A SYSTEM OF PARTICLES. 265 



SECTION III. 



Combination of the Vibratory Motion of Particles icith the 

 Motion of Translation. 



31. In the preceding Section we have considered the forces repnl- 

 sive: though, as far as their mutual action on eacli other is concerned, 

 there appears to be no reason for so doing; indeed it appeared from 

 considerations connected with light that the etiier, at least, is an excep- 

 tion to this rule. The difficulty attending the hypothesis of attractive 

 forces consists in the apparent instability of a system of such particles. 



This difficulty, however, is readily obviated, as the following con- 

 siderations sufficiently evince. 



32. If the particles have the cubical arrangement which I have 

 before adopted, it is clear that the action of the forces on any par- 

 ticle, moved slightly from its position of equilibrium, would tend to 

 bring it back. And if a series of particles in a given plane be 

 simultaneously moved, they, in like manner, would be brought back. 

 But another case presents itself wliich is not so easily solved, viz., 

 that, in which a series of particles in one plane are moved simul- 

 taneously at right angles to that plane. We will then endeavour to 

 find what is the force exerted on a particle in these circumstances. 



33. Take the position of equilibrium of any particle, so displaced, 

 as the origin of co-ordinates: let x, y, s be the co-ordinates of any 

 other particle, at the distance r, suppose the displacement to be throuo-Ii 

 the space a, and that the force varies inversely as the square of the 

 distance, then the attraction on this particle to carry it forward, is 



2 yr; -^~ — — — -3 taken to infinity. 



