920 
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. 
M. Aveustin Louis Caucuy has been long known 
whic wae 28 one of the ablest and most prolific mathematical 
mathemati- Writers of this century. Besides numerous and im- 
cal labours, portant memoirs, on nearly every branch of pure 
and applied mathematics, published in the Journal 
de V’Ecole Polytechnique, and the Memoirs of the In- 
stitute, he has published, in a separate form, Ezer- 
cises des Mathematiques 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; 
MATHEMATICAL AND PHYSICAL SCIENCE. [Diss. VI. 
facts to the ordinary laws of polarization by reflec- Theory of 
tion, As early as 1814 (Philosophical Transactions, os 
1814, p. 230), Sir David Brewster had remarked that tion, in. 
such highly refractive substancesas Realgar, Diamond, cluding the 
and Chromate of Lead, do not polarize, at any angle, ease of 
the whole of the reflected light. Mr Airy afterwards =o 
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; ° 
and last of all, M. Jamin showed that all transparent M. Jamin. 
substances polarize 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 coeficient 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’s 
stances whose index of refraction is nearly 1°46, that dified by sf 
of the glass which he examined. The complication Green and 
is held to arise from the existence of vibrations by M- 
(556.) 
M. Cauchy 
auchy. 
(557.) 
Green’s 
account of 
his method. 
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 Abbé Moigno? in France, M. Radicke *in 
Germany, and Professor Powell‘ 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. 
I shall first mention some seemingly exceptional 
(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° (not long before his death), 
is so far incomplete that it involves only one constant. 
M. Cauchy’s investigations, published two years later,’ 
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 refrangibility (dispersion) 
of light has ever been felt to be one of the most 
real as well as prominent difficulties in admitting 
1 Cambridge Transactions, vol. ix. 4 
3 Handbuch der Optik, Band i., 1839. 
5 See Moigno Rep. d’Optique, p. 1385. 
8 Cambridge Tr tions, vol. vii. 
ire d’Optique Moderne. 1847-50. 
4 The Undulatory Theory as applied to the Dispersion of Light. 1841, 
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 
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 Mécanique Analytique, and which appears to be more especially applicable to problems that relate to the motions of systems 
of an immense number of otra mutually acting on each other. One of the advantages of this method, of great importance, 
is, that we are necessarily 
conditions which are requisite and suficient for the complete solu 
A consideration of the candid admissions of the preceding paragraphs (especially the last sentence) 
ed by the mere process of the calculation, and, with little care on our part, to all the equations and 
tion of any problem to which it may be applied.” 
; will lead the reader to see 
how short a way a theory of so general a kind—the chief characteristic of which consists in parse) every troublesome physical 
enquiry—can go towards explaining the relations of Light to Matter; yet it may be of use by i 
cating the kind of solutions 
which more restricted hypothesis may be expected to give of the laws of phenomena. 
7 Comptes Rendus de l’ Acad. des Sciences. 
(559.) 
Theory of 
dispersion. 
é 
