490 M. Verdet on the Optical Properties developed in 



If the closed conductor be submitted to the action of any num- 

 ber of magnetic poles, the electromotive forces respectively de- 

 veloped by these different poles will be united, and their sum 

 represented by 



F=2/i C/^ cos t-Jw 00 * V )' 



This ecpiatiou can evidently be put in this form, 



Or if we call R and R' the resultants of the actions which the 

 magnetic poles would exercise on the unit of magnetic fluid 

 placed in o and in o 1 , x and w' the angles made by these resultants 

 with the normals to the conductor, we shall have 



EwioSeS*, RW' = S^jf. 



If, as is supposed, the magnetic action is the same at all 

 points of the conductor and of the space which it traverses when 

 displaced, the two resultants R and R' would be constant through- 

 out the extent of the conductor, and equal to one another. Calling 

 w the total area of the conductor, we should have 



; F=o)R(cos a— cosa'). 



If «=0, «' = 90°, we have 



F = ft)R; 



i. e. if the plane of the closed conductor is at first perpendicular 

 and then parallel to the magnetic action, the total electromotive 

 force is proportional to the area of the conductor and this mag- 

 netic action itself. 



During the displacement of the conductor, the induced cur- 

 rent is at each instant proportional to the electromotive power 

 developed in the conductor, and consequently a quantity of elec- 

 tricity proportional to this force passes through any section 

 whatever of the wire. Hence it follows, that the total quantity 

 of electricity which passes through any section of the wire during 

 the whole duration of the movement is proportional to the total 

 electromotor force. It is then proportional to the magnetic 

 action in the case just considered. Now this total quantity of 

 electricity is precisely the only thing relative to the induced 

 current which we can measure by the aid of the galvanometer : 

 it is often described, but falsely, under the name of intensity of 

 the induced current ; we shall designate it simply by the expres- 

 sion induced current; thus the proposition demonstrated above 

 could be thus enunciated, under the conditions already defined, 

 the induced current is proportional to the magnetic action. 



