Saturday, 22 September 2941 T.A.: Birthday on the floating raft

The barrel-rider illustrated by Horus Engels, 1957

The Greater Bear over the Long Lake on 22 September,
simulated in the "Stellarium" freeware

Sorry, guys, you are celebrating at the wrong day. Since the months of the Shire calendar do not have the same length as those of our Gregorian calendar, Bilbo's (and Frodo's) birthday was not yesterday, but it is today, on 22 Halimath = 23 September, see the table below.

Anyway, on this day, in 2941 T. A., Bilbo just managed to get, invisible, on the raft that the Elves had made out of their barrels. Despite his worsening health condition, he spent the day on-board until, after sunset, the raft arrived at Lake-Town. Once all Dwarves had been released from their barrels, they entered Esgaroth officially and requested shelter, which was willingly granted by the men of Esgaroth.   

Since the weather was fair, a very young moon, about two days old, will have been visible in the west at sunset. This was exactly one lunation (one full cycle of the lunar phases) before Durin's Day of 2941 T. A. When Bilbo released the Dwarves, he noticed the Greater Bear in the sky at late night but no moon any more. The text of "The Hobbit" is fully consistent with the lunar phases here.

P. S.: Happy Hobbitday to you all!

Days in the Gregorian calendar (white) and in the Shire calendar (yellow)