812 Transactions of the Society. 



viz. for the lower angled systems, the use of somewhat wider 

 apertures than can be fully utilized by the total amplifications for 

 which the systems are constructed, or — what is the same thing — 

 will recommend the use of lower powers with a given aperture than 

 is indicated by the corresponding figures of N of Table I. The 

 surplus of aperture which is thus left unemployed in regard to the 

 delineating power is utiHzed in promoting the illuminating power 

 (or the brightness of the image), at least when narrow incident 

 pencils are required for proper illumination of the objects. On the 

 other hand, it has been shown that the said benefit is practically 

 confined within somewhat narrow limits. 



As I have said already, I am fully aware of the uncertainty of 

 the numerical data on which the above computations are based, 

 which uncertainty will scarcely ever be overcome in a matter like 

 that in question. Though in my opinion the figures advanced 

 above will conform as nearly as possible to the present state of the 

 Microscope, I should make no serious objection if any other 

 observer arrived at figures which difi'er from mine by twenty or 

 even thirty per cent., bearing in mind the interference of so many 

 elements of individual judgment. I do not, therefore, lay any 

 great stress upon the numerical details ; the reader may try to 

 improve them, or take them as a mere exemplification of general 

 principles, illustrating their application to actual systems. What 

 I insist upon is only that the theory of the Microscope is com- 

 petent to indicate a distinct guide for the rational construction of 

 objectives on the principle of proper economy of the independent 

 capabilities of the systems (delineating power and amphfying 

 power) ; that this principle leads necessarily to a certain propor- 

 tion between aperture and focal length ; and that this proportion 

 may be determined with such a degree of approximation as is 

 required for a practical guide, at all events sufficient for showing 

 the hmits between rational and irrational aims. 



In my opinion the question discussed here is of some general 

 importance in regard to microscopy. It will, of course, do no 

 harm that systems of lenses should be made of any design 

 whatever and according to any particular taste, and full liberty 

 must always be conceded in that respect. On the other hand, 

 however, the Microscope has an important vocation as an aid to 

 scientific research, and microscopical science is therefore fully 

 justified in demanding that the prominent feature in the improve- 

 ment of the instrument should always be to render it as useful 

 as possible for its primary purpose, and that no hobbies of any 

 kind should be permitted to take the lead in microscopical optics. 

 In order to prevent this, and to secure progress in the direction of 

 useful aims, the discussion of the question of the " rational " con- 

 struction of objectives cannot be dispensed with. 



