Fremling Field Notebook 1970 - 1977

ya Rol

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TLYz

3

48

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cz

0 3.00

4.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 12.00 24 00

17.00 18.00 19.00 20.00 21.00 22.00 23.00 41.0 24 00 42.00 35 00

2600 27.00 31 00 3.00 31.00 49.00 60.00 32.00 50.00 33.00 34.00 39.00 60 00 38.00 47.00 48.00

47.00

48.00

49.00

50.00 ,I

I

i

I

1 A IES SM STAKES Pt CROSS-SECTIoN(; LOPE 1 To 1. ROADWAY or ANY WItE

.1 2 0.10 1.10 2.10 3.10 4.10 5.10 8.10 7.10 8.10 9.10 10.10 11.10 12.10 13.10 14.10 15.10 186.10 17.10 18.10 19.10 20.10 21.10 22.10 23.10 24.10 25.10 26.10 27.10 28.10 29.10 30.10 31.10 32.10 33.10 34.10 35 10 36.10 37.10 38.10 39.10 40.10 41.10 42.10 43.10 44.10 45.10 46.10 47,10 48.10 49.10 50.10

0.00 1.00

I

0.2C0 2.20 .

3.20 4.20 5.20

.3 .4 0.30 2.30 3.30 4.30 6.30

1.40

.5* .6 17 0.50 1.50

2.40 3.50 3.40 4.50 4.40 5.40 5.50 6,.40 6.50 7.50 7.40 7.20 7.30 8.

8.30 8.40 8.50 9.40 9.

9.30 9.50 10.26 10.30 10.40 10.50 11.50 11.20 11.30 12.50 12.20' 12.30 13.50 13.

13.30 13.40 14.50 14.2 14.30 14.40 15.30 15.40 15" 15.50 16 20 16.30 16.40 17.50 17 20 17.30 17.40 18.50 12 .0 18.30 18.40 19.30 19.40 19.1 19.50 20.40 20.50 20 20.30 22.40 21.50 21.20 21.30 21.40 22.50 22.20 22.30 23.20 23.30 23.40 23.50 24.30 24.20 24.40 24.50 25.20 25.30 25.40 25.50 26.40 26.50 26.20.128.30 27.20 27.30 27.40 27.50 28 201 28.30 28.40 28.50 29.20 29.40 29.50 3029.30 30 30.20 .

30.50 30.40 31.20 31.30 31.40 31.50 32 20 32.30 32.40 33.201~33.30 33.40 34 20f 34.30 34.40 34.50 35.50 35.20 45.30 35.40 36.50 46.30 38.40 36.20 37.20 37.30 37.40 37.50 42.50 38.20 38.30 38.40 38.50 39.20 39.30 39.40 39.50 40.20 40.30 40.40 40.650 41.20 '41.30 41.40 41.50 42.20 42,.30 42.40 42.50 43.20 43.30 43.40 44.20 44.30 44.40 44.50 45.40 45.50 46.50 46.20 1 .30 46.40 417.30 47.40 47,50 47.20 48,50 48.30 48.40 48,20 49.20 49.30 49.40 49.50 03 50.40 50.50 50.20 I II r

11.40

0.60 0.70 1.70 1.60 2.70 2.80 3.70 3.60 4.70 4.60 5.70 5.60 6.60 6.70 7.60 8.60 9.80 9.70 10.60 10.70 11.60 11.70 12.70 12.60 13.60 13.70 14.60 14.70 15.60 15. 70 16.60 16.70 17.60 17.70 18.60 18.70 19.60 19.70 20.60 20.70 21.70 21.60 22.60 22.70 23.60 23.70 24.60 24.70 25.60 25.70 26.60 26.70 27.60 27.70 28.60 28.70 29.80 29.70 30.60 30.70 31.70 31.60 32.60 32.70 33.60 33.70 34.60 34.70 35.70 35.60 36.60 36.70 37.60 37.70 38.60 .38.70 39.60 39.70 40.60 40.70 41.60 41.70 42.60 42.70 43.60 43.70 44.60 44.70 45.60 45.70 46.60 46.70 47.60 47.70 48.60 48.70 49.70 49.60 50.70 50.60 ll

F .8 0.80 2.80 3.80 4.80

s5.80

7.80 8.80 9.80 10.80 11.80 12.80 13.80 14.80

0.90 1.90 2.90 3.90 4.90 5.90 6.90 7.90

10.90 11.,90 12.90 13.90 14.90 15.90 16.90 17.80 17.90 18.90 18.80 19.80 19.90 20.80 20.90 21.90 21.80 22.90 23.80 23.90 24.90 24.80 22.80 25.80 25.90 26.90 26.80 27.90 28.90 28.80 29.90 29.80 30.90 30.80 31.90 31.80 32.90 32.80 33.80 33 90 3490 34.80 35.90 35.80 36.90 36.80 37.90 37.80 38.90 38.80 39.80 39.90 40.80 40.90 41.80 41 90 42.90 43.90 44.80 44.90 45.80 45.90 46.80 46.90 47.90 47.80 48 80 48.90 49.80 49.90 50.80 50.90

Distance of slope stake from side or shoulder stake for any width roadway, slopDe1 to 1. It ground is nearly level the cut or 11 at aide stake Is located by the double entry method in left

column and top row. he nnumbe+.n body of table In same row and column g ves distance from s not level estimate the difference n elevation between the side stake to slope stake. It gro fill. Add this amoun to side stake and slope stake, lower arget by this amout If cut, elevte cut or f1 and find distance In tae. Set up rod at this point, and line of ight should cut trget l it does not make the alight austment necessary.

IMPROVED

TABLES

AND

INFORMATION ....

:I:I

:::

:~~:

--

-

i

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

TABLE II TRIGONOMETRIC FORMULAE. LA = LMOP LB =LPON = LOPL R=OB= c=1 a sn = a = sos B= LP sin A= a c

1

b =

sos A

c

I

=b

sin B= OL

MQ tan A= a-- =-b OM

MQ = MQ= cotB= MQ

cot At . NT

NT = tan B = NT

NT I

ON

sec A

versA=

OQ- sc B= OQ

== N

csc A=

OP

1

--- = OT = sec B= OT

= LM= covers B=

OP-LP covers A= OPP = OP-LP = vers B OP exsec A = PQ = coexse B coexsec A = PT = exsec B

sin A=

1-Cos A

2

2 cos Ao ,+CosA

sin 2 A= 2 sin A cos A cos 2 A= cos t A-sin' A sin C' sin B sin A LawofLines = Law of i nes a B C Law of Cosines c'=a'2 +b' -2 ab cos C a__/ (A+1) tan Law of Tangents a-b tan 1/i(A-B)

TABLE 1I -

Continued

TRIGONOMETRIC 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. Let a+b+c =s, (s-a) (s-b) (s-c) -r s 2 cos ' A

(s-a) bc

r

tans A =

s-a

tan 't B= tan '/ C =

r

s-b

r s-c

Area of a triangle: Area = 11. ab Sin C Area = s (s--a) (s-b) (s-c) PRISMOIDAL .FORMULA.

Vol.

-

+(B+b+4M)

h = altitude; b, B =bases; M = midsection TABLE III

INCHES AND FRACTIONS OF AN INCH IN DECIMALS OF A FOOT 0

'/i

.0052 '/s .0104 s/e .0156 '/4 .0208 /is .0260 */s .0313 7'ss.0365 I .0417 Ise .0469 1/s.0521 11/,e.0573 ;4 .0625 I/ise .0677 '/s.0729 3I/ie .0781 1 .0833 0

1

2

3

4

5

6

7

8

9

10

.0885 .0938 .0990 .1042 .1094 .1146 .1198 .1250 .1302 .1354 .1406 .1458 ,1510 .1563 .1615 .1667

.1719 .1771 .1823 .1875 .1927 .1979 .2031 .2083 .2135 .2188 .2240 .2292 .2344 .2396 .2448 .2500

.2552 .2404 .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 .4792 .4844 .4896 .4948 .5000

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

.5885 .5938 .5990 .6042 .6094 .6146 .6198 .6250 .6302 .6354 .6406 .6458 .6510 .6563 .6615 .6667

.6719 .6771 .6823 .6875 .6927 .6979 .7031 .7083 .7135 .7188 -7240 .7292 .7344 .7396 .7448 .7500

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

.8385 .8438 .849 .8542 .8594 .8646 .8698 .8750 .8802 .8854 .8906 .8958 .9010 .9063 .9115 .9167

1

2

3j

4

6

71

8

9

10

5

11 .9219 1/is .9271 1s .9323 '/ .9375 .9427 .9479 .9531 7/1 .9583 .9635 9/s .9688 6/ .9740 "'/s .9792 .9844 3/ .989 s .9948 1.000 11

Deg.

