616 DR W. PEDDIE ON 



Third Series of Experiments. 



Since, in the preceding series, large values of the initial range had alone been used, 

 the third series was undertaken with the object of testing the constancy of the product 

 nb when the initial angle was small. The results are contained in Table V. The 

 wire was not fatigued by oscillation before each experiment. In the first two experi- 

 ments, the value of 6 was large, and a comparison of the values of n, in these cases, 

 with the values of n in similar cases in the first and second series of experiments, shows 

 that the effect of the great fatigue induced in the second series has persisted through- 

 out the period of four and a-half months which elapsed between the completion of the 

 second series and the commencement of the third. 



Constancy of the Product nb. 



When the product nb is made as small as 180, the convexity, towards the origin, 

 of the curves in which log. (x + a) is plotted against log. y is usually distinct ; when the 

 product is as large as 250, the concavity, towards the origin, of these curves is also 

 in general distinct. Thus the evidence that the product had, throughout the second 

 and third series of experiments, a constant value not much different from 200 is 

 of considerable strength. It is confirmed also by the results of the first series as 

 given in Table III. Although these data were not determined with special precautions 

 to obtain the best result, the products, with very few exceptions, fall within the 

 limits just specified. In the particular exception 3.8.94 (l), the scale readings differed 

 greatly, and for no obvious reason, from the readings got in the experiment 3.8.94 (3) 

 under nearly identical conditions. And, in the exception 4.8.94 (1), the scale readings 

 differed greatly from those which were obtained in the experiment 3.8.94 (4) under 

 the same conditions. These two exceptions stand alone, in this respect, in all the series 

 of observations. A new determination of the quantities n, a, and b was made, so as to 

 give products of n and b not greatly differing from 200. 



The results are given in Table VI. In almost every case these values of the 

 quantities were found to give better agreement with the results of observation than the 

 values given in Table III. This was, for example, the case in the experiment 4.8.94(2). 



Variation of n and b. 



A comparison of the values of n and b in Tables IV., V., and VI. shows that the effect 

 of increased initial range is of the same kind as the effect of fatigue. Fatigue causes a 

 distinct and persistent increase in the value of n, and increase of the initial range also 

 causes an increase in the value of n. Probably, if the wire were fatigued day after 

 day by oscillation to a large and definite extent for a considerable period, a definite 

 relation between n and Q would become apparent. In the present series of experi- 

 ments, no such relation can be established, for it is impossible to separate the effects 

 of increased initial range and of fatigue. This is well brought out in fig. 2. The 



