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INDEX OF CURVE AND REDUCTION TABLES Table

I-SLOPE STAKE

Table

II-STADIA CORRECTION AND HORIZONTAL DISTANCES

Table

III-TRIGONOMETRIC FORMULAE

Table

IV-NATURAL TRIGONOMETRICAL FUNCTIONS CURVE FORMULAE

Table

V-TANGENTS AND EXTERNALS TO A 10 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 IOTHS 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 ANY WIDTH.SIDESLOPES 1/

TO 1.

SLOPE STAKE

SIDE ISTAKE

SIDE ISTAKE

I

16.2

C.L. ; SLOPE STAKE

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24.3

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10.7 16.05

_ Distance out from Side or Shoulder Stake. j= 0

1.1

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TABLE II. STADIA CORRECTION AND HORIZONTAL DISTANCES STADIA REDUCTIONS FOR READING 100 Horizontal Correction

in Elevation

18°-30' 19°-00' 19°-30' 20v°-00' 20°-30'

10.1 10.6 11.2 11.7 12.3

30.1 30.8 31.5 32.1 32.8

12.1 13.8 15.5 17.10 17.9

21°-0a 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

12°-00' 12°-30' 13°-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' 24o-30 25°-00' 25°-30'

15.9 16.5 17.2 17.9 18.6

36.6 37.2 37.7 38.3 39.0

13-30' 14v0-00' 14°-30' 15O00' 15-30

5.5 5.9 6.3 6.7 7.2

22.7 23.4 24.2 25.0 25.8

26'-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

16°-00' 16-30' 17°--00' 17°-30' 18°-00'

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' 30o00'

22.8 23.5 24.3 25.0

41.9 42.4 42.9 43.3

Difference

VerticalAnge

0.1 0.3 0.5 0.8 1.1

3.5 5.3 7.0 8.7 10.4

1.5 1.9 2.5 3.0 3.3

Vertical Angle

orint Coraection

2000' 3-00' 5o-0aJ 6°--00'

7°-00P 8°-00' 9°-00'

10°-00' 10°-30' 11-00'

110-30'

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

.......... 66 .......... 132 ........ 198 264 .......... ........ 330 .......... 396 .......... 462 .......... 528 .......... 594 .......... 660

in Elevation

210-30,

260-30' 27O00'

Feet to Chains 100 200 300 400 500 600 700

.... 1.515 .... 3.030 .... 4.545 .... 6.060 .... 7.575 .... 9.090 .... 10.606

800 .... 12.121 900 .... 13.636 1,000 .... 15.151

Difference

TABLE III. TRIGONOMETRIC FORMULAE

B

B

c

C A

b

Right Triangle Solution of

a

For Angle A.

B

A

A

b

A

a

C

b

Oblique Triangles Right Triangles

a b C a tan= -, cot = asee , = -, cosec = -

sin = -, cos = -

Given a, b

Required A, B,o

a tan A = b-= cot B,

0

A, B, b

sin A = a =cosB,b=V(c+a)

A, a

B, b,a

B = 90°-A, b = a cot A, c =

A, 6

B, a, c

B = 90°-A, a = btanA,

A, c

B,

as,

Given B, a

A,

A, a, b

a, 6,

=

co

B,

A, b, a

1---

A.

coe A.

, O

B, C

sin B

A, B, 0

Area Area

a sin O in A sin

,C = 180°-(A + B), a

a

A+B=180--C,tan (A--B)=(a-b)tan

=

, area =

area = b

sin A

(A-,-B

be

,sin JA=1

=

a

sin A

,C= 180--(A+B)

sin jB== S,

(-a) =

B = 90°-A, a = asin A, b = c cos A, SSolution of Oblique Triangles a sin B Required sin A ,C= 180-(A + B), bb, a, C Ssin A

C A,

6, c

V1 +

., b

C

a

= a

V(s-a)

(s-b)(s-c)

sin A

2 2

A,B, C,a Area

area

a sin B sin-C sinA

REDUCTION TO HORIZONTAL Horizontal distance = Slope distance multiplied by the cosine of the vertical angle. Thus: slope distance =319.4 ft. ° Vert. angle-5 10'. From Table. IV. cos 5O 10'= 9959. Horizontal distance - 319.4 .9155= 318.09 ft. . v distance times (I-cosine of vertical angle). With the same figures as in the preceding example, the followIng result is obtained. Cosine 5 10'=.999.1 -. 950=.0041. Horizontal distance 319.4x.0041=1.31. 319.4-1.31= 31.09 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: rase=14 ft.. slope distance=302.6 ft. Horizontal distance=302.6- 1 =302.6-0.32-302.28 ft. 2 x 302.6

TABLE IV. NATURAL TRIGONOMETRICAL FUNCTIONS Angle

Si

Ten.

Sac.

Cosec.

Angle

Sin.

Tean.

Sec.

Coses.

Cotg.

Cosin.

