326 M. L. Pupin—Studies in the EH lectro-magnetic Theory. 
Art. XXX VI.—Studies in the Hlectro-magnetic Theory.—I. 
The law of electro-magnetic flux ,* by M. I. Purr, 
Ph.D., Columbia College, New York. 
THE law of electro-magnetic flux is a short expression for the 
well-known quantitative relations between electromotive force 
and electric flux on the one hand and magnetomotive force 
and magnetic flux on the other. Ohm?’s law is a part of it. 
These relations are statements of experimental facts which 
we know to hold true for constant and slowly varying forces. 
The object of this investigation is to show the exact position 
which this law occupies in Maxwell’s electro-magnetic theory; 
to point out its limitations; to show that Maxwell’s electro- 
magnetic theory of light demands a more general form of this 
law; and finally, to presenta general form of this law of which 
both its ordinary form and also those forms which were assumed 
hypothetically in some of the recent developments of the 
electro-magnetic theory of light are special cases. 
1. Lhe two fundamental laws of Maxwell’s Electro-dynamics. 
A brief statement of Maxwell’s electro-magnetic theory seems 
desirable in this discussion. For the sake of brevity none but 
its most essential features will be presented, and that in such a 
way as to emphasize as forcibly as possible the essential differ- 
ences between this theory and the older electro-magnetic 
theories. 
The essential features of the Maxwellian theory are reducible 
to two, which may be ealled its two characteristic features. 
These two characteristic features can be exhibited in a very 
simple manner by considering the gradual change in form and 
in meaning which the following two well known experimental 
laws, relating to magneto-electric and to electro-magnetic 
induction, undergo as we pass from the views of old electric 
theories to those of the Maxwellian theory. These laws I 
choose to state in the following form for reasons which will 
be evident presently :— | 
First law :—A varying magnetic field induces a field of elec- 
tric force in all electric conductors within its region. The 
electromotive force around any simple circuit} of this induced 
* Read in abstract before the Am. Assoc. Adv. Science at its Springfield meet- 
ing, Aug. 30, 1895. 
{+ The expression simple circuit needs an explanation. Consider any point of 
the field. Pass a plane through it and in this plane draw an infinitely small area 
around the point under consideration. If the boundary of this elementary area 
be such that none of its points contain more than one branch of the boundary 
curve, then this boundary curve is a simple circuit around this point. 
