12 PROCEEDINGS OF THE CANADIAN INSTITUTE, 
15. If F is the image of K, and K’ of F’, then on the a axis of 
Fig. 8 we have 
BK EP = tS. E'S a 
Hence 
2h 
Also, if T, T’ are conjugates such that FT = F’T’, then 
il DA lM Sly 
It thus appears that the middle point of FF’ also bisects the lines 
KK’, SS’, RN’, R'N, TT’ and (vide § 28) VV’. 
16. The method of § 6 may be applied as follows to a system 
of lenses. 
Let there be any number of lenses L,, L,,... whose principal 
foci are (F,, F’,), (F,, F’,) ..., and whose principal planes cut the 
common axis in (A, A’), (B, B’)... 
Let (Ry, R,), (R,, R,.)... be pairs of conjugate points such that 
RyF, = 6, RF’, = &,, R|F, = 6, ... In like manner let (P,, P;), 
(P,, P.), .. . be any other set of conjugate points such that R,P, = 
Po RP, = p's, - - 
Then (§ 7) 
Doe Be 
Po Pa 
ad 8 ae 
= -t |_| = 1, &e 3 
Tg ae 
from which by eliminating p, = — p’'), p» = — p»,... we get an 
equation of the form 
Peni we 
Pony: 
where f = R,F, /’, = R,,F’, F,F’ being the principal foci of the 
system. 
17. The principal foci F, F’ of a system of lenses may be deter- 
mined geometrically as in § 8. 
Thus, let there be two lenses L,, L,, whose principal foci are 
(F,, F’,), (F., F’.), and principal points (R,, R’,), (R,, R’,). Then 
(Fig. 9), since parallel rays on emergence come from F;, F, is the 
image of Fin L, Hence the line joining X, and F, on the y axis 
gives F on the @ axis. 
