. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools . t identicalw^ith that in § 33, a. b. Assume that it is desired to change the forward tangent(as above) but to retain the same radius. In Fig. 27 {R2 — R1) cos J2 =^2^ J lR2-Ri) cos J2 =0^n\ x = 02n — 02n ={R2 — Ri)(cos ^2 — Dit2—iXi (24) The is moved backioard along the sharper curve anangular distance of J2~^2 = ^i~^/- In case the tangent is moved inward rather than outward,the solution will apply by transposing J2 and ^2- Then we§hall have cos J/ = cos J2 + 15 D (25) 39
. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools . t identicalw^ith that in § 33, a. b. Assume that it is desired to change the forward tangent(as above) but to retain the same radius. In Fig. 27 {R2 — R1) cos J2 =^2^ J lR2-Ri) cos J2 =0^n\ x = 02n — 02n ={R2 — Ri)(cos ^2 — Dit2—iXi (24) The is moved backioard along the sharper curve anangular distance of J2~^2 = ^i~^/- In case the tangent is moved inward rather than outward,the solution will apply by transposing J2 and ^2- Then we§hall have cos J/ = cos J2 + 15 D (25) 39. ALIGNMENT. 41 The is then moved forward. c. Assume the same case as (b) except that the larger radiuscomes first and that the tangent adjacent to the smaller radiusis moved. In Fig. 28 (R2-R1) cos J, =0{a\(i^2-Ei)eosi/=0iV. x=0^^n—0{ri= (R2—Ri)(cos J/—cos ii). cos J/ = cos ii + ^- -Ji: (26) The is moved forward along the easier curve an angular distance of J/ —il = i2~^2In case the tangent is moved inward, transpose as before and we have. cos i/ = cos Ji — R2—R1 (27) The is moved backward d. Assume that the radius-of one curve is to be altered with-out changing either tangent. Assume conditions as in Fig. 29. For the diagrammatic solutionassume that R2 is to be increasedby O2S. Then, since J?, mustpass through 0^ and extend be-yond Oj a distance O^S, thelocus of the new center must lieon the arc drawn about 0^ ascenter and wnth OS as locus of O2 is also givenby a line 0/p parallel to BVand at a distance of R2 (equalto S .. ) from it. Thenew center is therefore at theintersection Oo. An arc with ra-
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