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INDEX OF CURVE AND REDUCTION TABLES Table Table

I-SLOPE STAKE II-STADIA CORRECTION AND HORIZONTAL DISTANCES

Table III-TRIGONOMETRIC FORMULAE Table

IV-NATURAL TRIGONOMETRICAL FUNCTIONS CURVE FORMULAE

Table

° V-TANGENTS AND EXTERNALS TO A 1 CURVE

USEFUL RELATIONS Table

VI-INCHES TO DECIMALS OF A FOOT

Table VII-MINUTES IN DECIMALS OF A DEGREE Table VIII-MIDDLE ORDINATES OF RAILS Table

IX-SHORT RADIUS CURVES

Table

X-RODS IN FEET, IOTHS AND 100THS OF FEET

Table XI-LINKS IN FEET, 10THS AND 100THS OF FEET

TABLE I. SLOPE STAKE

DISTANCES FROM SIDE STAKES FOR CROSS-SECTIONING ROADWAY OF ANYWIDTH.SIDESLOPES11/2TO 1.

SLOPE STAKE

SIDE ISTAKE

i 1----

,,

1

'

SIDE ISTAKE I

I

i

1- L. C.

Distance out from Side or Shoulder Stake.

0 .1 1 .1 000 0 151 0.80 1.50 165 1 80 8.00 8.15 8.80 4.50 465 4.80 6.00 6 15 6.80 7 50 7.65 7.80 9 00 9 15 9.80 10.5010 65 10.80 12.00 12 15 12.80 13 50 13.65 18 80 15.00 15 15 15 80 16 50 16 65 16 80 1800 18.153 18.30 19 50 19 65 19.80 21.00 21 15 21.80 22 50 2265 2280 24.00 2415 24 30 25.50 2565 25.80 27.00 27 15 27.30 28650 2865 2880 8000 80 15 30.30 31 50 31 65 31.80 3300 33 15 33 30 3450 8465 84.80 86.00 86 15 36.80 87.5037.65 37 80 3900 39 15 39.80 4050 4065 40 80 42 00 42 15 42.30 48-50 4365 43.80 4500 45 15 45.80 46.5046.65 46.80 4800 48.15 48.30 49.50 49 65 49.80 51 00 51.15 51.30 52 50 52.65 52.80 5400 54.15 54.30 5550 5565 55.80 57.00 57.15 57.30 5850 58.65 58 80 60 00 60.15 60 30

.3 .4 1.5

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8.

.61 .7

0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.95 2.10 2.25 2.40 2.55 2.70 2.85 345 3.60 S75 8.90 4.05 4.20 435 4.95 5 10 525 540 5.55 5.70 5.85 6.45 6.60 6 75 6.90 7.05 7.20 7.35 7.95 8.10 8.25 8.40 8.55 8.70 8.85 9.45 9.60 9.75 9.90 10.05 10.20 10.35 10.95 11.10 11.25 11.40 11.55 11 70 11.85 12.45 '12.60 12.75 12.90 13.05 13.20 13.35 18 95 14.10 14.25 14.40 14 55 14.70 14.85 15 45 15.60 15.75 15.90 16.05 16.20 16 35 16.95 17 10 17.25 17.40 17.55 17.70 17.85 18 45 18.60 18 75 18.90 19.05 19.20 1985 19.95 20.10 20.25 2040 20.55 20.70 20.85 21.45 21 60 21.75 21.90 2205 2220 2235 2295 28.25 23.40 23.55 23.70 23.85 2445 24.60 24.75 2490 25 05 25.20 25.85 25 95 23.10 2625 2640 26.55 26.70 26.85 27 45 27.60 27.75 27.90 28.05 2820 28.85 28.9529.10 29.25 29.40 29.55 29.7029.85 30.45 30.60 30.75 30.90 81.05 31.20 31.85 31.95 82 10 3225 32.4032.55 8270 8285 33 45 33.60 3375 33.90 34.05 84.20 34.35 34.95 35.10 85 25 35 40 35.55 35.70 3585 36 45 36.60 36.75 36.9037.05 37.20 37.35 87.9538.10 38.25 38.40 38.55 88.70 38.85 89 45 3960 39.75 39.90 40.05 40.2040.35 40.95 41.10 41.25 41 40 41.55 41.70 41.85 42.45 42.6042 75 42.90 48.05 43.20 48.35 43 95 44.10 4425 4440 44.55 44.70 4485 4545 45.60 45.75 45.90 46.054620 46.85 46 95 47.10 47.25 47.40 47.55 47.70 47.85 4845 48.60 48 75 48.90 49.05 49 20 49.35 49.95 50.10 50.25 50.40 50.55 50.7050.85 51.45 51.60 51.75 51.90 52.05 52.20 52.85 52.95 53.10 53.25 58.40 583.55 53.7058.85 54 45 54.60 54.75 54.90 55.05 55.20 55.85 55.95 56.10 56.25 56.40 56.55 56.7056.85 57 45 57.60 57.75 57.90 58.05 58.20 5835 58.95 59.10 59 25 69.40 5955 59.70 59.85 60 45 6060 60.75 6090 61.05 61 20 61.35 ,

,

,

,

TABLE II. STADIA CORRECTION AND HORIZONTAL DISTANCES STADIA REDUCTIONS FOR READING 100 Vertical Angle erticl Angle

I

20-0a

3o-00' 4°-00' 5°-O 6°-00'

Horizontal Correction

Difference in Elevation

Horizontal Correction

VerticalAngle

Difference in Elevation

0.1 0.3 0.5 0.8 1.1

3.5 5.3 7.0 8.7 10.4

18°-30' 19°-00, 19°-30" 20-00' 20°-30'

10.1 10.6 11.2 11.7 12.3

30.1 30.8 31.5 32.1 32.8

1.5 1.9 2.5

21-00a 210-30, 22°-00' 22°-30' 23o-00'

12.8 13.4 14.0 14.7 15.3

33.5 34.1 34.7 35.4 36.0

10°-00'

3.0

10°-30'

3.3

12.1 13.8 15.5 17.10 17.9

110-00,

3.6 4.0 4.3 4.7 5.1

18.7 19.5 20.3 21.1 21.9

23°-30' 24°-00' 24°-30' 25°-00' 25v°-30'

15.9 16.5 17.2 17.9 18.6

36.6 37.2 37.7 38.3 39.0

5.5 5.9 6.3 6.7 7.2

22.7 23.4 24.2 25.0 25.8

26°-00' 26°-30' 27°-00' 27°-30' 28°-00'

19.2 19.9 20.6 21.3 22.0

39.4 39.9 40.5 41.0 42.0

7.6 8.1 8.5 9.0 9.5

26.5 27.2 28.0 28.7 29.4

28°-30' 29°-00' 29°-30' 30°-00'

22.8 23.5 24.3 25.0

41.9 42.4 42.9 43.3

7°--00'

80 -00' 90 -00,

110--30, 12°-00' 12-30' 13°-00'

13°-30'

14°-00' 14°-30' 15°-00' 15o--3a1

16°-00' 16°-30' 17°-00' 17

-30'

18-00'

Chains to Feet 1 2 3 4 5 6 7 8 9 10

........ 66 ..........

132 198 .......... ....... 264 ........ 330 ..........

396 ........

462 .......... 528 ..........

594 ......... 660

Feet to Chains 100 ....

1.515

....

3.030

300 ....

4.545

400 ....

500 ....

600 ....

