TORSIONAL OSCILLATIONS OF WIRES. 613 



The first negative elongation does not entirely destroy the positive set. The second 

 positive elongation increases it, and the second negative elongation does not entirely 

 remove this increase ; and so on. Thus the conditions under which successive oscilla- 

 tions occur are continually varying, and one cannot therefore assume without proof 

 that the oscillations are symmetrical about a fixed point. As a matter of fact, the 

 present experiments have shown that there is a fixed point of symmetry. 



If an arbitrary scale reading /3 be chosen as the zero in any one experiment, 

 and if successive positive and negative elongations a, y, be read from this zero, the 

 point about which the oscillations are symmetrical must be jB + (a — y)/2. A number 

 of results, which show that this quantity is practically constant in any one experiment, 

 are given in Table I. The dates of the experiments are given in the left-hand column. 

 The number of complete oscillations which had taken place since the commencement 

 of the experiment are given in the first row. and the corresponding values of the 

 quantity /3+ (a — y)/2 appear in the various rows and columns underneath. The last 

 column contains the values of the zero which were observed when the oscillations were 

 stopped. 



There may be an error of ±0*1 in any of the calculated quantities. In the columns 

 headed \ and 1, the error may be much greater, because the elongations decreased with 

 great rapidity at first. 



General Outline of Experiments. 



Three series of experiments were carried out. The first of these, extending from 

 the date 12.7.94 to the date 4.8.94, consisted of forty-two experiments. The treatment 

 of the wire throughout this period was as nearly uniform as possible, and the initial range 

 of oscillation was varied considerably in the different experiments. On those days on 

 which small initial ranges only were used, the wire was oscillated with a large initial 

 range after the observations were completed, so as to preserve the uniformity of 

 treatment. 



A second series, made between the dates 16.7.95 and 26.7.95, consisted of thirteen 

 experiments. The main object was the investigation of the effect of fatigue. The wire 

 was oscillated for some time, through as large a range as was possible with the given 

 range through which the lever could be turned, before each experiment was begun — 

 the number of complete oscillations varying from 1 to 200. 



A third set, in which the initial ranges were on the whole smaller than those 

 previously employed, consisting of ten experiments, was obtained between the dates 

 9.12.95 and 24.12.95. 



Before the second set was begun, the wire was oscillated, with a large initial range, 

 once or twice per day for about three weeks. Before the third set was begun, it was 

 similarly oscillated, about once per day, for five or six weeks. 



In those experiments in which the initial range had as great a value as could be 

 attained conveniently, the range fell to about half its initial value in one oscillation. 



