82 HISTORY OF OPTICS. 







:n such cases ; and thus explained, so far as an empirical law of phc 

 .nomcna went, the curious and various forms of the colored curves. 

 This law, when simplified by M. Biot. 3 made the tint proportional to 

 the product of the distances of the point from the two poles. In the 

 following year, Sir J. Ilerschel confirmed this law by showing, from 

 ai'tual 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 eqnal to a constant 

 quantity. 4 He also reduced to rule some other apparent anomalies in 

 phenomena of the same class. 



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

 tion of the two rays produced by double refraction in biaxal crystals, 

 a circumstance which has a close bearing upon the phenomena of 

 depolarization. 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 discovered from the theory the true laws of 

 double refraction, it appeared that the above rule is inaccurate, although 

 in a degree which observation could hardly detect without the aid of 

 theory. 5 



There were still other classes of optical phenomena 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 of this twist being different for different colors ; 

 a result which was afterwards traced to a modification of light differ- 

 ent both from common and from polarized light, and subsequently 

 known as circular polarization. Sir J. Herschel had the good fortune 

 and sagacity to discover that this peculiar kind of polarization in 

 quartz was connected with an equally peculiar modification of crystal- 

 lization, the plagihedral faces which are seen, on some crystals. 

 obliquely disposed, and, as it were, following each other round the 

 crystal from left to right, or from right to left. Sir J. Herschel found 

 that the riyht-handed or left-handed character of the circular polariza- 

 tion corresponded, in all cases, to that of the crystal. 



In 1815, M. Biot, in his researches on the subject of circular polari- 

 sation, was led to the unexpected and curious discovery, that this pro- 



Mem. lust. 1818, p. 192. 4 Phil. Trans. 1819. 



6 Fresnel. Mem. Inst. 1827, p. 162. 



