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K51 <br />31 <br />VIII <br />TABLE II. - Radii, Ordinates and Deflections. Chord- 100 ft. <br />Deg. <br />Radius <br />Ilid <br />Ord.' <br />Tan. <br />Dist. <br />Def. <br />Dist. <br />lief' <br />for <br />1 Ft. <br />Deg. <br />Radius <br />?lid. <br />Ord, <br />Taa <br />Dist. <br />Def. <br />Dist. <br />Def. <br />'Cr <br />1 Ft. <br />12 <br />ft. <br />It. <br />ft. <br />ft. <br />! <br />10 59' <br />it. <br />ft. <br />ft. <br />ft. <br />34° <br />0`10' <br />34377. <br />.036 <br />.1451 <br />.291 <br />0.05 <br />7' <br />819.0 <br />1.528 <br />G.105 <br />12.21 <br />2.i0 <br />20 <br />17189. <br />.073 <br />.291 <br />.592 <br />0.10 <br />20' <br />781.5 <br />1.600 <br />6.395 <br />12.79 <br />2.20 <br />30 <br />11459. <br />.109 <br />.436 <br />S73 <br />0.15 <br />130, <br />764.5 <br />1.637 <br />6.540 <br />13.05 <br />2.25 <br />40 <br />5594.4 <br />.145 <br />.5S2 <br />1.164 <br />0.20 <br />40 <br />747.9 <br />1.673 <br />6.655 <br />13.37 <br />2.30 <br />50 <br />6875.5 <br />.182 <br />.727 <br />1.454.0.25 <br />5° 50' <br />8 <br />716.8 <br />1.740 <br />6.970 <br />13.95 <br />2.40 <br />1 <br />5729.G <br />.218 <br />.573 <br />1.74:; <br />0.30 <br />20 <br />GS8.2 <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 />G74.7 <br />1.555 <br />7.411 <br />14.52 <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 />2.00 <br />30 <br />3819.5 <br />.327 <br />1.309 <br />2.615 <br />0.45 <br />9 <br />637.3 <br />1.965 <br />7.646 <br />15.69 <br />2.70 <br />40 <br />3437.9 <br />.30.1 <br />1.454 <br />2.909 <br />0.50 <br />20 <br />614.6 <br />2.037 <br />5.136 <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 />2864.9 <br />.430 <br />1.745 <br />3.490 <br />0.60 <br />40 <br />:193.4 <br />2.110 <br />5.426 <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 />.7,73.7 <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 <br />2.292 <br />9.150 <br />18.30 <br />3.15 <br />30 <br />2292.0 <br />.545 <br />2.181 <br />4.303 <br />0.75 <br />11 <br />52_1.7 <br />2.402 <br />9.585 <br />19.1G <br />3.30 <br />40 <br />214S.8 <br />.582 <br />2.327 <br />4.65-1 <br />O.go <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.G20 <br />10.45 <br />20.91 <br />3.60 <br />2 <br />1910.1 <br />.655 <br />2.618 <br />5.235 <br />0.90 <br />30 <br />.159.3 <br />2.73350 <br />10.S9 <br />21.77 <br />3.75 <br />10 <br />1509.6 <br />.691 <br />2.763 <br />5.526 <br />0.05 <br />13 <br />441.7 <br />2.539 <br />11.32 <br />22.6-1 <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 />6.103 <br />1.05 <br />14 . <br />410.3 <br />3.05S <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 />3.165 <br />12.62 <br />25.24 <br />-1.35 <br />50 <br />1495.0 <br />.536 <br />3.345 <br />6.659 <br />1.15 <br />l5 <br />3S3.1 <br />3.277 <br />13.05 <br />26.11 <br />4.50 <br />4 <br />1432.7 <br />.873 <br />3:490 <br />0.980 <br />1.20 <br />30 <br />370:8 <br />3.3S7 <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 />3.490 <br />13.92 <br />27.84 <br />4.80 <br />20 <br />1322.5 <br />.945 <br />3.715 <br />7.561 <br />1.30 <br />30. <br />348.5 <br />3:60G <br />14.35 <br />23.70 <br />4.95 <br />30 <br />1273.6 <br />.9S2 <br />3.926 <br />7.852 <br />1.35 <br />17 <br />338.3 <br />3.716 <br />14.75 <br />29.56 <br />5.10 <br />40 <br />1228:1 <br />1.01S <br />4.071 <br />8.143 <br />1.40 <br />18 <br />319.6 <br />8.935 <br />15.64 <br />31.29 <br />5.40 <br />50 <br />1185.8 <br />1.055 <br />4.217 <br />5.433 <br />1.45 <br />19 <br />302.9 <br />4.155 <br />16.51 <br />33.01 <br />5.70 <br />S <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 />6.60 <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 />15.22 <br />36.44 <br />G.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 />38:1G <br />6.60 <br />30 <br />1042.1 <br />1.200 <br />4.795 <br />9.596 <br />1.65 <br />23 <br />250.8 <br />5.035 <br />19.94 <br />39.87 <br />0.90 <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.OSS <br />10.18 <br />1.75 <br />25 <br />231.0 <br />5.476 <br />21.64 <br />43.28 <br />,1 .50 <br />6 <br />9.55.4 <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.SO <br />10 <br />929.G <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 />1.352 <br />5.524 <br />11.05 <br />1.90 <br />28 <br />206.7 <br />6.139 <br />24.19 <br />48.3S <br />8.40 <br />30 <br />851.9 <br />1.418 <br />5.GG9 <br />11.34 <br />1.95 <br />29 <br />199.7 <br />0.360 <br />25.64 <br />50.07 <br />8.70 <br />40 <br />559.9 <br />1.455 <br />5.514 <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 cora of length (C) is equal to .0012 C2 <br />multiplied by the middle ordinate taken from the above table. Thns, if it <br />desired to bond a 30 ft. rail to fit a 10 degree curve, its middle ordinate should <br />be .0012X90OX2.183 or 2.3G inches. <br />TABLE III. Deflections for Sub Chords for Short Radius Carves. <br />Degree <br />of <br />Curve <br />Radius <br />50 <br />sub chord , <br />f. = sin of z def. ang a <br />Length <br />of are <br />for 100 ft. <br />sin. l'def. ang. <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 Ft. <br />30° <br />193.18 <br />I° 5I'. <br />12 <br />2° 58' <br />3° 43' <br />]OI.Ij <br />320 <br />181.39. <br />10 59' <br />2° 25' <br />3° 10'3° <br />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 />360 <br />161.So <br />2° 13 <br />20 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 />146.39 <br />2°27' <br />2° 57` <br />3055' <br />4° 54' <br />IO2.o6 <br />420 <br />139.52 <br />20 34'30 <br />05 <br />4° 07' <br />5oos, <br />102.29 <br />44° <br />133.47 <br />2°41' <br />3° 13' <br />4°is, <br />5°22' <br />102.53 <br />46-0 <br />127.97 <br />2° 48' <br />3° 21' <br />4° 29' <br />50 g6' <br />102.76 <br />48° <br />122.92 <br />2° 55' <br />30 29' <br />4° 40' <br />5° 50' <br />103.00 <br />50° <br />118.31 <br />3° 02' <br />3° 38 <br />4° 51' <br />6004 1 <br />103.24 <br />520 <br />114.06 <br />3° 09' <br />3.° 46' <br />5° 02' <br />60 17' <br />103.54 <br />54 <br />110.31 <br />3° 16'3° <br />54' <br />S° 13' <br />6° 31' <br />103- 84 <br />560 <br />io6.5o <br />3°22' <br />4° 02' <br />50 23' <br />6° 44' <br />104.14 <br />58° <br />103.14 <br />30 29' <br />4° 10' <br />5° 34' <br />6° 57' <br />104.43 <br />6o° <br />100.00 <br />3° 35' <br />4° 18 <br />50 44' <br />7' 11' <br />104.72 <br />IX <br />l <br />CURVE YORINIULAS <br />T= R tan # I R= T cot. z I Chord def. =chords <br />T _ 5o tan 4 I 50 R <br />Sin. J D R = <br />50 Sin. Y D No. chords = I <br />R E= R ex. sec <br />5o tan % 'I <br />Sin. Tan. def. = z chord def. <br />ln.ID = T E=T tan <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. h'Iultiply the given distance by .01745 (dcf. for I° for i ft. <br />see Table IL), and divide given deflection by the product.. <br />Rule 2. 