170 Dr Searle, Experiments with a prism of small angle 
6 is positive, the point of intersection of QR and XS is on the 
same side of RS as A is, and this is true whatever the angle of 
incidence of QR at R. If BAC is exactly t7, QR and SX are 
Fig. 13. 
parallel and then PQ and XY are parallel also. When, however, 
QR and SX are not parallel, we must take account of the refrac- 
tions at Q and X. Let MQM’, NXWN’ be the normals at Q and X. 
Then sin PQM=ysin RQM’ and sin YXN=ps1n SXN’, where 
1s the refractive index of the prism. Now it is easy to place the 
prism so that the ray PQ which falls upon it from the auto- 
Scions goniometer is nearly normal to BC, and then, if BAC 
is nearly $7, the ray XY will also be nearly normal to BC. We 
may then use the angles instead of their snes and then 
PQM =pRQM’ and YXN=pSXN’, 
and thus the angle between PQ and YX is pw times the angle 
between QR and SX, we. it is 240. The angle between PQ and 
YX is measured by the goniometer by the method of §§ 10, 11 in 
exactly the same way as for the double mirror, If this angle be w 
radians, then y= 26, and the error in the angle BAC is W/2u 
radians. The method indicated in Fig. 12 is used to decide 
whether BAC is greater or less than a right angle. The refractive 
index of the prism must be found by an ordinary spectrometer. 
§ 14. Practical example. The following results were obtained 
with a prism whose angles were nearly 90°, 45°, 45°. The same 
goniometer was used as in § 12. 
The refractive index of the prism was measured by a spectrometer. 
Using one of the smaller angles, the angle (7) was found to be 44° 59’ and the 
minimum deviation (D) was 25° 32’, Hence 
_ sin 5 3(D+7) _ sin 35° 15"5 
sin $7 “sin 22° 29'°5 
The readings on the glass scale of the images due to the prism were 7°70 
and 7°88 cm.; half the difference is 0:09 cm. ‘The value of > is 
0-09/f=0-09/35-09 = 0:00256 radians. 
When the burner was placed so as to illuminate the face AB and not the face 
AC, the surviving image U (Fig. 12) was to the left of W, z.e. on the opposite 
side to the burner. The angle of the prism is therefore greater than a right 
angle. Hence, if A be the angle BAC, 
A=hrt+/2n=1 01 +0:00256/3-018=3 m +0:00085 radians 
=O" 29). 
= 1509) 
