802 
MR. H. TOMLINSON ON THE INFLUENCE OF STRESS AND 
when vibrating under the influence of torsional elasticity. It is pointed out (a) that, 
though no change of volume or shape can be produced without dissipation of energy, 
because of the accompanying change of temperature, estimates founded on the thermo¬ 
dynamic theory of elastic solids suffice to prove that the loss of energy due to this 
cause is small in comparison with the whole loss of energy which has been observed in 
many cases of vibration. ( h ) That, as a result of experiments in which a spring was 
vibrated alternately in air of ordinary pressure and in the exhausted receiver of an 
air-pump, there is an internal resistance to its motions immensely greater than the 
resistance of the air. Hence it is concluded that with solids as with liquids there 
exists an internal resistance to change of shape depending upon the rapidity of the 
change. The results of Thomson’s experiments are briefly as follows :—■ 
(a.) The loss of energy in a vibration through one range was greater, the greater the 
velocity but the difference between the losses at low and high speeds was much 
less than it would have been, had the resistance been approximately as the rapidity of 
the change of shape. 
(6.) When the weight of the vibrator was increased, whilst its moment of inertia 
was maintained constant, the viscosity was always at first much increased ; but then, 
day after day, it gradually diminished and became as small in amount as it had been 
with the lighter weight. 
(c.) A wire which was kept vibrating nearly all day, from day to day, after several 
days showed very much more molecular friction than another kept quiescent except 
during each experiment.! 
The investigation was continued with much smaller degrees of maximum angular 
distortion, to discover, if possible, the law of the molecular friction, and, so far as the 
irregularities depending upon previous conditions of the elastic substance allowed any 
simple law to lie indicated, it was proved that, as with fluids, the diminution of range 
per equal numbers of oscillations bore a constant ratio to the diminishing range. But, 
on the contrary, as with the larger angular distortions, the relation between the law of 
subsidence in two sets of oscillations having different periods, with the same elastic 
body in the same circumstances, was not that which would occur if the molecular 
resistance were simply proportional to the velocity of the change of shape in the 
different cases. If the molecular friction followed this simple law, the proportionate 
diminution of range per period would he inversely as the periods.^ This proportion 
was not found to hold good, but the loss of energy was, in fact, as it would be if the 
result were wholly or partially due to the “elastische Nachwirkung’’—elastic after¬ 
working—as the Germans call it. 
* I shall be able to show that this is not the case if we eliminate the effect of the resistance of the air. 
t This so-called “fatigue of elasticity” does not occur if the oscillations are kept well within the 
limits of elasticity.'—H. T. 
t There is a slip in § 36 of ‘ Encycl. Brit.,’ 9th edit., Art. “Elasticity,” in which article Sir William 
Thomson refers to his previously-mentioned memoir; the words “ directly as the square roots of the 
periods ” should he “ inversely as the periods.” 
