achromatic compound Microscope. 177 



If the radiant is now made to approach the glass so that the 

 course of the rayfdeg shall be more divergent from the axis, 

 a3 the angles of incidence and emergence become more nearly 

 equal to each other, the spherical aberration produced by the 

 two will be found to bear a less proportion to the opposing er- 

 ror of the single correcting curve a c b ; for such a focus there- 

 fore the rays will be over-corrected. 



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 pro- 

 duced by them will recover its original proportion to the op- 

 posite error of the curve of correction. When / has reached 

 this point/", (at which the angle of incidence does not ex- 

 ceed 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/ 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 achro- 

 matic 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 aplantic pencils may con- 

 verge after traversing the glass, and that their foci for a 

 radiant may be on opposite sides of it, the principle how- 

 ever of the two foci remaining unaltered. See Fig. 5. 



To try this principle under a great change of circumstances, 



\EW SKUIES, VOL. V. NO. I. JULY 1831. M 



