G14 DR W. PEDDIE ON 



First Method of Determining the Constants. 



In the first determination of the values of the quantities n, a, and b in the expres- 

 sion y"(.c + «) = b, use was made of the equations — 



.<•„ - .'■ 



.r + Xo - 2j\, 



where y 1 = my. 2 = m 2 y 3 , a suitable value being assigned to m. Three sets of values of 

 y 3 , y , and y x were chosen. These were respectively 5, 10, 20 ; 4, 8, 16 ; and 4, 7, 

 12 "25 in all the cases in which the values of the quantities n, a, and b were determined 

 by this method with two exceptions. In the experiment of date 16.7.94, the sets 

 chosen were 5, 10, 20 ; 6, 10, 167 ; and 5, 8, 12'8 ; in that of date 4.8.94 (2) the sets 

 were 3*5, 7, 14, and 4, 7, 12*25. These constant sets were chosen in order that, as far as 

 possible, the determination of the quantities n, a, and b might be made under like 

 conditions in the different cases. The arithmetical means of the values obtained for 

 n, a, and 6 were then taken. It was hoped that, in this way, it might be possible to 

 make out a systematic variation in the value of n as the value of the initial range was 

 varied. But no indication of any change could be found, though the initial range was 

 varied from its greatest value to about one-quarter of its greatest value ; and the 

 variety of the results obtained showed that any change which really existed was entirely 

 hidden by irregularities arising in the observations themselves. 



The columns headed n, a, and b in Table II. contain the averages ; those headed 

 n v n. 2 , and n 3 contain respectively the values of n as calculated from the three sets of 

 values of y in the order specified above ; and the column headed gives the values of 

 the initial range. Although these results are not subsequently employed, they are 

 tabulated because they verify the conclusion, made in the first paper, that there is a 

 slow diminution in the value of n as the oscillations die away. 



Second Method, of Determining the Constants. 



Since a method of evaluating the quantities n, cc, and b, dependent on the selection 

 of particular points on the experimental curves, seemed to be incapable of sufficient 

 accuracy for the indication of systematic variations in the value of n, it became necessary 

 to use a method which gives values suiting, on an average, all points of any curve. 

 Such a method is at once evident if we write the equation in the form — 



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



If the proper value of a be chosen, and if values of log. (x + a) be plotted vertically, 

 while corresponding values of log. y are plotted horizontal, the points thus obtained lie 

 on an average on a straight line, and the tangent of the angle which this line makes 



