determining the dispersive ratio of glass, ^c. 265 
lens, consider these rays as converging towards the back 
surface to a focus f ; and from this surface a part of them 
will be reflected to a focus/'; which will be expressed by 
J 2 f — r' ■ 
y 
This, by substituting for /, its preceding value, and making 
= -11— becomes 
I + X 
/' = 
r r 
r r 
2 r- 
X + i 
r' 
z r — y r' 
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 r 
1 
m 
■ (1 —yg (I +3')/' * 
Or substituting for /', we obtain 
(I “3/) »•' 
7-= W. 
2 (* +3') — 
r 
And of course by simply inverting the lens, or changing 
r to r', we have (calling the other measured focus n) 
(I —y) r 
z (i + y- 
n. 
Let (p be the measured solar focus by refraction; then 
1 4- being the index, we have 
(t“+ ~ 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 
