336 MM. I. Pupin—Studies in the Hlectro-magnetic Theory. 
refer in particular to the following investigations and reserve a 
more detailed discussion of this matter for a future occasion : 
Von Helmholtz, Wied. Ann. xlviii, pp. 389 and 723, 1893. 
Goldhammer, Wied. Ann. xlvil, pp. 93 and 265 soxlwiy ae wile 
1892. Drude, Wied. Ann. xlvi, p. 353, 1892; xlviii, Dp: 129 
and p. 356; xlix, p. 960, 1893... Mbert, Wied. Ann. xlviii, p- 
iL, 1893; li, p- 268, 1894. 
3. Hetension of the law of flux. 
The question arises now, can we without resorting to any 
hypotheses not already contained in Maxwell’s electro-magnetic 
theory find a more general and satisfactory form for the law of 
flux? This question can be answered in the affirmative, pro- 
vided that by a law of flux we mean a quantitative relation 
between the electric force and the electric flux on the one 
hand and the magnetic force and magnetic flux on the other. 
Consider two large conductors insulated from each other by 
a perfect non-conductor. Let one of them be connected to 
one pole of a galvanic cell and the other to the other pole. 
We know that as soon as these conductors are connected in the 
manner described an integral transient current takes place 
whose value depends on the capacity of the conductors. The 
work of the cell appears half as heat in the conducting parts 
and half as potential energy in the dielectric. If Q be the 
integral current and E the electromotive force of the cell, then 
EQ=total work of the cell. 
4EQ=potential energy stored in the dielectric. 
Let X, Y, Z be the components of the intensity of the electro- 
motive reaction at any point of the dielectric and at any 
moment during the flow of the integral current. 
rer fag ah 
F ‘dt? dt? GE. 
electric Pies ae current at the same point and time, then 
fif(she 42) dr= EQ 
where dz is an saahitey ante of the dielectric. The inte- 
gration extends over the whole dielectric field and over the 
interval of time from the start to the completion of the integral 
current. It is evidently immaterial how X....and/.. 
vary during the flow of the integral current ; the final resultant 
potential energy in the dielectric is, according to experiment, 
always the same and equal to 4EQ. According to their phys- 
ical character X.......are, of course, finite, continuous, 
and singly-valued functions of ‘the time ; we can ‘apply, there- 
fore, to the indicated integration all the rules of calculus which 
be the components of the intensity of the 
re. eS . 
