8 
BRITISH ASSOCIATION.— 1835. 
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. 
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 in different 
media, which was found necessary for the theory, seems to accord, 
better than the supposition of a varying density, with the phenomena 
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 formulae 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 , tom. 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.] 
