232 
MR. STOKES ON THE THEORY OF CERTAIN 
from the thick end, so that the same formulae will apply to both of the arrangements 
mentioned in art. 2. 
If we put the formula (2.) will apply to the experiment in which a plate of 
glass or mica is held so as to cover half the pupil of the eye when viewing a spectrum 
formed in any manner, the plate being held perpendicularly to the axis of the eye. 
The effect of the small obliquity of incidence of some of the colours is supposed to 
be neglected. 
The number of bands which would be determined by means of the formula (2.) 
would not be absolutely exact, unless we suppose the observation taken by receiving 
each fixed line in succession at a perpendicular incidence. This may be effected in 
the following manner. Suppose that we want to count the number of bands between 
F and G, move the plate by turning it .round a horizontal axis till the bands about 
F are seen stationary ; then begin to count from F, and before stopping at G incline 
the plate a little till the bands about G are seen stationary, estimating the fractions 
of an interval at F and G, if the bands are not too close. The result will be strictlv 
the number given by the formula (2.). The difference, however, between this result 
and that which would be obtained by keeping the plate fixed would be barely sen- 
sible. If the latter mode of observation should be thought easier or more accurate, 
the exact formula which would replace (2.) would be easily obtained. 
7. Suppose now the nearer face of the retarding plate made to rest on the nearer 
inner face of the hollow prism, and suppose one of the fixed lines, as F, to be viewed 
at a minimum deviation. Let (p, <p' be the angles of incidence and refraction at the 
first surface of the fluid, i, i' those at the surface of the plate, 2 s the angle of the 
prism. Since the deviation of F is a minimum, the angle of refraction (p'p for F is 
equal to s, and the angle of incidence <p is given by sin sin ‘P'f, and is the angle 
of incidence for all the colours, the incident light being supposed white. The angle 
of refraction <p' for any fixed line is given by the equation sin^'=- sin <p=— sin s ; 
then i=2s — ip', and i' is known from the equation 
(jb' sin sin z (3.) 
The retardation is given by either of the formulae 
R=T (j!a' cos 7 — |U; cos z). . (5.) 
These formulae might be deduced from that given in Airy’s Tract, modified so as 
to suit the case in which the plate is immersed in a fluid ; but either of them may be 
itnmediately proved independently by referring everything to the wave’s front and 
not the ray. 
By multiplying and dividing the second side of (5.) by cos i, and employing (3.), 
we get R=T sec i sec i versin (i—i') (6.) 
