'llieory of Jufractioii in (Jtn^es. 467 



(3) Present Jlieories. 



The theory tir^t oiven by Lorentz ^, and the more general 

 theory o£ Voigt f, hoth depend on the hypothesis that the 

 molecule may be regarded as composed of a greater or 

 less number of electrical doublets, and includes the view 

 that an atom may be regarded as consisting of a positively 

 charged particle and a large number of comparatively small 

 negatively charged particles, there being no charge on the 

 whole. 



The doublets are supposed to be capable of vibrating in a 

 number of definite periods, which correspond to spectral 

 lines. The periods must therefore be regarded as inde- 

 pendent of temperature. 



The result readily follows that 



where h is a constant depending on the gas, p is the density, 

 and/(^^) is a function of the frequency of the waves and of 

 the free periods of vibration of the molecule. 



This view is therefore capable of explaining the general 

 features which I have called (B) and (C), but cannot be 

 made to explain (A) and (D). 



Before passing to a modified theory, it may be pointed out 

 that a formula of the preceding form may be obtained by 

 regarding the molecules simply as obstacles which differ in 

 their properties from the surrounding aether. If we take the 

 formulEe for the waves scattered from a spherical obstacle J, 

 and use Lord Rayleigh's method §, we readily obtain 



where N is the number of particles per unit volume, 

 T „ volume of a particle, 

 Kq ,, dielectric constant for the aether, 

 Ki „ „ „ particle, 



k „ electrical conductivity of the particle, 

 pI'2'tt ,, frequency of the waves. 



A like result holds for particles of any shape^ provided the 

 dimensions of the particle are small compared with a wave- 

 length. 



* Annalen cler Physik, ix. p. 641 (1880) ; also ' Theorie Elect, de 

 Max ice 11.^ 

 t Ibid. Ixvii. p. 34o (1899). 

 X Quart. Journ. Math. No. 121, p. 36 (1899). 

 § Phil. Marr. (-j) xlvii. p. 37o (1899). 

 2 H2 



