360 Bumstead — Reflection of Electric Waves at the 



If now we are dealing with plane waves, propagated along 

 straight and perfectly conducting guides parallel to the axis of 

 z, then E and H are in planes perpendicular to z and cut 

 each other orthogonally at all points. The actual form of the 

 lines of electric and magnetic force may, of course, vary greatly 

 with the shape and size of the guides, but, if we follow any 

 plane in the wave, the line integral of E from one guide to 

 the other is independent of the path, so long as we stay in the 

 plane ; and, with this understanding, it may be called the dif- 

 ference of potential between the wires, Y. In like manner, 

 the line integral of H about a closed circuit embracing one of 

 the wires is a constant, and equal to 47rl where I is the current 

 in the wire at this point. It should be observed that this cur- 

 rent has nothing directly to do with the current C in (1), but 

 is, from the present point of view, to be regarded merely as 

 the line integral of the magnetic force. 



The advantage in using the scalars, Y and I, instead of the 

 vectors, E and H, in treating plane waves, is apparent, since 

 Y and I vary only with the coordinate along the wire, ^, and 

 the problem reduces to one dimension. Equations (1^) and (2^) 

 become, respectively, 



_J=SV + GV (3) 



~ V-=LI -|-47rFI (4) 



dz ^ ' 



where S and L are the capacity and inductance of the system, 

 Gr is the total electric conductance of the medium from one 

 wire to the other, and F is the total magnetic conductance of 

 the medium in circuits about the two wires following the lines 

 of magnetic force ; all these being measured per unit length 

 along zr 



It is immediately apparent from these equations that the 

 rate of dissipation of energy in a wave plane, whose thickness 

 is dz^ is GYWs due to the electric conductivity, and ^.irYVdz 

 due to the magnetic conductivity ; and both take place through- 

 out the plane. 



The approximate equivalence of magnetic conductance in 

 the medium and electrical resistance in the guiding wires is 

 thus made evident. If we now have no magnetic conduc- 

 tivity in the medium, but a resistance, JR per unit length, in 

 each wire, where R = ^ttF, we shall still have the same dissi- 

 pation per second in the plane, viz : RIV/s, and things will go 

 on apjproximately as before. In fact, if we use one of the old 

 theories, which ignore the action of the medium, to investi- 



■^ See Heaviside, Electromagnetic Theory, vol. i, p. 384, where, however, a 

 difEerent system of units is employed. 



