Reflection and Refraction o^ Light. 165 



He then argued that incomplete polarization must be due 

 to the fact that these expressions differ slightly from zero, and 

 that their value must be negative, in order that the pressural 

 waves should be insensible at a distance from the interface for 

 all angles of incidence. 



In a memoir published in 1840 and in the Exercises 

 oV Analyse et de Physique* , this mistake was corrected, and the 

 true condition p/(m + n)=p , l(m l -t-n')}xas given; but, appa- 

 rently led astray by his original mistake and by a desiref 

 (afterwards given up, Compt. Rend, xxviii. p. 125) to make 

 complete polarization depend on the properties of the refracting 

 medium alone, and not on any relation between the two 

 media, he still adopted the solution 



m + n = = m, , + n'; 



though he mentioned J also the true solution, viz. that the coeffi- 

 cient of compressibility of the aether is infinite, and the wave- 

 lengths of the pressural waves in the two media are equal. 



Assuming that the aether is incompressible, the polarization 

 of the reflected ray will be elliptical when the wave-lengths of 

 the pressural waves are unequal, and we get 



M 



-GH/#+'> 



where \ u , X" are the wave-lengths of the pressural waves in 

 the two media. This is Eisenlohr's suggestion; but the 

 form in which he made it does not show that it involves the 

 absolute incompressibility of the aether. If X n /X" = X/X ! , we 

 get Green's formula. Eisenlohr§ says that this assumption 

 is absolutely untenable : it is, however, as Green shows, a 

 direct consequence of the assumption made by him, and in- 

 volved in Cauchy's conditions, viz. the identity of the statical 

 properties of the aether in the two media. 



Further than that, if we assume only the equality of the 

 rigidities, the equations of condition become (8), (96) ; whence 



B" ~ p -^ ' 

 and if the aether is incompressible, 



^-1 



M = 



/* 2 -rl 



* C. R. x. p. 357. Ex. d J An. et de Phys. i. p. 233. 

 f C. R. ix. p. 727. % Ibid. x. p. 358. 



§ Pogg. Ann. civ. p. 358. 