TABLE

IV -RADII,

Radius

Mid. Ord.

Tan. Offset

ORDINATES AND Da rmeco Def. for t 1 Foo

Des.

Radios

Mid. Ord.

Tan. Offset

Def. for 1 Foot

1.2 0" 10' 20 30 40 50

34377.5 17188.8 11459.2 8594.42 6875.55

.036 .073 .109 .145 .182

.145 .291 .436 .582 .727

0.10 0.15 0.20 0.25

5729.65 4911.15 4297.28 3819.83 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 .582 .618

1.745 1.891 2.036 2.181 2.327 2.472

0.,0 0.65 0.70 0.75 0.80 0.85

1910.08 1?09.57 1719.12 1637.28 1562 88 1494.95

.655 .691 .727 764 .800 836

2.618 2.763 2.908 3.054 3.199 3.345

0.00 0.95 1.00 1.05 1.10 1.15

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

3.490 3.635 3.718 3.926 4.071 4.217

1.20 1.25 1.30 1.35 1.40 1.45

1146.28 1109.33 1074.88 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 1.65 1.70 1.75

955.37 029.57 905.13 881.95 859.92

1.309 1.348 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

0.05'

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

716.78 688.16 674.69 661.74

1.746 1.819 1.855 1.892

6.976 7.266 7.411 7.556

2.40 2.50 2.55 2.60

637.28 614.56 603.80 593.42

1.965 2.037 2.074 2.110

7.848 8.136 8.281 8.426

2.70 2.80 2.85 2.90

573.69 546.44 521.67 499.06 478.34 459.28 441.68 425.40 410.28 396.20

2.183 8.716 2.292 9.150 2.402 9.585 2.511. 10.02 2.620 . 10.45 2.730 10.89 2.839 11.32 2.949 11.75 3.058 12.18 3.168 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 1ia08 19.94 20.79

6.00 8.30 8.60 6.90 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

" :-~----":li--Note.

ton Chord Deflection

-22 times tangent deflection.

(1) c = (3) (4) (5) (7

V TABLE V CURVE FORMUL)E FOR SIMPLE CURVES COMPILED BY J. CALVIN LOCKE, C. E. (2) C = ia's+b "

c = #2R (R - 1 (R-+b) (R--b) = V2R (R-Ri-b'" c = 2 m (2R-m) c = 2R sin '/ I (6) c = 2T cos Vs I e= R exsec '/s I e =tan (8) R tantan '/ (9) e =T tan /. I

(10) b-(11) b

a (2R-a)

V(c+

c c-

-

-R )

=

c--

4

(12) b= Rsin I (13) b = a cot '/ I a2 b 'c d c'-+4m' (15) R= (14) R = 2m 8m 2a 2a ) (16) d = R (2R-}(2R+c) 2R-c) = VR (2R-4R2--c (18) d= 2R sin 1/e I

(17) d = (20) m

R2(R- R'

TV

(19) m-.

.R)

d*

2

-

(21) m = R vers I, 1 (22) m = R sin 1/ I tan 'f4 I (23) m = 1/ ctan ' I (24) a =e2R (25) a'= R -- f(R+b) (R--b)= R - J/R'-b' (2 a (29) a (32) 1

2 R (sin' ' I)* (27) a -=Rvers I (28 a = R sin I tanI/ (31) T~ R tan =/lI (30) a = T sin 1 I b tan X57.295780 X 57.295780 (33) R =

=/y

(34) L = IR X 0.01745329 (36 Area Seg.2

(35) L =

LR--R2 sin I

LR-Rb

2

2

d-3

TABLE VI

SINES, COSINES, TANGENTS, COTANOENTS tan

sin

tan

sin

tan

sin

0'

10'

10' 20'

20'

30'

30' 40'

0 0000 1 175 2 349 3 523 4 698 5 872 6 1045 7 219 8 392 9 564

00000029 01750204 349 378 524 552 699 777 875 901 1051 1074 228 248 405 421 584 593

00290058 0204 0233 78 407 553 581 729 756 904 929 1080 1103 257 279 435 449 614 622

00580087 0233 0262 407 436 582 610 758 785 934 958 1110 1132 287 305 465 478 644 650

00870116 262 291 437 465 612 640 787 814 963 987 1139 1161 317 334 495 507 673 679

01160145 291 320 466 494 641 669 816 843 992 1016 1169 190 346 363 524 536 703 708

014589 320 88 49587 67086 84685 1022 84 198 83 376 82 55481 73380

30

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

il rl 4 793 794 763 765 944 937 974 965 2126 2108 2156 2136 309 278 339 306 493 447 524 476 711 644 679 616 867 784 899 812 3057 952 3089 939 249 3118 281 3145 443 283 476 311

823 822 2004 994 186 2164 370 334 555 504 742 672 931 840 31213007 314 173 508 338

8581 2035 2022 217 193 401 363 586 532 773 700 962 868 3153 3035 346 201 541 365

883 2065 247 432 617 805 994 3185 378 574

I 880 2051 221 391 560 728 896 3062 228 393

5 91479 2Q95 78 278 77 462 76 64875 836 74 3026 73 217 72 411 71 607 70

20 420 21 584 22 746 23 907 244067 25 226 26 384 27 540 28 695 29 848

640 448 839 611 4040 773 245 934 452 4094 63 253 877 410 5095 566 317 720 543 874

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

772 973 4176 383 592 806 5022 243 467 696

557 719 881 4041 200 358 514 669 823 975

805 60 4006 68 210 67 417 66 62865 84164 5059 63 280 62 50561 735 0

774 5025 175 249 324 494 471 745 6 7002 760 265 901 536 6041 813 180 8098 316

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

851 5075 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

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

6009

tan

sin

tan

40'

sin

50'

tan

4

p sin

S 0'

50'

969 59 6208 58 453 70356 959 55 7221 54 49053 766 52 8050 51 34250

591 539 64249 40 428 391 450 441 472 491 494 54 517 41 561 693 583 744 604 796 26 847 648 899 670 95248 9110 756 9163 777 9217 799 9271 47 42 691 9004 713 9057 734 43 820 325 841 380 862 435 884 490 905 545 926 601 46 827 7030 884 7050 942 45 44 947 657 967 713 988 770 7009 45 7071 1.0000 7092 1.0058 7112 1.0117 133 1.0176 153 1.0235 173 1.0295 44

4

60'

60' 50'

cos

cot

cos

50' 40' cot cos

40' 30'

30' 20'

cot

cot

cos

cos

20' cot

10'

cos

10'

cot

TABLE VI (continued)

SINES, COSINES, TANGENTS, COTANGOENTS (continued) sin

a 0'

tan

sin

ten

0'

10'

10' 20'

sin

tan

sin

20' 30'

tan

sin

tan

30' 40'

40'

sin 50'

tan 50' y

46 7193 1.0355 7214 1.0416 7234 1.0477 7254 1.0533 774 1.0599 47 314 .0724 333 .0786 353 .0650 373 .0913 392 .0977 48 431 .1106 451 .1171 470 .1237 490 .1303 509 .1369 49 547 .1504 566 .1571 585 .1640 604 .1708 623 .1778

7294 1.0661 43 412 .1041 42 528 .1436 41 642 .21847 40

50 51

7753 1.276 39 862 .123 38

660 1.1918 7679 1.1988 7698 1.2059 7716 1.2131 7735 1.2203 771 .2349 790 .2423 808 .249!

