74 THEORY OF THE MICROSCOPE. 



the angle of incidence of the aberrant pencil. In the Campani 

 eye-piece the real image is not, therefore, formed in the plane of 

 the field-lens, but above it. 



By similar reasoning it may be shown, that the displacement 

 of the centre of curvature to the right (which a shallow eye-lens 

 presupposes) requires, as the condition of aplanatism, that the 

 distance of the two lenses shall be less than the focus of the 

 upper lens. In this case ah arrangement is applied to the eye- 

 piece, which agrees in principle with that of Ramsden, in that 

 the real image is formed in front of the lower lens. 



It is therefore possible to combine single lenses in different 

 ways to form an aplanatic system under the given conditions. A 

 strict fulfilment of the conditions is, in general, possible only for 

 particular pencils, just as the elimination of spherical and 

 chromatic aberration in the objective is limited theoretically to 

 particular inclinations and colours. An eye-piece which is 

 aplanatic for the violet rays, cannot, as a rule, be so for the 

 red, since both the position of the centre of curvature and the 

 distance of the lenses depend upon the refrangibility of the 

 rays. The point p in the figure is evidently removed the further 

 to the left the greater the refrangibility of the rays, while q, as 

 we may suppose, does not change its position ; moreover, the 

 focus of the eye-lens is different for each colour. The confusion 

 thus produced in the case of the refraction at the lower surface 

 of the eye-lens, depends, of course, upon the dispersive power of 

 the glass, but it is further dependent upon the actual position of 

 the point p, in which the prolongations of the differently-coloured 

 pencils cut the axis. If p lies for all colours to the left of the 

 centre of curvature, an eye-piece which is aplanatic for violet or 

 central rays will move the marginal points of the red image a 

 little too far outwards, because the point of divergence b for this 

 colour is still situated within the focus. The field of view would 

 therefore appear with a red fringe. This chromatic aberration is, 

 however, equalized by the refraction at the upper lens-surface, 

 for here the violet rays are inclined more strongly towards the 

 axis than the red rays. It is evident, also, that this counter- 

 action will preponderate if all the rays are refracted to the axis 

 by the combined action of the lens. The red margin of the field of 

 view is consequently converted into a blue one in the final image. 



The same result is obtained, if the point p, with regard to all 



