90 



in their individuality. In other words, no matter what might be 

 the real distance between any two dots or lines on a diatom 

 they must, by optic?^l means, be so rendered to the eye, when 

 looking down the microscope, that they did not appear closer 

 together than -iw of an inch. It was more convenient for them 

 to be magnified a little more, so as to be sepai-ated apparently 

 by a greater interval, because in that case these Avliose eyes 

 were not absolutely normal would see them better ; but anyhow 

 they must not apparently be separated by an interval of less 

 than 0^4^ of an inch. The lines on Amphipleura pelhccida were 

 mostly about 100,000 to the inch, so to see them with the micro- 

 scope the entire optical arrangement must result in magnifying 

 at least 400 diameters, because 400 x 250 = 100,000. Now, how 

 did the author obtain his magnification, and what was it ? He 

 used a ~ in. objective and a 27 eyepiece. Well, that equalled a 

 magnification of 1620, because the initial magnifying power of 

 a Jin. was about 60, and 60 x 27 = 1620. He had, therefore, 

 plenty of magnification. But what about the N.A. — the second 

 condition ? 



Abbe's law, which was based on mathematical considerations 

 admitting of no controversy, declared that, with the smallest 

 possible beam of truly axial illumination, the number of lines 

 to the inch capable of being resolved = A. x N.A. where \ is 

 the number of wave-lengths to the inch of the light actually 

 used. Putting this into actual figures, seeing that there are 

 about 47,500 to the inch for visual light, it was found that 

 47,500 X "95 gave 45,125 lines to the inch as the theoretical 

 limit — a long way off" 100,000. In other words, the lines must 

 not be closer than ^yy.ry of an inch. But with oblique light 

 this formula was doubled and became 2A "95, or 90,250 to the 

 inch, or y^^l^jo ^^ ^^^ ^^^^^ apart. It was evident, then, that 

 Mr. Merlin could not have seen lines yooVo^ °^ even tto^xto" ^^ 

 an inch, apart without oblique light, using only a |ths cone of 

 axial illumination ; and this justifies the original remark that 

 his specimen must have been a coarsely marked one. It was 

 theoretically possible that the author might possess a photo- 

 graphic eye, so to speak : one that received impressions in the 

 violet-blue ray as well as ordinary individuals did in the yellow- 

 green or so-called " visual ray," but he had never heard of such 

 a case. 



