THEORY OF THE MICROSCOPE. 



sect the perpendicular passing through c in the cardinal focal points. 

 Let r c v = 60, the aperture of the objective, and p c q = 30, 

 that of the diaphragm ; then the path of 

 the rays may be easily determined in ac- 

 cordance with the principles laid down in 

 the Introduction. The ray drawn through 

 the focal point parallel to v c, after re- 

 fraction, proceeds parallel to the axis ; the 

 ray incident from below, in a direction 

 parallel to q c, is so refracted that it cuts 

 the upper focal plane in the same point 

 as the prolongation of q c. By this ray 

 the marginal rays of the pencils (both 

 incident and emergent), which contribute 

 to the illumination of the point 0, are 

 determined. All rays which are deflected 

 to the right or left to a greater angle than 

 those shown in the figure, meet either 

 on the margin of the diaphragm or on 

 that of the object. We can just as 

 easily construct the effective pencils 



for any other points. For instance, the limiting point of the 

 central shadow is determined by a line drawn parallel to v c 

 through i. 



If we suppose the figure turned round 180, it will evidently 

 illustrate the course of the rays for the combination of the dia- 

 phragm of 60 with the objective of 30. The limiting lines 

 between light and shadow remain as before ; and if the pencils 

 proceeding from the object remain homocentric, after the re- 

 fraction in the objective, as assumed for both cases, there is 

 nothing that could explain any appreciable alteration in the 

 image, either in distinctness or amount of light. It is, there- 

 fore, perfectly correct to say that the magnitude of the angle 

 of aperture in objectives has, in respect to their dioptric 

 functions, neither more nor less signification than the magnitude 

 of the aperture of the diaphragm. It may be further inferred 

 that the advantages which the former possesses are either of a 

 purely practical nature, or are due to circumstances which have 

 no connection with the dioptric formation of the images. 



In order to determine all cases practically possible, we must 



FIG. 42. 



