148 Mr. S. H. Burbury on the 



such that 



and therefore 



^ 2 = %> ^=^,&c, 



7 ^ , I'll 1^22 



d = *±-D T--- 



and thence by a known proposition * we find 



^=2a 1? ^ = &i2, &c, andD = i; 

 and therefore 



F fa . . . c n ) = K (2tt)2 VD . e -< 2a nr+ 6 >^+ • • ■> 



= K(2?r)2 A /p. e -(^ 1 2 -i-6i2^+...) # 



To determine K we have 



jj . . . F (c x . . . c n ) dc x . . . dc„ = 1. 



That is, since 



n 



JJ * VD 



and 



F ( Cl . . . c n ) =-^-n VD.e-^ 24 - 6 ^^" . 



(2tt)2 



(5) Again, 



(2tt)2 jj 



= -yY = Xi by hypothesis. 

 Similarly, 



and therefore _ -. 



(o c = fo x 5 



and these results are true whatever be the form of the func- 

 tion/^ . . . x n ). 



* Todhunter, Theory of Equations, 2nd edition, p. 393. 



«i' 



