598 
Proceedings of Royal Society of Edinburgh. [sess. 
Note on Mr Joseph O. Thompson’s Results regarding 
Vibrating Wires. By Dr W. Peddie. 
(Read June 19, 1899.) 
In 1865 Lord Kelvin published the results of experiments which 
first made evident “ a very remarkable fatigue of elasticity, accord- 
ing to which a wire which has been kept vibrating for several hours 
or days through a certain range came to rest much quicker when 
left to itself than when set in vibration after it has been at rest for 
several days and then immediately left to itself.” On the strength 
of Lord Kelvin’s statement this elastic fatigue of metals has been 
regarded as a definitely ascertained fact. But, quite recently 
( Physical Review , March 1899), Mr Joseph O. Thompson has 
published a paper “On the period and logarithmic decrement 
of a continuously vibrating wire,” in which he states that it seems 
probable that “for constant temperature and constant amplitude 
the logarithmic decrement is constant.” This conclusion is based 
upon his observation that the logarithmic decrement, in the case 
of a copper wire, when the amplitude of vibration varied from 
about 185° to 175°, had the same value after it had been continu- 
ously vibrated through the average arc of 180° for fifty consecutive 
hours as it had at the commencement of that period. Observations 
upon other metals seemed to support the conclusion. 
Lord Kelvin also stated that fatigue caused an increase of the 
period of vibration. Mr Thompson finds that “no matter what 
metal was used, no matter whether the arc of vibration was as 
small as 20° or as high as 200°, no matter whether the wire was 
long or short, thick or thin (provided of course the breaking strength 
of the wire was at least twice the weight of the disc), the result was 
uniformly the same, namely, that ivhen temperature and amplitude 
of vibration remained constant , the period of vibration was a constant 
quantity .” 
Mr Thompson, after having reached the above conclusion regard- 
ing the logarithmic decrement, proceeds to determine, if possible;, 
