COLOURS OF CRYSTALLINE PLATES. 143 



mon nor plane-polarized light, but possess all the characters which 

 are impressed upon a polarized ray by two total reflexions from 

 glass at an angle of about 50. 



The refraction of quartz, then, in the direction of its optic axis, is 

 wholly different from that of every other known crystal. In other 

 directions, the two pencils into which a single ray is divided were 

 supposed to obey the ordinary laws, and to be plane-polarized in 

 opposite planes. This supposition has been overturned by Pro- 

 fessor Airy ;* and it has been shown that the two pencils in quartz 

 are, each of them, elliptically polarized, the elliptical vibrations of 

 the two rays being in opposite directions, and the greater axes of 

 the ellipses being in the principal plane, and perpendicular to it, 

 respectively. The ratio of the axes, in these ellipses, is the same 

 in the two rays, f but varies with their inclination to the optic 

 axis, being a ratio of equality when the direction of the ray 

 coincides with the axis, and increasing indefinitely with their incli- 

 nation to that line according to some unknown law. As to the course 

 of the refracted rays, Professor Airy finds that it is still determined 

 by the Huygenian law ; but that the sphere and spheroid, which 

 determine the velocity and direction of the two rays, do not touch, as 

 in all other known uniaxal crystals, the latter surface being contained 

 entirely within the former. This position is certainly a startling 

 one. The two sheets of the wave-surface being thus absolutely 

 separated, there is a complete interruption of continuity in passing 

 from the velocity of one ray to that of the other ; a result which 

 does not hold in any other case with which we are acquainted. It 

 is however necessary to the explanation of the phenomena ; for 

 the interval of retardation does not vanish with the inclination of 

 the ray to the axis. Professor Airy has given an elaborate calcu- 

 lation, founded on these hypotheses, of the forms of the rings, &c., 

 displayed by quartz in plane-polarized and circularly polarized 



* "On the Nature of the Light in the two rays produced by the double refraction 

 of Quartz." Cambridge Transactions, 1831. 



t In the Supplement to this paper Professor Airy has explained a highly ingenious 

 method of determining experimentally the relation between the ellipticity and the dirvc- 

 tion of either of the rays. This method depends upon a remarkable effect which he 

 had been led to expect from theory : namely, a sudden change of half an undulation 

 in the interval of retardation, and therefore a change of half an ordrr in the rings 

 when the im-idftit light is elliptically polarized. From the results of some experiments 

 conducted in this method, Professor Airy seems to think that the ratio of the axes in 

 the ordinary ray approaches more nearly to one of equality than in the extraordinary 

 ray. 