826 .2572 844 .2647

53 986 54 8090 55 192 56 290 57 387 58 480 59 572

.3270 8004 .3764 101 .4281 206 .4826 307 .5399 403 .6003 496 .0643 587

.3351 8021 .3848 124 .4370 225 .4919 323 .5497 418 .6101 511 .6753 601

.3452 8039 .3934 141 .4460 241 .5013 339 .5597 434 .6212 526 .6864 616

.3514 .4019 .4550 .5108 .5697 .6319 .6977

8056 158 258 355 450 542 631

.3597 .4106 .4641 .5204 .5798 .6426 .7090

80l3 175 274 371 465 557 646

.3680 ,4193 .4733 .5301 .5900 .6534 .7205

36 35 34 33 32 31 30

60 660 1.7321 8675 1.7437 8689 1.7556 8704 1.7675 61 746 .8040 760 .8165 774 .8291 788 .8418 62 829 .8807 843 .8940 857 .9074 870 .9210 63 910 .9626 923 .9768 936 .9912 949 2.0057 64 988 2.0503 9001 2.0655 9013 2.0809 9026 .0965 65 9063 .1445 075 .1609 088 .1775 100 .1943 66 135 .2460 147 .2637 159 .2817 171 .2996 67 205 .3559 216 .3750 228 .3945 239 .4142 68 272 .4751 283 .4960 293 .5172 304 .5386 69 336 .6051 346 .6279 356 .6511 367 .6746

8718 1.7797 802 .8546 884 .9347 962 2.0204 9038 .1123 112 .2113 182 .3183 250 .4342 315 .5605 377 .6985

8732 1.7917 29 816 .8676 28 897 .9486 27 975 2.0353 26 9051 ,1283 25 124 .2286 24 194 .3369 2 261 .4545 22 325 .5826 21 387 .7228 20

70 71 72 73 74 75 76 77 78 79

9436 492 546 596 644 689 730 769 805 838

9446 2.8770 19 502 3.0475 18 555 .2371 17 605 .4495 16 652 .6891 15 696 .9617 14 737 4.2747 13 775 .6382 12 811 5.0658 11 843 .5764 10

397 2.7475 9407 2.7725 9417 2.7980 9426 2.8239 455 .9042 465 .9319 474 .9600 483 .9887 511 3.0777 520 3.1084 528 3.1397. 537 3.1716 563 .2709 572 .3052 580 .3402 588 .3759 613 .4874 621 .5261 628 .5656 636 .6059 659 .7321 667 .7760 674 .8208 681 .8657 703 4.0108 710 4.0611 717 4.1126 724 4.1653 744 .3315 750 .3897 757 .4494 763 .5107 781 .7046 787 .7729 793 .8430 799 .9152 816 .1446 822 5.2257 827 5.3093 833 5.3955

80 9848 5.6713 9853 5.7694 9858 5.8708 9863 81 877 6.3138 881 6.4348 886 6.5606 890 82 903 7.1154 907 7.2687 911 7.4287 914 83 925 8.1443 929 8.3450 932 8.5555 936 84 945 9.5144 948 9.7882 951 10.078 954 85 962 11.430 964 11.826 967 12.250 969 86 976 14.300 978 14.924 980 15.605 981 87 986 19.081 988 20.206 989 21.470 990 88 994 28.636 9995 31.242 9996 34.368 997 89 9998 57.290 9999 68.750 9999 85.940 9999

s

60

cos

60' 50'

cot cos

50'

cot

40'

cos

40' 30'

cot cos

2.8502 3.0178 .2041 .4124 .6470 .9136 4.2193 .5736 .9894 5.4845

5.9758 9868 6.0844 9872 6.6912 894 .8209 899 7.5958 918 7.7704 932 8.7769 939 9.0098 942 10.385 957 10.711 959 12.706 971 13.197 974 16.350 983 17.169 985 22.903 992 24.542 993 38.189 997 42.964 9998 114.58 1.000 171.88 1.000

30' cot

20'

cos

20'

ct

10'

cos

6.1970 .9682 7.9530 9.2553 11.059 13.727 18.075 26.432 49.104 343.77

10'

cot

9 8 7 6 5 4 3 2 I 0

TABLE VII Deflections for Sub Chords for Short Radius Curves e

sub chord = sin of

Radius

of

d___

Curve

__

sin. def. ang.

30o 32.

340° 36 38o 40 42 ° 44 ° 46°

12.5 Ft.

193.18

1

181.39 171.0 161.8o 153.58 146.19

1 59' 2 6'' 2° 13

122.92

48

° °

I

52

54° 560 5o 6o

14.0o6

101.15

343'

I'

3 58'

101.33

2 27' 34 2° 41 ° 2° 48' 55

30 29

4

3 02'

3 38

4O

3

5

10o3.14

3029' 3 35'

So3° 22'

T = R tan I 50 tan jI S ."DR D Sin.

46'

3054 4o02' 4Io'

33

4 12 4 26'

Ioi.48

3 3 3 4 4

55'

40o' 454

4

29' 401

101.85 2.06 102.29 102.53 102.76

30 21'

5

4 18'

R

Io.66

5 o' 5022?

5 36'

'

534' ° 5 44'

103m00 o0324

50'

5

I5

6004' 6017'

1o3-54

6 3I' 644

I10384 104.14 104-43

657' °

7

11'

Chord def.

1o4.72

chord'

D Sin. 1D

E=R

I

07' 18'

02'

5°

= T cot.

Sin.D=R Sin.

are

58'

309'

)

of

for 100 ft.

3

3° 16'

D = Sotan 5tE

25 Ft.

2

Io0. I Io6.5

100oo.00

20 Ft.

17'

2

118.31

°

2025' 20° 331 2041' 20 49' 2° 57' 3o05' 3 13 3 21

2

51'

°

133.47 127.97

Length .

_

15 Ft.

20 201

139.52

def. angle

_o

sec

=T tan ( I

R I

No.chords=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 .o01745 (def. for l for I ft. see Table II.), and divide given deflection by the product.

Rule 2. Multiply given deflection by 573, anddivide the product by the given distance.

To find deflection for a given angle and distance. Multiply the angle by .01745, 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.

Given Base Ioo, Alt. 1o.1o+2oo=*5. 00o-.5=Ioo.5 hyp.

Given Hyp. 1oo, Alt. 25.252 2oo=3.125. Xoo-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 0.574 d, where d is the distance in miles.

The correction for curvature alone is closely, jd=. The combined correction isnegative.

PROBABLE ERROR. Ifdt, d ,d3 , etc. are the discrepancies of various results from the mean, and ifId*=the sum of the squares of these differences and n=the number of observations, then the probable error of the mean= gd0.6

TANGENTS AND EXTERNALS TO A le CURVE

TABLE VIII I

T

go 10' 20' 30'

10' 20' 30'

50.00 58.34 66.67 75.0183.34 91.68 100.01 108.35 116.68 125.02 133.36 141.70 150.04 158.38 166.72 175.06 183.40 191.74 200.08.

208.43 216.77 225.12 33.47 241.81 250.16 258.51 266.86 275.21 283.57 291.92 300.28 308.64 316.99 325.35 333.71 342.08 350.44 358.81 367.17 375.54 383.91 392.28 400.66 409.03 417.41 425.79

40'

434.17

50'

442.55

40'.

50' go 10' 20' 30' 40' 50' So 10' 20' 30' 40' 50' o

4

10' 20' 30' 40' 50' 10' 20' 30' 40' 50' 60 10' 20' 30' 40' 50' 70

10' 20' 30' 40' 50'

go9

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

450.93 459.32 467.71 476.10 484.49 492.88 501.28 509.68 518.08 526.48 534.89 543.29

-

I

I I=0

E

1.024

So

C.

