. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools. By Walter Loring Webb . , = 0 — O^n — O^n = {R^ — P,)(cos z/^ — cos z//). Xcos /^/ = cos Z/^ — n __ p . . (24) §39. ALIGNMENT. 41 The P. C. C. is moved hackward along the sliarper curve anangular distance of ^/ — ^^ — z^i — /^/. In case the tangent is moved inward rather than outward,the solution will apply bj transposing A^ and ^/. Then wewill have cos A = cos ^. + p _ p- . . (25) Tlie P. C. C. is then moved for-ward. c. Assume the same case as (b) ex-cept that the larger ra
. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools. By Walter Loring Webb . , = 0 — O^n — O^n = {R^ — P,)(cos z/^ — cos z//). Xcos /^/ = cos Z/^ — n __ p . . (24) §39. ALIGNMENT. 41 The P. C. C. is moved hackward along the sliarper curve anangular distance of ^/ — ^^ — z^i — /^/. In case the tangent is moved inward rather than outward,the solution will apply bj transposing A^ and ^/. Then wewill have cos A = cos ^. + p _ p- . . (25) Tlie P. C. C. is then moved for-ward. c. Assume the same case as (b) ex-cept that the larger radius comes firstand that the tangent adjacent to thesmaller radius is moved. In Fisr. 28 (i?2 — R,) cos J, = 0,71; (i?, - B,) cos zf/ = 0;n,. n^-^ Fig. 28. X = 0/n - 0^71 = (P, - i?,)(cos z// _ cos ^,). cos /I/ = COS A, + p^^_^> . . (26) The P. C. C. is moved forward along the easier curve anangular distance of ^/ —. /i^ = /l^ — A^, In case the tangent is moved inward, transpose as before andwe have cos Al = cos A^ — X . (27) The P. C. C. is moved hachioard. d. Assume that the radius of one curve is to be altered witli-out changing either tangent. Assume conditions as in Fig. the diagrannnatic solution assume that P, is to be in- 42 RAILROAD CONSTRUCTION. 39. creased by O^S, Then, since ^/ must pass through 0, and ex-tend beyond 0, a distance 0,S, the locus of the new centermust lie on the arc drawn about 0, as center and with OS as radius. The locus of 6*/ is also givenby a line O^j? parallel to ^ F and at adistance of ^/ (equal P. CO.)from it. The new center is thereforeat the intersection 0^\ An arc withradius i?/ will therefore be tangent atJj and tangent to the old curve ^^r^-chiced at
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