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XVI. On the Theory of certain Bands seen in the Spectrum. 
By G. G. Stokes, M.A., Fellow of Pemhrohe College, Cambridge. 
Communicated by the Rev. Baden Powell, M.A., F.R.S., 8fc. 
Received May 25, — Read May 25, 1848. 
Some months ago Professor Powell communicated to me an account of a new 
case of interference which he had discovered in the course of some experiments on 
a fluid prism, requesting at the same time my consideration of the theory. As the 
phenomenon is fully described in Professor Powell’s memoir, and is briefly noticed 
in art. 1 of this paper, it is unnecessary here to allude to it. It struck me that the 
theory of the phenomenon was almost identical with that of the bands seen when a 
spectrum is viewed by an eye, half the pupil of which is covered by a plate of glass 
or mica. The latter phenomenon has formed the subject of numerous experiments 
by Sir David Brewster, who has discovered a very remarkable polarity, or apparent 
polarity, in the bands. The theory of these bands has been considered by the Astro- 
nomer Royal in two memoirs “ On the Theoretical Explanation of an apparent 
new Polarity of Light,” printed in the Philosophical Transactions for 1840 (Part II.) 
and 1841 (Part L). In the latter of these Mr. Airy has considered the case in 
which the spectrum is viewed in focus, which is the most interesting case, as being 
that in which the bands are best seen, and which is likewise far simpler than the 
case in which the spectrum is viewed out of focus. Indeed, from the mode of ap- 
proximation adopted, the former memoir can hardly be considered to belong to the 
bands which formed the subject of Sir David Brewster’s experiments, although the 
memoir no doubt contains the theory of a possible system of bands. On going over 
the theory of the bands seen when the spectrum is viewed in focus, after the receipt 
of Professor Powell’s letter, I was led to perceive that the intensity of the light 
could be expressed in finite terms. This saves the trouble of Mr. Airy's quadratures, 
and allows the results to be discussed with great facility. The law, too, of the 
variation of the intensity with the thickness of the plate is very remarkable, on 
aceount of its discontinuity. These reasons have induced me to lay my investigation 
before the Royal Society, even though the remarkable polarity of the bands has been 
already explained by the Astronomer Royal. The observation of these bands seems 
likely to become of great importance in the determination of the refractive indices, 
and more especially the laws of dispersion, of minerals and other substances which 
cannot be formed into prisms which would exhibit the fixed lines of the spectrum. 
2 H 
MDCCCXLVIII. 
