View of the Undulatory Theory of Light. 19 



tegration; but it will suffice, among the different motions 

 which the system may receive, to consider those in which the 

 displacements remain the same for all the molecules situated 

 in a plane parallel to a given plane ; and in the investigation 

 of phaenomena which are restricted to the conditions of this 

 sort of motion, we shall find that simpler differential equations 

 may be substituted for those above referred to. The deduc- 

 tion of these equations, and the establishment of a general ma- 

 thematical theory of such vibratio?is of molecules of an elastic 

 medium as shall account for the phaenomena of homogeneous 

 light, form the subject of another memoir in the fifth volume, 

 commencing at p. 19, and extending through the remainder of 

 the forty-ninth, the fiftieth and fifty-first livraisons of the same 

 work, published in 1830. 



The investigation is left apparently incomplete in the fifty- 

 first number, and it does not appear that any continuation of 

 the series has since been printed. 



In 1830, however, M. Cauchy published a separate tract, 

 entitled " Memoire sur la dispersion de la lumiere," in which, 

 after referring to the investigations contained in his former 

 memoirs, in which the propagation and polarization of light 

 are explained, he observes that the fundamental expressions 

 are only approximate. Those differential equations which are 

 employed in the fourth volume for deducing the theory of 

 waves (as we have already observed), are derived from others, 

 yet more general, in the third. These equations, however, 

 suffice for the laws of homogeneous light. But it struck the 

 author's friend, M. Coriolis, that possibly some of the terms 

 which had been neglected in the approximation might in- 

 clude what was necessary for extending the theory to light of 

 different refrangibility ; or, in other words, for overcoming the 

 greatest and indeed only formidable objection which has 

 hitherto stood in the way of the complete application of this 

 theory. M. Cauchy on examination found this idea fully 

 verified, and has proceeded in this memoir to give the com- 

 plete investigation of it. 



He takes up the subject from its first principles, and de- 

 duces the fundamental equations of motion, which (with a 

 slight difference of form) are the same as those established in 

 his third volume. He thence proceeds, without adopting the 

 same simplifications as those before used, to the integration 

 of these expressions. In the course of this process he arrives 

 at the same conclusions before established respecting the pro- 

 pagation of plane waves, and further develops those condi- 

 tions by which the relation between the length of the undu- 



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