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^LIBRARY OF CONGRESS.^ 
 
 f [SMITHSONIAN DEPOSIT.] ' 
 
 ? UNITED STATES OF AMERICA.! 
 
THE 
 
 PRACTICAL SURVEYOR'S GUIDE, 
 
 THE NECESSARY INFORMATION TO MAKE ANY PERSON 
 OF COMMON CAPACITY, 
 
 A FDaSHED LAND SIJRYEYOE, 
 
 WITHOUT THE AID OF A TEACHER. 
 
 BY 
 
 ANDREW DUNCAN, 
 
 LAND SURVEYOR AND CIVIL ENGINEEB. 
 
 iDl 
 
 PHILADELPHIA: 
 
 HENRY CAREY BAIRD, 
 
 (successor to e. l. caret.) 
 
 LONDON: 
 
 LOW, SON & CO. 
 
 1854. 
 
Entered, according to act of Congress, in the year 1854, by 
 
 HBNRY^CARET BAIRD, 
 
 In the Clerk's OfiSce of the District Court of the United States, for 
 
 the Eastern District of Pennsylvania. 
 
 STEBEOTYPED BY SLOTE & MOONEY, 
 
 Philadelphia. 
 
 ^^p 
 
 s-s-siso 
 
ADYEETISEMENT. 
 
 The intention of the Author of the following 
 synopsis is to furnish a cheap, small book contain- 
 ing the best practical information hitherto pub- 
 lished and scattered through many eminent authors, 
 nearly all of which he has carefully studied, and 
 having had more than thirty years' experience as a 
 Surveyor, &c., has often had occasion to carry 
 large works in order to have at hand the things 
 necessary in the immediate field practice of sur- 
 veying, levelling, profiling, calculating excava- 
 tions, embankments, &c. To render the book as 
 cheap as possible, the tables shall be only those 
 that are really wanted, but- by which all things in 
 common practice can be readily done, viz : Lati- 
 tude and departure, for four pole chains. A table 
 of natural sines, cosines, and tangents, which are 
 most useful for finding the radius of curves, degree 
 of curvature, &c., on railroad and other curves, 
 their application in finding grades, cuttings, fil- 
 lings, &c., will, it is hoped, prove useful. 
 
 (iii) 
 
iv Advertisement. 
 
 Geometrical demonstrations are avoided, except 
 in a few cases, the design of the writer being to 
 furnish a short treatise, to direct at once to what 
 is required. 
 
 The work will be comprised in four divisons : 
 
 1st. The arithmetical calculation of plane figures. 
 
 2nd. The calculation of surveys taken with the 
 compass and chain by latitude and departure, with 
 various methods of proof. 
 
 3d. The method of plotting, enlarging and di- 
 minishing maps, with remarks on copying and 
 embellishing. 
 
 4th. Levelling, profiling and calculating cuttings 
 and embankments, the use and application of the 
 tables, together with many other useful things 
 applicable in practice. 
 
PREFACE. 
 
 The following compilation is made in consequence of the 
 undersigned not having met with any work on Surveying 
 sufficiently concise, and instructive in the several details, 
 necessary to qualify properly the practical surveyor. Many 
 of the works already published contain subjects not neces- 
 sary in such treatises ; such as Geometry, Plane Trigo- 
 nometry, &c., which subjects, it is taken for granted, all 
 who intend to become proficients have studied prior to 
 reading Surveying. They are also found not to contain 
 instruction that in recent improvements the surveyor re- 
 quires to know. Many of these things the compiler of this 
 short treatise, will endeavour to supply ; also, many other 
 necessary things, which, in his long experience, he has 
 found indispensable to the correct practitioner. He has 
 collected the most necessary insti-uction in leveling and 
 profiling, with a new and speedy plan of setting grades 
 on rail and plank roads. The method of inflecting curves, 
 not hitherto sufficiently explained. The description and 
 design of a new instrument whereby distances are found 
 at once without any calculation, A new method of sur- 
 veying any tract of land by measuring one line through 
 it, with a geometrical demonstration of the same. A geo- 
 metrical method of correcting surveys taken with the Com- 
 1* (v) 
 
vi Preface. 
 
 pass, to fit them for calculation, with a table of corrections 
 for certain distances, but applicable to all. A short method 
 of finding the angles from the courses, and vice versa. 
 The method of surveying with the Compass through any 
 mine or iron works, and to correct the deflections of the 
 needle by attraction. Description of an instrument by the 
 help of which any gentleman may measure a map by inspec- 
 tion, without calculation. A new and short method of calcu- 
 lation, wherein fewer figures are used than in the common 
 method ; also, the Pennsylvania method. Tables of diff'er- 
 ence ■ of Latitude and Departure, made expressly for two 
 pole chains, but which can also be used with four poles. 
 The method of correcting the diurnal variation of the 
 needle, most useful in tracing the boundaries of surveys, 
 a complete description of which is given with the reason 
 for using 57-3° and how it is found. Various methods of 
 plotting and embellishing maps. The most correct method 
 of laying ofi" lots with a pole, plummets, &c. Description 
 of a new Compass which the compiler has contrived for 
 that purpose, and which is made by Reid & Sons, Smith- 
 field street, Pittsburgh. 
 
 The compiler does not deny that he has borrowed from 
 many authors those things he has found best adapted to 
 the completion of a work adequate to make a finished 
 American Surveyor, of which an unprejudiced and en- 
 lightened public are the best judges. 
 
 ANDREW DUNCAN, 
 
 Land Surveyor and Civil Engineer, 
 
 Office, Odeon Building, Fourth St., Pittsburgh, 
 
PRACTICAL SUEYEYOE'S GUIDE. 
 
 Problem First. 
 To reduce two pole chains and links to four pole 
 ones. 
 
 If the number of chains be even, the half of 
 them will be four pole ones, to which annex the 
 given links. Thus : 
 
 1. In 16 chains, 37 links of two pole chains 
 how many four pole ones : 
 
 2)16. 37 
 
 Ans. 8.37 
 
 But if the number of chains be odd, take half 
 of them and add 50 to the links. Thus : 
 2)131.40 
 
 Ans. 65.90 
 
 Problem Second. 
 To reduce four pole chains and links to two pole 
 ones. Double the chains and annex the links if 
 
 (9) 
 
10 The Surveyor's Guide. 
 
 they be less than 50, but if they exceed 50, add one 
 to double the chains and take 50 from the links. 
 
 C, L. 
 
 Thus : 16. 25 of four poles, how many two pole 
 chains. 
 
 16.25 . 
 
 2 
 
 Ans. ^32.25 
 
 C. L. 
 
 2d. In 19.87 four pole chains how many two 
 
 pole ones. 
 
 : 19.87 
 2.50 
 
 Ans. 39.37 
 
 To reduce two pole chains and links to perches 
 and decimal of a perch, multiply the chains by 
 
 C. L. 
 
 two and the links by four, thus: In 16.37 how 
 
 many perches. 
 
 16.37 
 2. 4 
 
 Ans. 33.48 
 
 Article First — of Areas. 
 A square is a plane figure having four equal 
 sides and four right angles. To find the contentj 
 
The Surveyor's Gtuide. 11 
 
 multiply the side into itself aB;d the product is the 
 content. 
 
 Example. 
 Required the area of the square A B C D, one 
 of whose sides is 25 chains 95 links. 
 
 Fig. 1. 
 
 25.95 
 25.95 
 
 12975 
 23355 
 12975 
 5190 
 
 A 
 
 A. K. P. 
 
 67. 1. 14.44 
 
 A. 67.34025 
 4 
 
 C 
 
 25.95 
 
 R. 1.36100 
 40 
 
 
 P. 14,44000 
 
 
 
 A parallelogram is a four sided figure whose 
 opposite sides and angles are equal. To find the 
 area multiply one of the sides by the p.erpendicular 
 demitted from one of its opposite, angles. 
 Example. 
 
 Required the area of the parallelogram A B 
 
12 The Surveyor's Guide. 
 
 C D, the length of which is 15 chains, and height 
 
 C. L. 
 
 12 64. 
 
 Fig. 2 
 
 12.64 
 
 A. R. p. 
 
 18.3. 33.6 
 
 D 
 
 15 00 ( 
 
 12.64 
 15 
 
 
 6320 
 1264 
 
 Acres, 
 
 18,960 
 
 Roods, 
 
 3.840 
 40 
 
 Perches, 38,600 
 
 The content of an oblong piece of ground and 
 one side are frequently given to find the other. 
 Divide the area in perches by the given side, gives 
 the side required which is easily reduced into 
 chains and links. 
 
 If a lot contains 507 perches and is 14.25 long, 
 what is its width. 
 
The Surveyor's Guide. 13 
 
 29)507 '17.4827 
 29 
 
 .25+12.06=8 37.06 
 
 217.0000 
 203 
 
 140 
 116 
 
 240 
 232 
 
 80 
 58 
 
 220 
 
 203 
 To draw maps of these figures is too obvious to 
 require any explanation. 
 
 5th. When the sides of the above figures are 
 given in feet and inches, reduce the inches to deci- 
 mal of a foot. Then multiply the length by the 
 breadth and divide the product by 43560, the 
 number of feet in an acre, the quotient will be the 
 acres and decimal of an acre, which may be redu- 
 ced to roods and perches by multiplying by 4 for 
 the roods and 40 for the perches, pointing off the 
 proper number of decimal places each time, thus : 
 
 A lot of land is 600 feet 4 inches long and 240 
 2 
 
14 The Surveyor's Guide. 
 
 feet 3 inches wide, how many acres does it contain. 
 600.333.X240.25=144230.00325 
 
 This divided by 43560. gives 3.31106 or 3 1 0^9.76 
 
 4 
 
 1.24424 
 40 
 
 9.76960 Ans. 
 
 6th. A trapezium is a four sided figure the oppo- 
 site sides of which are neither equal nor parallel. 
 To find the content, measure a diagonal and two 
 perpendiculars to the opposite corners, multiply 
 the diagonal by half the sum of the perpendicu- 
 lars, and the product will be the area. 
 Example. 
 
 Let A B C D be any trapezium, having A C 80 
 perches, and the perpendiculars as in the figure. 
 
The Surveyor's Guide. 
 
 15 
 
 25 
 20 
 
 2)45 
 
 22.5 
 80 
 
 160)1800,0(li.l.00 Ans. 
 160 
 
 200 
 160 
 
 40)40(1 
 40 
 
 7th. A triangle is a figure having three sides 
 and three angles, any side may be called the base, 
 having the base and perpendicular given. Multi- 
 ply the base by half the perpendicular, or the base 
 by the whole of the perpendicular, and take half 
 the sum. 
 
 Example. 
 
 LetABCbeany 
 triangle whose base 
 is 100 two pole ch's 
 and 15 links, and 
 perpendicular 40 
 
16 The Surveyor's Guide. 
 
 chains and 20 links, required the content in 
 
 acres. 
 
 100 15 
 2 4 
 
 40 20 200.6 perches and decimal. 
 
 2 4 40.4 half the perpendicular. 
 
 2)80 8 8024 
 
 8024 
 
 40 4 A. R. P. 
 
 160)8104.24(50 2 24.24 Ans. 
 800 
 
 40)104 
 80 
 
 24 
 
 8th. Having the three sides given to find the area 
 rule, add the three sides together and take half 
 the sum, from which subtract each side severally, 
 multiply the half sum and three remainders con- 
 tinually into each other, and the square root of 
 the product will be the area. 
 
 The most satisfactory proof of the above rule 
 is the following : 
 
 Let A B C be any triangle, B C its base, A B the 
 greatest side, and A C the least, and let P be half 
 
The Surveyor's Guide. 17 
 
 the perimeter. In A B take A D=A C, join D C 
 and draw A E perpendicular to D C and E G pa- 
 allel to B C cutting A B 
 in G, with tlie centre G 
 and radius G E describe 
 a circle cutting A B in L 
 and A B and E G pro- 
 duced in K and H. Join 
 H B and produce A E, Kg. 5. 
 
 H B till they meet in M. Since A D=A C and 
 the angles at E are right, the squares of A E, 
 E D are equal 2 A E,+2 E and .-. E D=E C or 
 D 0=2 D E. Hence by similar triangles D G E, 
 D B 0, B 0=2 G E=E H, and B is also paral- 
 lel to E H .-. H B M is parallel to E D and 
 (Euc. 1st 29th) the angle B M E=D E A, viz : a 
 right angle, and H E being a diameter, M is a 
 point in the circle. But from similar triangles 
 D G E, D B 0, D B=2 D G, to each of these 
 equals add A D+A 0=2 A D, and B A+A 0=2 
 A G, to each of which equals add B 0=2 G E=2 
 G K .-. A B+A 0+B 0=2 A K or A K is =P, 
 half the perimeter. Now the area of the triangle 
 A B 0=area A D 0+area B D 0=A EXD E+ 
 
18 
 
 The Sueveyor's Guide. 
 
 M EXD E (B M being parallel to D C)=A MXD 
 E. But by similar triangles A D E, A M B : A 
 E : E D :: A M to M B, and by equi-multiples 
 the first multiplied by third : the second multiplied 
 by the third :: the second X by the third : the 
 second X by the fourth. Hence, A EXA M : E 
 DXA M :: E DXA M : E DXM B, i. e. the area 
 of the triangle is a mean proportional between 
 A EXA M, and E DXM B. Now E DXM B = 
 P— A BXP— A C, and A EXA M=A LXA K= 
 PXP — B 0. Hence the area of the triangle is : 
 ^fPXP— A BXP— A GXP— B 0, which is the rule. 
 
 Example. 
 9th. Suppose the 
 sides to be measur- 
 ed by a four pole 
 chain and be 
 
 AB 10.64) 
 A C 12. 28 y 
 BO 9. 00 J 
 
 Sum 31.92 
 
 I sum 15. 96 
 
 5. 32 first remainder. 
 3. 68 second do. 
 
 6. 96 third do. 
 
 Fig. 6 
 
The Surveyor's Guide. 19 
 
 15.96X5.32X3.68X6.96=2174.71013216(46.6337 
 16 
 
 
 A. R. 
 
 4 2 
 
 616 
 
 
 
 926)5871 
 5556 
 
 And since 
 10 square 
 4 pole ch's 
 make one 
 acre, this 
 becomes 
 
 
 9323)31501 
 27969 
 
 
 93263)353232 
 
 279789 
 
 
 932667)7344316 4.66337 
 6528669 4 
 
 
 p. 
 26. 
 
 2.65348 
 40 
 
 The content is 
 
 26,13920 
 
 If the sides are in perches and decimal, divide 
 the square root of the products of the half sum 
 and three remainders by 160, and the quotient 
 will be the acres, and the remainder divided by 40 
 will be the roods. 
 
 The same may be more readily done by loga- 
 rithms, for as the addition of logarithms serves for 
 
20 
 
 The Surveyor's Guide. 
 
 the multiplication of their corresponding numbers, 
 and that the number answering to the half of a lo- 
 garithm will give the square root of the number of 
 that logarithm, it follows that half the sum of the 
 logarithms of half the sum of the sides, and the 
 three remainders will give the area, thus : 
 Half sum, 15.96 log. 1.20303 
 
 First remainder, 5.32 
 Second " 3.68 
 Third « 6.96 
 
 " 0.72591 
 " 0.56585 
 " 0.84261 
 
 2)3.33740 
 
 Square four poles 46.63 
 Or, 4.663 
 4 
 
 1.66870 
 
 2.652 
 40 
 
 
 26.080 4 2 26 as before. 
 
 10th. When the three sides are given and the 
 angles are required, call either side on which the 
 perpendicular will fall from the o^pposite angle the 
 base, then as the base is to the sum of the other 
 two sides so is the difference of those sides to the 
 difference of the segments made by the perpen- 
 dicular, then half that difference added to half the 
 
The Surveyor's Guide. 
 
 21 
 
 Bum gives the greater, and substracted the less, by 
 
 •which means it is divided into two right angled 
 
 triangles, the hypothenuse and one leg of each 
 
 being given, the angles are easily found by plane 
 
 trigonometry. 
 
 Example. 
 Let A B C be ^ \ Kg. 7 
 
 any triangle hav- 
 ing the sides giv- 
 en as follows,viz : 
 A B 88, B C 54 
 and A C 108 to find the angles. 
 
 A B=88 Then as 108 : 142 :: 34 
 B C=54 34 
 
 142 sum 
 34 difference. 
 
 568 
 426 
 
 108)4828.000(44.703 diff. of the 
 432 segments at the base. 
 
 22.351 half diff. 
 
 508 
 432 
 
 760 
 756 
 
 400 
 324 
 
22 The Surveyor's Guide. 
 
 Then half the base 54+22.351=76.351, the 
 greater segment A B, and 54—22.351=31.649 the 
 less segment. 
 
 The triangle is now divided into two right angled 
 
 triangles, the hypothenuse and base in each being 
 
 given to find the angles, as follows : 
 
 AsAB 88 1.9444827 
 
 : Rad. 90° 10.0000000 
 
 :: A D 76.351 1.8828147 
 
 11.8828147 
 1.9444827 
 
 : Sine A B D 60°.ll' 9.9383320 
 
 And 90— 60°.11'=29°.49'=-Angle BAD. In 
 the same way C B D is found to be 35°. 53' its com- 
 plement 54°.07'=/' B CD. 
 
 Now A B D=60°.ll' 
 C B D=35 .53 
 
 Angle A B C= 
 
 =96 
 
 .04 
 
 t 
 
 A= 
 
 29 
 
 .49 
 
 L 
 
 C- 
 
 54 
 
 .07 
 
 180 .00 Proof as the three angles 
 of every plane triangle are equal to 180° per 32d 
 of the 1st of Euclid. 
 
 lltli. Many things occur to the practical sur- 
 
The Surveyor's Guide. 23 
 
 veyor in the triangle, some of which I shall take 
 notice of in this place. It often happens in prac- 
 tice that the two sides and their included angle are 
 given to find the other angles and side. 
 
 Rule. — As the sum of the sides is to their differ- 
 ence so is the tangent of half the sum of the oppo- 
 site angles to the tangent of half the difference ; 
 this half difference added to half the sum of the 
 angles at the base gives the greater, and sub- 
 tracted the less. Then aa sine of either of the 
 base angles is to its opposite side, so is sine of the 
 contained angle to the required side. 
 Example. 
 
 Let AC 
 
 =80, B G 
 
 =110,and 
 
 /^ ACB 
 
 102°.30'to 
 
 find A B 
 
 c 
 and the angles A and B. 
 
 Side B C 110 From 180 
 Side AC 80 take /: C= 102.30 
 
 Sum 190 2)77.30 sum of base 
 
 angles. 
 
 Diff. of sides 30 | sum -38.45 
 
24 
 
 The Surveyor's Guide. 
 
 Then as 190 log. 2.2787536 88°.45' 
 : 30 " 1.4771213 7 .13 
 
 :: Tag't 38°.45' 9.9044910 
 
 45 .58 U A 
 
 11.3816123 — 
 
 2.2787536 31 .32 B 
 
 ::Tag'tofidiff.7°.13' 9.1028587 
 
 Then as sine B 31°.32' 
 
 : AC 80 
 
 :: sine C 102.30 
 Or its supplem't 77.30 
 
 9.7184971 
 1.9030900 
 
 9.9895815 
 
 11.8926715 
 
 9.7184971 
 
 To A B 149.34 2.1741744 
 
 12th. Again, it often happens that the area 
 must be found from the foregoing data, in that 
 case multiply the two sides together, and that pro- 
 duct by the natural sine of \ the contained angle, 
 gives the area. 
 
 Example. 
 
 Let ABC 
 
 be a triangle 
 
 having the 
 
 side A C 13 
 
 chains, A B 4. 
 
 7c. 501. and /- B A C 42° to find the area. 
 
The Surveyor's Guide. 25 
 
 7.5 
 13 
 
 225 
 75 
 
 97.5X.334565 half the nat'l sine of 42°= 
 
 A. R. P. 
 
 32.62 square four pole chains = 32 19.2 Ans. 
 
 Demonstration. 
 Let fall the perpendicular B. D. 
 A B : B D :: rad : sine A 
 .-. B D=ABXsine^A 
 
 Rad But rad.=l. 
 
 .*. B D=A B=sine. Multiply each side by 
 ACandBD. AC=AB. Sine A.XA C 
 But A C. B D— the area. Hence, 
 
 A B. A C. Sine A=area, which is the rule. 
 
 13th. Let B A C be a triangular farm, and P a 
 well of water. It is required to draw a line or 
 fence from the well that will divide the farm 
 equally between two partners; 
 
26 
 
 The Surveyor's Guide. 
 
 Fig. 10. 
 
 E D 
 
 Find D the middle of the base, B C, and from 
 P take a course of P D. Again set your instrument 
 at A, and take the same course A E ; cause a pole 
 to be set at E, a line or fence from E to P will 
 bisect the farm, which is easily demonstrated from 
 the figure. See Bland. 
 
 14th. Again, suppose the well P, to be situated 
 within the farm, and it be required to divide it 
 equally between three occupants, so that each may 
 have the use of the well. a 
 
 In fig. 11 di- 
 vide the base B 
 C, into three 
 equal parts in 
 D and E. Set 
 your instrument 
 at P, and take ^ 
 
 Fig. 11. 
 
The Suevetor's Guide. 
 
 27 
 
 the courses P D and P E. Remove your instru- 
 ment to A, and take A F the same course as P D, 
 and A G the same as P E. Cause stakes to be driven 
 at F and E in a straight line between B and C. 
 Fences from F, G, and A, to P, trisect the farm, 
 ■which is plain from the figure. 
 
 15th. To find the area of a Trapezoid Rule, 
 multiply half the sum of the parallel sides by the 
 perpendicular distance between them, and the pro- 
 duct is the area. 
 
 Let figure 12 be a 
 Trapezoid ; if A D be q ..-,- 
 bisected in E, and E 
 F drawn parallel to 
 
 A B or C D, it also j Kg. 12. 
 
 bisects B C in F. — 
 Through F draw ^G 
 H parallel to A D. 
 
 It is evident the triangles, B F G, and F C H, 
 are similar and equal. (26th Euclid, 1st.) .-. E F, 
 half the sum of the sides, multiplied by the per- 
 pendicular distance between them, A B, gives 
 the area. 
 
28 
 
 The Surveyor's Guide. 
 
 Being surveying on the side of a bog, and want- 
 ing four acres to make up a division, and seeing A 
 
 A 50 , C 
 
 B would pass through a pond, I found A C fifty 
 chains, and L C 56*^; how far must I measure 
 from C towards B, so that the triangle ABC, 
 may contain four acres. 
 
 Since A C X C B X i the natl. sine of 56°=4 
 acres, it follows that 4 acres divided by the pro- 
 duct of one half the natl. sine of 56° into A C, 
 gives B C the required side. Thus : 
 
 50X4=200 perches X, 4145188=82.9 ; and 640 
 perches in 4 acres, divided by 82.9=7.72 per the 
 length of B C, and in like manner any other simi- 
 lar case can be done. 
 
 17th. Sometimes it is found necessary to ob- 
 tain the area of a trapezium from having the 
 diagonals and the angle of intersection given. 
 
The Surveyor's Guide. 29 
 
 Rule — Half the product of the diagonals multi- 
 plied by the natural sine of the angle of intersec- 
 tion, will be the area. 
 
 Example. 
 If the two diagonals of a trapezium be 40.15, 
 and 60.13 chains the /- of intersection 75° 45', 
 what is the area. J of 40.15X60.13=1207.1097= 
 half the product of the diagonals, and 1207.1097X 
 96923=(natural sine of 75°45')=1169.966934531== 
 
 A. R. P. 
 
 the area, in square four pole chains, or 116. 3. 39. 47. 
 Answer. 
 
 18th. To find the area of a trapezium, when 
 each side and the angle of intersection of the 
 diagonals are given. Rule — Square each side of 
 the trapezium ; add together the squares of each 
 pair of opposite sides ; subtract the less from the 
 greater; multiply the diflference by the tangents 
 of the angle of intersection. One fourth of the 
 product will be the area. 
 
 Example. 
 
 What is the area of a trapezium, the sides of 
 which are 10, 13, 7.16, 8.32, and 10.05 chains 
 respectively, and the V of intersection of the 
 diagonals 52° 15'. 
 
30 The Surveyor's Guide. 
 
 (10.13)=102.6169 
 ( 8.32)= 69.2224 
 
 171.8393=Sum of sqs. of opposite sides. 
 
 (15.05)=226.5025 
 ( 7.16)= 51.2656 
 
 277.7681=Suni of sqs. of other sides. 
 
 105.9288 Difference, 
 Multiplied by .32288=1 the natural tangent, 
 
 34.20290944 or 
 
 A 3. 1 .27,23 perches. 
 
 For a demonstration of the foregoing, see Cfib- 
 son's Surveying, hj Trotter. 
 
 19th. To find the area of a trapezium, when the 
 four sides are severally given, and also the sum 
 of any two opposite angles. B,ule — From half the 
 sum of the four given sides, subtract each seve- 
 rally ; multiply the four remainders continually 
 together ; from the result subtract one half the 
 continual product of the four sides, multiplied by 
 unity, increased by the natural cosine of the sum 
 of the given angles. The square root of the 
 result will be the area. 
 
