WEBSTER. — PROPERTIES OE THE ETHER. 521 



(38) or f f j {H-ak}- (/S5H • ds. 



00 



But since V-H = V-H = 0, 



the surface integral 



(39) J J(H-6'H).r/S 



is the same over any cap of the parallelogram circuit as over any 

 other; and since 



(40) Vx5H = 5E+ 5(pp), 

 the line integral 



(41) fdk'ds 



+ 

 is the same around any line of the vector 6H as on any other. There- 

 fore the integral (38) is 



(42) r r AH-OT-r/sir j^H.f/si. 



Any cap Any line 



But by Stokes' Theorem, the line integral is 



(43) pp-r/cr, 



while the surface integral over the plane cap is, 



(44) f/r'x(H — GH)-5r, 

 so that (36) becomes 



(45) pp.(/o-f/r'x(H — G'H)-5r 

 = pr/r'-r/o-px(H — GH)-5r 



(46) = px(H- ak}'8Tdc. 



+ + 



Substituting - K'dTde for 8U, (33) now becomes 



(47) r{px(H - Gk)'8Tdr + (E — 6'E)-5n/r + K-5rf/('|(// = 0, 



