314 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
The relations e < being essentially positive, the requisite com- 
pensation can only take place when the deviations «,, «, have 
opposite signs, that is to say when the two mixed liquids turn 
the plane of polarization of the type ray in different directions. 
The essential oils of turpentine and of lemon are in this case: 
the first turns the planes of all the rays towards the left, the 
second towards the right of the observer. 
With respect to the proportions of the mixture, let V, be the 
volume of the first liquid occupied by the weight P,, at the 
temperature at which the experiment is performed, and V, the 
analogous volume occupied by the weight P,, we shall evidently 
have P, = V, 8,3; P. = Vooo 
These expressions of the weights P,, P, being substituted in our 
equation of condition, the densities disappear, and there remains 
a, V, + % V,=0; 
that is to say, the two liquids must be mixed in volumes reci- 
procally proportional to the deviations which they produce, in 
tubes of equal length, on the type ray for which their actions 
are to be compensated. 
17. I have published the details of a similar experiment on 
the essential oils of lemon and of turpentine, in the Comptes 
Rendus de ? Académie des Sciences, t. ii. p. 540 et seg. 1 shall 
only relate here the general results. The compensation was 
established for the red ray, transmitted through a glass co- 
loured by the protoxide of copper. The compensation was very 
exact for it when the mixture had been effected in the rela- 
tions of volume indicated by the formula. But it was not quite 
exact for the other rays of the spectrum; for, on placing the 
principal section of the analysing prism in the primitive plane 
of polarization of the incident pencil, the extraordinary image, 
which should have been null if the compensation of the devia- 
tions had been general, was feebly but sensibly apparent; so 
that on moving the prism a little to the right or the left of that 
primitive azimuth, feeble signs of coloration were distinctly ob- 
served in the extraordinary image, which soon disappeared when 
the azimuth continued to increase in the one or other direction. 
This experiment proves, therefore, that the dispersion of the 
planes of polarization is not effected rigorously, but only very 
nearly, according to the same law in the two oils, and doubtless d 
also in other substances possessing rotatory powers. Thus the 
