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i
<br />I
<br />TABLE II.=Radii, Ordinates and.Deflections. Chord -='100 ft.
<br />Mid Def. , Mid. Tan. Def. Def.
<br />Deg, . Radius Tan. Def. for Deg. Radius OrdDistfor
<br />Ord. Dist. Dist. 1 Ft. . , Dist. 1 Ft,
<br />ft.. t, ft. ft. ft, ft. ft, ft.
<br />0°10' 34377. 036 .145 .291 0.05 7' 819.0 1.528 'G. 105 12.21 2.10
<br />20 17189. 073 .291 582 0.10 20' 781.8 1.600 .6.395 12.79 2.20
<br />30 11459. ,109 .436 •873 0.15 30 764.5 1,637 6.540 13.08 2,25
<br />40 8594.4.145 .582 1.164 0.20 40 747.9 1.673 6,685 13.37 2.30
<br />50 6875.5 ,182 ,727 1.454 0.25 8 716.8 1.746 6.976 13.95 2,40
<br />1 5729:6 .218 .873 1,745 0.30' 20 688.2 1.819 7.266 14•,53 2.50
<br />10 4911.2 .255 1.018 2.036 0.35 30 674.7 1.855 :7.411 14.82 2.55
<br />0.40 40 661.7 1.892 :7.556 15,11 2.60
<br />20 4297.3 .291 1.184 2.327
<br />30 3819.8 ".327 1.309 2.618 0.45 9 637.3 1.965 7.846.15.69 2.70
<br />40 3437.9 .364 1.454 2.909 0.50 20 614.6 2.037 8.136 16.27 2.80
<br />50 . 3125.4 .400 1,600 3,200 0.55 30 603.8 2:074 8.281 16.56 2.85
<br />8 • 2864.9 .436 1.745 3.490 0.60 40: 593.4 2.110 8.426 16.85 2.90
<br />10 2644.6 '.473 1.891 3.781 '0.65 10 573.7 2.183 '8.716,17.43 3.00
<br />20 2455.7 :509 2.03G 4.072 0.70 30 546.4 2.292 9.150 18.30 3.15
<br />30 2292,0 ,545 2,181. 4363 0.75 11 521.7 2,402 '9.585 19.16 3.30
<br />40 2148.8 ',582 2.327. 4,.654 0.80 30 499.1 2.511 10.02 20.04 3:45
<br />b0. 2022..85 -12• 478,3 2,620 10.45 20.913.60
<br />4 .618 2,472 4.945 0
<br />E 1910.4 .655 2.618 5.235 0.90 , :30 459.3 2,730 10.89 21.77 3.75
<br />0.95
<br />10- 1809.6 .691 2,763 5.526 13 441.7 2,839 11.32 22.64 3.90
<br />20 .1719.1 .727 2,908 5.817 1.00 30 425.4 2,949 11.75 23.51 4.05
<br />30. 1637.3 .764 3,054 6.108 1.05 14 410.3 3,058 12.18 24.37 4.20
<br />40 1562,9 .800 3,199 6.398 1.10 30 396.2 3,168 12.62 25.2.4 4.35
<br />50 1495.0 _,836 3,345 6.689 1.15 15` 383.1 3,277.13.05 26.11 4:50
<br />1432.7 '.873 3.490 6.950 1.20 30 370,8 3,387 13.49' 26.97 4.65
<br />-10 1375.4 ,909 3,635 "7.271 1.25 '16' 359.3 3,496 13.92 27.84 4.80
<br />20 1322.5 ,.945 3,718 7.561 1.30 30 348.5 3,606 14.35 28.70 4.95
<br />30 -1273.6 .9823,926 7,852 1.35, 17 338.3 3,716 "14.78 29.56 5.10
<br />40 1228,1 1,018 4.071 8.143 1.40 18. 319.6 3,935 15.64 31.29 5.40
<br />50' 1185.8 1,055 4.217 8,433 1.45 19 302.9 4.155 16.51 33.01 5.70
<br />6 1146.3 1.091 4.362 g•724 1.50 20' 287.9 4.374 17.37 34.73 6.00
<br />10 1109.3 1.127 4.507 9.014. 1.55 21 274.4 4.594 18:22 36.44.6.30
<br />20 1074.7 1.164 4.653 .9,305 1.60. `22` 262.0 4,814 19.08 38,16 6.60
<br />30 1042.1"1,200 4,798 9.596 1.65 23 250.8 5.035 19:94 39.87 6.90
<br />40 1011.5 1,237 4.943 9,886 1.70 24 240.5 5.255 20.79 41.58 7.20
