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VIII <br />TA13LU IL - Radii, Ordinates and Deflections. Chord =100 ft.rX <br />'CURVE FORMULAS <br />Deg. <br />Radius <br />Mid. <br />Ord, <br />Tea. <br />Diet. <br />DcI. <br />Dist. <br />Def r' <br />1 F� <br />Deg. <br />Rad us <br />Mid. <br />Ord. <br />Tas <br />Diet, <br />Def. <br />Dist. <br />Dai' <br />1 Ft. <br />2° 58' <br />t. <br />ft. <br />32° <br />181.39 <br />1° 59' <br />2° 25' <br />t, <br />ft. <br />ft. <br />ft. <br />171.01 <br />0'10' <br />34377. <br />.036 <br />.145 <br />.291 <br />0.05 <br />7° <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 <br />11459. <br />.1U9 <br />.436 <br />.873 <br />0.15 <br />30 <br />704.5 <br />1.637 <br />6.540 <br />13.08 <br />2.25 <br />40 <br />859-t.4 <br />.145 <br />.582 <br />1.164 <br />0.20 <br />40 <br />747.9 <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 />716.8 <br />1.746 <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.L0 <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 />1361.7 <br />1.892 <br />7.556 <br />15.11 <br />2.60 <br />30 <br />3810.8 <br />.327 <br />1.300 <br />2.618 <br />0.45 <br />9 <br />637.3 <br />1.065 <br />7.846'15.69 <br />2.70 <br />40. <br />3137.9 <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 />8.281 <br />16.56 <br />2.85 <br />2 <br />28644.9 <br />.436 <br />1.74.5 <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 />.5092.036 <br />4.0720.70 <br />30 <br />516.4 <br />2.292 <br />0.150 <br />18.30 <br />3.75 <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 />0.585 <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 />478.3 <br />2.620 <br />10.45 <br />20.91 <br />3.60 <br />9 <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 />1S09.6 <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 />4.0.5 <br />30 <br />1037.3 <br />.704 <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 />6.689 <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 />6.950 <br />1.20 <br />30 <br />370.8 <br />3.387 <br />13.49 <br />26.97 <br />4.65 <br />40 <br />'1375.4 <br />.909 <br />3.635 <br />7.271 <br />1.25 <br />16 <br />359.3 <br />3.496 <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 />14.35 <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 />16.64 <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 />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.•} <br />.594 <br />18.22 <br />36144 <br />6..30 <br />20 <br />1074.7 <br />1.164 <br />4.653 <br />9.305 <br />1.60 <br />ltd <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 />20.79 <br />41.58 <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 />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 />7.80 <br />10 <br />929.6 <br />1.346 <br />5.379 <br />10.76 <br />1.85 <br />27 <br />214.2.918 <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 />.139 <br />24.19 <br />48.38 <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 />103.2 <br />6.583 <br />25.88 <br />51.76 <br />9.00 <br />Tho middle ordinate in inches for any cord of length f0) 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 .0012X90OX2.183 or 2.36 inches. <br />TABLE TIL Deflections for Sub Chords for Short Radius Curves. <br />Degree <br />of <br />Curve <br />Radius <br />50 <br />sin:9 cid.ang. <br />34 sub chord <br />R = sin of i def. angle <br />h <br />of arc <br />for 100 ft. <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 Ft. <br />30° <br />193. IS <br />I° 51' <br />2°17' <br />2° 58' <br />3°43' <br />101.15 <br />32° <br />181.39 <br />1° 59' <br />2° 25' <br />3° l0' <br />3° 58' <br />for .