18 



CONSTRUCTION OF THE MICROSCOPE. 



ence at c d: in either case the image will have a certain degree of 

 indistinctness; and the difference between the focal points of their cir- 

 cumferential and central rays is termed the spherical aberration. It 



fig. 9. 



therefore becomes apparent that, to produce the desired effect, the cur- 

 vature of the lens is required to be increased around the centre, so as 

 to bring the rays which pass through it more speedily to a focus ; and 

 to be diminished towards the circumference, so as to throw the focus 

 of the rays influenced by it to a greater distance. This condition is in 

 a measure fulfilled in the meniscus form of lens, which is shown to be 

 the segment of an ellipsoid instead of a sphere. 



But the ellipse and the hyperbola are curves of this kind, in which 

 the curvature diminishes from the central ray, or axis, to the circum- 

 ference b; and mathematicians have sliown how spherical aberration 

 may be entirely removed by lenses whose sections are ellipses or hy- 

 perbolas. This curious discovery we owe to Descartes. 



If a I, a I' for example, fig. 

 10, be part of an ellipse whose 

 greater axis is to the distance 

 between its foci //as the in- 

 dex of refraction is to unity, 

 then parallel rays r /', r" I in- 

 cident upon the elliptical sur- 

 face I' a I, will be refracted by 

 the single action of that sur- 

 face into lines which would, 

 meet exactly in the farther 

 focus/ if there were no second surface intervening between la I and/ 

 But as every useful lens must have two surfaces, we have only to describe 

 a circle I a I' round /as a centre, for the second surface of the lens I' I. 

 As all the rays refracted at the surface I a I' converge accurately 

 to/ and as the circular surface Id 1? is perpendicular to every one of 

 the refracted rays, all these rays will go on to /without suffering any 



10. 



