The Rev. J. H. Jellett on the Equilibrium and Motion of an Elastic SoliJ. 183 

 This being supposed universally true, we shall have, as is easily seen, 



F=/(a;7j,z, x',y',z', |' _ ^, ^' _ ^, f' - f ). 

 Let p, e, be the polar co-ordinates of ?«' xvith regard to m; then since 

 a;' = a- + psin0cos(p, y' = y + p sin 6 sin 0, z'=z + pcose; 

 it is plain that the foregoing expression for cc may be written 



^=/(^<y,2, p,e,(f>, I'- 1, ^'_,,, f'-f). 



Hitherto no assumption has been made either with respect to the macmitude 

 of the distance between the particles m, m', or with respect to that of the dis- 

 placements I, ^ f , ^', ,/, ^'. But previously to proceeding further, it is neces- 

 sary to make the following suppositions: 



(1.) That the greatest distance between two particles which are capable 

 of acting upon one another, or, as it is ordinarily termed, the radius of mole- 

 cular activity, IS indefinitely small compared with the intensity of the force 

 generated. 



(2.) That the sphere of molecular activity contains, nevertheless, an inde- 

 nnitely gi-eat number of particles. 



From the first of these assumptions, combined with the supposition that 

 the displacements follow some regular law, we have 



quantities of higher orders being neglected. 

 For the same reason, 



F=F,+A{^'-^)+B{^'-r,) + C{^'~Q. (B) 



This expression consists, as will be seen, of two distinct parts, namely F„ 