<br />50 982.6 1,273 5.088 10.18' 1.75. '.25. 231,0 5,476 21,64 43,28 7.50
<br />8, 955.4 1,309 5,234 10.47 1.80 26 222,3 5.697 22.50 44.99 7:80
<br />10 929.6 1.346 5.379 10.76 1.85 27, 214.2 5.918 23.35 46.69 8.10
<br />20 905.1 1,382 5.524 11.05 1-9028 206.7 6,139 24.19 48.38 8.40
<br />30 881.9 1,"418 5.669 11.34 1.95 29 199.7 6.360 25.04 50.07 8,70
<br />40 859.9 1,455 5.814 11.63 2.00 30, 193.2 6.583125:8 8 51.76 9.00
<br />The middle ordinate in inches for any cord of length (C) is equal to .0012 C'
<br />multiplied by the middle ordinato taken from the above table. Thus, if it
<br />desired to bend it 30 ft. rail to fit a 10 degree curve, its middle ordinate'shonid
<br />be .0012X900X2:183 or 2.36 inches,
<br />TABLE III. 11„flartinns for Sub Chords for Short Radius Curves.
<br />7egree
<br />of
<br />Curvesin,
<br />Radius
<br />50
<br />i def, an g
<br />12.5
<br />1°
<br />y4
<br />Ft.
<br />SI,
<br />sub chord
<br />�-
<br />15
<br />20.171
<br />Ft.
<br />sin of
<br />'J def.
<br />angle
<br />31'
<br />Length
<br />of arc
<br />for 100 ft.
<br />20 Ft.
<br />25 Ft.
<br />30'
<br />193.18
<br />2058"
<br />-3043'
<br />101,15
<br />32°
<br />181.39
<br />1°
<br />59,
<br />2
<br />25
<br />3
<br />Io
<br />3
<br />58
<br />I0I.33
<br />34°
<br />r71.01
<br />2°
<br />06'
<br />20
<br />33�
<br />30
<br />zI1
<br />40
<br />12'
<br />IOI.¢S
<br />360
<br />161.8o
<br />2°
<br />13'
<br />2°
<br />41,
<br />3°
<br />33,
<br />4°
<br />26
<br />io1.66
<br />38°
<br />153.58
<br />z °
<br />20
<br />2
<br />49
<br />3
<br />44
<br />4
<br />40
<br />I0I.85
<br />40°
<br />146.19
<br />2°�7'
<br />16
<br />°
<br />2
<br />,
<br />57
<br />°
<br />3
<br />55
<br />°
<br />4
<br />54
<br />102.06
<br />42'
<br />139.52
<br />2o34,
<br />,
<br />30
<br />05�
<br />40
<br />071
<br />50
<br />08�
<br />Ioz.29
<br />°
<br />I 47
<br />o
<br />2°
<br />41,
<br />3
<br />13
<br />¢
<br />18
<br />5.22
<br />38
<br />102.53
<br />6°
<br />4
<br />123
<br />7.97
<br />2°
<br />48,
<br />3°
<br />029/
<br />zI'
<br />4°
<br />29'
<br />S°
<br />36'
<br />102.76
<br />°
<br />¢8°
<br />I22.9z
<br />2°55,
<br />59
<br />3°3'
<br />10,
<br />4°51'
<br />o'
<br />6°04'
<br />o'
<br />103-00
<br />50
<br />118.31
<br />3
<br />Oz
<br />60
<br />1 1,0000
<br />Io3.24
<br />520
<br />114,06
<br />30
<br />09;
<br />5°
<br />�3'.
<br />6°
<br />110.11
<br />3°
<br />54�
<br />3i'
<br />Io3.84.
<br />55°
<br />1o6.5o
<br />3°
<br />22,
<br />40
<br />02/
<br />5 0
<br />23'
<br />60
<br />44'
<br />IO¢, 14
<br />0
<br />1
<br />4°
<br />10
<br />5°
<br />44,
<br />11,
<br />104
<br />60°
<br />100.000
<br />3°
<br />35�
<br />18'
<br />7°
<br />I .72 .
