Fremling Field Notebook 1965 - 1966

Fm ..

..

a.

.

, ,

ws

n .L' !

e

e

'2+O .

.

DraTANcz FOM

_.__.

SIm STAS

CO

Fo

SLOPS 1 TO 1. ROADWAY OF AN~

0

.2

.1

0.00 0.10 0 1 1.00 1.10 21 .00 2.10 1 3.00 13.10 4 4.00 4.10 85 .00 5.10 S6.00 36.10 7.00 7.10 8 8.00 8.10 9.10 9 9.00 10 10.00 10.10 11 11.00 11.10 12 12.00 12.10 13 13.00 13.10 14 14.00 14.10 15 15.00 15.10 18 1.00 16.10 i7 17.00 17.10 14 18.00 18.10 19.10 19 19.00 20 2I0.00 20.10 41 48.00 21.10 9 40.00 22.10 23.00 23.10 24 24.00 24.10 25 25.00 25.10 26 26.00 26.10 '27.00 2710 27 28 28.00 2810 29 29.00 29.10 o30 0.00 30.10 31 31.00 31.10t 32 32.00 s2.10 33 33.00 33.10 34 .00 34.10 85,00 35 10 35 36 00 86.10 3 37 37.00 37.10 8.00 38.10 38

39 40 41

89.00 40.00 41.00

44 45 4 47

44.00 45.00 48.00 47.00

42 43

48 49 50

39.10 40.10 41.10

42.00 43.00

42.10 43.10

48.00 49.00 60.00

48.10 49.10 50.10

0.20 1.20 2.20 3.20 4.20 5.20 6.20 7.20 8.20 9.20 10.20 11.20 12.20 13.20 14.20 15.20 16.20 17.20 18.20 10.20 20.20 21.20 22.20 23.20 24.20 25.20 26.20 27.20 28.20 29.20 30.20 31.20 3220 33.20 34 20 35.20 36.20 37.20 38.20

39.20 41.20 40.20 42.20 43.20

44.20 45.20 46.20 47.20

44.10 45.10 48.10 47.10

48.20 49.20 50.20

.3

.4

.5

33.30 34.30 35.30 36.30 37.30 38.30

0.40 0.50 1.40 1.60 2.50 2.40 3.40 3.80 4.40 4.50 5.40 5.0 6.40 36.50 7.40 7.50 8.40 8.50 9.40 9.50 10.40 10.50 11.40 11.50 12.40 12.50 13.40 13.50 14.40 14.80 15.40 15.50 16.40 16.50 17.40 17.50 18.40 18.50 19.50 19.40 20.40 I 20.50 21.40 21.50 22.50 22.40 23.40 23.0 24.40 24.50 25.50 25.40 26.40 26.50 27.40 27.50 28.40 28.60 29.40 29.50 30.50 30.40 31.40 31.50 32.40, 32.5 33.40o 33.50 34.40 34.50 35.40 35.50 36.40 38.50 37.40 37.50 38.40 38.50

42.80 43.30

42.40 43.40

0.30 1.30 2.30 3.30 4.30 5.30 6.30 7.30 8.30 9.30 10.30 11.30 12.30 13.30 14.30 15.30 18.30 17.30 18.30 19.30 20.30 21.30 22.30 23.30 24.30 25.30 26.30 27.30 28.30o 29.30 30.30 31.30

32.30

39.30 40.30 41.30 44.30 45.30 46.30 47.30

48.30 49.30 0.30

39.40 40.40 41.40

39.50 40.50 41.50

42.50 43.50

44.40 44.50 45.40 45.50 46.40 46.50 47.40 47.50 48.,4048.50 49.40 50.40

49.50 50.50

S-SEcromN

o

WtIva

.6

39.60 40.60 41.60

39.70 40.70 41.70

44.60 45.80 .46.80 47.60

44.70 45.70 46.70 47.70

42.60 43.60

48.60 49.80 0.0

.8

.7

0.70 0.60 1.60 1.70 2.60 2.70 3.60 3.70 4.60 4.70 5.60 8.70 6.80 3.70 7.60 7.70 8.60 8.70 9.60 9.70 10.60 10.70 11.60 11.70 12.60 12.70 13.60 13.70 14.70 14.60 15.60 15.70 16.60 18.70 17.60 17.70 18.60 18.70 19.60 19.70 20.80 20.70 21.60 21.70 22.60 22.70 23.0 23.70 .750 24.60 24.70 25.70 25.60 2.60 26.70 27.60 27.70 28.60 28.70 29.70 29.60 30.60 0.70 31.0o 31.70 32.6 32.70 0 33.70 33.0 34.60 34.70 35.60 35.70 38.60 38.70 37.80 37.70 38.60 .38.70 42.70 43.70

48.70 49.70 50..70

9

0.80 1.80 2.80 3.80 4.80 5.80 0.80 7.80 8.80 9.80 10.80 11.80 12.80 13.80 14.80 15.80 16.80 17.80 18.80 19.80 20.80 21.80 22.80 23.80 24.80 25.80 26.80 27.80 28.80 29.80 30.80 31.80 32.80 33.80 34.80 35.80 38.80 37.80 38.80

0.90 0 1.90 1 2.90 2 3 3.90 4.90 4 5.90 8 8.90 8 7.90 7 8 8.90 9 9.90 10.90 10 11.90 11 12.90 12 13.90 13 14 14.90 15.90 15 16.90 16 17.90 17 18.90 18 19.90 19 20.90 20 21.90 21 22.90 22 23.90 12 24.90 24 25.90 25 26.90 26 27.90 27 28.90 28 29.90 29 30.90 30 31.90 3 32.90 32 33.90 33 4.90 34 35.90 35 36.90 36 37.90 37 38.90 38

42.80 43.80

42.90 43.90

39.80 40.80 41.80 44.80 45.80 46.80 47.80

48.80 49.80 50.80

39.90 40.90 41.90

39 40 41

44.90 45.,90 46.90 47.90

44 45 48 47

42 43

48.0 48 49.90 49 50.90 I 50

Diatace of slope stake from side or shoulder stake for any width roadway, slope 1 to i1. It ground Is nearly lee the cut or ll at side stake is located by the double entry method in left column and top row. le number in body of table in same row and column gives dIstance from side stake to slope stake. If ground is not level estimate the difference in elevation between the side stake and slope stake, lower target by this amount if out, elevate If flU. Add this amount to cut or fill and find distance in table. Bet up rod at this point, and line of sight should cut target.

If It does not make the alight adjustment necessary.

-

I"

-

~-~P~III

II

=s

H

Q/jii/ns/f&et4k

tZ

D

D-

~

JA 64/&4'Y~d7'

mx;,QQ

hL

IMPROVED

TABLES

AND

INFORMATION

DIRECTIONS FOR USE OF TABLES TABLE No. XIV Distance of slope stake from side or shoulder stake for any width roadway, slope 1Yl to 1.

If ground is nearly level, the cut or fill at side stake is located by the double entry method in left column and top row. The number in body of table in same row and column gives distance from side stake to slope stake. If ground is not level estimate the difference in elevation between the side stake and slope stake, lower target by this amount if cut, elevate if fill. Add this amount to cut or fill and find distance in table.

Set up rod at this point, and line of sight should cut target. If it does not make the slight adjustment necessary.

TABLE No. VIII 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.

N

TABLE

II

TRIGONOMETRIC FORMULAE.

LA

LB =LPON = LOPL R= OB = c= 1

= LMOP

sin A

a

c b sos A=c a tan A = b cot A sec A = csc A =

-

a

= a= sos B = LP 1 b b = sin B = OL l MQ = MQ = MQ = cot B = MQ OM I NT = NT= tan B -=NT

-OM 1 OT OT .

ON 1

=OQ

= csc B = OQ

= OT = sec B = OT

vers A= L LM = covers B+ : OP OP-LP covers A = =. OP-LP = vers B OP exseA = PQ = coexsec B coexsec A = PT - exsec B / 1-Cos A I/ Cos A sin t/s A = 2 cos It/A = 2 sin 2 A= 2 sin A cos A cos 2 A cos A-sin A sin A sin B sin C' Law of Lines a ' =. a B C Law of Cosines c2=a'+b'-2 ab cos C Law of Tangents a

a-b

= tan 'I, (A+B) tan 'Ia (A-B)

TABLE II - Continued TRIOONOMETRIC FORMULE (continued)

in any triangle: Given a, b, C; to find c, B, A. Use Law of Lines.

Given A, B, c; to find a, b, C. Use Law of Lines.

