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THE AMERICAN^ MONTHLY 



[July, 



are shown to be indispensable for all 

 observations upon minute structure 

 for which high powers are necessary; 

 but it will be desirable first to point 

 out the erroneous interpretations 

 upon which the third view (as to all- 

 round vision and dissimilar images) 

 has been founded, and for this pur- 

 pose it will be necessary to refer to 

 the paper by Dr. Royston-Pigott, 

 F.R.S., in which the subject is dealt 

 with.* 

 ******* 



Now, it is necessary to say plainly, 

 this view is founded upon a funda- 

 mental error, "belonging," to use 

 Professor Abbe's words, "to the 

 venerable relics of the past naive pe- 

 riod of microscopical science, which 

 was characterized by an unshaken 

 conviction in the validity of the hy- 

 pothesis that microscopical vision is 

 in all essential respects the same 

 thing as ordinary vision." The "all- 

 round vision," by virtue of which we 

 are supposed, when looking at a min- 

 ute cube, to see at the same time the 

 top and all the sides (with the result 

 of rounding off the corners and an- 

 gles !), does not really exist, as can 

 be shown by the application of the 

 simplest laws of geometrical image 

 formation. The different obliquities 

 of the rays in an objective of wide 

 aperture cannot give rise to any all- 

 round vision, for in the microscope 

 there is no difference of perspective 

 attendant upon oblique vision as with 

 the naked eye. The difference of pro- 

 jection of successive layers which ex- 

 ists is ineffective, except in the case of 

 binocular vision. This absence of 

 perspective may be readily establish- 

 ed by examining an object alternate- 

 ly by an axial and an oblique ray; it 

 will be found that there is no shorten- 

 ing of the lines in the latter case, and 

 no capacity in the microscope, there- 

 fore, for " all-round vision." Indeed 

 if this theory were correct, micro- 

 scopical vision, even of plane objects 



*Proc. Roy. Soc. xxxi (1881) pp. 260-78. 



and with very moderate apertures, 

 would be entirely destroyed. 



Equally mistaken is the second 

 branch of the view which I am con- 

 sidering, viz., that a wide aperture 

 must, in the nature of things, impair 

 definition on account of the increase 

 thereby produced, in the dissimilar 

 images received through the several 

 parts of the objective. In support of 

 this view, illustrations drawn from 

 stereoscopic vision are adduced, 

 which admittedly does depend upon 

 the dissimilar images formed by the 

 right and left-hand halves of the ob- 

 jective ; but, as Professor Abbe has 

 shown, the dissimilarity of images 

 presented by an objective of wide 

 aperture is a dissimilarity in the pro- 

 jection of successive layers only, and ' 

 this is not effective unless we produce 

 these images by different portions of 

 the aperture separately and conduct 

 them to different eyes, as in binocular 

 microscopes. The sole effect of the 

 wider aperture, when the images are 

 not so separated, is a reduction in the 

 depth of vision — to confine us to the 

 vision of thinner objects, not to im- 

 pair the definition of what is seen 

 when the objects are within the range 

 of penetration. 



If we pass to practical experience, 

 v/e shall find that the principles which 

 theory establishes are amply confirm- 

 ed. All who have worked with wide- 

 angled objectives cannot fail to have 

 recognized the great fact of modern 

 practical optics, the perfection of de- 

 finition obtained with such glasses — 

 a fact which has been verified by such 

 authorities as Mr. Dallinger, who, so 

 long ago as 1878, stated of a new 

 ^-inch homogeneous-immersion ob- 

 jective of the wide aperture of 1..25 

 that " the sharpness and brilliancy of 

 the definition which this lens yields 

 is absolutely unsurpassed in my ex- 

 perience." 



The question of the power of reso- 

 lution supposed to be possessed by 

 small apertures can also be brought 

 to a very simple practical test by 

 those who believe in that view exhib- 



