The great law of perfectly elastic bo dies is, that their relative velocity will re main the same before and after collision; that is, perfectly elastic bodies will re cede from one another after the stroke, with the same velocity that they came to gether. Many curious phenomena may be explained from this property in bo dies.
If the ivory ball A, (fig. 10.) weighing two ounces, strike with the velocity 16 against B at rest, weighing also two oun ces, the body B will move forward after the stroke with the velocity 16, A remain ing at rest in its place. The reason of this is, that the body A loses one half of its motion by striking the equal body B, tied the other half by the elasticity 'of B recovering its former figure. From this experiment, several curious phenomena arise : thus, if a row of shovel-board pieces (that is, metalline cylinders of about half an inch in height, and two inches diameter) be laid upon a smooth table, and you take a single piece, and drive it against the row, the last piece of the row will fly off; for if A (fig. 11.) strike the row of pieces; B, C, D, E, F, G, H, I, in the direction A a, then will the last piece fly off to i with the same ve locity that.A struck B : and whatever be the velocity of A, no other piece but the 'last piece I will fly off. But if you take two pieces, as A and B, (fig. 12.) and strike them together against the row C,D E, F, G, H, I, the two last pieces, H and I, will fly off from the other end of the row, with the same velocity that A and B made the stroke.
If three or more pieces are made use of to make the stroke, the very same num.
ber will fly off from the other end of the row ; and it is to be observed, that the same will happen with equal elastic balls, suspended in a row by strings of the tame length.
Again, if the elastic body A, (fig, 13.) weighing four ounces, strike the quies cent body B, weighing only two ounces, with a velocity equal to 12 ; then will the velocity of A, after the stroke, be 4, and that of B 1,6. Just the reverse of this happens when a lesser body strikes against the greater : in which case, the striking, or lesser body, will be reflected with one-fourth of its first motion, and the greater be carried forward with a motion which is as 16.
The magnitude and motions of spheri cal bodies perfectly elastic, and moving in the same right line, and meeting each other, being given, their motion after reflection may be determined thus : let the bodies be called A and B, and the re spective velocities a and b ; then, if the bodies tend the same way, and A, moving swifter than B, follows,it, the velocity bf the body A, after the reflection, will be a A—a.B.-1--2 bB , , , „ anu tnat OI t neD Guy li== A ± B a A — b but if the bodies meet, A + B then changing the sine of b, the velocity of A will bea A—aB-2bB --; and that A+1.1 A + B 2 aA.-I-bA—bB of B : and if either .
of these happen to come out negative, the motion after the stroke „tends the contrary way to that of A before it ; which is also to be understood of the motion of the body A in the first case.