The President's Address. By Prof. P. Martin Duncan. 151 



and therefore has the larger or smaller aperture, according as the 

 diameter of the beam emerging from it is greater or smaller. 



As Fellows of this Society we may, I think, be proud of the able 

 communications, relating to this subject, which were published last 

 year in the April and June numbers of the Journal. 



Numerical Aperture. 



The abandonment of the angular notation for aperture neces- 

 sarily follows, as soon as the correct view of aperture is appreciated ; 

 for when we know that the apertures of three objectives are, for 

 instance, as 98, 126, and 138, no one would insist that they should be 

 designated 157°, 142°, and 130°. A notation can have no title to 

 be considered a scientific one, which denotes things as the same 

 when they are really different (60° in air and oil) or different when 

 they are the same (180° in air and 82° in oil). 



Until, however, the " law of aplanatic convergence " had been 

 demonstrated by Professor Abbe, no principle had been established 

 by which the ratio between emergent beam and focal length, could 

 be conveniently denoted. 



It would not be possible for me to condense, without a sacrifice 

 of intelligibility, the steps by which he subsequently showed, in a 

 very beautiful manner, that the ratio in question can be expressed 

 by the product of the refractive index of the medium in front of the 

 objective, and the sine of half the angle of aperture, that is by 

 n sin u. 



Taking for our unit the capacity of an objective for collecting 

 the whole hemisphere of rays from an object in air (i. e. the case of 

 a dry objective of 180° angle) we obtain the " numerical " notation, 

 which commencing with the lowest numbers advances as far as 1 • 52 

 with oil-immersion objectives, and by the use of which not only are 

 apertures compared in the same medium, but in different media also, 

 and we see whether they are smaller or larger than the maximum 

 of a dry objective. 



It is gratifying to find that the reproach hitherto attaching to 

 microscopists, for the use of a misleading notation, is, thanks to the 

 efforts of this Society, being rapidly removed, and that the initials 

 N.A. are no longer so mystic a symbol as they have been. I under- 

 stand that many of the opticians have decided to use the numerical 

 notation in the future issues of their catalogues, which is a step in 

 the right direction, which we shall hope to see generally followed. 



Whilst on this subject I may point out how important it is 

 that in observations with high-power objectives, their aperture as 

 well as magnifying power should be stated. Whether a large or 

 a small aperture has been used, may make a very material diffe- 

 rence in the value to be attached to the results described. 



