An apology for a missed reference.
It has been brought to our attention that our tight constrain of 12590–12800 seconds on the value of
obtained in our paper
1
was pre-empted by Tanikawa and Sôma.
2
Unfortunately, we were unaware of their paper, and had we known of it, we would certainly have acknowledged their result and referenced it. In mitigation of our omission, we would like to point out that our approaches to the subject are complementary rather than tautological.
In their analysis, Tanikawa and Soma considered both
and the tidal acceleration (
) of the Moon as variables. In one section of their analysis, they fixed the value of
to that in the contemporaneous Jet Propulsion Laboratory ephemerides and thereby obtained nearly the same constraints on
that we did later. However, in our approach we treated the observational account of the eclipse from Rome as circumstantial and used our most recent model of the behaviour of
3
to determine whether the eclipse could have been total at Rome. An important element in our discussion was the detail and circumstances of Livy’s account of the eclipse as seen in Rome.
We apologise to Tanikawa and Soma for omitting to acknowledge their paper of 2004.
