Eeplanation of Talbot’s Bands. 5) 
disturbance at F would be a succession of impulses corre- 
sponding to the half period of the original impulse. _ There 
is light at F, but it is light which belongs to the overlapping 
spectrum of the second order. As regards the wave-length 
AX under consideration, there is darkness. The difficulty, if 
it is still felt to be one, may be avoided by considering a 
grating giving rise to the “corrugated waves” of Lord 
Rayleigh*. I have called these gratings “ simple gratings,” 
as all other gratings may be imagined to be made up of 
superposed simple gratings. The light of a simple grating 
is concentrated into the two spectra of the first ordery. 
Tt may readily be shown that any device which gets rid of 
the spectra of different orders will change impulses which 
were originally in one direction into disturbances which are 
alternately in one and the other direction, so that no further 
question can arise as to the way in which, according to the 
view here adopted, the dark bands are formed in Talbot’s 
experiment. 
3. The proposition proved in § 1 allows us to extend the 
investigation to the case where the spectrum is produced by a 
prism. Inthe immediate neighbourhood of a given wave- 
length, the spectrum may be taken to be a normal one, and 
there can be no intrinsic difference between the bands seen 
in this case and those observed when a grating of the 
same resolving power is used. It has been shown by Lord 
Rayleigh that in all questions relating to resolving power 
the number of lines in the grating has to be replaced in the 
dp. 
dn’ 
thickness of the prisms, » the refractive index, and A the 
wave-length. It follows at once that the retardation which 
- gives black bands is for prisms 
ease of prisms by ¢ where ¢ is the aggregate effective 
14 
pM. 
4, It is interesting to follow out the modus operandi of a 
prism when an impulse is transmitted through it. For the 
sake of simplicity we may confine ourselves to the case 
that the law of refraction is such that the group velocity 
is independent of the wave-length. If the impulse be con- 
fined to the wave-front W F (fig. 3) before entering a refracting 
substance, it will at a given time in its passage through it 
* ‘Encyclopedia Britannica,’ “ Wave Theory,” and ‘Collected Works.’ 
+ Phil. Mag. xxxvii. p. 509 (1894). 
