52 LECTURE vr. 



iiishing their distance. For it may be shown, from the principles of the compo- 

 sition of motion, that any force, acting in this manner, will cause each of the 

 two bodies to describe a space proportional to the magnitude of the other 

 body : thus a body of one pound will move through a space twice as great as 

 a body of two pounds weight, and the remaining parts of the original distance 

 will still be divided in the same proportion, by the original centre of inertia, 

 Avhich therefore still remains the centre of inertia, and is at rest. And it fol- 

 lows also, that if the centre of inertia is at first in motion, its motion will not 

 be aftected by any reciprocal action of the bodies. 



This important property is very capable of experimental illustration ; first 

 observing, that all kr^^wn forces are reciprocal, and among the rest the action 

 of a spring: we place two unequal bodies so as to be separated when a spring- 

 is set at liberty, and we find that they describe, in any given interval of time, 

 distances which are inversely as their weights ; and that consequently the 

 place of the centre of inertia remains unaltered. They may either be made to 

 float on water, or may be suspended by long threads ; the spring may be de- 

 tached by burning a thread that confines it, and it may be observed whe- 

 ther or no they strike at the same instant two obstacles, placed at such dis- 

 tances as the theory requires ; or if they are suspended as pendulums, the arcs 

 ■\^'hich they describe may be measured, the velocities being always nearly pro- 

 portional to these arcs, and accurately so to their chords. (Plate II. Fig. 30.) 



The same might also be shown of attractive as well as of repulsive forces. 

 For instance, if we placedourselves in a small boat, and pulled a rope tied to a 

 much larger one, we should draw ourselves towards the large boat with a mo- 

 tion as much more rapid than that of the large boat, as its weight is greater 

 than that of our own boat; arid the two boats would meet in their common 

 centre of inertia, supposing the resistance of the water inconsiderable. 



Having established this property of the centre of inertia, as a law of motion, 

 we may derive from it the true estimate of the quantity of motion in differ- 

 ent bodies, in a much more satisfactory manner, than it has usually been ex- 

 plained. For since the same reciprocal action produces, in a body weighing 

 two pounds, only half the velocity that it produces in a body weighing one 

 pound, the cause being the same, the effects must be considered as equal, and 



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