-33 <br />34° <br />171.01 <br />2° 06' <br />2° 33' <br />3° 21' <br />4° 12' <br />I01.48 <br />36° <br />161.8o <br />2° 13' <br />2° 41' <br />3° 33' <br />4° 26' <br />lot .6G <br />380 <br />153•.58 <br />2° 20' <br />2° 49' <br />3° X14' <br />4° 40' <br />Io1.8i <br />400 <br />146.19 <br />2°27' <br />2°S7' <br />3°55' <br />4° 54' <br />102.o6 <br />42° <br />139.52 <br />2034' <br />3° 05' <br />4° 07' <br />S° 08 <br />102.29 <br />44° <br />133-47 <br />2°'41 I <br />3° r3' <br />4° 18'. <br />g° 22' <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 />2° 55' <br />3° 29' <br />4° 40' <br />S° 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 />3° 09' <br />3° 46' <br />5° 02' <br />6° 17' <br />103.54 <br />'S4°110.11 <br />.8000 <br />3° 16' <br />3° 54' <br />5° 13' <br />6° 31' <br />103.84 <br />56° <br />io6.50 <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 />5° 34 <br />6° 57 <br />104.43 <br />60° <br />100.06 <br />3° 35' <br />4° 18' <br />50 44' <br />7° 11' <br />I 104.72 <br />T= R tan i 1 R= T cot. I chords <br />T = 5o tan 2 I Chord def.. _ <br />Sin. 2'' D 50 It <br />R - 3 <br />Sin. ' 50 <br />2 Sin. 2 D <br />D = No. chords = 1 <br />T. E = R ex. sec I. D <br />Sin. 'a D = 5o tan I I' E = T�tan ; 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 1. Multiply the given distance by .01745 (def. for ]° 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 />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the <br />base. Add quotient to base for hypotenuse. <br />Given Base loo, Alt. 10.102_200=.5. 100d-.5=100.5 hyp. <br />Given Hyp. 100, Alt. 25.252=200=3.125. 100-3.125=o6.875 =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 11, 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, 3d2. The combined cor- <br />rection is negative. <br />PRO13ABLE ERROR. If d1,d2, da, etc. are the discrepancies of various <br />results from the mean, and if V2=the'sum of the squares of these differ- <br />ences and n=the number of observations, then the probable Error of the <br />mean =F,d 2 <br />10.67453 ,1(n-]) <br />SOLAR EPHEMER1s. 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, 3x6 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 />11 <br />.0167 <br />IV <br />.1833 <br />211 <br />.3500 <br />31' <br />.5167 <br />411 <br />.6833 <br />51' <br />.8500 <br />.0333 <br />12 <br />.2000 <br />22 <br />.3667 <br />32 <br />.5333 <br />42 <br />.7000 <br />52 <br />.8667 <br />3 <br />.0500 <br />13 <br />.2167 <br />23 <br />.3833 <br />33 <br />.5:500 <br />43 <br />.7167 <br />53 <br />.8833 <br />4 <br />.06167 <br />14 <br />.2333 <br />24 <br />.4000 <br />34 <br />.5667 <br />44 <br />.7333 <br />54 <br />.9000 <br />' 5 <br />.083:3 <br />15 <br />.2500 <br />25 <br />.4167 <br />35 <br />.5833 <br />45 <br />.7500 <br />55 <br />.9167 <br />6 - <br />.1000 <br />16 <br />.2667 <br />26 <br />.4333 <br />36 <br />.6000 <br />46 <br />.7067 <br />56 <br />.9333 <br />7 <br />.1167 <br />17 <br />.2533 <br />27 <br />.4500 <br />37 <br />.6167 <br />47 <br />.7533 <br />57 <br />.9.500 <br />8 <br />.1333 <br />I8 <br />.3000 <br />28 <br />.4667 <br />38 <br />.6333 <br />48 <br />.8000 <br />58 <br />.9667 <br />9 <br />.1500 <br />19 <br />.3167 <br />29 <br />.4833 <br />39 <br />.6-500 <br />49 <br />.8167 <br />59 <br />.9833 <br />10 <br />.1667 <br />20 <br />.3333 <br />30 <br />.5000 <br />40 <br />.6667 <br />50 <br />J .8333 <br />60 <br />1.0001) <br />TABLE. \'.---Inches in Decimals of a Foot. <br />1-16 3-3'2 �,v 3-I6i 1.1 5-16 3i 14 4e %i <br />.0052 .0078 .0101 .01:56 .0208 .0260 .0313 .0117 .0521 .Of�_'S ` .0729 <br />1 I " 3 I -1 I 5 I 6 7 8 I 9 I 10 I 11 <br />.0833 .1667 .2.500 .3.3 .4107 .5000 .5833 .6667 .7500 .8333 .9167 <br />