118 Lord Bayleigh [March 24, 



the D-lines are seen widely separated with the naked eye — hut the 

 aperture is inconveniently small (^-inch). In the new instrument 

 exhibited the prisms (supplied by Messrs. Watson) are larger, so that 

 a line of ten prisms occupies 20 inches. Thus, while the resolving 

 power is much greater, the dispersion is less than before 



In the course of the lecture the instrument was applied to show 

 the duplicity of the reversed soda lines. The interval on the screen 

 between the centres of the dark lines was about half an inch. 



It is instructive to compare the action of the glass powder with 

 that of the spectroscope. In the latter the disposition of the prisms 

 is regular, and in passing from one edge of the beam to the other 

 there is complete substitution of liquid for glass over the whole 

 length. For one kind of light there is no relative retardation ; and 

 the resolving power depends upon the question of what change of 

 wave length is required in order that its relative retardation may be 

 altered from zero to the quarter wave length. All kinds of light for 

 which the illative retardation is less than this remain mixed. In 

 the case of the powder we have similar questions to consider. For 

 one kind of light the medium is optically homogeneous, i.e. the re- 

 tardation is the same along all rays. If we now suppose the quality 

 of the light slightly varied, the retardation is no longer precisely the 

 same along all rays ; but if the variation from the mean falls short of 

 the quarter wave length it is without importance, and the medium 

 still behaves practically as if it were homogeneous. The difference 

 between the action of the powder and that of the regular prisms in 

 the spectroscope depends upon this, that in the latter there is com- 

 plete substitution of glass for liquid along the extreme rays, while in 

 the former the paths of all the rays lie partly through glass and 

 partly through liquid in nearly the same proportions. The difference 

 of retardations along various rays is thus a question of a deviation 

 from an average. 



It is true that we may imagine a relative distribution of glass and 

 liquid that would more nearly assimilate the two cases. If, for 

 example, the glass consisted of equal spheres resting against one 

 another in cubic order, some rays might pass entirely through glass 

 and others entirely through liquid, and then the quarter wave length 

 of relative retardation would enter at the same total thickness in both 

 cases. But such an arrangement would be highly unstable ; and, if 

 the spheres be packed in close order, the extreme relative retardation 

 would be much less. The latter arrangement, for which exact results 

 could readily be calculated, represents the glass powder more nearly 

 than does the cubic order. 



A simplified problem, in which the element of chance is retained, 

 may be constructed by supposing the particles of glass replaced by 

 thin parallel discs which are distributed entirely at random over a 

 certain stratum. Wo may go further and imagine the discs limited to 

 a particular plane. Each disc is supposed to exercise a minute re- 

 tarding influence on the light which traverses it, and they aro sup- 



