The Eev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 193 



(P- 1) {Q: - 1) {R" - 1)-EQ:'{P- 1) -P"Ii{Q'-\)-QP'{R"-l) 



+ FQ"R+ P"QR'=.0. (Q) 



We shall next proceed to consider the two hypotheses which have been 

 most frequently made by writers upon this subject, namely: — 1. That the sum 

 of the internal moments may be represented by the variation of a single func- 

 tion. 2. That the force which one molecule exerts upon another is a force of 

 attraction or repulsion. 



Hypothesis of the Existence of a single Function V, by whose Variation the Sum 

 of the internal Moments of the Body may be represented. 

 8. This condition gives the equation 



The three expressions (H), p. 187, must, therefore, when added together, give 

 a complete variation. Now if we examine the value of Z there given, we shall 

 see that the first six terms, those, namely, which are multiplied by 



-^^"a'l ^^■'a'l ^7"^'! ^/Jia'' ^ a,o' 1 ^a^a' ) 



form in themselves a complete variation, namely, 



^ I --'^^'"■dF- + ^^^'^'df + ^^^'^-d^^^'-'Ty dz 



Similarly in the values of M and N the terms multiplied by 



respectively, form complete variations in themselves. 

 Let us now consider the term in the value of .£ 



" " dx dx 

 Corresponding to this term, we have in the value of M 



dk dh, 



