Count a change that a ruler cannot resolve
Michelson’s 1907 lecture explains how changing an optical path carries a fringe through repeated bright and dark states. Those cycles compare a mechanical displacement with a light wavelength. A mirror displacement changes the round-trip path twice as much, so confusing path difference with mirror travel doubles the inferred length.
The measurement connects a source, an optical geometry and a material standard. A fringe is not itself a universal length unit until the wavelength and the medium in which it propagates have been specified.
Sources: [1]
A spectral line can contain more than one frequency
The lecture reports a search among many gas and metal-vapor radiations. Broad or multiple lines lost useful interference visibility as the path difference increased. Red cadmium light was unusually suitable for comparing the metre with a wavelength.
This is why a fine translation stage was insufficient. A changing source spectrum can wash out or modulate the same fringes being counted. Michelson used visibility as information about spectral structure as well as a practical limit on length comparison.
Sources: [1]
Visibility is a comparison of two intensities
For an ideal two-beam measurement, visibility is the difference between maximum and minimum intensity divided by their sum. Unequal beam powers, polarization mismatch and background reduce it even when the source is coherent. A low value is therefore not a unique measurement of spectral width.
For a stable source, visibility as a function of optical delay constrains first-order coherence. Converting the full interferogram into a spectrum requires a known delay coordinate, finite-window treatment and response correction. A single disappearing fringe supplies much less information.
Sources: [1]
Repeatability is not the whole uncertainty
Michelson compared determinations made by different observers and at different times. Agreement tested reproducibility, but refractive index, thermal expansion, alignment and the reference standard still governed accuracy. The historical result did not define today’s SI metre.
The 1907 award concerns optical precision instruments and the measurements made with them. Reducing it to the ether-drift null result hides the spectroscopy and metrology that the lecture actually develops.
Try the two failure modes separately
Read the lecture’s length-standard comparison beside its discussion of visibility. In the linked interferometer, first vary displacement with a fixed source, then vary source coherence with fixed geometry. A lost fringe and a shifted fringe ask different questions.
Sources: [1]