MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
25 
We have therefore exactly the same equations to combine as before, with the sole 
exception that occupies the place of a l ; we have therefore only to make this 
simple change in the value of sin 0 P and we obtain 
sin 0,= ( 1 -j-s) .— ^ sin 0 
1 a? a 
2t r 2 /i 2 
p — — 7 j — avu cos 0 
i 27 r 2 /i 2 
j) — — r- ava cos 
a 6 
sin 2 (Q-Sj) 
sin 2 (9 + 9,) 
27 r 2 /i 2 . sin 2 (29) 
».= — 5 - am cos fl,. . a - . - . - — 
/ ; « 3 1 1 sin 2 (9 + 9,) 
with the same expressions for the comparative brightness as before. See No. 16. 
23. The first of the above equations, compared with the Cartesian law of refraction, 
regarded as an experimental truth, shows that s is independent of 0 ; in fact 
— “/ 
s= 
a, a sin i 
1 , 
and since by the Cartesian law is independent of 0, it follows that s is also inde- 
pendent of 0. This quantity must therefore be regarded as a certain coefficient of 
absorption, depending mainly on the constitution of the crystal and the period of the 
incident ray, possibly also in some degree on the orientation of the ray, or the posi- 
tion of the plane in which its vibrations are performed, with regard to certain fixed 
planes in the crystal, or refracting medium, whether solid or fluid. The theoretical 
determination of this coefficient can only result from a more perfect theory of reso- 
nance than has hitherto been given, and it is hoped that some of the great modern 
analysts will turn their attention in this direction. 
If we denote the former refractive index % or by as before, and the altered 
a 3 a ; ?lU ; * 
refracted index 
. „ •-? or — 1 — by a., we shall have 
(1 +s)a l 3 a t 1+s §,a, Jrp 
/x 
t*»=TTs- 
This very simple formula, now given for the first time, demonstrates the rule I 
have before enunciated, namely, 
The solar rays can exercise no action upon any medium through which they are trans- 
mitted without an accompanying diminution of the refractive index. 
24. To estimate the effect of this diminution upon the intensities (i 1 , i t ) of the 
reflected and refracted rays, unity as before representing the intensity of the incident 
primary ray, we have 
., _p' sin 2 (9 — 9 ( ) 
1 p sin 2 (9 + 9 ; ) 
MDCCCLIV. 
E 
