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.
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