of Refraction, Reflexion, and Extinction. 281 



procedure rests on a scheme of differential equations deter- 

 mining the laws of propagation of light in material media. 

 On the view here being developed, these laws of course 

 continue to apply and therefore must be derivable from the 

 molecular standpoint. It will then serve to bring out more 

 clearly the scope of the foregoing calculation if we show 

 that our solutions are consistent with the fundamental 

 Maxwell-Lorentz equations. To examine this point it will 

 be convenient to recapitulate some of the results previously 

 obtained. We have : 



(H,) = 0, (H y )=t^5 ; e «-^^ (H ,) = 0, (9) 



(P. t )=-;na<V^-^+<?>, (P y )=o, (P,)=o. (10) 



These equations merely reiterate our foregoing results : 

 (6) and (10) of § 5 and (3), § 2 ; (E x ), (H x ) etc. represent 

 as before the components of the actual electric and magnetic 

 field at a point in the medium and (P x ) etc. are the com- 

 ponents of the polarization electrically induced. It may 

 now be immediately verified that (8), (9), and (10) satisfy 

 the well-known Maxwell-Lorentz equations as usually 

 formulated. 



§ 7. A slightly different form may be given to the fore- 

 going equation (7), § 6, namely : 



A m v 2 — a: 2 — 1 



as 



J:7rN — 



(V— AT — l) 2 + Av 2 K 2 ' 



3// 3 



4ttN 



e'~ (V — k' 2 — 1 ) - + ±v 2 k 2 



Equation (2) includes as a particular case Lord Rayleigh's 

 celebrated formula of extinction ; for assuming « to be very 

 small in comparison with v — 1 we have from (2)*, if we 

 retain the leading term only : 



vh §n A 8t7 3 



m 



* Of. Bulletin Int. de C Acad i 7 . Sc. de Cracovie for L909, p. 9i0, 



