364 Mr Herschel on Achromatic Object-Glasses: 
adjustment of the foci; and to go beyond this point, with the 
ordinary materials, seems hopeless. I would recommend, then, 
to the optician who has been fortunate enough to procure fine 
specimens of glass, on the working of which he thinks it worth 
while to bestow much pains (especially if he should have, enough 
for several object-glasses), to determine the ratio of the disper- 
sive powers of his flint and crown glasses, by a direct experi- 
ment on small portions of his materials, working them into a 
small object-glass, having the ratio of the focal lengths of its 
component lenses, as nearly as he can guess, in the proportion of 
their dispersions, but leaving rather a preponderance on the side 
of the thrown or convex lens, and then by degrees reducing tlie 
curvature of one of the surfaces of this, till he obtains the near- 
est possible approach to perfect achromaticity, i. e. till the purple 
and green fringes surrounding a white object on a black ground^ 
appear in it as above described, when thrown one way or the 
other out of focus (using a pretty strong magnifier). Let him 
then determine accurately, by eoeperiment, the focal length of 
each of his two lenses, and -dividing the one by the other, he 
will obtain a dispersive ratio (ratio of the dispersive powers), on 
■M'hich he may calculate with perfect security in his future ope- 
rations. If he know the exact radii of his tools, he may at the 
same time determine the refracting powers of the media. 
These data once obtained, we are prepared to determine from 
theory the radii of the several surfaces which,^ in a telescope of 
given focal length, shall destroy that imperfection which arises 
from the spherical figure. This problem is well known to be 
of the kind called indeterminate, or admitting an infinite variety 
of solutions. In consequence, an unlimited variety of combina- 
tions of lenses, free from spherical aberration, may be discover- 
ed ; and to fix our choice among them, is a matter of consider- 
able delicacy, as well as importance. Various constructions have 
been proposed by different writers. Thus, D’Alembert has 
given one, in which he destroys the spherical aberration, not 
merely for rays of mean refrangibility, but for those of all co- 
lours ; but this, however refined in theory, is quite useless in 
practice, as is also another construction investigated by the same 
author, in which the aberration of rays diverging from a point 
vof the axis is annihilated, and the field (so far as the object-glass 
