B 
flare spots in photography. 217 
calculate the six secondary focal lengths from the quantities 
M, N, M,, N, and W by §11, we shall find that one of the 
observed values of the six secondary focal lengths will agree with 
any selected one of the calculated values, and so we can decide 
which two surfaces acted as reflectors in each case. 
813. Practical example. The following is a record of 
measurements made by G. F. C. Searle, using two meniscus 
spectacle lenses of nominal powers of one dioptre and of one-half 
dioptre. Barlow’s tables of reciprocals were used; the powers are 
given to the nearest 0:00001 cm... 
The primary power of each lens was found from the distances of 
an object and its image from the lens. 
The primary power of AX B; w=767°6 cm., v=111°36 cm. 
Hence 
M=1/u + 1/v = 0:001303 + 0:008980 = 0:01028 cm.~' = 1-028 dioptre. 
For primary power of CLD; w=633°5 cm., v= 306-7 cm. 
Hence 
N =1/u+1/v = 0-001579 + 0:003261 = 0:00484 cm.* = 0-484 dioptre. 
The secondary power of each lens was found on the optical bench 
by the minimum distance method. 
For secondary power of AX 4; minimum distance = 4m, = 56:48 cm. 
Hence M,=1/m,=1/14:12 = 0-07082 cm.-1. 
For secondary power of CLD; minimum distance = 4n,. = 120°58 em. 
Hence WV, =1/n, =1/30-145 =0-03317 em.-1. 
Radius 6 of lens AK B = — 46°44 cm. 
Radius ¢ of lens CLD = — 35°18 cm. 
The signs are negative since the surfaces are concave. 
Hence W=—2 (1/6 + 1/c) =2 (0021533 + 0028425) = 0-:09992 cm.~?. 
By § 11, the six secondary powers of the system are given by 
the following equations: 
Poo = M +N, = 001028 + 0:03317 = 004345 em.“4. 
Pyp=M +N, + W=0-01028 + 0:03317 + 0:09992 =0:14337 cm.-1. 
F,,4=M,+ N,+ W =0-07082 + 003317 + 0:09992 =0°-20391 cm.-1. 
Fo, =M +N + W=0-01028 + 0:00484 + 0:09992 = 0-11504 cm.7. 
Po, =M,+N + W=0-07082 + 0-00484 + 0:09992 =0°17558 cm. 
F,,=M,+N = 0:07082 + 0-00484 = 007506 aii. 
The following table gives the minimum distance between the cross- 
wires and each of the secondary images. The corresponding focal 
length, f,, is one-quarter of this distance and the corresponding power 
Ff, is 1/f,. The power calculated from M, NV, M,, N., W is entered in 
