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VIII <br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft. <br />Deg. <br />Radius <br />Mid. <br />Ord. <br />Tan. <br />Dist, <br />Def. <br />Dist. <br />for <br />r <br />1 FG <br />Deg. <br />Radius <br />Mid.. <br />Ord <br />Ten <br />Dist, <br />Def. <br />Dist. <br />Dol. <br />1 r t. <br />2°58' <br />3°43' <br />101.15 <br />32° <br />181.39 <br />1° 59' <br />2° i5' <br />3° to' <br />t. <br />t; <br />t. <br />171.01 <br />0'10' <br />34377. <br />.036 <br />.145 <br />.291 <br />0. On <br />1" <br />819.0 <br />1.528 <br />6.105 <br />12.21 <br />2.10 <br />20 <br />17189. <br />.073 <br />.291 <br />.582 <br />0.10 <br />20' <br />781:'8 <br />1.600 <br />6.395 <br />12.79 <br />2.20 <br />30 <br />11459. <br />.109 <br />.436 <br />.873 <br />0.15 <br />30 <br />764'.5 <br />1.637 <br />6.540 <br />13.08 <br />2.25 <br />40 <br />8594.4 <br />.145 <br />.582 <br />1.164 <br />0.20 <br />40 <br />747.9 <br />1.673 <br />'G.685 <br />13.37 <br />2.30 <br />50 <br />6875.5 <br />.182 <br />.727 <br />1.454 <br />0.25 <br />8 <br />716.8 <br />1.746 <br />6.976 <br />M 95 <br />2.40 <br />1 <br />5729.6 <br />.218 <br />.873 <br />1.745 <br />0.30 <br />" 20 <br />688.2 <br />1.819 <br />7.266 <br />14.53 <br />2.;0 <br />10 <br />4911.2 <br />.255 <br />1.018 <br />2.036 <br />0.35 <br />30 <br />674.7 <br />1.855 <br />7.411 <br />14.82 <br />2.55 <br />20 <br />4297.3 <br />.291 <br />1.164 <br />2.327 <br />0.40 <br />40 <br />661.7 <br />1.892 <br />7.550 <br />15.11 <br />2.00 <br />30 <br />3319.8 <br />.327 <br />1.300 <br />2.618 <br />0.45 <br />9 <br />637.3 <br />1.9655 <br />7.846 <br />15.69 <br />2.70 <br />40 <br />3137.9 <br />.364 <br />1.454 <br />2.009 <br />0.50 <br />20 <br />614.6 <br />2.037 <br />.S. 136 <br />16.27 <br />2.S0 <br />50 <br />3125.4 <br />.400 <br />1.600 <br />3.200 <br />0.55 <br />30 <br />G03.8 <br />2.074 <br />'S.281 <br />16.50 <br />2.85 <br />2 <br />2861.9 <br />.436 <br />1.745 <br />3.490 <br />0:60 <br />40 <br />593.4 <br />2.110 <br />8.426 <br />16.85 <br />2.90 <br />10 <br />2644.6 <br />.473 <br />1.891 <br />3.781 <br />0.65 <br />10 . <br />573.7 <br />2.153 <br />5.716 <br />17.43 <br />3.00 <br />20 <br />2155.7 <br />.509 <br />2.036 <br />4.072 <br />0.70 <br />30 <br />546.4 <br />2.202 <br />9'.150 <br />18.30 <br />3.1:5 <br />30 <br />2292.0 <br />.545 <br />2.181 <br />4.3G3 <br />0.75 <br />11 <br />521.7 <br />2.402 <br />9.555 <br />10.16 <br />3.30 <br />40 <br />2148.8 <br />.562 <br />2.327 <br />4.6554 <br />0.80 <br />30 <br />499.1 <br />2.511 <br />10.02 <br />20.04 <br />3.45 <br />50 <br />2022.4 <br />.618 <br />2.472 <br />4.0.15 <br />0.85 <br />'12 <br />478.3 <br />2.620 <br />10.45 <br />20.91 <br />3.60 <br />S <br />1910.1 <br />.655 <br />2.618 <br />5.235 <br />0.90 <br />30 <br />459.3 <br />2.730 <br />10.89 <br />21.77 <br />3.75 <br />10 <br />1809.6 <br />.691 <br />2.763 <br />5.526 <br />0.95 <br />13 <br />441.7 <br />2.839 <br />11.32 <br />22.64 <br />3.90 <br />20 <br />1719.1 <br />.727 <br />2.908 <br />5.517 <br />1.00 <br />30 <br />425.4 <br />2.949 <br />11.75 <br />23.51.4.05 <br />30 <br />1037.3 <br />.704 <br />3.054 <br />6.108 <br />1.05 <br />14 <br />410.3 <br />3.058 <br />12.18 <br />24.37 <br />4.20 <br />40 <br />1562.9 <br />.800 <br />3.199 <br />6.398 <br />1.10 <br />30 <br />396.2 <br />3.168 <br />12.62 <br />25.24 <br />4.35 <br />50 <br />1195.0 <br />.836 <br />3.345 <br />,6.689 <br />1.15 <br />15 <br />383.1 <br />3.277 <br />13.05 <br />26.11 <br />4.50 <br />! <br />1132.7 <br />.873 <br />3.490 <br />6.950 <br />1.20 <br />30 <br />370.9 <br />3.387 <br />13.49 <br />26.97 <br />4.65 <br />10 <br />1375.4 <br />.909 <br />3.635 <br />7.271 <br />1.25 <br />16 <br />339.3 <br />3.496 <br />13.92 .27.84 <br />4.80 <br />20 <br />1322.5 <br />.945 <br />3.718 <br />!7.561 <br />1.30 <br />30 <br />348.45 <br />3.606 <br />14.35 <br />28.70 <br />4.95 <br />30' <br />1273.6 <br />.982 <br />3.926 <br />7.852 <br />1.35 <br />17 <br />338.3 <br />3.71 Cr <br />14.78 <br />29.56 <br />5.10 <br />40 <br />1228.1 <br />1.018 <br />4.071' <br />8.143 <br />1.40 <br />18 <br />319.6 <br />3.935 <br />15.64 <br />31.29 <br />5.40 <br />50 <br />1185.8 <br />1.055 <br />4.217 <br />8.433 <br />1.45 <br />19 <br />302.9 <br />4.155 <br />16.51 <br />33.01 <br />5.70 <br />5 <br />1146.3 <br />1.091 <br />4.362 <br />8.724 <br />1.50 <br />20 <br />287.0 <br />4.374 <br />17.37 <br />34.73 <br />6.00 <br />10 <br />1109.3 <br />1.127 <br />4.507 <br />9.014 <br />1.55 <br />21 <br />271.4 <br />4.594 <br />18.22 <br />36.44 <br />6.30 <br />20 <br />1074.7 <br />1:164 <br />4.653 <br />9.305 <br />1.60. <br />22 <br />202.0 <br />4.814 <br />19.08 <br />38.16 <br />6.60 <br />30 <br />1042.1 <br />1.200 <br />4.798 <br />9.590 <br />1.65 <br />23 <br />250.8 <br />5.03.5 <br />19.94 <br />39.87 <br />6.90 <br />40 <br />1011.5 <br />1.237 <br />4.943 <br />9.886 <br />1.70 <br />24 <br />240.5 <br />5.255 <br />20.79 <br />41.58 <br />7.20 <br />50 <br />=982.6 <br />1.273 <br />5.088 <br />10.18 <br />1.75 <br />25 <br />231.0 <br />6.476 <br />21.64 <br />43.28 <br />7.50. <br />s <br />955.4 <br />1.309 <br />5.234 <br />10.47 <br />1.50 <br />26 <br />222.3 <br />5.697 <br />22.50 <br />44.99 <br />7.50 <br />10 <br />929.6 <br />1.346 <br />5.379 <br />10.76 <br />1.85 <br />27 <br />214.2 <br />.918 <br />23.35 <br />46.69 <br />8.10 <br />20 <br />905.1 <br />1.382 <br />5.524 <br />11.05 <br />1.90' <br />28 <br />206.7 <br />.139 <br />24.19 <br />48.38 <br />8.40 <br />30 <br />•881.9 <br />1.418 <br />5.669 <br />11.34 <br />1.95 <br />29 <br />199.7 <br />6.360 <br />25.04 <br />50.07 <br />9.70 <br />40 <br />859.9 <br />1.455 <br />5.814 <br />11.63 <br />2.00 <br />30 <br />193.2 <br />6.583 <br />25.58 <br />51.76 <br />9.00 <br />The Middle ordinate }'n inches forany cord of length (C) is equal to .0012 C' <br />multiplied by the middle ordinate token from the above table. Thus, if it <br />desired to bend a 30 ft. rail to fit a 10 degree curve, its twiddle ordinate should <br />be .0012X900X2.1&1 or 2.36 inches. <br />TALE III. Deflections for Sub Chords for Short Radius Curves. <br />Degree <br />of <br />Curve' <br />Radius <br />50 <br />sin.'' def: ang. <br />M sub chordLength <br />I <br />R = sin of def. angle <br />of arc <br />for 100 ft - <br />t.30` <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 Ft. <br />30' <br />193.18 <br />1051' <br />2°17' <br />2°58' <br />3°43' <br />101.15 <br />32° <br />181.39 <br />1° 59' <br />2° i5' <br />3° to' <br />3° 58' <br />I01.33 <br />34° <br />171.01 <br />2° o6' <br />2° 33' <br />3° 21' <br />,4° 12' <br />101.48 <br />36° <br />16t. 8o <br />2° 13' <br />2° 4!' <br />3° 33' <br />4° 26' <br />loi.66 <br />38° <br />153.58 <br />2° 20' <br />2° 49' <br />3° 44' <br />4° 40'. <br />10I :85 <br />400 <br />1¢6.19 <br />z° 27' <br />2° 57' <br />3°,55' <br />4° 54' <br />102.o6 <br />42° <br />139.52 <br />2° 34 <br />3° 0,5' <br />4.07 ' <br />5° 08 <br />162.29 <br />44° <br />133.47 <br />2° 411 <br />3° 13' <br />4° 18' <br />S° -2' <br />roi:53 <br />46° <br />127.97 <br />2° 48' <br />3° 21' <br />4 29' <br />5° 36' <br />102.76 <br />48° <br />122.92 <br />2° 55' <br />3° 29 <br />4° 40' <br />S° go' <br />103:00 <br />50° <br />118.31 <br />3° 02' <br />3° 38' <br />q° 51' <br />6° 04' <br />103.24 <br />52° <br />a 14.06 <br />3° 09' <br />3° 46' <br />5° 02' <br />6° 17' <br />103.54 <br />54° <br />110.11 <br />3° 16' <br />3° 54' <br />:) 13' . <br />6° 31' <br />103.84 <br />56° <br />io6.5o <br />3° 22' <br />4° 02' <br />5°23 <br />6° 44' <br />104.14 <br />58° <br />103.14 <br />3° 29' <br />4° 10' <br />5° 34' <br />6° 57' <br />14443 <br />6o° <br />Ioo.00 <br />3° 35' <br />40 18' <br />5° 44 <br />. 