427 
1910-11.] Energy in Torsionally Oscillating Wires. 
angle not differing much from 180°. It was further found that this could 
not he done in every case with the same value of a for the two portions, 
but, by choosing a slightly different value of a, in every case the points 
could be brought to lie on two straight lines. The doubling of the line, as 
will be seen when the metals are considered separately, was found to depend 
upon controllable conditions, e.g. in brass it occurred when the metal had 
been brought to a certain temperature in the neighbourhood of 375° C. In 
most cases it was found that the value of n was greater in the line drawn 
through the points corresponding to the smaller oscillations. 
Experiments on Brass Wire. 
In the present series of experiments brass was the material most studied 
in detail, and, for the purpose of experiment, lengths of brass wire, approxi- 
mately one millimetre in diameter,* were used. The length was in each 
case chosen so that, from clamp to clamp on the torsion apparatus, there 
should be exactly one foot of wire. It was found in a subsequent experi- 
ment, however, that change of length had no effect on the constants a and 
n, although b might differ considerably. In an experiment on 6 inches of 
brass wire, the values of a and n were found to be equal to those got with 
12 inches of the same wire. The reason can readily be seen, as follows. 
If we postulate that the loss of potential energy in a breaking down of 
molecular groups is proportional to a power of the angle of torsion, we can 
approximately write (Peddie, Phil. Mag., July 1894) the loss of energy per 
swing in the form 
— hydy =py m dx. 
Now, in a wire of half length, k is doubled for the same value of y ; and the 
loss of energy, with the same y at half length, is half of what it would have 
been in the wire of whole length at 2 y. But in the wire of whole length at 
2 y the loss is 
m y m dx. 
- 2hjdy =p2 m ~ l y m dx 
— Tcydy = p2 m ~ 2 y m dx, 
y m - 2 (*+ a )= 2 = 5 ^ 2 )’ 
y n ( x+a )=fn'l 
The empirical law was found to hold over a very long range at the ordinary 
temperature. In all cases the points lay, with the proper value of a, in 
Thus 
so 
i.e. 
* -0975 cm. 
