grow in old tim- bers, younger trees, and a bushy underwood, the evil becomes very appa- rent of such a mixed system. By cutting and removing the full grown trees, a very great damage is inflicted on the smaller growths of every kind, and the younger trees when put in full possession of the ground, form only the half crop which the land is able to bear. In this way the evil is perpetuated, and each succeeding gene- ration grows to damage the following vegetable increase. The most effec- tual way is to cut everything completely from the ground, and to plant afresh with the suitable plants, and attending for some two or three years that the young trees that are planted be not overpowered by the thick and rapid growth of the underwood, and the shoots from the old stools which possess the vivacious principle. These exuberances are very use- ful in sheltering and drawing into a tall growth, the plants that are in- serted in the ground, provided the density be not allowed to choke the growth of the young trees-this danger exists only for a short time, and is easily avoided. Felling tim- bers, and barking oaks. Hard timbers and firs are best felled in the end of the year, and removed before the spring growth is commenced. The ground is planted with young trees in the same winter. Oaks being cut for barking in the early summer, the planting of the land with fresh growths is delayed to the next winter, when the process is repeated, as above de- scribed. In every case the clearing of the ground must be complete, save some few choice trees in the corners or fences of the plantation, which may adorn the scenery and enliven the landscape. The remnants must be few, and all others are indiscriminately removed. Copse woods. Copse or coppice is a plantation of trees that rise to a certain. growth of years, when the stems are all cut and sold for the re- spective purposes of use. The trees are of the vivacious kinds, that send forth shoots from the old stools after the growth is cut, and the most rapid in vegetation are necessarily preferred. The whole tribe of fir trees, or the coniferous division of plants is wholly excluded, and the choice falls on the oak, ash, elm, willow, and chesnut. The fir plants are deficient in the vivacious principle, and those trees are most eligible which shoot readily from the stools and prosecute a vigorous growth. ON LANDED PROPERTY. 959 Inferior lands are generally converted into copses, as banks, Various in rocky declivities, barren wastes, and flooded grounds. In the the situation. first formation the plants are inserted as for a timber plantation that has been already treated, and the stems are immediately cut close by the ground. Sometimes a year is deferred between the planting and cutting, but with no convincing advantage. The growths are ever more rapid and vigorous from a cut stem than in the natural stalk from the nursery. This fact is generally well understood, and the practice adopted in the case of a new copse wood being formed, and the strongest plants in the nursery are used, as they, when cut, send out the most healthy and vigorous shoots, which in the shortest time are led into the form of the useful purposes that are required. The sets are two feet apart as for timber, the near contiguity being equally required in order to induce the quick and upright vertical growth. The vegetations that are not able to attain the height of the upper reach, are dwindled into the inferior purposes, as will be afterwards detailed. Planting. the produce. Copse woods mostly prevail in the hop-growing districts of England, and these localities are chiefly situated on the chalk formations, where coal is not found as fuel. The hop plant requires a pole to support the twining stem, around which it climbs and fastens by means of tendrils. This purpose uses the tallest and stoutest growths of the coppice. Fuel demands for its most urgent purpose the use of all the inferior stems, branches, and bushes, or all the growths that are inapplicable to any other purpose by reason of want of strength and bulk. The intermediate growths occupy the middle purposes of stakes for fencing and for making sheep hurdles, and this use becomes in many places the principal application. Copses generally attain the full growth of the purposes for Purposes of which the articles are used in the time of ten to fourteen years, when the produce is sold by auction or private bargain in a fixed sum of money by the acre of land. The purchaser cuts the timber in every shoot or bush of any kind, applies it to his own purposes, and removes the whole articles outside the plantation by the first of May, when the young shoots from the stools will sustain damage by the trespass of any intrusion. The brushwood that grows on the earthen mound or fence belongs to Manufacture the purchaser, who plashes a new fence with the thorns which of the woods. he cuts for his purpose. The fence is not included in the measurement of the ground, and the purchaser gets the stems that grow upon the mound for the trouble of plashing the new fence. The growths are cut from the stems by an upward slanting cut of the axe, and the face of the cut must be clean and even, that no roughness occur to lodge wetness and lead to decay. The new shoots rise from the seam of the wood and bark, and the more sloping extent of cut will produce a greater number of fresh vege- tations. But a medium is to be observed, as the stool will not support to maturity a disproportionate number of shoots. The eye of experience will easily fix the proper elevation of the cut. In the southern counties of England a quantity of woodlands belongs to most farms, which are cut at the proper season, and used by the farmer as 960 ON LANDED PROPERTY. 氤 Best pro- any other crops on his lands. This arrangement supplies the farmer with firewood, and also with fencing and hurdle stakes, and the de- perty of them mand for hop poles in his vicinity will add to the accommoda- tion afforded by the woodlands. But it may be better policy that the landlord manages all the woods as his own care, and the farmer can buy the fuel and stakes he may want at the periodical sales of the articles. The landlord would thus employ a fixed number of special workmen under an experienced and trusty foreman, who will be employed during the year in cutting copses, felling timber, barking oak, and upholding fences. The cuttings will be duly separated into the purposes of use carried outside the plantation, whereon a fixed day the disposed lots are vended by auction, or previously sold by private treaty, and the time of removal is expressly certified. The landlord has thus the certainty of the lasting object being duly provided, and can make what alterations he pleases at any time. Old stools to A long continued cutting of the stools of copse wood forms a be removed. dense tuft or collection of the ends of the shoots upon the old stool, in the cavities of which the water lodges and induces decay. In these overgrown cases, the whole collection is best removed by cutting the old stem close by the ground with a saw, and slanting the cut upwards, so as to prevent a lodgment of any kind being made upon the incision. This operation presents a fresh source of shoots, and very often most wonder- fully renovates the condition of the stools. When a lengthened age has wholly debilitated the production of suitable growths from the stools, it is the best way, as in the case of full grown timber trees, to dig and remove the old stumps wholly from the ground, and to plant with nursery sets, as at first, the entire area of the plantation. The sets must be placed in fresh ground, and not in the holes whence the stools are removed. This reno- vation is the same as making a new coppice. Copses and Though it is very customary, it is still highly objectionable, timbers to be to grow together the trees for timber, and the undergrowth for separate. coppice purposes. The timber trees stand widely, and the branches spread in an extensive lateral expansion, the stem never rises to a height of bole to constitute utility, and covers a large shade, under which the copse wood does not thrive, but dwindles into an inferior growth. This is an object of daily observation, and requires to be removed by copse woods occupying the ground in the one purpose, and timber trees to have the same privilege with any underwood that may rise, being cut for use at the seemingly proper periods. This arrangement is very simple and easy, and provides each purpose separately, as they do not thrive in union, and suffer mutually by the intrusion on each other's abode. Best trees for copses. In the hop growing districts, and on the copse lands of the best quality, the most eligible trees are oak, ash, and Spanish chesnut. The ash is quickest in growth, but not very durable as a hop- pole, the oak rises slower but lasts longer, while the chesnut very often excels both these plants, in being more durable than the ash, and wanting the fault of the oak,in being brittle and unwooded in the upper end of the stem. On dry banks and on rocky declivities, the birch and the hazel ON LANDED PROPERTY. 961 · Varied ac- cording to soil. form a good undergrowth of stakes and fuel, but never rise into hop-poles, for which purpose the oak, ash, and chesnut are the most valuable trees. On lands that are damp and moist, even after a complete surface draining, the alder grows well, and affords hop-poles of the first quality, and stakes for the fence and hurdles. On the lowest grounds, the willow tree yields the largest produce, and hop-poles are often obtained of the best sort. The ash obtains the widest range of growth, as it thrives well on all soils, from the flooded ground to the sandy waste; but the inferior growths of it are not equal in quantity to that of the hazel and birch, and on chalky lands the beech exceeds all others in bulk and produce, though it is chiefly adapted for fire-wood. It seldom rises to the height of good stakes. The trees now mentioned are adapted for any va- riety of soils that may occur, and present a selection which suit the occu- pation of any lands in Britain. Digging of land not necessary. Copses not pruned. No advantage attends any preparation of the ground for trees by being dug or trenched, especially on high situations; expe- rience has shown that the growth may be superior on trenched lands for the space of five or six years, when it falls to the standard of the unprepared grounds. The sole attention in making plantations of any kind for timber or copses, is directed to complete fencing, open draining of the surface where wetness prevails, and roads of twenty feet in width traversing the grounds in the convenient directions, by which to obtain access for any purpose. The only work to be done till the timber is full grown is to remove occasionally the trees that are smothered by the taller growths, and use the stems for some purpose before the decay performs a total uselessness. No pruning or thinning is to be done in copse woods, as the thick growth is necessary to promote the tall and straight form of the poles and stakes, which would spread laterally into branches if room was given for that purpose. The full growth is reached in ten to fourteen years; and the value of copses varies from £8 to £20 per acre, according to the quantity and quality of the produce, and the price of the different articles in the locality. In many places, the poorer lands. of all sorts pay as much rent as the cultivated grounds, where the small necessary attention is bestowed. Many wastes in the districts value of the wanting coal might be well used in copse woods, and especially rocky declivities, on which no other improvement ever can be done. The first expense is comparatively small, and though the times of payment are far between, the return is more certain than yearly crops of vegetables, and the casualties are much less numerous. The yearly cost is something, and is covered by a very small produce and a low price. woods. Seeds of trees that fall to the ground germinate and strike roots into the soil, from which timber arises that is better in quality than the trees that grow from the plants of the nursery. This fact is well known in every timber growing quarter of the known world. When the timber is used by the saw and chisel of the workman, the operator can tell if the materials had grown from the seed or the plant, the former being cleanest in the fibre, and presenting a smoother surface from the action of the tools. It 962 ON LANDED PROPERTY. from seeds. Timber best follows that the seeds of trees be thickly scattered on the land which is to be planted and allowed to germinate and strike roots into the ground as in nature's way. The seeds are mixed in a large va- riety, so that success be the more certain, and sown by hand in at least four bushels on an acre. It will be advantageous that the grass on the surface be not consumed by any animals for some years before the seeds are sown, but allowed to fall and decay yearly, which will afford a bed of ve- getable earth for the germination of the seeds and attaching of the roots to the ground. The young plants will grow in a thick condition as from the inserted stems; the thriving individuals will rise and form the crop; and the inferior growths will dwindle into underwood, or be altogether extirpated. The quantity of seeds must be very ample, and when a failure is observed in the first and second years, another sowing must be done in a smaller quantity, and every means used to obtain a full crop on the ground. All vermin that eat tender shoots and gnaw the barks of trees must not be present; and the fencing of the sown grounds must be very secure. The collection of seeds for use will supersede the nursery, and a very considerable expense will be saved. Nature has shown the way; and the results are superior to the mode that is now followed, which employs much more time, and expends a larger cost. The stem of the nursery being cut close by the ground when the tree is planted, sends forth a vigorous shoot, which grows far more luxu- riantly than the old stem; and this shows the superiority of every growth from the position where the vegetation is to be permanent, and the seed is more vivacious than any stem. To be sown on the ground. Portland; his authority The above detailed system of very thick planting, which promotes an upright straightness of growth, and kills the under-branches without the mangling of the pruning process, is founded on nature in the first place, Duke of and has been illustrated by the practice of the Duke of Portland on his extensive landed estates, in the counties of Nottingham and Northumberland, and in Ayrshire, in the west of Scotland. His Grace is known as the originator of several most correct practical maxims on various agricultural subjects, which are introduced and practised with a most extensive benefit, and are never disturbed by any of the evanescent theories of the day. Our opinion has ever admired the planting of trees, as now detailed, and for which an appeal is made to his authority; the system has an unerring law of nature for its base, and reason for its guide. On the subject of planting acorns and placing young trees, his Grace writes in a private letter on the matter :— “Fine large acorns produce very superior plants for some years; but I do not think I have seen that superiority disappear till after the expiration of more than seven years. Communica- tion. "I am quite satisfied that the effect of double trenching is to operate a permanent benefit. I did not see this effect in a plantation till it was twenty years old. It was by mere accident I discovered that effect; but I have since acted upon it extensively, and subsequent experience has con- firmed the truth of the appearances. The roots of the plants work more ON LANDED PROPERTY. 963 easily, get sooner out of reach of the effects of the sun, and the rain sinking deeper into the earth, is not so soon evaporated." In the matters of planting and draining, our work has adopted his Grace's practice, as the most just in principle, and efficacious in the result. CHAPTER VII. MEADOWS AND EMBANKMENTS, BEDS OF RIVERS, WATER COURSES, AND FLOODED GROUNDS. Meadows, or low grounds. LANDS that are low in position and flat on the surface are exposed to floods of water, which usurp the dominion of the ground, and damage the productive quality of the soil, owing to the time of the possession by the watery element. This damage equally ensues, whether the ground be in an arable condition or used in a state of grass, for the starvation of the land by the water, produces a low state of tem- perature in the soil, which continues for some time, and very much retards vegetation. These grounds are mostly grazed by animals, during the periods when the inundations of water are abser '; but in many cases, the arable condition would be very profitable, it the presence of the water could be averted. The low position of the inundated grounds, presents a formidable barrier to the removal of the water, as the descent induces a sluggish motion, and retards the escape after the liquid has been directed into a proper channel. This obstacle has exerted much influence on the operations of embanking, and has very much Embanking. perplexed the arrangements for the purpose. Where the fall of the ground affords a quick descent of the water, the process is com- paratively very easy, as it only remains to provide a channel and turn the water into it. In other cases, the channels are over-charged and burst by the bulk of water, or are always full, and throw back the water into the smaller outlets. Embanking may be justly termed the first branch of engineering that has been practised by the human race. Observation soon showed to the eye, that low grounds were the most fertile that were situated along the sea shore, and on the banks of rivers, and that the quality was damaged by the inundations of water on the surface, and that the area was gradually lessened by the invasion of rivers, seas, and lakes. Measures were not long in being used, for the purpose of averting the damage; and the monuments yet remain over all the countries of the ancient The first world, where arts and sciences were brought into life, and engineering ; cradled into use. The alluvial shores, wide plains, and fertile deltas, are found to be protected against waste and temporary damage, and the confined water is directed in small channels for the purpose of conferring 964 ON LANDED PROPERTY. in Holland; the benefits of irrigation on the grounds that are secured from the ravages of nature. Every country of modern Europe exhibits the marks of this ancient art—the dikes of Holland, are marvels of human industry —and the embankment of the river Po in Italy shows a skill and application of the practice that excites universal admiration. In the former country, the ocean, inland seas, and rivers, are prevented and confined within proper limits: the sediment of mud that is carried by the rapid torrents from the higher grounds, sinks in the channel of the rivers and raises the course of the water above the surrounding level, where the inhabitants have their homes, in Italy; and cultivate the grounds. A rupture of these banks would inundate a whole region of country, devastate the property, and probably drown many thousands of people: yet such is the feeling of security produced by the skill and labour of centuries, in devising and repairing these artificial mounds, that no dread is ever expressed, and a bank of mud is felt sufficient to repel the floods of rivers and the storms of the ocean. The river Po rushes impetuously from high grounds into the valley of Lombardy, and runs during the half of its course of 300 miles into the Adriatic sea, over a country of alluvial flat, where the descent is small, and the course is slow and sluggish; the bulk of the water is much swollen by the dissolved snows of the Alps, and the torrents carry along vast quantities of fine earth that is torn from the high grounds which, on reaching the low country where the water moves slowly, or almost stagnates, sinks to the bottom as sediment, consolidates, and elevates the bed of the river. This natural course of centuries has raised river Po; the channel of the water above the surrounding country, and embankments were raised at an early age in order to guard the labours of man from the ravages of the unloosened waters. These banks are models of skill and industry-of ingenuity in the plan, and of perseverance in the maintaining of the bulwarks. with the in Britain. In Britain, the embanking of grounds exposed to damage and degradation, seems to have been begun at an early period of time, though probably not before the Roman conquest. The Romney marsh and the flat grounds of the estuary of the Thames, may have been the work of the Romans, who had attained much knowledge of the art, and were ever ready to communicate their acquirements to the victims of their conquering policy. After the retreat of these improving adventurers, the art of embanking slept in the general slumber of the human mind for the dark period of one thousand years, and revived in the sixteenth century, along with the universal resurrection of arts and sciences, men and manners: foreign intercourse showed the policy of Holland, which country sent engineers to Britain, who commenced with the draining and embanking of the fens of Lincolnshire, where the sea comes far inland by reason of the flatness of the alluvial formation of the country, and the de- scending rivers are prevented the discharge of the waters into the sea which are consequently thrown back upon the surface of the ground. Two centuries of repeated attempts have scarcely sufficed to complete the emancipation ON LANDED PROPERTY. 965 of these overflowed districts; but the operations have very much conduced to advance the skill of the art of embanking, and have shown the principles in many different forms. Three uses There are three applications of the use of embankments, in guarding the encroachments of the sea, in turning away occasional of embank- floods of water from the surface of flat lands, and in preventing ing; rare with the the waste of alluvial lands by the invasion of rapid streams or torrents that tear, waste, and carry away the soft and unresisting earthy accumu- lation of tender ingredients. The shores of the sea are most generally either rocky or sandy, which are useless for cultivable purposes of any kind, and the cases are not many where the ocean intrudes on grounds that are worth any cost and labour in the defence. There are some few instances of such an occurrence, but the greater part Ocean. happens in the case of inland seas or estuaries that penetrate the country, and on the sides of which the alluvial flats have been formed that require to be protected. In these situations, the force of the sea is much less than of the open ocean-the tides rise gently, and the winds have a very diminished effect. The tides are not impelled by furious winds blowing in the same direction, and the mixture of fresh water very much lessens the power of the briny liquid. But the barriers to be opposed are the same in both cases, as the resistances come forward in the same manner, and are formed of similar elements. Embanking is based upon very simple principles, but the application of them to practice requires both skill and experience. The fundamental principle is, that a liquid presses upon any resisting solid, not by any dimensions, or general properties of the fluid, but solely with a General prin- force proportionate to its depth. Hence when a perpendicular ciples. bank is opposed to a body of water, it has to sustain the pressure of the depth of the body, and undiminished by any assistance that can be given at it. This is a fixed law of fluids, and carries along with it the simplest conviction of practice. It only remains to convert the deep pressure laterally into a shallow depth vertically, and thus reduce the opposition from an impinging force into a rolling harmlessness of motion. On this principle, soft materials being hardened into a body, are equally useful with the hardest rocks, or even walls of cemented masonry; and have the surface so levelled and crusted, as that the ripple of the rolling water does not make a breach, or form any beginning of damage. Banks are made with compacted earth, in the dimensions of three feet of base to one of perpendicular height. The slope is set to the sea, and covered with turf, the pieces of which are fastened to the surface by means of hooked wooden pegs. This growth of grassy surface presents the best of all materials on which waters roll without doing damage, and it is fed by the alternate benefits of being dry and having a watery covering. The mound may be six or eight feet wide on the top, and have a slope to the land of one and a half feet of base to one of height, or about one-half of the seaward slope; the whole construction being quickly and carefully covered with turf, and being duly attended and repaired, will Best mate- rials. 966 ON LANDED PROPERTY. very soon become a grassy barrier of much strength, which will bear an intrusion beyond its appearance. It is a law both of theory and of experience that the greater slope of a Slope of bank, the more effectually it performs the object of its purpose, banks. and its end as a resisting surface. There is no precise rule for the degree of slope, because it depends on the nature of the materials of the bank, and on the degree of exposure to the winds, waves, and currents of the tide; but it should rather be above than below the average now stated, of three feet of base to one of height, and in no case below two to one, even where the resistance appears to be very much reduced in force. The height must be above the highest known rise of waters, which must not wash over the top of the bank, and the slope height may be six feet above the water line. Much care is required in forming the slope of the bank to the sea, in order to prevent any breach, or abrasion of the surface; the earth is beaten hard with mallets, and the grassy turf is best taken from the sea shore, when the plants will be proper to the maritime situation, and may be chiefly the sea carex, the upright sea lyme grass, the sea rushy wheat grass, and certain kinds of the sedge. The creeping roots of the plants extend beneath the surface, bind the loose earth of the bank, so as to enable it to resist the continued action of the waves. A thin coating of straw, and sometimes fascines of osiers, or branches of any kind are pinned down on the bank to form a kind of thatch; but How secured. the simple turf, when laid with care on a well prepared bank, is the most sufficient. Front pro- Where banks are exposed to high rolling tides that are driven in fury by storms of straight in-blowing winds, the necessity occurs of driving into the ground two rows of piles in three or four yards between, and filling the empty space with the largest stones that can be found. This front barrier being placed in twenty feet distant from the grassy bank, will act as a breakwater; the fury of the waves is broken by it, the water passes through the loose mass of stones, gathers in a placid body between the barrier and the bank, and rolls upon the latter like a standing pool that is gently moved by a force that is distant and little troublesome. Where stones are scarce and wood abounds, the piles may be driven into the ground almost close together, when the quantity of them will constitute tection: the barrier, but stones are preferable where found within a reasonable distance. The bottom of the grassy bank will be in no danger of being undermined from the quiet re-assemblage of broken waters as by the furious lashings and peltings of the merciless beat of briny waves that search every access, and explore every crevice. To prevent the very smallest entrance into the bank being obtained, in case of there being no breakwater erected, the bottom of the bank in the grassy turf, must underlie the slimy ground of the shore, and the hardened mud on which the water rolls must overlap the turf of the base of the mound, and conduct the roll of the water from its own slope to the grassy bank without any obstacle intervening at the junction of the mound with the shore. If the water beats against any resistance, it will soon make its way, and an entry ON LANDED PROPERTY. 967 banks: once found will quickly lead to an overwhelming destruction. The whole secret lies in making water always roll upon the resistance, but never to impinge against it. Where streams of water from the country must pass through the bank into the sea, a suitable opening must be left in openings in the mound, and built with solid masonry, of the size to permit the free egress of the largest quantity of water ever known to demand ad- mittance; when the tide is ebb, the discharge is free and easy through this opening of the fresh water from the land; and when the tide rises, it will, if unrestrained, pass through the orifice and inundate the flat lands which the bank was erected to defend. To prevent this intrusion, a gate of thick boards strengthened with iron bars, is suspended by hinges to shut the opening as closely as the wood and stone wall can be fitted to join. The running water from the country pushes the gate before it, and keeps it open, and runs freely into the sea-when the tide rises, a heavier force of water rolling against the gate shuts it, by which the sea water is excluded, and the fresh water from the land is confined inside the bank till the tide recedes, when the gate is opened by its superior weight against the receding tide, and the congregated waters escape through the opening. This arrangement provides a bed inside the barrier in which the assemblage of fresh water rests without doing harm during the presence of the tide outside; but, except during very heavy land floods, the quantity will be vastly inferior to the tides that were formerly admitted, and there- fore much surface will be secured from overflowing. This simple mechanism is applied to one river flowing into another as well as running into the sea; the inferior stream is overpowered by the greater pressure of the main river, but being collected inside a mound, and a gate being provided, it will open the sluice when it equals in weight the quantity of water outside, and flow away. But the waiting con- gregation of waters is often inconvenient. gates or sluices: open and shut with the tide. A more costly, but a generally more effectual mode, consists in leaving no opening in the bank; but collecting the inside waters, and erecting a steam pump, by the constant working of which the river is hoisted over the barrier in continued discharges. This mode is essential in cases where the country is below the level of the sea, as is frequent in Holland and in the fenny districts of England. The steam is superior to the windmill, or to any power yet known, by reason of the steadiness and constancy with which it acts: and the pump is preferable to wheels and buckets, in being less cumbersome, easier managed, and less liable to accident. Pumps. When the raising of an embankment occurs on ground that is covered by every tide that flows, the difficulty is very perplexing in securing the works as it proceeds, against the tides, and also against the storms and gales that may occur. The near completion of the work is frequently thrown back to a beginning by some slight breach, which leads to an over- throw of the whole structure. Practical skill and resources are im- peratively necessary in the chief operator who directs the works, and caution and foresight are nowhere more in request. The most secure 968 ON LANDED PROPERTY. way is to make a temporary fence by means of piles and stones in front of the mound being erected, which will break the storms, and guard from damage the erection till the work be completed, when the protection may be removed. The dam, if not wholly close, will at least turn away the chief parts of the water. Such a guard is almost indispensable where the water is a regular attendant. Alluvial valleys. These descriptions guard against the overflowings of land by tidal estuaries, that are often augmented by fresh water floods of the streams or rivers that flow into the arms of the sea. The flatness of the alluvial valley permits the ascent of the tide, and the lateral low surface of the ground allows the spreading of the commingled waters. Where the tide of the sea cannot rise the ascent of the country, the allu- vial valleys still remain very flat, and the rivers that flow through them are slow and sluggish in the course, and when swollen by heavy falls of rain, or by melted snows, the adjacent meadows are overflowed by the excess of water, and damaged by the cold application. The protection of these grounds from damage, occupies the next attention. Beds of rivers. Rivers are the great natural channels for conveying the surplus waters of the globe to the ocean, which is the general receptacle. The hollows and sinuosities of the earth generally regulate their course, depth, and width of channel, and are all dependent upon physical laws, which are as usual seen to be connected with a purpose or design. The channels are variously excavated: when it is wide, the velocity of the water is reduced; when contracted, the water runs faster, and the depth increases; the current is retarded by a tortuous channel, and quickened by a straight course: when the water undermines a bank, it is only hewing out a more suitable channel, and the tide is sought to be shut out by a bar of mud being thrown across the mouth of the outlet. These adaptations are termed the regimen by engineers, and so far from being the result of chance, is dependent upon laws that permit the usual investigation. When these operations of the river interfere with the works of man, reason instructs him to facilitate the natural operations, or present obstacles to their accomplishment as shall suit his own purposes. A trough is the natural channel of a river, and the deviations from this form are occasioned by steep banks, a barrier of rocks, or greater or less resistance of the surface strata, when the stream of water is diverted into pools, shallows, and eddies, and excavation of the banks. The solidity and permanence of the banks depend in part on the inclination of the surface, the hardness, tenacity, and smoothness of the materials, and on the degree of parallelism that is preserved between the course of the bank and the impinging current. Tortuous courses of bodies of water pre- sent an angle of resistance to the moving fluid, which being enlarged in volume acts with violence against an earthy accumulation, tears the mass, and carries away the dissolved materials. The flat soils of alluvial formation are gradually wasted and reduced in the superficial area by these invasions of watery bodies, and the protection of the cul- tivated lands becomes a business of constant attention. In waters of any Tortuous courses. ON LANDED PROPERTY. 969 banks. considerable depth, the most efficient protection of the banks, is made by driving one or more rows of strong and lengthy poles deeply into the bottom of the river, at the distance of about eight or ten feet from the bank, and filling the intervening space with very large stones. The row of piles must be placed in a direction of presenting to the moving waters as sharp an angle of contact as can be obtained, as this provision very much relieves the pressure, and throws off the impending weight. In the absence of large stones, baskets of strong osiers are filled with small stones and sunk in the bed of the vacant space behind the piles, and in Defence of other cases, bundles of brushwood are placed behind the piles, and held in the position by ligaments of some kind being fastened around the stakes in this position, the sediment lodges among the twigs, and consolidates into an earthy bank. The large piles of wood by which the whole provision is sustained, must be used in quantities as may appear to be necessary from the materials that can be obtained. The weight of large stones very soon finds a bed of repose-it only remains to have two rows of piles fronting the river, which will prevent the rolling of the stones into the deep trough of the channel-small stones will require the front piles to be thickly planted, and also cross rows at no great distances extending to the bank. The placing of the piles must be thicker for brush- wood, the bundles of which are pressed and held down by planks modes. that are joined to the driven piles. A very effectual defence is erected by forming a slope bank of stones and planks, extending from the top of the bank of the river forwards to the bottom of the water, of which the surface is lozenged with cross and longitudinal planks of timber. The water rolls upon this sloping surface, as upon the grassy banks that have been de- scribed, and though it be costly, it forms the most complete barrier that can be furnished. But in the most cases, the rows of piles, with some hard or consolidating materials, placed behind, will be adopted. Various Straight and courses. When waters run in a straight course, little or no damage is done to the banks which confine the current: but when the bed circular is narrow and the line crooked, the water is broken or displaced in the particles, and the agitation that is produced carries forward violence and destruction to all opposing obstacles. The course of rivers must be straight, or as nearly so as possible, and all attempts to alter or improve the line of currents must approach to that design. All bends of rivers must be assimilated to the straight line by using the largest circular sweep that can be got, and the barriers that are presented to an impinging current, must not offer a right-angled resistance, but receive the force in a sharp divergence, and throw off the brunt of the violence. This adoption forms an approach to the straight line, and though not straight itself, it throws the water into straight course till it meets a similar obstacle, when it is similarly treated. In making new courses for water, or in improving old ones, it is a grand blunder to confine the current; water spread abroad is very harmless, and damage arises from large collections that are confined in the movement and agitated in the course. A tendency must Beds must be ever be manifested to widen rather than contract the beds of widened. 30 970 ON LANDED PROPERTY. rivers, and to straighten the lines of course whenever a bare possibility exists. Necks of land may be often cut through with advantage in order to obtain a straight course, even at a present sacrifice of value in the land that may be used: the gradual damages of future waste will reach the amount and exceed the present expenditure. Flooded grounds. Mounds. The notice now made provides against the damage done by the force of currents of water rushing against the banks of soft earths that are unable to resist the pressure; an injury is also sustained by meadow lands being occasionally flooded by swollen rivers, which overflow the banks and stag- nate the waters on the adjoining grounds. Summer floods will often come during hay harvest and sweep away the cocked and tedded hays, or mix with sands and mud the unmown herbage, and render it useless for any purpose. These floods being spread abroad are not violent in the action or large in force; the intrusion is easily averted, and the direction controlled. A bank is raised of the materials of the ground on the perpendicular height of three feet, which will overtop the highest flood that may occur. The base will extend ten feet towards the river, which will afford a very gradual slope of vertical height. The mound may be almost perpendicular on the field side, as the bank has not to sustain a force pressing directly upon it, as in the case of the tides of the sea that rise with a constant appointment; it lies in the direction of the current of the river, and has only to support the weight of a fluid body that glides along its exterior, but does not exert an action upon its constructed strength. It has only to show the course to the water, and not to impede or obstruct it; the outspread water is restrained, but not denied any prescribed course. The bank must recede some little dis- tance from the bank of the river, and be so directed along its course as to avoid any abrupt turning or hollows where the waters can lodge and press with weight; the exterior slope must be convex, and the line must be uni- formly gradual in the bendings, and afford the water an easy rolling motion, without any ripple or displacement of the particles. The bank is constructed of hard rammed earths, that are covered with grassy turfs, and may be one yard in width on the top. Care must be used that the embankment is continued to the first current of the overflowing, in order that the water does not get behind the mound and render it of little avail. In alluvial countries, as now described, the grounds are flat, Hilly lands. and the currents of water are slow, and hence the means of pre- vention of harm are adapted to these qualities. Rivers of greater or less magnitude, that flow from hilly countries, are rapid in the course from the fall of the ground, and liable to very sudden risings of water, by reason of heavy rains in the mountains: the impetuous course continues till the flat country is reached, and before that period, much damage is done by the raging waters rolling against the banks, tearing away the loose soil in the narrow alluvial valleys through which the river flows, which very often amounts to a total alteration of the course, when a bed of gravel is left for the new bed that is taken from the cultivated lands. These hilly grounds and narrow valleys produce more bendings Much wasted ON LANDED PROPERTY. 971 than happen in wide plains, and the soil being mostly of gravelly loam, the waste is easy, and the demolition very quick. The gravel which is carried along by the torrent is usually heaved against one side of the channel, which being obstructed, the water is driven to the other side, and with the whole force and weight it undermines and tears the soft alluvium of which the flat lands are formed. The power of the water is most pro- digiously augmented by the narrow channels which are formed between the natural banks and the mounds of rolled gravel which shifts with the floods and lies where deposited. The furious rush of these impetuous torrents requires to be opposed by the strong erection of very hard materials. Solid stone work is the best resistance, built of squared blocks, with or without mortar, and raised to a height beyond the highest rise of the waters. The form of the bulwark is square, and longer in the face to the river than in the breadth to the land, and must be very firmly based on the solid substratum that is reached by digging through the alluvial mass of gravels and loose earths. The bar- rier is called a jetty, and is placed to receive the current of the Stone jetties water at a sharp angle of divergence, and to throw it off easily, and almost without seeming to stop the direction of the stream. An ob- tuse angle of divergence will throw the force of the water against the opposite bank; and if the bed of the stream be narrow, the water will break it, and probably cause a damage equal to that which is sought to be pre- vented. The jetty must throw the current of water into a mid-channel, and not against either bank; and consequently, the face of the stone work must be in a straight line with the mid-channel, into which the water is wished to be directed. The force of the current being broken against the jetty, the water will require to flow for a considerable distance to break the ere a new force is acquired, unless the fall of the country be current. very great; and when a fresh current is formed which threatens danger to the bank, a jetty is there built, which turns the stream as before into mid- channel and clear of either bank. In this way the stream is conducted from jetty to jetty in a harmless torrent till it reaches the placid flow of the level country, when it is directed by the embankments of the former description. It is useful to protect jetties in front where the streams are very power- ful, by placing large stones in a loose position at the base of the wall, and raised to the height of the ordinary quantity of water. The bottom of the heap may extend to three or four yards into the stream, and taper to one stone at the top where the loose aggregation leans against the jetty. The weight of each single block must be sufficient to secure for itself an im- moveable bed, and defy the force of the water to change the position. In the substratums of clay and alluvial earths, strong and lengthy wooden piles may be driven into the bed of the stream, as has been men- Piles of tim- tioned before, and a defence formed between them and the jetty; but in many substrata the driving of piles is difficult, and the loose aggre- gation of stones will be preferred. Both ends of the jetty must taper backwards into the bank with a wall like itself, in order to prevent at the ber. 972 ON LANDED PROPERTY. upper end the ingress of water behind the building, and at the under end the eddying of the stream into a corner, which may become the receptacle of waters that may seek a new channel. The whole volume of the stream must be directed into a mid-channel, and without any scattering of the sheet of water towards either of the banks. The collected stream will wear a channel for itself by the weight of its volume, and for that purpose every encouragement must be given to direct it in a mass. This direction is very peculiarly applicable to streams that descend an alluvial valley from higher grounds, where the banks are in composition soft and easy of demolition, and where the rapidity of the torrent soon excavates to be always a bed for the water. It is not here meant to confine the bed of kept. any river of water, but in certain cases to direct the body of water in a mid-channel, which will keep it from running against the banks and tearing away the land. Mid-channel Water- courses Watercourses are beds of rivers on a small scale, that traverse estates, farms, and plantations, on their way to join the main rivers that lead to the ocean. A surface of undulations and sinuosities very often compels a tortuous course of the waters, and a formation of gravel or of soft alluvium of ground gives way to the floods and torrents that run in the bended course that has been excavated. These torrents are chiefly from floods of rain and the melting of snows, and are confined from doing harm at the bendings of the course by driving into the ground with heavy mallets a row or two of strong stakes in one to two feet distant, and weaving a fence with the branches of trees in the manner of a basket. The space between the row of stakes and the bank is filled with the largest stones that can be found, among which the water passes and deposits a sediment, which in time fills the crevices, and the mass becomes a solid. The wicker work having the tail of the branches in the direction of the current, directs the water very quickly and smoothly along the guarded, wattled fence, and the wall being open to the passage of the water through it, no solid resistance is offered to the current, but rather a breakwater, which directs but does not obstruct the course. Small rivu- lets that are only periodical streams of any size, are fenced in and rivulets. this way by upright walls of wicker work backed with stones; and larger brooks are guarded with a sloped wall, as has been before de- scribed. This slope is well formed with strong stakes driven into the ground, the vacuities being filled with stones from the shingly bed of the stream, and the top covered with long branches of trees, with the tails pointing with the current, and fastened to the stakes by the natural hooks of the branches, or by ligaments, or by cross beams nailed to the stakes. Heavy stones being laid upon the top will add much to the solidity of the structure. In the course of time, the proper grasses will grow and form a matted turf, along which the floods of water will run with much ease and tranquillity. Very good walls are formed in this way; the materials are generally ready, the performance requires little skill and the expense is not great. 4 ON LANDED PROPERTY. 973 embanking. The principles of embanking are few and very simple, and Simple prin- admit an easy application. Water should run in a course as ciples of straight as can be obtained, and have a wide channel rather than a narrow bed. The bendings of rivers are guarded by barriers of piles and stones, and the impetuous currents of mountain streams are diverted into a mid-channel by jetties of stone masonry, against which the water rushes at a very sharp angle of divergence. The risings of tides and floods into deep formations of water are averted from doing harm by means of earthen mounds covered with grassy turf, on which the waters roll, but against which they do not impinge and press with the weight of their depth. This last principle forms the chief remembrance of embanking. The difficulties of execution will be proportionate with the circumstances of the locality, in position, materials, and labour. Irrigated Irrigated grounds constitute a very beneficial adaptation of lands that are situated to undergo the special application. In ground. dry hot countries the artificial supply of moisture was early adopted as a mode of increasing the fruits of the ground, and the practice has been in some degree continued in many countries in which circumstances permitted the use. The Romans used water extensively both on arable and grass lands, and from them the application has descended to the present day. In Britain, irrigation attracted much notice within the last hundred years; and there was scarcely left a brook, rill, or stream that was not converted to that purpose wherever it could possibly be used. The advantages consist in raising an early grass in the spring, Great advan- in growing a large crop of hay, and in producing an abundant tages. lattermath for the grazing of animals. In some places these advantages are very great, and compensate the heavy expenses of formation and up- holding. The full benefit of flooding suppose a dry hot climate, and an easy command of water, and a position of the lands to admit the ingress and egress of the water, and an application at a moderate expense. These indispensable requisites will show that, comparatively speaking, few situa- tions admit that mode of improvement. dows. Irrigated lands are divided into two kinds—catch and flow meadows : the former lying on a declivity, and catching the water in its descent from the higher grounds; and the latter raised artificially, to allow the water to flow over them. In catch work, the water is conducted by a Catch mea- level course to the higher part of the ground, and divided into rills, which are stopped at intervals to make the water flow with a rip- ling motion over the surface, for which purpose all inequalities must be levelled, and the stops duly regulated, in order to throw an equal quantity over the whole space. If the declivity be considerable, the rills must be cut in a diagonal direction to follow the fall of the ground, so as to convey the water most regularly, and with a uniform motion, and in an equal quantity over the surface; if the ground be more flat and even, straight and parallel cuts will answer the purpose. When the water has passed over the whole space, it is conveyed away in an open ditch into a brook 974 ON LANDED PROPERTY. or river; or if the ground admits, it may irrigate another division of catch or flow meadow before it be finally lost. Flow mea- dows. In flow meadows, the land is generally flat or nearly so, and must be raised into ridges of ten to fifteen yards in width, with open drains between them, and rills cut along the top of the ridges, with a longitudinal fall to cause the water to flow along them, and with a de- clination of the sides of the ridges to the catch drains sufficient to make the water run briskly over the surface. The main or conducting drain passes along the head or upper end of the flow work, and discharges a quantity of water into the rills along the tops of the ridges, regulated by the volume they can contain, and which is thrown by the artificial stops in the rills evenly and regularly over the sides of the ridges. It passes into the catch drains, which convey it into an open ditch, brook, or river, where it is carried away. The expense of forming watered meadows has been stated at £5 to £20 and upwards per acre; the latter kind being much more expensive than the former, which in many situations can be done at a moderate cost. The annual expense has been stated at £6 an acre, and the produce at £9; leaving a profit of £3 an acre, after paying £2 10s. for rent, included in the expenses. Expense. Returns. watering. In the general management of irrigated lands, the water is admitted in November, after the surface has been eaten very bare, and the gates, sluices, drains, and rills have all been put into working order. Practice varies in the time the land is allowed to be under water during the winter months; some allowing ten to fourteen days; others, two, three, or four weeks; gradually lessening the time to a few days till the beginning of Seasons of March. A month's watering may be given in November and December, with some days between each time, and in January and February for a week at a time, and latterly for four or five days. The lands should be laid as dry as possible between the waterings, and it has been much recommended to avoid raising a white scum by too much water- ing, and to turn off the water instantly, as damage ensues from a noxious quality in the scum, and the risk of the meadow being exposed to frost in that state. But many experienced irrigators never found any damage from that cause. In the beginning of March, there is generally sufficient grass to admit sheep to feed, and the meadow will be allowed a time to dry and consolidate before the admission of any stock. It is customary to fold the flocks on adjoining arable lands, and to graze the meadows from ten o'clock to five, when the dews will be off the grass. The herb- age may be eaten close till the first of May, when the water is admitted for a few days, and again laid dry for hay. After the crop is removed, dairy cows and young cattle are admitted to graze till October, as summer watering has long been supposed to rot the sheep. The second crop of hay has been cut, but it is generally weak and flaccid in quality; and even the first crop, if not cut quickly in the season, often becomes coarse and unpalatable. Use of the herbage. Irrigation is a very beneficial way of using land in places that suit the ON LANDED PROPERTY. 