The Surveyor's Guide. 31 
 
 Remark. 
 
 In the application of this theorem, it must be 
 carefully remembered that the cosine of an angle ' 
 is positive when that angle is in either the first or 
 fourth quadrants, and negative when it is in the 
 second or third quadrants. For a demonstration 
 of this beautiful theorem, see also, Grihson, hy 
 Trotter. 
 
 N. B. When the sum of the opposite angles is 
 180°, that is, when the trapezium can be inscribed 
 in a circle, the above rule is simply : frop half the 
 sum of the given sides, subtract each side seve- 
 rally ; multiply the four remainders continually 
 together, and extract the square root, gives the 
 area. 
 
 Example. 
 
 " One morning in May I went to survey, 
 
 As soon as bright Sol I espied ; 
 
 I measured round a four cornered ground. 
 
 In the margin see the length of each side ; 
 
 The angle at B, together with D, 
 
 An hundred and fifty degrees ; 
 
 The meadow's content is all that I want, 
 
 Assist me kind youths, if you please." 
 
32 
 
 The Surveyor's Guide. 
 
 A B 15.60 
 B C 13.20 
 C D 10.00 
 D A 26.00 ch'ns. 
 
 2)64.80 sum. 
 
 32.4=J sum. 
 
 rig. 14. 
 
 16.80=lst remr. S=half the sum. 
 
 19.20=2d do. of the sides. 
 
 22.40=3d do. 
 6.40=4th do. 
 
 Whence (s-A B)X(s-B C)X(s-C D)X(s-D A)= 
 32.4X16.8X19.2X22.4X6.4-46242.2016=46242. 
 2016 
 And A B. B C. C D. D A.X(l+cos. 150°) 
 
 That is 15.60X13.20X10.00X26.00 
 
 -X0.1339746=3586.4464 
 
 Difference=42655.7552 
 The square root of 42655.7552 is 206, 5327= 
 
 A. R. P. 
 
 area in square four pole chains, or 20. 2. 24,55232. 
 
 N. B. This problem is taken from Deighan's 
 
 Arithmetic, vol. second, page 148, and the answer 
 
 A. K. p. 
 
 there given is 21. 2. 00,64, which is obtained by 
 taking the trapezium to be inscribed in a circle, 
 which is not the case. 
 
The Surveyor's Guide. 33 
 
 When the opposite angles of a quadralateral are 
 equal to two right angles, a circle can be described 
 about it. The rule to find the area, then, is : mul- 
 tiply the half sum, and four remainders continually 
 together, and extract the square root, for in that 
 case l+cos.(A+B)=0. 
 
 21st. To find the area of a circle having the 
 diameter given. Rule — Square the diameter, and 
 multiply by .7854, and you have the area. 
 
 22d. To find the area of an ellipsis. Rule — 
 Multiply the transverse and conjugate diameters 
 together, and that product by .7854, and you have 
 the area. 
 
 28d. To find the area of a parabola. Rule — 
 Multiply the height by the breadth, and take two- 
 thirds of the product ; you have the area. 
 
 24th. To find the area of a segment of a para- 
 bola. Rule — Multiply the base of the segment by 
 the altitude thereof, and two-thirds of the product 
 gives the area. 
 
 25th. To find the area of a field or lot, which is 
 found to be the frustum or zone of a parabola, 
 included by two parallel right lines, and the inter- 
 cepted curves of the parabola. Rule — Add the two 
 
34 The Sukveyor's Guide, 
 
 parallel ends, divide the square of either of these 
 ends by this sum, add the quotient to the other 
 end, multiply this sum by the altitude of the frus- 
 tum or distance of the ends, take two-thirds of the 
 product, and it gives the area. 
 
TRIGONOMETEICAL SURVEYING. 
 
 26th. It was not my intention to say any thing 
 concerning this branch of surveying, as it is too 
 extensive a subject for this small work ; but as 
 some young readers may not have met with any 
 thing on that subject, I will present them with an 
 outline of how that grand operation is conducted. 
 
 When an entire country, or part of a country, 
 containing one or more counties is to be surveyed, 
 it is done by triangulation, and the application of 
 the rule given in the 12th section of this work. A 
 line of some miles in length is measured and re- 
 measured in order to prove its accuracy, on some 
 plane or heath which is nearly level, first having 
 been traced by a transit instrument, and poles 
 placed in an exact straight line, to guide the meas- 
 urers, as A B in the annexed figure, which is assu- 
 med as the base of the operations. A number of 
 hills and elevated spots are selected, on which sig- 
 nals can be placed, suitably distant and visible 
 
 (35) 
 
36 
 
 The Surveyor's Guide. 
 
 one from another. Thus, ifACDEBHG 
 F, &c., be several objects, the situations of which 
 
 D 
 
 Fig. 15. 
 
 are to be laid down on a map, and they are 
 within the lines, ACDEBHGF, accu- 
 rately calculated. It is supposed that the stations 
 A and B are chosen such as that all the others can 
 be seen from each of them. Then from the ex- 
 tremity A, measure the angles E A B, D A B, 
 CAB, &c., H A B, G A B, F A B, &c. And 
 from the other extremity B, measure the angles, 
 CBA,DBA,EBA, &c.,FBA, GBA,HBA, 
 &c. And as the common base, A B, and the seve- 
 ral angles of all the triangles are now known, the 
 sides, A C, A D, A E, &c. may be determined by 
 simple proportion, for as the natural sine of 
 
The Surveyor's Guide. 37 
 
 A C B : A B : : sine C A B : C B and so is sine ABC 
 to C A, and so through all the triangles, the three 
 sides being thus found in each triangle, the area is 
 easily found, as shown in section 8th of this trea- 
 tise. But to insure accuracy the objects C D E, etc., 
 should be all intersected from some third station, 
 O in the base A B, otherwise the figure may ap- 
 pear in the plotting to be right when it is not so, 
 and there will be no means of knowing whether 
 the angles have been correctly taken without going 
 over the work again. 
 
 27th. Here follows an example of a triangle con- 
 
 A. R. p. 
 
 taining a mean area of 1135.2.12.79. The] sides 
 of which were traced by a transit instrument, and 
 poles placed at the several points marked thus O ; 
 this being done, the respective distances of the 
 sides were ascertained by a mean of measures as 
 follows, viz : 
 
 B A 14643 links, or 9664.38 feet, A C 17814 
 links, or 11777.24 feet, B C 16588 links, or 10948. 
 08 feet. The angles were taken by a theodolite 
 as they are marked in the figure. 
 
 Now to determine the area of the triangle, A 
 BC: 
 
38 
 
 The Surveyor's Guide. 
 
 50°.1S'.21', 
 
 Fig.IO. 
 
 /'^^ 
 
 14643 Unks, or 9664.38 feet. 
 
 1st. From the data, A B, and the three angles of 
 the known formula 
 
 A B^Xsine BXsine A, a r p' 
 
 =1135.2.27.18 
 
 2 sine C. 
 2d, by B C, and the three angles, 
 
 the area will be 1135.3.029 
 
 3d, by C A, and the three angles, 
 
 the area will be 1135.0.38.6 
 
The Surveyor's Guide. 39 
 
 4th, by data A B, and the two 
 adjacent angles, we have by the 
 known formula, 
 
 A B^Xsine BXsine A, 
 
 2 sine (B+A) 
 The area will be 1135.2.25.7 
 
 5th, and by B C, and the two ad- 
 jacent angles 1135.3.01.9 
 6th, by a similar formula from A 
 C, and the two adjacent angles, 
 the area will be 1135.0.37.99 
 7th, by data A B, and the adja- 
 cent angle A, and the remote an- 
 gle C, we have by the known 
 formula, 
 
 (A B)^Xsine AXsine (C+A) 
 
 2 sine C area, 1135.2.27.8 
 
 8th, by a similar formula from hav- 
 ing A B, and the angles, B and 
 C; area 1135.2.28.2 
 
 9th, by having C B and the angles, 
 
 C and A; area 1135.3.03.58 
 
 10th, by having C B and the angles 
 
 B and A: area 1135.3.04.38 
 
40 The Surveyor's Guide. 
 
 11th, by a similar formula data C 
 A, and the angles, C and B, gives 
 the area 1135.0.39.66 
 
 12th, by a similar formula from da- 
 ta C A, and the angles A and 
 B; area 1135.1.00.12 
 
 13th, by data A BXB C, and the 
 contained angle, we have 
 
 A BXB CXsine B-1135.2.35.06 
 
 2 
 
 14th, by A CXA B, and the con- 
 tained angle 1135.1.32.92 
 
 15th, by A CXB C, and their con- 
 tained angle C 1135.2.00.79 
 
 16th, by data, A BXB C, and the 
 angle, A, we have by a known 
 formula, B AXsine A 
 
 BC. 
 
 =sine C, and A BXB C, sine (A+O) 
 
 2 area 1135.2.394 
 
 17th, by the application of similar 
 formula to the data, A BXB C, 
 and angle, C ; area 1135.2.30.4 
 
The Surveyor's Guide. 41 
 
 18th, by A' CXC B, and angle, A, 1136.0.19.51 
 19th, by A CXB C, and angle, B, 
 
 the area will be 1135.0.19.89 
 
 20th, by A CXB A, and angle, B, 
 
 the area will be 1135.1.10.5 
 
 21st, by A CXB A, and angle, C, 
 
 the area will be 1135.3.05.16 
 
 22d, by the usual rule from the 
 
 three sides, s. s — a. s — b. s — c. 1135.2.14.7 
 
 Now the various data exhibited in this triangle 
 have been ascertained with the same relative de- 
 gree of precision ; and the different areas deduced 
 therefrom have been subjected to the same loga- 
 rithmic process, till the figure has been exhausted ; 
 there is no reason to suppose that any one of them 
 is nearer to the truth than another ; and taking a 
 
 A. R. p. 
 
 mean of the results we have 1135.2.12.97 for the 
 nearest approximation to the true area. 
 
 But suppose we consider the triangle as spheri- 
 cal, and the admeasurement of the sides as the 
 lengths of three arcs of three great circles of the 
 sphere ; and, according to Sir Isaac Newton, the 
 diameter of the earth to be 41,798,177 feet, we 
 will then have, as the circumference of a great 
 
 4* 
 
42 The Surveyor's Guide. 
 
 -circle of the earth is to 360°, so is the length of 
 C B to the number of degrees or minutes, &c., 
 contained in the arch, C B, viz : 
 
 As 131312964.37 
 And do. 
 And do. 
 
 360°:: 11757.24 : l'.56".03868=archC A. 
 do.:: 9664.38 :r.35".38309= " AB 
 do. :: 10948.08 : r.48".05263== « B C. 
 
 Now let b a c, represent the sides of any spheri- 
 cal triangle, and e the spherical excess, we have by 
 Lhuiller's theorem. Tangent ^ E= 
 
 Tan. a+b+c. tan. a+b — c. tan. a — b+c. tan. — a+b+c. 
 
 i 4 ' ~4 4 
 
 And by restoring to a b and c, their deter- 
 mined values, we find 
 
 a+b+c =0° .1' .19". 8686 
 
 a+b— c=0° .0' .32" .1771' 
 
 a— b+c=0° .0' .21" .8493 
 
 And, — a+b+c=0° .0' .25" .842£ 
 
 Whence the log. tangt. of 0° .1' .19" .8686= 6.5879531 
 
 of .0' .32" .1771= 6.1931205 
 
 of .0' .21" .8493= 6.0250065 
 
 of .0' .25" .8423= 6.0979010 
 
 2)24.9039811 
 
 Log. of i the spherical excess= 2.4519905 
 The arc corresponding to this log. will be found 
 
The Surveyor's Guide. 43 
 
 to be ,00584 parts of a second, consequently the 
 spherical excess is 02336 of a second, and bj a 
 well known theorem, As 180° : the area of one- 
 quarter the surface of the sphere : : the spherical 
 excess to the area of the spherical triangle, viz : 
 
 As 180° 31500428420,3 the area of a great cir- 
 cle of the earth in statute acres : : 023360 to 
 
 A. R. p. 
 
 1135.2.11.3 being J perch less than the mean 
 area, which is in defect, but should be in excess ; 
 but this is accounted for by the hills on the land 
 not being taken into account ; the difference, how- 
 ever, is insignificant, and shows that the difference 
 between a plane and spherical triangle of conside- 
 rable dimensions is very inconsiderable. See Crib- 
 son s Surveying ly Trotter. 
 
 28th. How to measure a tract of land by measu- 
 ring a base line through it, and not departing from 
 that line, and yet finding all the distances round 
 the land, their courses, and angles of the field, and 
 the area, never before published. 
 
 In order to do this expeditiously, the surveyor 
 should be provided with an instrument having two 
 telescopes, one of which is movable, and the other 
 fixed, by which he can at any time take half a right 
 
44 The Surveyor's Guide. 
 
 angle from the base line, and also a right angle ; 
 he must also have an active assistant with a flag- 
 staff, to hold at the corners as he proceeds with the 
 measurement on the base line. Let ABODE 
 T M G H A be any tract of land that is to be sur- 
 veyed, let the base K L, be traced through it 
 with a transit instrument, and poles set perpen- 
 dicularly, to be visible from one to another. Set 
 your instrument at L, on the base line, which in 
 this survey bears N 40 E. A theodolite and com- 
 pass attached is the best instrument for this 
 method ; adjust your instrument, and let L be the 
 point where 45° inflected from the base L K will 
 cut the flag-staff; at the corner H, commence 
 chaining towards K, and five chains you find 45° 
 degrees deflected from the base line to the flag- 
 staff at B, on the left, will bisect it, which note in 
 your field-book by an oblique line to the left, ma- 
 king an angle as near 45° as the eye can judge ; at 
 9.30 half a right angle to the right will cut a pole 
 at G, and at 12.00 came the fence ; at 13.20 half 
 
 C. L. 
 
 a right angle will cut C, and at 19.15 you find a 
 right angle will intersect H. Now it is evident 
 
 C. L. 
 
 that you are 19.15 distant from H, for H 19.15. L 
 
The Surveyor's Guide. 
 
 45 
 
 is an isosceles triangle, and .*. you mark 19.15 on 
 the perpendicular. The next perpendicular is at 
 
 20, and the half right angle having been taken at 
 
 c. 
 
 5 on the chain line, 20 — 5=15=the distance to B. 
 
 0. L. 
 
 Again at 32.35 you find half a right angle bisects 
 
46 The Surveyor's Guide. 
 
 the pole at D, and at 33.20 a right angle inter- 
 
 c. L. 
 sects at G, and 33.20— 9.30-=30.40=the length of 
 
 the perpendicular which set on it. At 34.20 you 
 find the next perpendicular on the left to 0, and 
 the one-half right angle having been taken at 13. 
 20 .-. 34.20— 13.20=21.o''o the distance to C ; pro- 
 ceeding in this way you have 43.35 — 32.35=11 
 chains to D, and 51.30— 35,40=15.40=the dis- 
 tance to M, and 57.40—38.30=19.10 to F, and 
 60— 5T.40=2.10=the perpendicular of the last A 
 within the fence on the right and 62.30—60=2.30= 
 the perpendicular without the fence ; also, 62.30 — 
 41=21. 30=the distance to E, which A is to be 
 ducted out of the area of the last trapezoid on the 
 left. Thus you have found with very little trouble 
 all the requisites for calculating the area of the 
 land, and it may be remarked, that you might have 
 commenced at the corner B and noted where the 
 two perpendiculars fell at 19.15 and 20 and as you 
 proceeded on your base line take back sights at 
 the proper distances to intersect the poles at B and 
 H, and the distances from where the perpendicu- 
 lars would fall to these several points would be the 
 chains and links to be placed thereon. The dis- 
 
The Surveyor's Guide. 47 
 
 tances all round the land, can be accurately found, 
 for in the present case n/(A a^)+(a H")= A H, 
 and r Gr, and r H being given V{r G^)+(r IP)=H Gl- 
 and so on all round the land, and seeing that the 
 courses of A a and a H are given, the course of A 
 H may be readily found, for having the distance 
 and difference of latitude and departure, the course 
 is given in the tables ; also, the internal angles 
 can be easily found, for in the ^ A a H A a : 
 Ead. : : a H : tang't a A H, and so with the A 
 B b A. Hence, the angle B A H, is known, and 
 it is evident the same holds good all round the 
 land, the bases and perpendiculars of all the 
 right angled triangles being found from the base 
 line and can be marked on the sketch as the sur- 
 veyor proceeds. The same may be done with a 
 good compass, for having the course of the base 
 line, the courses of the normals to right and left 
 are known, and the course of J a right angle being 
 once ascertained on the right and left of the base 
 will always serve to find the points on the base 
 where they are to be taken ; but this would require 
 many trials and waste time, whereas, an instru- 
 ment showing J a right angle will save much time. 
 
48 The Surveyor's Guide. 
 
 Thus, in a plane country, the scientific reader will 
 acknowledge the plan completely available, and 
 the surveyor can calculate the content of the land 
 on the margin of his book while his needle is set- 
 tling, and be able to answer the farmer satisfac- 
 torily, who thinks a surveyor should be able to tell 
 the content the moment he has the last distance 
 measured. 
 
 The plotting and calculation of a survey taken 
 on the above plan is so obvious as to require no 
 explanation, seeing all the figures are either right 
 angled triangles or trapezoids, to find the area of 
 which is shown in figure 12th. 
 
 29th. The most correct method of correcting 
 the difierence of latitude and departure in surveys 
 taken with the compass, to fit them for calculation, 
 some authors divide the difi"erences proportionally 
 among all the stations ; but as there may be some 
 stations in a survey really correct, any alteration 
 in them would make them incorrect, so that the 
 altering of the legs of stations in surveys where 
 land is of great value, is a matter of considerable 
 importance. 
 
The Surveyor's Guide. 49 
 
 i^ 
 
 Pig.] 
 
 Problem. 
 
 To find what may be the error in the difference of latitude 
 and departure of a given station arising from the inacu- 
 racy of practice : 
 
 Let the right angled triangle A B D, fig. 18th, 
 represent a station "with its difference of latitude 
 and departure; if the angle A be the bearing, then 
 will the leg A D, be the difference of latitude, and 
 the leg B D, the departure ; but if the angle at B 
 be the bearing, then will the leg B D, be the differ- 
 ence of latitude, and D A the departure. Let the 
 small angle B A b represent the error committed 
 in taking the bearing, which may amount 7|- min- 
 utes, and the small part B e or E b, the error com- 
 mitted in chaining, in proportion to the whole line 
 AB, or A e, as 0.5 is to 5.00, (for in measuring the 
 6 
 
50 The Surveyor's Guide. 
 
 length of lines, there may be an error committed 
 of half a link in 10 chains ; (this is found by expe- 
 rience), and let e a, b d, and E c be drawn parallel 
 to B D, and B n o, and res, parallel to D A. 
 
 Case 1st. Suppose A B to be the true bearing 
 and length of a station, and A b the one found by 
 observation. Now it is plain that instead of the 
 triangle A B D, we shall have by observation the 
 triangle A b d, so that there is an error of the 
 quantity n b, by which the leg B D is increased, 
 and an error of the quantity B n, by which the leg 
 A D is decreased, and the contrary may be sup- 
 posed, if A b be the true distance and bearing and 
 A B that found by observation; but when the 
 angle at A is very small, D d may be supposed 
 equal to (0). 
 
 Case 2d. Suppose the true length and bearing 
 of a station to be A e, and that found by measur- 
 ment to be A B the bearing exact. Now it is 
 plain that the leg e a is increased by the error 
 r B, and that the leg A a, is increased by the error 
 r e or a D, and the quantities or errors by which 
 each leg is increased are in proportion to the legs 
 
The Suevetor's Guide. 51 
 
 themselves, that is, B r : e a : : r e : A a, and as 
 B e is to A e. 
 
 Case Sd. Suppose A e the true bearing and 
 length of a station, and A b the same, found by 
 observation. This supposes a compound error both 
 in chaining and bearing, and that the error in the 
 bearing increases the smallest angle in respect of 
 the bearing and its complement. Here we see 
 that when the leg A a is increased to A D by the 
 error in chaining, as in the last case, it shall, at the 
 same time, be brought back to A d by the error in 
 the bearing, as in case 1st. Therefore, the leg A a 
 will be increased by the quantity r e — B n, or de- 
 creased by the quantity B n — r e; but r e is 
 greater than B n, when the angle at A is, small ; 
 and B n is greater than r e, when the angle is 
 near 45°; for they become equal when the angle 
 is about 25°; but at the same time the leg e a will 
 be increased to d b, by the error b S=b n+B r. 
 
 Case 4th. Suppose A E the true distance and 
 bearing, and A B that found by observation ; this 
 supposes the error in the bearing to decrease the 
 smallest angle. Now it is evident that the longer 
 leg A c is increased by the error B o or D c, and 
 
52 
 
 The Surveyor's Guide. 
 
 the shorter leg decreased by the error E o. But 
 B o=B n+r e (for r e=ii o) and E o=b n — B r. 
 These errors are easily found in numbers by con- 
 sidering the figure, and that they are always pro- 
 portional to the length of the stations. 
 
 Here follows a table of errors in links and deci- 
 mals, calculated for a station of 30 two pole 
 chains, and for the different angles and their com- 
 plements, under which they are placed, but which 
 can be changed to any other length, by altering 
 them in the same proportion as are the stations. 
 
 BAb=i°error 
 in bearing. 
 
 88 
 
 ?2 
 
 78 
 
 23 
 67 
 
 32 
 
 58 
 
 42 
 
 48 
 
 45 
 
 B e 1.5 links error in chain- 
 ing. 
 
 bn= 
 Bn= 
 
 3.2 
 0.0 
 
 3.1 
 0.7 
 
 3.0 
 1.4 
 
 2.8 
 1.7 
 
 2.2 
 
 2.3 
 2.3 
 
 Error in short Leg. ] Case 
 Error in long Leg. J 1st. 
 
 Br= 
 r e= 
 
 0.0 
 1.5 
 
 0.3 
 1.5 
 
 0.6 
 1.4 
 
 0.8 
 1.3 
 
 1.0 
 1.1 
 
 1.0 
 1.0 
 
 Error in short Leg. ] Case 
 Error in long Leg. J 2d. 
 
 bs=(bn4-Br) 
 ad=(Bn^re) 
 
 3.2 
 1.5 
 
 3.4 
 0.8 
 
 3.6 
 0.0 
 
 3.6 
 0.4 
 
 3.4 
 1.1 
 
 3.3 
 1.3 
 
 Error in short Leg. ) Case 
 Error in long Leg. J 3d. 
 
 Eo=(bn-B r) 
 B o==(Bn+r e) 
 
 3.2 
 1.5 
 
 2.8 
 2.2 
 
 2.4 
 
 2.8 
 
 2.0 
 3.0 
 
 1.4 
 3.3 
 
 1.3 
 3.3 
 
 Error in short Leg. 1 Case 
 Error in long Leg. J 4th. 
 
 CORROLLARY. 
 
 Hence we may adopt the following rules for 
 altering the legs of stations in the correcting of 
 surveys : 
 
The Surveyor's Guide. 53 
 
 Rule First. 
 When the course, or angle, is either great or 
 small ; or when the difference of latitude and de- 
 parture are found in the beginning of the tables, 
 then the shortest leg may be increased or decreased 
 by any quantity not greater than 3.2 links, and 
 the longest leg increased by any quantity not 
 greater than 1.5 links. 
 
 Rule Second. 
 
 When the latitude and departure are found about 
 the [middle of the tables, or when the angle is 
 about 20° under or over 45°, then the shortest 
 leg may be increased by any quantity not greater 
 than 3.6, or rather 4 links, and the longest leg 
 left unaltered, which is, when the error in the 
 bearing increases the angle opposite the smallest 
 side ; but when contrary, the longer leg may be 
 increased by any quantity not greater than 3 
 links, and the shorter leg decreased by 2 links. 
 Rule Third. 
 
 When the difference of latitude and departure 
 are found in the latter part of the tables, or when 
 the bearing is about 45°, then either of the legs 
 
54 The Surveyor's Guide. 
 
 (they being nearly equal) may be increased or de- 
 creased by any quantity not greater than 3 links, 
 and the other leg by 1.4 links, but when one leg is 
 increased the other must be decreased. 
 
 These rules are on the supposition that the 
 chaining is always too long, which, in practice, I 
 have nearly always found to be the case ; but when 
 a surveyor has reason to think otherwise, he may 
 alter the rules to his opinion, not only in respect 
 to this, but also relative to the quantity of the 
 errors. 
 
 A description of an instrument by which any person, though 
 unskilled in surveying, may measure a map, or part of a 
 map, almost at one view : 
 
 Get a piece of good glass about 8 or 9 inches 
 long, and 6 or 7 inches broad, and divide it into 
 small oblong rectangles of eight-tenths of an inch 
 by 5 five-tenths, as fig. 19th. By laying this in- 
 strument (which I call a computor) on a map you 
 can tell with very few figures, sometimes with the 
 eye only, how many of the rectangles are con- 
 tained in the map, and consequently, how many 
 acres. When the map is laid down by a scale of 
 20 perches to an inch, then each rectangle will be 
 
The Surveyor's Guide. 
 
