98 Mr. SAMUEL HUNTER, 

Fig. 1. 
different dispersive powers an achromatic telescope could be 
formed. 
“This made me,” he writes, “ take reflexions into consideration, 
and finding them regular, so that the angle of reflexion of all 
sorts of rays was equal to their angle of incidence, I understood 
that by their mediation optick instruments might be brought to 
any degree of perfection imaginable, provided [1] a reflecting 
substance which would polish as finely as glass, and [2] reflect as 
much light as glass transmits, and [3] the art of communicating 
to ita parabolic figure be also attained.” Here Sir Isaac gives us 
the three requisites to a good reflecting telescope, but it is with 
the last alone we have to do at present. 
Let us first see why the figure must be parabolic. Suppose 
the rays A and A’, B and B’ fall on a segment of a sphere, A and 
A’ being more remote from the axis than B and B’, C being the 
centre of curvature, Sir Isaac found that the angle of inci- 
dence AAC was equal the angle of reflection DAC. So also the 
angle BBC=EBC. Hence parallel rays falling on a true 
spherical surface come to a focus at different points, accord- 
ing to their distance from the axis of curvature DC. Now 
if the curve at A could be flattened a little, as indicated by 
the dotted line, it is clear that the angle of incidence, AAC, 
could be made=the angle EAC and all the rays would come to a 
focus at the same point E. The curve of which that holds good 
is called a parabola. The difference between these two curves 
