FIRST ORDINARY MEETING. 11 
From these relations we find 
w d',d', ee Sis fe 
% share dyad, 
Hence if w = w,, each of the nth equalities becomes equal to 1, 
and the points R,, R,, the principal points of the system. 
Piast w= 2, dd, —f, fj, and d.d,.—/',f . 
Also, since AR, =f’, — d’,, BR, =f, — d,, we have 
d+d,=f,+h—e 
-and the values of the principal focal lengths become 
fe 
1 2 Z Ji th—e 
11. Now let R, R’ be the principal points, F, F’ the principal foci 
-of a thick lens ; so that we have 
TIPS ty nh, AS fae GE) 
ie 
Fig 6, in which X is the point (f,/’), exhibits the method of 
finding the conjugate of a given point. 
12. Conjugate points will be nodal points N, N’ when on the x 
axis we have NN’ = RR’. This will evidently happen when (Fig. 
6) the line through X makes FN = FX. RN (=/f' —/f) on the x 
axis will then be equal to R’N’ on the y axis. 
lf distances are measured from the nodal points N, N’, coeation 
f 
(4) becomes = + = 1, in which /’, p are measured from N, and 
f, p’ from N’ ; a ae conjugate points are determined as in Fig. 7. 
13. These mete make the existence of self-conjugate points 
‘manifest. Thus in Fig. 7, if S is such a point, we have 
BS, hs —/7 , ES -— WS — FE — 2h. 
Hence FS, F’S are the roots of s* — 2hs + ff’ = 0, and the self- 
conjugate points are at equal distances from F, F’. 
14. Fig. 8 exhibits the construction when one of the self: conjugate 
points is taken as origin. 
From the similar triangles PP’P, S’P’X, and also PSP, FSF, we 
obtain the relations 
