2Cl6 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 



particular men, as that would lead me into too great a length : I shall therefore 

 content myself with observing, that the laws of collision, which have been 

 investigated by mathematical philosophers, are principally of 3 kinds ; viz. those 

 relating to bodies perfectly elastic ; to bodies perfectly unelastic, and perfectly 

 soft; and to bodies perfectly unelastic, and perfectly hard. To avoid prolixity, I 

 shall consider in each, only the simple case of 2 bodies which are equal in weight, 

 or quantity of matter, striking each other. Respecting those which are perfectly 

 elastic, it is universally agreed that, when 2 such bodies strike each other, no 

 motion is lost; but that in all cases, what is lost by one is acquired by the other: 

 and hence, that if an elastic body in motion strike another at rest, on the stroke 

 the former will be reduced to a state of rest, and the latter will fly oft" with an 

 equal velocity. In like manner, if a non-elastic soft body strike another at rest, 

 they neither of them remain at rest, but proceed together from the point of 

 collision with exactly one half of the velocity that the first had before the stroke ; 

 this is also universally allowed to be true, and is fully proved by very good expe- 

 riments on the subject. 



Respecting the 3d species of body, that is, those that are non-elastic, 

 and yet perfectly hard ; the laws of motion relating to them, as laid down 

 by one species of philosophers, have been rejected by another ; the latter alledg- 

 ing, that there are no such bodies to be found in nature to try the experiment 

 on ; but those who have laid down and assigned the doctrine that would attend 

 the collision of bodies of this kind, if they could be found, have universally 

 agreed, that if a non-elastic hard body was to strike another of the same kind 

 at rest, that, in the same manner as is agreed concerning non-elastic soft bodies, 

 they neither of them would remain at rest, but would in like manner proceed 

 from the point of collision, with exactly one half of the velocity that the first 

 had before the stroke : in short, they lay it down as a rule attending all non- 

 elastic bodies, whether hard or soft, that the velocity after the stroke will be 

 the same in both, viz. one half of the velocity of the original striking body. 

 Here is therefore the assumption of a principle, which in reality is proved by no 

 experiment, nor by any fair deduction of reason that I know of, viz. that the 

 velocity of non-elastic hard bodies after the stroke must be the same as that 

 resulting from the stroke of non-elastic soft bodies; and the question now is, 

 whether it is true or not ? 



Here it may be very properly asked, what ill effects can result to practical men, 

 if philosophers should reason wrong concerning the effects of what does not exist 

 in nature, since the practical men can have no such materials to work on, or 

 misjudge of? But it is answered, that they who infer an equality of effects be- 

 tween the 2 sorts, may from thence be misled themselves, and in consequence 

 mislead practical men in their reasonings and conclusions concerning the sort 



