150 BROOM ALL : 



But at B the circle and transition have common taugency, 

 so that equating 



ill" _!l_ 



Ro ~ 2R. 



and therefore 



Lc ^ - - ^9) 



2 



(G) The relationship between the transition curve and 

 the circular curve with which it is to connect is expressed by 

 the equations 



So - — or R.. — -('O) 



2R,- 2S.- 



This can be shown as follows : If a perpendicular is erected 

 at the midpoint of the chord BD we have 



4R,. 



1- » ., Ic 



Sc = — ^ or Re -^ 



2R 2S. 



(H) Since the offsets increase as the cube of the dis- 

 tance and AB -^ 2AK there results 



EF- i^ C.) 



