168 CELESTIAL MECHANICS. I. lU. 13. 



may either be made to float on water, or may be suspended 

 by long threads: the spHng may be detached by burning 

 a thread that confines it, and it may be observed whether 

 or no they strike at the same instant two obstacles, placed 

 at such distances as the theory requires ; or, if they are 

 suspended as pendulums, the arcs which they describe may 

 be measured, the velocities being always nearly propor- 

 tional to these arcs, and accurately so to the chords, which 

 are as the square roots of the verse sines, representing the 

 heights of ascent. 



300. Definition. '''270.'' The joint 

 ratio of the masses and velocities of any two 

 bodies is the ratio of their momenta. 



301. Theorem. "271:' The momentum 

 of any body is the true measure of the quan- 

 tity of its motion. 



For the same reciprocal action produces in a double 

 body half the velocity, the common centre of inertia remain- 

 ing at rest ; and, the cause being the same, the effects 

 must be considered as equal: and when the reciprocal 

 force varies, the velocity of both bodies varies in the same 

 ratio. 



Scholium 1. We may also demonstrate experi- 

 mentally, by means of Mr. Atwood's machine, that the 

 same momentum is generated, in a given time, by the same 

 preponderating force, whatever may be the quantity of 

 matter moved. Thus if the preponderating weight be 

 one sixteenth of the whole weight of the boxes, it will fall 

 one foot in a second, instead of 16, and a velocity of two 

 feet will be acquired by the whole mass, instead of a 



