THEORY OF ELECTROMAGNETISM. 
747 
B. Modifications necessary on account of Hysteresis. 
71. This seems to be the place to consider what bearing the phenomena of hysteresis 
have upon such theories as the present. No theory of electromagnetism can be 
considered complete unless it takes this important group of facts into account. I do 
not here propose to give a theory of hysteresis—so that the present theory must be 
in this sense confessed incomplete—but it is necessary to notice what modifications 
ought strictly to be made in the assumptions hitherto adopted. 
Professor Ewing (‘Phil. Mag.,’* V., vol. 30 [1890], p. 205), has given a theory 
which adapts itself to dynamical methods such as the present. In his theory the 
phenomena of hysteresis depend upon the fact that groups of molecules can have 
various stable configurations, different groups at any instant having very different 
degrees of stability. The stability of a group is liable by variation of H and 'F to 
break down, so that the group takes up another configuration of greater or less 
stability, and the oscillations which necessarily ensue on the change result to our 
senses in the production of heat. On this view hysteresis is a phenomenon that 
prevents us, if we would take full account of the facts, from ignoring certain coordi¬ 
nates we have hitherto ignored. We can, however, go on ignoring these coordinates 
if we suppose l not to have a constant form in terms of the variables not ignored 
above, but a form which depends on the particular state as to these groups of mole¬ 
cules of an element of volume. We must, then, suppose certain variables—call them 
hysteresis-coordinates—which define the relative numbers of groups of different kinds. 
Of these l will be a function, but they are not of the nature of ordinary dynamical 
coordinates. Their value merely determines the instantaneous form of l as a function of 
ordinary coordinates, so that if one or more of the hysteresis-coordinates change, the 
form of l changes and a new dynamical era begins. In fact, they are very analogous 
to 6, and like 6 they must not be varied when the dynamical coordinates are varied 
in order to obtain the equations of motion. A mathematical development of Professor 
Ewing’s theory may be supposed to furnish the nature of these variables, and experi¬ 
ment must then be appealed to at once to test the theory, and if the test be favour¬ 
able, to find the exact form of l in terms of the variables. And from the mathematical 
development, or that combined with experiment, we must look to find the laws of 
variation of the hysteresis coordinates when H and 'F vary. 
72. This, of course, is only to be looked upon as an ideal procedure of events, 
which, perhaps, for many years cannot come about. Meanwhile, tentative hypotheses 
as to the nature of these variables might be made. For instance, it might be 
assumed that l is always correctly given by equation (1), § 59 above, and that the 
vector I 0 is the sole hysteresis coordinate. In this case g, (and K ?) would, of course, 
be assumed a function of I 0 as well as of 'F. Though this is probably much too 
* Or ‘Nature,’ Oct., L891, p. 566. 
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