202 J. W. Gibbs — Equilibrmm of Heterogeneous Substances. 



tory phases, they may not still have a theoretical significance. If so, 

 the consideration of the subject from this point of view, may assist 

 us, in such cases, in discovering the foi-m of the fundamental equation 

 with reference to the ultimate components, which is the only equation 

 required to express all the properties of the bodies which are capable 

 of experimental demonstration. Thus, when the phase of a body is 

 completely determined by the quantities of n independently vari- 

 able components, with the temperature and pressure, and we have 

 reason to suppose that the body is composed of a greater number 

 n' of proximate components, which are therefore not independ- 

 ently variable (while the temperature and pressure remain constant), 

 it seems quite possible that the fundamental equation of the body 

 may be of the same form as the equation for the phases of dissi- 

 pated energy of analogous compounds of n' proximate and n ultimate 

 components, in which the proximate components are capable of 

 independent variation (without variation of temperature or pressure). 

 And if such is found to be the case, the fact will be of interest as 

 affording an indication concerning the proximate constitution of the 

 body. 



Such considerations seem to be especially applicable to the very 

 common case in which at certain temperatures and pressures, regarded 

 as constant, the quantities of certain proximate components of a 

 mass are capable of independent variations, and all the phases pro- 

 duced by these variations are permanent in their nature, while at other 

 temperatures and pressures, likewise regarded as constant, th^ quan- 

 tities of these proximate components are not capable of independent 

 variation, and the phase may be completely defined by the quantities 

 of the ultimate components with the temperature and pressure. There 

 may be, at certain intermediate temperatures and pi*essures, a condi- 

 tion with respect to the independence of the proximate components 

 intermediate in character, in which the quantities of the proximate 

 components are independently variable when we consider all phases, 

 the essentially transitory as well as the permanent, but in which these 

 quantities are not independently variable when we consider the 

 permanent phases alone. Now we have no reason to believe that the 

 passing of a body in a state of dissipated energy from one to another 

 of the three conditions mentioned has any necessary connection with 

 any discontinuous change of state. Passing the limit which separates 

 one of these states from another will not therefore involve any dis- 

 continuous change in the values of any of the quantities enumerated 

 in (99)-(103) on page 143, if >y/,, wig, . . . m„, //j, //g? • • • yWn are 



