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    The Oxford English Dictionary gives the earliest recorded published date for log-book as being between 1679 and 1681:
    Log-book : a. Naut. A book in which the particulars of a ship’s voyage (including her rate of progress as indicated by the log) are entered daily from the log-board. Hence a journal of travel.
    a1679 Sir Jonas Moore, A new systeme of the mathematicks, (1681) vol I p271: ‘This account ruff taken off the Log-board, ought to be entred into a Book called a Traverse Book or Log Book.’
    1753 Chambers’s Cyclopaedia Suppl.: ‘Log-book, at sea, a book ruled and columned like the log-board.’
    1791 James Boswell, Life of Dr. Johnson vol II anno 1779, p309: ‘My Chester truly a log-book of felicity.’
    1813 Theatrical Inquisitor vol II p362: ‘It [the voyage] was divested of all log-book lumber.’
    1821 Lord Byron Diary in Works (1846) pp677/1: ‘This additional page of life’s log-book.’
    1889 W. C. Russell Marooned vol II chap iii p76: ‘The mate’s log-book was upon the table.’

    Log : Naut. and derived senses. An apparatus for ascertaining the rate of a ship’s motion, consisting of a thin quadrant of wood, loaded so as to float upright in the water, and fastened to a line wound on a reel. Hence in phrases to heave, throw the log, (to sail or calculate one’s way) by the log. Said also of other appliances having the same object.
    1574 William Bourne, A regiment for the sea (1577) ch xiv. 42b: ‘They hale in the logge or piece of wood again, and looke how many fadome the shippe hath gone in that time.’
    1644 Henry Manwayring, The sea-mans dictionary: or, An exposition and demonstration of all the parts and things belonging to a shippe: together with an explanation of all the terms and phrases used in the practique… (1644) at Logg-line: ‘One stands by with a Minut~glasse, while another out of the gallery lets fall the logg.’
    1669 Samuel Sturmy, The mariners magazine: or, Sturmy’s mathematical and practical arts. Whereunto is annexed, A compendium of fortification (by P. Staynred) (1669) vol IV chap ii p146: ‘We throw the Log every two Hours.’
    1769 William Falconer, An universal dictionary of the marine … A new edition, corrected (1780): ‘It is usual to heave the log once every hour in ships of war.’
    1834 Captain Frederick Marryat Peter Simple vol 1 chap xii p156: ‘It’s now within five minutes of two bells, so we’ll heave the log and mark the board.’

    Traverse-book n. (also travis-book) a log-book.
    a1679 Moore (1681) ibid
    1728 Chambers’s Cyclopaedia at Log: ‘They are enter’d into the Log-Book, or Traverse-Book, ruled and column’d just as the Log-Board is.’

    Log-board : n. a hinged pair of boards on which the particulars of a ship’s log are noted for transcription into the log-book.
    1669 Sturmy The mariners magazine (1669) ibid: ‘Next we will work the Courses of the Log-board.’
    1834 Marryat Peter Simple (1834) ibid: ‘O’Brien reported the rate of sailing to the master, marked it down on the log-board, and then returned.’
    1867 William Henry Smyth The sailor’s word-book: an alphabetical digest of nautical terms 1st edition (1867)
    Justin Reay