975 results. application, and where water can be led to the grounds, and the surface of the land made uniformly level at a reasonable expense. The chief benefits attend a dry soil and a warm climate, though advantages are not wanting in cold latitudes and under watery climes. The fertilization that is im- parted arises principally from the protection of the ground during winter from colds and frosts, and to the higher temperature which the ground obtains. Anlysis of soft and hard waters gave no result on which to found a preference, and no difference could be observed between the clear water of the spring and the sedimentary liquids of a still water brook. No doubt thirsty lands under a dry climate will imbibe very beneficial moisture from the waters that run over the surface, but which must not stag- Various nate upon the ground so as to cause starvation and excess; the movement must be constant and uniform, and neither loitering nor mean- dering. The use of irrigation on cold lands and under stormy climates produced an overgrowth of rushes and aquatic herbs; the practice retro- graded, and is now confined to the select localities, where the proper eligi- bilities are found. The stream of water must be constant and abundant, capable of being commodiously applied, and also having a ready escape from the grounds after the purpose has been effected. All these provisions will be examined and ascertained before an irrigation is attempted. The soil and its capabilities must be duly accounted: if it be strong General in nature and will be grateful of a higher temperature, or thirsty and will be benefited by a large application of moisture. The probable expense will be also estimated, and the expected result will be placed in opposition. It is not a general use of the land, as so many attendances are required to be present. When these requisites abound, the use of water has very largely repaid the application. capabilities. CHAPTER VIII. LAND DRAINING, OPEN AND COVERED,-PLAN, EXE- CUTION AND ARRANGEMENT BETWEEN LANDLORD AND TENANT. lands. It was very early observed by the cultivators of the earth, that moisture formed one of the essential elements of vegetation, and another obser- vation was not much longer in being made, that an excess of it pro- duced the opposite effect, retarded vegetation, and ultimately Draining of caused sterility and barrenness. In the early ages of agricul- ture, little or no attention was paid to the remedy of this damage which the land sustained: but as population increased, the wants to be supplied became more urgent, and application was made to remove the cause of this damage among the other operations of improvement. The first at- 976 ON LANDED PROPERTY. First concep- tions. Stones for filling the trenches. tention was directed to the removal of springs, which are formed by out- bursts of water from the under strata of the earth, forced upwards by pres- sure from a higher quarter. It is found that water flows in the permeable strata of the earth, as sands and gravels, and as these strata lie irregularly, unevenly, and interruptedly, the water finds or forces outlets upwards, as it is stopped in its course by impervious substances, and impelled by the pressure of its own body from a more elevated quarter. Attention was early directed to the interception of these outlets, and con- venience suggested the mode of making trenches in the ground, and thus conveying away the water underneath the operations that were acted upon the surface. In order to afford a current room for the water, stones were used to make a small square culvert in the bottom of the trench, and over it was laid a quantity of smaller stones which were covered by a turf and earth, and this operation finished the process. In places where stones were not abundant, or could not be found at all, other mate- rials have been used for being laid in the bottom of the trench, to afford a vacuum in which the water may flow, as stubble, straw twisted into ropes, and brushwood; and when the latter substance is put into neat bundles, and firmly tied together, and well trodden into the trench, which is sloped in the sides and narrowed downwards, drains have been found to run very well for many years, when filled with that material: but stones are in every case preferable, being the strongest material, and the most durable. Very many and most valuable improve- ments were made by this process; springs were intercepted and diverted; bogs and quagmires were rendered firm ground. Much waste land was re- claimed which was previously rendered nearly useless by the repeated inter- ruptions caused by watery outlets. The observation of these causes and remedies was afterwards extended to the damage inflicted on land by at- mospheric wetness, from the clayey nature of the land retaining too long the moisture that falls from the heavens, and thereby retarding the opera- tions of cultivation, and lessening the quantity and quality of the vege- table productions. It was early known that clay is not permeable to water, and consequently water will not flow into the trenches but from a short Frequent distance on either side of them, on the very wet and tenacious drainage. clay lands which abound in this kingdom. On this principle is founded the modern system of frequent draining, in which the drains are placed at short distances from each other in order that the water may flow into some one of them and not remain on the land. The wetness caused by the rains from the heavens has been too often attributed to springs from below; an insufficient number of drains has been made in order to divert them: the cause lay in a different quarter, and the land remained wet as before. The knowledge of the true cause of wetness has crept very slowly into the agricultural world; in many instances it is yet unknown, and very far from being generally acted upon. The very general desire of doing things with little trouble, and at little cost, has added much to the belief of water rising from below the ground being the cause of wetness; a few drains were reckoned sufficient, which gave little trouble to the mind or to ON LANDED PROPERTY. 977 the purse. A better knowledge is now being obtained, but not rejecting the former where found to be prevalent and necessary. Tapping of A system of draining wet lands by tapping the springs, was much esti- mated some few years ago. It consisted in boring large auger holes in low grounds into the tail of the stratum in which the water flowed, and from which it burst upwards in higher grounds and drawing the water to the auger holes. The plan succeeded or failed according as the strata in which the water flowed were regular or irregular, continuous or inter- springs rupted. Failures were most frequent, as might be expected; and for the pur- pose of carrying away surface water the plan was wholly useless. Even where it succeeded, it was seldom very strikingly more beneficial than the old mode of running a drain to each spring, for this drain in its course fre- quently intercepted other sources of wetness, or the surface water that flowed near its course. The specific success was confined to the springs flowing in sands and gravels, and where they formed the sole source of wetness. Draining of lands on that system has been altogether discontinued for a long time past. now disused. The modern system of draining differs from the old only in making a greater number of drains, and hence it is often called the frequent sys- tem. The same shape of the drains, the same mode of digging, and mostly of filling, yet prevail. The frequency of the drains carries off all the surface water, and intercepts the springs on the land, if any exist, and thus effectually answers both purposes. In the modern system of draining, three things are chiefly to be con- sidered: the frequency of the drains, the depth, and the mode of filling. The frequency of the drains will depend on the tenacity of the upper soil, and the nature of the subsoil, if it be pervious, impervious, or mixed. In pervious and mixed subsoils, the water will flow into a cavity from a distance in the permeable strata, and consequently the drains may be farther apart; but in tenacious soils, and in compact impervious subsoils, the water will not percolate or flow to any distance, and conse- Frequency of quently the drains must be nearer to each other in order to afford drains, a ready egress to the superabundant moisture. The most tenacious clay soils may not require a nearer distance than four yards: some writers state five yards as the closest draining that any lands may require; but in pure plastic clays which form the extreme cases, it is better to err on the safe side, and to have rather more drains than too few, and thus repeat the old error of a non-effective performance. A distance of five yards will drain very wet lands, but instances are not wanting where four yards may be required. A distance of not more than eight yards will be required to drain the most permeable soils and subsoils, and the general distance of four to eight yards may be stated as being required for the soils and cli- mate of Britain, ranging between these two numbers, according to soil and situation. Of these circumstances, the practitioner must judge from appearances; in many cases the herbage will give a fair idea of the nature of the soil; aquatic plants indicating the superabun- dance of moisture from below, and the altitude or hilly nature of the how indi- cated. 978 ON LANDED PROPERTY. country will give intimation of the quantity of rain that may be expected to fall, and of the number of drains that may be required when both cir- cumstances are considered. The skill and judgment of the chief operator must be duly and very fully exercised on these points. A local knowledge is best; but as it is very seldom to be got, the next best, or that of practice and experience must be used. Mistakes are often committed from want of the observation and consideration which these two points Much judg- ment re- require the two essential points on which the whole matter quired. rests. On no point in the practice of agriculture is there more room for the exercise of skill and judgment, for a mistake is productive of much more mischief than in most other cases, being widely spread in its effects, and difficult of remedy. Depth of The depth of the drains must also be regulated by the nature of the soil, and the dryness or humidity of the climate. In pure clays, where the effect of the drain is wholly confined to the carrying away of surface water, the drains cannot be too shallow, provided they are not disturbed by the plough or the feet of the animals. All the moisture or water to be carried away lies on the surface, and consequently the readier access it finds to the drains the better. But impervious and mixed subsoils, where the under-water flows in horizontal or vertical strata, the drains may be deeper, in order to find a firm foundation for the materials with which the drain is filled; though the propriety is questioned, and is certainly very questionable, of cutting drains any deeper than where the water drains, is first found, and there to commence filling the drain, always supposing a firm foundation to be first found. Deep drains require more materials to fill them, and create more expense, both in filling and in dig- ging; but in permeable soils, they may be useful in draining water which may flow in a stratum that edges or throws water upwards between the drains. Drains removed to a depth beyond the reach of the surface water, are wholly useless for the purpose of removing it, and much money and useless labour have been expended in digging downwards to cure the evil, when the remedy lay wholly upon the surface. In our climate, and upon the generality of our soils, a depth of two to three feet may be stated as a two to three fair average; water lying or flowing below that depth can in- flict no damage on the upper soil, and if the drains are made deeper, they may be removed beyond the reach of the surface water. Various depths have been mentioned by writers, and even by practical men, which are not worth much discussion, as they seem to have pro- ceeded more from fancy and bare matter of opinion, than to be grounded on experience or on any specific solid fact. The depth now stated is sufficient to intercept the permeable strata, and does not require any large quantity of materials to fill it to a proper depth from the top, or render it accessible to the surface water, and these are the very special purposes of draining, viz., to carry away the surface water, and at the same time drain the under-water that lies within the reach of damaging the upper soil. feet. Stones have ever been universally preferred for the purpose of filling ON LANDED PROPERTY. 979 drains, but in many countries they are not found, and other materials have been used, as brushwood, stubble, and twisted straw. Modern invention has supplied the place of stones, and by the substitution of tiles, which are composed of puddled clay moulded into the proper shape, and then baked in an oven or kiln, to a hardness that resists the action of the Materials of vicissitudes to which they are exposed. This invention must be filling. reckoned one of the most valuable of modern times, for it converts matter into the means of improving itself, and the most tenacious clay into a mode of making itself productive. The ductile quality of clay allows it to be moulded into any form, which in the present case is about twelve inches long, and arched into a span of four inches. Other dimensions are used, but the shape now given has been found to be well adapted for the purpose. The width of the drains at the top may be about two feet, sloping to six inches in width at the bottom, in which the tile of four inches is laid. It has been found by experience that the constant percolation or oozing of water on the bottom of a drain, even of a hard and tenacious clayey nature, creates a softness in which the thin edge of the tile gradually sinks and obstructs the arched passage, as- sisted by the superincumbent weight of the filling materials. This cir- cumstance has rendered necessary the use of soles or flat tiles that are laid below the arched tile to prevent the sinking, and in common practice, a piece of a broken sole is laid below the meeting corners of the arched tiles, and bears the pressure of both. A quantity of straw, or a turf laid with the grassy side downwards, is put over the tile, and the excavated earth being thrown promiscuously to fill the drain, the process is finished. Width of drains. used. In the filling of drains with stones, the materials are broken with ham- mers, to the size of the largest road metal, either in the quarry where the stones are dug, or on the sides of the drains where the unbroken materials are laid. Stones dug from a quarry are preferable to stones gathered on the surface of the ground, as they afford more angular points, stones, how and consequently a greater number of interstices in the drains; when the stones are broken on the sides of the drains, the bruised materials are very conveniently lifted into the drains by means of baskets, without any earth getting intermixed. When they are dug and broken in a quarry, earth or rubbish of some sort will generally get mixed with them, and it is essential that no earth get into the drains. A screen is very easily constructed and placed on a wheelbarrow to be moved along the side of the drain as it is filled, provided with a wide screen to turn the stones into the drain, and a narrower one to throw on the ground the rub- bish that passes through the wider bars of the upper screen. The carts come alongside the screen, into which the stones are thrown from the carts by hand shovel, the large bulks run into the drain, and the rubbish falls on the land; and with care and attention very sufficient work is made. But in general it may be recommended, that the stones be laid unbroken on the sides of the drains; that they be broken on a platform of boards, filled into baskets, and placed into the drains, and immediately covered 980 ON LANDED PROPERTY. them. Covering of with turf and earth. It is necessary that the drains be not allowed to remain long open and unfilled, nor the stones be al- lowed to lie uncovered after being put into the drains. In this operation, as in all others of a similar nature, systematic dispatch must be studied, the different operations must go on simultaneously, and be so arranged, that the execution of one part does not overreach the other, in order that the unfinished portion may sustain no damage. The earth crumbles into drains lying open, and causes labour in shovelling it out before the stones are put in and the same objection holds with stones placed in drains and lying uncovered. It is very convenient when land can be drained in a state of grass, on account of the superior cleanliness and neatness with which the work can be performed. This very great advantage will most amply compensate Grassy turf for any additional expense incurred in digging the drains during useful. the hard season of summer, which may sometimes happen, and sometimes not. The lines of the drains being first marked by pegs or turves, the unbroken stones may be laid alongside at convenience; the grassy turf must be pared off thinly, and laid aside, and carefully pre- served for covering the broken stones; the drains may then be dug to the full depth, and immediately filled with the broken stones to the height of twelve to sixteen inches from the top; the stones levelled with an iron rake, and the grassy turf laid neatly over them, and the earth shovelled in upon it. The broken stones should be put into baskets, and handed to a man standing in the drain, who will empty them in the proper place, level the stones, and lay the grassy turf neatly over them; and it is essen- tial that this part of the business shall be performed by a confidential person specially appointed for the purpose, and whose contract bears a greater remuneration for the proper execution of it. The quarrying and breaking of the stones, the digging of the drains and the filling of the earth, may be let to be done by contract; but the filling of the drain with stones, and the laying of the turf over them, should be performed by a fixed daily or weekly remuneration, where there is no induce- ment to hurry over the work imperfectly, as is generally the case in contract work. Work that is exposed to view may be mended when seen to be imperfectly performed, but a drain when covered is hid for ever, and the mischief remains. Much draining has been spoiled and money uselessly expended by the work being improperly executed on an erroneous system: contract work requires a sharp oversight, and in what- ever way draining is performed, it claims much attention, being easy to spoil, and difficult to remedy. Filling most carefully done. In digging drains it is advantageous that the cavity is sloped to a very narrow bottom, as the stones, in being put into the drain, catch on the sloped sides, and form a kind of artificial arch, and afford a greater cavity, or more interstices below. When tiles are used, the bottom of the drain may be made the breadth of the tile, or a little more. Broken stones laid in a drain over the tile about a foot in depth, has been called the “ ne plus ultra" of draining, as it affords a clear pas- ON LANDED PROPERTY. 981 "Ne plus ultra" of draining. Tiles. sage for water in the tile, and the upper space occupied by the stones is open and porous for extracting and conveying the water downwards. In the case of the tile alone being used, and covered, as it generally is, with straw, or a thin grassy turf, these substances are soon compressed and decay, and then there is only the space occupied by the tile, about four inches in height, to form a drain, both to extract and carry away the water. When stones are used, the half of the depth of the drain is filled, and thus affords an interstitial cavity of fifteen inches, for the purpose of receiving and discharging water. This circumstance constitutes the superiority of stones over tiles for the purpose of draining : they also form a stronger drain, and are more durable. Tiles are preferred where there is a constant current of water; in such cases, where stones are used, a square culvert should be set with broken stones, of a size proportioned to the quantity of water it may have to contain. It is necessary that a constant current of water have a free unbroken course. The receiving drain at the lower end of the field, must be wide, and have ample space both in width and depth-a depth of some inches below the common drains, and a width sufficient to contain a square set culvert of large unbroken stones to convey the whole quantity of water from the drainage; if one culvert be insufficient, two may be made; and in the case of tiles, if one large tile, which are made for the purpose, be insufficient, two may be placed, if necessary. These re- ceiving drains must be conducted with great care, where the common drains are discharged into them, built with solidity, and have a covering of broken stones and grassy turf over them. If the current of water be large or rapid, care must be taken that the bed of the current is secured by laying soles or thin stones. . filling. When drains are being dug, it may be advantageous to lay on one side of the drain the porous upper soil which is first 'excavated, and on the other side, the subsoil which will be of a different nature. After the grassy turf or straw is laid neatly over the stones or tiles, this earth may be shovelled into the drain, and may be mixed, or the one Earthy preferred to the other. Where the subsoil is very clayey and tenacious, the upper soil may be first put in, and the subsoil put on the top, as the action of the air and the operations of cultivation may pre- vent its consolidating and denying a passage to the water downwards, as often happens when it is put undermost in the drain. But no damage may happen from both kinds being put in promiscuously, unless the clay be very tenacious. A depth of fifteen inches of earth, over the stones or tiles will be sufficient to admit subsoil ploughing, and may not be too deep and deny a passage to the water. Digging. When the pressure of other business over the farm does not allow the full combination of the operating force on the point of draining, it will be very convenient to dig the drains to half the depth, and to excavate the part that is left at the time when the materials are brought forward and broken, and then the two operations of digging and filling can go on together. It is of very great consequence that a drain 982 ON LANDED PROPERTY. be filled with stones immediately on being dug, on the same day, if possible. Direction. Drains are generally run in three directions, upright, aslant, and across; and each mode has its advocates, according as circumstances have favoured the operations. Cross draining can only be done when the de- clivity of the land favours the descent of the water in that direction, and then it becomes a kind of upright draining, being upright to the fall of the water. The across and slant directions have an advantage in the ruts of the plough crossing the drains, and thus conveying the water to be carried off, while in the upright direction the ruts and the drains run parallel, and consequently the water may remain longer on the land before reaching the drains. A preference may be justly given to that direction, which causes the ruts of the plough to cross the drains, for it seems natural to suppose that the water will, by that means, make a quicker escape. But much land has been and is yet drained, by placing a drain in each furrow Furrow between the ridges, at distances of four to twenty yards, and keeping the open furrow over the drain; and it is contended that it forms the most effectual mode of drainage on pure clay lands, and that the drains must be no deeper than places them beyond disturbance by the plough and the horses' feet. The ridges are shaped and raised to a convexity to throw the water to the furrows, and it is there quickly let into the drains. This mode is still largely practised in many places, and it has proved both effectual and durable. draining. The Duke of Portland was among the first practitioners in Britain, of the furrow draining, or frequent system; and the mode of placing the Duke of Portland's method. drain in the open furrow made by the plough, and sinking the cavity no deeper than beyond disturbance by the implements of cultivation, has always been used, and is yet followed over all His Grace's estates, and was seen in full operation by the author of this work on the stiff alluvial clays in Ayrshire, in the west of Scotland, on the estate of that nobleman. After all that has been done, spoken, and written on the subject of frequent draining, the above practice may form the sim- plest and most effectual mode that is yet known; and His Grace's very true and most just opinion on the subjects, is very deserving of being recorded:—“That on all purely clay soils, the drains can- not be too shallow, provided they are not disturbed." Place the drains in point of number within the quick reach of the water, and afford to the water as quick a descent to the cavity after it has reached the surface of the drain. These two provisions constitute complete drainage, and both must exist, as one is useless without the other. His maxim. Circular or pipe tiles have lately been introduced, which Pipe tiles. fit into each other at the ends, and thus form an uninterrupted channel. The diameter has been reduced so low as one inch-much too small an orifice to form a drain. The largest tiles are sometimes deficient in forming a cavity large enough to form a drain, and experience has taught all drainers to increase rather than diminish the size and capacity of the open portion of the drain. It is on this account that stones are so very ON LANDED PROPERTY. 983 much preferable to tiles, in forming an interstitial cavity of broken stones in place of four inches afforded by the tile, for the purpose of draining and carrying away the water. Pure clay soils admit the stones to be small broken, as there is no current or muddy oosing of water to require large passages. But in mixed subsoils of sands and gravels, where are found outlets and oozings of water, the stones may be of a larger size, as they form larger openings and in- terstices for the passage of the muddy liquid. On soft bottoms where the stones sink by their own weight, it is necessary that some flat substance be laid underneath them. Soles are used in tile-draining; and for stones, slates have been very much recommended, and no doubt will prove to be very effectual, but the expense will be considerable, and flat shaped stones may be used, or any rough unbroken stones may be thrown into the drain till a bottom be formed by their weight sinking them, and then the broken materials may be put into the drain as usual. These points require much attention in draining; a neglect even in one single place may defeat the purpose of an entire length of drains, cause obstructions, and much expense and labour in removing them. Soles for sands and gravels. The very first object to be considered in commencing the operation of draining, is an outlet for the collected water, and for this purpose, the brooks or rivulets must be very carefully examined, deepened, and straightened, where it is necessary; the second consideration is the large drain, whether covered or open, that receives the water from the small field drains, and conveys it to the brook. It must be of sufficient width and depth, and convey the water freely away, without any stoppage or obstructions. An experienced operator will commence with these exami- nations, on which depends in a very great degree the success of the intended scheme. Hill drain- ing. Very much good has been effected on the Cheviot mountains and the Southern Highlands of Scotland in improving the sheep pastures, by cutting open drains for surface water with the spade, in large sods from sixteen to eighteen inches wide, and laying them on the under side, as the drains are chiefly run along the slanting sides of mountainous grounds. The cut is then cleared out to the depth of about fifteen inches, and the loose earth is likewise thrown to the lower side, so as to make a bank. These drains by removing the surface water, have proved of essential service in preventing the rot among sheep in moist pastures. An early bite of grass may be procured for the sheep by throwing the water over convenient grounds by way of irrigation, and these two advantages make this kind of draining one of the most useful improvements of the present day. When springs of water are found in land to be drained, it will happen that the straight lines of the drains will pass on each side, and leave the outlet untouched; in that case, a drain must be cut, and run with the necessary declivity from the set drain to the spring, and a tile must be laid, or a square culvert set with stones, to convey the current to the drain ; 984 ON LANDED PROPERTY. Springs of water inter- cepted. and if the current of water be strong and constant, it will require a tile, or a stone culvert to convey it to the receiving drain at the end of the field. An oozing of water will find a way among broken stones; but it is much better that a current have a free course in a tile or culvert. The ends of all drains that remain open should be built up firmly with square stones to the height of the drain, leaving a square mouth of discharge for the water. The joining of small drains with re- ceiving drains must be made of the same height, and covered with the same turf and earth; and all such work must be done by an experienced confidential person, and the whole carefully overlooked and superintended by the chief operator. In no agricultural business whatever is more care and attention necessary than in draining, and nowhere does carelessness and neglect operate more forcibly and to greater disadvantage. All drains covered. It is advantageous that all drains or ditches be covered, that no open drains remain anywhere visible within the enclosure of a field. Covered drains admit the plough close to the fence, and allow the live stock to obtain the shelter of the hedge by standing close to it. The expense of draining, like that of every other operation and per- formance, will vary according to circumstances as the cost and distance of the carriage of the materials, and the price of labour required to apply and adapt the materials to the purpose. A variation in draining will also happen from the greater or smaller number of drains that are required on an acre of land, and this circumstance itself must vary according to the extreme or moderate wetness of the soil. All these circumstances com- bined require a wider range of figure than at first sight would appear to be necessary, and to the reasons above given there must be added the nature of the soil, if it be hard or soft for digging. The expense will range from £4 to £8 per acre, according as the favourable or unfavourable circumstances may predominate; an average may be stated in £5 or £6 Expense of an acre, when the drains are five or six yards apart, which draining; width will drain moderately wet lands. This estimate is con- fined within the hedges of the field to be drained, all exterior operations, as the cutting of open ditches, and of water courses, must be charged to the account of general expenditure. The expense of draining being very considerable, and the nature of the improvement being permanent, it is both natural and reasonable that it be performed at the expense of the party who has a permanent interest in the land on which the improvement is performed. A yearly tenant of land is debarred by common sense from making any outlay of which he cannot reap the full fruits in the year of tenure; a farmer with a short lease is not much better situated. A lease of not less than twenty years, falls. at least, is required to justify such a costly improvement as draining at the expense of the tenant, that he may have a fair chance of being reimbursed for his outlay of capital. A farmer, even with a lease, has only a temporary interest in the land he occupies-it is contrary to human nature to expect that he will take as much trouble in the per- formance as if he had an interest at stake, and consequently the cost of the on whom it ON LANDED PROPERTY. 985 improvement reverts on the proprietor who enjoys the perpetuity of the value. Accordingly, the most equitable arrangement seems to be that the improvement be effected at the cost of the proprietor, the tenant paying a yearly interest for the money expended, and the cartage of the materials as an equivalent for the benefit he may derive from the improvement that has been effected. The work being done by the proprietor's own workmen, he has the greater security that it is properly done; a vast advantage over the draining being entrusted to persons who have only a temporary interest in the performance. Various arrangements Various ar- have been made between landlord and tenant; as the former rangements. giving the tiles, and the latter digging the drains and filling them; and otherwise each party paying half the expense. The most common, and the most equitable arrangement consists in the landowner making all the outlay, and the farmer paying five per cent. interest on the outlay, during the period of twenty years: and otherwise, the tenant pays 5s. or 6s. an acre for the drained lands, along with the rent, in half-yearly payments. This last mode will give the landowner three-and-a-half to four per cent. yearly, for the money expended, which may be sufficient when the national funds are taken as a model. This last arrangement was from the first adopted, and is still used by the Duke of Portland, whose excel- lent practice has been already mentioned on several rural under- takings. His methods and calculations are never exceeded by any subsequent attempts, but remain as rocks fixed in the bottom of the sea, that are never lifted up and down by tides. In all arrangements, the proprietor must have the work done by his own agency both in labour and superintendence, as he has the security of its being permanently effected. The farmer by doing a stated portion of the performance, buys the yearly fruits of the improvement, and at the end of twenty years, the negotiation is terminated, and the improved ground becomes an article of commerce in the altered condition which has been imposed upon it. A wealthy tenant may be induced by a lease of twenty or twenty-five years to drain lands at his own cost which are the property of another person; but the cases are few, and there is yet a great aversion to grant the necessary security which is essential to the business. Security begets confidence, and confidence promotes that thirst and eager desire of remuneration which does not exist unless self-interest be enlisted in the cause, and which so effectually ensures the advancement and economical termination of any intended scheme. Terms of agreement regulate the moral ex- citement, which is keen or blunt as the conditions may be encouraging or unfair between the parties. Duke of Portland's method of all ways the most equitable. The draining of lands that are wet, either from springs of water from below the ground, or from the aluminous composition of the soil holding the moisture too long, and causing damage to vegetation, or as often happens from both causes must precede all other improvements that may be intended to be undertaken under the circumstances now described. Experience will direct whether a thorough frequent draining be necessary to prevent the damage of a general wetness, or a less frequent drainage 3 P 986 ON LANDED PROPERTY. Value of to carry away the hurtful effects of springs, aided by a partial wetness of the soil; but in every case the drainage should be more frequent than less frequent, in order to produce at once a sure and certain result. No pro- prietor of land ever can find a more profitable or a safer invest- draining, ment for money-he has the security on his own property, in addition to the improvement of it; and it has been stated, as an average calculation, that land thoroughly drained, and properly managed other- wise produces three crops in two years, in comparison with the former produce. The farmer has the advantage of more produce from his lands, the texture improved, and more easily wrought and accessible, and a more grateful and a sweeter herbage. The circumstance of draining rendering lands easier and sooner accessible at the different periods of working, is a recommendation of itself sufficient to show the great value of the improve- ment, besides the increase of produce in every crop that grows. Experience has not yet recorded the fact, if draining has in any case converted stiff clay lands into turnip loams: if it has happened any where, it may have arisen from a constitutional near alliance of the soil, or from the nature of it approximating to loam, and wanting only the abstraction of the water, and but little alteration in the texture. Clay soils may probably be placed beyond that degree of alteration. on any lands. It has been objected to draining that it destroys the viscous tenacity in the land, so necessary to the production of wheat and beans, and may carry off in the shape of water the saline and soluble salts in the soil. But these evils may exist only in imagination and anticipation, and may in effect be only partial, and may not detract much from the general value of draining. The effects of it have been found so very superior to that of the viscous tenacity and that of the soluble salts in the wet state of the land, that little hesitation will be entertained which of the two conditions of the land must be preferred for practice. Objections It is certain that draining has not in every case been attended not tenable. with success, and that in many instances it has been accompanied with loss of capital. This result may be ascribed to two general causes: the want of knowledge or caution in the application of the system to prac- tice, and to the defective execution of the works, in cutting and filling the drains, and in the materials used. True economy consists in getting work well done, not in the cheapness of execution; and a very general mistake is constantly committed in placing the tiles too deep, and too small a quantity of porous materials over them; thus repeating the old error of having useless drains deeply imbedded in compact clay, and beyond the reach of the surface water. But the occasional failures of draining are not more frequent than other miscarriages, the chance of which attaches to proceedings of every kind. A neglected execution will mar any purpose, and a careless application almost renders a failure to be Failures few. certain. In order to derive the full effects of draining, it must be followed by an improved treatment of the land in every respect, as to cropping and ma- nuring, in order to repair the damage they may sustain by the supposed ON LANDED PROPERTY. 987 of draining. General, loss of tenacity and of saline soluble matters. When land is drained in a state of grass, there will be fresh matters in the soil for decomposition, and then the liberal application of calcareous matters becomes very highly necessary and desirable. It has been admitted in all ages of the world, that the draining of marshes and of stagnant waters is highly Consequences conducive to health and salubrity; and we may very reasonably suppose that the close draining of wet lands, though performed on a smaller scale, will operate in a similar manner. It carries away or pre- vents the generation of the pestilential miasms that originate in distem- pered and poisonous bodies, and lime arrests the noxious effluvia that tend to rise more or less from every soil at certain seasons of the year, and de- composes them, or causes the elements to assume new forms of chemical combination, in which they no longer exert the same injurious influence on animal life. How beautiful a consequence of agricultural skill that the health of the community should be promoted by the same methods which most largely increase the produce of the land! Can it be doubted that the All-benevolent Creator of the world places this consequence so plainly before mankind as a stimulus to further and more general improvements, to the application of other knowledge still to the amelioration of the soil? What noble employment for the mind of man! By the use of his reason, his energies, and his capital, he affords in the first place, employment for his fellow-creatures, then an increase of food and of health to the human race; and lastly, a remuneration to himself. What more can his heart desire? There is nothing wanting to satisfy either the selfish or the philanthropic mind. A very heavy and unextinguishable responsibility rests on those persons who possess the means and the of conferring such invaluable benefits on the human race, and neglect the very valuable opportunity of lightening the debts of property to poverty ; and who continue ignorant and unwilling, or incapable of action, in spite of the warnings of science and the sanctions of experience. Under the wide expanse of heaven there is not and cannot be a more gratifying em- ployment than the improving the condition of the human race; Universal, and as the physical condition must ever precede the moral, the improvement of which we are now treating, must claim a prominent place among the agencies that may be employed in effecting that object. There is a huge difference between the employment we are now describing and the many fooleries that engage the attention of the human race, that de- grade the intellect, vitiate the morals, and debilitate the bodies of men. Here is employment, food, and health, to be derived from a source the most rational under heaven-from the cultivation of the earth, the inalien- able patrimony of the human race. It is not a little surprising that any draining should remain unperformed, the proofs of the beneficial effects being so many, so strong, and undeniable. The results, as we have shown, are not confined to the benefit of the individual who performs the opera- tion; they swell into national importance, and claim the attention of the philosopher and statesman, as well as of the cultivator and owner of the soil. Every interest must give way to the general power to every grade of society, 988 ON LANDED PROPERTY. < interest; but here is no opposition, or any jarring contention, for every party is benefited, and the general good promoted. The labourer finds employment; the farmer obtains an increase of produce; and the land- owner gets his property improved in value, and a remuneration for his capital; the nation enjoys a climate improved and salubrified by and compre- the process, and an increase of food, the essential element of life, hensively. on the regular and ample supply of which articles the prosperity of any social community almost wholly depends. individually CHAPTER IX. MINERALS-WORKING AND VALUE. MINERAL property is very frequently the most valuable part of a landed estate. The income is generally steady and secure, and not so uncertain as the revenue of the capitalist and the trader. Extensive mining infers the advancement of a large capital; and an adequate knowledge of the sub- ject should be present before commencing too rashly in the works of dig- Minerals. ging minerals. There are many cases in which the land-owner may profitably embark his capital in mining; but in most cases it is preferred to lease out this species of property to others, who advance the capital and follow mining as a profession. The metals of Britain are-copper, tin, lead, and iron. The useful minerals are-lime, coal, clay, and building stones. Copper lies chiefly in the older rocks of primary and transition, and is found in many con- ditions, but chiefly in the ores of sulphurets. The most important of the ores of copper is copper-pyrites or yellow copper ore, which is a compound of sulphuret of copper, and sesqui-sulphuret of iron. It is found in granite, the trap rocks, and even in the lava of recent volcanoes. Although more difficult to be reduced than iron, it was more extensively employed by the ancients, who understood the art of hardening it, so as to form cutting instruments, by mixing it with tin and other metals. Copper, The primary and transition deposits of Cornwall, that are intersected by porphyries and other plutonic rocks, afford the richest mines of copper that are now worked, which lie in the tract of country between Truro and the Land's End. The veins traverse the slaty rocks or killas of the pro- vincial nomenclature, and are collected into groups, and do not cover a large extent of surface. The directions are various in which the veins run their course, which is never vertical, but at an angle with the horizon. The depth is not known, the search being generally abandoned on account of the poverty of the vein, or the increased expenses of sinking. The average width is three feet, some are six and even ten or in Cornwall; ON LANDED PROPERTY. 989 twelve, with smaller ramifications. The length is under two miles, though some reach to seven. The depth is great, extending to 1650 feet below the surface of the ground, and many cases approach to that level. The driftways and levels under ground amount in the aggregate to hundreds of miles. The mines extend under the bed of the sea; and the dashing of the waves, and the rolling of the pebbles and fragments of rock, are heard by the workmen in the excavations below. A very rich mine of copper was wrought in Anglesea, which for twelve years, from 1773 to 1785, lowered the price of the metal throughout Europe. The produce diminished, and the mine is now only moderately productive. Some other places afford copper in limited quantities—as Devonshire, Derbyshire, and Staffordshire, the Wicklow Mountains, and the Isle of Man. The transition mountains of Scotland show a in Argyle- small quantity; and a mine has been opened in the Zetland shire. Islands. No rock above the coal in Britain contains copper; but in Ger- many, beds of what are called copper-slate exist in the new red sandstone. The brass of the Romans meant copper, which must have been very early worked in this country. The Crown gave up its right to all the baser metals in 1688, when England did not produce sufficient copper for its own use; and the copper coinage of native metal did not appear till 1717. From this period the increase of copper has been amazing, and now exceeding 14,000 tons, being in the one-half exported, and over one million of money in value. Smelting. Sulphur, iron, and other substances are associated with cop- per, and require, in being separated from it, a much more com- plicated series of operations than iron or lead. The smelting establish- ments are quite distinct from the digging of the metal, which is sent to the former as a raw material, to be prepared by a different division of labour and of firm. The same hands do not often possess both undertakings. The metal of copper is very malleable, and may be hammered into plates of great fineness. The substance is of great value in the arts. Iron only exceeds it in tenacity, which is superior to that of gold, silver, and platinum. The alloy equals the single value-three parts of copper and one of zinc form brass; one hundred parts to ten of tin, it forms bronze and gun-metal; with twenty-five of tin, it forms bell-metal; with thirty-five of tin, it forms optical speculæ, which were formerly used as mirrors. Quality. Value. Very few localities can be expected to yield copper in any workable quantity. The value is inferior only to the precious metals, and the mineral is very profitable on an estate of land; but much caution is due to the engagement in working it, and must ever be done under the direc- tion of a skilful engineer. Tin is a scarce metal, yet was early known to the nations of Europe, who seem to have derived the supply from the inhabitants of Tyre. It occurs in the primary rocks, in veins, or disseminated, and in two mineral species, the peroxide, called tin stone, or tin ore, and the cupreous, sul- phuret or bell-metal ore. The metal is abundant in Cornwall, and is 990 ON LANDED PROPERTY. found on the continent of Europe, and in the East Indies. In Cornwall Tin. the veins extend from a line to several feet in thickness, and are of unknown depth, being wider in the softer rocks than in the granite. The veins are wrought by vertical shafts and by drifts under- ground that extend for many leagues. Stream tin or grain tin is gathered in the ravines and valleys, where it lies mixed with sand and gravel in grains or larger fragments up to twenty pounds in weight. The ore is separated by washing, and sells at a lower price than the block tin of the veins. The purifying of tin is a tedious process; the ore is first reduced to powder by stampers, and washed and sifted, so as to separate the tin from the other mixtures. The heat of a furnace then banishes the sulphur and arsenic from their combinations, and washing separates the substances. The ore is then fused by lime and coal; the lime combines with the earthy matters, and the coal reduces the oxide to the metallic state. It Working. is again further purified by fusion, and cast into blocks, which are stamped for commerce. About 4300 tons of tin are produced in Corn- wall, of which the one-half is exported. The locality of tin is very limited, and forbids any hope of a successful search in Britain. Some deposits of stream-tin may probably occur in the primary districts of the west of Scotland and Ireland. Quantity. Lead : Lead exists only in one abundant ore, which is the sulphuret or galena, or lead glance. The mineral occurs in veins of va- rying thickness, in the primary or transition districts, partially in the old red sand stone, abundantly in the mountain limestone, but sparingly in the coal measures, or the superior formations. The chief positions in Britain are the slaty and greywacke hills, which stretch across the island from St. Abb's Head to the Irish sea; in Derbyshire, Shropshire, Devon- shire, and Cornwall; in the Isle of Man; in Denbighshire and Flintshire; and in some parts of Ireland. The mines have been worked in Scotland since 1540 with considerable profit, in the slaty and greywacke rocks of the counties of Dumfries and Lanark. The thickness of the veins varies from four to ten feet and upwards. where found. The elevated country near the Cheviot hills, in the north of England, around Crossfell, where the meeting happens of the counties of Northum- berland, Durham, North Riding of Yorkshire, Cumberland, and Westmoreland, contains the mines of lead that are the richest in England. The number is 175, and have been, or are now worked. The rock of mountain limestone, with its accompanying strata of sandstone and slate, contains the mines which are situated in the five counties. The directions of the veins are various, and are sometimes very slender, and at other times thick, as fifteen feet or more. The best are in the limestone; and the quantity and quality are contracted in the slate and sandstone. Trap in dikes intersect the veins, which are very productive, and have much increased the value of the landed property. The oldest mines are in Derbyshire, and the richest in North Wales, which yield fully one-fourth of all the lead in the kingdom. Many or all ON LANDED PROPERTY. 