300 PHILOSOPHICAL TRANSACTIONS. |_ANNO 17»2. 



of their velocity; the square root of which being 10, will be the velocity of the 

 two non-elastic soft bodies after the stroke, being just one-half of the original 

 velocity, as it is constantly found to be. But in the non-elastic hard bodies, no 

 power being lost in the stroke, the mechanic power will remain after it, as before 

 it, = 3200; this, in like manner, being divided by l6, the double quantity of 

 matter, will give 200 for the square of the velocity, the square root of which is 

 14.14 &c. for their velocity after the stroke, which is to 10, the velocity of the 

 non-elastic soft bodies after the stroke, as the square root of 2 to 1 ; or as the 

 diagonal of a square to its side.* 



It remains therefore now to be proved, that precisely half of the mechanic 

 power is lost in the collision of non-elastic soft bodies; for which purpose my 

 mind suggested the following reflections. In the collision of elastic bodies, the 

 effect, seemingly instantaneous, is yet performed in time; during which time the 

 natural springs residing in elastic bodies, and which constitute them such, are 

 bent or forced, till the motion of the striking body is divided between itself and 

 the body at rest; and in this state the two bodies would then proceed together, 

 as in the case of non-elastic soft bodies; but as the springs will immediately re- 

 store themselves in an equal time, and with the same degree of impulsive force 

 with which they were bent in this reaction, the motion that remained in the 

 striking body will be totally destroyed, and the total exertion of the two springs, 

 communicated to the original resting body, will cause it to fly off with the same 

 velocity with which it was struck. 



On this idea, if we could construct a couple of bodies in such a way, that 

 they should either act as bodies perfectly elastic; or, that their springs should at 

 pleasure be hooked up, retained, or prevented from restoring themselves, when 

 at their extreme degree of bending; and if the bodies under these circumstances 

 observed the laws of collision of non-elastic soft bodies, then it would be proved, 

 that one-half of the mechanical power, residing in the striking body, would be 

 lost in the action of collision; because the impulsive force or power of the spring 

 in its restitution being cut off, or suspended from acting, which is equal to the 

 impulsive force or power to bend it, and which alone has been employed to com- 

 municate motion from one body to the other, it would make it evident, that one- 

 half of the impulsive force is lost in the action, as the other half remains locked 

 up in the springs. It also follows, as a collateral circumstance, that be the im- 

 pulsive power of the springs what it may from first to last, yet as one-half of the 

 time of the action is by this means cutoff, in this sense also it will follow, that 



• This erroneous conclusion is deduced by Mr. S. from his false rule, for finding the velocities of 

 bodies after impact. The true rule is the same for all non-elastic bodies, whether hard or soft. If 

 die bodies adhere and move together with one common velocity immediately after the stroke, that 

 velocity must bj the half of the velocity before the sttoke, as found in the note above ; whatever the 

 nature of the bodies may be. 



