ACHROMATIC COMPOUND MICROSCOPES. 
195 
But if f still approaches the glass, the angle of incidence continues to 
increase with the increasing divergence of the ray, till it will exceed that of 
emergence which has in the mean while been diminishing, and at length the 
spherical error produced by them will recover its original proportion to the 
opposite error of the curve of correction. When f has reached this point f", 
(at which the angle of incidence does not exceed that of emergence so much 
as it had at first come short of it,) the rays again pass the glass free from 
spherical aberration. 
If f be carried from hence towards the glass, or outwards from its original 
place, the angle of incidence in the former case, or of emergence in the latter, 
becomes disproportionately effective ; and either way the aberration exceeds 
the correction. 
These facts have been established by careful experiment : they accord with 
every appearance in such combinations of the plano-convex glasses as have 
come under my notice, and may I believe be extended to this rule ; — that in 
general an achromatic object-glass, of which the inner surfaces are in contact, 
or nearly so, will have on one side of it two foci in its axis, for the rays 
proceeding from which it will be truly corrected at a moderate aperture ; that 
for the space between these two points, its spherical aberration will be over- 
corrected, and beyond them either way under-corrected. 
I am not aware that an exception is to be made for any 
quality of glass or curves that are likely to be used for the 
microscope : but I apprehend a case may occur, if the flint 
glass is convexo-concave and the convex lens united to its 
concave side, that neither of the aplanatic pencils may con- 
verge after traversing the glass, and that their foci for a 
radiant may be on opposite sides of it, the principle however 
of the two foci remaining unaltered. 
To try this principle under a great change of circum- 
stances, and to prove in what manner it was applicable to 
another most simple form of the object-glass, having made 
a magnified tracing of the curves of one of Utzschneider’s*, 
and drawn a ray through it from its longer aplanatic focus, 
* See Figure p. 194. 
2 c 2 
