458 Prof. Maxwell and Mr. F. Jenkin on the Elementary 



proposition can easily be established when the laws of magneto- 

 electric induction have been understood (31). 



31. Magneto-electric Induction. — Let a conducting circuit be 

 placed in a magnetic field. Let C be the intensity of any cur- 

 rent in that circuit ; E the magnitude of the electromotive force 

 acting in the circuit. Let the circuit be so moved that the 

 number of lines of magnetic force (11) passing through it is 

 increased by N in the time t, then (23) the electromagnetic 

 forces will contribute towards the motion an amount of work 

 measured by CN. Now Q, the quantity of electricity which 

 passes, is equal to Ct ; so that the work done on the current is 

 EQ or CE£. By the principle of conservation of energy, the 

 work done by the electromagnetic forces must be at the expense 

 of that done by the electromotive forces, or 



CN + CE*=0; 

 or dividing by Ct, we find that 



N 

 E=-y; (15) 



or, in other words, if the number of lines of force passing through 

 a circuit be increased, an electromotive force in the negative 

 direction will act in the circuit measured by the number of lines 

 of force added per second. 



If R be the resistance of the circuit, we have by Ohm's law 

 ( quation 6) E = CR; and therefore 



N = -E/=-RC*=-RQ; .... (16) 

 or, in other words, if the number of lines of magnetic force 

 passing through the circuit is altered, a current will be produced 

 in the circuit in the direction opposite to that of a current 

 which would have produced lines of force in the direction of 

 those added, and the quantity of electricity which passes, multi- 

 plied by the resistance of the circuit, measures the number of 

 additional lines passing through the circuit. 



The facts of magneto-electric induction were discovered by 

 Faraday, and described by him in the First Series of his " Expe- 

 rimental Researches in Electricity/' read to the Royal Society, 

 November 24th, 1831. 



He has shown* the relation between the induced current and 

 the lines of force cut by the circuit, and he has also described 

 the state of a conductor in a field of force as a state the change 

 of which is a cause of currents. He calls it the electrotonic 

 state; and, as we have just seen, the electrotonic state may be 

 measured by the number of lines of force which pass through 

 the circuit at any time. 



* Experimental Researches, 3082, &e, 



