Chat. XXI.] THE HEAVENS. 279 



PROPOSITION XXXVIII. 



Problem. — To determine the interaction of revolving 

 forces. 



1. Two equal forces revolving in the same direc- 

 tion, in the same plane, will mutually revolve each 

 other ; so that they will both revolve in an orbit 

 whose diameter will be the radius of either of the 

 orbits in which one endeavours to revolve the other. 



2. If two equal forces revolve in planes at right 

 angles to each other, the one whose axis lies in the 

 plane of the rotation of the other will be revolved by 

 the latter. 



3. If two equal forces revolve in opposite direc- 

 tions in the same plane they cannot revolve each 

 other, unless the equilibrium of their forces be dis- 

 turbed by the action of some extraneous force. 



4. Let each of the foregoing couples be revolved 

 by the action of a greater central force of rotation. 



And let this central force rotate in the same plane 

 and in the same direction as the bodies m Section I. 



Then, when these latter are equidistant from the 

 central force, they are equally acted on by it, and 

 therefore remain at their normal distance from each 

 other. 



But, as they advance in their orbital motions 

 round each other, the one approaches and the other 



