Arthur,
Observing the length of the sidereal day (a stars transit) and
comparing it to the length of the solar day (the suns transit) seems to
me a very good suggestion for a possible method employed. If these daily
differences were measured and then summed an equation of time connecting
sidereal time to solar time and visa-versa could be constructed. For
reference, the maximum difference between the mean solar day length and
the apparent solar day length is about 30 seconds and occurs in late
December. The diference between the regular rate of a sidreal day and
our fictious mean solar day is, of course, not far apart. The graph of
the summed time differences vs declination i.e., the analemma, would
then not be far apart either.
Part of my interest in all of this is knowing how much technology would
have been needed to measure these differences and wether it was measured
first with an analytical solution provided later. This is not assuming
then that the analytical construct of a mean solar day already existed.
In Dava Sobel's excellent book, "Longitude", about the struggle of John
Harrison to construct a clock for determining longitude, she points out
that the equation of time was known before Harrison. This puts a
milestone for the awareness of the equation of time, a.k.a. the
analemma, at about 1690.
Still hoping then, someone has the history of its discovery and its
possible evolution.
Regards,
Luke
