MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
27 
whence 
Consequently 
. 2k. [\ + s) sin 25 
1 (1 + s) sin 25 + (1 + s') sin 25, 
2t i 2 k 2 a 
q — — avco cos 9 
7 "6 
2 7T 2 # 2 
= — ^ avco cos 
l f (1 + s) sin 23 — (1 + s') .sin 25, V 
[(1 + s) sin 25+ (1 + s') sin 25, J 
25. If j' j, denote 
that of the incident 
2 7T 2 # 2 
= — am cos - 
a. 
2(1 + s) .sin 25 
(1+s) sin 25+ (I + s') sin 25, 
the comparative brightness of the reflected and refracted rays, 
secondary ray being represented by unity, we shall have 
(1 + s) sin 25 — (1 +s') .sin 25, V 2 
(1 + s) sin 25 + (1 + s') sin 25, J 
rs . ot cos 5 q. 
j nz q -f- q — •±i 
21 w cos 5, 1 co cos 5 cos 5, q 
a 3 </, A-, 2 1 sin 5, /c, 2 
«, 3 a k 2 1+s sin 5 k 2 ’ 
• 4 sin 5, [ (1+s) sin 25 l 2 
1+s sin 5 \(1 +s) sin 25 + (1 +s ; ) sin 25, J 
If then i' be — tan2 (^~^I as the experiments of Brewster and Arago would lead us 
J tan 2 (6 + 5,) 1 
to infer, in all such cases at least we must have s' =s. In fact, being equi- 
valent to sinol+sin^^’ we cou ^ not ^ ave exact agreement between theory and expe- 
riment unless 
(1 + s) sin 25 — (1 +s') sin 25, sin 25— sin 25, 
(1 + s) sin 25 + (1 + s') sin 25, sin 25+ sin 2.Q’ 
that is, unless (1 +s) sin 2Asin 20, — ( 1 +s J ) sin 2Asin 20, 
= — (1 +s) sin 29 sin 29 t +(1 +a') sin 20 sin 20,, 
that is, unless 2(1 +s)=2(l or s=s'. 
7T 
Neither without this condition would j vanish when 9+9=-, or 20, =x— 29, for in 
f s — s' V 2 
that case the expression for j becomes C ^ A • 
26. It is extremely natural to suppose that the effect upon the medium is mainly, 
if not entirely, operated by the refracted ray in its passage into the medium, after its 
separation from the reflected ray ; and as s and s' denote the ratios that is to 
say, the ratio, for each case, in which the vis viva entering the medium distributes 
itself between the particles of the medium and the particles of the ether interfused 
amongst them, we ought to expect that in an isotropical medium, like that under 
e 2 
