164 Dr Searle, Experiments with a prism of small angle 
where J is the length from the centre of the pivot to the edge of 
the goniometer scale, and the angles are expressed in radians. 
Equations (12) and (13) then give w andi. For water 
M, = 1°3334 — 0:00009 (¢ — 15), 
where ¢ is the centigrade temperature. For temperatures near 
15°C. it will suffice to take w,=4 and »—-1=H. 
The method may be employed to find the refractive index of 
a liquid such as a salt solution. If this has the refractive index 
#», and if 2D, be the change of deviation when the prism is turned | 
round in the solution, which is contained in the tank, then, by (13), 
D = ID; = (Ms ah Da, 
and thus fs = 14D = D3) eee (14) 
If the auto-collimating device of the goniometer is used, the | 
collimator may be dispensed with. A plane mirror of good quality 
is placed with its face approximately perpendicular to the axis of 
the goniometer arm when the latter is in its central position. The | 
goniometer wire is then made to coincide with its own image in _ 
each case. | 
§7. Practical example. The following observations were 
made, using the same prism as in § 4. The auto-collimating 
method was used. The value of 7 was 40 cm. 
Observations for D, Prism in air. 
Edge towards left. Readings 11-37, 11:37, 11:37. Mean 11:370cm. 
Edge towards right. Readings 8-41, 8:40, 8-40. Mean 8-403 cm. 
Hence D=$ (11°370 — 8:403)/40=2'967/80=0-03709 radians. 
Observations for D,. Prism in water at 20°C; p,=4. 
Edge towards left. Readings 10°39, 10°38, 10°38. Mean 10383 cm. 
Edge towards right. Readings 9°30, 9-30, 9:30. Mean 9-300 cm. 
Hence D,=$ (10°383 — 9°300)/40= 1:083/80=0-01354 radians. 
By (18), we have for the angle of the prism 
j-T Ws (003709 — 0:01354)=0-07065 radians=4° 9/9, 
[Ll 
By (12), we have for the refractive index of the prism 
_4D-—D, _ 4x 0:03709/3 — 001354 
DZD IN; 03 709-0 01e54 
Observations for D,. Prism in saturated solution of sodium chloride. 
Edge towards left. Readings 10-28, 10:28, 10:27. Mean 10-277 cm. 
Edge towards right. Readings 9:44, 9:45, 9:45. Mean 9:447 cm. 
Hence D,=$ (10:277 — 9:447)/40=0:830/80=0:01038 radians. 
By (14), we have for the refractive index of the salt solution 
Hg=1-+(D— Dz)/i=1 +0-02671/0:07065 =1°378. 
§ 8. Determination of the angle and refractive index of a 
prism by primary and secondary images. When a ray which 
enters a prism ABC by the face AB meets the face AC, the 
greater part of the light is refracted out through that face, but 
some is reflected back into the prism. If this reflected light 
=1°525. 
