POLARISED LIGHT THROUGH DOUBLE REFRACTING CRYSTALS. 187 



3. When a = and £= \. 



4. When a = J and /3 = 0. 



To compare our results with the experiments, we observe that for a given 

 thickness of the crystal p is a function of the kind of light, so that in passing 

 from one end of the spectrum to the other the value of p increases (or dimi- 

 nishes) in a continuous manner. When the film is thick, p will make several 

 entire revolutions within the spectrum. When it is thin, there will be only one 

 or two, or a fraction of a revolution. Take the case of a thick film, then there 



will be a certain set of black bands when /3 = ^ — a. We may call these No. 1. 



For these p = 2mr. 



When ft — ? + a there will be another set of black bands, No. 2, inter- 

 mediate in position to No. 1. For these _p = (2 n + 1) n. 



When /3 = or „ the system of bands vanishes. 



When (3 = — a the black bands of No. 1 become bright and of maximum 

 intensity. 



When /3 = a the black bands of No. 2 become bright and of maximum 

 intensity. 



When a = I" all these phenomena are at their greatest distinctness. 



In turning the analyser there is simply a dissolution of one system into the 

 other, without motion of the system of bands in the case of a single plate of 

 crystal. But if we place the crystal with its ■axis inclined 45° to the plane of 



primitive polarisation, and place above this a film of retardation ~ with its axis 



parallel to the original polarisation, then we have as before for the light emerg- 

 ing from the first crystal, 



of = c — r= cos (nt + p) y' = c— y= cos nt . 



Resolving these rays in the direction of the axis of the second film, we have 



x" = o c (cos (nt + p) + cos nt\ 



y" = g c (cos (nt + p) — cos nt) , 

 and since x" is retarded |" it becomes 



x" = s c (sin (nt + p) — sin nt j , 



