250 
Mr. Barlow on the rules and principles for 
We have thus the focal length of the plate and flint lens. 
Assume now for the ratio of tlie radius of the inside surface 
to the outside surface of the flint i : lo, that is, 
Let r" r"' : : 1 : lo or q' — lo then 
r" — f d — ■ = iL— ^ = 27-19 concave, 
r"'= f d [i-\-q')=z^v9, X-60 X 11= 271-9 concave. 
Therefore to find the values of the letters employed in 
formula (14.) for the aberration, we have, r" ■=— 27*19 r' = 
— 271 * 45 , 
, fa' + I)/" q' 
q = 10, c' = ^ ^ 
a'/" 
C — 
r 
80 
a 4 1 
27-19 
•6 
I -6 
= 4*03 
~ — 2-94 
= *375. 
These values substituted in the expression 
(C 4 q'Y C 4 (<<' 4 2) q 
{a c — q')^ ^ c (a'c' 4 «' + i) 
c' + I )* (c + 2 — b.') q' 
(/.c'41)^ 
give in numbers 
49-84 
a d 
(!?’ + «) 
+ 
49-84 23-06 
•38-3 ^ —47-45 I ^ -515 X -66 _ 
25 30 5 ^'iS ( " 
2 283 ^ 403 
73 =p 
If now we were to employ the equations given for deter¬ 
mining the value of q, this value of p must be substituted 
in the equation answering to a = -515; but making use of 
the table, we must find the nearest value to p in the first 
column above and below 1*73, and thence the correspond¬ 
ing value of q. Here, since the values of q answering 10 
pz= 1-70, and 1-75, are the same, for a = -510, and a~ -520, 
we may infer they are the same for = *515 ; hence, 