6.060 7.575 9.090

200

700 .... 10.606 800 .... 12.121 900 .... 13.636

1,000 .... 15.151

TABLE III. TRIGONOMETRIC FORMULAE B C A

B

C

a

C

a

b

A

B a

b

A

b y b 0 Right Triangle Oblique Triangles Solution of Right Triangles a b a b For Angle A. sin, Cos= b, tan ,cot -, sec-,, Sb

Given a, b

a

tan A =

A, B, b

sinA = a-=cosB, b=

= cot B, c =

0

B, b, a

B = 90 -A,

Given

Required

Sasin B

A, B, a

b, c, C

sin A

A, a A, b A, a

b

a

Required A, B ,o

2

j

C

ecosec

b'

a

= a

(c+a)(o--a) =o

b = a cot A, c

e

= -

1--2

a

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sin A

b sin A

a sin C

A, a, b

B, e, C

sin B=

a, b,

A, B, a

A+B=180*-- C, tan # (A-B)=(a-b)tan I (A-B) a+b a sin C sin A

C0

A, B, aC

a

0

,C = 180 -(A

sin jB=,v 8= a2

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area =

A

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=a- 2

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+ B), o =

, area =

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(a-

s

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2

A, B, C,a Area

area =

a sin B sin C 2 sin A

REDUCTION TO HORIZONTAL Horizontal distance -=Slope distance multiplied by the cosine of the vertical angle. Thus: slope distance =319.4ft.

aso

,

Vert. angle-5" 10'. From Table. IV. cos 5 10'= 9959.

Horizontal distance - 319.4%.. 995 = 31809 ft.

Horizontal distance also - Slope distance minus slope distance times (I-cosine of vertical angle). With the

same figures as in the preceding example, the following result is obtained. Cosine 50 10- .959. 1-.9959=.0041.

Horizontal distance 319.4X.0041 =1.31. 319.4-1.31= 31809 ft.

When the rise is known, the horizontal distance is approximately:-the slope distance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.. slope distanee=302.6 ft. Horizontal distance=3026-- 14 14 =302.8-0.32302.28 ft.

2 X 302.6

TABLE IV. NATURAL TRIGONOMETRICAL FUNCTIONS Angle

Se.

Cosec.

Sin

Tan.

0 .0029 .0058 .0087 .0116 .0145

0 .0029 .0058 .0087

343.8 171.9

401161.0001

85.94

.0145 1.0001

Cotg.

Angle

Cosin.

00

Sin.

Tn.

S.c.

Cosec.

Cotg.

Coin.

7.185 7.040 6.900 6.766 6.636 6.512

7.115 6.968 6.827 6.691 6.561 6.435

.99027 .98986 .98944 .98902 .98858 .98814

68.76

1. .99998 .99996 .99993 .99989

1392 .1421 .1449 .1478 .1507 .1536

1.0098 1.0102 1.0107 1.0111 1.0115 1.0120

114.6

.0175 .0175 0204 .0204 .0233 .0233 .0262 .0262 .0291 .0291 .0320 .0320

1.0002 1.0002 1.0003 1.0003 1.0004 1.0005

57.30 49.11 42.98 38.20 34.38 31.26

.99985 99979 .99973 .99966 .99958 .99949

.1564 .1593 .1622 .1650 .1679 .1708

1.0125 6.394 6.314 .98769 1.0129 6.277 6.197 .98723 1.0134 6.166 6.084 .98676 1.0139 6.059 5.976 .98629 1.0144 5.955 5.871 .98580 1.0149 5.855 5.769 .98531

.0349 .0378 .0407 .0436 .0465 .0494

.0349 .0378 .0407 .0437 .0466

1.0006 1.0007 10008 1.0010 1.0011 10012

28.65

.99939 .99929

24.56 22.93 21.49 20.23

.99917 .99905 .99892 .99878

.1736 .1765 .1794 .1822 .1851 .1880

1.0154 1.0160 1.0165 1.0170 1.0176 1.0181

5.759 5.665 5.575 5.488 5.403 5.320

.0523

.0524 1.0014 .0553 1.0015 0582 1.0017 .0612 1.0019 .0641 10020 .0670 1.0022

19.11 18.10 17.20

.99863 .99847 .99831 .99813 .99795 99776

.1908 .1937 .1965 .1994 .2022 .2051

1.0187 1.0193 1.0199 1.0205 1 0211 1.0217

5.2415.145 .98163

.2079 .2108 .2136 .2164 .2193 .2221

1.0223 1.0230 1.0236 1.0243 1.0249 10256

4.810 4.745 4.682 4.620

.0552 0581 .0610 .0640 0669

4495

.0698 .0699 .0727 .0756 .0758 .0785 .0787 .0814 .0816 .0843 .0846

2645

16.38 15.64 14.96

5.671 5.576 5485 5.396 5.309 5.226

.98481 .98430 .98378 .98325 .98272

.98218

5.066 4.989 4.915 4.843 4.773

.98107 .98050 .97992 .97934 .97875

4.705 4.638 4.574 4.511 4.560 4.449 4.502 4.390

.97815 .97754 .97692 .97630 .97566 .97502

5.164 5,089 5416 4.945 4.877

1.0024 1 0027 1.0029 1.0031 1.0033 1.0036

14.34 13.76 13.23 12.75 12.29

11.87

.99756 .99736 .99714 .99692 .99668 .99644

.0872 .0901 .0929 .0958 .0987 .1016

.0875 1.0038 .0904 1.0041 .0934 1.0043 .0963 1 0046 .0992 1.0049 .1022 1.0052

11.47 11.10 10.76 10.43 10.13 9.839

.99619 .99594 .99567 .99,40 .99511 .99482

.2250 .2278 .2306 .2334 .2363 .2391

1.0263 1.0270 1.0277 1.0284 1.0291 1.0299

4.445 4.390 4.336 4.284 4.232 4.182

4.331 4.275 4.219 4.165 4.113 4.061

.97437 .97371 .97304 .97237 .97169 .97100

.1045 .1074 .1103 .1132 .1161 .1190

.1051 .1080 .1110 .1139 .1169 .1198

1.0055 1.0058 1.0061 1.0065 1.0068 1 0072

9.567 9.309 9 465 8.834 8.614 8.405

.99452 .99421 .99390 .99357 .99324 .99290

.2419 .2447 .2476 .2504 .2532 .2560

1.0306 1.0314 1.0321 1.0329 1.0337 1.0345

4.133 4.086 4.039 3.994 3.949 3.906

4.011 3.962 3.914 3.867 3.821 3.776

.97030 .96959 .96887 .96815 .96742 .96667

.1219 .1248 .1276 .1305 .1334 .1363

.1228 1.0075 .1257 1.0079 .1287 1.0082 .1317 1.0086 .1346 1.0090 .1376 1.0094

8.206 8.016 7.834

.99255 .99219 .99182 .99144 .99106 .99067

.2588 .2616 .2644 .2672 .2700 .2728

1.0353

3.864 3.732 .96593

4729

Cosin

Cotg.

Cosec.

7661 7.496 7.337

Soc.

Tan.

Sin.

Angle

Cosin. Cotg.

10361 3.822 3.689 .96517 1.0369 3.782 3.647 .964$0 1.0377 1.0386 1.0394

Cosec.

3.742 3.606 .96363 3.703 3.566 .96285 3.665 3.526 .96206

Sac.

Ton.

Sin.

Angle

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS Angl

Sion

Tn.

Sec.

.2867 .2899 .2931 .2962 .2994 .3026

Cotg.

Cosin.

