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If if we do not have hard evidence for the clock on Bilbos Mantelpiece, we have a picture by Tolkien of Bilbos hall ["Pictures by JRR Tolkien"; no 20: "The Hall at Bag-End, Residence of B. Baggins Esquire"]. In this picture we have two obviously mechanical clocks. On left beside the door showing six o'clock and one to the right with pendulum and two wieghts on a chain which shows to my great surprise seven o'clock.
Taking into account that Tolkien said that Hobbingen is on the latitude of Oxford then a difference of 1 hour in day time corrospondes to an distance of roughly 1500 km or 932 miles.
This is more or less the straight distance from Hobbing to the middle of Mirkwood. That means that he clock beside the door in Bilbos hall showed the Rhovanion time while that at his side wall showed Eridor time!
For the dwarvish reconing of time I assume that since the sundown on Dúrin's day was so improtant they would also recon time from sundown to sundown.
Therefore it might be a hobbitish invention to count day from midnight to midnight.
Respectfully
Findegil
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