,36 
MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
s — s' 
4(1+*) 
+ s + s') 2 ^’ 
9~\2 + * + «'} 9 
tan y — — oo, except when s'=s, in which case tan y'=^. 
Further, tan y,= 2 + g+ J j • tan y. 
We see therefore that t here is no reflected ray of the first class, nor any of the second 
class if ,?'=.$ ; in that case tan y,= tan y, and q,=q- The vis viva communicated to the 
fluid arises therefore entirely from the primary component wave, which imparts to it 
the vis viva ~ — p ; the orientation remains in this case unchanged; but if a' differs 
from s the case is different; in that case the secondary beam produces a slight 
reflected ray whose vis viva = 
s—s' 
q, and whose orientation is — -, so that its 
|_2+s + s'j 
vibrations, like those of its parent ray, lie in the secondary plane. The orientation 
(y ( ) of the refracted ray is given by the formula 
, * 2(1 +*) 
tan y ; 2 + « + s' 
whence 
tan y, — tan y—\ 0 
i—J 
2 + s + s' 
.tan y. 
The plane of vibration is therefore rotated in the positive or negative direction, that 
is, according to our conventions, from left to right, or from right to left according as 
s is greater or less than s', that is, according as the primary or secondary refracted 
ray exerts a greater action on the fluid. 
The quantity of vis viva expended on the fluid is in this case 
, , s 4s'(l+s) 
v,+*?,=-nr/+ (2 + s + s y ?> 
which must be employed in working some effect or other upon the fluid. 
If we suppose that s and s' are constant for every thin stratum of fluid of the same 
vertical height <$|, since the effect ought to vanish with we may suppose 
s—s 
2 + s + S 
and regarding y as a function of |, we have 
j =*$% ; 
tan y ; — tan y = § tan y = ^ tan y . 
Consequently 
whence 
d . 
Js 7 
tan y 5 
loge tan y=o-|+ log £ tan C, or 
tan y— tan C.s^. 
In this equation C is the initial value of y at the surface of the fluid, or at the surface 
of a crystal which possesses the property in question. The circular polarization, as 
