Mechanical Theory of Circular and Elliptic Respiration. 403 
better, to find my equations supported by a similar theory, and their 
form at least countenanced by the like mechanical analogy. Be- 
sides, I recollected that Fresnel himself, in his Memoir on Double 
Refraction, had indicated a ‘‘helicoidal arrangement,” or something 
of that sort, as a probable cause of circular polarization (Mémoires 
de I’Institut, tom. vii. p. 73); and as this was an hypothesis of 
the same kind as the other, only not so general, I was prepared to 
find that the supposition of an arbitrary arrangement, whatever 
might be thought of its physical reality, would lead to equations of 
the same form as those which I had assumed. Upon trial, however, 
the very contrary proved to be the case, for though it was possible 
to obtain additional terms, containing differential coefficients of the 
third order, multiplied by the same constant C, yet this constant 
always came out with the same sign in both equations, whereas a 
difference of sign was essential for the expression of the phenomena. 
I had no sooner arrived at this result, than I perceived it to be fatal 
to the theory of M. Cauchy, and to afford a demonstration of its 
insufficiency, not only in the particular application which I had made 
of it, but in all its applications, For the hypothesis which I used 
was, in fact, identical with that theory, in the most general form 
of which it is susceptible, when unrestricted by any particular sup- 
position as to the arrangement of the ethereal molecules ; and there- 
fore the fundamental conception of the theory could not be true, as 
it not merely failed to explain a large and most remarkable class of 
phzenomena—those of circular and elliptical polarization—but abso- 
lutely excluded them, and left no room for their existence. It fol- 
lowed from this, that the mechanical explanation, which the same 
theory was supposed to have given, of the phenomena of rectilinear 
polarization and double refraction in crystals, could not be well 
founded ; indeed, as I have said, I had always distrusted it, and that 
for various reasons, of which one has been already mentioned, and 
another was suggested by the forced relations which M. Cauchy had 
found it necessary to establish among the constants of his theory, and 
by which he had compelled, as it were, his complicated formulas to 
assume the appearance of an agreement (though, after all, a very 
imperfect one) with the simple laws of Fresnel. 
Such were the conclusions at which I arrived, and the reflections 
which they forced upon me, nearly six years ago. ‘They have been 
frequently mentioned in conversation to those who took an interest 
in such matters, and their general tenor may be gathered from what 
I have elsewhere written (Transactions of the Academy, vol. xviii, 
p- 68); but I did not think it worth while to publish them in detail, 
change its density, and therefore propagates to a distance transversal vi- 
brations only; while ordinary elastic fluids transmit only normal vibrations, 
and ordinary solids admit vibrations of both kinds. This hypothesis also 
includes the supposition that the density of the ether is unchanged by the 
presence of ponderable matter. As to M. Cauchy's third ray, with vibra- 
tions nearly normal to the wave, there is no reason to believe that it has 
even the faintest existence ; but it is necessarily introduced by his identifi- 
npg of the vibrations of light with those of an indefinitely extended elastic 
solid, 