Oiven"a, b, c; to find A, B, C. s (s-a) (s-b) (s--c) Let a+b+c 8

2

(s-a)

cos /I,A tan 1f/ A -= r

a-a

tan /s B =

r

s-b

tan 1/s C

r

s-c Area of a triangle: Area -

'/, ab Sin C

Area =

(s--a) (s-b) (s-c)

PRISMOIDAL.FORMULA. Vol. -

(Bb-+4M)

h = altitude; b, B = bases; M = midsection TABLE III INCHES AND FRACTIONS OF AN INCH IN DECIMALS OF A

FOOT 0

1

/, .0052 /s .0104 /i,.0156 /'4 .0208 /i .0260 ,s .0313 a .0365 is.0417 'e .0469 I/s .0521 t/s .0573 14 .0625 s .0677

.0885 .0938 .0990 .1042 .1094 .1146 .1198 .1250 .1302 .1354 .1406 .1458 ,,1510 S.0729 .1563 ,s .0781 .1615 1 .0833 .1667 0

1

2

3

4

5

6

.1719 .1771 .1623 .1875 .1927 .1979 .2031 .2083 .2135 .2188 .2240 .2292 .2344 .2396 .2448 .2500

.2552 .2604 .2656 .2708 .2760 .2813 .2865 .2917 .2969 .3021 .3073 .3125 .3177 .3229 .3281 .3333

.3385 .3438 .3490 .3542 .3594 .3646 .3698 .3750 .3803 .3854 .3906 .3958 .4010 .4063 .4115 .4167

.4219 .4271 .4323 .4375 .4427 .4479 .4531 .4583 .4635 .4688 .4740 .42 .4844 .4896 .4948 .5000

.5052 .5104 .5156 .5208 .5260 .5313 .5365 .5417 .5469 .5521 .5573 .5625 .5677 .5729 .5781 .5833

2

3

4

5

6

7

8

.5885 .6719 .5938 .6771 .5990 .6823 .6042 .6875 .6094 .6927 .6146 .6979 .6198 .7031 .6250 .7083 .6302 .7135 .6354 .7188 .6406 *7240 .6458 .7292 .6510 .7344 .6563 .7396 .6615 .7448 .6667 .7500 7

8

9

10

.7552 .7604 .7656 .7708 .7760 .7813 .7865 .7917 .7969 .8021 .8073 .8125 .8177 .8229 .8281 .8333

.838 .8438 .8496 .8542 .8594 .8646 .8698 .8750 .8802 .8854 .8906 .8958 .9010 .9063 .9115 .9167

9

10

11 .9219 '/e .9271 i/. .9323 '/it .9375 .9427 .9479 .9531 7/, .9583 1/ .9635 '/ss .9688 '/s .9740 th .9792 .9844 usg .989 ,js 9948 ". e 1.000 1

s,

11

Deg.

00

10' 20 30 40 50

TABLE

IV

-RADI

Radius

Mid. Ord.

Tan. Offset

ORDIATES AND DFLaCTIoXNS Def. for

1

.036 .073 .109 .145 .182

.145 .291 .436 .582 .727

8729.65 10 4911.15 20 4297.28 30 3819.83 40 3437.87 3125:36

.218 .255 .291 .327 .364 .400

.873 1.018 1.164 1.309 1.454 1.600

0.30 0.35 0.40 0.45 0.50 0.55

2864.93 2644.58 2455.70 2292.01 2148.79 2022.41

.436 .473 .509 .545 .618

1.745 1.891 2.036 2.181 2.327 2.472

0.60 0.66 0.70 0.75 0.80 0.85

1910.08 1F09.57 1719.12 1637.28 1562.88 1494.95

.655 .691 .727 764 .800 836

2.818 2.763 2.908 3.054 3.199 3.345

0.90 0.95 1.00 1.05 1.10 1.15

Note.

.582

Radius

Mid. Ord.

Tan. t

0.05'

0.10 0.15 0.20 0.25

.873 1432.69 1375.40 .909 1322.53 .945 1273.57 .982 1228.11 1.018 1185.78 1.055

3.490 1.20 3.6835 1.25 3.718 1.30 3.926 1.35 4.071 1.40 4.217 1.45

11468.28 1109.33 1074.68 1042.14 1011.51 982.64

1.091 1.127 1.164 1.200 1.237 1.273

4.362 4.507 4.653 4.798 4.943 5.088

1.50 1.55 1.60 1.85 1.70 1.75

955.37 "929.57 905.13 881.95 859.92

1.309 1.346 1.382 1.418 1.455

5.234 5.379 5.524 5.669 5.814

1.80 1.85 1.90 1.95 2.00

Chord Deflection -2 times tangent deflection.

Dt. for

Foot 1

Foot

34377.5 17188.8.

11459.2 8594.42 6875.55

8

Deg.

819.02 781,84 764.49 747.89

1.528 1.600 1.637 1.673

6.105 6.395 6.540 6.685

2.10' 2.20 2.25 2.30

718.78 688.16 874.69 661.74

1.746 1.819 1.855 1.892

6.976 7.286 7.411 7.556

2.40 2.50 2.55 2.60

687.28 614.56 608.80 593.42

1.965 2.087 2.074 2.110

7.848 8.136 8.281 8.426

2.70 2.80 2.85 2.90

573.69 546.44 521.87 499.06 478.34 459.28 441.68 425.40 410.28 396.20

2.183 2.292 2.402 2.511.

2.620 2.730 2.839 2.949 3.058 3.188

8.716 9.150 9.585 10.02 10.45 10.89 11.32 11.75 12.18 12.62

3.00 3.15 3.30 3.45 3.60 3.75 3.90 4.05 4.20 4.35

383.07 370.78 359.27 348.45 338.27 319.62 302.94

3.277 3.387 3.496 3.606 3.716 3.935' 4.155

13.05 13.49 13.92 14.35 14.78 15.64 16.51

4.50 4.65 4.80 4.95 5.10 5.40 5.70

287.94 274.37 262.04 250.79 240.49

4.374 4.594 4.814 5.035 5.255

17.37 18.22 19.08 19.94 20.79

8.00 8.30 6.60 8.90 7.20

231.01 222.27 214.18 206.68 199.70 193.18

5.476 5.697 5.918 6.139 6.360 6.583

21.64 22.50 23.35 24.19 25.04 25.88

7.50 7.80 8.10 8.40 8.70 9.00

TABLE V CURVE FORMUL/E FOR SIMPLE CURVES COMPILED BY J. CALVIN LOCKE, C. E.

(1) c =

a'+b'

(2) c -=

Ra

(3) c =- 2R (R - /(R+b) (R-b) = f2R (R--b(4) c = 2 m (2R-m) (6)c = 2T cos sI (5) c=2Rsin /

(7) e= R exsec 1/s2

)

() e= Ttan/

VI (8) e= Rtan/ I tan1/4 b(2R-a)

(10)

(11) b =

(c+

(12) b= Rsin I a==+b" (14) R--2a (16) d =

. c2R - 4s (13) b= acot'a/I I c'+4m' dR c*( 8m 2m 2a

R (2R-(2R+c) 2R-c) =

(17) d =2Rm (20) m -

18) d

R

R (2R-

2R sin / 1

R+

-R

c2) (19) m =

=R R

W

c'

1 (21) m = Rvers 1 /z 1 (22) m = Rsin1 /s tan '/fI (23) m = I c tan ' I (25) a = R- f(R+b) (R--b) = R - R-b' (24) a = --

(27) a= R vers l

112 1 (26) a = 2 R (sin 1

(29)a b tan

(32) I

/

1l (30) a= T sin I

X 57.295780

(34) L = IR X 0.01745329 (36 Area

Seg. sin I 36 AreaLR-R' 2

(33) R

(28 a = R sin Itan 1'I

(31) T= R tan 1/sI

L X 57.295780

(35) L =8d-c LR-Rb 2Seg. 2

TABLE VI

SINES, COSINES, TANGENTS, COTANGENTS tan sin 40' 50'

tan t 50' -

0087 0116 262 291 437 465 612 640 787 814 963 987 1139 1161 317 334 495 507 673 679

0116 291 466 641 816 992 1169 346 524 703

0145 89 32088 495 87 670 86 846 85 1022 84 198 83 376 82 554 81 733 80

823 822 2004 994 186 2164 370 334 555 504 742 672 931 840 3121 3007 314 173 508 338

853 2035 217 401 586 773 962 3153 346 541

851 2022 193 363 532 700 868 3035 201 365

883 880 2065 2051 247 221 432 391 617 560 805 728 994 896 3185 3062 378 228 574 393

914 2Q95 278 462 648 836 3026 217 411 607

79 78 77 76 75 74 73 72 71 70

673 475 872 638 4074 800 279 961 487 4120 699 279 913 436 5132 592 354 746 581 899

706 502 906 665 4108 827 314 987 522 4147 734 305 950 4462 5169 617 392 772 619 924

739 529 939 692 4142 854 348 4014 557 173 770 331 986 488 5206 643 430 797 658 950

772 557 973 719 4176 881 383 4041 592 200 806 358 5022 514 243 669 467 823 696 975

805 4006 210 417 628 841 .5059 280 505 735

69 68 67 66 65 64 63 62 61 60

5812 5050 6048 200 289 348 536 495 787 640 7046 783 310 925 581 6065 860 202 8146 338

851 5975 6088 225 330 5373 577 519 830 664 7089 807 355 948 627 6088 907 225 8195 361

890 5100 6128 250 371 398 619 544 873 688 7133 831 400 972 673 6111 954 248 8243 383

930 5125 6168 275 412 422 661 568 916 712 7177 854 445 995 720 6134 8002 271 292 406

969 6208 453 703 959 7221 490 766 8050 342

59 58 57 56 55 54 53 52 51 50

s sin S 0'

tan sin 0' 10'

tan sin 10' 20'

tan 20'

sin 30'

0 0000 I 175 2 349 3 523 4 698 5 872 6 1045 7 219 8 392 9 564

0000 0029 01750204 349 378 524 .552 699 727 875 901 1051 1014 228 248 405 421 584 593

0029 0058 02040233 378 407 553 581 729 756 904 929 1080 1103 257 279 435 449 614 622

