144 TESTING THE MICROSCOPE. 



measurements, in which D sometimes becomes less than m d, 

 wholly untouched. 



It may therefore be considered certain that there are Microscopes 

 which, in spite of their imperfections, accomplish more with low 

 powers in comparison with a healthy eye, than a perfect, ideal 

 instrument should accomplish according to theory. It is evident 

 that this paradoxical phenomenon can be explained only by 

 peculiarities which distinguish microscopic observation whether 

 the refracting lenses are more or less perfect from vision with 

 the naked eye. We may mention as such peculiarities: (1) the 

 microscopic production of images due, as regards detail, to inter- 

 ference ; (2) the difference of brightness dependent upon the angle 

 of aperture, which has already been discussed ; (3) the chromatic 

 aberration of these pencils of light, which it is known can never 

 be quite eliminated ; (4) their spherical aberration. 



Of these four points and we know of no others the first is 

 of preponderating influence, as might be expected. For, as above 

 remarked, the microscopic structure-image is formed through in- 

 terference, and the image-forming pencils of light which graze the 

 margin of the objective-aperture are so narrow that the aberra- 

 tions of the eye cannot produce any appreciable error. The 

 sharpness of the image on the retina is therefore necessarily 

 increased to a still higher degree than by diminishing the cones of 

 light reaching the eye by circular diaphragms. These diaphragms, 

 however, have a favourable influence. If, for instance, we look 

 through a small aperture of about 1 mm. in diameter at the 

 page of a book, or its image, the printing appears decidedly 

 clearer, and the letters seem blacker and more sharply defined. 



The second of these points, as experimental testing immediately 

 shows, is unimportant, for the phenomenon remains the same even 

 when, by a suitable adjustment of the illumination, the brightness 

 of the microscopic image is so modified that the naked eye has a 

 considerable advantage. Just as little can the spherical aberra- 

 tion, mentioned as point (4), turn the scale, as the eye does not 

 produce a noticeable aberration of the marginal rays of pencils of 

 light, which are incident approximately in the direction of its 

 axis, 1 and consequently the compensation of such an aberration 

 by means of an opposite one of the incident rays cannot take place. 



1 Cf. Fick, " Medizinische Physik," 1st ed. p. 310, and Wagner's " Hand- 

 worterbuch der Physiologic," article " Das Sehen," by Volkmann. 



