CONSTRUCTION OF THE MICROSCOPE. 23 



using the meniscus form of lens, which is the segment of 

 an ellipsoid instead of a sphere. 



The ellipse and the hyperbola are curves of this kind, 

 in which the curvature diminishes from the central ray, or 

 axis, to the circumference b ; and mathematicians have 

 shown how spherical aberration may be entirely removed 

 by lenses whose sections are ellipses or hyperbolas. For 

 this curious discovery we are indebted to Descartes. 



If a I, a I', for example, fig. 10, be part of an ellipse 



Fig. 10. 



whose greater axis is to the distance between its foci // as 

 the index of refraction is to unity, then parallel rays 

 r I', r" I incident upon the elliptical surface I' a I, will be 

 refracted by the single action of that surface into lines 

 which would meet exactly in the farther focus /, if there 

 were no second surface intervening between I a V and/! 

 But as every useful lens must have two surfaces, we have 

 only to describe a circle I a V round /as a centre, for the 

 second surface of the lens I ' I. 



As all the rays refracted at the surface I a V converge 

 accurately to /, and as the circular surface I a V is perpen- 

 dicular to every one of the refracted rays, all these rays 

 will go on to/ without suffering any refraction at the circular 

 surface. Hence it should follow, that a meniscus whose 

 convex surface is part of an ellipsoid, and whose convex 

 surface is part of any spherical surface whose centre is in 

 the farther focus, will have no appreciable spherical 

 aberration, and will refract parallel rays incident on its 

 convex surface to the farther focus. 



