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VIII <br />TABLE Il. - Radii, Ordinates and Deflections. Chord =100 ft. <br />Deg. <br />Radius <br />Mid. <br />Ord. <br />Tan. <br />Diss. <br />Det.. <br />Dist. <br />Def' <br />for <br />I Ft. <br />Deg.: ;Radius <br />20 Ft.* <br />fid. <br />Ord. <br />Tan. <br />Dist. <br />Def. <br />Dist. <br />Def. <br />for <br />1 Ft. <br />^° 17' <br />ft. <br />ft. <br />ft. <br />ft. <br />? <br />1° 59' <br />ft. , <br />ft. <br />it. <br />ft, <br />34° <br />0'10' <br />34377. <br />.036 <br />.145 <br />,291 <br />0.05 <br />7° <br />519.0 <br />1.525 <br />' 6.105 <br />12.21 <br />2.I0 <br />20 <br />17189. <br />.073 <br />.291 <br />.582 <br />0.10 <br />20' <br />751.8 <br />1.600 <br />6,393 <br />12.79 <br />2.20 <br />30 <br />11459. <br />.109 <br />.436 <br />S73 <br />0.15 <br />30 <br />764.5 <br />1.637 <br />6.540 <br />13.03 <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 />6.61;5 <br />13.'d7 <br />2.30 <br />50 <br />GS75.5 <br />.182 <br />.727 <br />1.454 <br />0.25 <br />8 <br />716.8 <br />1.746 <br />6.076 <br />13.95 <br />2.40 <br />1 <br />5729.6 <br />.213 <br />.873 <br />1.745 <br />0.30 <br />20 <br />GS3.2 <br />1.819 <br />7.26E <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 />601.7 <br />1.592 <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 />G37.3 <br />1.965 <br />7.84G <br />15.69 <br />2.70 <br />40 <br />3437.9 <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 />8.251 <br />16.56 <br />2.85 <br />2. <br />28(A.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 />8.71G <br />17.43 <br />3.00 <br />20 <br />2.155.7 <br />.509 <br />2.03G <br />4.072 <br />0:70 <br />30 <br />546.4 <br />2.292 <br />9.350 <br />18.30 <br />3.15 <br />30 <br />2292.0 <br />.545 <br />2.151 <br />4.363 <br />0.75 <br />11 <br />521.7 <br />2.402 <br />9.585 <br />19.1G <br />3.30 <br />40 <br />2148.8 <br />.5S2 <br />2.327 <br />4.654 <br />0.80 <br />30 <br />499.1 <br />2.511 <br />10.02 <br />20.01 <br />3.45 <br />50 <br />2022.4 <br />.6118 <br />2.472 <br />4.945 <br />0.85 <br />39. <br />478.3 <br />2.6320 <br />10.45 <br />20.91 <br />3.60 <br />3 <br />1910.1 <br />.655 <br />2.G1S <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 />^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 />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 />3.055 <br />12.18 <br />24.27 <br />4.20 <br />40 <br />1562.9 <br />.800 <br />3.109 <br />6.398 <br />1.10 <br />30 <br />396.2 <br />3.165 <br />12.62 <br />25.24 <br />4.35 <br />50 <br />1495.0 <br />.836 <br />3.345 <br />G.6SO <br />1.15 <br />15 <br />353.1 <br />3.277 <br />13.05 <br />26.11 <br />4.50 <br />4 <br />1432.7 <br />.873 <br />3.400 <br />6.980 <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 />3.400 <br />13.92 <br />27.54 <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 />3.606 <br />14.35 <br />23.70 <br />4.95 <br />30 <br />1273.6 <br />:982 <br />3.926 <br />7.552 <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 />1.01S <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 />2S7.9 <br />4.374 <br />17.37 <br />34.73 <br />6.00 <br />10 <br />1109.3 <br />1.127 <br />4.507 <br />0.014 <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 />9.30:; <br />1.60 <br />22 <br />262.0 <br />4.814 <br />19.OS <br />38.1G <br />6.60 <br />30 <br />1042.1 <br />1.200 <br />4.798 <br />9.596 <br />1.65 <br />23 <br />250.5 <br />5.035 <br />19.94 <br />39.57 <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 />41.53 <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 />43.25 <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 />7.50 <br />10 <br />929:6 <br />1.346 <br />5.379 <br />10.7G <br />1.85 <br />27 <br />214.2 <br />5.918 <br />23.35 <br />46.60 <br />S.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 />S.40 <br />30 <br />881.9 <br />1.4135.669 <br />11.34 <br />1.95 <br />29 <br />199.7 <br />6.360 <br />25.04 <br />50.07 <br />5.70 <br />40 <br />859.9 <br />1,455 <br />5.814 <br />11.63 <br />2.00 <br />30 <br />193.2 <br />(1.533 <br />25.83 <br />51.76 <br />9.00 <br />The middle ordinate in inches for any cord of length (C) is equal to0013 C2 <br />multiplied by the middle ordinate talion from the above table. Thus, if it <br />desired to hend a.30 ft. rail to fit a 10 degree curve, its middle ordinate should <br />be .0012X90OX2.183 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 />M sub chord _ <br />R = sin of i def. angle <br />Length <br />of arc <br />for 1C0 ft. <br />- <br />sin.'s def. ang. <br />12,5 Ft. <br />IS Ft. <br />20 Ft.* <br />25 Ft. <br />30° <br />193. iS <br />1° 51' <br />^° 17' <br />2° 58' <br />3° 43' <br />101.15 <br />32° <br />131.39 <br />1° 59' <br />2° 25' <br />3° lo' <br />3° 58' <br />101.33 <br />34° <br />171.01 <br />2°o6' <br />2°33' <br />3°3I' <br />Y° I2' <br />101.48 <br />36° <br />161.80 <br />2° 13' <br />2° 41' <br />3° 33' <br />4° 26' <br />101.66 <br />38° <br />153.58 <br />2° 20' <br />2° 49' <br />3° 44' <br />4° 40' <br />101.85 <br />40° <br />146.19 <br />2°27' <br />2°51 <br />3°55' <br />4° 54' <br />IO2.o6 <br />42' <br />139.52 <br />2° 341 <br />3° o5' <br />4 07' <br />5'08' <br />102.29 <br />44° <br />123.47 <br />2° 41' <br />.3 I3' <br />4° 18' <br />5° 22' <br />102.53 <br />.4333 <br />127.97 <br />2° 48' <br />3° 21' <br />4° 29 <br />5° 36' <br />1o2.76 <br />4S° <br />122.92 <br />2° 55' <br />3° 29' <br />4° 40' <br />;° 50' <br />103. co <br />5o° <br />IIS. 31 <br />3° 02' <br />3° 3S' <br />4° 51' <br />6° ea' <br />103.2_[ <br />52° <br />114.x6 <br />3° 09' <br />3° 46' <br />5° oa' <br />6° 17' <br />1103.54 <br />54° <br />110.11 <br />3° 16' <br />3° 5T' <br />S° 13' <br />6° 31' <br />103.84 <br />56° <br />Io6.5o <br />`i4 <br />3°22' <br />4'02' <br />5°23' <br />6°44' <br />104,14 <br />58° <br />10 <br />3° 29' <br />4° io' <br />S° 34' <br />6° 57' <br />Io4-43 <br />6o° <br />100.00 <br />3° 35' <br />4° 18' <br />5° 44' <br />7° If' <br />104..72 <br />IX ' <br />CURVE FOR'THULAS <br />T= R tan +4 I R= T cot. I chords <br />50 tan I _ Chord def. R <br />T 'Sin. +> D R 50 <br />50 D I <br />Sin. � D = ' Sin. 