 55 
 
 16 perches by 10, or one acre ; and if the map be 
 40 perches to an inch, then each rectangle will be 
 32 perches by 20, or 4 acres ; and if by 80 per- 
 ches to an inch, then each rectan- 
 gle will contain 16 acres. This 
 instrument would be useful to 
 gentlemen and others not very 
 well skilled in surveying, to 
 measuriB a map, or part of a 
 map that they wished to know 
 the content of nearly. It is 
 easily used. The sides of the ^^s- 19. 
 
 glass must be made to coincide with as many of 
 the lines on the map as possible, and the broken 
 squares can be estimated by the eye, or a square 
 inch horn. 
 
 Description and design of a new instrument by wliicli dis- 
 tances can be found at once, without any calculation ; 
 
 Let a brass semi-circle (fig. 26) of about 9 inches 
 radius, have its inner edge or limb, divided into 
 90 equal parts, beginning at N and counting up- 
 wards 10, 20, 30, &c., to 90 at Z, and each of 
 these divisions subdivided into 6 equal parts. Let 
 
56 The Surveyor's Guide. 
 
 the outer limb be divided into degrees and 6th 
 parts of a degree, marking the degrees from the 
 middle of the limb, both ways, 10, 20, 30, &c., 
 to 90 at N and Z. Let also, the middle space be- 
 tween the outer and inner limbs, be marked from 
 Z to N, 10, 20, 30, 40, &c., to 180 at K 
 
 Let this semi-circle be fixed to the middle of a 
 box ruler B D, about S^ feet long, an inch and a 
 half broad, and of a convenient thickness. The 
 inner breadth of half this rule must be level with 
 the surface of the semi-circle, but the outer half 
 must be higher about two-tenths of an inch. On 
 the outer half there must be fixed a thin brass 
 scale of an equal length and breadth with the box 
 ruler, the breadth of which scale is to be divided, 
 by lines drawn from end to end, into three equal 
 parts, and the length into inches, half inches, and 
 tenth of an inch ; the inches are to be drawn di- 
 rectly across the whole breadth, and marked 1, 2, 
 3, 4, &c., both ways to B and D ; the half inches 
 are to be drawn across the middle and innermost 
 third, and the lOths only across the inner third. 
 Let there be on one end of this scale an inch, and 
 on the other end half an inch, each divided very 
 
The Surveyor's Guide. 57 
 
 exactly into 10 equal parts diagonally, that the 
 lOths and centesms which may happen in the 
 operations, on the square and indices hereafter to 
 be described, may be exactly measured on them by 
 a pair of dividers. The reason for raising the 
 outer half of the box ruler above the inner half 
 two-tenths of an inch, is to make room for the in- 
 dices A b and A d, which are to be fixed to the 
 centre of the semi-circle, and there to open and 
 shut as occasion requires, like the legs of a sector. 
 Those indices are about 26 inches long, three- 
 fourths of an inch broad, and about two-tenths 
 thick; their breadth is to be divided into three 
 equal parts, and their length into inches, half 
 inches, and tenths, as the brass scale before men- 
 tioned. The inches are to be marked from the 
 center A, with 1, 2, 3, 4, &c., to b and d, and the 
 tenths drawn across the inner third. Each of 
 those indices must have a small screw nut with a 
 pin or bit of wire upon it, which pin may, by the 
 screw nut, be fixed exactly to any division on them 
 in order to suspend the label, or ruler T Y, which 
 has a thin piece of brass with a small hole in it, 
 exactly fitting the aforesaid pin, and is to be fixed 
 
58 The Sueveyor's Guide. 
 
 also to any division of the ruler, as occasion re- 
 quires. Let this label, or ruler, be about two feet 
 long, and of the same breadth and thickness as the 
 indices A b and A d, and divided after the same 
 manner as they are, only the tenths are to be 
 drawn across the inner edge, as well as across the 
 inner third of the breadth, and the inches are to 
 be marked 1, 2, 3, 4, &c., from C to T and Y, 
 making C T eighteen inches, and C Y six. The 
 like divisions are to be made on the side of the 
 square K X, beginning at the inner edge of the 
 brass ruler at K, marking the full inches on the 
 upper side, 1, 2, 3, 4, &c., to 24 ; the tenths are 
 to be drawn across the upper third and the upper 
 edge. Let this instrument be fixed on a tripod 
 with a ball and socket like those of a common sur- 
 veying instrument, but very strong, in order to 
 have it very firm ; and let there be sights which 
 may, as occasion requires, be fixed on the diame- 
 ter, indices, and ruler T Y, of the the same kind 
 with those of a surveying instrument. 
 
 N. B. The ball and socket must not be fixed 
 exactly under the center of the semi-circle, but some 
 distance from it, on the cross-bar which goes from 
 
The Surveyor's Guide. 
 
 59 
 
 the center to the middle of the limb, as -well to sup- 
 port the head of the instrument more easily by be- 
 ing nearer its center of gravity, as to make room 
 for an air level, which must be fixed exactly under 
 the diameter or ruler A B, so that when the semi- 
 circle is turned vertically the diameter may be 
 fixed horizontally. 
 
60 The Surveyor's Guide. 
 
 The use of the Instrument in measuring distances : 
 Example. 
 
 Let it be required to find the distance from the 
 house at A to the castle, (fig. 27) or to any part 
 thereof, as the weather-cock on the top of the 
 spire at C. 
 
 Having set up your instrument at A, turn it 
 about till through the sights on the diameter, you 
 see a mark set up at B, and having fixed the di- 
 ameter in that position, turn the moving index till 
 through the narrow slit of a small sight fixed on 
 the center, you see the hair in the other sight cut 
 the spire at C, then fixing the index in that posi- 
 tion to the limb of the semi-circle, measure with a 
 four pole chain in a straight line from A to B ; 
 and having marked the chains and links of that 
 distance on the diameter and placed the ruler with 
 the sights on it exactly to that distance, by means 
 of the small pin and hole mentioned before, set up 
 your instrument at the end of the distance you 
 measured (which you may make full chains if you 
 please) and turn it about till through the sights on 
 the diameter you see a pole at the first station A, 
 and having fixed it in that position, turn the ruler 
 on the pin which is fixed at the former distance on 
 
The Surveyor's Guide. 61 
 
 the diameter, till through the sights on it you see 
 the vane at C ; then will the part of the index a c, 
 cut by the inner edge of the ruler, give the dis- 
 tance A C from the house to the spire at C, which 
 was to be found ; and if there be occasion, the dis- 
 tance from the mark at B to the spire will be found 
 on the ruler at the intersection of the index ; all 
 of which is plain from the similarity of the trian- 
 gles ABC and a. pin. c, or that formed by the 
 diameter, index, and ruler, from Cor. 1st 4 Euc. 
 Book 6th. Thus the surveyor can find the distance 
 of any or all the particular objects he can see and 
 may wish to set down in his map, and by turning 
 the instrument vertically by means of a notch in 
 the socket, inaccessible heigths can, in like manner, 
 be readily ascertained in the same manner. 
 
 Example in Measuring Distance. 
 
 Let it be required to find the distance from the 
 house at A to the castle, (fig. 27) or to any part 
 thereof, as the weather-cock at the top of the spire 
 at C. 
 
 Having set up your instrument at A, turn it 
 about till through the sights on the diameter, you 
 see a pole at B, and having fixed the diameter in 
 
62 
 
 The Surveyor's Guide. 
 
 that position, turn the moving index till through 
 the narrow slit of a small sight fixed on the center, 
 you see the hair in the other sight cut the spire at 
 C ; then fix the index in that position to the limb 
 of the semi-circle and measure with your chain of 
 100 links in a straight line from A to B, which 
 mark on the diameter, and place the ruler, having 
 the sights on it exactly on that distance by means 
 of the small pin and hole before mentioned ; set 
 up the instrument at the end of the measured dis- 
 tance, and turn it about till through the sights on 
 
 Pig. 27. 
 
 the diameter you bisect the pole at A, and having 
 fixed it in that position, turn the ruler on the pin 
 which is fixed at the former distance on the diame- 
 ter, till through the sights you see the vane at C ; 
 then will the part of the index, a c, cut by the in- 
 
The Surveyor's Guide. 63 
 
 ner edge of the ruler, give the distance A C from 
 the house to the spire at C. 
 
 And in like manner by directing the ruler to 
 any other objects from A, and noting the degrees 
 cut by the ruler on the limb, and directing from 
 B to each object, the distance from A vrillbe shown 
 as before explained, and thus the surveyor fur- 
 nished with such an instrument, can from the end 
 of his first station, tell the length of his diagonals 
 to as many corners as he can see from that point. 
 Also, by turning the instrument vertically, heights 
 can be determined in the same manner. 
 
 I would recommend the surveyor to use a com- 
 pass, having the limb divided into 360°, and the 
 bottom of the box into four 90's ; then in taking 
 the courses, if N. W., the limb and quarter com- 
 pass are the same ; but if in the S. W. quarter, 
 the sum of the degrees on the limb and quarter 
 compass are 180° ; and in S. E. quarter, the dif- 
 ference of the degrees on the limb and quarter 
 compass make 180° ; lastly, if in the N. E. quar- 
 ter, the sum of the quarter compass and limb 
 make 360. A surveyor should prove all his courses 
 by this rule before he quits his instrument. 
 
64 The Sueveyor's Guide. 
 
 Problem. 
 Given the bearings of any two stations of a 
 survey, thence to determine the angle made by 
 those stations. Rule — Deduct the preceding bear- 
 ing from the succeeding, according as the remain- 
 der is greater or less than 180°. Add — or+180° 
 (as the case may be) and you have the required 
 angle. 
 
 N. B. The angle found by the above rule will 
 be internal if the polygon lie towards the right 
 hand in the traverse ; and external, if toward the 
 
 left. 
 
 Example First. 
 Required the several angles of the polygon 
 A B C D E F G, the courses of the sides being, viz : 
 
 Kg. 28. 
 
 1 
 
 A B 2691° 
 
 or 
 
 S. E. 
 
 891 
 
 2 
 
 B C 2511 
 
 or 
 
 S. E. 
 
 711 
 
 3 
 
 C D 252f 
 
 or 
 
 S. E. 
 
 72| 
 
 4 
 
 D E 162^ 
 
 or 
 
 s. w. 
 
 in 
 
 5 
 
 E F 77| 
 
 or 
 
 N.W. 
 
 77f 
 
 6 
 
 FG 30| 
 
 or 
 
 N.W. 
 
 30^ 
 
 7 
 
 GA 5f 
 
 or 
 
 N.W. 
 
 5f 
 
The Surveyor's Guide. 65 
 
 From 2511 From 77| 
 
 take 269J take 162^ 
 
 —18 —841 
 
 +180 +180 
 
 Sum 162=Ang. ABC. Sum 95i=Z. DBF 
 
 From 252| From 30| 
 
 take 2511 take 77f 
 
 +li —47 
 
 +180 +180 
 
 Sum 1811=/. BCD. Sum 133=/: E F G 
 
 From 162i From 5| 
 
 take 252| take 30| 
 
 —901 _25 
 
 +180 +180 
 
 Sum 891= A C D E. Sum 155=/. F G A 
 
 From 2691 
 take 5| 
 
 Rem. 2631 
 —180 
 
 Sum 
 
 Now 180° multiplied by the number of sides 
 6* 
 
66 The Surveyor's Guide. 
 
 any polygon minus 360°, equals the sum of the in- 
 ternal angles .-. 180X7= 160 and 1260—360=900 
 So 83|+162+181i+89J+95i+133+155=900°. 
 Proof. 
 
 Next. Having the bearing of any station and 
 all the internal angles of any polygon, thence to 
 determine the courses of each of the other stations 
 in the regular order of succession, viz : the land 
 lying to the right hand as you surround it. Rule : 
 According as the given angle is+or — than 180° ; 
 add the preceding bearing, succeeding angle, and 
 +or — 180° (as the case may be ;) their sum will be 
 the succeeding bearing or course. 
 
 Note. — It sometimes happens that the result 
 will be more than 360° ; in this case take 360° 
 from it and the remainder will be the course of the 
 succeeding station. 
 
 Example. 
 
 Take the course of A B 269i or S. 89i E, in the 
 preceding figure, and the angles as there found, 
 viz : 
 
The Surveyor's Gcjide. 67 
 
 269^ 162i 
 
 162 95J 
 
 +180 +180 ^ 
 
 611J 4371 
 
 Deduct 360 360 
 
 Cou. of B C 251| or S TIJ E. Cou. of E F 77| or N 77f "W 
 
 251i 77f 
 
 ISli 133 
 
 --180 +180 
 
 Cou. of C D 252f or S 72$ E. 390f 
 
 252f 
 
 360 
 
 fj Cou. of F G 30| or N 30| W 
 
 +180 
 
 30| 
 
 522i 155 
 
 Deduct 360 +180 
 
 Cou. of D E 162i or S 17| W. 365f 
 
 360 
 
 Cou. of G A 5forN.5|W. 
 
 5f 
 83f 
 +180 
 
 Cou. of A B 269 J or S 89 J E. 
 
 being the' same as that given ; therefore, a proof 
 of the correctness of the work. And thus the sur- 
 veyor has a sure method of avoiding the inconve- 
 nience of the needle being drawn from its true 
 position by mines or other causes, and also correct 
 the diurnal variation ; for no matter how much 
 
68 The Surveyor's Guide. 
 
 the needle may be attracted at any station, the 
 angle will be correct by taking a back and fore 
 sight at every station, and having the true course 
 of the first station. All the others can be found 
 by the foregoing rules. And to know if any at- 
 traction exists at the first station, take a course in 
 a different direction from your chain line ; go to 
 the object bisected, or to some convenient distance 
 in that direction, and take a back sight ; if that 
 agree with the fore sight, you may safely conclude 
 that no attraction exists at either ; but should it 
 differ, make trial in some other direction, in like 
 manner, till you find what station the attraction is 
 in ; but by using a good theodolite all such trouble 
 is avoided. 
 
 In every survey that is truly taken, the sum of 
 the Northings is equal to the sum of the Southings, 
 and the sum of the Eastings to the sum of the 
 "Westings. 
 
 Let a b c e f g h represent a plot or parcel of 
 land ; let a be the first station, b the second, c the 
 third, and so on. Let N S be a meridian line, then 
 will all lines parallel thereto, which pass through the 
 
The Surveyor's Guide. 
 
 69 
 
 y c 4 
 
 several stations, be aj 
 meridians also, as a o, 
 b s, c d, &c., and the 
 lines b 0, c s, d e, 
 &c., perpendiculars 
 to these, will be east 
 or west lines or de- n"T 
 parture. The northings e i+g o+h g=a o+b s+ 
 c d+f r, the southings ; for let the figure be com- 
 pleted, then it is plain that g o+h g+r k=a o+ 
 b s+c d and e i — r k=f r; if to the former part 
 of this first equation e i— r k, be added, and f r 
 to the latter, then g o+h g+e i=a o+b s+c d+f r ; 
 that is, the sum of the northing is equal to the sum 
 of the southings. 
 
 The eastings c s+q a=o b+d e+i f+r g+o h, 
 the westings for a q+y o (a z)=d e+i f+r g+o h, 
 and h o=c s — y o. If to the former part of this 
 first equation c s — y o, be added, and b o to the 
 latter, then c s+a q=o h+d e+i f+r g+o h ; that 
 is, the sum of the eastings is equal to the sum of 
 the westings. 
 
 Now, as there is many methods of calculation, 
 and every man chooses one in preference to all 
 
70 
 
 The Surveyor's Guide. 
 
 others, I shall here show the method which I have 
 always practiced, being, I think, least liable to 
 mistakes, although not the shortest, as shall be 
 hereafter shown. 
 
 1^ 
 
 
 
 : : o : : : 
 
 1.00 
 2.00 
 2.00 
 2.00 
 1.00 
 
 s 
 
 
 IJjj igllJ i 
 
 : : : 
 
 i 
 
 ^ 
 
 O 
 -* 
 
 
 iii 1 1! 
 
 ilil 
 
 
 i 
 
 
 
 : : : 
 
 
 11 
 
 ogooooooooooooo 
 
 
 
 
 
 
 
 
 g|§|§ :|g| :J : 
 
 o 
 
 sSsiijiiS 
 
 
 lis 
 
 o 
 
 k 
 
 11^3333333331331 
 
 1 
 
 
 
 "Si 
 
 rH « «) ■* >0 -iO i^- 00 OS C 
 
 r-l <N M 'il i« 
 
 
 
 
 
 
 
 
 
 o o 
 3 I 
 
 CQOQ 
 
 In the above method the northings and south- 
 ings, eastings and westings, being corrected by the 
 
The Surveyor's Guide. 71 
 
 foregoing rules, set the sum of the northings, or 
 southings at the top of the column titled latitude, 
 then continually add the northings and subtract 
 the southings, or add the southings and subtract 
 the northings, and the last number will always be 
 the same as the first, which is a proof of so much 
 of the work. Then add the first and last latitudes 
 together, and place their sum opposite to the first 
 station in the column under latitudes, added, and so 
 continue to add every two adjoining latitudes, and 
 place their sum in a line with the latter, then mul- 
 tiply each of these numbers by the particular 
 easting or westing belonging to that station, and 
 place the product in the column of east or west 
 area, as the case may be, and the difference of 
 these two columns divided by two, will be the con- 
 tent of the survey. In this method there is no 
 danger of making mistakes from indirect stations, 
 and by using the eastings, and westings, in the same 
 manner as you did the northings, and the south- 
 ings, you can prove the work, and find the area 
 four different ways. 
 
72 
 
 Surveyor's Guide. 
 
 ANOTHER METHOD, WHEREIN FEWER FIGURES ARE 
 USED, NEVER BEFORE PUBLISHED : 
 
 The Eastings and Westings, Northings and South- 
 ings, are here corrected according to the foregoing 
 rules, and placed as usual, as follows : 
 
 CALCULATION OF THE NOTES ON THE SUCCEEDING 
 PAGE. 
 
 1 1 1 1 Lata. IDoub. Semi 1 1 1 
 N. 1 S. |li. N.|L.S. 1 added. 1 Eectangle.l E. 1 W. 1 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 
 I 
 
 
 2.76 
 4.44 
 0.77 
 4.38 
 
 2.76 
 7.20 
 
 5.15 
 4.38 
 0.00 
 2.60 
 2.96 
 6.31 
 
 ...... 
 
 2.76 
 9.96 
 9.53 
 4.38 
 2.60 
 6.56 
 9.27 
 8.74 
 3.29 
 1.58 
 4.51 
 5.29 
 1.77 
 
 +4.4712 
 +11.9520 
 + 20.5848 
 — 1.9272 
 14.3520 
 —10.3416 
 
 1.62 
 1.20 
 
 0.44 
 
 1*86 
 
 Bx.E 
 2.16 
 
 '6.38 
 'l.34 
 
 15.40 
 
 
 
 
 
 
 Ex. S. 
 2.60 
 0.36 
 3.35 
 3.34 
 2.11 
 
 Indirect. 
 
 
 
 
 
 6.04 
 2.70 
 0.59 
 0.99 
 3.52 
 1.77 
 0.00 
 
 +59.1426 
 + 17 4800 
 
 Ex.W 
 9 nn 
 
 
 '"o.'io 
 
 2.53 
 
 —4.4086 
 
 +5.6564 3.58 
 +5.4120 1.20 
 
 Indirect 
 
 1.75 
 1.77 
 
 +5.0784 
 +4.4958 
 
 0.96 
 2.54 
 
 15.40 
 
 
 Ex. N. 
 
 
 15.28 
 )ouble t 
 
 15.28 
 le sum 
 
 )f th 
 
 aindi 
 
 rect, 
 
 165.3026 
 33.3548 
 
 
 
 131.9478 
 
 
 65.9739 Angular.spaces. 
 
The Surveyor's Guide. 
 
 73 
 
 11.76 Parallel breadth. 
 12.35 Meridianal breadth. 
 
 5880 
 3528 
 2352 
 1176 
 
 145.2360 Content of 
 65.9739 
 
 parallelogram. 
 
 7,9.2621 
 4 
 
 
 3.70484 
 40 
 
 
 28.19360 
 
 A.R. P. 
 
 7.3.28.19, the same as on nest page. 
 
 Nl 
 
74 
 
 The Surveyor's Guide. 
 
 The foregoing plot and calculation may not be 
 unacceptable to the reader, being as complicated a 
 figure as could be easily met with. 
 
 A new and concise method of Calculation, wherein fewer 
 figures are used than in the common methods : 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 "i'eo 
 
 0.36 
 3.35 
 3.34 
 2.11 
 
 "l."75 
 1.77 
 
 S. 
 
 2.76 
 4.44 
 0.77 
 4.38 
 
 E. 
 
 1.62 
 
 1.20 
 
 "6.44 
 
 W. 
 
 M. D. 
 162 
 
 D. D. 
 
 Area. 
 
 Deduction. 
 
 "2.I6 
 
 "s.'si 
 "e.'ss 
 "i'.u 
 
 3.24 E. 
 4.44 E. 
 2.28 E. 
 2.72 E. 
 2.80 W. 
 0.94 W. 
 7.32 W. 
 5.32 W. 
 6.66 W. 
 3.08 W. 
 1.88 W. 
 0.92 W. 
 1 62 E 
 
 4.86 E. 
 
 7.68 E. 
 
 6.72 E. 
 
 5.00 E. 
 
 0.08 W. 
 
 3.74 W. 
 
 8.26 W. 
 12.64 W. 
 11.98 W. 
 
 9.74 W. 
 
 4.96 W. 
 
 2.80 W. 
 
 0.70 E. 
 
 13.4136 
 34.0992 
 
 5.1744 
 
 21.9000 
 
 2080 
 
 1.3464 
 27.6710 
 42.2176 
 25.2778 
 
 
 
 
 
 
 
 1.86 
 
 
 
 "o!40 
 2.53 
 
 2.00 
 
 "■3.58 
 1.20 
 0.96 
 2.54 
 
 
 
 3.8960 
 
 12.5488 
 
 
 4.9000 
 
 
 
 1.2390 
 
 
 
 
 15.28 15.28 15.40 15.40 
 
 17.6838 
 
 A. R. r. 
 
 7 3 28.19 
 
 2,0)15,8.5242 
 
 7,9.2621 
 4 
 
 3,7.0484 
 40 
 
 This method may be called a compound of 
 Burgh's and Gibson's, without being intimately 
 connected with either. It allows the first meridian 
 to pass at any distance from the first station not 
 less than the first latitude or first departure. 
 
The Surveyor's Guide. 75 
 
 This example supposes the first meridian to pass 
 at the distance of the first Easting from the first 
 station of the survey, and the M. D. column is 
 completed by one single addition of the Eastings, 
 or one single subtraction of the Westings, to or 
 from each preceding one, agreeably to the nature 
 of the signs. The D. D., or double distance col- 
 umn, is completed by adding the first and last, 
 and placing their sum in a line with the first East- 
 ing or Westing, and then adding every two ac- 
 cording to the signs, and placing their sum in a 
 line with the latter, marking E. or W. as the case 
 may be. Then the Eastings X by the Southings, 
 and the Westings X by the Northings, must be put 
 into the area column ; but, the Westings X by the 
 Southings, and the Eastings X by the Northings, 
 must be put into the deduction column, the diflfer- 
 ence is double the area of the survey. 
 
 The following is a method of calculation first 
 published by Noble, the inventor, and is a very 
 superior plan when well understood, but requires 
 considerable attention to distinguish the indirect 
 stations, as the areas belonging to them must be 
 deducted. A little practice will enable the learner 
 to know both them and the four extremes, viz : 
 
76 The Surveyor's Guide. 
 
 N. S. E. and W. That author's description of a 
 semi-rectangle is a figure limited by the latitudes 
 of both ends of the station, the station itself, and 
 a section of the parallel from which the latitudes 
 are measured, equal to the departure ; and when 
 the last mentioned is indirect, the semi-rectangle 
 is indirect also, viz : Indirect or retrograde sta- 
 tions are those stations, in respect of the rest, 
 which bear backward or contrary to the natural 
 succession of the four quarters of the compass. 
 
 If, in proceeding Southerly from the extreme 
 point jSTorth, there happen a station to turn North- 
 erly, or, in proceeding Northerly from the extreme 
 point South, there happen a station to turn South- 
 erly, such stations are indirect or retrograde sta- 
 tions. The same may be said of stations that 
 turn after the like manner in proceeding from the 
 extreme points E. and W. of the survey. The 
 extreme points, N. S. E. or W. of a survey, are 
 the ends of those stations which run more to the 
 N. S. E. or W. than any other stations in the survey. 
 
