The first actual attempt to make the wave length of sodium light a
standard of length was made by Peirce.[1] This method involves two
distinct measurements: first, that of the angular displacement of the
image of a slit by a diffraction grating, and, second, that of the
distance between the lines of the grating. Both of these are subject to
errors due to changes of temperature and to instrumental errors. The
results of this work have not as yet been published; but it is not
probable that the degree of accuracy attained is much greater than one
part in fifty or a hundred thousand. More recently, Mr. Bell, of the
Johns Hopkins University, using Rowland's gratings, has made a
determination of the length of the wave of sodium light which is claimed
to be accurate to one two hundred thousandth part[2]. If this claim is
justified, it is probably very near the limit of accuracy of which the
method admits. A short time before this, another method was proposed by
Mace de Lepinay.[3] This consists in the calculation of the number of
wave lengths between two surfaces of a cube of quartz. Besides the
spectroscopic observations of Talbot's fringes, the method involves the
measurement of the index of refraction and of the density of quartz, and
it is not surprising that the degree of accuracy attained was only one
in fifty thousand.
[Footnote 1: Nature, xx, 99, 1879; this Journal, III, xviii, 51, 1879.]
[Footnote 2: On the absolute wave lengths of light, this Journal,
III, xxxiii, 167, 1887.]
[Footnote 3: Comptes Rendus, cii, 1153, 1886; Journal, de Phys.,
II, v, 411, 1886.]
Several years ago, a method suggested itself which seemed likely to
furnish results much more accurate than either of the foregoing, and
some preliminary experiments made in June have confirmed the
anticipation. The apparatus for observing the interference phenomena is
the same as that used in the experiments on the relative motion of the
earth and the luminiferous ether.
Light from the source at s (Fig. 1), a sodium flame, falls on the
plane parallel glass, a, and is divided, part going to the plane
mirror, c, and part to the plane mirror, b. These two pencils are
returned along _cae_ and _bae_, and the interference of the two is
observed in the telescope at e. If the distances, _ac_ and _ab_, are
made equal, the plane, c, made parallel with that of the image of b,
and the compensating glass, d, interposed, the interference is at once
seen. If the adjustment be exact, the whole field will be dark, since
one pencil experiences external reflection and the other internal.
If now b be moved parallel with itself a measured distance by means of
the micrometer screw, the number of alternations of light and darkness
is exactly twice the number of wave lengths in the measured distance.
Thus the determination consists absolutely of a measurement of a length
and the counting of a number.
The degree of accuracy depends on the number of wave lengths which it is
possible to count. Fizeau was unable to observe interference when the
difference of path amounted to 50,000 wave lengths. It seemed probable
that with a smaller density of sodium vapor this number might be
increased, and the experiment was tried with metallic sodium in an
exhausted tube provided with aluminum electrodes. It was found possible
to increase this number to more than 200,000. Now it is very easy to
estimate tenths or even twentieths of a wave length, which implies that
it is possible to find the number of wave lengths in a given fixed
distance between two planes with an error less than one part in two
millions and probably one in ten millions. But the distance
corresponding to 400,000 wave lengths is roughly a decimeter, and this
cannot be determined or reproduced more accurately than say to one part
in 500,000. So it would be necessary to increase this distance. This
can be done by using the same instrument together with a comparer.
The intermediate standard decimeter, lm (Fig. 2), is put in place of
the mirror, b. It consists of a prism of glass one decimeter long with
one end, l, plane, and the other slightly convex, so that when it
touches the plane, m, Newton's rings appear, and these serve to
control any change in the distance, lm, which has been previously
determined in wave lengths.
The end, l, is now adjusted so that colored fringes appear in white
light. These can be measured to within one-twentieth of a wave length,
and probably to within one-fiftieth. The piece, lm, is then moved
forward till the fringes again appear at m. Then the refractometer is
moved in the same direction till the fringes appear again at l, and so
on till the whole meter has been stepped off. Supposing that in this
operation the error in the setting of the fringes is always in the same
direction, the whole error in stepping off the meter would be one part
in two millions. By repetition this could of course be reduced. A
microscope rigidly attached to the carriage holding the piece, lm, would
serve to compare, and a diamond attached to the same piece would be used
to produce copies. All measurements would be made with the apparatus
surrounded by melting ice, so that no temperature corrections would be
required.
Probably there would be considerable difficulty in actually counting
400,000 wave lengths, but this can be avoided by first counting the wave
lengths and fractions in a length of one millimeter and using this to
step off a centimeter. This will give the nearest whole number of
wave lengths, and the fractions may be observed directly. The centimeter
is then used in the same way to step off a decimeter, which again
determines the nearest whole number, the fraction being observed
directly as before.
The fractions are determined as follows: The fringes observed in the
refractometer under the conditions above mentioned can readily be shown
to be concentric circles. The center has the minimum intensity when the
difference in the distances, ab, ac, is an exact number of wave
lengths. The diameters of the consecutive circles vary as the square
roots of the corresponding number of waves. Therefore, if x is the
fraction of a wave length to be determined, and y the diameter of the
first dark ring, d being the diameter of the ring corresponding to one
wave length, then x = y²/d².
[Illustration:
----- +---+
|c | |
| | |
| | |+-------------------------+
| | || |
| | || |
| | |+-------------------------+ l
| | | 2.
| | | m
| +---+
| ______
| +-------------| |---+
| /\ /\ | +-----------| __|-+ | _
a|/ / / / | | | b | | | | |
S----------/\/__d/ / | | | | | | | | |
/ /| / /-----| |-----------|-| ||||||||||| |
| \/ | | | | | | | | |
_|_ | | | | | | |_|
| : | | +-----------|___|----+ | m
e| : | +-----------------------+
| : |
|_ _| 1.
U
]
There is a slight difficulty to be noted in consequence of the fact that
there are two series of waves in sodium light. The result of this
superposition of these is that as the difference of path increases, the
interference becomes less distinct and finally disappears, reappears,
and has a maximum of distinctness again, when the difference of path is
an exact multiple of both wave lengths. Thus there is an alternation of
distinct interference fringes with uniform illumination. If the length
to be measured, the centimeter for instance, is such that the
interference does not fall exactly at the maximum--to one side by, say,
one-tenth the distance between two maxima, there would be an error of
one-twentieth of a wave length requiring an arithmetical correction.
Among other substances tried in the preliminary experiments were
thallium, lithium, and hydrogen. All of these gave interference up to
fifty to one hundred thousand wave lengths, and could therefore all be
used as checks on the determination with sodium. It may be noted that in
case of the red hydrogen line, the interference phenomena disappeared at
about 15,000 wave lengths, and again at about 45,000 wave lengths; so
that the red hydrogen line must be a double line with the components
about one-sixtieth as distant as the sodium lines.--_Amer. Jour.
Science._
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[RURAL NEW YORKER]