991 Quantity. these mines have been worked out or destroyed by inundations. The aver- age yearly produce of lead in Britain is about 50,000 tons, and at £20 per ton the value is about one million sterling. About one-third of the produce is exported. Lead-glance is the chief ore, and the extraction of the metal is not very difficult. The sulphur is driven off as acids, and the metal is Working. oxidated by the action of a powerful heat; a part of the sulphuric acid combines with the metal, and forms sulphate of lead, to reduce which quicklime and coal are added during the process; the lime combining with the sulphuric acid, and the carbon of the coal abstracting the oxygen of the metallic oxide. The metal being reduced, is collected in vessels, from which it is cast into large ingots termed pigs, and is ready for commerce. Silver, iron, and copper, are in a small quantity mixed with common lead. The silver is extracted, when the quantity defrays the expense; but the amount and value are inconsiderable in this country. Risk of Mining. The hazards are large of mining and smelting, and metal- liferous veins are irregularly disposed, sometimes disappear, and are cut off when the indications appear of the largest returns. They are consequently placed beyond the calculation of coal and stones, which lie in beds, and admit an approximate relation of the raw material with the ex- terior approach. The number and thickness of the veins must determine the expediency of working, and the proprietor will be guided by the best advice on the subject. Iron. Iron is the most useful of all the metals, and enters every- where into the composition of the larger masses of mountain rocks, and in combination with oxygen, sulphur, silica, and other sub- stances, forms many mineral species. The ores are numerous, but two of them furnish the useful metal in magnetic iron and clay ironstone. The former yields the iron of Sweden and Norway, and occurs in beds or single crystals in the older rock formations, and combines the two oxides of red and black. The ironstone is found in the coal measures of Britain, of which the whole consumption is supplied from that quarter. It is a happy ad- vantage, the coal and lime necessary for the smelting the ore are found together, as the geological deposit has placed the formations. Iron occurs in beds, that are from one inch to a foot in thickness, and alternate with shale, limestone, and coal. The ore is put into large fur- naces, where a powerful heat is raised by common coal mixed with lime as a flux. The oxygen is banished by the heat, while the lime Where found combines and carries off the foreign matters in a fusible com- pound called slag. The melted metal by its density sinks to the bottom, where it escapes by a hole plugged with sand and clay; the slag floats upon the surface, and escapes by an aperture in the side of the furnace. The process of fusion goes on continually, as fresh matter is constantly supplied from above. The liquid matter received from the furnace is run into moulds of sand, and then it forms the pig-iron of commerce. Working. The furnaces are square at the bottom, where the metal collects, and 992 ON LANDED PROPERTY. Smelting. then swell outward to their greatest diameter, when they contract to the commencement of the chimney. They are built with bricks or stone, and lined with fire bricks; the hearth at the bottom being a hard infusible stone. A tunnel head, or an external gallery, at the beginning of the upper part of the chimney, contains square openings with iron doors, by which the furnace is charged with materials. A most intense degree of heat is raised by blowing pipes, which are driven by steam power, and holes introduce the streams of air in the lower and nar- rower part of the furnace. The fuel is coke or common bituminous coal; and a saving of these matters in the one-third to one-half is effected by heating the air before entering the furnace, by passing it through heated pipes that are placed between the furnace and the blowing apparatus : iron is more brittle produced in this way than by means of coke and cold air. Before being put into the furnace, the ore has been exposed Furnaces. in heaps to the air, for the purpose of banishing water, carbonic acid, and sulphur. Ironstone, coal, and limestone, are then introduced in twenty cubic feet of coal to the corresponding quantities of iron and lime. The liquid metal is usually drawn off every twelve hours; and the furnace being once ignited, is never again extinguished till it needs reparation. The metal is conveyed into its moulds under a shed by the side of the furnace. The iron is impure as it comes into the first melted condition, containing foreign bodies, chiefly carbon, and is hence regarded as a carburet. It is fusible, and may be moulded into many fabrics. It becomes tenacious and ductile, but more infusible, and formed into soft or malleable iron by a further series of processes, by which it is freed of its carbon and other impurities. Pig-iron. The pig-iron is fused in a peculiar kind of furnace, and formed into a slab, which is rendered brittle by throwing water upon it. Being broken into pieces, a reverbatory furnace subjects it to the operation of puddling, which consists in stirring it while in a liquid state, when a large disengagement will happen of carbonic oxide, as is known by the blue flame. Balls are then formed of the iron, and forged by heavy hammers, or are passed while hot between a series of grooved rollers. This condition is called mill-bar iron. The forging is continued by welding pieces of it together, and the properties are further acquired of malleability, ductility, and cohesiveness. Steel. The iron thus prepared is the valuable substance of malleable iron, fusible only by the most intense heat that can be produced by any artificial means. The malleability is of any temperature, and in- creases with the heat applied; when red hot, it may be hammered into any forms, and welded or joined in any fashion. It is very ductile, and may be drawn into thin wires, when the supporting power exceeds all other metals. Combined with carbon, iron forms steel. Iron is generally melted where it is found, as coals and lime are in contiguity. The mines of Britain are in North and South Wales, ON LANDED PROPERTY. 993 Shropshire, Staffordshire, and Derbyshire; and in Scotland, in the vallies of Forth and Clyde. Mines in Britain. The improvements of the smelting processes, and the use of the steam engine, have increased the iron trade most amazingly, from the middle to the close of last century, and the facility of an increased production had the usual effect of diminishing the price, and this result enlarged the con- sumption by introducing iron into many other purposes of use. The de- mand now must limit the production, as Britain seems capable of supplying the entire consumption of the world. Rent or royalty. The mines of iron are let upon lease for a stipulated rent or royalty. The royalty is not reducible to rule, but must vary with the nature and richness of the mine, and other circumstances that affect the value of the produce. The land-owner may sink the new mine, and work it till the value can be approximated, when a tenancy can be negotiated. Very long leases are generally granted to companies or wealthy individuals, who make every erection, and perform all business at their own cost, without any demand on the original inheritance. Coal Coal is a very inflammable body, composed chiefly of bitumen with other matters, with much carbon in the hard varieties. The formation lies in great irregular basins, the strata dipping to some common centre, or general axis, and are found in the sandstones of the secondary class of rocks, which succeed the unstratified deposits. Where this rock is not deeply covered by the upper formations, the coal approaches the surface, and was early discovered for the purpose of fuel. It forms the chief mineral wealth of Britain, and employs a large portion of the shipping and mariners of the island. The regularity of the strata of coal is very often disturbed and intersected by dikes, fissures, and irruptions of igneous rocks, as traps, basalt, porphyries, and interjected argillaceous matters, which are found in every geological deposit from the granite to the chalk. These barriers run in various directions, vertical, oblique, and often right-angled to the stratum of coal; and are known by different names as dikes, slips, faults, and troubles, according as the dislocation of the stratum is greater or less, and affects the proceedings of the mine largely or in a small degree. mines. Boring. Coal is best discovered by boring, and the natural indications must be such as to induce that trial being made. Professional borers contract for the work, and are paid 5s. for the first five fathoms; 10s. or more for the second; 15s. or more for the third, and so on, in the same proportion for every five fathoms, or thirty feet in depth. The essential purpose of boring is to ascertain the depth and thickness of the mineral seams in the tract to be surveyed. The depth of the covering over the coal and the thickness of the strata, must be ascer- tained, and also the dip or inclination, which the coals assume in the extent of the surface ground. Declivities admit a day-level being made, which will draw off the water into lower ground, when it is best five or six feet in height, and four feet wide, built and arched with stones or bricks. Water will flow into every excavation made in the ground, Depth. 994 ON LANDED PROPERTY. Levels. either from the looser earth of alluvial covering, or from the seams of solid strata through which it may permeate. In level situations, no in- clination can be found, and pumps are necessary in order to raise the water from the bottom of the excavation to the surface, on which it is floated away into brooks or rivers; or it is discharged into a day-level, which has been described. In great depths, there is a large mechanical stress in the length of the piston rods, and the increase of weight and strength in other parts of the pump, when water is raised from the bottom, and therefore it is necessary to have a series of pumps, the lowermost throwing the water into a cistern, whence another higher pump draws it to a second cistern, and so on to the dis- charging orifice. The cylinders of the pumps are fifteen and eighteen Pumps. inches diameter. Engine pits. Coals are reached by an engine pit, circular in form, and divided by partitions into parts, as the purposes may require, in placing the pump, for ventilation, and for raising the coals. The engine pit is frequently placed at the tail or lowest dip of the inclined strata below ground, to which the water flows, and the coals are raised at other places that are pointed by convenience. The coal pits are circularly lined with masonry, through the depth of the loose covering of the surface; the rocks below afford a solid boundary, and not unfrequently the wall is continued from top to the bottom, or planks of wood or thick boards are substituted. Sheathings of cast iron prevent the influx of quicksands, which were formerly thought to be fatal and altogether insurmountable. A peculiar arrangement joins the different segments. Water pre- Water will flow into the pit that is being sunk, which must vented. be removed by pumps that are successively lowered downwards as the works proceeds. A pump will very conveniently raise water to the height of twenty-five fathoms, so that three pumps will be required for the depth of seventy-five fathoms. The cisterns that receive the water at the stated distances, are fixed in the excavations made to receive them in the sides of the pit, as the excavation goes on; and the pumps are used in the first place to raise the water that flows into the pit that is being dug: they are afterwards placed in the position which they are to occupy. In some pits, the water is carried to the fixed cisterns by means of spiral boxes carried round the sides; but in all larger pits, the entry of water is prohibited by the cast iron sheathing that has been mentioned. The sinking of the engine pit constitutes the first grand work of the mine, and is termed the winning of the colliery. When the mine is won, the further operations consist in working the mineral, the division and economy of labour, the ventilation of the mine, and the removal of the water. In the vast coal field of the Tyne, the mineral lies deep under a bed of alluvial debris, and large depths must be sunk to reach and excavate the workable One engine pit with the necessary machinery, has expended, £50,000; and even £80,000 and £100,000 have been in special cases, used in these purposes. Nothing could justify such large outlays, but the high value of this rich coal, which it has maintained for Cost of sink- seams. ing. ON LANDED PROPERTY. 995 centuries, and the seemingly inexhaustible source of the supply, which appears to meet the continued and increasing demand. In that locality, mining is seen in the perfected science, and engineering is exhibited on a scale of grandeur. coal, The coal lies in seams that are more or less inclined from the horizontal direction and which are parted by strata, which are more or less argilla- ceous, siliceous, or calcareous; the lower is floor, and the upper the roof, and the coal is parted from each, by thin seams of dry powder Seams of or clay; and the coal itself is intersected by series of subordinate partings, parallel to the main ones, consisting of a soft carbonaceous matter which blackens the fingers, and varying in thicknesss from a line to an inch and half. The mass is also cut by backs and cutters, which extend transversely at right angles to the line of dip, and longitudinally in the line of dip, and these divisions facilitate the working of the coal, and affect the methods of working. Two methods are used in working coals-one way leaves Ways of dig- pillars to support the roof, and which remains in permanency, ging. or being removed, the roof falls in and fills the mine; the second mode allows the roof to fall in regularly as the work proceeds. The first mode is the most common, and the most generally applicable. The engine pit is at once sunk to the most extreme depth, from which a mine is run which is termed the dip head level, and to it all the water in the mine s directed. A series of excavations is conducted in the line of ascent upwards, and another at right angles to these. The pump raises the water from the lowest level, roads are directed in various quarters, and one fourth part or more is left of the standing mass in order to support the roof. The progressive excavations of the coal divide the mine into numerous passages, which are called rooms or thirlings, and communicate with one general passage, that leads to the place in the bottom of the pit, by which the coal is to be elevated. This road is a double railway of cast iron, on which are run low trucks on four wheels, called rolleys, Roads and and are dragged by one horse, several trucks being hooked together. The excavated coal is placed in tubs, technically termed corves, made of osiers, or of hammered iron. They are put on small trucks with low wheels called trams, which are dragged through the low and narrow passages by manual labour. Each truck carries a tub or corf, con- taining four to six cwts. Boys drive the corves from the workings to the mainway, and lads drive the trucks along the mainway to the shaft. trucks. The miners, or hewers, work separately in assigned portions of work. The coal is brought down with light picks of iron, by wedges and drills, and sometimes with gunpowder. The room being scanty for work, the body reclines or sits, and in narrow seams, the back is flat on the pave- ment. The hire is by the quantity excavated, and the miner Hired- assists in loading the corves, which on reaching the mainway, are examined by the superintendent, and being passed his sanction, several corves are hooked together, the train is drawn by a horse rapidly along quantity. 996 ON LANDED PROPERTY. the railway. Where the inclination is great, inclined planes, with ma- chinery are substituted for animal power. The corves having reached the bottom of the shaft, a strong rope with hooks and chains attaches a certain number, which are raised to the pit mouth by means of the rope being coiled round a beam which is revolved by a horse walking in a circular pathway; in all large mines, steam power Elevation by relieves the use of animals. The corves are unhooked by at- machinery. tendants at the mouth of the pit, and dragged on rails to the place of deposition of the load. The empty corves are lowered by the elevating power working in another direction. Ventilation is very necessary in every work underground, and fresh air must be made to circulate in every part of the excavation. Air pits are provided in the shape of wooden boxes, which communicate with the open air, or with some large opening that receives from it the necessary respirations. Coal mines are very dangerously infested with destructive vapours that issue from the pores and fissures of the coal, and which accumulate in two dangerous gases, of carbonic acid gas, and light carburreted hydrogen. The former receives the name of coal damp, or choke damp; and the latter of fire damp, or foul air. Gas in pits. Carbonic acid being heavy, falls to the ground, and rolls along like water, in the lower part of the works, rising by degrees to the higher. It issues abundantly from the seams and fissures, forming a stratum of a foot or two at the bottom of the excavation, while a pure air is respirable above it. In the air above it, a candle burns clear; in the stratum, it is instantly extinguished. This gas is pernicious to human life, either pure or mixed with atmospheric air: when a candle will not burn in it, it is instantly fatal. Hence the precaution of lowering a candle to try the quality of the gas, and also the modern safe-guard of the miner carrying a Safety lamps. lamp which by the faint burning warns the approach of danger. The general air of mines has a quantity of this gas, but does not prove deleterious. Fire damp. The fire damp of mines is sub-carburreted hydrogen, and burns with a strong yellow flame. When abundantly present, it detonates with violence, and hence the danger of the explosion. Being light it flies to the higher part of the works, and hangs like a canopy over the heads of the workmen. A small quantity of it mixed with the common air, creates no inconvenience; but when pure, and without almost any mixture, respiring life does not exist in it. If ignited by the contact of a burning lamp, a terrible explosion takes place, attended with much devastation and loss of life. The gas is not ignited by any tem- perature below that of flame, and flame cannot be communicated through narrow tubes of metal. Hence a lamp was constructed by Sir H. Davy, the celebrated chemist, which is covered with a tall cylinder of fine wire that from the fineness of the texture does not greatly obstruct the light, while it admits sufficient air from without to support the combustion. When brought into contact with the inflammable air of the Now less dangerous. ON LANDED PROPERTY. 997 mine, the air enters the lamp and supports combustion, but the flame of the lamp does not pass through the covering of wire gauze, and inflame the explosive atmosphere without. In extreme cases, air which enters the lamp will take fire, and the intense heat will oxidate the wires, and cause them to fall into pieces. This safeguard of a lamp against explosions, is not wholly perfect-but it has greatly reduced the number of explosions, and would still lessen the accidents, if due caution was observed. Miners are careless, and often open the lamps to trim them in spite of every admonition and the many fatal examples. coals Private gain and public interest are equally concerned in the working of coal mines. A just rent can always be got for coal in proportion to the quantity of saleable produce, and the royalty varies from Royalty on one-sixth or more, to one-fifteenth, according as the mine is level free, or requires an engine pit. When other minerals, as ironstone, are wrought along with the coal, a separate royalty is charged on the special article. The lease must describe the situation and extent of the mine, with a map made and signed by both parties. The mode of working the mine, the maintenance of the levels, and other general regulations, are also agreed, the landlord builds the specified accommodations, the lessee upholds them, and leaves all in tenantable order when he vacates the possession. The moveable machinery is erected by the tenant, and the landlord can buy it at the valuation of mutual referees. known from sale. The royalty is ascertained from the sworn books of sale by the tenant, and the owner may appoint his own agents as checks the books of for his interest: and he can send into the mine at any time, surveyors to see that the mine is properly wrought, and all things are attended. The working must not touch any other mine by ten fathoms, nor go underneath any specified buildings; all pits must be arched over, and surface damages paid. Other conditions will arise from local circum- stances, and occurring attachments. When coals are discovered, the proprietor of the ground sinks the pit, makes the levels, and puts all into current going order for operations. The mine is then let for a yearly rent: or a long lease on very Lease is long. equitable terms is given to the wealthy individual, or a public company, which uses the possession nearly as its own. In other cases, the proprietor is the sole agent, works the mine, and gets all profits. The charge of royalty is the most just and equitable for both parties, as it depends on the quantity sold, and does not rob one to pay another in an uncertainty. The quantity of coals excavated yearly in Britain reaches 35,000,000 of tons, and at 10s. of an average price the value amounts to £18,000,000. The one-half of the price belongs to the labour that has brought the coal to the mouth of the pit, and the other for the carriage to the port of delivery. The capital engaged in coal mining exceeds £10,000,000. The single seams of coals vary in thickness from one foot to forty, and the aggregation of a coal bed from that to 200 feet. The condition of the mining population has been much improved by private benevolence, and special acts of legislation. 998 ON LANDED PROPERTY. Lime. Lime exists in many combinations, but mostly as a car- bonate, or an earthy base in combination with carbonic acid gas. The highly indurated and crystalline kinds form marbles; and the softer constitute the common compact limestone, magnesian stone, oolite limes, and chalk. All these rocks, being subjected to a strong heat above redness, yield the gas which holds the stone together, and becomes a light cinder, which on being slaked with water falls into fine powder. The mixture with sand becomes mortar for building walls of stones and bricks and the powder is used as manure for land. Lime is mostly a flat rock, and lies in horizontal beds, that are divided by seams, and cross fissures, and differs largely from the veins from which minerals are extracted. Where the rock is uppermost in position without any stratified body being superimposed except the alluvial covering, the excavation of the stone is done by open cast, that is, in the manner of a quarry. An outlet for the water is first to be found in the natural descent of the ground-if none exists, a low point must be formed, and a pump placed over it, which will discharge the water into some opening or out- let. The earthy covering of the rock must be raised by spade, and wheeled by barrows to some side where no interference will be made with the works. When the limestone lies deep, the mining of the rock proceeds in the manner of coals. The rock of lime generally yields to the pick, hammer, and wedge: otherwise, it is bored and blasted with gunpowder. Working. Burning. Furnaces are built for the purpose of calcining limestone, in the ellip- tical form, narrowing to the bottom where the calcined lime is withdrawn. The egg-shape is used, when the wider end must be at the top, in order to receive the raw materials of broken stones. The exterior wall of the furnace is of thick masonry, and the inside lined with fire brick, or stones capable to resist a high temperature, and erected on a convenient ground to receive the stones that are intended to be burnt. It should stand at the bottom of a slope if possible, and the top level with the mixed stones, which are put at once into the furnace, and the low ground gives access to the removal of the cinders of the lime as they are drawn from the opening at the bottom of the furnace. When a suitable situation is at a moderate distance, a railway will convey upon trucks, the stones to the furnace. The stones are broken by hammer into a convenient size, and put into the furnace with alternate layers of coals or wood. The fire being applied below ascends upwards, consumes the fuel, and banishes the gas from the stone, which is drawn and carried from the eye of the kiln, in a constant regularity with the filling of the stones into the top of the furnace. In this way the work never stops, and the supply is constant. It is computed that, in a well-constructed kiln, one bushel of the best coal will produce three of lime, and from one-third to Drawing of one-half, according to the constitution of the lime, may be withdrawn every day. These proportions will vary, and as much as two-thirds may be withdrawn by extending the height of the kiln, lessening its diameter, and diminishing the width of the top. But cinders. ON LANDED PROPERTY. 999 the calcination will be less gradual and perfect than when more time is allowed, and a smaller quantity withdrawn. Royalty. The proprietor may keep in his own hands the working of limestones; but it is generally let at a royalty that varies from one-sixth to a fourth of the proceeds, according to the quality and sale of the lime, and the distance and cost of fuel. When the royalty is extended to show an average of years, a lease may be granted, as for a farm of land, upon the moderated calculation that should direct the assumptions of value. Building stones are sufficiently strong to resist the pressure of any force applied to them, and durable to oppose disintegration from the power of chemical changes and external agents. Hardness and tenacity compose the first quality, and the texture forms the second. The closeness of the grain, the homogeneity of the mass, and in certain cases the specific gravity, indicate durability, and afford the only direction of judgment, independently of experience. A loose earthy texture is very unfavourable to durability. Building stones. Building stones are of all kinds, from the primitive granite to the upper- most formation of chalk. The secondary formation of flat rocks affords the most useful articles, as the beds are flat and horizontal, and are tra- versed by seams and fissures, which very much facilitate the excavation of the stones. Sandstones and limestones are the best rocks for mak- ing walls; and the varieties are many, and the qualities discordant. They are certainly inferior to the crystalline rocks in a very long dura- bility; but the use is more general from the facility of being raised, and formed into any shape of blocks. Limestones are of better practical value than sandstones. quarry quarries. Beds of rocks that are workable, will lie on flat grounds, or in the sides of declivities. In both cases, the lowest point must be sought where to begin the excavation, and to it the water will flow and be discharged. A road must be made to lead into the opening from the nearest approach of the common thoroughfare, of which the ascents must be easy, and Working of the inclinations gentle. Where a permanent use of the for stones is anticipated, the earthy covering must be removed and wheeled to some convenient deposition, in which no interference will be made with the future operations. If the quality allows, the earthy matters may be mixed with lime for a compost manure: at least, the uppermost stratum may suit this purpose. Where a short purpose is required in digging stones, the earth may be laid behind the operations, and thus fill up the excavation, which will again become arable ground. A depth and width of face of rock will be preserved according to the dip and inclination of the strata. When the beds sink downwards, and no outlet can be Shaping for dug to vent the water, a pump must be erected to raise the li- use. quid, and discharge it over the intervening height into a running declivity. The stones are separated and raised in blocks by sledges, picks, wedges, and hand-levers; and in case of the harder rock, gunpowder is applied to burst the rock into fragments. The nature of the rock, the direction of 1000 ON LANDED PROPERTY. the strata, and the lines of cleavage, adapt the modes of working to the peculiar conformations. Quarries of stones are but little valued, except in some few cases where favourable circumstances concur to demand the use. The quality then must be very superior, the transport ready, and the sale constant and permanent. These junctions very seldom meet. When a stone quarry is worked in ordinary circumstances, the royalty varies from one-third to two- fifths of the sales, leaving two-thirds to three-fifths for the expenses and profit of the lessee. A yearly rent may be imposed, after an approximation has been learned of the probable value from the bygone practice. Royalty. Slates are a primary formation of rocks, crystalline, hard, and durable, Slates. and are laid in vertical strata, thin and fissile, with laminar openings. They are used for roofing houses and are very ex- tensively quarried in Wales, and in the west of Scotland. The larger rocks are parted by wedges and levers, and the fragments by hand tools into smaller sizes. Slates are only found in the primary districts, and are wrought on a royalty, as may be due to the demand. Flagstones, wrought. Clay. Flagstones are used for laying pavements, private roads, and the floors of houses. The rock is found from the primary schist to the uppermost sandstone, in which formation it chiefly abounds, and constitutes a very useful article. The bed is raised in the natural divisions, which are afterward separated into use, as can be effected, The quarry is conducted as formerly described for building stones, and the royalty or yearly value is fixed in the same way. The stone is mostly siliceous, with a base of clay and sometimes with limestone. Clay is an alluvial formation that is of vast extent in some flat countries, and the presence of it can be traced from the decomposition of soft felspar in the primary rocks, to the sub-ærial deposit of fresh water alluvium, attending every formation, and contributing very large- ly to mark the connections that serve to exhibit the various stages of the ascending series of deposits. Argillaceous schistus is the first type of the body of clay, and from that primary rock, in the form of shale of very various qualities and conditions, clay is an accompaniment of every deposit, and a very strong indication of the increasing existence of soft materials in the structure of the globe. The first deposits of clay that are exposed to view, are very viscous and tenacious in the texture, from hav- ing been suspended in, and deposited by marine water, as is clearly indi- cated by the presence of the spoils of the ocean. Other beds are much more friable, having been washed by fresh water, and deposited by its agency. Finer kinds. The finer clays, or those that are most pure in silica and alumina, are used in making porcelain and pottery, and the more mixed sorts are manufac- tured into bricks and tiles. For both purposes, the essential quality is the kneadable property, by which when moistened, the clay can be led into any shape by hand or tool. Porcelain clay is the finest; pottery is made of the second quality; and bricks and tiles pro- ON LANDED PROPERTY. 1001 ceed from the inferior qualities. The first kinds of clay are the decompo- sitions of the older rocks, in veins or small beds, whence the substance is excavated like metals, and sent to the special manufactory. It forms a very distinct employment, and is not of great extent in Britain. Inferior qualities. The inferior clays are mixed with other substances, from having been exposed to different combinations, and to the affections of external agencies. The foreign substances are lime, iron, manganese, potassa, and bitumen, in very different quantities and combinations, most of which substances tend to make the clay fusible. A certain degree of fusibility is required both in pottery and bricks, in order that the ma- nufactured article may be rendered capable of resisting the absorption of moisture; and in all the natural clays, even the purest employed in the arts, the foreign bodies exist in them to the degree of producing fusion. at certain temperatures. Very early ages of the world used vitrified or fused clay in the forma- tion of vessels, and the use of brick as a substitute for stone in building seems to have had a very early date. Clay for bricks. Clay that is fit for bricks is found in many parts of Britain: it must be free of stones, plastic, and capable of forming a stiff paste with water. Lime is added to some clays to produce a tendency to fusion, and is used as powdered chalk, or marl. Sand also is used for the purpose of preventing too great a contraction of the clay in the fur- nace, and it must be as siliceous as possible. The quantity is soon deter- mined by experience, and must not make the bricks brittle. The best clays are those which already contain the portions of lime and sand that are necessary for the above purposes. Coal cinders are added to clay, and prevent the contraction of clay in burning, in the same manner as sand; the iron of the clay is de-oxidised, and the bricks are yellow, a colour which is valued in building, and the durability is increased. Certain clays resist high temperatures, and constitute fire bricks, as the constituent mat- ters exist in some definite proportion. This clay is scarce, and is chiefly found in the shales of the coal formation. Digging. The beds of manufactured clay are several feet thick, or lie in very ir- regular deposits. In certain cases, it is dug and used at once; but most generally and beneficially, it is raised from the bed or clay pit, laid in shallow heaps before winter and in quantity enough for the work of one year. The harder matters will be reduced by exposure to the air, the parts will be blended together, and the whole mass will be mollified. In most cases, one winter's exposure will prepare the clay; but in some instances, two, and sometimes three, are required; and in all cases, a long exposure is beneficial. The clay is several times turned over and moistened with water, and if sand or lime be re- quired, this is the best stage of the process for mixing them intimately with the clay. Straw or turf is frequently laid over the clay after being prepared in this way. Soil and stones are carefully removed when the clay is moved from the bed. The clay mill or pug mill next cuts the clay into minute shreds, as it 3 Q 1002 ON LANDED PROPERTY. Working. passes downwards through the action of arms and knives, which are im- pelled by the power of horses or steam. The clay is then ready for being moulded into any shape, either by manual labour, or by ma- chinery. The clay is thrown with some force into the mould, smoothed over the top by a ruler of wood, which compresses the clay, and fits it to the mould. This is the mould for flat articles; for bended and arched purposes, a slice of clay is fitted over the mould, and pressed down upon it: the moulds being removed, the shaped clay is placed on the shelves of a drying shed. An expert moulder will form 5000 bricks in a day, and 1500 to 2000 draining tiles. Bricks for drying are Drying. built in walls with alternate interstices, which allow the circu- lation of air: but for drying tiles, shelves are used in long sheds of various sizes, as the extent of works may require. An ordinary work will need a shed of 150 feet long, 18 feet wide, and 6 feet high. The sides of the shed are hung with canvas cloth, which is run up on rollers, when the screen is not wanted to prevent the effects of frost. The roofing may be of slates, tiles, thatch, or boards, as the climate may require. The tiles must remain in the shed till sufficiently dry to bear the heat of the kiln. This time will vary from four to eight days, according as the weather may be dry or moist. Baking kilns are of two kinds; clamps for preparing common bricks, and close kilns which harden tiles for roofing and draining. The clamp is an oblong heap of bricks placed above each Burning. other longitudinally and transversely, leaving intervals for the passage of the air: fuel chambers are formed on the ground of fire-bricks, entering from the opposite sides of the heap: from these flues, cross ones are carried at right angles into the intervening spaces. The fuel is put into the chambers, ignited, and the clamp is gradually heated from the bottom upwards. More or less fuel, and the enlarging or diminishing the orifices of the fire-places, will regulate the combustion, which is slow at first, and gradually increased to the required intensity, and after a suitable time, the furnaces are closed, the fires extinguished, and the bricks allowed to cool. Kilns. The close kilns act upon the same principle, and the heat being con- fined within walls, can be raised to a greater intensity by an equal expen- diture of fuel. An oblong building with a set of fuel chambers along the sides, which are prolonged into flues, contains the tiles placed interstitially from the bottom to the arched roof, and best when set on end. Cross flues of fire-bricks convey the heat uniformly over the extent, and the vapour or heated air escapes at the top by vents for the special purpose. The fire is put into the chambers, and the heat ascend- ing warms, dries, and bakes the tiles of clay, by the rising current of air, and by the contact of the tiles with one another. The slow fire is gradu- ally increased, and kept burning till the tiles are baked, which will require about seventy-two hours, according to the construction of the kiln, and the degree of heat maintained. When the tiles are baked, the fires are extinguished, and the mass is allowed to cool. Different constructions and ON LANDED PROPERTY. 1003 operations are used in making kilns which are more or less perfect, and may yet be much improved. Tiles. Draining tiles are now mostly made by machines, of which the most approved are those of Mr. Anislie and Mr. Etheredge. The clay passes. between rollers, and hence into apertures which contain the mould that is wished, and from which the clay comes in the shape of the intended use. Some differences exist in the construction of the machines, but the purpose is effected as above mentioned. It is doubt- ful if any advantage is gained by the use of machinery in this respect. The article is not so well manufactured, and cheapness never can consti- tute true economy. For draining tiles a good article is essential, as the damage is removed from view, and is placed beyond repair. An insuf- ficient preparation is beyond all other things to be avoided. Quantity. The manufacture of bricks, in Britain, exceeds fifteen hundred millions yearly. The production in England, and the economy of la- bour exceed all other countries, but not the quality of the article, being inferior to Holland. Brick grounds are rendered useless by the dig- ging of clay for any future application, at least for a long period of time; and the land may be sold for that use, a lease granted for a cer- tain extent of ground, or a royalty claimed on a specific num- ber of manufactured articles. Rent, CHAPTER X. EXPENSES OF AN ESTATE-REGULATIONS OF DIS- BURSEMENTS—AND RELATION OF THE PRIATE EXPENDITURES. APPRO- Expenditure on a landed estate. It is a fixed law of nature that all bodies tend to change con- dition, which terminates in a total decay and disappearance from a state of being. This tendency exists in all formations, whether organic or devoid of functional progressions; and is quick or slow, according as the natural constitution may be soft and pervious, or compact, hard, and durable. Inorganic bodies are slow in decay, but are liable to a disintegration of the parts, which impairs the quality and de- feats the purpose of use. Vegetable bodies are quicker to decompose from the greater number of component parts, and the natural quality of the different kinds that are produced. Slow growths are the most durable, as the parts are more exposed in the congregation, and hardened by the ex- ternal influences of affection. The inorganic creation does not allow these circumstances, and the condition is less changeable, but still liable to nature's general law. When these materials are used for the purposes of utility, the Materials for best quality that can be procured is chosen for the special appli- repairs. 1004 ON LANDED PROPERTY. cation, and adapted as the most experienced knowledge is able to direct. Stones and For the building of houses and walls of any kind, stones are preferred to bricks, in all cases where the former materials can be got within the bounds of a reasonable expense. But in alluvial countries, and where the distance of carriage and other circumstances render difficult the provision of stones, the use of bricks is adopted; and being an artificial production, that material for walls becomes more easily decomposed, especially if the clay be indifferent in quality, and the manufacture into bricks has been improperly executed. Not only the getting of these materials forms a chief consideration, but the quality as to fitness and durability must con- stitute a very large item in the estimate that is being made of bricks. any undertaking that requires the use of the materials. Expense being equal, or so nearly balanced, as that the superior eligibility of stones is able to cover the difference, no hesitation can happen which of the ar- ticles will be used; and a consideration may be added of the extended superiority which the harder material will evince beyond the present cal- culation of the applied utility. Where the cost of stones does not exceed fifty per cent. more than bricks, the choice will be justified of the rocky body, as the durability will recompense the surplus in requiring less re- pairs, and in constituting a better erection in every point of view. But where the balance of cost amounts to nearly one hundred per cent., the brick must be chosen, as that amount may never be repaid during a long currency of the necessary repairs. If the stone be sandy, and belong to the soft deposit of rocks, the decay will soon com- mence; exposure very much affects earthy aggregations that have not been removed beyond the influence of its power by the force of fire or a very minute cement. This quality is soon determined by experience, and has a very large effect in determining the eligibility of building materials, as the choice may happen in different localities. Bricks must be calcu- lated in the same way, not only in the primary cost, but in a strict rela- tion of the future value, as shown in the quality of duration. This attachment to any article will very much adjust the equilibrium against a greater original expense of purchase. Sandstones. Timbers. The use of timbers is regulated by the same rules of consi- deration as the choice of stones and bricks. The hard woods are used for purposes that are exposed to external actions which promote decay, and the softer qualities are adapted for use in situations that are covered from damage, and sheltered from violence. The timber roofing of houses being covered from exposure, is constructed of firs, which, being kept dry, are nearly equal to the hard woods. Timbers kept in one state, wet or dry, will last long; it is the change of conditions, from wet to dry, and from dry to wet, that tries the constitution of the timber, and which marks the quality of quick and soft decay. Friction, or the attriting con- tact of other bodies, in constant or frequent applications, imposes on tim- ber the special adaptation of purposes, as it requires a quality similar to that which resists decay. All posts sunk into the ground are required to ON LANDED PROPERTY. 1005 Decays and be of hard timbers, and very much of the inside furniture of barns, stables, and cow-sheds, and also of cottages and dwelling houses. In all cases of exposure, or a more frequent use, hardness must be repairs. applied, and the best quality of it selected. Reason and conventional agreement have established the relation be- twixt landlord and tenant, or the permanent and temporary occupier of the soil, that the former affords the raw materials with which to uphold the decays of nature, and the farmer puts the articles into form, and places the adaptations into use; and also that general decays, or a universal failure of any permanent articles, are wholly replaced by the landlord ; the farmer doing such a part of the work as the agreement has understood, or a posterior arrangement may dictate. But for the purpose of restoring and upholding all the small decays and tendencies to damage that may occur during the lease, the farmer gets, without price, from the owner of the soil, felled timber, lime, stones, and bricks, at the respective places of manufacture, which are carried to the required uses and timeously applied. On a neglected estate, where decays and dilapidations have been Total dilapi- allowed to progress, and to escape observation and attention, this expense to the landlord will amount to a sum; but under all correct and systematic management, the item will be trifling, except it may be for once in ten or fifteen years, when a wholly new erection of buildings, or some part of a farmery becomes necessary; then a due allowance must be made by scattering the special sum expended on that point over the lease of the farm, and distributing it on the general outlay. A notice of it must be taken before and after the event, and by contracting the outlay of some years, prevent the expenditure of the special year from exceeding the average of the general arrangement. In this way an equitable distribu- tion is created and maintained. The upholding and restoring of decays of perishable materials, includes the preservation and restoring of watercourses and beds dations. General repairs. of rivers, the repairing of roads, the repairing of very old fences, or the making a new one in its place, and all purposes of repair in which any wholly new undertaking is not performed. Such expenses will inevitably occur in every case of using the surface of the earth, and the more vigi- lantly the wants are noticed and supplied, the expense will be less, and the general benefit will be greater. The very beginning of a want must be checked, that it may not grow into a gap of wide dimensions, in which more means may be spent than would have repaired many beginnings. These things require an active and vigilant superintendence, and a prompt and spirited execution. Circumstances of locality and special position will very much influence the amount of expenditure that may be required for the purpose of up- holding in current-going order of a proper and sound condition all the articles of decay which a landed estate will present to that department. The size of the farms, in being small or large, will affect the cost of the repairs of houses; the intersection of the estate by brooks or rivers will require a greater or less expense, as the courses are few or many, Prompt exe- cution. 1006 ON LANDED PROPERTY. and the roads are sometimes so arranged as to make a sum of some magnitude in the upholding. Very much will depend on the activity of management that is displayed, and the orderly system that is adopted in the vigilance of detection, and the promptitude of supplying the inci- pient deficiencies that may occur. The economy of this management con- sists not in withholding the outlay that is necessarily required in order to save expense, but in doing promptly what must be done in due time and in the proper place. No greater fault than neglect can occur in the management of business, especially when the growth of the evil proceeds increasing as time progresses. Per centage In all ordinary cases of circumstantial attachments, and where of cost. a tolerable exact system of management has been adopted and prevailed for some time, the sum of five per cent on the rental of the estate is found sufficient to uphold the retrograding condition that attends the articles of use in realizing the value of the ground. But where a dilapi- dated condition has been allowed, and where local circumstances demand a corresponding attention, a variation rises to ten per cent., denoting an average of seven or eight in cases of the medium circumstances of attach- ment and position. If a sum near to ten per cent. be required for a time, it may soon be reduced by a vigilant attention and enlightened system of management; and if that figure be exceeded by reason of some previous negligence, the extent may soon be curtailed within that sum; and the better way may be not to exceed it in any case, but to proceed gradually, and accomplish yearly what can be done with that amount of money, always executing in the first place the most necessary requirements. This mode may answer better than to make a very large expenditure in one year, and do nothing in the next, except when imperative circumstances require such a course of proceedings as has happened, and no doubt will again In these cases, the average expenditure must be regulated by the occur. In a course of years. course of five years; beyond which time no extra amount beyond the allowed medium should be carried forward to embarrass the next period of that amount of years. Each year must be kept as nearly as possible to the sum that is allowed and fixed for the special purpose; and no proceedings of any kind are to be left to uncertainty where they can be fixed. Extras and accidents will require deviations which are soon ascertained by the lapse of experience, and reduced to the original regu- lation, and made a part of it. As was before observed, the replacing of an old erection of any kind by a new structure, falls under the department of upholding the decays, for a similar thing stood there before, whereas a new erection understands that nothing of the kind had ever before appeared. The execution of wholly new undertakings on a landed estate takings. deserves a consideration that is widely different from the repairs that are required to uphold the value that is being derived. That depart- ment of outlay admits no dispute, it only needs a regulated disposal. Original executions will be various: in making new roads, new planta- tions of trees, cutting watercourses, or new beds for rivers, consolidating farms, and erection of dwelling-houses for tradesmen and mechanics-these New under- ON LANDED PROPERTY. 1007 Waste grounds. Plantations. objects require a very careful and attentive consideration of the concomi- tant and combining circumstances which may seem to justify the execution. It must be very readily granted that all grounds that cannot be ploughed, or any way improved, and which do not yield a natural pasturage of some little value, should be planted with trees, as a crop of timber may be got of some degree of quality, and the land is improved for the future arable cultivation, if wished to be restored, and if the surface formation will allow the use of the ground for the use of aration. If water can be conveyed to irrigate the surface, the value may be well used in that way; or if the ground can be improved by a top-dressing with composts, the planting with trees may not be eligible. But precipitous grounds, rocky declivities, and slopes that are beyond practical use, do not admit one moment's hesitation in being converted into a plantation of timber or copse wood, according as the nature of the ground and the demand of the locality may direct. A coppice will return a value in eight or ten years, when the circumstances are mediately favourable, and at most in fourteen years, when the best use of the growths requires a lengthened duration to attain the necessary maturity. The quickest return in value from timber trees comes in about thirty years from the fir tribe of plants: the hard timbers will require a period of nearly sixty years be- fore any part of the expense is returned which has been incurred. During that time the outlay lies dormant at compound interest, and in sixty years will be quadrupled in amount, and doubled in thirty years. All these considerations must be duly and very carefully weighed in estimating the propriety of an undertaking in planting trees, and discover if the use of money could not be more beneficial in some other expenditure. But many situations will occur where no other use of the ground can be devised, or is rationally possible, and then the calculation comes to be the extent to which the execution may proceed at one time, or at distant intervals. A large performance may throw a burden on the property that is too heavy for its position, and the improvement may be too extensive to form a pro- portionate part of the aggregated extent. The amount must be New things duly regulated by the circumstances of the proprietor, and the special capital that can be spared to the purpose of general improvements. A certain quantity of money should be allowed for this special purpose, in all cases where the requirements are in existence; and but few situations are found where the wants do not happen. New plantations are not by any means to be included in the charge of five to ten per cent. for the pur- pose of upholding the current-going value of landed property; that allow- ance only supports a value, and does not create any source of deriving an income. All creations that are wholly new, are to be entered in an ac- count that is altogether disconnected with any other rendition, and distinct. the outlay is sunk for many years, and a heavy interest charge. comes against the proceeds that may be realized. It is true, that a trifling expense is incurred yearly in carrying forward the increase of plantations, in keeping clear the courses of water, and maintaining the fencible con- dition of the boundary walls. This balance, though small, assists in ren- 1008 ON LANDED PROPERTY. 1 dering more tolerable the long period of time during which no value is derived from plantations of trees. Loans of money used in three ways-drain- It may be again observed, that all grounds that are physically beyond any other purpose of application, cannot be too soon planted with trees, in tim- ber or copses, which may be very beneficially mixed in the position of enclosures, but not in the plants being placed in mixture. There is no doubt that loans of money now granted by government to drain wet lands will soon be extended to the two purposes of erecting farm buildings and planting waste grounds, and both uses are ing, planting, fully as necessary as the removal of superabundant water; and no more just and beneficial burden can be imposed on landed property than the performance of these three purposes, which increase the quantity of the necessaries of life, salubrify the air, add to the lasting value of the property as an article of commerce, encourage the letting of it for temporary use, shelter the country, adorn the scenery, and contribute in a variety of ways to the comforts of the people. and building. Extra pur- The raising of new embankments, and the cutting of water- poses. courses in an original direction, forms another item of general expenditure to be charged to the account of improvements. The return arises from the estimated advantage that will accrue from the performance in a larger abundance of some articles in a certain quarter than would have been produced or were grown if the new work had not been done. This calculation must go beyond a barely ideal existence if at all possible to be attained; the accruements must be clearly obvious, and almost firmly tan- gible, in order to justify the expenditure on points that require to show certainties in the returns. These executions require a yearly charge in upholding the useful condition, and consequently, the inducements of per- formance must be stronger on that account than where one action suffices for a long period of time. These occasional or probably constant repairs are included in the charge of upholding the current revenue of the pro- perty, and must be put under the regulation that apportions the yearly amount of that expenditure. The cutting a river course may be divided by two parties that possess the opposite sides of the river, and will be mutually benefited by the alteration, when each side of the banks will be defended by the proprietor, and the cost included in the charge of yearly repairs. The building of new jetties of stone works, in order to throw the course of waters into a mid-channel, and save the banks from being wasted, will go to the charge of upholding, as the want of the article may incur a much greater outlay in erecting the same protection after an extensive evil has been done. These structures for the purpose of preventing future evils that may be of a great, but are still of an uncertain magnitude, differ from the requirements that are needed for the purpose of warding off constant occurrences, as floods of water and rise of tides; the latter operation being once done, the repetition is unnecessary; in the for- mer case, the uncertainty of coming storms renders a constant employment in the protection of the alluvial banks. Such employments are to be added to the account of protections, as distinguished from total alterations, Rivers. ON LANDED PROPERTY. 