of the Theri)wdyn<(mic Prirperties of Substances. 385 



can be di\'i(UHl into two parts, of wliicli one represents the homoge- 

 neous states, the other tliose which are not so. We shall see that, 

 when the former part of the surface is given, tlie latter can readily be 

 formed, as indeed we might expect. We may therefore call the for- 

 mer part the primitive surface, and the latter the derived surface. 



To ascertain the nature of the derived surface and its relations to 

 the primitive surface sufficiently to construct it when the latter is 

 given, it is only necessary to use the principle that the volume, 

 enti'opy, and energy of the whole l)ody are equal to the sums of the 

 volumes, entropies, and energies res})ectively of the parts, while the 

 pressure and tempci'ature of the whole ai'c the same as those of each 

 of the parts. Let us commence with the case in Avhich the body is in 

 part solid, in part liquid, and in part vapor. The position of the 

 point detei'mined by the volume, entropy, and energy of such a com- 

 pound will be that of the center of gravity of masses jiroportioned 

 to the masses of solid, liquid, and vapor jdaced at the three points of 

 the primitive surface which represent respectively the states of com- 

 plete solidity, complete liquidity, and cora})lete vaporization, each at 

 the temperature and pressure of the compound. Hence, the part of 

 the surface which represents a compound of solid, liquid, and vaj^or is 

 a plane triangle, having its vertices at the points mentioned. The 

 fact that the surface is hei'e plane indicates that the pressure and tem- 

 perature are here constant, the inclination of the plane indicating the 

 value of these quantities. Moreover, as these values are the same for 

 the compound as for the three different homogeneous states corres- 

 ponding to its diiferent portions, the plane of the triangle is tangent 

 at each of its vertices to the primitive surface, viz : at one vertex to 

 that part of the primitive surface which represents solid, at another 

 to the part representing liquid, and at the third to the part represent- 

 ing vapor. 



When the body consists of a compound of two different homogene- 

 ous states, the point which represents the compound state will be at 



active forces are so balanced, that the shghtest change of force will j^roduce motion 

 in either direction. 



Another limitation is rendered necessary by the fact that in the following discus- 

 sion the magnitude and form of the bounding and dividing surfaces are left out of 

 account ; so that the results are in general strictly valid only in cases in which the 

 influence of these particulars may be neglected. When, therefore, two states of the 

 substance are spoken of as in contact, it must be understood that the surface dividing 

 them is plane. To consider the subject in a more general form, it would be necessary 

 to introduce considerations which belong to the theories of capillarity and crystalliza- 

 tion. 



