Railway Curves. 



135 



Example, Fig. V. 



Supposing the distance DB or d = 285, and the demi-tangent EC 

 or h— 31, and that the angle a = 38° 20', and the angle 

 /3 =29° 30' — Required, the common radius of the two curves, 

 and the length and position of the chords. 



a 38° 20' 

 /3 29° 30' 



by sin. 

 by cos. 



dn 2 = 



by 2 0-3010300 



9-7466237 cos, 

 9-9987084 



0-3010300 



, 9-9189996 



9-9987084 



sum 67° 50' 



diff. 8° 50' 



by m = 0-0463621 



bycZ 

 by dn = 



222415-87 by dn 2 = 



0-2187380 byn 



half sum 33° 55' 

 half diff. 4° 25' 



2-4548449 





= 2-6735829 

 2 





= 5-3471658 



by m 2 = 0-0927242 and mr = 2738268 

 by n 2 = 0-4374760 and n 2 = 1-23801 



4 - 3-976278 = -023722 the denr. 



d. 



2h- 



285 

 62 



347x223=i> 



by q = 2-3751513 

 by 347 = 2-5403295 

 by 223 = 2-3483049 



by pq = 3-2637857 



222415-87 =Ansr. 

 ;>2 = 1835-6326 



224251-5026 



root = 473-552 

 nd=471-61 



The numr. 1-942 



r= 81-865 Answer. 



2) 

 by = 5-3507354 



by root = 2-6753677 



by numr. = 0-2882492 

 - denr. = 2-3751513 



by r= 1-9130979 



