RELATIVE DISPLACEMENT OF CIRCUITS. 553 



Consider the first term of the integral, and replace the partial 



"v* 

 erentials 



term becomes 



differentials and by their values taken from equations (2); this 



or 



Analogous results will be obtained by treating the second and 

 third terms in the same way. We may, moreover, observe that we 

 have 



^rr+F <fr = F-, 



and that the groups of this form disappear when the integral is 

 extended to a closed circuit. 



The value of the electromotive force reduces then to 



- 



Each of the three groups contained in the parenthesis represents 

 the electromotive force which, at a given instant, acts on unit length 

 parallel to one of the axes. If, further, we suppose that the field 

 contains electrical masses giving a potential \//, the most general values 

 of the components P\ Q', J? of the electromotive force will be 



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