28 On th UNEQUAL 
D; fo that DF reprefents the greateft linear aberration in this 
cafe. - 
AGAIN, let GH (Fig. 11.) reprefent a concave lens, receiving 
the parallel rays SH, RK, which it refraéts 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 HX 
produced backward, will interfect the axis’ in fome point P 
nearer to the lens than its focus, P N being’ the linear aberra- 
tion. : 
Ir 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 moft aberration. Hence, to render the 
aberrations DF (Fig. 10.) and PN (Fig. 11.) equal, the fo- 
cal diftance of the convex muft 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 imthe 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 object. 
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 iffuing from S are made to converge by 
the convex; and when the aberrations DF and PN 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 
