1898 - 99 .] Dr W. Peddie on Vibrating Wires. 599 
how Lord Kelvin could have obtained results so different. He 
finds that the value of the decrement at a given range depends 
essentially upon the magnitude of the maximum oscillation pre- 
viously given to the wire ; and he suggests that the increased value 
of the decrement may have been due to an accidental increase of 
maximum range. 
I scarcely think that the suggested explanation is probable. I 
think rather that Lord Kelvin’s results and conclusions are un- 
assailable. A considerable number of experiments were made by 
the students working under Lord Kelvin’s directions. In order 
that the explanation should hold, it would be necessary to assume 
that, in each case, too large an initial oscillation was given to the 
fatigued wire while the unfatigued wire was correctly oscillated. 
There does not seem to be any sufficient reason for assuming such 
a condition persistently. 
In the series of experiments which I have made upon the tor- 
sional oscillations of an iron wire {Trans. Roy. Soc. Edin ., 1896 
and 1898), the results show a distinct effect of fatigue upon the 
rate of decrease of oscillations and entirely corroborate Lord 
Kelvin’s results. No attempt was made to investigate the effect of 
fatigue upon the period of oscillation. 
If y be the range of oscillation, while x is the number of oscilla- 
tions made since the commencement of the experiment, the equation 
y n {x + a) = b, 
where a, n, and b are constants in any one experiment, holds with 
great accuracy throughout a large range. This gives as the value 
of the logarithmic decrement the quantity 
_ l <fy = 1 » 
y dx no 
In the papers referred to, I have shown that the value of b may, 
by suitable treatment regarding fatigue, be diminished to one-half 
of its initial value while n is not much different from unity. Thus 
the logarithmic decrement may be doubled. In more recent ex- 
periments, not yet published, I have obtained still greater varia- 
tions. 
I found that it was possible to have the product nb sensibly con- 
stant * that, in general, log. nb is practically proportional to n in 
