106 Mr. Arry on the use of Silvered Glass 
It appears surprising that no attempt has been made to remove 
the inconveniences attached to the use of glass reflectors. It 
occurred to me some time since that in Gregory’s or Cassegrain’s 
telescope, supposing the mirrors constructed of silvered lenses the 
radii of whose surfaces were different, the chromatic aberration 
of one mirror might be corrected by that of the other. For example, 
suppose the great mirror to be a meniscus silvered on its convex 
side: since the convergence of the rays is caused partly by the 
refraction of the meniscus through which they pass twice, and 
partly by the reflection at the silvered surface, the violet rays 
will converge sooner than the red, but the aberration will not 
be so great as if the convergence were occasioned entirely by 
refraction. Now if the small mirror be so constructed that its 
chromatic aberration may be equal to that of the great mirror 
but in the opposite direction, that is, so that the focal length for 
violet rays may be greater than that for red rays, as much as the 
focal length of the great mirror for red rays is greater than that 
for violet rays, the rays of all colours will after the second re- 
flection converge to the same distance from the small mirror, 
and will therefore form an image free from chromatic aberration. 
This may be effected by using for the small mirror a concayo- 
convex lens, silvered on its convex side. For since the refraction 
tends to make the rays diverge, and the reflection to make them 
converge, the convergence produced, being the excess of the latter 
above the former, is greater for red than for violet rays, and con- 
sequently the focal length is greater for violet than for red rays. 
In this manner by a proper adjustment of the surfaces, the rays 
of all colours m each pencil may always be made to converge 
and form an image at the same distance from the small mirror. 
It is yet desirable to correct if possible the spherical aberra- 
tion by the use of spherical surfaces only. The method by which 
the chromatic aberration is corrected naturally suggested a mode 
