ZOOLOGY AND BOTANY, MICKOSCOPY, ETC. 687 



whicli set limits to tlie depth-perspective in microscopic vision — on 

 the influence of the medium in which the object is, on the influence 

 of the aperture-angle of the objective, or of the incident illuminating 

 pencils, and on the influence which the very unequal extent of 

 accommodation of the eyes of different individuals must have on the 

 capacity for stereoscopic vision especially with low powers — in 

 particular it leads to a rule of cjeneral application which should 

 always be applied where stereoscopic observation is concerned, which 

 is — use always the loicest amplification sufficient for distinctly recog- 

 nizing the object, and in observations with transmitted light employ 

 as narrow a pjencil as is compatible with sufficient illumination of 

 the image. 



In conclusion, we may refer to the general importance in micro- 

 scopical investigations which this disproportion of ampdification in the 

 three-dimensional image of all optical instruments possesses. The 

 foregoing considerations point to the over-amplification of depth- 

 dimension as an obstacle for a more extended application of stereo- 

 scopic observation. It should, however, be pointed out that whilst this 

 peculiarity hinders and limits the direct appreciation of solid forms, 

 yet it to the same degree supports and extends the indirect recognition 

 of space relations. When with increase of amplification the depth- 

 perspective of the Microscope becomes more and more flattened, at the 

 same time the images of difi'erent planes stand out from each other in 

 an equal degree more perfectly, and are in the same degree clearer and 

 more distinct. With an increase of amplification the Microscope 

 acquires more and more the property of an optical raicrcAorae, which 

 presents to the observer's eye sections of the object of a fineness and 

 sharpness that no instrument could produce by mechanical means. 

 The over-amplification of the depth is the foundation of this capacity 

 in the Microscope, which enables the observer by successive adjust- 

 ments for a series of consecutive planes to construe the solid forms 

 of the smallest natural objects with the same certainty as he is 

 accustomed to see with the naked eye the solid forms of macroscopic 

 objects. It cannot be doubted that this positive gain from the 

 peculiar action of opjtical systems is a far greater advantage in the 

 general scientific use of the instrument than could ever be expected 

 from an extended application of stereoscopic observation. 



ti^ Since the original publication of the above paper, Professor 

 Abbe has sent us the following brief summary of the jjrincipal formulfe 

 which are the basis of the preceding discussions. 



(1) The over-amplification of the dejdJi in the solid microscopical 

 image results from a general proposition, which may be expressed in 

 the following way. Let A and B denote two points on the axis of an 

 optical system on the side of the object, and 8 their distance ; M the 

 linear amplification of a plane object at A, N the linear amplification 

 of a similar object at B, and o* the axial distance of the two images on 

 the other side of the system ; n and n* the refractive indices of the 

 media in front and at the back : then we have always 



n, 



2 z 2 



