CHAPTER XIII. 



EQUATIONS OF ELECTROMAGNETIC FIELD. 

 ELECTROMAGNETIC WAVES. 



243. Localized Electric Force of Induction. In the 



preceding chapter we have developed the theory of current induc- 

 tion in linear circuits, on the basis of the treatment of a set of 

 currents as a mechanical cyclic system, and we have thus arrived 

 at equations which are justified by experiment. We have found 

 for the electromotive force of induction in any circuit, 



d fiT\ dp 



where p, the electro-kinetic momentum corresponding to the circuit, 

 is by the results of 226 defined as the total flux of magnetic 

 induction through the circuit, that is the surface integral 



(2) p = { cos (nx) + S 3JI cos (ny) + S JJ cos (nz)} dS 



over any cap bounded by the circuit. 



If we consider the electromotive force around the circuit as 

 made up of electric forces acting at each point of the circuit, just 

 as in 166 we considered the electromotive force due to electro- 

 static action as the line-integral of the electrostatic field-intensity, 

 we may here consider the electromotive force as a line-integral 

 around the circuit, 



(3) E { = l(Xdx + Ydy + Zdz} = JF cos (Fds) ds. 



The vector F whose components are X, Y, Z is a quantity of 

 the same nature as the electric field-intensity, and we shall not in 

 future distinguish whether it is of electrostatic or electrodynamic 

 origin. If we apply Stokes's theorem to the line-integral in (3) we 



