. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . lated. Example. Given R = or Z> = 1° 10, and .1 = 4° 40, tofind c. Here, by the first formula, c =^ sin. 4° 40 = ,^ , , ^ , 100 sin. 43 40 Isy the second formula, c — gin \o iq = , 70. ProblCDll. Given the angle of intersection K C B = 1 [fig. 23),and the distance
. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . lated. Example. Given R = or Z> = 1° 10, and .1 = 4° 40, tofind c. Here, by the first formula, c =^ sin. 4° 40 = ,^ , , ^ , 100 sin. 43 40 Isy the second formula, c — gin \o iq = , 70. ProblCDll. Given the angle of intersection K C B = 1 [fig. 23),and the distance CD = h from the intersection point to the curve in thedirection of the centre., to find the tangent A C = T, and the radius A G= R. Solution. In the triangle ^ D C we have sin. CA D : sin. A D C =^ CD: AC. Bnt CAD = ^AOD = ili^ 2, III. and VI.), and as the sine of an angle is the same as the sine of its supplement, sin. A D C == sin A D E = cos. DA E = cos 4 /. Moreover, CD = b and A C = T. Substituting these values in the prectrding pro- b cos, -^ ^portion, we have sin. ^ I: cos. ^ I = b : T, or T = ^.^ \*j^ ; whence (Tab. X. 33) MISCELLANEOUS PROBLEMS. 19 ^- T =h cot. \ I. To find R, we have (§ 5) R = T cot. ^ I. Substit iting for T ifcfalue just found, wc have ^ R = b cot. ^ 7 cot. ^ 2. Fig. 23. hxample. Given 7 = 30°, 6 = 130, to find Tan! R. Here h = 130^7=7° 30 7 = 15° 72 = 71. Problem. Given the angle of intersection KC B = 1 [Jig. 23). %nd the tangent A C = T, or the radius A 0 = R, to find C D -^ b. Solution. If T is given, we have (§ 70) T = h cot. ^ 7, or 6 =T lot i/ .•.h= r tan. 17. If R is given, we have (§ 70) R = b cot. ^7 cot. |^7, or 6R eot ^ Jcot. i / ..b = R tan. ;J 7 tan. ^ 7. 50 CIRCULAR CURVES. Example. Given /= 27°, T= 600 or 7^ = 2499 lb, to IHere b = 600 tan. 6° 45 = 71 01, or i = tan. 6° 45tan. 13° 30 = 1 72. Problem. Given the angle of interse
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