608 GENERAL THEORIES. 



the elementary electromotive force becomes 



The total electromotive force produced in the circuit s' by the 

 circuit s, is obtained if we integrate this expression in reference to 

 s and to s'. As the intensity I is merely a function of the time, and 

 as the limits of the integral are themselves independent of the time, 



(9) 



We shall have then (353) 

 (10) E 



_d C Ci^r^r 

 ~~d* J J ^^ 



rr-M 



JJ r 



A 1 J r dt dt 



/ / 



which gives the general expression (518) of the electromotive force 

 produced in a circuit by an external current. We shall find in like 

 manner the other cases of induction. 



626. VARIOUS ATTEMPTS AT A THEORY. Numerous attempts 

 have been made, after the example of Weber, to bring under one 

 and the same theory the phenomena of statical electricity, of per- 

 manent currents, and the effects of induction, and to establish a 

 connection between electricity, magnetism, and light. 



Gauss expressed the opinion that electrical actions cannot take 

 place instantaneously, and that we should have a key to electro- 

 dynamical phenomena, if we could discover the law of the propa- 

 gation of electrical forces. 



Guided by these considerations, several mathematicians have 

 treated the problem. For instance, the phenomena of induction 

 may be explained by assuming that the electrical potential is 

 propagated in a medium with a certain velocity which would be the 

 same as that of light, according to B. Riemann, or of a totally 

 different order, according to the theory of C. Neumann. 



M. Betti compares the action of currents to that of a system of 

 elementary magnets tangential at every point to the contour of the 

 circuit, and periodically polarized in opposite directions, and he 

 considers the magnetic force as transmitted in the medium with a 

 certain velocity. 



