158 EFFECT OF VARIOUS PROCESSES 



by a sufficiently slow variation of the external coordinates, 

 just as approximate thermodynamic equilibrium may usually 

 be attained by sufficient slowness in the mechanical operations 

 to which the body is subject. 



We now pass to the consideration of the effect on an en- 

 semble of systems which is produced by the action of other 

 ensembles with which it is brought into dynamical connec- 

 tion. In a previous chapter * we have imagined a dynamical 

 connection arbitrarily created between the systems of two 

 ensembles. We shall now regard the action between the 

 systems of the two ensembles as a result of the variation 

 of the external coordinates, which causes such variations 

 of the internal coordinates as to bring the systems of the 

 two ensembles within the range of each other's action. 



Initially, we suppose that we have two separate ensembles 

 of systems, E and E z . The numbers of degrees of freedom 

 of the systems in the two ensembles will be denoted by n^ and 

 n 2 respectively, and the probability-coefficients by e^ and e"*, 

 Now we may regard any system of the first ensemble com- 

 bined with any system of the second as forming a single 

 system of ^ + n z degrees of freedom. Let us consider the 

 ensemble ( J? 12 ) obtained by thus combining each system of the 

 first ensemble with each of the second. 



At the initial moment, which may be specified by a single 

 accent, the probability-coefficient of any phase of the combined 

 systems is evidently the product of the probability-coefficients 

 of the phases of which it is made up. This may be expressed 

 by the equation, 



e w = 6 V e v , (455) 



or n* = in' + ^ ( 456 ) 



which gives r^z = ij/ + iya'- (457) 



The forces tending to vary the internal coordinates of the 

 combined systems, together with those exerted by either 

 system upon the bodies represented by the coordinates called 



* See Chapter IV, page 37. 



