MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
33 
we see therefore in general why particular rays should be selected for absorption, with- 
out any insensible gradation, and why some lines of absorption, those corresponding 
to unison for example, should be more strongly marked than others; and these pre- 
liminaries being conceived, then comes the equation 
sin ^=(1+$)^ sin 0, 
which explains how those rays which undergo absorption are turned out of their places 
and deflected towards the less refracted end of the spectrum, and in some cases, 
though with intensities so diminished as to be imperceptible, far beyond the limits of 
the visible spectrum. In fact as s increases, the above equation shows that 0 { increases. 
The refracted ray is therefore turned more from the normal, or deviates less from its 
original course than it would do if there were no absorption, in which case a = o. 
The intensities of the reflected and refracted rays, both in the primary and secondary 
planes, will of course be diminished by the loss of vis viva, as is further apparent from 
the expressions which have been obtained for i', i n j ! and^', in Nos. 24 and 25, namely, 
sin 2 (6 — 9,) . 4 cos 2 0 sin 0 sin fl / 
' ~ sin 2 (0 + 0,)’ l ‘~ I " Ts sin 2 (0 + 0,) 
., | ( 1 + s) sin 20 — ( 1 4- s') sin 20, 1 2 
J | (1 +s) sin 20 + (1 -I -s') sin 20, j 
• 4 sin 0, J (l+s)sin20 | 2 
1 +s sin0 |_(1 + s) sin 20 + (1 +s') sin 20, J 
where it maybe observed that and diminish rapidly as s increases. Without 
the turning action above mentioned, the lines of absorption might exist indeed in a 
less marked manner, but the turning action fairly dismisses the weakened rays out 
of their places, and these places, if occupied at all, will be occupied by stray rays of a 
different colour from their immediate neighbours, presenting a faint tinge of the 
colour which has been turned from a remote space on the more refracted end of the 
spectrum. And this, I consider, is the true explanation of the phenomenon discovered 
by Brewster, and cited by Draper, p. 85 ; that red light exists in the violet spaces 
of the solar spectrum and blue light in the red : provided the red light in the violet 
spaces be regarded as the extreme violet, deflected towards the purple part of the 
spectrum ; for the extreme violet rays, to my own eyes at least, scarcely differ in 
colour from the extreme red. 
In the celebrated Memoire ofM. Cauchy’s (1836, cited by Beer, Einleitung in die 
hohere Optik, p. 209, and reproduced in theExercices d’Analyse Mem. tom. i. p.288), 
the velocity of undulation is given by a rapidly converging series of the form 
d 2 = A 0 -(- A 2 -^+A 4 ^ 4 + &c., 
A A 
in which I have thought it right not to include a 2 , a 4 , &c. under the unknown con- 
stants A 2 , A 4 , so as to exhibit to the eye the rapidity of convergence. As a first 
approximation, we have 
a= CA 0 , 
MDCCCLIV. 
F 
