PHENOMENA OF DIPOLARIZED LIGHT. 423 



the tint proportional to the product of the distances 

 of the point from the two poles. In the following 

 year, Sir J. Herschel confirmed this law by showing, 

 from actual measurement, that the curve of the 

 isochromatic lines in these cases was the curve 

 termed the lemniscata, which has, for each point, 

 the product of the distances from two fixed poles 

 equal to a constant quantity 4 . He also reduced to 

 rule some other apparent anomalies in phenemona 

 of the same class, 



M. Biot, too, gave a rule for the directions of 

 the planes of polarization of the two rays produced 

 by double refraction in biaxal crystals, a circum- 

 stance which has a close bearing upon the pheno- 

 mena of dipolarization. His rule was, that the one 

 plane of polarization bisects the dihedral angle 

 formed by the two planes which pass through the 

 optic axes, and that the other is perpendicular to 

 such a plane. When, however, Fresnel had dis- 

 covered from the theory the true laws of double 

 refraction, it appeared that the above rule is inac- 

 curate, although in a degree which observation 

 could hardly detect without the aid of theory 5 . 



There were still other classes of optical pheno- 

 mena which attracted notice ; especially those which 

 are exhibited by plates of quartz cut perpendicular 

 to the axis. M. Arago had observed, in 1811, that 

 this substance produced a twist of the plane of 

 polarization to the right or left hand, the amount 

 4 Phil. Trans. 1819. 5 Fresnel, Mem. Inxl. 1827, p. 162. 