1.0403 1.0412 1.0423 1.0429 1.0438 1.0448

3.487 3.450 3.412 3.376 3.340 3.305

.96126 .96046 .95964 .95882 .95799 .95715

1.0946 1.0961 1.0975 1.0989 1.1004 1.1019

.3057 .3089 .3121 .3153 .3185 .3217

1.0457 1.0466 1.0476 1.0485 1.0495 1.0505

3.271 3.237 3.204 3.172 3.140 3.108

.95630 .95545 .95459 .95372 .95284 .95195

1.1034 1.1049 1.1064 1.1079 1.1095 1.1110

12.366 2.351 2.337 2.323 2.309 2.295

2.145 2.128 2.112 2.097 2.081 2.066

.90631 .90507 .90383 .90259 .90133 .90007

.3249 .3281 .3314 .3346 .3378 .3411

1.0515 1.0525 1.0535 1.0545 1.0555 1.0566

3.078 3.048 3.018 2.989 2.960 2.932

.95106 .95015 .94924 .94832 .94740 .94646

1.1126 .2.281 1.1142 2.268 1.1158 2.254 1.1174 2.241 1.1190 2.228 1.1207 2.215

2.050 2.035 2.020 2.006 1.991 1.977

.89879 .89752 .89623 .89493 .89363 .89232

.3443 .3476 .3508 .3541 .3574 .3607

1.0576 1.0587 1.0598 1.0608 1.0619 1.0631

2.904 2.877 2.850 2.824 2.798 2.773

.94552 .94457 .94361 .94264 .94167 .94068

1.1223 1.1240 1.1257 1.1274 1.1291 1.1308

2.203 2.190 2.178 2.166 2.154 2.142

1.963 1.949 1.935 1.921 1.907 1.894

.89101 .88968 .88835 .88701 .88566 .88431

.3640 .3673 .3706 .3739 .3772 .3805

1.0642 1 0653 1.0665 1.0676 1.0688 1.0700

2.747 2.723 2.699 2.675 2.651 2.628

.93969 .93869 .93769 .93667 .93565. .93462

1.1326 1.1343 1.1361 1.1379 1.1397 1.1415

2.130 2.119 2.107 2.096 2.085 2.073

1.881 1.868 1.855 1.842 1.829 1.816

.88295 .88158 .88020 .87882 .87743 .87603

.3839 1.0711 .3872 1.0723 .3906 1.0736 .3939 1.0748 .3973 1.0760 .4006 1.0773

2.605 2.583 2.560 2.539 2.517 2.496

.93358 .93253 .93148 .93042 .92935 .92827

1.1434 1.1452 1.1471 1.1490 1.1509 1.1528

2.063 2.052 2.041 2.031 2.020 2.010

1.804 1.792 1.780 1.767 1.756 1.744

.87462 .87321 .87178 .87036 .86892 .86748

.4040 .4074 .4108 .4142 .4176 .4210

1.0785 1.0798 1.0811 1.0824 1.0837 1.0850

2.475 2.455 2.434 2.414 2.394 2.375

.92718 .92609 .92499 .92388 .92276 .92164

1.1547 2.000 1.1566 1.990 1.1586 1.980 1.1606 1.970 1.1626 1.961 1.1646 1.951

1.732 1.720 1.709 1.698 1.686 1.675

.86603 .86457 .86310 .86163 .86015 .85866

.4245 .4279 .4314 .4348 .4383

1.0864 1.0877 1.0891 1.0904 1.0918 1.0932

2.356 2.337 2.318 2.300 2.282 2.264

.92050 .91936 .91822 .91706 .91590 .91472

1.1666 1.1687 1.1707 1.1728 1.1749 1.1770

1.924 1.932 1.923 1.914 1.905 1.896

1.664 1.653 1.643 1.632 1.621 1.611

.85717 .85567 .85416 .85264 .85112 .84959

Cosec.

Sec.

Ton.

Sin.

.4417

Cosin.

Cotg.

Cosec.

Cosec. Soc.

Ton.

Sin.

Angle

Ingle

Sin.

Cosin.

Tan.

Cog.

Sec.

Cosec.

Cotg.

Cosin.

2.459 2.246 .91355 2.443 2.229 .91236 2.427 2.211 .91116 2.411 2.194 .90996 2.396 2.177 .90875 2.381 2.161 .90753

Angle

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS Angle

Sin.

Cosin.

Tan.

Cog.

Sec.

Cosec.

Cotg.

Cosin.

Angle

Sin.

Tan

Sec.

Cosec.

Cotg.

Cosin.

1.1792 1.1813 1.1835 1.1857 1.1879 1.1901

.84805 .84650 .84495 .84339 .84182 .84025

1.2868 1.2898 1.2929 1.2959 1.2991 1.3022

.77715 .77531 .77347 .77162 .76977 .76791

1.1924 1.1946 1.1969 1.1992 1.2015 1.2039

.83867 .83708 .83549 .83389 .83228 .83066

1.3054 1.3086 1.3118 1.3151 1.3184 1.3217

.76604 .76417 .76229 .76041 .75851 .75661

1.2062

.82904 .82741 .82577 .82413 .82248 .82082

1.3251

1.2086 1.2110 1.2134 1.2158 1.2183

.75471 .75280 .75088 .74896 .74703 .74509

1.2208 1.2233 1.2258 1.2283 1.2309 1.2335

.81915 .81748 .81580 .81412 .81242 .81072

1.3456

1.2361 1.2387 1.2413 1.2440 1.2466 1.2494

.80902 .80730 .80558 .80386 .80212 .80038

1.3673

1.2521 1.2549 1.2577 1.2605 1.2633 1.2661

.79864 .79688 .79512 .79335 .79158 .78980

1.3902 1.3941 1.3980 1.4020 1.4061

1.4101'

.71934 .71732 .71529 .71325 .71121 .70916

1.2690 1.2719 1.2748 1.2778 1.2808 1.2838

.78801 .78622 .78442 .78261 .78079 .77897

1.414

.70711

Cosec

Sec.

Ton.

Sin. Angle

1.3284 1.3318 1.3352 1.3386 1.3421

.74314 .74120 .73924 .73728 .73531 .73333

1.3492 1.3527 1.3563 1.3600 1.3636

.73135 .72937 .72737 .72537 .72337 .72136

1.3711 1.3748 1.3786 1.3824 1.3863

Cosin.

Cotg.

Cosec.

Sec.

Tan.

Sin.

Angle

CURVE FORMULAE

CURVE TABLE Table of Tangent and External to a 1 Curve

Angle of Intersection I

;

a

To find Tangent and External for curve of any other degree, divide by degree of curve and add correction found in column of corrections.

Degree of curve with a given I may be found by dividing tangent, (or external), opposite I by given tangent, (or external).

The distance from a point on the tangent to the curve is very nearly the square of the tangent length divided by twice the radius.

CURVE FORMULAS 50 sin % D

Radius : Length of Curve: L

= 100

D

--. 0174533 X A X R also L= Degree of Curve: D = 100

L L

Tangent:

T = R tan % A

Long Cord:

LC

=-2R sin % A

Middle Ordinate: M =

External :

E

=

R (1-Cos % A) Ttan

rA

TABLE V. TANGENTS AND EXTERNALS TO A 10 CURVE i T 10

E

=10o

10' 20' 30' 40' 50'

50.00 58.34 66.67 75.01 83.34 91.68

.218 .297 .388 .491 .606 .733

10' 20' 30' 40' 50'

100.01 108.35 116.68 125.02 133.36 141.70

.873 1.024 1.188 1.364 1.552 1.752

10' 20' 30' 40' 50'

150.04 158.38 166.72 175.06 183.40 191.74

1.964 2.188 2.425 2.674 2.934 3.207

10' 20' 30' 40' 50'

200.08 208.43 216.77 225.12 233.47 241.81

3.492 3.790 4.099 4.421 4.755 5.100

10' 20' 30' 40' 50'

250.16 258.51 266.86 275.21 283.57 291.92

5.459 5.829 6.211 6.606 7.013 7.432

2*

30

40

5P

60 10' 20' 30' 40' 5,0'

300.28 7.863.

