The Rev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 197 



are evidently identical with the system of equations (R). The theorem, as 

 stated above, is, therefore, true. 



10. The total number of constants in />+ i/+iV being fifty-four, it is evi- 

 dent that the number oi distinct constants contained in cF, and, therefore, in 

 F, will be 



54- 18 = 36. 



Now V, which is, as we have seen, a homogeneous quadratic function of the 



nine quantities 



d^ li^ d^ di] dy d^ d£ d^, d^ 



dx' dy' dz' dx' dy' dz' dx' dy' dz' 



will contain in general forty-five terms, and therefore, if it be subjected to no 

 restriction, forty-five distinct constants. The function at which we have arrived 

 is not, therefore, in its most general form. In fact, if we examine the composi- 

 tion of the terms in the value of Z (H), we see that the quantities 



Similarly, in the value of if we should 



with the common coefficient ^^j,^- These coefficients being, by the equations 

 (R), identical, the four terms enumerated above may be written 



d)] di^ d£, dcrj d>] dc^ d£, dhj 

 dy dz dz dy dz dy dy dz j' 



B,..H'^:^+'^^ 



di) d^ dij d^ 

 dy dz dz dy 



Hence it is evident, that the terms in V containing 



dfj d£, dv] d£, 

 dij dz ' dz dy' 

 will be of the form 



2d 2 