0058 0233 407 582 758 934 1110 287 465 644

0087 0262 436 610 785 958 1132 305 478 650

10 736 11 908 12 2079 13 250 14 419 15 588 16 756 17' 924 18 3090 19 256

763 765 944 937 2126 2108 309 278 493 447 679 616 867 784 3057 952 249 3118 443 283

793 794 974 965 2156 2136 339 306 524 476 711 644 899 812 3089 939 281 3145 476 311

20 420 21584 22 746 23 907 24 4067 25 226 26 384 27 540 28695 29 848

640 839 4040 245 452 663 877 5095 317 543

448 611 773 934 4094 253 410 566 720 874

30 5000 31 150 32 299 33 446 34 592 35 736 36 878 37 6018 ,8 157 39 293

774 6009 249 494 745 7002 265 "536 813 8098

5025 175 324 471 16 760 901 6041 180 316

tan sin 30' 40'

0145 320 494 669 843 1016 190 363 536 708

40 428 391 450 441 472 491 494 54T 41 561 693 583 744 604 796 626 847 42 691 9004 713 9057 734 9110 756 9163 43 820 325 841 380 862 435 884 490 44 947 657 967 713 988 770 7009 827 45 7071 1.0000 7092 1.0058 7112 1.0117 133 1.0176

517 591 539 642 648 899 670 952 777 9217 799 9271 905 545 926 601 7030 884 7050 942 153 1.0235 173 1.0295

S 60'

60' 50'

50'

40'

40'

30'

30'

20'

20'

10'

10'

Scos

cot

cot

cos

cot

cos

cot

cos

cot

cos

cot

cos

49 48 47 46 45 44

.4

TABLE VI (continued)

SINES, COSINES TANOENTS COTANENTS (continued) sin tan sin tan sin tan O' I10' 110' I20'I 20' 0' 1.0355 .0724

tan 30"

tan 40' ni

a40'

50'P

50'

1.0416 7234 1.0877 .0786 353 .0850 .1171 470 .1237 ..1571 585 .1640

1.0533 1.059 .00913 7274 392 .0977 .1303 S09 .1369 .1708 623 .1778

660 1.1918 7711 .2349 880j .2799 986 .3270 8090 .3764 S192 .4281 290 .4826 3871 .5399 480 .6003 572, .6643

1.1988 .2423 .2876 .3351 .3848 .4310 .4919 .5497 .6107 .6753

1.2131 7735 1.2203 7753 862 844 .2647 .2572 969 .3032 951 .3111 .3514 8056 .3597 8073 175 .4019 158 .4106 274 .4550 258 .4641 .5108 311 355 .5204 465 .5697 450 .5798 542 .6426 557 .6319 646 .697 631 .7090

660 746 829 910 988 9063 135 205 272 336

1.7321 .8040 .8807 .9626 2.0503 .1445 .2460 .3559 .4751 .6051

1.7437 8689 1.7556 .8165 774 .8291 .8940 857 .9074 .9168 .9912 2.0655 9013 2.0809 .1609 088 .1775 .2637 159 .2817 .3750 228 .3945 293 .5172 .6279 356 .6511

1.7797 8732 1.7417 .8418 802 .8546 816 .8676 .9210 884 .9347 897 .9486 2.0057 962 2.0204 975 2.0353 .0965 9038 .1123 9051 ,1283 124 .2286 .1943 112 .2113 194 .3369 .29981 182 .3183 .4142 250 .4342 261 .4545 325 .5386 315 .5605 .6746 387 377 .6985

397 455 511 563 613 659 703 744 781 816

2.7475 .9042 3.0777 .2709 .4874 .7321 4.0108 .3315 .7046 .1446

2.7725 9417 2.7980 .9319 474 .9600 3.1084 528 3.1397. .3052 580 .3402 .5261 628 .5656 .7760 674 .8208 4.0611 717 4.1126 .3897 757 .4494 .7729 793 .8430 5.2257 827 5.3093

2.8239 9436 .9887 492 3.1716 546 596 .3759 6.6059 644 689 .8657 4.1653 730 .510385 769 805 .9152 5.3955 838

9848 877 903 925 945 962 976 986 994 9998

5.6713 6.3138 7.1154 8.1443 9.5144 11.430 14.300 19.081 28.636 57.290

5.7694 9858 5.8708 6.4348 886 6.5606 7.2687 911 7.4287 8.3450 932 8.5555 9.7882 961 10.078 11.826 967 12.250 14.924 980 15.605 20.206 989 21.470 31.242 9996 34.368 68.750 9999 85.940

5.9758 9868 6.0844 9872 6.143270 894 .8269 899 .9682 6.6912 7.5958 918 7.7704 932 7.9530 8.7769 939 9.0098 942 9.2553 959 11.059 10.385 957 10.711 12.706 971 13.197 974 13.727 16.350 983 17.169 985 18.075 22.903 992 24.542 993 26.432 38.189 997 42.964 9998 49.104 114.58 .000 '171.88 1.000 343.77

7193 314 431 547

60

.1106 .1504

60" cot

l

I

I

7698 1.2059 808 .2497 916 .2954 8021 .3452 124 .3934 225 .4460 323 .5013 418 .5591 511 .6212 601 .6864

50' 40' cot cos

40' cot

30' cot

20'

cos

7294 1.0561 412 .1041 528 .1436 642 .1847

1.2176

.2723 .3190 .3680 .4193 .4733 .5301 .5900 .6534 .7205

2.8502 9446 502 3.0475 3.0178 .2041 555 .2371 605 .4495 .4124 652 .6891 .6470 696 .9617 .9136 4.2193 737 4.2747 775 .6382 .5736 .9894 811 5.0658 5.4845 843 .5764

20' cot

10'

cos

10' cot

TABLE VII Deflections for Sub Chords for Short ladius Curves.

1egree

Radius

Curve

sin. J def. ang.

30o 32 34

193.18 181.39 171.O1

sub chord 12.5 Ft. °

for 100 ft.

3 43 ' 3 58 ° 4 12

101.15

2 41

3 33

4

2

Io1.66 o101.85 102.06

2 ° 33'

344'

440'

2 57

3 55'

4 54

305

4

153.58

40

146.19

42

139.52

20 34

44

133.47

460

127.97

248

480 50 ° 52 54

122.9

1I18.31

2 55' 3 02'

I14.o6 0.11

3 09 3316

560

zo6.50

3 22'

58

103.14 100oo.oo00

3 29' 335

4 4

60

T

5tan

Sin.

k D = 50

Sin.

JD

Sin.

2 41'

25

49'

I

5

8

40

3 3

21 29'

29 4 40'.

5 36' 50 50'

4 5'

60 04 6

3

502' 13

42'

5' 23'

631' 6 44'

5

60 57

3° 38''

3

' 18

E =T tan

I

34 44'

101.48

102.29 102.53 102.76

o8'

13'

50 ER Re sec

RE

07'

101.33

6'

3

5 22'

7

°

13.00

103.24

I7'

103.54 I103.84

104.14 104.43 104.72

'

Chord def. = chord

R = T cot. I I R = Sin. D

D

= 5 ta

17'

20

380

161.8o

25 Ft.

20581 31 o0' 321'

°

1059 2°06' 2 13 2o 20 2 27

36

def. agle

20 Ft.

2

51'

sn f

15 Ft.

I

No.chords = I

D

Tan. def.=

chord def.

The square of any distance, divided by twice the radius, will equal the distance from tangent to curve, very nearly.

To find angle for a given distance and deflection. ° Rule I.

Multiply the given distance by .01745 (def. for

for i ft.

see Table II.), and divide given deflection by the product.

Rule 2. Multiply given deflection by 57.3, and divide the product by the given distance.

To find deflection for a given angle and distance. Multiply the angle by .o1745, and the product by the distance.

GENERAL DATA RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the

base.

Add quotient to base for hypotenuse.

2 Given Base ioo, Alt. 1o.Ozo o=.5. ioo0.5=Ioo.5 hyp.

Given Hyp. 1oo, Alt. 25.252+2oo0=3.125. Ioo-3.125=96.875=--Base.

Error in first example, .oo2; in last, .045.

To find Tons of Rail in one mile of track: multiply weight per yard

by II, and divide by 7.

LEVELING. The correction for curvature and refraction, in feet and decimals of feet is equal to 0.574ds , where d is the distance in miles.

The correction for curvature alone is closely, id2. The combined correction is negative.

PROBABLE ERROR. If d,3, d, d, etc. are the discrepancies of various

results from the mean, and if 7d=-the sum of the squares of these differences and n=the number of observations, then the probable error of the d mean= 0.6745 7_d)

TANGENTS AND EXTERNALS TO Ale CURVE.

TABLE VIII T

E

I

1=100

T

E

to 10' 20' 30' 40'.

