442 ON- APEETFEE AND DEFINITION OF MICIIOSCOPE OBJECT GLASS. 



viewed through a microscope armed with objectives of given 

 angular aperture, under the several conditions of illumination by- 

 red, blue, and mean rays of the spectrum. Of course this formula, 

 and all calculations made from it, must exceed any possible actual 

 performance, even on the assumption of perfect construction of lenses 

 and exact fulfilment of the conditions necessary to perfect amplifica- 

 tion, definition, and brightness of image. Helmholtz does not apply his 

 formula to measure distmctness of definition of points, lines, spaces, 

 or surfaces, but simply to find how closely two lines (or a series of 

 lines) may be approximated before '' interference " waves blot out 

 the separate impression of these lines on the retina, and to mark 

 this nearest approach as the measure of extreme limit of resolution. 



But Mr. Sorby, in referring to his table, says : — *' The examina- 

 tion of this table will clearly show the value of aperture in 

 ' defining ' lines at very small intervals on flat objects like 

 diatomaceae, though in practice the advantage may be entirely 

 counterbalanced by other (?) disadvantages in the case of a 

 diff'erent class of objects." 



The readers of Professor Helmholtz's essay will scarcely acquiesce 

 in the correctness of a statement which attributes increase of 

 *' definition " to larger angular aperture, unless the term 

 *' definition" be understood in a more liberal than literal sense, 

 as meaning freedom from diffraction effects. Eut it must be borne in 

 mind that diff'raction phenomena in the microscope arise from two 

 distinct sources, and affect the microscope image in two very 

 different ways. The diffraction which is occasioned when a brightly 

 illumined image is viewed through a small optical aperture (and 

 such is the case in the microscope) annuls, by interference of wave 

 undulations, the vision of very minute objects, or produces false 

 images by distortion. There is here no question of '' definition," 

 but of seeing or not seeing, and, if seen, of true or false representa- 

 tion. It is a question of ''resolving" or not ''resolving" the 

 object. The second mode in which diffraction affects the microscope 

 image is when, from some peculiarity in the object, e.g., structural 

 particles or finely ruled lines, &c., some illuminating rays are split 



