NavList:

Frank,
My quote from the 1851 edition was because I have that available in my book-shelf.
However, in the first edition of Bowditch, from 1802, the same statement is found on page 129: "...; hence the length of a knot ought to be 51 feet; each of these knots is divided into 10 fathoms. If the glass be only 28 seconds in running out, the length of the knot ought to be 47 feet and 6 tenths."  Further on, page 237, "...in the second and third columns are the knots and fathoms the ship is found to run per hour. Some navigators do not divide the knot into ten fathoms, but onto half knots only, ...". In the example on page 244 it is clear that Bowditch used tenths of a knot. 

Don Seltzer rightly points out that the lengths between knots did differ quite a lot. Norwood, in his Seaman’s Practice from 1636 recommends 50 feet for a half-minute glass. Maskelyne, in British Mariner’s Guide from 1763 says that prior to Norwood 42 feet was common for a 30 second glass; Nares, in his Seamanship from 1882 gives 47.1 feet for 28 seconds; a difference of 20%. Different lengths between different knots on the same log-line was proposed in Sweden in 1836, based on the fact that as more line was let out the slip of the chip decreased. I do not know if this kind of line was widely used or not. Roswall, in his Navigation from 1824, recommends different lengths for different latitudes. Between the equator and 30° latitude he states 46 Swedish fot, from 30° to 60° 47 or 48 fot, above 60° 49 fot. For 30 seconds. A Swedish fot is slightly shorter than an English foot. Don says the log-line was only marked for integer knots. At least in Sweden it was common to also have half-knot marks. I have myself used such half-knot lines.

Modris Fersters excerpt from the Investigator logbook is interesting in that only even numbers for F were used. That means that speed was recorded only to the nearest quarter of a knot. This makes sense as the precision in measured speed is not too great.

I have again looked into the log of Bounty, and am convinced that they used the F column to mark ⅛ of a knot. In the file I used, https://whalesite.org/pitcairn/fatefulvoyage/logbooks.html there seems to be a few typing or transcription errors, but on the average ⅛ gives reasonable results. In the Remarks for 1 December 1787, it is stated that “The Log will always be marked in proportion of fifty feet to Thirty Seconds of Time”.

In an interesting article by Frank Scott, “Speed, Navigational Accuracy and the ‘Ship Log’ “, in the Mariner’s Mirror 92:4 pages 477-481, 2006, Scott writes “The division into eights or tenth of a knot seldom equated to true fathoms but was recorded under the heading of ‘fathoms’ “.

Frank, your statement that the F column shows sixth parts of miles (in an hour) is interesting. Where have you seen that? Yes, I care, seriously. The study of old logbooks gives an insight into how navigation was actually performed, and shows different practices among different masters. It is important input for nautical research.
Lars