38 
MR. POWER ON THE ABSORPTION OF THE SOEAR RAYS, ETC. 
38. I return to the subject of reflexion and refraction. In the genera! theory I 
have taken the case of a dense refracting medium, as it is usually termed (though I 
think it will turn out that it should rather be termed a rare refracting medium), in 
which *^0 > 1, or y J; > 1. But all the steps will hold, mutati.s mutandis, when p,< 1, 
and it may be convenient to exhibit the formulae adapted to that hypothesis. They 
are as follows : — 
For the primary wave, 
hi — sin (0 ,-0) 
h sin (0, + 6) 
h, sin 29 
It sin (9, + 0) 
p' sin 2 (9,-9) 
p sin 2 {9 , + 9) 
Pi 1 sin 20, sin 2 9 
p l+s sin 2 (9 1 + 9) 
For the secondary wave, j= 
*/_ 
(1 +s') sin 20,— (1 + s) sin 29 
(1 + s) sin 2 0, + (1 + s) sin 29 
2(1 +s) sin 29 
k (1 + s') sin 2 0, + (1 + s) sin 29 
q 1 J (1 + s / ) sin 20 ,— (1 + s) sin 201 2 
q |(1 +S 1 ) sin 29, + (1 +s) sin 26] 
q, 4(1 + s) sin 20, .sin 29 
q ((l+s') sin 29,+ (l + s) sin 20) 2 
To which must be added, 
1 1+5 
sin sin 0— — -sin 6 
1 F, F 
. i . ( 1 +T) sin 20 , — ( 1 +s) sin 20 sin( 0 ,+ 0 ) 
' ‘ (1 +s') sin 29, + (1 +s) sin 20 sin (0,— 9) 
2.(1 +s).sin (0 + 0 ,) 
Vi * aia 7' ^ _| _ 5/ ) . s in 20,+ (l +s) sin ‘20 
I have thought it right to give the whole series of formulae for the convenience of 
persons who may be possessed of the means to test them experimentally, and I may 
mention that it is more particularly in the refracted rays that they differ from the 
formulae of Fresnel; it is therefore to the latter that I must principally look for the 
experimental verification of this theory. 
It mav be as well to write down the formulae for the secondary wave in case s and 
s' are equal, or very small when unequal. They are as follows : — 
k' tan (0,-0) 
k tan (0,+ 9) 
k, 2 sin 20 
k sin 20 ,+ sin 20 
