62 On the Spherules which compose the Ribs of the Scales 



depends chiefly on the curved areas, BDB, ADA, formed by- 

 completing the square, A B, B A, and in the difference between 

 the areas of the two inscribed semicircles and the square, i. e. 



between the area of a square and its inscribed circle, i. e. between 

 l'OOOO and 0*7854 for a square of diameter 1, or 0-2146, i.e. 

 one-fifth nearly ; so that the combined areas of these curved 

 notches are only about Atli of the corresponding square, or, allowing 

 for the breadth of a Nobert's line, we may at least say one-fourth. 

 The double notches therefore which really enable the eye in such 

 minute objects to discriminate the beaded form, are four times smaller 

 in area than the space corresponding to Nobert's lines ruled at a 

 similar rate. 



On precisely the same principle, when first diatoms began to be 

 studied, the lines formed by shadows disposed in lines were much 

 more easily made out than the beading projecting the shadows. It 

 would be interesting if some of our Fellows would work at this 

 question of the comparative easiness of distinguishing lines drawn 

 at the same rate of closeness, or of defining rows of spherules in 

 close contact. The retina repeats, as it were, the sensation all 

 along the line which is seen ; and a much fainter line can be 

 distinguished than dots in close proximity, which if dotted on paper 

 and removed to a distance quickly run into a line, whilst finer dark 

 lines drawn at the same intervals as the dots still remain visible. 

 Of course the case is quite altered if brilliant dots be used, as these, 



