1899.] on Transparency and Opacity. 119 



posed to be so numerous that it is improbable that a ray can pass the 

 plane without encountering a large number. A certain number (»t) of 

 encounters is more probable than any other, but if every ray en- 

 countered the same number of discs, the retardation would be uniform 

 and lead to no disturbance. 



It is a question of Probabilities to determine the chance of a pre- 

 scribed number of encounters, or of a prescribed deviation from the 

 mean. In the notation of the integral calculus the chance of the 

 deviation from m lying between + r is * 



— I 



J 



where t = r j y (2 m). This is equal to '84 when t= 1*0, or 

 r = tj (2 m) ; so that the chance is comparatively small of a deviation 

 from m exceeding + y* (2 m). 



To represent the glass powder occupying a stratum of 2 cm. 

 thick, we may perhaps suppose that m = 72. There would thus be a 

 moderate chance of a difference of retardations equal to, say, one-fifth 

 of the extreme difference corresponding to a substitution of glass for 

 liquid throughout the whole thickness. The range of wave lengths in 

 the light regularly transmitted by the powder would thus be about 

 five times the range of wave lengths still unseparated in a spectroscope 

 of equal (2 cm.) thickness. Of course, no calculation of this kind can 

 give more than a rough idea of the action of the powder, whose dis- 

 position, though partly a matter of chance, is also influenced by me- 

 chanical considerations ; but it appears, at any rate, that the character 

 of the light regularly transmitted by the powder is such as may reason- 

 ably be explained. 



As regards the size of the grains of glass, it will be seen that as 

 great or a greater degree of purity may be obtained in a given thick- 

 ness from coarse grains as from fine ones, but the light not regularly 

 transmitted is dispersed through smaller angles. Here again the 

 comparison with the regularly disposed prisms of an actual spectro- 

 scope is useful. 



At the close of the lecture the failure of transparency which arises 

 from the presence of particles small compared to the wave length of 

 light was discussed. The tints of the setting sun were illustrated 

 by passing the light from the electric lamp through a liquid in which 

 a precipitate of sulphur was slowly forming, f The lecturer gave 

 reasons for his opinion that the blue of the sky is not wholly, or even 

 principally, due to particles of foreign matter. The molecules of 

 air themselves are competent to disperse a light not greatly inferior 

 in brightness to that which we receive from the sky. 



[E.] 



* See Phil. Mug. 1899, vol. xlvii. p. 251. t Op. eit. 1881, vol. Xii. p. 9G. 



