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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
I,_
.9 I
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
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b = a cot A, c
e
= -
1--2
a
sin A. sin A. co= A, tan b = a B = 90°--A, B, a, a cos A. B=90°-A, a = csin A, b= ecos A, B, a, b olution of Oblique Triangles a sin (
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
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,C = 180 -(A
sin jB=,v 8= a2
Area
area =
A
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=a- 2
Area
+ B), o =
, area =
atxc , C=180*-(A+B) (s-a)
(a-
s
b c sin A 2
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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