308.64 8.307 316.99 8.762 325.35 9.230 333.71 9.710 342.08 10.202

10' 20' 30' 40' 50'

350.44 358.81 367.17 375.54 383.91 392.28

10.707 11.224 11.753 12.294 12.847 13.413

10' 20' 30' 40' 50'

400.66 409.03 417.41 425.79 434.17 442.55

13.991 14.582 15.184 15.799 16.426 17.065

10' 20' 30' 40' 50'

450.93 459.32 467.71 476.10 484.49 492.88

17.717 18.381 19.058 19.746 20.447 21.161

100 10' 20' 30' 40' 50'

501.28 509.68 518.08 526.48 534.89 543.29

21.887 22.624 23.375 24.138 24.913 25.700

70

80

90

LI

E

10 20 30 40 50

551.70 560.11 568.53 576.95 585.36 593.79

26.500 27.313 28.137 28.974 29.824 30.686

120 10 20' 30' 40' 50'

602.21 610.64 619.07 627.50 635.93 644.37

31.561 32.447 33.347 34.259 35.183 36.120

.006

652.81 37.070 130, 10' 661.25 38.031 20' 669.70 39.006 30' 678.15 39.993 40' 686.60 40.992 50' 695.06 42.004

10 C. T .13 E .011

11

10 C.

T .06 E .003

15°C. T .09 E .004

14* 10' 20' 30' 40' 50'

703.51 711.97 720.44 728.90 737.37 745.85

754.32 10 762.80 20 771.29 30 , 779.77 40 788.26 50 796.75

150

°

805.25 10 813.75 20' 822.25 30 830.76 40' 839.27 50' 847.78

16

20" C. T .13 E .006

1-20

T

°

°

856.30 10' 864.82 20' 873.35 30' 881.88 40 890.41 50' 898.95

17

180

907.49 10' 916.03 20' 924.58 30' 933.13 40 941.69 50' 950.25

+

15° C. T .19 E .017

30' 1087 E 102.35 50 1105.1 105.60

1113.7 10' 1122.4 20' 1131.0 30' 1139.7 40' 1148.4 50' 1157.0

220

107.24 108.90 110.57 112.25 113.95.

115.66

+ 5o C. T .10 E .013

°

1165.7 117.38 10 C. 10' 1174.4 119.12 T 20' 1183.1 120.87 30' 1191.8 122.63 .19 E 40' 1200.5 124.41 50' 1209.2 126.20 .025

230

10' 20' 30' 40' 50' °

25

10' 20' 30'

40' 50'

1217.9 1226.6 1235.3 1244.0 1252.8 1261.5 1270.2 1279.0 1287.7 1296.5 1305.3 1314.0

128.00 129.82 131.65 133.50 135.35 137.23

15" C. T 139.11 141.01 .29 142.93 E 144.85 146.79 .038 148.75

26 56.309. 1322.8 150.71.

57.498 10' 1331.6 152.69 58.699 20' 1340.4 154.69 59.914 30' 1349.2 156.70 ° ° 61.141 20 C. 40' 1358.0 158.72 20 C. T 62.381 50' 1366.8 160.76 T ° .26 .39 27 63.634 1375.6 162.81 E E 64.900 10' 1384.4 164.86 .022 66.178 20' 1393.2 166.95 .051 67.470 30' 1402.0 169.04 68.774 40' 1410.9 171.15 70.091 50' 1419.7 173.27

958.81 967.38 975.96 984.53 993.12 1001.7

30 C 200 r 10' T 20' .19 30' E 40' 50' .008

1010.3 1018.9 1027.5 1036.1 1044.7 1053.3

88.389 89.888 91.399 92.924 94.462 96.013

1428.6 10' 1437.4 20' 1446.3 30' 1455.1 40' 1464.0 50' 1472.9

280

°

29

1481.8

10' 1490.7 20' 1499.6 30' 1508.5 40' 1517.4 50' 1526.3

175.41 ° 177.55 179.72 25 C. T 181.89 184.08 .49 186.29 E 188.51 .065 190.74 192.99 195.25.

197.53 199.82 °

°

°

T = R tan V2I

1061.S 97.577 1070.6 99.155

30.

°

10' 20' 30' 40' 50'

°

19

IE

40' 1096.4 103.97

E

240

49.441 50.554 51.679 52.818 53.969 55.132

T

20- 1079.2 100.75

T .06

71.421 ° 72.764 74.119 25 C. T 75.488 76.869 .32 78.264 E .028 79.671 81.092 82.525 83.972 85.431 86.904

°

25 C. T .16 E .007,

10

5" C.

°

43.029 44.066 45.116 46.178 47.253 48.341

I

30 C. T .39 E .034

300

10' 20, 30' 40' 50'

= R exsec %I

1535.3 1544.2 1553.1 1562.1 1571.0 1580.0

202.12 204.44 206.77 209.12 211.48 213.86

30 C. T .59 E .078

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 10 CURVE I 31*

T

1-40

E EE

1589.0 1598.0 1606.9 1615.9 1624.9 1633.9

216.3 218.7 221.1 223.5 226.0 228.4

1643.0 1652.0 1661.0 1670.0 1679.1 1688.1

230.9 233.4 235.9 238.4 241.0 243.5

1697.2 1706.3 1715.3 1724.4 1733.5 1742.6

'1"

.

-=50.

T

I

387.4 390.7 394.1 397.4 400.8 404.2

51"

10' 20' 30' 40' 50'

2142.2 2151.7 2161.2 2170.8 2180.3 2189.9

420 10' 20' 30' 40' 50'

2199.4 2209.0 2218.6 2228.1 2237.7 2247.3

407.6 411.1 414.5 418.0 421.4 425.0

52

246.1 248.7 251.3 253.9 256.5 259.1

430

2257.0 2266.6 2276.2 2285.9 2295.6 2305.2

428.5 10" C. 432.0 T 435.6 439.2 .34 442.8 E 446.4 .075

530

10' 20' 30' 40' ,50'

1751.7 1760.8 1770.0 1779.1 1788.2 1797.4

261.8 264.5 267.2 269.9 272.6 275.3

440,

2314.9 2324.6 2334.3 2344.1 2353.8 2363.5

450.0 453.6.

457.3 461.0 464.6 468.4

54

10' 20' 30' 40' 50'

1806.6 1815.7 1824.9 1834.1 1843.3 1852.5

278.1 280.8 283.6 286.4 289.2 292.0

10' 20' 30' 40' 50'

2373.3 2383.1 2392.8 2402.6 2412.4 2422.3

472.1 475.8 479.6 483.4 487.2 491.0

10' 20' 30' 40' 50'

1861.7 1870.9 1880.1 1889.4 1898.6 1907.9

294.9 297.7 300.6 303.5 306.4 309.3

460 10' 20' 30' 40' 50'

2432.1 2441.9 2451.8 2461.7 2471.5 2481.4:

37* 10' 20' 30' 40' 50'

1917.1 1926.4 1935.7 1945.0 1954.3 1963.6

312.2 315.2 318.1 321.1 324.1 327.1

470

2491.3 2501.2 2511.2 2521.1 2531.1 2541.0

494.8 498.7 502.5 506.4 ° 510.3 20 C. 514.3 T .68 518.2 E 522.2 526.1 .151 530.1 534.2538.2

38*

1972.9 1982.2 1991.5 2000.9 2010.2 2019.6

330.2 333.2 336.3 339.3 342.4 345.5

2551.0 2561.0 2571.0 2581.0 2591.0 2601.1

542.2 546.3 550.4 554.5 558.6 562.8

10' 20' 30' 40' 50' °

32

10' 20' 30' 40' 50' 330

10' 20' 30' 40' 50' 340

10' 20' 30' 40' 50' 35° 10' 20' 30' 40' 50' °

36

410

5" C. T .13 E .023

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50' 10' 20' 30' 40' 50'

