Simple Apparatus for Use in Applied Mathematics. 601 
short and when the ball is not magnetised. After each observation the ball 
is demagnetised. 
This apparatus does not involve any dynamical knowledge of quantities 
which the beginner cannot determine for himself. 
II. — Standardizing a Gtiven Vibrator. 
Another difficulty which presents itself to the beginner is that he must 
assume the time of vibration of some vibrator when he is asked to determine 
velocities and accelerations of trolleys, etc. 
Fig. 2. 
The piece of apparatus figured enables the student to determine the 
period of vibration of the vibrator (Fig. 2). 
The pendulum vibrates perpendicularly to the direction of motion of the 
trolley, and thus crosses the trace of the vibrator after definite intervals of 
time. 
The trolley is given a light tap so that it moves with practically uniform 
velocity under the pendulum and vibrator. 
When the velocity is small a large number of vibrations will be recorded 
on the paper. 
The brush of the pendulum and that of the vibrator are set as closely 
together as possible. 
If the pendulum's zero is at a and the vibrator's at b, then in going from 
A to c it executes n oscillations, and the vibrator executes m oscillations in 
an equal distance measured from b. 
Hence = ^, where Tp is the period of the heavy rigid pendulum, t^ 
