Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

320 PROF. MICHELSON, THE ECHELON SPECTROSCOPE.
or putting dn= unity,
d =................................................(IV ).
s
The quantity d\/X = E corresponding to this is found by substituting this value of
dO in (II), whence
E=...................................................(V ).
Hence the limit of resolution is the nth part of the distance between the spectra.
This fact is evidently a rather serious objection to this form of spectroscope. Thus in
observing the effect of increasing density on the breadth of the sodium lines, if the
broadening be of the order of \/bt the two contiguous spectra (of the same line) will
overlap. As a particular case, let us take t = 7 mm., E= 17000 It will be impossible
to examine lines whose breadth is greater than the fourteenth part of the distance
between the D lines. It is evidently advantageous to make t as small as possible.
Now the resolving power, which may be defined by -, is proportional to the product
Wt. Consequently, in order to increase it as much as possible it is necessary to use
thick plates, or to increase their number. But in consequence of the losses by the
successive reflections, experience shows that this number is limited to from 20 to 35 plates,
any excess not contributing in any important degree to the efficiency.
I have constructed three echelons, the thickness of the plates being 7 mm., 18 mm. and
30 mm. respectively, each containing the maximum number of elements-that is, 20 to 35,
and whose theoretical resolving powers are therefore of the order of 210,000, 540,000 and
900,000 respectively. In other words, they can resolve lines whose distances apart are the
two-hundredth, the five-hundredth and the nine-hundredth of the distance between the
D lines.
Consequently the smallest of these echelons surpasses the resolving power of the best
gratings, and what is even more important, it concentrates all the light in a single
spectrum.
The law of the distribution of intensities in the successive spectra is readily deduced
from the integral
s/2
A = cos pxdx,
J - s/2
27r
where p= -.
sin2 wr - 0
Hence I = A2 =
(4O)2