ZOOLOGY AND BOTANY, MICEOSCOPY, ETC. 683 



2 "OS mm. with 10 times amplification. 



all the amplifications being referred to the conventional distance of 

 250 mm. 



These figures would be uniformly increased in the ratio of 

 3 : 4 or 2 : 3 if the object is supposed to be in water or in balsam. 

 For a more short-sighted eye, but capable of great accommodation, 

 the limits of vision being 200 and 100 mm., the above values for the 

 depth would have to be increased in the ratio of 2 : 3 ; on the other 

 hand, for a long sight in which distinct vision only reaches to 500 mm. 

 as the nearest point, they must be decreased in the proportion of 

 5 to 3. The construction of the Microscope (apart from its total 

 amplification) has nothing at all to do with these effects. 



Secondly. The perception of depth is assisted by the insensibility 

 of the eye to small defects in the union of the rays in the optic image, 

 consequently small circles of confusion in the vertical image. As a 

 result of this, in a fixed adjustment of the Microscope and a fixed con- 

 dition of accommodation of the observer's eye, transverse sections of 

 the object which are a little above and below the exact adjustment are 

 nevertheless seen without sensible or at any rate prejudicial indis- 

 tinctness. The total amount of depth so obtained is the so-called depth 

 of focus of the Microscope. In order to determine it numerically, the 

 allowable magnitude of the circles of confusion in the microscopical 

 image must be defined by the visual angle under which they may 

 appear to the eye. In accordance with experience, 1 minute of arc 

 would denote the limit for very sharply defined vision, 2 to 3 minutes 

 for vision still pretty distinct, and 5 to 6 minutes the limit for vision 

 only just tolerable. If the amount of the allowable indistinctness is 

 determined in this way, the focal depth depends further only upon the 

 refractive index of the medium in which the object is, the amplifica- 

 tion and the angle of aperture of the Microscope for the angle of 

 the admitted pencil if the whole aperture is not filled with rays), but 

 is quite independent of all other circumstances. Its value may be 

 computed for each particular case from a simple formula, according 

 to which it is directly proportional to the refractive index of the 

 object medium and inversely proportional to the " numerical aperture " 

 of the objective, as also to the first power of the amplification. To 

 take an example ; assume the visual angle of allowable indistinctness 

 to be fixed at 5', and the aperture-angle of the image-forming pencils 

 to be 60'^ in air (corresponding to a numerical aperture of • 50), the 

 depth of focus of an object in air will then equal 



