length of a thick mirror 125 
lines on S in turn, the interval between successive lines being 
constant, and the scale reading of the arm is taken in each case. 
From these readings the mean distance, d cm., on the goniometer 
scale corresponding to s cm. on the glass scale is found. The 
distance, / cm., from the centre of the pivot of the goniometer to 
ithe edge of the goniometer scale is also measured. Then, if ¢ be 
the angle corresponding to s cm. on the glass scale, 6 = d/l radians, 
for small angles. Then by (9), since 6 = 4, 
Pf B90 SSD SSCs voccreccogdosranvavee (10) 
The thickness of the scale S has no influence on the result. 
The rays emerging from the mirror system pass through S, but 
their directions are unchanged by the passage. 
§ 10. Practicai example. The following results were obtained 
by G. F. C. Searle using the same mirror system as was used by 
Mr Heath in § 6. 
Length of goniometer arm, i.e. distance from centre of pivot to edge of 
scale =/= 40-00 cm. 
When the glass scale was set in the focal plane, with its divided face 
turned towards the mirror system, the following readings were obtained : 
| | | 
(eRcadine: ot: | Reading of | Readtne ae | Reading of | Change of goniometer 
ieee Bek goniometer | laa eels goniometer | reading for 1 cm. on 
8 seale leet scale glass scale 
| | 
4:0 cm. 6°58 cm. | 5:0 cm. 10°59 cm. 4-01 
45 | 859 } 5) 12°59 4:00 | 
5:0 _ 10-59 | 6:0 14:60 | 4-01 
Mean 4:007 cm. 
Two other sets of observations, each with a fresh setting of the glass 
scale, gave the mean values 4:010 and 4030. Taking the general mean, 
d=4:016 cm. 
Hence, by (10), since s=1, 
f=sl/d=40/4:016=9:96 cm. 
Distance A/F’ of glass scale from vertex A=f+h=9°59 cm. 
Hence h=959 —9:96= — 0°37 cm. 
The values found by Mr Heath were f=10-07, h= —0°47 cm. 
§ 11. A special system. An interesting system may be formed 
by a convex lens and a plane mirror, the distance between the lens 
and mirror being greater than the focal length of the lens; the 
distance may be conveniently about twice the focal length. With 
this system the two real self-conjugate points, viz. the “centre” and 
9—5 