T

2732.9 2743.1 2753.4 2763.7 2773.9 2784.2

E

I=60j

2794.5 2804.9 2815.2 2825.6 2835.9 2846.3

618,4 622.8 627.2 5o C. 631.7 T 636.2 .21 640.7 E 645.2 .056 649.7 654.3 658.8 663.4' 668.0

2856.7 2867.1 2877.5 2888.0 2898.4 2908.9

672.7 10" C. 677.3 T 682.0 686.7 .42 E 691.4 696.1 .112

2919.4 2929.9 2940.4 2951.0 2961.5 2972.1

700.9 705.7 710.5 715.3 720.1 725.0

2982.7 2993.3 3003.9 3014.5 3025.2 3035.8

729.9 734.8 739.7 744.6 749.6 754.6

°

15"C. T .40 E .070

?0"

C. T .53 E .093

450

10' 20' 30' 40' 50'

15" C. T .51 E .116

10' 20' 30' 40' 50' 550

10' 20' 30' 40' 50' 56

°

3110.9 3121.7 3132.6 3143.4 3154.2 3165.1

759.6 764.6 769.7 774.7 20 C. 779.8 T 784.9 .84 E 790.1 795.2 .225 800.4 805.6 810.9 816.1

3176.0 3186.9 3197.8 3208.8 3219.7 3230.7

821.4 826.7 832.0 837.3 842.7 848.1

3241.7 3252.7 3263.7 3274.8 3285.8 3296.9

853.5 858.9 864.3 869.8 875.3 880.8

3308.0 3319.1 3330.3 3341.4 3352.6 3363.8

886.4 30 C. 892.0 T 897.5 1.27 903.2 E 908.8 914.5 .340

3046.5 10' 3057.2 20' 3067.9 30' 3078.7 40' 3089.4 50' 3100.2

570

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50' 390

10' 20' 30' 40' 50' 40" 10' 20' 30' 40' 50'

480

25

10' 20' 30' 40' 50'

C.

58

25" C. T .85 E .189

2029.0 2038.4 2047.8 2057.2 2066.6 2076.0

T .67 E 348.6 .117 351.8 354.9.

358.1 361.3 364.5

490

10' 20' 30' 40' 50'

2611.2 2621.2 2631.3 2641.4 2651.5 2661.6

566.9 571.1 575.

579.5 583.8 588.0

2085.4 2094.9 2104.3 2113.8 2123.3 2132.7

367.7 30" C. T 371.0 374.2 .80 377.5 E 380.8 384.1 .141

500 10' 20' 30' 40' 50'

2671.8 2681.9 2692.1 2702,3 2712.5 2722.7

592.3 30" C. T 596.6 600.9 1.02 605.3 E 609.6 614.0 .227

T= R tan I

10' 20' 30' 40' 50' 590

10' 20' 30' 40' 50' 600

10' 20' 30' 40' 50'

E=Rexsec'/21

°

25 C. T 1.05 E .283

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 1 CURVE I

T

E

3375.0 3386.3 3397.5 3408.8 3420.1 3431.4

920.2 925.9 931.6 937.3 943.1 948.9

3442.7 10' 3454.1 20' 3465.4 30' 3476.8 40' 3488.3 50' 3499.7

954.8 960.6 966.5 972.4 978.3 984.3

.080

990.2 996.2 1002.3 1008.3 1014.4 1020.5

10' C. T

610 10' 20' 30' 40' 50' °

62

630 10' 20' 30' 40' 50'

3511.1 3522.6 3534.1 3545.6 3557.2 3568.7

=70 + 5 C. T .25 E

1032.8 1039.0 1045.2 1051.4 1057.7

3650.2 10' 3661.9 20' 3673.7 30' 3685.4 40' 3697.2 50' 3709.0

1063.9 1070.2 1076.6 1082.9 1089.3 1095.7

°

65

66

10' 20' 30' 40' 50' °

67

10' 20' 30' 40' 50' °

68

10' 20' 30' 40' 50'

3720.9 3732.7 3744.6 3756.5 3768.5 3780.4 3792.4 3804.4 3816.4 3828.4 3840.5 3852.6 3864.7 3876.8 3889.0 3901.2 3913.4 3925.6

690 3937.9 10' 3950.2 20' 3962.5 30' 3974.8 40' 3987.2 50' 3999.5 70

°

10' 20' 30' 40' 50'

7201

.51 E .159

730 10' 20' 30' 40' 50'

T

800

E

4086.9 4099.5 4112.1 4124.8 4137.4 4150.1

1308.2 1315.6 1322.9 1330.3 1337.7 1345.1

4162.8 4175.6 4188.5 4201.2 4214.0 4226.8

1352.6 1360.1 1367.6 1375.2 1382.8 1390.4

4239.7 4252.6 4265.6 4278.5 4291.5 4304.6

1398.0 1405.7 1413.5 1421.2 1429.0 1436.8

+

T

4011.9 4024.4 4036.8 4049.3 4061.8 4074.4

740

150C. T .76 E .240

1452.5 1460.4 1468.4 1476.4 1484.4

4396.5 10' 4409.8 20' 4423.1 30' 4436.4 40' 4449.7 50' 4463.1

1492.4 1500.5 1508.6 1516.7 1524.9 1533.1

°

1102.2 76 4476.5 1108.6 10' 4489.9 1115.1 20' 4503.4 ° 1121.7 20 C 30' 4516.9 40' 4530.4 1128.2 T 50' 4544.0 1134.8 1.02 ° 77 4557.6 E 1141.4 1148.0 10' 4571.2 20' 4584.8 1154.7 .31 1161.3 30' 4598.5 1168.1 " 40' 4612.2 1174.8 50' 4626.0

1541.4 1549.7 1558.0 1566.3 1574.7 1583.1

10' 20' 30' 40' 50'

4980.7 4995.4 5010.0 5024.8 5039.5 5054.3

1862.2 1871.8 1881.5 1891.2 1900.9 1910.7

10'C. 83 T 10' 20' .61 30' E 40' .220 50'

5069.2 5084.0 5099.0 5113.9 5128.9 5143.9

1920.5 10 C. 1930.4 T 1940.3 .72 1950.3 1960.2 E 1970.3 .299

10 20' 30' 40' 50'

.30 E

.110

°

82

4639.8 10' 4653.6 20' 4667.4 30' 4681.3 40' 4695.2 50' 4709.2

1643.0 1651.7 1660.5 1669.2 1678.1 1686.9

1591.6 1600.1 1608.6 1617.1 1625.7 1634.4

84

15' C. T .91 E

850 10' 20' 30' 40' 50'

.332

°

86

10' 20' 30' 40' 50'

20C T 1.22 E

870 10' 20' 30' 40' 50'

.445

°

88

78a

4723.2 10' 4737.2 20' 4751.2 30' 4765.3 40' 4779.4 50' 4793.6

1695.8 1704.7 1713.7 172237 1731.7 1740.8

10' 20' 25 C. T 30' 1.53 40' 50' E .558 89" 10' 20' 30' 40' 50'

1265.0 30' C. 1272.1 T 1279.3 1.54 1286.5 1293.6 E 1300.9 .485

4807.7 800 10' 4822.0 20' 4836.2 30' 4850.5 40' 4864.8 50' 4879.2

1749.9 1759.0 1768.2 1777.4 1786.7 1796.0

30' C. 900 T 10' 1.84 20' 30' E 40' .671 50'

°

T-=Rtan V21

.149

°

5159.0 1980.4

10' 20' 30' 40' 50'

1181.6 1188.4 1195.2 25, C. T 1202.0 1208.9 1.28 1215.8 E 1222.7 .403 1229.7 1236.7 1243.7 1250.8 1257.9

79

°

°

4330.7 4343.8 4356.9 4370.1 4383.3

°

75

1=90

1805.3 + 1814.7 1824.15"C. 1833.6 T 1843.1 .36 1852.6 E

4317.6 1444.6

10' 20' 30' 40' 50'

E

4893.6 4908.0 4922.5 4937.0 4951.5 4966.1

81°

5, C. T

°

3591.9 3603.5 3615.1 3626.8 3638.5

°

10' 20' 30' 40' 50'

20' 30' 40' 50'

3580.3 1026.6

10' 20' 30' 40' 50'

710

16'

°

64

I

E=Rexsec VT

5174.1 5189.3 5204.4 5219.7 5234.9

1990.5 2000.6 2010.8 2021.1 2031.4 150C.

