TORSIONAL OSCILLATIONS OF WIRES. 615 



with the horizontal axis is numerically equal to the value of n. The equation then 

 gives the value of b if values of x and y, corresponding to a point on the line, are 

 inserted in it. If too large a value of a has been assumed, the line will be curved from 

 the origin ; if too small a value has been assumed, the line will be curved towards the 

 origin. 



First Series of Experiments. 



In the above way the constants were determined in all the cases included in the first 

 series of experiments after the date 24.7.94. The results are given in Table III. It is 

 evident that there is no stronger indication of systematic variation in the values of the 

 quantities than was given by the former method of determination. On the whole, the 

 value of n seems to be greater when the initial range is small. But no stress can be 

 laid on this result, for, when the range is small, a possible error in an observed value of 

 y is a large fraction of its total amount. Again, possible observational errors cause 

 the graph to appear practically straight throughout a considerable extent, although 

 different values of a are chosen in plotting it ; and this causes an uncertainty in the 

 deduction of the values of n and b which increases when the initial range is small. 

 The values of n and b, given in the table, were those which were obtained from the 

 first assumed probable value of a which made the graph sufficiently straight. 



Second Series of Experiments. 



It became evident that it was necessary to carry out another series of experiments, 

 under distinctly different conditions, in order to re-test the question of systematic 

 variation, or to determine if the results obtained in the two series had any aspect 

 in common. The results of the second series are contained in Table IV. The numbers 

 which are given in that table are not, in some cases, those which were at first adopted. 

 But theory indicated, as w T ill be found subsequently, that the product nb might be 

 constant, and it was seen to be so nearly constant throughout such a large number 

 of the cases, that, in those cases in which its value differed much from the average, 

 a recalculation of the quantities was made — a being altered in such a way as to make 

 nb take a value not much different from that observed on the average in the other 

 cases. It w T as in general found that the change thus made brought the calculated 

 values of y into closer agreement with the observed values. 



Throughout this series, large initial ranges of oscillation were employed, and the 

 various experiments practically differed only in the amount of fatigue to which the 

 wire was subjected. The amount of fatigue is indicated in the column headed N, 

 which gives the number of complete large oscillations which were given to the wire 

 before the observations were commenced. The effect of fatigue in diminishing b and 

 increasing n is very marked. That it is also persistent is evident on a comparison 

 of the cases in which N had the value 1, and of the two cases in which N had the 

 value 50. 



