VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 29P 



be the same as would result from the collision of two soft ones; that is, if it can 

 be bona fide proved, that one-half of the original power is lost in the stroke of 

 soft bodies by the change of figure, as was very strongly suggested by the 

 mill experiments; then, since no such loss can happen in the collision of 

 bodies perfectly hard, the result and consequence of such a stroke must be 

 different. 



The consequence of a stroke of bodies perfectly hard, but void of elasticity, 

 must doubtless be different from that of bodies perfectly elastic: for having no 

 spring, the body at rest could not be driven off with the velocity of the striking 

 body, for that is the consequence of the action of the spring or elastic parts be- 

 tween them, as will be shown in the result of the experiments; the striking body 

 will therefore not be stopped, and as the motion it loses must be communicated 

 to the other, from the equality of action and reaction, they will proceed toge- 

 ther, with an equal velocity, as in the case of non-elastic soft bodies: the ques- 

 tion therefore that remains is, what that velocity must be? — It must be greater 

 than that of the non-elastic soft bodies, because there is no mechanical power 

 lost in the stroke. It must be less than that of the striking body, because, if 

 equal, instead of a loss of motion by the collision, it will be doubled. If there- 

 fore non-elastic soft bodies lose half their motion, or mechanical power, by 

 change of figure in collision, and yet proceed together with half the velocity, 

 and the non-elastic hard bodies can lose none in any manner whatever; then, as 

 they must move together, their velocity must be such as to preserve the equality 

 of the mechanic power unimpaired, after the stroke, the same as it was before it. 



For example, let the velocity of the striking body before the stroke be 20, 

 and its mass or quantity of matter 8; then, according to the rule deduced from 

 the experiments in the tract on Mechanic Power (see exper. 3 and 4) that power 

 will be expressed by 20 X 20 = 400, which X 8 = 3200; and if half of it is 

 lost in the stroke,* in the case of non-elastic soft bodies, it will be reduced to 

 l600; which -7- l6 the double quantity of matter, will give 100 for the square 



* But, it may be said, if half of it is not lost by the stroke, what then becomes of Mr. S.'s rule ? 

 And what good reason has he to suppose that the half, or indeed any part, of the power or momentum 

 of any body is lost by the stroke? In fact, Mr. S. bewilders and puzzles himself about a thing 

 which he calls mechanical power, which is proportional to the height or space that a body falls through 

 to acquire its velocity, which is known to be proportional to the square of that velocity. Whereas 

 the real force or momentum of a body in motion, or with which it strikes any obstacle, is a quite 

 different thing, being proportional to the velocity in a given body, or to the product of die velocity 

 and the body, no part of which is lost by the stroke, but remains the same after the stroke as before 

 it. And hence, instead of Mr. S.'s complex and unnatural way of computing the common velocity 

 of the two bodies after the stroke, the rule is very plain and simple ; viz. divide the momentum, 

 20 x 8 = 160, by the sum of the two bodies, 8 + 8 = 16', and the quotient 10, is their common 

 velocity after the stroke. 



a Q 2 



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