Dr. Oliver Lodge on Opacity, 405 



H is reflected positively and E negatively. A perfectly con- 

 ducting barrier is a perfect reflector ; it doubles the magnetic 

 force and destroys the electric force on the side containing 

 the incident wave, and transmits nothing/' 



[I must here interpolate a remark to the effect that though 

 it can hardly be doubted that the above boundary conditions 

 (tangential continuity of both E and H) are correct, yet 

 in general we cannot avoid some form of sether-theory 



Whenever ox is zero it follows that R has no circulation but is 

 the derivative of an ordinary single-valued potential function, whose 

 dV =X.dx-{- Ydy-\-Zdz. In electromagnetism this condition is by no means 

 satisfied. E and H or H and E are both full of circulation, and their 

 circuits are interlaced. Fluctuation in E by giving rise to current causes 

 H ; fluctuation in H causes induced E.] 



Now differentiating only in a direction normal to a plane wave 

 advancing along a; the operator Vv becomes simply idjdx when applied 

 to any vector in the wave-front, the scalar part of v being nothing. 



So the second of the above fundamental equations can be written 



■ dE_ dH 



~ l d^~^W 



dE 



so, ignoring any superposed constant fields of no radiation interest, E and 

 II are vectors in the same phase at right angles to each other, and their 

 tensors are given by E = pvYL. 



Similarly of course the other equation furnishes H=KvE; thus giving 

 the ordinary K^v 2 = l, and likewise the fact that the electric and mag- 

 netic energies per unit volume are equal, |KE 2 =^H 2 . 



A wave travelling in the opposite direction will be indicated by 

 E= -pvH; hence, as is well known, if either the electric or the 

 magnetic disturbance is reversed in sign the direction of advance is 

 reversed too. 



(The readiest way to justify the equation E=^wH, a posteriori, is to 

 assume the two well-known facts obtained above, viz. that the electric 

 and magnetic energies are equal in a true advancing wave, and that 

 0=1/ >J pK; then it follows at once.) 



Treatment of an insulating boundary. — At the boundary of a different 

 medium without conductivity the tangential continuity of E and of H 

 across the boundary gives us the equations 



E, + E 3 = E 2 

 H 1 + H 3 =H 2 , 



where the suffix 1 refers to incident, the suflix 2 to transmitted, and 

 the suffix 3 to reflected waves. 



H^-r-Hg may be replaced by /»v(Ej - E 3 ), since the reflected wave is 

 reversed ; so we shall have, for the second" of the continuity equations, 



^E. 2 =mnE 2 ; 