5250.3 5265.6 5281.0 5296.4 5311.9 5327.4

2041.7 T 2052.1 1.09 2062.5 E 2073.0 2083.5 .450 2094.1

5343.0 5358.6 5374.2 5389.9 5405.6 5421.4

2104.7 2115.3 2126.0 2136.7 2147.5 20 C. 2158.4 T 1.45 2169.2 2180.2 2191.1 .603 2202.2 2213.2 2224.3

5437.2 5453.1 5469.0 5484.9 5500.9 5517.0 5533.1 5549.2 5565.4 5581.6 5597.8 5614.2 5630.5 5646.9 5663.4 5679.9 5696.4 5713.0

2235.5 2246.7 2258.0 25°C. 2269.3 T ?280.6 1.83 E 2292.0 E 2303.5 .756 2315.0 2326.6 2338.2 2349.8 2361.5

5729.7 5746.3 5763.1 5779.9 5796.7 5813.6

2373.3 30'C. 2385.1 T 2397.0 2.20 2408.9 2420.9 E 2432.9 .910

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 10 CURVE ll

110

T

E

8336.7 8362.7 8388.9 8415.1 8441.5 8468.0

4386.1 4407.6 4429.2 4450.9 4472.7 4494.6

8494.6 8521.3 8548.1 8575.0 8602.1 8629.3

4516.6 4538.8 4561.1 4583.4 4606.0 4628.6

8656.6 8684.0 8711.5 8739.2 8767.0 8794.9

4651.3 4674.2 4697.2 4720.3 4743.6 4766.9

10' 20' 30' 40' 50'

8822.9 8851.0 8879.3 8907.7 8936.3 8965.0

4790.4 4814.1 4837.8 4861.7 4885.7 4909.9

1150 10' 20' 30' 40' 50'

8993.8 9022.7 9051.7 9080.9 9110.3 9139.8

4934.1 4958.6 4983.1 5007.8 5032.6 5057.6

1160

9169.4 9199.1 9229.0 9259.0 9289.2 9319.5

5082.7 5107.9 5133.3 5158.8 5184.5 5210.3

1170 10' 20' 30' 40' 50'

9349.9 9380.5 9411.3 9442.2 9473.2 9504.4

5236.2 5262.3 5288.6 5315.0 5341.5 5368.2

7886.2 4018.2 7910.4 4037.8 7934.6 4057.4 7959.C04077.2 7983.5 4097.1 8008.0 4117.0

1180

10' 20' 30' 40' 50'

9535.7 9567.2 9598.9 9630.7 9662.6 9694.7

5395.1 5422.1 5449.2 5476.5 5504.0 5531.7

1090 10' 20' 30' 40' 50'

8032.7 8057.4 8082.3 8107.3 8132.3 8157.5

4137.1 4157.3 4177.5.

4197.9 4218.4 4239.0

119' 10' 20' 30' 40' 50'

9727.0 9759.4 9792.0 9824.8 9857.7 9890.8

5559.4 5587.4 5615.5 5643.8 5672.3 5700.9

1100

8182.8 8208.2 8233.7 8259.3 8285.0 8310.8

4259.7 4280.5 4301.4 4322.4 4343.6 4364.8

9924.0 9957.5 9991.0 10025.0 10059.0 10093.0

5729.7 5758.6 5787.7 5817.0 5846.5 5876.1

I

.

T

E

6950.6 6971.3 6992.0 7012.7 7033.6 7054.5

3278.1 3294.1 3310.1 3326.1 3342.3 3358.5

7075.5 7096.6 7117.8 7139.0 7160.3 7181.7

3374.9 3391.2 3407.7 3424.3 3440.9 3457.6

7203.2 7224.7 7246.3 7268.0 7289.8 7311.7

3474.4 3491.3 3508.2 3525.2 3542.4 3559.6

1130

10' 20' 30' 40' 50' 104' 10' 20' 30' 40' 50'

7333.6 7355.6 7377.8 7399.9 7422.2 7444.6

1140

2751.3 2764.8 2778.3 2792.0 2805.6 2819.4

1050

7467.0 7489.6 7512.2 7534.9 7557.7 7580.5

3576.8 3594.2 3611.7 3629.2 3646.8 3664.5 15 C. T 3682.3 3700.2 1.56 3718.2 E 3736.2 3754.4 .806 3772.6

6363.4 2833.2 10' 6382.1 2847.0 20' 6400.8 2861.0 30' 6419.5 2875.0 40', 6438.4 2889.0 50' 6457.3 2903.1

1060

3791.0 3809.4 3827.9 ° 3846.5 3865.2 20 C. T 3884.0 2.08 3902.9 E 3921.9 3940.9 1.08 3960.1 3979.4.

3998.7

=100

I

T

E

910 10' 20' 30' 40' 50'

5830.5 5847.5 5864.6 5881.7 5898.8 5916.0

2444.9 2457.1 2469.3 2481.5 2493.8 2506.1

1010 ..

920

5933.2 5950.5 5967.9 5985.3 6002.7 6020.2

2518;5 2531.0 2543.5 2556.0 2568.6 2581.3

102*

I

10' 20' 30' 40' 50'

10' 20' 30' 40' 50' 10' 20' 30' 40' 50'

6037.8 2594.0 10 C. 10' 6055.4 2606.8 T 20' 6073.1 2619.7 30' 6090.8 2632.6 .86 40' 6108.6 2645.5 E 50' 6126.4 2658.5 .401 940 6144.3 2671.6 10' 6162.2 2684.7 20' 6180.2 2697.9 30' 6198.3 2711.2 40' 6216.4 2724.5 50' 6234.6 2737.9 930

950

10' 20' 30'

40' 50'

6252.8 6271.1 6289.4 6307.9 6326.3 6344.8

10' 20' 30' 40' 50'

96*

970

10' 20' 30'

40' 50' 980 10' 20' 30'

10' 20' 30' 40' 50'

°

20 C T 1.74 107* 6476.2 2917.3 E 10' 6495.2 2931.6 6514.3 2945.9 .809 20' 6533.4 2960.3 30' 40' 6552.6 2974.7.

50' 6571.9 2989.2

6591.2 6610.6 6630.1 6649.6 40', 6669.2 50' 6688.8

3003.8 3018.4 3033.1 3047.9 3062.8 3077.7

6708.6 3092.7 10' 6728.4 3107.7 20' 6748.2 3122.9, 30' 6768.1 3138.1 40' 6788.1 3153.3 50' 6808.2 3168.7

990

1030

1080 °

25

C

T 2.18 E 1.02

10' 20' 30' 40' 50'

7603.5 7626.6 7649.7 7672.9 7696.3 7719.7 7743.2 7766.8 7790.5 7814.3 7838.1 7862.1

5° C.

