1813.] 



Imperial Institute of France. 



22f 



ought to polarize under a perpendicular incidence. The limits 

 of partial polarization^ calculated after this result, for the plates 

 of sulphate of lime, and measured in millimetres, are as follows : 



Thickness at which the polarization is not yet sensible : 

 0-0029548 mm. (0-00011633 inch.), answering to the ver?/ 

 Mack of Newton. 



Thickness at which the plate polarizes all the incident light : 

 0-031144 mm. (0-00122614 inch.), white of the first order. 



Thickness at which the plate ceases to give colours : 

 0-45173 mm. (0-01778461 inch.), mixture of all the rings. 



We see that it cannot be said that the action of these plates 

 becomes feebler in proportion as their thickness diminishes, since 

 at the thickness of of a millimetre (0-00118 inch.) they 

 polarize the whole incident light ; while at the thickness of -j^^^ 

 they polarize only a part. In the first case we have O = o. if 

 we place the principal section of the rhomboid in the plane of 

 the polarization of the ray, and turn the axis of the plate in an 

 azimuth of 45°, we shall have a = o, i = 45°. Then our 

 formulas give = o, = E. That is" to say, that the ordi- 

 nary image observed across the rhomboid has vanished, and that 

 the extraordinary image contains all the light transmitted. 

 Therefore, when the axis of the plate is placed in an axis of 45°, 

 the pencil which it polarizes has its axes of polarization turned 

 in the azimuth of 90°. We shall see hereafter that this result is 

 general : whatever be the azimuth i, the polarization produced 

 by the plate takes place in the azimuth 2 i. Hence the reason 

 why the separation of the two colours by the rhomboid is most 

 complete in the position a — o, i = 45°. 



The same laws and the same formulas apply generally to plates 

 of mica, and of rock crystal, cut parallel to the axis of the 

 crystals ; but the imperfect superposition of the plates of mica 

 produces a greater difference in the thickness of the plates which 

 polarize the same colour, when they are taken from different 

 crystals. The same thing holds with those plates of mica which 

 have no principal sections. Rock crystal presents, likewise, some 

 variations in the analogous thicknesses between one crystal and 

 another ; but the relation between the thicknesses and the colours 

 always hold good in homogeneous pieces, when they are split 

 into different fragments. When the rock crystal is very regularly 

 crystallized, the tliickness of the plates which polarize the same 

 colour are exactly, or very nearly, the same as in pure sulphate 

 of lime; at least this was the case in the regular pieces of these 

 substances which M. Biot compared. 



After having considered the phenomena which take place under 

 a perpendicular incidence, M. Biot examines those which arise 

 when the incidence is oblique. These, while their law remains 

 unknown, appear altogether irregular and anomalous. Accord- 

 ing as the plate is inclined one way or other, according as its 



