for the Mirrors of Reflecting Telescopes. 107 
of correcting the spherical aberration also: namely, by making 
the spherical aberration of one mirror equal and opposite to that 
of the other. From the investigation it appears that the determi- 
nation of the radii of the surfaces proper for this purpose depends 
on the solution of a cubic equation, and therefore the correction of 
the spherical aberration is always possible. This will enable us to 
employ so large an aperture that the objection founded on the 
loss of light will be entirely removed. 
In the construction of the telescope it is necessary to attend 
to another consideration, the nature of which may be thus explained. 
The apparent distance of an object seen through a telescope from 
the center of the field of view, depends on the angle made by 
the axis of the pencil of rays, when it enters the eye, with the 
axis of the telescope. Now when the axis of the pencil which 
is reflected from the great mirror is incident on the small mirror, 
the refraction of the concavo-convex lens, which forms the small 
mirror in the Gregorian construction, will disperse the axes of 
the differently coloured pencils: the axis of the red pencil will 
meet the first eye-glass at a greater distance from the axis of the 
telescope than that of the violet pencil. The refraction of the 
first eye-glass would make these axes intersect at a distance 
greater than its focal length. If then no other eye-glass were 
interposed, the axes of red and violet pencils would enter the 
eye in different directions, and the image formed by the red rays 
would appear more distant from the center of the field of view, 
than the image formed by the violet rays: that is, objects near 
the edge of the field of view would be coloured. This will be 
removed by placing a concave lens near the eye, which will cause 
the axes of pencils of all colours to enter the eye parallel to each 
other. By similar reasoning a combination of eye-glasses may 
always be found, which will produce an image perfectly free 
from colour. 
02 
