402 



Mr. Alex. McAulay. On the 



[Apr. 28, 



The other most important features of the fundamental assumptions 

 are first those already described with reference to the electric co-ordi- 

 nates, and the expression for the current in terms of the displacement, 

 and, secondly, the manner in which are treated the two currents, 

 conduction and dielectric (the latter being inappropriately on the 

 present theory denominated the " displacement current"). If there 

 are (and physicists seem agreed on the point) two independent 

 currents whose sum appears in the equation 4 ttO = YyH, and whose 

 sum obeys the laws of incompressibility, it seems to me of the nature 

 of a truism that there must be also two independent electric displace- 

 ments, whose sum obeys the laws of incompressibility. I, therefore, 

 from the very beginning recognise two displacements, d and k, which 

 I call, for want of better names, the dielectric and conduction dis- 

 placements.* This naturally leads to the contemplation of two 

 independent kinds of electro-motive force. This last, however, is 

 subsequently satisfactorily disposed of. 



Before leaving the fundamental assumptions let me remark that, 

 though in some important respects the present theory may seem to 

 differ from Maxwell's, it will be found, I think, that just where the 

 difference seems to be most marked, is Maxwell's theory most vague. 

 All the differences, if they really be such, have been forced on me 

 unwillingly in the attempt to put into definite form what I take to be 

 the essence of Maxwell's theory. At any rate the results, though 

 not in every respect identical with Maxwell's, are yet so nearly 

 identical that the true matter for surprise is that they differ so 

 little and in such unimportant ways from his. 



It must be added, to prevent misconception of my own views, that 

 I by no means consider proven, what I regard as the key to Maxwell's 

 theory, and what I have strictly adhered to in this paper, the assump- 

 tion that under all circumstances 4ttC = YyH. My position rather 

 is that, while the assumption may or may not be true, it is desirable 

 to investigate as generally as possible what must be true, and what 

 cannot be true if the assumption is made. In other words, I do not 

 think that Maxwell's theory has yet had a fair trial, even at the hands 

 of mathematicians, and the present paper is an attempt to provide 

 more ways and means than hitherto have been available, for such a 

 trial. The methods adopted are equally applicable to other sets of 

 fundamental assumptions. 



* Perhaps it would be better to call them the elastic and frictional displacements, 

 or the reversible and irreversible displacements. I wish, to leave this point open for 

 those better qualified tc decide. Of the three sets of terms suggested above, the last 

 seems to me the best. The only reason for adopting in the present paper the names 

 given in the text is to imply the origin of the assumption that there are two such 

 displacements. Of course, if we call the two displacements reversible and irre- 

 versible, we must also call the corresponding currents reversible and irreversible. 