T .51 E .268

°

10' 20' 30' 40' 50' 1120

10' 20' 30' 40' 50' 10' 20' 30' 40' 50'

10' 20' 30' 40' 50'

°

°

6828.3 3184.1 30 C 10' 6848.5 3199.6 T 20' 6868.8 3215.1 2.62 6889.2 3230.8 40' 6909.6 3246.5 50' 6930.1 3262.3 1.22

1000

111

10' 20' 30' 40' 50'

T = R tan W/2 I = Rtan L

30 C. 1200 T 10' 20' 3.14 30' E 40' 1.63 50',

E = Rexsech/2 E = R exsec 1/lI

I=120

°

5o C. T .62 E .360

10

°

C.

T 1.25 E .721

15 C.

T 1.93 E 1.09

°

20 C. T 2.52 E 1.46

°

25 C. T 3.16 E 1.83

°

30 C. T 3.81 E 2.20

USEFUL RELATIONS Lineal feet X.00019 = miles Lineal yards X.0006 = miles Square inches X.007 = square feet Square feet X.111 = square yards Square yards X.0002067 = acres Acres X 4840 = square yards Cubic inches X.00058 = cubic feet Cubic feet X.03704 = cubic yards Links x.22 = yards Links x.66 = feet Feet X 1.5 = links 360 ° = 21600' = 1296000" Radius = are of 57.2957790 ° Arc of 1" (radius = 1) = .017453292 Arc of 1' (radius = 1) = .000290888 Arc of 1" (radius = 1) = .000004848 Curvature of Earth's surface = about 0.7 feet in 1 mile Curvature in feet = 0.667 (Dist. in miles)' Difference between arc and chord length, 0.05 feet in 11 % miles Probable error of a single observation = 0.6754 Error in chaining of 0.01 feet in 100 feet: Due to1. Length of tape error of 0.01 feet 2. Alignment. One end 1.4 feet out of line 3. Sag of tape at center of 0.61 feet.

4. Temperature difference of 15" 5. Difference of pull of 15 lbs.

SQUARE MEASURE 144 sq. inches = 1 sq. ft.

9 sq. ft. = 1 sq. yard 301/ sq. yds. = 1 sq. rd.

40 sq. rds. = 1 rood.

4 roods = 1 acre 640 acres = 1 sq. mile.

SURVEYORS' MEASURE 7.92 inches = 1 link.

25 links = 1 red.

4 rds. = 1 chain.

10 sq. chains or 160 sq. rods = 1 acre.

640 acres = 1 sq. mile.

36 sq. miles (6 miles sq.) = 1 township.

n -i

TABLE VI. INCHES TO DECIMALS OF A FOOT

0

Ia.

1

2

3

4

5

6

7

8

9

11

10

In.

0 Foot .0833 .1667 .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167 0 1-32 .0026 .0859 .1693 .2526 .3359 .4193 .5026 .5859 .6693 .7526.8359 .9193 1-32 1-16 .0052 .0885 .1719 .2552 .3385 .4219 .5052 .5885.6719 .7552 .8385 .9219 1-16

32 .0078 .0911 .1745 .2578 .3411 .4245 .5078 .5911 .6745 .7578 .8411 .9245 3-32 1-8 .0104 .0938 .1771 .2604 .3438 .4271 .5104 .598 .6771 .7604 .8438 .9271 1-8

5-32 .0130 .0964 .1797 .2630 .3464 .4297 .5130 .5964 .6797 .7630 .8464 .9297 5-32

8-16 7-32 1-4 9-32 5-16

.01561.09901.1823 .0182 .1016 .1849 .0208 .1042 .1875 .0234 .1068 .1901 .0260 .1094.1927

.2656 .2682 .2708 .2734 .2760

.3490 .3516 .3542 .8568 .3594

.423 .4349 .4375 .4401 .4427

.5156 .5182 .5208 .5234 .5260

.5990 .6016 .6042 .6068 .6094

.6823 .6849 .875 .6901 .6927

.7656 .7682 .7708 .774 .7760

.8490 .8516 .8542 .8568 .8594

.9382 .949 .9375 .9401 .9427

8-16 7-32 1-4 9-32 6-16

11-32

.

1953 .2786 .3620 .4453 .5286 .6120 .6953 .7786 .8620 .9453 11-32 .0286 .1129

13-32 7-16

.0339 .1172 .2005 .2839 .3672 .4505 .5339 .6172 .7005 .7839 .8672 .9505 13-32 .0365 .1198 .2031 .2865 .3698 .4531 .5365 .6198 .7031 .7865 .8698 .9531 7-16

17-32

.0443 .1276 .2109 .2943 .8776 .4609 .5443 .6276 .7109 .7943 .8776 .960

3-8

.4479 .5313 .6146 .6979.7813 .8646 .9479 3-8

.0313 .1146 .1979.2813 .36

15-32 .0391 .1224 .2057 .2891 .8724 .4557 .5391 .6224 .7057 .7891 .8724 .955715-32 1-2 .0417 .1250 .2083 .2917 .3750 .4583 .5417 .6250 .7083 .7917 .8750 .9583 1-2 9-16 19-32 5-8 21-32 11-16 23-32

.0469 .1302 .2135 .0495 .1328 .2161 .0521 .1354 .2188 .0547.1380 .2214 .0573.1406 .2240 .0599 .1432 .2266

.2969 .2995 .3021 .3047 .3073 .3099

. 802 .4635 .5469 .8828 .4061 .549 .3854 .4688 .51 .3880 .4714 .5547 .3906 .4740 .5573 .3932 .4766 .5599

.6302 .6328 .6354 .6380 .6406 .6432

.7135 .7161 .7188 .7214 .7240 .7266

.7969 .7995 .8021 .8047 .8073 .8099

.8802 .8828 .8854 .8880 .8906 .8932

17-32

.9635 9-16 .9661 19-32 688 5-8 .9714 21-32 .974011-16 .9766 23-32

3-4

.0625 .1458 .2292 .3125 .3958 .4792 .5625 .6458 .7292 .8125 .8958 .9792 8-4

27-, 7-8 29-32

.0703 .1536 .2370 .3203 .4036 .4870 .5703 .6536 .7370 .8203 .9036 .9870 27-32 .0729 .1563 .2396 .3229 .4063 .4896 .5729 .656.7396 .822 .9063.9896 7-8 .0755 .1589 .2422 .3255 .4089 .4922 .5755 .6589 .7422 .8255 .9089 .9922 29-32

25-32 .0651 .1484 .2318 .3151 .3984 .4818 .5651 .6484 .7318 .8151 .8984 .9818 25-32 13-16 .0677 .1510 .2344 .3177 .4010 .4844 .5677 .6510 .7344 .8177 .9010 .9844 13-16 15-16 .0781 .1615 .2448 .3281 .4115 .4948 .5781 .6615 .7448 .8281 .9115 .9948 15-16 81-82 .0807 .1641 .2474 .3307 .4141 .4974 .580 .6641 .7474 .8307 .9141 .9974 31-82 0

1

2

8

4

5

6

7

8

9

10

11

TABLE VII. MINUTES IN DECIMALS OF A DEGREE 0'30" 1 00 30 2 00 30 3 00 30 4 00 30 5 00 30 6 00 30 7 00 30 8 00 30 9 00 30 10 00

.00833 .01667 .02500 .03333 .04167 .05000 .05833 .06667 .07500 .08333 .09167 .10000 .10833 .11667 .12500 .13333 .14167 .15000 .15833 .16667

