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TA13LE H. - Radii, Ordinates and Deflections- Chord =100 ft. <br />Deg. <br />Radius <br />Mid. <br />Ord. <br />Tan. <br />Diet. <br />Def. <br />Dist. <br />De' <br />1f Ft <br />Deg. <br />Radius <br />Mid. <br />Ord <br />Taa <br />Dist. <br />Def. <br />Dist. <br />Def. <br />)f Ft. <br />2° 58' <br />t. <br />It. <br />ft. <br />Lt. <br />1° 59' <br />2° 25' <br />It. <br />t. <br />it. <br />ft. <br />' <br />0'10' <br />34377. <br />.036 <br />.145 <br />.231 <br />0.05 <br />7° <br />819.0 <br />1.528 <br />6.106 <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 />4.0 <br />859 t.4 <br />.145 <br />.582 <br />1.16;4 <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.;.0 <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 />2.00 <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 />2.60 <br />30 <br />3819.8 <br />.327 <br />1.300 <br />2.618 <br />0.45 <br />9 <br />637.3 <br />1.965 <br />7.846 <br />1:5.69 <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.S0 <br />50 <br />3125.4 <br />.400 <br />1.600 <br />3.200 <br />0.55 <br />30 <br />G03.8 <br />2.074 <br />8.281 <br />16.56 <br />2.85 <br />2 <br />2861.9 <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 />261.1.6 <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 />.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 />3.1.1 <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.;0 <br />40 <br />2118.8 <br />.582 <br />2.327 <br />4.654 <br />0.80 <br />30 <br />499.1 <br />2.511 <br />10.01'. <br />20.04 <br />3.45 <br />50 <br />2022.4 <br />.6t8 <br />2.472 <br />4.945 <br />0.85 <br />12 <br />479.3 <br />2.620 <br />10.45 <br />20.91 <br />3.60 <br />If <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 />21.77,3.75 <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 />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 />G. IDS <br />1.05 <br />11 <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 <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 />46 <br />1132.7 <br />.873 <br />3.490 <br />I6.9S0 <br />1.20 <br />30 <br />370.8 <br />3.387 <br />13.49 <br />26.97 <br />4.615 <br />10 <br />1375.4 <br />-.909 <br />3.035 <br />; 7.271 <br />1.25 <br />.16 <br />359.3 <br />3.496 <br />13.92 <br />27.84 <br />4.90 <br />20 <br />1322.5 <br />.945 <br />3.718 <br />7.661 <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 />5.111 <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 />31.29 <br />5.•10 <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 />16.51 133.01 <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 />271.4 <br />4.594 <br />18.22 <br />361.44 <br />Q.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 />19.03 <br />35.16 <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 />1.7.i <br />25 <br />231.0 <br />5.476 <br />21.64 <br />43.28 <br />7.50 <br />4 <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.S0 <br />10 <br />929.6 <br />1.346 <br />5.379 <br />10.76 <br />1.85 <br />27 <br />214.2 <br />.918 <br />23.35 <br />46;.6;9 <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 />851.9 <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 />4U <br />859.9 <br />1.455 <br />5.814 <br />11.63 <br />2.00 <br />30 <br />193.2 <br />6.583 <br />25.58, <br />51.76 <br />9.00 <br />The middle ordinate in inches for any cord of length (0) is equal to .0012 W <br />multiplied by the middle ordinate taken from the above table. Thus, if it <br />desired to bend a.10 ft. rail to fit it 10 degree curve, its lniddlo ordinate should <br />be .0012X90oX2.181 or 2.36 inches. <br />TABLE III. Deflections for Sub Chords for Short Radius Curves. <br />Degree <br />of <br />Curye <br />Radius <br />50 <br />sin, l def. ang. <br />31, sub chord = sin of ' def. an le <br />.R• g <br />Length <br />of arc <br />for 100 ft. <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 Ft. <br />30° <br />193.18 <br />1° 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° to' <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 />161.8o <br />2° 13' <br />2°.41' <br />3° 33' <br />4° 26' <br />101.66 <br />380 <br />153.58 <br />2° 20' <br />2° 49'3° <br />44' <br />4° 40' <br />101-8.5 <br />400 <br />146.19 <br />2° 27' <br />?