822 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



the same attractive force as before, so that no change of effect is 

 produced. The effects of the two other pairs must be considered 

 separately. 



The atom H is more distant from J than from M, for its distance 

 from M is less than 90°, since it is the hypothenuse of a right 

 angled spherical triangle, of which the sums of the two legs is 

 90°, while the distance from H to J is greater than 90°, l)eiug the 

 hypothenuse of a right angled spherical triangle, of which one 

 side is 90°+ C J, and the other, the distance A H. 



The resultant attractive force exerted by J and M upon H, 

 therefore, is not in the direction H G. It is, however, since a 

 straight line drawn from M to J will cut tiirough G, in the plane 

 of a great circle of the sphere, and we may decompose it into two 

 forces, one in the line H G, and the other tangent to the sphere at 

 H, forming nearly a right angle with the direction A H, and tend- 

 in «• to cause H to divero;e a little from its orbit to the left of its 

 direction of motion. 



This component of the forces exerted is the only one that can 

 disturb the stability of the system, for the momentum and central 

 attraction will keep the atoms in their orbits, and by amplifying 

 or reducing the orbits, preserve an equilibrium between the cen- 

 tripetal and centrifugal forces. 



In like manner it may be shown that H is more strongly 

 attracted towards I than towards L, and the tangential component 

 of the resultant attractive force will be equal in amount to that of 

 M and J, but its direction will be so nearly that of A H, that the 

 component of divergence may be disregarded as being the indefi- 

 nitely small portion of an indefinitely small quantity, and the 

 whole tangential component may be considered as expended in 

 accelerating the velocity of H in its orl)it. 



By similar reasoning we find that while each of the atoms H, J 

 and L above the dynamical equator diverge a little to the left of 

 the circular orbits represented, Avhen viewed from without, I, K 

 and M, below the equator, diverge to the right. Continued action 

 of the same kind will take place upon H in the same direction, but 

 with less and less disturbing power, as the motion of M takes it 

 more and more in the rear of H, and that of I more and more to 

 the right. The effect upon each of the other atoms is obviously' 

 similar. 



In the meantime all the atoms are approaching the dynamical 

 equator, and must cross it simultaneously, since the acceleration 



