72 THE MICROSCOPE. 



image are admitted from a field of N nim. in the first 

 case, and of ^ mm. in the second. As the " opening " 

 of the objective is estimated by the diameter (and not 

 by the area) the higher power lens admits twice as 

 many rays as the lower power, because it admits the 

 same number from a field of half the diameter, and, in 

 general, the admission of rays by the same opening, 

 but different powers, must be in the inverse ratio of 

 the focal lengths. 



In the case of the single lens, therefore, its aperture 

 is determined by the ratio between the clear opening 

 and the focal length. The same considerations apply to 

 the case of a compound objective, substituting, however, 

 for the clear opening of the single lens the diameter of 

 the pencil at its emergence from the objective, that is, 

 the clear utilized diameter of the back lens. 



All equally holds good whether the medium in which 

 the objective is placed is the same in the case of the 

 two objectives or different, as an alteration of the 

 medium makes no difference in the power. 



Thus we arrive at a general proposition for all kinds 

 of objectives: 1st, when the power is the same, the 

 admission of rays (or aperture) varies with the diame- 

 ter of the pencil at its emergence; 2nd, when the 

 powers are different, the same aperture requires differ- 

 ent openings in the ratio of the focal lengths, or 

 conversely with the same opening the aperture is in 

 inverse ratio to the focal lengths. We see, therefore, 

 that just as in the telescope the absolute diameter of 

 the object-glass defines its aperture, so in the micro- 

 scope the ratio between the utilized diameter of the back 

 lens and the focal length of the objective defines its 

 aperture also, and this is clearly a definition of aperture 

 in its primary and only legitimate meaning as " open- 

 ing ; " that is, the capacity of the objective for admit- 

 ting ravs from the object and transmitting them to the 

 image. 



If, by way of illustration, we compare a series 

 of dry and oil-immersion objectives, and commencing 

 with small air angles, progress up to 180 air angle, 

 and then take an oil -immersion of 82 and progress 



