122 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



rays *; the existence of normal vibrations seems to 

 be proved by the ingenious experiments of M. Jamin, 

 showing that at no angle is light perfectly polarized 

 by reflection. The more we see of these diversities 

 arising in the progress of science, the less are we 

 disposed to found on merely mathematical conclu- 

 , sions from an assumed constitution of elastic bodies ; 

 the more, on the other hand, do we admire the ad- 

 mirable sagacity of Fresnel the real Newton of 

 modern optics few of even the least of whose sug- 

 gestive anticipations have fallen to the ground. 

 (556.) M. AUGUSTIN Louis CAUCHY has been long known 

 M. Cauchy as one o f ne a ]jl es t an d most prolific mathematical 

 inatlfenmti- w "* ers ^ ^ s century. Besides numerous and im- 

 cal labours, portant memoirs, on nearly every branch of pure 

 and applied mathematics, published in the Journal 

 de I'Ecole Polytechnique, and the Memoirs of the In- 

 stitute, he has published, in a separate form, Exer- 

 cises des Mathematigues in two series of volumes ; 

 and for many years scarcely a weekly meeting of the 

 Academy of Sciences occurred without a mathema- 

 tical memoir of this prolific author being laid on the 

 table, and subsequently printed in the Comptes Ren- 

 dus. The integral calculus and other parts of ana- 

 lysis form the subjects of a large part of these writings; 

 but the theory of hydrodynamics in the earlier, and of 

 optics in the later part of his career, are largely re- 

 presented. So diffuse and desultory a mode of publi- 

 cation has been little favourable to those who wish to 

 make themselves acquainted with what has been ac- 

 complished by M. Cauchy. The scientific world is in- 

 debted to Abbe Moigno in France, M. Radicke 3 in 

 Germany, and Professor Powell 4 in England, for ana- 

 lyzing in part his optical labours. As the present 

 brief notice is evidently inadequate to include even 

 the most superficial view of the whole, I shall say a 

 few words upon two of his theoretical researches on 

 light, which have attracted most general attention. 

 The first is upon the theory of Reflection and Re- 

 fraction, framed so as to include the phenomena of 

 metallic reflection ; the second is upon the Dispersion 

 of Light. 

 (557.) I shall first mention some seemingly exceptional 



facts to the ordinary laws of polarization by reflec- Theory of 

 tion. As early as 1814 (Philosophical Transactions, * e ^ * 

 1814, p. 230), Sir David Brewster had remarked that tion> in _ 

 such highly refractive substances as Realgar, Diamond, eluding th 

 and Chromate of Lead, do not polarize, at any angle, case of 

 the whole of the reflected light. Mr Airy afterwards m ' 

 showed that light reflected from diamond near the 

 maximum polarizing angle, possesses qualities re- 

 sembling those of light reflected from metals. The 

 same view was more generally stated by Mr Dale ; 5 

 and last of all, M. Jamin showed that all transparent M. Jamin. 

 substances polai'ize elliptically the light which they 

 reflect, the difference of " phase " of the two compo- 

 nent vibrations increasing from 180 at a perpen- 

 dicular incidence, to 360 at an incidence of 90 ; and 

 that the laws of reflection at transparent surfaces, as 

 also in the case of metals, depend upon two con- 

 stants the index of refraction and the coefficient of 

 ellipticity. And he has determined in numerous 

 cases the values of these constants. 



Thus Fresnel's theory of reflection requires un- (558.) 

 doubted modification. It only holds true for sub- Fresnel'i 

 stances whose index of refraction is nearly 1-46, that di g e( i ^ 

 of the glass which he examined. The complication Green and 

 is held to arise from the existence of vibrations b / M> 

 (called normal) in the direction of transmission of the 

 luminiferous wave, such as those which produce the 

 effects of Sound in air, and which produce certain 

 effects on Light at the bounding surfaces of two 

 media. In the theory of Fresnel, as also in those of 

 Maccullagh and Neumann, this influence is neglected. 

 To Green and to M. Cauchy belongs the merit of lay- 

 ing down a more comprehensive theory. Mr Green's 

 theory, published in 1837 6 (not long before his death), 

 is so far incomplete that it involves only one constant. 

 M. Cauchy's investigations, published two years later, 7 

 embrace the phenomena of metallic reflection by the 

 introduction of the two constants mentioned above, 

 thus completing the theory of reflection and refrac- 

 tion both for transparent and metallic surfaces. 



The fact of the unequal rcfrangibility (dispersion) 

 of light has ever been felt to be one of the most 

 real as well as prominent difficulties in admitting 



(559.) 



* Repertoire cTOptique Moderne. 1847-50. 



4 The Undulatory Theory as applied to the Dispersion of Light. 1841. 



1 Cambridge Transactions, vol. ix. 

 3 Handbuch der Optik Band i., 1839. 

 5 See Moigno Rep. d'Optique, p. 1385. 

 p , 6 Cambridge Transactions, vol. vii. The following extract from this able paper shows the independence of physical assump- 



. - tions which characterizes these ultra-mathematical optical theories : " . . . We are so perfectly ignorant of the mode of action 

 '. 'jt, j of the elements of the luminiferous ether on each other, that it would seem a safe method to take some general physical [?] 

 ' principle as the basis of our reasoning. . . . The principle selected as the basis of the reasoning contained in the follow- 

 ing paper is this : In whatever way the elements of any material system act upon each other, if all the internal forces exerted 

 be multiplied by the elements of their respective directions, the total sum for any assigned portion of the mass will always be 

 the exact differential of some function. But this function being known, we can immediately apply the general method given in 

 the Mecanique Analytique, and which appears to be more especially applicable to problems that relate to the motions of systems 

 of an immense number of particles mutually acting on each other. One of the advantages of this method, of great importance, 

 is, that we are necessarily led by the mere process of the calculation, and, with little care on our part, to all the equations and 

 conditions which are requisite and sufficient for the complete solution of any problem to which it may be applied." 



A consideration of the candid admissions of the preceding paragraphs (especially the last sentence) will lead the reader to see 

 how short a way a theory of so general a kind the chief characteristic of which consists in eluding every troublesome physical 

 enquiry can go towards explaining the relations of Light to Matter; yet it may be of use by indicating the kind of solutions 



which more restricted hypothesis may be expected to give of the laws of phenomena. 

 7 Comptes Hindus de VAcad. des Sciences. 