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

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

10' 20' 30' 40'

50' 5io

10' 20' 30' 40' 50' go

10' 20' 30' 40' 50' 70

10' 20' 30' 40' 50' So

10' 20' 30' 40' 50' go

10' 20' 30' 40' 50' 100 10' 20' 30' 40' 50'

50.00 .218 .297 58.34 66.67 .388 ;+c 75.01 .491 50 C. T' .606 83.34 .733 .03 91.68 100.01 .873 .001 108.35 1.024 116.68 1.188 125.02 1.364 133.36 1.552 141.70 1.752 150.04 1.964 100 C yo 158.38 2.188 T 166.72 2.425 .06 2.674 175.06 E 183.40 2.934 .003 191.74 3.207 200.08 3.492 208.43 3.790 216.77 4.099 225.12 4.421 933.47 4.755 241.81 5.100 150 C. T 250.16 5.459 .09 258.51 5.829 E 266.86 6.211 .004 275.21 6.606 283.57 7.013 291.92 7.432 300.28 7.863 308.64 8.307 316.99 8.762 325.35 9.230 200 C. 333.71 9.710 T 342.08 10.202 .13 E 350.44 10.707 358.81 11.224 .006 367.17 11.753 375.54 12.294 383.91 12.847 392.28 13.413 400.66 13.991 409.03 14.582 25o C. T 417.41 15.184 425.79 15.799 .16 '434.17 16.426 E 442.55 17.065 .007 450.93 17.717 459.32 18.381 467.71 19.058 476.101 19.746 484.49 20.447 492.88 21.161 300 C. T 501.28 21.887 509.68 22.624 .19 E 518.08 23.375 526.48 24.138 .008 534.89 24.913 543.29 25.700

~

T

I

I1=200

"

-

I 1=3P

"

noi

10' 20' 30' 40' 50'

120o 10' 20" 30' 40' 50' 180 10' 20' 30' 40' 50' 14o 10' 20' 30' 40' 50' 150 20' 30' 40' 50' 10' 20' 30' 40' 50' 170o 10' 20' 30' 40' 50' 18o 10' 20' 30' 40' 50' io 10' 30' 40' 50' 200 10' 20' 30' 40' 50'

T=. R tau 'IaI

551.70 560.11 568.53 576.95 585.36 593.79 602.21 610.64 619.07 627.50 635.93 644.37 652.81 661.25 669.70 678.15 686.60 695.06 703.51 711.97 720.44 728.90 737.37 745.85 754.32 762.80 771l29 779.77 788.26 796.75 805.25 813.75 822.25 830.76 839.27 847.78 856.30 864.82 873.35 881.88 890.41 898.95 907.49 916.03 924.58 933.13 941.69 950.25 958.81 967.38 975.96 984.53 993.12 1001.7 1010.3 1018.9 1027.5 1036.1 1044.7 1053.3

26.500 27.313 28.137 28.974 29.824 30.686 31.561 32.447 33.347 34.259 35.183 36.120 37.070 38.031 39.006 39.993 40.992 42.004 43.029 44.066 45.116 46.178 47.253 48.341 49.441 50.554 51.679 52.818 53.969 55.132 56.309 57.498 58.699 59.914 61.141 62.381 63.634 64.900 66.178 67.470 68.774 70.091 71.421 72.764 74.119 75.488 76.869 78.264 79'.671 81.092 82.525 83.972 85.431 86.904 88.389 89.888 91.399 92.924 94.462 96.013

10

+ T

.06

ES 006

10' 20' 30' 40' 50' 220 10' 20' 30'

40' 50' 100 C. 230 10' 20' .13 30' E .011 40" 50' 20' 30' 240" 40' 10' 150 C. 50' T 250 .19 10' E 20' .017 30' 40' 50'

20

0

C.

T .26 E

.022

10' 20' " 2S30' 40' 50' 270 10' 20' 30' 40'

50' 280 250 C. 10' T 20' .32 30' E 40' .028 50' 290 10' 20' 30' 40' ° 30 C. 50' T 300 .39 10' E 20' .034 30' 40' 50'

1061.9 1070.6 1079.2 1087.8 1096.4 1.105.1 1113.7 1122.4 1131.0 1139.7 1148.4 1157.0 1165.7 1174.4 1183.1 1191.8 1200.5 1209.2 1217.9 1226.6 1235.3 1244.0 1252.8 1261.5 1270.2 1279.0 1287.7 1296.5 1305.3 1314.0 1322.8 1331.6 1340.4 1349.2 1358.0 1366.8 1375.6 1384.4 1393.2 1402.0 1410.9 1419.7 1428.6 1437.4 1446.3 1455.1 1464.0 1472.9 1481.8 11490.7 1499.6 1508.5 1517.4 1526.3 1535.3 1544.2 1553.1 1562.1 1571.0 1580.0

E= R exsec112i

97.577 99.155 100.75 102.35 T 103.97 105.60 .10 E 107.24 .013 108.90 110.57 112.25 113.95 115.66 117.38 100 C. 119.12 T 120.87 .19 122.63 E 124.41 .025 126.20 128.00 129.82 131.65 133.50 135.35 137.23 150 C. T 139.11 .29 141.01 E 142.93 .038 144.85 146.79 148.75 150.71 1'152.69 154.69 156.70 200 C. 158.72 T 160.76 .39 E 162.81 164.86 .051 166.95 169.04 !171.15 173.27 175.41 177.55 250 C. T 179.72 181.89 .49 184.08 E 186.29 .065 188.51 190.74 192.99 195.25 197.53 199.82 300 C. T 202.12 204.44 .59 E 206.77 209.12 .078 211.48 213.86

TABLE VIII TANGENTS AND EXTERNALS TO A 10 CURVE

I 310 10' 20' 30' 40' 50' 820 10' 20' 30'

40' 50'

$s8

10' 20'

30' 40' 50' 340

10' 30' 40' 50" 350 10' 20' 30' 50' $86o

10' 20' 40' 50'

7o0

10' 20' 30" 40' 50' 88o 10' 20' 30' 40' 50' 390 10' 20' 30' 40' 50' 400 10' 20' 30' 40' 50'

T

E 1=400

1589.0 216.3 1598.0 218.7 1606.9 221.1 1615.9 223.5 1624.9 226.0 1633.9 228.4 1643.0 230.9 1652.0 233.4 1661.0 235.9 1670.0 238.4 1679.1 241.0 1688.1 243.5 1697.2 246.1 1706.3 248.7 1715.3 251.3 1724.4 253.9 1733.5 256.5 1742.6 259.1 1751.7 261.8 176Q.8 264.5 1I.0 267.2 1779.1 269.9 1788.2 272.6 1797.4 275.3 1806.6 278.1 1815.7 280.8 1824.9 283.6 1834.1 286.4 1843.3 289.2 1852.5 292.0 1861.7 294.9 1870.9 297.7 1880.1 300.6 1889.4 303.5 1898.6 306.4 1907.9 305.3 1917.1 312.2 1926.4 315.2 1935.7 318.1 1945.0 321.1 1954.3 324.1 1963.6 327.1 1972.9 330.2 1982.2 333.2 1991.5 336.3 2000.9 339.3 2010.2 342.4 2019.6 345.5 2029.0 348.6 2038.4 351.8 2047.8 354.9 2057.2 358.1 2066.6 361.3 2076.0 364.5 2085.4 367.7 2094.9 371.0 2104.3 374.2 2113.8 377.5 2123.3 380.8 2132.7 384.1

t

T

E I=50o

2142.2 387.4 2151.7 390.7 2161.2 394.1 2170.8 397.4 2180.3 400.8 404.2 2189.9 2199.4 407.6 2209.0 411.1 2218.6 414.5 2228.1 418.0 421.4 2237.7 425.0 2247.3 2257.0 428.5 10' 2266.6 432.0 440 20' 2276.2 435.6 30' 2285.9 439.2 442.8 40' 2295.6 50' 2305.2 446.4 450.0 2314.9 44o 10' 2324.6 453.6 20' 2334.3 457.3 461.0 30' 2344.1 2353.8 464.6 50' 2363.5 468.4 472.1 450 2373.3 475.8 10' 2383.1 479.6 20' 2392.8 483.4 30' 2402.6 40' 2412.4 487.2 50' 2422.3 491.0 2432.1 494.8 460 10' 2441.9 498.7 502.5 20' 2451.8 30' 2461.7 506.4 510.3 40' 2471.5 50' 2481.4 514,3 518.2 470o 2491.3 522.2 10' 2501.2 526.1 20' 2511.2 530.1 30' 251.1 2531.1 534.2 2541.0 538.2 542.2 480 2551.0 546.3 10' 2561.0 2571.0 550.4 20 554.5 30' 2581.0 40' 2591.0 558.6 50' 2601.1 562.8 566.9 490 2611.2 10' 2621.2 571.1 575.3 20' 2631.3 30' 2641.4 579.5 583.8 40' 2651.5 588.0 50' 2661.6 592.3 500 2671.8 10' 2681.9 596.6 20' 2692.1 600.9 30' 2702.3 605.3 609.6 40' 2712.5 50' 2722.7 614.0 410

+ 10' 20' So C. 30' T .13 40' E 50' .023 420 10' 20' 30' 40' 50' 100 C. .26 E .046

150 C T .40 E .00

20* C.

T

.53 E.

250 C.

T .67 .117

300

C.

.80 E .141

T=R tntit I

E

I

51o 10' 20' T 30' 40' .17 E 50' .037 52o 10'

50 C.

30' 40' 50' 100 C. 530 10' T 20' .34 30' E .075 50'

540

10' 20' 30' 40'

150 C. 50' T 550 .51 E * 10' .116 20' 30'

40'

I.

200

C.

