A manual of the principles and practice of road-making: comprising the location, construction, and improvement of roads, (common, macadam, paved, plank, etc.) and rail-roads. By W. M. Gillespie ...

408 APPENDIX C.
PROBLEM II.
Given two intersecting tangents, and also the tangential angle, i e.,
given Do and 60, to find t. (Fig. 1.)
t = c tan. p D~
2 sin. 6"
PROBLEM III.
Given two intersecting tangents, and also the distance from the
vertex to a point through which the curve must pass, i. e., given D~ and
I c, to find t and 8~. (Fig. 1.)
sin. 5~ = d tan. Do tan. D, and t = IC. cot. D~.
2ic
tan, x D-. tan. DtD
Conversely, c I a t., and I c= t tan. ~ D~o
2 sin. d~
PROBLEM IV.
Given two intersecting tangents, and also a point through which the
curve must pass, i. e., given D~ and the co-ordinates of P, to find 5 and
AL. (Fig. 4.)
Find F A and A I as in General Problem IV.
tan. - D~
sin. 6 = c 2 _ 2
2AI
CASE B.-To START FROM A GIVEN TANGENT, AND PASS
THROUGH A GIVEN POINT.
PROBLEM V.
Given this tangent and point, and also the starting point. (Fig. 6.)
1. Given A z and I A z, to find 6 and I A.
= sin. I A ZA Z.in. C~ = c I A and A I -
A Z 2 Cos. I A Z
Approximately, = IAZ
A Z in chains)'
sin. I A Z
Conversely, A z C= C — I
sin. 8~