. to connect them by a curve passing a given distance from the the angle LCB = 31° 44, and C E = 50 feet, to find the I Locating Side Tracks, Etc. 379 radius MA, By geometry, the angle A M E = | L C B = 15° 52. IlgA, ^y ^ m By logarithms we have : As external secant 15° 52 = ^ L C B S-aOlTSO Is to 50 1-698970 So is R. . . . 10-000000 To M A=1262=:R. of a 4° 32f curve 3-101181 60 50 By natural external secants ex. sec. 15° 62 039603 1262 ft. Case 2d. To find the tangent AC, or C B; or point of curve. By logarithms:
. to connect them by a curve passing a given distance from the the angle LCB = 31° 44, and C E = 50 feet, to find the I Locating Side Tracks, Etc. 379 radius MA, By geometry, the angle A M E = | L C B = 15° 52. IlgA, ^y ^ m By logarithms we have : As external secant 15° 52 = ^ L C B S-aOlTSO Is to 50 1-698970 So is R. . . . 10-000000 To M A=1262=:R. of a 4° 32f curve 3-101181 60 50 By natural external secants ex. sec. 15° 62 039603 1262 ft. Case 2d. To find the tangent AC, or C B; or point of curve. By logarithms: AsR 10 000000 Is to AM =1262 .... 3-101181So is tangent 15° 62 ... 9-453668 To AC = 388-8 .... 2-664849 By natural tangents: 1262 X (natural tangent 15° 52 = -26546) = 388 feet= C A = C B. 380 Formula for Running Lines, PROPOSITION VI. Fig. located a curve connecting two tangents, it is required to movethe middle of the curve any given distance, either towards or fromthe vertex. Let the angle TLG = 36° = whole amount of curvature; the. arc A B C = 1200 feet; the radius A N = G N = 1910 feet, and IB= B F = 10 is required to find the radii H M and E have by logarithms: External secant 18° = half of 36° = A N L S-YSYISS Is to 10 1-000000 So isR 10000000 To difference of radii = 183 feet . 2^2847 By natural external secants: -^rr 183 ft. •0546-95 1910 + 183 = 2093 = MH = radius of a 2° 44 curve;and 1910 — 183 = 1727 = 0E= radius of a 3° 19 natural tangents:183 X (natural tangent 18° = -32429) = 69-4 = HA = AE. Locating Side Tracks, Etc. 381 PROPOSITION VIL Fig. is required to locate a tangent from an inaccessible point on a curve. Let A B C be the given curve with a R. of 1637 feet curving 3° 30per 100 feet; C the inaccessible point. Assume a point B, if con-venient, at a given distance, say 300 feet, from C. Throw off atangent, and measure, at right angles therefrom, B E = external Fig. 6,
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Keywords: ., bookcentury1800, bookdecade1850, booksubjectenginee, bookyear1856
