92 
the speed of the cylinder by means of the chronograph, for, having once found a 
good average value for the velocity of impact for a certain height of drop, the 
velocity of the cylinder at any other impact from the same height of drop can be 
found trom the inclination of the impact curve. 
Thus ade — hn 
Ve 
Vi 
and Ve = 
tan a 
It may also be noted that the amount of mutual compression at impact is at 
least approximately given by the extent to which the curve sinks below the zero 
line. 
By making the moment of inertia of the cylinder large, its speed during the 
time of contact may be considered as constant. It should be noted that the 
results do not depend upon the friction between the block and the guides, for we 
are concerned only with the actual velocities just before and just after impact, no 
matter how they are attained. 
PRELIMINARY TESTS WITH THE APPARATUS. 
The method here employed for the determination of the coefficient of restitu- 
tion, consists in principle, in the dropping of a mass on a plate so large that the 
motion communicated to it may be neglected, so that the relative motion is merely 
that of the block. As a matter of fact in the arrangement adopted, the stationary 
plate is only about ten times as large as the block, but it is so solidly clamped to 
the base of the massive structure that it is assumed to be practically immovable. 
It might however be suspected that the result would depend upon the stationary 
block, i. e., its mass, or its vertical thickness, for evidently if it were too thin it 
would in reality be on the elasticity of the base beneath it that the force of rebound 
would depend. 
To test this point, a short beam of well-seasoned cherry was taken whose 
cross-section was a rectangle, one side of which was three times as long as the 
other, so that the beam was three times as thick in one direction as that in the 
other. The actual dimensions of the beam were 2’— 13’— 43”. 
If these thicknesses for the stationary mass be too small, it should be shown 
by the coefficient of. restitution being different for impacts in the direction of the 
greater thickness and in the direction of the smaller thickness. The impinging 
block used was also cherry, the grain being vertical and the impinging surface 
turned into a hemisphere of 7 centimeters radius. The value of e found with the 
greater thickness of the beam vertical was .35 and with the smaller thickness 
