189I.] NEW-YORK MICROSCOPICAL SOCIETY. 81 



interpolated ones (proceeding from above downward) are at first 

 very small, then larger but rectangular and twice as long as wide, 

 making the pattern one of alternate dots and rectangles; as we 

 pass to the right the rectangles run into each other obliquely, mak- 

 ing a wavy white line, the dots of the alveoli proper being in the 

 bends of the line, very much as in the longitudinal fibrils of 

 print No. ii. This change, distortion, and multiplication of the 

 dots is so entirely within our common experience in diatom- 

 study that I have no hesitation in explaining the longitudinal 

 striated appearance in this patch as the result of the redupli- 

 cating of the dots by the intercalation of the rectangular ones, 

 making in fact broken lines which on so small a scale are suffi- 

 ciently even to make continuous ones to the naked eye. On the 

 other side of the midrib in the same print (No. 12) the rectangles 

 and round dots are of nearly equal size, but they still make a faint 

 longitudinal striation, diverging a little from the midrib as we 

 pass from left to right. 



We thus have an ocular demonstration how a striated appear- 

 ance may be made out of a tessellated one, when there is no 

 question of continuous fibrils. Yet even this does not prove 

 that the fibrils are not there. Of course all visual appearances 

 under the microscope have their cause in the structure of the 

 object, considered in relation to the laws of transmitted and 

 reflected light. The puzzle often is to tell what to attribute to 

 each factor. I do not think it difficult to account for the tessel- 

 lated appearance of dots and squares with alternate blue and red 

 color. To do so may require us to refer to some elementary 

 matters in diatom-marking. 



Dr. Brebisson, at a very early day, divided the regular dotted 

 markings of diatoms into three classes: i, Quadrille rectangle 

 droit (in squares parallel to midrib, e.g., Pleurosigma balticuni); 

 2, Quadrille rectangle oblique (in squares oblique to midrib, e.g , 

 jP. /<7/v;/^j//;;/); 3, ^«/;2r^//r^ (quincunx or lozenge of 60° smaller 

 angle, e.g., P. angulatuni). This classification has been a good 

 deal neglected, but has good claims to remembrance, and will 

 assist me in explaining the phenomena before us. 



In Mr. Smith's print No. 6 is well shown what I regard as the 

 normal scheme of areolation of P. formosum. It will be seen to 

 be a reticulation with meshes as nearly square as nature gives us 



