British Association for the Advancement of Science. 295 



Irish Academy ;)also a similar account of his new theory of varying 

 orbits. 



He likewise explained to the Section the method of investigation 

 pursued by Mr. G. B. Jerrard, for accomplishing the solution of 

 equations of the fifth or of higher degrees*. 



A short Account of some recent Investigations concerning the Laws of 

 Reflexion and Refraction at the surface of Crystals. By Mr. 

 M'Cullagh. 



To understand the nature of the general problem which a com- 

 plete theory of double refraction requires to be solved, let it be sup- 

 posed that a ray of light is reflected and refracted at the separating 

 surface of an ordinary medium and a doubly refracting crystal, 

 the light passing out of the former medium into the latter. This 

 limited view of the subject is taken merely for the sake of clearness 

 of conception ; since we might suppose that both media are crystal- 

 lized, without increasing the difficulty of the problem. The question, 

 it is obvious, naturally divides itself into two distinct heads. The 

 first relates to the laws of the propagation of light in the interior of 

 either of the two media, before or after it has passed their separating 

 surface ; and this part of the subject has been fully treated, accord- 

 ing to their different methods, by MM. Fresnel and Cauchy. The 

 second division of the subject had been left completely untouched. 

 It relates to the more complex consideration of what takes place at 

 the separating surface of the media, the laws according to which 

 the light is there divided between the reflected and refracted rays, 

 including a determination of the attendant circumstances indicated 

 by the wave theory, with regard to the vibrations in the reflected 

 and refracted rays. In the case above mentioned, when the incident 

 light is polarized, there are four things to be determined, namely, 

 the magnitude and direction of the reflected vibration, with the mag- 

 nitudes of the two refracted vibrations. The four conditions neces- 

 sary for this determination are furnished by two new laws, which 

 could not be easily stated without entering too much into detail. 

 The results, applied to determine the polarizing angle of a crystal 

 in different azimuths of the plane of reflection, agree very closely 

 with the admirable experiments of Sir David Brewster on Iceland 

 spar. In the course of these experiments it was observed that the 

 polarizing angle remained the same when the crystal was turned half 

 round (through an angle of 180°), although the inclination of the re- 

 fracted rays to the axis of the crystal was thereby greatly changed. 

 This remarkable fact is a consequence of the theory. After some 

 complicated substitutions in the primary equations, the value of the 

 polarizing angle is found to contain only even powers of the sine or 

 cosine of the azimuth of the plane of reflection, and therefore a 

 change of 180° in the azimuth produces no change in the polarizing 

 angle. 



* See our last number, p. 202. — Edit. 



