216 
PROFESSOR POWELL ON A NEW CASE OF 
character of the bands, and the limits of thickness, as well as which of the two 
arrangements before described, will produce them, it is necessary to consider more 
precisely the relative refractions of the plate and medium, or the amount and direc- 
tion of the retardation ; and it is found that on such considerations we obtain an 
expression which includes these conditions ; — the difference of sign corresponding to 
the two arrangements : while it assigns the number of bands which will be formed be- 
tween any two given rays, or throughout the whole spectrum, with a given thickness 
of the plate. 
(13.) In the comparison of theory and observation, the broad facts, — that bands 
will be produced in the respective cases by the one or the other arrangement, — as 
well as their general character, — show an entire agreement with theory. 
The more precise comparison of the number of bands formed throughout the 
spectrum, or within certain definite spaces of it, though in some cases unavoidably 
imperfect from the difficulty of distinguishing the bands, yet upon the whole gives 
accordances as good as perhaps can be expected. 
(14.) When plates of doubly-refracting crystals are employed, the calculation for 
the extraordinary ray in particular directions in the crystal, becomes more eomplex, 
involving the laws of crystalline refraction. 
In all cases a small error in the index causes a comparatively large difference in 
the calculated numbei’ of bands. But, from whatever cause, in these last instances 
the application of theory is, as yet, less satisfactory than in others ; at least in the 
instance of calc-spar. 
(15.) The first observation of the general phenomenon reminded me of the pre- 
cisely analogous result obtained by Baron von Wrede, though in a manner so totally 
different*; in which two portions of light, unequally retarded the one by reflexion 
from the ^^r^^, the other from the second surface of a plate of mica, impinge jointly 
on a prism, whence results a spectrum crossed with bands ; while the author’s pro- 
found analysis (founded on the hypothesis of the internal reflexions of a ray among 
the molecules of a medium) opens an extended analogy between these cases and 
those of the absorption of definite rays by media in general. 
(16.) There is also obviously a general analogy between these phenomena and 
those observed by Mr. Fox Talbot and Sir D. Brewster, on partially intercepting 
the sj)ectrum by a plate of mica covering half the pupil of the eye ; — especially in the 
circumstance, that here also the plate must be applied towards one side of the prism, 
which corresponds to what has been described as a species of polarity. In those 
experiments the retardation is the difference of the retardations of the plate of mica 
and of a plate of air which would be contained between the surfaces of the mica pro- 
duced : in mine it is the difference of the retardation of the glass and of an equal 
thickness of the liquid medium of the prism. 
* Taylor’s Foreign Scientific Memoirs, vol. i. part 3, p. 487. 
