SPHERICAL ABERRATION FOR A SYMMETRICAL OPTICAL SYSTEM. 
61 
The suffixes here have a different meaning to that which has been previously 
ascribed to them, but no confusion is likely to arise on this account. 
The values are as follows, f denoting the focal length of the lens, /, f A the focal 
lengths of the surfaces, so that 
0 27 (ft— l) 
1 
A u = 
Ai = 
A 2 = 
fi = ri/{n-l), f\ = -rj(n- 1 ) 
. fi±p r + (»±mr _ 2n{1+n+ („+1 _ <£ 
J i /i / J i J 
2n a (n—i) 3 L - + 4 + 1 > s ^ - 4,i ( 1 + +«“) / + '‘ 2 ( ,l + 1 ) s 
W-ir [' TzT" +6 ( " +1 r b, +2n (1+ " + ” 2)/ (i + 7, 
A 3 = Ai with fi and f 3 interchanged 
A 4 - Ag ,, ,, ,, 
1 
4ft 3 (n—l) 2 
— ( 4 + ^) + 2 (n 2 —n+l) ^ + n(n— l) 2 7— ft 2 (n 2 —n + 1) 
/1 A 73/ J 1 /1 
Bi = 
B 2 = 
• /I 1 
'/, + /) +6 ( " ,+ 1 ) j&i +B( "“ w A 7 /J 
(»-!)’ t“ A (/. + /J +6 (n * + " +1 3m(k +1 )2 ii + 3 ” 2 (n ’"“ +1) . 
B 3 = a 4 
C rt — B 0 —f— 4 A 1 
Ci — Bi—^A 2 
C 2 = B 2 + f—f A 3 
K 
8(ft— l) 4 
_ (vr —n+ l) (/ +/// ” . (ft + l)“ ri J ft ( n 2 —n+ l),/ 3 l 
• //■ »* 7 I/,* /, s J 
ft 
/• K+3» s +» + 2(»‘+y+i)/. |+£ | ^ + (» +1 )>(» s -«+i) A 
n 
l /i 3 
/ 1 * 
-/(ft 2 -ft+l)j| 
ft' 
7b 
E 1 = 
8 (ft-l) 4 
_ 6 (ft 3 -n+l) ( fi±£)f 5 (ft + I)“ ,m f 5ft 6 (ft 3 -ft+ l ) nf 3 ] 
/3/1 5 7 I/3/1 3 /T /1 5 J 
ft 
/ 3 (4(ft 3 + 3ft 2 + n) (n + 1 ) 4 + 8 {n i + n 2 + 1) , y f A } 
”7 1J} + ft + Ui+1) ft J 
, f 2 f 67,4(w+l) 2 (7+l) , 2(n-l) 2 {n 2 + n+l)f 3 \ 
71/7 / 2 / 3 J 
/ [ 2ft (27 + n + 2 ) | 7+ I) 4 / 1 + // 3 ^ +1 )2 
n 
VOL. CCXXI.-A. 
/ 3 1 / 
K 
