218 Dr Searle, Experiments illustrating 
the last column but one and the last column shows which two sur faces 
acted as reflectors. 
Minimum Focal Observed Calculated 
distance length power power Reflectors 
em. cm. em.—! em. 
19°46 ~ 4:865 0:20555 0:20391 DA 
22°82 5705 0-:17528 0:17558 CA 
2D 6:978 0:14331 0:14337 DB 
34°76 8690 PIL 0 // 0-11504 CB 
53°22 13°305 0:07516 0:07566 BA 
91-86 BIE NSD 0:04354 0:04345 DC 
It will be seen that there is tair agreement between the observed 
and the calculated values of the secondary powers. 
§14. Secondary focal lengths for a system of n thin lenses 
in contact. The method of § 11 is easily extended to n thin 
lenses in contact. Let P (Fig. 6) be the object and Q a secondary 
image. let the lenses be A,K,B,, A,K,B,...A,K,B,. Let 
f4,--- Pn be the refractive andiees and i alt Bee) fs dae powers of the 
lenses. Let the radii of the surfaces of the lenses be ‘ay, 0; c/a One 
the radii being counted positive when the surfaces are convex as 
in Fig. 6. Let the distance of the edges K,... K,, from the axis 
be h. Let X, Y be points on PK,, QK, such that PX = PA,, 
OV = 057, Let the planes of the edges of the first and last lenses 
cut the axis in M,, M,; let PM, = u, “hn let QM, = v. 
Since F, = (w, — 1) 1/a, + 1/0,) and since A,B, = 4h?(1/a, + 1/6,), 
we have 
A, By = $h2F;/ (pa. — 1), 
and similarly for the other lenses. 
