912 
liant discoveries which, literally for years, remained 
unknown in England to those most interested and 
solicitous to learn them. Thus Sir D. Brewster 
learned first in February 1814 that Malus had in 
March 1811 published the discovery of the polar- 
ization of light by refraction, which he also had made ; 
whilst Arago’s experiments on coloured polarization 
were likewise unknown to him through the same 
want of international communication. 
(522.) The work on Philosophical Instruments, men- 
Treatise OD tioned above, contains, besides what its name more 
ort ya particularly imports, numerous observations on re- 
instru-  fractive and dispersive powers, including the disco- 
ments. very of substances more refractive than diamond, 
and less so than water. It also describes the pro- 
perty of some agates to transmit light polarized in 
only one plane. The imperfect polarization of light 
by metals and by a serene sky had been anticipated 
by Malus and Arago. 
(523.) From this time (1813) Sir David Brewster became 
cer on? regular contributor to the London Philosophical 
optical sub- Transactions, which, as well as those of Edinburgh, 
jects. contain a series of elaborate experimental investi- 
gations due to him, which have hardly been sur- 
passed, It is difficult to overrate the importance of 
these researches, whether for the intrinsic interest 
of the phenomena they reveal, or for the significance 
of the empirical laws by which their author, with 
a rare sagacity, succeeded in classifying facts, and 
afforded a sure basis for farther generalization. The 
number and variety of these researches is so ex- 
ceedingly great, and in many cases so impossible 
to explain without entering into minute detail, that 
I shall, in accordance with the plan of this essay, 
merely indicate some of the most generally impor- 
tant by arranging them in groups. Such are— 
I. The laws of polarization by reflection and re- 
fraction, and other quantitative laws of phenomena. 
II. The discovery of the polarizing structure in- 
duced by heat and pressure. 
III. The discovery of crystals with two axes of 
double refraction, and many of the laws of their phe- 
nomena, including the connection of optical structure 
and crystalline forms. 
IV. The laws of metallic reflection. 
V. Experiments on the absorption of light. 
(525.) I. Malus had failed to discover a connection be- 
spd of Po tween the angle at which light is completely po- 
ization : . : 
by reflec larized by reflection, and the other known optical 
tion. properties of bodies. In 1814, Sir D. Brewster 
discovered the beautiful and simple law, “that the 
index of refraction is equal to the tangent of the 
angle of polarization.’ He had suspected it much 
(524.) 
Enumera- 
of the most 
important. 
MATHEMATICAL AND PHYSICAL SCIENCE. 
[Diss. VI. 
sooner, but he had been baffled by the irregular re- 
sults obtained by reflection from glass, whose sur- 
face he found to undergo an almost imperceptible 
chemical change. He further observed that it is 
only in bodies of low refractive power that the po- 
larization is sensibly complete, a result of great im- 
portance, which has been too much overlooked until 
the recent and valuable paper of Jamin on the same 
subject. He deduced as a corollary, that at the 
maximum polarizing angle the incident and refracted 
rays are at right angles to one another, and also 
Malus’s experimental result that the rays reflected 
from the first and second surfaces of plates are 
simultaneously polarized. He further discovered the 
fact that light may be completely polarized (as to 
sense) by a sufficient number of reflections at any 
angle, and drew the conclusion that the whole light 
undergoes some change at each reflection, in opposi- 
tion to the view of Malus, who maintained that, 
except at the polarizing angle, a portion of the light 
is polarized, and the rest is unchanged. 
Sir David Brewster independently observed the po- _(526.) 
larization of light transmitted obliquely throughglass, Imperfect 
and he calculated the number of plates necessary — 
polarize it with sensible completeness. All these 
researches he resumed some years after (Phil, Trans. 
1830), endeavouring to give a photometric estimate 
of the effects of reflection and refraction under all 
circumstances. The results as regards partially po- 
larized light may still be considered as subject to 
doubt, His skill in obtaining a mathematical repre- 
sentation of the phenomena was again displayed ina 
number of laws connecting the experimental results.? 
II. Malus had observed that a vast number of (527.) 
substances depolarized light more or less completely ; Polarizing 
and Arago found feeble traces of chromatic polar-ycturs 
ization in some specimens of glass, But the more glass; 
definite characters of the beautiful phenomena of 
glass not perfectly annealed (which proved to be of 
unexpected importance) were noticed, independently, 
by Sir D. Brewster and Dr Seebeck of Nurnberg. 
The Jatter had priority in publication,” but the former 
correctly referred them to their immediate cause— 
the constraint produced by rapid cooling. Sir D. 
Brewster noticed that the unannealed glass which 
forms what are called Prince Rupert’s Drops, had a 
remarkable power of depolarization; and he also 
observed subsequently that the plates of glass be- 
tween which he was in the habit of squeezing heated 
wax and resins, for the purpose of optical examina- 
tion, transiently communicated tints to polarized 
light. These observations, duly developed, proved 
on the one hand that glass (and generally refracting 
1 Thus he found that the effect of refraction on the plane of polarization of the incident light may be expressed by this 
simple formula—cotan a’= cotan a cos (i—7’), where a and a’ are the azimuths of the planes of polarization of the incident 
and refracted rays measured from the plane of reflection, and ¢ and? the angles of incidence and refraction. This result, ad- 
mirably verified by experiment, is also conformable to Fresnel’s theory. 
® In Schweigger’s Journal for 1813, vol. vii. I have not been able to find in this paper (which contains the first account of 
the beautiful symmetric coloured figures displayed in cubes and cylinders of glass) the smallest trace of the true cause of the 
phenomenon, viz., the sudden or partial cooling of the glass. 
44 
