Mechanical Theory of Circular and Elliptic Polarization. 409 
[of molecules] so essentially different from each other” as the 
zthereal fluid and an clastic solid*. (See Annales de Chimie, 
tom. xliv. p.432.) The remark, however, did not meet with much 
attention from mathematicians, who were, perhaps, not disposed to 
scrutinize too closely any hypothesis which gave transversal vi- 
brations as a result. Besides, the hypothesis appeared to go much 
‘further, as it offered prima facie explanations of a great variety of 
phznomena; it was one to which calculation could be readily ap- 
plied, and therefore it naturally found favour with the calculator ; 
and as to M. Poisson’s objection, it was easily removed by a change 
of terms, for when the elastic solid was called an “ elastic system,” 
there was no longer anything startling in the announcement that 
the motions of the ether are those of such a system. The hypo- 
thesis was therefore embraced by a great number of writers in every 
part of Europe, who reproduced, each in his own way, the results 
of M. Cauchy, though sometimes with considerable modifications. 
Every day saw some new investigation purely analytical—some 
new mathematical research uncontrolled by a single physical concep: 
tion—put forward as a ‘‘ mechanical theory” of double refraction, 
of circular polarization, of dispersion, of absorption; until at length 
the Journals of Science and Transactions of Societies were filled with 
a great mass of unmeaning formulas. This state of things was partly 
occasioned by the great number of ‘‘ disposable”’ constants entering 
into the differential equations of M. Cauchy and their integrals ; for 
it was easy to introduce, among the constants, such relations as 
would lead to any desired conclusion; and this method was fre- 
quently adopted by M. Cauchy himself. ‘Thus, in his theory of 
double (or rather triple) refraction, given in the works already cited 
{p. 402), he supposes three out of his nine constants to vanish, and 
assumes, among the other six, three very strange and improhable 
relations, by means of which each of the principal sections of his 
wave-surface (considering only two out of its three sheets) is re- 
duced to the circle and ellipse of Fresnel’s law; and the three prin- 
cipal sections being thus forced to coincide, it would not be very 
surprising if the two sheets were found to coincide in every part with 
the wave-surface of Fresnel. The coincidence, however, is only ap- 
proximate; but M. Cauchy is so far from being embarrassed by this 
circumstance, that he does not hesitate to regard his own theory as 
rigorously true, and that of Fresnel as bearing to it, in point of ac- 
curacy, the same relation which the elliptical theory of the planets, 
in the system of the world, bears to that of gravitation (Mémoires de 
? Institut, tom. x. p. 313). Nor is he at all embarrassed by the su- 
pernumerary ray belonging to the third sheet of his wave-surface ; 
he assumes at once that such a ray exists, though it was never seen, 
* As the theory of M. Cauchy (Mém. de [ Institut, tom. x.) had been 
communicated to the Academy of Sciences some months before the period 
(October, 1830) at which M. Poisson wrote, there can be no doubt that 
M. Poisson’s remark was directed against that theory, though he did not 
expressly mention it. 
Phil. Mag. S. 3. Vol. 22. No. 146, May. 1843. 2E 
