Decembee 27, 1895.] 



SCIENCE. 



877 



magnet, a current will also be induced in 

 the loop. Again, leaving everything un- 

 changed and changing the shape of the loop 

 only a current will result. In each case the 

 magnetic flux through any surface bounded 

 by the loop is varied, and this variation of 

 the flux produces, according to Faraday's 

 researches, an electro-motive force in the 

 loop. The law connecting the two may be 

 stated as follows : 



The electro-motive force around the 

 boundary line of any elementary area is pro- 

 portional to the magnetic current, or, what is 

 the same thing, to the rate of variation of 

 the magnetic flux through that area. 



This law is the fundamental law of the 

 Faraday-Maxwell theory which describes 

 the dynamic element in our view of the 

 electric force. Although the form of this 

 law is essentially the same here as it was 

 in the old theories its meaning is radi- 

 cally different. The old theories be- 

 lieved that unless the boundry line men- 

 tioned above consisted of a conductor, no 

 electro-motive force around this boundry 

 would be called into play by the variation 

 of the magnetic flux. In the modern theory 

 this limitation is removed. The current in 

 the loop produced by the variation of the 

 magnetic flux is an evidence that electo- 

 motive reactions are set up in the dielectric 

 surrounding the loop, and this reaction 

 manifests itself as a conduction current 

 when the loop consists of a conducting 

 material. N"ow an electro-motive reaction 

 in the dielectric is impossible without a 

 previous electric flux, hence every variation 

 of the magnetic flux is accompanied by an 

 electric flux, just as every variation of the 

 electric flux is accompanied by a magnetic 

 flux. The law connecting the variation of 

 the flux of one type to the integral flux of 

 the other type is formally the same in each 

 case. 



The question, How does the reaction of the 

 magnetic field against a change of the cur- 



rent in any part of it manifest itself? is now 

 easily answered. Evidently since this change 

 of the current is accompanied bj' a propor- 

 tional change of the magnetic flux in every 

 part of the field the reaction will be an elec- 

 tro-motive reaction against the electro-mo- 

 tive force tending to produce this change in 

 the current. It is evident also that the 

 electro-motive reaction is proportional to the 

 rate of change of the current ; that is to say, 

 the current seems to behave like a moving 

 body in consequence of its inertia. For a 

 moving body opposes an inertia reaction 

 against every force tending to change its 

 velocity, and this inertia reaction is, ac- 

 cording to N"ewton's second axiom, equal 

 to the rate of change of momentum. Hence 

 the striking formal resemblance between 

 the laws of electro-magnetic and magneto- 

 electric induction and the laws of inertia 

 reactions of a connected material system. 

 This is the second essential feature of the 

 modern electro-magnetic theory which 

 Maxwell emphasized by his mechanical 

 models, illustrating the actions going on in 

 the electro-magnetic field. 



Summing up the foregoing brief account 

 of the Faraday-Maxwell theory, we can say 

 that, broadly speaking, this theory rests on 

 two laws : a. The law of flux. h. The law 

 of the variation of the flux. These two 

 laws are formally the same as they were in 

 the old theory, but their meaning is radically 

 diflerent. This difierence has been brought 

 about by a substitution of a new view of the 

 electric and of the magnetic force in place of 

 the doctrine of direct action at a distance, 

 the view, namely, that electric and mag- 

 , netic forces at any point of space are reac- 

 tions due to the physical state of the dielec- 

 tric in that point. This state is completely 

 determined by the fluxes in that point and 

 the rates of variation of the fluxes in every 

 point of the field. 



The account of the ordinary electro-mag- 

 netic phenomena in which the electro-mag- 



