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



NOTE ON ARTICLE 12. 



On a reperusal of Article 12, it appears to me that I have not stated with sufficient 

 accuracy the distinguishing characteristic of a system of attracting and repelling mole- 

 cules, and I think it, therefore, necessary to add a few words in explanation of what I have 

 there said. 



The supposition that the molecular force is a function of the distance may have one 

 of two meanings, namely: — 1. That all molecules situated at the same distance from m 

 exert upon it a force of the same intensity. 2. That the force which any one molecule 

 in exerts upon m cannot be changed, except by altering the distance between these two 

 molecules. If we recollect that the symbol d denotes a passage from one molecule to 

 another, and S the displacement of the same molecule; and if we use the latter in its most 

 general sense, as applied to any displacement, virtual or real, we may represent the first 

 hypothesis by the equations 



de ' d^ "' 



and the second by 



Sd ' S<p 



It is in the latter of these significations that the second hypothesis made in Article 12 is to 

 be understood. 



Now it has been shown in the text, that if the sum of the internal moments be capable 

 of being represented by the variation of a single function, we must have 



since p is indefinitely small. If then we use the symbol S to denote an increment pro- 

 duced by a real displacement, we shall have 



and, therefore. 

 Hence 