.1392 .1421 .1449 .1478 .1507 .1536

1.0098 1.0102 1.0107 1.0111 1.0115 1.0120

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

1.0001 1.0001

114.6 85.94 68,76

1.0002 1.0002 1.0003 1.0003 1.0004 1.0005

57.30 49.11 42.98 38.20 3438 31.26

.99985 99979 .99973 .99966 .99958 .99949

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

1.0125 1.0129 1I0134 1.0139 1.0144 1.0149

6.394 6.277 6.166 6.059 5.955 5.855

6.314 6.197 6.084 5.976 5.871 5.769

.98769 .98723 .98676 98629 .98580 .98531

1.0006 1.0007

28.65

1I.008

24.56 22.93 21.49 20.23

.99939 .99929 .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

5.671 5.576 5.485 5.396 5309 5.226

,98481 .98430 .98378 .98325 .98272 .98218

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

1.0187 1.0193 1.0199 1.0205 10211 1.0217

5.241 5.145 .98163

15.64 14.96

.99863 .99847 .99831 .99813 .99795 99776 .99756 .99736 .99714 .99692 .99668 .99644

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

1.0223 1.0230 1.0236 1.0243 1.0249 1.0256

4.810 4.745 4.682 4.620

1.0036

14.34 13.76 13.23 12.75 12.29 11.87

1.0038 1.0041 1.0043 1 0046 1.0049 1.0052

11.47 11.10 10.76 10.43 10.13 9.839

.99619 .99594 .99567 .99540 .99511 .99482

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

1.0263 1.0270 1.0277 1.0284 1.0291 1.0299

1.0055 1.0058 1.0061 1.0065 1.0068 1 0072

9.567 9.309 9 065 8.834 8.614 8.405

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

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

1.0075 1.0079 1.0082 1.0086 1.0090 1.0094

8.206 8.016 7.834

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

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

171.9

1.0010 1.0011 1.0012 1.0014 1.0015 1.0017 1.0019 1 0020 1.0022 1.0024 1.0027 1.0029 1.0031

1.0033

Cog

Cosin.

1. 1. .99998 .99996 .99993 .99989

343.8

CI-IF

Cotg.

2645

19.11 18.10 17.20

1638

7661 7.496 7.337

VI.Sc I Tan. SinAnle J

u.

5.164 5.089 5016 4.945 4.877

5.066 4.989 4.915 4.843

4.773

4.705 4.638 4.574 4.511 4.560 4.449 4.502 4.390

<4.445

.98107 .98050 .97992 .97934 .97875 .97815 97754 .97692 .97630 .97566 .97502

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

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

1.0353 1 0361 1.0369 1.0377 1.0386 1.0394

3.864 3.822 3.782 3.742 3.703 3.665

3.732 .96593 3.689 .96517 3 647 .96440 3.606 .96363 3.566 .96285 3.526 .96206

Cotis.Cosec.

Sec.

Ton. SijhAndI

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS AIi

ia.

C(iL

Tn.

SLc.

SCot.

Cse.

C1Co

osin

n

Sin.

TS

Coa

$*c.

Cosi.

1.0403 1.0412 1.0423 1.0429 1.0438 1.0448

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

1.0946 1.0961 1.0975 1.0989 1.1004 1.1019

2.459 2.443 2.427 2.411 2.396 2.381

.91355 .91236 .91116 .90996 .90875 .90753

1.0457 1.0466 1.0476 1.0485 1.0495 1.0505

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

1.1034 1.1049 1.1064 1.1079 1.1095

1.1110

2.366 2.351 2.337 2.323 2.309 2.295

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

1.0515 1.0525 1.0535 1.0545 1.0555 1.0566

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

1.1126 1.1142 1.1158 1.1174 1.1190 1.1207

2.281 2.268 2.254 2.241 2.228 2.215

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

1.0576 1.0587 1.0598 1.0608 1.0619 1.0631

.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

.89101

1.0642 1 0653 1.0665 1.0676 1.0688 1.0700

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

1.1326 2.130 1.1343 2.119 1.1361 2.107 1.1379 2.096 1.1397 2.085 4823 .5505 11.1415 2.073

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

1.0711 1.0723 1.0736 1.0748 1.0760 1.0773

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

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

1.0785 1.0798 1.0811 1.0824 1.0837 1.0850

92718 92609 92499 92388 92276 92164

1.1547 1.1566 1.1586 1.1606 1.1626 1.1646

2.000 1.990 1.980 1.970 1.961 1.951

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

1.0864 1.0877 1.0891 1.0904 1.0918 1.0932

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

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

Cott'.Coe

s-

TL

Sin

Cms. Cotg cose S..

.88968 .88835 .88701 .88566 .88431

ITom. Sin AnteI

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS Ag

Si.

Cosin.

Tn.

Cotg.

S.

Coec.

lot.

Angle

Cosin.

Sin.

Ten

Sc.

Cosec

Cotg.

osin

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

1.2086 1.2110 1.2134 1.2158 1.2183

.82741 .82577 .82413 .82248 .82082

1.3251 1.3284 1.3318 1.3352 1.3386 1.3421

.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 1.3492 1.3527 1.3563 1.3600 1.3636

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

1.2361 1.2387 1.2413 1.2440 1.2466 1.2494

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

1.3673 1.3711 1.3748 1.3786 1.3824 1,3863

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

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

Sc

Tan.

Sin.

Angle

Cosin.

Cotg.

Cosec.

Soc.

Tan.

Sin.

