THEORY OF ELECTROMAGNETISM. 
755 
Professor J. J. Thomson [‘Applications,’ § 17 (4)] magnetic coordinates independently 
of electric coordinates. It is interesting to note in this connection that Professor 
J. J. Thomson (ibid., § 59) working on somewhat different lines from this paper, has 
also found that thermomagnetic phenomena have a distinct bearing on the equation 
477 C = VVH. His conclusion is that this equation must be given up, and that 
instead we shall have 
VVH = 4ttC + (4tt/ 3) B (@SVd - S@V. d), 
B being here assumed to be a scalar. He assumes that thermomagnetic phenomena 
are reversible. 
84. The first equation that challenges attention is (16). It might be thought that 
it was a truism that B should remain constant in a steady field. This, however, is 
not the case. If the steady increase of B implied by this equation does not produce 
a steady increase in some physical quantity which can be measured directly, the field 
will remain steady in the ordinary sense though B increases. Now the physically 
measurable phenomena depending on B can be conveniently divided into three groups, 
(1) the stress at the point — which leads to mechanical phenomena capable of measure¬ 
ment, (2) the effect it has in modifying the value of H at all points of the field — 
which again leads to mechanical phenomena capable of measurement, (3) its effect on 
the induction of currents. As to (1) it is certainly true that in many instances above 
B does occur in the expression for the stress at a point, but this is in the case of 
solids purely a mathematical result. By equation (27) § 55 we see that the rate 
of variation of B will in general have no effect on the stress at a point. With regard 
to (2) the question must be asked, how does the value of B affect the values of H, C, 
&c., at points other than that considered? The answer is — solely by reason of the 
equations SYB = 0, [SUVB]' 0+6 = 0, where it must be remembered B is an explicit 
function of H, C, &c. If then the rates of variation SVB [SUrB] ((+6 due to g are 
zero, the steady increase of B,, will not produce a steady increase of H, C, &c., at any 
point of space. But these conditions are insured by equations (17), (18). Hence we 
see that B rj need not cause time variation of any mechanical phenomena. As to (3) 
the only electric effect of B (due to — A in E) is one which remains constant so long 
as B remains constant, and, therefore, does not affect the steadiness of the field. 
Hence equation (16) presents no difficulty. 
Equations (15), (17), and (18), however, do present very formidable difficulties. 
It has been stated that the influence of B on the electromagnetic quantities of the 
field is due to the equations SVB = 0, [SUz/B] a+6 = 0. It must now be added that 
the manner in which it thus affects the field depends on the form of its expression in 
terms of H, C, &c. Now unless the principal term in B is one depending on H only, 
the behaviour of the body in question would not at all approximate to the magnetic 
behaviour we know that bodies exhibit. For instance, we know that bismuth 
always behaves very approximately as if it were non-magnetic. This requires that 
5 d 2 
