Theories of Microscopical Vision. By A. E. Conrady. 615 



is there really any danger of our seeing two or three lines where 

 there is but one ; of seeing crossed lines wrongly spaced, and 

 running in a direction totally different from their actual direction 

 in the object, etc., etc. ? 



2. Granting that, in order to obtain perfectly truthful images 

 all diffracted light must be used, how is the immense improve- 

 ment of images with only a slight increase of N.A. accounted for ? 



3. What is the explanation of the greatly improved images 

 obtained with " solid " illuminating cones of considerable aperture ; 

 do these images deserve the confidence which they inspire ? 



The object of this paper is to attempt to answer these and 

 similar questions : to show how the image is built up according to 

 the diffraction theory under the usual conditions of observation, 

 and in how far it is likely to be truthful or the reverse, and thus 

 to rob the theory of its hidden terrors and to make it acceptable 

 to practical microscopists. 



It will be necessary to have an ideal image with which to 

 compare those yielded by diffraction ; it would be absurd to use 

 the exact image of geometrical optics as a standard, as this is 

 absolutely unattainable with light of finite wave-length. I shall, 

 instead, use the image which the object would yield with the same 

 objective if it were rendered self-luminous. That it is the most 

 faithful image practically possible, and has the further advantage 

 of being easily deduced by adding to all bright outlines of the 

 geometrical image the fuzzy fringe representing overlapping 

 spurious discs. 



It will soon be noted that I apply Abbe's principle in a some- 

 what different manner to that familiar from the existing explana- 

 tions. I do so because, in my opinion, it makes it easier to arrive 

 at the 'practically important deductions from the fundamental 

 principle in a straightforward manner. It is not done with a view 

 to belittling the great physicist, nor does it imply any flaw in his 

 own treatment of the subject. On the contrary, I trust that this 

 paper may be of some assistance in convincing those who have 

 looked on the Abbe theory as sterile and devoid of practical utility, 

 that this theory, when applied" to ordinary working conditions, 

 explains every peculiarity of the microscopical image, and is, 

 indeed, the only theory that can be applied with safety. And I thus 

 hope to remove many doubts as to its importance, and to demon- 

 strate to microscopists that, even if Prof. Abbe had never given 

 us anything else, his theory of microscopic vision alone should 

 secure him immortal fame. 



I shall at first follow Prof. Abbe's lead by assuming light 

 reaching the object in practically parallel rays or plane waves, 

 discussing afterwards how the results are modified when condensers 

 are interposed, and I shall limit the present paper to the considera- 

 tion of perfectly regular and perfectly plane simple gratings ; and 



2 u 2 



