REFRANGIBILlTr of LIGHT. 27 



When both fides of a lens are convex, and the proportion of 

 their convexities is as one to fix, if the mod convex fide be ex- 

 pofed to parallel rays, the aberration will exceed the thicknefs 

 of the lens one fourteenth, which is the fmalleft pofllble aber- 

 ration of any convex lens. 



If it is required to increafe the aberration, this may be done 

 by grinding one fide of the lens convex, and the other fide con- 

 cave, to a longer radius. Such a lens, with its concave fide 

 turned towards parallel rays, will have more aberration than 

 any plano-convex or double convex lens of the fame focal di- 

 ftanCe. 



Hugenius proceeds to fhew, that the fame aberration is pro- 

 duced by concave lenfes as by fimilar convex ones. When a 

 plano-concave lens is expofed to parallel rays, with its plane fide 

 outward, the external ray of the pencil, being produced back- 

 ward after refraction, will interfect the axis of the lens nearer 

 to it than its focus, by four times and a half the thicknefs of 

 the lens. But if its concave fide be expofed to the parallel rays, 

 the aberration will only exceed the thicknefs of the lens one 

 fourteenth part. A double concave, whofe radii are as one to 

 fix, with the moft concave fide turned outward, difperfes the 

 rays with the leaft aberration ', and a concave menifcus, with 

 its convex fide outward, produces more aberration than any 

 plano-concave or double concave lens, of an equal focal di- 

 ftance. 



These are fufficient data for correcting the aberration from 

 the fpherical figure, in cafes where both a convex and concave 

 lens are required, in the conftruction of the compound object- 

 glafs. 



Ficj. 10. Let AB reprefent a convex lens receiving a pencil of 

 rays from the object S, and converging rays incident near the axis, 

 as S T, to the point F ; and external rays, as S B, to the point 



D 2 Dj 



