532 Proceedings of Philosophical Societies. [March^ 



xvliat order the parts of this matter are disposed, nor at what 

 distance they are from each other, provided always that the axes 

 of the plates be parallel to each other. For example, if we 

 take a plate of mica, or of sulphate of lime, which, referred to 

 the table of Newton, poksnzes the^ indigo of the third order ; 

 this plate may be mechanically divided into several other thinner 

 ones, which polarize other colours belonging to rings higher up 

 in the table : but when the light passes all these plates in succes- 

 sion, the colour polar- ed by them all togeth ;r will always be the 

 indigo of the third orde , in v/hat way soever they- are placed 

 above each other. M. Bic ■ announced, likewise, that when the 

 axes of the plates were made to cross at right angles, the colour 

 appeared to him to be that which resulted from the difference of 

 their thicknesses, instead of from tlie sum. This opinion was 

 afterwards verified, and fully confirmed^ by means of a morei 

 exact apparatus. 



This property constitutes the object of a third memoir, read by 

 M. Biot on the 30th of November, 1812: and this memoir 

 itself is only the prelude of a dissertation, in which M. Biot 

 proposes to reduce to mechanical causes, and to one general fact, 

 all the phenomena that he has observed, as well as the formulas - 

 that express them. 



After having recalled the principal circumstances of theSe 

 phenomena, and the formulas which he had deduced from them, 

 he shows from these formulas that the plates of sulphate of lime, 

 of mica, and of rock crystal, exposed to a polarized ray with a 

 perpendicLilar incidence, do not polarize the light upon which 

 they act, according to the direction of their axes, but according 

 to a direction which foriiis a double angle with the axis of polari- 

 zfiti -5 of (he incident ray : so that if the azimuth of the axis of 

 tilt . ■ 't- 5 in respect of the plane of polarization, be 2 i, the 

 lumio rs nioiecules which the plate polarizes do not turn their 

 axes of polarization in the azimuth ?, but in the azimuth 2 i. 

 He shows t'iie constant and unforeseen agreement of this result 

 with the plienomena. Tiiis constitutes the first foundation of his 

 theory. 



Studying, then, the variations of colours polarized by the 

 plates under different inclinations, he shows that these phenofc- 

 mena seem occasioned by the opposite action of two forces 

 analogous to those v/hich occasion double refraction ; witli this 

 difference, that of these two forces, which proceed from two 

 rectangular axes, the one tends to increase the polarizing force 

 of the plate, and the other to weaken it: so that by modifying 

 the action of these two axes by inclination, you may make the 

 plate act at pleasure, either as thicker or thinner. Sometimes 

 even a third axis, perpendicular to the plates, joins its action to 

 that of the two preceding; and as it is inclined so as to favour 

 either the one of the other, it increases the action of the plate 