T .001

4.421

4.755 5.100 15o C T 5.459 .09 5.829 E 6.211 6.606 .004 7.013 7.432 7.863 8.307 8.762 9.230 20g C, 9.710 T 30.202 .13 E 10.707 11.224 .006 11.753 75C 12.294 12.847 13.413 13.991 14.582 25* C 15.184 T 15.799 .16 16.426 E 17.065 .007 17.717 18.381 19.058 19.746 20.447 21.161 300 C T 21.887 22.624 .19 E 23.375 24.138 .008 25.700

551.70 560.11 568.53 576.95 585.36 593.79 602.21 610.64 10' 20 619.07 120" 30' 627.50 40' 635.93 50' 644.37 1o0 652.81 10' 661.25 20' 669.70 30' 678.15 40' 686.60 695.06 5' 10"

1.188 1.364 1.552 1.752 1.%4 100 C 2.188 T 2.425 .06 2.674 E 2.934 .003 3.207 3.492 " 3.790 4.099

24.913

-

no

.218 .297 .491 .606 .733 .873

T

10' 20' 30' 40' 50'

ggo

14o

711.97 720.44 728.90 737.37 745.85 754.32 350 10' 762.80 20" 771.29 30' 779.77 40' 788.26 50' 796.75 16° 805.25 10' 813.75 20' 822.25 30' 830.76 40' 839.27 50' 847.78 856.30 370 10' 864.82 20' 873.35 30' 881.88 40' 890.41 50' 898.95 18o 907.49 10' 916.03 20' 924.58 30' 933.13 40' 941.69 50' 950.25 19o 958.81 10' 967.38 20' 975.96 30' 984.53 40' 993.12 50' 1001.7 1010.3 200 10' 1018.9 20' 1027.5 30' 1036.1 40' 1044.7 50' 1053.3

T=Rtan

10' 20' 30' 40' 50'

/IuI

I20

E= 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

21O 10' 20' So C. 30' T 40' .06 50' E ,.006 22o 10' 20' 30' 40' 50' 100 C. 230 10' T 20' .13 30' E 40' .011 50' 240 10' 20'

+

150 C. 50' T .19 25e 10' E 20' .017 30' 40' 50' 26o

10' 20' 20o C. 30' 40' T 50' .26 E 270 .022 10' 20' 30' 40' 50' 280 250 C. 10' T 20' .32 30' E 40' .028 50' 290 10' 20' 30' 40' 50' 300 C T 300 .39 10' E 20' .034 30' 40' 50' I'

T

H

E

=30

1061.9 97.577 1070.6 99.155 1079.2 100.75 + 1087.8 102.35 50 C. T 1096.4 103.97 1105.1 1105.60 .10 E 1113.7 107.24 .013, 1122.4 108.90 1131.0 110.57 1139.7 1112.25 1148.4 113.95 1157.0 115.66 1165.7 117.38 10o C. 1174.4 119.12 T 1183.1 120.87 .19 1191.8122.63 E 1200.5 124.41 .025 1209.2 126.20 1217.9 128.00 1226.6 129.82 1235.3 131.65 1244.0 133.50 1252.8 135.35 1261.5 137.23 150 C. T 1270.2 139.11 .29 1279.0 141.01 E 1287.7 142.93 .038 1296.5 144.85 1305.3 146.79 1314.0 148.75 1322.8 150.71 1331.6 "152.69 1340,4 154.69 1349.2 156.70 1358.0 158.72 1366.8 160.76 1375.6 162.81 1384.4 164.86 1393.2 166.95 1402.0 169.04 1410.9 171.15 1419.7 173.27 1428.6 175.41 1437.4 177.55 250 C. T 1446.3 179.72 1455.1 181.89 .49 E 1464.0 184.08 1472.9 186.29 .065 1481.8 188.51 1490.7 190.74 1499.6 192.99 1508.5 195.25 1517.4 197.53 1526.3 199.82 1535.3 202.12 1544.2 204.44 1553.1 206.77 1562.1 209.12 1571.0 211.48 1580.0 213.86

E= R exsec ja4I

TABLE

1 o10

10' 20' 30' 40' 50' 30

10' 20' 30' 40' 50'

$30

10' 20' 30' 40' 50'

34o0

VIII TANGENTS AND EXTERNALS TO A I° CURVE T

1589.0 1598.0 1606.9 1615.9 1624.9 1633.9 1643.0 1652.0 1661.0 1670.0 1679.1 1688.1 1697.2 1706.3 1715.3 1724.4 1733.5 1742.6 )751.7

10'

20'

1770.0

30' 40' 50'

1779.1 1788.2 1797.4 1806.6 1815.7 1824.9 1834.1 1843.3 1852.5 1861.7 1870.9 1880.1 1889.4 1898.6 1907.9 1917.1 1926.4 1935.7 1945.0 1954.3 1963.6 1972.9 1982.2 1991.5 2000.9 2010.2 2019.6 2029.0 2038.4 2047.8 2057.2 2066.6 2076.0 2085.4 2094.9 2104.3 2113.8 2123.3 2132.7

350

10' 20' 30' 40' 50' 360 10' 20' 30' 40' 50' 370

10' 20' 30' 40' 50' 38 10' 20' 30' 40' 50' 390

10' 20' 30' 40' 50' 400

10' 20' 30' 40' 50'

E I=40o I 216.3 218.7 221.1 223.5 226.0 228.4 230.9 233.4 235.9 241.0 243.5 246.1 248.7 251,3 253.9 256.5 259.1 261.8 264.5 267.2 269.9 272.6 275.3 278.1 280.8 283.6 286.4 289.2 292.0 294.9 297.7 300.6 303.5 306.4 305.3 312.2 315.2 318.1 321.1 324.1 327.1' 330.2 333.2 336.3 339.3 342.4 348.6 351.8 354.9 358.1 361.3 364.5 367.7 371.0 374.2 377.5 380.8 384.1 T

So C. T .13 E .023

100 C. .26 E

.046

410 10' 20' 30' 40' 50' 42o 10' 20' 30' 40' 50' 430

10' 20' 30' 40' 50' 440

15o C. T .40 E .070

10' 20' 30' 40' 50'

450

10' 20' 30' 40' 50' 46 10' 20' 30' 200 C 40' T 50' .53 E 470 .093 10' 20' 30' 40' 50' 480 10' 250 C 20' 30' .67 40' 50' .117

T 2142.2 2151.7 2161.2 2170.8 2180.3 2189.9 2199.4 2209.0 2218.6 2228.1 2237.7 2247.3 2257.0 2266.6 2276.2 2285.9 2295.6 2305.2 2314.9 2324.6 2334.3 2344.1 2353.8 2363.5 2373.3 2383.1 2392.8 2402.6 2412.4 2422.3 2432.1 2441.9 2451.8 2461.7 2471.5 2481.4 2491.3 2501.2

2541.0 2551.0 2561.0 2571.0 2581.0 2591.0 2601.1 490 2611.2 10' 2621.2 20' 2631.3 30' 2641.4 40' 2651.5 50' 2661.6 300 C 500 2671.8 T 10' 2681.9 .80 20' 2692.1 E 30' 2702.3 .141 40' 2712.5 50' 2722.7 = T R a I.I=Rexe = R tanI

~ ~

IIo=500

B 387.4 390.7 394.1 397.4 400.8 404.2 407.6 411.1 414.5 418.0 421.4 425.0 428.5 432.0 435.6 439.2 442.8 446.4 450.0 453.6 457.3 461.0 464.6 468.4 472.1 475.8 479.6 483.4 487.2 491.0 494.8 498.7 502.5 506.4 510.3 514.3 518.2 522.2 526.1 530.1 534.2 538.2 542.2 546.3 550.4 554.5 558.6 562.8 566.9 571.1 575.3 579.5 583.8 '588.0 592.3 596.6 600.9 605.3 609.6 614.0

+

So C. T .17 E .037

100 C, T

.34 E .075

150 C. T .51 E .116

1

2732.9 2743.1 2753.4 2763.7 40' 2773.9 50' 2784.2 2794.5 10' 2804.9 20, 2815.2 30' 2825.6 520 40' 2835.9 50' 2846.3 2856.7 53o 10' 2867.1 20' 2877.5 30' 2888.0 40' 2898.4 50 2908.9 54o0 2919.4 10" 2929.9 20' 2940.4 30' 2951.0 40' 2961.5 50' 2972.1 2982.7 550 10' 2993.3 20' 3003.9 30' 3014.5 40' 3025.2 50' 3035.8 3046.5 560 3057.2 3067.9 20' 30 3078.7 40' 3089.4 50' 3100.2 3110.9 570 10' 3121.7 20' 3132.6 30' 3143.4 40' 3154.2 50' 3165.1 580 10' 3186.9 20' 3197.8 30' 3208.8 40' 3219.7 50' 3230.7 3241.7 10' 3252.7 20' 3263.7 30' 3274.8 40' 3285.8 50' . 3296.9 3308.0 600 10' 3319.1 20' 3330,3 30 3341.4 40' 3352.6 50' 3363.8 510 10' 20'

