428 DR W. PEDDIE ON 



The numbers in the last row agree sufficiently well with those in the second to 

 justify the adoption of the general formula 



?/ 103 (x+ 1 -4 + ?/„-'■■») = 100 



for the representation of the results of the whole series of experiments made under 

 the condition of equal large fatigue. 



Table II. contains a comparison, in the case of each experiment, of the results of 

 observation with those of calculation. The middle column in each case contains the 

 observed values of y, when x has successively the values 1, 2, 3, 5, 7, 10, 15, 20, 25, 

 30, 35, 40, 45, and 50. The numbers in the left hand column are those calculated 

 for the same values of x, with the values of a, n, and b, given in Table I. ; those in 

 the right hand column are the corresponding values obtained by means of the general 

 formula just given. The latter have been kindly calculated for me by Mr W. Thomson, 

 formerly Donald Fraser bursar in the Physical Laboratory. In practically all cases, 

 excepting the one in which the initial range had its largest value, the numbers in the 

 third column agree at least as well with those in the second as do those in the first. 



Discussion of the Initial Manges in Previous Experiments. 



If we take the data for the experiments detailed in Tables IV. and V. of the Second 

 Paper (Trans. R.S.E., 1896), and calculate from them, for these experiments, the values 

 of p in the expression 



y n (x+p + by - n ) = b, 



we get interesting evidence of the effect of magnitude of initial range and of fatigue 

 upon the value of p. The results are given in Table III. In the first set, the initial 

 range, y , is fairly constant. The numbers in the column headed N give the number 

 of large oscillations to which the wire was subjected before readings were taken. 

 These numbers, therefore, to some extent, indicate the amount of fatigue. They do 

 not do so entirely, since the effect of previous fatigue persists to some extent from day 

 to day. This is indicated by the smaller values of p on succeeding dates, when N had 

 a given value. When fatigue is small, p bears a large ratio to a ; when fatigue is 

 great, p bears a small ratio to a. 



In the second set, fatigue was practically constant while the initial range varied 

 between wide limits. As was to be expected, p practially vanishes in comparison with 

 a when the initial range is very small, so that the curve y n (x + a) = b is very flat. 



Re- calculation of Data in Table I. of the First Paper. 

 The values of n, a, and b, given in Table I. of the First Paper (Philosophical Mag- 



