680 SUMMARY OF CURRENT RESEARCHES RELATING TO 



" that the latter are of first-rate quality and used with high eye-pieces, 

 " and the question comes up, ' How high may the eye-piece be ? ' Our 

 " own impression is, that the same circumstances which prevent the 

 " successful construction of high objectives will prevent the construc- 

 " tion and employment of high eye-pieces. Just where the limit lies 

 " it may be difficult to state, but we doubt the efficacy of any eye-piece 

 " higher than a one-eight. This, with an objective of one-tenth would 

 " give 8000 to 10,000 diameters, and this seems to be about the limit 

 "arrived at by our best workers." 



Conditions of Microstereoscopic Vision—" Penetration." — It is 

 well known that, although binocular Microscopes have been devised 

 which allow the use of high j)Owers, there is always a very marked 

 falling off in the stereoscopic eifect. Several unsuccessful attempts have 

 hitherto been made to elucidate this on theoretical grounds. Professor 

 Abbe has, however, now published * an elaborate discussion of the con- 

 ditions of microstereoscopic vision which clears away the difficulties 

 which have attended the previous considerations of the subject. 



In an introductory part he points out that the stereoscopic effect 

 of binocular observation in the Microscope is fettered by restrictions 

 which are not in any way caused by the action of the particular 

 stereoscopic apparatus, but arise from the general laws of microscopic 

 vision. The direct appreciation of solid forms in binocular vision 

 obviously cannot extend further than the delineation of them goes. 

 It is only when an object can be seen in all its parts in one field of 

 the Microscope (that is, under one focussing) that a true stereoscopic 

 image of it is obtained. So long as only a small part of the object is 

 visible simultaneously with any distinctness, no stereoscopic apparatus, 

 however perfect, can bring into view the form of the whole. Now as 

 the amplification is increased the Mici'oscope continually loses in 

 depth, and this decrease in depth (starting with the lowest powers) 

 is not simply proportional to the amplification, but is in a very much 

 greater ratio. Thus with an amplification of 300, the depth is not 

 the iV*^ ^^ *^** wiih 30 times, but about the ^V*^ ^^^Jt so that an 

 entirely disproportional loss of depth takes place, and it is only when 

 we pass beyond the medium powers that the further decrease becomes 

 approximately proportional to the amjilification. But already with 

 an amplification of not more than 300 times the absolute depth of the 

 image scarcely amounts to the hundredth of a millimetre, and with 

 1000 times not even to a micromillimetre. The thickness of the 

 object which can be seen in one field of the Microscope therefore 

 decreases more and more with increase of amplification, at first (com- 

 mencing from the lowest powers) very rapidly, and not in a less 

 degree until the depth of vision has become very small. The scope 

 for stereoscopic observation must always be restricted in the same 

 ratio. Only under relatively low amplifications is a direct solid 

 view of those objects possible whose depth is a considerable fraction 



* ZeitKchr. f. Mikr., ii. (1880) p. 207. 



