152 Mr. J. Walker on Cauchy's Theory of 



equations of condition at the interface, which was given in a 

 lithographed memoir published in 1836. This method assumes 

 a change in the equations of motion near the interface to a 

 distance comparable with the radius of the sphere of activity 

 of a molecule, and leads to the following theorem : — 



"Etant donnesdeux milieux ou deux systemes de molecules 

 separes l'un de l'autre par le plan de yz, supposons que des 

 equations d'equilibre ou de mouvement generalisees de maniere 

 a subsister pour tous les points de Fun et de l'autre systeme 

 et meme pour les points situes sur la surface de separation, 

 Fon puisse deduire une equation de la forme 



=(h) 



dx* ' 



», ® designant deux quantites finies, mais variables avec les 

 coordonnees xy z. On aura, pour x = 0, 



d% da' 



* = *', 



dx dx 



en admettant que Ton prenne pour premier et pour second 



membre de chacune des formules les resultats que fournit la 



reduction de x a zero, dans les deux valeurs de la fonction 



da 



-j- ou s? relatives aux points interieurs du premier et du 



second systeme." 



The equations of condition resulting from the application of 

 this theorem were published in Cauchy's memoir on Dispersion 

 in the same year*. They express that the linear dilatation of 

 the aether normal to the interface is the same for both the 

 media, and that the rotations in the three coordinate planes 

 of a particle at the interface is the same, whether the particle 

 is considered as belonging to the first or second medium. 



The method of deducing these conditions was given in a 

 memoir presented to the French Academy on October 29, 

 1838f . This memoir has never been published ; and all we 

 know is that the method involved the assumption that the 

 velocity of propagation of the pressural w r aves is very great 

 compared with that of the distortionalwavesj. In 1842 Cauchy 

 showed that these conditions lead to FresnePs formula3§. 



The final theory was published in detail f| in the years 1838 

 and 1839, and is contained in the 8th and 9th volumes of 

 the Comptes Rendus, and in the Exercises oV Analyse et de 



* Mem. sur la Dispersion, § 10. f Comptes Rendus, vii. p. 751. 



\ Ibid. x. p. 905. § Ibid. xv. p. 418. 



|| The idea seems to be prevalent that we are indebted to the German 

 reproductions for our knowledge of the details of Cauchy's method. 



