100-102] FORMULAE FOR OVARY ELLIPSOID. 147 



external region. As particular cases of the formula (9) we 

 note 



The definite-integral form of Q n shews that 



(10), 



where the accents indicate differentiations with respect to f. 



The corresponding expressions for the stream-function are 

 readily found ; thus, from the definition of Art. 93, 



&amp;lt;ty =s _]L_&amp;lt;ty &amp;lt;ty__d 



dsf -& ds^ ds^~^ds^ ............... 



whence 



Thus, in the case of (7), we have 



whence 



The same result will follow of course from the second of equations 

 (12). 



In the same way, the stream-function corresponding to (8) is 



102. We can apply this to the case of an ovary ellipsoid 

 moving parallel to its axis in an infinite mass of liquid. The 

 elliptic coordinates must be chosen so that the ellipsoid in question 



102 