 Though most surveys have those four extreme 
 points, yet there are some where one and the same 
 station may be the greatest extreme N., and at 
 the same time the greatest extreme East or West ; 
 
The Surveyor's Guide. 77 
 
 or one and the same station may be the extreme 
 South, and likewise the extreme East or West. 
 The circumscribing parallelogram of a survey is a 
 rectangle or parallelogram circumscribing the body 
 of the land, whose four sides, passing through the 
 four extremes N. S. E. and W. of the survey, are 
 two meridians and two parallels of latitude. 
 
 The angular spaces are the areas contained 
 between the sides of the circumscribing paralello- 
 gram, and the stations of the land surrounded, 
 which, deducted from the area of the second parall- 
 elogram, leaves the content of the survey. 
 
 Now in order to find the area of those angular 
 spaces, the four extremes must first be ascertained. 
 This an experienced hand can see at once by 
 examining his field-book, which, being known, you 
 must find the latitude of each station in the survey 
 from the extreme points North and South ; thus, 
 having found and corrected your latitudes and 
 departures, and placed them as in the following 
 table, write in a line with N, and also the South 
 extreme as in the following table. Now, begin- 
 ning at each of these extremes. North and South, 
 continue to add the Northings, and subtract the 
 Southings to find the latitude of each station to 
 7* 
 
78 The Surveyor's Guide. 
 
 the extreme point West, but you must still add 
 the Southings and subtract the Northings to the 
 extreme point East. When the latitude of every 
 station is thus found, and placed in their proper 
 columns, add every two latitudes next each other, 
 and put their sum in a line with the latter station 
 in the column marked L. A., and each sum or 
 number in this column is the length of a rectangle, 
 which is double the semi-rectangle of each station. 
 It is no matter at which of the two latitudes you 
 begin, so that you place their sum in a line with 
 the latter or succeeding station ; but it is common 
 to begin by adding the first and last' stations to- 
 gether, and placing their sum in a line with the 
 first station ; then add the first and second, and 
 place it in a line with the second, and so on 
 till the column is filled. Then each number must 
 be multiplied by its corresponding Easting or 
 Westing, and the products put in the column 
 marked D. S., or double semi-rectangle of each 
 station. If the Easting or Westing be direct, 
 then this product must be marked + ; but if it be 
 indirect, with the negative sign — , and the sum 
 of all the affirmatives, abating the sum of all the 
 negatives, will be the content of all the angular 
 
The Surveyor's Guide. 
 
 79 
 
 spaces. But, to find tlie length and breadth of 
 the circumscribing parallelogram, note that from 
 the sum of all the Northings or Southings you 
 must deduct the sum of all the Northings or South- 
 ings that have indirect diiference of latitude, 
 •which will give one side, and the same must be 
 done with the Eastings and Westings to find the 
 other side. The length and breadth of the parall- 
 elogram being thus found, they must be multiplied 
 together, and from their product take the content 
 of the angular spaces, and the remainder will be 
 the content of the survey. 
 
 TAKE THE FOLLOWING EXAMPLE IN NUMBERS. 
 
 
 N. 
 
 S. 
 
 L.N. 
 
 L.S. 
 
 1 
 
 
 5.75 
 
 
 0.00 
 
 ? 
 
 30.28 
 
 9n 
 
 
 
 30.28 
 
 3 
 
 
 
 m 51 
 
 4 
 
 9.04 
 
 
 6.17 
 
 48.55 
 
 5 
 
 4.66 
 
 
 1.51 
 
 
 6 
 
 151 
 
 
 0.00 
 
 
 
 
 6.78 
 
 6.78 
 
 
 8 
 
 
 17.46 
 
 24.24 
 
 
 9 
 
 
 12.97 
 
 37.21 
 
 
 10 
 
 
 11.76 
 
 48.97 
 
 6.75 
 
 5.75 
 
 30.28 
 
 69.79 
 
 88.06 
 
 7.68 
 
 1.51 
 
 6.78 
 
 31.02 
 
 61.45 
 
 86.18 
 
 -076.5900 
 
 -468.7344 
 
 -687.4315 
 
 -626.1066 
 
 +088.9344 
 
 +020.2340 
 
 +049.8330 
 
 +268.3230 
 
 — 233.5100 
 
 +739.4244 
 
 11.58 
 13.40 
 7.35 
 
 .58 
 
 13.32 
 
 15.48 
 
 9.85 
 
 7.11 
 
 2)2792.1013 49.56 49.56 
 
 1396.0506=Ang. spaces. 
 
 In this example there are no indirect stations 
 in the Northings or Southings, 54.72 is the me- 
 ridianal breadth of the survey. But station 9th 
 being indirect in the parallel breadth, must be 
 
80 The Surveyor's Guide. 
 
 deducted from the sum of the Easting or Westing 
 to find the other side of the circumscribing par- 
 allelogram. Thus : 
 
 49.56 Sum E. or W. 
 3.80 Indirect. 
 
 45.76=Parallel breadth. 
 54.72=Meridianal breadth. 
 
 91.52 
 32032 
 18304 
 
 22880 
 
 2503.9872 Content of circum. parallelogram. 
 1396.0506 " of the angular spaces. 
 
 1107.9366 
 4 
 
 3.17464 
 40 
 
 6.98560 110.3.06.98, the content. 
 
 In this example you may see that the four ex- 
 tremes are the 6th, 1st, 10th, and 4th stations. 
 You can also see that the two latitudes of the 
 extreme West is equal to the two latitudes of the 
 extreme East, that is 6.17+48.55=48.97+5.75, 
 which is a proof to so much of the work. 
 
The Surveyor's Guide. 
 
 81 
 
 If you begin with the Eastings and Westings, 
 and proceed as you were directed, all along with 
 the Northings and Southings, you can find the 
 content of the survey in like manner, and so prove 
 the work. 
 
 To survey with the compass througli any mine, or other 
 cause for drawing the compass needle off its parallelism : 
 
 The diurnal variation of the needle is known 
 to every practical surveyor, but is easily cor- 
 rected by examining the time of the day when the 
 courses of long stations were taken ; as from about 
 8 o'clock in the morning till about 2 in the after- 
 noon, the needle varies Westerly to from about 
 7'08" to about 13'2r', as shown in the following 
 table. The surveyor can make such allowance as 
 will (all other errors apart) insure a complete 
 clase. 
 
 MEAN DIURNAL VARIATION FOR EVERY MONTH IN 
 THE YEAR. 
 
 January, 
 
 0" 7'08" 
 
 July, 
 
 0"13'14" 
 
 February, 
 
 8'58" 
 
 August, 
 
 12'19" 
 
 March, 
 
 ivn" 
 
 September, 
 
 11'43" 
 
 April, 
 
 12'26" 
 
 October, 
 
 10'36" 
 
 May,' 
 
 13'00" 
 
 November, 
 
 8'09" 
 
 June, 
 
 13'2F 
 
 December, 
 
 6'58" 
 
82 The Surveyor's Guide. 
 
 Now, in surveying with the compass detatched 
 from a Theodolite, both back and fore sights 
 should always be taken ; and to make sure that no 
 attraction exists in the first station, take a course 
 in a contrary direction to some object, go to that 
 object and take a back sight ; if the fore and back 
 sight agree you may be satisfied that no attraction 
 is at your first station ; but should they not agree, 
 you must then, from the latter station, repeat the 
 like process till you find at which of them the 
 attraction exists ; if, at the first station, either 
 note its quantity, which allow on the next course, 
 as in tracing old boundaries ; or pay no attention 
 to it at the starting, but continue to take the fore 
 and back sights throughout, and as at any station 
 the needle will be as much attracted at the fore as 
 the back sight, the angles can all be truly found as 
 formerly shown, and thence the true courses for 
 calculation by latitude and departure. Thus may 
 the expert surveyor traverse any city, mountain, or 
 other place containing mines or other substances 
 which attract the needle, about which I have heard 
 many complaints. 
 
The Surveyor's Guide. 
 
 83 
 
 Now to plot the last given notes, and in like 
 manner any other survey similarly prepared : — 
 Having the length and breadth of the circumscri- 
 bing parallelogram, let it be drawn by the same 
 
 scale you intend to lay down' your map by, and 
 beginning at either of the extremes, as 1, lay off 
 your latitude as l.a 5.575, and at right angles to 
 that, the departure of that station or Westing a.2 
 13.32, and join their extremities with the line 1 2, 
 
84 The Surveyor's Guide. 
 
 which is the distance. The next station is N. W. 
 Draw toward the North 2.b parallel to the sides 
 of your parallelogram, and on it lay 30.28, your 
 next Northing, and at right angles thereto toward 
 the West 15.48, your next Westing, and join 2 and 
 3, which is your next distance, and so on all round, 
 and as your Northings are equal to your Southings, 
 and your Eastings to your Westings, your last 
 departure, whether East or West, will fall into the 
 point of beginning, as T.l. This is the most expe- 
 ditious mode of plotting surveys, and can be made 
 use of in the most extensive work, and is much 
 superior to protraction by parallels and a metallic 
 protractor. The mechanical methods of finding 
 area, shown by many authors, I do not think well 
 to notice, as none of them can be depended on for 
 accuracy. 
 
 OF LOTTING OR LAYING OUT TOWNS, &C. 
 
 Regarding this kind of surveying, little can be 
 said more than giving some general directions con- 
 cerning the method of operation, as every man has 
 mostly predetermined the manner in which he 
 intends to have his property cut up into lots. 
 Provide yourself with a 20 or 25 feet pole, ten 
 
The Surveyor's Guide, 85 
 
 skivers with sharp points and thin edges, two brass 
 plummets with steel points hung to fine cords ; 
 then having fixed poles so as to direct you in a 
 straight line, and set them perpendicular by the 
 help of your plumb, direct your assistant to hold 
 one end of your pole in the straight course, with 
 his plummet hanging over the extremity, whilst 
 you hold yours touching the end of the pole which 
 you hold, and the point of your plummet exactly 
 over the starting point ; when both plummets are 
 steady, order your assistant to stick, and exactly 
 where the point sticks, he sticks one of his skivers 
 edgewise and slanting, so as that you can, when 
 you arrive at it, hang the point of your plummet 
 exactly over the edge of the skiver, and your 
 assistant again sticks his plummet in the ground, 
 and a skiver as before, and so on to the end. By 
 measuring carefully in this manner, property can 
 be laid out with great accuracy. 
 
 Almost every man has his own method of keep- 
 ing his field-book, but the following method, which 
 I have always adopted, is, I think, best calculated 
 to prevent confusion in extensive surveys, for as 
 writing backward and chaining forward are con- 
 trary, it is more congenial, and natural, to both 
 8 
 
86 
 
 The Surveyor's Guide. 
 
 write and chain forward, by beginning at the bot- 
 tom of the page. 
 
 N. B. It may not be unacceptable to the reader 
 to see these notes, calculated by Noble's method, 
 as on page 47. 
 
The Survetor's Guide. 
 
 87 
 
 Maple 
 
 ® 
 
 60.00 
 35.10 
 
 N.77fW. 
 
 Tin Oak 
 0-5 
 
 
 
 
 W. 0. 
 
 (5) 
 
 
 
 
 
 
 Stump. 
 
 «i«, 
 
 
 
 
 
 1 
 
 41.40 
 
 
 
 
 
 162i 
 
 
 
 
 
 "a 
 
 S.17IW. 
 
 
 
 
 
 1 
 1© 
 
 (4) 
 
 To a stone. 
 
 i 
 
 1 
 
 3 
 
 
 To the place of 
 
 m 
 
 36.40 
 
 18.48 
 
 "^ 0.6 
 
 33.00 
 
 
 
 
 heginning. 
 
 
 © 
 
 
 1 
 
 @ 
 
 
 
 21.00 
 
 
 7.10 
 
 R. 0. 
 
 
 S 
 
 S. 0. 
 
 
 3.24 
 
 0.15 to a Pine 
 
 
 
 
 N. 5f E. 
 
 @ 
 
 
 15.00 
 
 0.10 
 
 
 (7) 
 
 
 7.00 
 2521 
 
 S. 72JE. 
 
 toChesiiut 
 
 
 
 
 
 ^ 
 
 
 J^ 
 
 
 1 
 
 (3) 
 
 To a post. 
 
 1 
 
 36.25 
 23.00 
 
 To a post. 
 Chesnut. 
 
 B.Oali 
 
 41.00 
 
 s 
 
 26.00 
 4.00 
 
 Dogwood 
 
 1 
 
 n 
 
 
 1 
 
 2511 
 
 S. 71|E. 
 
 (2) 
 
 2olo 
 26U 
 
 chains to a 
 hickory 
 
 10.00 
 
 7.00 
 
 N.30fW. 
 
 (6) 
 
 0.10 to a Beech 
 
 Shellbark 
 mckory. 
 
 m 
 
 
 S.89|E. 
 
 tree. 
 
 
 66.00 
 
 
 
 
 
 
 Stream North 
 
 
 (1) 
 
 
 
 62.00 
 
 36 West. 
 
 Begins at a White Oak on. Squire Hays' Estate. 
 
S8 The Surveyor's Guide. 
 
 The foregoing method of keeping a field book, 
 I think, is the most convenient I have seen. The 
 following is the calculation of the notes corrected 
 by the foregoing rules. 
 
 
 
 P. 
 
 
 
 Lat. 
 
 
 
 
 
 
 1 
 
 
 Poles. 
 
 N. 
 
 S. 
 
 32.05 
 
 L.A. 
 
 E. Area. 
 
 W. Area. 
 
 E. 
 
 W. 
 
 S.89V 
 S.7i4Ie. 
 
 10.00 
 
 
 0.10 
 
 31.95 
 
 64.00 
 
 640.0000 
 
 
 10.00 
 
 
 2 
 
 20.50 
 
 
 6.55 
 
 25.40 
 
 57.35 
 
 1115.4575 
 
 
 
 
 3S.7a^E. 
 
 18.40 
 
 
 5.50 
 
 19.90 
 
 45.30 
 
 795.9210 
 
 
 17.57 
 
 
 4S.17gw. 
 
 20.90 
 
 
 19.90 
 
 0.00 
 
 19.90 
 
 
 126.9620 
 
 
 6.38 
 
 5 N.77gW. 
 
 6 N.30^Vy. 
 
 7 N. 53| E. 
 
 33.00 
 
 6.9+ 
 
 
 6.9+ 
 
 6.94 
 
 
 223.8150 
 
 
 .32.25 
 
 18.25 
 
 15.fiS 
 
 
 22.62 
 
 29.56 
 
 
 275.7948 
 
 
 9.33 
 
 9.48 
 
 9.03 
 
 
 32.05 
 
 54.67 
 
 51.3898 
 
 1 0.94 
 
 
 Double axea, 
 
 626.5718 47.96 47.96 
 
 2.0)1976.1965 in square four pole 
 chains. 
 
 A.R. V. 
 
 98.3.0957 
 
 
 
 Lat. 
 
 Lat. 
 
 Lats. 
 
 DouWe Semi- 
 
 
 
 N. 
 
 S. 
 
 South. 
 
 North. 
 
 Added. 
 
 rectangles. 
 
 E. 
 
 W. 
 
 
 0.10 
 
 
 0.10 
 
 0.10 
 
 —1.0000 
 
 10.00 
 
 
 
 6.55 
 
 
 6.65 
 
 6.75 
 
 +131.2S75 
 
 19.45 
 
 
 
 5.50 
 
 19.90 
 
 12J5 
 
 18.80 
 
 4-330.3160 
 
 17.57 
 
 Ex.E. 
 
 Ex. S. 
 
 19.90 
 
 00.00 
 
 
 19.90 
 
 —128.9620 
 
 
 6.38 
 
 6.94 
 
 
 6.94 
 
 
 6.94 
 
 +22:!.S150 
 
 
 32.25 
 
 15 68 
 
 
 22.62 
 
 9.43 
 
 29.56 
 
 ■f275.7M8 
 
 Ex. W. 
 
 9.33 
 
 9.43 
 
 North. 
 
 
 . 00.00 
 
 9.43 
 
 +8.8&42 
 
 0.94 . 
 
 
 32.05 32.05 
 Content of the angular spaces, 
 
The Surveyor's Guide. 
 
 47.96 Parallel breadth. 
 
 32.05 
 
 23980 
 9592 
 
 14388 
 
 1537.1180 Content of circum. parallelogram. 
 549.0197 " of the angular spaces. 
 
 988.0983 
 4 
 
 3.23932 
 40 
 
 9,57280 
 
 A. R. P. 
 
 98.3.95.73 the same as before. 
 
 There are no indirect stations in the above, but 
 were the longitudes made use of instead of the 
 latitudes, the last station would be indirect; and 
 here also it may be seen that the sum of the oppo- 
 site latitudes, against the extremes East and West, 
 are equal, viz : 12.15+19.90=32.05 and 22.62+ 
 9.43=32.05. 
 
 Of the Tracing of Old Hearings. 
 
 Gummer, in his work on Surveying, gives the 
 general number 57.3°, for doing this which many 
 8* 
 
90 The Surveyor's Guide. 
 
 work with, although it is not correct, but comes 
 out pretty near the truth when the chain line is not 
 very long. 
 
 To find this number, say 6.2831853 (the circum- 
 ference of a circle whose diameter is 2) : 360° :: 1 
 : 57.3° nearly. Now if two corners are known, 
 and can be both seen, set your compass at one of 
 them, and direct your sights to the other ; the dif- 
 ference between that shown by your needle, and 
 that shown in the deed, will be the variation to be 
 allowed on each course round the land, supposing 
 all those given in the deed to have been correctly 
 taken at the time the survey was made, which fre- 
 quently happens not to be the case. If the two 
 corners cannot be seen from each other, run the 
 course and distance given in the deed, and observe 
 if the point you arrive at, joined to the corner, 
 form an Isoseless triangle, which will be the case 
 if all be right ; otherwise some mistake has been 
 made in the distances, which must be corrected. 
 Then take the pendicular distance to the given 
 corner, and say : As the measured distance is to 
 the distance to the corner, so are 57.3° to the 
 number of degrees, minutes, or seconds, as the 
 case may be, which will be the variation. Or, 
 
The Sukveyor's Guide. 91 
 
 more accurately. As the distance to where the 
 perpendicular was taken is to radius, so is the dis- 
 tance to the corner to the tangent of the variation. 
 In running your trial line, you will be told you are 
 wrong, and that you don't understand your busi- 
 ness, and all such stuff, will be sounded in your 
 ears ; but pay no attention to such nonsense, for it 
 is to be regretted that too many men are so igno- 
 rant as to think that a Surveyor can, by some 
 mysterious means, direct his compass on the exact 
 line, and find all the courses as if by magic. It 
 often happens that the corners runs through clumps 
 of trees or other obstructions through which you 
 cannot chain. In such a case I have often chosen 
 an opening some degrees to right or left of the 
 fence, and at certain distances driven posts till I 
 found a perpendicular to the corner. Then, as 
 the whole distance is to the perpendicular, so is 
 each distance from the beginning to the perpen- 
 dicular distance from the measured line to the 
 fence, which, being correctly laid ofi", and posts 
 driven at their extremities, will point out the true 
 boundary. 
 
 Of Levelling. 
 The art of levelling consists in finding or tra- 
 
92 
 
 The Surveyor's Guide. 
 
 cing a line on a given portion of the earth's sur- 
 face, parallel to the horizon at all points. The 
 subject is too extensive to be comprised in this 
 small treatise. I shall give an example, which it 
 is hoped will enable the reader to do anything of 
 that nature that may come in his way. Any one 
 desirous of being fully informed on that subject, 
 should consult Bruff's Engineering, where every 
 information on that subject can be obtained. Re- 
 garding the adjustment of the level, which is a 
 simple matter, let the practitioner always place his 
 level in the middle, between the back and fore- 
 sights, and keep the bubble in the middle of the 
 divisions, and all will be right. 
 
The Surveyoe's Guide. 
 
 93 
 
 FIELD BOOK DISTANCES, MEASURED WITH A ONE 
 nUNDRED FEET CHAIN. 
 
 Efleva- 
 tion. 
 
 Back 
 sight. 
 
 Fore 
 sight. 
 
 Depres- 
 sion. 
 
 Total 
 elevat'Q 
 Datum 
 100 feet. 
 
 Dis- 
 tance. 
 
 ...... 
 
 1.11 
 
 6.S4 
 5.73 
 8.10 
 8.15 
 5.80 
 5.00 
 5.01 
 4.05 
 4.98 
 6.12 
 2.25 
 7.77 
 3.95 
 6.30 
 1.60 
 4.24 
 6.74 
 2.17 
 4.60 
 5.36 
 
 5.73 
 8.10 
 8.15 
 5.80 
 5.00 
 4.55 
 4.05 
 4.98 
 6.12 
 6.67 
 7.77 
 
 13.52 
 6.30 
 
 10.80 
 4.24 
 6.74 
 
 10.20 
 4.60 
 5.36 
 5.99 
 
 
 100. 
 101.11 
 
 98.74 
 98.69 
 101.04 
 101.84 
 102.29 
 103.25 
 102.32 
 101.18 
 100.63 
 95.11 
 89.36 
 87.01 
 82.51 
 79.87 
 77.37 
 73.91 
 71.48 
 70.72 
 70.09 
 
 .00 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 ] On cross road 50 
 J ft. W. N. 54 W. 
 1 Side of ravine, 30 
 J feet deep. 
 10. bottom 10 ft.wd. 
 1 Top of bank on 
 J other side. 
 
 1 Middle of stream, 
 i N. 57 W. 
 
 2.37 
 0.05 
 
 
 2.35 
 0.80 
 0.45 
 0.96 
 
 
 
 
 0.93 
 1.14 
 .55 
 5.52 
 5.75 
 2.35 
 4.50 
 2.64 
 2.50 
 3.46 
 2.43 
 0.76 
 0.63 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5.67 
 
 104.76 
 
 134.67 
 104.76 
 
 35.58 
 5.67 
 
 100.... 
 70.09 
 
 1 Dati 
 [therec 
 r giving 
 J accura 
 
 im at top, from wHoh. 
 uoed level is deducted, 
 a third proof of the 
 
 29.91 
 
 29.91 
 
 29.91 
 
 cy of the work. 
 
 The fall in the following section fi'om 1 to 21 
 is 29.91 feet; this divided into 2100 feet, the 
 whole distance gives 1 in 70.21, the regular grade ; 
 and to find the grade in degrees, it will be as 2100 
 is to radius :: 29.91 to the tangent of the angle in 
 this case 0° 49' nearly. Here it will be observed 
 
94 
 
 The Surveyor's Guide. 
 
 that the difference between the datum line and any 
 grade, is th.e height above or below the base line, 
 running through the first station. If the ordinate 
 be greater, the difference is above base ; if less, 
 below. Some old fashioned levellers follow a more 
 intricate plan. Thus 101.11—98.74=2.37—1.11 
 =1.26 above; again, 98.74—98.69=0.05, and 
 1.26+0.05=131 below, and so on. But this re- 
 quires too much thought, when to add and when 
 to subtract ; whereas the other method is done by 
 one subtraction. 
 
 Scale of length, 800 feet to 
 
 To LAY OUT A HOAD ON A REGULAR GrADE UP 
 
 A Hill. 
 Set your instrument at the starting point, level 
 it, and set the vane on your levelling rod to the 
 exict height of the centre of your glass. Ele- 
 
The Surveyor's Guide, 
 
 95 
 
 vate your grading instrument to the number of 
 degrees you intend your road to be. Send forward 
 your rod to any place where the cross wire will cut 
 the middle of the vane, and there drive a post, and 
 on it mark grade, and so on to the end of the 
 road. And to find the cuttings and fillings, the 
 follotving plan is the most convenient. Set your 
 instrument on the starting point, measure very 
 exactly the height of the centre of the glass, and 
 send your rod to the first point where cutting or 
 filling is required. Elevate your instrument to 
 the grade, mark where it cuts the rod, and the dif- 
 ference of the height of the instrument and height 
 on the* rod, will be the cutting or filling. If the 
 height of the instrument exceeds that on the rod, 
 the difierence is cutting, and per contra. 
 
 Example : 
 
 In the above cut the height of instrument is 4 
 feet ; height of rod, 2 ; diiference, 2 cutting. 
 
96 Surveyor's Guide. 
 
 Again, height of instrument, 4, and back sight to 
 rod 5 ; difference, 1 to be added to last, gives 3 
 of cutting at instrument. Fore sight, 3 ; differ- 
 ence to be added to last, gives 4 feet cutting at the 
 rod ; but now, height of instrument, 5 ; back sight, 
 2 ; difference, 3 ; which, deducted from 4, leaves 
 1, and so through the whole. 
 
 To Inflect in Curves on Rail Roads and 
 Others. 
 
 The curves most in use at the present time, are 
 those of a circle. The angle made at the angular 
 point of the tangents is always given — the length 
 of your tangent is also given. To find the radius, 
 multiply the natural tangent of half the contained 
 angle by the length of the tangent of your curve, 
 and the product will be the radius of the curve. 
 
 To find the degree of curvature, divide half the 
 chord to be inflected by the radius of the curve, 
 and it gives the natural sine of the degrees of cur- 
 vature. 
 
