ROTATION OF LIGHT IN BISULPHIDE OF CARBON. 
361 
diffused by imperfect translucency of the optical apparatus. If cZE denote the 
smallest perceptible difference, the value of oZE/A is in favourable circumstances as 
low as yg- or x 7 >oj which means that with a sufficient total brightness differences of 
this amount may be apparent to observation. 
Let us now consider the values of cZE corresponding to different methods of pro¬ 
cedure. If the analysing Nicol be adjusted for extinction of the original light, the 
comparison is between the brightness which cannot be got rid of (H 0 ) and (H o +/t0 2 ).* 
Near the limit of discrimination, to which case we may confine our attention, hQ 2 is 
small relatively to H 0 , and thus we may take 
cZE=A 
liQ^ 
Ho' 
The procedure just considered is that which would naturally be adopted to render 
evident a small quantity of light of given amount, viz., to isolate it and compare it 
with the best attainable darkness. But in the present problem the circumstances are 
peculiar in that we are able to deal with phases. Now if we regard the amplitude 
(a) of the feeble light as given, putting a?=h6 2 , we may produce more effect from it 
by combining it with other light in the same phase of amplitude (/3) than by isolating 
it. The comparison is then between brightnesses (a+/3) 3 and /3 3 , or as a is very 
small, between /3 2 -\-2a/3 and /3 3 . Thus 
cZE=A 
2 a/3 
/3 3 + /3 0 2 ’ 
in which /3 0 3 is written H 0 . 
The light of amplitude /3 is obtained in the simplest possible manner by merely 
rotating the analysing Nicol through a small angle, and the only question is how to 
exhibit the comparison light which shall not be affected, when /3 is changed to (/3 + a). 
For this purpose we may divide the field of view into two halves with an oblique 
mirror in which is seen by reflection a feeble light, of the same colour and coming 
ultimately from the same source. 
It is possible that an instrument upon this principle might be made to work 
satisfactorily,! but the half-shade polarimeters of Jellet and Laurent seem to be 
in most respects preferable. In them the comparison is between (y3+a) 3 and (/3—a ) 3 , 
so that 
cZE=A 
4 a/3 
/3 3 + /3 0 2 ’ 
representing twice as great a sensibility. The only thing to be said upon the other 
side is that the division line in these instruments can hardly be made as invisible as 
the sharp edge of a mirror may be. 
* We may imagine the presentation of the two brightnesses to be consecutive, or more favourably 
that both are seen at once, half the field of view being occupied by a black body seen after reflection in 
an oblique mirror, whose edge forms the dividing line. 
f Readings would of course be taken in both the positions (one on either side of extinction) which 
give a match with the comparison light. 
