50 Trans. Acad, Sci. of St. Louis. 



which is the equation to the ellipsoid whose volume is 



4 

 F = -5 nra^b cos a. 

 o 



This is the volume of the prolate spheroid generator multi- 

 plied by cos a. 



It may also be seen from equation (12) that the oblate 

 spheroid is derived from the prolate spheroid when 



or 



that is when 



a2(l + sina) = 62 



1 + sm a = — 5 



or 



sin a = -K — 1 = -^ e % 



a = arc sm I — -e^l. 



A casual examination will show, that the ellipsoid may be 

 derived from the oblate spheroid by the method of Isogonic 

 Transformation. In fact, the method may be applied to any 

 figure through its equation, or, simply by graphics. 



There is no indication at present that this method of trans- 

 formation admits of any practical application. 



Issued May 16, 1901. 



