TORSIONAL OSCILLATIONS OF WIRES. 433 



curves obtained by plotting log (x + a) against log y, when the initial oscillation is 

 small, though a straight line passes with considerable accuracy in the neighbourhood of 

 the points, leaving as many points on one side as on the other on the average, yet almost 

 absolute accuracy would be obtained by drawing two lines meeting at a vejy slight 

 inclination — the smaller value of n corresponding to the smaller oscillations. The 

 crossing point of these lines may possibly indicate an angle of torsion, such that 

 molecular groups which break at a less angle have recovered from fatigue, while those 

 which break at a greater angle have not yet recovered from fatigue. I first observed 

 this in the experiment 17.11.97 (1), but it was found subsequently in other experiments, 

 and had also occurred in previous experiments, as detailed below. 



It first appeared in the experiment 3.11.97 (2) with y =12'8, and it appears 

 slightly also in the succeeding experiment 4.11.97 (1) with y = 20'7. It occurred also 

 in the experiment 9.11.97. In the case of the three experiments of date 10.11.97, it 

 appeared markedly in the first, very slightly, if at all, in the second, and not at all in the 

 third — each experiment apparently aiding in its obliteration. The initial angles in 

 these cases were 13*1, 11*0, and 11*2 respectively. It could not be said to be evident 

 in the experiment 11.11.97 (2). 2/ = 9*3, which followed immediately after the experi- 

 ment 11.11.97 (l), 2/ = 35*6 ; and it did not appear in the experiment 12.11.97 (1), 

 y = 9'4, which was immediately preceded by 40 large oscillations. In the experiment 

 15.11.97 (1), y Q = 8'6, made after the wire had remained at rest for three days, it again 

 appeared markedly, the point of junction of the two lines corresponding to an angle 

 about one and a half times as large as that indicated in the experiment 10.11.97 (1). 

 It could not be observed in the experiment 16.11.97 (1), which followed a large oscilla- 

 tion on the preceding day, though it would appear if a smaller value of a were chosen. 

 But a smaller value of a would increase the value of n, and it is to be noticed that the 

 values of n and b, found for that experiment and the preceding one, are abnormally 

 large (see 18.11.97 (1)). As already mentioned, the peculiarity appears in the experi- 

 ment 17.11.97 (1), y = 14'3, the wire having been considerably fatigued on the preceding- 

 day. It did not appear in the subsequent experiments on that date. It was evident in 

 the experiment 18.11.97 (l), y = 9'8. In the succeeding experiment on the same date, 

 <y = 10, it was also apparent, but the joining point of the lines occurred at a smaller 

 angle. It could not be said to appear in any of the succeeding experiments. In these 

 the initial range was very small, or very large ; or, the initial range being of inter- 

 mediate size, the experiments were made when the wire had been only slightly oscillated 

 for some days, in which case the joining point might be expected to occur at smaller 

 angles than those which were observed. 



The phenomenon, although not very readily observed, occurs with such persistency 

 that I scarcely think that it can be due to accidental causes. The facts that the joining 

 point occurs at a larger angle when fatigue is small than when it is large, and that 

 repetition of an experiment with small initial range makes the joining point pass to 

 smaller angles, seem to indicate that there is a fairly sharply-marked limiting angle, 



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