11lultipiy 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 T'RIAKGLES. Square the altitude, divide by twice the <br />base. Add quotient to base for hypotenuse. <br />Given Base Ioo,Alt. 10 -IO" -=200=.5. 100-{-.5=300.5 hyp. <br />Given Hyp. loo, Alt. 25.25 =200=3.125. 100-3.125=96.875=Base. <br />Error in first example, .002; 1n last, .045. <br />To find Tons of Rail in one mile of trach` multiply weight per yard <br />by 33, and divide by 7. . <br />. LEVELING. The correction for curvature and refraction, in feet <br />and decimals of feetis equal to 0.574d" -, 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 d„ d_ ds i etc• are the discrepancies Of Var10llS <br />results from the mean, and if Ed==the sum of the squares of these differ- <br />ences and n=the number of observations, then the probable error of the <br />mean= 7-d2 <br />SOLAR EPHE3iFRIS. Attention is Called to the Solar Ephemeris for <br />the current year, published by lieu tel fi Esser Co., and furnished free of <br />charge upon request, which is 3,h.59 in., with about 90 pages of data very <br />useful to the Surveyor; such as the adjustments cf 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 f ormulas; Natural and Logarithmic Functions; <br />and Logarithms of Numbers. <br />.T.- T1.r in T)rr.im�la of n. Degree. <br />1' <br />.0167 <br />11' <br />u.1833 <br />21' <br />.3500 <br />31' <br />5161 <br />41' 6833 <br />51' .6500 <br />2 <br />.0333 <br />12 <br />.2000 <br />22 <br />.3667 <br />^2 <br />.5333 <br />42 .7000 <br />5' .8333 <br />53 <br />3 <br />.0500 <br />13 <br />.2167 <br />23 <br />.3533 <br />33 <br />.5500 <br />43 7107 <br />54 <br />4 <br />.0667 <br />14 <br />.2333 <br />24 <br />.4000 <br />34 <br />.5667 <br />44 .'333 <br />' <br />.9000 <br />55 <br />5 <br />0833 <br />15 <br />.2500 <br />25 <br />.4107 <br />35 <br />.5,133 <br />45 .7"000 <br />.9167 <br />56 <br />fi <br />.1000 <br />10 <br />.2667 <br />26- <br />.4333 <br />36- <br />.60004C.. <br />.7067 <br />.9333 <br />57 '.9500 <br />7 <br />.1167 <br />17 <br />.2S33 <br />27 <br />.4500 <br />37 <br />.6167 <br />47 .7533 <br />58 <br />8 <br />.1333 <br />18 <br />.3000 <br />28 <br />.4667 <br />38 <br />.6333 <br />4s 5000 <br />.9667 <br />59 <br />9 <br />.1500 <br />19 <br />.3167 <br />29 <br />.4533 <br />39 <br />.6500 <br />• 49 SIG7 <br />.9833 <br />60 1.0000 <br />10 <br />116,67 <br />20 <br />.3333 <br />30 <br />.5000 <br />40 <br />.6667 <br />50 8333 <br />TABLE V. - <br />Inches lnDecimals Of a 1'00t. <br />1-16- <br />0052 <br />3-32 <br />.0078 <br />;•8 3-16 <br />.0104 .0156 <br />;y <br />.0208 <br />5-16 <br />.026;0 <br />.0313 <br />rs <br />.717 .0521 <br />is 'Yg <br />.06;25 .0729 <br />t4S33 <br />z <br />.]667 <br />.2500 .3333 <br />.4167 <br />.5000 <br />.5833 <br />.6667 .7500 <br />to 11 <br />.8333 .9167 <br />