for the Mirrors of Refiecting Telescopes. 111 
n—1 
n> 
hence by (5), s=2.n—1 r+anR-D+ >} (r+D)?.(r+n+1.D) 
(n—1.r+nR—D)?* ——— 20-1 Dy»? 
SS ae Se EN ies Pe r-—) x 
(2.0F1.R+ 71, -"**p)h 
n n 
(8). The thickness is neglected, as its intreduction would 
not sensibly alter either term of the expression for 2. 
(9). Let @ be the distance of the focus of emergent rays 
from the surface; then n=8; therefore da = — a’dz, and da= — a%éz, 
nearly. Let © and F denote the values of 2 and a, when the 
incident rays are parallel; then dF = — F?dZ, and 5F=-— F°8 8. 
(10). That the chromatic aberration in-a telescope may be 
destroyed, it is necessary that the images formed by rays of 
different colours after reflection from the small mirror be equally 
distant from that mirror. If now we suppose rays of all colours 
diverging from the place at which the second image is formed, 
to be incident on the small mirror, the rays of each colour after 
reflection will converge to the point in which an image is formed 
by rays of the same colour reflected from the great mirror. Let 
a be the distance of the first image from the small mirror, F 
the focal length of the great mirror, 4 the distance between the 
mirrors, 7 the distance of the second image from the small 
P 1 5s : : 
mirror, and = the radii of the unsilvered and silvered surfaces 
of the small mirror; since b=a+F we have 5a+édF=0. But by 
(7), - = 2.n—1.p+2np'—D, neglecting at present spherical aberra- 
tion; therefore da = — 2a° (p+p') dn, since by supposition D is the 
same for all colours: similarly })F=—2F? (r+R)én. Substituting 