'No. chords = - <br />R E= R ex. sec. 1 I D <br />Sin. D = 5° tT ' I E = T tan 41 'Tan. def. = s 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. l'fultiply the given distance by .01745 (def. for r° for I 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 TRIANGLE'S. Square the altitude, divide by twice the <br />Iiase. Add quotient to base for hypotenuse. <br />Given Base-ioo,Alt.10.102+200=.5. IOO+.5=100.5 hyp. <br />Given Hyp. 3oo,Alt. 25.252=200=3.125.1oo-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 1i, 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, id 2. The combined cor- <br />rection is negative. <br />PROVABLE ERROR. If dt, d„ ds, etc. are the discrepancies of various <br />results from the mean, and if Y'd2=the sum of the squares of these differ- <br />ences and r -=the number of observations, then the probable error of the <br />mean= ± 0.63745 Ede <br />7 n (n-1) <br />SOLAR Erfi riIER1s. Attention is called to the Solar Ephemeris for <br />the current year, published by heuffel'& Esser Co., and furnished free of <br />charge upon request, which is 3}x5H 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 declinatio-n; arithmetic constants; English and 1lietric <br />conversions; trigonometric formulas; Natural and Logarithmic Functions; <br />and Logarithms of 2\ --umbers. <br />T.1BLE W. - i1inutes in Decimals of a Degree. <br />1' <br />0167 <br />11' <br />1833 1121' <br />3500 <br />131 <br />5167 <br />41' <br />6833 <br />.51' <br />5500 <br />2 <br />i2 58 % <br />12 <br />U0:i3 <br />'» <br />3667 <br />3? <br />5333 <br />42 <br />.7000 <br />52 <br />.1667 <br />3 <br />.038 <br />13 <br />.2000 <br />,2167 <br />2:1 <br />.3333 <br />33 <br />.5500 <br />43 <br />.7167 <br />53 <br />SS33 <br />4 <br />.0500 <br />11 <br />.2333 <br />24 <br />.4000 <br />"4 <br />.5"67 <br />41 <br />.7333 <br />54 <br />9000 <br />6 <br />.0667 <br />15 <br />2500 <br />25 <br />.4167 <br />35 <br />.5333 <br />463 <br />7500 <br />55 <br />.9167 <br />6 <br />.0533 <br />i <br />16 <br />.2667 <br />2G <br />.4333 <br />33 <br />.6000 <br />46 <br />.7667 <br />56 <br />.9333 <br />7 <br />.1000 <br />1.7 <br />.2533 <br />27 <br />4500 <br />31 <br />G167 <br />47 <br />.7 33 <br />57 <br />9500 <br />8 <br />.1167 <br />18 <br />.3000 <br />28 <br />.4667 <br />38 <br />.0333 <br />48 <br />.8000 <br />58 <br />.966'7 <br />9 <br />,1333 <br />.1500 <br />19 <br />.3167 <br />19 <br />.4533 <br />39 <br />.6500 <br />49 <br />1 <br />59 <br />.9833 <br />10 <br />.1667 <br />20 <br />.3333 <br />30 <br />.5000 i <br />40 <br />W7 <br />50 <br />5333 <br />co <br />1.0000 <br />TABLE V. - <br />Inches in Decimals of a Foot. <br />1-163 <br />3-32 <br />!§ <br />3 -IG <br />I <br />5-163 <br />ie <br />i2 58 % <br />U0:i3 <br />.0075 <br />.0101 <br />.0156 <br />.0208 <br />.0.630 <br />.0313 <br />.0117 . Ci.521 <br />.0625 <br />.0_720 <br />1 <br />2 <br />34 <br />5 <br />6 <br />7 <br />S 9 <br />i0 <br />11 <br />.0833 <br />.1667 <br />.25pD <br />3333 <br />.4167 <br />.5000 <br />.5833 <br />.6Efi 7510 <br />.5333 <br />.9167 <br />