10'

200 C. .68 E .151

250 C.

T .85 E .189

300 G T 1.02 E .227

T

E = R exsec l 1

E I=too 618.4 622.8 627.2 631.7 636.2 640.7 645.2 649.7 654.3 658.8 663.4 668.0 672.7 677.3 682.0 686.7 691.4 696.1 700.9 705.7 710.5 715.3 720.1 725.0 729.9 734.8 739.7 744.6 749.6 754.6 759.6 764.6 769.7 774.7 779.8 784.9 790.1 795.2 800.4 805.6 810.9 816.1 821.4 826.7 832.0 837.3 842.7 848.1 853.5 858.9 864.3 869.8 875.3 880.8 886.4 892.0 897.5 903.2 908.8 914.5

5o C. T .21 E .056

100 C.

T .42 E .112

C. 150 'gSOC T .0

.168

200 C. T .81 .225

T 1.05 E 2.83

300 C.

1.27 E

"I

TABLE VIII TANGENTS AND EXTERNALS TO A 1 CURVE. I

T

I=700

E

3375.0 920.2 3386.3 925.9 3397.5 931.6 3408.8 937.3 3420.1 943.1 3431.4 948.9 3442.7 954.8 3454.1 960.6 3465.4 966.5 3476.8 972.4 3488.31 978.3 3499.7 984.3 3511.1 990.2 3522.6 996.2 3534.1 1002.3 3545.6 1008.3 3557.2 1014.4 3568.7 1020.5 3580.3 1026.6 3591 9 1032.8 3603.5' 1039.0 3615.1 1045.2 3626.8 1051.4 3638.5 1057,7 6So0 3650.2 1063.9 10' 3661.9 1070.2 20' 3073.7 1076.6 30' 3685.4 1082.9 40' 3697.2 1089.3 50' 3709.0 1095.7 3720.9 1102.2 660 10' 3732.7 1108.6 20' 3744.6 1115.1 30' 3756.5 1121.7 40' 3768.5 1128.2 50' 3780.4 1134.8 670 3792.4 1141.4 10' 3804.4 1148.0 20' 3816.4 1154.7 30' 3828.4 1161.3 40' 3840.5 1168.1 50' 3852.6 1174.8 68g 3864.7 1181.6 10' 3876.8 1188.4 20' 3889.0 1195.2 30' 3901.2 1202.0 40' 3913.4 1208.9 50' 3925.6 1215.8 3937.9 1222.7 10' 3950.2 1229.7 20' 3962.5 1236.7 30' 3974.8 1243.7 40' 3987.2 1250.8 3999.5 1257.9 50' 4011.9 1265.0 10' 4024.4 1272.1 20' 4036.8 1279.3 30' 4049.3 1286.5 40' 4061.8 1293.6 50' 4074.4 1300.9 610 10' 20' 30' 40' 50' 820 10' 20' 30' 40' 50' 630 10' 20' 30' 40' 50' 64o 10' 20' 30' 40' 50'

I

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 4476.5 760 10' 4489.9 20' 4503.4 30' 4516.9 40' 4530.4 50' 4544.0 4557.6 770 10' 4571.2 20' 4584.8 30' 4598.5 40' 4612.2 50' 4626.0 4639.8 780 10' 4653.6 20' 4667..4 30' 4681.3 40' 4695.2 50' 4709.2 4723.2 10' 4737.2 20' 4751.2 30' 4765.3 40' 4779.4 50' 4793.6 4807.7 800 10' 4822.0 4836.2 4850.5 40' 4864.8 50' 4879.2 710

10' 20' So C. 30' T 40' .25 50' E .080 720 10' 20' 30' 40' 50' 100 C. 730 10' T 20' .51 30' E 40' 159 50' 740 10' 20' 30' 40' 15 C. 50' T6 750 10' E 20' .240 30' 40' 50'

+

200 C, T 1.02 E .321

250 C.

T 1.28 E .403

300 C.

E-

T

1.54

E

.485

T

Rtan/ni

E

I=800 1

go 1308.2 10' 1315.6 20' 1322.9 + 30' 1330.3 T 40 1337.7 .30 1345.1 50' E 82o 1352.6 .110 10' 1360.1 20' 1367.6 1375.2 30' 1382.8 40' 1390.4 50" 1398.0 100 C. 830 10' 1405.7 T 20' 1413.5 61 30' 1421,2 1429.0 40' 1436.8 50' 840 10' 20' 30' 40' 50' 1484.4 850 1492.4 .91 1500.5 10' 1508.6 .332 20' 30' 1516.7 1524.9 40' 50' 1533.1 860 1541.4 1549.7 10' 20' 30' 20o C. 40' T 50' 1.22 E 1591.6 870 .445 1600.1 10' 20' 1608.6 30' 1617.1 40' 1625.7 50' 1634.4 88o0 1643.0 10' 250 C. 20' 1660.5 T 30' 16697421.53 1678.1 40' E 50' .558 1686.9 8g0 1695.8 10' 1704.7 20' 1713.7 30' 1722.7 1731.7 40' 1740.8 300 C. 50' T 1749.9 900 1.84 10' E 20' .671 1777.4 30' 1786.7 40' 1796.0 50' E=Reusec3/

T

E

4893.6 4908.,0 4922.5 4937.0 4951.5 4966.1 4980.7 4995.4 5010.0 5024.8 5039.5 5054.3 5069.2 5084.0 5099.0 5113.9 5128.9 5143.9 5159.0 5174.1 5189.3 5204.4 5219.7 5234.9 5250.3 5265.6 5281.0 5296.4 5311.9 5327.4 5343.0

1805.3 1814.7 1824.1

I

=900

1833.6 So C.

1843.1 .36 1852.6 E 1862.2 .149 1871.8 1881.5 1891.2 1900.9 1910,7 1920.5 100 C. 1930.4 T 1940,3 .72 1950.3 E 1960,2 .299 1970.3 1980,4 1990.5 2000.6 2010.8 2021.1 2031.4 150 C. 2041.7 1.09 2052.1 2062.5 .E 2073.0 .450 2083.5 2094.1

535$.6

5374.2 5389.9 5405.6 5421.4 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 5729.7 5746.3 5763.1 5779.9 5796.7 5813.6

2136.7 20 0 C. 2147.5 T 2158.4 1.45 E 2169.2 2180.2 .603 2191.1 2202.2 2213.2 2224.3 2235.5 2246.7 250 C. 2258.0 T 2269.3 1.83 2280.6 E 2292.0 .756 2303.5 2315.0 2326.6 2338.2 2349.8 2361.5 300 C. T 2373.3 2385.1 2.20 E 2397.0 2408.9 .910 2420.9 2432.9

TABLE VIII TANGENTS AND EXTERNALS TO A 10 CURVE

I tT I' 910

10' 20' 30' 40' 50' 920 10' 20' 30' 40' 50' 980 10' 20' 30' 40' 50' g40 10' 20' 30' 50' .50

10' 20' 30' 40' 50'° 88 0 10' 20' 30' 40' 50' 570

10' 20' 30' 40' 50' 980 10' 20' 30' 40' 50' 10' 20' 30' 40' 50' 1000 10' 20' 30' 40' 50'

5830.5 5847.5 5864.6 5881.7 5898.8 5916.0 5933.2 5950.5 5967.9 5985r3 6002.7 0020.2 6037.8 6055.4 6073.1 6090.8 6108.6 6126.4 6144.3 6162.2 6180.2 6198.3 6216.4 6234.6 6252.8 6271.1 6289.4 6307.9 6326.3 6344.8 6363.4 6382.1 6400.8 6419.5 6438.4 6457.3 6476.2 6495.2 6514.3 6533.4 6552.6 6571.9 6591.2 6610.6 6630.1 6649.6 6669.2 6688.8 6708.6 6728.4 6748.2 6768.1 6788.1 6808.2.

