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XIV. — On Torsional Oscillations of Wires. By Dr W. Peddie. (With Two Plates.) 



(Read 20th June 1898.) 



This paper is in continuation of two others, on the same subject, previously 

 communicated to the Society. In the First Paper (Philosophical Magazine, July 1894) 

 it was shown that the formula 



y"{x + a) = b, 



where n, a, and b are constants in any one experiment, represents with accuracy 

 the relation between y, the range of oscillation, and x, the number of oscillations 

 which have taken place since torsion was first applied and the wire was left to itself, 

 so that the oscillations gradually diminished. The apparatus employed, and the 

 method of observation used, were identical with those described in the Second Paper 

 above referred to. The wire which was experimented upon was the same as that used 

 on the previous occasions. Its length, as given in the First and Second Papers, was 

 89*1 cm. A measurement made on the date 19.10.1897, in the course of the last 

 series of experiments described in the present paper, showed that the length had 

 become 89*3 cm. This increase was doubtless due to the fact that the heavy lead 

 oscillator had been left attached to the wire during the whole of the intervening 

 period. On the date given, it was also found that, with the same oscillator as was 

 used in the experiments first described, ten oscillations were performed in 81 seconds, 

 when the range was large, while 79 seconds were occupied when the range was small. 

 This observation verified the result stated in the First Paper, that the period slightly 

 increases as the range increases. It also showed that the wire was practically in the 

 same condition as it was at first, in so far as elastic qualities are concerned ; for the 

 corresponding periods were only slightly less in earlier experiments, the difference 

 being largely accounted for by the slight increase of length of the wire. 



In the First Paper, the above equation was also deduced as an approximation, from 

 the assumption that the defect of the potential energy of the system, at any given 

 distortion, from the value which it would have had in accordance with Hooke's Law, 

 was proportional to a power of the distortion. It was pointed out that the value 

 of n seemed to approximate to zero when the range of oscillation was very small ; 

 and that, when n becomes zero, the equation changes form and becomes the well- 

 known exponential equation, which was first proved by Lord Kelvin to hold when 

 the oscillations are small. 



An improved method of calculating the values of the quantities n, a, and b was 



VOL. XXXIX. PART II. (NO. 14). 3 T 



