OF AN ENSEMBLE OF SYSTEMS. 37 



words. Let us therefore suppose that in forming the system 

 C we add certain forces acting between A and .5, and having 

 the force-function e AB . The energy of the system C is now 

 A + B + ABI an d an ensemble of such systems distributed 

 with a density proportional to 



(96) 



would be in statistical equilibrium. Comparing this with the 

 probability-coefficient of C given above (95), we see that if 

 we suppose e AB (or rather the variable part of this term when 

 we consider all possible configurations of the systems A and B) 

 to be infinitely small, the actual distribution in phase of C 

 will differ infinitely little from one of statistical equilibrium, 

 which is equivalent to saying that its distribution in phase 

 will vary infinitely little even in a time indefinitely prolonged.* 

 The case would be entirely different if A and B belonged to 

 ensembles having different moduli, say A and 5 . The prob- 

 ability-coefficient of C would then be 



which is not approximately proportional to any expression of 

 the form (96). 



Before proceeding farther in the investigation of the dis- 

 tribution in phase which we have called canonical, it will be 

 interesting to see whether the properties with respect to 



* It will be observed that the above condition relating to the forces which 

 act between the different systems is entirely analogous to that which must 

 hold in the corresponding case in thermodynamics. The most simple test 

 of the equality of temperature of two bodies is that they remain in equilib- 

 rium when brought into thermal contact. Direct thermal contact implies 

 molecular forces acting between the bodies. Now the test will fail unless 

 the energy of these forces can be neglected in comparison with the other 

 energies of the bodies. Thus, in the case of energetic chemical action be- 

 tween the bodies, or when the number of particles affected by the forces 

 acting between the bodies is not negligible in comparison with the whole 

 number of particles (as when the bodies have the form of exceedingly thin 

 sheets), the contact of bodies of the same temperature may produce con- 

 siderable thermal disturbance, and thus fail to afford a reliable criterion of 

 the equality of temperature. 



