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F-11 <br />;II ;I <br />VIII <br />•TABLE IL -Radii, Ordinates and Deflections. Chord=100 it. <br />Deg. <br />Radius <br />Mid. <br />Ord. <br />Tan. <br />Dist.. <br />Def. <br />Dist. <br />Def <br />I for <br />1 or <br />Deb. <br />Radius <br />Mid. <br />Ord. <br />Tan <br />Dist. <br />Def. <br />Dist. <br />for <br />1 r t. <br />2° 17, <br />ft. <br />It. <br />ft. <br />ft. <br />181.39 <br />i° J9' <br />ft. <br />ft. <br />it. <br />ft. <br />34° <br />0°10' <br />34377. <br />.036 <br />.145.291 <br />4° 12' <br />0.05 <br />7- <br />819.0 <br />1.525 <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 />747.0 <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 />71G.8 <br />1.740 <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 />G74.7 <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 />1.592 <br />7.556 <br />15.11 <br />2.60 <br />30 <br />3810.8 <br />.327 <br />1.309 <br />2.618 <br />0.45 <br />9 <br />G37.3 <br />1.965 <br />7.846 <br />15.69 <br />2.70 <br />40 <br />3437.0 <br />.364 <br />1.454 <br />2.009 <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 />3 <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 />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 />9.150 <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 />50 <br />2022.4 <br />.618 <br />2.472 <br />4.945 <br />0.85 <br />12 <br />473.3 <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 />10.89 <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 />1710.1 <br />.727 <br />2.90S <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 />1495.0.836 <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 />d <br />1432.7 <br />.873 <br />3.490 <br />6.980 <br />1.20 <br />30 <br />370_8 <br />3.357 <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 />1G <br />359.3 <br />3.49G <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 />14.3.5 <br />28.70 <br />4.95 <br />301273.6 <br />.982 <br />3.926 <br />7.802 <br />1.3:, <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 />31.20 <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 />B <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 />30.87 <br />G.90 <br />40 <br />1011.5 <br />1.237 <br />4.943 <br />9.$86 <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 />.5.688 <br />10.18 <br />1.75 <br />25 <br />231.0 <br />5.476 <br />21.64 <br />43.28.7.50 <br />B <br />10 <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 />20 <br />929.6 <br />905.1 <br />1.346 <br />1.382 <br />5.379 <br />5.524 <br />10.76 <br />11.05 <br />1.85 <br />1.90 <br />27 <br />28 <br />214.2 <br />206.7 <br />5.918 <br />6.139 <br />23.35 <br />24.19 <br />46.69 <br />48:38 <br />8.10 <br />8.40 <br />30 <br />881.9 <br />1.418 <br />5.GG9 <br />11.34 <br />1.95 <br />29 <br />199.7 <br />6.360 <br />2.5.04 <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 />25.83 <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 />of <br />Curve <br />Radius <br />50 <br />A sub chord = sin of 1 def. angle <br />R <br />ength <br />of arc <br />for 100 ft. <br />sin. z def. ang.. <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 Ft. <br />30°. <br />193.13 <br />1°51' <br />2° 17, <br />2° 58' <br />3' 43' <br />IOI.15 <br />32° <br />181.39 <br />i° J9' <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 />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. i9 <br />2° 27' <br />20 57 <br />3° 55 <br />40 54' <br />IO2.