ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 693 



discusses the effect of observing the two different images with a single 

 eye (when each point of the object is seen in one direction only), and 

 the difficulties attending the recognition of the respective distances of 

 parts of an object with one eye. With true solid vision with two eyes 

 they must constantly be accommodated according as we desire to see 

 the nearer, central, or more remote parts of the object. With apparent 

 stereoscopic vision this is not, however, necessary. 



Finally, the author expresses his opinion as to the value of bino- 

 culars as follows : — " For the solution of natural problems the author 

 cannot expect much of the stereoscopic Microscope since the sharpness 

 of the image leaves much to be desired.* Its use for instruction is, 

 moreover, rendered very difficult in that each observer must regulate 

 not only the focus but also the lateral distance of the eye-pieces. 

 Nevertheless, for microscopical objects of complicated form the instru- 

 ment may here and there prove useful." 



Miniatured Images. — In the President's Address (ante, p. 158) a 

 brief reference is made to the unsatisfactory character of experiments 

 made on miniatured images — spider-lines, for instance, " miniatured to 

 the fourteenth part of the hundred-thousandth of an inch." The 

 illusory character of all conclusions on the subject of microscopical 

 vision, which are based on the observation of miniatured images, is 

 demonstrated by the following discussion, which we extract from some 

 notes on the subject by Professor Abbe. 



Fig. 133. 



Let (Fig. 133) be an object — a grating or wire gauze, or spider- 

 line, Q its miniature image, projected by means of an objective S, 2 the 

 objective of the Microscope by which this miniature image is observed, 

 and P the re-enlarged image which is finally seen through the eye- 

 piece. The linear aperture of the objective 2 may be denoted by a ; 

 the corresponding aperture-angle by cv; the angle of convergence of 

 the delineating pencils at the image P by v ; the angle of divergence 

 of the pencils admitted from O by u ; the distance of from S by d, 

 and the distance of the final image from 2 by 8 (these distances being 

 measured from the posterior principal foci of the two objectives which 

 will practically be very near to the back lenses), and / and <f> the 

 equivalent focal lengths of S and 2 respectively. All the conditions 

 of the observation are now strictly defined. 



* In the particular case, on account of the interposition of the prism and 

 additional eye-piece combination. 



