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PEOCEEDINaS OF THE SOCIETY. 



written, and proceeded : — " It is almost superfluous to remark that 

 this gentleman understands perfectly what he intended to convey, 

 and carefully protected himself by qualifications and explanations 

 of his statements, where, had he not done so, room might have 

 been found for misrepresentation. For instance, at p. 140, vol. i,, 

 I find the following, viz. : — 



" C. ' It is intended simply and solely to show the fallacy of the 

 supposed limit of 2 y assigned to the aperture within a medium.' And 

 at p. 139, the value of y is given as = 40° 59' ; but Professor Stokes 

 nowhere asserts that there is such a limit with a dry lens, for the 

 simple reason, no doubt, that there is no such limit, and he is far too 

 astute to ' travel beyond the record,' 



" Who is responsible for promulgating the fallacy in question I am 

 not aware ; but I can perhaps make a good guess as to how it arose. 

 I quote also the following from p. 139, which I find in Professor 

 Stokes's paper, viz, : — 



" D. ' To disprove an alleged proposition, the shortest and least 

 invidious plan is often to show by one or more particular instances 

 that it is untrue.' 



" This I propose doing with regard to ' the supposed limit ' of 2 y 

 in air, and I shall take the liberty of copying Professor Stokes's 

 diagram from p. 141, vol, i,, and of adding thereto some few lines in 

 illustration of my argument, using the same letters of reference as 

 those on the original so far as they go, 



" 0, Fig, 32, is the centre of the large segment of the sphere HAL. 

 The rays Q H-Q L diverging from the focus Q within the glass (or 

 medium) are refracted at H towards K, and at L towards M, as if 

 they proceeded from q, the angle H 5 L being 81° 58'. 



Fig. 32. 



Fig. 33. 



" It is assumed by Professor Stokes that Q is a real focus of no 

 aberration, and that achromatism, &c., will be dealt with by the back 

 combinations ; and it is further suggested that in order to make the 

 lens of practical use, the excessively large segment of a sphere here 

 depicted shall be reduced to a hemisphere, leaving the space between 

 the lines H L and B C as working distance for balsam, covering-glass, 

 and immersion fluid. 



