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XVIII. — On Torsional Oscillations of Wires. By Dr W. Peddie. With Two Plates. 



(Read 16th March 1896.) 



About two years ago I communicated to this Society a paper on the above subject, 

 which was printed in the Philosophical Magazine (1894). The object of the investiga- 

 tions therein discussed was the determination of the law of decrease of torsional oscilla- 

 tions when the range of oscillation was large in comparison with the palpable limits 

 of elasticity. An equation of the form 



t/'(x + a) = b, 



where y represents the range of oscillation, and x represents the number of oscillations 

 which have taken place since the commencement of the observations in any one 

 experiment, was found to give an exceedingly close representation of the results. The 

 values of the quantities n, a, and b depend on the magnitude of the initial oscillation, 

 and on the previous treatment of the wire. It was also found that, when the oscilla- 

 tions were allowed to die away to a sufficient extent, the value of n tended to 

 diminish. The oscillations were practically isochronous. 



It was shown further that the above formula could be deduced from the assumptions 

 (1) that the loss of energy per oscillation is proportional to a power of the angle of 

 oscillation, and (2), that, apart from this loss, Hooke's Law is obeyed. The latter 

 assumption may be regarded as completely justified by the observations of G-. Wiede- 

 mann, who showed that, after a rod has been " accommodated " by a few twists, in 

 opposite directions alternately, to a given maximum, Hooke's Law was followed in 

 all subsequent twists in one direction so long as the original maximum was not 

 exceeded. The accuracy of the former assumption is therefore to be gauged by the 

 completeness with which the formula suits the results of observation. 



The conditions under which the resilience has maximum or zero values were 

 discussed, and an expression, connecting the angle of " set " with the angle of torsion, 

 was also deduced, and was tested by means of Wiedemann's observations, the agree- 

 ment being very complete. And it was further pointed out that the well-known law 

 of " compound interest," found by Lord Kelvin to hold in the case of very small 

 oscillations, follows as a particular case when 7^ = 0. 



The initial range had nearly a constant value in all the experiments discussed 

 in the first paper, and therefore no attempt could be made in it to consider the 

 variations of the parameters n, a, and b, consequent on changes in the initial conditions. 

 In the present paper, three separate sets of experiments are described. Full confirma- 

 tion is given of the accuracy of the above formula, and the nature of the variations 

 of the parameters is investigated. 



VOL. XXXVIII. PART III. (NO. 18). 4 Q 



