In Rivendell, Elrond observed that the moon-letters on Thrór's Map must have been under the same crescent Moon at Midsummer that was then in the sky. The Moon's phase recurs like this on a cycle of almost exactly nineteen years, so we can calculate back to find the likeliest date the Map was made, a calculation that gives us two possible dates. These particular moon-letters must have been inscribed either in III 2770 (that is, the same year that Smaug drove the Dwarves from Erebor) or nineteen years later in III 2789 (just before Thrór gave the Map to his son Thráin). Either date would fit the established timeline, but if Elrond is right about the crescent Moon, one of these two dates must be the correct one.