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VIII ' <br />-'TABLE II.- Radii, Ordinates and Deflections. Chord =too ft. <br />Deg. <br />'Radius <br />I Mid. <br />Ord. <br />Tan. <br />Dist. <br />Def: <br />Dist. <br />Dem' ' <br />1 h t. <br />Deg. <br />gadius <br />Mid. <br />Ord. <br />Tan, <br />Dist. <br />Del. <br />Dist. <br />Def. ; <br />1r <br />1° <br />t. <br />ft. <br />it. <br />ft. <br />' <br />3° <br />ft, <br />ft. <br />ft, <br />ft. <br />1° <br />0 <10' <br />34377. <br />.036 <br />.145 <br />291 <br />0.05 <br />V <br />819.0 <br />1.525 <br />6.105 <br />12.21 <br />2.10 <br />20 <br />17189. <br />.073 <br />.291 <br />:552 <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.a"40 <br />13:03 <br />2.25'1.' <br />40 <br />8594.4 <br />.145 <br />.552 <br />1.161 <br />0.20 <br />40 <br />747.9 <br />1.673 <br />6.685 <br />13.37 <br />2.30 <br />.50 <br />0875.5 <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 />.573 <br />1.745 <br />0.30 <br />20 <br />658.2 <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 />14.52 <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 />1.592 <br />7.556 <br />15.11 <br />2.G0;. <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 />7.546 <br />15.69 <br />2.70 <br />40 <br />3437.9 <br />.364 <br />1.45.1 <br />2.909 <br />0.50' <br />20 <br />614.6 <br />2.037 <br />8.136 <br />16.27.2.50 <br />110.11 <br />50 <br />3125.4 <br />.400 <br />1.000 <br />3.200 <br />0.55 <br />30 <br />G03.S <br />2.074 <br />5.251 <br />16.56 <br />2.85 <br />2 <br />2864.9 <br />.436 <br />1.74. <br />3.490 <br />0.00 <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 />3.751 <br />0.65 <br />10 <br />573.7 <br />2.153 <br />5.716 <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 />9.1,50 <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 />9.555 <br />19.10 <br />3.30 <br />40 <br />2145.8 <br />.582 <br />2.327 <br />4.654 <br />O.SO <br />30 <br />499.1 <br />2.511 <br />10.02 <br />20.01 <br />3.45 <br />50 <br />2022.4 <br />.618 <br />2.472 <br />4.945 <br />0.85 <br />12 <br />475.3 <br />2.620 <br />10.45 <br />20.91 <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 />10.59 <br />:;1.77 <br />3.75 <br />10 <br />1809.6 <br />.691 <br />2.763 <br />5.5261 <br />0.95 <br />13 <br />441.7 <br />2.539 <br />11.32 <br />^'2.64 <br />3.90 <br />20 <br />1719.1 <br />.727 <br />2.008 <br />5.817 <br />1.00 <br />30 <br />425.4 <br />2.949 <br />11.75 <br />3.51 <br />4.05 . <br />30, <br />.1637.3 <br />.764 <br />3.054 <br />6.10S <br />1.05 <br />14 <br />410.3 <br />3.05S <br />12.13 <br />2.1,37 <br />4.20 <br />40' <br />1.1562.9 <br />.5003.199 <br />G. 398 <br />1.10 <br />30 <br />366.2 <br />3.165 <br />12.62 <br />25.24 <br />4.35 <br />50 <br />1495.0 <br />..836 <br />3.345 <br />6.659 <br />1.15 <br />15 <br />383.1 <br />3.277 <br />13.05 <br />26.11 <br />4.50 <br />4 <br />1432.7 <br />.573 <br />3.490 <br />6.950 <br />1.20 <br />30 <br />370.5 <br />3.357 <br />13.49 <br />26.97 <br />-1.65 <br />10 <br />1375.4 <br />.009 <br />3.635 <br />7.271 <br />1.25 <br />1G <br />359.3 <br />3.496 <br />13.92 <br />27.84 <br />4.50 <br />20 <br />1332.5 <br />.945 <br />3.715 <br />7. 