traced upon the Surface of the Sphere. 



277 



V. 



To find the equation of a great circle on the sphere, which shall cut two 

 given meridians at given angles. 



Let PF, and PF 7/ be the meridians ; M, and M y/ the points where the 

 great circle sought shall cut them ; TT e, and e tl the two angles of the 

 triangle formed by that circle and the given meridians and /? ft the 

 third. If we put, for the moment, TT e, = A, t lt = B, /3 /; /3,=.C, and 

 A + B + Czz2S, we have 





, ,r-6,+ g-fl,-ft 



, C= g -: 



S = 



C,+ ^ + ft/ ft 



.(1.) 



Also, cot a a 



cot a, = 

 VOL. XII. PART I 



n 



