408 FOURTH RErouT — 1834. 



other directions, the two pencils into which a single ray is di- 

 vided, were supposed to obey the ordhiary laws, and to be 

 plane-polarized in opposite planes. This supposition has been 

 overturned by Professor Airy *, and it has been shown that the 

 two pencils in quartz are, each of them, elUiJlically-imlarized ; 

 the elliptical vibrations of the two rays being in opposite direc- 

 tions, 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 inclination to that line ac- 

 cording to some unknown law. As to the course of the re- 

 fracted rays. Professor Airy finds that it is still determined by 

 the Hujrgenian law ; but that the sphere and spheroid, which 

 determine the velocity and direction of the two i"iys, do not 

 touch, as in all other knoAvn 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 ex- 

 planation 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 calculation founded on these hypo- 

 theses, of the forms of the rings, &c. — displayed by quartz in 

 plane-polarized, and circularly-polarized light, and in any posi- 

 tion of the analysing plate ; and he has found the most strik- 

 ing agreement between the results of calculation and those of 

 observation . 



We yet want a mechanical theory which will accoimt for the 

 peculiar form of the wave- surface just alluded to. Fresnel seems 

 to have thought that the difference of the velocities of the two 

 rays in the direction of the axis might be physically explained 



• " On the Nature of the Light in the two rays produced by the double re- 

 fraction of Quartz," Cambridge I'ransactions 1831. 



f In the Supplement to this paper Professor Airy has explained a highly in- 

 genious method of determining experimentally the relation between the ellip- 

 ticity and the direction 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 there- 

 fore a change of half an order in the rings, when the incident 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 ap- 

 liroaches more nearly to one of equality, than in the extraordinary ray. 



