Burton. — On the Mlninium Visible in the Microscojje. 253 



Now £a is = the conjugate focal length p' less the principal focal 

 length/, or p' - f. Eef erring to diagram (1), we see that 



a a' ov p q = sin a . /. 



Since for the fii'st diffracted pencil sin a = \ ^ d, d being the distance 

 of the striae in the object, the above formula becomes 



j,j.JP'-f)-Kl^.d; 



./ -^ 



d '' 

 or, since 



p' - f^f= the magnifying power ni) 

 .-.BP^m.d, 



i. e. the distance of the visible striae in the real image of the object 

 is equal in this case to the distance of the actual diffracting elements 

 of the object multiplied by the magnifying power of the objective. 



If the direct ray A is screened off, then the first of the equations 

 just given becomes 



that is to say, since a' a" = 2 a a', JS P is halved, or striae will be seen, 

 the intervals of which are half the intervals of the set seen in the 

 first case. The reduction of the intervals of the visible striae may be 

 carried further by screening off all the spectra of the first, second, &c., 

 orders. 



It has been shown in treatises on Interference Phenomena that 

 rows of dots, individually of any form whatsoever, will, if of sufficient 

 minuteness, behave as if they were actual striae, both species of inter- 

 cepting systems producing identically the same phenomena. It mat- 

 ters not whether the dots in question consist of actual absorbing 

 particles, of transparent elevations or depressions in a uniform mem- 

 brane or shell, or of mere differences of refractive powers between 

 adjoining portions of the same substance, the effect on the luminous 

 undulations is the same in all cases of similar arrangement. All the 

 markings seen on different species of diatomaceae for instance might 

 have been previously drawn by a person who had never seen a diatom 

 in the microscope, had the grouping and distance i?iter se of the spectra 

 seen at the upper focal plane of the objective been communicated to 

 him. The diffracting obstructions originating the known appearances 

 may belong to any of the classes just enumerated, but we do not 

 know, and we never shall know hi/ mere microscopical inspection, what 

 the diffractive structures really are. 



Lastly, it is easily seen that, as the visibility of minute detail de- 

 pends on the diffraction spectra produced thereby, the limit of visibility 

 is attained when diffraction ceases, or, in other words, when the angle 

 a becomes equal to 90° for spectra of the first order. Referring to 

 diagram (1), we see that this occurs when al -a i = \ of the light 



