ON AN ENSEMBLE OF SYSTEMS. 163 



e/ _ e," + ej - e 2 " + etc. = W. (480) 



If E Q , E v and JE 2 are the only ensembles, we have 



^< ,-_, ( -,_-, 0i (481) 



It will be observed that the relations expressed in the last 

 three formulae between IF, e x e/', e 2 ' e 2 ", etc., and @ 1? 

 2 , etc. are precisely those which hold in a Carnot's cycle for 

 the work obtained, the energy lost by the several bodies which 

 serve as heaters or coolers, and their initial temperatures. 



It will not escape the reader's notice, that while from one 

 point of view the operations which are here described are quite 

 beyond our powers of actual performance, on account of the 

 impossibility of handling the immense number of systems 

 which are involved, yet from another point of view the opera- 

 tions described are the most simple and accurate means of 

 representing what actually takes place in our simplest experi- 

 ments in thermodynamics. The states of the bodies which 

 we handle are certainly not known to us exactly. What we 

 know about a body can generally be described most accurately 

 and most simply by saying that it is one taken at random 

 from a great number (ensemble) of bodies which are com- 

 pletely described. If we bring it into connection with another 

 body concerning which we have a similar limited knowledge, 

 the state of the two bodies is properly described as that of a 

 pair of bodies taken from a great number (ensemble) of pairs 

 which are formed by combining each body of the first en- 

 semble with each of the second. 



Again, when we bring one body into thermal contact with 

 another, for example, in a Carnot's cycle, when we bring a 

 mass of fluid into thermal contact with some other body from 

 which we wish it to receive heat, we may do it by moving the 

 vessel containing the fluid. This motion is mathematically 

 expressed by the variation of the coordinates which determine 

 the position of the vessel. We allow ourselves for the pur- 

 poses of a theoretical discussion to suppose that the walls of 

 this vessel are incapable of absorbing heat from the fluid. 



