﻿42 Dr. W. Peddie on 



three days. Between the experiments F and h x experiments 

 were performed every day — twelve experiments in all, some 

 with large, some with small, oscillations. 



Test of the Empirical Formulae. 



In the following table a comparison is made of observed 

 results in each experiment with the results calculated from 

 the formulae. In the upper row are given values of y common 

 to all the experiments. 



These figures show that the correspondence between the 

 observed results and the results derived from the empirical 

 formulae is very close, and that it holds throughout a large 

 range of values of x. The curves in fig. 1 show this even 

 more clearly. 



All the results given in Table II. for each experiment with 

 the exception of P were observed within ten minutes after 

 starting the oscillations. All the results given for P were 

 observed within thirteen minutes. Within these time-limits, 

 therefore, the quantity n in the equation is practically constant. 

 Yet, since from that table we see that the value of n may 

 diminish from 1*32 to 1*18 in the course of twenty-four hours, 

 we cannot assume that n will not vary in amount in any one 

 experiment until the vibrations cease to be observable. As 

 a matter of fact, it does so vary. 



Variations in the Value o/n. 



From Table I. it appears that when a fresh wire is oscillated 

 with a given initial maximum range on different occasions, 

 the quantity n at first increases in magnitude and ultimately 

 reaches a value which remains constant so long as the treat- 

 ment of the wire from day to day is fairly uniform. This 

 value is exceeded if the given initial range be exceeded, or if 

 the wire be " fatigued " by long-continued oscillation ; but 

 the previous steady value of n is soon reacquired. 



If the empirical formula above used be correct, any two 

 values of y corresponding to a constant difference in x must 

 satisfy the condition 



~~^ 2 = constant (2) 





If too large a value of n be used in this equation, the value of 

 the quantity on the left-hand side will increase when the values 

 of y x and y 2 decrease. If too small a value be used, the 

 quantity will decrease when y } and y 2 decrease. 



