28 On the UNEQUAL 



D ; fo that D F reprefents the greateft linear aberration in this 

 cafe. 



Again, let G H (Fig. n.) reprefent a concave lens, receiving 

 the parallel rays S H, R K, which it refracts in the lines H X 

 and KV. This ray KV being produced backward, will interfect 

 the axis of the lens nearly at the point N, which is called the 

 virtual focus of the concave ; and the external ray H X 

 produced backward, will interfed the axis in fome point P 

 nearer to the lens than its focus, P N being the linear aberra- 

 tion. 



It may here be obferved, that the convex is in that pofition 

 which produces the leaft aberration, and the concave in the po- 

 fition which produces mod aberration. Hence, to render the 

 aberrations DF (Fig. 10.) and PN (Fig. n.) equal, the fo- 

 cal diftance of the convex mud be much fhorter than that of 

 the concave ; and if the diftances of the points F and N from 

 the convex and concave lenfes be required to be the fame, as 

 reprefented in the figures, then muft the object be placed much, 

 nearer to the convex. Hence the image of the near object S» 

 is reprefented at the fame diftance from the convex lens in fi- 

 gure tenth, as the virtual focus of the concave in figure ele- 

 venth, where it is reprefented as receiving parallel rays, which 

 are fuppofed to come from an infinitely diftant objecl. 



Now, when the diftance between K. and N, which is the 

 point from which parallel rays are made to diverge by the con- 

 cave lens, is equal to the diftance between T and F, which is 

 the point to which rays ifluing from S are made to converge by 

 the convex ; and when the aberrations D F and P N are alfo 

 equal ; I fay, that in this cafe, if the two lenfes be placed con- 

 tiguous, in the manner reprefented in the twelfth figure, parallel 

 rays, incident on thefe lenfes, will be converged to the point S, 

 without any aberration of the external ray. 



For 



