8 Mr. Tovey on the Relation between the Velocity and 
my method worthy of a place in your Journal, I shall pro- 
bably send you a continuation of the subject. 
Let m,m’, m', &c. be the masses of the particles of ether; 
let the rectangular coordinates of m be 2, y,2; those of m’, 
xv+Axr,y+Ay, z+ Az; of m', r+ Az’, yt Ay, z+Az, &e. 
Let r = /(Az?+ Ay?+3s?), 7) = /(Aa!?+ Ay’? + Az’?), &c. 
Suppose the masses to be all equal, and the force of one par- 
ticle on another to be a function of their distance multiplied 
by m3; and suppose each particle to be influenced only by the 
attractions or repulsions of the other particles; then as the 
cosines of the angles which 7 makes with the positive direc- 
A A A seh 
tions of z, y, 2 are =, —, = we have (by the princi- 
ples of statics), when the system is in equilibrium, 
m= me Aai=s0; mz, £1) Ay = 0, 
me 20) he O (1.) 
The sums = extending to all the particles within the sphere 
of the attractive or repulsive influence of the particle m, which 
may be any particle of the system. 
Now, suppose the system to be disturbed, and that at the 
end of the time ¢, the displacements of m, in the directions of 
2, Y, % be &, 7, $; and those of m’, E+ AE, y+Ayn, $+A’; and 
suppose Aé, Ay, A to be so small that we may neglect their 
squares and rectangles; then the distance of these particles 
being r+ Ar = oy [(Axv+A£)?+ (Ay+An)?+(Az+A8)*], 
we have 
_ ArAf+ AyAn+ Az AE 
Ps 
The cosines of the directions which » + Ar makes with those 
Axv+Ake Ay+An Az+AT. 
r+Ar? r+Ar? r+Ar ’ 
write X, Y, Z for the sums of the components of the forces 
acting on m, in the directions of 2, y, z, we have 
Ar 
of z,y, z will be and if we 
he J (r+4r) 
= 7 2 Sis der (Aaw+ A€), 
“4A 
Yame, SOTA ay san) (2.) 
T= m2 Lets) (Az+AQ). 