6828.3 6848.5 6868.8 6889.2 6909.6 6930.1

T E

1010 6950.6 2444.9 10' 6971.3 2457.1 5t20' 6992.0 2469.3 50 C. T 30' 7012.7 2481.5 40' 7033.6 2493.8 .43 2506.1 50' 7054,5 E 2518.5 .200 1020 7075.5 2531.0 10' 7096.6 2543.5 20' 7117.8 30' 7139.0 2556.0 2568.6 40' 7160.3 2581.3 50' 7181.7 2594.0 100 C. 1030 7203.2 2606.8 10' 7224.7 T 2619.7 20' 7246.3 .86 2632.6 30' 7268.0 E 2645.5 .401 40' 7289.8 2658.5 50' 7311.7 2671.6 1040 7333.6 2684.7 10' 7355.6 2697.9 20' 7377.8 2711.2 30' 7399.9 2724.5 40' 7422.2 50' 7444.6 2737.9 150 C. T 7467.0 2751.3 1.30 105 2764.8 10" 7489.6 E 20' 7512.2 2778.3 .604 2792.0 30' 7534.9 2805.6 40' 7557.7 2819.4 50' 7580.5 2833.2 1060 7603.5 2847.0 10' 7626.6 2861.0 20' 7649.7 2875.0 200 C 30' 7672.9 2889.0 T 40' 7696.3 2903.1 1.74 50' 7719.7 E 2917.3 .809 1070 7743.2 10' 7766.8 2931.6 2945.9 20' 7790.5 2960.3 30' 7814.3 40' 7838.1 2974.7 2989.2 50' 7862.1 3003.8 1080 7886.2 3018.4 25 C. 10' 7910.4 20' 7934.6 3033.1 T 30' 7959.0 3047.9 2.18 3062.8 40' 7983.5 E 8008.0 3077.7 1.02 3092.7 1090 8032.7 3107.7 10' 8057.4 3122.9 20' 8082.3 3138.1 30' 8107.3 3153.3 40' 8132.3 3168.7 50' 8157.5 300 C 8182.8 3184.1 1100 T 3199.6 2.62 10' 8208.2 20' 8233.7 3215.1 E 30' 8259.3 3230.8 1.22 40' 8285.0 3246.5 3262.3 50' 8310.8 TJ

Ya1

3278.1 3294.1 3310.1 3326.1 3342.3 3358.5 3374.9 3391.2 3407.7 3424.3 3440.9 3457.6 3474.4 3491.3 3508.2 3525.2 3542.4 3559.6 3576.8 3594.2 3611.7 3629.2 3646.8 3664.5 3682.3 3700.2 3718.2 3736.2 3754.4 3772.6 3791.0 3809.4 3827.9 3846.5 3865.2 3884.0 3902.9 3921.9 3940.9 3960.1 3979.4 3998.7 4018.2 4037.8 4057.4 4077.2 4097.1 4117.0 4137.1 4157.3 41717.5 4197.9 4218.4 4239.0 4259.7 4280.5 4301.4 4322.4 4343.6 4364.8

=11I + 50

110.

T .51 E .268

100 C .103 E .536

15e C.

T i1.56 E .806

20o C. T 2.08 E 1.08

250

C.

T 2.61 E 1.36

300

10' 20' 30' 40' 50'

C.

C.

T 3.14 E 1.63

1120

10' 20' 30' 40' 50' 1130 10' 20' 30' 40' 50' ifo 1140 10' 20' 30' 40' 50' 1150 10' 20' 30' .w 40' 50' 1160 ito 10' 20' 30' 40' 50 117A. 10' 20' 30' 40 50' 1180 10' 20' 30' 40' 50' 1190 10' 20' 30' 40' 50' 1200 10' 20' 30' 40' 50'

E=Rexsec

1

T E 1 8336.7 4386.1 8362.7 4407.6 8388.9 4429.2 8415.1 4450.9 8441.5 4472.7 468.0734494.6 8494.6 4516.6 8521.3 4538.8 8548.1 4561.1 8575.0 4583.4 8602.1 4606.0 8629.3 4628.6 8656.6 4651.3 8684.0 4674.2 8711.5 4697.2 8739.2 4720.3 8767.0 4743.6 8794.9 4766.9 8822.9 4790.4 8851.0 4814.1 8879.3 4837.8 8907.7 4861.7 8936.3 4885.7 8965.0 4909 9 8993.8 4934.1 9022.7 4958.6 9051.7 4983 1 9080.9 5007.8 9110.3 5032.6 9139.8 5057.6 9169.4 5082.7 9199.1 5107.9 9229.0 5133.3 9259.0 5158.8 9289.2 5184.5 9319.5 5210.3 9349.9 5236.2 9380.5 5262.3 9411.3 5288.6 9442.2 5315.0 9473.2 5341.5 9504.4 5368.2 9535.7 5395.1 9567.2 5422.1 9598.9 5449.2 9630.7 5476.5 9662.6 5504.0 9694.7 5531.7 9727.0 5559.4 9759.4 5587.4 9792.0 5615.5 9824.8 5643.8 9857.7 5672.3 9890.8 5700.9 9924.0 5729.7 9957.5 5758.6 9991.0. 5787.7 10025.0 5817.0 10059.0 5846.5 10093.0 5876.1

+

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C.

T

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lonC. T 1.25* 721E

721

150 C. T 1.93 E 1 09

200 C. T 2.52 E 1.46

C. T 3.16 E

250

1.83

300 C.

T 3.81 E 2.20

TABLE IX MIDDLE ORDINATES OF RAILS Length of Rail (feet) C

R

o'Feet 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 6 7

17189 8594 5730 4297 3438 2865 2456 2149 1910 1719 1563 1433 1323 1228 1146 955.3 819.0

301

28 Inch Inch

1 26 X24 ch

22 2o 11 c

Inch InchInch

.08 .07 .06 .05 .04 .16 .14 .12 .10 .08 .24 .20 .18 .15 .13 .31 .27 .231 0117 0 .39 ,34 .29 .25 .21 .47 .41 .35 .30 .25 .55 .48 .41 .35 .29 .63 .55 .47 .40 .33 .71 .62 .53 .45 .38 .78 .68 .59 .50 .42 .86 .75 .65 .55 .46 .. 94 .82 .71 .60 .50 1.02 .89 .77 .65 .55 1.10 .96 .83 .70 .59 1.18 1.03 .89 75 .63 41 1.23 1.06 .90 .76 1.65 1.44 1.24 1.05 .89

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

it

R

O

feet

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

716.8 637.3 573.7 521.7 478.3 441.7 410.3 383.1 359.3 338.3 319.6 302.9 287.9 262.0 240.5 222.3

ln

1.88

2s Ina

1.64 2.12 1.84 2.36 2.05 2.59 2.26 3.83 2.47 3.05 2.66 3.30 2.87 3.54 3.08 3.76 3.28 4.00 3.48 4.21 3.67 4.45 3.89 4.70 4.09 5.16 4.44 5.64 4.92 6.07 5.29

26

nch 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 4.58

24 122 20 Inch lach Iach 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 3.88

1.01 1.14 1.27 1.39 1.54 i.66 1.78 1.91 2.04 2.16 2.28 2.41 2.54 2:80 3.04 3.29

.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 2.70

TABLE X

SHORT RADIUS. CURVES Feet

Feet

Angle

Angle

for 1 Foot

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 '-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 find length of curve divide angle from P. C. to P. T. by central angle of chord, and multiply by length of chord.

