A SYSTEM OF PARTICLES. 23', 



SECTION I. 



Interpre/afiofi of the Equations corresponding to Vihratory Motion. 



1. Let the mass of a particle of medium A, estimated by its 

 repulsion at the distance unity, be represented by P\ that of a par- 

 ticle of medium H, estimated in like manner, by Q; and the moving 

 force of a particle of A on a particle of H by 3/, which is also the 

 moving force of a particle of IB on one of A. 



We will first consider the motion of a particle of medium A. 



Let .r, y, s be its co-ordinates when at rest, 



X -^r Ix, y + ly, z -v Sz those of another particle of the same medium, 



X + Ax, y + i\y, x + As those of a particle of B\ 



r = \/lx' + If + W, 

 R = V^x- + Ay- + Ass^ 



Let the same quantities at the end of the time / become 

 X + a, y, z. 



x + a + ^x + Sa, y + Sy, x + Sz. 

 X + a + Ax + Aa, y + Ay, z + As. 

 r + Sr. 

 R + aR. 

 (the motion being in the direction of the axis of x) 

 and let the function which expresses the force be r(pr. 



The action of the particles of A on the particle in question parallel 

 to X, is evidently the sum of all such expressions as the following, 



P'.(p{r + ^r) (Sx + Sa) ; 



and that of the particles of B on the same particle the sum of 



M.(p(R + AR){Ax + Aa), 



