296 British Association for the Advancement of Science. 



The two new laws above mentioned, on which the theory de- 

 pends, occurred to the author in the beginning of last December ; 

 but, owing to an oversight in forming one of the equations, they 

 were not fully verified until the beginning of June. 



In this theory it is supposed that the vibrations of polarized light 

 are parallel to the plane of polarization, according to the opinion of 

 M. Cauchy. This is contrary to the views of Fresnel, whose theory 

 of double refraction obliged him to adopt the hypothesis that the 

 vibrations are perpendicular to the plane of polarization. It is 

 further supposed, that the density of the vibrating aether is the same 

 in both media ; and this hypothesis of a constant density indifferent 

 media, which was found necessary for the theory, seems to accord, 

 better than the supposition of a varying density, with the phaenomena 

 of astronomical aberration. 



If we conceive the three principal indices of refraction for the 

 crystal to become equal, we shall obtain the solution of a very simple 

 case of the general problem with which we have been occupied, — 

 the case of an ordinary refracting medium, such as glass. This 

 simple case, it is well known, was solved by Fresnel. The fore- 

 going theory leads to a simple law, expressing all the particulars of 

 the case, but differing with regard to the magnitude of the refracted 

 vibration, from the formulas of Fresnel. The law may be stated, 

 by saying that the refracted vibration is the resultant of the incident 

 and reflected vibrations ; the first vibration being the diagonal of a 

 parallelogram of which the other two vibrations are the sides, just 

 as in the composition of forces. The plane of this parallelogram is 

 the plane of polarization of the refracted ray. It is to be remem- 

 bered, that the vibrations in each ray are perpendicular to the ray 

 itself, and parallel to its plane of polarization. 



This simple case has also been considered by M. Cauchy, in a 

 short paper inserted in the Bulletin Universel, torn. xiv. ; but it does 

 not seem to have been observed by any one that his solution is er- 

 roneous. His formula for light polarized parallel to the plane of 

 reflexion, is that which belongs to light polarized perpendicular to 

 the plane of reflexion and vice versa. 



Mr. Whewell read his report on the Mathematical Theories of 

 Electricity, Magnetism, and Heat. 



[This report will be printed in the next volume of the Transac- 

 tions of the Association.] 



On certain points connected with the recent Discoveries relative to 

 Radiant Heat. By Professor Powell. 



In this communication the author expressed his particular satis- 

 faction in finding that M. Melloni (in his second memoir) describes 

 a repetition of the experiment originally made by him, and recorded 

 in the Philosophical Transactions, 1825, with perfect success, by 

 means of his extremely delicate apparatus. The confirmation is 



