CHAPTER XVI. 



LAWS OF FALLING BODIES. 



IT has already been shown that the actual quantity of 

 motion of two bodies approaching each other in con- 

 sequence of their mutual gravitation must be the same in 

 the one body as in the other, no matter what the actual 

 difference in their masses may be. We have already, 

 therefore, ascertained the fundamental law of falling 

 bodies; so that what follows can be but the rendering 

 explicit of what is already implied in this primary law. 



Indeed, there has already become explicit this much: 

 That mass and velocity are the necessary reciprocal fac- 

 tors of the total quantity of motion of any and every 

 body. If, therefore, in any pair of bodies gravitating 

 toward each other, the one has twice the mass of the other, 

 it will at any given moment in their approach toward 

 each other have acquired but half the velocity of that 

 other, and at the end of any given time will have passed 

 through but half the distance traversed by the other 

 body in the same time. In case they meet, it is evident 

 that the double mass will have traversed one-third the 

 original distance of separation, while the smaller mass will 

 have traversed the remaining two-thirds. If the masses 

 are' to each other as one to one thousand, the less will 

 approach the greater with a velocity a thousand fold that 

 with which the greater will approach the less, and in case 

 they continue their approach undisturbed until they 



