M. I. Pupin—Studies in the Electro-magnetic Theory. 341 
pendent of the periodicity of these waves, and therefore fails to 
account for some of the most important optical phenomena 
like dispersion, absorption, etc. These phenomena we know 
to be due to the dependence of the optical constants of a sub- 
stance on the periodicity of waves ; hence, if Maxwell’s electro- 
magnetic theory is to become a satisfactory theory of light, it 
must be extended so as to represent the electro-magnetic con- 
stants of a substance as functions of the periodicity of the 
impressed electro-magnetic forces. This extension of the Max- 
wellian theory will affect, therefore, the law of flux only, and 
not the first part of this theory, since this part does not and 
should not contain any reference whatever to the nature of the 
medium of which the electro-magnetic field is composed. 
This opinion is confirmed by the recent developments of the 
electro-magnetic theory of light, since in these the law of flux 
and not the two fundamental laws of Maxwell’s theory appear 
in a modified form. Besides, itis obvious that Maxwell’s form 
of the law of flux holds true for constant and slowly varying 
forces only. In every other case its application is only tenta- 
tive. The second part of the Maxwellian theory should, there- 
fore, be considered as a tentative and therefore approximate 
description of the laws of propagation of electro-magnetic dis- 
turbances. A more accurate description of these laws must 
proceed from a more general form of the law of flux, a form 
which will hold true for forces of all periodicities. That such 
a form of the law of flux actually exists is rendered highly 
probable by considering the most general relation between the 
electric and magnetic forces and their fluxes which will satisfy 
Maxwell’s fundamental hypotheses, and also the observed fact 
that the electric, respectively magnetic, energy of the medium 
through which an integral electric, respectively magnetic, cur- 
rent has passed is a quadratic function of that integral current. 
This general relation is expressed by the forms (C) and (D) 
deduced above. 
Maxwell’s provisional form of the law of flux is a special 
case of this general relation. This general relation suggests 
also that many other forms of the law of flux are permissible 
in which those physical constants which determine the propa- 
gation of an electro-magnetic disturbance appear as functions 
of the periodicity of the disturbance. But these constants are 
not specific inductive capacity, magnetic permeabilities and 
resistivity of the medium. 
It still remains to be shown that according to Maxwell’s 
electro-magnetic theory a law of flux containing explicitly 
the periodicity of the impressed forces is not only admissible 
but also necessary. When that is shown, then this theory 
will have fulfilled one of the most essential conditions which 
every satisfactory theory of light must fulfill. 
Effingham Park, West Islip, L. I., Aug. 20, 1895. 
Am. Jour. Sci—Tuirp Series, Vou. L, No. 298—OctToBER, 1895. 
