174 CELESTIAL MECHANICS. I. ill. 14. 



and the horse and the weight would approach each other, 

 with equal quantities of motion. And this is what we 

 mean by the reciprocality of forces, or the equality of 

 action and reaction. 



304. Theorem. " 285.'' If two gravi- 

 tating bodies be suspended at constant dis- 

 tances from each other and from a given 

 point, they will be at rest when their centre of 

 inertia is in the vertical line passing through 

 the point of suspension : and the equilibrium 

 will be stable when the centre of inertia would 

 ascend in quitting the vertical line, tottering 

 when it would descend, and neutral when it 

 cannot quit it. 



jy Suppose the bodies A and B, of which 



^<:;^;^^T\ C is the centre of inertia, to be sus- 



C^^""-<\ pended from D by the threads AD, BD, 

 B and to be retained at the distance AB by 

 the rod AB, and let C be in the vertical line DC. Let the 

 force of gravity be represented by DC, then AD will 

 represent the action of the thread, and AC the pressure 

 exerted by A on any obstacle at C (241); and in the same 

 manner BC will represent the pressure of B in the 

 direction BC, supposing the weights A and B equal, and 

 each represented by DC ; but since they are unequal, the 

 ratio of their masses must be compounded with that of 

 the relative forces, and A.AC will represent the actual 

 force of A, and B.BC that of B ; but these products, by 

 the supposition, are equal, since A : B=;BC : AC (298); 



