Law of Distribution of Energy, 157 



These conditions being satisfied the system will, on free 

 interchange of energy, pass out of the varied state into the 

 normal state. And it can be now shown that the function B 



= jj . . ./(>! . . . ff n ){log/(a?i . . . x v ) — l}dx l ...dx n 



diminishes in the process. 



For let B be the value of B in the normal state, when 



_nS 



f(x x . . . x n ) = Ce 2T, B its value when 



_«s 



/fa ... *,)=Ce ™l + q. 

 Then B-B = 



Oil . . . e 2T 1 + q (log 0— or — 1 + log 1 + q)dx x . . . dx n 



C( -— wS 



— C ... e 2i'(l g'C- ^ — l)dx x . . . dx n 



rr nS 



= C • • • e^mi + qlogl + qdxx . . . dx n 



= C ... e~w{l + q \ gl + q-.q}dx 1 . . . da? n , 

 because 



C . . . e'Wqdxi . . . dx r = 0. 



Now since 1 + q is positive, 1 + q log 1 + q — g is necessarily 

 positive, unless q = 0, and is then zero ; B — B is therefore 

 positive. And given T and the coefficients a 1; 5 12 , &c, B has 



nS 



its least possible value when q=0 } or f(x x . . . x n ) =Ce 2T . 

 And this least possible or minimum value differs by a con- 



n \/D 

 stant from log C or log | (J^J ~~| j . 



Further, j- (B — ■ B ) = log (1 + q), and therefore B — B dimin- 

 ishes as q approaches zero. 



The Second Law of Thermodynamics, 



(17) In stationary motion the minimum function has th e 



value / n \f */D 



13 = ( ~™ r j plus a constant. 



It is a function of T and the parameters a t , b l2 , &c, or any 



