or 
to a lever arm. By a crossbar placed at any desired height, this lever is tripped 
up as the block descends, the pencil is released and shot forward by the tension of 
rubber bands so as to press against the paper-covered cylinder. Were the cylinder 
at rest, the pencil would merely describe a vertical line, turning back on the 
same line at the moment of impact. When the cylinder is in rotation the 
_ pencil describes a curve which is abruptly reversed at the moment of impact. As 
the block usually bounces several times before coming to rest, this curve consists 
of successive loops meeting at sharp angles which correspond to the successive 
impacts. This will be fully understood by a glance at the record sheet shown on 
the wall. If now we draw tangents to these curves at a point of impact, and 
denote by Vi the velocity of the block immediately before impact, by Vr its 
velocity immediately after impact and by Vc the velocity of the surface of the 
cylinder at the moment of impact, then— 
Ve y 
=a 4 
Ve tan @ a’ 
——— —— ’ 
Vi tan @ y 
: Ve x 
Del Vr ae : ‘ 
or, if x’ be taken equal to x, we have e= crs ~—, the coefficient being consid- 
/ f] y — 
ered negative, since Vr is a negative quantity. Thus the actual velocity need 
not be known so far as the determination of e is concerned, and the process is 
reduced to the drawing of two tangent lines and the measuring of the ordinates 
corresponding to equal abcissae measured from the point of impact. 
To enable us to find the time of contact during impact, or, briefly, the dura- 
tion of impact, it is necessary to know the speed of the cylinder. Now once in 
each rotation of the cylinder it thrusts up a vertical wire attached to the short arm 
of a lever, causing the longer arm to descend and complete an electric circuit and 
give a record on the drum of an electro-chronograph. The speed of the drum is 
determined by a parallel record of the time of vibration of a second’s pendulum 
which completes another electric circuit whenever it passes through the vertical. 
The electro-chronograph thus used is one made by the Geneva Society, of Switz- 
erland; its drum can be made to rotate once in a second under the control of a 
Foucault regulator. From the curve exhibited it is plain that the impinging 
bodies compress each other during the first period of contact, and upon separation 
they more or less regain their original forms; so that at each rebound a portion 
of the line traced by the pencil when at rest is intercepted between the curves 
traced by the pencil. Dividing the length of the portion so intercepted by the 
product of the circumference of the cylinder and the number of revolutions per 
second we have the duration of contact. It is not necessary always to determine 
