1912-13.] Fuller Test of the Law of Torsional Oscillation. 177 
XVII. — On a Fuller Test of the Law of Torsional Oscillation. By 
Janies B. Ritchie, B.Sc., Carnegie Research Scholar in Physics, 
University College, Dundee. Communicated by Professor W. Peddie. 
;(MS. received November 18, 1912. Read November 18, 1912.) 
Test of a Modification of the Formula. 
It has been shown in a former paper * that an equation of the form 
y n (x + a) = b 
can be applied to give close representation of results in the determination 
of the law of decrease of torsional oscillations of wires of different materials, 
when the range of oscillation is large in comparison with the palpable 
limits of elasticity. In the equation as written 
y = the range of oscillation. 
x — the number of oscillations since the commencement of observa- 
tions. 
n, a , and b = quantities, constants for any one experiment, their numerical 
values depending on the initial conditions of the wire in 
question, and its subsequent treatment. 
This empirical equation was deduced by Dr Peddief on the supposition 
that the loss of potential energy when the wire is twisted through an 
angle, 6 say, is due to the rupture of molecular configurations, and is 
proportional to a power of the angle of torsion. Thus, the potential 
energy during the twist 0 being represented in accordance with Hooke's 
Law, as 
Y = ±k0 2 (1) 
we obtain on taking the loss into account, 
Y = \W-p(T ( 2 ) 
This loss of energy per swing was taken as being small in comparison 
with the total energy, so that it was practically equal to kO d6, and hence 
equation (2) took the form 
- Ic6d6 = p6 m dt (3) 
where dt is the time of an outward swing. 
The integral is 
0 n (t + 1 0 ) = b . 
W 
VOL. XXXIII. 
* Proc. Roy. Soc. Edin ., vol. xxxi. p. 424. 
t Phil. Mag., July 1894. 
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