PROPERTIES OF THE ELECTROMAGNETIC FIELD. 



The electromotive force corresponding to the contour is then 

 Ufrcos=( - \dydz. 



On the other hand, this expression should also represent the 

 flow of magnetic induction through the circuit dydz from the 

 negative face ; as the expression for this flow is i&dydz, the com- 



ao -m 



ponent /*X is equal to . 



The other components of magnetic induction parallel to the 

 y axis and the x axis, will satisfy analogous conditions, which is 

 given by the equation 



Let us now consider any given closed circuit ; we may divide 

 the surface into elements by two series of arbitrary curves. If we 



make the summation Jds cos e of the electromotive forces along 



the contour of all the elements, we shall obtain the total flow of 

 magnetic induction across the circuit, and this sum will reduce to 

 the single terms furnished by the primitive contour, for the sum 

 of the portions of the curve common to two contiguous elements 

 is null. The total electromotive force of a circuit, only depends 

 then on the values of the components F, G, and H at the 

 different points of the contour, and these components are con- 

 nected with the magnetic induction by the equations (2). 



568. We may observe that the component F represents at a 

 given point, and for unit length parallel to the x axis, the total 

 electromotive force which corresponds to the suppression of the 

 field. This electromotive force may also be regarded as the in- 

 tegral, in respect of time, of the elementary electromotive forces 

 which correspond to the gradual suppression of the field. The 



