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On this day, in 2789 T. A., Thrór, dethroned King of the Mountain, wrote the moon-letters on his map. It was within the last year of Thrór's life before he was slain by Azog.

On this day, in 2865 T. A., the moon-letters became visible for the first time. Thrór's map was in the hands of Gandalf the wizard, but it did not occur to him to hold the map against the moonlight. It may have been a cloudy evening, anyway.

On this day, in 2941 T.A., the moon-letters became visible for the second time. Elrond detected them and read them aloud.

On all three days, the moon was "a broad silver crescent", a description that survived all revisions of "The Hobbit" unscathed. The best fit with the other lunar phases stated in the book is a moon that is 6 days and 9 hours old at 7.00 p.m. of midsummer's eve, with an illumination that is about 45 %, looking like the image given here ( ) that I just shot with my daughter's camera on 10.45 p.m. CEST. The deviation of the lunar phase that Elrond saw from that which Thrór saw at the same time of the day in 2789 T.A. is 11.8 hours, clearly a tolerable error margin.

(I cannot give the details of the calculations here; if you are interested, they are all included in my companion volume "The Moon in 'The Hobbit'", ISBN: 149756056X.)

The dates of 2789 and 2865 T.A. emerge from calculating the Callippic Cycle backwards, a period of 76 years after which the lunar phase repeats on the same day, with a deviation of a few hours. In ancient Greece, the Callippic Cycles were applied to base calendars on, with the first year of the first Callippic cycle beginning at the summer solstice of 330 BC. It may be plausible to assume that the Dwarves of Erebor used a similar calendar to devise the moon-letters.

Midsummer's day: Leaving Rivendell

It is a clear day on this day, in 2941 T.A., as the Company with Gandalf and Bilbo finally leave Rivendell (in whatever timeline) and head into the Misty Mountains.

Karen Fonstad calculates an average distance of 4 miles per day for this leg of the journey, but does not take the attested lunar phases into account. We will see later this month that they suggest a faster progress.

How interesting! That Tolkien should have ensured that he correctly used the lunar phases in his stories is, on reflection, as expected as it is delightful to discover :-)

He did so in retrospect, alas, and he had some odd misconceptions about the motions of the moon, though quite by chance he got it 90% right. My blog contains by now the almost completed Hobbit timetable, and I am right now in the process of editing it into an extended edition of my book, "The Moon in 'The Hobbit'".

Ah - perhaps the moon's journeyings prior to the Fourth Age were a little different :-D

Maybe. The lunar period would have had to be about 20 minutes shorter than now to make the phases in "The Hobbit" match with those of "LotR". *gr*