The Eev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 203 



f d^ ^d^ d^ 



+ a^pA cos oi j-_ + cos jS, ^ + cos 7, -r- 



, ( dn ^ dn dti\ 



+ 6,p,(^cosa,^+cos^,^ + cos7>^j 



+ c, p, (^cos a, ^ + cos /3, -A + cos 7, ^j , 



where /o is the force which is independent of the displacements of any one of 

 the three particles. First let it be supposed that/o is independent of the dis- 

 placements of any other particle.* Then, as the foregoing expression represents 

 that part of the modifying force which results from the relative displacement 

 of m", it seems that the most general supposition which we can make as to the 

 aggregate effect of all the particles is, that it is estimated by multiplying this 

 expression by some function of the polar co-ordinates of ?«", as also by the ele- 

 ment of the mass^ and integrating through the whole sphere of molecular acti- 

 vity. It is easily seen, that the result of this process will be an expression of 

 the form 



dx ^ dy ' dz 

 dx ^ dy ^ dz 



^^'di^^'Ty^^'Tz' 



where E,,, A^, Bi, &c., are definite integrals depending upon the constitution 

 of the medium, being in general of the form 



/(.r, y, z, p., e, <j>). 



Hence the general value of i^ ( (D), p. 185) will become 



* It is easily seen, that this supposition does not limit the generality of the result. 

 VOL. XXU. 2 E 



E, + A,-r- + A,- + A,- 



