116 J. RHEINBERG ON THE BLACK AND WHITE DOT PHENOMENON. 



upon it. The reasons are that the black spots get more 

 concentrated if the bands are prolonged slightly below the 

 surface plane, and so become rather more distinct and sharp. 

 Distinctness and sharpness is what the eye unconsciously makes 

 for. At the surface plane the dark spots are larger than the 

 perforations, because they form an outside as well as an inside 

 ring ; slightly lower down they overlap and do not cover an area 

 quite so large, thereby conforming more nearly to the real 

 diameter of the perforations. 



This again is more simply explained by a diagram. Let Fig. 7 

 represent bands crossing each other at an angle. A reference to 

 Figs. 1 and 2 will show that the position of the upper-surface 

 plane of a diatom would be correctly shown by the line A B, 

 and that e g and f h might be taken as the two walls which 



B 



Fig. 7. 



a vertical section of a perforation shows. But it is in the 

 plane C D, slightly below A B, where the greatest overlapping and 

 consequent concentration of darkness (or light) occurs, and which 

 would appear most distinct. And the distance m n in this plane 

 corresponds more nearly to the real size ef of the opening than 

 does ^ Z in the plane A B.* 



It will already have been gathered from this paper that the 

 black dot represents the best image. There is no doubt to my 

 mind that this is in the great majority of cases correct. The 

 statement is qunlified, however; because from numerous diagrams 

 which I have made following out the passage of the light through 



* As a section of a perforation shows two walls, we have four bands 

 issuing from each perforation ; but the opposite walls of the perforations 

 are mostly so close together that the bands overlap and appear as two only. 

 For this reason the black dots have no white centre, as Fig. 7 might seem 

 to show. 



