——= oe 
MES ait 
M. I. Pupin—Studies in the Electro-magnetic Theory. 339 
" f/ da dB dy a 
Soa. + 3,b,+ yye,de—faef( ae “- oer thie )ar= 4LC 
0 
The first integral refers to the state of the field when the elec- 
tric current has become constant and therefore the magnetic 
integral current has ceased to flow. The value of this integral 
ean be easily shown to be LC* and we have, therefore, 
bens ss-uclie db _d de dy\) 
The same relations can be deduced from this integral as from 
(C). If the dielectric of the field is absorptive then the last’ 
integral equals the heat developed in the field. We can put, 
therefore 
wy fite fi (at a) +. ( | ) +( dro 
as the most general relation between the magnetic force and 
the magnetic flux. 
Equations (C) and (D) are the consequence of the following 
premises :—First, the hypotheses by means of which we pass 
from the two experimental laws of electro-magnetic and magneto- 
electric induction to Maxwell’s two fundamental laws are cor- 
rect. Second, it is an experimental fact that the electric energy 
of the field is proportional to the square of the integral electric 
and the magnetic energy is proportional to the square of the 
integral magnetic current which has passed across the field. 
Third, the principle of conservation of energy is applicable to 
the processes just described. 
Since these equations (C) and (D} contain as a special case not 
only that form of the law of flux which Maxwell employed in 
the second part of his electro-magnetic theory, but also a large 
variety of other forms of that law, in which the physical con- 
stants which determine the propagation of an electro-magnetic 
disturbance appear as functions of the periodicity of the im- 
pressed forces, and since forms of the law of flux of the same 
type as these latter forms were assumed hypothetically in 
most of the recent developments of the electro-magnetic theory 
of light because they lead to a tolerably satisfactory explana- 
tion of the phenomena of dispersion, absorption, rotation of 
the plane of polarization,—it follows that we can accept these 
two equations as the most general expression for the law of 
electro-magnetic flux. 
Summary. 
The main points of this essay can be summed up as fol- 
lows: 