.68

E

.151

250 C.

T .85 E .189

50' 560 10' 20' 30 40' 50' 570

10' 20' 30' 40' 50' 580 10' 20' 30' 40' 50' 590

10' 20' 30' 50' 0 30 C. 600 T 10' 1.02 20' E 30 .227 40' 50'

R exsec '12

T

E

2732.9 618.4 2743.1 622.8 2753.4 627.2 2763.7 631.7 2773.9 636.2 2784.2 640.7 2794.5 645.2 2804.9 649.7 2815.2 654.3 2825.6 658.8 2835.9 663.4 2846.3 668.0 2856,7 672.7 2867.1 677.3 2877.5 682.0 2888.0 686.7 2898.4 691.4 2908.9 696.1 2919.4 700.9 2929.9 705.7 2940.4 710.5 2951.0 715.3 720.1 2961.5 2972.1 725.0 2982.7 729.9 2993.3 734.8 3003.9 739.7 3014.5 744.6 3025.2 749.6 3035.8 754.6 3046.5 759.6 3057.2 764.6 3067.9 769.7 3078.7 774.7 3089.4 779.8 3100.2 784.9 3110.9 790.1 3121.7 795.2 3132.6 800.4 3143.4 805.6 3154.2 810.9 3165.1 816.1 3176.0 821.4 3186.9 826.7 3197.8 832.0 837.3 3208.8 3219.7 842.7 3230.7 848.1 853.5 3241.7 3252.7 858.9 3263.7 864.3 869.8 3274.8 875.3 3285.8 880.8 3296.9 886.4 3308.0 3319.1 892.0 3330.3 897.5 903.2 3341.4 3352.6 908.8 3363.8 914.5

]=too 5 C. T .21 E .056

100 C. T .42 E .112

150

C.

E .168

250 C.

1.05 E 2.83

300 C.

1.27 E .340

TABLE VIII TANGENTS AND EXTERNALS TO A 1 CURVE. 1

T

1

1

1=70D

710 3375.0 920.2 610 10' 10' 3386.3 925.9 + 20' 20' 3397.5 931.6 SOC. 30' 937.3 3408.8 T 40' 40' 3420.1 943.1 50' 50" 3431.4 948.9 .25 620 3442.7 954.8 .080 720 10' 10' 3454.1 960.6 20' 20' 3465.4 966.5 30' 30' 3476.8 972.4 40' 40' 3488.3 978.3 50' 50' 3499.7 984.3 680 3511.1 990.2 10o C, 7830 10' 10' 3522.6 996.2 T 20' 20D' 3534.1 1002.3 .51 30' 30' 3545.6 1008.3 E 40' 40' 3557.2 1014.4 159 50' 50' 3568.7 1020.5 3580.3 1026.6 740 640 10' 10' 3591,9 1032.'8 20' 3603.5 1039.0 3615.1 1045.2 30' 3626.8 1051.4 40' 3638.5 1057.7 150 C 50' T 3650.2 1063.9 650 so .76 750 3661.9 1070.2 10' E 50' 3673.7 1076.6 20' 20' .240 3685.4 1082.9 30' 30' 40' 40' 10' 3697.2 1089.3 50' 10' 3709.0 1095.7 20' 30' 3720.9 1102.2 76o 40' 3732.7 1108.6 10' 50' 3744.6 1115.1 20' 3756.5 1121.7200 C 30' 60 40' T 10' 3768.5 1128.2 50' 20' 3780.4 1134.8 1.02 30' 3792.4 1141.4 E 770 40' 3804.4 1148.0 .321 10' 50' 3816.4 1154.7 20' 3828.4 1161.3 30' 870 40' 10' 3840.5 1168.1 50' 20' 3852.6 1174.8 30' 3864.7 1181.6 780 40' 3876.8 1188.4 25o C. 10' 20' 3889.0 1195.2 T 30' 3901.21202.0 1.28 40' E 10' 3913.4 1208.9 50' .403 3925.6 1215.8 50' 50' 20' 30' 3937.9 1222.7 7go 69o 40' 3950.2 1229.7 10' 10' 20' 20' 3962.5 1236.7 30' 30' 3974.8 1243.7 40' 40' 3987.2 1250.8 50' 50' 3999.5 1257.9 300 C T 4011.9 1265.0 800 10' 4024.4 1272.1 1.54 E 20' 4036.8 1279.3 .485 1286.5 30' 4049.3 40' 4061.81293.6 50' 4074.4 1300.9 I

30'

~~--~-~-

I

E =R naI

I==80l

T

E

4086.9 4099.5 4112.1 4124.8 1137.4 4150.1 4162.8 4175.6 4188.5 4201.2 4214.0 4226.8 4239.7 4252.6 4265.6 4278.5 4291.5 4304.6 4317.6 4330.7 4343.8 4356.9 4370.1 4383.3 4396.5 4409.8 4423.1 4436.4 4449.7 4463.1 4476.5 4489.9 4503.4 4516.9 4530.4 4544.0 4557.6 4571.2 4584.8 4598.5 4612.2 4626.0 4639.8 4653.6 4667.4 4681.3 4695.2 4709.2 4723.2 4737.2 4751.2 4765.3 4779.4 4793.6 4807.7 4822.0 4836.2 4850.5

1308.2 1315.6 1322.9 1330.3 1337.7 1345.1 1352.6 1360.1 1367.6 1375.2 1382.8 1390.4 1398.0 1405.7 1413.5 1421.2 1429.0 1436.8 1444.6 1452.5 1460.4 1468.4 1476.4 1484.4 1492.4 1500.5 1508.6 1516.7 1524.9 1533.1 1541.4 1549.7 1558.0 1566.3 1574.7 1583.1 1591.6

4864.8

4879.2

I

+ 50 C. T .30 E .110

100 C. T .61 E .220

150 C. TI .91 .332

20o C. T 1.22 E .445

1608.6 1617.1 1625.7 1634.4 1643.0 1651.7250 C. 1660.5 T 1669,2 1.53 1678.1 E .558 1686.9 1695.8 1704.7 1713.7 1722.7 1731.7 1740.8 30+ C. T 1749.9 1759.0 1.84 E 1768.2 .671 1777.4 1786.7 1796.0

tanE

N

T

Bt=90*

4893.6 1805.3 4908,0 1814.7 4922.5 1824.1 4937.0 1833.6 4951.5 1843.1 40" 50' 4966.1 1852.6 4980.7 1862.2 820 10' 4995.4 1871.8 20' 5010.0 1881.5 30' 5024.8 1891.2 40' 5039.5 1900.9 50' 5054.3 1910.7 5069.2 1920.5 830 10' 5084.0 1930.4 20' 5099.0 1940.3 30' 5113.9 1950.3 40' 5128.9 1960.2 5143.9 1970.3 50' 5159.0 1980.4 84o 10' 5174.1 1990.5 5189.3 2000.6 20' 30' 5204.4 2010.8 40' 5219.7 2021.1 50' 5234.9 2031.4 5250.3 2041.7 850 10' 5265.6 2052.1 20' 5281.0 2062.5 30' 5296.4 2073.0 40' 5311.9 2083.5 50' 5327.4 2094.1 5343.0 2104.7 8860 10' 5359.6 2115.3 20' 5374.2 2126.0 30' 5389.9 2136.7 5405.6 2147.5 40' 5421.4 2158.4 50' 5437.2 2169.2 870 10' 5453.1 2180.2 20' 5469.0 2191.1 30' 5484.9 2202.2 40' 5500.9 2213.2 5517.0 2224.3 50' 5533.1 2235.5 88 10' 5549.2 2246.7 20' 5565.4 2258.0 30' 5581.62269.3 40' 5597.8 2280.6 50' 5614.2 2292.0 5630.5 2303.5 890 10' 5646.9 2315.0 20' 5663.4 2326.6 30' 5679.9 2338.2 40' 5696.4 2349.8 50' 5713.0 2361.5 5729.7 2373.3 900 10' 5746.3 2385.1 20' 5763.1 2397.0 30' 5779.9 2408.9 40' 5796.7 2420.9 50' 5813.6 2432.9 810 10' 20' 30'

=Ruec'I

+ T .36 E .,149

100 C. T .72 E .299

15o C. ST

1.09 .450

20oC. T 1.45 .603

C. T 1.83

25

E

.756

300 C. T 2.20 E .910 +

TABLE VIII

I T to

10' 20' 30' 40' 50' 10' 20' 920 30' 40' 50' 93o0

10' 20' 30' 40' 50' 940 10' 20' 30' 40' 50' 10' 20' 30' 40' 50' 950 "0 10' 20' 30' 40' 50' 10' 20' 30' 40' 50' .7.

