338 MM. I. Pupin—Studies in the Electro-magnetic Theory. 
470 
47 
| ee 
f 47 
A= | 47 _ cq | 4 
era | 
as another possible set of relations. 
Here A=a,—a,p'+a,p'—.... 
B=b,—b,p'+b,p'—.... 
C=c,—c¢,p'+¢,p'—.... 
In this permissible form of the law of flux the constant which 
corresponds to specific inductive capacity is a function of the 
periodicity. A large variety of other relations can easily be 
found all of which will satisfy the integral equation. 
If the dielectric is absorptive then the value of the integral 
does not vanish but equals the heat developed in the dielectric. 
Hence in general 
eo 
cxf af | (2-0B) + (0-0) + (0-09) hare 
\ 
contains all the possible forms of the law of flux relating to 
the electrical force and the electric flux, which are consis- 
tent with Maxwell’s hypotheses and with the quadratic form of 
electropotential energy. 
A similar relation between the magnetic force and the mag- 
netic flux can be obtained. Consider a loop of wire in which 
a galvanic cell sets up a current. From the moment of closing 
' the circuit up to the time when the current becomes constant 
magnetic energy is stored up in the medium. The final 
amount of magnetic energy will be in the well known notation 
W=3LC’ | 
Let a, 8,7 be the components of the intensity of the mag- 
netomotive reaction at any point of the field and at any 
moment during the flow of the magnetic integral current. 
tat da db de 
er da? Beale 
magnetic current.at the same point and the same moment, then 
t 
gt’, "DE NGG ara 
Integrating by parts we obtain 
be the components of the intensity of the 
