ual 
160 Dr Searle, Experiments with a prism of small angle 
the prism through a small angle about a horizontal axis per- 
pendicular to the plane of the three spheres. 
The marked face of the prism is placed against the spheres’ 
and the two goniometer readings corresponding to reflexion at the 
front face and to reflexion at the back face are taken. The angle 
between the two positions of the arm is the angle @ in Fig. 3. 
Keeping the marked face still in contact with the spheres, the 
prism is turned through 180° about a horizontal axis perpendicular 
to the plane of the spheres and the observations are repeated, 
thus furnishing a second value of @; care must, of course, be taken 
not to move the clamp. The angle between the two positions of | 
the arm corresponding to reflexion at the front face is equal to 20. 
The goniometer readings are reduced to radians by aid of the 
Table where necessary. The observations may be repeated with 
-the unmarked face of the prism in contact with the spheres; to 
ensure quite independent readings, the goniometer stand may be 
slightly moved from its first position. 
The refractive index is then found by the formula 
je =Sin'6/sin- 2, 02 ce eee eee (2) 
§ 4. Practical example. The following observations were 
made by G. F. C. Searle. 
Distance of goniometer scale from pivot = 40°00 cm. 
The central reading of the goniometer is 10°00 cm. 
The letters #’ and B indicate readings corresponding to reflexion at the 
front and back faces of the prism respectively. 
(i) Marked face in contact with spheres: 
Mark to right. Mark to left. 
F,=730cem. 6,=1159 cm. f,=12°92 cm. 6,=8°62 cm. 
(ii) Unmarked face in contact with spheres: 
Mark to right. Mark to left. 
He — (0S cman o.—Nileso ent: F,=12-70iem. 2, —8 em: 
The deviation of the arm from its central position for F, is — 2°70 cm. 
and the angle is --tan~!(2°70/40) or —tan—!0-06750. By the Table the 
angle is — (0°06750—0-00010) or —0:06740 radians. In the same way F, 
corresponds to a deviation of 007287 radians, and hence 
21=0-06740 + 007287 =0'14027 radians. 
Similarly we find from /, and B,, 
6=0:10713, 
and from /, and B,, 6=0°10736, 
the mean being 0°10725 radians. 
The readings /',, B; and #,, By, give the values 
21=0714027, 6=0:10725 radians. 
The mean values are 
4=0-07014 radians=4° 11, @=0°10725 radians=6° 8-7. 
Hence, by (2), 
p=sin 6/sin 7= 17528. 
