152 BkOOMALL : 



T =- AK f- DS 4 MX or 



I _ I 



T = — cosIX-— ) f- Re tan — t MS tan — 

 2^3' 2 2 



KR . • , 



Since MS ^ and AF — AE approximate! v 



4 



1, I ^' """ """ I 



T — — -f- R. tan — ' iL tan — or 



2 242 



T = — + R,- tan — + tan — (approximately) 



2 2 12 2 



Whence, by (.10) 



T= — + R.. tan — f tan — (13) 



2 2 24R, 2 



This formula makes it possible to locate A and A', and 

 the field work is now easy. With the transit at A and A' 

 lay out the two transition curves, working toward the central 

 curve in each case. The ten deflections for the ten chords 

 assumed for AB and A'B' will be 



d, = .1' X 

 d, = .2' X 



*i 



S^ 

 3 



Sc 



3 



d, = .3' X — etc. 

 3 



the value of S<- expressed in radians, being found from equa- 

 tion (10). After having located the two transition curves a 

 circular curve is run in between B and B' in the usual way. 

 To locate the instrument in the direction of the common tan- 

 gent at the point of central curve B or B', set up, for exam- 

 ple, at B, sight on A with inverted telescope and turn off the 



