ZOOLOGY AND BOTANT, MICROSCOPY, ETC. 685 



With 



The over-amplification of the depth-dimension, inherent in the 

 optical formation of the image, produces therefore, as the amplifica- 

 tion increases, a more and more unfavourable relation between the 

 depth and width of the object-space accessible to accommodation. 

 Whilst with 10 times amplification the relation is about that of a 

 pretty thick book, with 3000 times amplification it equals only a 

 single leaf of the book. 



The other constituent of the depth of vision, the deptJi of focus, on 

 the other hand, shows an essentially different relation, because the 

 effect of over-amplification is here directly compensated by the 

 narrowing — proportionally to the amplification of the Microscope — 

 of the pencils passing from the eye-piece to the eye. For the limits 

 of perfectly distinct vision by varying accommodation, it is obviously 

 a matter of indifi'erence whether the pupil receives narrow or wide 

 pencils. But the increase in the circles of confusion when the near 

 or distant points of distinct vision are overstepped is proportional to 

 the diameter of the image-forming pencil at its entrance into the eye. 

 The result of this is, that in spite of the over-amplification of the 

 depth-dimension, the solid space recognizable by virtue of the focal 

 depth maintains a constant relation between breadth and thickness 

 as long as the same angle of aperture and the same object medium 

 are considered, and as long as a fixed limit is retained for the 

 allowable circles of confusion. 



For an effective aperture of ■ 50, air as medium, and 5' as the 

 allowable visual angle of the circles of confusion, this constant 

 relation of depth to the diameter of the field of view corresponding to 

 the depth of focus is ■^^, consequently a very small fraction, not- 

 withstanding that a pretty wide latitude is here allowed for indis- 

 tinctness. 



The depth is increased to about -^^ when under the same 

 assumptions in other respects the object is supposed to be in balsam, 

 and it may be further raised in a considerable proportion when the 

 much smaller angles of aperture are taken into account which are 

 available with lower amplification or with illumination by narrow 

 pencils. These examples show this much however, that when the 

 amplification is low the focal depth in every case falls very much 

 into the background as compared with the accommodation depth, 

 which even for eyes with small capacity of accommodation must 

 still retain a considerable magnitude, whilst inversely imder very 

 high amplifications the ef&cacy of accommodation falls more and more 

 behind the small but constant effect of focal depth. 



Combining the preceding figures we have the following table 

 showing the total depth of vision from 10 to 3000 times. 



Ser. 2.— Vol. I. 2 Z 



