THERMODYNAMIC PROPERTIES OF SUBSTANCES. 39 



Properties of the Surface relating to Stability of Thermodynamic 



Equilibrium. 



We will now turn our attention to the geometrical properties of 

 the surface, which indicate whether the thermodynamic equilibrium 

 of the body is stable, unstable, or neutral. This will involve the 

 consideration, to a certain extent, of the nature of the processes which 

 take place when equilibrium does not subsist. We will suppose the 

 body placed in a medium of constant pressure and temperature ; but 

 as, when the pressure or temperature of the body at its surface differs 

 from that of the medium, the immediate contact .of the two is hardly 

 consistent with the continuance of the initial pressure and temperature 

 of the medium, both of which we desire to suppose constant, we will 

 suppose the body separated from the medium by an envelop which 

 will yield to the smallest differences of pressure between the two, but 

 which can only yield very gradually, and which is also a very poor 

 conductor of heat. It will be convenient and allowable for the pur- 

 poses of reasoning to limit its properties to those mentioned, and to 

 suppose that it does not occupy any space, or absorb any heat except 

 what it transmits, i.e., to make its volume and its specific heat 0. By 

 the intervention of such an envelop, we may suppose the action of the 

 body upon the medium to be so retarded as not sensibly to disturb 

 the uniformity of pressure and temperature in the latter. 



When the body is not in a state of thermodynamic equilibrium, its 

 state is not one of those which are represented by our surface. The 

 body, however, as a whole has a certain volume, entropy, and energy, 

 which are equal to the sums of the volumes, etc., of its parts.* If, 

 then, we suppose points endowed with mass proportional to the 

 masses of the various parts of the body, which are in different thermo- 

 dynamic states, placed in the positions determined by the states 

 and motions of these parts, (i.e., so placed that their co-ordinates are 

 equal to the volume, entropy, and energy of the whole body supposed 

 successively in the same states and endowed with the same velocities 

 as the different parts), the center of gravity of such points thus 

 placed will evidently represent by its co-ordinates the volume, entropy, 

 and energy of the whole body. If all parts of the body are at rest, 

 the point representing its volume, entropy, and energy will be the 

 center of gravity of a number of points upon the primitive surface. 

 The effect of motion in the parts of the body will be to move the 

 corresponding points parallel to the axis of e, a distance equal in 

 each case to the vis viva of th^ whole body, if endowed with the 



*As the discussion is to apply to cases in which the parts of the body are in (sensible) 

 motion, it is necessary to define the sense in which the word energy is to be used. We 

 will use the word as including the vis viva of sensible motions. 