10' 30" .17500 11 00 .18333 30 .19167 12 00 .20000 30 .20833 13 00 .21667 30 .22500 14 00 .23333 30 .24167 15 00 .25000 30 .25833 16 00 .26667 30 .27500 17 00 .28333 30 .29167 18 00 .30000 30 .30833 19 00 .31667 30 .32500 20 00 .33333

20' 30" 21 00 30 22 00 30 23 00 30 24 00 30 25 00 30 26 00 30 27 00 30 28 00 30 29 00 30 30 00

.34167 .35000 .35833 .36667 .37500 .38333 .39167 .40000 .40833 .41667 .42500 .43333 .44167 .45000 .45833 .46667 .47500 .48333 .49167 .500000

30' 30" .50833 31 00 .51667 30 .52500 32 00 .53333 30 .54167 33 00 .55000 30 .55833 34 00 .56667 30 .57500 35 00 .58333 30 .59167 36 00 .60000 30 .60833 37 00 .61667 30 .62500 38 00 .63333 30 .64167 39 00 .65000 30 .65833 40 00 .66667

40' 30" .67500 41 00 .68333 30 .69167 42 00 .70000 30 .70833 43 00 .71667 30 .72500 44 00 .73333 30 .74167 45 00 .75000 30 .75833 46 00 .76667 30 .77500 47 00 .78333 30 .79167 48 00 .80000 30 .80833 49 00 .81667 30 .82500 50 00 .83333

50' 30" .84167 .85000 51 00 30 .85833 52 00 .86667 .87500 30 .88333 53 00 .89167 30 .90000 54 00 30 .90833 .91667 55 00 30 .92500 56 00 .93333 30 .94167 57 00 .95000 30 .95833 58 00 .96667 30 .97500 59 00 .98333 30 .99167 60 00 1.00000

TABLE VIII. MIDDLE ORDINATES OF RAILS

Length of Rail (feet) C o0

R Feet

0-20 17189 0-40 8594 1-0 5730 1-20 4297 1-40 3438 2-0 2865 2-20 2456 2-40 2149 3-0 1910 3-20 1719 3-40 1563 4-0 1433 4-20 1323 4-40 1228 5 1146 6 955.3 819.0 7

30 28 26 24 22 20 Inch Inch Inch Inch Inch Inch

C o

.08 .16 .24 .31 .39 .47 .55 .63 .71 .78 .86 .94 1.02 1.10 1.18 1.41 1.65

8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26

.07 .14 .20 .27 .34 .41 .48 .55 .62 .68 .75 .82 .89 .96 1.03 1.23 1.44

.06 .05 .1 .10 .18 .15 .23 .20 .29 .25. .35 .30 .41 .35 .47 .40 .53 .45 .59

.50

.65 .71 .77 .83 .89 1.06 1.24

.55 .60 .65 .70 .75 .90 1.05

.04 .08 .13 .17 21 .25 .29 .33 .38 .42 .46 .50 .55 .59 .63 .76 .89

.03 .07 .10 .13 .17 .20 .23 .27 .31 .35 .38 .42 .45 .48 .52 .62 .73

R Feet

30 28 26 24 22 20 Inch Inch Inch Inch Inch Inch

716.8 1.88 1.64 1.42 637.3 2.12 1.84 1.60 2.05 1.78 573.736 521.7 2.59 2.26 1.95 478.3 3.83 2.47 2.15 441.7 3.05 2.66 2.30 410.3 3.30 2.87 2.48 383.1 3.54 3.08 2.68 359.3 3.76 3.28 2.83 338.3 4.00 3.48 3.02 319.6 4.21 3.67 3.18 302.9 4.45 3.89 3.36 287.9 4.70 4.09 3.55 262.0 5.164.44 3.84 240.5 5.64 4.92 4.20 222.3 6.07 5.29 4.58

1.20 1.01 .84 1.35 1.14 .94 1.50 1.27 1.04 1.65 1.39 1.15 1.81 1.54 1.26 1.96 1.66 1.36 2.10 1.78 1.46 2.26 1.91 1.57 2.40 2.041.67 2.57 2.161.78 2.70 2.281.87 2.86 2.41 1.98 3.00 2.54 2.09 3.30 2.80 2.29 3.59 3.04 2.50 3.88 3.29 2.70

TABLE IX. SHORT RADIUS CURVES Radius Feet 35 45 50 60 75 100 120 150 190 200 225 240 250 275 288 300 350 376 400 410

ChObord Central Feet Angle 10 10 15 15 15 20 20 20 25 25 25 25 25 25 50 50 50 50 50 50

16-26 12-46 17-16 14-22 11-30 11-30 9-34 7-39 7-32 7-10 6-25 5-58 5-44 5-12 9-58 9-32 8-12 7-40 7-10 7-00

Deflection Angle

Deflection for 1 Foot

8-13 6-23 8-38 7-11 5-45 5-45 4-47 3-49 3-46 3-35 3-12 2-59 2-52 2-36 4-59 4-46 4-06 3-50 3-35 3-30

49.3 38.3 34.5 28.8 23.0 17.3 14.3 11.5 9.15 8.6 7.7 7.2 6.9 6.2 6.0 5.7 4.9 4.6 4.3 4.2

To find length of curve divide angle from P. C. to P. T. by central angle of chord, and multiply by length of chord.

TABLE X. RODS IN FEET, IOTHS AND 100TIIS OF FEET

Feet

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

16.50 33.00 49.50 66.00 82.50 99.00 115.50 132.00 148.50 165.00 181.50 198.00 214.50 231.00 247.50 264.00 280.50 297.00 313.50 330.00

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

346.50 363.00 379.50 396.00 412.50 429.00 445.50 462.00 478.50 495.00 511.50 528.00 544.50 561.00 577.50 594.00 610.50 627.00 643.50 660.00

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a

Feet

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

1336.50 1353.00 1369.50 1386.00 1402.50 1419.00 1435.50 1452.00 1468.50 1485.00 1501.50 1518.00 1534.50 1551.00 1567.50 1584.00 1600.50 1617.00 1633.50 1650.00

Feet

Feet

Feet

o

676.50 61 1006.50 693.00 62 1023.00 709.50 63 1039.50 726.00 64 1056.00 742.50 65 1072.50 759.00 66 1089.00 775.50 67 1105.50 792.00 68 1122.00 808.50 69 1138.50 825.00 70 1155.00 841.50 71 1171.50 858.00 72 1188.00 874.50 73 1204.50 891.00 74 1221.00 907.50 75 1237.50 924.00 76 1254.00 940.50 77 1270.50 957.00 78 1287.00 973.50 79 1303.50 990.00 80 1320.00

TABLE XI. LINKS IN FEET, IOTHS AND 100THS OF FEET .

Feet

.

Feet

.

Feet

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.66 1.32 1.98 2.64 3.30 3.96 4.62 5.28 5.94 6.60 7.26 7.92 8.58 9.24 9.90 10.56 11.22

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

11.88 12.54 13.20 13.86 14.52 15.18 15.84 16.50 17.16 17.82 18.48 19.14 19.80 20.46 21.12 21.78 22.44

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

23.10 23.76 24.42 25.08 25.74 26.40 27.06 27.72 28.38 29.04 29.70 30.36 31.02 31.68 32.34 33.00 33.66

Feet

52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68

34.32 34.98 35.64 36.30 36.96 37.62 38.28 38.94 39.60 40.26 40.92 41.58 42.24 42.90 43.56 44.22 44.88

Feet

69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

45.54 46.20 46.86 47.52 48.18 48.84 49.50 50.16 50.82 51.48 52.14 52.80 53.46 54.12 54.78 55.44 56.10

Feet

86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

56.76 57.42 58.08 58.74 59.40 60.06 60.72 61.38 62.04 62.70 63.36 64.02 64.68 65.34 66.00 66.66 67.32

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