THERMODYNAMIC PROPERTIES OF SUBSTANCES. 35 



must be such, namely, as shall not be affected by any of the changes 

 mentioned above. For example, we may find properties which concern 

 the plane v = (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 ij = 0, or e = 0, 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 parts, 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 which are 



not Homogeneous. 



This mode of representation of the volume, entropy, energy, pressure, 

 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, therefore, that 



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

 body, to which dv, dy, and rfe 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 that 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 different 

 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 this paper, experience justifies us in assuming the above con- 

 dition (that either of the two states existing in contact can pass into the other without 

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

 one of the 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 com- 

 pound 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 pressure 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 main- 

 tained by friction differs from that of a frictionless machine in which the active forces 

 are so balanced, that the slightest change of force will produce motion in either 

 direction. 



Another limitation is rendered necessary by the fact that in the following discussion 

 the magnitude and form of the bounding and dividing surfaces are left out of account ; 



