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SIMPLE APPAEATIJS FOE USE IN APPLIED MATHEMATICS. 
By J. Steph. van der Lingen. 
(From the Applied Mathematics Laboratory, South African College.) 
(Eeceived April 9, 1915.) 
1. — Apparatus for Finding " g." 
Teachers of applied mathematics generally find some difficulty in 
satisfying the queries of students who desire to have some definite idea 
about the acceleration of a freely falling body. 
The following is a brief description of a simple piece of apparatus which 
does not involve assumptions of dynamical quantities which the beginner 
cannot determine for himself (see Fig. 1). 
The axis, a, of a rigid pendulum is firmly screwed on to a board on a 
wall. 
Vertically above a a clamp, f, is screwed on a fixed board so that the rod, 
s, may be clamped at various heights above or below a. 
The rod, s, carries an electro-magnet, m, which is connected electrically to 
T T by means of flexible wire. 
Below B, the movable bob of the pendulum, a light platform, p, is 
clamped by screws on to the rod. 
At H, the centre of p, an hole is cut so that a steel ball may fall freely 
through it. 
When the rod of the pendulum is hooked by the catch, c, an electric 
current passes through r, the variable resistance, and m. 
R is varied until the steel ball is just held up by m. 
On releasing the pendulum at c the ball begins to fall. 
The height (h) of m above h is increased or decreased according as the 
ball falls to the left or right of h until the ball just falls through h. 
A piece of paper with a central line on it is now placed over h, and the 
ball at M slightly inked at its lowest point. 
The height of m is now set so that the ball falls on the central line. 
The height "h " is now measured, and also the diameter of the ball. 
The time of vibration is now found by observing the time that the 
pendulum takes to make a hundred vibrations. 
The beginner immediately sees that the ball fell through a height " h " 
