326 
DR. BREWSTER ON ELLIPTIC POLARIZATION. 
the sign + being used for the red or least refrangible rays, and — for the blue 
or most refrangible. 
For the same reason, in calculating the phases of an elliptically polarized ho- 
cos (i 4- i 1 ) 
mogeneous ray by means of the formula tan <p 
we must deter- 
cos (i — i 1 ) 1 
mine /' from the formula sin i 1 = the sign + being used for the red or 
sin i 
least refrangible, and — for the blue or most refrangible rays. 
As the theoretical considerations upon which M. Fresnel is said* to have 
constructed his formula, did not present to him the above anomaly, it would be 
in vain for me to seek an explanation of it. I may just mention, however, that 
at the second surfaces of bodies the angle of maximum polarization, or tan — 
is necessarily less for the least refrangible than for the mean rays, which is the 
reverse of what takes place at the first surface ; and since the limit of total re- 
flexion whose sine is or since the sphere of circular polarization commences 
sooner for the least than for the most refrangible rays, it might be expected 
that the angle of maximum circular polarization should be less for these rays, 
as I have found to be the case. 
Although we do not understand the nature of the forces by which metals 
reflect the two oppositely polarized pencils, yet they act exactly like the 
second surfaces of transparent bodies when producing total reflexion. Setting 
out from a perpendicular incidence, the least refrangible rays begin to suffer 
the double reflexion sooner than the mean ray, and they sooner reach their 
maximum of elliptic polarization, thus exhibiting the inversion as it were of 
the spectrum, which we have noticed. 
The theory of elliptic vibrations as given by Fresnel, will no doubt embrace 
the phenomena of elliptic polarization; and when the nature of metallic action 
shall be more thoroughly examined, we may expect to be able to trace the 
phenomenon under consideration to its true cause. 
Allerly, February 19///, 1830. 
' I am acquainted with M. Fresnel’s formula only from the account given of it by Mr. Hersciiel. 
