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.

318 PROF. MICHELSON, THE ECHELON SPECTROSCOPE.
I am aware of the difficulties to be encountered in the attempt to put this idea
into practical shape, and it may well be that they are in fact insurmountable-but in
any case it seems to be well worth the attempt.
Meanwhile the idea suggested itself of avoiding the difficulty in the following way:
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FIG. 2.
Plates of glass (Fig. 2), accurately plane-paralleled and of the same thickness, were
placed in contact, as shown in Fig. 2. If the thicknesses were exactly the same,
and were it not for variations in the thickness of the air-films between the plates, the
retardations of the pencils reflected by the successive surfaces would be exactly the
same, and the reflected waves would be in the same conditions as in the case of a
reflecting grating-except that the retardation is enormously greater.
The first condition is not very difficult to fulfil; but in consequence of dust particles
which invariably deposit on the glass surfaces, in spite of the greatest possible precautions, it is practically impossible to insure a perfect contact, or even constancy in
the distances between surfaces*.
If now instead of the retardation by reflection we make use of the retardation by
transmission through the glass, the difficulty disappears almost completely. In particular
the air-films are compensated by equivalent thicknesses of air outside, so that it is no
longer necessary that their thickness should be constant. Besides, the accuracy of
parallelism and of thickness of the glass plates necessary to insure good results is now
only one-fourth of that required in the reflection arrangement.
In Fig. 3 let ab = s, the breadth of each pencil of rays; bd = t, the thickness of each
element of the echelon; 0, the angle of diffraction; a, the angle adb; m, the number of
waves of length X corresponding to the common difference of path of the successive
elements. The difference of path is mX = t-ac.
t
Now ac = — cos (a + 0),
cos a v
* Nevertheless I have succeeded with ten such plates, phenomena such as the Zeeman effect, the broadening of
silvered on their front surfaces, in obtaining spectra which, lines by pressure, etc.-but evidently the limit has been
though somewhat confused, were still pure enough to show nearly reached.