INTENSITY OF ORDINARY AND EXTRAORDINARY RAYS. 405 
about 6°5 times. M. Cauchy in these remarkable results refers 
to experiments which he instituted with M. Hessler of Gritz, 
which however merely showed “ that the escaping ray gradually 
disappeared as the incident ray was caused to make a less and 
less angle.” I have in vain endeavoured to observe any increase 
in the intensity of the escaping ray at the instant of total re- 
flexion. 
The disagreement of M. Cauchy’s formula (a.) with that of 
Fresnel is alone sufficient to show that it is opposed to experi- 
ment. M. Cauchy has assumed the square of the magnitudes 
of the refracted ray and incident light as the proportion of in- 
tensities, instead of the proportion of their actual power. Con- 
sequently, if D,? and D,? in M. Cauchy’s formula expresses the 
intensity of the refracted light, its value must be multiplied by 
some factor, which expresses the relation of the mass, which is 
set in motion by the same undulation in the incident and re- 
fracted light. 'The introduction of this factor gives the correc- 
tion of the formula (a.). I find it by dividing Fresnel’s formula 
by M. Cauchy’s, 
cos q sing 
sin @ cos} 
Hence it is seen that the new principle from which M, Cauchy 
has deduced his formula, is essentially based on the supposition 
that the luminiferous zther possesses the same elasticity in diffe- 
rent media, and that the refraction of the light is produced by its 
varying density alone. This is Fresnel’s hypothesis. Its inade- 
quacy, or rather inadmissibility, in crystalline substances, induced 
me to give it up, and to regard the refraction of light as produced 
by the difference in elasticity alone, as may be seen in my treatise 
published in the Transactions of the Berlin Academy, “On the 
Influence of the surfaces of Crystals on reflected Light, and 
the Intensity of the ordinary and extraordinary Ray.” I return 
to the main object of this communication, 7. e. to detail the 
methods which I adopt for ascertaining experimentally the dis- 
tribution of light falling upon the surface of a transparent cry- 
stalline medium, between the reflected, the ordinary, and the 
extraordinary rays. 
Suppose the incident light, the intensity of which is P?, to be 
polarized at right angles to the plane of polarization. The re- 
flected light is also polarized, but there is no ground for suppo- 
sing that it is polarized at right angles to the plane of incidence ; 
_ experiment shows the contrary; thus I decompose it into one 