1009 which first confer a benefit, and then require a yearly charge to enable the continuance. Roads The making and maintenance of roads does not in every case form a separate charge on landed property. The turnpike roads are managed by commissioners, who need no local assistance: the public roads of local use are, or intended to be, supported by a fixed charge on the ren- tal of each farm, which is to this day, in most places, badly arranged, and imperfectly executed. But when a new road is formed, or an old one re- constructed, the proprietor of the land is always expected to bear a chief part of the expense; when the item must be charged to an expenditure for which no value may ever be got, but an improved passage of use, and a benefit conferred on the public at large. It would be a very superior arrangement that all the roads on any estate of land be managed by the chief direction of the agent on the property, and the acting power under the delegated by him to a subordinate in office under his surveil- agent's care. lance. In that case, the whole expense would fall on the landlord and the farmers; the latter bearing the one-half of the expenditure, and the other moiety attaching to the owner. This outlay on the property must be charged to the yearly per centage of use, as it goes to uphold the current value of the property in the provision of roads, which form the first consideration in the lasting improvements in any country or division of territory. Ano- ther arrangement will charge the land-owner with making all the A beneficial roads, and that the farmers uphold them; but most of the neces- arrangement. sary roads are now made in Britain, and the landlord would escape the fair contribution. But where new roads are required, the owner must bear the original outlay, and also the future share of the necessary repairs. The charge made on the rent of each farm for the purpose of roads, will be paid to the agent at the half-yearly audits of rent. The mode is used in some few instances of the roads being managed by the estate agent, and the benefits are very evident and frankly acknowledged. The farmers being only temporary occupiers of the ground, no part of their funds must be applied to the structure of permanent erections; the land-owner is the liable person, and also for a fair share of the future requirements to up- hold the value. The landlord gives a share in upholding buildings on a farm by giving raw materials in lime, stone, and timber; so in upholding roads, after his cost has made them, a share must come from his property to maintain the articles in use. This charge, where it is come into use, will be included in the per centage of repairs. Bridges. The building of bridges is generally a private concern of the land-owner, or of subscription among the neighbouring pro- prietors, when the possession of it evidently assists their advantage. At all events, such a thing is wholly beyond the province of the farmer, and it is also removed beyond the charge of repairs: it is an original edifice, and needs no future amendments that can form a charge. The owner of the property is always expected to make the largest contribution, and very justly in many cases, as his property will be most largely benefited by the erection. But instances are not wanting where the public will be 1010 ON LANDED PROPERTY. equally, if not more, advantaged than the property itself by the projected means of traffic, when the owner of the soil may be allowed an equality Singly or with other subscribers. If any landed property does not exist doubly useful on both sides of the bridge, the advantages are not so large to the benefit of the patrimony; the bridge is only a public transit through the estate; but when both sides belong to the same property, it is a means of communication, and becomes doubly valuable. All these considerations occur in estimating every kind of outlay on the estate of land; the private advantage to the owner, the general benefit to the country, the charge re- quired to derive undiminished the current-going yearly revenue, the amount that can be allowed to general improvements which promise a distant return, and what sums the extent and value of the property are able to give in extras, as contributions and subscriptions, for objects of public utility. It is an important point to fix the relation of the several points of ex- penditure on an estate of landed property, or the respective amount of the items which constitute the gross outlay over the whole extent. For this purpose it is necessary to ascertain the most valuable points of outlay, or those which return the quickest value for the money that is ex- Purposes of outlay. pended, and the steadiness of the source which forms the spring of revenue. Two items constitute the chief outlay on landed property—— farms and the plantations. The last point is contained in two departments, or the making of plantations, and the cost of protecting those that have been made, dividing the outlay into two accounts, which must not be con- founded together, but separately arranged; the two amounts being added together will show the gross outlay in the department of plantations. The growing of timber makes slow returns, and at distant periods of time; the thinnings, if any, consist of worthless under-growths, which fetch little money, and do not repay any part of the original cost, if the value upholds the current item of expense. But on most estates, a quantity of timber will be found that is full grown and ready for sale, and by a certain quantity of yearly value from that source, the current- going expense will be covered, and a surplus be derived for the rent of the land. When oak timber is produced, a double chance occurs in the wood and bark as articles of value, in obtaining a revenue from the plan- tations, which contributes very much to the value of the grounds. A yearly fall of timber is to be recommended in all cases where the articles are found; if not yearly, then in the time of two or three years, a sum of money, less or more, must be got from that use of the land. The regula- tion is imperative, that on all estates which contain woods of the proper age, an income be derived from the sales of timber which shall cover the cost of upholding, and if possible, a surplus be accumulated that will de- fray the expense of making new plantations, in some part, if not the whole of the outlay. From the revenue of the plantations a per cent- from them. age must be deducted for the current-going expenditure, which will not be large, but still forming an item. The very varying conditions of estates of land in quantity and quality of timber, and the uncertainty of Woods. Revenue • ON LANDED PROPERTY. 1011 the value of the article, render impossible any nomination of the amount of the per centage; the sale being large or small, adds to the difficulty, and the figure must be left to the circumstances of each particular case that occurs. Where no timber exists that can be sold, then the cost falls upon the rental of the estate, when the average per centage for the purpose of plantations will not exceed two to three per cent., or about one- None but an third of the cost in upholding the current value of the farmed outlay. lands; and it will require an estate of some magnitude, and woods of very considerable extent, to use that allowance, except in cases of making altera- tions and improvements beyond the currency of procedure. In this calcu- lation there are not included the timber of pleasure grounds, or of parks and policies; these places are isolated from common touch, and are not de- pended on by any estimate of value. All hedge-row timbers over the estate are contained in the calculation, and the same purposes of use are attached. Copse woods, if any, are comprehended in the account, and ranked with timbers in the general estimate. On estates of old improvement that are proportionately Young plan- wooded and enclosed, a yearly rental should be derived from the tations. produce sold, or at least the current expenses should be paid by the arti- cle which requires the protection of cost. Cases will occur of under-age plantations, when no value can be got, but must be waited for till the tim- ber is matured for use. A yearly item will then be expended in the pro- tection of the plantations, which will vary with the many circumstances of extent of grounds, situation, locality of the fields, and the exposure of situation. Rent of lands The yearly revenue that is steadily derived from the lands that are let in farms of temporary occupation, requires an atten- tion much wider than that of plantations, and a larger allowance in pro- portion to the value of the source of income. The produce of land being yearly in its nature, the value is annually derived; and as the recurrence is steady, and not liable to any omissions, the more attention is required that no wants be allowed which may impair the yearly revenue in the necessary attachments. Plantations are in general an improving department, at least to a certain age; the appurtenances of a farm are decaying from the very day of erection, and demand the care of upholding in order to continue the income that is got from their use. This very essential difference renders necessary a much larger allowance for the support of the most valuable department, and as it constitutes the chief part of the property, it must be first considered, and have the proper estimation. A per centage on the gross rental of the estate in five per cent. has been found to uphold the sufficient in cases of well-regulated estates, and of business judi- ciously administered, where former carelessness creates no large demands, and fortuitous circumstances have no large possession. A variation to ten per cent. has been allowed to meet the cases of extraordinary demand that arise from natural causes, and from the bad administration of former offi- cials, or from some undefinable or incontrollable cause which may have ceased after a time, and then the work of regeneration must commence. Per centage value. 1012 ON LANDED PROPERTY. But these extremes of extra charge are not to be included as common de- mands, and should be noticed as examples to be avoided rather than models of imitation. Few or no cases should reach the medium figure of seven and a half per cent., which shows an outlay beyond the justness of good regulations and a sound apportionment. At the same time, few or no Not to be ex- estates will need less than five per cent., unless a niggardly par- simony be allowed to exercise its sway, and create many wants to demand on some future day an expenditure much beyond the amount of savings which it is able to show at the present time. This policy but too often prevails, and is attended with much loss and inconvenience. ceeded. By taking seven and a half per cent. as the average allowance for upholding an estate, and the cost of the plantations at one-third of that sum, there is got the figure of ten per cent. as the amount of these two expenditures on landed property. Cost of gar- Gardens, policies, and pleasure grounds, form a part of the dens, policies appropriated use of an estate of land, and require a proportionate and pleasure allowance for the maintenance. These establishments form an grounds. article of luxury rather than use, and no tangible revenue is de- rived from them; yet a burden is created on the landed estate, and a con- sideration is due to the department when the parts of any estate of land are regulated in calculation. Plantations make a return in some annual sums, or in more years' amount, or a large value is obtained from a general fall of grown timber, which must be distributed over the years in which no income was derived. But gardens and reserve grounds never show a return of any value; the whole produce disappears, and the cost of pro- duction must come from another source, or the rental of the property. The extent of these appropriations will depend on the extent of the property, the family of the owner, and if the domestics are constantly resident; but in general cases, a per centage of two and a half per cent. will suffice for a genteel and moderate establishment, where prudence and economy are duly entertained. Thus, two and a half per cent., added to ten per cent., as shown before, makes twelve and a half per cent. for the current-going yearly cost of supporting the yearly value of a landed estate, and allowing two and a half per cent. for extras in contributions and subscriptions for purposes connected with the property, there is got the sum of fifteen per cent., as the gross estimate of maintaining a landed estate. The average may be stated at ten to fifteen per cent. Whole per centage. ON LANDED PROPERTY. 1013 CHAPTER XI. VALUATION OF LANDED PROPERTY; OF THE SOIL, OF HOUSES, OF WOODS, OF MINERALS, OF MANORIAL RIGHTS, OF ROYALTIES, AND OF FEE FARM RENTS*. valued. LAND having become an article of commerce is raised and depressed in value by the same laws and contingencies as other commodities that are used for profit and advantage. The value of a landed estate, as Land how the subject of sale or purchase, is primarily determined by the free rent which is produced from the use of it. This rent may be calculated from certain assumed rates of farm produce-but the simple determination proceeds from the marketable value of the land, or the amount which can be got for it by the farmers of occupation. The probable rent is diminished by all the burdens which affect the land, as land-tax, poor's rates, tythes, and any other burdens which fall upon the land, and not upon any other securities. The net rent thus obtained, is to be multiplied by such a number of years' purchase as land produces at the time in the market. This expression shows the amount of interest which the buyer calculates upon receiving from his purchase- Interest of money. Thus, if the number is twenty-five, or if the purchaser pays twenty-five for every £1 of free rent, being in common language twenty-five years' purchase he will receive four per cent. for 25 : 1 :: 100: 4. purchase. If the market price be three years' purchase, he will receive three and one-third per cent. for 30 : 1 :: 100 : 31. The common rate of interest should determine the number of years' pur- chase; but the demand for land, as compared with other securities exerts the same influence, as in all other cases of transactions in selling property. When the sum of five per cent. constituted the rate of interest in this country, the common calculation reckoned land to sell at twenty-five years' purchase, or, in other words, that it should yield four per cent. of interest. But this proportion is not now upheld by land—the market rate of interest scarcely exceeds three per cent., and land is sold at prices which does not even reach that figure. When it is wished or fixed to have a certain rate of interest Per centage from land, the number of years that will yield the amount being expected. multiplied into the net rental, the product will exhibit the amount of the purchase-money, which must be increased by the estimate of woods, mines, or other adjuncts, and diminished by all incumbrances that may exist. The present value must be ascertained, as in the case of annuities, and the amount deducted. An annuity of £100 yearly for ten years, * See also examples of practice, pp. 620-631. 1014 ON LANDED PROPERTY. Leases of much con- sideration. payable half-yearly, and at the rate of three and a half per cent. interest, is worth £837 12s. 10d. to be deducted, and so on with all similar cases. A heavy consideration is due to the leases of land, if the rents seem equitable, or low, that no advantage may be expected, when the holdings expire, or that a rise of rental is evident. Leases which are long in expiry are generally reckoned adverse to the selling of land, as the chance is distant of deriving any advantage that may occur. But no large calculation can be founded on these probabilities, which are at best uncertainties, unless the rental be very palpably under the average of the common estimate. In that case, and where several cases are found, an inducement may be formed to advance the offer of purchase, as a realization is evident of the increased amount. Farms that are underlet, and which are held by lease, constitute an annuity in the amount of the yearly deficiency, and the same thing as if the money was paid to a recipient quarter, instead of not receiving it from a source of proper value. If a farm have ten years of lease unexpired, and the rent be evidently £100 too low, then the sum of £837 12s 10d. is to be deducted from the purchase-money which was shown before to be the present value of £100 for ten years paid half-yearly, and reckoning in- terest at three and a half per cent. These deficiencies on the wants of the Encum- brances. realized value, are encumbrances upon the property, and tell heavily against the market value of land. But such cases do not often occur, as values of every kind have now been well ascertained, and in a period of time and under circumstances which exclude the rational ex- pectation of any great change. Condition of The general condition of an estate of land will very largely the estate influence the amount of the value, in its being forward in con- dition, well regulated, and under the due administration. If the appur- tenances of the farms show extensive dilapidations, and will immediately require a large outlay of money to execute the necessary repairs; if the roads. show an incommodious condition, and need any considerable restoration; if the plantations exhibit a state of neglect, are open and exposed to depreda- tions; and if the fences are broken down, damaged, and misthriven, too few in number, and ineffectual in the purpose, a very large drawback will be formed by the aggregation of such items, and the money that has been saved by the parsimony of neglect, will now be deducted in a greater sum from the expected amount of sale. Articles that are exposed to view for the purpose of vendition, must be exhibited in the very soundest possible condition, as the flaws are the objects of observation, and are always magnified rather than lessened, or even fairly estimated. A hurried preparation does not exhibit the proper and necessary train of enticing appearances, that are necessary to secure an approbation of willing invest- ment: the newly raised exhibitions are seen through, and raise a suspicion of other coverings being purposely used. Only a long and continuously persevered administration of care and economy, can exhibit a landed property to the eye of purchase in the garb that will both suit the fancy and please the judgment: show an article must be sound and pleasurable. ON LANDED PROPERTY. 1015 for the delight of the mind, as well as profit to the pocket. In making these preparations, it is only necessary to consult the current condition, in articles of lasting utility, and of durable pleasure. These purposes suit both views, of present possession and of future dismemberment. Many, or nearly all estates of land that are of any considerable extent, possess houses that pay rent, either in single tenements, or in congregated villages. The property is more perishable than the land Houses pay- which is cultivated, and repairs are regularly required to sup- ing rent. port the tenantable condition. The per centage on the rent of houses to uphold decays, is to be deducted from the yearly amount: but it is generally included in the general per centage over the estate, and is not separated in a distinct account, except the village be large, and yields a revenue that deserves a classified consideration. In that case, a distinct view is shown of the different values got from land and houses-the expense of maintaining the serviceable condition of each species of property, and the net revenue from each source, when the purchase cost can be distinguished. The decaying nature of houses requires a larger interest than lands, and consequently a smaller number of years' purchase. The interest being calculated at seven and a half per cent. in the common estimate, the number of years will be about thirteen and a half on the purchase number. The general number is below that figure, and falls even so low as one-third of the calculation in diminution. Villages In many situations, houses pay a very encouraging rent of a property in land. In manufacturing districts, in convenient fishing stations on the sea coast, and in places where mechanics abound, the erection of cottage dwellings becomes a good outlay of money-the rents are small, and easily raised, and are generally well paid. The source of employment and the means must be first discovered, and the permanency of the undertakings. When these provisions exist in a moderate degree, no more beneficial ornament can be conferred on a landed property than a number of conveniently located and suitably provided cottage dwellings, showing health and contentment, and nursing the bonds of union, and the sinews of the nation's strength. All such habitations must be under the management of the landlord, and not placed under the dominion of any farmer, except where the domiciles answer the express purpose of lodging the labourers of the farm. In that case, the property ranks as a provision of the farm, and is merged into the value of that de- mer's care. partment. In sequestered localities that are removed from the conveniences of the parish village, and where farms of land are regularly constituted, it would be very advantageous and beneficial to establish a village by the means of the proprietor, import the raw materials, export the produce, employ labour, and circulate money. A value would be given to the property, and if circumstances are moderately favourable, the adverse ones may be turned into sources of nutrition. not the far- The foregoing remarks only apply to houses that yield a rent, or are capable of yielding a revenue, and not all to the houses of the farm, which instead of being placed to the value of the land in the proper number, are to 1016 ON LANDED PROPERTY. Separate be deducted from the purchase-money, when they are seen to be deficient in the necessary provision. The amount that may be estimated to erect the required habitations must be deducted from the number of years' purchase. Woods are determined in value on several data: full-grown timbers are estimated by the selling price, lessened by the cost of felling, and the ex- penses of sale. The improved condition of the land may be reckoned, when an arable state of the ground is intended to be done; but it is mostly replanted with young trees. A calculation can be formed of the number of trees on an acre of ground, and local experience will be able to form a value of the single trees, and thence of the acre, and of the total number of acres in the plantation. It is best that the seller has the trees felled by his own work- men; and in some cases, an eligibility may occur, that the trees be dragged outside the wood by the same employment; but if this last per- formance be not done by the seller's execution, the felling of the trees is very properly done by that part of the transaction. Distinctive marks separate the trees, so that no confusion happens. Lots of bulk to suit a variety of purchase, may be laid outside the wood, and sold in divisions, or by the measured foot. And as before observed, it is much best, that the owner has the trees brought to that position, and that no purchaser enters the plantation. woods. When woods are not full grown, but vary in age from the year of being planted to the time of maturation, a different mode of valuation must be adopted. The cost of producing woods is usually applied as a mode of valuing young trees, and when the age of timbers approaches the full growth of use, the value of the wood when felled may be learned from Young plan- the knowledge of the value of timber, and the corresponding tations. deduction must be made in the number of years that will elapse till the maturity be attained. The land will be improved for the purpose of pasturage; and this consideration may form an item of some value in the estimate. The amount of the original expense of forming a plantation is increased by the accumulated interest from the time of out- lay to the time of sale, the amount of the annual rents, with interest from the period of planting to the time of sale, and the value of the land on which the wood is growing, because the cost of the land on which the wood is planted, is part of the cost of production. If land worth 10s. an acre has been planted with trees for twenty years, at £5 an acre of original cost, the value of the timber in this way will be as under :- Valuation. £. s. d. The sum of £5 principal and interest at 3 per cent for twenty years 9 19 0 The amount of 10s. per annum at the same interest and time The value of the land at 10s. an acre, at thirty years' purchase Value of the wood in twentieth year, per acre 14 2 10 15 0 0 39 1 10 This mode of valuing woods is not eligible, unless the age of the trees ON LANDED PROPERTY. 1017 be very young, or under ten years, when the approximation can be better made from the existing circumstances than from the distant value of the matured article. The calculation only shows what the cost has been to the seller of the land to bring into the present condition the article which is offered for sale; but it affords no index to the value of the materials after the lapse of many years, during which time the purchaser gets no revenue, and has to wait the expected return. The age of Age of thirty thirty years will bring to maturity the general average of plan- years. tations of fir trees, and sixty years may be allowed for the use of the hard woods, as oak, ash, and elms. In unmixed congregations of trees, the calculation will be based on these simple periods of time; but where the woods are of mixed kinds, an opinion must be formed of the relative quantities of each sort, and then assume an average number of years in which the maturity will be reached. This assumption may be forty-five years, which may be divided into three periods: 1, of simple growth; 2, of accelerated growth; 3, of matured growth: and each period must be attached with a definite portion of the ultimate value. The simple division of the return into three parts would not be a fair apportionment, for the trees during the first period of time will not attain any- thing like one-third of the matured value, and consequently a periods. reduced item must be attached. The middle division of time will in- crease the most rapidly, and will push the trees to the full height, and commence the hardening of the timber into the useful consistence. The third, or last period, will bear the largest value, as the timber gradually attains the matured state. A notice must be taken of the quality of the soil to carry out the growths of the earliest periods, and of the exposure to allow the statures; for not unfrequently the first growths are encou- raged by favourable circumstances which do not exist when an advanced stage of existence is attained. Observation will not fail to intrude the necessary deductions on this point. Three General objects. The first object is to compute the number of trees on an acre of ground, which may be averaged by observing the distance between each standard that prevails over the extent of the plantation. Then the probable value must be ascertained of the timbers when full grown, and felled for sale. The age of the plantation being known, and the time of full maturity fixed, as before explained, there may be given to the latter division of time, seven-tenths of the aggregated value of the timbers when sold, one-fifth of the same sum to the middle division of time, and one-tenth to the first fifteen years of the growth of the trees; and if the sale happens when the age is about thirty-five years, or nearly to seven or eight, then one-tenth is to be taken from the third division of the age, and added to the first apportionment. This becomes necessary, from the greater value which has been attained by the young growths in seven or eight years, than if the valuation happened at the time of three or four years; and the last stage of maturity is less in value at thirty-five years than if the calculation was made between forty and forty-five years. Be- sides these data, other contingencies will occur to influence the calcula- 3 R 1018 ON LANDED PROPERTY. tions, which must be alive to every observation, and open to every suggestion. use. Growing woods of any age that is below the condition of immediate use Woods below seldom or never in this country realizes the full value in case of sale, being reckoned a dead stock which the proprietor cannot use, or remove, or cut down without damaging his estate in the very essen- tial provisions of shelter and embellishment. Such acts would inflict a damage on the general value of landed property that would many times exceed the amount of any sum that may be shown by calculation, even the most correct and the most substantially founded, and hardly would any diminution of value compensate the loss or want of one of the chief ornaments of nature, as shown in clothing the earth with vegetable growths of low and high dimensions. In most cases of young woods, the plan- tations are generally reckoned a most necessary appendage to them. any extent of landed property, of which the value is scarcely entertained; but if wanting, the value would be largely accounted and urged as an abatement. The justness of the complaint cannot be denied, and urges the demand on all proprietors that the provision be not in any case neglected. The price of growing woods, however it may be estimated, resolves itself into a simple bargain, of what the seller can get for it, and on what sum the purchaser is inclined to give, after he has consulted his convenience, and has prudently weighed the combination of circumstances which occurs to justify the purchase of the property. The cultivated lands and woods constitute the solid basis of landed pro- Price of Land and wood, chief sources. perty; the other sources of revenue are only attachments, that are evanescent in the nature, less durable in the fixity, and more exposed to chances and accidents of disruption. The chief at- tention must be paid to these two sources of revenue, as they form the only permanent foundation of any sound procedure. The intrinsic qual- ity of any soil, and the value derived from it, are no doubt, the primary points of regard, as by them is fixed the sum of the revenue; but many cases will occur, where an extended view must be taken of the capabilities of the natural provisions as inducing the probability of profitable under- takings beyond the present realizations. The susceptibility of future Susceptibi- lity of im- provement. improvements is a quality in landed property that is often more valuable than the present condition of profit, for it holds out the chances that may occur during the progress of undertakings which frequently much exceed the original calculations. The presence of woods and of dwellings on the estate are essential to its existence as a patrimonial inheritance, or a source of revenue; without them, land is only a dreary waste possessing neither shelter against the storm, or food against the natural cravings. The strength of a nation is founded on the number of its people, and an estate rests for value on the number of its appurtenances, and the state of the establishment which is maintained. The existing state or manner in which lands lie, makes all the differences imaginable in the estimates of value and produce. The situation has very great influence, being near to towns, convenient to manufactures, or con- ON LANDED PROPERTY. 1019 nected with an advancing condition of elements. The temperature of situation is also a matter of notice, as it affects very much the value both of lands and woods. The social position of an estate of land Social posi- must also be considered, if the community be liberal-minded, tion of an or prejudiced, frugal in habits, or lax and dissipated. The habits estate. of industry and of social affection must not be overlooked, and if the capable improvements of the district be fully performed, or are only being commenced, or half-way progressed. In a case of large improvements being done, the supply of labour, and the demand for produce will be taken into account, and the conveniencies that are seen of making these provisions, as is possible in many cases, where the necessity may dictate. The probability of creating a revenue, as well as the certainty of getting an income ready-made, will weigh the scale of judgment in the ratio of the considerations that are brought to bear upon the subject, and a greater number of these items occur in the purchase and value of landed Probability property than in most other human transactions. The seller of a revenue. must be aware of the circumstances that will bring forward these consi- derations, and have the articles for sale in the best possible condition that can remove objections which act in any way to detract from the value of the commodity. Woods and buildings are the foremost of the appur- tenances of landed property, and no reasonable expenditure must be with- held, in order to make the provision of these two articles, that is conform- able with the property and the attending circumstances. Buildings are required to uphold the current going value of the land, and timbers are needed to construct and uphold the buildings, and both objects being ar- tificial productions, can be raised on almost any lands in Britain. Articles of fancy and show are not required beyond the precincts of the pleasurable demesne; the provision over the estate must suit the circumstances of use, and lead to advancement. In making planta- tions, care is to be used that no encroachment is made on arable purposes, as the value of woods is posterior to the growing of yearly crops, which supply the daily wants of recurring use. A due proportion must be ob- served of the present with the future purposes, unless the grounds show a large amount of useless surfaces over cultivable lands, when the expe- diency admits no doubt of the speedy conversion of wastes into some shape of utility. No articles of show. Mineral property of any kind is always reckoned a valuable Mineral pro- appendage to an estate of land. If none of the valuable metals perty. are found to enhance the value of the surface ground, and even coals being altogether absent, there may still exist a sufficient quantity of clay and building stones with which may be supplied the current wants of the pro- perty in the manufactured article of bricks and stones for walling. The presence of these articles, though none are sold to raise a yearly revenue, is a very large convenience to any estate of land, as it abrogates the neces- sity of foreign purchase, and tends to the constitution of the property as being self-contained. A self-supporting property conveys a title to eligi- bility, and the necessary articles being present, will form a pre-eminence. 1020 ON LANDED PROPERTY. A mine and land of a similar value. over those that must be wrought for foreign use, and which have to supply the want of the materials that are constantly required. The value of these adventitious articles of property is variously affected by the ascertained continuation of the mineral substances, or the apprehended exhaustibility, View of the the prospect of the value being maintained, and if the support articles. of the undertaking rests upon the solid grounds of suitable ac- companying provisions. If the foreign export be none, the value of coal, clay, and building stones will be very considerable; and with the total want of coal, which is the most general case, the attachment of building materials will have a due attention. The quantity and quality of surface ground, which may be destroyed for use in working the minerals, must not escape the notice of valuation; the allowance in money for the destruction will detract a something from the value in all cases where the use of the surface infers a price of any amount. The annual revenue that is derived from a mine, is held to pay the same interest on the purchase- money as the soil of the earth, and it is liable to the same de- duction in a per centage for the yearly upholding of the current going order. In some cases, this charge will exceed that of land that is let in farms, as the movements of action are quicker and more fre- quent, and the frictions and collisions are much more numerous of the different bodies that are in use. This consideration, the probable ex- haustion of the article, and the uncertainty of demand, impose upon mineral property a cheaper purchase than of land in the full proportion of one-half the amount. The surface of the ground can be seen, examined, and esti- mated, and the possible and probable capabilities are estimated in prospect, the use of it can never fail while the human race exists, and all the artifi- cial repositories of money are trifling safeguards in comparison with the improved utility of the natural patrimony. Minerals are an adjunct to it, and a very valuable one; but the use is much hidden, and the continuation but differ uncertain. Hence, though the net produce of mines does add to in prospect. the aggregated sum of the purchase-money of a landed estate, the reckoning must be separately made, and the entertainment different. The chief consideration rests upon the continuation of the rent at the pre- sent reported value; the extension is a matter of choice in any improve- ments that may be contemplated to make on the property. The probability of this object, however, will conduce to flatter the prospects of purchase, if not over-estimated by the selling party, and put forward at an extrava- gant estimation. A thing that may be done is of uncertain amount, as the doing of it is exposed to many contingencies that are beyond all cal- culation; on these points, any fixed data give way to the best assumptions. Calculating land to fetch at present twenty-four years' pur- purchase in chase, which may be beyond the average, except in very prime qualities of soil and circumstances, minerals may be put down at twelve years' purchase, and the net revenue being multiplied by that figure, will give the amount to be added to the proposed offer for the pos- session of the estate. Years of mines. Manorial rights. Manorial rights or claims exist over lands that are not en- closed, but have been left open to the purposes of different ON LANDED PROPERTY. 1021 usages. When the disruptions happened of the large congregations of landed purposes that had long existed in Britain, large tracts of ground were appropriated to general use, with reservation of certain rights to some superior person who adjoined the property, and who contemplated his own possession of it at no very distant time, by granting the use of it upon re- tainable conditions. Some lands were used in common pasturage that was open to the adjoining grounds of cultivation, and the lord of the manor had the mines and quarries reserved for his use. Wooded grounds yielded the pasturage to the adjoining tenants, and the growing timbers are the property of the lord; and as manors of land came originally from the crown, the lords who held them gave away to lesser lords the similar pos- sessions, and retained the claims over them, which have been called mano- rial rights. Quit-rents, escheatments, and heriots were established, which yet exist in a very diminished degree. Quit-rents, or quiet-rents, is a certain small rent, payable by the tenants of manors in token of subjection, and by which the tenant goes quiet and free. It was an- ciently called white-rent, because paid in silver money, and differing from rent-corns. Escheatments are a fall of the land to the lord of the manor, by reason of the extinction of the blood of the tenant in the want of heirs, or by the commission of treason or felony. The original conditions being broken, the gift resulted back to the lord who gave it. Heriot is a personal chattel, due to the lord on the death of the tenant, and is no charge on the lands, but merely on the goods and chattels : the lord chooses any article that may appear good. Fines were also imposed by the higher lords upon their dependents for the alienation of the land that was given them. Quit-rents. Heriots. These feudal relics are yet found in South Britain, where ancient usages drag a lengthened existence beyond the rest of the kingdom. Heriots will depend on the probable chances of human life, and on the value of the ar- ticles that can be taken. One seizure in thirty years may ap- One in thirty proximate the chance of the property, which may place the pur- years. chase in that of ten to fifteen years. It is uncertain what articles are liable, and the value cannot be named. The timber trees that grow on pastured lands are counted and valued by the age, as in the enclosed plantations ; and there must be taken into account the probability of how many may succeed in growing in future years, as the young shoots are constantly ex- posed to browsing animals. The value does not form a large figure in the estimate of property in land. Royalty. Royalty is the claim of the crown over the mines that were wrought as its property, and was continued by the owners who succeeded as possessors. It consists of a fixed part of the value of each article that is sold by weight or measure, and was charged for the liberty to work and sell the materials. It was a prerogative of the crown, which descended to the next in power, or the owners of the soil, as they existed in titled or inferior gradations; the distinction was continued, as it implied both the profit and pride of superiority. When mines are dug and carried into a current-going condition by the landlord's expense, and the approxi- mated value has been ascertained, a fixed yearly rent may be agreed be- 1022 ON LANDED PROPERTY. tween the parties; but when speculation enters upon the undertaking, a royalty on the sales constitutes the safest ground of action, and must have a lease of suitable duration to warrant the outlay. After the expiring of the first lease, which will generally fix the future value, a yearly rent may supersede the royalty, or it may be continued by mutual option. A free rent. A royalty is a revenue that is free of all deductions, as the costs of every kind in working and upholding the currency of action falls upon the tenant, and the landlord gets the stipulated part by the trouble of receiving it. But the exhaustible nature of the property, and the uncertainty of demand, fall equally upon both parties; and the pur- chase value of the owner's share is reduced to the number of twelve years in the half of property in surface ground. Royalty is the net rent, calcu- lated posterior to the cost to the tenant of upholding materials, and there- fore both ways arrive at the same value to the owner, and do not alter the amount of the purchase-money. Fee-farm value. Fee-farm rents are due from tenures without homage, and rent is a free which belonged to the heirs for ever. The feoffment contained very special articles of agreement, one of which was the power of the feoffer and his heirs to enter into the possession of the lands upon the rent not having been paid for two years. The rent was one-third or one-fourth of the value, and some conditions of performance were imposed, as upholding churches and chaplains; but no fealty or service was done to the superior, as it was a removal of burdens from himself, and for which he allowed a means of performance. This trifle is free of any deduction, and may be added in the yearly amount of the unincumbered rent of the land. The likings of superiority yet continue these relics, though they are now both few and unimportant. The foregoing modes and items of valuation may be illustrated by an example of the statements that have now been given, General va- An estate of land is let into farms, which yield a gross rental luation of an of £15,000 yearly. The net-rent must be shown on which to cal- culate the purchase-money after the burdens have been deducted: Gross rental estate. Burdens-Allow 12 per cent. for upholding the current- going order, as previously shown Net rental £15,000 1,875 £13,125 Which is formed wholly from the surface ground, and is augmented by the following items :— Royalty of mines, which is free of burdens Manorial rights by estimate Fee-farm rents Surface-rents Rent Yearly. £350 150 50 550 13,125 £13,675 ON LANDED PROPERTY. 1023 The net-rent, with the manorial rights and fee-farm rents, is the sum of £13,325, at twenty years' purchase Royalty of £350 yearly, at ten years' purchase Purchase-money Purchase- money. £266,500 3,500 £270,000 Land bears a low interest. The woods are included in the surface-rents of the ground, and estimated as shown before, and placed under the reduction that has been explained. Land is computed to fetch the lowest interest of any stock in this country with relation to the purchase-money. The burdens, outlay, and trouble, anent the possession of it, are very considerable; and though the former may be ascertained with a very fair exactness, there are other expenses attending it which escape the common estimates of de- duction. The nature and extent of the estate, its present and past condition, the state of the tenantry, the conditions of leases, and other circumstances, will exert an indirect influence, and not very small, on the eligibility of an investment in land. Annual hold- ings and short leases incur more expense than where long leases prevail: frequent changes produce wants and desires by reason of the ob- jects being exposed to view. In addition to the regular expenditure which can be estimated, there is always a calculation of casual matters and un- avoidable accidents, which fall upon landed property beyond any other kind of capital. It is very common to hear complaints of the great expenses of landed property, which are in many cases very true, and are much owing to the careless attention and system of neglect with which the pos- session is managed. The full value of landed property can only be derived by maintaining it in good order, and for this purpose the requisite Must be in expenditure must not be withheld, and the judicious and rela- good order. tive application of it is to be preserved with the most scrupulous attention. If a small revenue is derived from a well-ordered and replenished estate of land, much less will be obtained from a neglected property, which is daily sliding downwards, and will soon arrive at total worthlessness. An improvident management will soon destroy any property without a trace of the fortune that has been lost, while a foreseeing and ready outlay for all necessary objects will always secure a well-paid present in- Is easily de- come, and promote ultimate improvement of the estate. Incom- stroyed. petency is never more clearly shown than in the so-called economy of withholding the means to repair deficiencies and make them durable, when larger gaps will arise from the neglect, and in refusing an expenditure which would add some new sources, and also prevent the casualties of recurrence. In this way much of the expenses on land is heedlessly incurred. The inducements to acquire landed property ever remain to be very strong, notwithstanding the low interest that accrues, and the expenses that are attached. It possesses a more durable security than other kinds of capital; there is a fair expectation of a future increase of value, and there are many pleasing associations connected with the solid and enduring possession of a landed estate. Land much desired. Is a firm security. 1024 ON LANDED PROPERTY. However much the thirst of gain may frequent the crowded ports of com- merce, and haunt the walks of trade, no sooner has a large fortune been realized than it looks towards the land as the safest security. A rural re- tirement has ever formed a chief delight of the human race, and no wealth is able to find an equal, or to substitute the enjoyments. Superiority is ever pleasing to the mind, and there is more room in the vacant country than in the crowded town, where to show the exercise of power and the influence of wealth. The possession of land conveys with it very peculiar associations of inherited liking and pleasing recurrence, and there are at- A gratifying tached to it many feelings of some little importance, which employment. employ the fancy and divert the judgment. A proprietor of land is pleased to employ a happy labour, and to pay it; gratification associates with the learning of the clergy and teachers of the neighbourhood, and the justice and the magistrate are delighted to assist in dispensing rationality as law on disputed points, and to contribute in the advancement of morality. The residence becomes highly pleasing, and the employment most truly useful. CHAPTER XII. LAND STEWARD AND FARM BAILIFF: QUALIFICATIONS AND DUTIES. Land THE land steward is a comparatively new official employment, having superseded the old manorial courts of audit, in which lawyers were necessarily employed. The post now requires a well educated steward and enlightened civilian, who is divested of the trammels and prejudices of a dogmatic craft, and whose mind has been very largely liberalized by a varied and comprehensive education. In the present days of enlightened and very rapidly progressive improvement of every kind, degree, and quality, it is most essentially necessary, that “the” person to whom the possessor of land has delegated the power of superin- tendence and direction over his property, be very intimately acquainted with the most approved modes of cultivating the possession, drawn from a systematic education and a regularly confirmed experience. For this purpose, the education must be commenced from boyhood; and especial His educa- care must be used, that the prejudices and trammels of the antiquated customs of a craft be not allowed to usurp the place of liberal ideas, and of reasonable and enlightened entertainments. In addition to the utmost extent of the usual education called "schooling,” which is necessary to any profession, there is to be recommended for practical use and ornamental possession, a pretty extensive classical edu- cation, by which is meant a very considerable knowledge of, and ac- tion. ON LANDED PROPERTY. 