Mr Herschel 071 Achromatic Ohject-Glds'ses. '’ 5G5 
is concerned) rendered equally perfect in every part. Such re- 
finements must be regarded as merely visionary, correcting in-* 
conveniences which have never been felt in practice, and leaving 
unsatisfied other, more essential conditions. A much better con- 
struction was devised by Clairaut, in which the two internal sur- 
faces are worked to equal radii, the one convex, the other con- 
cave, so as to admit of the two glasses being cemented together, 
and thus avoid the loss of light, by reflection at two surfaces 
Clairaut, however, has employed in his computations indices of 
refraction (1.600 and 1.55) higher, especially the latter, than 
what are now easily met with ; and when the average values, 
those likely to occur most frequently, are employed, the con- 
struction becomes imaginary for the more dispersive kinds of 
glass ; and within the limits for which it is real, the radii change 
so rapidly, as to render it difficult to interpolate between their 
calculated values ; so that this construction loses much of its real 
advantage to the artist who is no algebraist. > 
In the construction proposed in my paper, the destruction of 
the spherical aberration is insured, not only for parallel rays, 
but also for those which diverge from objects placed at any mo- 
derate finite distance, so as to produce a telescope equally perfect 
for terrestrial and astronomical purposes. This is the condition ^ 
introduced to render the problem determinate; but the advan- 
tage afforded by it, would not alone be such as to induce us to 
adopt it, in preference to many others which might be devised, 
were it not that the radii resulting from it are such as to satisfy 
other and much more important practical conditions, which may 
be shortly stated as follows. 
The curvatures assigned in this construction to all the 
•surfaces are moderate ; more so, indeed, than in any other hi- 
therto proposed on true theoretical grounds, for an aplanatic 
object-glass. 
^dly^ In this construction, the curvatures of the two exterior 
surfaces of the compound lens, of given focal length, vary with- 
in extremely narrow limits, by any variation in either the refrac- 
* Should Dr Wollaston’s ingenious mode of centering glasses, by the reflected 
images, ever come into general use (of which, from its facility and neatness, there 
can be little doubt), this destruction of the interior reflections will, instead of an 
advantage, become a source of inconvenience. 
