OF ELLIPTIC POLARIZATION. 
313 
The influence of the metal in modifying the rings was a maximum at 73°, 
as shown in Plate XI. fig. 1. exactly as if they had been crossed by a positive 
crystalline film which polarized a quarter of a tint, or the pale blueish white 
of the first order, and whose axis was situated in a plane +45°, or that which 
bisects the planes of the two pencils oppositely polarized by the metal. The 
influence of the metal, or the tint which it polarizes, diminishes gradually from 
73° to, 90°, where it vanishes, and consequently where the rings recover their 
symmetry and their tints. At this limit the position of the axis of the equiva- 
lent film is A B (fig. 2.), a line still bisecting the planes of the two oppositely 
polarized pencils. In fig. 2. the rings are not represented of their own shape, 
but just as they are beginning to be invaded by the metallic action as at an 
incidence of 86° or 87°. At incidences from 73° to 0° the opposite effect takes 
place, the rings recovering their symmetry at 0°, and the position of the axis of 
the equivalent film being now vertical, and bisecting the planes of the two 
oppositely polarized pencils. The form of the rings before they recover their 
symmetry is shown in fig. 3. 
At all intermediate angles of incidence the axis A B has intermediate posi- 
tions ; and calling A the inclination of the axis to the plane of reflexion, we 
shall have A = <p +45°, 
<p being positive or + from 90° to 73°, and negative or — from 73° to 0°. 
The intensity of the metallic tint, so to speak, or of the positive equivalent 
plate T, will be T = * ^ = (^) . 
Hence we see the error of the proposition hitherto maintained, that an in- 
crease of incidence, reckoning from the perpendicular, produces the same 
effect as an increase of thickness in thin crystallized plates. 
When the rings are combined with two reflexions at 73° in silver, or 73° in 
steel, they do not suffer the slightest change, the principal section of the prism 
being placed in the plane —39° 48' with silver, and —17° with steel. By 
two reflexions, however, between 7 3° or 73° and 90°, an effect is produced on 
the rings which increases gradually in silver from 73° to 82° 30', and diminishes 
from 82° 30' to 90°. At 82° 30' the effect is the same as after a single reflexion 
at 73° ; for since four reflexions at 82° 30' restore the elliptically polarized ray, 
two reflexions at the same angle must have produced complete elliptical polari- 
2 s 2 
