ACHROMATIC COMPOUND MICROSCOPES. 
197 
union of the spectrum, they usually continue nearly the same for the whole 
space between the foci, and for some distance beyond them either way. 
The places of these two foci and their proportions to each other, depend on 
a variety of circumstances. In several object-glasses that I have had made for 
trial, — plano-convex, with their inner surfaces cemented, their diameters the 
radius of the flint lens, and their colour pretty well corrected, — those composed 
of dense flint and light plate have had the rays from the longer focus emer- 
ging nearly parallel ; and this focus has been not quite three times the distance 
of the shorter from the glass : with English flint the rays have had more con- 
vergence, and the shorter focus has borne a rather less proportion to the longer. 
If the inner surfaces are not cemented, a striking effect is produced by mi- 
nute differences in their curves. It may give some idea of this, that in a glass 
of which almost the whole disk was covered with colour from contact of the 
lenses, the addition of a film of varnish so thin that this colour was not de- 
stroyed by it, caused a sensible change in the spherical correction. 
I have found that whatever extended the longer aplanatic focus, and in- 
creased the convergence of its rays, diminished the relative length of the 
shorter. Thus by turning to the concave lens the flatter instead of the deeper 
side of a convex lens, whose radii were to each other as 31 to 35, the pencil of 
the longer aplanatic focus, from being greatly divergent, was brought to con- 
verge at a very small distance behind the glass ; and the length of the shorter 
focus which had been one-half that of the longer, became but one-sixth of it. 
The direction of the aplanatic pencils appears to be scarcely affected by dif- 
ferences in the thickness of glasses, if their state as to colour is the same. 
One other property of the double object-glass remains to be mentioned ; 
which is, that when the longer aplanatic focus is used, the marginal rays of 
a pencil not coincident with the axis of the glass are distorted, so that a coma 
is thrown outwards ; while the contrary effect of a coma directed towards the 
centre of the field is produced by the rays from the shorter focus. These 
peculiarities of the coma seem inseparable attendants on the two foci, and are 
as conspicuous in the achromatic meniscus, as in the plano-convex object- 
glass. 
Of several purposes to which the particulars just given seem applicable, I 
must at present confine myself to the most obvious one. They furnish the 
