applicable to Heat. 125 



pulsions, which act inversely as the square of the distance, is 

 named, irrespective of the sign, the reciprocal potential of the 

 system of points. As it is advisable to have a convenient name* 

 for the case in which the attractions and repulsions are governed 

 by any law whatever, or, more generally still, for every case in 

 which the work accomplished in an infinitely small motion of the 

 system may be represented by the differential of any magnitude 

 dependent only on the space-coordinates of the points, I propose 

 to name the magnitude whose differential represents the negative 

 value of the work, from the Greek word epyov (work), the ergal 

 of the system. The theorem of the equivalence of vis viva and 

 work can then be expressed very simply ; and in order to exhibit 

 distinctly the analogy between this theorem and that respecting 

 the virial, I will place the two in juxtaposition : — 



(1) The sum of the vis viva and the ergal is constant. 



(2) The mean vis viva is equal to the virial. 



In order to apply our theorem to heat, let us consider a body 

 as a system of material points in motion. With respect to the 

 forces which act upon these points we have a distinction to make : 

 in the first place, the elements of the body exert upon one another 

 attractive or repulsive forces; and, secondly, forces may act 

 upon the body from without. Accordingly we can divide the 

 virial into two parts, which refer respectively to the internal and 

 the external forces, and which we will call the internal and the 

 external virial. 



Provided that the whole of the internal forces can be reduced 

 to central forces, the internal virial is represented by the formula 

 above given for a system of points acting by way of attraction or 

 repulsion upon one another. It is further to be remarked that, 

 with a body in which innumerable atoms move irregularly but in 

 essentially like circumstances, so that all possible phases of mo- 

 tion occur simultaneously, it is not necessary to take the mean 

 value of rcj)(r) for each pair of atoms, but the values of r<f>{r) may 

 be taken for the precise position of the atoms at a certain moment, 

 as the sum formed therefrom does not importantly differ from 

 their total value throughout the course of the individual motions. 

 Consequently we have for the internal virial the expression 



^2<r<f>(r). 



As to the external forces, the case most frequently to be con- 

 sidered is where the body is acted upon by a uniform pressure 

 normal to the surface. The virial relative to this can be expressed 



* The term force-function, besides some inconvenience, has the disad- 

 vantage of having been already used for another magnitude, which stands 

 to the one in question in a relation similar to that in which the potential- 

 function stands to the potential. 



