The earlier copyright dates would apply to chapters 4-20, which were
serialized in 7 installments in _Atlantic Monthly_ from November 1874
to July 1875. The rest of the composition was done for the Mississippi
book, save those pieces like the Karl Ritter story which had been
composed for _A Tramp Abroad_.
Although the copyright issue is fairly straightforward, the composition
question has been the subject of debate because MT incorporated a lot
of "found" material as well--that is, not stuff he composed but
"borrowed" not always with attribution. For a rather thorough
examination of all of this see Horst Kruse, _Mark Twain's Life on the
Mississippi_ (Amherst, 1981).