JOUENAL 



OF THE 



ROYAL MIOROSCOPIOAL SOCIETY. 



JUNE 1884. 



TEANSACTIONS OF THE SOCIETY. 



VIII. — On the Estimation of Ajoerture in the Microscope. 

 By the late Charles Hockin, jun.* 



CBead Uth June, 1882.) 

 Plate VII. 



I HAVE read with much interest the papers by Prof. Abbe and Mr. 

 Crisp on the aperture of Microscope objectives, in which is shown 

 the great increase in aperture obtained with immersion over dry 

 objectives. 



It is not a little strange that at a date so long subsequent to the 

 introduction of immersion objectives, any microscopist should be 

 found maintaining that it is impossible for an immersion objective 

 to have an aperture in excess of that of a dry objective of 180^. As, 

 however, this has been asserted (and apparently seriously), it maybe 

 worth while to add a few observations to those contained in the 

 papers referred to, the form in which Professor Abbe has put both his 

 definition of numerical aperture and also his proof of the identity 

 of his formula for numerical aperture with his definition, allowing of 

 further elucidation, and from a somewhat difierent point of view. 



Professor Abbe defines the numerical aperture of an objective 

 as " the ratio of the linear semi-opening to the focal length." This 

 ratio is expressed in his notation by n sin u, where w is half the 

 aperture-angle of the objective, and n the refractive index of the 

 medium in which the object is placed. In the proof of the identity 

 of the formula n sin u with the definition, Professor Abbe has been 

 as concise as possible, referring to other works for the demonstra- 

 tion of all those formulae of which he has need, which have been 

 already published ; so that the exact sense of the terms used in the 

 definition comes out only in the course of the demonstration. 



* This paper has been delayed in publication in consequence of the lamented 

 death of the author, and the want of two of the diagrams, now supplied. The 

 late Mr. Charles Hockin, jun., was an electrician and mathematician of con- 

 siderable repute, and was a high Wrangler of his year. 



Ser. 2.— YoL. IV. 2 A 



