NUMERICAL APERTURE. 7 



innumerable form of Fungi ; — all present a very wide field indeed. 

 The smaller Crustacea appear to have engaged little attention from 

 our members. Amongst Insects, the Diptera alone would furnish 

 an enormous field for work. How few of the ' Saws of Saw-flies ' 

 have yet been satisfactorily identified ! And though so many 

 forms are to be met with among the Miscellanea of Cabinets, this 

 is as nothing compared with what remains to be done at them. The 

 Acari are numerous ; — practically inexhaustible, and most urgently 

 require such work as our members might profitably take up. 



" And so we might go on. Let but a kindly feeling prevail 

 amongst our members towards one another, a readiness to help for 

 the love of science, and present difficulties in the real study of the 

 minuter forms of life will easily be overcome and vanish." 



IRumerical aperture* 



By the Hon. J. G. P. Vereker. 



AMONG English Text Books on the Microscope, the only 

 one, as far as I know, which defines what is now known 

 as " Numerical Aperture " is the last edition of Carpenter 

 on the Microscope : although the subject has been fully 

 debated by the " Koyal Microscopical Society," and described in 

 its Journal. 



As, however, many members of the " Postal Microscopical 

 Society " may not have followed these discussions, it may prove 

 of interest to them that I should give an account of what this 

 term means. I send, therefore, an article on it, both ^or the 

 above reason, and also because a clear appreciation of it is 

 most important. 



The ideas of microscopists have lately undergone consider- 

 able development, owing to the investigations of Professor Abbe, 

 which have led him to define the laws of aplanatic combinations, 

 and also to put forth his diffraction theory of microscopic vision ; 

 and these investigations may be considered amongst the most 

 important advances in modern optics. 



Owing to his theories, the older plan of measuring the 

 aperture of objectives by mere angular magnitude has been 

 found to be unsatisfactory ; and probably the aperture will in 

 future be very generally expressed numerically. 



