determining the dispersive ratio of glass y &c. 259 
(c + q')* C + (a" + 2) q' 
(a'c —‘ c (a' c' + a' + i) 
{c'+ i)^ (c' + 2 — 6) g' 
(6c'+i)® c' 
gives in numbers 
( + '569 — 33 ' 54 ) X — -0851 = 2-805. 
This ansNvers to q = 3-064 ; and then 
r =z fa {q +i) = 19‘913 
r*z= fa Li-l—LL= 6-499 
These numbers agreeing so very exactly with Mr. Her- 
scHEL^s, was satisfactory; for although no doubt I believe 
could be entertained relative to either principle of computa¬ 
tion, yet it was highly pleasing to me to see so close an 
agreement in the results of two numerical processes founded 
on such widely different bases, 
24. In these numbers, however, we have an example of the 
inconvenience, (to which I have referred, p. 240), of rigidly 
enforcing a fourth condition ; for the concave of the flint 
being less deep than the corresponding plate convex radius, 
it was thought necessary to alter these numbers : this was 
done by changing r" z= 6-66 to r" = 6-58, and r' = 6-50 to 
r' = 6-61, which was the least alteration we could make in 
the contact surfaces to have the concave the deeper of the 
two; the other radii were necessarily altered to r == 19-0, 
and r'" = 32-5 ; so that our actual experimental radii were 
r = 19 0 7 r" = —- 6 58 ) 
r'= 6-6i3 r'"=-{- 32-5 3 
the focal length and dispersive ratio, that is, the ratio of the 
