Quetelefs Rings and other Allied Phenomena. 837 



however, instead of water, a little benzol is let in between 

 the plates, many more rings are visible, and their appearance 

 is very greatly improved. 



It should also be remarked that when observations of 

 Quetelet's rings are made with the air-film, there is a marked 

 and progressive diminution in their visibility as we pass 

 from the case o£ normal incidence to that in which the film 

 is very obliquely held. This diminution is not due to the 

 structure o£ the field, as the influence of the latter may be 

 sufficiently reduced by using relatively thin films, and yet 

 the effect continues to persist. This deterioration of the 

 visibility of the rings with increasing obliquity -of incidence 

 is also influenced in a very marked degree by the structure 

 of the film. The thinnest and most uniform films show the 

 effect to a much less degree than the relatively coarser 

 films. 



7 . Theory of the Phenomena. 



The effects described in the preceding section are not 

 explicable on the theory put forward by Stokes, Lommel, 

 and Exner. According to these authors, the interferences 

 observed are supposed to be those of the two sets of waves 

 diffracted at the dimmed surface of the mirror, in one case 

 at entry and in another case at emergence. The two dif- 

 fractions are supposed to occur independently, no given 

 portion of the wave-front being affected both at entry and 

 emergence. Stokes shows in his paper that on these assump- 

 tions, the two diffracted waves which each particle gives 

 rise to should be of equal intensity and are in permanent 

 phase-relation, so that the interference-minima should be 

 perfectly black. That this is not always the case shows 

 that the theory is imperfect. The assumption that no given 

 portion of the wave-front is affected both at entry and 

 emergence, though plausible when we are dealing with small 

 opaque particles very sparsely distributed on the surface of 

 the mirror, is inappropriate in other cases, as, for instance, 

 when the particles are densely distributed, and is not at all 

 permissible when the diffraction is due to a more or less 

 continuous film of heterogeneous structure on the surface of 

 the mirror. In such circumstances every portion of the 

 wave-front is affected both at entry and emergence, and the 

 theory developed by Stokes ceases to be applicable. 



In the cases in which Quetelet's rings are formed In- 

 breathing upon the mirror or by tarnishing its surface with 



