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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 />Def. <br />Dist.1 <br />for <br />Ft. <br />Deg. <br />Radine <br />lid. <br />Ord. <br />an. <br />Dist. <br />Def. <br />Dist. <br />Dor <br />Diet. <br />1 Ft. <br />193.18 <br />1° 51' <br />20 17' <br />2° 58' <br />30 43' <br />I01.15 <br />32° <br />t. <br />ft. <br />x ft. <br />t. <br />3° 58' <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 />688.2 <br />1.819 <br />7.268 <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 />2.327 <br />0.40 <br />40 <br />661.7 <br />1.892 <br />7.556 <br />15.11 <br />2.60 <br />30 <br />3819.8 <br />.327 <br />1.309 <br />2.618 <br />0.45 <br />9 <br />637.3 <br />1.965 <br />7.846 <br />15.69 <br />2.70 <br />40 <br />.3437.9 <br />.364 <br />1.454 <br />2.909 <br />0.50 <br />20 <br />614.6.2.037 <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 />603.8 <br />2.074 <br />8.281 <br />16.56 <br />2.85 <br />2 <br />2864.9 <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 />2.183 <br />8.716 <br />17.43 <br />3.00 <br />20 <br />'2455.7 <br />'.509 <br />2.036 <br />4.0720.70 <br />30 <br />546.4 <br />2.292 <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 />521.7 <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 />20.04 <br />3:45 <br />60 <br />2022.4 <br />.618 <br />2.472 <br />4.945 <br />0.85 <br />12 <br />478.3 <br />2.620 <br />10.45' <br />20.91 <br />3.60 <br />a <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 />396.2 <br />3.168 <br />12.62 <br />25.24 <br />4.35 <br />50 <br />1495.0 <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 />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 />.982 <br />3!926 <br />7.852 <br />1.35 <br />17 <br />338.3 <br />3.716 <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 />8 <br />1146.3 <br />1.091 <br />4.362 <br />8.724 <br />1.50 <br />20 <br />287.9 <br />.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 />274.4 <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 />262.0 <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 />28 <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 />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 />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 />.918 <br />2335 <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 />8.70 <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 middle ordinate `n inches for any cord of length (C) is equal to .0012 C' <br />multiplied by the middle ordinate taken from the above table. Thus, if it <br />desired to bends, 30 ft. rail to fit a 10 degree curve, its middle ordinate should <br />be .0012X900X2.183 or 2.36 inches. <br />.TABLEJIL . Deflections for Sub Chords for Short Radius Curves. <br />Degree <br />of <br />R iliussuItb <br />chord <br />. = sin of j def. angle <br />Length <br />a arc <br />Curve <br />sin. j def. ang. <br />12,5 Ft. <br />15 Ft. <br />20 it. <br />25 Ft. <br />for 100 ft. <br />300. <br />193.18 <br />1° 51' <br />20 17' <br />2° 58' <br />30 43' <br />I01.15 <br />32° <br />181.39 <br />1° 59' <br />20 25' <br />3° 10' <br />3° 58' <br />101.33 <br />34°171.01 <br />13 <br />2° 06' <br />2° 33' <br />3° 21' <br />4° 12' <br />101.48 <br />36° <br />161.8o2° <br />i3' <br />2° 4i: <br />3° 33' <br />4° 26' <br />ioi.66 <br />380 <br />153.58 <br />2° 20' <br />•2° 49' <br />30 44' <br />4° 40' <br />iof .85 <br />40° <br />146. i9 <br />2° 27' <br />2° 57 <br />.3° 55' <br />4° 54' <br />102.06 <br />420 <br />139.52 <br />2° 34 <br />3° 05' <br />4° 07' <br />50 o8 <br />102.29 <br />-440 <br />133.47 <br />2°41' <br />3°,13' <br />4°18' <br />50 22' <br />102.53 <br />460 <br />127.97 <br />2° 48' <br />3° 21' <br />4° i9' <br />.5° 36' <br />102.76 <br />'480 <br />122.92 <br />20 55' <br />'3029' <br />"40• 40' <br />S° 50' <br />103.00 <br />50° <br />118, 31 <br />3002 <br />3° 38' <br />4° 51' <br />6° 04 <br />103.24 <br />o <br />52 <br />114.06' <br />o , <br />3 09 <br />o r <br />3 46 <br />o: , <br />S oa <br />o , <br />G 17 <br />103.54 <br />54° <br />110-11 <br />3° 16' <br />3° 54,;5° <br />13' <br />6°.31' <br />103.84 <br />56°. <br />io6.5o <br />3° 22' <br />°02' <br />4002 1 <br />5023' <br />60 44' <br />104:14 <br />58° <br />03.14 <br />3°29' <br />4* 10 <br />S°34' <br />6° 57' <br />104.43 <br />600 <br />100.00 <br />30 35. <br />4° i8' <br />5° 44' <br />.70 11' <br />104-72 <br />Ix <br />:CURVE FORMULAS <br />T= R tan 211 R= T cot. 2' I chord' <br />50 tan 12 .I Chord, _ <br />T = Sin. z D 50 R <br />R= <br />Sin. a `D .' 50 Sin. '1 D No. chords = I <br />R 1 E= R ex. sec -I'I D <br />Sin. -'a D = So tan. 2 I <br />T E = T•tan I I Tan. def. = j 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 .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 fora 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 altitude, divide by twice the <br />base. Add quotient to base for hypotenuse. <br />Given Base loo, Alt. 1o.102-200=.5. loo+.5=ioo•5 hyp• <br />Given Hyp. too, Alt. 25.252-200=3.125. 100-3.125=96.875=Base. <br />Error in first example, .002; in last, .o45• <br />To find Tons of Rail in one mile of track: multiply weight per yard <br />by I I, 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, 'd2. The combined cor- <br />rection is negative. . <br />PROBABLE ERROR. If d,, 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= �d2 <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, 3ax6 in:, ,has. about 190 pages of data :very <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; t stadia measurements; <br />magnetic declination; arithmetic constants, etc. <br />TAnr R TV _ -Minutes in Decimals of a'�Deeree. <br />1t <br />.0167 <br />111 <br />.1833 <br />211 <br />.3500 <br />311 <br />.5167 <br />411 <br />.6833 <br />511 <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 />4 <br />.0667 <br />14 <br />.2333 <br />24 <br />.4000 <br />34 <br />.5667 <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 />.0333 <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 />.1667 <br />1 20 <br />1 .3333 It <br />30 <br />1 .5000 11 <br />40 <br />1 .6667 11 <br />50 <br />1 .8333'11 <br />60 <br />11.0000 <br />TABLE V. -Inches in Decimals of a Foot. <br />1-16332 3-16 1 5-16 % se �6 <br />.0052 I .0078 ..0104 .0156 I/y .0208 I .0260 .0313 .0417 .0521 .0625 .0729 <br />1 2 3 4 5 6 7 8 9 10 11• <br />.0833 .1667 .2500 .3333 .4167 .5000 1833 .6ti67 .7500 .8333 .4167 <br />