1879.] for a rectangular parallelepiped. 291 



or e-^^-^^'i'^e^[2ai{x-x)t, e-'^""^] 



1 //7r\ ^ / X — X 



2aV \t^\ 2a 



Therefore U = -^ / va x 



Sabc Jo t 





1 p i^OL-t 





or putting - for i, 



""-McL^'- 



tr« 





^ - ^1 - -4c^^^^ /) /„i+Zi ."^^' 



The function ^3 (x, q) satisfies the differential equation 

 d^6^ {x, q) _ ^ dd^ (x, q) 



dx' " ,, T' 



and therefore 



cZa;'^'^^V 2a '^ ) ^ dt A 2a ' ' 7' 

 Vol. III. Pt. vii. 22 



