59 8 ELECTRICAL UNITS. 



615. PHYSICAL CONCEPTION OF THE VELOCITY a. We may 

 give a physical representation of the velocity a which expresses 

 the ratio of the electrical units in the two systems. 



Suppose, for instance, that a sphere of radius R, or a con- 

 denser of the same capacity, were charged in such a manner that 

 its electrical potential is equal to unity, and is discharged n 

 times in the time / through a conductor ; the mean strength of the 



current . in electrostatic units will be - . If we determine n in 

 such a manner that the strength of this current is equal to the 

 electromagnetic unit, the expression will represent the number 



of electrostatic units of electricity which are contained in an 

 electromagnetic unit ; that is to say, the value of #, and this 

 expression is a velocity. 



616. Maxwell points out another mode of representing this, 

 based on the hypothesis that the external action of an electrical 

 mass in motion is equivalent to that of a current. 



Consider a plane covered with a uniform charge of electricity 

 of density <r, and moving in its own plane with a velocity u. 



Each band of unit breadth, and parallel to the direction of the 

 motion, is the equivalent of a current whose intensity is <ru in 



electrostatic measure, and - - in electromagnetic measure. Sup- 

 pose, now, that a second plane parallel to the first, at a distance 

 <5, moves in the same manner, and in the same direction, with a 

 velocity u', and let a-' be its density. Two kinds of actions are 

 produced between these planes ; an electrostatic repulsion in virtue 

 of charges of the same kind, and an electrodynamic attraction due 

 to parallel currents in the same direction. 



Let us now take in the second plane a band of length /, and 

 of infinitely small breadth b, and in the former plane an unlimited 

 band of breadth dx, at a distance x, from the projection of the 

 band bl. The electromagnetic action exerted by this unlimited 

 band on the first situated at the distance \/<5 2 + x 2 , is expressed 

 by (480) 



vu ar'u' T / <r<r'uu' T dx 



2 dx b = = 2 bl-===, 



and its component df along the perpendicular to the plane is 



cra-'uu' , , ^" !V 



df= 2 bl 



a 2 



