26 THE MICEOSCOPE. 



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 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 achrom- 

 atic 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 whicli 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. 



" The longer aplanatic focus may be found, when one of the 

 plano-convex object-glasses is placed in a microscope, by short- 

 ening the tube, if the glass shows over-correction; if under-cor- 

 rection, by lengthening it, or by bringing the rays together, 

 should they be parallel or divergent, by a very small good 

 telescope. The shorter focus is got at by sliding the glass 

 before another of sufficient length and large aperture that is 

 finely corrected, and bringing it forwards till it gives the re- 

 flection of a bright point from a globule of quicksilver, sharp 

 and free from mist, when the distance can be taken between 

 the glass and the object. 



* * The longer focus is the place at which to ascertain the 

 utmost aperture that may be given to the glass, and where, in 

 the absence of spherical error, its exact state of correction as 

 to color is seen most distinctly. 



" The correction of the chromatic aberration, like that of the 

 spherical, tends to excess in the marginal rays; so that if a 



