152 Mr, S. H. Burbury on the 



where D is the determinant of ^ 2%, ^p& 12 , &c, and then 



in the redistributed system the law will be 



F(o 1 ...e„) = Ce-» 



as before, and will remain unaffected by any further redistri- 

 bution. In stationary motion, therefore, F (cj . . . cj has the 



_«s 

 form Ce 2T , with a quadratic function for S, whether the 

 initial distribution /(^i . . . a? J has that form or not. 



This assumes that the process of redistribution of the 

 original systems has been carried out completely. If it be 

 carried out only partially, as for instance if only a portion of 

 the original systems be subjected to the process, the distribu- 

 tion in the new system will approximate more and more to 



«s 



the permanent form Ce 2T , according as the redistribution 

 is more complete. And by successive partial redistributions 

 it will ultimately be reduced to the permanent or stationary 

 form. 



(10) The processes which we have supposed to take place 

 successively may, of course, take place simultaneously. 

 Further, we may suppose the whole process of redistribution 

 to take place at a given rate per unit of time. Finally, our 

 results will not be affected if the variables in any association 

 undergo any other series of changes during the same time, 

 provided these changes do not on average alter S. 



(11) By the method of art. 8 energy is conserved in the 

 final result, but is not conserved in each separate process, 

 because generally S', the energy which we suppose to be 

 received by a system in the new distribution, is not equal to 



-±— — 2 ' ' ' - , the energy which the contributing systems 



part with. That may create a difficulty in the application of 

 the method to a physical system, even although, when the 

 contributing systems are rapidly oscillating and in different 



phases, it may be that S' = — 2 m* " on the average 



of a very short time. 



(12) If our associations be material systems fixed in space, 

 we may suppose the energy, S, of oscillation to be transmitted 

 through space — i. e. aether — in waves with conservation of 

 energy, so that the energy of a wave which passes per 

 unit area and time through a spherical surface of radius B 



