Mb maxwell, ON FARADAY'S LINES OF FORCE. 51 



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 volfa-electric or magneto-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 phenomena produced 

 by currents of electricity. For reasons which will immediately appear (71) 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 discovered 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 mathematical 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 form that its nature and properties may be 

 clearly explained without reference to mere symbols, and therefore I propose in the following 

 investigation to use symbols freely, and to take for granted the ordinary mathematical 

 operations. By a careful study of the laws of elastic solids and of the motions of viscous 

 fluids, I hope to discover a method of forming a mechanical conception of this electro-tonic 

 state adapted to general reasoning -f-. 



Part II. On Faraday's "Electro-tonic State." 



When a conductor moves in the neighbourhood of a current of electricity, or of a magnet, 

 or when a current or magnet near the conductor is moved, or altered in intensity, then a force 



" (3172) (3269). I tion of Electric, Magnetic and Galvanic Forces. Camb. and 



t See Prof. W. Thomson On a Mechanical Representa- I Dub. Math. Jeur, Jan. 1847. 



7 2 



