[ ] 
improving and perfedling Catadioptrical Telefcopes, 
by making the Speculums of Glafs, inftead of Metal 2 
in the following Manner : 
Fig. i; 
Fn 
A 
E 
BU 
B 
C 
Let the Figure ^BC^DE F reprefent the Section of 
a concavo-convex Speculum, whofe two Surfaces 
are Segments of unequal Spheres 5 call the Radius of 
the Sphere, to which the concave Side is ground, 
a 5 and the Radius of the convex Surface, which 
muft be quickfilver’d over, ej let BE be the Axis 
of the Speculum, or a Line perpendicular to both 
the Surfaces; and therein let P be the principal 
Focus, or Point where parallel Rays of the moft 
refrangible Kind are collefted, by this Speculum j 
and ^the Focus, or Point of Concourfe, of fuch 
Rays as are leaft refrangible ; to wit, after they 
have fuffer’d two Refraftions, at entering into, and 
pairing out of, the concave Surface E)EF^ and 
alfo one Reflexion from the convex Surface ABC: 
If the Radius of Concavity be greater than the Ra- 
dius of Convexity, as we will in the firfl; Place fup- 
pofe, then P will fall nearer the Vertex of the Spe- 
culum than the Point and the Interval will 
be the greateft Aberration, or Error, occafioned by 
the Separation, or unequal Refradion, of the greateft 
and leaft refrangible Rays, after their Emergence 
from 
