ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 681 



of the diameter of the field. Even with medium powers of 200-300 

 only very thin objects can be seen in relief, and with high powers 

 we are confined to objects, the depth of which does not exceed a few 

 micromillimetres. 



It is seen, therefore, that fairly satisfactory stereoscopic observa- 

 tion cannot be extended in general beyond moderate amplifications, 

 not even when the binocular apparatus allows the use of high powers. 

 As soon as these become necessary stereoscopic perception is limited 

 to objects of so little depth that a plastic view of them can hardly be 

 productive of any scientific advantage, although effective images are 

 still possible with suitable objects. It follows therefore, that in regard 

 to the more difficult problems of microscopical observation, any sub- 

 stantial aid by means of binocular vision is necessarily precluded. 



The following is a full translation of Professor Abbe's paper so 

 far as it relates to the theoretical question, with, however, some modi- 

 fications and additions by himself : — 



The questions which relate to (7epi/i-perspective or visual space (as 

 distinguished from field) in microscopical vision have never hitherto 

 been elucidated, though their solution constitutes the data for a 

 proper notion of the conditions of micvo-stereoscopic vision. 



The delineation of solid objects by a system of lenses is, by virtue 

 of the most general laws of optical delineation, subject to a peculiar 

 disproportion in amplification. The linear amplification of the depth- 

 dimension (parallel to the axis of the optical system) is when object 

 and image are in the same medium, always equal to the square of the 

 linear amplification of the dimensions at right angles to the axis ; 

 and if the object is in a more highly refracting medium than air, it is 

 equal to this square divided by the refractive index of the medium. 

 In every case, therefore, it will be found that in proportion to the 

 lateral amplification there is a progressive and with high powers a 

 rapidly increasing over-amplification of the depth of the three-dimen- 

 sional image. When, for example, a particular transverse section of 

 the object is magnified 100 times in breadth, the distance between the 

 planes of parts lying one behind the other is magnified 10,000 times, 

 at the corresponding points on the axis, when the object is in air, 7500 

 times when it is in water, and still as much as 6600 times when it 

 is in Canada balsam. 



The excessive distortion above described with high amplifications 

 would not, however, of itself so much hinder the correct appreciation 

 of solid forms in the microscopical image as might apjDcar at first 

 sight. For by virtue of the geometrical character of optical image- 

 formation, the solid image maintains a correct perspective in spite of 

 the over-amplification of the one dimension, although this perspective 

 with high amplifications becomes extremely abnormal — to some extent 

 comparable to that which results in ordinary vision by a large object 

 being placed close to the eye. Since, however, the appreciation of 

 solid forms is in no case merely a matter of sensation, but always 

 originates in an act of conception, the peculiarity in the optical 

 image referred to would not prevent the solid object being correctly 



