THEORY OF ELECTROMAGNETISM. 
765 
streams due to ordinary electric resistance and thermoelectric phenomena. The 
original form of zz is more suitable for that purpose. We assume then that the only 
heat effects are due to purely electrical causes. In this case, if the faces of the plate 
are thermally similar, we may assume that S i® has opposite values at points situated 
symmetrically on opposite sides of the plane midway between the faces of the plate. 
The effect of mS i® will be then merely to make the current stronger or weaker in 
the middle of the plate than near the faces, and, therefore, to increase the apparent 
resistance of the plate. We have already seen that unless P (assumed invariably to 
be a scalar in this connection) be independent of the strain, SK -1 © is zero, so that the 
whole expression on the right of equation (31) is zero. If, however, P be independent 
of the strain, the term in VKH in equation (31) would indicate a Hall effect. The 
presence of SK -1 © in this term, however, serves to show that probably this is not 
the true explanation of the Hall effect. 
The Halt, effect may be explained by saying that there is an electromotive force 
A VKH, where h may be called the coefficient of the Hall effect. It has been found 
experimentally that this coefficient is by no means independent of TH—that, in fact, 
in certain cases it changes sign when a definite strength of magnetic field is reached. 
The above work indicates how, on the present theory, we may seek to explain such 
an effect. For this purpose it must be remembered that equations (30) and (31) are 
only true if g is the only term in x which involves H. 
97. Let us now assume that the electric resistance is a function of H, and let us 
incorporate in g the term of x thus depending upon H. We must add a term 
— SKrK/2 to the former value of g ; r being a function (of Class II. of § 9) of 0, 'F and 
H. For the sake of definiteness give r the form — 6SHcH, where b, c are functions 
of the same classes as B and C respectively. Thus, as can be easily seen, to get 
r or r" from r we have merely to change b, c and H into b', c , and K' or b", c", and 
H" respectively. Equations (8a), (9a), (13a), and (16a) must now be changed to 
g = - SKst© + SK6KSHcH/2.(32), 
E^= -sr© + 6KSHcH.(33), 
6f g = - SK (2 [0] + 3 [1] + 4 [2]) © + 2SK6KSHcH - . (34), 
V4tt = VBK© - 2CHSK0 — cHSK6K.(35). 
Hence, in place of equation (28) we now have 
Si (VBK© - 2CHSK© - cHSK&K) =0.(36). 
Assuming B, C, b, c, to be all scalars, and putting, as is permissible in this case, 6=1, 
instead of equation (29) we have 
