THEORY OF ELECTROMAGNETISM. 
6 95 
The “ conduction ” current is measured by the current of foreign liquid, and the 
“displacement” current (indicated in the present paper by the term “dielectric” 
current) by that of the original liquid. In a simple conductor there is nothing to 
distinguish foreign from original liquid, and the conduction current in this case is 
represented by the whole liquid current. 
A similar but not identical analogy will hold in the theory now advocated. For 
fixed matter the whole of the foregoing would be true, but not for moving matter. 
The liquid in the present analogy must not be incompressible, but must have a 
property in connection with matter which corresponds to the property of an incom¬ 
pressible liquid with reference to space. An incompressible liquid is one of which 
only one definite quantity can occupy an assigned space. In the present analogy we 
must say, instead, that the liquid is contained by matter, and that a given portion of 
matter always contains the same quantity of liquid. If by any means we pump 
foreign liquid into this portion, then an equal quantity of liquid must pass out of 
the boundary of that portion of matter into neighbouring matter, and thus in the 
present analogy as in the former, electric displacement will have for analogue the flux 
of the liquid, but not as in that case, across a surface fixed in space, but across a 
surface fixed relatively to matter. 
Similar remarks apply to currents. 
E. Plan of the Paper. 
16. It will conduce to clearness to give some account here of the objects and aims 
of what is to follow. The part of the paper succeeding this introduction is in three 
main divisions : The groundivork of the theory; The establishment of general results. 
and The detailed examination of these results. 
The groundwork of the theory, though not the longest of these, calls for most 
attention here. It is divided into two parts, Fundamental assumptions and Pre¬ 
liminary dynamical and thermodynamical considerations. I do not propose to give 
here a resume of the different parts, but to call attention to certain prominent features. 
The two most important of the fundamental assumptions are, perhaps, first, that in all 
cases 477-0 = WEE, which I take to be one of the most characteristic features, if not the 
most characteristic, of Maxwell’s theory, and secondly, that the modified Lagrangian 
function per unit volume, though, of course, it contains H, does not contain any term 
involving magnetic moment per unit volume or magnetic induction. Neither of these 
assumptions seems to be at variance with Maxwell’s, and, as hinted, the first is 
taken up mainly because it is a fundamental feature in his theory. From the first it 
follows that C must obey the laws of incompressibility, and this naturally leads to 
the assumption that D also invariably obeys those laws. The second leads to very 
important consequences, which, I believe, have not before been traced, and which I 
wish to call attention to here. Though not put quite in this form below they amount 
to this, that H V/, where l is the modified Lagrangian function per unit volume of the 