1025 Classical. quaintance with, the ancient writers of Greece and Rome; from the perusal of which may be drawn the most liberal sentiments, and also the most elegant and ingenious, and which never fail to exert a most favourable influence on the professional transactions of any kind or degree with which they come into contact. They also tend very powerfully to create and promote that graceful affability of manner which is necessary for every person engaged in general business of a superior kind, where proper courtesy to inferiors, and the deferential respect that is due to superiors, are most imperatively required to constitute a negotiating "medium," for arranging and carrying on the business of the property. The use of a knowledge of these languages is un- deniable in producing the aptitude of correct speaking and writing, than which there is not a more useful or ornamental part of a polite education. And no qualification more clearly shows the fitness of any person for a business" occupation than the readiness with which ideas and concep- tions are entertained, and the correctness with which they are quickly clothed with a becoming verdure of language, that is at once Command of clear and intelligible, expressive and decorous, and which sends language. afloat in the commercial world as a current coin the very commonest transactions of business. Nothing more effectually contributes to the agreeable and faithful discharge of a mixed duty, than a graceful and pleasing affability of manner, and the prompt and correct use of the tongue and of the pen at all times, and on any occasions that may occur; and to produce these requisites, no branch of learning is more efficacious than an intimate acquaintance with the language and ideas of Greece and Rome, the two great theatres of human glory, from whom every succeeding enlightened nation has very unwillingly borrowed, and which many more have not yet equalled or approached. The common conversation of every person that is employed in the higher world of business, his inter- course with society, both vulgar and refined, his epistolary and business correspondence, and even his daily communications with servants and domestics, will be elevated and dignified, and even rendered more clear and intelligible, by being largely interspersed and ornately commingled with the "lactea ubertas" of Livy, and the "immortalis velocitas" of Sallust. curator Physical sciences Among the branches of education which are necessary to be cultivated by the person to perform the office of land steward, or the and administrator" of landed property, an especial notice is due to chemistry, botany, geology, and natural history, as being all of them more or less intimately connected with the nature and organization of the particular species of property with which the management is charged. The studies and a fair knowledge of each branch are very often required to be exercised in the specific application where the use is attended with very beneficial effects. But if occasions never happen to call forth the use of them, the general knowledge that is created never fails to have a very beneficial effect on the other branches that are exercised. Such studies enlarge the circle of know- able. very value- 1026 ON LANDED PROPERTY. ! ledge, ennoble the sentiments, refine and exalt the ideas, and insensibly lead the mind to form elevated conceptions of every object and transaction that is presented to its comprehension and negotiation. The mind is whetted to vivacity of conception and action by the attrition of exciting causes; by the number and power of the mental stimulants that have been poured into the intellectual "sensorium," where by the action of fusion and amalgamation, a current of refined matter is produced and emitted, which improves every object that is touched, and burnishes with a brighter polish every transaction which is performed. It promotes every affair, and brightens every business. A most powerful incentive to the acquisition of general learning is, that Learning it gives to the possessor of it a commanding position in society; gives power. power is most gratifying to the mind of man, and the mental is so much more pleasurable than the material form of it, that it is exercised without the infliction of pain, and in its development it is innocuous, and meets with opportunities of conveying benefits to others, than which latter employment no exercise can be more agreeable to human benevolence. A corresponding station in society is essentially necessary for every person who is engaged in a respectable and useful employment; and it can neither be attained nor upheld without that enlargement and refinement of the mind which flows from a general education, and which alone can entitle Professional any individual to the proud distinction. The position in society education ; must be graced by the man, and not the man by the position. A general education points unerringly to the paths of eminence; it infuses virtue into every sentiment, and imparts a grace to every action. The fundamental part of a professional education, must be that of the art or practice which is intended to form the occupation of the individual, and as the business of a land steward will be chiefly confined to the superintendence and direction of agricultural matters, it is most imperatively necessary that the person receives a practical education of the first order, and thus get ac- quainted with every detail and all the minutiae of the art. This education must be the most improved, the most enlightened, and the most approved, which the age and country can afford; and care is necessary that this practice be not instilled at any age too young for the discrimination of ideas, and when the pliant ductility of the mind is too apt to receive and set down as the most incontrovertible truths the practices which only constitute the trammels and antiquated prejudices of the craft. The mind is thus stamped from without, instead of being moved from within, and enlightened: becomes a passive recipient instead of an active exponent. Originality is wholly destroyed. To prevent this very common result of the general system of education, the study of practical agriculture is made to form the last part of a general education; and the branches formerly mentioned are previously acquired, in order that they may, by the power of their influence, liberalize the sentiments, and tend to neutralize the usual effects of an early infusion of prejudices and dogmas, which very often completely defy all future eradication, and produce very baneful results. On the other hand, equally as much care and caution must be used, that liberal and ON LANDED PROPERTY. 1027 the overheated fancies of scientific lore be not allowed to take the place of "rational" practice, and overturn the best laid schemes of scientific prudence and discretion. The one part of learning must balance & moderate; and improve the other; practice must show the results of every rational, and well conceived theory-and general learning will enlighten the con- ceptions, and by deduction show the feasibility of every scheme. Thus the two seemingly opposite elements of learning tend most materially to benefit each other; the meeting of the materials in the mind produce the the scintillations and coruscations that are so very necessary for the arrangement and transaction of affairs, and which illuminate every path and brighten every progress. If the mind be not stored to plenitude with valuable learning, it will quickly be occupied with lumber, trash, and trifles. mathematic; A general education never can be mentioned, without a very “special recommendation being always given to the study of mathematics properly so called. The word comprehends a wide range, and the branch must be extensively studied; for no education can be reckoned in any way complete without it; by it the mind is early accustomed to strict discipline: it learns to distinguish between causes and effects, to demand evidence for every fact, and a demonstration for every truth; and it dispels that very ignoble and infectious art of "believing " without evidence. Mathematics infuse a systematic order into every arrangement, and arrive by a strict method to every conclusion. No con- fusion is allowed; every thing is clearly placed, and produced from a regular concatenation. And so it must be in business, the arrangement must be methodical and clear, and the performance will be orderly, and the dispatch of it will be regular. A correct and wholesome discipline of the mind, is imparted by the studies of mathematics: it re- discipline of strains the vagaries of fancy, and curbs the licentiousness of an unbridled impetuosity at the same time, very pleasant truths are unfolded, and a trustworthy confidence derived in the ultimate results of any undertaking. These observations will apply to the practice of any liberal profession. the mind. Two stages of life will acquire the practical knowledge of agriculture; the first will be previous to the acquisition of the polite and liberal learn- ing, and the other after that valuable acquisition has been made. Not less than two years should be allowed to each term of the apprenticeship. The first period will teach the mechanical drudgery of the business; and the second will look at agriculture with liberal views, and enlightened optics. Some years must then elapse in the acquisition of varied scientific know- ledge, and in maturing and ruminating the practices that have been witnessed. No person must commence the office of land steward under the age of thirty years, or more; at which time the ideas will Age of busi- be matured, the experience extended, and the habits confirmed. ness. An early age only employs a raw inexperience and an immaturity of intellect that can add dignity to no employment, and is productive of much mischief. 1028 ON LANDED PROPERTY. During the first term of the apprenticeship, the juvenile attention will be employed in the operations of daily farming, in the participation of the manual and bodily labours, of which an intimate knowledge is requisite. The second period of learning, will direct and superintend the employ- ments, attend markets, fairs, and shows, at which much general knowledge may be acquired. A very material part consists in gathering a correct knowledge of the breeding and use of the improved animals of the farm, which now forms a very prominent part of the rural occupation. the juvenile No branch of practical knowledge can be found more useful, or more conducive to the interest of landed property, and to the advancement of cultivation: no part of the employment is more rational or more truly delightful. Tyroship of course. Varied learning. After the mind has been opened and liberalized by the study of the polite arts and of elegant literature, the attention must be most earnestly directed to the acquisition of the varied branches of knowledge, which will not only reflect a lustre on the profession, but will conduce most powerfully to the beneficial and satisfactory progress of the professional undertakings. The practical ideas must be concentrated and fixed; the habits of business must be chosen and formed; and the whole character must be graced with affability of manner and frankness of behaviour, which engage the attention of all who may approach, and always leave a very pleasing prepossession of remembrance. In the multiform varieties of a general business, no quality of the mind is attended with more beneficial impressions; it disarms hostility, and often wholly changes the frowns of opposition and the appearances of conflict. It is a quality of inestimable value; by it professional ignorance is often shrouded in a veil, and mistakes are slurred over, and pass unnoticed. When exerted along with other necessary acquisitions of office, it adds a brilliancy to every conception; and in business it gives a relish to every employment, and a passport to every intrusion. In promoting this very useful quality, a general education will be found to exert very powerful effects; and also in giving to the mind a stretch of liberality that is so necessary Courtesy. to every person who is engaged in the busy world, and whose attention is more particularly directed to the fruitful progress of a specific description of property. Early inculcated prejudices and rooted anti- pathies exert a most baneful influence on every human affair, and very often completely baffle all attempts of removal. For this purpose, a com- prehensive and varied education should be very early introduced, which, by presenting to the mind the most varied assemblage of objects and opinions, will accustom it to the very useful task of analyzing and choosing, and will prevent the pernicious extremity of one idea or practice usurping the undisputed possession of the mind. Most men, or rather all men, have their crotchets, and the sooner and the more earnestly they set about the removal of them, the better. The mind is not sufficiently trained, nor the habits confirmed, for arranging and conducting an extensive and responsible business, till nearly the age of forty years, or considerably turned of thirty. Till that age, the constant Crotchets must be avoided. ON LANDED PROPERTY. 1029 employment must be to gather information, and provide a Age of forty stock of knowledge for future use, by acting in subordinate suitable. capacities. years A chief agent that has been thus qualified resides upon the estate of land, and not very distant from it; and in addition to the duties of the agency, may be charged with the direction of a practical farm, which the proprietor may or should carry forward, in order to show to the tenantry an example of the most enlightened practice. On this farm, all new theories, and rational experiments are proved on a suitable scale, as will not interfere with general results, and at the same time are sufficient to test the feasibility of the schemes that may be propounded. Such an establishment is very necessary in order to develope the resources of the pro- A farm perty which is entrusted to the charge and possession of indi- necessary. vidual capacity. The powerful spur of self-interest will also come into action; for wherever labour is judiciously employed, the recompense is certain from such quarters. The duties of a chief agent on the days of audit in the receipt of rents, will be found in the last chapter of this work, along with the forms of notices, receipts, and cash books. The salary of such an agent Salary fixed. is generally at £300 or £400 yearly, according to the extent of the charge. A fixed sum is better than a per centage on the intromissions: it establishes a certainty which is useful in all cases. It also prevents any attempts on the part of the agent to increase unduly the amount of the rental, in order to raise his own emolument, than which insidious mode of managing any business, nothing can be more detrimental to the property, and disgraceful to the individual. All such temptations must be very carefully removed. All monies are paid by the chief agent, and no arrangements are made, nor any undertaking carried forward without his privity and direction. The fixation and direction of all undertakings must be centered in one person, along with all subordinate departments; confusion will otherwise ensue, attended with clashings and collisions, and attempts at independence, which invariably produce damage to every concern that is interested. All accounts must be reduced into one collection, where the accounts are easily examined and viewed in connection. A properly adjusted establishment of a chief agent and his subordinates, resembles the staff of the general of an army, where the duties are most clearly chalked out for each depart- ment, and the means allowed for accomplishing the orders that Regulations. are given. In the conferences with subordinate officers, the agent must listen attentively to every suggestion that comes from the de- partments of office, and form an opinion from the statements that are given and joined with his own reflection on the separate points. He must always appear to be superior to the need of advice, and at the same time be open and willing to receive the hints and observations that may occur in the course of discussion. A friendly urbanity of disposition goes very far to promote that degree of willing cheerfulness, which so very power- fully advances the onward progress and fruitful termination of every un- 1030 ON LANDED PROPERTY. dertaking to which unity of purpose and cordiality of support are essen- tially requisite. Visits fre- quent. An agent must not be far distant from an estate of land, in order to enable a frequent and personal inspection of every proceeding, and of getting acquainted with the characters of individuals, and of directing every subordinate department. A constant and very mi- nute surveillance must be exercised by him in every particular affair; and upon no account and in no affair must he rest satisfied with reports, nor allow the interested motives of those persons who approach him to influence his opinions or bias his judgment. To act upon hearsay, even on the most trivial occasion, shows a very great weakness in the powers of per- ception, and a disposition much too easy in the nature of compliances to enable the manly part to be called forth, than which no qualification is more required in the arduous situation of being placed between opposite and very often conflicting elements. A very vigorous enquiry must be made into the bearings of every affair, the truth must be discovered, and the decision and the future proceedings must be thereon made and directed. Nothing more effectually degrades a man placed in a responsible situation, than opinions crudely formed with hasty decisions, and actions impru- Steadiness dently executed, which are soon found to be wrong in tempe- of purpose. rament, and hurtful in the consequences. Perhaps in few or no offices of employment is there greater occasion for affability of manner, courtesy of bearing, calmness of judgment, and decisive energy of action when the resolution has been coolly formed. Hastiness and vacillation are equally the proofs of imbecility, that is most truly disqualifying for such an office. It must be laid down, and most tenaciously and inflexibly upheld as a fundamental maxim, that an estate agent must be an agriculturist of the most improved grade. Land-owners have committed most prodigious mistakes in employing lawyers, commercialists, or some similar persons, often of a nondescript character, whose sole object is ever to levy a sum of rental at any risk, and at the same time are utterly regardless of the source whence the profit is derived. Professional ignorance prevents any attention being paid to the furtherance of the art which supplies the revenue, and other engagements distract the necessary attention, even were it available and useful. The estate is seen only when the rents are due, and not again till that period returns: a manor bailiff is seldom kept, and no inspecting visitations are used. Under such treatment, all perishable articles fall into a state of ruin, as buildings, fences, roads, and the land itself; the rent is drawn so long as it can be got, and when the collection is no longer possible, a considerable sum of money is required to put the property into a vendible condition, which might have been wholly prevented by judicious regulations, and a timely interference, with a constant and vigilant surveillance. Very different must be the results to any landed property from the labours of a specially educated and duly constituted agent, whose time must be constantly occupied in the business of his remunerated employment, keeping accounts within doors, Ignorance ruinous. ON LANDED PROPERTY. 1031 where also will be devised the schemes of improvement, and the means of accomplishing every undertaking. The personal inspection, very fre- quently repeated, will include the farms, plantations, and roads, and also the interior policies, except where the resident family take that depart- ment under a special direction. Faults and mistakes must be put right without delay, and the whole exercise is a most agreeable occu- Exercise pation for a rational being, and very necessary for upholding pleasant. the value of the property. Even when a manor bailiff is kept, the visita- tions of the chief agent, are no less necessary; reports are apt to produce an improper bias, and misstatements are best removed by the evidence of the senses. In such inspections, a very patient and polite attention is re- quired to all opinions and suggestions that may be given and stated, in pro and con; hints are got from such sources, and information needs every source of obtaining a proper knowledge. No person is degraded by listen- ing to remarks from any quarter; something may be gained, and nothing is lost, and common civility is exercised. The due authority of the chief agent controls the inferior departments on the estate, and there must be impressed the proper sense of that ar- rangement. Much confusion will ensue from this subordination not being properly understood and acted upon; co-operation Authority. will be disarranged, and malevolence and lurking hostility will be engen- dered. The chief agent must use his power "discreetly;" make his ar- rangements "judiciously and practicably;" give his orders "civilly," but "firmly and energetically;" convey the necessary censures "authoritatively, but blandly;" commend "freely, but duly restrictive;" and in every case. to judge coolly and dispassionately, and act decidedly and firmly. An ample supply of prudent discretion and a very great command of temper, are most essential requisites in such an employment, in order to meet the very frequent rebuffs and mortifications, arising from the perpetual colli- sion of jarring interests, which naturally converge to the agent's position, This point very often forms the most arduous part of the official duty. Department. In such situations, nothing is more necessary and becoming than the propriety of appearance and behaviour that belongs to the grade of society in which any individual may be placed. The land agent is exposed to the frequent contact of superiors and inferiors, and to both these grades, the proper deportment must be correctly exercised. To the for- mer, a respect is due from the station in society, which expects opinions and proofs to be rendered with professional firmness, and sugges- tions offered with caution and prudence, as each special case may require. In such cases, an over-eagerness and heatedness are much to be avoided, which serve to produce irritation, and mar the face of proceedings. To- wards inferiors, courtesy and affability are absolutely indispensable, in order to secure the goodwill and affection of the operatives in every un- dertaking, and who form the muscles and sinews of every active operation, Harshness must in all cases be avoided, even though the amount of pro- vocation may apppear to justify the exercise: conciliation must form and cement the attachment; harshness will sever it. - 1032 ON LANDED PROPERTY. Correspon- The last, but not the least important, part of the duty of a land steward, is the correspondence, or communication with his employer, who is the owner of the property. The position in society often removes dence. the land-owner wholly beyond any notice of the concern, and even his constant or temporary residence does not enable him to enter into any considerable knowledge of the business: the drudgery forbids it. The knowledge and judgment of the agent come into full play, as upon his opinions and course of proceedings, the prosperity of the property, and necessary welfare of the subordinate parts do in a great measure depend. The most enlightened professional knowledge must be joined with a cool and reflective judgment, and used with equal energy on trivial matters as on large undertakings. A varied education has been largely recom- mended in order to raise the ideas and elevate the conceptions above the mole-eyed plodding in the mud of vulgar practices and of obsolete pre- judices, and of the clay-born sympathies that keep within the gin-horse track of daily routine. Judgment must systemize the conceptions, and steadiness must direct the attainment of every business and objects that may be contemplated. Correctness. The owner of a landed property being necessitated to rely on the esti- mate and representations of the land-steward, and to give his sanction almost wholly to his calculations, there occurs the most pressing necessity that these estimates of opinion be composed on a very firm basis, and after a most mature reflection. Hasty decisions and crude calculations must be most carefully avoided, for the consequent mis- carriages do much mischief, both directly and indirectly; they are exposed to contempt, and tend to prevent any future attempts of a similar nature; they also induce the proprietor to distrust the trustworthy confidence that Trustworthi- ever should be reposed in an agent, and to think his own inter- ference becomes the more necessary, and also to hear and con- sider other opinions on the subjects that come under consideration. The agent thus loses his proper "status" on account of these former misgivings, and also the confidence that is necessary to the undertaking and executing the beneficial improvements on the property. Envy and malevolence are ever ready to exert their evil offices whenever the least opening occurs. To prevent these gaps of offence, the most careful attention is required. ness. The general and professional education of the agent must enable him to form ideas and concoct plans which will bear a severe investigation, and stand the test of the most rigid scrutiny. The language of conveyance must be clear, and easily understood, pithy and short: the answers will consequently be the quicker obtained and the easier followed. The agent's mind must be wholly occupied with his occupation, devising modes of necessary improvements, arranging the execution, and obtaining the con- sent and sanction of the proprietor, after there have been bestowed upon. them the necessary explanations and elucidations. In this way, the uni- versal benefit will be most usefully promoted. The farm bailiff is a most useful person in the management and culti- vation of landed property. It has been observed that there may be, or. ON LANDED PROPERTY. 1033 Farm bailiffs. should be, a farm conducted practically on most estates of land by the proprietor, and of which the charge will devolve on the agent. He delegates the resident power to a practical person for the pur- pose of executing the orders he may receive, and conducts every practical business from these orders, and his own special judgment. This person must have been bred from boyhood in the constant exercise of agricul- tural operations: at least to have acquired a most thorough knowledge of the nature and extent of each. It is most essentially necessary that he is a perfect master of every practical process in cultivation; for when a per- son is thus acquainted with any performance from personal expe- His qualifi- rience, he is much better qualified to describe it, and to give directions on the subject, than if the recommendations were the mere re- sults of observation, however acute and penetrating. In addition to these primary qualifications, the farm bailiff must possess as much education as enables him to keep a correct account of the daily labour on the farm, and of the corns in the granary as it is thrashed and sold. The form of the wages book is subjoined. cations. • 3 s 1034 WAGES BOOK. | Number. Names of Wages Business. per Persons. Employed. Day. WAGES BOOK. An Account of the Names of Persons in the employment of and Weekly Labour and Wages for Four Weeks, from the day of Monday. Tuesday. Wednesday. Thursday. Friday. Saturday. Amount per Week. £ s. d. Wednesday. | Thursday. | Friday. Monday. Tuesday. Saturday. Amount per Week. £ 's. d. ~ Wednesday. Thursday. Monday. Tuesday. Friday. Saturday. , at to the Amount per Week. £ s. d. day of and of their Daily 185 | Wednesday. Thursday. Monday. | Tuesday. Saturday. Friday. Amount per Week. £ s. d. Observations showing how each Person is Employed. ON LANDED PROPERTY. 1035 The account is rendered monthly: the amount of the money is given to him, which he pays to the respective parties. The other accounts are given in as the transactions take place, and entered in the general farm account in which the weekly wages are entered in one sum, of wages. Duties. as per bill" In order to ensure sobriety and steadiness as much as possible, it is better that a farm bailiff be a married person; for of all requisites in such an office, steadiness may be termed the very first, both in kind and degree; and in order to give encouragement to attention and activity, the wages given must be liberal, and constitute a sufficient re- ward for the tear and wear of the body and mind that are exerted in such an office. The dwelling house must be suitable, with a garden attached, and the keep of a cow is part of the salary, with a stye for pigs. The sa- lary is usually £60 to £80 in money, the use of a saddle horse, and the usual appendages. The duty of the farm bailiff is to arrange and direct the whole pro- cesses of the farm, after consultation and concurrence of the chief agent who may have the chief direction. It is necessary that he is in the stables in the summer mornings soon after five o'clock, from 1st of March to 1st of October, when the harvest will be concluded. The necessary orders are given to the ploughmen, and the feed of oats is given to the horses from a locked chest, of which he keeps the key; and the same quantity is put into nose bags, and hung in the stables to be given to the horses during the interval of two hours for dinner. The bailiff sees all the teams of horses leave the stables at a quarter before six o'clock, which allows the work in the field to be commenced at six precisely. Labours. The time stops at eleven, begins again at one, p. m. stops at six, and so on; after that hour the bailiff is again in the stables, and feeds the horses with oats from the locked chest as in the morning. This finishes the necessary attention to the horses' labour. Inspections. After every order is given in the mornings and seen to be acted upon, the bailiff proceeds at seven o'clock to take the charge of the weeders of the crops, or hoers of turnips, in lads and women, and by a very constant attendance, he procures the duty of this branch of operators as firmly, as steadily, as conciliatory lenity will allow. From this employment, however, he must steal a march, once or twice in the day, to inspect the other works that may be proceeding, as ploughing, digging of ditches, road making, or any other business on the farm. His absence must be short, as "trifling" day-labourers require much care. A steady sense of duty will not allow any harshness beyond the proper obtaining of value for value. When due explanations are given, and no suitable return is made, the total separation is much better than the adoption of any coer- cion or vindictive proceedings. The bailiff sees the teams leave the stables at a quarter before one, p.m., when he takes his post with the daily labourers till the hour of six o'clock. In the evenings, after that hour, the bailiff may arrange with the servants the work of the morrow, always allowing the probable disarrangement by the weather, and other 1036 ON LANDED PROPERTY. An under bailiff accidents. On large farms, in order that the bailiff may have greater liberty of moving about, and inspecting the works of the farm, a steady labourer is selected to attend the gang of women and lads ; and during winter, this person feeds the thrashing machine, and per- forms all the barn work. He leads the sowing of the grain crops, sows the turnips, and in harvest, he becomes the chief builder of the ricks of grain. This person is a most useful addition on farms of 300 acres, and upwards. He frees the chief bailiff of the most troublesome part of the farming drudgery, and usually gets one-fourth more wages than the ploughman. The hay and corn harvests will require the constant attendance of the manager of every farm, and the turnip season is equally imperative in its demands for his presence. He must not be confined to any spot, or parti- cular department of notice, but must move constantly about, and see that all operations are progressing, and are duly executed. During these times, all foreign business is laid aside, and the home matters are the sole concern, A very chief care of the farm bailiff consists in his keeping every tool of the farm in the best acting order, the dead stock always in complete readiness, and the living implements in high spirits, and full of order. life and activity. The former is done by a vigilant attention, and the latter by kind treatment and conciliation. A harsh bailiff will lose his employer many acts of returning kindness: encouragement leads mankind; but harshness and brutality produce obduracy and retaliation. Tools in ON LANDED PROPERTY. 1037 FARM ACCOUNT BOOK. 1852. INDEX. A. Folio. B. Barn 2 Cattle Cash • Expenses for Labour Farm Servants Granary C. D. 9 4 E. 5 LO F. 13 G. 3 Horses H. 8 1038 FARM ACCOUNT BOOK, 1852. DR. Rick Yard. (1) Wheat. Barley. Oats. Beans. Peas. Date. Folio. Ricks. Ricks. Ricks. Ricks. Ricks. Nov. To Crop, 1852 . 7 10 16 4 3 1852. Date Folio. This account shows the ricks that are thrashed, DR. Barn. (2) Wheat. Barley. Oats. Beans. Peas. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Nov. 16 1 To Rick Yard . 15 6 1852. Date. Folio. Nov. 20 2 To Barn This account shows the progress o DR. Granary. (3) Wheat. Barley. Oats. Beans. Peas. £ s d. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. 15 6 This account will, at any time, sho FARM ACCOUNT BOOK, 1039 1852. Date. Folio. Contra. CR. (1) Wheat. Barley. Oats. Beans. Peas. Ricks. Ricks. Ricks. Ricks. Ricks. Nov. 16 2 By Barn . 1 and those that remain of each grain crop. 1852. Date. Folio. Contra. CR. (2) Wheat. Barley. Oats. Beans. Peas. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Nov. 20 3 By Granary. 15 6 thrashing and storing the crop of grain. 1852. Contra. CR. (3) Wheat. Barley. Oats. Beans. Peas. Date. Folio. £ s. d. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Qrs. Bus. Nov. 304 & 14 By Sale 30 0 0 10 0 the quantity of grain on hand. 1040 FARM ACCOUNT BOOK. 1852. Date. Folio. DR. Cash. (4) £ S. d. Nov. 30 3 & 14 To Cash for 10 qrs. of Wheat, at 60s. . 30 0 0 8 وو "" To Cash for One Foal. 15 0 0 1852. Date. The balance of this general cash account will DR. Expenses for Labour. Folio. (5) £ S. d. This account shows the expenses of labour only, and saves 1852. DR. Petty Expenses. Date. Folio. (6) વા £ 8. d. This account shows the smaller incidental expenses, and the amount FARM ACCOUNT BOOK. 1041 1852. Date. Folio. Contra. CR. (4) 48 £ S. d. Dec. 1. 5 10 By Cash paid Monthly Wages Bill . 23 14 3 8 "" "" By Cash paid for One Horse . 25 0 0 show the final balance of all transactions. 1852. Date. Folio. Contra. CR. (5) £ S. d. Dec. 1. 4 By Monthly Bill of Labour 23 14 3 time in examining the general cash account for that 1852. Date. Folio. purpose. Contra. CR. Dec. 8. 4 By Expenses at Market is carried to the general cash account quarterly or half yearly. £ જે S. (6) હું d. 0 7 6 1042 FARM ACCOUNT BOOK. 1852. Date. Folio. 1852. Date. Folio. DR. Manure Account. £ 48 S. (7) d. This account shows the money DR. Horses. (8) 48 £ S. d. Horses. Mares. Foals. : To Stock on Farm 300 0 0 8 2 3 4 To Purchase 25 0 0 1 0 0 1852. Date. Folio. : 0: : DR. Cattle. £ S. d. This account shows the dealings (9) Bulls. Cows. Oxen. Heifers. To Stock on Farm 500 0 0 1 14 18 15 To Purchase 16 0 0 0 2 0 This account shows the numbers and value FARM ACCOUNT BOOK. 1043 1852. Date. Folio. Dec. 10. Contra. OR. (7) £ 8. d. By Cash for 10 loads of Dung, at 4s. 2 0 0 spent for any manures. 1852. Date. Folio. : Contra. CR. (8) £ S. d. Horses. Mares. Foals. 4 By Sale 15 0 0 0 0 1 By Death. 20 0 0 1 0 0 among horses, the number and values. 1852. Date. Folio. :. : : Contra. CR. (6) વા £ 8. d. Bulls. Cows. Oxen. Heifers. By Sale 24 0 0 0 0 0 3 By Death 14 0 0 1 0 0 of the transactions among cattle. 1044 FARM ACCOUNT BOOK. 1852. Date. Folio. : DR. Sheep. £ રે (10) 8. d. Rams. Ewes. 1 year's 2 years' To Stock on Farm 0 0 0 2 300 150 120 To Purchase 60 0 0 60 0 This account shows every 1852. Date. Folio. DR. Swine. (11) મે £ 8. d. Boars. Sows. Pigs. Hogs. To Stock on Farm 60 0 อ 1 3 16 10 ... 1852. Date. Folio. General Loss on Stock. (12) Horses. Cattle. Sheep. Swine. £ S. d. By Death. 1 1 1 2 38 00 This acccount collects all losses on dead and live stock, and shows the amount. FARM ACCOUNT BOOK. 1045 1852. Date. Folio. : : : :. (10) Contra. CR. £ 8. d. Rams. Ewes. 1 year's. 2 years'. By Sale 60 0 0 0 0 0 40 By Death 1 10 0 0 1 0 0 lealing among sheep. 1852. Date. Folio. .... 1852. Date. : : Contra. CR. (11) £ 4+ S. d. Boars. Sows. Pigs. Hogs. By Sale 3 0 0 0 0 0 2 By Death 0 10 0 0 1 0 Goods from Farm as below. House. Stables. Folio. Beef. Mutton. l'ork. Hams. Cheese. Poultry. Eggs. Milk. : st. 40 Butter. Price. £ s. d. Oats. Hay. Straw. Price. (12) Garden. £ s. d. £ s. d. qrs. tns. 4s. 800 100 20s. 10 00 Load 2 80s.|| 8| O | 0 ||10 Dung||2|0|0 This account shows the goods sent from the farm for the use of a resident family. 1046 FARM ACCOUNT BOOK. 1852. Date. Folio. 1852. Date. Folio. DR. A. B., Farm Servant. 48 To Payment. 2 • S. d. Wheat. Barley. (13) Oats. qrs. bus. qrs. bus. qrs. bus. 00041016 This account is fitted for payments in kind; when the wages DR. J. D., Corn Factor. (14) બ £ 8. d. Nov. 30 3 To 10 qrs. of Wheat at 60s. 30 0 0 This account shows all debts that may exist in business when no This form of Farm Book-keeping may be enlarged or contracted to suit any circumstances of use, and columns may be added as required. Double entry is adopted, as it affords the most clear and effectual check FARM ACCOUNT BOOK. 1047 1852. Date. Folio. : Account Current. CR. By 1 yr's conditions £ S. d. Wheat. Barley. (13) Oats. bus. qrs. qrs. bus. qrs. bus. 10000 34 40 10 6 are wholly in money, they appear in the monthly bill. 1852. Date. Folio. His Account Current. Nov. 30. 4 By Cash. • • credit is given for the goods sold. Each dealer requires a column. (14) 4+ £ 8. d. ས 30 0 0 and exposition of business. A simple entry merely states a bare fact; the double entry certifies the negociation, and vouches the transaction of the business. 1048 ON LANDED PROPERTY. F CHAPTER XIII. MANOR BAILIFF, WOODREEVE, GARDENER, AND GAME- KEEPER THEIR POSITION AND DUTIES. Manor bailiff. WHERE landed property is extensive, and lies in a wide circuit, the head agent of superintendence is removed beyond the drudgery of the inferior work, and retires to the higher duties. A constant residence is not made on the estate, but only the necessary visits, or an occasional abode for a period of the year. A subordinate authority and management is delegated to the manor bailiff, who lives in the centre of the estate, and performs all the lower duties, and attends the minor concerns. Such a person is essentially required wherever there is attempted to show a well-managed estate of land, as the detailed works of any undertaking constitute the perfection which is formed by the seeming trifles of attach- ment. All large establishments demand a staff of action that is efficiently constituted and systematically organized; and a methodical exactness must pervade every branch of the departments, even to the minutia that nearly escape observation. The profitable development of every large under- taking mainly depends on the constitution of the managing authority, and the mode and manner by which the action can be exerted, or is allowed to show an efficiency. The arrangement must be made with judgment, and directed with much care. The manor bailiff resides in some convenient central part of Residence. the estate, where a suitable house is provided, with the necessary attachments, and attended with a quantity of land sufficient to maintain a saddle horse and a couple of cows. The money salary is usually £80 yearly. He must be a steady trustworthy person, respectable, and well educated, thoroughly acquainted with the most enlightened agriculture in every branch and detailed appurtenance, and equal to any keeping of ac- counts. His time will be constantly occupied with the business of the estate, in arranging the performances with the chief agent, and Occupations. superintending the execution. The wants of the farmers will first be made known to him, when he will hear the statements that are made, examine the grounds of validity, and judge the feasible sufficiency of being laid before the head agent for his approval or rejection. His own opinion must accompany every proposition; and it is most highly necessary that he is raised above partiality of representation, and the listening to re- ward. The vigilance of the chief agent must be ever awake on this point. An over-intimacy with any person or persons is to be discouraged, as it begets jealousy and destroys confidence. The preference is never to be shown to any individuals in priority of being served, except upon some ON LANDED PROPERTY. 1049 Qualifica- tions. Proposals. very sufficient grounds, such as superior management, the greatest number of wants, or the want of repairs for the longest time. As all the buildings and repairs of houses will be entrusted to the manor bailiff, his knowledge. must comprehend these performances, and be able to point im- perfections, and check abuses. Measurement of works of all kinds must be familiar to him, and also of lands on the small scale of fields and pieces of land. If the farmers or workmen have complaints of wrong in the bailiff, the chief agent hears and decides the case; and if he prefers complaint against any person of the estate, the case is settled by the same arbitrament. The agent must exercise a keen enquiry and a sound dis- cretion in deciding what may be purposely concealed from his knowledge. For the purpose of new buildings and repairs, the manor bailiff proposes plans and receives estimates from workmen, un- less the estate be large enough to keep in employment the necessary oper- ators of every department. These plans and estimates being sanctioned and signed by the chief agent, the works are commenced, carried on, and finished under the bailiff's superintendence, who draws money from the superior, with which to pay the subsisting money of the employed labour, and the balance that may be owing when the work is finished, measured, calculated, approved, and balanced with the money received. The value of the timber used is paid to the woodreeve on the estate, or bought from abroad, if none is grown that is suitable. The operations and items of de- tail will much employ the time of one person on an estate of land of the medium extent. Visits to farms. A very particular part of the employment of a manor bailiff consists in his visiting twice in the year every field of land on each single farm on the estate, and noting the management which is practised by the farmer. One visit is made in March or April, when the spring operations are being done, and the other in October, when the harvests are all finished, and the sowing of wheats is progressing. By riding round each field the condition of the gates and fences is observed, the neglects are noticed, and the improvements commended. An entry- book, carried in the pocket, contains these notices and memorandums, which require a convenient pen-case and ink-holder to be provided for the purpose, and to form a constant company. The rotations of cropping on each field of land must be very carefully noticed and entered in a book that is specially provided and adapted for the use of the bailiff: the size is a pocket folio of convenient bulk, containing on the left-hand leaf a plan of the farm on a reduced scale, with the fields num- bered in a regular order and coloured, to distinguish grass from arable grounds, and woods from meadows. The right-hand leaf which is opposite the former, contains the number of years in single columns, which form the lease of the farm, in which is written the crop which the land bears in that year, as marked by the figure in the regulated order of seasons. This book is contrived and used for the express purpose of the chief agent and owner of the estate being able to know at any time the system of cropping, which is practised without the necessity of a personal inspection. A copy Uses of a field-book. 3 T 1050 ON LANDED PROPERTY. of the book being sent the owner of the estate to any distance, the know- ledge is transmitted of the arable management on which the prosperity of the estate is chiefly dependent. The use of the book is best made in the autumn visit of the manor bailiff, as at that time the land will most clearly show the effects of the system of cropping, if any injurious rota- Twice-a-year tion has been followed and allowed, or a good one adopted and persevered. The introduction of any improper management is checked at once, and the manor bailiff must be able to judge of the admission or re- jection of the proposed innovation, report to the chief agent, receive the matured opinion, and return the verdict to the farmer; not that the farmer is to be confined within the narrow limits that may be chalked out by any superintendents, or checked by their ideas, but there is a most imperative necessity that the intrinsic worth and quality of the property receive no damage, and that the policy be not retrogressive, if it is not advancing. This is the duty of all persons who are in charge of property, and land has the very peculiar attachment of being easily damaged, but not recovered Correctly kept. without much time and expense. The manor bailiff comes into the room of the chief agent in observing and reporting the changes of use, and the benefits or damage of progress. The visits of the manor bailiff will discover if the open drains, or large cuts for the conveyance of water, are duly opened to answer the purpose, Is a general and if the receiving outlets of frequent drained lands are in the inspector. proper discharge of the purpose. As was before observed in this chapter, the fences will form an object of interest, as ruined fences seldom admit being recovered, and new ones are long in being reared into use. In fact, every proceeding on the surface of the ground comes within the notice of the manor bailiff, who is a general inspector of every business, and performs a special part that is marked for his personal execution. Though the plantations are under the management of a special director, who is entrusted with that department, yet an observation must be taken of the condition of that branch of property, and of the mode in which it is managed and protected. The manor bailiff can observe and report of these and similar concerns, without exciting any malevolence or hostility, always observing a prudent discretion, and a courteous demeanour. As these de- partments are all under the jurisdiction of the chief agent, the delegation of the manor bailiff invests him with the surveillance of the whole parts of the landed concern. All roads under his charge. The few cases of putting under the management of the manor bailiff the making and repair of all the roads on the estate where he is located, have proved the beneficial effects of the arrange- ment in the improved condition of the roads, and the lessened charge of expenditure. The necessities of the paths of transit create a charge on the rent of the farmers, which is fixed on the pound of payment by the chief agent, who collects the money at the half-yearly audit, and places it in a fund to be used as the manor bailiff may require. He will appoint the number of workmen, as the work to be done will demand, and station them in dwel- And are well lings upon or near to the localities on which the work is re- done. ON LANDED PROPERTY. 1051 quired. The digging of materials may constitute an extra item, and engage a contract agreement, or by special bargain; but the upholding of roads will employ a quantity of fixed labour throughout the year, which will mainly apportion the charge on the pound of rent to the farmer. The inspection of roads and farms is done at the same time, and becomes a business at once valuable and agreeable. This employment will form a distinct account in the hands of the manor bailiff, in which he will be debtor for all monies received, and creditor for all amounts paid. The making of new roads will be distinct from repairs, and must have a separate page, and a distinct consideration. The manor bailiff conveys to the farmers all notices of infor- Gives notice mation that are necessary, and that by special delivery of hand. of rent days, Even where fixed rent days prevail, the chief agent prepares and signs with his own hand a letter of notice to each farmer some two or three days previous, and sends the whole bundle to be singly delivered to each tenant by the manor bailiff. The form of these circulars will be given elsewhere. This delivery of notice is a part of the official routine of business, which is never to be neglected, even though the omission may seem to be harmless: it keeps attention alive, awakens interest, and by exhibiting care on one side of any concern, generally obtains a similar re- turn from the opposite quarters. On the rent days, the manor bailiff sits closely by the chief agent, who receives the money, counts it after him, places the parcels in proper order, and keeps a separate account of the amount. If time allows, any observations on either side betwixt the agents and the farmer may be mentioned and settled, but affairs of any magnitude are best discussed at a meeting of special appointment. At all and attends these occasions the manor bailiff is an essential presence, as he punctually. has seen the grounds of the request, and has heard all the urgencies and remonstrances that can be advanced. The duties of the manor bailiff are separated from practical farming, yet the person must be capable of surveying that department; and if he does not intermeddle, his observations may still be useful. The roads and fences of any farm that is used by the landlord are equally under his care, as if let to a tenant, and he must exercise the same diligence to promote the advantage and sustain the utility. The young fences that are being reared on the estate till grown for the use of the farmer, are under the manage- ment of the manor bailiff, who has workmen located conveniently for the purpose, or the day-labourers on the roads may act in both capacities, and be separately accounted. Both purposes may be served by one arrange- ment, as one surveillance comprehends the objects to be done. When the draining of lands is being done on the estate, the whole charge of the execution may devolve on the manor bailiff, draining his unless the extent of the property and the nature of it is able to afford, and requires a special appointment for the purpose. A gang of workmen may be kept for the separated purpose of draining, or the other workmen under the bailiff's jurisdiction may be used for draining when the performances can be so arranged so as not to get into contact and Fences and charge. 1052 ON LANDED PROPERTY. create confusion. The bailiff must be competent on the subject of draining, and actively acquire and promote intelligence on that very important point of rural management. The leader of the workmen must be trustworthy in the absence of the bailiff; the course of the drains will be directed by their opinion, and the cavities filled as they direct. Where a manufactory of tiles is placed on the estate, the chief management may rest with the manor bailiff, with competent foremen to direct every separate branch of the business. These appointments will render the per- son a very responsible individual, and who has the power of very much promoting both practical utility and social contentment. These two objects constitute the chief aim of every human employment. And tile making. Is the prac- The office of manor bailiff now described, lodges on the properties of land that are extensive, to employ and maintain the highest orders of agency, and the value can afford the deduction of the cost. All estates should have a practical person constantly resident, and large extents pos- sess that requisite in the manor bailiff, as the chief agent may be tical agent. distant, and have similar employments, of which he incurs the responsibility without performing the drudgery. On smaller extents of landed property, the practical resident may perform every duty, assisted by a servant to carry messages and deliver written notices. The manor bailiff must be possessed with a sound judgment, enlightened views, and a conduct that rises above every symptom of partiality or under-cloak deal- ing. Every thing must be fairly and faithfully represented, and no reser- vation made of any points that require an open disclosure. He is better when free of any social connections with the population of the estate, and removed beyond mixing in any dealings with the farmers. An independent Must be in- position must be maintained which can equal the appearance of dependent. superiors, and escape the unbecoming familiarity of inferior grades. Very much of the smooth and agreeable management of an estate of land will depend on the manor bailiff, who is placed on large extents for the express purpose of maintaining the connexion between the chief agent and the departments of operation. A very steady activity is re- quired, which assigns each work the necessary portion of time, and upholds the performance of every duty in the proper period of appointment. Steadi- ness is almost the first of virtues in such employments, no display of un- common energies on some particular occasions, and no momentary fits of unusual performances, though probably very valuable in themselves, can compensate for the derelictions of laxity and carelessness which succeed the periods of exertion. A vigilant observation and a steady execution constitute the foremost qualities of recommendation in any charge of operative performances. Woodreeve. Woodreeve is a person who acts as steward of any woodlands, and the defender and manager. The term is nearly obsolete, and comes from a word of the Saxon language, which conveys the above meaning. In former times, the woods were mostly planted by the seeds of nature, and the woodreeve merely ranged the grounds in order to debar any intrusion, and to preserve the wild beasts for the purposes of pleasure ON LANDED PROPERTY. 