426 DR W. PEDDIE ON 



described in the Second Paper. That method was employed in the calculations to be 

 given subsequently. Since 



n log y + log (x + a) = log b, 



if log (x + a) be plotted against log y, the corresponding points lie on a straight line 

 which intersects the axis along which log y is measured at an angle whose tangent 

 is n — provided that the proper value of a is used. The value of b can then be 

 obtained. If a wrong value of a be used, the points will not lie on a straight line. 

 If too large a value of a is taken, the curve on which they lie is convex towards the 

 origin ; if too small a value is taken, the curve is concave towards the origin. In 

 this way the true values of the constants are obtained in any experiment. Fig. 1 

 illustrates the method. 



First Series of Experiments. 



Previous attempts to separate the effects of the magnitude of the initial oscilla- 

 tion and of fatigue upon the values of the quantities n and b had not been success- 

 ful. An attempt was therefore made to eliminate entirely the effect of magnitude 

 of range by inducing very great fatigue in the wire. Before this was done a 

 single experiment was made on the date 8.6.96, the wire having practically not 

 been oscillated since the conclusion, on the date 24.12.95, of the third series of 

 experiments described in the Second Paper. After the date 8.6.96, the wire was 

 oscillated three or four times per week, by from 20 to 40 complete oscillations of large 

 magnitude, until the date 10.7.96, when 150 large oscillations were given. Then, on 

 the dates 14.7.96 and 15.7.96, respectively, 40 and 5 large oscillations were given. No 

 readings of the decrease of range with increase of number of oscillations, when the 

 wire was left to itself so that the oscillations died away, were taken on any of these 

 occasions — the object being merely to induce excessive fatigue as a permanent condition 

 in the wire. Such readings were taken on ten succeeding occasions. On each occasion 

 the wire received 25 complete large oscillations, and was then brought to rest before 

 being started anew in oscillation, when the readings were commenced. 



Table I. gives the results obtained, the quantities a, n, and b being calculated in 

 the manner already referred to. The magnitude of the initial range y varied greatly 

 in different experiments. The table also includes the results of the experiment made 

 on the date 8.6.96. These show that the wire was practically in the same condition 

 that it had been left in at the conclusion of the previous experiments. On the other 

 hand, the results of the experiments made under conditions of great fatigue of the 

 wire show a marked change in the state of the wire. The value of the product nb 

 has attained a practically constant value, about equal to one -half of its previous value. 

 The values of n and b are practically constant also, though the initial range varies 

 greatly. The double sets of results given under two dates correspond to slightly 

 different inclinations of the line in the diagram used to determine n and b. 



