traced upon the Surface of the Sphere. 



sis 



cot K = cot 2^ cot | 



6 



-< 



2 

 / 



(1-) 



From (1.) we get, by taking cot ' of each side of each equation, and 

 adding the results, 



v 



= cot- 1 cot cot 



v "V _ 



_+ cot- 1 cot I cot JL__ , . 



.(2.) 



or, taking cotan of each side, it is, after slight reduction, 



X 



1 2 



cot -- = 



S X 7+0 7 * 7+0 - 7 



COS 2 K COS 



_ COS _ -- sin - _ sin 



Sln 



cos 



v . v f 7 + . 

 |sm| {cos !^- ri 



6 



6 . 



cos* ^ (cos + cos 7) sin* ~ (cos cos 7) 



sin sm 7 

 cos cos x + cos 7 



sm % 



.(3.) 



7T 



Or, reducing (3.), and putting ^ ^ for x. it becomes ultimately 



. E E . , . E . , 



cos 7 sm = cos sm 7 cos <p sm sm <p cos 



.(4.) 



This is the equation of a circle (Vid. I. 1.), the co-ordinates of whose 

 centre and whose radius are found from these equations, viz. 



K=.0, 



E 



tan X = tan cosec 7, 



E 



cos 7 sm 



P = 



.(5.) 



A ,E 



VI cos 1 cos 7 



7 



These results perfectly correspond with those obtained by LEGENDRE, 

 as above referred to, when the difference of notation is attended to. 



