420 
Proceedings of the Royal Society of Edinburgh. [Sess. 
In this form, viz. Driving Force minus Frictional Force equal to Effective 
Force, the meaning of the equation can be grasped even by a student whose 
dynamical knowledge is small. 
With the present apparatus it was found necessary to determine a 
several times before and after each determination of a ; with an apparatus 
of more satisfactory construction this would probably be unnecessary. 
To get k, the radius of gyration, the pulley wheel was removed from its 
position on the friction rollers and was attached to bi-filar suspensions. 
Three separate determinations gave k — 4‘221, 4205, 4'230, giving a mean 
k = 4*218. This, with the weight P = 440 g, and the radius y> = 6T94 cm., 
k 2 
gives for the equivalent mass of the pulley P^ = 20*5 g. 
V 
The inertia of the four friction rollers was found from their dimensions 
and their weights to be one-tenth of that of the pulley wheel itself. As their 
angular speed is less than one-tenth that of the pulley, their total kinetic 
energy is less than one-thousandth of the kinetic energy of the pulley, and 
has therefore been left out of account in the subsequent calculation of g. 
] c 2 
A graphical evaluation of P— made in the usual way from the results 
appended, by plotting 7 against 2L + w and reading off the intercept on 
a-\-a 
the load axis, led to a value 21*2 g. 
A graphical method may also be adopted for ascertaining the fraction of 
a revolution at the beginning in finding a, and at the conclusion in finding 
a. If R is the number of revolutions from and to rest respectively, we have 
R . 
rp2 
in each case a constant, and so x, the unknown fraction of a revolution. 
can be at once obtained by plotting (0, 1, 2, 3, etc.) R against TJ, TJ, T*, TJ, 
etc., where T 0 , T v etc., are the times of x, 1 + x, 2 + x, etc., revolutions. In the 
a measurements this fraction is reduced to the smallest possible value by 
initial adjustment of the level of the release magnet, but one has no control 
over its value in the a determinations. As a rule, however, it is not 
necessary to evaluate x, the incomplete part of a revolution, in the deter- 
mination of a and a ; it is sufficient to plot squares of times from beginning 
and end respectively against number of complete revolutions, and the pro- 
ducts of the slopes of the resulting straight lines into twice the effective 
distance of one revolution at once give the acceleration and retardation 
required. This was the procedure adopted in obtaining the results com- 
municated in this paper : the experimental points, as long as the speed did 
not become excessive, lay exactly on a straight line, whose slope could 
easily be found to 1 in 1000. 
