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TRANSACTIONS OF THE SECTIONS. 7 
city, he has traced a relation to the constant arcs of restoration after two metallic 
reflexions, determined by Sir D. Brewster (Phil. Trans. 1830). 
The change of plane cannot yet be explained by theory; though the empirical 
formulas of Prof. MacCullagh appear to give a good representation of it, when the 
data for steel resulting from that investigation are introduced into the author’s for- 
mula. 
—- 
On a New Polarity of Light, with an Examination of Mr. Airy’s Explanation 
of it on the Undulatory Theory. By Sir Daviv Brewster, F.RS LL. & E., 
M.R.I.A. 
Notwithstanding the great power of the undulatory theory in explaining phz- 
nomena, and its occasional success in predicting them, I have never been able to 
consider it as a representation of that interesting assemblage of facts which consti- 
tute physical optics. When a theory of high pretensions, and remarkable for its 
powers of accommodation, is found incapable of explaining whole classes of well-ob- 
served and distinctly marked phenomena, those who have discovered or studied these 
phznomena may be excused for withholding from it their assent, and for not wholly 
abandoning older, though Jess popular views, which were sanctioned by such 
authorities as those of Newton and Laplace. It has fallen to my lot to lay before the 
public several of the facts to which I refer; but as it is not the object of this notice 
to discuss the general merits of the undulatory theory, I shall mention only two of 
those classes of facts which the undulatory theory has failed to explain. The first 
of these, which was communicated to the Royal Society about fifteen years ago, em- 
braces the phenomena of transverse fringes which cross the fringes produced by 
grooved surfaces, and produce, both in common and homogeneous light, a series of 
phenomena equally beautiful and singular. In these phenomena we witness the 
extraordinary fact, that a stripe of polished metal is incapable, at various angles of 
incidence, of reflecting a single ray of homogeneous light; while, at intermediate 
angles of incidence, it reflects that light freely. The undulatory theory has never 
ventured to explain these phenomena, and I feel confident that they are beyond its 
power; and hence the phenomena-themselves have excited no notice, and have 
shared the fate of all such intractable discoveries as refuse submission to the prevail- 
ing theory of the day. Thesecond group of phenomena which the undulatory theory 
is equally incapable of explaining, present themselves in looking at a perfect solar 
Spectrum, or a diffraction spectrum, through the edge of a thin plate of glass, quartz, 
or mica. If we cover one-half of the pupil of the eye with such a plate, and thus 
view the spectrum so that the rays which pass by the edge of the plate may interfere 
‘with those which pass through it, then if the plate is on the same side as the violet 
space, the spectrum is seen crossed with numerous black and nearly equidistant bands, 
parallel to Fraunhofer’s fixed lines, and, generally speaking, increasing with the thin- 
ness of the plate; but if the plate is on the same side as the red space, no bands 
whatever are seen, though all the other conditions of their production are the same. 
When the transparent plate is very thin the fringes of thin plates are produced, 
whether we cover the half or the whole of the pupil; but these have nothing to do 
with the phenomenon under consideration. The singular fact of the fringes being 
seen only in one position of the plate appeared to me to indicate a new polarity in the 
simple elements of light. I therefore communicated it to the British Association at 
Liverpool, in 1836; and in 1837 I submitted to the same body additional observa- 
tions, which excited some discussion. The singular phenomena contained in these 
notices, though pressed upon the attention of the supporters of the undulatory 
theory, remained unexplained for more than ¢hree years. They at last attracted the 
regard of Prof. Airy, in October 1839, when that distinguished mathematician re- 
peated my experiments; and in 1840 he made them the subject of an elaborate me- 
moir, constituting the Bakerian Lecture of that year, entitled, ‘On the Theoretical 
Explanation of an apparent New Polarity in Light.’ [Sir D. Brewster read the parts 
of Prof. Airy’s paper which could be readily understood by the Section.] Previous 
to the publication of this ingenious paper, Prof. Airy gave an account of it at the 
meeting of the British Association in Glasgow, in 1839. On that occasion I made 
a few observations upon it; but specially marking the fact, that whereas Prof. Airy’s 
