of the Spherical Conic. 

 Fig. 1. Fig. 2. 



353 



(and therefore i/l + c 2 = ,/i + c 2 + c __ vl*c 2 ~e=|Y 



then for the limiting value of ft we have 



sin 2 £= ^ = '3846, sin £=-62, or /3=38° nearly. 



In the first figure (3 is less, in the second figure greater than this 

 value : the form for the limiting value is obvious from a compa- 

 rison of the two figures. 



1 take the opportunity to mention the following theorem, 

 which is perhaps known, but I have not met with it anywhere ; 

 viz. any three circles, each two of which meet, may be considered 

 as the stereographic projections of three great circles of the 

 sphere. In fact suppose, as above, that the projection is made 

 on the plane of a great circle, and calling this the principal circle, 

 the projection of any other great circle meets the principal circle 

 at the extremities of a diameter of the principal circle. It fol- 

 lows that the theorem will be true, if, given any three circles each 

 two of which meet, a circle can be drawn meeting the given 

 circles, each of them at the extremities of a diameter of the circle 

 so to be drawn. It is easy to see that the required circle has 

 for its centre the radical centre (point of intersection of the 

 radical axes) of the given circles, and that the radius is the 

 ' Inner Potency ' of the point in question in regard to each of the 

 three given circles. In particular the three circles having for 

 centres the vertices of an equilateral triangle, and the side for 

 radius, may be considered as the stereographic projections of 

 three great circles of a sphere. This is a very ready mode of 

 delineation of a spherical figure depending on three great circles 

 of the sphere. 



2 Stone Buildings, W.C., 



March 21, 1863. 



