172 



TESTING THE MICROSCOPE. 



VI. 



DETERMINATION OF THE ANGLE OF APERTURE. 



SINCE the power of discrimination of Microscopes increases and 

 diminishes with the aperture, as was shown above, the latter 

 belongs to the factors which must be taken into consideration in 

 testing instruments. Its determination may be made in very 

 different ways ; yet all methods which have been proposed by the 

 microscopists are essentially equivalent. They cannot possibly 

 have any other basis than the easily understood phenomena, 

 which have reference to the known path of rays in the 

 Microscope; one diagram will therefore suffice to verify and 

 elucidate the most different methods of testing. 



FIG. 101. 



Let A, B, and C (Fig. 101) be the three pairs of principal 

 planes of the objective, field-lens, and eye-lens respectively, and 

 let F and F' be the focal planes belonging to A, and p the centre 

 of the field of view. If, then, m p n is the angle of aperture of the 

 objective, an illuminating cone of equal aperture is, of course, 

 necessary to fill it entirely ; it is also evident that any small por- 

 tion of the cone will illuminate the surface-element p, according 

 to the degree of its intensity. If, therefore, a source of light of 

 slight extent (whether it be a diaphragm illuminated by the mirror, 

 or the illuminating apparatus itself, or the distant flame of a lamp, 

 &c.) is moved in the direction from a to I, or conversely from 

 b to a, the object p appears to be illuminated as long as the source 

 of light is situated wholly or partially within the space limited by 

 the angle a p b = m p n. Outside this angular space the rays 



