OF ELECTRO-DYNAMIC FORCES. 529 



Hence the induction, during the element of time dt, i. e. the 



product of this element of time into the acting electromotive 



force, becomes 



a a.ci' Q( J • 



= — - . — cos cos & . ai, 

 2 r 



consequently the induction for any period of time in which the 

 intensity of the induced current increases by i, whilst r, 8 and 

 9' remain unchanged, is 



a ccoJ . ^ ^, 



= — - . Z cos © COS 0'. 



2 r 

 The positive value of this expression denotes a current induced 

 in the element «' in the direction of «', which with the produced 

 right line r forms the angle ©' ; the negative value denotes an 

 induced current in the opposite direction. 



When the two elements « and a! are parallel, and 6 = g', the 

 above expression, when the intensity of the current is increasing, 

 or where the value of i is positive, has a negative value, i. e. when 

 the intensity of the current is on the increase in a, a current is 

 excited in «' in an opposite direction to that of the inducing 

 current. The reverse applies when the intensity of the current 

 diminishes. Both results agree with well-known facts. The 

 proportionality of the induction to the variation of the intensity 

 i of the inducing current is also in accordance with experiment. 



Lastly, if we return from the consideration of these two distinct 

 kinds of voltaic induction to the general case, where at the same 

 time the intensity of the inducing current is variable and the 

 two conductors are in motion as regards each other, the electron 

 motive force exerted by the variable element of a current upon 

 the moved element of a conductor is found to be simply as the 

 8um of the electromotive forces which would occur — 



1. If the element of the conductor were not in motion at the 

 moment under consideration ; 



2. If the element of the conductor were in motion, but the 

 intensity of the current of the induced element did not alter at 

 the moment under consideration. 



