114 J. RHEINBEllG ON THE BLACK AND WHITE DOT PHENOMENON. 



in the upper-surface plane of the diatom just at or near one of 

 the edges of the vertical walls forming the partition. 



It will further be observed in Figs. 1 and 2, and also in 

 Figs. 4 and 5, that the rays which impinge on to one of the 

 vertical partitions are thrown back upon themselves. A change 

 of phase occurs where they are then reflected, and if we take any 

 point where one of these rays meets one of the unre fleeted rays, 

 we find the two have travelled the same length of path, and, 

 being now in opposite phase, they cancel one another and produce 



darkness. Thus darkness is formed in the surface plane of the 

 diatom both sides of the partition, though due to different causes 

 in the two cases,* 



We have got, in fact, two bands of darkness, which issue 

 upwards at an angle to each other from the horizontal plane 

 in which the top of the vertical partition lies. In the case of 



* To obtain the complete result of a cone of light impinging on the 

 diatom, the three figures, 1, 2, and 3, or 4, 5, and 6, must be superposed. 

 The relative amounts of light and darkness at various points on or above 

 the surface plane of the diatom can in this way be estimated. Of course, 

 where the rays are crossing each other in any place, great care must be 

 taken to note whether one set has or has not suffered total reflection, 

 because the change of phase accompanying this wholly alters the result. 