080 10' 20' 30' 40' 50' 20' 30' 40' 50' 100x 10' 30' 40' 50'

TANGENTS AND EXTERNALS TO A 1* CURVE

E I3p

5830.5 2444.9 5847.5 2457.1 5864.6 2469.3 5881.72481.5 5898.8 2493.8 5916.0 2506.1 5933.2 2518.5 5950.5 2531.0 5967.9 2543.5 5985*3 2556.0 6002.7 2568.6 6020.2 2581.3 6037.8 2594.0 6055.4 2606.8 6073.1 2619.7 6090.8 2632.6 6108.6 2645.5 6126.4 2658.5 6144.3 2671.6 6162.2 2684.7 6180.2 2697.9 6198.3 2711.2 6216.4 2724.5 6234.6 2737.9 6252.8 2751.3 6271.1 2764.8 6289.4 2778.3 6307.9 2792.0 6326.3 2805.6 6344.8 2819.4 6363.4 2833.2 6382.1 2847.0 6400.8 2861.0 6419.5 2875.0 6438.4 2889.0 6457.3 2003.1 6476.2 2917.3 6495.2 2931.6 6514.3 2945.9 6533.4 2960.3 6552.6 2974.7 6571.9 2989.2 6591.2 3003.8 6610.6 3018.4 6630.1 3033.1 6649.6 3047.9 6669.2 3062.8 6688.8 3077.7 6708.6 3092.7 6728.4 3107.7 6748.2 3122.9 6768.1 3138.1 6788.1 3153.3 6808.2 3168.7 6828.3 3184.1 6848.5 3199.6 6868.8 3215.1 6889.2 3230.8 6909.6 3246.5 6930.1 3262.3

-t-

50 C. T .43 E

101o0 10' 20' 30' 50'

o

102 10' 20' 30' 40' 50' 10OC. 103o 10' T 20' .86 30' E 40' .401 50' 1040 10' 40' 150 C. 50' T 1.30 1050 E 20' .604 30' 40' 50' 1080 10' 20' 200 C 30' T 40' 1.74 50' .809 107o 10' 20' 30' 40' 50' 10' 20' 30' 2.18 1.02E 40' 50' 1.02 1090

25*C

20' 30' 40' 50' 300

C.

2T 2.62 E 1.22

T 1E =10

I

10' 30' 40' 50'

6950.6 6971.3 6992.0 7012.7 7033.6 7054.5 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 7603.5 7626.6 7649.7 7672.9 7696.3 7719.7 7743.2 7766.8 7790.5 7814.3 7838.1 7862.1 7886.2 7910.4 7934.6 7959.0 7983.5 8008.0 8032.7 8057.4 8082.3 -8107.3 8132.3 8157.5 8182.8 8208.2 8233.7 8259.3 8285.0 8310.8

T=Rtan Vt1

3278.1 3294.1 + 3310.1 5* C. 3326.1 T 3342.3 .51 E 3358.5 3374.9 .268 3391.2 3407.7 3424.3 3440.9 3457.6 3474.4 10o C 3491.3 T 3508.2 .103 3525.2 E 3542.4 .536 3559.6 3576.8 3594.2 3611.7 3629.2 3646.8 3664.5 150 C T 3682.3 1.56 3700.2 E 3718.2 .806 3736.2 3754.4 3772.6 3791.0 3809.4 3827.9 3846.5 20O C 3865.2 T 3884.0 2.08 E 3902.9 3921.9 1.08 3940.9 3960.1 3979.4 3998.7 4018.2 4037.8 250 C. 4057.4 T 4077.2 2.61 4097.1 E 4117.0 1.36 4137.1 4157.3 4177.5 4197.9 4218.4 4239.0 30 C. 4259.7 T 4280.5 3.14 4301.4 1.63E 4322.4 1.63) 4343.6i 4364.8

V12 I- T e 11

111 10' 20' 30' 40' 50' 112o 10' 20' 30' 40" 50' 1138 10' 20' 30' 40' 50'

0 114

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

117A 10' 20' 30' 40' 50' 1180 10' 20' 30' 40' 50' 1190 10' 20' I30' 40' 50' 1200 10' 20' 30' 40' 50'

E =Rexsec'I1

8336.7 8362.7 8388.9 8415.1 8441.5 6468.0 8494.6 8521.3 8548.1 8575.0 8602.1 8629.3 8656.6 8684.0 8711.5 8739.2 8767.0 8794.9 8822.9 8851.0 8879.3 8907.7 8936.3 8965.0 8993.8 9022.7 9051.7 9080.9 9110.3 9139.8 9169.4 9199.1 9229.0 9259.0 9289.2 9319.5 9349.9 9380.5 9411.3 9442.2 9473.2 9504.4 9535.7 9567.2 9598.9 9630.7 9662.6 9694.7 9727.0 9759.4 9792.0 9824.8 9857.7 9890.8 9924.0 9957.5 9991.0.

10025.07 10059.0 10093.0

4386.1 4407.6 + 4429.2 5o C. 4450.9 T 4472.7 .62 4494.6 E 4516.6 .3 4538.8 4561.1 4583.4 4606.0 4628.6 4651.3 10 C. 4674.2 T 4697.2 1.25 4720.3 7E 4743.6 721 4766.9 4790.4 4814.1 4837.8 4861.7 4885.7 4909 9 150 C. T 4934.1 1.93 4958.6 E 4983 1 109 5007.8 5032.6 5057.6 5082.7 5107.9 5133.3 5158.8 200 C. 5184.5 T 5210.3 2.52 E 5236.2 5262.3 1.46 5288.6 5315.0 5341.5 5368.2 5395.1 5422.1 250 C. 5449.2 T 5476.5 3.16 5504.0 E 5531.7 1.83 5559.4 5587.4 5615.5 5643.8 5672.3 5700.9 5729.7 300C. T 5758.6 5787.7 3.81 E 5817.0 5846.5 2.20 5876.1

TABLE IX MIDDLE ORDINATES OF RAILS

Length of Rail (feet) C 0-20 0-40 1-0 1-20

1-40

2-0 2-20 2-40 3-0 3-20 3-40 4-0 4-20 4-40 5 7

R Feet 17189 8594 5730 4297 3438 2865 2456 2149 1910 1719 1563 1433 1323 1228 1146 819.0

30 28 26 Inch Inch I

.08 .07 .06 .05 .16 .14 .12 .10 .24 .20 .18 .15 .31 .27 .23 .20 39 34 .29 .25 .47 .41 .35 .30 .55 .48 .41 .35 .63 .55 .47 .40 .71 .62 .53 .45 .78 .68 .59 .50 .86 .75 .65 .55 .94 .82 .71 .60 1.02 .89 .77 .65 1.10 .96 .83 .70 1.18 1.03 .89 75 1.65 1.44 1.24 1.05

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

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

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

28 26 124 I22 20 nch Inch inch Inch Inch

R 130 feet

24I2211 20 C ch inc Inch ch 0

716.8 637.3 573.7 521.7 478.3 441.7 410.3 383.1 359.3 338.3 319.6 302.9 287.9 262.0 240.5

1.88 2.12 2.36 2.59 3.83 3.05 3.30 3.54 3.76 4.00 4.21 4.45 4.70 5.16 5.64

1.64 1.84 2.05 2.26 2.47 2.66 2.87 3.08 3.28 3.48 3.67 3.89 4.09 4.44 4.92

1.42 1.60 1.78 1.95 2.15 2.30 2.48 2.68 2.83 3.02 3.18 3.36 3.55 3.84 4.20

1.20 1.35 1.50 1.65 1.81 1.96 2.10 2.26 2.40 2.57 2.70 2.86 3.00 3.30 3.59

1.01 1.14 1.27 1.39 1.54 1.66 1.78 1.91 2.04 2.16 2.28 2.41 2.54 2:80 3.04

.84 .94 1.04 1.15 1.26 1.36 1.46 1.57 1.67 1.78 1.87 1.98 2.09 2.29 2.50

TABLE X

SHORT RADIUS CURVES

Raus .

Feet

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

Chord Feet 10 10 15 15 15 20 20 20 25 25 25 25 25 25 50 50 50 50 50 50

Central

Deflection

16-26 12-46 17-16 14-22 11- 30 1-30 9-34 7-39 7-32 7-10 6-25 5 58 5 44 5-12 9-58 9 -32 8-12 "-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

Angle

Angle

Deflection

for

1 Foot

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

TABLE XI INCLINED DISTANCE OF 100 FT. REDUCED TO HORIZONTAL. Slope ooo' 15' 30' 45' 1 00 15 30 45 2 00 15 30 45 3 00 15 30 45 400 15 30 45 5 00 15 30 45 600 15 30 45 7 00 15 30 45

HDisotan 100.000 99.999 99.996 99.991 99.965 99.976 99.966 99.953 99.939 99.923 99.905 99.885 99.863 99.839 99.813 99.786 99.756 99.725 99.692 99.657 99.619 99.580 99.5460 99.497 99.452 99.406 '99.357 99.307 99.255 99.200 99.144 99.087

Ior

Correction

Rise

Slope

0.000 0.001 0.004 0.009 0.015 0,024 0.034 0.047 0.061 0.077 0.095 0.115 0.137 0.161 0.187 0.214 0.244 0.275 0.308 0.343 0.381 0.420

0.000 0.004 0.009 0.013 0.017 0.022 0.026 0.031 0.035 0.039 0.044 0.048 0.052 0.057 0.061 0.065 0.070 0.074 0.078 0.083 0.087 0.092 0.096 0.100 0.105 0.109 0.113 0.118 0.122 0.126 0.131 0.135

8*OQ' 15' 30' 45' 9 00 15 30 45 10 00 15 30 45 11 00 15 30 45 1200 15 30 45 13 00 15 30 45 14 00 15 30 45 15 00 15 30 45

0.503 0.548 0.594 0.643 0.693 0.745 0.800 0.856 0.913

tal

99.027

98.965 98.902 98.836 98.769 98.700 98.629 98.556 98.481 98.404 98.325 98.245 98.163 98.079 97.992 97.905 97.815 97.723 97.630 97.534 97.437 97.338 97.237 97.134 97.030 96.923 96.815 96.705 96.593 96.479 96.363 96.246

Correction

Rise

0.973 1.035 1.098 1.164 1.231 1.300 1.371 1.444 1.519 1.596 1.675 1.755 1.83 1.921 2.008 2.095 2.185 2.217 2.370 2.466 2.563 2.662 2.763 2.866 2.970 3.077 3.185 3.295 3.407 3.561 3.637 3.754

0.139 0.143 0.148 0.1 1 0.156 0.161 0.16 0.169 0.174 0.178 0.181 0.18 0.191 0.195 0.199 0.204 0.208 0.212 0.216 0.221 0.225 0.229 0.233 0.238 0.242 0.246 0.250 0.255 0.259 0.263 0.26?