7° u' <br />104.72 <br />IX <br />CURVE FORMULAS <br />T ='R tan 21 R = T cot. ' l chord' <br />T = 56 to n l f Chord def. = <br />Sin. Z D It = 00 R <br />So Sin. all I . <br />Sin: a D = I\o..chords = <br />R E =Rex. sec ; l D <br />Sin. z D" = 'o tat I E = T tan a 1 Tan. def. = z 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 fo'r a given distance and deflection. <br />Mule 1. Multiply the given distance by .01745 (def, for i° fur I ft. <br />see Table II.), and divide given deflection liy the product. <br />Rule 2. Multiply given deflection by 57.3, and divide the prodtict by <br />the given distance. <br />To.find deflection fora given angle and distance. Multiply the angle . <br />by .01745i and the product by the distance. <br />GENERAL DATA <br />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the <br />base. Add quotient to base for hypotenuse. <br />Given Base loo, Alt. 10.101=2Oo=.5: 100-5-.5=100.,5 hyp. <br />Given -Hyp. loo, Alt. 25.25'-=200=3.125. 100-3.125=96.875=Babe. <br />-Error in first example, .002; in.last, .045. <br />find nd Tons of Rail in one mile of track: multiply weight per yard. - <br />by i f, and divide by 7. <br />LEVELING. The correction for -curvature and refraction, '-in *fevt <br />and decimals of feet is equal to 0.574d2, where d is the distance in nlilils. <br />The correction for curvature alone is closely, ^d2. The combined cor- <br />rection is negative. <br />PROBABLE ERROR. If dl, d2, da, etc. are'the discrepancies of various <br />results from the mean, and if Ede=the sum of the squares of these differ- <br />ences and n=the number of observations, then the probable error of the <br />mean <br />-0.6745 n(n-1) <br />SOLAR EPHEMERis. Attention is called to the Solar. Ephemeris for <br />the current year, published by Keuffel & Esser Co., and furnished upon <br />request. This handy booklet, Mex6 in., has about 190 pages of data eery <br />useful to. the Surveyor; such as the adjustments of transits, levels and Solar <br />attachments; directions and tables for determining the meridian and the <br />latitude from observations on the sun and Polaris; stadia measurements; <br />magnetic declination; arithmetic constants, etc. <br />TABLE IV.-N1inutes in Decimals of a Degree. <br />1' <br />.0167 <br />ll' <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 />.36657 <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 />4 <br />.06567 <br />14 <br />.2333 <br />24 <br />.4000 <br />34 <br />.5667 <br />44 <br />.7333 <br />54 <br />.9000 <br />5 <br />.0933 <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 />.0167 <br />47 <br />.7833 <br />57 <br />;1.;00 <br />8 <br />.1333 <br />1S <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 />.49.5167 <br />59 <br />9833 <br />10 <br />.1667 <br />20 <br />.3333 <br />30 <br />.5000 <br />40 <br />.6667 <br />50 <br />.8333 <br />1 60 <br />1.0000 <br />'1 mu.1c V. --Inches in Decimals of a Foot. <br />1-163-32 %.v 3-16 �i 5-164e <br />OO.i2 l .0079 .0104 `.0136 .0208 .0260 .0313 ( .0117 f .05'!1 .0625 .0720 <br />1 I 2 3 I 1 I 5 . I 6 i3:133 A167 .5000 .5933 .6 I S I 9 10 1] <br />.0833. .1607 .2500 .667 .7.100 .8333 <br />1 1, <br />