FRESNEL'S THEORY OF DOUBLE REFRACTION. 211 



appeared, on looking through the aperture 

 in the second surface. When the aperture 

 in the second plate was ever so slightly 

 shifted, so that the line connecting the two 

 apertures no longer coincided with the line 

 MO, the phenomenon rapidly changed, and 

 the annulus resolved iself into two separate 

 pencils. 



The incident converging cone was also formed by a lens 

 of short focus, placed at the distance of its own focal length 

 from the surface ; and in this case, the lamp was removed to a 

 distance, and the plate on the first surface dispensed with. 

 The same experiments were repeated with the sun's light; 

 and the emergent rays were even thrown on a screen, and 

 thus the section of the cone observed at various distances from 

 its summit. 



In the first experiments there was a considerable discre- 

 pancy between the results of observation and theory, both as 

 to the magnitude of the cone, and some other circumstances 

 of its appearance. These discrepancies were found to arise 

 from the sensible magnitude of the little aperture on the second 

 surface of the crystal, which suffered rays to pass which were 

 inclined to the line OM at small angles. Accordingly, the 

 magnitude of the observed cone required a correction before 

 it could be compared with the results of theory : when this 

 correction was applied, the agreement of the observed and 

 theoretical angles was found to be nearly complete. 



(221) The rays which compose the emergent cone are all po- 

 larized in different planes ; and these planes were found to be 

 connected by the following law, namely, " the angle between 

 the planes of polarization of any two rays of the cone is half the 

 angle between the planes containing the rays themselves and the 

 axis" This remarkable law was, in the first instance, dis- 