° 57' <br />3°55' <br />4° .94' <br />102.06 <br />42° <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 />46° <br />127.97 <br />2° 48' <br />.3° 21' <br />4° 29' <br />S° 36' <br />102.76 <br />48° <br />122.92 <br />2° 55' <br />3° 29' <br />4° 4o' <br />5° 50' <br />103.00 <br />50° <br />118.31 <br />3° 0'-' <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° oz' <br />6° 17' <br />103.54 <br />54° <br />110. 1 t <br />3° 16' <br />30 54' <br />50 13' <br />Ga 31' <br />103-84 <br />56° <br />1o6.50 <br />3° 22' <br />4 02' <br />5° 23 <br />6 44 <br />104.14 <br />58° <br />103 14 <br />3° 29 <br />4° lo' <br />5° 34 <br />.I <br />6° 57 <br />104.43 <br />60° <br />Ifio.00 <br />3° 35' <br />4° 18' <br />S° 44' <br />7 11' I <br />104:72 <br />CURVE FORMULAS Ix <br />T= R tan I I R= T cot. 'I chord' <br />T _ 50 tan I I Chord def. = <br />Sin. ill R 50 R <br />= <br />Sin. z D = 50 Sin. $ D No. chords = I <br />R E = R. ex. sec 1 D <br />Sin. 12 [) = 50 tan Z I <br />1. E = T tan # I Ta n. clef. = I 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 .01745 (def. for I° for I It. <br />see Table 1I.), 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 too, Alt. 10.10'-200=.5. 100-.5=100.5 Ihyp. <br />Given Hyp. too, Alt. 25.25'-200=3.125. 100-3-125=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 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..574d2,.where d is the distance in miles. <br />The correction for curvature alone is closely, d2. The combined cor- <br />rection is negative. <br />PROBABLE ERROR. If c11, d2, da, etc. are the discrepancies of various <br />results from the mean, and if Zdl=the sum of the squares of these differ- <br />ences and If =the number of observations, then the probable error of the <br />mean= 1dI <br />-0.6745 n(n_1) <br />SOLAR EPHE\fERls. 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, 3'6xG 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 />1' <br />.0167 <br />111 <br />.1533 <br />21' <br />.3500 <br />311 <br />.5167 <br />41' <br />.6833 <br />51' <br />.8500 <br />2 <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 />.21617 <br />23 <br />.3S33 <br />33 <br />.5500 <br />43 <br />.7167 <br />53 <br />.8333 <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 />.2:100 <br />25 <br />.4167 <br />35 <br />.5833 <br />45 <br />.7500 <br />55 <br />.9167 <br />6 <br />.1000 <br />l6 <br />.2667 <br />26 <br />.4333 <br />36 <br />.6000 <br />46 <br />.7667 <br />56 <br />.9333 <br />7 <br />.1167 <br />17 <br />.2333 <br />27 <br />.4500 <br />37 <br />.6167 <br />47 <br />.7533 <br />57 <br />.9500 <br />8 <br />.1333 <br />l8 <br />.3000 <br />28 <br />.1667 <br />38 <br />.6333 <br />48 <br />.8000 <br />58 <br />.9667 <br />9 <br />.1500 <br />19 <br />.3167 <br />29 <br />.4333 <br />39 <br />.6500 <br />49 <br />.S167 <br />59 <br />.983: <br />10 <br />.1667 <br />20 <br />.3333 <br />30 <br />.:;000 <br />40 <br />.6667 <br />50 <br />.5333 <br />60 <br />1.0000 <br />I:vn1.F, V. -Inches in Decimals of a Pout. <br />1-16 3-32 ;-s 3-16 1..1 5-16 '.e 5' 9e '/4 ' <br />.005. .0078 .0101 .0136 .0208 .0_610 .0313 .0117 .0:521 .063:; .0729 <br />1' I 3 I 3 I1 - :? 4 I 7 I 5 9 10 11 <br />.0833 .166, .2600 .3333 .4167 .+.nun .5833 .6667.7,500 .8333 .916; <br />