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

 and, therefore, since no such term can occur in N', we shall have in 



L + M+iV, 

 the group 



rf)/ di^ . d^ dlri 



ax dd' ' d.v dx ^ ^ ' 



Now if Z + M + 7V be a complete variation, it is plain that this expression 

 must have been derived from a single term of the form 



dx dx' 



Taking the variation of this term by the ordinary rule, and comparing it with 

 (Q'), we have the condition 



Proceeding in a similar way with the remaining terms, we find altogether 

 eighteen equations of condition, namely. 



(R) 



These equations may be more briefly written as follows : 



III {A cos p' -B cos a') (I' - ^) (,/ - ,,) dm = 0, 



JJJ(C cos a' -A cos 7') (r - W - dm = 0, (S) 



III (B cos y'-C cos ,3') (./ - y) (f - ^ dm = 0. 



For if we substitute for 



their values (C), and perform the integrations with regard to dm, the first of 

 the foregoing equations may be written 



