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 ah^ration. It 



therefore hecomes 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 shown how spherical aberration 

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

 perbolas. This curious discovery we owe to Descartes. 



Hal, a I' for example, fig. 

 jL-''^ 10, be part of an ellipse whose 



greater axis is to the distance 

 between its foci y/ as the in- 

 dex of refraction is to unity, 

 then parallel rays r V, r" I in- 

 cident upon the elliptical sur- 

 face?' a Z, will be refracted by 

 the single action of that sur- 

 face into lines which would 

 meet exactly in the farther 

 focus yj if there were no second surface intervening between I a I' and/! 

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

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

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

 tof, and as the circular surface IdV is perpendicular to every one of 

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



fig. 10. 



