308 
DR. BREWSTER ON THE THENOMENA AND LAWS 
These observations are represented by the formula, tan 0 = tan a . tan x; a 
being the angle of restoration when 6, the inclination of the plane of primitive 
polarization, is 45°. 
I have not given the values of 0 from 45° to 00°, because it is difficult to 
ascertain even in strong lights when the evanescence commences. At 90° the 
action of the first plate is 0 , so that at this limit the angle of restoration is the 
angle at which the elliptic polarization is no longer visible, from the smallness 
of the angle of incidence, an angle which varies with the intensity of the light 
employed. 
Hitherto we have attended only to the phenomena produced by two similar 
metals. When the metals are dissimilar, the one silver and the other steel, I 
found that at the mean maximum polarizing angle of 74°, the inclination of the 
39 ° 48 ' + 17 ° 
plane of the restored ray was 28° 30'. But 28° 24' = : ^ 3 80 that the 
inclination is an arithmetical mean between that of silver and that of steel. 
By four reflexions at 74° the inclination was reduced to 14°, while by four 
reflexions at about 83° and 58° the inclination was 21^°, nearly equal to 
28 ° 30 ' + 14 ° 
- 5 , according to the formula in page 297- By thus combining dis- 
similar metals we may produce elliptic polarization of all degress of intensity 
intermediate between those produced by similar metals. 
As the circular polarization of total reflexion is the limiting case of elliptical 
polarization, it becomes important to establish by experiment their intimate 
connexion and almost perfect similarity. Upon combining metallic and 
total reflexions this was at once evident ; and I found in general that circular 
polarization of any intensity, as produced by either one or more reflexions from 
glass, may always be restored to rectilineal polarization by one or more me- 
tallic reflexions, provided the latter are all made at angles less than the maxi- 
mum polarizing angle, and that the two classes of reflexions are performed in 
coincident planes. 
As this takes place throughout the whole range of total reflexion from 41° 
to 90°, it follows that total differs from metallic reflexion in its not having 
two opposite kinds of circular polarization, like the two opposite kinds of 
elliptical polarization which take place on each side of the maximum polari- 
zing angle of metals. But notwithstanding this, the circular like the elliptic 
