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



Green's equations gives the reflection total at all angles of 

 incidence. For this result there is no experimental evidence 

 at present, except in the case of silver. The same will result 

 from Lord Rayleiglr's extension of Green's theory, unless, as 

 seems scarcely probable, the refractive index of the pressural 

 waves is a complex quantity. 



VI. 



In August 1850* Cauchy published the outlines of the 

 result of applying his method to the case of reflection at 

 the surface of an isotropic medium which possesses rotatory 

 power. 



The displacements in the upper medium are taken as 



f = A oe (™+t>y-<»tW=i + A y fo(-«*+ty-»')^=i + B ll a u e^ a " x+ ^- (at) " / ~ 1 , 



V — — Q e (cuc+by-u>t)V=I + f^Q e (-ax+by-a>t)V~l . 



and those in the lower medium, since there will be two 

 refracted waves circularly polarized in opposite directions, 



P = AJbeWB+ty'^-i + AJbe {a * x+by ~ <at) * / -~ l + B"a"e (a " x+by ~ ,at)V -- l f 



f = — V^T . AJ — g(«i^+^-"*)^=i + /y/31 A 2 ' — e {a * x + b y-»v v:ri . 



Substituting these values in the equations of condition re- 

 sulting from the principle of continuity, we get 



b(A+A,- AJ-AJ) =B"/-B/, 

 -(A-A> + A 1 V + A 2 V=^(B"-B // ), 

 6{(A-A>-A 1 V-A 2 V} = (BV 2 -B A 2 ), 

 - (A + A> 2 + A x V 2 + A 2 « 2 ' 2 = 5(B V- B /y a'0, 



c + c=(-A /A/+ ^)v-i, 



(is; 



<?. R. xxxi. pp. 160, 225. 



