THEORY OF ELECTROMAGNETISM. 
767 
H except by reason of the term g, so that of equation (35) now stands for the full 
value of b. SVa and [SUFa] a+i are arbitrary. Let us, since it does not affect any 
physically measurable quantity, assume them both to be zero. Since b = VVa, 
[Vc?Sa ] a+6 = 0 , if we considered an analogue in which b stood for an electric current, 
477a would be the magnetic force due to the currents in a space containing no magnets. 
This analogue will serve to give us a very fair general idea of the effect of — a in E. 
Since [equation (35)] every term of b contains K, b will be confined to conductors 
where there are conduction currents. Thus, in the same conductor we shall have the 
“ real current ” and the “ current of the analogue.” The current of the analogue 
may be disposed with reference to the real current in one of three ways. It may be 
mainly parallel to the real current, or it may circulate round the real current 
mainly at right angles to it, or it may circulate round it spirally. In the first 
and third cases we see by the analogy that there would be an electromotive force due 
to a in the general field approximately parallel everywhere to the part of the magnetic 
force due to the real current. In the conductor itself, then, the resulting electro¬ 
motive force would cause the real current to move spirally, and would, therefore, 
apparently increase the resistance. In the second and third cases we see by the 
analogy that there would result effects due to the local state of affairs, so that where 
b was large there the effect of a on E would be large. In a case of this sort we should 
have to examine further before we could say what the local effect would be. 
It is easy to see that in the experiments for determining the quantities con¬ 
nected with the Hall and. thermomagnetic effects, the second of the above cases 
very approximately represents the state of affairs. For, by equation (35), it is only in 
the plate, where © or H is very large compared with the rest of the circuit, that b 
will have a sensible value. Hence there must be a strong local current of the 
analogue, that is, a current which does not go round the circuit parallel to the 
real current. 
It follows that the main physical effects of a are those that were considered in 
dealing with the Hall effect. 
E. Contact Electromotive Force. 
99. Our knowledge of this is not very accurate, but, besides the fact that contact- 
force certainly exists, and that it has been in numerous individual cases measured 
with fair accuracy, the following seems to stand out with considerable certainty. 
If the (apparent) electromotive force from one material, a , to another, b, when they 
are in contact be denoted by a | b, then the equation 
a|6d-6|c+c|a = 0.(1) 
is true if all three materials are conductors, but is not true if they are not all 
conductors. 
