ih 
M. LI. Pupin—Studies in the Electro-magnetie Theory. 333 
electro-magnetic waves in a substance can be accounted for by 
the electro-magnetic theory by assuming that the electro-mag- 
netic constants of the substance are different in different direc- 
tions. There seems to be no strong evidence against the 
assumption that Maxwell looked upon this form of the law of 
flux as merely a first approximation to truth. 
We are ready now to describe the sources of indirect experi- 
mental evidences in favor of the hypotheses on which rest the 
two fundamental laws of Maxwell’s electro-dynamics. It seems 
desirable, however, to make first the following slight digres- 
sion. Combining the two fundamental laws with the law of 
flux and considering, for the sake of brevity, that the medium 
is isotropic and non-absorptive, we obtain: 
ER =| OY opr | 
Sate, whe Gedy Nas’ 
ice es ef 
ot ae of) OY | 
V di Say eae) + (B). 
Equations (A) and (B) and similar equations for absorptive and 
anisotropic media are very often called the mathematical state- 
ment of the two fundamental laws of Maxwell’s electro-dynainics. 
Such a presentation of the Maxwellian theory seems not only 
entirely unnecessary but also misleading. Tor the hypotheses 
by means of which Maxwell passed from the two experimental 
laws of magneto-electric and of electro-magnetic: induction to 
the two fundamental laws of his electro-dynamics have very 
little if anything to do with what may or may not be the com- 
plete form of the law of flux as stated above, not even if we 
choose to accept Maxwell’s mechanical models of the electro- 
magnetic field as correct representations of what is going on in 
such a field. In these models the constants K, yw, &, have a 
definite mechanical meaning, but this meaning does by no 
means lead to the conclusion that for all periodicities of the 
impressed forces equations (A) and (B) are equivalent to that 
mathematical statement of the two fundamental laws in which 
the current and the forces appear as fundamental vectors, and 
no reference whatever is made to the physical constants of the 
field. Equations (A) and (B) should, therefore, be treated as 
an adulteration of Maxwell’s fundamental laws, the foreign 
element in this adulteration being that form of the law of flux 
which Maxwell employed. This adulteration may do, and as 
