86 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
Iu the case of a dry system n Q = 1, and 
N x + N 2 + N 3 = L, + L 2 + L 3 = 0. 
b t =b 2 = + 1. 
A' = A = 0. 
And tlie reciprocal focal distance <£ comes from 
HI — I 7) — 1 
* = -4— («* - <w + “4 — - Q a)- 
“l "2 
In order to pass from a system of infinitely tliin lenses calculated as 
above to a system with finite thickness, one must calculate a paraxial ray 
passing through selected thicknesses and d 2 with ascertained radii, 
and form the expressions 
Whence 
and cr , o-', Q are taken from the calculation of the paraxial ray. 
T, the expression of the chromatic aberration and 8 2 are no longer 
zero, whilst o-' 3 becomes considerably greater than the cr' 3 belonging to 
the general calculation. Now with the values Q and o- taken from the 
through-calculation, the following equations are built up : 
= ( — )(l + 2d 1 or 2 -f-2d 2 o- 3 ). 
SQi \% V 
Sdr'g 
8 Q 2 
(-- -Vl+2d 2 a 3 ). 
\n l n 2 ) x 
8^ = I _ L 
8 Q 3 n 2 
~ = N, - 2 [d, Q 2 N 2 + (d, + d 2 ) Q 3 HJ (I - I). 
^ = n 2 (1-2^ 2 )-^ 2 Q 3 N 3 (1-1). 
^ = N 3 (X-2d J <T 2 -2d 2 <r 3 ). 