Angle

CURVE FORMULAE

CURVE TABLE Table of Tangent and External to a 10 Curve

A

Angle of Intersection I

Long Cord

o

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 also L=

=

100

.0174533 X A X R

Degree of Curve: D

=

100

L L

Tangent:

T = R tan % A

Long Cord:

LC = 2R sin % A

Middle Ordinate: M = R (1-Cos % A) External :

E=

T tan 3 A

TABLE V. TANGENTS AND EXTERNALS TO A 10 CURVE 1 10 20 30 40 50 2*

10' 20' 30' 40, 50,

3'

4

50.0C 58.34 66.6 75.01 83.34 91.6E 100.01 108.35 116.68 125.02 133.36 141.70

°

=10

I

.218 .297 .388 .491 .606 .733 .873 1.024 1.188 1.364 1.552 1.752

150.04 10' 158.38 20 166.72 30' 175.06 40' 183.40 50' 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

°

50

10' 20' 30' 40'

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

6'

7'

8'

9'

°

10

I

501.28 10' 509.68 20' 518.08 30' 526.48 40' 534.89 50' 543.29

°

+

11

5 C. .001

10°C. T .06 E .003

15 C. T .09 E .004

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

13*0 10' 20' 30' 40' 50'

652.81 661.25 669.70 678.15 686.60 695.06

37.070 38.031 39.006 39.993 40.992 42.004

703.51 43.029 14* 10' 711.97 44.066 20' 720.44 45.116 30' 728.90 46.178 40' 737.37 47.253 50' 745.85 48.341 °

15

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

°

20 C. T .13 17* E 10' .006 20' 30' 40' 50', °

30 C. T .19 E .008

1-

u20* 21'

551.70 26.500

12'

°

25 C. T .16 E .007

E

18 10' 20' 30' 40' 50'

754.32 762.80 771.29 779.77 788.26 796.75

49.441 50.554 51.679 52.818 53.969 55.132

805.25 813.75 822.25 830.76 839.27 847.78

56.309. 57.498 58.699 59.914 61.141 62.381

856.30 864.82 873.35 881.88 890.41 898.95

63.634 64.900 66.178 67.470 68.774 70.091

907.49 916.03 924.58 933.13 941.69 950.25

71.421 72.764 74.119 75.488 76.869 78.264

958.81 967.38 975.96 984.53 993.12 1001.7

79.671 81.092 82.525 83.972 85.431 86.904

1010.3 1018.9 1027.5 1036.1 1044.7 1053.3

88.389 89.888 91.399 92.924 94.462 96.013 E= E=

°

19 10' 20' 30' 40' 50' °

20

R tan Vl.1 - Rtan T =

10' 20' 30' 40' 50'

°

10' 20' 30' 40' 50'

1113.7 1122.4 1131.0 1139.7. 1148.4 1157.0 1165.7 1174.4 1183.1 1191.8 1200.5 1209.2

117.38 10oC. 119.12 T 120.87 .19 122.63 E 124.41 126.20 .025

1217.9 1226.6 1235.3 1244.0 1252.8 1261.5

128.00 129.82 131.65 133.50 135.35 137.23

10' 20' 30' 40' 50'

1270.2 1279.0 1287.7 1296.5 1305.3 1314.0

139.11 141.01 142.93 144.85 146.79 148.75

10' 20' 30' 40' 50'

1322.8 1331.6 1340.4 1349.2 1358.0 1366.8

150.71. 152.69 154.69 156.70 158.72 20* C. 160.76 T .39 162.81 E 164.86 166.95 .051 169.04 171.15 173.27

°

23

10' 20' 30' 40' 50' 10' 20' 30' 40' 50' 25'

°

26 °

20 C. T .26 E .022

°

27

10' 20, 30' 40' 50' °

28 °

25 C T .32 E .028

ZIu=30.

97.577 + 99.155 5° C. 100.75 T 102.35 103.97 .10 105.60 E 107.24 .013 108.90 110.57 112.25 113.95. 115.66

24'

15' C. T .19 E .017

E

1061.9 1070.6 1079.2 10878 1096.4 1105.1

22'

10 C. T .13 E .011

T

10' 20' 30' 40' 50'

30' 576.95 28.974 40' 585.36 29.824 50' 593.79 30.686

16

°

TIL

10' 560.11 27.313 20' 568.53 28.137

T .03

°

21.887 22.624 23.375 24.138 24.913 25.700

L

10' 20' 30' 40' 50' °

29

10' 20' 30' 40' 50'

1375.6 1384.4 1393.2 1402.0 1410.9 1419.7

1481.8 1490.7 1499.6 1508.5 1517.4 1526.3

175.41 177.55 ° 179.72 25 C. T 181.89 184.08 .49 186.29 E .065 188.51 190.74 192.99 195.25. 197.53 199.82

1535.3 1544.2 1553.1 1562.1 1571.0 1580.0

202.12 30 C. T 204.44 206.77 .59 209.12 E 211.48 213.86 .078

1428.6 1437.4 1446.3 1455.1 1464.0 1472.9

°

30 C. 30' 10' T 20' .39 30' E 40', 50' .034 1 R exsec R exsec VI

15 C. T .29 E .038

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

IT

10' 20' 30' 40' 50'

