284 Aviericati Quarterly Microscopical Journal. 



methods is as close as could be desired." I have also found 

 Abbe's apertometer supported by Tolles's traverse-lens in measur- 

 ing apertures. 



224 Regent Street, 



London, May 27, 1879. 



APERTURE, ANGULAR AND NUMERICAL. 



BY R. HITCHCOCK. 



Within the past twelve months the attention of microscopists 

 has been directed to great improvements in objectives and the 

 methods of using them. The subject of angular aperture has 

 also taken a new phase, and its discussion has been characterized 

 by careful consideration of the points involved ; consequently, 

 all are gradually, but certainly, reaching the same conclusions. 

 The differences of opinion which still exist relate only to minor 

 points, which experiments will soon decide, when a full and 

 rational explanation of the subject can be given. This seems to 

 be an appropriate time, therefore, to direct attention to the most 

 prominent results of recent observations. 



There is no longer any misunderstanding of the proper mean- 

 ing of the expressions balsam angle and air angle. The terra 

 180° is no longer used, as it once was, and blindly accepted by a 

 few in its literal sense. It is used by Prof. Abbe, but always as 

 expressing a theoretical limit ; and in this sense is, indeed, a use- 

 ful and necessary term. Far different was its meaning when 

 Mr. Tolles attempted to prove not only that it was possible to 

 realize this angle in practice, but one even greater, which was 

 designated + 180". We mention Mr. Tolles because he is res- 

 ponsible for much of the confusion which has surrounded this 

 subject. In this case, as in many others, positive assertion has 

 often obtained the advantage over sound reasoning. In order to 

 avoid confusion, it seems desirable to explain the application of 

 the terms to those who are not perfectly familiar with the distinc- 

 tion between air and balsam angles. 



The balsam angle of a dry objective is an expression liable to 

 mislead, for balsam angle, glass angle and angle in fluid are 

 generally employed — although inaccurately — as synonyms, and 

 refer properly to the angle of light which enters the front lens of 

 the objective. To say that the balsam angle of a dry lens is 77.5°, 



