6 
of the light being stopped, when the formule give a reflexion 
very nearly total. 
The value of &’—6, or the difference of phase, increases 
from 0° to 180°. Whena plane-polarized ray is twice reflected 
from a metal, it will still be plane-polarized if the sum of the 
values of &—8 for the two angles of incidence be equal 
to 180°. 
It appears from the formule that when the charaeter- 
istic y is very small, the value of & will continue very small 
up to the neighbourhood of the polarizing angle. It will 
pass through 90°, when mm’=1; after which the change will 
be very rapid, and the value of & will soon rise to nearly 180°. 
This is exactly the phenomenon which Mr. Airy observed 
in the diamond. 
Another set of phenomena to which the author has ap- 
plied his formule are those of the coloured rings formed be- 
tween a glass lens and a metallic reflector; and he has thus 
been enabled to account for the singular appearances de- 
scribed by M. Arago in the Memoires d Arcueil, tom. 3, 
particularly the succession of changes which are observed 
when common light is incident, the intrusion of a new ring, 
&c. But there is one curious appearance which he does not 
find described by any former author. Itis this. ‘Through 
the last twenty or thirty degrees of incidence the first dark 
ring, surrounding the central spot which is comparatively 
bright, remains constantly of the same magnitude; although 
the other rings, like Newton’s rings formed between two glass 
lenses, dilate greatly with the obliquity of incidence. This 
appearance was observed at the same time by Professor 
Lloyd. The explanation is easy. It depends simply on this 
circumstance, (which is evident from the table,) that the angle 
180°—@’, at these oblique incidences, is nearly proportional 
to cos 2. 
As to the index of refraction in metals, the author con- 
jectures that it is equal to 
cos 