1589.0 1598.0 1606.9 1615.9 1624.9 1633.9

216.3 218.7 221.1 223.5 226.0 228.4

32* 10' 20' 30' 40' 50'

1643.0 1652.0 1661.0 1670.0 1679.1 1688.1

230.9 233.4 235.9 238.4 241.0 243.5

10' 20' 30' 40' 50'

1697.2 1706.3 1715.3 1724.4 1733.5 1742.6

246.1 248.7 251.3 253.9 256.5 259.1

34' 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

35'

1806.6 278.1 1815.7 280.8 1824.9 283.6 1834.1 286.4 1843.3 289.2 1852.5 292.0

310

°

33

10' 20' 30' 40, 50'

5o C. T .13 E .023

10o C. T .26 E .046

2794.5 2804.9 2815.2 2825.6 2835.9 2846.3

645.2 649.7 654.3 658.8 663.4 668.0

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

53,

2856.7 2867.1 2877.5 2888.0 2898.4 2908.9

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

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'

2919.4 2929.9 2940.4 2951.0 2961.5 2972.1

700.9 705.7 710.5 715.3 720.1 725.0

2373.3 2383.1 2392.8 2402.6 2412.4 2422.3

472.1 475.8 479.6 483.4 487.2 491.0

550 10' 20' 30' 40' 50'

2982.7 2993.3 3003;9 3014.5 3025.2 3035.8

729.9 734.8 739.7 744.6 749.6 754.6

2432.1 2441.9 2451.8 2461.7 2471.5 2481.4

10' 20' 30' 40' 50'

3046.5 3057.2 3067.9 3078.7 3089.4 3100.2

10' 20' 30 40' 50'

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

56

10' 20' 30' 40' 50'

10' 20' 30' 40' 50'

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

10' 20' 30' 40' 50'

2551.0 2561.0 2571.0 2581.0 2591.0 2601.1

542.2 546.3 550.4 554.5 558.6 562.8

58* 10' 20' 30' 40, 50'

3176.0 3186.9 3197.8 3208.8 3219.7 3230.7

821.4 826.7 832.0 837.3 842.7 848.1

49, 10' 20' 30' 40' 50'

2611.2 2621.2 2631.3 2641.4 2651.5 2661.6

566.9 571.1 575.3 579.5 583.8 588.0

59'

3241.7 3252.7 3263.7 3274.8 3285.8 3296.9

853.5 858.9 864.3 869.8 875.3 880.8

50* 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

3308.0 3319.1 3330.3 3341.4 3352.6 3363.8

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

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

50'

2257.0 2266.6 2276.2 2285.9 2295.6 2305.2

44 , 10' 20' 30' 40' 50'

42'

43* 10' 20' 30' 40'

°

45

10' 20' 30' 40' 50'

330.2 333.2 336.3 339.3 342.4 345.5

48

10' 20' 30' 40' 50'

2029.0 2038.4 2047.8 2057.2 2066.6 2076.0

348.6 351.8 354.9. 358.1 361.3 364.5

10' 20' 30' 40' 50'

2085.4 2094.9 2104.3 2113.8 2123.3 2132.7

367.7 371.0 374.2 377.5 380.8 384.1

°

39'

40'

47

+ 5 C. T .17 E .037

°

.67 E .117

T =Rtan

10' 20' 30' 40' 50' °

°

25" C.

30' C. T .80 E .141

1--,6

520 10' 20' 30' 40' 50'

10' 20' 304 40' 50'

1972.9 1982.2 1991.5 2000.9 2010.2 2019.6

10' 20' 30' 40' 50'

E

618,4 622.8 627.2 631.7 636.2 640.7

°

15 C. T .40 E .070

T

2732.9 2743.1 2753.4 2763.7 2773.9 2784.2

10' 20' 30' 40' 50'

37'

I

51s 10' 20' 30' 40' 50'

387.4 390.7 394.1 397.4 400.8 404.2

46'

10' 20' 30' 40' 50'

E-=.0 Ej

2142.2 2151.7 2161.2 2170.8 2180.3 2189.9

1861.7 294.9 1870.9 297.7 1880.1 300.6 1889.4 303.5 1898.6 306.4 0'° C. 1907.9 309.3 T 1917.1 312.2 .53 1926.4 315.2 E 1935.7 318.1 1945.0 321.1 .093 1954.3 324.1 1963.6 327.1

36'

38

41

15° C. T .51 E .116

°

25 C. T .85 E .189

°

57'

10' 20' 30' 40' 50' °

1z

60' 10' 20' 30' 40' 50'

E=Rexsec'/2I

°

°

25 C. T 1.05 E .283

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 1 ° CURVE 1=7o 3375.0 3386.3 3397.5 3408.8 3420.1 3431.4

920.2 925.9 931.6 937.3 943.1 948.9

620 10' 20' 30' 40' 50'

3442.7 3454.1 3465.4 3476.8 3488.3 3499.7

954.8 960.6 966.5 972.4 978.3 984.3

630

3511.1 3522.6 3534.1 3545.6 3557.2 3568.7

990.2 996.2 1002.3 1008.3 1014.4 1020.5

10' 20' 30' 40' 50'

