230 
MR. STOKES ON THE THEORY OF CERTAIN 
actual length in air, § the retardation measured by phase, M the retardation measured 
by the number of waves’ lengths, so that 
It. 
— R, M=-R; 
then when M is an odd multiple of the vibrations produced by the two streams, 
when brought to the same focus, will oppose each other, and there will be a minimum 
of illumination ; but when M is an even multiple of ^ the two streams will combine. 
and the illumination will be a maximum. Now M changes in passing from one 
colour to another in consequence of the variations both of R and of X ; and since the 
different colours occupy different angular positions in the field of view, the spectrum 
will be seen traversed by dark and bright bands. It is nearly thus that Mr. Talbot 
has explained the bands seen when a spectrum is viewed through a hole in a card 
which is half-covered with a plate of glass or mica, with its edge parallel to the fixed 
lines of the spectrum. Mr. Talbot however does not appear to have noticed the 
polarity of the bands. 
Let h, k be the breadths of the interfering streams ; then we may take 
, . 27r , . /2it , \ 
«sin — A: sin f — g'j 
to represent the vibrations produced at the focus by the two streams respectively, 
whieh gives for the intensity I, 
I = (A-}-A‘Cosf)'^-4-(^sin^)2=A2_j_^2_j_2/jA:cos^, (1.) 
which varies between the limits (Ji — kY and {h-^-ky. 
5. Although the preceding explanation is imperfect, for the reason already men- 
tioned, and does not account for the polarity, it is evident that if bands are formed at 
all in this way, the number seen in a given part of the spectrum will be determined 
correctly by the imperfect theory ; for everything will recur, so far as interference 
is coneerned, when M is decreased or increased by 1, and not before. This points 
out an easy mode of determining the number of bands seen in a given part of the 
speetrum. For the sake of avoiding a multiplicity of cases, let an acceleration be 
reckoned as a negative retardation, and suppose R positive when the stream which 
passes nearer to the edge of the prism is retarded relatively to the other. From the 
known refractive indices of the plate and fluid, and from the circumstances of the 
experiment, calculate the values of R for each of the fixed lines B, C . . . . H of the 
spectrum, or for any of them that may be seleeted, and thence the values of M, by 
dividing by the known values of A. Set down the results with their proper signs op- 
posite to the letters B, C . . . denoting the rays to which they respectively refer, and 
then form a table of differences by subtracting the value of M for B from the value 
for C, the value for C from the value for D, and so on. Let N be the number found 
in the table of differences corresponding to any interval, as for example from F to G : 
then the numerical value of N, that is to say, N or ~N, according as N is positive 
