212 Proceedings of Royal Society of Edinburgh. [sess. 
On Torsional Oscillations of Wires. By Dr W Peddie. 
(Read June 20, 1898.) 
{Abstract.) 
This paper is in continuation of two others, on the same subject, 
previously communicated to the Society. It consists of two parts, 
the first experimental, the second theoretical. 
The wire which was experimented upon was the one which was 
used in the previous experiments, and the apparatus was that 
described in the latter of the communications above referred to. 
In the first paper {Phil. Mag., 1894) it was shown that the 
equation 
y u {x + a) = b, 
where n, a, and b, are constants in any one experiment, represents 
to a very high degree of accuracy the relation between y, the range 
of oscillation, and x, the number of oscillations. In the second 
paper {Trans. R. S. E ., 1896), the result of attempts to determine 
the nature of the dependence of n upon (1) magnitude of initial 
oscillation, (2) amount of “ fatigue ” of the wire, were described. 
It was found to be impossible, under the subsisting conditions as 
to fatigue, to separate the effects of fatigue and initial range. 
The first series of experiments described in the present paper 
was conducted under the condition of excessive fatigue of the wire. 
The effect of magnitude of initial range was found to be practically 
eliminated. Thus it was possible to express all the results of that 
series by a general formula, of the above type, in which n and b are 
absolutely constant, while a is given in terms of the initial range. 
In the second paper above alluded to, it was shown that, through- 
out the series of experiments therein described, the product nb 
might be regarded as constant. And it was pointed out that this 
was, so far, an accident depending on the size of the scale-unit. 
The importance of the result lay in the fact, that a scale-unit 
which made the product constant could be found ; and that, if the 
product were constant, a critical angle of oscillation, at which the 
