Forced Vibrations of Electromagnetic Systems. 135 



If 5=0, these are the equations of electric and magnetic force 

 in a nonconducting dielectric. If therefore the new g be of 

 such magnitude as to make s = 0, we cause disturbances 

 to be propagated in the conducting dielectric in identically 

 the same manner as if it were nonconducting, but with a uni- 

 form attenuation at a rate indicated by the time-factor e~ qt . 



5. Undistorted Plane Waves in a Conducting Dielectric. — 

 Taking z perpendicular to the plane of the waves, we now 

 have, as special forms of (23), (24), 



-^=(4tt£-Kp)E, (28) 



-^- = (4^ + ^)H,. . . .'. (29) 



E being the tensor of E, parallel to x, and H the tensor of H, 

 parallel to y, and both being functions of z and t. 



Given E = E and H = H at time £=0, functions of z only, 

 decompose them thus, 



2/^Eo + ^Ho, (30) 



2/ 2 =E -^H (31) 



Here f x makes the positive and f 2 the negative wave, and at 

 time t the solutions are, due to the initial state, when s = 0, 



-E = e-" t \f 1 (z-vt)+f 2 (z + vt)\, . . . (32) 



f ivR=e-' t \f 1 (z-vt)-f 2 (z + vt)\. ... (33) 



The only difference from plane waves in a nonconducting 

 dielectric is in the uniform attenuation that goes on, due to 

 the dissipation of energy, which is so balanced on the electric 

 and magnetic sides as to annihilate the distortion the waves 

 would undergo were s finite, whether positive or negative. 



6. Practical Application. Imitation of this Effect. — When 

 I introduced* the new property of matter symbolized by the 

 coefficient g, it was merely to complete the analogy between 

 the electric and magnetic sides of electromagnetism. The 

 property is non-existent, so far as I know. But I have more 

 recently found how to precisely imitate its effect in another 

 electromagnetic problem, also relating to plane waves, making 

 use of electric conductivity to effect the functions of both k 

 and g in §§4 and 5. In the case of § 5, first remove both 

 conductivities, so that we have plane waves unattenuated and 

 undistorted. Next put a pair of parallel wires of no resistance 

 in the dielectric, parallel to z, and let the lines of electric force 



* See second footnote, p. 130. 