 Thus, in the annexed figure, where the radius is 
 140, and the cord to be inflected 100. 140)50, 
 000000 (.357142 is the natural sine of 20° 55'= 
 the degrees of curvature. 
 
The Surveyor's Guide. 
 
 97 
 
 Demonstration. 
 
 The angle A D C, is a right L=to A D B, and 
 A C B is common to the two triangles, ABC and 
 A D B. Hence LAC D=B A DJ, the L angle 
 of deflection. Now set your instrument at A, 
 direct your index to E, turn it towards the curve 
 
 E 
 
 till 20° 55' are told on the limb, holding the end 
 of your chain at A; let the assistant hold the 
 chain tight, and move round till the other end 
 comes in the line of the perpendicular wire of the 
 
98 The Surveyor's Guide. 
 
 telescope at G, and then fix a pin. Again, if 
 nothing intervene to prevent your seeing, inflect 
 from A E, double the said /., and fixing one end 
 of the chain at G, let the other be stretched to 
 come in contact with the telescope at H, and so on 
 through the whole. If H cannot be seen from A, 
 move the instrument to G, and take a back sight 
 to A, and inflect double the L of the degrees of 
 curvature from G K, which will fall into H. 
 
 I have met with some calling themselves engi- 
 neers, who adopt the following plan. They divide 
 57.,3°X60-=3438' by the radius of the circle, mul- 
 tiplying the quotient by the number of feet in the 
 chord, and divide by 60 for double the angle ; but 
 this is erroneous. I remember having met with a 
 person who declared that the angle found by this 
 rule was the true angle of deflection. I gave him 
 the tangent 100, and the radius 100 feet, and he 
 did it by this rule, viz: 100)3438(34.38X100= 
 3438+60=57° 18'. In this instance the L made 
 by the tangent and chord is only 45°, so that in- 
 stead of inflecting in 100 feet, this 57° 18' would 
 •fall below the chord. Nor is the half of it cor- 
 rect, viz: 28° 39'. For by the true method 
 100)50(=,5, the natural sine of 30° the true angle. 
 
The Surveyor's Guide. 99 
 
 It remains to find the length of the curve A G 
 H F. The circumference of a circle whose di- 
 ameter is 2, is 6.2832 nearly. Hence as 360° : 
 6.2882 :: 1 : .01745, &c. This number, multi- 
 plied by the degrees in the arc, and by the radius 
 of the curve, gives the length of the arc, thus : 
 
 01745 
 11 
 
 17450 268.1^' the length of the arc, and 
 1745 so of any other. 
 
 1,91950 
 140 
 
 7678000 
 191950 
 
 268,73000 
 
 The two following problems may be amusing to 
 some readers, viz : 
 
 A gentleman has a lot 40 perches long and 30 
 perches wide. He thinks the ends may be so ap- 
 plied, as that when their extremities are joined, the 
 area may be the greatest possible. The perpen- 
 
100 The Surveyor's Guide. 
 
 dicular breadth, and the length of the unknown 
 side are required. 
 
 Answer: Breadth, 26.815 nearly. 
 Length of the unknown side, 66.904 nearly. 
 
 Problem Second. 
 
 A plank road is to be made from the city A to 
 the town B, 20 miles asunder. A straight road is 
 so situated that a perpendicular from A to it is 10 
 miles, and from B 6 miles. The plank road must 
 touch the straight road in such a point as to be 
 the shortest possible by that route, the length of 
 the plank road, the point of contact, and radius 
 of the curve having 200 feet tangent, are required. 
 
 Answer : Length of the plank road, 25.298 
 The distance of the point of contact 
 
 from A, 12.2474 
 
 And from B, 7.3484 
 
 Badius of the curve having 200 feet tangent, 
 245 feet nearly. 
 
 This note to be placed after the calculation of 
 the large triangle. It is there shown that the area 
 of any plane triangle, the three sides of which are 
 given, is A B^. Sine B. Sine A 
 
 C 2 Sine C. Which is thus 
 
 proved BAA 
 
The Surveyor's Guide. 101 
 
 It has been already shown that B C. B A. Sine B. 
 
 2 
 
 equal area of the triangle, .*. B C. A C. Sine C. 
 =area. 
 
 2 
 
 Hence B C. B A. Sine B=B C. A C. Sine C. 
 
 Multiply each side by B A, and we have 
 
 B C. B A^. Sine B=B C. A C. B A. Sine C. 
 
 Divide this equation by B C, we have 
 
 B A^. Sine B=A C. B A. Sine C. 
 
 Multiply each side by Sine A .•. 
 
 B A^. Sine B. Sine A=A C. B A. Sine A. Sine C. 
 
 Divide this by Sine C, and 
 
 B A^. Sine B. Sine A. 
 
 ■ =A C. B A. Sine A.=twice 
 
 SineC 
 the area, and therefore 
 
 A B^. Sine B. Sine A 
 
 =:Area 
 
 2 Sine C 
 To find the perpendicular ordinates from the 
 chord 6 of any arc of a railroad, in order to set off 
 the curve correctly and speedily, without the help 
 of an instrument, suppose it to be a 20° curve, the 
 tangent 200. Find the radius, as formerly taught ; 
 multiply the radius by the natural co. sine of half 
 the vertical angle, and you have J the chord. 
 
102 
 
 The Sukveyor's Guide. 
 
 Multiply the radius by the natural sine of the 
 same angle, and you have the distance from the 
 centre to the middle of the chord, a constant num- 
 ber to be deducted. Now take any distance, sup- 
 pose 10 feet, at which you choose to erect your 
 
 ordinates, and from the semi-chord subtract this 
 number, square the remainder, and subtract it 
 from the square of the radius ; extract the square 
 root, from which take the aforesaid constant num- 
 ber, and the remainder is the ordinate to be 
 rightly applied, and so proceed till you arrive at 
 
The Surveyor's Guide. 103 
 
 the middle of the chord ; then the difference be- 
 tween the said constant number and the radius, is 
 the versed sine or greatest ordinate, and now you 
 are prepared to lay off the other side of your 
 curve, and all this can be done in a few minutes in 
 the field. 
 
 Example. See last figure. 
 
 Nat. tangent of 80°=5.67128 
 200 
 
 1134,25600=Iladius, 1134. 
 Nat. CO. sine of 80° =,17365 
 
 5671280 
 6805536 
 3402768 
 7939792 
 1134256 
 
 196,96355440=Semi-chord, 197. 
 
 Nat. sine of 80° 1134 
 
 ,9848 
 
 9072 
 4536 
 
 9072 
 10206 
 
 lllfi 7fi.R9 Distance from centre to said 
 J.1AU, (UO^ cliord=1117. 
 
104 The Surveyor's Guide. 
 
 From 1134 
 Take 1117 
 
 17= Versed sine FE— From 197 
 Take 10 
 
 (187^=34969 
 From (1134)^=1285956 
 Take ( 187)^= 34969 
 
 1250987=1118 
 From which take 1117 
 
 1 ft. the 1st ordinate. 
 
 Again, for the 2d ordinate, 197— 20=(177)^ 
 
 =31329 and 1285956 
 — 31329 
 
 (1120 From 1120 
 
 v/ 1254627 Take 1117 
 
 1 
 
 — 3=the next. 
 
 21)25 
 21 
 
 222)446 
 444 
 
 2240)227 
 
 Ordinate. All this is plain from the figure, and 
 "when the radius and constant subtrahend are 
 
The Surveyor's Guide. 
 
 10^ 
 
 found (which is on]j the work of a minute) all the 
 others are nearly had at sight. This I consider 
 quite superior to any other method now in practice. 
 Otherwise thus : Let the radius, versed sine, 
 chord, and constant quantity D E, be found as 
 
 
 before, divide the semi-chord into any number of 
 parts as e f g h i. From E C deduct one of the 
 parts i C, leaves E i^m F, then D F=(radius) 
 squared — (m F)^=(m Df the square root of which, 
 minus the constant quantity, E D, gives the ordi- 
 nate i F, and in like manner all the others are 
 found, and thus the curve can be laid off in a few 
 minutes in the most accurate manner, (by the 47th 
 of the first of Euclid.) 
 
106 
 
 The Sukveyor's Guide. 
 
 Problem. 
 Let A B C be a right angled triangle, the hy- 
 pothenuse of which is 35, and the difference be- 
 tween the area of the enscribed square (one of 
 c whose angles coin- 
 cides with the right 
 angle of the trian- 
 gle) and the area 
 of the A is 150. 
 Required the sides 
 of the triangle. 
 
 Solution. 
 
 Put A E=x and D F=y. Then per 4th Euc. 
 6th, y : y :: X : f =C F, f +x y=DoubIe the 
 area of the Ag A D E and D F C .-.=300 or 'f + 
 2 X y=600. Also f+ Y=B C and x+y= A 
 B. Now (l'+jy+{x + yy=S5^ viz; |:+? + y^ 
 +y+2 X y=1225 
 
 Deduct 'f +2 X y=600 
 
 5+2 y^+x^-=625 Ex't the square. 
 Root and -^'+x=25 or 
 
 y^+x^=25 x=A 1)^=5 ^/ x. 
 
The Surveyor's Guide. 107 
 
 Hence 5 \/ x : x :: 35 : x+y, and by divi- 
 ding the first and third by 5. x| : x :: y x+y 
 and :: are their squares, x : x^ :: 49 . x^+y^+ 
 2 X y. Multiply the extremes and means, and 
 
 49 x2=x3+x yH-2 x^ y-j-by x and 
 From 49 x =x''+y=2 xy ; but 25 x=j^+x^ .-. 
 Take 25 x =x'+y^ 
 
 24 X = 2 X y or 
 24 = 2 y and 
 
 y =12 the side of the square. 
 And the sides of the angle are 21 and 28. 
 
 28 
 21 
 
 28 
 56 
 
 2)588 
 
 294=area of A. 
 Deduct, 144 
 
 150=area of the 2 A's. 
 
108 
 
 The Surveyor's Guide. 
 
 1 TABLES OP LATITUDE AND DEPARTURE. i 
 
 1 
 1 
 
 N. S. 
 
 E.W. 1|N. S. 
 
 E.W. 
 
 N. S. 
 
 E.W. 
 
 N. S. 
 
 E.W. 
 
 89i 
 
 
 Oi 
 0.9999 
 
 19i 
 
 Oi 
 0.9999 
 
 89i 
 
 o.i 
 
 
 
 0.0043 
 
 0.0087 
 
 0.9999 
 
 0.0131 
 
 2 
 
 
 
 1.9999 
 
 0.0087 
 
 1.9999 
 
 0.0174 
 
 1.9998 
 
 0.0262 
 
 3 
 
 
 
 2.9999 
 
 0.0131 
 
 2.9998 
 
 0.0261 
 
 2.9997 
 
 0.0.392 
 
 4 
 
 
 
 3.9999 
 
 0.0174 
 
 3.9998 
 
 0.0349 
 
 3.9996 
 
 0.0623 
 
 5 
 
 
 
 4.9999 
 
 0.0218 
 
 4.9998 
 
 0.0436 
 
 4.9995 
 
 0.0654 
 
 6 
 
 
 
 5.9999 
 
 0.0262 
 
 5.9997 
 
 0.0623 
 
 6.9994 
 
 0.0785 
 
 7 
 
 
 
 6.9999 
 
 0.0305 
 
 6.9997 
 
 0.0611 
 
 6.9993 
 
 0.0916 
 
 8 
 
 
 
 7.9999 
 
 0.0349 
 
 7.9997 
 
 0.0698 
 
 7.9992 
 
 0.1047 
 
 9 
 
 1 
 
 
 
 8.9999 
 
 0.0393 
 
 8.9996 
 
 0.0785 
 88J 
 
 8.9991 
 
 0.1178 
 
 1° 
 
 89° 
 
 li 
 
 0.9997 
 
 88S_ 
 0.0218 
 
 li 
 
 li 
 
 88i 
 0.0305 
 
 0.9998J0.0174 
 
 0.9996 
 
 0.0262 
 
 0.9995 
 
 2 
 
 1.9997! 0.0349 
 
 1.9995 
 
 0.0436 
 
 1.9993 
 
 0.0523 
 
 1.9990 
 
 0.0610 
 
 3 
 
 2.9995|0.0523 
 
 2.9993 
 
 0.0654 
 
 2.9989 
 
 0.0785 
 
 2.9986 
 
 0.0916 
 
 4 
 
 3.9994 
 
 0.0698 
 
 3.9990 
 
 0.0872 
 
 3.9986 
 
 0.1047 
 
 3.9981 
 
 0.1221 
 
 6 
 
 4.9992 
 
 0.0872 
 
 4.9988 
 
 0.1090 
 
 4.9982 
 
 0.1309 
 
 4.9976 
 
 0.1527 
 
 6 
 
 5.9991 
 
 0.1047 
 
 5.9985 
 
 0.1309 
 
 5.9979 
 
 0.1570 
 
 6.9972 
 
 0.1832 
 
 7 
 
 6.9989 
 
 0.1221 
 
 6.9983 
 
 0.1627 
 
 6.9976 
 
 0.1832 
 
 6.9967 
 
 0.2137 
 
 8 
 
 7.9988 
 
 0.1396 
 
 7.9981 
 
 0.1745 
 
 7.9972 
 
 0.2094 
 
 7.9962 
 
 0.2443 
 
 9 
 
 1 
 
 8.9886 
 
 0.1570 
 
 8.9978 
 
 0.1963 
 
 8.9969 
 
 0.2356 
 
 8.9958 
 
 0.2748 
 
 2° 
 
 88° 
 
 2i 
 
 87S 
 0.0392 
 
 2i 
 0.9990 
 
 87i 
 0.0436 
 
 2i 
 
 87i 
 
 0.9994,0.0349 
 
 0.9992 
 
 0.9988 
 
 0.0479 
 
 
 1.9987 0.0698 
 
 1.9984 
 
 0.0785 
 
 1.9981 
 
 0.0872 
 
 1.9977 
 
 0.0959 
 
 3 
 
 2.9981 0.1047 
 
 2.9977 
 
 0.1178 
 
 2.9971 
 
 0.1308 
 
 2.9965 
 
 0.1439 
 
 4 
 
 3.9975 0.1396 
 
 3.9969 
 
 0.1570 
 
 3.9962 
 
 0.1745 
 
 3.9964 
 
 0.1919 
 
 .-i 
 
 4.9969 0.1745 
 
 4.9961 
 
 0.1963 
 
 4.9952 
 
 0.2181 
 
 4.9942 
 
 0.2399 
 
 6 
 
 5.9963 
 
 0.2094 
 
 5.9954 
 
 0.2355 
 
 5.9943 
 
 0.2617 
 
 5.9931 
 
 0.2878 
 
 7 
 
 6.9957 
 
 0.2443 
 
 6.9946 
 
 0.2748 
 
 6.9933 
 
 0.3053 
 
 6.9919 
 
 0.3358 
 
 a 
 
 7.9951 
 
 0.2792 
 
 7.9938 
 
 0.3141 
 
 7.9924 
 
 0.3489 
 
 7.9908 
 
 0.3838 
 
 9 
 
 1 
 
 8.9945 
 
 0.3141 
 
 87° 
 
 8.9930 
 3i° 
 
 0.3533 
 
 86.1 
 0.0567 
 
 8.9914 
 
 0.3926 
 
 8.9896 
 
 0.4318 
 
 3° 
 
 H 
 
 86i 
 0.0610 
 
 3i 
 
 86i 
 
 0.9986 
 
 0.0523 
 
 0.9984 
 
 0.9981 
 
 0.9978 
 
 0.0654 
 
 ? 
 
 1.9973 
 
 0.1047 
 
 1.9968 
 
 0.11.34 
 
 1.9963 
 
 0.1221 
 
 1.9957 
 
 0.1308 
 
 3 
 
 2.9959 
 
 0.1570 
 
 2.9952 
 
 0.1701 
 
 2.9944 
 
 0.1831 
 
 2.9936 
 
 0.1962 
 
 4 
 
 3.9945 
 
 0.2093 
 
 3.9935 
 
 0.2268 
 
 3.9925 
 
 0.22421 
 
 3.9914 
 
 0.2616 
 
 fi 
 
 4.9931 
 
 0.2617 
 
 4.9919 
 
 0.2835 
 
 4.9907 
 
 0.3062 
 
 4.9893 
 
 0.3270 
 
 fi 
 
 5.9918 
 
 0.3140 
 
 5.9903 
 
 0.3402 
 
 5.9888 
 
 0.3663 
 
 5.9871 
 
 0.3924 
 
 7 
 
 6.9904 
 
 0.3664 
 
 6.9888 
 
 0.3968 
 
 6.9869 
 
 0.4273 
 
 6.9850 
 
 0.4578 
 
 S 
 
 7.9890 
 
 0.4187 
 
 7.9871 
 
 0.4535 
 
 7.9861 
 
 0.4884 
 
 7.9829 
 
 0.6232 
 
 9 
 
 8.9877 
 E.W. 
 
 0.4710 
 
 N. S. 
 
 8.9866 
 E.W. 
 
 0.5102 
 
 9.9832 
 E.W. 
 
 0.6494 
 
 N. S. 
 
 8.9807 
 E.W. 
 
 0.6886 
 
 N. S. 
 
 N. S. 
 
The Surveyor's Guide. 
 
 109 
 
 TABLES OP LATITUDE AND DEPARTURE. j 
 
 
 
 N. S. 
 
 E. W. 1 iN. S. 
 86° 4i 
 
 E.W. 
 
 K S. 
 
 E. W. 
 
 N. S. 
 
 E.W. 
 
 85i 
 
 
 4° 
 
 85S 
 
 4i 
 
 85i 
 
 41 
 
 
 1 
 
 0.9976 
 
 0.0698' 0.9972 
 
 0.0741 
 
 0.9969 
 
 0.0784 
 
 0.9965 
 
 0.0828 
 
 
 2 
 
 1.9951 
 
 ).1395l 11.9945 
 
 0.1482 
 
 1.9938 
 
 0.1569 
 
 11.9931 
 
 0.1656 
 
 
 3 
 
 2.9927 0.2093ii2.9917' 
 
 0.2223 
 
 2.9907 
 
 0.2354 
 
 12.9897 
 
 0.2484 
 
 
 4 
 
 3.9902 
 
 0.2790! '3.9890 
 
 0.2964 
 
 3.9977 0.31381 
 
 13.9863 
 
 0.3312 
 
 
 5 
 
 4.9878 
 
 0.34881 !4.9862 
 
 0.3705 
 
 4.9846 
 
 0.3923 
 
 4.9828 
 
 0.4140 
 
 
 6|5.9854 
 
 0.4185 ,5.9835 
 
 0.4446 
 
 5.9815 
 
 0.4707 
 
 5.9794 
 
 0.4968 
 
 
 7l6.9829 
 
 0.4883' 6.9807 
 
 0.51871 
 
 '6.9784 
 
 0.5492 
 
 6.9759 
 
 0.5796 
 
 
 8 
 
 7.9805 0.5580 17.9780 
 
 0.59281 
 
 7.9753 
 
 0.6277 
 
 I7.9725 
 
 0.6625 
 
 
 1 9 
 
 8.9780|0.6278l 
 
 8.9752 
 5i 
 
 0.6670 
 
 84|"- 
 
 8.9722 
 5i 
 
 0.7061 
 
 8.9691 
 
 0.7453 
 
 
 
 5° 
 
 85° 1 
 
 84i 
 
 5i 
 
 84i 
 
 
 1 
 
 0.9961 
 
 0.0S71 
 
 0.9958 
 
 0.0915: 
 
 0.9954 
 
 0.0958 
 
 0.9949 
 
 0.1002 1 
 
 
 2 
 
 1.9923 
 
 0.1743 
 
 1.9916 
 
 0.1830' 
 
 |1.9908 
 
 0.1917 
 
 1.9899 
 
 0.2004 
 
 
 I ^ 
 
 2.9884 
 
 0.2615 
 
 2.9874 
 
 0.2745: 
 
 2.9862 
 
 0.2875 
 
 2.9849 
 
 0.3006 
 
 
 4- 
 
 3.9846 
 
 0.3486 
 
 3.9832 
 
 0.3660: 
 
 '3.9816 
 
 0.38.34 
 
 3.979^" 
 
 0.4008 
 
 
 1 5 
 
 4.9808 
 
 0.4358 
 
 4.9790 
 
 0.4575 
 
 '4.9770 
 
 0.4792 
 
 4.974S 
 
 0.5009 
 
 
 6 
 
 5.9769 
 
 0.5229 
 
 5.9 748 jo. 5490 
 
 5.9724 
 
 0.5751 
 
 5.9698 
 
 0.6011 
 
 
 
 6.9731 
 
 0.6101 
 
 6.9706!o.6405 
 
 6.9678 
 
 0.6709 
 
 6.9648 
 
 0.7013 
 
 
 ' 8 
 
 7.9692 
 
 0.6972 
 
 7.9664 
 
 0.7320 
 
 :7.9632 
 
 0.7668 
 
 7.9597 
 
 0.8015 
 
 
 ; 9 
 
 i 
 
 1 
 
 8.9654 
 
 0.7844' 
 
 8.9622 
 
 i « 
 
 0.9940 
 
 0.8235 
 
 :8.95S6 
 
 0.8626 
 
 8.9547 
 
 0.9017 
 
 
 6° 
 
 0.9945 
 
 84 
 
 83i 
 
 6i 
 
 83i 
 0.1132 
 
 1 6i 
 
 83i 
 01175 
 
 
 0.1045 
 
 0.1088 
 
 0.9935 
 
 ,0.9930 
 
 
 1 2U.9S90 
 
 0.2090 
 
 1.9881 
 
 0.2177 
 
 1.9871 
 
 0.2264 
 
 1.9861 
 
 0.2351 
 
 
 3 2.9836 
 
 0.3136 
 
 ,2.9821 
 
 0.3266 
 
 2.9807 
 
 0.3396 
 
 I2.9792 
 
 0.3526 
 
 
 i 4 
 
 3.9781 
 
 4181; 
 
 3.9762 
 
 0.4355 
 
 3.9743 
 
 0.4528 
 
 '3.9723 
 
 0.4701 
 
 
 5 
 
 4.9726 
 
 0.5226 
 
 14.9703 
 
 0.5443 
 
 4.9678 
 
 0.5660 
 
 14.9653 
 
 0.5877 
 
 
 fi 
 
 5.9671 
 
 0.6272 
 
 15.9643 
 
 0.6532 
 
 5.9614 
 
 0.6792 
 
 15.9584 
 
 0.7052 
 
 
 7 
 
 6.9616 
 
 0.7317 
 
 6.9584 
 
 0.7621 
 
 6.9550 
 
 0.7924 
 
 6.9515 
 
 0.8228 
 
 
 8 
 
 7.9562 
 
 0.8362 
 
 '7.9524 
 
 0.8709 
 
 7.9486 
 
 0.9056 
 
 7.9445 
 
 0.9403 
 
 
 9 
 
 1 
 
 8.9507 
 
 0.9408 
 83° 
 
 ^8.9465 
 
 0.9798 
 
 8.9421 
 
 1.0188 
 
 8.9376 
 
 1.0578 
 
 
 7° 
 
 n 
 
 82i 
 
 0.9914 
 
 S2i 
 
 1 ri 
 
 0.9908 
 
 82i 
 0.1348 
 
 
 0.9925 
 
 0.1218 
 
 0.9920 
 
 0.1262 
 
 0.1305 
 
 
 2 
 
 1.9851 
 
 0.2437 
 
 11.9840 
 
 0.2524 
 
 ;i.9S29 
 
 0.2610 
 
 |1.9817 
 
 0.2697 
 
 
 3 
 
 2.9776 
 
 0.3656 
 
 ,2.976( 
 
 0.3786 
 
 :2.9743 
 
 0.3916 
 
 !2.9726 
 
 0.4045 
 
 
 4 
 
 3.9702 
 
 0.4874 
 
 i.3.9680 
 
 0.5048 
 
 :3.9657 
 
 0.5221 
 
 13.9635 
 
 0.5394 
 
 
 5 
 
 4.9627 
 
 0.6093 
 
 4.9600 
 
 0.6310 
 
 4.9572 
 
 0.6526 
 
 14.9543 
 
 0.6742 
 
 
 6 
 
 5.9553 
 
 0.7312 
 
 5.952( 
 
 0.7572 
 
 5.9487 
 
 0.7831 i 15.9452 
 
 0.8091 
 
 
 7 
 
 6.9478 
 
 0.8531 
 
 16.9440 
 
 0.8834 
 
 6.9401 
 
 0.9137 
 
 6.9361 
 
 0.9439 
 
 
 8 
 
 7.9404 
 
 0.9750 
 
 17.9360 
 
 1.0096 
 
 7.9315 
 
 1.0442 
 
 7.9269 
 
 1.0788 
 
 
 918.9329 
 
 1.0968 
 
 8.9280 
 
 1.1358 
 
 8.923(. 
 
 1.1747 
 
 8.9178 
 
 1.2136 
 
 
 |e.w. 
 
