7 6 VISION WITH THE COMPOUND MICROSCOPE 



determined by the fact that no resolution can be effected unless at 

 least two diffraction pencils are admitted, and the admission of these 

 we have seen is absolutely dependent on the aperture of the objective. 



The rule given by Professor Abbe for determining the greatest 

 number of lines 'per inch which can be resolved by oblique light will 

 be found (taking any given colour as a basis) to be equal to twice 

 the number of undulations in an inch multiplied by the numerical 

 aperture. 



To those who have studied this subject it will be seen that the 

 ' numerical aperture ' here takes the place of what was formerly the 

 * sine of half the angle of aperture ; ' and it has the effect of giving 

 the proposition a broader generality. By using the ' sine of half 

 the angle of aperture,' the proposition is only true with the addition 

 that the number of undulations be calculated from the wave-length 

 within the special medium to which the angle of aperture relates. 



In introducing the numerical aperture instead of the sine of the 

 angle, the latter (the sine) is increased in the proportion of 1 : n 

 (n standing for the index of the medium), and that has the same 

 effect as increasing the other factor the number of undulations. 



What the colour employed should be is only capable of individual 

 determination, since the capacity for appreciating light varies with 

 different individuals. 



If, for instance, we take '43/u in the solar spectrum as being 

 sufficiently luminous for vision, we find the maximum so far as 

 seeing is concerned to be 118,000 to the inch (the object, in this 

 case, being in air) ; but as the non -luminous chemical rays remain 

 in the field after the departure of the visible spectrum, a photo- 

 graphic image of lines much closer together might be produced. 



AIR 



FIG. HO. 



This important subject can scarcely be considered complete, even 

 in outline, without a brief consideration, in their combined relations, 

 of apertures in excess of 180 in air and the special function these 

 apertures possess. 



1 . Suppose any object composed of minute elements in regular 

 arrangement, such as a diatom valve ; and, to confine the considera- 

 tion to the most simple case, suppose it illuminated by a narrow 



