﻿44 Dr. W. Peddie on 



We shall apply this test to the results of experiment C (not 

 given in Table I.), in which the initial range was only about 

 80, and 300 oscillations were observed. The values of y for 

 which x has the values 10, 20, 30, 40 are respectively 44*9, 

 31-9, 25*3, and 21-1. The values of the left-hand side of (2), 

 with w=l, for the stretches of x 10-20, 20-30, 30-40, are 

 respectively 0*0091, 0*0082, 0*0078. Hence the true value 

 of n for this part of the curve is greater than unity. The 

 values ofy for which x has the values 80, 160, 220, 300 are 

 respectively 13*5, 7*9, 6, 4*4. The values of the left-hand side 

 of (2) , with n— 1, for the stretches of x 80-160, 220-300, are 

 respectively 0*052 and 0*061. Hence, in this part of the curve, 

 where the oscillations are small relatively to the initial range, 

 the true value of n is less than unity. If in this part of the 

 curve we take n=*05, we get, instead of 0*052 and 0*061, the 

 quantities 0*083 and 0*068 respectively ; so that n exceeds 

 0*5. 



We shall next apply equation (2) to the results of experi- 

 ments R and S, performed at the dates 15-11-93 and 17-11-93 

 respectively. As in the experiments given in Table I., the 

 initial range was about 125. Previous to the former date the 

 wire had been left at rest with the lead ring appended since 

 the date 19-7-93, i. e. during a period of nearly four months. 



In the curve R the values of y for which x has the values 

 10, 20, 30, 40 are respectively 38*8, 29, 22*9, 18*8. The 

 values of the left-band side of (2), for »=1, over the three 

 stretches of a? 10-20, 20-30, 30-40, are respectively 0*0087, 

 0*0092, 0*0095. For n = 0*5 the numbers are 0'002o, 0*0024, 

 0*0021. Hence n is greater than 0*5 and less than unity. 



In the curve S, at the same values of x, the values of y are 

 36*6, 26*9, 21*1, 17*3; and the values of the left-hand side 

 of (2) are 0*0098, 0*0102, 0*0104. Hence n is less than 

 unity. The diiferences of these numbers are 0*00022 and 

 0*0002. The corresponding differences in R are 0*0005 and 

 0*0003. Hence n is larger in S than in R. 



The " Compound Interest " Law, 



There can be no doubt that, when the range of oscillation 

 is " much smaller than the palpable limits of elasticity," the 

 decrease of range per oscillation bears a constant ratio to the 

 range itself. This was first shown by Lord Kelvin and, more 

 recently, was confirmed by Tomlinson. When the range is 

 increased this law no longer holds, the logarithmic decrement 

 becoming larger. 



In experiment C the observations were continued for a 

 much longer time than in any other experiment, yet the stage 