0.211

For each foot take one one-hundredth of each reading.

TABLE XII

MINUTES IN DECIMALS OF A DEGREE. 030" 1 00 30 2 00 30 3 00 30 400 30 5 00 30 6 00 30 7 00 30 8 00 30

.00833 .01667 .02500 .03333 .04167 .05000 .05833

10'30" 11 00 30 12 00 30 13 00 30

.17500 .18333 .19167 .20000 .20833 .21667

.075001 .08333 .0167 .10000 .10833 .11667 .12500 .13333 .14167

30 15 00 30 16 00 30 17 0 30 18 00 30

233 .24167 30 .25000 25 00 330 .25833 .26667 2600 .27500 30 00 .29167 30 .30000 28 00 .30833 30

.15833 33 0 .166612000

.32500 30 .33333f3000

.06667 14

20'30" 21 00 30 22 00 30 23 00 30

900 .15000 1900 ' 316672900

30 1000

.34167 30'30" .35000 31 00 .35833 30 .3666732 00 .37500 30 .38333133 00 .39167 30 .4 074400 .40833 30 .41667 35 00 0 .40 .43333 36 00 .44167 30 .45000 37 00 .45833 30 .46667 38 00 .47500 30

.50833 .51667 .52500 .53833 .54167 .55000 .55833

40'30" 41 00 30 42 00 30 4300 30

.57500 30 .583334500 30 .59167 .60000 4600 .60833 30 .61667 47 00 .62500 30 .63333 48 00 .6167 0

.48333 3900 .05000 49 00 .49167 30 .5833 30 .50000 4000 .667

.67500 ,68333 .69167 .70000 .70833 .71667

50'30" 51 0 30 52 00 30 5300 30 .3500 5400 .74167 30 .750005500 .75833 30 .76667 56 00 .77500 30 .78333 57 00 .79167 30 .80000 5800 .80833 30

.81667 5900 .82500 30 00

.84167 .85000 .85833 .86667 .87500 .88333 .89167 .90000 .90833 .916657 .92500 .93333 .94167 .95000 .95833 .96667 .97500

.9833

.99167 00

TABLE XI II-CORRECTIONS

FOR TANGENTS AND EXTERNALS

These corrections are to be added to the approximate values, found by dividing the tangent, or externalfor a I1 curve (Table VIIIIby the degree of curve, in order to obtain the true tangents, or externals. Intermediate values may be obtained by interpolation.

FOR TANGENTS ADD Daonau or CUnva

Central

t10

15e° 0 16° 80

1l.

10'

50

03 04 06 .08

.06 10 .13 16

200 250

09 13 16 19 14 19 24 .29 19 .26 .32 .39 24 .33 40 49

°

40°

.22 .34 .45 .58

.25 .39 .51 67

1.36 1.54 1.72 1.91 2.10 2.29 2.48 1.52 172 1.92 2.142.352.562.77 14 1.71 1.94 2.17 2.38 2.60 2.83 3.07 1.88 2.13 2.38 2.63 2.88 3.13 3.39

.51 76 1.02 .56 .831.12 .1 .91 1.22 66 1.00 1.33

1.28 1.54 1.401.69 1.53 1.84 1.68 2.02

1.80 2.06 1.98 2.27 2.15 2.46 2.38 2 7

T70 T76 800 860

25 .27 30 33

.51 .57 .63 .69

1.09 1.19 1.30 1.6

700

.991.091.20 1.291.39 1.04 129 1.42 1.54 1.66 1.34 1.49 1.64 1.79 1.94 1.52 1.70 1.872.04 2.21

1.19 1.32 1 1.64

65

°

39 49 .59 .69 79 .89 70 .81 .92 47 .58 .9 .53 .67 .80 .93 1.06 1.20 60 76 91 1.06 1.21 1.37 .85 1.02 .95 1.14 1.05 1.27 1.16:1 40

17 .34 19 38 .21 42 23 46

65

.31 34 38 42 .48 58 .63 .68 .51 .53 .65 .72 79 .84 .90 .83 90 .991.06 1.14

.88 76 .84 .93

60°° 66 600°

500 55o 60

45

.28 .45 .58 .75

10 19 .29 11 22 .34 13 .26 .40 15 .30 44

o

40 45O

30O 35

1.45 1.83 1.552.00 1.74 2.18 2.08 2.61

2.33 2.60 2.88 2.57 2.873.16 2 78 3.10 3.44 3.053.40 3.77

2.20 2.57 2.94 3.32 3.70 2.40 2.80 3.20 3.61 4.02 2.62 3.06 3.954.40 3.14 3.674.21 4 76 5.31

3.16 3.44 3.473.78 3.78 4.12 4.14 4.55

3.72 4.09 4.46 4 8Q

4.91 5.38 5.85 7 01

5.32 5.83 6.34 7 60

4.10 4.50 4.404.98 4.88 5.37 5 86 6.43

900° 95 100° 110

86 .72 39 79 .43 .86 51 1.03

10

62 1.25 1 93 2.52 3.16 3.81 4 45 5.11 5.77 6 44 7 12 7.80 8.5019 22

FoR EXTERNALS ADD Central

Angle

5o

100

200

25

DEonEz

or

350

40

300

10 15 10 S"

.001 .003 .00 .009

80

.013 .025 .018 .035 .023 .046 .030 .00

.038 .054 .070 .093

.051 .072 .093 .119

.065 .086 .117 .153

.078 .109 .141 .184

.116 .142 .168 .204

.151 .188 .225 .273

.189 .236 .283 .343

°

45

°

50

550

60

°

65.

70

°

.012 .032 .051 .083

.014 .035 .057 .093

.015 .017 .018 .020 .039 .043 .047 .051 .063 .070 .076 .083 .106 120 127 135

.090 .131 .172 .216

.103 .153 .203 .254

.116 .175 .234 .289

.129 .197 .265 .325

.149 .213 .277 .351

.170 .230 .290 .378,

6o

.037 .048 ,60 .056 .007

.227 .283 .340 .412

.266 .332 .398 .483

.305 .381 .457 .554

.345 .420 .516 .625

.34 .479 .575 .697

.425 .530 .636 .711

.467 .50 .550 .582 .641 .700 .697 .774 .851 .84 .922 1.01

70 T75 80° 86

.080 .159 .240 .321 .403 .485 .095 .182 .286 .383 .480 .578 .110.220 .332 .445 .558 .671 .128 .259 .391 .524 .657 .790

.568 .678 .787 .926

.652 .777 .903 1.06

.735 .877 1.02 1.20

.819 .977 1.13 1.34

.906 1.07 1.25 1.47

.994 1.18 1.38 1.62

1.08 1.29 1.50 1.76

1.17 1.39 1.62 1.91

1.38 1.62 1.85 2.48

1.54 1.80 2.06 2.76

1.70 1.99 2.28 3.05

1.87 2.18 2.50 3.35

2.03 2.38 2.73 3.66

2.20 2.58 2.96 3.96

40 46" °

0 S5"

9o0 95 100 110 10

°

.075 .093 .112 .135

.149.299 .174 .350 .200 .401 .28 .36

.004 .006 .007 .008 .009 .010 .014 .018 .023 .027 .017 .022 .028 .034 .038 .027 036 .046 .056 .065

CUvaE

.011 .029 .045 .074

85 °

.003 .007 .011 .018

1.5

°

.450 .522 .604 .806

.603 .756 .910 1.07 1.22 .706 .985 1.06 1.25 1.43 .809 1.01 1.22 1.43 1.64 1.08 1.35 1.63 1.91 2.20

.179 .247 .315 .411

.188 .264 .341 .445

.360 721 1.08 1.45 1.82 2.19 2.57 2.95 3.33 3.72 4.11 4.50 4.91 5.32

S

-A

L""7

/Zr?

Tac2,r4L J~A6 _

k~

dn~~~

L~~&7i/6AJ~j,

71-1

~

~-6'A-i

kY4~i "" Q~ - t

-""

i

9

7

4

y Q

q~#LA45 ~7 ?4<Y/ AZC ).

it

2&9g ;A

YLi4

/14f

~

C'9r" !

c 13 L4~

~7

7i--~r 2 C,

i

r

cc

~a~e-4

4Q-/4r4'

'

a

L'"~I~

. Aly

S

~L~PCL~L-~p

~t~L~i. 3.

lle/

I/

77I

&~VU~

t

M7L

~c~i~/,~z1116L~ .

c /2

rs6&J, ~pO~S~a ~fA~

bY 4Z

QAL_~PIZ~

1W3 24 444

t Id2]

>4 -P~~64zi9a4

1iP~gf7

&c

x 657c~

~d~cBak-lo

.

;4

t

Cana( Cq ron

~jc

14 -

1

,/

Ia.

a/tj re

Ljlc~-f~c

\Y

e tj5S M

-e

Co.

