528 Transactions of the Society. 



stated that he had observed a minute rill on the moon with his 

 8-in. achromatic, and withheld the information that the aperture 

 had been stopped down to 3 in. Now, as an 8-in. will show a 

 rill on the moon § of a mile wide, and a 3 -in. a rill If miles wide, 

 his statement would not be of much value, for his audience will 

 think he is talking about a rill § of a mile wide, whereas the one 

 he saw must have been at least 2\ times wider. 



As it is impossible to practically use the full aperture of 

 most microscope objectives, a table, constructed upon an assump- 

 tion that a narrow portion at the periphery of a lens is the de- 

 termining factor for the limit, can only lead to wrong conclusions. 

 If, to refer back to our hypothetical astronomer, it had been the 

 accepted practice in the astronomical world to diminish the 

 aperture of a telescope object-glass 1\ times before estimating its 

 limit, no false impression would have been produced among the 

 audience ; but the audience of the biologist, on the other hand, 

 having been informed by the table at the end of the Journal that 

 the screen limit for a 1*3 N.A. is 135,800 lines to an inch, is 

 led to believe that the discovered structure is much smaller than 

 it really is. In the Journal for 1893, p. 17, there is a table, "con- 

 structed to meet the every-day wants of the practical microscopist," 

 which gave the resolving limit for objectives with a f cone ; k was 

 46,666, and c was 1 ■ 333, therefore the limit for N.A. 1 • was 70,000 

 lines to an inch. During the thirteen years since that table was 

 written, although apochromatic objectives remain pretty much as 

 they were then, cheap semi-apochromats have been greatly im- 

 proved, and some containing fluorite can now be purchased at a 

 very moderate price, which in point of excellence run even 

 apochromats very closely. In this interval, too, Mr. H. J. Grayson 

 has produced his wonderful band-plates, which have greatly aided 

 the practical establishment of a more accurate limit. It was 

 thought better to draw up a new table, for the same purpose as the 

 old ; and as it was to be a table of " working limits," rather than 

 one of absolute limits, c was made 1 * 3, so the difference between 

 the two tables is not great. The limit in the following table 

 will only be exceeded by a very few apochromats of super-excellent 

 quality. 



A reference to the table shows that the structure discovered by 

 our biologist must have been a good deal less than 104,500 lines 

 to the inch, because that figure is the screen limit for a 1 ' 3 N.A. 

 with nearly a ^ cone, and that if this quantity be halved, for, say, a 

 § cone, the result will not be so very far from the truth. 



It would be an excellent plan if the announcement of any 

 microscopical discovery were accompanied not only with a descrip- 

 tion of the objective and magnifying power, as at present, but also 

 with the Grayson band resolved, without the alteration of any of 

 the adjustments except the focus : e.g. an investigator having made 



