1 905-1906.] Address by the President. 329 



and delicate workmanship which these object-glasses require, 

 they are necessarily very expensive, but a kind called semi- 

 apochromatic, and which are also very good, can be bought at 

 a very reasonable price. 



We have now reached the end at present of the evolution 

 of microscope object-glasses, but it may be well to explain 

 a few technical terms applied to them. 



Numerical Aperture. — This denotes the ability of an object- 

 glass to collect and utilise a greater or less number of rays of 

 light, and is expressed in figures followed by the letters N. A. 

 Before the invention of immersion-lenses the expression used 

 was angular aperture, and was expressed by an angle of so 

 many degrees. But when immersion-lenses came into use, it 

 was found that the expression angle of aperture did no longer 

 denote the same quantity in the three different kinds of lenses 

 — dry, water-immersion, and oil-immersion. Under Fig. 1, 

 Plate XXV., we saw that an angle of 52° (26° -f 26°) in oil 

 and of 60° (30° -|- 30°) in water were both equal to an angle 

 of 84° (42°-H42°) in air. That is, the whole of the rays of 

 light collected by an angle of 84° in air could be taken up 

 by an angle of 60° in water and of 52° in oil. What was 

 wanted was an expression which would denote the same 

 equivalent in all the three media. Professor Abbe, to whom 

 microscopy owes so much, solved the problem, and adopted 

 the expression numerical aperture. Numerical aperture, then, 

 is the sine of half the angle of aperture multiplied by the 

 refractive index of the medium — that is, in air by 1, in water 

 by 1*33, and in oil by 1"52 ; and by limiting the result to 

 two figures, it will be found that '67 is the numerical aperture 

 for each of the three different angles. From what has been 

 said, it is evident that immersion-lenses can be made of a 

 much greater numerical aperture than dry lenses, and are thus 

 capable of collectiug and utilising a much greater number of 

 rays of light. Thus, while the theoretical maximum angle of 

 aperture for each of the three different kinds of lenses is 180°, 

 the numerical apertures are very different, being for air 1, for 

 water 1'33, and for oil 1"52. The greater the numerical 

 aperture of an object-glass, so much the greater, other things 

 being equal, is its resolving power. 



