1896.] and Rontgen's X Rays. 59 



Take the case of a plane wave, when we may put 



X — A sin — - (&> — (lx + my + nz)), 

 A, 



2tt 

 Y = B sin — (o) — (lx + my + nz)), 



A. 



9_ 



Z = G sin — (&) — (£# + ?n?/ + nz)), 

 A, 



substituting these values in equation (1) we get 



fiK {ft) - ( pi + qm + rn)) 2 A = A - ^ [IA + mB + nC], 

 fxK {&) - (pi + qm + m)} 2 B = B -m {I A + mB + nG), 

 fj,K {&) - (pi + qm + rn)} 2 C = G - n {I A + mB + nG\. 

 Eliminating A, B, G we find that either 



*JfxK (&) — (pi + qm + rn) = \, 

 or &) — (pl + qm + rn) =0. 



If we take the first solution, we have 

 IA +mB + nG = 0, 



i.e. the wave is a transverse wave ; while if we take the second 

 solution, we have 



l _ m _ n 



A = B = G' 



I m n 



This represents a normal wave, the direction of propagation 

 coinciding with the direction of the electric intensity, the velocity 

 of wave propagation is equal to the component of the velocity 

 of the ether in the direction of the electric intensity. If there is 

 only the normal wave, then since 



dY = dX dZ_dY dX = dZ 



dx dy ' dy dz ' dz dx 



the magnetic force will vanish. Since, however, 

 dX dY dZ 

 dx dy dz 



is not zero throughout the wave, the volume density of the 

 electrification is not zero ; thus the wave could not be propa- 

 gated through space devoid of matter, nor could the wave be 

 propagated without dissociation through an insulator unless the 

 wave length were comparable with molecular distances. 



