116 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



curious phenomena to anything like a law. It was 

 evident almost from the first, that the axes in ques- 

 tion (which he termed axes of no polarization) are 

 only the resultants of remoter fundamental actions of 

 the crystalline constitution. For example, these 

 axes vary in position according to the colour of the 

 light used to display them ; their position within the 

 crystal varies (as was shown by Mitscherlich) with 

 the temperature of the body, nor is it obviously 

 related to any of the geometrical lines of crystalliza- 

 Law of the tion. Sir David Brewster succeeded in finding the 

 tints. j aw o f the tints expressed upon the surface of a 

 sphere of which the directions of the two axes form 

 diameters. M. Biot expressed the law more ele- 

 gantly by saying, that the tint developed by a biaxal 

 crystal in any ray, is proportional to the product of 

 the sines of the angles which the ray in question 

 makes with the two optic axes. The tints are con- 

 sequently arranged round the two poles of the axes, 

 in a series of curves resembling the figure 8, having 

 each this property, that the product of the sines of 

 the angular distances of each point of one curve from 

 the two poles is equal to a constant quantity. Such 

 curves are called lemniscates, and are beautifully 

 seen in nitre, especially when viewed by homoge- 

 neous light. 



(532.) -A. series of researches of the most elaborate 

 Relation of description led Sir David Brewster to this addi- 

 optical cha- tional and admirable discovery, viz., that the optical 

 crystalline characters of single refraction, double refraction 

 forms. with one axis, and double refraction with two axes, 

 have reference invariably to the primitive crystalline 

 form of the mineral, and that the complexity of the 

 optical character is as invariably related in degree to 

 the complexity of the crystalline figure. Cubical and 

 regularly octahedral crystals (as rock salt and fluor 

 spar) being possessed of perfect symmetry in three prin- 

 cipal directions, possess also simple refraction. Crys- 

 tals with one predominant line or axis of symmetry 

 as rhombohedrons, octahedrons with square bases, 

 right prisms with square or hexagonal bases have a 

 single axis of double refraction. Such, for instance, are 

 Iceland spar, zircon, ice, beryl. Finally, all crystals 

 unsymmetrical in the three principal directions, in- 

 cluding prisms and octahedrons whose bases are 

 not square, and those which are oblique, have two 

 axes of double refraction. The rarity and minute- 

 ness of many crystals, the difficulty of cutting them, 

 and when cut, of detecting their optic axes, evi- 

 dently made the research one of extreme labour, yet 

 highly remunerative, not only through the discovery 

 of the general principle, but by the vast amount of 

 beautiful and varied optic displays witnessed in the 

 course of it. Sir David Brewster was nearly, if not 

 quite, alone in this research, and after a short resis- 

 tance on the part of some mineralogists, his principle 

 of discrimination of primitive forms of crystallization 

 by optical characters has been perfectly established. 

 (533.) ! The action of metals on the light which they 



reflect is very peculiar. Malus, who at first believed Laws of 

 that they were incapable of polarizing it in any de- m ^ tall ! ( 

 gree, afterwards changed his opinion, and inge- 

 niously suggested that whilst transparent bodies 

 reflect, at the polarizing angle, light polarized only in 

 one plane, metals reflect rays oppositely polarized 

 and then mixed. Sir David Brewster has the merit 

 of having, after several unsuccessful attempts, de- 

 duced the leading empirical laws of metallic polari- 

 zation, having been partly guided (as he states in his 

 paper in the Philosophical Transactions for 1830) 

 by Fresnel's remarkable experiments on circular 

 polarization produced by total reflection in glass 

 (see Art. 491). Having found qualities somewhat 

 analogous in light reflected one or several times from 

 metallic plates at various angles depending on the 

 nature of the substance, he gave to the light so re- 

 flected the name of elliptically polarized light. It 

 was afterwards satisfactorily proved by Mr Airy that 

 the light so named by Sir D. Brewster is in fact 

 identical in its qualities with the elliptically polar- 

 ized light of Fresnel. 



The subject of metallic polarization is rather too (534.) 

 abstruse to be explained in a popular way ; and the Metal . lic 

 phenomena produced with depolarfzing plates of clif-j^" 

 ferent metals are not so well known as, according to 

 their discoverer, they deserve to be. My limits only 

 permit me at present to state that the care and accu- 

 racy of Sir D. Brewster's results are unquestionable; 

 that they have formed almost the sole data upon 

 which M. Cauchy and other mathematicians have 

 based their theories of metallic reflection ; and that, 

 by generalizing the more limited views entertained by 

 Fresnel as to the constitution of media and the nature 

 of reflected light, they have been mainly instrumental 

 in fixing the later views of optical writers as to the 

 precise phenomena of polarization as produced, not 

 only by metals, but by other substances. To these 

 views I shall briefly advert in the next section. 



The laws of the reflection of light at crystallized (535.) 

 surfaces have also been studied by Sir D. Brewster. 

 In this case observation is still in advance of theory. 



V. Of Sir David Brewster's experiments on the (535. 

 absorption of light we must speak much more Absorpti 

 briefly. White light is coloured or analyzed by ofli s ht - 

 refraction (as in a prism) ; by simple interference, as 

 in Newton's rings ; by double refraction combined 

 with polarization. But it is also decomposed in a 

 way which, primarily at least, seems different from 

 all these, by passing through coloured, or ratner, 

 colouring media, whether solids, liquids, or gases, 

 as red glass, ink, chlorine. This, the most familiar 

 mode of coloration, is the most difficult to account 

 for, and has been (on account of its obscurity) less 

 studied than the others. In some instances, the 

 complementary colour (that which, added to the 

 transmitted tint, makes up white light) is entirely 

 absorbed or lost ; in other cases it is reflected at or 

 near the first surface of the medium. Sometimes 



