20 
MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
completely determines the reflected and refracted rays. The vis viva of the reflected 
ray will thus have for its expression 
2w 2 /i 2 „ sin 2 (0-0.) 
— 3 - avu cos 6. ■ 
or sin 2 (0 + 0y) 
If ts be the area of the pupil, we must alter the above in the ratio m :acos0, the 
section of the reflected beam, which gives 
27t 2 /< 2 sin 2 (0 — dj) 
a 3 Qm sin 2 (0 + 0,) 
for the quantity of vis viva which enters the eye and is afterwards condensed on the 
retina ; the corresponding expression for the incident ray is 
2tt 2 A 2 
- — s— am. 
a? 
If then we denote the brightness of the incident ray by 1 , that of the reflected ray 
will be represented by 
sin 2 (0 — 0 ; ) 
sin 2 ’(0 + 0 ; ) 
In like manner the vis viva of the refracted ray is 
27 r 2 A 2 sin 2 (20) 
am cos 
o u y 
Oif * 
sin 2 (0 + £ 
and the portion which would enter the eye, could it be placed so as to receive it, is 
sin 2 (20) 
2 t r 2 /* 2 
af sm 2 (0 + 0 ; ) 
giving for its comparative brightness the expression 
a, sin 2 (20) 
that is. 
a 3 a " sin 2 (0 + 0 ; )’ 
sin & t 4 sin 2 0. cos 2 ( 
or 
sin 0 sin 2 (0 + 0 ; ) 
4 cos 2 0 . sin 0 sin 0 ; 
sin 2 (0 + 0 ; ) 
16. Let us now take the component wave whose vibrations are performed in the 
secondary plane. Any displacement being represented by the equation 
27T 
z — k sin — (at-\-x-\-c), 
proceeding exactly as before, we shall have, on the supposition that no vis viva is lost, 
k 2 a cos 0 k ,2 a cos 0 /c 2 f/ ; cos 0 y 
The motion of a particle in the surface of separation regarded as performing its 
phase to the incident ray is 2 ir/rvcos (2wvt), which, as before, must be statically equi- 
valent to 2 nk’v cos ( 2 %vt) and cos (2th >t) ; but the directions of these three motions 
