110 Mr. Arry on the use of Silvered Glass 
r+D_ a@ (r+D)’.(n—1 r+n’—1D) 
n 2 n° 
= Date as 
and 2 =2—4y—— 4 2 2 (rp Dy. (rtm FID). 
: 1 : 
(4). 2”. For the reflection ; 2 be the distance of the focus 
after reflection from the reflecting surface, measured in the same 
direction ; r the radius of that surface; then in the formula just 
found making = —1, putting —R for r (since the rays are incident 
on the concave surface) and —2 for D, we find 
2 2 
y=—-2R-2 + >.2(R+2)*.(—R)= ~2R-2->.2R.(R+2). 
(5). 3”. For refraction at emergence; let : be the distance 
of the focus of emergent rays, measured in the opposite direction ; 
1 
in the same formula put B for n,-—r for r, y for D; 
1 
ol = — 
=e (y-r).(-r+2 + 1 -y) 
rod, oe 
n n° 
——_—_— a: — ——— 
=n-1.r—ny—>-.n.n—1 (y-r)y.(n+1.y—nr). 
(6). From (3) R+2 approximately = “—t r+R— = 
n—1 D 
n 
r+ — 
n 
therefore by (4), 7 Sy Ey ia 
{2 (r+ DY. (+m F1 D)F2R. (ee 
(7). From (6), y-r approximately = —2R - =" _ 
2n?—1 n+1 
+ D: 
n n 
7 
n+1.y-nr=— 2.n+1.R- 