1053 and of the chace. Improvements were totally unheeded, and the reeve merely took the charge of protecting and defending the spontaneous pro- ductions of nature. A more settled order of society introduced other ideas of wooded property, and the system gained ground of making wholly new plantations of trees, and of much improving the old grounds that were occupied as forests. The reeve now became a regularly employed attach- ment of the landed property, and his duties were marked and defined as a subordinate in office to the chief agency. The feudal superiority was sunk into a useful appendage, and the haughty air of independence was lowered into the economical arrangement of a gra- duated subordination. His office. duties. fences. On large estates, and on those which do not employ a manor bailiff, the woodreeve is placed in charge of the whole plantations on the property and of the nurseries where such things exist. The dwelling must adjoin the largest portion of the woods, or be central as possible to the divisions of wooded lands, and have the accommodation of the grounds to keep a saddle horse and two cows, with the necessary small buildings. The money salary is £80 yearly. He will direct the felling and selling of Position and timber in the proper seasons, receive all monies, and account for it to the chief agent. The planting of new grounds is a chief employ- ment during the fresh months of winter; and the fencing of the grounds, and the protection of the young trees, constitute a part of professional duty that is not exceeded in value by any other department in the management of landed property. Whole growths of trees may be destroyed beyond recovery by the trespass of cattle during one single day, and no remedy can be found except by planting afresh the ground with trees in the quan- tity destroyed. The whole plantation fences over the estate In woods and belong to the province of the woodreeve; for, as observed in the article “Lease,” the farmer has only to protect his fields, and the landlord who makes a plantation of young trees must protect the property he has enclosed for his own purposes. These fences require a most vigilant at- tention, and a constant outlook for the commencement of dilapidations, which may lead to gaps and entries of intrusion. A supply of ready ma- terials in stakes and bars is a very necessary preparation, and so located as to be easily applied when needed for the neighbouring woods. The judgment of the woodreeve will be exercised in making these preparations, than which there can be no better fitness for office. The felling of oak trees and of peeling the bark will, on some estates, form a busy time with all woodmen, and is generally very profitably employed. The sale of these articles is managed by the woodreeve, and the receipts duly accounted. The winter sales of other timbers are similarly done, and rendered in the amount. The accounts kept by the woodreeve are only a debtor and cre- ditor pages of receipts and payments, and rendered periodically to the chief agent, and placed by him in the proper department. It has been adopted to place under the charge of the wood- reeve all the road-side fences on the estate, in order that they may add to the beauty of the scenery, from being better kept Roadside fences his care; 1054 ON LANDED PROPERTY. than the cares of the farm might contemplate. The arrangement is good, only it will add some little item to the expense of the department of woods, but which will be inconsiderable in comparison with the improvements that may be effected. The gates of these roadside fences will be under the same care as the hedges, and both objects being kept in neat and efficient order will form an object of much pleasure and utility. It relieves the farmer of some part of the many burdens of his situation, and forms a step towards the suggestion in the article "Lease," that all the fences on an estate be managed by the care of the land-owner. The roadside fences have exhibited a very marked improvement from being under the charge of the woodreeve, in the few cases where the arrangement has been adopted, and it is reasonable to expect a similar condition of all other fences that are placed under the same authority. Whenever permanent objects are discussed, the land-owner's interest is ever foremost, and must take the brunt of the required expenditure in upholding the condition. A farmer patches a permanent article to make it serve his temporary purpose; the landlord erects and maintains the objects to serve the present time, and to extend the utility to future usages. and probably all other fences. A nursery of some extent is very usefully kept on most estates of land that have a moderate extent, and though trees sufficient to supply exten- sive wants may not be raised, some number will be ready to meet moderate demands, and young thorns may be raised in any quantity to supply the wants of the estate. The nursery is the peculiar province of the wood- reeve, and is best managed by labourers specially designed for the purpose. His day workers, The arrangements of the estate will allow the woodreeve a number of workmen which experience may find to be adequate to accomplish the quan- tity of work that has to be performed. The number will be altogether dependent on the extent and condition of the plantations; if the positions be distant and enclosures small, and need much planting, and if the timbers be old, and much felling is to be done. In many cases, much work is done by contract, and the number of day labourers is reduced; but some operations do not admit being contracted, and are best done by daily oversight. The felling and topping of timber trees may be contracted, as the work is visible, and does not admit being imperfectly performed, and then concealed from view; and the raising of new fences may also be contracted, and let to the constantly employed labourers under the woodreeve, and these persons will be alternately paid by the day, or by the job, as the nature of the different works may require or allow. The gang of labourers must always be headed by a trustworthy indivi- dual, who receives the commands of the woodreeve, and who is mainly responsible for the proper execution of every job of performance, whether done by contract or day labour. Before contract work is exten- sively embraced, a confidence must be established between the parties, and a belief that neither one is overreaching the other, but that the establishment is made and carried on for mutual benefit. These under- standings contribute very powerfully to the furtherance and prosperous result of any undertaking, and society is soldered and cemented by the and job men. ON LANDED PROPERTY. 1055 kind treatment and adequate remuneration which are practised by the employers to the employed, which has ever formed, and yet constitutes the heavy burden which remains to be discharged. The labourers must be all conveniently lodged in cottages over the estate, and not assembled in one place, but scattered singly, or in two dwellings together, and so placed as to exercise a surveillance over the woods, detect trespass, inspect the fences in the daily walks, and report promptly to the woodreeve, who will as readily issue the necessary directions to have the remedies supplied. The living of labourers in villages is very objectionable, idle single cot- congregations are encouraged, and gossiping assemblages spend tages useful. time and divert the attention. The dwellings must be placed so as to communicate readily, and afford an inspection of some utility whenever the labourer leaves his home, whether he traverses a bye-way, or walks along the public road: the eye cannot be opened, without looking on some object of interest. A woodreeve with four or six men should man- age the woods of a pretty extensive estate; but the number is wholly dependent on the quantity of wooded lands and the age of the timbers, and the extra work that may be attached to the department of the wood- reeve. In the event of the land-owner assuming the management of the fences on the sides of the roads, as has been suggested, and probably of the whole fences of the estate, the charge of the woodreeve will His foremen. be most prodigiously increased, and a delegation of authority will accrue to some trustworthy foremen, who will act under him, and un- dertake the charge and management of an assigned portion of work. The localities must be divided with judgment, and appointed with discretion. As before observed, all the dwellings must be planted with the view and for the express purpose of enabling a surveillance of some kind or degree being done by every operator in whatever capacity he may act, and under whatever charge his labour is exerted. Very much toil and trouble may be saved to the chief agents by arranging every subordinate as a part of the employment, and not as a driven slave, who toils for a grudged pittance, but as a willing actor, who is stimulated by motive, and impelled by gratitude. This is the only way of rendering human nature useful, and willing to apply its energies, by showing an interest in being em- ployed, and a reward for exertion. Discontent should be wholly removed, and contentment is not at all beyond the reach of attainment. In the notice of woods as a part of landed property, it was observed that the expense of that department rested wholly with the nature of the estate, as it may be stocked with old timbers, or half-grown plantations, or is in an incipient condition, and require much original expen- Woods, diture. In the two latter cases, no revenue will be derived young or old. from the wooded grounds, and the whole cost of the woodreeve's depart- ment will fall upon the estate as a primary outlay. A stock of full-grown timbers on any estate is an item of very considerable value, and enhances the price of the property more than the presence of it might suppose. Where a moderate quantity of timbers is ready for sale, such a portion should be yearly vended, as will cover the expense of the Sale of tim- ber. 1056 ON LANDED PROPERTY. Gardeners. woodreeving, in the current-going item of outlay for repairs and ne- cessary upholding; but the raising of new fences, and the making of new plantations, and all original work, must form a part of the general ex- penditure, unless a special fall of timber can be made to meet the outlay of money. If the yearly sale does not cover the whole cost of the wood- men, the greater part, or some portion being paid, will proportionally relieve the general burdens of the estate. Whenever a bare possibility exists, some relief must be given, but not to detract from future values by a premature use of the articles. This blunder may and has been done, and requires to be guarded against. Where no timbers are found for sale, the establishment of woodreeve will be reduced correspondingly, unless large doings are contemplated, and ample extraneous funds are at command. Gardener's office is wholly confined to the inside walled grounds, and the pleasure walks, roads, and shrubberies, that surround the gardens, and manorial residence. The department is most usually excluded from the inspection of the land agent, and wholly directed by the family of the estate. Nevertheless, a notice may be made of the ar- rangement which may seem just and equitable of that item in reference to a landed property. The expense of luxuries is seldom calculated and never regarded, consequently a much larger cost is attached to that depart- ment than appears in any part of the property. A garden of four acres is a provision for an estate of a very respectable extent, and allowing one man to an acre of ground, the head gardener will require four men em- Duties and ployed within the walls; and if the outer appendages are large, expense. as roads, walks, lawns, and shrubberies, two or three more hands will be required to keep all things in the state of trim neatness, which the practice of gardening understands. The average of six men with a head gardener, will require the sum of £300 yearly of maintenance only, exclusive of wants of seeds and flowers, which are uncertain and contingent. The employment of land in gardening, pays no rent in return for outlay, and is only to be placed to the account of unpaid luxury, that is both necessary and useful. Gamekeeper is an appendage of landed property, which is reckoned to be equally required with the other charges of protection. There is no doubt that the preservation of game animals, and a tolerably abundant supply of the different articles of that kind, forms, and even may consti- tute, a very great inducement to the possession of land, and Gamekeeper. were the arrangement not carried to a provoking extreme, no challenge would be given to the right of possession in the passing flights of rest on the grounds where the animals alight. Both pleasure and profit can easily be derived from that source of occupation, provided a relaxa- tion and forbearance were extended to conciliate and not exasperate the feelings of a jealous inferiority. The department of gamekeeping is most generally managed by the landlord's own special arrangements, but like gardening, it may be noticed, and the relation stated with the other estab- lishments on landed property. One head gamekeeper will require about £100 a year, for his mainten- ON LANDED PROPERTY. 1057 ance, a pony, cow, house, and garden. Two assistants will be needed in £100 more, which will make £200 to be the yearly cost of maintaining the protection of game. The erection of extra establishments, and food for the animals that is given in the plantations, will form another calcu- lation: the above is given as a medium thing, and to suit mo- Arrangement derate views on that point. The estimate now given for that and expense. purpose, and likewise for the establishment of gardening, will no doubt fall very short of the general costs that are incurred on these points; but as they are matters of fancy rather than use, and promoted by whim rather than utility, a moderate approximation is stated, without regard of special arrangements. Agent's judgment, The establishments of gardening and gamekeeping do not always, or rather very seldom, fall under the direction of the chief agent on an estate of landed property; but as the expenses are part of his disburse- ments, the notice is not to be omitted of the uses to which the money is applied. It may sometimes be his requested duty to give his opinion of the amount which should be incurred on each particular point of outlay, to make the arrangements, and to settle the estab- lishments; and then his judgment will be called into action, in disposing the parts to suit the particular purposes, and in allotting the distribution of the general charge on the property as the different values may require. It is true that the two departments now mentioned, are almost a domestic concern, and need not the inclusion in the estate concern, but as the landed value supports every department, the very household arrangements must be made conformably and partake the same regulations with the other branches of the landed economy. The land and woods must have the first care, as they form the source of revenue which upholds all con- cerns: the other branches must be contented with such appor- tionments as the respective values and necessities may seem to require, and are able to justify. The chief agent must pre- pare an advice on all these points, which if used, may lead to pleasurable results; and if not adopted, it may not be less valuable, to be honored with a rejection. in making arrange- ments. Whatever arrangements may be made in the case of the gardener and gamekeeper on any landed property, the chief agent must have the whole direction of the manor bailiff and woodreeve, as these offices do not form an independent separation, but are merely delegations of the business of the chief agent, and of which he retains the responsible execution. Hence a very regular subordination must be established and maintained by an understood dependence upon him, except in cases of last resort, when an appeal may be necessary to the owner of the property. These deputies are appointed by the approving knowledge by the landlord for their qualifications, and are moved by his convenience. No despotism must be exercised by the agent, but his authority must be supported in all reasonable jurisdictions, which are equitably dispensed. His just authority. 1058 ON LANDED PROPERTY. CHAPTER XIV. FIXED DAYS OF AUDIT-HALF-YEARLY PAYMENTS OF RENTS-FORM OF NOTICES, RECEIPTS, AND OF CASH BOOKS, GENERAL MAP OF ESTATES, AND OF EACH SEPARATE FARM-CONCLUDING OBSER- VATIONS. Days of FIXED days of audit are best adapted to the systematic management of landed property, where nothing must be left to uncertainty that can be fixed, but all proceedings go on in the most undisturbed order. Audit The times of receiving rents are of considerable import in the management of a landed estate, and the fixed periods are not less desirable. The days of audit are most generally arbitrary, and conveyed to the notice of the tenantry, in a precept from the receiving agent on the property. No doubt the known period of the year lets the farmer under- stand that the time of payment is approaching, and warns him to make a timeous preparation for the coming damage. Still he may trust to some little postponement of the day of audit, and neglect his diligence, and he may plead an excuse of not knowing the exact time for the neglect of fixed and observed. readiness. Some other business of the agent may interfere, and induce the putting aside the rent-day for some time, and a vague- ness is by this means introduced which is hurtfully extended into the other ramifications of business. Alterations of the day may follow, and lead into a month posterior to the customary time of clearing obligations. Such shufflings very much impair the efficiency of business, and totally disqualify any person from acting in the capacity of receiver of rents. Business hangs in suspense, uncertainty is prolonged, and accounts of every kind are kept behind, and fail to show the exact currency of affairs, in the purpose for which they are established. The closely kept state of accounts is the chief recommendation of any establishment, and no dilato- riness must be allowed in the very least tittle of amount. Activity is the soul of business, and punctuality with dispatch carry forward the whole machinery at the proper speed and rate of advancement. payments. The best experience has established the payment of money rents half- Half-yearly yearly, or in equal halves, at the end of every six months, after the entry to the farm, and during the currency of the lease. No better mode of management has been devised, and it obtains the approba- tion of both parties in the giver and receiver. The best time of entry has been shown to be in May, in the middle of the month, or on the first day of the summer quarter of the year. The first half-year expires ON LANDED PROPERTY. 1059 in November, and in that month the first moiety of the rent is due. But to avoid the appearance of an anxious eagerness, and to indulge the con- fidence in the mutual transactions, that neither party expects any trickery or demur, a quietus of one month is given to the tenantry, and short as it may be, the utility, is not below an estimate. The middle of December, or the fifteenth day of the month, is fixed as the permanent day of audit, with the postponement till Monday, when the fifteenth day is a Sunday, and also if it falls upon a Saturday. Such assemblies give rise to hilarity which is sometimes extended to late hours, and all occasions should be avoided of unfitting the mind for the day of holy rest. The same day of the month of June, will be six months distant, and divides the year into equal portions. purpose of December and June. In June These times of the year, June and December, do not seem to be exceeded in fitness by any other periods, for the rendering the value that is derived from the use of the land. the farmer has received the sales of the grain crops, thrashed and vended during winter, and also the proceeds of the winter-fed beef, which will meet the half-yearly rent, and leave a surplus to aid the next payment. In December, the clip of wool, and the sales of all the summer-fed animals, will come into hand, and under particular circumstances, these receipts will exceed the values of the winter half-year. In grass-land districts, almost the whole proceeds of the season will be obtained at this time of the year, from cheese, wool, and grass-fed beef and mutton. And Best periods the period of the month of December, gives an ample time to the necessary transactions being done to meet the demand upon the farmer. No disadvantage is imposed upon him, of disposing any stock under value in order to meet the rent-day; and in June, he has had sufficient time to convert into money the grains of corn farms, and the winter values of beef and mutton, upon the lands that form the mixed cultivations of Britain. No faults have ever been urged against these periods of the year, where the times are duly observed, and regularly attended. Omissions and neglect may disturb, but not destroy the eligibility. of the year. Arrears, The times of paying the rent of lands being fixed, and a month's quietus being given, it is very necessary that it be understood that no arrears are allowed, but that the full amount of the rent is expected on the day appointed, as all arrangements are made with that express view: nothing more contributes to embarrass any business than a number and a multiplicity of payments, which equally annoy and disturb both parties; the landlord never knows his income, and the farmer is per- petually bustling with payments. A mistaken lenity often leads to these confusions, and the demanding rents at improper seasons; the over-renting of farms, and an improper choice of tenants, tend to the embarrassments which involve much disagreeable communication, and create a very un- profitable state of affairs. To promote the non-existence of any back dues, an especial care must be used to place the tenant in a position to meet the exactness that is required, and to choose tenants who are capable and willing to use the necessary exertion under the circumstances that permit 1060 ON LANDED PROPERTY. not to be allowed. the attainment. Arrears of rent are a certain index of bad management, probably on both sides of the business; but if other exactitudes are per- formed under the same circumstances, a suspicion may be inferred that the tenant is failing in duty, and requires to be observed: the land under his temporary use will be in arrear of management, and defalcations will spread into every branch of the undertaking. Nothing is more to be avoided in the management of any landed property; when the cash-book shows few or no arrears, the assurance is certain of the prosperous and thriving condition, that the landlord enjoys his income, and the tenants share the fruits of the arrangement. But when the contrary happens, when the column of arrears equals the receipts, and stands constantly filled with a full amount of figures, the sus- picion is just, that the property is on the back ground, and the value and condition is diminishing. In a general view, arrears are most dis- graceful to the superintendency of an estate, and many evils grow out of them. They encourage idleness and extravagance among indolent and thoughtless tenants, and are a disheartening burden to the industrious. To a receiver they are the cause of much trouble, and to a proprietor they are doubly embarrassing, as being the cause of intricate accounts, and of an uncertain income. The remedy for arrears, as of every other malady, is to be suited to the Causes and cause. If it arises from over-renting, reduce the rent to an remedy. estimated fairness. If it be owing to over-indulgence, or to real misfortune, or to the known poverty of an ill-chosen tenant, and there is no prospect of the arrears ever being paid up-wipe it off. On the contrary, if the defaulter has substance, and there is a probability of his being able, one day or other, to clear the debt, lay it aside, and wait until a good year of fruits, or other favourable incident, occur for enforcing the payment. Standing arrears must be expunged, and current arrears prevented: the former by using means of due consideration, and the latter by establishing strict regulations to insure the punctuality of every pay- ment. But when extraordinary circumstances do occur, judgment will be immediately called into action, and matured into an arrangement by the exact circumstances of the case. The occurrences of this nature require a just compensation, which no reasonable proprietorship ever can deny, or think of refusing. When the tenants are exact on the rent days, and pay the value of the farms readily and cheerfully, an equal willingness of promptitude must meet the occurring wants, and thus ensure the continuance of the strict and well-regulated system of de- portment. Fire, tempests, loss of stock by accident, and other unavoidable calamities may befall the lower class of tenants, when it may be not only cruelty, but a very bad policy to demand the whole rent in the usual ful- ness of payment. Such cases are easily managed; a very bad crop of grains, or a large decline of prices, even though temporary, will, and must, induce a relaxation of the fixed rules, which are again observed, when the occasion of their being loosened, has passed away. Exceptions occur in every arrangement, and fixities are all liable to be shaken in their Prompt doings, ON LANDED PROPERTY. 1061 and no arrears. position. Arrears are a defilement to the rental of an estate, and con- stitute a stain both on the proprietorship and management of the pos- session. Every payment that is in arrear shows a want of arrangement in some quarter to meet the demand; it may be too large for the means, or the latter are not duly provided for the occasion; neglect is seen on both sides, too much is asked and cannot be found, and a fair value is not provided by reason of improvidence and an aversion to an honest exactness. A month before the day of audit, the chief agent will address to each individual farmer on the estate, a circular note signed by his own hand, reminding the tenant of the rent-day, and requesting his attendance. The bundle of letters goes to the manor bailiff, who delivers from his own hand, each letter to the special direction, which very much enforces the official notice contained in the circular. A trusty servant on Written small estates, acts for a manor bailiff, as such a person is occa- sionally employed in carrying orders and messages. The note runs thus:- Sir, notice. Fordhall House, 12th May, 1852. or Esq., falls I beg to remind you that the day of audit for the receiving the rents of your landlord, Earl of on the usual day of Tuesday, 16th of June, of this year, on which day the half-yearly rents due on 15th May, will be gathered in the King's Hotel, Wayford, at ten o'clock, A.M., when your punctual attendance is most respectfully requested, by, sir, Your very obedient servant, A B., Accredited agent and receiver. To Mr. G. F- Tenant in Fordhouse. This notice is delivered to every person on the estate, who pays a rent of any amount. Day ap- all parties, Precisely at the place and hour appointed, the chief agent arrives with his clerk, who has prepared the proper stamp receipts for each payment of money, and has had them signed by the receiver. The manor bailiff and woodreeve join the company in a suitable pointed for apartment, to which the farmers are introduced singly and in succession: a seat for a few minutes, gives the money rent to the receiver, who counts it, gives it to the manor bailiff, who also counts it, and if they both find the same amount, the clerk hands the stamped receipt to the farmer, who makes a suitable obeisance of mutual satisfaction, and retires. Another tenant is introduced, and is similarly treated, and so on till the number is exhausted. The clerk makes a scroll note of each receipt of money with the name of the payer; the money is put into parcels of twenty paper notes and of twenty gold sovereigns, which are all again counted by the agent and bailiff, after the business of receiving is over, and when the amount which they count agrees with the sum of the clerk's scroll account, 1062 ON LANDED PROPERTY. Proceedings. the business is complete. When they disagree, a repetition is done, and the mistake discovered. It is very convenient when the banker of the proprietor lives in the town in which the rents are received, as he attends with his clerk, counts and receives the money, and gives the agent the note of transfer of the amount to the credit of his employer. When this arrangement cannot be done, the money remains with the agent till next day, when it is carried by him to the bank of the property in the special locality. The security of the money for one night rests with the agent, manor bailiff, and woodreeve, sleeping in adjoining rooms, the former being central, and having the cash in the apartment. The cases are most numerous where the latter way is adopted, as only large properties and contiguous market towns afford the convenience of a bank. But most landed estates of any considerable extent will employ this arrangement. Receipts. The receipts given in return for money rents, are worded thus:- Received on account of Earl of Wayford, 16th June, 1852. or Esq., the sum of eighty pounds sterling, from Mr. G. F., tenant in Fordhouse Farm, being the half-year's rent of that farm due on 15th May last, by the said Mr. G. F. £80 Signed A. B., Accredited agent and receiver. When partial payments are made and arrears do occur, a stamp is not required, and an acknowledgment is given on plain paper, stating the particulars, and writing on the left hand corner, the rent of the farm, the sum received, and the arrears due. Thus: Rent £180 Paid 100 Arrears £80 This note will agree with the agent's book, and prevents the possibility of any mistakes. The receiving agent fills up the general cash-book of the estate from the scroll pages of the day of audit, placing every receipt of money in the proper assignment, and any disbursements to the proper account of use. Cash-book and copy sheet. These are the employments of his home retirement, where with his clerk he adjusts the items, and schemes the regulated ex- penditures. Where it is not convenient for the proprietor to see the general books of the estate, a copy sheet of each year's proceedings is regularly sent him. It is not unfrequent that the landlord treats the tenants with a dinner at least once a year; and it may happen in June or December, as may ON LANDED PROPERTY. 1063 Dinner. No business audit-day. be arranged. In that case, when the farmer is bowing retire- ment from the audit-room with the receipt for the rent in his hand, the agent will be glad to see him again at four, five, or six o'clock, as the hour may be fixed for dinner. At the other half-yearly audit when a dinner is not given, a glass of wine is handed to the tenant in the audit- room, when the money has been paid, and the receipt delivered; and this acknowledgment ends the intercourse for that day. It is best arranged that little or no public business is done by the agent on the on the days of audit; the money matters will very sufficiently occupy the attention, and the memory must not be crowded with a multi- tude of proposals, which may be too hastily considered, and improperly regarded. On such occasions, advantage may be taken of a hurried em- ployment to convert into promises the probably unguarded words of passing observation, and which require a much more grave consideration than can be bestowed upon any subject in these hurried moments of occu- pation. But on the last-mentioned day of audit a leisure may be got for the hearing and answering the appeals and proposals of the tenantry; and in long cases, the answer can be afterwards returned through the manor bailiff. Separate days, or one in every half-year, may be appointed for the purpose of hearing proposals, and meeting demands, which may be fixed as are the audit-days, and have the same consideration given to their importance. In some instances, the days of audit are held at the mansion of the proprietor, when the same forms of business are observed as at the public resorts. The subjoined form of a cash-book for an estate of land, may be altered in any way to suit the circumstances of attachment, and may afford the grounds of adoption in most cases. Books. 1064 ESTATE CASH BOOK. Crop 1852.] Posses- Names of sors' Rent. Farms. Names. 4 DR. Estate Cash Book. s.d. Date. Cash Received. £ 48 s. d. £ s. d. Arrears. £ s. d. s.d. Newstead A. B. Money 280 0 0 15th Half Burdens, June Year's if any Rent...140 O 0 15th Dec. Ditto... 140 0 0 280 0 0 280 00 Grange E. F. Money 600 0 0 15th Half Burdens, June Year's if any Rent... 300 300 0 0 15th 600 0 0 Dec. Cash... 240 00 540 0 0 By E. F. 60 00 This Book shows the rents received, the arrears, the expenses on each farm, and the whole charge of upholding the estate. It may be continued to any extent, and have attached to it the general receipts of money from ESTATE CASH BOOK. 1065 Crop 1852.] Contra. CR. Date. Expenses. £ S. d. બે £ S. d. £ 8. d. 18th July By Cash paid the Carpenter's Bill for Repairs, as by Ac- count rendered………….. 55 17 0 55 17 0 16th Sept. By Cash paid the Mason's Bill for Repairs by account...... 15 6 6 By Cash paid the Carpenter's Account 10 8 0 80 25 14 6 Total ....... 81 11 6 other quarters, and also the general expenses. Abstracts of each de- partment being joined together will show the result of the whole proceedings. 3 U 1066 ON LANDED PROPERTY. Brevity and simplicity of arrangement constitute the essence of the art of keeping accounts, which are to be so designed as to afford at any time from a slight inspection, a clear and satisfactory view of the existing state of affairs. There must be no dilatoriness of entry of the very minutest trifle; every transaction must be recorded within twenty-four hours after being done, and show the negotiation in the place of proper exhibition. Nothing is left till to-morrow which can be done to-day, and each night must show the business of every kind arranged as it has been done, and duly noted. No other way is able to direct the current of affairs in the proper channel, or control the tendency to go awry. Short and The following very concise and simple form of a book of receipts and payments, may be found useful in certain places of an extent clear. not very large, and where the proceedings require to be closely shown, and narrowly guarded. Its chief use consists in giving a view of gross receipts and disbursements, and showing the balance of money that remains in hand. It is a concise abstract of general proceedings, and has been found very useful under circumstances which require an understand- ing of that nature. Account in respect of Receipts and Payments at month, or from weeks ending for one 1852. Dr. Cr. Receipts. Dates. Particulars of sums paid and received. Payments. 4+ £ S. d. બે £ S. d. It is conveniently and very beneficially arranged that there be attached to the residence of the manor bailiff, an office-room of public resort, at which the bailiff is found on most days of the week and settles the business of the estate that requires the transaction of being put into the form of writing. This office of two apartments in the outer and inner rooms, may be joined with, or placed at a small distance from, the dwelling- Bailiff's office. house of the bailiff, and to it the chief agent may be appointed to come on the fourth Wednesday of every month, or any other day or week as may be eligible. The farmers and all the subordi- nate agents know this appointment, and attend it, when reports are made and suggestions heard and settled. The manor bailiff and woodreeve ON LANDED PROPERTY. 1067 Where to meet and consult, refer all matters to be settled at this meeting, and the tenants look to it as the termination of all cogitations and proposals. In this office are kept all the books of general reference, and the maps, which require very often to be consulted. On estates of the smaller extent, the agent will be of the minor grade, and perform the whole business of agency and of the bailiff; the office will be attached to his own dwelling, and answer the purpose above described. When he resides at a distance, an occasional residence may be found on the estate, when the monthly attendance at the bailiff's office will be more convenient, and more easily attended. may be the place of audit. In some cases of landed property on which the idea of hospitality is not entertained or largely distributed, the office at the residence of the manor bailiff or inferior agent, may serve as the place of audit, and the rents can be received in the two rooms of office. This arrangement does not abandon the monthly day of meeting at the office, as it is exclusively devoted to the receipt of money, and the other time to the transaction of contingent business. The residence of the proprietor may have an office attached, where every agency is done: on largely extended estates, the offices of business may be two or three in number, in order to suit the distances of detachments. At each place the agency must occasionally attend in order to inspect the demands that are made, and to diffuse a spirit of good order and emulation. In these offices, there must be lodged the necessary provisions for the transaction of business, as maps, rentals, books of accounts, registers, and receptacles of business that has been transacted. No person must carry away on any occasion, or for any purpose, a paper of any kind from the office, without leaving in its place, a memorandum, stating by whom it was taken, and for what purpose, and when it will be returned, in order that it may be traced in case it should not be brought back. This regulation should be written in large letters, and suspended in the most conspicuous place of the office. Such an injunction requires a positive enforcement. Rent-roll. A rent-roll is required on every estate of land, or a statement of the gross value of the property, ranged in the order of the farms, and other sources of revenue, as woods, mines, rights, and fines. This general view of increase is best arranged in columns, as being most perspicuous; and for a schedule of farms the following are proper :— 1. The mark of the farm in the general map. 2. The names of the farms. 3. The contents, or admeasurements of each. 4. The names of the present tenants of each. 5. The amounts of the existing rents. 6. The outgoings, if any, by the proprietor. 7. The expiration of the lease. The farms are best arranged geographically, in the natural order in which they lie on the estate, and thus appear on the rent-roll. The general roll- map of the estate, the book of maps, the large rotation book of maps, and the pocket-book of maps, must all agree in having the farms similarly 1068 ON LANDED PROPERTY. marked, and arranged in the same order, and also in the receiver's general cash-book, and in fact, on every occasion of the farms being placed in order of any kind, a systematic mode of proceeding must be adopted, prac- tised, and enforced; and when neglected or infringed, it has to be imme- diately restored. Maps of Books and Estates of land must be mapped in the whole extent by a compe- tent surveyor, or of the districts, or officiaries into which estate. a large extent may be divided. These provisions will be lodged on rollers, and unfolded on the floor of the office when a general consul- tation is required. On a reduced scale from this map, there is constructed a book of maps, in which each separate farm is contained on a leaf which extends over the whole book when opened, and the middle of it bends into the centre of the book when it is folded. This volume forms a ready re- ference to each single farm, and can be carried to any place to single be examined on the spot for the purpose of certification. In the reduced scale of one-half of these maps of estates, the general book of rotations is made, having on the right-hand side the plan of the farm, and on the left the rotations of cropping during the currency of the lease, as has been shown in the duties of the manor bailiff. And on all suitably reduced scales from these plans, the pocket-book of maps and ro- tations is constructed, so as to be convenient, and easily portable. All these plans being fitly done in one copy by a professed surveyor, can be copied into any useful number by an official who has received an educa- tion that enables the performance. At every office on an estate of land, there must be lodged within its walls, the book of maps, and the rota- tion books of the districts which lie within the circuit of the officiary; reference will be constantly necessary, and the provisions must be had. The original copies of professional skill will remain at the chief office, the others are copied as substitutes. maps of The plantations are separately mapped, and shown in the office or offices to which the position of the woods appertains. And when a new planting of trees has been done, a plan is made of the plantation ground, plantations. in order to answer the special purpose of necessary references. The woods are ranged in the numerical order, and a book with columns con- tains the extent of each plantation, the age of the timbers, the time of last cuttings, and the money got from sales, with the respective dates attached. The quantity of hedge-row trees on each farm may be entered in a simi- lar book, and accounted as they may be cut down and disposed for use, or sold. The manor bailiff and the woodreeve prepare and keep these books, and the chief agent examines and approves. On the inferior agencies, these performances fall upon the steward himself. These cases often join the duties of bailiff and woodreeve in one person, who will assist in upholding the provisions that have been mentioned. Accounts. On every estate of land there must be established laws and usages, to which both parties are liable, though no written contract subsist on the subject. Though these laws may be imperfect, they ought to be strictly observed, until better regulations are found: moral justice demands the ON LANDED PROPERTY. 1069 exactness. performance of these duties, and the example must be set of integrity and good faith to the tenants. The proprietor and agent must show the model; for if these persons break customs and covenants, what can be said to a farmer who follows the example? It is no more than common prudence to fulfil with scrupulous exactness every covenant and agreement, A scrupulous and every promise that has been made, even to the meanest cot- tager or labourer on the property, in order to inspire the same principle into the conduct of every person that is concerned. Not only good faith must be preserved, but good offices; and frequent acts of kindness must liberalize the minds of the tenants, and not with any loss, but with a posi- tive advantage to the estate. Spirited improvers must be denied no rea- sonable request, and should have favors voluntarily conferred upon them. Estates, like men, acquire good or bad characters, and not from Character the quality of the soil, but from the conduct that is observed in the arrangement and treatment of the negotiations. A skilful farmer of capital will rarely fix his abode on an estate of bad repute; while on the contrary, a contest will happen to obtain a footing on a property of estab- lished character. Nothing can well add more to the permanent respect- ability of a family of rank and fortune than having the estates occupied by a wealthy and respectable tenantry. established. The good management of a landed estate requires the assistance of a law officer, as solicitor, or attorney. This person is employed as an assistant when required, as is medical aid when specially necessary. Judicious re- gulations and timely advice without interference will almost prevent any serious divisions on the estate; yet cases will occur from the frailties of human nature, and in a state of civilized society, and of established pro- perty. The lawyer is best engaged on large properties to manage all legal affairs for a yearly stipend, which may be sometimes exceeded, but oftener below the mark. The land surveyor is employed when the pro- fessional service is required, and is often a useful person as an arbitrator or referee. of business. In every business between man and man, the affairs must be No arrear made pleasurable, and transacted cheerfully, as the matters oc- cur, and never delayed, till by accumulation the performance is difficult and irksome. Dispatch is essential before misunderstandings; idle tales, and groundless surmises have time to intervene, sour the mind, and pro- duce a distant coolness. Barriers are thus raised, which nothing but the mystic law may remove. No tricks or artifice to take advantage like gamblers round a table, but an honest desire to find the point of equity and right, must be the chief motive; and when honest men, who have character to lose, meet to settle any business, the difficulty very quickly vanishes. An umpire may be necessary at times, but the occasions will be few. On the part of persons in power, a conduct of a somewhat peculiar mark has to be observed, in order to give no offence to superiors, to please the equals, and to conciliate inferiors. A demeanour at once respectful and firm must be exhibited by agents, in order to procure respect and observance of regulations. No arrogant Conduct of persons in power. 1 1070 ON LANDED PROPERTY. haughtiness nor austerity of manner must debar the approach of solicita- tion, nor must an improper familiarity allow the intrusion of every petty squabble or request that may suppose itself worthy to be heard. The for- mer line of conduct prevents the necessary access of presence, and the latter crowds every avenue with trifling advances. No quality is more Firm decision hurtful in an agent of any kind than the want of a firm decision; essential, the resolves must be decided and adhered to with pertinacity. Inferiors must be taught into a respectful submission, but no slavish cringing, which wholly destroys the independence of mind which must ever accompany the use of any rational faculty. A courteous affability must be very largely entertained with every person, of whatever rank or station, that requires to use the agency of the estate in any way; no cold repulsion is to be used, nor a feeling of disdain be manifested, unless on the proper occasions, which must be well settled and authenticated. A demeaning familiarity must be very carefully avoided, as it tends most powerfully to lose esteem, to sink respect, and never fails to beget con- tempt for the object of its exercise. There is a happy medium of conduct which pleases superiors and conciliates the lower stations of life; it is a most valuable acquisition, as it procures confidence from the for- memory. mer and attaches the latter, who form the supporting ground- work of society. In the days of audit, or at any other times, the agent of extensive business must not trust to promises in a crowded memory, but reduce every business into writing, when it is of the possible import. An occupation being arranged in this way, and the habits of transaction being adapted to the circumstances of the position, and a systematic organization being on every point established, there is only wanting the polite affability and courteous demeanour which gilds every object and burnishes every business, gives oil to the wheels of affairs, and lubricates every transaction. and a clear Moral re- Such an important subject as the charge of landed property cannot be dismissed without a parting admonition to the holders of these offices. In many cases the total absence, only a temporary residence, and the occupa- tion of the land-owner in legislature, leaves to the agent the almost uncon- trolled direction of the estate; while in almost every instance of an agency of repute, the advice of the professional adviser is as it ought to be-deci- sive of the system that is adopted. The agent will see that he is entrusted with the physical and moral condition of a portion of his fellow- sponsibility creatures, who have a claim or vested right to be employed, of an agent; maintained, and educated by the property of which he has the administration. His employer has bought a certain part of the develope- ment of its resources, and this being the acting portion, must have its every direction made to tend to the chief points of attachment. This em- ployment becomes a very serious concern to a rational being, who must assume a corresponding lofty standard of morality in every sense and mean- ing of the word. The agent has to hold in constant perspective the employment of the people, and a competency of support; the education, moral and religious, accompanied with such a remuneration to his employer ON LANDED PROPERTY. 1071 and most important charge. as will justify the progress of the undertakings. These purposes form a most important charge to be invested in any one person, and re- quire a thoughtfulness the most serious, and a calculation the most profound. It is no every-day affair, or passing concern, but a matter the most valuable of all the varieties of occupation. Those persons who write about man, and the different states and stages of his existence-moral, social, and political-would do well to remember two things: the cultivation of the earth, and the supply of the necessaries of life; for they uphold or overturn all their ideal fabrics. INDEX. A. Abutments, wings, and spandrils Accommodation land, valuation of of labour on land. Accounts of subordinate land agency Acre decimal table Addition of vulgar fractions proof of Adjustment of rents (On Landed Property) Advertising of farms Age for business men Agent's judgment (On Landed Pro- perty) Age of plantations Agreement between auctioneer and purchaser at sale by auction Agreements and leases, law re- lating to • Agreement for a farm PAGE PAGE • 406 Appraisements, law relating to 749 586 under distress 781 869 Appraisers' oath in cases of distress 781 1068 Approaches to bridges 409 226 Appropriation of land 857 • 5 Arches and Counterforts 405 2 backing to 405 over reservoir 489 872 Arch over road of the farm yards 931 • 894 Areas, computation of 326 1027 Arithmetic 1 1057 proof of first four rules Arrangement of crops on land 2 909 1017 estate expenses 1057 farmeries 930 764 Arrears of rent of landed property Artesian wells and springs 1059 467 765 Artificers' work 541 770 Artificial manures 890 857 984 Art of ploughing Ashlar work. 968 Aspect of farmeries 906 403 935 • 895 752 1031 Alienation of land All drains should be covered. Alluvial valleys Altered policy (On Landed Property) Alternate system of cultivation of land. 862 Assignation of lease Auction, law of Alternation of plants Amount of fine to be paid for renew- ing any number of years lapsed in a lease originally granted for ten years Amount of fine to be paid for renew- ing any number of years lapsed in a lease originally granted for twenty years Amount of fine to be paid for renew- ing any number of years lapsed in a lease originally granted for twenty-one years Amount of fine to be paid for renew- ing any number of years lapsed in a lease originally granted for forty years Amount of fine to be paid for renew- ing with one life the lease of an estate originally granted on three lives. Angles and right lines, and their rectangles. 603 Back drainage of houses Backing to Arches Bad farming. arrangment of farmeries. 604 Bailiff's business office Baking of tiles • Ballasting and laying permanent sidings of a railway 605 Ballasting and laying permanent way of a railway Bankruptcy, its effect on a lease Barley used in rotation of crops 606 Bedfordshire, agricultural custom 910 908 Authority of a land agent B. 455 405 874 927 1066 1002 417 413 895 911 of 625 Beds of rivers Beech trees 968 • 951 607❘ Beet root 904 Benefit of leases on landed property 875 173 Berkshire, agricultural custom of 625 • Angular mensuration 193 Best forms of farmeries. 929 Apartments of agricultural dwellings 922 materials of embankment 965 1074 INDEX. Books of estate agency Best soils, cropping of times of paying rent of land trees for copses Block in course work PAGE 917 Concrete foundation PAGE 487 1059 489 960 Condition of lease of land 403 Conditions of sale, freehold property 881 761 1034 leasehold property 764 reference on farmeries and goods and chattels 764 cottages Boring of coal 940 Condition of tenantry 993 943 a landed estate 1014 Boulders, or field stones 948 Conic sections 216 Box sextant • 286 Consent by tenant to hold over un- Bricks, quality of 488 der distress 780 Bricklayers' prices 676 Constant water supply 465 quantities &c. work 547 Construction of water closet 459 541 Contents of railway cuttings and Brickwork 402 489 embankments, methods of com- puting the 380 Bridges 1009 Continued use of badly arranged culverts, &c. 402 farmeries 927 and highways, dilapida- tions of Buckinghamshire, agricultural cus- Coping and string courses 406 740 Copper 988 Coppersmiths' prices 705 Burdens on land tom of Builders' prices Building stones Burning of lime • Butt jointed pipes. • 625 Copse woods. 958 660 not formed. 961 • 999 Copying maps 860 Corners of fields should be planted 998 Cornwall, agricultural custom of 461 Cost of sinking coal pits pleasure grounds 335 946 626 • 994 1012 • Cottages 935 C. Cambridgeshire, agricuitural cus- tom of designs for 833 on farm, valuation of 586 Counterforts and arches 405 Capacity of sewers 625 451 Covering of drains 980 land 915 453 Cow shed 926 Capital required in farming 893 Cross staff 229 Capping top of reservoir 486 Crooked ridges on land to be made Carpenters and Joiners' work 551 straight 903 prices 660 Cube root, extraction of 10 Casting of iron pipes 468 Cultivation of land lessened 865 Catch-water meadows 973 defined 898 Causes of arrears of rent of land 1060 Culverts 411 Cement, Roman Centring of arches 404 Cumberland, agricultural custom of 489 Curvature of the earth and refrac- 626 Cesspools 468 tion, table of 161 Character of estate established 1069 Curvature of the earth and refrac- Cheshire, agricultural custom of 626 tion, the use of the table of 36 Choice of a tenant of land 892 • Customs duties 823 Circles, &c. • 178 Custom of the County of Bedford 625 Circular protractor 319 Berks 625 Clap gates 953 Bucks 625 Classical education of land steward 1025 Cambridge 625 Clay 1000 Cheshire 626 for bricks 1001 Cornwall 626 • Cleansing sewers by manual labour 454 Cumberland 626 Coal 993 Derby 626 Cocks for water supply • 470 Devon 626 Collected reference to maps 324 Dorset 626 Colonial surveying 424 Durham 626 Complaint before justices to recover Essex 626 possession 785 • Glo'ster 626 Computation of areas 326 • Computing scale tables • 328 330 Hereford Hertford Hants 626 • 627 627 · Concrete, composed of 404 Huntingdon 627 INDEX. 1075 PAGE PAGE Custom of the County of Kent Lancaster Leicester bridges 627 Dilapidations of highways and 627 740 627 Dip of the horizon, table of 141 Lincoln 627 the use of the • Middlesex. 627 tables of 29 Norfolk Northamp- • 627 Direction of roads on estates 943 drains 982 ton 627 Discharge of water flowing through Custom of the County of Northum- pipes. 