308 On Optical Combinations of Crystalline Films. 



This last figure is interesting, because we can see that the 

 result must be some polygonal or roughly circular central 

 figure with some sort of a cross, surrounded by eight detached 

 figures or eyes. I am sorry I cannot work this out mathema- 

 tically ; but with whole-wave and somewhat greater retarda- 

 tions it is pretty easy to trace it in one's own mind. It is so, as 

 you perceive; and you also see that the preparation and figure 

 can be rotated without very sensible change, which also fol- 

 lows from theory, and is a somewhat remarkable result, after 

 what we saw at the commencement, with such thick films. 

 And now, to show the effect of thickness, here is a precisely 

 similar preparation of eight films superposed at a successively 

 rotated angle of 45°, but built up of f A, films. Circular 

 polarization here comes into play; and the effect is totally dif- 

 ferent in every way. The last of these crossed micas is built 

 up of twelve f A, films, thus — 



x + + + + x 



You see the total difference in figure from any thing before, 

 and the scope for endless variety, which I must not further 

 pursue. 



Still more beautiful, but perhaps less interesting, are the 

 combinations of mica- and selenite-films discovered experi- 

 mentally by Norremberg. As he observes, if we call the three 

 axes of elasticity in any crystal x, y, z, then selenite-films 

 contain x and z, while mica on the other hand contains y 

 and z ; and it is easy to see that if preparations are built up 

 of both elements, very fine coloured fringes mast result, dif- 

 fering very greatly in character according to whether the x of 

 the selenite is parallel to the z of the mica or crosses it. As 

 far as I remember, however, Norremberg and Reusch seem to 

 have said that the characters of the fringes defy all prediction. 

 This is perhaps hardly true, even apart from mathematical 

 analysis, which I am unable to give, and which the mere 

 beauty of these combinations is scarcely worth. For it is 

 easy to perceive that if a single selenite be placed between 

 two thick micas, we must have very nearly the usual biaxial 

 figure, with some little modification in the eyes or rings, but 

 chiefly distinguished from the simple mica by rich colour. 

 That is so here. But if we alternate several parallel selenites 

 between parallel micas of less thickness, so as to give the sele- 

 nite functions of elasticity more comparative influence, then 

 it is evident that the modified lemniscate curves, or what is 

 still traceable of them, must be either brought nearer together 

 or more widely separated, and that we shall thus obtain 

 curved fringes having their approximate origin in the original 



