# Mathematics of the Paper Location of a Railroad Mathematics of the Paper Location of a Railroad
J C L John Charles Lounsbury Fish
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We now scale the map for a rough check on these computed bearings and distances.
4. COMPUTE CENTRAL, ANGLES OF CURVES. It is evident from the map that the central angle for curve No. 1 is Ai = ^ P]VI + ^v!V 2 = 63 39 ' + 45 58/ = 109 37/ ; and the central angle for curve No. 2 is Aa = ^Vj + ^V 2 PC 3 = 45 58 ' + 78 36/ = 124 34/ - We roughly check these values by scaling the map with the protractor.
5. COMPUTE TANGENT - DISTANCES OP CURVES. Using a "table of tangent-distances for a 1. Curve" we
... find the tangent-distance for curve No. 1 is Ti = 1, 355; and for curve No. 2, T 2 = 1, 364.
We obtain a rough check on these by scaling. If in any case the value of A is beyond the limits of the table, of course the tangent-distance must be computed from the formula: T = R tan A/2.
6. COMPUTE CURVE LENGTHS. Length of curve is equal to one hundred times the ratio of central angle to degree of curve.
Length of curve No. 1 is Lj 100 Ai / I>i = 100 (109 370/6 = 100 (109. 62) / 6 = 1, 827.
8 Length of curve No.

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