traced upon the Surface of the Sphere. 



Differentiating (7), we obtain 



397 



_ cos 6 K cos (p d (p sin 9 K sin '(f) d 6 



COt /x -^ ~ "7 "j"~j~ 



sin (pa (p 



dB 



or cot \= cos 6 Kcotd) sin0 K. - 



d(p 



(9-) 

 (10.) 



Differentiating again, we have 

 d(pd?0 



3 - ( ., 

 ind Klcotd>d6+ 

 ( 



Or writing it 



. 

 

 J 



cos 



d(p 



Bsin0 K+ A cos 6 K = ................. . 



we can successively determine , \ and ? in terms of <t> and the 'differen- 

 tial coefficients. 



From (12) we have 



tan 6 K = 



sin 6 K - 



cos 



6 K = 



B 



(13.) 



These inserted in (9) give 



B cos (b d d) + A sin <b d 6 

 cot \ = qp . ^ ",^^-Lr- 



sm 



A 2 + B 2 



sin(f>d(f) A/ A 2 + B 2 



V A 2 sin 2 ^ (d 2 + d 2 ) + 2 AB sin cos d<p d6 + 

 B cos (p d (p + A sin. (p d 6 



sin \ = -f- - 



COS A. = Zfl , 



and finally 



^ (B cos (p d(p + sin (p d 6) cos (p + sin 2 (pd(p 



(14.) 



cos p = 



A 2 + B* 



A 2 sin f 



+ 2 AB sin (p cos (pd(pdd + B 2 d</> 2 



B d (ft + A sin (p cos (p d 6 



' v A 2 sin 2 ^ ((/</>* + d0 2 ) + 2 AB sin cos d<d + B 2 d(p* 



. (15.) 



