ABSTRACT BY THE AUTHOR. 355 



the suffixed letter, as in the preceding cases, indicating that the 

 quantity which it represents is constant. This condition, in connection 

 with that of uniform temperature, may be shown to be equivalent 

 to (1) or (2). The difference of the values of \^ for two different 

 states of the system which have the same temperature represents the 

 work which would be expended in bringing the system from one 

 state to the other by a reversible process and without change of 

 temperature. 



If the system is incapable of thermal changes, like the systems 

 considered in theoretical mechanics, we may regard the entropy as 

 having the constant value zero. Conditions (2) and (4) may then 

 be written 



and are obviously identical in signification, since in this case \fs = e. 



Conditions (2) and (4), as criteria of equilibrium, may therefore 

 both be regarded as extensions of the criterion employed in ordinary 

 statics to the more general case of a thermodynamic system. In fact, 

 each of the quantities e and \{s (relating to a system without 

 sensible motion) may be regarded as a kind of force-function for 

 the system, the former as the force-function for constant entropy 

 (i.e., when only such states of the system are considered as have 

 the same entropy), and the latter as the force-function for constant 

 temperature (i.e., when only such states of the system are considered 

 as have the same uniform temperature). 



In the deduction of the particular conditions of equilibrium for 

 any system, the general formula (4) has an evident advantage over 

 (1) or (2) with respect to the brevity of the processes of reduction, 

 since the limitation of constant temperature applies to every part 

 of the system taken separately, and diminishes by one the number 

 of independent variations in the state of these parts which we have 

 to consider. Moreover, the transition from the systems considered 

 in ordinary mechanics to thermodynamic systems is most naturally 

 made by this formula, since it has always been customary to apply 

 the principles of theoretical mechanics to real systems on the sup- 

 position (more or less distinctly conceived and expressed) that the 

 temperature of the system remains constant, the mechanical properties 

 of a thermodynamic system maintained at a constant temperature 

 being such as might be imagined to belong to a purely mechanical 

 system, and admitting of representation by a force-function, as follows 

 directly from the fundamental laws of thermodynamics. 



Notwithstanding these considerations, the author has preferred in 

 general to use condition (2) as the criterion of equilibrium, believing 

 that it would be useful to exhibit the conditions of equilibrium of 

 thermodynamic systems in connection with those quantities which 



