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VIII <br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft. <br />Deg. <br />i� <br />Orld. <br />Det. <br />Dist. <br />e. <br />Dor <br />1 Ft. <br />Deg. <br />.Radius <br />Mi <br />Dist <br />Dist. <br />ef- <br />for <br />I Ft. <br />193.18 <br />1°51' <br />2° 17' <br />t.t. <br />3° 43' <br />Iol - 15 . <br />320 <br />181.39 <br />t. <br />ft. <br />ft. <br />30 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 />201 <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 />7.266 <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 />3137.9 <br />.364 <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 />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 />2155.7 <br />.509 <br />2.036 <br />4.072 <br />0.70 <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 />it <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 />50 <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 />3 <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 .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 />1502.9 <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 />4 <br />1132.7 <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 />5 <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 />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 />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 />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 />16 <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 />206.7 <br />6.139 <br />24.19 <br />48.38 <br />8.40 <br />30 <br />881.9 <br />1.418 <br />5.669 <br />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 in 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 bend a 30 ft. rail to fit a 10 degree curve, its middle ordinate should <br />be .0012X900X2.183 or 2.36 inches. <br />TABLE III. , Deflections for Sub Chords for Short Radius Curves. <br />Degree <br />Radius <br />M2 sub Ichord=sin of def. angle <br />of arc <br />Curve <br />sin. i def, an g. <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 Ft. <br />for 100 ft. <br />302 <br />193.18 <br />1°51' <br />2° 17' <br />2° 58' <br />3° 43' <br />Iol - 15 . <br />320 <br />181.39 <br />i° 59' . <br />20251 <br />3° Io' <br />30 58' <br />101.33 <br />340 <br />171.01 <br />2° 06' <br />2° 83' <br />3° 21' <br />4° 12' <br />101.48 <br />36° <br />01.8o <br />2° 13' <br />2° 41' <br />30 33' <br />40 26' <br />io1.66 <br />380153.58 <br />24 <br />2° 20' <br />2° 49' <br />3° 44' <br />4° 40' <br />101.85 <br />.40° <br />i46.ig <br />2° 27' <br />_ <br />2057' <br />3° 55' <br />4° 54 <br />102.o6 <br />420 .. <br />139.'52 <br />20 34' <br />30 05' <br />4° 07' <br />5° o8 <br />102.29 <br />44° <br />133.47 <br />2°-;41' <br />30 13' <br />4°18' <br />5° 2z' <br />102.53 <br />46° <br />127.97 <br />2048' <br />3,21' <br />4°29' <br />S°36' <br />Io2.76 <br />480 :. <br />122.92 <br />20 55' <br />3° 29'' <br />4° 40' <br />5° 50' <br />103.00 <br />- 5o°: <br />118.31 <br />3° 02': <br />30 38' <br />4°51' <br />6° 04' <br />103.24 <br />52° : <br />i14.06 <br />3° 09' <br />3° 46' <br />5° 02, <br />6° 17' <br />103.54 <br />54° <br />II0.11 <br />3° 16' <br />30 54' <br />5° 13'. <br />6° 31' <br />103.84 <br />-56° <br />1106.50 <br />3022 <br />4° 02' <br />S° 23'. <br />6° 44' <br />104.14 <br />580: <br />1103.14 <br />30 29, <br />4' 10' <br />5034 <br />6o 57' <br />104"43 <br />60 <br />100.00 <br />3035 <br />4 18 <br />5 44 <br />7 II <br />104.72 <br />IX <br />CURVE FORMULAS <br />= Rtan zI 1 <br />So tan 1 I R= T cot. 2' I chord' <br />T = 5 2 50 Chord def. = R <br />Sin. 2 D R = <br />Sin. s D = 50 - Sin. a 3 <br />D No. chords = I <br />R E= R ex. sec a I D <br />Sin." z D _ 5o tan <br />z I E _ .T tan } I Tan. def. = 2 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 1 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 altitude, divide by twice the <br />base. Add quotient to base for hypotenuse. <br />Given Base loo, Alt. 10.102-200=.5. 100+:5=1oo.5 hyp. " <br />Given Hyp. loo, Alt. 25.252=200=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 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, 8d'.. The combined cor- <br />rection is negative. <br />PROBABLE ERROR. If di; d2, d3, etc. are the discrepancies of various <br />results from the mean, and if 2A2 =the sum of the squares of these differ- <br />ences and-n=the number of observations, then the probable error of the <br />mean = 2;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, 38x6 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; stadia measurements; <br />magnetic declination; arithmetic constants, etc. <br />TABLE IV. -Minutes in Decimals of a Degree. <br />1t <br />.0167 <br />11/ <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 />.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 />S. <br />.I333, <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 11 <br />30 <br />1 .5000 11 <br />40 <br />1 .6667 11 <br />50 <br />1 .8333 11 <br />60 • <br />1.0000 <br />TABLE V. -Inches in Decimals of a Foot. <br />1-16 3-32 Y 3-16 Y 15-16 <br />.0052 I .0078 .0104 .0156 .0208 j .0260 .0 13 I .0417 .0 21 .08 5 I .07 9 <br />1 2 3 4 5 I 6 7 8 9 10 1 <br />083 3 .1667 .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167 <br />