 N. S. IE. W. 
 
 N. S. 
 
 E. W. 
 
 N. S. 
 
 E. W. 
 
 N. S. 
 
 1 
 
 
 
110 
 
 The Surveyor's Guide. 
 
 j TABLES OF LATITUDE AND DEPARTURE. jj 
 
 1 
 
 N. S. 
 
 E.W. 
 
 N. S. 
 
 E. W. 
 ~81i~ 
 
 N. S. 
 
 E. W. 
 
 N. S. 
 
 E. W. 
 
 "81i 
 0.1521 
 
 8° 
 0.9902 
 
 82 
 
 8i 
 
 8i 
 
 81i 
 0.1478 
 
 8i 
 0.9883 
 
 0.1391 
 
 0.9896 
 
 0.1435 
 
 0.9890 
 
 2 
 
 1.9805 
 
 0.2783 
 
 1.9793 
 
 0.2870' 
 
 1.9780 
 
 0.2956 
 
 1.9767 
 
 0.3042 
 
 3 
 
 2.9708 
 
 0.4175 
 
 2.9689 
 
 0.4305 
 
 2.9670 
 
 0.4434 
 
 2.9651 
 
 0.4564 
 
 4 
 
 3.9611 
 
 0.5567 
 
 3.9586 
 
 0.5740 
 
 3.9560 
 
 0.6912 
 
 3.9534 
 
 0.6085 
 
 5 
 
 4.9513 
 
 0.6959 
 
 4.9483 
 
 0.7175 
 
 4.9451 
 
 0.7390 
 
 4.9418 
 
 0.7606 
 
 6 
 
 5.9416 
 
 0.8350 
 
 5.9379 
 
 0.8605 
 
 5.9341 
 
 0.8868 
 
 5.9302 
 
 0.9127 
 
 7 
 
 6.9319 
 
 0.9742 
 
 6.9276 
 
 1.0045 
 
 6.9231 
 
 1.0347 
 
 6.9186 
 
 1.0649 
 
 8 
 
 7.9221 
 
 1.1134 
 
 7.9172 
 
 1.1479, 
 
 7.9121 
 
 1.1825 
 
 7.9069 
 
 1.2170 
 
 9 
 
 1 
 
 8.9124 
 
 1.2526 
 
 8.9069 
 
 1.2914 
 
 8.9011 
 
 1.3303 
 
 8.8952 
 
 9i 
 0.9855 
 
 1.3691 
 
 80i 
 0.1693 
 
 9° 
 
 81 
 
 9i 
 
 80i 
 
 9i 
 0.9863 
 
 804 
 
 0.9877 
 
 0.1564 
 
 '0.9870 
 
 0.1607 
 
 0.1650 
 
 2 
 
 1.9754 
 
 0.3129 
 
 ;L9740 
 
 0.3215 
 
 1.9726 
 
 0.3301 
 
 1.9711 
 
 0.3387 
 
 3 
 
 2.963] 
 
 0.4693 
 
 :2.9610 
 
 0.4822 
 
 2.9589 
 
 0.4951 
 
 2.9566 
 
 0.6080 
 
 ■4 
 
 3.9508 
 
 0.6257 
 
 3.9480 
 
 0.6430 
 
 3.9451 
 
 0.6602 
 
 3.9422 
 
 0.6774 
 
 5 
 
 4.9384 
 
 0.7822 
 
 4.9350 
 
 0.8037 
 
 4.9314 
 
 0.8252 
 
 4.9278 
 
 0.8467 
 
 6 
 
 5.9261 
 
 0.9386 
 
 5.9220 
 
 0.9644 
 
 6.9177 
 
 0.9903 
 
 5.9133 
 
 1.0161 
 
 7 
 
 6.9138 
 
 1.0950 
 
 6.9090 
 
 1.1252 
 
 ,6.9040 
 
 1.1553 
 
 6.8989 
 
 1.1854 
 
 8 
 
 7.9015 
 
 1.2515 
 
 7.8960 
 
 1.2859 
 
 17.8903 
 
 1.3204 
 
 7.8844 
 
 1.3548 
 
 9 
 
 1 
 
 8.8892 
 
 1.4079 
 
 ,8.8830 
 
 1.4467 
 
 8.8766 
 
 1.4864 
 
 794 
 0.1822 
 
 8.8700 
 
 101 
 0.9824 
 
 1.5241 
 
 79i 
 0.1866 
 
 10° 
 
 80° 
 0.1736 
 
 i lOi 
 
 791 
 0.1779 
 
 ! lOi 
 11.9832 
 
 0.9848 
 
 0.9840 
 
 2 
 
 1.9696 
 
 0.3473 
 
 ,L9681 
 
 0.3559 
 
 0.9665 
 
 0.3645 
 
 1.9649 
 
 0.3730 
 
 3 
 
 2.9544 
 
 0.5209 
 
 2.9521 
 
 0.5338 
 
 2.9497 
 
 0.5467 
 
 2.9473 
 
 0.6595 
 
 4 
 
 3.9392 
 
 0.6946 
 
 ,3.9362 
 
 0.7118 
 
 13.9330 
 
 0.7289 
 
 3.9298 
 
 0.7460 
 
 s 
 
 4.9240 
 
 0.8682 
 
 4.9202 
 
 0.8897 
 
 4.9163 
 
 0.9112 
 
 4.9123 
 
 0.9325 
 
 6 
 
 5.9088 
 
 1.0419 
 
 5.9042 
 
 1.0676 
 
 5.8995 
 
 1.0933 
 
 5.8947 
 
 1.1190 
 
 7 
 
 6.8937 
 
 1.2155 
 
 i 6.8883 
 
 1.2456 
 
 ,6.8828 
 
 1.2756 
 
 6.8772 
 
 1.3056 
 
 8 
 
 7.8785 
 
 1.3892 
 
 17.8723 
 
 1.4235 
 
 17.8660 
 
 1.4579 
 
 7.8596 
 
 1.4920 
 
 9 
 
 1 
 
 8.8633 
 
 1.5628 
 
 8.8564 
 
 1.6015 
 
 ~7SF 
 0.1951 
 
 18.8493 
 
 1 114 
 0.9799 
 
 1.6401 
 
 8.8421 
 
 1.6786 
 
 m 
 
 0.2036 
 
 11° 
 
 79 
 0.1908 
 
 1 Hi 
 
 784 
 0.1993 
 
 111 
 
 0.9816 
 
 0.9808 
 
 0.9790 
 
 2 
 
 L9633 
 
 0.3816 
 
 1.9616 
 
 0.3902 
 
 1.9598 
 
 0.3987 
 
 1.9581 
 
 0.4073 
 
 3 
 
 2.9449 
 
 0.5724 
 
 '2.9424 
 
 0.5853 
 
 12.9398 
 
 0.5981 
 
 2.9371 
 
 0.6109 
 
 4 
 
 3.9265 
 
 0.7632 
 
 13.9231 
 
 0.7804 
 
 13.9197 
 
 0.7975 
 
 3.9162 
 
 0.8146 
 
 5 
 
 4.9081 
 
 0.9540 
 
 4.9039 
 
 0.9755 
 
 4.8996 
 
 0.9968 
 
 4.8952 
 
 1.0182 
 
 6 
 
 5.8898 
 
 1.1449 
 
 5.8847 
 
 1.1705 
 
 5.8796 
 
 1.1962 
 
 6.8743 
 
 1.2218 
 
 y 
 
 6.8714 
 
 1.3357 
 
 6.8655 
 
 1.3656 
 
 6.8595 
 
 1.3956 
 
 6.8533 
 
 1.4265 
 
 i 8 
 
 7.8530 
 
 1..5265 
 
 7.8463 
 
 1.5607 
 
 7.8394 
 
 1.5949 
 
 7.8324 
 
 1.6291 
 
 1 9 
 
 1 
 
 8.8346 
 E.W. 
 
 1.7173 
 
 8.8271 
 
 eTw" 
 
 1.7558 
 N. S. 
 
 8.8193 
 
 ettv: 
 
 1.7943 
 
 N. S. 
 
 8.8114 
 E. W. 
 
 1.8327 
 
 nTsT 
 
 N. S. 
 
The Surveyor's Guide. 
 
 Ill 
 
 TABLES OF LATITUDE AND DEPARTURE. 1 
 
 1 
 
 N. S. 
 
 12° 
 
 0.9781 
 
 E.W. 
 
 N.S. 
 12i 
 
 E. AY.I 
 
 0.2122 
 
 N. S. 
 
 E. W. 
 
 N. S. 
 
 E. W. 
 
 ~77r 
 
 78° 
 
 12i 
 
 77i 
 
 12s 
 
 0.2079 
 
 0.9772 
 
 0.9763 
 
 0.2164 
 
 0.9753 
 
 0.2207 
 
 2 
 
 1.9563 
 
 0.4158 
 
 1.9544 
 
 0.4242 
 
 1.9526 
 
 0.4329 
 
 1.9507 
 
 0.4414 
 
 3 
 
 2.9344 
 
 0.6237 
 
 2.9317 
 
 0.6365 
 
 2.9289 
 
 0.6493 
 
 2.9260 
 
 0.6621 
 
 4 
 
 3.9126 
 
 0.8316 
 
 3.9089 
 
 0.8487 
 
 3.9052 
 
 0.8657 
 
 3.9014 
 
 0.8828 
 
 5 
 
 4.S907 
 
 L0396 
 
 4.8861 
 
 L0609 
 
 4.8815 
 
 1.0822 
 
 4.8767 
 
 L1035 
 
 6 
 
 5.8689 
 
 1.2475 
 
 5.8634 
 
 1.2730 
 
 5.8578 
 
 1.2986 
 
 5.8520 
 
 1.3242 
 
 7 
 
 6.8470 
 
 1.4554 
 
 6.8406 
 
 1.4852 
 
 6.8341 
 
 1.5151 
 
 6.8274 
 
 1.5449 
 
 8 
 
 7.8252 
 
 1.6633 
 
 7.8178 
 
 1.6974 
 
 7.8104 
 
 1.7315 
 
 7.8027 
 
 1.7656 
 
 9 
 
 1 
 
 8.8033 
 
 1.8712 
 
 8.7951 
 13i 
 
 1.9096 
 
 8.7867 
 
 1.9479 
 
 8.7781 
 
 1.9863 
 
 76i 
 
 0.2377 
 
 13° 
 
 77° 
 
 76i 
 0.2292 
 
 0.9724 
 
 76i 
 
 13i 
 0.9713 
 
 0.9744 
 
 O.2249I 
 
 0.9734 
 
 0.2334 
 
 2 
 
 1.9487 
 
 0.4499 
 
 L9467 
 
 0.4584 
 
 1.9447 
 
 0.4669 
 
 1.9427 
 
 0.4754 
 
 3 
 
 2.9231 
 
 0.6749 
 
 2.9201 
 
 0.6876 
 
 2.9171 
 
 0.7003 
 
 2.9140 
 
 0.7131 
 
 4 
 
 3.8975 
 
 0.8998 
 
 3.8934 
 
 C.9168 
 
 3.8895 
 
 0.9338 
 
 3.8854 
 
 0.9507 
 
 5 
 
 4.8718 
 
 1.1248 
 
 4.8669 
 
 1.1460 
 
 4.8619 
 
 1.1672 
 
 4.8567 
 
 L1884 
 
 6 
 
 5.8462 
 
 1.34971 
 
 5.8403 
 
 1.3752 
 
 5.8343 
 
 1.4007 
 
 5.8280 
 
 1.4261 
 
 7 
 
 6.8206 
 
 1.5746! 
 
 6.8136 
 
 1.6044 
 
 6.8067 
 
 1.6341 
 
 6.7994 
 
 1.6638 
 
 8 
 
 7.7950 
 
 1.7996 
 
 7.7870 
 
 L8336 
 
 7.7790 
 
 1.8676 
 
 7.7707 
 
 1.9015 
 
 9 
 1 
 
 8.7693 
 
 2.0246 
 
 8.7604 
 
 2.0628 
 
 75f 
 0.2461 
 
 8.7515 
 
 2.1010 
 
 8.7421 
 
 141 
 0.9670 
 
 2.1392 
 
 75i 
 0.2546 
 
 14° 
 
 76° 
 
 14i 
 0.9692 
 
 m 
 
 75i 
 
 0.9703 
 
 0.2419 
 
 0.9681 
 
 0.2504 
 
 2 
 
 1.9406 
 
 0.4838 
 
 ,1.9385 
 
 0.4923 
 
 L9363 
 
 0.5008 
 
 1.9341 
 
 0.5092 
 
 3 
 
 2.9109 
 
 0.7258 
 
 2.9077 
 
 0.7385 
 
 2.9044 
 
 0.7511 
 
 2.9011 
 
 0.7638 
 
 4 
 
 3.8812 
 
 0.9677 
 
 3.8769 
 
 0.9846 
 
 3.872711.0015 
 
 3.8682 
 
 1.1084 
 
 5 
 
 4.8515 
 
 1.2096 
 
 4.8461 
 
 1.2308 
 
 4.8407|l.2519 
 
 4.8352 
 
 1.2730 
 
 fi 
 
 .').8218 
 
 1.4515 
 
 5.815411.4769 
 
 5.8089 1.5023 
 
 5.8023 
 
 1.5276 
 
 7 
 
 6.7921 
 
 1.6935 
 
 6.7846 
 
 1.7231 
 
 6.7770IL7527 
 
 6.7693 
 
 1.7822 
 
 S 
 
 7.7624 
 
 1.9354 
 
 7.7538 
 
 1.9692 
 
 7.7452 
 
 2.0030 
 
 7.7364 
 
 2.0368 
 
 9 
 
 1 
 
 8.7327 
 
 2.1773 
 
 75 
 0.'25S8 
 
 8.7231 
 
 2.2154 
 T4i" 
 
 8.7133 
 
 2.2534 
 
 8.7034 
 
 2.2914 
 
 15 
 0.9659 
 
 15i 
 
 15,} 
 
 74i 
 0.2672 
 
 15i 
 0.9624 
 
 741 
 0.2714 
 
 0.9648 
 
 0.2630 
 
 0.9636 
 
 ?. 
 
 1.9319 
 
 0.5176 
 
 1.9296 
 
 0.5261 
 
 1.9273 
 
 0.5345 
 
 1.9249 
 
 0.5429 
 
 3 
 
 2.8978 
 
 0.7765 
 
 2.8944 
 
 0.7891 
 
 2.8909 
 
 0.8017 
 
 2.8874 
 
 0.8143 
 
 4 
 
 3.8637 
 
 1.0353 
 
 3.8591 
 
 1.0521 
 
 3.8545 
 
 1.0689 
 
 3.8498 
 
 1.0858 I 
 
 ft 
 
 4.8296 
 
 1.2941 
 
 4.8239 
 
 1.3152 
 
 4.8182 
 
 L3362 
 
 4.8123 
 
 1.3572 1 
 
 6 
 
 5.7956 
 
 1.5529 
 
 5.7887 
 
 1.5782 
 
 5.7818 
 
 1.6034 
 
 5.7747 
 
 1.6286 
 
 7 
 
 6.7615 
 
 1.8117 
 
 6.7535 
 
 1.8412 
 
 6.7454 
 
 1.8707 
 
 6.7372'l.9001 
 
 
 7.7274 
 
 2.0706 
 
 7.7183 
 
 2.1042 
 
 7.7090 
 
 2.1379 
 
 7.6996 2.1715 
 
 9 
 
 8.6933 
 E.W. 
 
 2.3294 
 
 N. S. 
 
 8.6831 
 
 bTw: 
 
 2.3673 
 
 8.6727 
 E. W. 
 
 2.4051 
 
 8.6621 2.4430 
 
 N.S.I 
 
 N. S. 1 
 
 E. W. 
 
 N. S. !l 
 
112 
 
 The Surveyor's Guide. 
 
 TABLES OP LATITUDE AND DEPARTURE 
 
 
 1 
 
 N.S. 
 16° 
 
 E.W. 
 
 N.S. 
 
 E.W. 
 
 N.S. 
 16} 
 
 E.W. 
 
 N.S. 
 
 E.W. 
 
 73i 
 
 74 
 0.2756 
 
 16i 
 
 731 
 0.2798 
 
 73i 
 0.2840 
 
 16S 
 0.9575 
 
 0.9612 
 
 0.9600 
 
 0.9588 
 
 0.2882 
 
 2 
 
 L9225 
 
 0.5513 
 
 1.9201 
 
 ).5596 
 
 1.9176 
 
 0.5680 
 
 1.9151 
 
 ).5764 
 
 3 
 
 2.8838 
 
 0.8269 
 
 2.8801 
 
 0.8395 
 
 2.8765 
 
 0.8520 
 
 2.8727 
 
 0.8646 
 
 4 
 
 3.8450 
 
 L1025 
 
 3.8402 
 
 1.1193 
 
 3.8353 
 
 1.1361 
 
 3.8303 
 
 1.1528 
 
 5 
 
 4.8063 
 
 L3782 
 
 4.8002 
 
 L3991 
 
 4.7941 
 
 1.4201 
 
 4.7878 
 
 1.4410 
 
 6 
 
 5.7676 
 
 1.6538 
 
 5.7603 
 
 1.6790 
 
 5.7529 
 
 1.7041 
 
 5.7454 
 
 1.7292 
 
 7 
 
 6.7288 
 
 1.9295 
 
 6.7203 
 
 1.9588 
 
 6.7117 
 
 1.9881 
 
 6.7030 
 
 2.0174 
 
 8 
 
 7.6901 
 
 2.2051 
 
 7.6804 
 
 2.2386 
 
 7.6705 
 
 2.2721 
 
 7.6606 
 
 2.3056 
 
 9 
 1 
 
 8.6513 
 
 2.4807 
 
 8.6404 
 
 2.5186 
 
 8.6294 
 
 2.5661 
 
 m 
 
 0.3007 
 
 8.6181 
 
 m 
 
 0.9523 
 
 2.5938 
 
 17 
 0.9563 
 
 73 
 
 17i 
 
 721 
 0.2905 
 
 17i 
 0.9537 
 
 72i 
 0.3048 
 
 0.2924 
 
 0.9550 
 
 ?. 
 
 1.9126 
 
 0.5847 
 
 1.9100 
 
 0.5931 
 
 1.9074 
 
 0.6014 
 
 1.9048 
 
 0.6097 
 
 
 2.8689 
 
 0.8771 
 
 2.8651 
 
 0.8896 
 
 2.8611 
 
 0.9021 
 
 2.8672 
 
 0.9146 1 
 
 4 
 
 3.8252 
 
 1.1695 
 
 3.8201 
 
 1.1862 
 
 3.8149 
 
 1.2028 
 
 3.8096 
 
 1.2195 1 
 
 fi 
 
 4.7815 
 
 1.4619 
 
 4.7751 
 
 1.4827 
 
 4.7686 
 
 1.6035 
 
 4.7620 
 
 1.6243 i 
 
 fi 
 
 5.7378 
 
 1.7642 
 
 5.7301 
 
 1.7792 
 
 5.7223 
 
 1.8042 
 
 5.7144 
 
 1.8292 1 
 
 7 
 
 6.6941 
 
 2.0466 
 
 6.6851 
 
 2.0758 
 
 6.6760 
 
 2.1049 
 
 6.6668 
 
 2.1340 
 
 8 
 
 7.6504 
 
 2.3390 
 
 7.6402 
 
 2.3723 
 
 7.6297 
 
 2.4056 
 
 7.6192 
 
 2.4389 
 
 9 
 1 
 
 8.6067 
 
 2.6313 
 
 8.5952 
 
 18i 
 0.9497 
 
 2.6689 
 
 8.6834 
 
 2.7063 
 
 8.6716 
 
 2.7438 
 
 18° 
 
 72 
 0.3090 
 
 711 
 0.3131 
 
 18J 
 0.9483 
 
 71i 
 
 18i 
 0.9469 
 
 7U 
 
 0.9510 
 
 0.3173 
 
 0.3214 1 
 
 ? 
 
 L9021 
 
 0.6180 
 
 1.8994 
 
 0.6263 
 
 1.8966 
 
 0.6346 
 
 1.8939,0.6429 || 
 
 3 
 
 2.8532 
 
 0.9271 
 
 2.8491 
 
 0.9395 
 
 2.8460 
 
 0.9619 
 
 2.8408 
 
 0.96-13 
 
 4 
 
 3.8042 
 
 1.2361 
 
 3.7988 
 
 1.2527 
 
 3.7933 
 
 1.2692 
 
 3.7877 
 
 1.2857 
 
 ft 
 
 4.7553 
 
 1.5451 
 
 4.7485 
 
 L6658 
 
 4.7416 
 
 1.5865 
 
 4.7346 
 
 1.6072 
 
 fi 
 
 5.7063 
 
 1.8541 
 
 5.6982 
 
 1.8790 
 
 5.6899 
 
 L9038 
 
 6.6816 
 
 1.9286 
 
 7 
 
 6.6574 
 
 2.1631 
 
 6.6479 
 
 2.1921 
 
 6.6383 
 
 2.2211 
 
 6.6285 
 
 2.2501 
 
 8 
 
 7.6084 
 
 2.4721 
 
 7.6976 
 
 2.5053 
 
 7.6866 
 
 2.5384 
 
 7.6764 
 
 2.6716 
 
 9 
 1 
 
 8.5595 
 
 2.7812 
 
 71° 
 0.3255 
 
 8.5473 
 
 2.8185 
 
 7oa 
 
 0.3297 
 
 8.6349 
 
 2.8567 
 
 8.6224 
 
 2.8929 
 .70i 
 0.3379 
 
 19° 
 0.9455 
 
 19i 
 
 70i 
 073338 
 
 19i 
 0.9412 
 
 0.9441 
 
 0.9426 
 
 9 
 
 1.8910 
 
 0.6511 
 
 1.8882 
 
 0.6594 
 
 1.8853 
 
 0.6676 
 
 1.8823 
 
 0.6768 
 
 3 
 
 2.8366 
 
 0.9767 
 
 2.8323 
 
 0.9891 
 
 2.8279 
 
 1.0014 
 
 2.8233 
 
 1.0137 
 
 4 
 
 3.7821 
 
 1.3023 
 
 3.7764 
 
 1.3188 
 
 3.7706 
 
 1.3362 
 
 3.7647 
 
 1.3517 
 
 ^ 
 
 4.7276 
 
 1.6278 
 
 4.7204 
 
 1.6484 
 
 4.7132 
 
 1.6690 
 
 4.7069 
 
 1.6896 
 
 5.6731 
 
 1.9534 
 
 5.6645 
 
 1.9781 
 
 5.6568 
 
 2.0028 
 
 5.6471 
 
 2.0275 
 
 7 
 
 6.6186 
 
 2.2790 
 
 6.6086 
 
 2.3078 
 
 6.6985 
 
 2.3366 
 
 6.5882 
 
 2.3654 
 
 8 
 
 7.5641 
 
 2.6045 
 
 7.5527 
 
 2.6375 
 
 7.6411 
 
 2.6705 
 
 7.5294 
 
 2.7033 
 
 9 
 
 8.5097 
 
 eTw: 
 
 2.9301 
 N.S. 
 
 8.4968 
 E.W. 
 
 2.9672 
 
 N.S. 
 
 8.4838 
 
 3.0043 
 
 N.S. 
 
 8.4706 
 E.W. 
 
 3.0412 
 
 E.W. 
 
 N.S. 
 
The Surveyor's Guide. 
 
 113 
 
 tables oe latitude and departure. I 
 
 
 1 
 
 N. S. 
 20 
 
 E.W. 
 
 70 
 
 N. S. 1 
 "201" 
 0.9382 
 
 E.W. 
 
 N. S. 
 
 e. w. 
 
 69 i 
 0.3502 
 
 N. S. 
 
 E.W. 
 
