80 BUTLER ART. D 



purpose he uses the criterion in its second form, "both because 

 it admits more readily the introduction of the condition that 

 there shall be no thermal communication between the different 

 parts of the system, and because it is more convenient, as 

 respects the form of the general equations relating to equilib- 

 rium, to make the entropy one of the independent variables 

 which determine the state of the system, than to make the energy 

 one of these variables."* In order to apply the criterion it is nec- 

 essary to specify completely the possible variations of which the 

 energy of the system is capable, and for this purpose differential 

 coefficients, representing the change of energy of homogeneous 

 parts of the system with the quantities of their component 

 substances, must be introduced. The complete significance 

 of these quantities does not appear until a later stage. It is 

 thought that the discussion of the conditions of equiUbrium 

 in heterogeneous systems will be more easily followed if we first 

 define the auxiliary functions \p, f and x and derive the varia- 

 tions of the energy, and of these quantities, in homogeneous 

 masses. 



Let e, 7] and v be the energy, entropy and volume respectively 

 of a homogeneous body at a temperature t and pressure p. We 

 have seen that in any given state the energy and entropy of a body 

 are definite, but since it is only possible to measure differences of 

 energy and entropy, "the values of these quantities are so far 

 arbitrary, that we may choose independently for each simple 

 substance, the state in which its energy and entropy are both 

 zero. The values of the energy and entropy of any compound 

 body in any particular state will then be fixed. Its energy will 

 be the sum of the work and heat expended in bringing its 

 components from the states in which their energies and their 

 entropies are zero into combination and to the state in ques- 



tion; and its entropy is the value of the integral J — for any 



reversible process by which that change is effected." 

 The quantities \p, f and x, defined by the equations 



^ = 6 - iT,, (14) [87] 



f = ,-trj-^pv, (15) [91] 



X = e + vv; (16) [89] 



* Gibbs, I, 62. 



