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system of attracting or repelling molecules, and M. Cauchy 

 lias really clone nothing more than transfer to the lumiiiife- 

 rous ether both the constitution of the solid and differential 

 formulas of its vibration), still I should have been glad, in 

 the absence of anything better, to find my equations sup- 

 ported by a similar theory, and their form at least counte- 

 nanced by the like mechanical analogy. Besides, I recol- 

 lected that Fresnel himself, in his Memoir on Double Re- 

 fraction, had indicated a " helicoidal arrangement," or some- 

 thing of that sort, as a probable cause of circular polariza- 

 tion (Memoires de Vlnst'ilut, torn. 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 fonn 

 as those which I had assumed. Upon trial, however, the 

 very contrary proved to be the case, for though it was pos- 

 sible to obtain additional terms, containing differential co- 

 efficients 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 ar- 

 rived 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 parlicula;- application wliich I 

 had made of it, but in all its applications. For the hypo- 

 thesis which I used was, in fact, identical with that theory, 

 in the most general form of which it is susceptible, when un- 

 restricted by any particular supposition as to the arrange- 

 ment of the ethereal molecules ; and therefore the funda- 

 mental conception of the theory could not be true, as it not 

 merely failed to explain a large and most remarkable class of 

 phenomena — those of circular and elliptical polarization — but 

 absolutely excluded them, and left no room for their exist- 

 ence. It followed from this, that the mechanical explanation. 