442 berland 627 Disposal of material 401 Custom of the County of Nottingham 628 Distress, appraisement 781 Oxford 628 appraisers' oath 781 Rutland 628 consent by tenant to hold Shropshire Somerset 628 over. 780 • 628 Distress, notice of 780 Stafford 628 notice of, standing corn 781 Suffolk Surrey 628 warrant of 780 628 Diversion of roads in constructing a Sussex 630 railway 412 Warwick 630 Division of fractions 5 Westmore- proof of 3 land • 630 Dorsetshire, agricultural custom of 626 Custom of the County of Wilts 630 Dr. Angus Smith's preparation for Worcester. York, East 630 coating pipes 470 Drainage outfall 446 Riding 630 sewerage, and water sup- Custom ofthe County of York, North ply of towns 440 Riding 631 Draining necessary on clay lands 914 Custom of the County of York, West Riding of land 975 631 roads 944 Drain pipes, tender for 475 Drainage and water supply, prices D. of materials for 686 Drains, house 455 Danger from uncertainty of tenure in land Decays of houses junctions for 458 864 main 446 1005 pipe 445 • Decimals of an acre 6 447 226 of a pound sterling. reduction of • Declination of the sun, tables of 807 7 size of trapping of under bridges 450 459 407 171 Drawing of lime cinders 998 the use of Drilling of green crops 905 • the tables of 38 Drying of bricks 1002 Decorators' and paperhangers' prices 697 Dry stone walls 948 Defence of banks 969 Dung, free to incoming tenant of Deficiencies of cottages 936 farm. 890 Depth of drains 978 Dung used in broad cast and drilling 902 Derbyshire, agricultural custom of 626 Duodecimals 8 Description of a farmery 925 Durham, agricultural custom of 626 entails 860 Duties of farm bailiff 1035 Designs for houses, villas, cot- tages, &c. Dwelling house 922 833 of the farm 867 Devonshire, agricultural custom of 626 Differential coefficients, tables of 168 the use of E. the tables of 38 Digging of clay 1001 drains 981 Earthy filling of drains land 961 Dilapidations by mortgagee or Earthenware pipes Elevation by machinery Embanking 460 981 • 996 486 mortgagor 737 963 Dilapidations and nuisances 707 Embankments 400 • by tenants for life Enclosed grounds 947 • and years 714 Encumbered estates 862 1076 INDEX. 541 • cottages 940 Encumbrances Engine pits Entail of land Equitable privileges of farmers Erection of hedge fences Essex, agricultural custom of • Exactions from a farmer should be Estate valuation lenient Excavations and embankments for pipe laying • of foundation Excavators' work • Expense of pruning trees avoided PAGE 1014 | Flooded grounds 994 Flow meadows PAGE 970 974 860 Fluids, motion of, passing through pipes 442 879 Form of lease 94.9 626 577 872 398 479 408 957 sewers tender for railway works Formulæ for solving all the cases of a rectilineal triangle, of which three parts are known, tables of . Formulæ for solving all the cases of a rectilineal triangle, the use of the tables of Formulæ for the solution of quad- ratics and cubics, tables of . Formulæ for the solution of quad- 878 453 420 166 37 167 irrigation 974 draining 984 ratics and cubics, the use of the tables of 37 • Expenditure on landed property 1003 Experience of rotations. 920 Formulæ relating to two arcs or angles, tables of 164 Expired leases 895 Formulæ relating to two arcs or Exploration and trial levels 338 Extra buildings 923 Foundation of concrete. Extraction of cube root 10 square root 9 • Exudation of plants 921 vulgar F. Facts to assist the memory in mat- ters of valuation Failures, few in draining land Farm account book angles, the use of the tables of Fractions, addition & subtraction of sion of Fractions, reduction of . Functions of sewers Furniture of farm. Furnaces Furrow draining 37 487 LO 5 multiplication and divi- 5 4 3 • 451 866 992 982 • 616 986 1037 buildings 921 G. Farmeries 925 Farmer's dwelling, its accommo- Game 891 • dation 922 Gamekeeper 1056 Farmery covered 934 No. 1 930 Gardener Garden and Orchards 1056 867 No. 2 931 Gas in pits 996 • No. 3 934 Gas works, rating of 651 Farm homesteads, valuation of 583 Gates 952 labour, valuation of • 587 Feeding yards 926 Gathering grounds, for water supply General Board of Health, on sur- 462 Fee farm rent 1022 veys and maps 447 • Felling timber 958 General buildings on farms 868 Fences 870 • clearing of water-courses 915 in charge of the manor description of farm buildings 923 bailiff 1051 mistake in farmeries. 926 Fencing and ditching 393 objects in valuing plantations 1017 Field book for farm bailiff 1049 principle of embanking 965 levelling 311 repairs of houses 1006 setting out slopes 374 rule of size of farms 942 surveying 270 scheme of crops 889 valuation of tillages value of draining 987 and tenant right 632 valuation of an estate 1022 Filling in after pipe laying 480 Geometry, plane and solid 172 • of drains to be carefully done 980 practical 186 • Filter, the best one for water 464 Glaziers' prices 699 Fire damp 996 work 575 · Fishing Fixed sum of money for rent Fixtures on farms. Flagstones Flat measure, tables of . 891 Gloucestershire, agricultural cus- 877 Good husbandry defined Government loans of money 883 tom of 626 890 1000 • 528 Grain rents 862 884 · INDEX. 1077 Grain crops purchased Grand axiom of tenancy Grants of land Grass turf the best bottom of roads for covering drains. Grasses for cropping PAGE 881 | Interest of purchased estates 875 low of land 857 Intermittent supply of water PAGE 1013 1023 465 944 Inventory and valuation of tillages 980 and tenant right 636 916 Iron 991 Gravatt's level 308 Ironmongers' prices 677 Gravel. 488 Ironmongery 573 Great importance of fallowing 907 Iron pipes and castings, specifica- advantages of irrigation 973 tion for 468 value of leases 863 Iron, quality of 468 Grey, Mr., his practice in agriculture 882 Ironwork 407 891 Irrigated grounds. 973 911 Groined arches 489 Groups of cottages 940 J. Grubber working 905 • Gully gratings 481 Joiners' prices 660 Joints for pipes 461 Judgment required in planning H. farmeries 928 • Junctions for house drains 458 Hampshire, agricultural custom of 627 Junction of roads 945 • Hedge-row trees 951 Herefordshire, agricultural custom of Heriots. 626 K. 1021 Hertfordshire, agricultural custom of Kent, the agricultural custom of 627 627 Kilns 1002 Highways and bridges, dilapida- tions of 740 Hill draining 983 L. Holders of land for life. 861 Horizon, tables of the dip of . 14] Labour, hours 1034 the use of the tables of the Labourers' Cottages 868 dip of 29 Lancashire, agricultural custom of 627 House drains 455-456 Land and wood, chief sources 1018 junctions for 458 trapping of 459 Houses, designs for 833 bears a low interest differs from manufactures how valued • 1023 866 1013 paying rent 1015 Huntingdonshire, agricultural cus- is a firm security is easily injured 1023 1023 • tom of 627 is much desired 1023 Hydrants and screw cocks 480 measure, tables of 230 Hydraulics 440 measuring 219 Hydraulic tables (Ryde's), synopsis must be in good order 1023 of, second edition of 443 • plans for railways 380 Hydraulic tables (Ryde's), speci- men of surveying 257 444 the distinction of society 858 Hydrostatic bellows Hyperbolic and common logarithms, table of Hyperbolic and common logarithms, the use of the table of 440 valuation 577 Landlord and tenant 765 161 Landlord's aid in accidents Large farms. 887 942 35 Last years of tenure 890 Law of auction 752 I. Ignorance ruinous in agency relating to agreements and leases 765 Law relating to appraisements 749 1030 Laying and ballasting permanent Improved house drains. Improvements gradual in dwellings Inferior lands in rotation of crops 455 sidings of a railway 417 936 Laying and ballasting permanent 912 way of a railway 413 918 Laying drain pipes 479 Inferior qualities of clay Inspections by bailiffs 1001 Lead 990 1035 Lease defined 877 1078 INDEX. Lease for three years, or less, of a house Lease is heritable • is long of coal mines must have an issue of much consideration Leases and agreements Legumes and grasses used hardly of use. PAGE PAGE Maps and surveys for sanitary pur- 769 poses 447 892 Maps of estates 1068 997 Masonry 490 883 Masons' prices 674 1014 Materials for building houses. 924 765 filling drains 979 913 roads 943 914 Mathematical tables, use of 18 • used 912 Maturity of trees 957 918 May entry on farms 881 Leguminous plants 908 Meadows 963 Leicestershire, agricultural custom of 627 Means of farming should be known 893 Length of tenure • 864 Level, Gravatt's Measures and weights, mensura- 308 tion of 192 spirit. 299 Measuring bricklayers' work. 541 Troughton's 307 carpenters' and joiners' Y 301 work. 551 Levels 994 Measuring excavators' work 541 Levelling 296 glaziers' work 575 practical specimen of 314 hay ricks, tables for 638 staves • 309 iron work 573 the operation of 310 land 219 Lime 489 painters' work 573 998 paper-hangers' work 576 used 905 plasterers' work 571 Lining of puddle for reservoir Liquid draining of farmery List of grass seeds Loans of money Lincolnshire, agricultural custom of 627 sawyers' work 566 487 stonemasons' work 566 926 timber. 491 913 Memoranda to assist the memory 861 in matters of valuation 616 1008 Mensuration, angular 193 • bolic, table of Logarithms Logarithms, common and hyper- • Logarithms, common and hyper- bolic, the use of the tables of Logarithms for finding the horary angle or apparent time, table of. Logarithms for finding the horary angle or apparent time, the use of the table of Logarithms of numbers, tables of Logarithms, use of the table of Logarithmic sines, tangents, &c., tables of • Logarithmic sines, tangents, &c., use of the tables of Long dates at entry on farm Longer security necessary Longitude and time, tables of 13 of solids 197 of superfices 194 161 weights and measures 192 hyper- Meridional parts, tables of 132 35 the use of the tables of 26 34 41 158 Metropolis, subterranean survey Michaelmas entry on farms Mid-channels of water must be used Middlesex, agricultural custom of . Mineral property vey of 454 880 972 627 1019 • 15 Minerals 891 988 68 Mines of coal 993 Modes of ploughing 899 19 884 • Moon's altitude, tables of the cor- rection of 147 866 Moon's altitude, the use of the 142 tables of correction of 33 the use of the Moon's parallax, tables of 141 tables of 32 the use of the Longitude, tables of 140 the use of the tables of 29 tables of Moon's semidiameter, tables of the augmentation of 30 142 M. Main drains Moon's semidiameter, the use of the tables of the augmentation of Moral responsibility of an agent 31 1070 • • 446 Mortar 404 Mains and pipes for water supply, 488 size of 466 Manor bailiff. 1048 Manorial rights Mortgagee or mortgagor, dilapida- tions by 737 1021 Manufacture of the copse woods Motion of fluids passing through 959 pipes 441 INDEX. 1079 Motion of water Mounds Much judgment required in draining Much varied position of farms Multiple arcs, tables of expressions for • PAGE 453 Parish valuation, written in the PAGE 970 978 form prescribed by the Poor Law Commissioners 656 941 Parish valuation, Field Book re- commended for . 658 163 Parishes, valuation of • 647 Multiple arcs, the use of the ta- bles of Parliamentary plans and sections 345 37 Paved crossings 409 Multiplication, proof of of fractions 3 Paving. 547 5 Peaty soils 920 Pediometer 327 • N. Natural sines and cosines for agricultural labourers Pentagraph Permanent fencing 336 394 Piggery 930 787 Pig iron 992 Notice of distress Necessity of comfortable dwellings Neglected woods New designs of farm buildings necessary Norfolk, agricultural custom of Northamptonshire, agricultural cus- tom of Northumberland, agricultural cus- tom of Notation in arithmetic distress of standing corn. owner's intention to apply Piles of timber 971 940 Pipe drains 445-447 958 • laying, specification for 477 tender for 484 • 927 Pipes and castings, tender for 472 627 mains for water supply, size of 466 627 Pipes, coated 470 earthenware 460 627 iron 469 · 1 stoneware, tender for 475 780 Plane and solid geometry 172 781 trigonometry 200 Planes and solids 183 to justices to recover possession 785 Plans and sections, parliamentary 345 Notice to quit 774 Plantations 1007 Notices to be made of cultivation 898 Planting of trees 955 Nottinghamshire, agricultural cus- copses 959 tom of 628 Plasterers' prices 676 Nuisances 746 work 571 • and Dilapidations. • Numbers, the properties of Numerical reference to maps 10 707 Plotting, sections 323 | Plumbers' prices 326 surveys 316 689 Policy and security of tenant of land. 863 0. Polygons and quadrilaterals 176 Portland's, Duke of, mode of planting 962 Obligations of a lease 896 draining 982 Observances of a lease 897 • arrangement with Old timber stools removed 960 his tenants 985 • Opening in banks . 967 Possession, recovery of 782 • Origin of farms and leases 863 Potatoes 904 Original holding of land 859 | Poultry yard 931 Outfall drainage 446 • Practical geometry 186 Oxfordshire, agricultural custom of 628 Present worth of an estate, lease, or P. Painters' prices 694 work 573 Paperhangers' work 576 • Paperhanger and decorators' prices 697 Parallax in altitude of the sun and planets, tables of 143 Parallax in altitude of the sun and planets, the use of the ta- bles of 32 Parapet walls 406 Parish and estate surveying 258 annuity, for any number of years certain and in perpetuity, at the several rates of interest which a purchaser may thereby make of his money. Present worth of property held on a single life, as of a person in pos- session of a living or benefice, or the holder of a lease, estate, or annuity, according to the Nor- thampton table of mortality. Present worth of property held on a single life, as of a person in pos- session of a living or benefice, or the holder of a lease, estate, or 590 594 1080 INDEX. annuity, according to the Carlisle table of mortality Present worth of an estate, annuity, or a lease on two joint lives, ac- cording to the Northampton table of mortality Present value of an estate, annuity, or a lease, held on the longest of two lives, calculated according to the Northampton table of mortality Present worth of an estate, annuity, or a lease, held on the longest of three lives, according to the Nor- thampton table of mortality Present value of the perpetuity of one year's rent or fine, payable at intervals of years Present value of the reversion to a freehold estate, or a perpetuity, after any given number of years not exceeding sixty Present value of a reversionary estate in fee after the life of a person of a given age, at the several rates of 3, 4, 5, 6, 7, and 8 per cent. interest Present value of a reversionary estate in fee after the longest of two lives of given ages, at the several rates of 3, 4, 5, and 6 per cent. interest Present value of a reversionary estate or annuity on a single life, after any other single life now in possession, at the several rates of 3, 4, 5, and 6 per cent. in- terest Present value of a reversionary an- nuity on a single life, to be nominated at the death of a per- son now in possession, at the several rates of 3, 4, 5, and 6 per cent. interest PAGE • -stone-ware drain pipes PAGE Q. 596 Quadrilaterals and polygons 176 • Quality of copper iron 989 • 468 598 473 water 462 Quantity of bricks 1003 599 lead water 991 • 464 • 547 882 600 Quantities in brick-work, &c. Quitting and entering farms cuttings and embankments, methods of computing the con- R. 608 Rack rents Railway 609 tents of · Railway surveying works, tender for Railways, rating of Rain fall 611 guage Rating of railways, gas, and water works Receipts, form of • Recovery of possession 612 Rectangles, right lines, and angles Reduction of vulgar fractions • Refraction and curvature of the earth, the use of the tables of Refraction of the sun and stars, ta- bles of Refraction of the sun and stars, the 884 931 380 338 420 651 452 439 651 1062 782 173 4 Decimals 7 Reference to maps, collected. 324 numerical 323 613 Refraction and curvature of the earth, tables of . 161 36 • 144 614 use of the tables of 33 • Regulations on land 1029 Relative gradients, table of 379 age 615 Remarks on the construction of farm Price of young woods 1018 buildings 926 · Prices of builders' work 660 Rents must be equitable 870 materials for drainage and Rent defined 883 water supply 686 of lands 1011 Primogeniture 859 of woods 1010 Prismatic compass 283 roll 1067 Private roads 945 tends to rise rather than fall. 871 Proof of first four rules of arith- upon bricks 1003 • metic 2 Reserved capital of farmers 893 Properties of numbers Prospective view of farming opera- tions. Protractor, circular semi-circular Provision of water Puddle. Pumps • Purposes of outlay 10 Reservoir 967 Risk of mining 994 1010 Roads • 464 specification for 485 878 Residence of land agent 1048 319 Restrictions in farming 874 320 Right_lines, angles, and their rect- 870 angles 173 487 Rights of land 857 991 Rivers 1008 887 Present value of £1, payable at the death of a person of a given INDEX. 1081 PAGE PAGE Roads in mines woods 995 • 956 Skewbacks 489 on farm to be provided under the agent's care Slaters' work 869 Sloe 943 Slope of banks - 549 951 966 • 1009 Slopes 486 • Roadside fences Roman cement Root crops Rotation of crops • Royalty 1053 Social position of an estate 1019 404 policy necessary in the man- 908 agement of an estate 879 910 Socket pipes 461 919 Soffits of arches 489 993 Soles for sands and gravels 983 1011 Solid geometry 172 Rubble. Rules of management of a farm Rutlandshire, agricultural custom of Ryde's Hydraulic tables, synopsis 404 measure, tables of 495 888 Solids and planes 183 • 628 mensuration of 197 • Somersetshire, agricultural custom of 628 of second edition of Ryde's hydraulic tables, specimen of • 443 Sowing of wheat 902 444 Spandril of arches 487 Spandrils, abutments, and wings 406 Specialties of a lease 897 S. Specification for construction of railway works 392 • Salary, fixed of a land agent. 1029 Specification for iron socket pipes Sale by auction, conditions of sale of freehold property and castings 468 761 Specifications for pipe laying 477 Sale by auction, conditions of sale reservoir 485 of leasehold property 764 Specifications for stone-ware drain Sale by auction, conditions of sale pipes. 473 of goods 764 Spirit level 299 · Sale by auction, agreement 764 Springs and artesian wells 467 Sales of timber Sawyers' work Scorching soils 958 of water intercepted 984 566 Spring ploughing . 919 Square root, extraction of 899 9 Screw cock and hydrants 480 Stables. 925 • Seams of coal 995 Staffordshire, agricultural custom of 628 Seasons of watering 974 Stamp duties 809 Section, working · 361 Standing orders 339 Security the base of farming 866 Sterile clays 912 Seeded crops. 908 Stipulations of a lease 886 Semi-circular protractor 320 Stone 402 Sets of thorns laid on turf 951 imposts 406 • Setting out centre line of railway 350 -jetties 971 curves 351 Stonemasons' work 566 tables for. Setting out slopes. 362 specimen field book . 374 360 Stone-ware drain pipes, specification for Stone-ware drain pipes, quality of . tender for 473 473 475 • Setting out slopes, tables for • 375 Stones for filling trenches 976 widths of railways, how used 979 • canals, &c. Settlements made by the lease 362 Storage reservoir 464 879 Straight courses of water 969 Sewerage of towns 446 Stretch of primogeniture 860 drainage, and water sup- String courses and coping 406 ply of towns 440 Subterranean survey of the me- Sewers 451 • tropolis 454 cleansing of 454 Subtraction of vulgar fractions 5 form of 453 proof of 2 Sewer gratings 460 Succession in a farm lease 895 Short tenure for rich lands 879 Suffolk, agricultural custom of 628 Shropshire, agricultural custom of 628 Sunk fences 948 • Simple principles of embanking 973 Sun's declination, tables of 171 Single cottages useful 1055 the use of the ta- Size of drains 450-452-456 bles of 38 farms various 941 Superfices, mensuration of 194 water mains and pipes 466 Superficial or flat measure, tables of 528 3 V 1082 INDEX. PAGE PAGE Supply of water 461 Tables of logarithms and numbers. 41 Support of buildings 886 logarithms, use of. 15 Surplus earth 481 logarithmic sines, tan- Surrey, agricultural custom of 628 gents, &c. . 68 Surveying, colonial 424 Tables of logarithmic sines, tan- land 257 gents, &c., the use of 19 parishes and estates 258 Tables of Longitudes 140 railway 338 the use of 29 traverse 280 longitude and time 142 trigonometrical 271 the Surveyorship of roads 945 use of 32 • Surveys and maps for sanitary pur- Tables of Meridional parts 132 poses. 447 the use of 26 Sussex, agricultural custom of 630 moon's parallax 141 Swedish turnips 905 the use of 30 • Synopsis of second edition of Ryde's natural sines and cosines 787 hydraulic tables 443 parallax in altitude of the sun and planets. 143 Tables of parallax in altitude of the T. sun and planets, the use of Tables of refraction of the sun and 32 Tables for computing areas measuring hay ricks valuing hay ricks setting out curves setting out slopes 330 • stars. 144 638 Tables of refraction of the sun and 645 • stars, the use of 33 360 375 Tables of relative gradients solid measure 379 495 • Tables, hydraulic, synopsis of 2nd superficial or flat measure 528 edition of 443 the sun's declination 171 Tables, hydraulic, specimen of mathematical, use of. 444 trigonometrical equivalents 162 18 trigonometrical formulæ of augmentation of the moon's semidiameter. 142 for the solution of quadratics and cubics 167 Tables of augmentation of the moon's semidiameter, the use of Tables of common and hyperbolic logarithms Tables of trigonometrical expres- 31 sions. 165 Tables of unequalsided timber 516 161 Tables of common and hyperbolic logarithms, the use of useful numbers, with their logarithms 169 Tables of correction of the moon's altitude Tables of correction of the moon's altitude, the use of Tables of curvature of the earth and refraction Tables of curvature of the earth 35 Tables showing the amount of fine to be paid for renewing any num- ber of years lapsed in a lease originally granted for 10 years 147 161 and refraction, the use of 36 Table of decimals of an acre. decimals of a pound 226 sterling Table of differential co-efficients dip of the horizon. · the use of Table of expressions for mutiple arcs formulæ for solving all the cases of a rectilineal triangle, of which three parts are known Table of formulae relating to two arcs or angles • Tables of land measure logarithms for finding the horary angle or apparent time Tables of logarithms for finding the horary angle or apparent time, the use of . 807 168 141 33 Tables showing the amount of fine to be paid for renewing any num- ber of years lapsed in a lease originally granted for 20 years Tables showing the amount of fine to be paid for renewing any num- ber of years lapsed in a lease originally granted for 21 years Tables showing the amount of fine to be paid for renewing any num- ber of years lapsed in a lease originally granted for 40 years Tables showing the amount of fine to be paid for renewing with one life the lease of an estate origi- nally granted on three lives Tables showing the length of tim- ber of any scantling contained in a foot cube 29 163 • 166 164 230 158 • Tables showing the number of years' purchase upon the net rental, required to return a given rate of interest • 603 604 605 606 607 671 589 34 Tables showing the present worth INDEX. -1083 of an estate, lease, or annuity, for any number of years certain and in perpetuity, at the several rates of interest which a purchaser may thereby make of his money Tables showing the present worth of property held on a single life, as of a person in possession of a living or benefice, or the holder of a lease, estate, or annuity, ac- cording to the Northampton table of mortality Tables showing the present worth of property held on a single life, as of a person in possession of a living or benefice, or the holder of a lease, estate, or annuity, ac- cording to the Carlisle table of mortality Tables showing the present worth of an estate, annuity, or a lease held on two joint lives, according to the Northampton table of mor- tality Tables showing the present value of an estate, annuity, or a lease held on the longest of two lives, calculated according to the Nor- thampton table of mortality Tables of the present worth of an estate, annuity, or a lease, held on the longest of three lives, ac- cording to the Northampton table of mortality Tables showing the present value of the perpetuity of one year's rent or fine, payable at every interval of years Tables showing the present value of the reversion to a freehold estate, or perpetuity, after any given number of years not exceeding 60 Tables showing the present value of a reversionary estate in fee after the life of a person of a given age, at the several rates of 3, 4, 5, 6, 7, and 8 per cent. interest Tables showing the present value of a reversionary estate in fee after the longest of two lives of given ages at the several rates of 3, 4, 5, and 6 per cent. in- terest Tables showing the present value of a reversionary estate or annuity on a single life, after any other single life now in possession, at the several rates of 3, 4, 5, and 6 per cent. interest Tables showing the present value of a reversionary annuity on a single life, to be nominated at the death of a person now in PAGE 590 possession, at the several rates of 3, 4, 5, and 6 per cent. interest. Tables showing the present value of £1, payable at the death of a person of a given age Tables showing the price per foot run of scantlings of fir or other timber Tables showing the price to be charged for fir or other timber, in measured work 594 Temporary fencing Tapping of springs Tenants for life and years, dilapi- dations by . 598 Threshing machinery Tiles for draining Tortuous courses of water • PAGE 614 615 672 669 394 977 714 Tender for iron pipes and castings 472 pipe laying railway works 484 • 420 596 stone-ware drain pipes 475 • Terms of management of a farm 873 Theodolite 290 Thick planting 956 Three periods of the growth of woods 1017 934 981 Tiling 545-548 • Timber measuring 491 tables, solid measure 495 599 superficial or flat measure 528 Timber tables, unequalsided timber Time for outlay by the farmer 516 879 of entry on farms 880 600 planting 956 • paying rents of farms 884 Tin 990 968 608 Total dilapidations on an estate Trapping house drains 1005 459 Traverse surveying 280 955 • 338 • 174 271 200 307 391 903 903 tenure 878 Twenty years not too long 883 Two gates to every field of land 952 612 U. Unequalsided timber, tables of 516 Use of herbage from irrigation 974 lime 901 • 613 the mathematical tables 18 sun's declination 38 Use of the table of common and hyperbolic logarithms 35 Trees on an acre of ground Trial levels and exploration 609 Triangles Trigonometrical surveying Trigonometry, plane Troughton's level Tunnels Turnip lands 611 Turnips on clay lands Twenty years the best length of table for reducing the 1084 INDEX. for Use of the table of correction of the moon's altitude. • Use of the table of curvature of the earth and refraction Use of the table of dip of the horizon Use of the tables of logarithms PAGE Valuation of wood lands 33 Value of copper • draining woods Valuing hay ricks, tables for . Various modes of protecting banks results of watering lands arrangements of executing PAGE 586 989 986 36 961 645 29 969 15 975 • finding the horary angle or ap- parent time drainage 985 34 Velocity of fluids passing through Use of the table of logarithmic pipes 441 sines, tangents, &c. 19 Villages 1015 Use of the table of longitudes 29 Vulgar fractions 3 longitude and addition and sub- time 32 traction of. 5 Use of the table of meridional parts moon's parallax semidi- 26 30 Vulgar fractions, multiplication and division of . Vulgar fractions, reduction of 54 ameter 31 Use of the table of parallax in alti- tude of the sun and planets Use of the table of refraction of the sun and stars Use of the table of trigonometrical expressions 32 W. 33 Walls, how useful 949 Warrant of distress 780 37 to peace officers to take and give possession 786 Warwickshire, agricultural custom V. of 630 Waste grounds 1007 Validity of simple agreements Valuation memoranda to assist the 877 Water-closet, construction of 459 courses 972 memory 616 887 Valuation of a parish, written in filter. 464 the form prescribed by the Poor Law Commissioners flowing through pipes, dis- 656 charge of 442 Valuation of a parish, Field Book recommended for Water in motion 453 • 658 in pits 994 Valuation of accommodation land 586 • mains and pipes, size of 466 bricklayers' work 545 pipes, tender for 472 carpenters' and joiner' quality of 462 • work 556 quantity of 464 Valuation of cottages 586 supply 461 estates 577 and drainage, prices excavators' work 548 of materials for 686 farm homesteads 583 Water supply, drainage, and sew- farm labour 587 erage of towns 440 glaziers' work • 575 Water works, rating of. 651 ironmongery • 573 Ways of digging pits 995 land. painters' work paper hanging parishes • plasterers' work sawyers' work 577 Weeds in hedges 950 1016 Weights and measures, mensura- 575 tion of 192 576 Westmoreland, agricultural custom 647 of 630 572 Width of drains 979 566 Widths of ground required for slaters' work 550 railways and canals 362 stonemasons' work 569 • Width of roads 944 tillages and tenant Wiltshire, agricultural custom of 630 • right 625 Wings, abutments, and spandrils 406 Valuation of tillages, specimen of Field Book Winter ploughing 898 632 Wireworkers' prices 706 Valuation of tillages, specimen of inventory and valuation Wooden sleepers 416 636 Wood lands, valuation of 586 INDEX. 1085 Woodreeve Wood work • Woods and minerals below use clean cut Worcestershire, agricultural cus- PAGE 1052 tom of Working of clay • iron • lead lime quarries soils tin Working section • Y. PAGE 407 891 Y level 301 958 Years' purchase on net rental, table 1018 of 589 958 Years of purchase in mines Yorkshire, agricultural custom 1020 630 1002 of Young plantations 630 1010 991 1011 991 Young plants of trees 954 998 999 904 Z. 990 361 Zinc-workers' prices 703 LONDON: PRINTED BY G. PHIPPS, RANELAGH STREET, EATON SQUARE. ERRATA. Page 224 line 24, for IK 66 read IK 6. Page 467 line 9, for AA, fig. 194 read A A, fig. 187. LIST OF PLATES. 2 4 13 + General Diagrams. 5 Diagram Plan of the Parish of Sunbury. 6 } Diagrams for setting out Slopes. 8 Parliamentary Plan of a proposed Railway. 9 Parliamentary Section of a proposed Railway. 10 Land Plan of a proposed Railway. 11 Working Section of a proposed Railway. 12 General Diagrams. 13) Plans of House Drainage. 145 Plate.1. Fig. 1. Fig. 2. Fig. 3. Fig. 4 Fig. 5. D\ P. E -B Fig.6. Fig. 7. G H I D B E D Fig. 8. Fig.9. Fig.10. Z 1 2 7 V MLA A Fig.ll. B R/S B D a Fig.12. A Fig. 13. D Fig.14. A C Fig.15. $ E A F F A- -B C G Fig.16. G Fig.17. H A В C D B D B Fig.18. Fig.20. Fig.19. D P D B D Fig.21. C D B B Fig.22. D G Fig. 23. B E B C C Fig. 24. Fig.25. A B E F E D B D C H b. Fig.26. Fig.27. Fig.28 Fig.29 D Fig.30. E Fig. 31. Di B Fig.32. B Fig.33. R B Fig.34. F E C Р D B B E E Fig.35. Fig.36. B Fig.37. B C Fig.38. E Fig.39. R Fig.41. A B D D C F D D H B B B E G E H A Fig.40. Fig.42. Fig.4.3. Fig.44. D Fig.45. Fig 46. C Fig.47. A I D E K B F B E D G Bk F E IC B A F B Fig.48. F D Fig.49. B P E Fig.50 T Fig. 51. 1 6 0 2 B C D D Fig.63. P Fig.64. R Fig.65. B Fig.66 10 Р D D P E B C BA P D E D D G Fig.52. C E B D B B A D E Fig.53. Fig.54. Fig.55. Fig.56. Fig.57 Fig.58. Fig.59 Fig.60. Fig.61. Fig.62 t B B T B P P W K H G G B H B Fig.67. Fig.68. Fig.69. Fig. 70. B C D Fig. 72. Fig. 71. E- E E F A D F B A -C a F Fig. 73. E C Fig. 74. A Fig.75. Ad B D RC F 3 Fig.76. H B 1 1 B P I H G B 7 8 와 E 10 D 1 2 E G F ZA 12 D C Fig.77 4 C D E Fig. 78. F. 7 3 A R B Q 1. IS .3 3 5 7 B London, John Weale, Architectural Library:59 High Holborn 1853. A Fig. 7.9 B D Fig. 80. M S P F B I E T R N B Fig. 81. F D K B G H D II.A. Beever. sc. Plate 2. A- B AR Fig. 82. C di 2 3 Fig. 83. D 3 2 d I Fig. 84. Fig.85. B Fig.86. C Fig. 87. D Fig. 88. G C B Fig. 89. Fig.90. A-6 Å Ä Ä Ë B # 2 3 C 3 2 1 B E D B D D A E B K F A D B A E I A H G C DI D Fig.91. E Fig.101. D E F A B C D G 1 2 4 5 7 C Fig.lll. P Fig.92. Fig.93. A B B G C- G B F C E Fig.103. Fig.94. C Fig.95. -b.. E D A Fig.104. Fig.106. A H sec tan A rad B A T Fig.102. E M G B Fig.105. rad COS B see Crad B tan Fig.113. Fig.112. B A A A R D F H D « ด B C C E A Fig.117. x Cz T A Π Br Pi W R¹ Fig.107. Fig.96. C C Fig.108. A 0 1 H B E Fig.115. Fig.114. A Fig.116. D B E Fig.120. AAB E B D F R2 E H E Bi Fig.118. C² Y C D Fig.97. Fig.98. B Fig.108* IC2 D E I Fig.99 Fig.109. b AB d a Fig.100. b Fig.110. B Fig.121. I P Fig.122. C M Τ A F K 0 F B 172 X 772 D Fig.119. 13 Xx Q T A Pl I α e F K2 K I T K? E K L F K2 B T¹ E A T T B F TE B A E K K3 D 14 P2 X 13 D x K Jolm Weale, Architectural Library, 59, fligh Holborn, 1853. $2 Ꮓ Y -B2 E1 P2 h B WA.Beerer sc. Plate 3. C- Fig. 125. t Fig.126. B NIH 1 A A Fig. 127. B height a A mean B 460 Fig. 128. 1142 830 422 480 a Fig. 148. Fig.149. Fig.150. Fig.151. A B A C B G d B E AC H E G H D D a A Κ I Fig.147. F A E D Hƒ B Fig.145. E 'L I Fig. 130. Kẹ A E \130; 411 960 C Fig. 129. 750 395 F A 27 034 G 700 H 300 T100 M L K B 20 76 E 20 46 G 157 87 Fig. 131. 66 193 198 45 4 A Edward Ryde Del. 55 134 127 286 144 B 116 21 68 Fig.133 Fig. 135. B D K- 88 138 160 Ꭰ Fig.132. 46 198 E Fig. 134. 970 C A A B Fig.144. - Fig. 143. & Fig. 136. d b Fig. 137. a A A 38 Bø Fig. 146. G I H Fig.142. D C Ꭰ m ~ A Fig.154. 11 Fig.140. A Line 1. B Fig. 138. a b d 1 C B A a d' Fig. 139. h d B Fig.152. C Fig.155. B 23 72 1600-12 36 1636 13 End |1250 Fig.123. 1136 |1115 1050 3 a + & H <--230op--> Fig. 153. 730 19a 19 590P 29 a 1636–12 680 10 | 520 16 430 280 210 12 Q 2 326.5 Theod. 146.5 Bear. 13 1290-11 Line 2. D Line 3. Line 1. Line 4 E B Fig.141. A Main line London John Weale, 1853. C 8 Fig.124. K H P2 X 51 W. A. Beever. Sc. Plate 4. F Fig 156. A B D E G Fig.165. E C H Fig.157. Fig. 158. F L I K B A B K I Fig.166. E D Fig. 167. A C B Fig.169. G A B Fig.168. B E Fig.170. E C G Fig.172. T Fig. 174. F A B ž 1 ź N ♡ 13 20 4 Edward Ryde, del. ž 3 ž G B D C Fio.171. - 4을 5 152 ź 6 Ź 7 42 8 호 10 11 호 12 13 214 201- 7 18 9 10 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Fig.159. B A D B C Fig.160. B D C A B H Fig.161. D A C E F D Fig.162. D Ex C A Limb Vernier South Magnetic Meridian -North C D B Fig.176. B D Fig.175. 5 EDWARD RYDE 44 FEET TO ONE INCH PIMLICO 5 London, John Weale, 1853 . B Fig.163. L A M, F 44 FEE O OFFSET C D B Fig. 177. Fia.164. B A D 9 Fig. 173. E A C A 4 3 2 4 2 V 8 IV. A. Beever, $c . Plate 5 PARISH OF SUNBURY M LETON PARISH 1 a SHE PP E RT d ASHFORD a PARISH PARISH 12 FELTHAM 10 CHARLTON e 1 1 N PA t f 13: VI Ꮓ & HALLIFORD 且 S H R SCALE. 5 10 15 20 25 30 60 90 Chains n d Edw Ryde, del . H A N ០៧ གཤེའང་གངས་ m W ORTH W PARISH V u M A L T N London John Weale, 1853. E 11 P A R S AMPTON B H S PARISH t 1385. 1. 24. 943. I. 4. 313.0.25. REFERENCE. ARABLE LAND. MEADOW LAND. HOMESTEADS WOODS &c. TOTAL CONTENT 2641.3. 13. WA. Beever, Sc.. Plate 6.. A B A Fig. 1. 02 1 Dz a3 3 IC 1 Fig. 2. B ал bi az + B₂ a3 W4 b4 a5 bs 06 16 b a4 аг az al B bi bz A B₂ bs a 1 ag Fig. 3. F 0.6 dz b3 E Published by John Weale.59 High Holborn London 1853. ba V 6 (1.7 a6 as a4 it 3 Di b6 b5 124 13 12 a2 01 bi D AM.Lowry Se Plate 7 A B 0.1 az by b z Fig. 4. i 6 Va G bs a 15 a 3 bz 04 bs D6 E (6 as a3 a2 bó v3 ~ bz bi F a az b2 13 رم at BA .. 10 ว 06 bo ат bi 、 H 100 իգ as be 15 x W d.4 b az a2 be a 1 bi C D A B A B Published by John Weale. 59 High Holborn. London 1853. Fig. 5. a 4 a 3 Fig. 6. di (1.2 a 3 F F a 4 a れる C C D D JW. Lowry Sc. PARISH OF OF IDS WORTH 3. RAD FUR & Edr Ride Del. PARISH OF 6 Miles CHALTON 4. RAD. 4 FUR.2 CH. 7 # R a 7 7 Mites RAD.3 FUR, 0 Parish Boundary P R ISH 3 10 RAD. FUR. Limit of Deviation O F RAD. 4 7 FUR. 8 Miles MILE 2 Limit of Deviation Scale for General Plan. 20 40 60 3 80, Chains 1 Mile. J Scale for Enlargements. 1 2 3 4 .f 6 7 8 9 10 I 12 13 14 15 16 17 18 19 20 Chains - 4 of a Mile. London, John Weale, 1853. BURITO N 4 Tunnels RAD. SIFUR 9 Miles 1 2 5 0 BURITON Plate 8. Ïd. Beever, Sc. Edward Ryde, Del. 3 4 6 Cross Section. No 1. 1 1 + 1 1 Tin 66 Level Level of Rails 1 in 101 Greatest Inclination or present road 1 in 66. Greatest Inclination or road when altered. Level. t I IN 100 6 Miles 1 I 273 Public Road to be crossed on the Level. Level unaltered. f 1 I 1 I 1 } I DATUM LINE 200 feet below the Apex of the Mile Stone (marked 50 miles from London) shown on Plan 2 3 4 5 6 I IN 8 O 7 Public Road to be crossed on the Level. Level unaltered. 7 Miles 1 2 Horizontal o Public Road to be crossed on Level. Level unaltered. Occupation Road 1 1 ! 1 I ! 1 | 1 I 1 1 1 1 34 339 Under Bridge, 20 reet span 16 feet high. Public Road. Level unaltered. 30 73 I IN 96 الله 3 4 5 6 Seales 20 400 60 It Vertical 9 10 20 30 40 _00_80__700 London, John Weale, 1853. 200 Feet ? 8 Miles Cross Section, No 2. 1 I 1 in 30 1 in 55 1 in 30 1 1 in 198 Level of Rails Greatest Inclination of present road 1 in 55. Greatest Inclination of road when altered 1 in 30. 381 2 30_Chains = 1 Mile 14 26 3 4 5 10 9 74 TUNNEL 462 Yos IIN 122 Public Road. 197 Level unaltered. 73 24 Pond Under Bridge, 20 feet span, Public Road, Level unaltered. 16 feet high 18 1 1 1 ! Under Bridge, 20 reet span,16 rt. high Public Road. Level unaltered. 9 Miles 1 2 3 4 5 G Scales for Cross Sections. Horizontal e 7 2 3 70 15 Chains Vertical p 20 20 30 4 50 60 Feet II.A. Beever, Sc - 1 303 Public Road, to be raised 2 reet, and crossed on Level. See Cross Section N.“I. Public Road to be diverted Public Road to be diverted 14 Occupation Road 1 ! 1 1 1 1 | t 1 1 } 1 Plate 9. See Cross Section Nº 2. Turnpike Road to be raised 9reet and passed over Bridge. 30 feet Span, 16 feet High LAND PLAN. II 11 11 THE !! 11 || !! }} Testim 11 11 11 11 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 1 31. 32 33 34 35 36 12 0.3.33 9 MILES 0.2.13 37- 1 38. 2 39 30 #1 10.0.14 43 47 45 Diversion of Road 46 47. 48 11 0 49 9 7 8 1 30 30 3 0.1.13 52 53 54 55 56 57 58 1 59 0 2 14 61 6 29 62 63 64 65 66 5 0.1.11 67 68 69 5 71 0234 0.2.31 72 73 7.4 75 76 77 78 3.1.33 479 77 Edward Rrde, del. London John Weale, 1853. Plate 10. A 11 11 11 11 11 11 11 6 81 82 83 -84- 0.0.8 0.0.37 85-- go 87 88 89 7 791 نظام علم WA.Beever. Sc. above Datum Line Formation Level Heights of Edward Ryde Civil Engineer & Surveyor. 697 698 699 DATUM LINE Datum Line of Ground above Heights of Surface · 315.10 Embankment and Heights of Depths of Cutting 30.02 344.68 303.10 41.58 344.14 317.10 27.04 345.12 6 701 702 323.60 19.47 343.60 31.9.80 23.80 342.54 .54 323.00 19.54 342.01 341.48 323.60 18.41 324.10 17.38 340.95 323.80 17.15 340.42 322.80 17.62 -343.07 703 704 705 706 707 708 709 71 339.89 17.36 322.20 17.69 339.36 322.00 338.83 319.10 338.30 321.00 337.77 320.90 19. 73 Formation Level Upper Surface of Rails 17.30 16.87 337.24 320.50 16. 74 336.71 320.30 16 .41 336.18 320.00 16.18 335.65 319.50 16.15 335.12 319.10 16.02 334.59 318.90 334.06 318.50 15. 69 15.56 333.53 317.90 333.00 317.00 332.48 3.16.00 331.96 315.50 331.44 314.80 330.92 313.50 | 330.40 312.00 RATE 329.88 3.11.28 329.36 3.11.50 328.84 | 312.50 328.32 314.02 327.80 315.70 Pond 15.63 16.00 OF Under Bridge Foot Way! Under Bridge Public Road! 16 .48 16.46 16 .64 327.26 317.00 326.72 317.72 326.18 319.50 17.42 18.40 18.60 17.86 16.34 INCLINATION 325.64 321.10 325.10 322.00 324.56 322.00 324.02 322.80 London, John Weale, 1853. 14.30 12.10 10.26 Under Bridge Public Road! 9.00 6.68 4.54 3.10 2.56 1.22 IN / 22 0.00 322.94 323.94 1.00 322.40 323.90 1.50 323.48 323.48 WORKING SECTION. 321.86 322.50 0.64 321.32 321.10 0.22 Public Road 320.78 3.19.18 1.60 (Level Crossing) 324.24 318.00 2.24 319.70 317.00 2.70 319.16 316.10 3.06 318.62 315.50 3.12 318.08 3.15.30 2.78 317.54 315.00 2.54 317.00 315.10 1.90 316.46 316.46 0.00 315.92 318.22 2.30 315. 38 320.00 4.62 712 713 714 715 716 717 718 719 9 MILES 721 722 723 724 725 726 727 728 729 7.31 732 733 734 735 736 737 738 739 2 741 742 743 744 745 746 747 748 749 3 751 752 753 754 755 756 757 758 759 4 761 762 763 764 765 766 767 768 769 5 771 772 773 774 775 776 777 778 779 6 781 782 783 784 785 786 787 788 314.84 320.84 6.00 314.30 321.10 6.80 313.76 320.76 7.00 313.22 320.00 6.78 312.68 318.68 6 .00 312.14 316.70 4 56 30. 66 315.26 3.60 3IL. 10 315.70 4.60 310.60 315.90 5.30 310.10 317.10 7.00 309.60 318.60 9.00 309.10 320.50 П. 40 308.60 323.50 14.90 308.10 326.10 18.00 307.60 330.60) 23.00 Over Bridge 307.10 333.10 26.00 Occupation Road! 306.60 333.60 27.00 306.10 335.10 29.00 305.61 336.61 31.00 305.12 338.12 33.00 304.63 339.23 34.60 304.14 340.64 36.50 303.64 342.00 38.36 303.14 343.14 40.00 302.64 343.62 41.02 302.14 343.14 41.00 301.64 343.40 41.76 301.10 342.90 41.80 300.56 341.10 40.54 300.02 299.48 338.02 38.00 330.0 30.52 298.94 315.00 16.06 300.50 298.40 30.00 WA. Beever, Sc. 789 7 791 12.60 297.86 302.20 if 34 297.32 285.50 Π 11.82 296.78 281.70 15 .08 296.24 281.60 14 64 295.70 281.90 13. 84 Over Bridge Plate II. Fia. 173. a. Fio. 179. ( ་ Fig.180. ! 1 1 1 L B A B A Fia. 182. Fig.183. Fig.173c. E A F A B Fig. 187. parents IMPERMEABLE D Porous b Fig.173.b. IMPROVED SYSTEM OF BACK DRAINAGE. OLD SYSTEM OF HOUSE DRAINAGE. E A F B Fig.173k Fig.181. Fig. 184. Fig. 185. Fig. 173.d. d 00 H Edward Ride. Del . A B Di E: ( e Fig.186. Fig. 173.1. M SIZ 1 N B F C Plan Section Fig.173.e. Fig. 189. to C Fig. 188. Fia. 190. STREET Sewer Fig. 173. m. PARISH NO. 2. PARISH ALINE A PARISH PARISH NO.4. SEWER NO.3. Section PLAN SECTION Fig. 192 Fia. 193. B Fig. 194. PLAN Fig. 173. n. PARISH RAILWAY NO. 6. PARISH NO. 5. Plan Fig.191. STREE T C London, John Weale, 1853. DR B A A SECTION Fig. 195. Fig. 173. f. E RADIUS A 70 Fig.196. 20 B C Fig.173.h. Centre Stake ·36 18 -X- -40 12x Fig.173.i. Fig. 173.g F E B. NER SINE SINE D C M RADIUS Plate.12. E F In D d Α 'M' B IA. Beever. Sc . B a m N N Plates ! 1 1 ST 1 1 " 1 1 1 A N 1 } i 10 1 SEPARATE 12./ 11.4 12.0 1 1 1 1 1 DRE 1 1 1 量 1 1 } 1 1 1 } DRAINAGE. 06 B.M 11.92 ST TREET ST JOHN 10.3 10.8 1 12.0 44 1 W S R 1 1 1 1 1 1 1 ! 1 1 1 1 1 1 1 1 1 1 1 1 о 1 1 1 ན ! 1 1 1 1 11.8 A D } 1 1 1 1 1 1 1 1 W.S 1 } : 1 1 1 } 1 NOTE. W.S. WATER SUPPLY. S. SINK STONE. R.S. RAIN SPOUT. O. CLOSET. EDWARD RYDE, DEL. 1 1 1 1 1 Sa 1 1 量 Sa DS So S HARGING ON THE ST JOH 100 11.0 0000 TAN ココロ N S PL A CE YARD 10.5 9.3 10.0 D D O هد ་་་ t www The bo ST A ND R E E W W S TE RR A C 耳 O ច SCALES. FEET 10 10 20 30 40 50 100 FEET Τ LINKS 100 90 80 70 60 50 40 30 20 10 0 I CHAIN W. A. BEEVER.SC. London, John Weale, 1853 Plate 14. 1 1 1 1 1 1 ST 1 1 1 t 1 1 ANDR 1 1 1 E W 1 1- 1 1 S 1 IMPROVED BACK DRAINAGE. 12.2 II.4 ST JOHN S 10.8 S 12.1 12.0 1 ROAD 1 1 1 1 1 1 1 12.0 W.S 1 1 1 1 1 1 NOTE. W.S. WATER SUPPLY. S. SINK STONE. R.S. RAIN SPOUT. O. CLOSET. EDWARD RYDE, DEL. 1 薯 1 11.8 1 1 1 # R.S R.S OS W.S 10.3 TB.M RE E T 11.92 ST JO H NS PLACE 10.5 9.3 10.0 1602 Lolos 미 미 000 11.10 TAN Y ARD R.S R.SI R.S R.S R.S R.S R.S R.S DR.S R.Sh R.S 120 123) 124 125 124|126|125 12 3|1727120 12.5 ST 000 ANDREWS TERRACE R SCALES. FEET 10 0 10 20 30 40 50 LINKS 100 90 80 70 60 50 40 30 20 10 0 London, John Weale, 1853. V E R 100 FEET I CHAIN W. A. BEEVER.SC. NEW LIST LIST OF WORKS RECENTLY PUBLISHED, OR IN PREPARATION FOR PUBLICATION IN 1853, BY JOHN WEALE, 59, HIGH HOLBORN, LONDON. GREAT EXHIBITION BUILDING. The BUILDING erected in HYDE PARK for the GREAT EXHIBITION of the WORKS of INDUSTRY of ALL NATIONS, 1851: Illustrated by 28 large folding Plates, embracing plans, elevations, sections, and details, laid down to a large scale from the working drawings of the Contractors, Messrs. Fox, HENDER- SON, and Co., by CHARLES DOWNES, Architect; with a scientific description by CHARLES COWPER, C. E. In 4 Parts, royal quarto, now complete, price £1. 10s., or in cloth boards, lettered, price £1. 11s. 6d. ***This work has every measured detail so thoroughly made out as to enable the Engineer or Architect to erect a construction of a similar nature, either more or less extensive. The following is a List of the Subjects and Plates: CONTENTS. Origin of the Great Exhibition build- Main gutters and rain-water connec- | Louvres. ing. General description of the building. Columns. Girders and trusses. Wooden trusses. Cast-iron girders. Glass roof. Wrought-iron trusses. Plan of ground floor. Plan of galleries. Plan above galleries. South elevation. East elevation. Transverse section. Longitudinal section. Details of columns. Details of vertical diagonal bracing. Wood trusses and cast-iron girders. Wrought-iron trusses under roof. tions. Galleries. Staircases. Gallery railing. Transept. Lead flats. Outer walls, or sides of building. Ends of transept. LIST OF PLATES. Glass roof and Paxton gutters. Main gutters. Details of gallery, and ornamental bands on columns. Plans and section of staircases. Details of staircases. Ditto, and gallery railing. Details of transept roof. Details of lead flats. Setting out the building and fixing the columns. Proving girders and trusses. Hoisting girders and trusses. Hoisting transept ribs. Manufacture of the sash-bars. Miscellaneous details. Paxton's latest improvements in roofs. Outer walls, or sides of building. Details of ditto. Details of panels and joint-plates at ends of building. External elevation of semicircular head of transept end. Internal elevation of ditto. Details of ditto, and pedestals at south entrance. Wrought-iron trusses under transept Details of machinery for moving roof and lead flat. In octavo, cloth boards, price 9s. louvres. HYDRAULIC FORMULE, CO-EFFICIENTS, AND TABLES, For finding the Discharge of Water from Orifices, Notches, Weirs, Short Tubes, Diaphragms, Mouth-pieces, Pipes, Drains, Streams, and Rivers. BY JOHN NEVILLE, ARCHITECT AND C. E., MEMBER ROYAL IRISH ACADEMY, MEMBER INST. C. E. IRELAND, MEMBER GEOLOGICAL SOC. IRELAND, COUNTY SURVEYOR OF LOUTH, AND OF THE COUNTY OF THE TOWN OF DROGHEDA. This work contains above 150 different hydraulic formulæ (the Continental ones reduced to English measures), and the most extensive and accurate Tables yet published for finding the mean velocity of discharge from triangular, quadrilateral, and circular orifices, pipes, and rivers; with experimental results and co-efficients;-effects of friction; of the velocity of approach; and of curves, bends, contractions, and expansions;—the best form of channel;—THE DRAINAGE effects of long and shorT WEIRS, AND WEIR-BASINS;-extent of back-water from weirs ; contracted channels;-catchment basins;-hydrostatic and hydraulic pressure;-water-power, &c. &c. &c. 2 JOHN WEALE'S SIR JOHN RENNIE'S WORK ON THE THEORY, FORMATION, AND CONSTRUCTION OF BRITISH AND FOREIGN HARBOURS. 2 V Copious explanatory text, illustrated by numerous examples, in 2 Parts, at 128. cach, in-half-moroc007 price 312. 123. Vol Vols. very neat The history of the most ancient maritime nations affords conclusive evidence of the importance which they attached to the construction of secure and extensive Harbours, as indispensably necessary to the extension of commerce and navigation, and to the successful establishment of colonies in distant parts of the globe. To this important subject, and more especially with reference to the vast extension of our commerce with foreign nations, the attention of the British Government has of late years been worthily directed; and as this may be reasonably expected to enhance the value of any information which may add to our existing stock of knowledge in a department of Civil Engineering as yet but imperfectly understood, its contribution at the present time may become generally useful to the Engineering Profession. The Plates are executed by the best mechanical Engravers; the Views finely engraved under the direction of Mr. Pye: all the Engineering Plates have dimensions, with every explanatory detail for professional use. The following is a list of the Subjects engraved : MOLE, HARBOUR, and BREAKWATER of CHERBOURG, with details. 5 plates. Views of the ROYAL DOCKYARD at SHEERNESS. 4 plates. HARBOUR and Town of SHEERNESS, store-houses, &c. 2 plates. Graving and other docks, with details, pumping engines, and machinery, at SHEERNESS. 14 plates. CHATHAM DOCKYARD and the River Medway. Proposed NORTHFLEET DOCKS. PORTSMOUTH DOCKYARD and HARBOUR. 2 plates. WOOLWICH and DEPTFORD DOCKYAards. General view of PLYMOUTH and DEVONPORT. Chart of PLYMOUTH SOUND. DEVONPORT and KEYHAM DOCKYARds. DEVONPORT and PEMBROKE DOCKYARDS. View and plans of the VICTUALLING ESTABLISHMENTS at PLYMOUTH. 2 plates. RAMSGATE HARBOUR, plans and sections, lock-gates, slips, engine-house, and workshops. 6 plates. DOVER HARBOUR at various periods, and Harbour of Refuge. 4 plates. NEWHAVEN, RYE, and SHOREHAM HARBOURs. HULL DOCKS and HARBOUR, BRIDLINGTON HARBOUr. SCARBOROUGH HARBOUR. 2 plates. HARTLEPOOL BAY, HARBOUR, DOCKS, and Lock- GATES. 16 plates. CORK HARBOUR and MILFORD HAVEN. SUNDERLAND HARBOUR, and driving piles and dredg- ing. 3 plates. Mouth of the RIVER TYNE. LEITH DOCKS, harbour, pier, Martello tower, and ware- houses. 4 plates. BERWICK HARBOUR. BELL ROCK LIGHTHOUSE. TOWN and HARBOUR of PETERHEAD, and proposed harbour of Fraserburgh. GREAT GRIMSBY DOCKS and Wharfs. BAY of ARDROSSAN, proposed docks on the Broomie- law, and GREENOCK HARBour. PORT PATRICK HARBOur. DONAGHADEE HARBOUR. TOWN and HARBOUR of BELFAST. CARRICKFERGUS HARBOUR. DUBLIN BAy. DOUGLAS HARBOUR, Isle of Man. KINGSTOWN HARBOUR. HOWTH HArbour. HOLYHEAD HARBOUR. ABERDEEN. HOLYHEAD and PORTLand. HARBOURS of the DEE and MERSEY. LIVERPOOL. WHITEHAVEN. DELAWARE. Ponta-Delgarda. YARMOUTH, HARWICH, and Lowestoft. VENICE. 3 plates. ANCONA, TARENTUM, ANTIUM, BRINDISI, and Malaga. NAPLES. MESSINA and SYRACUSE. PORT PEIRæus. EGINA, GUMISHLA, STANCHIO, and BOURDRoon. TUNIS, SIDON, and TYRE. PALERMO and GIRGENTI. GENOA and CIVITA VECCHIA. CALAIS and DUNKIRK. BREST. CARLSCRONA and COPENHAGEN. CADIZ. TOULON and MARSEILLes. CORUNNA and FERROL. HAVRE and DIEPPE. CARTAGENA and CETTE. ALGIERS. CRONSTADT. DUNDEE, &c. &c. NEW LIST OF WORKS. 3 TREDGOLD ON THE STEAM ENGINE. Published in 74 Parts, price 2s. 6d. each, in 4to, illustrated by very numerous engravings and wood-cuts, a new and much extended edition, now complete in 3 vols. bound in 4, in elegant half-morocco, price Nine Guineas and a Half. THE STEAM ENGINE, IN ITS PROGRESSIVE AND PRESENT STATE OF IMPROVEMENT; Practically and amply elucidating, in every detail, its modifications and applications, its duties and consumption of fuel, with an investigation of its principles and the proportions of its parts for efficiency and strength; including examples of British and American recently constructed engines, with details, drawn to a large scale. The well-known and highly appreciated Treatise, Mr. TREDGOLD's national Work on the STEAM ENGINE, founded on scientific principles and compiled from the practice of the best makers—showing also easy rules for construction, and for the calculation of its power in all cases—has commanded a most extensive sale in the several English editions, and in Translations on the Continent. These editions being now out of print, the proprietor has been induced to enlarge and extend the present edition by practical examples of all kinds, with the most recent improvements in the construction and practical operations of the steam engine both at home and abroad. The work is divided into the sections named below, either of which may be purchased separately: working engineers will be thus enabled to select those portions which more especially apply to the objects upon which they may be respectively employed. Several scientific men, extensively and practically employed, have contributed original and really practical papers of the utmost utility; by which the value of this extended edition is much increased. A copious INDEX for reference is added. DIVISION A. Locomotive Engines, 41 plates and 55 wood-cuts, complete, making Vol. I. In half-morocco binding, price £2. 12s. 6d. DIVISION B. Marine Engines, British and American, numerous plates and wood-cuts, making Vol. II.; bound in 2 vols. half-morocco, price £3. 13s. 6d. DIVISION C to G. making Vol. III., and completing the work, comprising Stationary Engines, Pumping Engines, Engines for Mills, and several examples of Boilers employed in the British Steam Navy, in half-morocco, price £3. 13s. 6d. LIST OF PLATES. DIVISION A.-LOCOMOTIVE ENGINES. Elevation of the 8-wheeled locomotive engine and tender, the IRON DUKE, on the Great Western Railway. Longitudinal section of ditto. Plan, ditto. Transverse sections, ditto. Details of ditto: transverse section through working gear, transverse section and end view of tender; plan and section of feed-pump; plan and elevation of hand- pump; details of inside framing, centre axle, driving axle-box, regulation-valve, centre-beam stay, &c. Elevation of Crampton's patent locomotive engine and tender. Longitudinal section of ditto. Plan of ditto. Transverse sections of ditto. Elevation of the PYRACMON six-wheeled goods' engine on the Great Western Railway. Half-plan of the working gear of ditto. Elevation of a portion of the working gear of ditto. Diagrams, by J. Sewell, L. E., of resistances per ton of the train; and portion of engines of the class of the GREAT BRITAIN locomotive, including tender, with various loads and at various velocities; also of the additional resistance in tbs. per ton of the train, when the engine is loaded, to be added to the resistance per ton of the engine and tender when unloaded. Side and front elevation of an express carriage engine, introduced on the Eastern Counties Railway by James Samuel, C. E., Resident Engineer. Longitudinal and cross section of ditto. Plan of ditto; with plan and section of cylinders, details and sections, piston full size. Elevation of the outside-cylinder tank engine made by Messrs. Sharpe Brothers & Co., of Manchester, for the Manchester and Birmingham Railway. Section of cylinder and other parts, and part elevation of ditto. Longitudinal section of ditto. Plan of ditto. Transverse sections of both ends, with sectional parts. Mr. Edward Wood's experiments on the several sections of old and modern valves of locomotive engines,-viz. fig. 1, stroke commences; fig. 2, steam-port open; fig. 3, steam-port open; fig. 4, steam-port open; fig. 5, stroke completed, steam cut off, exhaustion com- mences; fig. 6, stroke commences; fig. 7, steam-port full open; fig. 8, steam cut off; fig. 9, exhaustion commences; fig. 10, steam completed. Ditto, drawn and engraved to half-size: fig. 1, old valve, -inch lap; fig. 2, 3-inch lap; fig. 3, 4-inch lap; fig. 4, 3-inch lap, Gray's patent; fig. 5, 1-inch lap. Elevation of a six-wheeled locomotive engine and tender, No. 15, constructed by Messrs. Tayleur, Vulcan, Foundry, Warrington, for the Caledonian Railway. Longitudinal section of ditto. Plan of ditto, engine and tender, with cylindrical part of boiler removed. Elevations of fire-box, section of fire-box, section of smoke-box of ditto. Elevations and sectional parts of ditto. Sectional parts, half-plan of working gear, ditto. Elevation of Messrs. Robert Stephenson and Co.'s six- wheeled patent locomotive engine and tender. Longitudinal section of ditto. JOHN WEALE'S TREDGOLD ON THE STEAM ENGINE. Plan and details of Stephenson's patent engine. Section of fire-box, section of smoke-box, front and back elevations of the same. Plan of a six-wheeled engine on the Birmingham and Shrewsbury Railway, constructed by Messrs. Bury, Curtis, and Kennedy, Liverpool. Longitudinal section of ditto. Sectional elevation of the smoke-box of ditto. Sectional elevation of the fire-box of ditto. Elevation of the locomotive engine and tender, PLEWS, adapted for high speeds, constructed by Messrs. R. & W. Hawthorn, of Newcastle-upon-Tyne, for the York, Newcastle, and Berwick Railway Company. Longitudinal section of ditto. This section is through the fire-box, boiler, and smoke-box, showing the tubes, safety-valve, whistles, steam and blast pipes, &c. Plan of ditto. Plan of the working gear, details, &c. &c. Forty-one plates and fifty-five wood engravings. DIVISION B.