ha 
M. I. Pupin—Studies in the Electro-magnetic Theory. 331 
Arde: 01: pOZ Aisi SKN.) 
eeGuae ai tay > aa) 
va=-(e-s) Lines) law, 
ADAG. oY 5x\; | 
ee -2), 
ey ae 
a oy be | 
ae = ay aes Seer condeliaa: 
in dh 66 6a | 
meee Se ay 
An immediate consequence of these two laws is the following 
important relation :— 
0 /da a 0 (db GO (dey 
Oa = oy | PLA (5) a 
Onn han ORG: do (dh 
Te (2) ay = wee (=) Bere 
_ That is to say, the magnetic and the electric currents follow 
the laws of flow of an incompressible fluid. Hence they form 
closed paths. This is one of the essential differences between 
the Maxwellian theory and the older electro-magnetic theories. 
Numerous other essential differences can be deduced directly 
from the two laws by a proper interpretation: of the physical 
meaning of the perfect formal similarity existing between them. 
One or two only of the several of these essential differences 
which were first pointed out clearly by Hertz,* should be men- 
tioned here, in order to show their general character. The mag- 
netic field induced by a loop of wire carrying an electric current 
(which we may call avarying electric solenoid) has the same form 
as the electric field induced by a varying magnetic solenoid which 
has the same geometrical configuration as the loop; hence just 
as two varying electric solenoids exert a magnetic force, so two 
varying magnetic solenoids exert an electric force upon each 
other. 
An experimental proof of the existence of the electric field 
of force induced by a varying magnetic solenoid would consti- 
tute a direct experimental evidence in favor of the Maxwellian 
theory. It is evident, however, that extremely serious and 
apparently insurmountable technical difficulties would be 
encountered by every attempt to verify experimentally this - 
relation and similar other reciprocal relations which, taken 
* Wied. Ann. xxiii, p. 84, 1884. 
