This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 edition. Excerpt: ... An interesting class of phenomena depending on the elasticity of matter is that of collision between elastic bodies. The laws governing these collisions were investigated by Newton and his contemporaries, who used the following method. The colliding bodies were spherical balls suspended by strings in the way shown in Fig. 81; the balls, after falling from given heights, struck against each other at the lowest point, and after rebounding again reached a certain height. By measuring these heights (and allowing, as Newton did, for the resistance of the air) the velocities of the balls before and after collision can be determined. Newton in this way showed that when the collision was direct--i.e., when the relative velocities of the two bodies at the instant of collision was along the common normal at the point of impact--the relative velocity after impact bore a constant ratio to the relative velocity before impact--the relative velocity being, of course, reversed in direction. Thus, if u, v are the velocities of the bodies before impact, u being the velocity of the more slowly moving body, while U, V are the velocities after impact, then V-V = e(v-u) (1) Fig. 81. where e is a quantity called the coefficient of restitution, and Newton's experiments showed that e depended only on the materials of which the balls were made, and not on the masses or relative velocities. A series of experiments were made by Hodgkinson, the results of which were in general agreement with Newton's. Hodgkinson found, however (Report of British Association, 1834), that when the initial relative velocity was very large e was smaller than it was with moderate velocity. Vincent has shown that the coefficient of restitution is given by the equation e = e0-bu, where - is...