290 Obituary Notices of Fellows deceased. 



system. This involved the existence for the system of a unique charac- 

 teristic relation of total differentials, which might well be called the 

 equation of Gibbs ; namely, 



E = p^v-H^i^nii + ^t 2 S m 2 + . . . 



where 00 represents H, which is not itself the differential of any 

 analytical function, and the other terms represent energy of expansion, 

 of adiabatic chemical change, and of other types, the co-efficients 

 0, p, pi, . . . being intensities which depend only on the state of the 

 system, not on its mass. The principle of Clausius is that, for self- 

 contained systems in which E does not vary, the trend of must be 

 upwards in spontaneous change ; thus at constant temperature the value 

 of p <5v + ju.1 & mi + /"2 ^m 2 + . . . must be negative ; therefore 

 at constant temperature the trend of E 00 must be downwards, con- 

 trasting with the case of constant energy when that of is downwards. 

 The stable equilibria at constant temperature are at the minima of this 

 function. If there is the additional restriction that the reactions occur 

 also under constant extraneous atmospheric pressure, so that p is con- 

 stant as well as 0, it is the modified available energy E + p v 

 that tends to a minimum ; and a similar simplification obtains if any 

 other force of the system is supposed to be maintained invariable. 

 The variation of this part of the energy, A or E 0, is wholly avail- 

 able mechanically between states at the same temperature ; for each 

 temperature it constitutes a potential energy function of the forces, 

 and was in fact afterwards named on that account the free energy 

 by Helmholtz. When states of the systems at different temperatures 

 are compared, the availability must be referred to some standard 

 entropy, as in the discussion above, and the idea becomes complex. 

 Free energies at different temperatures must thus not be compared as 



3A 



available relatively to each other ; but - is equal to the entropy 0, 



3A v6 



and 0&r- is, equal to H, so that the heat capacities of the system 



are determined directly in terms of A. It had, indeed, been pointed 

 out long before by Massieu, as Gibbs remarked, that this expression 

 E constituted a single function fully characteristic by itself of 

 the system, over the range of purely physical changes with which 

 thermodynamics was then concerned, in that all the thermal quantities 

 belonging to the system are involved in it and derivable from it by 

 differentiation. 



An important development, in this new science of chemical energetics, 

 was the discussion of the number of different states or phases that 

 could exist alongside each other with given materials, as depending on 

 the number of independent constituent substances that are actually 

 interacting; one result of this was the simple and invaluable phase 