3580.3 3591.9 3603.5 3615.1 3626.8 3638.5

1026.6 1032.8 1039.0 1045.2 1051.4 1057.7

65° 10' 20' 30' 40' 50'

3650.2 3661.9 3673.7 3685.4 3697.2 3709.0

1063.9 1070.2 1076.6 1082.9 1089.3 1095.7

660 10' 20' 30' 40' 50'

3720.9 3732.7 3744.6 3756.5 3768.5 3780.4

1102.2 1108.6 1115.1 1121.7 1128.2 1134.8

°

64

67. 10' 20' 30' 40' 50' 68

1181.6 1188.4 1195.2 1202.0 1208.9 1215.8

690 10' 20' 30' 40' 50'

3937.9 3950.2 3962.5 3974.8 3987.2 3999.5

1222.7 1229.7 1236.7 1243.7 1250.8 1257.9

70* 10' 20' 30' 40' 50'

4011.9 4024.4 4036.8 4049.3 4061.8 4074.4

1265.0 1272.1 1279.3 1286.5 1293.6 1300.9

4086.9 4099.5 4112.1 4124.8 4137.4 4150.1

1308.2 1315.6 1322.9 1330.3 1337.7 1345.1

72*

4162.8 4175.6 4188.5 4201.2 4214.0 4226.8

1352.6 1360.1 1367.6 1375.2 1382.8 1390.4

730

4239.7 4252.6 4265.6 4278.5 4291.5 4304.6

1398.0 1405.7 1413.5 1421.2 1429.0 1436.8

4317.6 4330.7 4343.8 4356.9 4370.1 4383.3

1444.6 1452.5 1460.4 1468.4 1476.4 1484.4

4396.5 4409.8 4423.1 4436.4 4449.7 4463.1

1492.4 1500.5 1508.6 1516.7 1524.9 1533.1

4476.5 4489.9 4503.4 4516.9 4530.4 4544.0

1541.4 1549.7 1558.0 1566.3 1574.7 1583.1

4557.6 4571.2 4584.8 4598.5 4612.2 4626.0

1591.6 1600.1 1608.6 1617.1 1625.7 1634.4

786 10' 20' 30' 40' 50'

4639.8 4653.6 4667.4 4681.3 4695.2 4709.2

1643.0 1651.7 1660.5 1669.2 1678.1 1686.9

790

4723.2 4737.2 4751.2 4765.3 4779.4 4793.6

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

10' 20' 30' 40' 50'

°

5 C.

T .25 E .080

10' 20' 30' 40' 50'

°

10 C. T .51 E .159

10' 20' 30' 40' 50' °

74

15 C. T .76 E .240

10' 20' 30' 40' 50' 750

10' 20' 30' 40' 50' °

76

200 C. T 1.02 3792.4 1141.4 E 3804.4 1148.0 3816.4 1154.7 .3i21 3828.4 1161.3 3840.5 1168.1 3852.6 1174.8

3864.7 10' 3876.8 20' 3889.0 30' 3901.2 40' 3913.4 50' 3925.6

1=800 71

610 10' 20' 30' 40' 50'

10' 20' 30' 40' 50'

°

25' C. T 1.28 E .403

10' 20' 30' 40' 50, °

77

10' 20' 30' 40' 50,

10' 20' 30' 40' 50' 30" C. T 1.54 E .485 T=

Rtan %I

°

10 20' 30' 40' 50'

5' C.

T .30 E .110

82* 10' 20' 30' 40' 50'

4893.6 4908.0 4922.5 4937.0 4951.5 4966.1

1805.3 1814.7 1824.1 1833.6 1843.1 1852.6

4980.7 4995.4 5010.0 5024.8 5039.5 5054.3

1862.2 1871.8 1881.5 1891.2 1900.9 1910.7

°

5069.2 1920.5 10 C. 830 10' 5084.0 1930.4 T 20' 5099.0 1940.3 .61 30' 5113.9 1950.3 40' 5128.9 1960.2 E 50' 5143.9 1970.3 .220 84

°

5° C. T .36 E .149

10 C. T .72 E .299

5159.0 5174.1 5189.3 5204.4 5219.7 5234.9

1980.4 1990.5 2000.6 2010.8 2021.1 2031.4 15"C. T 2041.7 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 2158.4

5437.2 5453.1 5469.0 5484.9 5500.9 5517.0

2169.2 2180.2 2191.1 2202.2 2213.2 2224.3

5533.1 5549.2 5565.4 5581.6 5597.8 5614.2

2235.5 2246.7 2258.0 2269.3 2280.6 2292.0

1695.8 1704.7 1713.7 1722.7 1731.7 1740.8

880 ° 10' 25 C. 20' T 30' 40' 1.53 50, E ° .558 89 10' 20' 30' 40' 50,

5630.5 5646.9 5663.4 5679.9 5696.4 5713.0

2303.5 2315.0 2326.6 2338.2 2349.8 2361.5

1749.9 1759.0 1768.2 1777.4 1786.7 1796.0

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

5729.7 5746.3 5763.1 5779.9 5796.7 5813.6

2373.3 2385.1 2397.0 2408.9 2420.9 2432.9

°

80

81

10' 20' 30' 40' 50'

