214 Proceedings of the Royal Society of Edinburgh. [Sess. 
is fairly regular. The irregularities which occur are not surprising when 
we bear in mind that we are dealing with the differences of small quantities 
of which the experimental errors are considerable. If, confining our 
attention to either the a- or the ^-differences, we plot each row in terms of 
the corresponding values of T, and each column in terms of the correspond- 
ing values of H, we get a series of zigzag lines which radiate in a roughly 
rectilinear manner from the origin. Let us assume that the a-differences 
tabulated in Table C can be represented in the form A H T, and that the 
^-differences can be represented similarly in the form B H T, where A and 
B are coefficients, each of which is the ratio of the sum of the corresponding 
set of differences to the sum of the products of the H’s and T’s. 
Thus we find that each a+difference has the value 
a-diff.= 0-0169 HT, 
and that each 6-difference is given by 
6-diff. =0-0138 HT. 
These may be written in the form 
T(H) = T(1 +0-0169 H) 
H(T) = H(1 +0-0138 T), 
where H is always positive and T is always negative. 
Thus T(H) is always negative and numerically greater than T, the ratio 
of the two being 1+0-0169 H. 
Again, H(T) is positive like H but less than the value of H in the ratio 
of 1 + 0-0138 T to unity until T attains the value —72 (=—1/0-0138). 
When the transverse effect has this critical value, which occurs in the 
neighbourhood of field 220 (see Table A), the values of H(T) vanish. For 
numerically higher values of T, H(T) becomes negative and goes on 
increasing numerically for increasing values of both H and T. 
We may now substitute for T and H in the formulae just given their 
values in terms of the magnetizing forces t and h. The formulae then 
become 
T(H) = — 
93 zf 2 A 1-35 h 2 \ 
12,800 + A 790 + /iV 
H(T) 
80 ft 2 
790 + h 2 
1-28 t 2 \ 
12,800 + tV ’ 
These two formulae embody the average results already shown in Table 
A. By their means we can calculate the values of the changes of resistance 
for various convenient combinations of the two fields, as given in the 
following tables : — 
