196 
MR. LISTER ON THE IMPROVEMENT OF 
which was ascertained after cementing the lenses ; I laid down a figure of the 
flint lens inverted, and by means of the angles of the other diagram projected a 
plano-convex z to be joined to its flat side. The new glass proved as achro- 
matic as the original, though the single radius of the plano-convex was more 
than one-third longer than corresponded with the curves of the former double 
convex lens : the two aplanatic foci showed themselves as before ; the longer, 
however, not in the place indicated by the ray drawn : but at a point F, 
about two-thirds more distant from the glass, and from which both surfaces 
of the flint lens bent the pencil outwards ; the shorter focus F" too becoming 
about half the length of the other, and the angle of incidence of its rays not 
equalling that of their emergence. 
The longer aplanatic focus may be found when one of the plano-convex 
object-glasses is placed in a microscope, by shortening the tube if the glass 
shows over-correction, if under-correction by lengthening it, or by bringing the 
rays together should they be parallel or divergent, by a very small good tele- 
scope. The shorter focus is got at by sliding the glass before another of suffi- 
cient length and large aperture that is finely corrected, and bringing it forwards 
till it gives the reflexion 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 colour 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 glass, which is achromatic with a 
moderate aperture, has its cell opened wider, the circle of rays thus added to 
the pencil will be rather over-corrected as to colour. 
The same tendency to over-correction is produced, if, without varying the 
aperture, the divergence of the incident rays is much augmented ; as in an 
object-glass placed in front of another : but, generally, in this position a part 
only of its aperture comes into use ; so that the two properties mentioned 
neutralize each other, and its chromatic state remains unaltered. If, for ex- 
ample, the outstanding colours were observed at the longer focus to be green 
and claret, which show that the nearest practicable approach is made to the 