15'C. T 850 5250.3 .91 10' 5265.6 20' 5281.0 E 30' 5296.4 .332 40, 5311.9 50' 5327.4 860

10' 20' 30' 40' 50'

°

20 C. T 1.22 E .445

870

E = R exsec V

10' 20' 30, 40' 50'

°

20 C. T 1.45 E .603

°

25 C. T 1.83 E .756

°

30 C. T 2.20 E .910

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

T

91" 10' 20' 30' 40' 50'

5830.5 5847.5 5864.6 5881.7 5898.8 5916.0

E

[=1000

h=

E

6950.6 6971.3 6992.0 7012.7 40' 7033.6 50' 7054.5

92 10' 20' 30' 40' 50'

5933.2 5950.5 5967.9 5985.3 6002.7 6020.2

2444.9 2457.1 2469.3 5" C. T 2481.5 2493.8 .43 2506.1 E 2518.5 .200 2531.0 2543.5 2556.0 2568.61 2581.3

93" 10' 20' 30' 40'

6037.8 6055.4 6073.1 6090.8 6108.6 6126.4

2594.0 10*C. 2606.8 T 2619.7 2632.6 .86 2645.5 E 2658.5 .401

940 10' 20' 30' 40' 50'

6144.3 6162.2 6180.2 6198.3 6216.4 6234.6

2671.6 2684.7 2697.9 2711.2 2724.5 2737.9

95" 10' 20' 30' 40' 50'

6252.8 6271.1 6289.4 6307.9 6326.3 6344.8

2751.3 2764.8 2778.3 2792.0 2805.6 2819.4

6363.4 6382.1 6400.8 6419.5 6438.4 6457.3

2833.2 106 2847,0 10' 20' 2861.0 2875.0 30' 40' 2889.0 20' C. T 2903.1 50' 1.74 ° 2917.3 107 E 2931.6 10' .809 2945.9 20' 30' 2960.3 40' 2974.7. 2989.2 50'

°

96*

10' 20' 30' 40' 50'

97" 10' 20 30' 40' 50'

6476.2 6495.2 6514.3 6533.4 6552.6 6571.9

101" 10' 20' 30'

103

102

°

10' 20' 30'

40' 50' °

10' 20' 30' 40' 50'

104* 10' 20' 30' 40 50' 15°C. T 105" 1.30 10' 20' E 30' .604 40' 50' °

°

98° 6591.2 10' 6610.6 20' 6630.1 30' 6649.6 40, 6669.2 50' 6688.8

3003.8 3018.4 3033.1 3047.9 3062.8 3077.7

99* 10' 20' 30' 40' 50'

6708.6 6728.4 6748.2 6768.1 6788.1 6808.2

3092.7 3107.7 3122.9 3138.1 3153.3 3168.7

100" 10 20' 30' 40 50

6828.3 3184.1 30 C. 110 T 10' 6848.5 3199.6 20' 6868.8 3215.1 2.62 6889.2 3230.8 30' 40' 6909.6 3246.5 50' 6930.1 3262.3 1.22 IT =Ka'/J = tan vl

108 10' 25 C. 20' T 30' 40' 2.18 50' E ° 1.02 109 10' 20' 30' 40' 50' °

°

7075.5 7096.6 7117.8 7139.0 7160.3 7181.7 7203.2 7224.7 7246.3 7268.0 7289.8 7311.7 7333.6 7355.6 7377.8 7399.9 7422.2 7444.6 7467.0 7489.6 7512.2 7534.9 7557.7 7580.5

T

E

50'

8336.7 8362.7 8388.9 8415.1 8441.5 8468.0

4386.1 4407.6 4429.2 4450.9 4472.7 4494.6

112* 10' 20' 30' 40' 50'

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

8822.9 8851.0 8879.3 8907.7 8936.3 8965.0

4790.4 4814.1 4837.8 4861.7 4885.7 4909.9

8993.8 9022.7 9051.7 9080.9 9110.3 9139.8

4934.1 4958.6 4983.1 5007.8 5032.6 5057.6

9169.4 9199.1 9229.0 9259.0 9289.2 9319.5

5082.7 5107.9 5133.3 5158.8 5184.5 5210.3

9349.9 9380.5 9411.3 9442.2 9473.2 9504.4

5236.2 5262.3 5288.6 5315.0 5341.5 5368.2

9535.7 9567.2 9598.9 9630.7 9662.6 9694.7

5395.1 ,5422.1 5449.2 5476.5 15504.0 5531.7

11 llo"

T

3278.1 3294.1 3310.1 5° C. 3326.1 T 3342.3 .51 3358.5 E 3374.9 .268 3391.2 3407.7 3424.3 3440.9 3457.6

111" 10 20' 30'

40'

°

3474.4 10"C. 113 3491.3 10' T 3508.2 20 3525.2 .103 30' 3542.4 40' E 3559.6 50' .536 ° 114 3576.8 3594.2 10' 3611.7 20' 3629.2 30' 3646.8 40' 3664.5 15 C. 50 T 3682.3 X115° 3700.2 1.56 10' 3718.2 20' E 3736.2 30' 3754.4 .806 40, 3772.6 50'

