J. RHEINBERG ON BLACK AND WHITE DOT PHENOMENON. 303 



that in the case of such single perforations or isolated objects, 

 more than two definite images can never be obtained, whilst in 

 the case of periodic structure under suitable conditions some 

 supplementary images —always very hazy — are obtainable, which 

 are due to the crossing of bands from elements which are 

 separated from one another. In the case of a single edge 

 without any adjacent perforation in the structures, I have never 

 been able to obtain more than two, and often only one image, 

 having any pretension to sharp definition. 



Now, let us see what is the general position of the question. 



We have the following theories to choose from : That the 

 chief and immediate causes of the appearances are — 



(1) Spherical aberration by reason of the objective acting in 



zones, each zone having its own focus within certain 

 limits. 



(2) A stenopaic, or pin-hole effect. 



(3) Crossing of bands, arising from diffraction (Dr. Johnston 



Stoney on Microscopic Vision, Philosophical Journal, 

 May, 1896, pp. 514-16.) 



(4) Crossing of bands (or rather cones) formed by reason of 



the difference of refractive indices of the media, in 

 accordance with the ordinary laws of total reflection 

 beyond the critical angle. 



So far as I know the above comprise all the theories brought 

 forward, and indeed it would be difficult to suggest any further 

 one. 



Let us, therefore, take them one by one. 



(1) The spherical aberration of any objective is easily 

 measurable, and is, under given conditions, a fixed quantity. 

 We should, therefore, expect, when using the same objective with 

 an almost full cone of light on diatoms mounted in the same 

 medium, without altering tube length, that the distances between 

 the black and white dots were the same. But what we do find 

 is that these distances are very variable. The distance between 

 the black dot and upper white dot in some styrax-mounted 

 specimens of Navicula lyra was about 6 /x (/x = 1 micron 

 = YoVo niillimetre) in Stauroneis phoenicenteron 3 yu, j in Actino- 

 cyclus Ralfsii it was in difterent specimens 4|, 7|, and 9 /a. 



Another point to observe is that the spherical aberration of an 

 objective usually shows at its worst when narrow cones of light 



