in Physical Optics. 93 
sity of their exact agreement with experiment in those pheeno- 
mena which depend upon the change of the algebraic signs, or 
upon the equality of intensity of the two kinds of light, or the 
evanescence of one of them. In all cases of this nature which 
have been examined, I believe the results have been found to be 
most satisfactory. The formula (A) is always positive while 
the angle of incidence changes from zero to 90° : (B) is negative 
at first and afterwards positive; vanishing entirely, in exact 
accordance with Brewster’s law, at the intermediate stage of 
7+ 2'= 90°. All this is shown by the Astronomer Royal in 
the Cambridge Transactions, vol. iv., in a series of very in- 
teresting experiments, to be in perfect agreement with nature. 
In the extreme case of7 = 90°, Professor Lloyd, in vol. xvii. 
of the Irish Transactions, by a very simple and elegant ex- 
periment, has proved that both (A) and (B) are rigidly exact, 
both as to their algebraic signs, and the relative magnitudes of 
the vibrations which they represent. In the other extreme case 
of z = 0°, I am not aware of any very satisfactory experiment 
of a direct nature, not depending on photometry, having been 
made. I beg therefore to. propose one, which I believe is 
perfectly new, and of such a nature as to be free from any ob- 
security or doubt as to the phenomenon to be observed. It 
will be remarked that when z is very nearly 90°, the formule 
(A) and (B) become 
heey imal pe, 
E+ ] e+ 1 
Now these are exactly equal, but of opposite signs, indica- 
ting that both species of light are reflected with equal inten- 
sities; but while the phase of that portion whose vibrations 
are perpendicular to the plane of reflection is unaffected, the 
phase of that portion whose vibrations are in the plane of re- 
flexion is accelerated or retarded by half an undulation. 
Consequently, if s7ght-handed circularly polarized light be in- 
cident nearly perpendicularly upon a plane surface of glass, 
Fresnel’s formule lead us to expect that the reflected light 
will be left-handed circularly polarized, and vice versd. I trust 
that the simplicity of the experiment here proposed, as well 
as its newness, will induce some one of your experimental 
correspondents to undertake it. The result, I have no doubt, 
will be the addition of another instance to the list of fulfilled 
predictions of the undulatory theory. 
Cambridge, Noy. 30, 1842. 
and —a. 
