22 
MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
giving for result 
e^_a, 4 sin 2 26 
a ; 3 a (sin 26 + sin 26 ; ) 2 ’ 
that is, 4 sin* (28) sin 8 
sin 6 (sin 26 + sin 2 6,) 2 
16 cos 2 6. sin 6 sin 6, 
or /. 
(sin 26+ sin 26) 2 
The rule to be followed in selecting the proper solution out of two possible 
ones, is to take that which causes the ray to deviate as little as possible from its 
original direction ; this is at least the most natural course, and accords with expe- 
rience in accounting for the phenomenon of polarization, as we shall immediately see ; 
the contrary choice would leave that phenomenon unexplained ; we have therefore 
no alternative but to adopt the second solution. 
17. It may be observed, by the way, that the expressions of the intensities 
sin 2 (6 —6,) tan 2 (6 — 6 ; ) 
sin 2 (6 + 6,) ’ tan 2 (6 + 6 y ) ’ 
which I have found for the reflected rays whose vibrations occur respectively in the 
primary and secondary planes, exactly coincide with those which Fresnel has found 
for the reflected rays whose vibrations are respectively performed in the secondary and 
primary planes ; while the expressions for the intensities of the refracted rays, with 
the same interchange of planes, only approximately coincide with those deduced by 
Fresnel. 
18. If 6-\-6 t =- the expression for the secondary reflected ray vanishes; hence it 
follows that the incident beam, resulting from the superposition of the two compo- 
nents, after reflexion at the particular angle which satisfies the condition 
will produce a reflected ray of the primary class, that is to say, a ray whose vibra- 
tions are performed entirely in the plane of incidence. 
If [Jj be the index of refraction, we have 
sin 6 « ; 3 « __ ga 
^ sin 6, a 3 « ; g i a t 
g>, ^ denoting the densities of the ether as it exists in the two media, for which the 
rates of undulation are respectively a, a r 
When ^=^—0, we have sin^=cos^, and therefore tanO-p, the law (first disco- 
vered by Brewster) which determines what is called the polarising angle, agreeably 
to experience. 
But after incidence at this angle, the beam resulting from the superposition of the 
two component rays, will, after reflexion, consist entirely of vibrations performed in 
the plane of incidence, and not, as Fresnel supposed, in a plane at right angles to 
this. 