56 1 <br />1.30 <br />30 <br />345.5 <br />3.606 <br />14.35 <br />28.70 <br />4.05 <br />30 <br />1273.6 <br />.982 <br />3.926 <br />7.552 <br />1.35 <br />17 <br />33S.3 <br />3.716 <br />14.7S' <br />29.50 <br />5.10 <br />40 <br />1228.1 <br />1.015 <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 />5.433 <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 />257.9 <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 />15.22 <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 />G.60 <br />30 <br />1042.1 <br />1.200 <br />4.798 <br />9.596 <br />1.65' <br />23 <br />2,50.8 <br />5.035 <br />19.94 <br />39.57 <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 />41.55 <br />7.20 <br />50 <br />952.6 <br />1.273 <br />5.085 <br />10.15 <br />1.75 <br />25 <br />231.0 <br />5.476 <br />21.64 <br />43.28 <br />7.50 <br />G <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 />5.91S <br />23.35 <br />46.69 <br />5.10 <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 />43.38 <br />5.40 <br />30 <br />SS1.9 <br />1.418 <br />5.669 <br />11.34 <br />1.95 <br />29 <br />109.7 <br />6.360 <br />25.04 <br />50.07 <br />8.70 <br />40 1 <br />859.9 <br />1.455 <br />5.514 <br />11.63 <br />2.00 <br />30 <br />103.2 <br />6.583 <br />25.85 <br />51.76 <br />9.00 <br />The middle ordinate in inches for any cord of length (C) is equal to .0012 C2 <br />multiplied by the middle ordinate taken from the above `able. ''1'hns, if it <br />desired to bend &30 ft. rail to fit a 10 degree curse, its middle ordinate should <br />be .0012X900X2.183 or 2.3G inches. <br />. TABLE III. 'Deflections for Sub Chords for Short Radius Curves. <br />Degree <br />of <br />Curve <br />It 50us <br />/1J sub chord = <br />R <br />sin of s def. angle <br />Length <br />of arc <br />for 100 ft. <br />sin. i def. ang. <br />12.5 Ft. <br />15 Ft.. <br />20 Ft. <br />25 Ft. <br />30° <br />• 193.15 <br />1° <br />51' <br />2° <br />17' <br />2' <br />58' <br />3° <br />4J' <br />101.15 <br />320 <br />181.J9 <br />1° <br />59' <br />2° <br />25' <br />3° <br />Io' <br />3° <br />58' <br />101.33 <br />34° <br />171.01 <br />2° <br />o6' <br />2° <br />33' <br />3° <br />2I' <br />4° <br />I2' <br />101.43 <br />36° <br />161'. 8o <br />2° <br />13' <br />2°:}f' <br />5 <br />3° <br />3J' <br />4° <br />26' <br />101.66 <br />380 <br />153.58 <br />2°20' <br />.7500 <br />s°49' <br />.9167 <br />3°44' <br />}°40' <br />1.01.85 <br />40° <br />146.19 <br />2°27' <br />4G <br />2°57' <br />56 <br />3°55' <br />7 <br />4'54' <br />17 <br />I62.o6 <br />42° <br />139.52 <br />2 <br />34' <br />3° <br />05' <br />4° <br />07' <br />5° <br />08' <br />102.29 <br />'44° <br />133.47 <br />°° <br />2 <br />41' <br />3° <br />13' <br />40 <br />18' <br />5° <br />22' <br />102.53 <br />46° <br />127.97 <br />2°48' <br />.4533 <br />3°21' <br />.6500 <br />4°29'• <br />.5167 <br />5°36' <br />.9533 <br />102.76 <br />.4R° <br />122.92 <br />z° <br />55' <br />3° <br />29' <br />4° <br />40' <br />5° <br />50' <br />103.00 <br />50° <br />118.31 <br />3° <br />02' <br />3° <br />38' <br />4° <br />51' <br />6° <br />04' <br />103.24 <br />52° <br />114.06 <br />3° <br />09' <br />3° <br />46' <br />5° <br />oz' <br />6° <br />17' <br />103.54 <br />54° <br />110.11 <br />3° <br />16' <br />3° <br />54' <br />90 <br />13 <br />.60311 <br />103.84 <br />560 <br />1o6.50 <br />3° <br />22 <br />4002 <br />, <br />5° <br />23' <br />6°47' <br />104.14 <br />58° <br />103.14 <br />3° <br />29' <br />4°10' <br />S°34' <br />6°57' <br />I04.43 <br />60° <br />100.00 <br />3°35' <br />4°18 <br />5°44' <br />7°11' <br />104.72 <br />IX <br />- CURVE FORTAIL'LAS - <br />T = R tan � I R = T cot.: I Chord def. = chorda <br />T _ 5o tan zi I 50 R <br />Sin. J. D R = <br />5o Sin. D I ". . <br />Sin. � D = _ No. chords = - . <br />R E= R ex. sec 1 I D <br />2 I <br />Sin. D = 50 tan I E'-_ T tan J I Tan. def. = a chord def. <br />The square of anydistance, divided by twice the radius, will equal <br />the distance from tangent Lo curse, very nearly. <br />To find angle fora given distance and deflection. <br />Rule 1. filultiply the given distance by .ot745 (def. for I° for I ft. • . <br />see Table IL), 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 ANGLE TRIANGLES. 'Square the altitude, divide by twice the <br />base. Add quotient to base for hypotenuse. <br />Given Base Ioo,Alt. 10.102_200=.5. Ioo+.5=Ioo.5 hyp• <br />Given Hyp. loo, Alt.25 252_200=3.I25_ foo-3.r25=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 0.5748, where d is the distance in miles. <br />The correction for curvature alone is closely, ;d-. The combined cor- <br />rection is negative. <br />PRosADLE ERROR. If d„ d., da, etc. are the discrepancies of various' <br />results from the mean, and if 682=the sum of the squares -of these differ- <br />ences and n=the number of observations, then the probable error of the <br />a <br />mean= + 0.6745-lIn_(n-1) \ <br />SOLAR EPHEMERIS. 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 3Jx51 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 frofn observations on the sun and Polaris; stadia meas <br />urements; magnetic declination; arithmetic constants; English and Metric <br />conversions; trigonometric f ormulas; Natural andLogarithmic Functions; <br />and Logarithms of Numbers. <br />TABLE I4. - il2linutes in Decimals of a Degree. <br />V <br />.0167 <br />11' <br />.1833 <br />21' <br />.3500 <br />3l' <br />.5167 <br />41' <br />f,S33 <br />bl' <br />5500 <br />2 <br />.0333 <br />12 <br />.2000 <br />22 <br />.3667 <br />32 <br />.5333 <br />42 <br />.7000 <br />52 <br />.'667 <br />:4 <br />.0500 <br />13 <br />.2167 <br />23 <br />.2533 <br />33 <br />.5500 <br />43.7167 <br />S 9 <br />53 <br />.5833 <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 />.5S33 <br />45 <br />.7500 <br />55 <br />.9167 <br />6.1000 <br />1G . <br />26 <br />.4333 <br />36 <br />.6000 <br />4G <br />.7667 <br />56 <br />.9333 <br />7 <br />.1167 <br />17 <br />.2667 <br />.2533 <br />27 <br />.4500 <br />37 <br />.6167 <br />47 <br />.7533 <br />57 <br />'.9500 <br />S <br />1333 <br />18 <br />.3000 <br />28 <br />.4667 <br />38 <br />.6333 <br />48 <br />.5000 <br />58 <br />.9667 <br />9 <br />.1500 <br />19 <br />.3167 <br />29 <br />.4533 <br />39 <br />.6500 <br />49 <br />.5167 <br />59 <br />.9533 <br />10 <br />.1667 <br />20 <br />1 .3333 1130 <br />1 .5000 11 <br />40 <br />1 .6667 <br />1 59 <br />.8333 <br />60 <br />1 1.0000 <br />x" <br />TABLE V. - <br />Inches in Decimals of a Foot. <br />1-]G <br />3-32 <br />3-1G <br />is <br />5-1G <br />y§ <br />i3 is <br />sa <br />.0052 <br />.0075 <br />.61104 <br />.015E <br />.0205 <br />.020:0 <br />.(131^, <br />.0417 .0521 <br />OG25 <br />_.0729 <br />1 <br />2 <br />3 <br />4 <br />5 <br />fi <br />7 <br />S 9 <br />1303 <br />0 <br />11 <br />.0533 <br />.IGG7 <br />2500 <br />.3333 <br />.4167 <br />.5000 <br />.5833 <br />..6607 .7500 <br />.5333 <br />.9167 <br />x" <br />