122 Dr Searle, The determination of the focal 
readings is again found; let this be ». Then, since a/b=m/n, 
we have, by (7), 
—m+n- 
The distance p = AC is found just as in § 5. 
It is not necessary that the microscope should be provided with 
a sliding carriage, but, if this 1s the case, the difference of the scale 
readings of the carriage will give the distance x which is required 
in Gauss’s method. If a glass scale is used to provide the points 
A and K, it will have no effect upon the value of a, since it 
displaces both K and its image through equal distances parallel to 
the axis. 
§8. Practical ecample. The following results were obtained 
by G. F. C. Searle using a system formed by a double-convex lens 
placed in front of a plane mirror. 
The lens was 1°2 cm. thick and was placed at about 2°8 cm. from the 
plane mirror which was formed of a piece of glass about 03 em. thick, 
silvered on the back. The focal length of the lens was about 20 cm. The 
plane mirror was not of very good quality and thus very accurate readings 
were impossible. A glass scale was used to provide the points to be observed. 
In the table m and correspond to 1 mm. on the glass scale. 
Glass scale seen directly Image of glass scale 
Scale readings Seale readings 
for 7 mm. ee for 4mm. 4n 
10-4 71:2 60'8 135 | 69:0 555 
12-05 le a3-0 61-0 180) was 55°7 
18:8 796 60:8 204 | 761 55-7 
20°7 81-6 60-9 300 | 85-0 550 
Mean value of 7m=60°88. Mean value of 42=55:48,. 
Hence m=8°70, n=13°87. 
Distance of centne C from vertex A, 20°16, 20-06, 20: 06, 20°02 cm. 
Hence p=20°08 cm. 
__ 13°87 x 20:08 
Mead lop Oh j/= = 93-57 12°34 cm 
By (6), h=p — 2f=20-08 — 24:68= — 4-60 cm, 
Hence the system is equivalent to an ideal concave mirror of focal length 
12°34 cm. placed with its surface 4°60 cm. behind the front Saehoae of the 
optical system. 
