240 
MR. STOKES ON THE THEORY OF CERTAIN 
14. The preceding investigation will apply, with a very trifling modification, to Sir 
David Brewster’s experiment, in which the retarding plate, instead of being placed 
in front of the object-glass of a telescope, is held close to the eye. In this case the 
eye itself takes the place of the telescope ; and if we suppose the whole refraction to 
take place at the surface of the cornea, which will not be far from the truth, we 
must replace fhy the diameter of the eye, and -vj/ by the angular extent of the portion 
of the spectrum considered, diminished in the ratio of m to 1, m being the refractive 
index of the cornea. When a telescope is used in this experiment, the retarding 
plate being still held close to the eye, it is still the naked eye, and not the telescope, 
which must be assimilated to the telescope considered in the investigation ; the only 
difference is that must be taken to refer to the magnified, and not the unmagnified 
spectrum. 
Let the axis of x be always reckoned positive in the direction in which the blue 
end of the spectrum is seen, so that in the image formed at the focus of the object- 
glass or on the retina, according as the retarding plate is placed in front of the ob- 
ject-glass or in front of the eye, the blue is to the negative side of the red. Although 
the plate has been supposed at the positive side, there will thus be no loss of gene- 
rality, for should the plate be at the negative side it will only be requisite to change 
the sign of g. 
First, suppose g to decrease algebraically in passing from the red to the blue. 
This will be the case in Sir David Brewster’s experiment when the retarding plate 
is held at the side on which the red is seen. It will be the case in Professor Powell’s 
experiment when the first of the arrangements mentioned in art. 2 is employed, and 
the value of N in the table of differences mentioned in art. 5 is positive, or when the 
second arrangement is employed and N is negative. In this case ra- is negative, and 
therefore — and therefore (15.) is the expression for the intensity. This 
expression indicates a uniform intensity, so that there are no bands at all. 
Secondly, suppose g to increase algebraically in passing from the red to the blue. 
This will be the case in Sir David Brewster’s experiment when the retarding plate is 
held at the side on which the blue is seen. It will be the case in Professor Powell’s 
experiment when the first arrangement is employed and N is negative, or when the 
second arrangement is employed and N is positive. In this case zd- is positive; and 
since tst varies as the thickness of the plate, g' may be made to assume any value from 
— (Ig-f/^-pA”) to -f-oo by altering the thickness of the plate. Hence, provided the 
thickness lie within certain limits, the expression for the intensity will be (16.) or (17.)- 
Since these expressions have the same form as (1.), the magnitude only of the coef- 
ficient of cos g', as compared with the constant term, being different, it is evident 
that the numbei- of bands and the places of the minima are given correctly by the 
imperfect theory considered in Section I. 
15. The plate being placed as in the preceding paragraph, suppose first that the 
breadths h, k of the interfering streams are equal, and that the streams are contiguous. 