-

°

=140"

10, C. T 1.25 E .721

15°C. T 1.93 E 1.09

116

7743.2 7766.8 7790.5 7814.3 7838.1 7862.1

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

7886.2 7910.4 7934.6 7959.C 7983.5 8008.0

4018.2 4037.8 4057.4 4077.2 4097.1 4117.0

118

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'

8182.8 8208.2 8233.7 8259.3 8285.0 8310.8

9924.0 5729.7 30 C. 4259.7 30 C. 120 T 4280.5 T 10' 9957.5 5758.6 4301.4 3.14 20' 9991.0 5787.7 3.81 4322.4 30' L0025.0 5817.0 E E 4343.6 40' L0059.0 5846.5 2.20 4364.8 1.63 50' 10093.0 5876.1 E =- R exec'/ E = R exsec Vz21

7603.5 7626.6 7649.7 7672.9 7696.3 7719.7

°

117 10' 20' 30' 40' 50' °

10' 20' 30' 40' 50' °

°

°

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

°

20 C. T 2.52 E 1.46

°

25 C. T 3.16 E 1.83

°

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 X4840 = 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 Are 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 are 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 301/4 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.

"

-

TABLE VI. INCHES TO DECIMALS OF A FOOT

lIa

0

1

2

4

8

5

6

7

8

9

10

11

In.

.4167. .5838 .6667 .7500 .8888 .9167 0 0 Foot .0888 .1667 .2500.8 .06s9 .1693 .2526.89 .4198 .5026 .585 .6693 .766 .869 .9198 1-82 1-32 .0 .0052 .0078 .0104 .0130 .0156 7-2 .0182 1-4 .008 9-82 .0284 5-16 .060 11-82 .0286 1-16 8-82 1-8 5-89 8-16

.0885 .0911 .0938 .0964 .0090 .1016 .1042 .1068 .1094 .1120

.1719 .252 .338885.4219 .502 .1745 .2578 .8411 .4245.507 4.4271 .5104 .1771 .2604. .1797 .2680.3464 .4297 .5130 .18238 .2656 .490 .4323 .5156 .1849 .2682 .8516 .449 .518 .187 .2708 .3542 .4375 .5408 .1901 .2734 .8568 .4401.5284 .19'27 .2760 .85941.4427.5260 .1953 .2786 .3620 .4453 .5286

.885 .6719 .7552 .8385 .911 .674 .7678 .8411 .5938 .6771 .7604 .848 .5964 .6797 .7630 .8464 .990 .6823 .766 .840 .016 .. 89 .7682 .8561 .6042 .5876 .7708 .8548 .6068.6901 .7734 .8568 .6094 .697 .7760 .8594 .6120 .6953.7786.860

.9219 1-16 8-8 .45 .9271 1-8 .9297 5-82 .923 8-16 .949 7-82 .9875 1-4 .9401 9-82 .9427 5-16 .9453 11-32

8..8

.0313 .1146 .1979 .2813 .8646 .4479 .5318 .6146 .6979 .7813 .8646 .9479 8-8

1-2

.0417 .0448 .0409 .0495 .0521

18-82 .0839 .1172 .2005 .2839 .8672 .4505 .5339 .6172 .7005 .7839 .8672 .9505 183-38 7-16 .0365 .1198 .2031 .2865 .698 .4531 .5365 .6198 .701 .785 .8698 .9531 7-16 15-82 .0891 .1224 .2067 .2891 .8724 .4557 .59 .6284 .7057 .7891 .8724 .9557 15-8

17-82 9-16 19-83 5-8

.1250 .1276 .1802 .1828 .1354

.2083 .2109 .2135 .2161 .2188

.2917 .2943 .2969 .2995 .3021

.8750 .8776 .8802 .3828 .3854

21-82 [.0 47 .1380 .2214 .304

11-16 -32 8-4 25-2

.05731.1406 .0599 .1432 .06256.1458 .0651 .1484

.4583 .541 .6250 .7083 .7917 .8750 .4009 .5448 .6276 .7109 .7943 .8776 .46 .546 .602 .7135 .796 .880 .4061 .5495 .6328 .7161 .795 .8828 .4688 .5521.64 .7188.8021 .8854

880 .4714 .554

.958831-2 .9609 17-32 .9635 9-16 .9661 19-8 .9688 5-8

.6380 .7214 .8047 .8880 .9714 21-32 .7240 .8073 .806 .9740 11-16

.6406 .5 .240 .807 .3906 .4740.557 .2266 .92 .4766 .55 .6432 .6458 .2292 .3125 .3958 .4792 . .2318 .3151 .3984 .4818 .551 .6484

.7266 .8099 .8982 .9766 23-8 -4 .7992 .8125 .858. .73188151 .884 .9818 25-2

183-16 .077 .1510 .2844 .3177 .4010 .4844 .5677 .6510 .7344 .8177 .9010 .9844 13-16

.6586 .7870 .820 .9036 .870 27.40 .4870 . 27-32 .0708 .1586 .2370.820 .20 7-8 .0729 .1563 .2396.3 9 .4068 .4896 .572 .6563 .7396 .8229 .9063 .9896 7-8 29-2 .0755 .1589 .2422 .256 .4089 .4922 .57 .6589 .7422 .826 .9089 .992 29-82 15-16 .0781 .1615 .2448 .8281 .4115 .4948 .5781 .6615 .7448 .8281 .9115 .9948 15-16

