ASG Proceedings of Philosophical Societies. ‘[Dee. 
ROYAL INSTITUTE OF FRANCE. 
Account of the Labours of the Class of Mathematical and Physicat 
Sciences of the Royal Institute of France during the Year ¥814. 
(Continued from p. 229.) 
MarnHEeMatTicAL Part. 
By M. le Chevalier Delambre, Perpetual Secretary. 2 
“We have already, in a preceding notice, briefly analyzed the 
memoir of M. Biot on A new Application of the Theory of the 
Oscillitions of Light, read to the Class at the end of 1813. “The 
author announces in it that he has extended to substances having 
the most powerful double refraction, as arragonite and calcareous 
spar, the researches which he had at first only applied to substances 
whose double refraction is so feeble that the images of the luminous 
points seen through plates with parallel surfaces, and three or four 
centimetres thick, which are not sensibly separated. He has found 
in that manner that in these crystals, as in all the others, the Juminous 
-molecules begin by oscillating round their centre of gravity toa 
certain depth, after which they acquire likewise a fixed polarization, 
which arranges their axes in two rectangular directions. ° 
To observe these phenomena in any crystal we must attenuate its 
polarizing force till the luminous molecules which traverse it make 
in its interior less than eight oscillations. We accomplish this either 
by forming with the given crystal plates sufficiently thin, or by in- 
clining them on an incident polarized ray so as to diminish the 
angle which the refracted ray forms with the axis of double refrac- 
tion; or, which is more convenient, by employing these ‘two 
metliods together. ‘ 
We accomplish the same thing by transmitting first the incident 
ray through a plate of sulphate of lime of the requisite thickness, 
the axis of which forms an angle of 45° with the primitive plane of 
polarization ; for when a ray is thus prepared, in order that it 
should be decomposed into coloured pencils, it is not necessary that | 
the polarizing force of the second plate should be very weak; it is 
sufficient that it diminishes in the requisite degree the first imprés- 
sions which it has received, in order that the difference of the 
number of oscillations produced in the two plates be less than 
eight, | eh REST 
We find, for example, that the polarizing force of Iceland spar 
is expressed by 18°6, if we take that of sulphate of lime for unity ; 
or there is required a thickness of sulphate of lime amounting’ to 
38°6, to destroy the modifications given to the rays of light bya 
thickness of 1 of Iceland spar. This ratio will be likewise that of 
Jeeland spar; for rock crystal acts exactly like sulphate of lime. 
This ratio will only be 17-7, according to other experiments of M. 
Malus. ‘The difference is insensible. M. Biot cannot decide which 
is accurate. All the other substances which he has been able ta 
