348 SUMMARY OF CURRENT RESEARCHES RELATING TO 



principles, with none of wLicli can, or in fact does, the angular aperturist 

 venture to disagree. His mistake has not been based on any ignorance 

 of those principles, but has simply arisen from a deep-rooted disinclina- 

 tion to modify former views — a disinclination which, not for the first 

 time in the history of science, has led those who are beset by it to deny 

 the plainest facts long after their truth has been established. 



Leaving now the consideration of the increased aperture of wide- 

 angled immersion objectives over dry objectives, we propose to deal 

 with the second question (which represents a problem that long 

 perplexed the minds of microscopists). On tohat principle does the 

 advantage derived from increased aperture depend ? That an increase 

 in the aperture of objectives is accompanied by an increase in their 

 performance has been established since the date of Dr. Goring's dis- 

 covery of the fact, and the true explanation, whatever it may be, is 

 of course independent of any consideration of apertures in excess of 

 180° angular in air or even of immersion objectives at all. The 

 question arises when we consider only dry objectives. 



Down to so late as 1870 all endeavours to give an answer to this 

 question had entirely failed. One of the ablest and most elaborate 

 of these attempts is that contained in the article "Angular Aperture" 

 in the ' Micrographic Dictionary,' but apart from the fact that it 

 starts with the fallacious assumption that the essential condition of 

 increased aperture is increased obliquity of the rays to the object, no 

 one can ever have risen from a perusal of that article, who was really 

 desirous of understanding the subject, without feeling the unsatisfying 

 character of the explanation attempted. That the true explanation 

 was still wanting was evident from the remarkable way in which all 

 microscopical authors avoided the subject, never getting beyond the 

 bare statement of fact that increased apertui-e in some way involves 

 increased resolving power. More than one microscopist devoted great 

 pains and labour to the endeavour to establish a consistent theory, 

 but all failed in consequence of having continued to consider micro- 

 scopical vision as essentially the same in principle as vision with 

 the naked eye, and so applying to the question only dioptrical con- 

 siderations. 



The crucial question which any explanation of the virtue of 

 increased aperture must face is the following, which on the old view 

 must necessarily be an insoluble paradox. How is it that we obtain a 

 greater effect by the increased obliquity of the incident illuminating 

 beam to the axis of the Microscope, even although at the same time 

 its obliquity to the object is decreased ? The ordinary explanation of 

 shadow and similar effects obviously fails here. 



(1) The Abbe Theory of Microscopical Vision. 



The solution of all the mystery was at last discovered by ap- 

 proaching the matter from a different point of view, and recognizing 

 what is now obvious, that in the case of the objects of minute size 

 with which the Microscope deals, and for the vision of which aper- 

 ture is necessary, the conditions of ordinary vision do not apply. 



When we consider waves of sound it is a well-recognized fact 

 that to produce an acoustic shadow the obstacle must be many times 



