340 MM. L. Pupin—Studies in the Electro-magnetie Theory. 
Maxwell’s electro-magnetic theory consists of two distinct 
parts. The essential elements of the first part are the law of 
induced electromotive force and the law of induced magneto- 
motive force. These two fundamental laws are an extension 
of the two experimental laws of magneto-electric and of electro- 
magnetic induction, which extension consists in adding to what 
is already contained in these experimental laws the hypotheses 
that the magnetic and the electric flux in dielectrics are not a 
mere mathematical fiction, as the older electro-magnetic theories 
supposed, but an actually existing state in the dielectric whose 
rate of variation through any imaginary surface in the dielec- 
tric is proportional to the reacting electro-motive, respectively 
magneto-motive force, induced around the circuit of the bound- 
ary line of this surface. The value of the reacting force is 
independent of the nature of the substance through which the 
circuit passes. Hence the physical constants of the electro- 
magnetic field (that is specific inductive capacity, etc.) do not 
appear in the first part of Maxwell’s electro-magnetic theory. 
~The second part of this theory takes account of these con- 
stants by adding to the two fundamental laws just mentioned 
the ordinary form of law of flux. The first two laws are a 
cross-connection between the varying flux of one type and the 
reacting force of the other type; the law of flux, on the other 
hand, is a direct connection between the force and the flux of 
its own type. Combining the two fundamental laws with 
the law of flux, we obtain the fundamental differential equa- 
tions of the second part of Maxwell’s electro-magnetic theory. 
These equations are a mathematical statement of the laws of 
propagation of an electro-magnetic disturbance through various 
media, exhibiting the remarkable fact that, on the one hand, 
the velocity of propagation of an electro-magnetic disturbance 
is approximately and the wave-form of propagation is exactly 
_ the same as in the case of light; on the other hand, however, 
the velocity of propagation of an electro magnetic wave 
through a non-absorptive dielectric is independent of its 
periodicity, a fact which does not hold true in the ease 
of light.* Hence although both parts of the Maxwellian 
theory agree well with experimental facts which were brought 
to light by the labors of Hertz and of other physicists 
who extended the Hertzian methods of investigation, yet this 
theory falls short of being a satisfactory theory of light, because 
it represents the propagation of electro-magnetic waves as inde- 
* An apparent exception to this isthe propagation of light through the most 
perfect of all dielectrics, namely, the ether in a perfect vacuum The velocity of 
propagation of light through this dielectric is, within the narrow limits of the 
visible spectrum, independent of the wave length. The question. however, 
whether all wave-lengths travel through pure ether with the same velocity has 
not yet been answered definitely. The statement. therefore, that the velocity of 
Hertzian waves in ether is the same as that of light is somewhat indefinite. 
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