This was done in the year of Nabonassar 578, and is thus described by Daniel.
We must assume, from the canon of Ptolemy, that it was Nabonassar who bowed himself before the weight of the arms of Assyria.
No war seems to have been waged between Tiglath-Pileser and Nabonassar.
Nabonassar had died and was succeeded by his son Nabu-nadin-zeri, who, after reigning for two years, was slain in a rebellion.
There is no reason to think that the observation of eclipses by the Babylonians commenced with Nabonassar.