-MARINE ENGINES, &c. Two plates, comprising figures 1, 2, and 3, Properties of Steam. Plan of H. M. screw steam frigate DAUNTLESS, con- structed by Robert Napier, Esq. Longitudinal elevation and transverse section of ditto. Longitudinal section at A B on plan, longitudinal section at CD on plan of ditto. Engines of H. M. steam ship TERRIBLE, constructed by Messrs. Maudslay, Sons, and Field, on the double- cylinder principle. Longitudinal sections of engines. Transverse section and end view of ditto. Transverse section through boilers of ditto. Plan of engines, showing also bunkers, paddles, &c. Oscillating engines of the Peninsular and Oriental Com- pany's steam vessel ARIEL, constructed by John Penn and Sons. Longitudinal section. Section at engines of ditto. Section at boiler of ditto. Plan at boiler of ditto. Section at air-pump-section at cylinder of ditto. Annular cylinder engines of the iron steam vessels PRIN- CESS MARY and PRINCESS MAUDE, constructed by Maudslay, Sons, and Field. Longitudinal section. Transverse section at engines of ditto. Section at boilers of ditto. Plan of engines of ditto, showing bunkers, paddles, &c. Plan of engines of H. M. steam vessel SIMOOM, Con- structed by James Watt & Co., of London and Soho. Longitudinal section of ditto. Cross section of ditto. Engine of the RED ROVER, side view and plan. Longitudinal section of ditto. Cross sections of ditto. Sheer draught and plans of vessel. Plan of the engine of H. M. steam frigate PHŒNIX. Longitudinal section of engine of ditto. Cross section of ditto. Engine of the RUBY steam vessel, elevation and plan. Sheer draught and plan of vessel. Plan of engine of the WILBERFORCE, Hull and London packet. Cross section of ditto and vessel. Longitudinal section of engines of ditto. Elevation of engines of ditto. Engines of the BERENICE, Hon. E. I. Co.'s steam vessel. Section of ditto. Sheer draught and plan, stern view, and body plan of vessel. View of the BERENICE, whilst at sea. Boilers of H. M. ships HERMES, SPITFIRE, and FIREFLY. Kingston's valves, as fitted on board sea-going vessels for blow-off injection, and hand-pump sea valves. Boilers of H. M. steam vessel AFRICAN. Morgan's paddle-wheels, as fitted in H. M. S. Medea. Side elevation of ditto. Plans of upper and lower decks of H. M. S. MEDEA. Sheer draught and profile of ditto. Morgan and Seaward's paddle-wheels, comparatively. Positions of a float of a radiating paddle-wheel in a vessel in motion, and positions of a float of a verti- cally acting wheel in a vessel in motion. Cycloidal paddle-wheels. Sailing of steamers in five points from courses. Experimental steaming and sailing of the CALEDONIA, VANGUARD, ASIA, and MEDea. Engines of H. M. steam ship MEGÆRA. Engine of the steam boat NEW WORLD, T. F. Secor & Co., Engineers, New York. Elevation and section. Elevations of cylinder and crank ends. Steam cylinders, plans, and sections. Details. Several sections of details. Details and sections. Details of parts. Plans and sections of condenser, bed-plates, air-pump bucket, &c. Details and sections, injection valves. Details, plan and elevation of beams, &c. &c. Details, sections of parts, boilers, &c. of the steam boat NEW WORLD. Sections, details, and paddles. Engines of the U. S. mail steamers ОHIо and GEORGIA. Longitudinal section. Elevations and cross sections of ditto. Details of steam-chests, side-pipes, valves, and valve gear of ditto. Section of valves, and plan of piston of ditto. Boilers of ditto, sections of ditto, Engine of the U. S. steamer WATER-WITCH. Sectional elevation. Steam-chests and cylinders of ditto. Boilers, sections, &c. of ditto. Boilers of the U. S. steamer PowHATAN. Front view and sections of ditto. Elevation of the Pittsburg and Cincinnati American packet BUCKEYE STATE. Bow view, stern view. Plan of the BUCKEYE State. Model, &c. of ditto, wheel-house frame, cross section at wheel-house, and body plan. Plan and side elevation of ditto. Sheer draught and plan, with the body plan, of the U.S. steam frigate SARANAC. Longitudinal section of ditto, cross section. Engines of the U. S. steamer SUSQUEHANNA. Elevation of the U. S. PACIFIC steam packet engine. Plan of ditto. Boilers of ditto, end views. Ditto ditto. Eighty-five engravings and fifty-one wood-cuts. NEW LIST OF WORKS. TREDGOLD ON THE STEAM ENGINE. DIVISION C. TO G., FORMING VOL. III. STATIONARY ENGINES, PUMPING Side elevation of pumping engine, U. S. dock, New York. End elevation of ditto. Elevation and section of the pumps, ditto.-2 plates. Boilers of pumping engines, ditto. Boilers, Details, &c. of pumping engines, ditto. Plan of the boilers, ditto. Isometrical projection of a rectangular boiler. Plan and two sections of a cylindrical boiler. Brunton's apparatus for feeding furnace-fires by means of machinery. Parts of a high-pressure engine with a 4-passaged cock. Section of a double-acting condensing engine. Section of a common atmospheric engine. On the construction of pistons. Section of steam pipes and valves. Apparatus for opening and closing steam passages. Parallel motions.-2 plates. Plan and elevation of an atmospheric engine. Elevation of a single-acting Boulton and Watt engine. Double-acting engine for raising water. Double-acting engine for impelling machinery. Maudslay's portable condensing engine for impelling machinery. Indicator for measuring the force of steam in the cylin- der, and diagrams of forms of vessels. Section of a steam vessel with its boiler, in two parts— diagrams showing fire-places-longitudinal section through boiler and fire-places. Isometrical projection of a steam-boat engine. Plan and section of a steam-boat engine. Ten horse-power engine, constructed by W. Fairbairn and Co.-4 plates. Forty-five horse-power engine, constructed by W. Fair- bairn & Co.-3 plates. Plan and section of boiler for a 20-horse engine, at the manufactory of Whitworth & Co., Manchester. Messrs. Hague's double-acting cylinder, with slides, &c. Sixty-five-inch cylinder, erected by Maudslay, Sons, and Field, at the Chelsea Water-works.-5 plates. Beale's patented rotary engine. Double-story boilers of H.M.S. DEVASTATION, 400 H. P. Refrigerator feed and brine pumps. Feed and brine apparatus, as fitted on board the West India Royal Mail Company's ships. Boilers of H. M. steam sloop BASILISK, 400 H.P. Boilers of the SINGAPORE, 470 H. P., Peninsular and Oriental Company. Original double-story boilers of the GREAT Western, Telescopic chimney, or sliding funnel, of H. M. ship HYDRA, 220 H. P. Seaward's patent brine and feed valves. Boilers of H. M. mail packet UNDINE, (Miller, Raven- hill, & Co.) 100 H. P. Cross sections of engines of H. M. mail packet UNDINE. Longitudinal elevation of ditto. Brine-pumps as fitted on board H. M. S. Medea, 220 H. P. (Maudslay, Sons, and Field.) Boilers of H. M. S. HYDRA, 220 H. P. 1 ENGINES, MARINE BOILERS, &c. 5 Plan of the four boilers, with the supplementary steam- chests and shut-off valves, of the AVENGER. Boilers of H. M. steam ship NIGER, 400 H. P., fitted by Maudslay, Sons, and Field. Experimental boiler, Woolwich Yard. [Sons, and Field.) Boilers of H. M. S. TERRIBLE, 800 H. P. (Maudslay, Boilers of the MINX and TEASER, 100 H.P. (trans- ferred to WASp.) Boilers of the SAMSON, 450 H. P. Daniel's pyrometer, full size. [and Field.) Boilers of the Desperate, 400 H. P. (Maudslay, Sons, Boilers of the NIGER (2nd plate). Boilers of H. M. S. BASILISK (2nd plate). Boilers of the UNDINE. Boilers of the Royal Mail steam ships ASIA and AFRICA, 768 H. P., constructed by R. Napier, Glasgow. Longitudinal and midship sections of ditto. Boilers of H.M.S. LA HOGUE, 450 H.P. (Seaward & Co.) H. M. S. SIDON, 560 H. P. Plan of telescope funnel. Boilers of H. M. S. BRISK, 250 H. P. Copper boilers for H. M. S. SANSPAREIL, 350 H. P. (James Watt & Co.) American marine boilers, designed and executed by C. W. Copeland, Esq., of New York, as fitted on board the American packets. Midship section of the hull of the steam packet PACI- Fic, New York and Liverpool line. Elevation of pumping engines of the New Orleans Water- works, U. S., arranged and drawn by E. W. Smith, Engineer, constructed at the Allaire Works, New York. Elevation of pumps and valves, chests, gearing, &c. Elevation at steam cylinder end. General plan of a turbine water-wheel in operation at Lowell, Massachusets, U. S., by J. B. Francis, C. E. Elevation of ditto.· Section of ditto. Plan of the floats and guide curves, ditto. Large self-acting surfacing and screw-propeller lathe, by Joseph Whitworth & Co., Manchester. Longitudinal section, showing arrangement of engine- room for disc engine applied to screw propeller, and Bishop's disc engine, by G. & J. Rennie, with details. Arrangement of engine-room for engines of 60 horse- power, for driving propellers of H. M. steam vessels REYNARD and CRUISER, constructed by Messrs. Rennie. Longitudinal section and engine-room. Ditto. Transverse section at boilers and at engines. Very claborate diagrams showing experiments and results of various paddle-wheels.--8 plates. Steam flour-mills at Smyrna, constructed by Messrs. Joyce & Co. Double cylinder pendulous condensing engine, side elevation. Side elevation, horizontal plan, ditto. Longitudinal section. Horizontal plan of mill-house and boilers. Transverse section through engine-house and mill. Boilers, longitudinal and transverse sections, front view. | Section through mill-stones, elevation of upper part, section of lower part, plan of hopper, &c. SUMMARY OF THE ILLUSTRATIONS. Vol. I. Locomotive Engines Plates. 41 Wood-cuts. 55 II. Marine Engines 85 51 III. Stationary Engines, Pumping Engines, Engines for Flour-Mills, Examples of Boilers, &c., &c. 100 58 Total 226 164 6 JOHN WEALE'S A NEW SURVEY OF LONDON: FULLY DEVELOPING Its Antiquity, History, and Architecture-Palatial and Ecclesiastical Structures-Public Build- ings-and its Social, Literary, and Scientific Institutions-various Galleries of Art-Parks, Pleasure Gardens, and Conservatories-Trade and Manufactures-Government and Municipal Arrangements-Railways, Canals, and Water Supply-and its Geography, Geology, and Natural History. Illustrated by a newly constructed whole sheet Map, and more than Two Hundred finely executed Engravings, from Original Drawings by the best Artists, of the most interesting subjects in the Metropolis and its Vicinage. Third edition, in 2 vols., 910 pages, small 8vo., in cloth boards lettered, price 10s. 6d., or in half-morocco elegant, 148., and in half-calf gilt, 12s. The following is a list of the Subjects more particularly treated of: Physical Geography of the Basin of Bridges. the Thames. Climate. Geology. Geology of the water-courses. Natural history. Statistics. Canals. Cemeteries. Club-houses. Colleges. Corporation of the City of London. Customs, dock and port of London. Spirit of the public journals-'The Royal dockyards. Times.' Legislation and government. Municipal arrangements. Police. Postal arrangements. Banking. Assurances. Duties on articles imported into Eng- land. Architecture of London-its history, &c. Ancient London. Temple church, St. Saviour's, and other ancient churches. Westminster Abbey church. Westminster Palace. Westminster Hall. Sepulchral architecture. Tudor churches. Ancient churches. Modern churches. Lincoln's Inn hall, and the other inns of court. St. Paul's cathedral. Sir Christopher Wren's churches. The public buildings of Inigo Jones and of Sir William Chambers. Arts, manufactures, and trade. Tables of the names, actuaries, and business terms of the several as- surance companies. Asylums. Bank of England. Baths and wash-houses. Bazaars and show-rooms. Model buildings for the poor. Breweries. Electric telegraph. Education. Engineers' workshops. Sir Thomas Gresham and the Royal Exchange. Galleries of Pictures: those of Lord Ashburton. Barbers' Hall. Bridewell Hospital. Thomas Baring, Esq. Society of British Artists. British Institution. British Museum. Duke of Buccleuch. Chelsea Hospital. Duke of Devonshire. G. Tomline, Esq. Dulwich College. Earl of Ellesmere. Foundling Hospital. School of Design. Greenwich Hospital. Vernon Gallery. Grosvenor Gallery. Guildhall, City. Hampton Court Palace. T. Holford, Esq. H. T. Hope, Esq. St. James's Palace. Kensington Palace. Marquis of Lansdowne. National Gallery. National Institution. Duke of Northumberland. Lord Overstone. Mr. Sheepshanks. Lord Garvagh. Galleries of Pictures: those of Earl de Grey. Earl Normanton. Sir Robert Peel. Queen's Gallery, Buckingham Pa- lace. Samuel Rogers, Esq. Royal Academy. Society of Arts. Society of Painters in Water Co- lours. Duke of Sutherland. Lord Ward. Duke of Wellington. Whitehall Chapel. Windsor Castle. Gas-works and gas-lighting in Lon- don. Gardens, conservatories, and parks. Halls. Hospitals. Jews' synagogues and schools. Learned societies. Museums. Public libraries. Lunatic asylums. Markets. Mercantile marine. Mint. Music, opera, oratorios, musical socie- ties, &c. Observatories. Panoramas. Patents for inventions in England. Public and private buildings. Prisons. Railway stations. Sewers of London. Thames tunnel. Union workhouses. Water supply of London. Excursions to the vicinity of London. Castle and stables at Windsor. Colleges of Cambridge and Oxford. &c., &c In one large Volume, with numerous Tables, Engravings, and Cuts, price me tramed, A TEXT BOOK For Agents, Estate Agents, Stewards, and Private Gentlemen, generally, in connection with Valuing, Surveying, Building, Letting and Leasing, Setting out, Disposing, and particularly describing all kinds of Property, whether it be Land or Personal Property. Useful to Assurance Companies Builders Landed Proprietors Stewards Auctioneers Appraisers Agriculturists Architects Civil Engineers Estate Agents Te-be published in the cours of the Spring of 1953, Surveyors Valuers, &c. NEW LIST OF WORKS. THE WORK ON BRIDGES OF STONE, IRON, TIMBER, AND WIRE. 7 In 4 Vols. bound in 3, described in pages 8, 9, 10 of the larger Catalogue of Publications; to which the following is the Supplement, now completed, entitled SUPPLEMENT TO THE THEORY, PRACTICE, AND ARCHITECTURE OF BRIDGES OF STONE, IRON, TIMBER, WIRE, AND SUSPENSION,' In one large 8vo volume, with explanatory text and 68 Plates, comprising details and measured dimensions, in Parts as follows: Part I. "" II. "" III. IV. 68. 68. 68. 10s. 20s. V. & VI. Bound in half-morocco, uniform with the larger work, price £2. 108., or in a different pattern at the same price. LIST OF PLATES. Cast-iron girder bridge, Ashford, Rye and Hastings Railway. Details, ditto. Elevation and plan of truss of St. Mary's Viaduct, Cheltenham Railway. Iron road bridge over the Railway at Chalk Farm. Mr. Fairbairn's hollow-girder bridge at Blackburn. Waterford and Limerick Railway truss bridge. Hollow-girder bridge over the River Medlock. Railway bridge over lagunes of Venice. Viaduct at Beangency, Orleans and Tours Railway. Oblique cast-iron bridge, on the system of M. Polonceau, over the Canal St. Denis. Blackwall Extension Railway, Commercial Road bridge. Ditto, enlarged elevation of outside girders, with details. Ditto, details. Ditto, ditto, and sections. Ditto, ditto, ditto. Richmond and Windsor main line, bridge over the Thames. Ditto, details. Ditto, ditto, and sections. Orleans and Bordeaux Railway bridge. Ditto, sections and details. Rouen and Havre Railway timber bridge. Ditto, details. Ditto, ditto, and sections. Viaduct of the Valley of Malauncey, near Rouen. Hoop-iron suspension bridge over the Seine at Suresne, department de la Seine. Hoop-iron suspension foot bridge at Abainville. Suspension bridge over the Douro, iron wire suspension cables. Ditto, details. Glasgow and South-Western Railway bridge over the water of Ayr. Ditto, sections and details. Plan of the cities of Ofen and Pesth. Sections and soundings of the River Danube. Longitudinal section of framing. No. 1 coffer-dam Transverse framing of coffer-dam. Sections of Nos. 2 and 3 of coffer-dam. Plan of No. 3 coffer-dam and ice-breakers. Plan and elevation of the construction of the scaffolding, and the manner of hoisting the chains. Line of soundings,-dam longitudinal sections. Dam sections. Plan and elevation of the Pesth suspension bridge. Elevation of Nos. 2 and 3 coffer-dams. End view of ditto. Transverse section of No. 2 ditto. Transverse section of coffer-dam, plan of the 1st course, and No. 3 pier. Vertical section of Nos. 2 and 3 piers, showing vertical bond-stones. Vertical cross section of ditto. Front elevation of Nos. 2 and 3 piers. End elevation of ditto. Details of chains. Ditto. Ditto and plan of nut, bolt, and retaining-links. Plan and elevation of roller-frames. Elevation and section of main blocks for raising the chains. Ditto, longitudinal section of fixture pier, showing tunnel for chains. Plan and elevation of retaining-plates, showing machine for boring holes for retaining-bars. Retaining link and bar. Longitudinal plan and elevation of cast-iron beam with truss columns. Longitudinal elevation and section of trussing, &c. Plan of pier at level of footpath. Detail of cantilevers for supporting the balconies round the towers. Elevation and section of cantilevers. Detail of key-stone and Hungarian arms. Front elevation of toll-houses and wing walls. Longitudinal elevation of toll-house, fixture pier, wing wall, and pedestal. Vertical section of retaining-piers. Section at end of fixture pier, showing chain-holes. Lamp and pedestal at entrance of bridge. Lamp and pedestal at end of wing walls. Separately sold from the above in a volume, price half-bound in morocco £1. 128. AN ACCOUNT, with illustrations, of the SUSPENSION BRIDGE ACROSS the RIVER DANUBE, BY WILLIAM TIERNEY CLARK, C.E., F.R.S. With Forty Engravings. 8 JOHN WEALE'S THE AIDE-MÉMOIRE TO THE MILITARY SCIENCES, Framed from Contributions of Officers of the different Services, and edited by a Committee of the Corps of Royal Engineers. The work is now completed. Abattis. Ammunition. Anemometer. Anti-Corrosion. Sold in 3 vols., or in 6 Parts, as follows: £. 3. d. Part I. A. to D., NEW EDITION 0 14 0 II. D. to F. 0 16 0 • III. F. to M. 0 16 0 IV. M. to P. • 0 14 0 V. P. to R. 0 16 0 VI. R. to Z. 1 0 0 4 16 0 The subjects amply and practically treated of are as follows: PART A. B. C. SKETCH OF THE SCIENCE AND ART OF WAR. Bombardment. Boom. Breach. Bridge, Masonry, Demolition of. Buffalo. Artillery. Attack of Fortresses and Posts. Appendix-Assault. Barometer. Bridge, Field. Pontoon. Boat. Rope. Boat and Rope. Cask. Trestle. Raft. Flying, Swing. Bullock. Cable, Chain. Camel. Hemp. Camp, Intrenched. Caponière. Capstan, Field. Carriages (Land and Sea Service). Castrametation. Chevaux-de-Frize. Combustion, Spontaneous. Command. Barricade. Barrier. Battery. Blindage. Block. Blockade, Military. Blockhouse. Boat. Pile and Spar. Flying, Trail. Reconstruction of. Field, Demolition of. PART D. E. F. Dam, temporary. Defence of buildings and villages. Defensive elements. Defence of fortresses. Defensive precautions. Defence of coasts. Defilade. Demolition of works and buildings. Demolition of artillery. Depression carriages. Derrick (sheers, &c.) Dialling Disembarkation and embarkation. Diving dress and apparatus. Draining. Electricity: Lightning conductor. Electrotype. Explosion of powder. Electric telegraph. Elephant. Embarkation. Engineer, military. civil. Epaulement. Eprouvette. Equipment of Artillery. Engineer. PART F. G. H. I. K. L. M. Compass. Contouring. Equipment, Naval. American. Musket-ball Cartridge. Escalade. Evolutions of infantry. artillery. cavalry. Fascine. Field sketching. Fire, vertical. precautions against. cart. Forage, bulk and weight of. Ford. Fortification, field. Fort, permanent. Fort, field. Fortress, permanent. Fraise. Furnace, shot. Fuze for mines. Gabion. Horse. Hurdle. Hut. Ice. Forts, detached. Fortresses, field, or places du moment. Galvanism. Fortification, permanent. Geognosy and Geology. Kyanizing and Burnettizing. Laboratory. Grenade. Levelling "" Coehorn's system. Guard-house, defensible. Loophole. Bastion do. Guerite. Machicoulis. "" Montalembert's do. Gun cotton. "" "" Magazine. Carnot's do. Gunner. " "" German do. "" "" relative value of. "" Fougass. Gunnery. Gunpowder. Heat, Mantlet. Manœuvres of cavalry. Marine artillery. horse artillery. NEW LIST OF WORKS. 9 Meteorology. Mining, military: Part 1. AIDE-MÉMOIRE TO THE MILITARY SCIENCES. Part II.-Practical operations. III.-Charges of mines. IV.-Counter or defensive mines. v.-Attack and defence of countermines. Appendix 1.-Mines for field ser- vice. II.-On breaching ex- periments. PART M. N. O. P. Appendix III. -On Ventilation. Mountain artillery. Mountain barometer. Mule for burden. Musket. Musketry fire and practice. Observatory, astronomical: Part 1. Part II.-Chronometers, &c. III.-Portable observatories. Iv.-Astronomical instru- ments. Observatory, Magnetical. PART P. Q. R. Appendix:-On the books and forms used. Ordnance, British. , construction of. Part 1.-Casting of iron ordnance. 11.-Brass do. III.-Machinery, Woolwich. Ordnance department. Oven, field. , permanent. Pah. Palanque. Palisade.- Parapet. Palæontology. Passage of rivers. Part 1.-Military operations, and the construction of tem- porary bridges. -Permanent bridges. III.-Ditto. Pendulum. Roads: Part II.-Maintenance of Mac- adamized roads. Rocket artillery. Sanitary precautions : -Fever as an army disease. II.-Cholera. Sap. Shrapnell shells, or spherical case. Shot garlands. Siege operations in India. -, irregular. and engineer equipment. Sod-work. Staff. Statistics. Steam engine. locomotive: I. On the consumption of fuel Penetration of projectiles. Petard. Planting trees. Point-blank. Pontoon. Position, military. retrenched. Pyrotechny, military. Quarry. Quartering of troops. Railway. Reconnoitring. Reports, military. River and inland navigation. Prisons, military: discipline and ma- Roads: nagement. PART R. S. T. V. W. Z. II. Resistances to Railway III. Trains. Qualifications of Engine Drivers and Fire-men. Iv.-Description of the LORD of THE ISLES and the LIVER- POOL locomotive engines. V. The Locomotive Engine Boiler. Stockade. Street fighting. Surveying : Trigonometrical survey. Ordnance survey of Great Britain and Ireland. Swimming. Tactics of the three arms. Tambour. Telegraph, field. and the evaporation of water. universal. 1 INDEX, AND LIST OF CONTRIBUTORS. Part 1.-Tracing and construction. Tête de pont. Trous de loup. Voltaic electricity: I.-Invention of the electric tele- graph. II.-Transmission of electricity to a distant place. III.-Patents granted prior to the year 1838. -Various telegraphs in use in England. The submarine telegraph. Water meadows, or irrigation: 1.—Historical sketch. II.-Machines for raising water. Water supply. Water-wheels. Weather. Wells. Zig-zag. THE ENGINEER'S AND CONTRACTOR'S POCKET BOOK, WITH AN ASTRONOMICAL ALMANACK, REVISED FOR 1852 1858 In morocco tuck, price 6s. 1854 CONTENTS. AIR, Air in motion (or wind), and wind-mills. Alloys for bronze; Miscellaneous alloys and composi- tions; Table of alloys; Alloys of copper and zinc, and of copper and tin. Almanack for 1852 and 1953, American railroads; steam vessels. Areas of the segments of a circle. Armstrong (R.), his experiment on boilers. Astronomical phenomena. Ballasting. Barlow's (Mr.) experiments. Barrel drains and culverts. Bell-hanger's prices. Blowing a blast engine. Boilers and engines, proportions of; Furnaces and chimneys; Marine. Bossut's experiments on the discharge of water by hori- zontal conduit or conducting pipes. Brass, weight of a lineal foot of, round and square. Breen (Hugh), his almanack. Bricks. Bridges and viaducts; Bridges of brick and stone; Iron bridges; Timber bridges. Burt's (Mr.) agency for the sale of preserved timber. 10 JOHN WEALE'S THE ENGINEER'S AND CONTRACTOR'S POCKET BOOK. Cask and malt gauging. Cast-iron binders or joints; Columns, formulæ of; Columns or cylinders, Table of diameter of; Hollow columns, Table of the diameters and thickness of metal of; Girders, prices of; Stancheons, Table of, strength of. Chairs, tables, weights, &c. Chatburn limestone. Chimneys, &c., dimensions of. Circumferences, &c. of circles. Coal, evaporating power of, and results of coking. Columns, cast-iron, weight or pressure of, strength of. Comparative values between the present and former measures of capacity. Continuous bearing. Copper pipes, Table of the weight of, Table of the bore and weight of cocks for. Copper, weight of a lineal foot of, round and square. Cornish pumping engines. Cotton mill; Cotton press. Current coin of the principal commercial countries, with their weight and relative value in British money. Digging, well-sinking, &c. Docks, dry, at Greenock. Draining by steam power. Dredging machinery. DWARF, Table of experiments with H. M. screw steam tender. Earthwork and embankments, Tables of contents, &c. Experiments on rectangular bars of malleable iron, by Mr. Barlow; on angle and T iron bars. Fairbairn (Wm.); on the expansive action of steam, and a new construction of expansion valves for condensing steam engines. Feet reduced to links and decimals. Fire-proof flooring. Flour-mills. Fluids in motion. Francis (J. B., of Lowell, Massachusets), his water-wheel. French measures. Friction. Fuel, boilers, furnaces, &c. Furnaces and boilers. Galvanized tin iron sheets in London or Liverpool, list of gauges and weights of. Gas-tubing composition. Glynn (Joseph), F.R.S., on turbine water-wheels. Hawksby (Mr., of Nottingham), his experiments on pumping water. Heat, Tables of the effects of. Hexagon heads and nuts for bolts, proportional sizes and weights of. Hick's rule for calculating the strength of shafts. Hodgkinson's (Eaton) experiments. Hungerford Bridge. Hydraulics. Hydrodynamics. Hydrostatic press. Hydrostatics. Imperial standard measures of Great Britain; Iron. Indian Navy, ships of war, and other vessels. Institution of Civil Engineers, List of Members of the, corrected to March 15, 1852. Iron balls, weight of cast; bars, angle and T, weight of; castings; experiments; hoop, weight of 10 lineal feet; lock gates; roofs; tubes for locomotive and marine boilers; weights of rolled iron. Ironmonger's prices. Just's analysis of Mr. Dixon Robinson's limestone. Latitudes and longitudes of the principal observatories. Lead pipes, Table of the weights of, Leslie (J.), C.E. Lime, mortar, cements, concrete, &c. Limestone, analysis of. Liquids in motion. Locomotive engines; Table showing the speed of an engine. Log for a sea-going steamer, form of. Machines and tools, prices of. Mahogany, experiments made on the strength of Hon- duras. Mallet's experiments on overshot wheels. Marine boilers; engines. Masonry and stone-work. Massachusets railroads. Mensuration, epitome of. Metals, lineal expansion of. Morin's (Col.) experiments. Motion; motion of water in rivers. Nails, weight and length. Navies-of the United States; Indian Navy; Oriental and Peninsular Company; British Navy; of Austria; Denmark; Naples; Spain; France; Germanic Con- federation; Holland; Portugal; Prussia; Sardinia; Sweden and Norway; Turkey; Russia; Royal West India Mail Company's fleet. New York, State of, railroads. Numbers, Table of the fourth and fifth power of. Paddle-wheel steamers. Pambour (Count de) and Mr. Parkes' experiments on boilers for the production of steam. Peacocke's (R. A.) hydraulic experiments. Pile-driving. Pitch of wheels. Table to find the diameter of a wheel for a given pitch of teeth. Plastering. Playfair (Dr. Lyon). Preserved timber. Prices for railways; paid by H. M. Office of Works, smith and founder's work. Prony's experiments. Proportions of steam engines and boilers. Pumping engines; pumping water by steam power. Rails, chairs, &c., Table of. Railway, American, statistics; railway and building contractor's prices; carriages. Rain, Tables of. Rammell's (T. W.) plan and estimate for a distributing apparatus by fixed pipes and hydrants. Rennie's (Mr. Geo.) experiments; (the late J.) estimate. Roads, experiments upon carriages travelling on ordinary roads; influence of the diameter of the wheels; Morin's experiments on the traction of carriages, and the destructive effects which they produce upon roads. Robinson (Dixon), his experiments and material. Roofs; covering of roofs. Ropes, Morin's recent experiments on the stiffness of ropes; tarred ropes; dry white ropes. Saw-mill. Screw steamers. Sewage manures. Sewers, castings for; their estimates, &c. Signs and abbreviations used in arithmetic and mathe- matical expressions. Slating. Sleepers, quantity in cubic feet, &c. Smeaton's experiments on wind-mills. Smith and founder's prices. Specific gravity, Table of. Steam dredging; Navigation; Tables of the elastic force; Vessels of war, of America; of England; of India; of several maritime nations. NEW LIST OF WORKS. 11 THE ENGINEER'S AND CONTRACTOR'S POCKET BOOK. Steel, weight of round steel. Stone, per tb., stone, qr., cwt., and ton, &c., Table of the price. Stones. Strength of columns; Materials of construction. Sugar-mill. Suspension aqueduct over the Alleghany River; Bridges. Table of experiments with H. M. screw steam tender DWARF; of gradients; iron roofs; latent heats; paddle-wheel steamers of H. M. Service and Post- Office Service; pressure of the wind moving at given velocities; prices of galvanized tinned iron tube; specific heats; the cohesive power of bodies; columns, posts, &c., of timber and iron; the comparative strength, size, weight, and price of iron-wire rope (A. Smith's), hempen rope, and iron chain; cor- responding velocities with heads of water as high as 50 ft., in feet and decimals; dimensions of the prin- cipal parts of marine engines; effects of heat on different metals; elastic force of steam; expansion and density of water; expansion of solids by in- creasing the temperature; expansion of water by heat; heights corresponding to different velocities, in French metres; lineal expansion of metals; motion of water, and quantities discharged by pipes of different diameters; power of metals, &c.; pressure, &c., of wind-mill sails; principal dimensions of 28 merchant steamers with screw propellers; of steamers with paddle-wheels; progressive dilatation of metals by heat, &c.; proportion of real to theoretical discharge through thin-lipped orifices; quantities of water, in cubic feet, discharged over a weir per minute, &c.; quantity of water discharged per minute; relative weight and strength of ropes and chains; results of experiments on the friction of unctuous surfaces; scantlings of posts of oak; size and weight of iron laths; weight in ths. required to crush 14-in. cubes of stone, and other bodies; weight of a lineal foot of cast-iron pipes, in tbs.; weight of a lineal foot of flat bar iron, in lbs.; weight of a lineal foot of square and round bar iron; weight of a superficial foot of various metals, in tbs.; weight of modules of elasticity of various metals; velocities of paddle-wheels of dif- ferent diameters, in feet per minute, and British statute miles per hour; showing the dimensions, cost, and price per cubic yard, of ten of the principal bridges or viaducts built for railways, and also the height of the boiling point at different heights;-to find the diameter of a wheel for a given pitch of teeth. Tables of squares, cubes, square and cube roots. Teeth of wheels. Temperature, of the relative indications of, by different thermometers. Thermometers, Table of comparison of different. Timber for carpentry and joinery purposes; Table of the properties of different kinds of. Tin plates, Table of the weight of. Tools and machines, prices of. Traction, Morin's experiments on. Tredgold's Rules for Hydraulics, from Eytelwein's Equation. Turbines, Report on, by Joseph Glynn and others. Values of different materials. Water-wheels. Watson's (H. H.) analysis of limestone from the quar- ries at Chatburn. Weight of angle and T iron bars; of woods. Weights and measures. West India Royal Mail Company. Whitelaw's experiments on turbine water-wheels. White's (of Cowes) experiments on Honduras mahogany. Wicksteed's (Thos.) experiments on the evaporating power of different kinds of coal. Wind-mills, of air, air in motion, &c. Woods. Wrought iron, prices. Zinc as a material in house-building. In One Volume 8vo, extra cloth, bound, price 9s. THE STUDENT'S GUIDE TO THE PRACTICE OF DESIGNING, MEASURING, AND VALUING ARTIFICERS' WORKS; Containing Directions for taking Dimensions, abstracting the same, and bringing the Quantities into Bill; with Tables of Constants, and copious memoranda for the Valuation of Labour and Materials in the respective trades of Bricklayer and Slater, Carpenter and Joiner, Sawyer, Stonemason, Plasterer, Smith and Ironmonger, Plumber, Painter and Glazier, Paper-hanger. Thirty-eight Plates and Wood-cuts. The Measuring, &c., edited by Edward Dobson, Architect and Surveyor. Second Edition, with the additions on Design by E. LACY GARBETT, Architect. CONTENTS. PRELIMINARY OBSERVATIONS ON DESIGNING ARTI- FICERS' WORKS. Preliminary Observations on Measurement, Valuation, &c.- On measuring-On rotation therein therein-On abstracting quantities-On valuation-On the use of constants of labour. BRICKLAYER AND SLATER. DESIGN OF BRICKWORK-technical terms, &c. Foundations-Arches, inverted and erect-Window and other aperture heads-Window jambs-Plates and internal cornices-String-courses-External cornices-Chimney shafts-On general improve- ment of brick architecture, especially fenestration. MEASUREMENT. Of diggers' work-Of brickwork, of facings, &c. DESIGN OF TILING, and technical terms. Measurement of Tiling-Example of the mode of keeping the measuring-book for brickwork. ABSTRACTING Bricklayers' and Tilers' work. Example of bill of Bricklayers' and Tilers' work. VALUATION of Bricklayers' work, Earthwork, Con- crete, &c. Table of sizes and weights of various articles-Tables of the numbers of bricks or tiles in various works -Valuation of Diggers' and Bricklayers' labour— Table of Constants for said labour. 12 JOHN WEALE'S DESIGNING, MEASURING, AND VALUING ARTIFICERS' WORKS. EXAMPLES OF VALUING. 1. A yard of concrete.-2. A rod of brickwork.- 3. A foot of facing.-4. A yard of paving.-5. A square of tiling. DESIGN, SLATING. MEASUREMENT, AND VALUATION OF CARPENTER AND JOINER. DESIGN OF CARPENTRY-technical terms, &c. Brestsummers, an abuse: substitutes for them Joists, trimmers, trimming-joists-Girders, their abuse and right use- -Substitutes for girders and quarter-partitions-Quarter-partitions-Roof-fram- ing-Great waste in present common modes of roof- framing-To determine the right mode of subdi- viding the weight, and the right numbers of bearers for leaded roofs-The same for other roofs-Prin- ciple of the truss-Considerations that determine its right pitch-Internal filling or tracery of trusses -Collar-beam trusses-Connection of the parts of trusses-Variations on the truss; right limits thereto To avoid fallacious trussing and roof- framing-Delorme's roofing; its economy on cir- cular plans-Useful property of regular polygonal plans-On combinations of roofing, hips, and valleys On gutters, their use and abuse-Mansarde or curb-roofs. DESIGN OF JOINERY-technical terms, &c. Modes of finishing and decorating panel-work-Design of doors. MEASUREMENT of Carpenters' and Joiners' work-Ab- breviations. Modes of measuring Carpenters' work-Classification of labour when measured with the timber-Classifi- cation of labour and nails when measured separately from the timber. EXAMPLES OF MEASUREMENT, arch centerings. Bracketing to sham entablatures, gutters-Sound- boarding, chimney-grounds, sham plinths - Sham pilasters, floor-boarding, mouldings - Doorcases, doors, doorway linings Dado or surbase, its best construction · Sashes and sash-frames (examples of measurement) - Shutters, boxings, and other window fittings - Staircases and their fittings. ABSTRACTING Carpenters' and Joiners' work. Example of Bill of Carpenters' and Joiners' work. VALUATION of Carpenters' and Joiners' work, Memo- randa. Tables of numbers and weights. TABLES OF CONSTANTS OF LABOUr. Roofs, naked floors Quarter-partitions, Labour on fir, per foot cube-Example of the valuation of deals or battens Constants of labour on deals, per foot superficial. CONSTANTS OF LABOUR, and of nails, separately. On battening, weather boarding-Rough boarding, deal floors, batten floors. LABOUR AND NAILS together. On grounds, skirtings, gutters, doorway-linings- Doors, framed partitions, mouldings — Window- fittings- Shutters, sashes and frames, staircases- Staircase fittings, wall-strings-Dados, sham co- lumns and pilasters. VALUATION OF SAWYERS' WORK. MASON. DESIGN OF STONEMASONS' WORK. Dr. Robison on Greek and Gothic Architecture Great fallacy in the Gothic ornamentation, which led also to the modern monkey styles ''Resto- ration' and Preservation. MEASUREMENT of Stonemason's work. Example of measuring a spandril step, three methods Allowance for labour not seen in finished stone -Abbreviations, Specimen of the measuring-book -Stairs, Landings, Steps, Coping-String-courses, Plinths, Window-sills, Curbs-Columns, Entabla- tures, Blockings-Cornices, Renaissance Niches. ABSTRACTING AND VALUATION. Table of weight of stone Table of Constants of Labour Example of Bill of Masons' work. PLASTERER. DESIGN OF PLASTER-WORK in real and mock Archi- tecture. Ceilings and their uses Unnecessary disease and death traced to their misconstruction - Sanitary requirements for a right ceiling Conditions to be observed to render domestic ceilings innoxious - Ditto, for ceilings of public buildings - Bar- barous shifts necessitated by wrong ceiling — Technical terms in Plasterers' work. MEASUREMENT of Plaster-work. Abbreviations --Abstracting of Plasterers' work Example of Bill of Plasterers' work. VALUATION. Memoranda of quantities of materials - Constants of Labour. SMITH AND FOUNDER. ON THE USE OF METAL-WORK IN ARCHITECTURE. Iron not rightly to be used much more now than in the middle ages Substitutes for the present extravagant use of iron- Fire-proof (and sanitary) ceiling and flooring- Fire-proof roof-framing in brick and iron-Another method, applicable to hipped roofs - A mode of untrussed roof-framing in iron only-A principle for iron trussed roofing on any plan or scale-Another variation thereof On the decoration of metallic architecture. MEASUREMENT of Smiths' and Founders' work. PLUMBER, PAINTER, GLAZIER, &c. DESIGN, &C. OF LEAD-WOrk. MEASUREMENT OF PAINT-WORK- Abbreviations. Specimen of the measuring-book-Abstract of Paint- workExample of Bill of Paint-work. VALUATION of Paint-work. Constants of Labour Measurement and Valuation of GLAZING Measurement and Valuation of PAPER-HANGING. - APPENDIX ON WARMING. Modifications of sanitary construction to suit the English open fire-More economic modes of warming in public buildings-Ditto, for private ones--Warm- ing by gas. NEW LIST OF WORKS. In 12mo., price 5s. bound and lettered, 13 THE OPERATIVE MECHANIC'S WORKSHOP COMPANION, AND THE SCIENTIFIC GENTLEMAN'S PRACTICAL ASSISTANT ; Comprising a great variety of the most useful Rules in Mechanical Science, divested of mathe- matical complexity; with numerous Tables of Practical Data and Calculated Results, for facilitating Mechanical and Commercial Transactions. BY W. TEMPLETON, AUTHOR OF SEVERAL SCIENTIFIC WORKS. Third edition, with the addition of Mechanical Tables for the use of Operative Smiths, Mill- wrights, and Engineers; and practical directions for the Smelting of Metallic Ores. GEOMETRY. To erect a perpendicular on a right line. To erect a perpendicular at the end of a line. To bisect a given angle. CONTENTS. To describe a circle through three given points out of a right line. To find the centre of a given circle. To find the length of any given arc of a circle. To draw a tangent to a circle. To draw lines towards the centre of a circle, the centre being inaccessible. To describe an arc of a circle. To describe an ellipse or oval. To describe an elliptic arch. To describe a parabola. To measure an intercepted line. To obtain the distance of an inaccessible object. To find the distance between two inaccessible objects. To design a beam of strongest section. To find the proper position for the eccentric in a steam engine. To determine the proper length of valve levers. To inscribe any regular polygon. To construct a square upon a right line. To form a square equal to a given triangle. To form a square equal to a given rectangle. To form a rectangle equal to a given square. To bisect any given triangle. To describe a circle in a given triangle. To form a rectangle in a given triangle. To make a rectangle equal to a given triangle. To make a triangle equal to a given quadrilateral. To form a square equal to a given circle. To form an octagon from a given square. To form a square equal to two given squares, or a circle equal to two given circles. To draw a line equal to any portion of a circle's circum- ference. To draw a spiral with uniform spaces. To draw a volute for the Ionic column. To draw a scroll for hand-rails. To find the angles and lengths of materials for pyramidal frustums. To describe the proper form of material by which to form a cone. Sector by which to obtain angles. GEOMETRY APPLIED TO MECHANICS. To delineate a vee-threaded screw. To delineate a square-threaded screw. To determine the proper forms for a pair of bevel wheels. Proportions for the construction of toothed wheels. To delineate wheels by orthographic projection. Delineation of an undershot water-wheel. DECIMAL ARITHMETIC. Definitions.-Reduction. Applied examples. Definitions of Arithmetical Signs. British Standard Measures.-British Special Measures. Decimal Approximations.-Decimal Equivalents. MENSURATION. To measure the surface of a square, rectangle, rhom- boid, &c. Two sides of a triangle given, to find the third side. Utility of triangles. To find the area of a triangle. Table of Polygons. Definitions of the circle.-Rules in relation to the circle. To find the diameter of a circle when any chord and versed sine are given. To find the length of any given arc of a circle. To find the area of the sector of a circle. To find the area of a circular ring. To find the area of an ellipse. To find the area of a parabola. To find the solidity or capacity of any cubical figure. To find the convex surface and solidity of a cylinder. To find the length of any cylindrical helix. To find the convex surface and solidity of a cone. To find the solidity or capacity of any frustum of a cone or pyramid. To find the solid contents of a wedge. To find the convex surface and solidity of a sphere or globe. To find the convex surface and solidity of the segment of a globe. To find the convex surface and solidity of a cylindrical ring. To determine the proper length of iron for a ring of given diameter. To determine the length of angle iron to form a ring of given diameter. To measure the capacity of a locomotive tender tank. Table of Specific Gravities and Properties of Metals. Table of Specific Gravities and Properties of Timber. Table of Specific Gravities of Liquids, Gases, &c. Weights of various measures of water. Table of the Weight of Square and Round Bar Iron. Table of the Weight of Flat Bar Iron. Table of the Circumferences of Circles, from 1 inch to 20 feet ths of an inch; advancing by an eighth. Table showing the Weight of a lineal foot of Malleable Rectangular or Flat Iron, from th of an inch to 3 inches thick; advancing by an eighth, and quarter of an inch, in breadth. Table showing the Weight of a lineal foot of Round Bar Iron, in avoirdupois qrs. tbs. oz., from 1th of an inch to 12 inches in diameter; advancing by an eighth of an inch. Table showing the Weight of a lineal foot of Square Bar Iron, in avoirdupois qrs. tbs. oz., from th of an inch to 12 inches; advancing by an eighth. Table containing the Circumferences for Angled Iron 14 JOHN WEALE'S NEW LIST OF WORKS. THE OPERATIVE MECHANIC'S WORKSHOP COMPANION. Table of Inclined Planes. Hoops, from 6 inches to 6 feet in diameter; ad- vancing by an eighth of an inch.-Angle outside. Table containing the Circumferences for Angled Iron Hoops, from 6 inches to 6 feet in diameter; ad- vancing by an eighth of an inch.-Angle inside. Proportional breadths for six-sided nuts. Table of the Weights of Sheet Iron, Copper, and Brass. Comparative weights of different bodies. Table of the Weights of Cast-Iron Pipes. Weights of leaden pipes. To find the weights of pipes of various metals. Weight of a cubic inch of various metals. Table of the Weights of Cast-Iron Balls. Table to facilitate the Measure of Timber. Table of Cubic or Solid Measure. To measure battens, deals, and planks. Table of Scantling Timber. INSTRUMENTAL ARITHMETIC. Explanation of the slide rule.-Numeration.—To mul- tiply by the slide rule.-Proportion.-Rule of Three Inverse.-Square and cube roots.-Measure of squares, rectangles, &c.-Measure of circles and polygons. Tables of Gauge-Points for the Slide Rule. Mensuration of solidity and capacity.-To compute the power of steam engines. Of steam engine boilers. COMMERCIAL TABLES. Tables by which to facilitate the Calculation of British Money.-Table of Equivalent Prices. Definitions. STRENGTH OF MATERIALS. Table of Tenacities, Resistance to Compression, &c. of Various Bodies. Table of Comparative Strength of Ropes and Chains. Table of Metallic Alloys. Resistance of bodies to lateral pressure. Table of Practical Data. To find the dimensions of a beam of timber to sustain a given weight.-To determine the absolute strength of a rectangular beam of timber. To determine the dimensions of a beam with a given degree of deflection. Cast-iron beams of strongest section. Of wooden beams, trussed. Absolute strength of cast-iron beams. Table of Dimensions for Cast-Iron Beams. To find the weight of a cast-iron beam. Resistance to flexure by vertical pressure. To determine the dimensions for a column of timber. Table by which to determine the Dimensions of Cast- Iron Columns. Resistance of bodies to twisting. Relative strength of metals to resist torsion. On the Smelting of Metallic Ores. Table of Squares, Cubes, &c. of Numbers. Definitions, &c. MECHANIC POWERS. Rules. First kind of lever. Second ditto. Third ditto. Lever on a safety-valve, &c.-Wheel and pinion, or crane.-Rules, &c.-The pulley, with applications.— Inclined plane. Table of Inclinations and Amount of Opposing Re- sistance. A. Delineation of Screws. The wedge. The screw.-The endless screw, or screw applied to a wheel. CONTINUOUS CIRCULAR MOTION. Definitions, &c.-Proportional diameters of wheels to the number of revolutions.-Of a train of wheels and pinions.-Diameters or number of teeth in wheels in proportion to their velocities.-To determine the proper diameters of wheels to given peculiarities.- To find the proportional wheels for screw cutting by a lathe. Table of Change Wheels for Screw Cutting. Diameters of small wheels. Table of the Strength of Wheels of Cast Iron. Table of the Diameters of Wheels to contain a given number of Teeth. FRICTION. PROPERTIES OF WATER AND AIR. Effects produced by water in its natural state. The pressure of fluids.--The hydraulic press.--The weights of bodies obtained by displacement of fluids. -The resistance of water to bodies passing through it.--Of water flowing through orifices.-Discharging of water by rectangular apertures.-Flowing of water through pipes. Table of the Diameters of Pipes for the Discharging of Water. Laws of the gravity of water.--Rules relating to water- wheels.-Turbines, their effects, &c.--Rule to calcu- late the powers of turbines.-Overshot water wheels, notice of. Effects produced by steam. Table of the Elastic Force of Steam.-Of the latent heat in steam.-Steam as a motive power.-Temperature of steam.- Expansive force of steam. Table of Hyperbolic Logarithms.-Condensation of steam.- Boiling points of impure water. Effects produced by air. Table of the Expansion of Air by Heat.-Table relating to Pumps.-Oxygen of the atmosphere.-Resistance of the atmosphere.-Table of Atmospheric Force.- Effect of wind-mills. STEAM ENGINE BOILERS. To determine the amount of heating surface in a boiler. -Of waggon-shaped boilers.-Of cylindrical boilers. - Marine boilers. Locomotive boilers. Heating powers of combustibles. Observations on the giving an order for a steam engine. Table of Dimensions for Steam Engine Cylinders. Units of nominal power.-To estimate the power of an engine. To determine the velocity for the piston of a steam engine. Table of Approximate Velocities for Pistons. Table for Parallel Motions. LOGARITHMS. Table of Logarithms. Table of Circumferences and Areas of Circles. Table of Square and Cube Roots of Numbers. Table of Per-Centage and Discount. LIST OF PLATES. B. Illustration to the Drawing of Bevel Wheels. C. Orthographic Projection. D. Applications of Mechanic Powers. E. and F. Parallel Motions. G. Elevation and Section of an Overshot Water-Wheel, constructed by Messrs. Donkin and Co. Details. H. K. Boilers of the 'Braganza' steam vessel, by Messrs. Bury, Curtis, and Kennedy. L. Locomotive Boiler. SERIES OF MR. WEALE'S RUDIMENTARY WORKS FOR THE USE OF BEGINNERS. 1s. • 2. NEW LIST FOR 1853. 1. Rudimentary Chemistry, by Prof. Fownes, F.R. S., including Agricultural Chemistry, for the use of Farmers. 4th edition. Natural Philosophy, by Charles 45. Rudimentary Treatise on Limes, Cements, Mortars, Concrete, Mastics, &c., by Geo. R. Burnell, C.E. • 1s. 46. the Art of Con- Tomlinson 1s. 3. Geology, by Lieut.-Col. Portlock, F.R.S., &c. 3rd edition structing and Repairing by H. Law, C.E. Common Roads, 1s. • 4, 5. 6. 1s. 6d. Mineralogy, by D. Varley, 2 vols. 2s. Mechanics, by Charles Tomlin- 47, 48, 49. the Construction • 38. son 1s. 50. • 7. Electricity, by Sir William Snow Harris, F. R.S. 3rd edition. • • 18. 8, 9, 10. 11, 11*. 12. 1s. 6d. Magnetism, by the same, 3 vols. 3s. 6d. History of the Electric Tele- graph, by E. Highton, C. E., double Part 28. Pneumatics, by Charles Tomlin- son. and Illumination of Lighthouses, by Alan Stevenson, C.E., 3 vols. the Law of Con- tracts for Works and Services, by David Gibbons, Esq. 51, 52, 53. 54. 1s. 13, 14, 15.-- Civil Engineering, by Henry Law, C. E., 3 vols. : and 15*. Supplement, 4s. 6d. Architecture (Orders of), by W. H. Leeds. 2nd edition. 1s. Architect Naval Architec- ture, Principles of the Science, by J. Peake, N.A., 3 vols. • 3s. Masting, Mast- making, and Rigging of Ships, by R. Kipping, 16 N.A. (in the press) 55, 56. • Navigation: the Sailor's Sea-Book.-How to keep the log. and work it off-Latitude and longitude- Great Circle Sailing-Law of Storms and Variable Winds; and an Explanation of Terms used, with coloured illustrations of Flags, 2 vols. 57, 58. the Principles of the Art of Warming and Ventilation, by Chas. Tomlinson, 2 vols. 16. 17. Ditto (Styles of), by T. Bury, 1s. 18, 19. Ditto (Principles of Design in), by E. L. Garbett, Architect, 2 vols. 28. 20, 21. Perspective, by G. Pyne, Artist, 2 vols. 3rd edition 28. 22. Art of Building, by E. Dobson, C.E. 1s. 59. 23, 24. Brick - making, Tile- R. Armstrong, C.E. making, &c., by the same, 2 vols. 28. 60, 61. 25, 26. Masonry and Stone-cut- ting, by the same, with illustrations of the preceding, in 16 4to. atlas plates 62. 28. 27, 28. Painting, or a Grammar 63, 64, 65. of Colouring, by George Field, Esq., 2 vols. 28. 29. Draining Districts and Lands 1s. 30. Draining and Sewage of 66. Towns and Buildings 1s. 31. Well-sinking and Boring, 67, 68. by G. R. Burnell, C.E. 1s. 32. the Use of Instruments, 33. by J. F. Heather, M.A. 3rd edition. Constructing Cranes, by 15. 69, 70. J. Glynn, F.R.S., C.E. 1s. 71. • 34. Treatise on the Steam Engine, by Dr. Lardner 1s. 35. 28. 28. • Steam Boilers, by 1s. Land and Engi- 18. neering Surveying, by T. Baker, C. E., 2 vols. 2s. Introductory patches of Rail- way Details, by R. M. Stephenson, C.E. Treatise on the Construction of Agricultural Buildings; on Motive Powers, and the Machinery of the Steading; and on Agricultural Field Engines, Machines, and Implements, 3 vols. (vol. 8 in the press) on Clay Lands and Loamy Soils, by Prof. Donaldson, A. E. on Clock and Watch- making, and on Church Clocks, by E. B. Denison, M. A., 2 vols. - • and Practical Treatise on Music, by C. C. Spencer, 2 vols. • Instruction for Playing the Piano-Forte, by the same • 38. 1s. 28. • 28. • 1s. 72, 73, 74, 75. — Treatise (A Manual of the Mollusca) on Recent Fossil Shells, by S. P. Woodward, and illustrations, 4 vols. (vols. 3 & 4 in the press) on Descriptive Geo- metry, by J. F. Heather, M.A., 2 vols. on Economy of Fuel, particularly with reference to Reverberatory Furnaces for the Manufacture of Iron and Steam Boilers. • 4s. 2$. 1s. Treatise on Steam as applied to General Purposes and Locomotive En- gines, by J. Sewell, C. E., 3 vols. 79**. Atlas of Plates illustrative of the 3 vols., in folio, and as a Drawing Book of Loco- motive Engines, price 7s. 80, 81. Rudimentary Treatise on Marine Engines, and on the Screw, &c., by R. Murray, C.E., 2 vols. • 3s. 28. 40. Art of Blasting Rocks and Quar- rying, and on Stone, by Lieut.-Gen. Sir J. Burgoyne, K.C.B., R.E. 2nd edition 36, 37, 38, 39.- Dictionary of Terms used by Architects, Builders, Civil and Mechanical Engineers, Surveyors, Artists, Ship-builders, &c., 4 vols. Art of Glass-Staining, by Dr. 1s. 76, 77. 77*. 4s. • M. A. Gessert 1s. • • 41. Essay on Painting on Glass, by 78, 79, 79*. E. O. Fromberg ls. 42. Treatise on Cottage Building 18. • 43. Tubular and Girder Bridges, and others, more particularly de- scribing the Britannia and Conway Bridges, with Experiments 44. by E. Dobson, C.E. 1s. Foundations, &c., 18. 16 MR. WEALE'S SERIES OF RUDIMENTARY WORKS. 80*, 81*. The Practice of Embanking Lands from the Sea, treated as a Means of Profitable Employment of Capital, by John Wiggins, F. G.S., Land Agent and Surveyor, 2 vols. . 82, 82*. Rudimentary Treatise on the Power of Water, as applied to drive Flour-Mills, by Joseph Glynn, F.R.S., C.E. 83. Haddon, M. A. 82**, 83*. 83**. 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