158 Dr Searle, Experiments with a prism of small angle 
r 
tan 6 @ tan é |} Cc tan 6» c 
0:01 000000 0:10 0:00033 0-19 0:00224 
0:02 0-00000 O-ll | 0°00044 0-20 0:00260 
0:03 0:00001 0°12 0:00057 0°21 0:00301 
0:04 000002 0°13 000072 0:22 0:00345 . 
0:05 000004 0°14 000090 0:23 0°00393 
0°06 0:00007 0°15 0:00111 0°24 0:00446 
0:07 0:00011 0:16 0:00134 0°25 0:00502 
0:08 0:00017 0°17 0:00161 
0:09 0:00024 0-18 000191 
§ 3. Measurement of the angle and the refractive index of 
a prism by the auto-collimating goniometer. Let ABC (Fig. 3) 
be a section of the prism by a principal plane and let the angle 
A B 
Fig. 4. 
BAC of the prism be 7 radians. Let P be a point on the face AC 
and let PK be perpendicular to the face AB. Let the ray KP 
on passing out of the glass into the air be refracted along PQ, 
making an angle @ with the normal PN. Then, since PK makes 
an angle 7 with the normal, we have, if w be the refractive index 
of the prism, 
sin @= mwsin2. 
The two directions PN and PQ are readily identified by 
optical means, for PN is the direction of a parallel beam of rays 
which returns along its own path after reflexion at AO, and PQ 
is the direction of a parallel beam which returns along its own 
path after two refractions at AC and one reflexion at AB. 
The angle ¢ of the prisin is easily found. For, if the prism be 
turned through two right angles about an axis perpendicular to 
the plane of the face AB, so that the section of the prism comes 
into the position shown in Fig. 4, the normal to the face AC 
