26 THEOKY OF THE MICKOSCOPE. 



by way of example, in a double-lens whose focal length = 8*773 mm. 

 Let the distance of the focal point from the first lens-surface 

 = 7*339, therefore, that of the anterior principal point of the same 

 surface = 1434 mm. ; and let the refractive index of the flint- 

 glass = 1*6 : 1 on these assumptions we get for the distance from 

 the axis, y, of a ray emerging from the focal point and inclined 

 at an angle of 14 after its passage through the lens: 



a. According to the trigonometrical calculation for the case of 

 the point of emergence of the ray approximately coinciding with 

 the point of intersection in the anterior principal plane, where, at 

 the same time, the path described in the crown-glass need not be 

 calculated separately, 



y = 7-339 . tan 14 + 1434 . tan 8 40' = 2'048 mm. 



b. According to the formula y = focal length x tan 14, 



y = 8-773 . tan 14 = 2-187 mm. 



Our lens is not, however, aplanatic for rays which emanate from 

 the focal point, but is noticeably over-corrected. The distance from 

 the axis of the ray refracted by the flint-glass proves, therefore, 

 somewhat too small; it may rise to about 2*07 mm. But, in 

 substance, nothing is altered thereby; the deviation as com- 

 pared with the tangent of the angle of inclination continues 

 the same. It is, further, evident that the amount of this varia- 

 tion increases and decreases with the angle of inclination of the 

 incident ray. 



1 Cf . the data for the second double-lens of the objective calculated in the 

 succeeding pages. 



