200 The Rev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 



Bodies composed of attracting and repelling Molecules. 



12. Two conditions may be supposed to be included in the supposition, that 

 the molecular force is a force of attraction or repulsion, namely : 



1. That the direction of the force is in the line joining the molecules. 2. That 

 the intensity of this force, for each pair of molecules, is represented by a function 

 of the distance. Retaining the former of these conditions, we may replace the 

 second by the hypothesis made in the foregoing section, namely, that the sum of 

 the internal moments may be represented by the variation of a single function. 

 For as the effect of the force is in this case to change the distance between 

 two molecules, if this force be represented by F, and the distance between the 

 particles by />, the moment of the force F will be 



Fcp, 



or dividing the force 2^ as before into i^o and F,, and putting p + p for the dis- 

 tance as changed by displacement, 



effective moment = F^cf\ 



and therefore the complete moment is expressed by 



l\lF,lp'dm, 



which cannot be a complete variation, unless 



F. ^fip'). 



Hence the proposition is evident. Instead, therefore, of defining the body to 

 be one composed of attracting or repelling molecules, we shall define it to be 

 " a body in which the molecular force acts in the direction of the line joining 

 the molecules, and in which the sum of the internal moments is represented by 

 the variation of a single function." We shall consider successively the simplifica- 

 tions which these two suppositions introduce into the general equations. 



The first hypothesis, that, namely, which regards the direction of the mole- 

 cular force, is mathematically represented by making 



a'^a, p'=p, y' = y. 



