of the Titer Diodynamic Properties of Substances. 389 



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

 then, we suppose points endowed witli mass proportional to the 

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

 modynamic states, placed in the positions determined by tlie states 

 and motions of tliese 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 effebt of motion in the parts of the body will be to move the 

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

 each case ti> the vis oiiut of the whole body, if endowed with the 

 velocity of the part represented ; — the center of gravity of points 

 thus determined will give the volume, entropy, and energy of the 

 whole body. 



Now let us suppose that the body having the initial Aolume, 

 entropy, and energy, v\ //', and t', is placed (enclosed in an envelop as 

 aforesaid) in a medium having the constant pressure P and tempera- 

 ture y, and by the action of the medium and the interaction of its 

 own parts comes to a final state of rest in which its volume, etc., are 

 y", ?/", f" ; — we wish to find a relation between tliese quantities. If 

 we regard, as we may, the medium as a very large body, so that 

 imparting heat to it or compressing it witliin moderate limits will 

 have no appreciable effect upon its pressure and temjjerature, and 

 write V, H, and E, for its volume, entrojiy, and energy, equation (1) 



becomes 



dE= Tdll—Pd I , 



Avhich we may integrate i-egarding P and T' as constants, obtaining 



E"^E'~ Tir'^TH'-PV"-\-PV', (a) 



where E\ E'\ etc., refer 'to the initial and final states of the medium. 

 Again, as the sum of the energies of the body and the surrounding 

 medium may become less, but cannot become greater (this arises from 

 the nature of the envelop supposed), we have 



e"^E"^^'-\-E'. (b) 



* 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 sensiltk vwtions. 



