MR, POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
35 
q' f (1 + s) sin 29 — (1 + s') sin 203' 2 
q |(1 + s) sin 20 4- (1 + s') sin 20, J 
q t 4. (1 + s).sin 20. sin 20, 
q { (1 + s ) sin 20 + (1 + s') sin 20, j- 2 
If for isotropical media we suppose .s' =s, the two last formulae become 
q' tan 2 .(0 — 0,) 
q tan 2 (0 + 0,) 
q t 4 sin20.sin20 / 
q 1 + s {sin 20 + sin 20 / } 2 
35. Lastly, if y, y , y j denote, as before, the orientations of the compound rays, 
regarded as plane polarized, that is according to the present theory, as performing 
their vibrations in a plane making the angles y, y', y ( with the plane of incidence, we 
shall have 
k 
tan y=;j 
. , k' V h , 
tan y —jy =- -- f tan 7 = 
tan y 
(] + s) sin 20 — (1 + s') sin 20, sin (0 + 0,) 
(l + s) .sin 20 + (1 +6') sin 20, sin (0 — 0,) 
k, k. h , 
,dn5 '' = i-; = *T ( tau5 ' 
or 
2(1 +s) sin (0 - 
u,li /• 
If s'=s, we get 
tan y = 1 , 
(1 +s) sin 20 + (I + s') sin 20, 
(0 + 0,) COS (0+0,)^ 
- = . tan y 
cos (0 — 0,) ' 
tan. (0 — 0,) sin (0 + 0,) 
tan(0 + 0y) sin (0 — 0,) 
tan y 
5111 10 f Vj) 
' ’ lil ^ 1 sin 20 + sin 20, 
2 si n (9 + 9,) 
in 20+ sin 20," ^ an ^ 
the same expressions which we obtained on the supposition that there was no absorp- 
tion, and which have been tested by Brewster and Arago. 
36. A most interesting application of this theory is the explanation it affords of 
the rotatory phenomena of polarization exhibited by certain liquids, as also by certain 
solids, some specimens of quartz, for instance, which are distinguished from each 
other by the known appellations of right-handed and left-handed quartz. 
Let us suppose that the liquid (a solution of sugar or of honey, for instance, both of 
which are found to possess this property) is divided by horizontal sections at a small 
vertical distance from each other, f being the depth below the surface of the fluid. 
Though there is no refraction or deviation as the rays pass from one stratum to another, 
nothing prevents us from making 0 in the formulae just found, which gives 
p'-O, 
P,= 
1 -{- S 