 69i 
 0.3543 
 
 
 69S 
 
 20i 
 
 201 
 
 
 0.9397 
 
 0.3420 
 
 0.3461 
 
 0.9366 
 
 0.9351 
 
 
 t 
 
 1.8794 
 
 0.6840 
 
 1.8764 
 
 0.6922 
 
 1.8733 
 
 0.7004 
 
 1.8703 
 
 0.7086 
 
 
 •6 
 
 2.8191 1.0261] 
 
 2.8146 
 
 1.0383 
 
 2.8100 
 
 1.0606 
 
 2.8054 
 
 1.0629 
 
 
 4 
 
 3.7588 1.36811 
 
 3.7528 
 
 1.3845 
 
 3.7467 
 
 1.4008 
 
 3.7405 
 
 1.4172 
 
 
 6 
 
 4.6985 
 
 1.7101 
 
 4.6910 
 
 1.7306 
 
 4.6834 
 
 1.7510 
 
 4.6757 
 
 1.7715 
 
 
 6 
 
 5.6381 
 
 2.0521 
 
 5.6291 
 
 2.0767 
 
 6.6200 
 
 2.1012 
 
 5.6108 
 
 2.1267 
 
 
 7 
 
 6.5778 
 
 2.3941 
 
 6.5673 
 
 2.4228 
 
 6.6567 
 
 2.4614 
 
 6.5459 
 
 2.4800 
 
 
 8 
 
 7.5175 
 
 2.7362 
 
 7.5055 
 
 2.7689 
 
 7.4934 
 
 2.8016 
 
 7.4811 
 
 2.8343 
 
 
 9 
 1 
 
 8.4572 
 
 3.0782 
 
 8.4437 
 
 3.1160 
 
 8.4300 
 
 3.1519 
 
 8.4162 
 
 3.1886 
 68i 
 
 
 21° 
 
 69° 
 
 21i 
 
 68i 
 0.3624 
 
 2U 
 
 68i 
 
 211 
 
 
 0.9336 
 
 0.3583 
 
 0.9320 
 
 0.9304 
 
 0.3665 
 
 0.9288 
 
 0.3705 
 
 
 2 
 
 1.8672 
 
 0.7167 
 
 1.8640 
 
 0.7249 
 
 1.8608 
 
 0.7330 
 
 1.857610.7411 1 
 
 
 3 
 
 2.8008 
 
 L0751 
 
 2.7960 
 
 1.0873 
 
 2.7913 
 
 1.0995 
 
 2.7864 1.1117 
 
 
 4 
 
 3.7343 
 
 1.4335 
 
 3.7280 
 
 1.4497 
 
 3.7217 
 
 1.4660 
 
 3.7162 1.4822 
 
 
 5 
 
 4.6679 
 
 L7918 
 
 4.6600 
 
 1.8122 
 
 4.6521 
 
 1.8325 
 
 4.6440 1.8528 
 
 
 6 
 
 5.6015 
 
 2.1502 
 
 15.5920 
 
 2.1746 
 
 5.5825 
 
 2.1990 
 
 6.6729 2.2233 
 
 
 7 
 
 6.5351 
 
 2.5086 
 
 6.5240 
 
 2.5371 
 
 6.5129 
 
 2.6665 
 
 6.5017 2.5939 
 
 
 8 
 
 7.4686 
 
 2.8669 
 
 7.4560 
 
 2.8995 
 
 7.4433 
 
 2.9320 
 
 7.4305 2.9644 
 
 
 9 
 
 1 
 
 8.4022 
 
 3.2253 
 
 8.3880 
 
 3.2619 
 
 8.3738 
 
 3.2985 
 
 67i 
 
 0.3827 
 
 8.3593 
 
 3.3360 
 
 
 22° 
 
 68° 
 
 22i 
 
 67i 
 
 22J 
 
 22i 
 
 67i 
 
 
 0.9272 
 
 0.3746 
 
 0.9255 
 
 0.3786 
 
 0.9239 
 
 0.9222 
 
 0.3867 
 
 
 2 
 
 1.8544 
 
 0.7492 
 
 1.8511 
 
 0.7673 
 
 1.8478 
 
 0.7654 
 
 1.844410.7734 
 
 
 3 
 
 2.7816 
 
 L1238 
 
 2.7766 
 
 1.1359 
 
 2.7716 
 
 1.1480 
 
 2.7666 
 
 1.1601 
 
 
 ' 4 
 
 3.70S7 
 
 1.4984 
 
 3.7022 
 
 1.5146 
 
 3.6956 
 
 L5307 
 
 3.6888 
 
 1.5468 
 
 
 fi 
 
 4.6359 
 
 1.8730 
 
 4.6277 
 
 1.8932 
 
 4.6194 
 
 1.9134 
 
 4.6110 
 
 1.9335 
 
 
 6 
 
 5.5631 
 
 2.2476 
 
 5.5532 
 
 2.2719 
 
 6.5433 
 
 2.2961 
 
 5.6332 
 
 2.3202 
 
 1 
 
 7 
 
 6.4903 
 
 2.6222 
 
 6.4788 
 
 2.6505 
 
 6.4671 
 
 2.6788 
 
 6.4564 
 
 2.7069 
 
 
 i 8 
 
 7.4175 
 
 2.9968 
 
 7.4043 
 
 3.0292 
 
 7.3910 
 
 3.0615 
 
 7.3776 
 
 3.0936 
 
 
 1 ' 
 
 i 1 
 
 8.3447 
 23 
 
 3.3715 
 
 8.3299 
 
 3.4078 
 
 8.3149 
 
 3.4441 
 
 8.2998 
 
 3.4803 
 
 66i 
 
 (L4027 
 
 
 67 
 
 23i 
 
 66S 
 
 23i 
 
 66i 
 0.3987 
 
 23i 
 
 
 0.9205 
 
 0.3907 
 
 0.9188 
 
 0.3947 
 
 0.9170 
 
 10.9163 
 
 
 . 5> 
 
 1.8410 
 
 0.7815 
 
 1.8376 
 
 0.7895 
 
 1.8341 
 
 0.7976 
 
 |l.8306 
 
 0.8055 
 
 
 
 2.7615 
 
 1.1722 
 
 2.7564 
 
 1.1842 
 
 2.7612 
 
 L1962 
 
 2.7469 
 
 1.2082 
 
 
 4 
 
 3.6820 
 
 1.5629 
 
 3.6762 
 
 1.5790 
 
 3.6682 
 
 L6960 
 
 3.6612 
 
 1.6110 
 
 
 5 
 
 4.6025 1.9537 
 
 4.5939 
 
 1.9737 
 
 4.5853 
 
 11.9937 
 
 4.5766 
 
 0.0137 
 
 
 fi 
 
 5.5230 2.3444 
 
 5.5127 
 
 2.3685 
 
 6.6024 
 
 2.3925 
 
 5.4919 
 
 2.4165*! 1 
 
 7 
 
 6.4435 2.7351 
 
 6.4315 
 
 2.7632 
 
 6.4194 
 
 2.7912 
 
 6.4072 
 
 2.8192 \ 
 
 S 
 
 7.3640 3.1258 
 
 7.3603 
 
 3.1579 
 
 7.3365 
 
 3.1900 
 
 7.2226 
 
 3.2220 
 
 
 9 
 
 i 
 
 8.2845|3.5166 
 
 8.2691 
 
 'e.'w 
 
 3.6527 
 
 8.2636 
 
 3.5887 
 N. S. 
 
 8.2378 
 
 3.6247 
 N. S. 
 
 
 e. W 
 
 IN.S. 
 
 N. S. 
 
 E.W 
 
 E.W 
 
 J 
 
114 
 
 The Surveyor's Guide. 
 
 TABLES OF LATITUDE AND DEPARTURE. jl 
 
 1 
 
 1 
 
 N. S. 
 
 E.W. 
 
 N. S. 
 
 E. W. 
 651 
 0.4107 
 
 N. S. E. W.| 
 
 N. S. 
 
 E. W. 
 '"651" 
 0.4186 
 
 24 
 0.9135 
 
 66 
 
 24i 
 
 24i 
 
 65i 
 
 24i 
 
 0.4067 
 
 0.9117 
 
 0.9099 0.4147 
 
 0.9081 
 
 ?. 
 
 1.8271 
 
 0.8135 
 
 1.8235 
 
 0.8214 
 
 1.8199 0.8294 
 
 1.8163 
 
 0.8373 
 
 8 
 
 2.7406 
 
 1.2202 
 
 2.7353 
 
 1.2322 
 
 2.7299 1.2441 
 
 2.7244 
 
 L2560 
 
 4 
 
 3.6542 
 
 1.6269 
 
 3.6470 
 
 1.6429 
 
 3.6398 1.6588| 
 
 3.6326 
 
 1.6746 
 
 ft 
 
 4.5677 
 
 2.0337 
 
 4.5588 
 
 2.0536 
 
 4.5498 
 
 2.0735 
 
 4.5407 
 
 2.0933 1 
 
 6 
 
 5.4813 
 
 2.4404 
 
 5.4706 
 
 2.4643 
 
 5.4598 
 
 2.4882 
 
 5.4489 
 
 2.5122 
 
 7 
 
 6.3948 
 
 2.8472 
 
 6.3823 
 
 2.8750 
 
 6.3697 
 
 2.9029 
 
 6.3570 
 
 2.9306 
 
 1 ^ 
 
 7.3084 
 
 3.2539 
 
 7.2941 
 
 3.2857' 
 
 7.2797 
 
 3.3175 
 
 7.2651 
 
 3.3493 
 
 9 
 1 
 
 8.2219 
 
 3.6606 
 
 8.2058 
 
 3.6965 
 
 8.1896 
 
 3.7322 
 
 8.1733 
 
 3.7679 
 
 64i 1 
 0.4344 
 
 25° 
 
 65 
 
 25i 
 
 64i 
 
 25i 
 
 64i 
 
 25i 
 0.9007 
 
 0.9063 
 
 0.4226 
 
 0.9044 
 
 0.4265 
 
 0.9026 
 
 0.4305 
 
 
 1 8126 
 
 0.8452 
 
 |L8089 
 
 0.85311 
 
 1.8052 
 
 0.8610 
 
 1.8014 
 
 0.8688 
 
 3 
 
 2.7189 
 
 1.2679 
 
 2.7134 
 
 1.2797 
 
 2.7077 
 
 1.2915 
 
 2.7021 
 
 1.3032 
 
 4 
 
 3.6252 
 
 1.6905 
 
 3.6178 
 
 L7063 
 
 3.6103 
 
 1.7220 
 
 3.6028 
 
 1.7376 
 
 ft 
 
 4.5315 
 
 2.1131 
 
 4.5223 
 
 2.1328 
 
 4.5129 
 
 2.1525 
 
 4.5035 
 
 2.1720 
 
 fi 
 
 5.4378 
 
 2.5357 
 
 15.4267 
 
 2.5594 
 
 5.4155 
 
 2.5831 
 
 15.4042 
 
 2.6064 
 
 7 
 
 6.3442 
 
 2.9583 
 
 6.3312 
 
 2.9860 
 
 16.3181 
 
 3.0136 
 
 6.3049 
 
 3.0408 
 
 S 
 
 7.2505 
 
 3.3809 
 
 7.2356 
 
 3.4125 
 
 17.2207 
 
 3.4441 
 
 7.2056 
 
 3.4752 
 
 9 
 1 
 
 8.1568 
 
 .3.8036 
 
 8.1401 
 
 3.839] 
 
 8.1233 
 0.8949 
 
 3.8746 
 
 8.1063 
 
 3.9096 
 
 63i 
 0.4501 
 
 26° 
 
 64° 
 
 26i 
 
 634 
 0.4423 
 
 63i 
 
 26.! 
 0.8930 
 
 0.8988 
 
 0.4384 
 
 0.8969 
 
 0.4462 
 
 
 1.7976 
 
 0.8767 
 
 [1.7937 
 
 0.8846 
 
 !1.7899 
 
 0.8924 
 
 1.7859 
 
 0.9002 
 
 1 S 
 
 2.6964 
 
 1.3151 
 
 2.6906 
 
 1.3269 
 
 |2.6848 
 
 1.3386 
 
 2.6789 
 
 1.3503 
 
 4 
 
 3.5952 
 
 1.7535 
 
 13.5875 
 
 L7692 
 
 13.5797 
 
 1.7848 
 
 3.5719 
 
 1.8004 
 
 ft 
 
 4.4940 
 
 2.1919 
 
 14.4843 
 
 2.2115 
 
 4.4746 
 
 2.2310 
 
 4.4649 
 
 2.2505 
 
 6 
 
 5.3928 
 
 2.6302 
 
 15.3812 
 
 2.6537 
 
 5.3696 
 
 2 6772 
 
 5.3579 
 
 2.7006 
 
 7 
 
 6.2916 
 
 3.0686 
 
 .6.2781 
 
 3.0960 
 
 6.2645 
 
 3.1234 
 
 6.2508 
 
 3.1507 
 
 8 
 
 7.1904 
 
 3.5070 i7.1750 
 
 3.5383 
 
 7.1594 
 
 3.5606 
 
 7.1438 
 
 3.6008 
 
 9 
 1 
 
 8.0891 
 
 3.9453 
 
 _6_3_ 
 
 0.4540 
 
 18.0718 
 
 I'm' 
 
 ' 0.8890 
 
 3.9806 
 0.4578 
 
 8.0544 
 
 4.0158 
 
 8.0368 
 
 4.0509 
 
 27i 
 
 62i- 
 0.4617 
 
 271 
 0.8850 
 
 62i 
 0.4056 
 
 0.8910 
 
 0.8870 
 
 ? 
 
 1 7820 
 
 0.9080 
 
 '1.7780 
 
 0.9157 
 
 1.7740 
 
 0.9235 
 
 1.7700 
 
 0.9312 
 
 3 
 
 2.0730 
 
 1.3620 
 
 2.6670 
 
 1.3736 
 
 ,2.6610 
 
 ,L3852 
 
 2.6550 1.3968 \ 
 
 ^ 4 
 
 3.5640 
 
 L8160 
 
 3.5561 
 
 1.8315 
 
 3.5480 
 
 L8470 
 
 3.5400 
 
 1.8624 1 
 
 1 '"^ 
 
 4.4550 2.2699 
 
 4.4451 
 
 2.2894 
 
 4.4350 
 
 2.3087 
 
 4.4250 
 
 2.3281 
 
 1 fi 
 
 5.3460 
 
 2.7239 
 
 5.3341 
 
 2.7472 
 
 5.3221 
 
 2.7705 
 
 5.3099 
 
 2.7937 
 
 1 7 
 
 6.2370 
 
 3.1779 
 
 6.2231 
 
 3.2051 
 
 6.2092 
 
 3.2322 
 
 6.1949 
 
 3.2593 
 
 8 
 
 7.1280 
 
 .3.6319 
 
 7.1121 
 
 3.6030 
 
 7.0961 
 
 3.6940 
 
 7.0799 
 
 3.7249 
 
 9 
 
 8.0191 
 E.W. 
 
 4.0859 
 N. S. 
 
 8.0011 
 1 E.W. 
 
 4.1209 
 N. S. 
 
 7.9S31 
 
 4.1553 
 
 N. S.- 
 
 7.9049 
 
 !e. W. 
 
 4.1905 
 
 'n. S. 
 
 E.W. 
 
The Surveyor's Gqide. 
 
 115 
 
 
 TABLES OP LATITUDE 
 
 AND 
 
 DEPARTURE 
 
 
 1 
 
 N. S. 
 
 28 
 0.8829 
 
 E. W. 
 
 62 
 0.4694 
 
 N. S. 
 28i 
 
 E. AV.i 
 
 611 
 0.4733 
 
 N. S. 
 
 E.W. 
 
 N. S. 
 
 2SJ 
 
 0.8766 
 
 E.W. 
 
 28,^ 
 
 6U 
 
 61i 
 
 0.8809 
 
 0.8788 
 
 0.4771 
 
 0.4810 
 
 2 
 
 L7659 
 
 0.9389 
 
 L7618 
 
 0.9466 
 
 1.7576 
 
 0.9543 
 
 L7534 
 
 0.9620 
 
 3 
 
 2.64S8 
 
 1.4084 
 
 2.6427 
 
 1.4199 
 
 2.6364 
 
 1.4315 
 
 2.6302 
 
 1.4430 
 
 4 
 
 3.5318 L8779! 
 
 3.5236 
 
 L8933 
 
 3.5153 
 
 1.90S6 
 
 3.5069 
 
 1.9239 
 
 5 
 
 4.4147 
 
 2.3474 
 
 4.4045 
 
 3.3666 
 
 4.3941 
 
 2.3858 
 
 4.3836 
 
 2.4049 
 
 fi 
 
 5.2977 
 
 2.8168 
 
 5.2854 
 
 2.8399 
 
 5.2729 
 
 2.8629 
 
 5.2604 
 
 2.8859 
 
 7 
 
 6.1806 
 
 3.2863 
 
 6.1662 
 
 3.3132 
 
 6.1517 
 
 3.3401 
 
 6.1371|.3.3669 
 
 8 
 
 7.0636 
 
 3.7558 
 
 7.0471 3.78661 
 
 7.0305 
 
 3.8173 
 
 7.013S 3.8479 
 
 9 
 
 1 
 
 7.9465 
 
 4.2252 
 
 7.9280 4.2599 
 29J 1 60i 
 
 7.9093 
 
 4.2944 
 60i 
 
 7.8905 
 
 29i 
 
 0.8682 
 
 4.3289 
 
 29 
 
 61 
 0.4848 
 
 29i 
 0.8703 
 
 60i 
 
 0.8746 
 
 :0.S725 
 
 0.4SS6 
 
 0.4924 
 
 0.4962 
 
 2 
 
 L7492 0.9696] 
 
 ,L7450 
 
 0.9772 
 
 1.7407 
 
 0.9848 
 
 1.7364 
 
 0.9924 
 
 3 
 
 2 6239 
 
 1.45441 
 
 ,2.6175 
 
 1.4659 
 
 2.6111 
 
 1.4773 
 
 2.6046 
 
 1.4886 
 
 4 
 
 3.4985 
 
 1.9392 
 
 3.4900 
 
 1.9545 
 
 3.4814 
 
 1.9697 
 
 3.4728 
 
 1.9849 
 
 5 
 
 4.3731 
 
 2.4240 
 
 4.3625 
 
 2.443 ll 
 
 4.3518 
 
 2.4621 
 
 4.3410 
 
 2.481] 
 
 fi 
 
 5.2477 
 
 2.9089 
 
 '5.2350 
 
 2.93171 
 
 5.2221 
 
 2.9545 
 
 5.2092 
 
 2.9773 
 
 7 
 
 6.1223 
 
 3.3937 
 
 (6.1075 
 
 3.4203 
 
 6.0925 
 
 3.4463 
 
 6.0774 
 
 3.4735 
 
 S 
 
 6.997013.8785 
 
 6.9S00 
 
 3.9090i 
 
 6.9628 
 
 3.9394 
 
 7.9456 
 
 3.9697 
 
 9 
 
 1 
 
 7.8716J4.3633 
 
 7.8525 
 
 30i 
 0.8638 
 
 4.3976 
 , 59i 
 i0.5038 
 
 7.8332 
 
 30i- 
 
 0.8616 
 
 4.4318 
 
 7.8138 
 30i 
 
 4.4669 
 
 30 
 
 60 
 0.5000 
 
 59i 
 0.5075 
 
 59i 
 
 0.S660 
 
 0.8594 
 
 0.5113 
 
 *? 
 
 I.7320I1.OOOO 
 
 L7277 
 
 !l.0076 
 
 1.7232 
 
 1.0151 
 
 L7188IL0226 
 
 8 
 
 2.59S1 
 
 1.5000 
 
 2.5915 
 
 1.5113 
 
 2.5849 
 
 1.5226 
 
 2.57S2;L5339 
 
 4 
 
 3.4041 
 
 2.2000 
 
 3.4552 
 
 2.0151 
 
 3.4465 
 
 2.0301 
 
 3.4376 
 
 2.0452 
 
 ,T 
 
 4.3301 
 
 2.5000 
 
 4.3192 
 
 2.5189 
 
 4.3081 
 
 2.5377 
 
 4.2970 
 
 2.5564 
 
 fi 
 
 5.1961 
 
 3.3000 
 
 5.1830 
 
 3.0226 
 
 5.1698 
 
 3.0452 
 
 5.1564 
 
 3.0677 
 
 7 
 
 6.0622 
 
 3.5000 
 
 6.0468 
 
 !3.5264 
 
 16.0314 
 
 3.5528 
 
 6.0158 
 
 3.5790 
 
 
 6.92S2 
 
 4.0000 
 
 6.9107 
 
 4.0302 
 
 6.8930 
 
 4.0603 
 
 6.8752 
 
 14.0903 
 
 9 
 1 
 
 7.7942 
 
 4.5000 
 
 59 
 0.5150 
 
 7.7745 
 
 31i 
 
 0.8549 
 
 4.5339 
 0.5188 
 
 :7.7547 
 
 4.5678 
 
 7.7346 
 
 31i 
 
 0.8503 
 
 4.6016 
 
 1-^ 
 0.8571 
 
 31i 
 
 68i 
 0.5225 
 
 58i 
 
 0.8526 
 
 0.5262 
 
 '>. 
 
 1.7143 
 
 L0301 
 
 1.709S 
 
 1.0375 
 
 L7053 
 
 L0450 
 
 1.7007 
 
 1.0524 
 
 q 
 
 2.5715 
 
 1.5451 
 
 2.5647 
 
 1.5563 
 
 2.5579 
 
 1.5675 
 
 2.5510iL5786 
 
 /| 
 
 13.4287 
 
 2.0602 
 
 3.4196 2.0751 
 
 3.4106 
 
 2.0900 
 
 3.4014 2.1048 
 
 5 
 
 14.2858 
 
 2.5752 
 
 4.2745 2.5939 
 
 4.2632 
 
 2.6125 
 
 4.251S 
 
 2.6311 
 
 fi 
 
 5.1430 
 
 3.0902 
 
 5.1295:3.1126 
 
 5.1158 
 
 3.1350 
 
 5.1021 
 
 3.1573 
 
 
 16.0002 
 
 3.6053 
 
 5.98443.6314 
 
 5.9685 
 
 3.6575 
 
 5.9525 
 
 3.6835 
 
 8 
 
 6.8573 
 
 4.1203 
 
 16.8393 4.1502 
 
 6.8211 
 
 4.1800 
 
 6.8028 
 
 4.2097 
 
 9 
 
 7.7145 
 
 4.6353 
 
 7.694214.0689 
 
 7.6738 
 
 4.7025 
 
 7.6532 
 
 4.7359 
 
 
 E. W 
 
 N. S. 
 
 E.W 
 
 1 N. S. 
 
 E.W. 
 
 1 N.S. 
 
 E.W 
 
 1 N.S. 
 
116 
 
 The Surveyors Guide. 
 
 
 TABLES OF LATITUDE AND 
 
 DEPARTURE 
 
 
 
 1 
 
 N. S. 
 
 E.W. 
 58° 
 
 N. S. 
 
 E.\Y. 
 
 N. S. 
 
 E.W. 
 
 57i 
 
 0.5373 
 
 N. S. 
 
 32i 
 
 0.8410 
 
 E.W. 
 "67i" 
 0.6409 
 
 
 32° 
 0.8480 
 
 32i 
 0.8457 
 
 57S 
 
 32i 
 0.8434 
 
 
 0.5299 
 
 0.6336 
 
 
 2 
 
 1.6961 
 
 1.0598 
 
 L6914 
 
 1.0672 
 
 1.6868 
 
 1.0746 
 
 L6821 
 
 1.0819 
 
 
 •6 
 
 2.5441 
 
 L5897 
 
 2.5372 
 
 1.6008 
 
 2.6302 
 
 1.6119 
 
 2.5231 
 
 L6229 
 
 
 4 
 
 3.3922 
 
 2.1197 
 
 3.3829 2.1344 
 
 3.3736 
 
 2.1492 
 
 3.3642 
 
 2.1639 
 
 
 5 
 
 4.2402 
 
 2.6496 
 
 4.2286 2.6681 
 
 4.2169 
 
 2.6865 
 
 4.2052 
 
 2.7049. 
 
