170 I'lril.USOPHlCAL TKANSACTIONS. [aNNO 1727. 



motion through lq, and retaining that through qm; producing therefore «m tt) 

 N, that MN may he = qm = v/2; and putting there a third similar spring, 

 forming with mn half a right angle, as mnr; so that MR be again =: cp ^ 1 ; 

 in like manner it is evident, that the motion through mr is entirely expended 

 on bending the spring n, the body in the mean time continuing to move with 

 the direction and velocity rn =: 1. In fine, if with this remaining velocity, it 

 should perpendicularly impinge on the spring o, it will entirely communicate the 

 rest of its force in bending it; and therefore the body itself will be brought to 

 a state of rest. From these premises it now appears, that the force of the 

 body c was so great, that by itself alone, it could precisely bend 4 such springs, 

 to bend each of which apart, there is required half the velocity of a body equal 

 to c itself, consequently, since the effect of the former is 4 times greater than 

 the effect of the latter, it is likewise evident, that the force of a body of 2 

 degrees of velocity, is 4 times as great as the force of the same, or an equal 

 body of one degree. 



In much the same manner I might demonstrate, that the body c with a velo- 

 city of 3 degrees may bend Q springs, to bend one of which there is one degree 

 of velocity required in that body; and in general, that the number of bent 

 springs is always the square of the number of the degrees of velocity; whence 

 therefore it will follow, that the forces of equal bodies are in a duplicate ratio 

 of their velocities, q. e. d." 



This argument is founded entirely on the commonly received doctrine of the 

 composition and resolution of forces, and not on any decisive experiments, 

 that have been actually made on this occasion. All that is proved from this 

 doctrine is, that a body moving with 2 degrees of velocity, may be made to 

 bend 4; with 3 degrees of velocity it may be made to bend g similar springs, 

 each destroying one degree of velocity in a perpendicular direction, before its 

 force is entirely spent, provided care be taken to alter the directions of the mo- 

 tion in every stroke but the last, after a certain manner; that had the same 

 body moved but with one degree of velocity in one direction, and that in a 

 perpendicular one, it would have lost all its force at once, and bent but one of 

 those springs ; which is far from proving the thing in question. 



To make the reasoning on this head conclusive, the two bodies should not 

 only be equal in quantity of matter, but alike in that material circumstance, 

 the direction of their motions; so that if one of the bodies move in a perpen- 

 dicular direction, the other should do so too; or if the one strikes in an ob- 

 lique direction, the other should do the same, and that in the same degree of 

 obliquity; and lastly, if one moves in several directions, the other should do 

 the same. But in the case before us, one is supposed to move only in one 