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° 22' <br />102.53 <br />460 <br />127.97 <br />2° 48' <br />3° 21' <br />4° 29' <br />5° 36' <br />102.76 <br />48° <br />122.92 <br />2° 55' <br />3° 29' <br />40 40' <br />5° 50' <br />103.00 <br />50° <br />118.31 <br />3° 02 <br />3° 38 <br />4° 51' <br />6° 04' <br />103.24. <br />52° <br />114.o6 <br />300 9' <br />3° 46' <br />5° O2' <br />6° 17' <br />103.54 <br />540 <br />IIO.II <br />3° 16' <br />3° 54' <br />S° 13, <br />6° 31' <br />I03.84 <br />56° <br />1o6.5o <br />3°22' <br />4° 02 <br />5° 23' <br />6° 44' <br />104.14 <br />580 <br />103.14 <br />3°29' <br />4°10' <br />S° 34 <br />6°57' <br />I04.43 <br />6o° <br />100.00 <br />3035 <br />4° 18' <br />1 50 44' <br />1 7° II' <br />104.72 <br />CURVE FORMULAS <br />T= R tan k h R= T cot. I chord' <br />_ 5o tan i I 2 Chord def. = R <br />T Sin. J D R = 50 <br />Sin. z <br />3 D <br />Sin. # D =''-0 ' No. chords = <br />R E =Rex. sec D. <br />; I <br />Sin. D = 50 tan $ I E = T tan I I Tan. def. = 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 .01743 (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 .oi745, 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 zoo, Alt. Io.lO2-'200=.5. 100-x-.5=IOO.5 hyp. <br />Given Hyp. ioo, Alt. 25.252=200=3.125: 100-3.125=96.875=13ase. <br />Error 1n first example, .00r, In last, .045• <br />To find Tons of Rail in one mile of track: multiply weight per yard, <br />by II, and divide by 7. <br />LEVELING. The correction for curvature and refraction, in .feet <br />and decimals of feet is equal to 0.574 d2, where d is the distance in miles. <br />The correction for curvature alone is closely, 302. The combined cor- <br />rection is negative. <br />PROBABLE ERROR. If d, , d-, ds, etc. are the discrepancies of various <br />results from the mean, and if 10=the sum of the squares of these differ- <br />ences and n=the number of observation -s; then the probable error of the <br />mean= ± Xd' <br />0.6745 <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 311x58 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 from observations on the sun and Polaris; stadia meas- <br />urements; magnetic declination; arithmetic constants; English and Metric <br />conversions; trigonometric formulas; Natural andLogarithmic Functions; <br />and Logarithms of Numbers. <br />TABLE IV. - Minutes in Decimals of a Degree. <br />1' <br />.0167 <br />11' <br />1833 <br />2V <br />.3500 <br />31' <br />.5167 <br />41' <br />.69.43 <br />51; <br />.8500 <br />2.0333 <br />Y2 % <br />12 <br />2000 <br />22 <br />.3667 <br />32 <br />.5333 <br />42 <br />.7000 <br />52; <br />5667 <br />3 <br />.0500 <br />13 <br />.2167 <br />23 <br />.3833 <br />33 <br />.5500 <br />43.. <br />.7167 <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 <br />.1000 <br />16 <br />,2667 <br />16 <br />.4333 <br />30 <br />.6000 <br />46 <br />.7667 <br />56 <br />.9333 <br />7 <br />.1167 <br />17 <br />.2533 <br />27 <br />.4500 <br />37 <br />.6167 <br />47 <br />.7933 <br />57 <br />.9500 <br />8 <br />.1333 <br />18 <br />.3000 <br />28 <br />.4667 <br />38 <br />.0333 <br />48 <br />.5000 <br />58 <br />.9667 <br />9 <br />.1590 <br />19 <br />.3167 <br />29 <br />.4833 <br />30 <br />.6500 <br />49 <br />.8167 <br />59 <br />.9833 <br />10 <br />.1667 <br />20 <br />.3333 <br />30 <br />.5000 <br />40 <br />.GG67 <br />50 <br />.5333 <br />c6 <br />1.0000 <br />TABLF. V. - <br />Inches in Decimals of a Foot. <br />1-16 <br />3-32 <br />%' <br />3-16 <br />Y4 <br />5-16H.5833 <br />Y2 % <br />31 <br />/s <br />.0052 <br />.0078 <br />.0104 <br />.0156 <br />.0205 <br />.0260.0117 <br />.0521 <br />.0625 <br />.0729 <br />1 <br />2 <br />3 <br />h <br />5 <br />68 <br />9 <br />10 <br />11 <br />.0833 <br />.1667 <br />.2300 <br />.3333 <br />.4167 <br />.5000 <br />.6667 .7500 <br />.8333 <br />.9167 <br />