traced upon the Surface of the Sphere. 287 



(p = 0, or $ = -TT. That is, in this case, the two poles of the equator fulfil 

 the conditions, and these alone. 



2do, If we take that particular meridian 6 ft, , we shall have 



*<= + (14) 



Avhich shows that (p may be of any value, or, in other words, the circle 

 sought is the meridian thus determined. 



Stio, If, instead of this, we take a, = \ , or rather tan a, = tan \ , we 



have also cos </> = j| ; or <f> may be of any value, whatever 6 may be. That 



is, the circle itself is indeterminate, being subjected in reality to a condi- 

 tion less in number than is necessary to define it. 



XI. 



To find the equation of a great circle which makes with a given me- 

 ridian at a given point in that meridian a given angle. 



Let e FLD be the given angle, a, ft the given point L, and LD 

 the circle sought. 



Let the equation be assumed, 



cotcj) = tan A cos (6 K) (1) 



Now, when 6 = ft, we have 



cot a = tan A cos (ft K) (%) 



oo 2 



