330 M. I. Pupin—Studies in the Hlectro-magnetic Theory. 
So far an electro-magnetic field of invariable geometrical con- 
figuration has been considered. It should be observed now 
that the two laws suffice to describe completely the inductive 
effects in an electro-magnetic field of variable geometrical con- 
figuration also. A field of variable geometrical configuration 
means, of course, a field in which the various sources of flux 
(like electrically or magnetically charged bodies and conductors 
carrying electric currents) are in relative motion with respect 
to bodies which are under the inductive action of these sources. 
According to these laws the inductive effects in any circuit 
depend on the rate of variation of the flux through that circuit 
and on nothing else; they are, therefore, independent of the 
particular method by which that variation is produced ; whether 
by varying the intensity of the field; or by motion of the 
various parts of the field; or by keeping everything constant 
and moving the circuit under consideration, it is immaterial. 
This is simply an extension of the experimental fact that the 
electromotive force induced in a conducting circuit follows the 
same law whether that electromotive force be induced by the 
motion of the circuit towards a magnet or by the motion of 
the magnet towards the circuit, or by keeping the two in fixed 
relative position and varying the strength of the magnet. 
The fundamental quantities in this theory are electric cur- 
rent and electromotive force on the one hand and magnetic 
current and magnetomotive force on the other. Calling 
them the fundamental vectors of the electro-magnetic field, 
we can say that the jirst characteristic feature of Maxwell’s 
electro-magnetic theory consists in the perfectly symmetrical 
form of cross-connection between its fundamental vectors, one 
of these cross-connections stating the law of induced magneto- 
motive force and the other stating the law of enduced electro- 
motive force. 
A symbolieal statement of these two laws shows this symme- 
try more clearly. 
Let X, Y, Z be the components of the induced electromotive 
intensity at any point of the field. 
Let a, 6, y be the components of the induced magnetomotive 
intensity at same point of the field. 
df dg dh 
dt? di’? dj’ | be the components of the intensity of the elec- 
Wo ee r tric and magnetic currents, respectively, at 
Te? de ae the same point. 
If the electric vectors be measured in electrostatic and the 
magnetic vectors be measured in electro-magnetic units, then, 
V being the ratio between the two, we can state symbolically 
the two laws as follows: 
Let 
