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VIII <br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 f t. <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 bends 30 ft. rail to fit 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 />Curve <br />Radius . <br />Mid <br />Ord. " <br />Tan. <br />Dist. <br />Def. <br />Dist. <br />D r'. <br />1Ft. <br />Deg. <br />$ad os <br />Mid. <br />Ord. <br />Tan <br />-Dist. <br />Def. <br />Dist. <br />ef. <br />Dfor <br />] Ft <br />20 58' � <br />3° 43' <br />101.15 <br />320 <br />581.39 <br />i° 59' <br />2° 25' <br />t. <br />t. <br />t. <br />t. <br />171.01 <br />0"101 <br />34377: <br />.036 <br />..145.291 <br />101.48 <br />0.05 <br />V <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 />30'11459.. <br />102.o6 <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 />6.68513.37 <br />102.76 <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 />13.9 5 <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 />20'614.6 <br />2.037 <br />8.136 <br />16.27 <br />2.50 <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 />2SU: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 />11 <br />521.7 <br />2.402 <br />9.585 <br />19.163.30 <br />46 <br />2148.8 <br />.582 <br />2.327 <br />4.654 <br />0.80' <br />0 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 <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 />.1195.0 <br />.836 <br />3.345 <br />6.6S9 <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 />8.635 <br />7.271 <br />1.25 <br />16 <br />3� 9 3 <br />3.406. <br />13.92_ <br />27.84 <br />4 S0 <br />20: <br />1322.5 <br />.945 <br />3.718 <br />7.561 <br />1.30. <br />36 <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 />4.155'16.51 <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 />20.7941.58 <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 />8 <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 />7.50 <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 />206.7 <br />6.139 <br />24.19 <br />45.38 <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 bends 30 ft. rail to fit 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 />Curve <br />Radius <br />sin. 19 def. ang. <br />'/2 sub chord= sin of 12 def. angle <br />of arc <br />for 100 ft. <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 Ft. <br />30° <br />193.18 <br />10 51' <br />20 17' <br />20 58' � <br />3° 43' <br />101.15 <br />320 <br />581.39 <br />i° 59' <br />2° 25' <br />3° Io <br />3° 58' <br />101.33 <br />34° <br />171.01 <br />2° 06' <br />2° 33' <br />3° 21' <br />4° 12' <br />101.48 <br />36° <br />161:80. <br />2° 13' <br />2° 41' <br />30 33' <br />4° 26' <br />IOI.66 <br />380_ <br />153.58 <br />2° 20' <br />2° 49' <br />3° 44' <br />4° 40' <br />ioi.85 <br />46°'46. <br />546. i9 <br />20 27' <br />2° 57' <br />30.55' <br />40 5f <br />102.o6 <br />420 <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 />5° 2z' <br />102.53 <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 />20 55 <br />3° 29' <br />4P 40- <br />5° 50' <br />103.00 <br />50' " <br />118.31 <br />3° oz'. <br />3° 38' <br />4° 51' <br />6° 64' <br />103.24 <br />52P <br />114.06 <br />3° 09' <br />3° 46' <br />5° O2' <br />6° 17' <br />103 - 54 <br />:54P 1 <br />IIO. I1 <br />30 16' <br />3° 54' <br />5° 13' <br />6° 31', <br />103.84 <br />56? I <br />io6.50 <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°Io' <br />5° 34'. <br />6° 57' <br />104.43 <br />600 <br />loo.00. <br />3°35' <br />4°18' <br />5°44' <br />70II1 <br />104.72 <br />IX <br />CURVE -FORMULAS <br />T= R tan i I R= T cot. ; I chord' <br />17 So tan -' I 50 ~ Chord def. = R <br />- - Sin. 12.D R = <br />Sin. z D = 50 Sin: D _ No. chords I <br />R' E Rex. sec ' I D <br />Sin.a D = So t T ' I E = T tan } 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 for a given distance and deflection. ' <br />1 Rule I.- Multiply the given distance by .01745 (def., for I° for I ft. <br />see Table P1.), and divide given deflection by the product. <br />j Rule 2: Multiply given deflection by 57.3, and divide the product by <br />1 the given distance. <br />To find deflection for a given angle an&distarice. Multiply the angle <br />by .61745, and the product by the distance. <br />e <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 Ioo,.Alt. 10.10' -'.200=.5. 100-{-.5=IOO.5 hyp. <br />Given Hyp. too, Alt: 25.25'_200=3.125..100-3.I25=96.875=Base. <br />Error in first example,..062; 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, .3d'. 'The combined cor- <br />rection is negative. <br />PROBABLE ERROR. If dl, d2, d3, 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 = d' <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 />1f .0167 111' .1833 211 .3500 311 '.5167 411 .6833 511 .8500 <br />l 2 .0333 12 .2000 22 .3667 32 .5333 42 .7000 52 .8667 <br />3 .0500 13. .2167 23 .3833 33 .5500 43• .7167 53 .8833 <br />I,. 4 .0667 14 .2333 24 .4000 34 .5667 44 .7333 54 .9000' <br />5 .0833 15 .2500 25 .4167 35 .5833 45 .7500 55 .9167 <br />6 .1000 .16 .2667 26 .4333 36 .6000 46 .7667 56 .9333 <br />7 :1167 17. .2833 27 .4500 37 .6167 47 .7833 57 .9500 <br />8 .1333 18 -:3000 28 .4667 38 .6333 48 .8000 58 .9667 <br />9 .1500 19 .3167 29 .4833 39 .6500 49 .8167. 59 .9833 <br />10 .1667 11 20 .3333 11 30 1 .5000 11 40 .6667 11'50' 1 .8333 11 .60 11.0000 <br />- TABLE V. -Inches in Decimals of a Foot. <br />1-16 3-32. Y 3-16% 5-16 % '� % % ?� <br />.0052 .0078 ( .0104 .01.6 I .0208 .0260 I .0313 .0417 .0521 .0625 I .0729 <br />1 2 3 4 5 6 7 8 9 10 11 <br />.0833 .1667 . .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167 <br />