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.

PROF. MICHELSON, THE ECHELON SPECTROSCOPE. 319
or, since 0 is always very small,
t
ac = -- (cos a- sin a)= t (1 -0 tan a),
COS a
and hence = ( - 1)t + s.........................................(I).
a, b
I i
i Il
i
/ I
/ / I
FIG. 3.
To find the angle corresponding to a given value d\, differentiate for X and we find
do0 1 d~sL
X = - [m -t -.
dX s \ t dx)
Putting in this expression the approximate value of
t
m = (-l),
we have dx/X = (/ -d....... (II).
For the majority of optical glasses b varies between 0'5 and 1'0.
The expression (II) measures the dispersion of the echelon. To obtain the resolving
power, put e = d/X for the limit. For this limiting value the angle 0 will be \/ns,
where n is the number of elements; whence ns = the effective diameter of the observing
telescope. Substituting these values we find
t...........................................( I II).
To obtain the angular distance between the spectra, differentiate (I) for m; we find
dmn s '