30

.80

TABLE XI

HORIZONTAL INCLINED DISTANCE OF 100 FT. REDUCED TO.03 Slope

tance

000' 15' 30' 45' 1 00 15 30 45 2 00 15 30 45 3 00 15 30 45 4 00 15 30 45 5 00 15 30 45 6 00 15 30 45 7 00 15 30 45

100.000 99.999 99.996 99.991 99.985 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 99.540 99.497 99.452 99.406 '99.357 99.307 99.255 99.200 99.144 99.087

istance

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 0.460 0.503 0.548 0.594 0.43 0.693 0.745 0.800 0.856 0.913

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

800' 15' 30' 45' 9 00 15 30 45 10 00 15 30 45 11 00 15 30 45 12.00 15 30 45 13 00

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 9.479 96.363 96.246

15

30 45 1400 15 30 45 15 00 15 30 45

Correction

Rise

0.973 1.035 1.098 1.104 1.231 1.300 1.371 1.444 1.519 1.596 1.675 1.755 1.837 1.921 2.008 2.095 2.185 2.277 2.370 2.406 2.563 2.662 2.763 2.866 2.970 3.077 3.185 3.295 3.407 3.521 3.637 3.754

0.139 0.143 0.148 0.152 0.156 0.161 0.165 0.169 0.174 0.178 0.182 0.18l 0.191 0.195 0.199 0.204 0.20 0.212 0.216 0.221 0.225 0.229 0.233 0.238 0.242 0.246 0.250 0.25 0.259 0.263 0.207 0.2

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

TABLE XII

MINUTES IN DECIMALS OF A DEGREE. 10'30" 11 00 30 12 00 30 13 00 30

.17500 .18333 .19167 .20000 .20833 .21667 .22500

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

0'30" 1 00 30 200 30 300 30

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

5 00

30 .0750011 30 .24167 30 .08333 15 00 .2500 25 0

6 00 .10000 16 00 30 .10833 30 700 .11667 17 00 30.12500 30 8 00 .13333 18 00

30 .14167

30

.26667 26 00 .27500 30 .28333 27 00 .29167 30 .30000 30 33 28 00

. 8

30

.32500

30

40'30" 41 00 30 4200 30 43 00

.67500 ,68333 .69167 .70000 .70833 .71667 .72500

50'30" 51 00 30 52 00 30 5300 30

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

.40833 30 .41667 35 00

.57500 30 .58333 45 00

.74167 30 .75000 55 0

.90833 .9167

.43333 36 .44167 30 .45000 37 00 .45833 30 .46667 38 00

.600004600 46 00 .60833 30 .61667 47 00 .62500 30 .63333 48 00

.76667 56 00 .77500 30 .78333 57 00 .79167 30 .80000 58 00

.93333 .94167 .95000 .95833 .96667

.47500

30 .64167

30 .80833

30

.49167

30

30

30

9 00 .15000 19 00 .31667 29 0 .48333 3 00 .65000 49 00 .81667 59 00 30 .15833 30

10 00 .16667 20 00

.3333330 00

.84167 .85000 .85833 .8667 .87500 .88333 .89167

.34167 30'30" .35000 31 00 .35833 30 .36667 32 00 .37500 30 .38333133 00 . 30

.65833

.50000 40 00 .66667 50 00

00

.82500

.83333 60 00

.97500

.98333 .99167

1.00000

TABLE XI

I-CoRRECTIONS FOR TANGENTS AND EXTERNALS

These corrections are to be added to the approximate values, found by dividing the tangent,or externalfor a 1 curve (Table VIII) by the degree of curve, in order to obtain the true tangents, or externals. Intermediate values may be obtained by interpolation.

FOR TANGENTS ADD or CUnVE

Dzoa

Central S5

10'

15'

20'

25o

30°

350 400

10° 15 ° 2o 26'

03 .06 04 10 06 .13 .08 16

09 14 19 24

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

8 85

10 19 11 22 13 .26 15 .30

.29 .34 44

39 47 .53 60

60 65"

17 .34 19 38 .21 42 23 46

.51 .57 .63 .69

.68 .85 1.02 1.19 76 .951.141.32 .84 1.05 1.27 1.49 .93 1.16 1 401.64

TVo To 80° 88o

25 .27 30 33

40°

46

50° 55

.40

49 .58 .67 76

45

65.

50 '

55o 60

.31 .51 .65 .83

.34 38 42 .4 .5 58 .63 .68 .72 79 .84 .90 90 .991.06 1.14

.22 .25 .28 .34 .39 46 .45 .51 .58 .58 67 .75

70'

.59 .69 79 .89 .99 1.09 1.20 1.29 1.39 .69 ,70 .81 .92 1.041.29 1.42 1.54 1.66 .80 .93 1.06 1.201.34 1.49 1.64 1.79 1.94 91 1.06 1.21 1.37 1.52 1.70 1.872.04 2.21 1.361.54 1.52 1.72 1.71 1.94 1.88 2.13

1.72 1.92 2.17 2.38

1.912.102.292.48 2.14 2.35 2.56 2,77 2.38 2.602.833.07 2.63 2.88 3.13 3.39

.51 761.02 1.28 1.54 1.80 2.06 2.33 2.60 .56 .83 1.12 1.40 1.69 1.982.27 2.57 2.87 .61 .911.221.531.842.152.462 783.10 66 1.00 1.33 1.68 2.02 2.36 2 7 3.05 3.40

2.88 3.16 3.44 3.72 3.16 3.47 3,78 4.09 3443.784.12 4.4 3.77 4.14 4.554 8(

1.09 1.45 1.83 2.20 2.57 2.94 3.32 3.70 1.19 1.55 2.00 2.40 2.80 3.20 3.61 4.02 1.30 21.74 22.18 32.62 33.063.503.0 67 4 2 43.95 4.40 1.56 .08 .61 .14 . . 1 76.31

4.104.504.91 4.404.985.38 4.88 5.37 5.85 5 86 6.437 01

5.32 5.83 6.34 7 60

90° 9S 10 110

36 .72 39 79 .43 .86 51 1.03

120

62 1.25 1 93 2.52 3.163.81 4 45 5.115.77 6 44 7 127.80 8.509 22 FOR EXTERNAL

Central Angle

ADD

DEonRz or Cav 20'

25'

30'

35'

40'

45'

50.

550

10' 15' 20

.001.003 .003 .007 .006 .011 .009 .018

.004 .010 .017 .027

.006 .014 .022 036

.007 .018 .028 .046

.008 .023 .034 .056

.009 .027 .038 .065

.011 .029 .045 .074

.012 .032 .051 .083

.014 .035 .057 .093

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

85

.013.025 .018.035 .023.046 .030.060

.038 .054 .070 .093

.051 .072 .093 .119

.065 .086 .117 .153

.078 .109 .141 .184

.090 .131 .172 .216

.103 .153 .203 .254

.116 .175 .234 .289

.129 .197 .265 .325

.149 .213 .277 .351

60s 85'

.046.093 .056 .112 .067 .135

.142 .188 .236 .283 .332 .381 .420 .479 .530 .582 .641 .700 .168 .225 .283 .340 .398 .457 .516 .575 .636 .697 .774 .851 .204 .273 .343 .412 .483 .554 .625 .697 .711 .845 .922 1.01

T0 T' 80 85'

.080 .159 .095 .182 .110.220 .128.259

.240 .286 .332 .391

90 95°° 100 110°

.149 .299 .174.350 .200 .401 .268 .536

.450 .522 .604 .806

120.

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

So 0°

40° 48

°

55

5e

10* 15'

.321 .383 .445 .524

.403 .480 .558 .657

.485 .578 .671 .790

.568 .678 .787 .926

.652 .777 .903 1.06

.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

60

.170 .230 .290 .378,

65'

.179 .247 .315 .411

70'

.188 .264 .341 .445

.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

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.AND THERE ARE HILTON HOTELS AROUND THE WORLD OPERATED BY HILTON INTERNATIONAL CO. RESERVATION S for all hotels can be made by contacing any Hilton Reservation Office (see telephone directory) any Hilton hotel or inn . .. or special reservation centers: New York, (212) 59-4500; Chicago, (312) 346-2772; Los Angees, (2131 628-6231; San Froncisco, (4151 771 -1200;Toronto, Canada (416-362-3771. .

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RECEIPT FOR CERTIFIED MAIL-300 (plus postage)

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DELIVER TO ADDRESSEE ONLY .

SPECIAL(extr DELIVERY fee required)

PS

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FEES

1. Shows to whom and date delivered ........... 1 65 With delivery to addressee only ............

2. Shows to whea, date and where delivered .. 3 With delivery to addressee only.

RETURN

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INSURANCE COVERAGE PROVIDEDNOT FOR INTERNATIONAL MAIL

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STICK POSTAGE STAMPS TO ARTICLE TO COVER POSTAGE (first class or airmai), CERTIFIED MAIL FEE, AND CHARGES FOR ANY SELECTED OPTIONAL SERVICES. (sfe front) 1. f you want this receipt postmarked, stick the gummed stub on the left portin side of the article, leaving the receipt attached, and present the article at a post office service window or hand it to your rural carrier. (no extra charge) 2. If you do not want this receipt postmarked, stick the gummed stub on the left portion of the address side of the article, date, detach and retain the receipt, and mail the article.

