352 Proceedings of Royal Society of Edinburgh. [skss. 
eyepiece as regards its rotation is ascertained after each setting to 
equal intensity of the two bright strips. The ratio of the bright- 
ness of the two strips is equal to the square of the tangent of 
the angle of displacement of the eyepiece, if the zero of the 
latter be that position in which the light of the under strip 
is completely extinguished. As the under strip is that due to 
the comparison beam, that is, to the beam that does not pass 
through the absorbing liquid, the tangent of the displacement 
angle is equal to the fraction of the incident light transmitted 
by the absorbing substance. 
It is to be noted that, in common with other polarising spectro- 
photometers, this instrument suffers from the defect that the light 
in passing through the main prism is partially polarised in a 
vertical plane, for which reason, when there is no absorbing sub- 
stance in the path of either beam, and when accordingly the 
analysing Nicol ought to give equality of illumination when set 
at an angle of 45°, it is found that the Nicol has to be turned 
round slightly from that position before the intensities of the two 
beams will exactly balance. The amount of this error, which 
depends on the refractive index of the glass of the prism, etc., 
can be calculated by Fresnel’s formulae, and in a case computed 
by the author it is about 4° 40'. As, however, it is hoped later on 
to publish some experiments on this subject, the mathematical 
discussion need not be entered into here. It only remains to be 
said, that the observations made with such instruments are to be 
reduced by assuming that a certain (constant) absorbing body has 
been permanently placed in the path of one of the beams. 
It should be noted that the two beams of light are in some 
ways asymmetric as they pass through the Wollaston prism, and 
hence it is possible that different fractions of the light may be 
transmitted in each case. As regards absorption the existence of 
such a crystal as tourmaline shows that this may be very different 
in the case of the ordinary and of the extraordinary rays. With 
the crystal mentioned the ordinary ray is practically non-existent 
after transmission through one or two millimetres of the substance, 
while the extraordinary ray in the same circumstances is only 
slightly absorbed. In the case of this instrument, however, the 
Wollaston prism is of quartz, which is a substance where no such 
