﻿46 - Dr. W. Peddie on 



Kelvin's and Wiedemann's Theories, 



Lord Kelvin said that the decay of the oscillations might 

 be due to viscous resistance, i. e. resistance to change of shape 

 depending on the rate of change, in which case the elasticity 

 is perfect within the limits of the experiment. On the other 

 hand he remarked that, if it were due to dependence of the 

 elastic resilient force on previous conditions of strain, the 

 phenomenon would be continuous with imperfectness of 

 elasticity, and this was indicated to some extent by the 

 phenomenon of " fatigue." 



His final experiments were made with small distortions, 

 within the palpable limits of elasticity, to test the former 

 theory. The loss of energy per vibration was greater than 

 could be accounted for by dissipation ensuing on change of 

 shape of an elastic solid, and it was also immensely greater 

 than that due to resistance of the air. He considered also 

 that the results showed a loss of energy much greater than 

 any that could be accounted for by imperfection of elasticity. 



Though the compound-interest law was precisely that which 

 would arise from viscous resistance, yet, in that case, the 

 logarithmic decrement should vary inversely as the period ; 

 but this was far from being so. Tomlinson finds that the 

 decrement is nearly independent of the period in the more 

 "non-viscous" metals, and that it increases markedly with 

 the period in other metals. Kelvin remarked that the result 

 was such as might be due to " after-action " or imperfection 

 of elasticity. 



Wiedemann's statical observations showed that a wire 

 which had once been twisted behaved in quite different ways 

 according as it was twisted to one side or the other of its 

 existing position of equilibrium ; whence he concluded that 

 u * the hypothesis according to which the decay of torsional 

 oscillations is due to internal friction depending on the velocity 

 alone, can no longer be maintained." Nor could the elastic 

 after-action alone account for it. He then stated his own 

 theory as follows : — Let the wire be u accommodated " by 

 frequent rotations to and fro (see the account of his experi- 

 mental results on p. 37), and therein at last be temporarily 

 twisted in the positive direction, describing an angle -ha, 

 while the molecules may be rotated so that the lower ends of 

 their axes, looked at from the axis of the wire, describe an 

 angle +a, say to the left. The direction of this rotation 

 follows from my magnetic experiments. If the wire be slowly 

 brought back into the permanent torsion-position -\-b, the 

 axes of the molecules will retain a portion +/3 of their rota- 



