ON FARADAY'S LINES OF FORCE. 187 



It is natural to suppose that a force of this kind, which depends on a 

 change in the number of lines, is due to a change of state which is measured 

 by the number of these lines. A closed conductor in a magnetic field may 

 be supposed to be in a certain state arising from the magnetic action. 

 As long as this state remains unchanged no effect takes place, but, when the 

 state changes, electro-motive forces arise, depending as to their intensity and 

 direction on this change of state. I cannot do better here than quote a 

 passage from the first series of Faraday's Experimental Researches, Art. (60). 



" While the wire is subject to either volta-electric or magno-electric 

 induction it appears to be in a peculiar state, for it resists the formation of 

 an electrical current in it ; whereas, if in its common condition, such a current 

 would be produced; and when left uninfluenced it has the power of originating a 

 current, a power which the wire does not possess under ordinary circumstances. 

 This electrical condition of matter has not hitherto been / recognised, but it 

 probably exerts a very important influence in many if not most of the phe- 

 nomena produced by currents of electricity. For reasons which will immediately 

 appear (7) I have, after advising with several learned friends, ventured to 

 designate it as the electro-tonic state." Finding that all the phenomena could 

 be otherwise explained without reference to the electro-tonic state, Faraday in 

 his second series rejected it as not necessary ; but in his recent researches * 

 he seems still to think that there may be some physical truth in his 

 conjecture about this new state of bodies. 



The conjecture of a philosopher so familiar with nature may sometimes be 

 more pregnant with truth than the best established experimental law disco- 

 vered by empirical inquirers, and though not bound to admit it as a physical 

 truth, we may accept it as a new idea by which our mathematical conceptions 

 may be rendered clearer. 



In this outline of Faraday's electrical theories, as they appear from a 

 mathematical point of view, I can do no more than simply state the mathe- 

 matical methods by which I believe that electrical phenomena can be best 

 comprehended and reduced to calculation, and my aim has been to present the 

 mathematical ideas to the mind in an embodied form, as systems of lines or 

 surfaces, and not as mere symbols, which neither convey the same ideas, nor 

 readily adapt themselves to the phenomena to be explained. The idea of the 

 electro-tonic state, however, has not yet presented itself to my mind in such a 



* (3172) (3269). 



242 



