146 The Aether as an Elastic Solid. 



the media on either side the interface. This implies in the 

 present case that the quantities 



tie* de z 



n and n 



dx ty 



are to be continuous across the interface : so we have 



n cos i'. (/' - 1") = n' cos r . /', ; n sin i.(f' + F) = n' sin r . f\. 



Eliminating /' we have 



F' _ sin (r - i) 

 f sin (r + i) 



Now this is Fresnel's sine-law for the ratio of the intensity 

 of the reflected ray to that of the incident ray ; and it is known 

 that the light to which it applies is that which is polarized 

 parallel to the plane of incidence. Thus Cauchy was driven 

 to the conclusion that, in order to satisfy the known facts 

 of reflexion and refraction, the vibrations of the aether must be 

 supposed executed at right angles to the plane of polarization 

 of the light. 



The case of a vibration performed in the plane of incidence 

 he discussed in the same way. It was found that Fresnel's 

 tangent-law could be obtained by assuming that e x and the 

 normal pressure across the interface have equal values in the 

 two contiguous media. 



The theory thus advanced was encumbered with many diffi- 

 culties. In the first place, the identification of the plane of 

 polarization with the plane at right angles to the direction of 

 vibration was contrary to the only theory of crystal-optics which 

 Cauchy had as yet published. In the second place, no reasons 

 were given for the choice of the conditions at the interface. 

 Cauchy's motive in selecting these particular conditions was 

 evidently to secure the fulfilment of Fresnel's sine-law and 

 tangent-law; but the results are inconsistent with the true 

 boundary-conditions, which were given later by Green. 



It is probable that the results of the theory of reflexion had 

 much to do with the decision, which Cauchy now made,* to 



*Comptes Rendus, ii. (1836), p. 341. 



