766 
MR, A. McAULAY ON THE MATHEMATICAL 
S/K" 1 ® — B _1 Si'H . (2CSK- 1 0 + c).(37), 
and in place of (31), 
E, ; - mSi© = — B -1 [KB [SK" 1 0 [A - C (H 2, + 2S HR)] - c (H 2 + S 2 iH)} 
+ i (2CSK- 1 © + c){(A - CPA) SiKH + BSKHSfH] 
+ YKE {(2CSK- 1 0 + c) (A - CH 2 ) + B 2 SK -1 0)] . . . . (38) 
which simplifies when SK -1 © is zero (which it certainly approximately is in the 
experiments made to determine the coefficient of the Hall effect, whether P be inde¬ 
pendent of V P or not) to 
E y - m'Si*0 = B -1 c[KB(H 2 + Sh'H) 
— i {(A — CH 2 ) SIKH + BSKHSiH} 
- YKH (A - CH 2 )].(39). 
Owing to the term in i on the right as well as the term in i on the left, there may 
be an apparent increase of resistance. The term in K shows that there will also be 
an increase — c (K 2 + Sh’H) in the resistance. The term in YKH shows that the 
present assumptions lead to a Hall effect, whose coefficient — — B _1 c (A — CH 2 ). 
With regard to the new term 2SK6KSHcH in equation (34), it should be noticed 
that since it is quadratic in K, it would have no influence on the apparent Thomson 
effect, but only upon the apparent resistance as measured by heat effects. 
That we can explain the Hall effect on the present theory is of some interest, 
because, as remarked in § 92 above, we cannot explain it on the present theory in the 
ordinary way. Nor can we hope to explain it by the term — K Vai in E [equations (29), 
§50, and (20), § 35] for Y k VYKH = V£Y£H = — 2H, whereas Y K V (kVx) = 0. It 
should be noticed that the difficulties in the way of explaining the Hall effect by a 
term — C'SCDH/2 do not apply to explaining the magnetic rotation of the plane of 
polarised light, since this is equally well explained by substituting d for D. 
98. One effect of g still remains for consideration. It is necessary to consider it if 
only to show that it leads to no results large enough to be experimentally tested. It 
also helps to show how the various interferences with the lines of flow, several times 
mentioned above, are mainly brought about. 
In writing down equation (9 a) it was mentioned that E (/ did not contain the part 
of a due to g. We have indirectly taken account of the effect of a y in part, by the 
considerations just given in leading up to the explanation of the Hall effect. We 
have not, however, thereby taken full account of a r To do this in the manner 
illustrated above, we should require to study the effect had in modifying the whole 
electromotive force instead of the part E r We proceed then, to a more general 
examination of the effect of the term — a^ in E. 
We will now drop the suffix g from a and b, since we shall not suppose x to contain 
