Modified Theory of Gravitation. 105 



perpendicular therefore to the direction of the quasi-electro- 

 motive intensity T, which we shall suppose to be measured 

 positively from left to right in the figure, 

 as indicated by the arrow. 



At any instant let 9 be (in electro- 

 magnetic measure) the surface-density of 

 electrification on the right-hand face, — 9 

 -f 9 being that on the left-hand face ; 9 will 

 evidently be a periodic function of the time 

 of the form 



9 = 9 ^, .... (75) 



where ? is a constant, in general complex. 



Between the faces of the slab there is, at any time t, a 

 conduction current whose density, referred to unit of area, 

 is ds/di, and a polarization current whose density is — ds/dt*, 

 the total effective current being thus zero. The same result 

 is otherwise evident ; for at any point exterior to the slab 

 the total electromotive intensity arising from the surface- 

 densities 9 and —9 vanishes at each instant. Hence outside 

 the slab there is no polarization and no polarization-current, 

 and of course no conduction-current; so that the total 

 effective current is zero outside the slab. The solenoidal 

 or " stream M character of the total current accordingly 

 necessitates a zero value for this vector within the substance 

 of the slab also. 



62. Thus everywhere, except near the edges of the slab 

 (which we ignore) magnetic force is absent, and electro- 

 magnetically speaking our system is without kinetic energy f. 

 There must of course be some kinetic energy involved in 

 the reciprocating relative motions of positive and negative 

 electrons, but this kinetic energy, even though a close enough 

 analysis would reveal its electromagnetic character, has no 

 place in the ordinary equations of electromagnetism, and a 

 moment's consideration suffices to indicate its excessive 

 minuteness. 



* Cf. Appendix A, § 49. 



f There will accordingly be no production of electromagnetic -waves, 

 except near the edges of the slab where the same simple conditions are 

 not realized. But in general electromagnetic waves will be produced 

 wherever there are bodies of dielectric or conducting material in the path 

 of the primary compressional waves. If the primary disturbance, as in 

 the foregoing table, is assumed to be periodic and of frequency 1*29 X 10 10 , 

 the electromagnetic waves, being cf the same frequency, will in free 

 aether have a wave-length of 2-33 cm. "Without having considered these 

 waves in any detail, I think it may be said that they will be quite 

 insignificant, provided the electromotive effects of the primary waves are 

 too slight to give rise to appreciable thermal phenomena. 



