114 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



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 on tioned above, contains, besides what its name more 

 io^hieal " particularly imports, numerous observations on re- 

 instru- tractive 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 

 His re- a regular contributor to the London Philosophical 

 opticaUub" 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 

 (524.) I. The laws of polarization by reflection and re- 



En umera- f rac tion, and other quantitative laws of phenomena. 



of the most TT ml -, .-, , . . , 



important. *** ^ ne 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- 



Law of po- t w een the angle at which light is completely po- 

 larization ,.,, ,? Til 1 J . -, 



by reflec- ianzed 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 



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 thro ugh glass, I n 'P erfe ct 

 and he calculated the number of plates necessary to ^ ^ 

 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 in a 

 number of laws connecting the experimental results. 1 



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- ? tr " cture , 



. . j T. i ln h ea ted 



ization in some specimens ot glass. But the more gi, iss ; 

 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 latter had priority in publication, 2 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 

 eimple formula cotan a' cotan a cos (t f), 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 i and i' the angles of incidence and refraction. This result, ad- 

 mirably verified by experiment, is also conformable to Fresnel's theory. 



2 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. 



