384 J^. W. G-ihhs on a Representation by Surfaces 



the plane y=0 (as that the whole surface must necessarily fall on the 

 positive side of this plane), but we must not expect to find properties 

 which concern the planes 7/=:0, or 6=z0, in distinction from others 

 parallel to them. It may be added that, as the volume, entropy, and 

 energy of a body are equal to the sums of the volumes, entropies, and 

 energies of its pai'ts, if the surface should be constructed for bodies 

 differing in quantity but not in kind of matter, the different surfaces 

 thus formed would be similar to one another, their linear dimensions 

 being proportional to the quantities of matter. 



Nature of that Part of the Surface which represents States lohich are 



not Iloinogeneous. 



This mode of representation of the volume, entropy, energy, pres- 

 sure, and temperature of a body will apply as well to the case in 

 which different portions of the body are in different states (supposing 

 always that the whole is in a state of thermodynamic equilibrium), as 

 to that in which the body is uniform in state throughout. For the 

 body taken as a whole has a definite volume, entropy, and energy, as 

 well as pressure and temperature, and the validity of the general 

 equation (1) is independent of the uniformity or diversity in respect 

 to state of the different portions of the body,* It is evident, there- 

 fore, that the thermodynamic surface, for many substances at least, 



* It is, however, supposed in this equation that the variations in the state of the 

 body, to whicli dv, di], and dz refer, are such as may be produced reversibly by expan- 

 sion and compression or by addition and subtraction of heat. Hence, when the body 

 consists of parts in different states, it is necessary tliat these states should be such as 

 can pass either into the other without sensible change of pressure or temperature. 

 Otherwise, it would be necessary to suppose in the differential equation (1) that the 

 proportion in which the body is divided into the different states remains constant. 

 But such a limitation would render the equation as applied to a compound of differ- 

 ent states valueless for our present purpose. If, however, we leave out of account 

 the cases in which we regard the states as chemically different from one another, 

 which lie beyond the scope of tliis paper, experience justifies us in assuming the above 

 condition (that either of the two states existing in contact can pass into the other with- 

 out sensible change of the pressure or temperature), as at least approximately true, 

 when one of tlie states is fluid. But if both are solid, the necessary mobility of the 

 parts is wanting. It must therefore be understood, that the following discussion of 

 the compound states is not intended to apply without limitation to the exceptional 

 cases, where we have two different solid states of the same substance at the same pres- 

 sure and temperature. It may be added that the thermodynamic equilibrium which 

 subsists between two such solid states of the same substance differs from that which 

 subsists when one of the states is fluid, very much as in statics an equilibrium which 

 is maintained by friction differs from that of a frictionless machine in which the 