<br />CURVE FORMULAS
<br />T=
<br />Rtan I R= T cot. a I Chord def. =.chorda
<br />T= 50 Sin, J D R= 60 R
<br />I D
<br />Sin. 11 D = 50 Sin, 2 No. chords = I `
<br />R E R ex. sec z I D
<br />5o tan ; I
<br />„Sin. A D= T E= T tan I I Tan. def. = a chord def.
<br />The square of any distance, divided by twice the radius, will equal
<br />the, distance from tangent to curve, very nearly.
<br />'To find angle for a given distance and deflection.
<br />Rule I: Multiply the given distance by .01945 (def. for I° for i ft.
<br />see Table II.), and divide given deflection by the product.
<br />'Rule 2. Multiply given deflection by 57,3, and divide the product by
<br />the given distance.
<br />To find deflection for a given angle and distance. Multiply the angle
<br />by .01745, and the product by the distance.
<br />GENERAL DATA
<br />RIGHT ANGLE TRIANGLES. 'Square the attitude, divide *by twice the
<br />base. Add quotient to base for hypotenuse. .
<br />Given Base loo, Alt. Io.Io2=200=.5. 100-{-.5=100,5 hyp.,
<br />Given Hyp. Ioo, Alt. 25.25z=lob=3.125. 100-3.125=96.875=Base.
<br />Error in first, example, .002; in last, .045•
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by If, and divide by .7.
<br />LEVELING. The correction for curvature and refraction, in feet
<br />and decimals of feetis equal to 0.574d2, where d is the distance in miles.
<br />The correction for curvature alone is closely, jda. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d,., da, da, etc. are the discrepancies of various
<br />results from the mean, and if 7 -de =the sum of the squares of.these differ-
<br />ences and n=the number of observations, then the probable eiror of the
<br />a.
<br />mean- ± 0.6745 1d
<br />n --(n- )
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co.,`and furnished free of
<br />charge upon request, which is 31,x58 in., with about 90 pages of data -very
<br />useful to the Surveyor; such as the adjustments of transits, levels and
<br />solarattachments; directions and tables for determining the meridian
<br />and the latitude from observations on the sun and Polaris;'stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and Metric
<br />conversions; trigonometric f ormulas; Natural -and Logarithmic Functions;
<br />and Logarithms of Numbers.
<br />- 'TABLE 1V. - Minutes
<br />TABLE V. -
<br />in"Decimals of a Degree.
<br />1'
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />.6833.
<br />51'
<br />.8500
<br />2,•
<br />.0333
<br />12
<br />,2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3
<br />,0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />:5500
<br />43
<br />:7167
<br />53
<br />.8833"
<br />L
<br />.0667
<br />14
<br />,2333
<br />24
<br />.4000
<br />34
<br />.5662
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />,0833
<br />15
<br />,2500
<br />25
<br />.4167
<br />35
<br />.5833"
<br />45
<br />:7500
<br />55
<br />:9167
<br />6.'
<br />.1000
<br />16
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000,
<br />46
<br />.7667
<br />56
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2833..
<br />27
<br />'.4500
<br />37
<br />.6167
<br />47
<br />,7833
<br />57
<br />,9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333_
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />.1500
<br />19
<br />'.3167
<br />29'
<br />,4833
<br />•39
<br />.6500
<br />49
<br />.8167
<br />59
<br />9833
<br />10,
<br />1 .1667 11
<br />20
<br />1 .3333.
<br />_
<br />30
<br />1 .5000
<br />11 40 1
<br />.6667
<br />.50
<br />.83331,
<br />60
<br />1 1,0000
<br />TABLE V. -
<br />Inches in Decimals of a root.
<br />"
<br />1-16332
<br />Y8
<br />3-16
<br />Y4
<br />5-16
<br />Y8
<br />Y8
<br />Y4
<br />0052
<br />.0078
<br />.6104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />.0417 J1521
<br />.0625
<br />1.0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6
<br />7
<br />8 9
<br />10
<br />11
<br />.,0833
<br />.1667
<br />.,2500
<br />,3333
<br />.4167
<br />..5000
<br />.5833
<br />-:6667 .7500
<br />.8333
<br />1 .9167-
<br />. 11
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