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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 />Hist. <br />Def. <br />Dist. <br />Def. <br />lfo . <br />Deg. <br />Radius <br />Mid. <br />Ord. <br />Tan <br />gist. <br />Def. <br />Dist. <br />Del. <br />i Ft. <br />14 <br />t. <br />ft. <br />It. <br />ft. <br />11 <br />I° 59' <br />ft. <br />ft. <br />ft. <br />ft. <br />34' <br />0°10' <br />34377. <br />.036 <br />.145 <br />.291 <br />0.05 <br />7. <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 />6.685 <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 />13.95 <br />2.40 <br />1' <br />5729.6 <br />.218 <br />.873 <br />1.745 <br />0.30 <br />20 <br />588.2'1.819 <br />103.54 <br />7.255 <br />14.53 <br />2.50 <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 />2.31_7 <br />0.40 <br />40 <br />661.7.1.892 <br />3° 35' <br />7.550 <br />15.11 <br />2.60 <br />.30 <br />3819.8 <br />.327 <br />1.309 <br />2.613 <br />0.45 <br />9 <br />637.3 <br />1.965 <br />7.84G <br />15.69 <br />2.70 <br />40 <br />3437.9 <br />.304 <br />1.454 <br />2.909 <br />0.50 <br />20 <br />614.6 <br />2:037 <br />8.136 <br />16.27 <br />2.80 <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 />8.281 <br />16:56 <br />2.85 <br />2 <br />2864.0 <br />.436 <br />1.745 <br />3.490 <br />0.60 <br />40 <br />593.4 <br />2.110 <br />8.426 <br />16.55 <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 />2.183 <br />8.716 <br />17.43 <br />3.00 <br />20 <br />2455.7 <br />.509 <br />2.036 <br />4.072 <br />0:70 <br />30 <br />546.4'2.29'2 <br />9.150 <br />18.30 <br />3.15 <br />30 <br />2292.0 <br />.545 <br />2.181 <br />4.363 <br />0.75 <br />11 <br />52 1. 7 <br />2.402 <br />9.585 <br />19.16 <br />3.30 <br />40 <br />2148.8 <br />.582 <br />2.327 <br />4.654 <br />0.80 <br />30 <br />499.1 <br />2.511 <br />10.02 <br />20.0.1 <br />3.45 <br />50 <br />2022.4 <br />.615 <br />2.472 <br />4.045 <br />0.85 <br />12 <br />478.3 <br />2.620 <br />10.45 <br />2D.01 <br />3.60 <br />.8 <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 />5.817 <br />1.00 <br />30 <br />425.4 <br />2.949 <br />11.75 <br />23.51 <br />4.05 <br />30. <br />1637.3 <br />.764 <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 />;ML 2 <br />3.168 <br />12.6.2 <br />25.24 <br />4.35 <br />50 <br />1495.0 <br />.836 <br />3.345 <br />6.589 <br />1.15 <br />15 <br />383.1 <br />3.277 <br />13.05 <br />26.11 <br />4.50 <br />L - <br />1432.7 <br />.873 <br />3.490 <br />6.980 <br />1.20 <br />30 <br />370.8 <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 />359.3 <br />3.496 <br />13.92 <br />27.84 <br />4.80 <br />.20 <br />1322.5 <br />.945 <br />3.718 <br />7.561 <br />1.30 <br />30 <br />348.5 <br />3.606 <br />14.35 <br />28.70 <br />4.95 <br />30 <br />1273.6 <br />.082 <br />3.926 <br />7.852 <br />1.35 <br />17 <br />338.3 <br />3.716 <br />14.79 <br />29.50 <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 />8 <br />1146.3 <br />1.091 <br />4.362 <br />8.724 <br />1.50 <br />20 <br />287.9 <br />4.374 <br />17.37 <br />34.73 <br />G:00 <br />.10 <br />1109.3 <br />1.127 <br />4.507 <br />9.014 <br />1.55 <br />21 <br />274.4 <br />4.594 <br />18.22 <br />36.44 <br />6.30 <br />20 <br />1074.7, <br />1.iG4 <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 />9.596 <br />1.65 <br />23 <br />250.8 <br />5.035 <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 />4t.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 />5.476 <br />21.64 <br />43.28 <br />7.50 <br />6 <br />955.4 <br />1.309 <br />5.234 <br />10.47 <br />1.80 <br />26 <br />222.3 <br />5.697 <br />22.50 <br />44.99 <br />7.80 <br />10 <br />929.6 <br />1.346 <br />5.379 <br />10.76 <br />1.85 <br />27' <br />214.2 <br />5.918 <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 />20G,7 <br />6.139 <br />24.19 <br />48.38 <br />8.40 <br />30 <br />881.9 <br />1.418 <br />5.669 <br />1.1.34 <br />1.05 <br />29 <br />199.7 <br />6.360 <br />25.0.1 <br />50.078.70 <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 />25.88 <br />51.76 <br />9:00 <br />The middlo ordinate in inches for any cord of lerii;th (C) is equal to .0013 C2 <br />multiplied by the middle ordinate taken from the above table. Thus, if it <br />desired to bend 0..30 ft. rail to fit a 10 degree curve, its middle ordinate should <br />be .0012X900X`-'.183 or 1.36 inches. <br />TABLE III. Deflections for Sub Chords for Short Radius Curves. <br />Degree <br />of <br />Cure <br />Radius <br />50 <br />1/ sob chord - sin of a def. angle <br />R <br />length <br />of arc <br />for 1,00 ft. <br />sin. sdef.ang. <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 FL <br />30° <br />193.18 <br />1° 51` <br />14 <br />2° 58` <br />3° 43`I0I.15 <br />2000 <br />32 <br />131.39 <br />I° 59' <br />2° 25' <br />3°10' <br />3°58` <br />101.33 <br />34' <br />171.01 <br />2°o6' <br />2°33 <br />3°21' <br />4° 12' <br />101.48 <br />360 <br />161.8o, <br />2° 13 <br />2° 41' <br />3° 33 <br />4°26' <br />IoI.66 <br />38° <br />153.58 <br />2°20' <br />2°49' <br />3° 44' <br />4°40' <br />101.85 <br />40° <br />146.19 <br />2°27' <br />z° 57, <br />3' 55' <br />4° 54' <br />102.06 <br />42' <br />139.52 <br />2'34' <br />3° 05' <br />4° 07` <br />5°08 <br />102.29 <br />44' <br />133.47 <br />2° 41' <br />3° 13' <br />4° 18' <br />S°.32' <br />102.53 <br />460 <br />127.97 <br />2° 48' <br />3° 2I' <br />¢ 29' <br />5° 36' <br />102.76 <br />48° <br />122.92 <br />2 ° 55 <br />3' �9r <br />4° 40 <br />5° 50' <br />103.00 <br />500 <br />118.31. <br />3° 02' <br />3° 38' <br />4° 51' <br />6° 04' <br />103.24 <br />52° <br />114.o6 <br />3° 09' <br />3° 46' <br />5° o2' <br />6° 17' <br />103.54 <br />54° - <br />110-11 <br />3° 16' <br />3' 54` <br />5° 13' <br />6' 31 <br />103.84 . <br />56° <br />io6. 50 <br />3° 22'. <br />4° 02' <br />S°.z3' <br />6° 44' <br />104, 14 <br />58° <br />103.14 <br />3° 29' <br />4` 1O` <br />5° 34' <br />60 37` <br />104.43 <br />600 <br />100.00 <br />3° 35' <br />4° 18' <br />• 5° 44' <br />7° 11' <br />104.72 <br />Ix <br />CURVE FORMULAS <br />T 3o tan I R = T cot. 21 Chord def. = chords <br />T - sin. � 2 50 <br />5o R. _ Sin. a D 1 <br />to J D =' No. chords - <br />1 = R ex. sec I D <br />Sin._J D = oo tarn ' I E - T tan J I 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 fora given distance and deflection. <br />Rule I. Multiply the given distance by .01745 (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 />RIGnT ANGLF TRIAN- rLES. Square the altitude, divide by twice the <br />base. Add quotient to base for hypotenuse. <br />Given Base loo, Alt. 10.1()2=200=.5. 100-}-.5=Ioo.5 hyp• <br />Given Hyp. foo, Alt. 25.252-200=3.125. loo-3.125=96.875=Base. <br />Error in first example, .002; in last, .045. <br />To find- Tons of Rail in one mile of trach: multiply weight per yard <br />by ri, and divide by 7. <br />LEVELING. The correction for curvature and refraction, in feet <br />and decimals of feet is equal to 0.574d2,where d is the distance in miles. <br />The correction for curvature alone is closely, �d The combined cor- <br />rection is negative. <br />PROBABLE ERROR. If di, d" d„ etc. are the discrepancies of various <br />results from the mean, and if Xda-the sum of the squares of these differ- <br />ences and n�the number of observations, then the probable error of the <br />mean= + 0.6745 Ida <br />n (n•-1) <br />SOLAR EPAFUERIS. 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 3.1,x5uz in., with about 90 pages of data very <br />useful to the Surveyor; such as the adjustments of transits, levels and <br />solar attachments; 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 formulas; Natural andLogarithmic Functions; <br />and Logarithms of Numbers. <br />TABiF IV. - Minutes in Decimals of a Decree. <br />1` <br />OIG7 <br />11' <br />.1833 <br />21' <br />.3600 <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 />.8607 <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 />.0667 <br />14 <br />.2333 <br />24 <br />.4000 <br />34 <br />.5667 <br />44 <br />.7333 <br />54 <br />.0000 <br />5 <br />.6833 <br />15 <br />.2500 <br />25 <br />.4167 <br />35 <br />.5833 <br />45 <br />.7500 <br />55 <br />91676 <br />.0167- <br />G <br />.1000 <br />16'. <br />.2667 <br />2G <br />.4333 <br />36 <br />.6000 <br />40 <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 />.0500 <br />S <br />-.1333 <br />18 <br />.3000 <br />28 <br />.4067 <br />33 <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 .11367 J1 <br />20 <br />.3333 1130 <br />1 .5000 11 <br />40 <br />1 .5667 1, <br />50 <br />1 .833311 <br />60 <br />1.0000 <br />TABLE V. - Inches in Decimals of a foot. <br />1-113 <br />3-32 <br />Y, <br />3-10 <br />X <br />5-16 <br />% <br />� % <br />% <br />N <br />.0052 <br />.0078 <br />.0104 <br />.0156 <br />.0208 <br />.0260 <br />.0313 <br />.0417 .0521 <br />.0625 <br />.0729 <br />1 <br />2 <br />3 <br />4 <br />5 <br />6 <br />7 <br />8 9 <br />lOr <br />11 <br />.0833 <br />.1667 <br />.2500 <br />.3333, <br />.4187: <br />.5000 <br />.5833 <br />.6657 .7500 <br />:8333 <br />.9167. <br />