S au

le va Ld

L+Oi- er

<2 ck If

SLet

arse

17,;4

(0&o Vi

veV

Co4

$ c.

(lc/ TIT

ierh) tit) a/

Tiume

ACYark f

(4ar7 4inePl fr7ee I

yaJrMon

(ioh

c0

(J11 yvers, 7%3

co-

14r~seI/4c~rI

/

Z/ Ma)crine

ij7 cL

rP

* ~jja

-

B~a~Y

iIX 4J7/vL 6

Dv~i

£,(J

6 q

0

-

ka',

e.P /cc/~

(9 0 1

Nil

56ZVe2 a

a

£-L

C-Pqf -

+1..s

A

4a ftie

4,. !

r~

L

v

d

6G4.#

/

1O-Je

dL Ah./0/+r U

*.

-t

.

r.K\

\f /&ww/td

J cV

/

v

aJl4 ST .

r

i 4

/2.

i/ 27

0

LJ -

II

c~. ;N

) ~o't24

6t

MC

5~7~- ~B

SeA

QIw

61(I(y (J6 f

I

a

~p~c~hvlB

a

1/7.

3.

4

KVnA9ma( d ~k~vzoteu

Ait-I

91f L7

V~L~Y oil

,a

,I

~eo ' i t t~Q

6n

e. jwo'

CPt

" n

S 55

~f~ r

In~

UAlt

T7ยง (QW,'Q

-T/ACad~f a,

6

I-I

Ld~

4{2Zc& t28 a

rI

tL 04>d Wu-tAaa? ~e

I1NdAt' VbC.

VL/7

'4.

~g-

~B

I 24

i~:a m4 2L

:1

;aar,

=13

~j-t --_

~t, d-~

Zk4

~a~~ ei~ a6

j

;Z41/~

V~2

ac~;

e LAA 'L

W-eMCL /A CI

A

a

Zi"a 11

ca2

F

r~v4zp-

z2 VA~B IJ

(s

RF '*

A-

o;~

-

aA

eAA 4

...

44

, i ยง,Q4'

--

4

,

v

โ ข

~ 1200

it~L~ 7L~

1 -

4 vUff S~6 q/\f~iCuL

(6

)-1 -

pl~k~7

4'q.g(L5~C

4ZI~~~ map

r

a

T1/ (;P

ct4~

(.

4AJ/

d

r~P&-4.

1w,

6luQf A

I

27,

I 6

CIS c.

"

i2 ~ ~

".

lz

r,/4N

A.~4L~4;

ML: P LSL~O~1.

4& 4,~I4a

A

/

,

. 112

d

aqC

I

~I$

nf

wA

*I1I ~ilao

~n':~B~c~4i,.J

2

/

s"r~,,~-,"I L

/

i

j

C:~,

4i"

(.r

f

/kii

.r..

i

5

r ,

J

*i---".

C

O

42

~;

/&/-

/

£

c

l r$ ~ e..

:L,/

~;c:= 6

c

// 6iJC

?.iB7 ~c

2dlq-tS

I4

I~I .r;*~

g~

7il %~1i.;-

7"4

d-;,, I

'

/

s~ e~c 6"-~

)f V

f

~

I/7/7 /fi( rr

00,

/;

C g

.

A J.

-i--

/

.

~/

7

~

,

1

- -'

Ij

Ki

(: /7

:;~<

I, I

_

)

i ;-

~ ~

c

I

:

i

J

.

- P'

iii;

f1~

Iv /

v 1~

/ i3,y

..

h

...

'K

r

iI

',I

r

A

,. ,,d:~_.-:-

..

Ij

~~®i _

i

:

(

s"

~ ~;.

:- -

E

,~x"'

IS"

v, a'---

,1,

/ /

/

:

1

7

(

(

(a

1

/

I

..

i*;c_

i

iI

,

f

-

i$

Ys-r

fi .

1

{ ,]-P :. ;

'

-

;

,

CL.

DISTANCES FROM SIDE STAKES FOR CROSS-SECTIONING. SLOPE 1/s TO 1. ROADWAY OF ANY WIDTH.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 36 37 39 40 41

42 43 44 45 46 47 48 49 50

0

.1

.2

.3

.4

0.00 1.50 3.00 4.50 6.00 7.50 9.00 10.50 12.00 13.50 15.00 16.50 18.00 19.50 21.00 22.50 24.00 25.50 27.00 28.50 30.00 31.50 33.00 34.50 36.00 37.50 39.00 40.50 42.00 43.50 45.00 46.50 48.00 49.50 51.00 52.50 54.00 55.50 57.00 58.50 00.00 61.50 63.00 64.50 66.00 67.50 69.00 70.50 72.00 73.50 75.00

0.15 1.65 3.15 4.65 6.15 7.65 9.15 10.65 12.15 13.65 15.15 16.65 18.15 19.65 21.15 22.65 24.15 25.65 27.15 28.65 30.15 31.65 33.15 34.65 36.15 37.65 39.15 40.65 42.15 43.65 45.15 46.65 48.15 49.65

0.30 1.80 3.30 4.80 6.30 7.80 9.30 10.80 12.30 13.80 15.30 16.80 18.30 19.80 21.30 22.80 24.30 25.80 27.30 28.80 30.30 31.80 33.30 34.80 36.30 37.80 39.30 40.80 42.30 43.80 45.30 46.80 48.30 49.80 51.30 52.80 54.30 55.80 57.30 58.80 60.30 61.80 63.30 64.80 66.30 67.80 69.30 70.80 72.30 73.80 75.30

0.45 1.95 3.45 4.95 6.45 7.95 9.45 10.95 12,45 13.95 15.45 16.95 18.45 19.95 21.45 22.95 24.45 25.95 27.45 28.95 30.45 31.95 33.45 34.95 36.45 37.95 39.45 40.95 42.45 43.95 45.45 46.95 48.45 49.95 51.45 52.95 54.45 55.95 57.45 58.95 60.45 61.95 63.45 64.95 66.45 67.95 69.45 70.95 72.45 73.95 75.45

4.00

51.15

52.65 54.15 55.65 57.15 58.65 60.15 61.65 63.15 64.65 66.15 67.65 69.15 70.65 72.15 73.65 75.15

.5

0.75 2.10 2.25 3.60 3.75 5.25 5.10 6.60 6.75 8.10 8.25 9.60 9.75 11.10 11.25 12.60 12.75 14.10 14.25 15.60 15.75 17.10 17.25 18.00 18.75 20.10 20.25 21.60 21.75 23.10 23.25 24.60 24.75 26.10 26.25 27.60 27.75 29,10 29.25 30.60 30.75 32.10 32.25 33.60 33.75 35.10 35.25 36.60 36.75 38.10 38.25 39.60 39.75 41.10 41.25 42.60 42.75 44.10 44.25 45.60 45.75 47.10 47.25 48.60 48.75 50.10 50.25 51.60 51.75 53.10 53.25 54.60 54.75 56.10 56.25 57.00 57.75 59.10 59.25 60.00 60.75 62.10 62.25 63.60 63.75 65.10 65.25 66.60 66.75 68.10 68.25 69.60 69.75 71.10 71.20 72.60 72.75 74.10 74.25 75.60 75.75

.6

.7

0.90 2.40 3.90 5.40 6.90 8.40 9.90 11.40 12.90 14.40 15.90 17.40 18.90 20.40 21.90 23.40 24.90 26.40 27.90.

29.40 30.90 32.40 33.90 35.40 36.90 38.40 39.90 41.40 42.90 44.40 45.90 47.40 48.90 50.40 51.90 53.40 54.90 56.40 57.90 59.40 60.90 62.40 63.90 65.40 66.90 68.40 69.90 71.40 72.90 74.40 75.90

1.05 2.55 4.05 5.55 7.05 8.55 10.05 11.55 13.05 14.55 16.05 17.55 19.05 20.55 22.05 23.55 25.05 26.55 28.05 29.55 31.05 32.55 34.05 35.55 37.05 38.55 40.05 41.55 43.05 44.55 46.05 47.55 49.05 50.55 52.05 53.55 55.05 56.55 58.05 59.55 61.05 62.55 64.05 65.55 67.05 68.55 70.05 71.55 73.05 74.55 76.05

AMERICANBLUE PRINT CO., INC.--NEW YORK

,.8 1.20 2.70 4.20 5.70 7.20 8.70 10.20 11.70 13.20 14.70 16.20 17.70 19.20 20.70 22.20 23.70 25.20 26.70 28.210 29.70 31.20 32.70 34.20 35.70 37.20 38.70 40.20 41.70 43.20 44.70 46.20 47.70 49.20 50.70 52.20 53.70 55.20 56.70 58.20 59.70 61.20 62.70 64.20 65.70 67.20 68.70 70.20 71.70 73.20 74.70 76.20

.9 1.35 2.85 4.35

5.85 7.35 8.85 10.35 11.85 13.35 14.85

16.35 17.85 19.35 20.85 22.35 23.85 25.35 26.85 28.35 29.85 .31.35 32.85 34.35 35.85 37.35 38.85 40.35 41.85 43.35 44.85 46.35 47.85 49.35 50.85 52.35 53.85 55.35 56.85 58.35 59.85 61.35 62.85 64.36 65.85 67.35 68.85 70.35 71.85 73.35 74.85 76.35

II