3. If you want a return receipt, write the certified-mail number and your name and address on a return receipt card, Form 3811, and attach it to the back of the article by means of the gummed eds. Endorse front of article RETURN RECEIPT REQUESTED. 4. If you want the article delivered only to the addressee, endorse it on the front DELIVER TO ADDRESEE ONLY. Place the same endorsement in line 2 of the return receipt card if that service is requested.

5. Save this receipt and present it if you make inquiry.

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BUSINESS PURPOSE OF THIS PORTION OF TRIP_ ___

ALLOCATION

BUSINESS

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REIMBURSED

ALWAYS OBTAIN ITEMIZED BILL FOR LODGINGS IF MORE THAN ONE EXPENDITURE IS INCLUDED

)

ROOM

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CITY

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ST. PAUL, STATE CAPiEOL 161 St. Anthony (1-94) ' ST. PAUL, MINNESOTA 55103

TELEPHONE 227-8711

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SUPPER CLUB HIGHWAY 61

MIESVILLE, MINNESOTA BETWEEN HASTINGS AND REDWING

PHONE (612) 437-3528

THIS RECEIPT IS PROVIDED FOR YOUR CONVENIENCE FOR TAX & PERSONAL RECORDS.

ACCOMMODATIONS FOR BANQUETS * PARTIES * PRIVATE DINING ROOM RESERVATIONS * OFF SALE BEVERAGES TELEPHONE (612) 437-3528 OR (507) 263-2263

THANK YOU!

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DELIVERED

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,,Descriptior)et.

Pieces

NOTICE TO BUYER:

(1)

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Do not sign this Agreement (set forth on the reverse side hereof) before you read

or if it

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to protect

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You are entitled to an exact copy of this Agreement at the time you sigr You have the right to pay at any time the full amount LAMPERT

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LUMBER COMPANYSAE

I have read the above notice, agree to the terms and conditions on the reverse side, and acknowledge receitDLVR of a copy of this Agreement.

Aon

A

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AGREEMENT

END CREDIT

OPEN

(Minnesota) REVOLVING

Buye,

a anapproved

Company(Laprt)

AGREEMENT

CHARGE

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credit

North Dakota)

customer

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Lampert Lme

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resienc, udertands that Lampert will issue monthly

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Buye ageesto

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Lampert within

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dateeiter () te full amount of the outstanding balance in his accuta tha bilin dae labeled "New Balance" on the billing statement), i hc balanc pnalty in ful, wihout even NO INACE CHARGE will be imposed, or (2) an installmenbae Ifpa Buer thefils ewo alane, lss oher cedit posed, ithi G a in which on te flloingpayment one onthfolowin hi schedule, bilingdate Buer event aree a FINANCEtHC to ay ampet willbe ncured s described below.

Ottniqg Balance

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CUSTOMER COUNTER

SUnited Parcel Service SHIPPING RECORD - COPY 1 UPS COPY - COPY 2 SHIPPER COPY PACKAGE INSERT - COPY 3

AMOUNT

AMOUNT

ENCLOSE THIRD COPY INSIDE PACKAGE PRIOR TO SHIPPING DO NOT WRITE BELOW THIS LINE TYPE CHARGE

CUSTOMER COUNTER

DATE TRANS

CHARGES AMOUNT TYPE

SC.O.D.

COD EX. VAL

EXCESS VALUATION PACKAGE

560

PKG

WHENTRACING THIS PACKAGE, GIVE ALL INFORMATION ON ABOVELINE UNLESS A GREATER VALUE IS DECLARED IN WRITING ON THIS RECEIPT, THE SHIPPER HEREBY DECLARES THE RELEASED VALUE OF EACH PACKAGE OR'ARTICLE NOT ENCLOSED IN A PACKAGE, COVERED BY THIS RECEIPT TO BE AS FOLLOWS: $100 FOR EACH PACKAGE OR ARTICLE. THE ENTRY OF A C.O.D. AMOUNT DOES NOT CONSTITUTE SUCH A DECLARATION. THE SHIPPER AGREES THAT TARIFF PROVISIONS UPON WHICH PARCEL RATES ASSESSED HEREON ARE BASED SHALL APPLY FOR ALL DELIVERIES TENDERED DURING THE SAME CALENDAR WEEK. CLAIM FOR LOSS OR DAMAGE MUST BE MADE WITHIN 9 MONTHS FROM THE DATE OF THIS RECEIPT. A CLAIM NOT MADE WITHIN THE TIME LIMIT SPECIFIED IS DEEMED WAIVED. CUSTOMER'S CHECK ACCEPTED AT SHIPPER'S RISK UNLESS NOTED ON C.O.D. TAG.

- -------- - -

-- --

AIR TRANSPORTATION OF ANY OF THE ABOVE PACKAGES IS PROVIDED BY UNITED PARCEL SERVICE CO., A DELAWARE STREET, 51 WEAVER CORPORATION, GREENWICH OFFICE PARK 5, GREENWICH. CT 6830, AN AIR FREIGHT FORWARDER HOLDING C.A.B. OPERATING AUTHORIZATION NO. 31.

U1227 EXP NCR-TC-1REV. 7.75

ThankYou Fpr Using

United ParcelService

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DSTANCES FROM SIDE STAKES FOR CIOSS-SECT SLOPE 1'I/ TO 1. ROADWAY OF ANY WIDTH.

0 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 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

.1

0.15 00.00 1.65 1.50 3.15 3.00 4.50 4.65 6.00 6.15 7.50 7.65 9.00 9.15 10.50 10.65 12.00 12.15 13.50 13.65 15.00 15.15 16.50 16.65 18.00 18.15 19.50 19.65 21.00 21.15 22.50 22.65 24.00 24.15 25.50 25.65 27.00 27.15 28.50 28.65 30.00 30.15 31.50 31.

31.65 33.00 33.15 34.50 34.65 36.00 36.15 37.50 37.65 39.00 39.15 40.50 40.65 42.00 42.15 43.50 43.65 45.00 45.15 46.50 46.65 48.00 48.15 49.50 49.65 51.00 51.15 52.50 52.65 54.00 54.15 55.50 55.65 57.00 57.15 58.50 58.65 60.00 60.15 61.50 61.65 63.00 63.15 64.50 64.65 66.00 66.15 67.50 67.65 69.00 69.15 70.50 70.65 72.00 72.15 73.50 73.65 75.00 75.15

.2

.3

.4

,.5

.6

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

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 15.95 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

0.60 2.10 3.60 5.10 6.60 8.10 9.60 11.10 12.60 14.10 15.60 17.10 16.60 20.10 21.60 23.10 24.60 26.10 27.60 29,10 30.60 32.10 33.60 35.10 36.60 38.10 39.60 41.10 42.60 44.10 45.60 47.10 48.60 50.10 51.60 53.10 54.60 56.10 57.60 59.10 60.60 62.10 63.60 65.10 66.60 68.10 69.60 71.10 72.60 74.10 75.60

0.75 2.25 3.75 5.25 6.75 8.25 9.75 11.25 12.75 14.25 15.75 17.25 18.75 20.25 21.75 23.2' 24.75 26.25 27.75 29.25 30.75 32.25 33.75 35.25 36.75 38.25 39.75 41.25 42.75 44,25 45.75 47.25 48.75 50.25 51.75 53.25 54.75 56.25 57.75 59.25 60.75 62.25 63.75 65.25 66.75 68.25 69.75 71.20 72.75 74.25 75.75

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

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

THE NATIONAL

BLANK

1.

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 28.20.

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 ' 6.70 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

BOOK COMPANY

HOLYOKE NEW YORK

.71 .8 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

MASSACHUSETTS CHICAGO

BOSTON

SAN FRANCISCO

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 64.35 65.85 67.35 68.85 70.35 71.85 73.35 74.85

176.35

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 21 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50