The Eev. J. H. Jellett on the Eguilibrium and Motion of an Elastic Solid. 205 



titles will furnish but otie term to the equations of motion. Thus, if the 

 quantities 



enter into L in the form 



d^(m d^ dl^ 



dz dy ' dy dz' 



A ^ ^+5^ ^ 

 dz dy dy dz ' 



the equations of motion will derive from them the single term 



It is evident, therefore, that the supposition 



will not restrict in any way the generality of these equations. We have seen 

 accordingly, that the principle of independent action gives to these equations 

 the greatest number of independent constants which they can have, without a 

 change of form. But the restriction may show itself in other ways. Thus, when 

 we assume that the simi of the internal moments may be represented by the 

 variation of a single function V, we find that in order to reconcile this suppo- 

 sition with the principle of independent action, it is necessary to assume further, 

 that the coefficients of Fare connected by nine equations of condition, and that, 

 therefore, that principle does not admit of the existence of a function V in its 

 most general form. This restriction has evidently been removed by supposing 

 the state of each molecule to be modified by the action of the surrounding 

 molecules. For, as we have just seen, this supposition enables us to obtain values 

 for L, M, N in which the coefficients are completely independent of each other ; 

 and, with regard to the particular case of physical optics, we infer, as before, 

 that if a luminous ether exist, whose constitution agrees with either of the hy- 

 potheses advanced by Professor I\Iac Cullagh and Mr. Geeen respectively, 

 each of the particles of that medium must be supposed to be capable of modi- 

 fying the force exerted by any other particle within its sphere of action. 



It is unnecessary to pursue the consequences of this principle further; 

 for, as we have already seen, all the varieties of the general equations of mo- 

 tion, to the consideration of which the present Memoir is specially devoted, 

 may be obtained from the more limited principle of independent action. ■- 



2e2 



