326 Mr. R. Hargreaves on Radiation 



which the components of translation enter into A 2 and B 2 , and 

 on that ground the calculations are deferred to a later stage. 



Electromagnetic Scheme. 



In the section of Electromagnetic theory presented here we 

 are concerned almost entirely with a moving standpoint. 

 Such a standpoint seems to be demanded for the consideration 

 of reflexion at a moving surface, and of refraction into a 

 moving dielectric. But it has further applications. When 

 radiation is viewed from a moving standpoint the energy 

 ceases to have purely the character of radiant energy; a part 

 of it assumes a mechanical character. That is, a part of the 

 energy is then radiant energy as interpreted from a moving 

 standpoint, and another part is kinetic energy; and this 

 latter is given by the scalar product of the translation and a 

 momentum belonging to the passage of radiation. 



For a dielectric there is a question of the coefficient in the 

 motional term of the energy, and two values claim considera- 

 tion. One gives a constant velocity of propagation for 

 electromagnetic waves, the other a modified velocity. Both 

 are regarded as actual, the former referring to waves origi- 

 nating in the dielectric, the latter to waves produced by the 

 impact of waves from outside on a moving dielectric. The 

 motion of the dielectric is a motion relative to the standpoint in 

 respect to which the originating wave shows a constant velocity. 



The modification is that of Fresnel's formula, and the 

 formula is here exact, not an approximation. This simplifies 

 the character of the equation for transit of energy in reflexion 

 and refraction. Lorentz's equations, when treated exactly, 

 involve a double refraction appertaining to the translation ; 

 i. e. the propagation of a plane wave is only possible for two 

 modes of polarization, defined by the directions of the trans- 

 lation and of the wave-normal. This introduces great 

 complication into the question of reflexion and refraction, 

 especially as neither velocity of propagation is so easy to deal 

 with as that of Fresnel's formula. 



§ 9. For the propagation of electromagnetic waves, the 

 scheme of equations referred to the moving standpoint is 

 taken to be 



Y dt~dy dz 9 Vdt ' dz dy>'- ^ L) 



X'-X = €M(vy-w0)[V, a ! -ct = € K(wY-rZ)/V, . . . (II.) 



with X' Y f a! ft' continuous at a surface of separation z = 

 constant. 



KX, . . . Ma, . . . are the components of electric and mag- 

 netic induction, X'... a! ... are the electric and magnetic 



