70 THE MICROSCOPE. 



proper definition of the term " aperture," bat had 

 assumed it to be synonymous with what was known as 

 " angular aperture." The angles of the pencils admit- 

 ted by objectives cannot however serve as a measure of 

 their apertures. When the medium in which they 

 work is the same, as air, it is not the angles but the 

 sines of those angles which enable the proper com- 

 parison to be made, thus : if two dry objectives admit 

 pencils of 60 and 180, their real apertures are not as 

 1 : 3, but as 1 : 2 only. When the media are different, 

 as air, water and oil, the angles are still more misleading, 

 as there may be three angles all with the same number 

 of degrees, and yet representing entirely different aper 

 tures. 



Whilst, however, those who insisted upon the increase 

 of the apertures of objectives with the increase in the 

 refractive index of the immersion fluid, were right in 

 their contention, a somewhat similar lack of proper 

 definition of the term aperture prevented the question 

 being at that time effectually disposed of. The whole 

 matter was, however, recently exhaustively dealt with 

 in the course of a renewal of the " aperture question," 

 before the Royal Microscopical Society, and in the 

 papers of Professor Abbe (of Jena), and Mr. Crisp 

 (Sec. R<. Micr. Soc.), printed in the journal of that 

 society, 1 the subject of aperture will be found to be 

 at last placed on a scientific basis. To follow the 

 question in all its details, reference must be made to 

 these papers, but a brief resume of the leading points 

 will be found instructive and useful. 



The first essential step in the consideration of aper- 

 ture is, as I have said, to understand clearly what is 

 meant by the term. It will be at once recognized that 

 its definition must necessarily refer to its primary 

 meaning of " opening," and must, in the case of an 

 optical instrument, define its capacity for receiving 

 rays from the object, and transmitting them to the 

 image. 



In the case of the telescope-objective, its capacity 

 for receiving and transmitting rays is necessarily mea- 



(1) Journ. R. Micr. Soc., I. (1881), pp. 303-60 and pp. 388-123. 