 
 6 
 
 5.0883 
 
 3.1795 
 
 5.0744 
 
 3.2017 
 
 5.0603 
 
 3.2238 
 
 5.0462 
 
 3.2458' 
 
 
 1 
 
 5.9363 
 
 3.7094 
 
 5.9201 
 
 3.7353 
 
 5.9037 
 
 3.7611 i 
 
 5.8873 
 
 3.7868 
 
 
 8- 
 
 6.7844 
 
 4.2394 
 
 6.7658 
 
 4.2689 
 
 6.7471 
 
 4.29841 
 
 6.7283 
 
 4.3278 
 
 
 9 
 1 
 
 7.6324 
 
 4.7693 
 
 7.6115 
 
 4.8026 
 56S 
 
 7.5905 
 
 4.8357 
 
 7.5694 
 33i 
 
 4.8688 
 '"56i 
 0.5566 
 
 
 33 
 
 57 
 
 33i 
 
 33i 
 0^8339 
 
 56^ 
 
 
 0.8386 
 
 0.6446 
 
 0.8363 
 
 0.6483 
 
 0.6519 
 
 0.8314 
 
 
 2 
 
 1.6773 
 
 L0893 
 
 1.6726 
 
 L0966 
 
 L6678 
 
 1.1039 
 
 1.6629 
 
 Lllll 
 
 
 3 
 
 2.5160 
 
 L6339 
 
 2.6089 
 
 1.6449 
 
 2.5017 
 
 1.6668 
 
 2.4944 
 
 L6667 
 
 
 4 
 
 3.3547 
 
 2.1786 
 
 3.3451 
 
 2.1932 
 
 3.3365 
 
 2.2077 
 
 3.3259 
 
 2.2223 
 
 
 5 
 
 4.1934 
 
 2.7232 
 
 4.1S14 
 
 2.7415 
 
 4.1694 
 
 2.7697 
 
 4.1573 
 
 2.7778 
 
 
 6 
 
 5.0320 
 
 3.2678 
 
 5.0177 
 
 3.2898 
 
 5.0033 
 
 3.3116 
 
 4.9888 
 
 3.3334 
 
 
 7 
 
 5.8707 
 
 3.8125 
 
 5.8540 
 
 3.8381 
 
 5.8372 
 
 3.8636 
 
 5.8203 
 
 3.8890 
 
 
 8 
 
 6.7094 
 
 4.3571 
 
 6.6903 
 
 4.3863 
 
 6.6711 
 
 4.4165 
 
 6.6618 
 
 4.4446 
 
 
 9 
 1 
 
 7.5480 
 
 4.9018 
 56° 
 
 7.5266 
 
 4.9346 
 
 7.5069 
 
 4.9674 
 
 7.4832 
 
 6.0001 
 
 
 34 
 
 34i 
 
 65S 
 
 34i 
 
 55i 
 0.5664 
 
 34S 
 
 56i 
 
 
 0.8290 
 
 0.5592 
 
 0.8266 
 
 0.5628 
 
 0.8241 
 
 0.8216 
 
 0.5700 
 
 
 2 
 
 L65S1 
 
 L1184 
 
 L6632 
 
 1.1256 
 
 1.6482 
 
 1.1328 
 
 1.6433 
 
 1.1400 
 
 
 1 3 
 
 2.4871 
 
 1.6776 
 
 2.4798 
 
 1.6884 
 
 2.4724 
 
 L6992 
 
 2.4649 
 
 1.7100 
 
 
 4 
 
 3.3162 
 
 2.2368 
 
 3.3063 
 
 2.2512 
 
 3.2965 
 
 2.2666 
 
 3.2866 
 
 2.2800 
 
 
 5 
 
 4.1452 
 
 2.7960 
 
 4.1329 
 
 2.8140 
 
 4.1206 
 
 2.8320 
 
 4.1082 
 
 12.8500 
 
 
 6 
 
 4.0742 
 
 3.3552 
 
 4.9595 
 
 3.3768 
 
 4.9447 
 
 3.3984 
 
 4.9299 
 
 13.4200 
 
 
 7 15.8033 
 
 3.9144 
 
 5.7861 
 
 3.9396 
 
 5.7689 
 
 3.9648 
 
 5.7515 
 
 3.9900 
 
 
 8 1 6.6323 
 
 4.4735 
 
 6.6127 
 
 4.5024 
 
 6.5930 
 
 4.5313 
 
 6.5732 
 
 4.5600 
 
 
 9 
 
 1 
 
 7.4613 
 ■350 
 
 5.0327 
 55 
 
 7.4393 
 
 5.0662 
 
 7.4171 
 35i 
 
 5.0977 
 
 54i 
 
 0.5807 
 
 7.3948 
 
 5.1300 
 "Hi" 
 0.6842 
 
 
 35i 
 
 541 
 
 351 
 
 
 0.8191 
 
 0.6736 
 
 0.8166 
 
 0.5771 
 
 0.8141 
 
 0.8116 
 
 
 1^ 
 
 1.6383 
 
 1.1472 
 
 1.6333 
 
 1.1543 
 
 1.6282 
 
 LI 614 
 
 1.6231 
 
 L1685 
 
 
 .S 
 
 2.4575 
 
 1.7207 
 
 2.4499 
 
 1.7314 
 
 2.4423 
 
 L7421 
 
 2.4347 
 
 1.7527 
 
 
 4 
 
 3.2766 
 
 2.2943 
 
 3.2666 
 
 2.3086 
 
 3.2565 
 
 2.3228 
 
 3.2463 
 
 2.3370 
 
 
 f> 
 
 4.0968 
 
 2.8679 
 
 4.0832 
 
 2.8867 
 
 4.0706 
 
 2.9035 
 
 4.0679 
 
 2.9212 
 
 
 fi 
 
 4.9149 
 
 3.4415 
 
 4.899? 
 
 3.4629 
 
 4.8847 
 
 3.4842 
 
 4.8694 
 
 3.5055 
 
 
 7 
 
 5.734] 
 
 4.0160 
 
 5.7165 
 
 4.0400 
 
 5.6988 
 
 4.0649 
 
 5.6810 
 
 4.0897 
 
 
 a 
 
 6.5632 
 
 4.5886 
 
 6.5331 
 
 4.6172 
 
 6.5129 
 
 4.6466 
 
 6.4926 
 
 4.6740 
 
 
 9 
 
 7.3724 
 
 6.1622 
 
 n". S. 
 
 7.349S 
 
 6.1943 
 
 7.3270 
 
 fETw: 
 
 5.2263 
 
 N. S. 
 
 7.3042 
 
 5.2582 
 
 NTs. 
 
 
 E. W. 
 
 N. S. 
 
 E.W 
 
 . 
 
The Surveyor's Guide. 
 
 117 
 
 TABLES OF LATITUDE AND DEPARTURE. j 
 
 1 
 
 ! 1 
 
 N. S. 
 
 E.W. 
 
 N. S. 
 
 36i 
 
 0.8064 
 
 E. AV. 
 
 "63i~ 
 0.5913 
 
 N. S. 
 
 E. W. 
 
 53i" 
 
 N. S. 
 
 E. W. 
 
 •53i 
 0.5983 
 
 36 
 
 0.8090 
 
 64 
 
 364 
 
 36S 
 0.8012 
 
 0.6878 
 
 0.803810.5948 
 
 \ 2 
 
 1.6181 
 
 1,1766 
 
 1.6129 
 
 1.1826 
 
 1.6077|l.lS96 
 
 1.6025 
 
 1.1966 
 
 3 
 
 2.4271 
 
 1.7634 
 
 2.4193 
 
 1.7739 
 
 2.4116 
 
 1.7845 
 
 2.4038 
 
 1.7950 
 
 4 
 
 3.2361 
 
 2.3511 
 
 3.2268 
 
 2.3662 
 
 3.2154 
 
 2.3793 
 
 3.2050 
 
 2.3933 
 
 5 
 
 4.0451 
 
 2.9389 
 
 4.0322 
 
 2.9566 
 
 4.0193 
 
 2.9741 
 
 4.0063 
 
 2.9916 
 
 6 
 
 4.8641 
 
 3.6267 
 
 4.8387 
 
 3.6478 
 
 4.8231 1.3.6689 
 
 4.8075 
 
 3.5899 
 
 7 
 
 6.6631 
 
 4.1145 
 
 6.6461 
 
 4.1391 
 
 6.6270 
 
 4.1638 
 
 5.6088 
 
 4.1883 
 
 8 
 
 6.4721 
 
 4.7023 
 
 6.4516 
 
 4.7304 
 
 0.4308 
 
 4.7686 
 
 6.4100 
 
 4.7866 
 
 9 
 1 
 
 7.2812 
 
 6.2901 
 63 
 
 7.2580 
 
 6.3217 
 
 521 
 0.6053 
 
 7.2347 
 
 5.3534 
 
 7.2111 
 
 5.3849 
 
 52i 
 0.6122 
 
 37 
 0.7986 
 
 37J 
 
 37i 
 0.7933 
 
 62i 
 0.6087 
 
 371 
 0.7907 
 
 0.6018 
 
 0.7960 
 
 2 
 
 1.6973 
 
 1.2036 
 
 1.5920 
 
 1.2106 
 
 1.5867 
 
 1.2176 
 
 1.5814 
 
 1.2244 
 
 3 
 
 2.3959 
 
 1.8054 
 
 2.3880 
 
 1.8159 
 
 2.3801 
 
 1.8263| 
 
 2.3721 
 
 1.8366 
 
 4 
 
 3.1945 
 
 2.4073 
 
 3.1840 
 
 2.4212 
 
 3.17.34 
 
 2.4350 
 
 3.1628 
 
 2.4489 
 
 5 
 
 3.9932 
 
 3.0091 
 
 3.9800 
 
 3.0266 
 
 3.9668 
 
 3.0438 
 
 3.9534 
 
 3.0611 
 
 6 
 
 4.7918 
 
 .3.61091 
 
 14.7760 
 
 3.6318 
 
 4.7601 
 
 3.6526 
 
 4.7441 
 
 3.6733 
 
 7 
 
 5.6904 
 
 4.2127 
 
 15.5720 
 
 4.2371 
 
 5.6635 
 
 4.2613 
 
 5.6348 
 
 4.2855 
 
 8 
 
 6.3891 
 
 4.8145 
 
 6.3680 
 
 4.8424 
 
 6.3468 
 
 4.8701 
 
 6.3265 
 
 4.8977 
 
 9 
 1 
 
 7.1877 
 
 6.4163 
 
 7.1640 
 
 6.4476 
 
 7.1402 
 
 5.4788 
 
 7.1162 
 
 5.5099 
 
 38° 
 
 62 
 
 38i 
 
 611 1 
 0.6191 
 
 51i 
 0.6225 
 
 38i 
 
 61i' 
 0.6269 
 
 0.7880 
 
 0.6156 
 
 0.7853 
 
 0.7826 
 
 0.7799 
 
 2 
 
 1.5760 
 
 1.2313 
 
 1.5706 
 
 1.2382 
 
 1.5662 
 
 1.2450 
 
 1.5598 
 
 1.2518 
 
 3 
 
 2.3640 
 
 1.8470 
 
 2.3559 
 
 1.8673 
 
 2.3478 
 
 1.8676 
 
 2.3397 
 
 1.8778 
 
 4 
 
 .3.1520 
 
 2.4626 
 
 3.1413 
 
 2.4764 
 
 3.1304 
 
 2.4900 
 
 3.1195 
 
 2.5037 
 
 5 
 
 3.9401 
 
 3.0783 
 
 3.9266 
 
 3.0955 
 
 3.9130 
 
 3.1125 
 
 3.8994 
 
 3.1296 
 
 6 
 
 4.7281 
 
 3.6940 
 
 4.7119 
 
 3.7146 
 
 4.6956 3.736] 
 
 4.6793 
 
 3.7555 
 
 7 
 
 5.5161 
 
 4.3096 
 
 5.4972 
 
 4.3337 
 
 5.4782|4.3576 
 
 5.4692 
 
 4.3815 
 
 8 
 
 6.3041 
 
 4.9253 
 
 6.2826 
 
 4.9528 
 
 6.2608 
 
 4.9801 
 
 6.2391 
 
 6.0074 
 
 9 
 1 
 
 7.0921 
 
 6.5409 
 
 7.0678 
 
 5.5718 
 
 ToF 
 
 7.0434 
 
 6.6026 
 
 7.0190 
 
 6.6333 
 
 50i 
 0.6394 
 
 39° 
 
 61 
 
 0.62931 
 
 39i 
 0.7716 
 
 50i 
 0.6361 
 
 39i 
 0.7688 
 
 0.7771 
 
 0.7744 
 
 0.6327 
 
 9. 
 
 1.5543 
 
 1.2586 
 
 1.5488 
 
 1.2654 
 
 1.5432 
 
 1.2621 
 
 1.6377 
 
 1.2789 
 
 3 
 
 2.3314 
 
 1.8880 
 
 2.3232 
 
 1.8981 
 
 2.3149 
 
 1.9082 
 
 2.3065 
 
 1.9183 
 
 4 
 
 3.1086 
 
 2.5173 
 
 3.0976 
 
 2.6308 
 
 3.0865 2.64431 
 
 3.0764 
 
 2.6678 1 
 
 1 •"> 
 
 3.885713.1466 
 
 3.8719!3.1635| 
 
 3.858ll3.1804| 
 
 3.8442 3.1972 i 
 
 1 fi 
 
 4.6629 
 
 3.7759 
 
 4.6463 
 
 3.7962 
 
 4.6297 
 
 3.8165 
 
 4.613013.8366 j 
 
 1 ^ 
 
 5.4400 
 
 4.4052 
 
 5.4207 
 
 4.4289 
 
 5.4014 
 
 4.4525] 
 
 6.3819'4.4761 | 
 
 8 
 
 6.2172 
 
 5.0346 
 
 6.1951 
 
 6.0616 
 
 6.1730 
 
 6.08861 
 
 6.1507 
 
 5.1165 
 
 9 
 
 6.9943 
 
 5.6639 
 
 6.9695 
 
 5.6943 
 
 6.9446 
 
 5.7247 
 
 6.9196 
 E. W. 
 
 5.7650 
 
 E.W. 
 
 N. S. 
 
 E.W. 
 
 N. S. 
 
 E.W. 
 
 N. S. 
 
 N. S. 
 
118 
 
 The Surveyor's Guide. 
 
 TABLES OF LATITUDE AND DEPARTURE. [ 
 
 1 
 
 N. S. 
 
 40° 
 
 0.7660 
 
 E. W. 
 50 
 
 0.6428 
 
 N. S. 
 
 E.W. 
 
 N. S. 
 
 E.W. 
 
 N.S. 
 
 E.W. 
 
 40i 
 0.-7632 
 
 49i 
 
 m 
 
 49i 
 
 401 
 0.7676 
 
 49i 
 
 0.6461 
 
 0.7604 
 
 0.6494 
 
 0.6527 
 
 2 
 
 1.5321 
 
 1.2856 
 
 L5265 
 
 1.2922 
 
 1.5208 
 
 1.2989 
 
 1.5161 
 
 1.3055 
 
 '6 
 
 2.2981 
 
 1.9284 
 
 2.2897 
 
 L9384 
 
 2.2812 
 
 1.9483 
 
 2.2727 
 
 1.9583 
 
 4 
 
 3.0642 
 
 2.5711 
 
 3.0529 
 
 2.5845 
 
 3.0416 
 
 2.5978 
 
 3.0303 
 
 2.6110 
 
 1 ^ 
 
 3.8302 
 
 3.2139 
 
 3.8162 
 
 3.2306 
 
 3.8020 
 
 3.2472 
 
 3.787-8 
 
 3.2638 
 
 6 
 
 4.5963 
 
 3.8567 
 
 4.5794 
 
 3.8767 
 
 J4.5624 
 
 3.8967 
 
 4.6464 
 
 3.9166 
 
 7 
 
 5.3623 
 
 4.4995 
 
 5.3425 
 
 4.6229 
 
 6.3228 
 
 4.6461 
 
 6.3029 
 
 4.6693 
 
 8 
 
 6.1284 
 
 5.1423 
 
 6.1059 
 
 5.1690 
 
 |6.0832 
 
 5.1956 
 
 6.0605 
 
 5.2221 
 
 9 
 1 
 
 6.8944 
 
 5.7851 
 
 6.8691 
 
 5.8151 
 
 481 
 
 6.8436 
 
 6.8460 
 48i 
 
 6.8181 
 
 5.8748 
 48i 
 6.6659 
 
 41 
 
 49 
 
 41i 
 0.7518 
 
 m 
 
 411 
 0.7460 
 
 0.7547 
 
 0.6560 
 
 0.6593 
 
 0.7489 
 
 0.6626 
 
 2 
 
 1.5094 
 
 1.3121 
 
 L5037 
 
 1.3187 
 
 1.4979 
 
 1.3252 
 
 L4921 
 
 1.3318 
 
 3 
 
 2.2041 
 
 1.9682 
 
 2.2555 
 
 1.9780 
 
 2.2468 
 
 L9879 
 
 2.2382 
 
 1.9976 
 
 4 
 
 3.0188 
 
 2.6242 
 
 3.0074 
 
 2.6374 
 
 2.9958 
 
 2.6505 
 
 2.9842 
 
 2.6635 
 
 5 
 
 3.7735 
 
 3.2803 
 
 3.7592 
 
 3.2967 
 
 3.7447 
 
 3.3131 
 
 3.7303 
 
 3.3294 
 
 6 
 
 4.5283 
 
 3.9364 
 
 4.5110 
 
 3.9660 
 
 4.4937 
 
 3.9757 
 
 4.4764 
 
 3.9953 
 
 7 
 
 5.2830 
 
 4.5924 
 
 6.2629 
 
 4.6154 
 
 6.2426 
 
 4.6383 
 
 5.2224 
 
 4.6612 
 
 8 
 
 6.0377 
 
 5.2485 
 
 [6.0147 
 
 6.2747 
 
 5.9916 
 
 6.3010 
 
 5.9686 
 
 6.3270 
 
 9 
 1 
 
 6.7924 
 
 5.9045 
 
 6.7666 
 
 5.9341 
 
 6.7406 
 
 5.9636 
 
 6.7145 
 '42i 
 
 6.9929 
 
 42 
 
 48 
 0.6691 
 
 42i 
 0.7402 
 
 471 
 0.6723 
 
 ,0.7373 
 
 m 
 
 0.676-6 
 
 47i 
 
 0.7431 
 
 0.7343 
 
 0.6788 
 
 2 
 
 1.4863 
 
 1.3383 
 
 1.4804 
 
 1.3447 
 
 11.4740 
 
 1.3512 
 
 1.4686 
 
 1.3576 
 
 3 
 
 2.2294 
 
 2.0074 
 
 '2.2207 
 
 2.0171 
 
 2.2118 
 
 2.0268 
 
 2.2029 
 
 2.0364 
 
 4 
 
 2.9726 
 
 2.6765 
 
 2.9609 
 
 2.6895 
 
 2.9491 
 
 2.7024 
 
 2.9373 
 
 2.7152 
 
 5 
 
 3.7157 
 
 3.34571 
 
 3.7011 
 
 3.3618 
 
 3.6864 
 
 3.3779 
 
 3.6716 
 
 3.3940 
 
 6 
 
 4.4589 
 
 4.0148 
 
 4.4413 
 
 4.0342 
 
 4.4237 
 
 4.0535 
 
 4.4059 
 
 4.0728 
 
 7 
 
 5.2020 
 
 4.6839 
 
 5.1815 
 
 4.7066 6.1610 
 
 4.7291 
 
 5.1402 
 
 4.7516 
 
 8 15.9452 
 
 5.3530 
 
 5.9218 
 
 5.3789, 5.8982 
 
 6.4047 
 
 6.874616.4304 || 
 
 9 
 
 6.6883 
 
 6.0222 
 47 
 
 6.6620 
 0.7283 
 
 6.0513 
 
 46i 
 0.6852 
 
 6.6355 
 1 43i 
 
 6.0803 
 
 6.6089 
 
 6.1092 
 
 1 
 
 43 
 0.7313 
 
 m\ 
 
 431 
 0.7223 
 
 46i 
 0.69i5 
 
 0.6S2oi 
 
 0.7253'0.6883| 
 
 ;^ 
 
 1.4627 
 
 1.3640| 
 
 1.45G7 
 
 1.3704 
 
 1.4507 
 
 1.3767 
 
 1.4447 
 
 1..3830 
 
 3 
 
 2.1941 
 
 2.0460 2.1851 
 
 2.05561 ;2.1761 
 
 2.0651 
 
 2.1671 2.0745 !j 
 
 4 
 
 2.9254 
 
 2.7280 2.9135'2.7407; '2.9015 
 
 2.7534 
 
 2.8894 2.7660 1 
 
 5 3.6568 
 
 3.4100 3.6418 3.4259| 
 
 3.6269 
 
 3.4418 
 
 3.6118 3.4576 || 
 
 6 i4.3881 
 
 4.09201 4.3702 
 
 4.1111 
 
 4.3622 
 
 4.1301 
 
 4.3342 
 
 4.1491 
 
 7 5.1195 
 
 4.7740 5.0986 
 
 4.7963 
 
 5.0776 
 
 4.8186 
 
 6.0565 
 
 4.8406 i 
 
 8 5.8508 
 
 5.4560 5.8269 
 
 6.4814 
 
 6.8030 
 
 6.5068 
 
 6.7789 
 
 5.5321 1 
 
 9 6.5822 
 
 6.1380! 6.5553 
 
 6.1666 
 
 N. S. 
 
 6.5284 
 E.W. 
 
 6.1952 
 
 6.6013 
 
 6.2236 
 
 N.S. 1 
 
 
 
 E. W. 
 
 N. S. 
 
 E. W. 
 
 N. S. 
 
 E.W. 
 
The Surveyor's Guide. 
 
 119 
 
 tables of latitude and departure. I 
 
 
 1 
 
 N". S. 
 
 E.W.I 
 
 N. S. 
 
 E.W. 
 
 N.S. 
 
 E.W. 
 
 45J 
 
 N. S. 
 
 E.W. 1 
 
 
 44° 
 
 46 
 
 Ui 
 
 45i 
 
 0.7132 
 
 44i 
 
 45i 
 0.7040 
 
 
 0.7193 
 
 0.6946 
 
 0.7163 
 
 0.6978 
 
 0.7009 
 
 0.7102 
 
 
 2 
 
 1.4387 
 
 1.3893 
 
 1.4326 
 
 1.3956 
 
 1.4266 
 
 1.4018 
 
 1.4204 
 
 1.4080 
 
 
 ■6 
 
 2.1580 
 
 2.0840 
 
 2.1489 
 
 2.0934 
 
 2.1397 
 
 2.1027 
 
 2.1306 
 
 2.1120 
 
 
 4 
 
 2.8774 
 
 2.7786 
 
 2.8652 
 
 2.7912 
 
 2.8630 
 
 2.8036 
 
 2.8407 
 
 2.8161 
 
 
 5 
 
 3.5967 
 
 3.4733 
 
 3.5815 
 
 3.4889 
 
 3.5662 
 
 3.5045 
 
 3.5509 
 
 3.5201 
 
 
 6 
 
 4.3160 
 
 4.1679 
 
 4.2978 
 
 4.1867 
 
 4.2795 
 
 4.2054 
 
 4.2611 
 
 4.2241 
 
 
 1 
 
 5.0354 
 
 4.8626 
 
 5.0141 
 
 4.8845 
 
 4.9927 
 
 4.9063 
 
 4.9713 
 
 4.9281 
 
 
 8 
 
 5.7547 
 
 5.5573 
 
 5.7304 
 
 5.5823 
 
 5.7060 
 
 5.6072 
 
 5.6816 
 
 5.6321 
 
 
 9 
 1 
 
 6.4741 
 
 6.2519 
 
 6.4467 
 
 6.2801 
 
 6.4192 
 
 6.3081 
 
 6.3917 
 
 6.3361 
 
 
 46 
 
 45 
 
 
 
 
 
 
 0.7071 
 
 0.7071 
 
 
 2 
 
 1.4142 
 
 1.4142 
 
 
 
 
 
 
 
 
 3 
 
 2.1213 
 
 2.1213 
 
 
 
 
 
 
 
 
 4 
 
 2.8284 
 
 2.8284 
 
 
 
 
 
 
 
 
 5 
 
 3.5355 
 
 3.5355 
 
 
 
 
 
 
 
 
 6 
 
 4.2426 
 
 4.2426 
 
 
 
 
 
 
 
 
 7 
 
 4.9497 
 
 4.9497 
 
 
 
 
 
 
 
 
 8 
 
 5.6569 
 
 5.6569 
 
 
 
 
 
 
 
 
 9 
 
 6.3640 
 
 6.3640 
 
 b7W. 
 
 
 
 
 
 
 
 E.W. 
 
 N. S. 
 
 N. S. 
 
 E.W. 
 
 N. S. 
 
 E.W. 
 
 N. S. 
 
 
TAELES OP SUEYEYS 
 
 THE USE OP THE FOREGOING TABLES IN RELATION 
 TO SURVEYS. 
 
 They show, by inspection, the alteration of lati- 
 tude and departure to every degree on the com- 
 pass, and that for any distance not exceeding 
 100.000 links. 
 
 In the uppermost rank of every division are 
 placed the several angles and their complements, 
 to 45°, including the quarter, half, and three- 
 quarters of degrees ; and in the left-hand column 
 are lengths of the measured lines of the field- 
 work, and in the common areas are the difference 
 of latitude and departure. 
 
 Examples. 
 Suppose the angle to be N. E. 27J degrees, and 
 the line in the field measured to 6 chains, and 
 it be required to find the Northings and Eastings 
 of that station, under 27J degrees, and answering 
 to 6 in left-hand column, the number in the com- 
 (120) 
 
The Surveyor's Guide. 121 
 
 mon area, 5.3221, -which shows the Northings ; 
 and under 621, (which is the complement to that 
 angle) opposite the same number in the side col- 
 umn, I find 2.7705, which shows the Easting of 
 that station. If the course be the same, and dis- 
 tance 60 chains, remove the decimal point one 
 place to the right-hand, and the latitude and de- 
 parture will be 53.221 27,705. 
 
 And if the line were 600 chains, the course 
 remaining the same, the Northings would be 532 
 chains, 21 links, and the Eastings 277 chains, 05 
 links. 
 
 If the measured line doth not consist of an ex- 
 act number of tens, as suppose its length to be 75 
 chains, 03 links, or 75 chains, 34 links, and the 
 course 27J° ; then under this angle, and opposite 
 
 c. 
 
 70 are 62.091 
 
 6 " 4.435 
 
 0.30 links 0.266 
 
 0.04 " 0.035 
 
 70 chains 32.822 
 
 5 " 2.308 
 
 0.30 links 0.138 
 
 0.04 " 0.018 
 
 Northing. 66.827 Easting 34.786 
 
 for 75 chains, 34 links. for 75 chains, 34 links. 
 
 And so for any other. 
 
 N. B. These tables will answer to ^° or 7J', an 
 arithmetical mean between |° and J°, or between 
 J° and f °. 
 
Ailjr;\/-.4, 
 
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