968 Transactions of the Society. 



XXIII. — On the limits of Resolution in the Microscope. 

 By Frank Crisp, LL.B., B. A., V.P. & Treas. Linn. Soc, Sec. E.M.S. 



(^Sead 11th Novemler, 1885.) 

 The claim is frequently made that lines have been resolved with a 

 particular aperture in excess of the maximum number per inch 

 given in the table at p. 325 of Vol. I. (1881) of the Journal. 

 Very few of these claims are supported by any definite data. If 

 it is Amphipleura pellucida that has served as the object, the lines 

 have not been counted, though it is known that different specimens 

 of the diatom vary in the closeness of the lines. The aperture of 

 the objective has been only roughly estimated, and there has been 

 a general deficiency of any kind of precision as to the essential 

 data, that has rendered it unnecessary to consider the claim seriously. 

 When a case is brought forward in which the lines have been 

 counted, the aperture measured, the obliquity of the incident beam 

 determined by observing its position within the clear aperture by 

 means of the auxiliary Microscope, and the predominant colour of 

 the effective light indicated, it will then, and not till then, be time 

 to re-examine the difiraction theory. 



There are, however, some features in connection with the claims 

 in question, which show that misapprehension exists as to the 

 limit of resolving power in the Microscope which it will be desirable 

 to clear away. 



There are three eases in which, as it is supposed, lines in excess 

 of the theoretical maximum have been resolved, and these are 

 (1) with monochromatic light, (2) with photography, and (3) with 

 sunlight. The case of sunlight is distinct from the other two, 

 which have a common explanation and which had better, therefore, 

 be dealt with first. 



The formula which gives the number of lines to the inch that 

 can be resolved by a given aperture, with the maximum obliquity of 



illumination, is S = ^r— where B is the distance apart of the lines, 

 A a 



\ the wave-length of the image-forming rays, and a the aperture 

 of the objective. It will be seen that to solve this equation a value 

 must be given to X or the wave-length. This of course varies 

 according to the portion of the spectrum made use of, the wave- 

 length of the red end being longer than that of the blue end. 

 The heading of the column of resolving power in the table ex- 

 pressly states that the figures apply to a value of X = • 52689 /* ; 

 that is to the line E. The figures therefore represent the resolving 

 power with ordinary white light. 



Now consider what takes place when for white light is sub- 

 stituted monochro7natic (hlue) light obtained by shutting off, or at 

 least considerably reducing, the red, yellow, and green rays by 

 an ammonio-sulphate of copper cell or other appropriate agent. 