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 10' 30" .01667 11 00 30 .02500 .03333 12 00 30 .04167 .05000 13 00 30 .05833 .06667 14 00 30 .07500 .08333 15 00 30 .09167 .10000 16 00 30 .10833 .11667 17 00 30 .12500 .13333 18 00 .14167 30 .15000 19 00 30 .15833 .16667 20 00

.17500 20' 30" .18333121 00 30 .19167 .20000 22 00 30 .20833 .21667 23 00 30 .22500 .23333 24 00 30 .24167 .25000 25 00 30 .25833 .26667126 00 30 .27500 .28333 27 00 30 .29167 .30000128 00 30 .30833 .31667129 00 .32500 30 .3333 30 00

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

30' 30" 31 00 30 32 00 30 33 00 30 34 00 30 35 00 30 36 00 30 37 00 30 38 00 30 39 00 30 40 00

.50833 .51667 .52500 .53333 .54167 .55000 .55833 .56667 .57500 .58333 .59167 .60000 .60833 .61667 .62500 .63333 .64167 .65000 .65833 .66667

40' 30' 41 00 30 42 00 30 43 00 30 44 00 30 45 00 30 46 00 30 47 00 30 48 00 30 49 00 30 50 00

.67500 .68333 .69167 .70000 .70833 .71667 .72500 .73833 .74167 .75000 .75833 .76667 .77500 .78333 .79167 .80000 .80833 .81667 .82500 .833338

50' 30" 51 00 30 52 00 30 53 00 30 54 00 30 55 00 30 56 00 30 57 00 30 58 00 30 59 00 30 60 00

.84167

.85000 .85833 .86667 .87500 .88333 .89167 .90000 .90833 .91667 .92500 .93333 .94167 .95000 .95833 .96667 .97500 .98333 .99167 1.00000

TABLE VIII. MIDDLE ORDINATES OF RAILS

Length of Rail (feet) C O f

R Feet

30 2828 6 24 22 20 InchInchInch Inch Inch Inch

C o

R 30 28 26 24 22 20 Feet Inch ch Inch Inch Inh lh

0-20 0-40 1-0 1-20 1-40 2-0 2-20 2-40 3-0 8-20 3-40 4-0 4-20 4-40 5 6

17189 8594 5730 4297 3438 2865 2456 2149 1910 1719 1563 1433 1323 1228 1146 955.

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

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

716.8 1.88 1.64 1.42 1.20 1.01 .84 637.3 2.121.84 1.60 1.35 1.14 .94 573.7 2.36 2.05 1.78 1.50 1.27 1.04 521.7 2.59 2.26 1.95 1.65 1.39 1.15 478.3 3.83 2.47 2.15 1.811.54 1.26 441.7 3.05 2 2.30 1.96 1.66 1.36 410.3 3.30 2.87 2.48 2.10 1.78 1.46 383.1 3.543.08 2.68 2.261.91 1.57 359.3 3.76 3.28 2.83 2.40 2.041.67 338.3 4.00 3.48 3.02 2.57 2.16 1.78 319.6 4.21 3.67 3.18 2.70 2281.87 302.9 4.45 3.89 3.36 2.86 2.41 1.98 287.9 4.70 4.09 3.55 3.00 2.54 2.09 262.0 5.16 4.44 3.84 3.30 2.80 2.29 240.5 5.64 4.924.20 3.59 3.042.50 222.3 6.075.29 4.58 3.88 3.29 2.70

7

819.

.07 .06 .14 .1 .20 .1 .27 .23 .34 .29 .41 .35 .48 .41 .55 .47 .62 .53 .68 .59 .75 .65 .82 .71 .89 .77 .96 .83 1.03 .89 1.23 1.

.05 .10 .15 .20 .25. .30 .35 .40 .45 .50 .55 .60 .65 .7 .75 .90

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

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

1.6 1.44 1.24 1.05 .89 .73

TABLE IX. SHORT RADIUS CURVES Badis Feet

OChorl IPeet

Central Angle

Deflection Angle

Deflection for 1 ]oot

35 45 50 60 75 100 120 150 190 200 225 240 250 275 288 300 350 376 400 410

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

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 And length of curve divide angle from P. C. to P. T. by central and multiply by length of chord. 2%

~~~;~)ii

~3~a

s~~~:

r"3"

gle of chord,

TABLE X. RODS IN FEET, 1OTHS AND IOOTIS OF FEET

- .1.

1

...

-

0

Fee

a

.-

Feet

........... ..;..a......-..........r...........-.---

0

If

Feet

r--

If

Feet

Feet

TALE XI. LINKS IN FEET, 10THS AND 100THS OF FEET

II

P'eet

_

I

C

z p1984

6.76 QIts343

~

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l;*

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w

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a

o

4.68 5.34 ;6.00

-

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1.38

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N---+

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7.42 8.08 8.74 9.40 0.06 0.72

2.04

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to v N

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wN-N

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o

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