with special reference to Cor once and Iridescent Clouds. 279 

 where z x = ira%/f\. 



To secure corresponding points, let 



7T 



z i — z ~"p 



and let us choose such values of R and a that the angular 

 distance from the sun is the same (=0) in both cases. For 

 this, 



a0 = 2R<9-V4; 



and, since by hypothesis z is great, aO amounts to several 

 wave-lengths ; and this equation is satisfied by nearly the 

 same values of a and 2R throughout the visible spectrum. 

 The ratio of the brightness of a water-cloud to that of an ice- 

 cloud is then SBPz^Jcfz 3 , or 2zjz. Thus the outlying spectra 

 from water-drops are about twice as bright as those from ice- 

 filaments, when the drops and the filaments occupy the same 

 fraction of the field of view, and corresponding spectra are at 

 the same distance from the sun. 



Influence of Transparency. 



We have incidentally assumed that drops of water and 

 needles of ice can be treated as opaque objects. Now if a 

 single hexagonal filament be placed with one of its faces 

 normal to the sun's rays, it is clear that the light, transmitted 

 through the part that behaves like a parallel plate, must inter- 

 fere with the light that passes on either side of the filament, 

 and should be taken into account. But with the varying 

 orientation of the filaments, the quantity and relative retarda- 

 tion of the transmitted light would alter to such an extent 

 that the practical result in the case of a cloud would merely 

 be the addition of so much white light. 



The case of a spherical drop of water does not admit of the 

 same variety. And it would seem that, when the size is uni- 

 form, the transmitted light should be taken into account. 

 The investigation would be complex, even if it be possible 

 with our present knowledge ; but we see at once that a large 

 part of the light must be retarded relatively to the uninter- 

 rupted light by about a third of the diameter of the drop. 

 Thus the character of the effect would change completely with 

 small changes in the size, and in ordinary clouds we shall not 

 be far wrong in treating the drops as opaque. It is probable 

 that the comparative poorness of water iridescences is partly 

 due to this cause. 



The legitimacy of adding the illuminations due to the dif- 

 ferent drops, without reference to phase, has been shown by 



