. 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 PROP
. 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,. a secant of arc B C ; then to find by logarithms the distance B E, we have: As radius 10*000000 Is to 0 0 =: 1637 3-214122 So is external secant 10° 30== angle COB . 8231221 To BE = 27-88 1-445343 By natural external secants: 1637 X (nat. ex. sec. 10° 30 = -017030) = 27* the line B E =r 27 88 feet at right angles to BII. Setthe instrument over E, and turn off the angle BEC = 79° 30 =complement of 10° 30. EOF will be the direction of the tangentrequired. Case there be no convenient accessible point between A andC, produce the curve to D, measure the external secant D F asbefore, place the instrument at F, and turn off the angle will give the direction of the tangent F C as before. Case the lines AI and I C be more practicable for operating 382 Formulae for Running Lines, than the curve A B C, calculate and produce the tangent from A toI, the vertex of the curve ABC, and turn off the angle KIF =A O C, and make I C = A I, as 4th
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Keywords: ., bookcentury1800, bookdecade1850, booksubjectenginee, bookyear1856
