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XII. — Hieories of Microscopical Vision : a Vindication of 



the Abbe Tlieory. 



By A. E. Cunrady, F.K.A.S., F.E.M.S. 



(Bead November 16th, 1904). 



In the early days of the compound Microscope, the performance of 

 the instrument was judged on the basis of geometrical optics, viz. 

 it was assumed that an optically perfect instrument should bear 

 unlimited magnification, and that the practical limitation of resolv- 

 ing and defining power was due to insufficient light, and especially 

 to the shortcomings of that long-suffering individual, the manufac- 

 turing optician. 



But when the undulatory theory of light became more generally 

 known and accepted, a direct connection between the power of 

 optical instruments and the wave-length of the light employed was 

 soon recognised as one of the obvious deductions from that theory. 



On the assumption of a self-luminous object and a limiting 

 aperture of 180° in air (N.A. 1*00, we should say now), the great 

 Hermann v. Helmholtz defined that limit for the Microscope in an 

 admirably clear and conclusive paper which must be read in the 

 original, or at least in a straightforward translation, to be appre- 

 ciated. 



On the basis of that tlieory, microscopical vision becomes 

 comparable with telescopic vision. Each point in the object is 

 represented by a " spurious or diffraction disc " in the image ; the 

 latter being composed of an immense number of overlapping 

 "spurious discs," which soften all outlines and suppress detail 

 below the theoretical limit of resolution, but produce an otherwise 

 faithful and exact representation of the object. 



It is, however, most important to bear in mind that this con- 

 venient and comforting theory assumes that the object behaves 

 like a self-luminous one, that is to say, that each point in the 

 object sends out regular spherical waves independently of all other 

 points, in the same way as the molecules of a white-hot object 

 would do. The opinion seems to be widely held that we can 

 satisfy that assumption by focussing a sharp image of the source 

 of light (usually a lamp flame) upon the object by means of a well 

 corrected condenser, and that by this procedure we can secure 

 images which give perfectly trustworthy indications of all resolv- 

 able detail in the object. 



If we could project a geometrically perfect image of a self- 

 luminous surface upon a very thin object, by a wide-angled con- 



