

of Refraction, Reflexion, and Extinction. 279' 



Hence the expression of the component along y of the actual 

 magnetic field at M becomes 



m ^ - 4? rNA(2) • hc Jn{t-h: + q) 



{ - >/} - i(6V-l) 6 



4- I A tt)J n (p-9) — 1 Jn(t—az+q) (Q) 



L t(6c-i)J • • v ; 



To prevent the occurrence in (9) of terms representing 

 " vacuum-waves'''' (which the medium is incapable of propa- 

 gating), precisely the same condition must be fulfilled which 

 is already satisfied in consequence of equation (5) above. 

 This should be observed in corroboration of our previous 

 result. Finally we have 



{n ^~ i(tfc 2 -l) .... {W) 



§ 6. Let us consider now an electron which is set vibrating 

 to and fro under the operation of an electric force E. Write 

 e for the charge on the electron and m for its effective mass.. 

 Let f be the component, in the direction of x, of the dis- 

 placement of the electron, reckoned from the position of 

 equilibrium ; let n represent a constant and 3 a definite 

 period of time of very short duration which in most cases 

 of interest may be put = 2e 2 j'dmc 3 . Confining ourselves to 

 vibrations in which •& is a very small fraction of the periodic 

 time 27r/n, we assume as the equation of motion in the 

 direction of x : 



m('f-3f+Vf)=*E a (1) 



[The second term of the left-hand member arises here 

 from damping due to radiation. In a celebrated paper, 

 Professor H. A. Lorentz has shown (I.e., pp. 103, 104) that 

 this simple form of expression, — 3f, is adequate whenever 

 the molecules of the substance, as in gases and liquids, can 

 be supposed to be irregularly distributed. The third term is 

 generally regarded as representing the component along x of 

 the " quasi-elastic 7 ' force supposed to connect the electron 

 to the system to which it belongs. The introduction of this 

 concept has not escaped criticism ; by some writers it is 

 considered as a gratuitous supposition, devoid of physical 

 significance. Arguing from analogy we might perhaps 

 invoke in its favour the well-known propositions deducible 

 from the theory of small vibrations performed, about an 

 equilibrium configuration, by a dynamical (holononricY 



