265 
determining the dispersive ratio of glass , &c. 
lens, consider these rays as converging towards the back 
surface to a focus /; and from this surface a part of them 
will be reflected to a focus/' ; which will be expressed by 
r, __ fr' 
J 2 f — r' 
This, by substituting for /, its preceding value, and making 
y 
— — becomes 
I + X 
f 
r r 
z r ■ 
2 r — - y r 
x -f i 
These rays will be refracted at the first surface to a focus 
which we suppose to have been measured. Let this mea- 
sured distance be m ; then by known principles for expressing 
the refraction at the surface of a rarer medium, we have 
— y 
m 
(i — y)r (i +y)/' ‘ 
Or substituting for /', we obtain 
( 1 — — y ) 
2 ( l +y)— 
■m. 
And of course by simply inverting the lens, or changing 
r to r', we have ( calling the other measured focus n ) 
(I —y)r 
— = n. 
2 (i + y ~~j 
r 
Let tp be the measured solar focus by refraction ; then 
l x being the index, we have 
x (~r + “?"•) ~ T" 
From which three equations, and the known relation be- 
tween y and x, the three required quantities x , r, and r' may 
be obtained. 
MDCCCXXVII. 
M m 
