180 
Proceedings of the Royal Society of Edinburgh. [Sess. 
where A = 1*5, this value of A being chosen so as to cause the values of y; 
taken to lie well over the range plotted. 
The values taken were 
# 1 = 62 , 0 y l = 2 - 40 
#2 = 23-0 log V\ = '38. 
# 3 = 6.0 
Now 
i.e., 
and 
2/i n P°gi/i + ^i + «)] =; 
A^^pog y 1 + log A + k'(x 2 + a)] = b, 
A w [log y 1 + log A + k'(x 2 + a)] = log y 1 + k'(x 1 + a), 
A n [2 log A + log y l + k\x 3 + a)] = log y 1 + log A + k’(x 2 + a). 
Using the contractions 
2 log A + log 2 /! = A, 
log A + log y 1 = B, 
we have 
A + k\x 3 + a) _ B + k'(x 2 + a) 
B + k'(x 2 + a) log y + k'fa + a) 
Now substitute various (likely) values of a, and find the corresponding 
values of h' from the resulting quadratic. 
Thus if a = 4, since A = *732 and B = *556, we get k' = ’ 32 or *002. 
Proceeding in this way, we find the following : — 
a 
k' 
a 
k' 
a 
V 
0 
T5 
6 
•88 
10 
- -35 
1 
T5 
6-5 
3-16 
11 
-•25 
2 
T5 
7 
7-45 
12 
-•20 
3 
•17 
7-5 
-2-50 
13 
-T5 
4 
•32 
8 
- 1T5 
14 
-T5 
5 
•47 
9 
- -65 
15 
-T5 
These values are seen plotted in diagram I. 
Again, 
A n [log y 1 + log A + k\x 2 + a)\ = log y + k'(x l + a) . . . (6> 
When a was equal to 5 in the original curve for soft copper, this value 
seemed on the whole to give the closest approximation to one straight line. 
Let a = 5 be tried in the further approximation. In this case k' — '47. 
Substituting in equation (6), we find 
n= 2-00. 
