222 The Mathematical Electricians of the 



CHAPTEK VII. 



THE MATHEMATICAL ELECTRICIANS OF THE MIDDLE OF THE 

 NINETEENTH CENTURY. 



WHILE Faraday was engaged in discovering the laws of induced 

 currents in his own way, by use of the conception of lines of 

 force, his contemporary Franz Neumann was attacking the 

 same problem from a different point of view. Xeumann 

 preferred to take Ampere as his model ; and in 1845 published 

 a memoir,* in which the laws of induction of currents were 

 deduced by the help of Ampere's analysis. 



Among the assumptions on which Neumann based his work 

 was a rule which had been formulated, not long after Faraday's 

 original discovery, by Emil Lenz,f and which may be enunciated 

 as follows : when a conducting circuit is moved in a magnetic 

 field, the induced current flows in such a direction that the 

 ponderomotive forces on it tend to oppose the motion. 



Let ds denote an element of the circuit which is in motion, 

 and let C ds denote the component, taken in the direction of 

 motion, of the ponderomotive force exerted by the inducing 

 current on d$, when the latter is carrying unit current ; so that 

 the value of C is known from Ampere's theory. Then Lenz's 

 rule requires that the product of C into the strength of the 

 induced current should be negative. Xeumann assumed that 

 this is because it consists of a negative coefficient multiplying 

 the square of C\ that is, he assumed the induced electro- 

 motive force to be proportional to C. He further assumed it to 

 be proportional to the velocity v of the motion; and thus 

 obtained for the electromotive force induced in ds the expression 



- ei-Cds, 

 where e denotes a constant coefficient. By aid of this formula, 



Berlin Abhandlungen, 1845, p. 1 ; 1848, p. 1 ; reprinted as Xo. 10 and 

 No. 36 of Ostwald's Klassiker-, translated Journal de Math, xiii (1848), p. 113. 

 t Ann. d. Phys. xxxi (1834), p. 483. 



