I hate to confuse anyone with the facts but the Oxford English Dictionary
2nd ed. has the following entry

dead reckoning

[dead /a./ V.]

The estimation of a ship's position from the distance run by the log
and the courses steered by the compass, with corrections for current,
leeway, etc., but without astronomical observations. Hence /dead/
latitude (q.v.), that computed by dead reckoning.

"*1613* M. Ridley /Magn. Bodies/ 147 Keeping a true, not a dead
reckoning of his course." "*1760* Pemberton in /Phil. Trans./ LI. 911
The latitude exhibited by the dead reckoning of the ship." "*1840* R.
H. Dana /Bef. Mast/ xxxii. 124 We had drifted too much to allow of our
dead reckoning being anywhere near the mark." "*1891* /Nature/ 3 Sept.,
The log, which for the first time enabled the mariner to carry out his
dead-reckoning with confidence, is first described in Bourne's ?Regiment
for the Sea?, which was published in 1577." "*1917* Bosanquet &
Campbell /Navigation for Aerial Navigators/ i. 4 In aerial
navigation+Dead Reckoning is the position arrived at as calculated from
the estimated track and the estimated speed made good over the
ground." "/Ibid./ 5 These data enable us to find a Dead Reckoning
position." "*1935* C. G. Burge /Compl. Bk. Aviation/ 477/1 Dead
reckoning+is a compromise between pilotage and navigation." "*1868*
Lowell /Witchcraft/ Prose Wks. 1890 II. 372 The mind, when it sails by
dead reckoning+will sometimes bring up in strange latitudes."


The log is the ships log - not a log in the water.

It is interesting to note the distinction between pilotage, navigation and
dead reckoning.