the Use of Nicol’s Prism. 323 
Inserting numerical values, we have 
mae ihe W='32a+‘24r? sinoosy, . . . (8) 
@,—0="64r cos , approximately... . . . (9) 
To render these formule intelligible to one who has not 
read through the investigation, we may remark that we 
have to deal with one plane fixed in space, viz. the plane con- 
taining the axis of rotation of the Nicol circle and the direction 
of the emergent light. 
6 and 180°+6@, are the readings of the circle in the two 
opposite positions, and @=0 when the principal plane of the 
Nicol is at right angles to the fixed plane. 
av is the angle between the plane of polarization and the 
fixed plane. :; 
ais the angle between the axis of rotation and the principal 
lane. 
. r is the angle between the axis of rotation and the emergent 
light. 
“The angles are supposed to be expressed in circular measure 
in these as in all the other formule. 
The first term on the right-hand side of equation (8) is 
a constant, and is therefore of no consequence in measuring 
a change of y. ‘The second term is a measure of the out- 
standing error. 
Let us suppose 
fo i Ol). 
Then 
"247? sin vr cos = 1’; 
but if w= —30°, 
the same=—1’. 
So in measuring a rotation of 60° we may be subject to an 
error of 2’ if the axis of rotation be inclined to the emergent 
light at an angle of 3°. To make sure that the error shall be 
less than 1’, the last-mentioned angle must be kept within 2°. 
Hquation (9) affords the means of deducing the value of r 
from the difference of readings in the two opposite positions. 
The second term of (8) is due to two main causes. One is 
that the rotation of the plane of polarization takes place about 
one axis, while the rotation is measured about another. The 
effect of this appears in the coefficient —4. The other part of 
the error is due to the values of y in the two opposite posi- 
tions not exactly neutralizing each other. This appears in 
the coefficient m—l. If these two causes had reinforced 
instead of counteracting one another, the resultant error would 
have been five times as large. 
