Light from Transparent Matter. 93 



Now cot 2 0, = t^ + cot 2 0, 

 sin 2 6 



cot *,= cot 0(1 +|^J appro*. 



Hence 



X={l + 2(/* 2 -l)sin 2 <9^,, 



Y = {l + (/, 2 -l)[^-2sin 2 ^} t/ , 



^__ X— Y _, 2 2 sin 2 2(9-1 /* 2 -l cos 4(9 



>|r'~X+Y "~ (/a j 4cos 2 " 2 I + cos20* ( yj 



From (19) we see that the reflected wave vanishes when 

 cos 40=0; that is, when 



*=8' or * ss T 



It appears, then, that on the hypothesis D=D', there would 



7T 07T 



be two polarizing angles (q> ~ respectively) whenever the dif- 



o o 



ference of refrangibility between the two media is small. Since 

 nothing of the sort is observed, we conclude that D cannot be 

 equal to D', and are driven to adopt Green's original view that 

 the rigidity of the aether is the same in all media. 



Results substantially equivalent to (19) have been already given 

 in a different form by Lorenz*, who, however, has not discussed 

 them, but simply says that they cannot be reconciled with Fres- 

 nel's formulae. Curiously enough he has taken the same particular 

 case for disproof which I, without a knowledge of his work, had 

 hit upon. Those who have done me the honour of reading my 

 papers on the action of small particles on light will understand 

 how I anticipated the two polarizing angles by the very different 

 process there employed. Lorenz draws the conclusion that the 

 elastic force of the aether is the same in all transparent uncrys- 

 talline substances as in vacuo, and that the vibrations of light 

 are performed normally to the plane of polarization. He might, 

 I think, have omitted the wovduncrystallinef. 



There is also another paper J by Lorenz on this subject, in 

 which he endeavours to account for the correction to FresneFs 

 tangent-formula required by experiment, by supposing that the 

 transition from the one medium to the other, instead of being 



* Pogg. Ann. vol. cxiv. t Phil- Mag. S. 4. vol. xli. p. 519. 



'+ Pogg. ^4nn. vol. cxi. 



