Dr Searle, Experiments with a prism of small angle 157 
plane mirror, those rays which fall normally upon the mirror will 
retrace their paths, and, after passing a second time through the 
lens, will come to a focus at the point in the focal plane from 
which they started. Other points in the focal plane will have 
Fig, 2. 
imverted images in that plane and thus an inverted image of the 
slit and wire will be seen. By properly adjusting the mirror about 
a horizontal axis, the lower edge of the image of the slit may be 
made to lie on the upper edge of the bar HF (Fig. 2), and then, 
by adjusting the arm of the goniometer or by turning the mirror 
about a vertical axis, the image of the wire may be made to 
coincide with the wire itself. 
The goniometer may, conveniently, be bolted to a table carried 
by a Compound Laboratory Stand (W.G. Pye and Co.); its height 
above the table is then adjustable. 
The goniometer does not measure angles directly but their 
tangents. If the indicating wire crosses the edge of the scale at 
a distance zcm. from the central division and if the angle between 
the displaced and the central positions of the arm is @ radians, 
then tan 0 =2/40, if the distance from the pivot to the edge of 
the scale is 40cm. The scale extends 10 cm. on either side of its 
central division so that the greatest value of tan @ is 0°25. When 
tan @ is known, @ can be found in degrees by trigonometrical 
tables or in radians by the series 
6 = tan 0—4 tan? 04+ 4 tan? 0 —..., ...eceseeee (1) 
provided |tan 6; < 1. 
The following Table, calculated to five decimal places by aid of 
the series, enables @ to be easily found when tan @ is known. 
It gives the value of c, the quantity which must be subtracted 
from tan @ in order to obtain the value of @ in radians. For values 
of tan @ not given in the Table, interpolation may be used. Thus, 
when tan 0 = 0:205, c = 000280 and thus 
6 = tan 6 —c = 0205 — 0:00280 = 0:20220 radians. 
The Table gives c with greater accuracy than the present experi- 
ments demand, but the extra figures are given in the hope that 
it may be useful for other purposes. 
11—2 
