60 



THEORY OF THE MICROSCOPE. 



surface of the lens, by / 3 , and that of the central portion of the 

 lens by (/ 3 ), the calculation for the first double-lens of the objec- 

 tive gives the following ratios : 



FIRST OBJECTIVE-LENS. 



From this table it is evident, in the first place, that the first 

 double-lens is approximately aplanatic for an object-distance of 

 51634 mm., but appreciably under-corrected for shorter distances, 

 since the marginal rays, produced backwards, cut the axis at a 

 greater distance than the central rays. It is, however, assumed 

 that the rays proceeding from the object-point reach the anterior 

 surface of the lens without deviation, which, it is well known, 

 is not usually the case. The ray passes through the fluid in 

 which the object is placed to the cover-glass and thence into air, 

 and is thus twice refracted before meeting the objective. The 

 divergence of the marginal rays is thus increased ; they appear 

 finally to emerge from a point which lies above the real object- 

 point, and which is the more remote from it, the thicker the 

 cover-glass and the greater the angle which the rays make with 

 the axis. We will hereafter investigate more exactly the effect 

 thus produced ; we need only premise that, in consequence 

 thereof, a somewhat shorter object-distance must be assumed for 

 the marginal rays, if the calculation is to hold good for the cases 

 which ordinarily occur. 



If we select *5 mm. as the object-distance (vide p. 31) of the 

 given combination of lenses, a diminution of about '005 mm. for 

 the marginal rays would produce a perfect equality of the focal 

 lengths / 3 and (/ 3 ). Of course this slight reduction of the object- 

 distance is not equivalent to the influence of ordinary cover- 

 glasses ; but, as no other combination approaches so nearly to 

 aplanatism of the objective, we may take it as the basis of further 

 calculations, and assume for the second and third double-lenses 

 the distances and refractive indices (vide- table on p. 34) which 



