156 Mr. 8. H. Burbury on the 



Again, in this case 



b 2a b . 

 . b 2a b 

 . . b 2a 

 b 



Therefore 



= (2a)-'0->= 1 ± ri (2a)'-'. 



Aj,, a 



and vanishes as r increases indefinitely. 



Part IV. 

 Boltzmann's Minimum Function. 

 (16) We have seen that, the law of distribution being 



nS 



O/J — 



2TD 



2TD 



n 



Y^, ,%\x 2 = ^, <fec, and S = T. 



xJ n L) 



Let ns consider a varied system in which with these same 



values of Xi #i#2> &c. the law of distribution is Ce 2~t 1 -f q y 

 where 1 + q is any positive function of # 1? x 2) &c, and q must 

 satisfy the following conditions, namely :— 



(1) In order that the number of systems may be the same 

 in the varied as in the normal state, 



rr* w§ pr %s 



... e~2T dx x , . . dx n = • • • e~2T 1 + qdxt . . . dx n 



or 



JT- 



nS 



qe 2Tdx 1 . . . dx n = 0. 



J3- 



(2) In order that the values of x^, w x x 2 , &c, may not be 

 altered, 



_nS CI _nS 



e st Xl 2 dw x . . . dx n — I I ... e wl + qx^dotx ...dw 



and therefore also 



? x . . . dae n = JJ ... e 2T lT^S^! . . . dx n . 



if... 



_nS 



e 2T Sfe 



