Law of Distribution of Energy. 147 



the index containing all squares and products of 0i.,.6 n ; 

 and therefore F(c x . . . c n ) 



a 2 



— TC" (V -{*i 2 ~2+ *i x JA+ ■ ■ ■ + Mi + • • • + C »M V-l} ,^ , 



the limits being + oo , and K being a constant to be found 

 by making jj . . . F(c x . . . c^dc x . . . dc n = 1. 

 (3) Now for two variables a?!, x 2 we find that 





i 2 . — _ . -,w 



do, 



-{^ +^A+^7f- +(eA+c ^ a) vri } 



2tt 



n/ 



_c,2 c 2 2 



ar 2 2 -^- — 2; 1 2;2C ) c 2 +^ 1 2 -j 



— 5 9 12 



1 ^O wlct/O 



where d is the determinant, 



d = 



x 



l ? 





and d n , d 12 , ^ 22 are its minors. 



We infer, and it can be proved, that the same law holds 

 for n variables. That is that if 



d = 



then 



^ 2 , 



<2?l#2j 



OG-^OCa. $2 } 





w*)Ub n 



X 



Jb (q . . . c w ) = K /-% e l d 2 d 



in which d lr is the minor formed by omitting the first row 

 and rth column of d, and its sign is such that 



d = Xi 2 d n + 2£ = 2 ^l^lr. 



(4) Now there exists a determinant 



2a ly bu . . . 6 ln 



6 12 , 2a 2 • • • b 2n 

 L2 



D = 



