A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 559 



Hence the quantity 



f/j-.dx s^dv -r T dz\ , 

 \(F- r + G~f-+H- r )ds 

 J \ ds ds dsj 



will be increased by the following increments, 



IdFdx , dFdy dFdz\ , 



a -y- -J- + -j- -77 + -j- -j. , due to motion of conductor, 

 \dx dt dy dt dz dt/ 



ds IdFdx , dGdy clH dz\ , 



' of circmt - 



The total increment will therefore be 



fdF_dG\dy_ (dH_d_F_\dz 

 *\dy dx) dt~ a ( dx ~ dz ) dt '/ 



or. by the equations of Magnetic Force (8), 



d dz 



If P is the electromotive force in the moving conductor parallel to x referred 

 to unit of length, then the actual electromotive force is Pa ; and since this is 

 measured by the decrement of the electromagnetic momentum of the circuit, the 

 electromotive force due to motion will be 



(65) The complete equations of electromotive force on a moving conductor 

 may now be written as follows : 



Equations of Electromotive Force. 



fl,t, 1 



. ___ 



" ~ dx 



dz dx\ dG d\ii 

 dt-' Y -dt)--dt-dy 



dx dy\ dll d\l> 



-'--~ 



The first term on the right-hand side of each equation represents the electro- 

 motive force arising from the motion of the conductor itself. This electromotive 



