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    Re: Sun Moon Lunars to 155 degrees
    From: George Huxtable
    Date: 2010 Apr 2, 16:36 +0100

    Brad wrote-
    
    "It is always a possibility that multiple octants were used, of course.  It
    was a scientific expedition and we do know (based upon earlier comments)
    that there were two octants on board."
    
    from George-
    
    Not quite so. We know of two SEXTANTS aboard Adventure, supplied by the
    Board of Longitude. These were immense, heavy, 15-inch-radius jobs, one by
    Dollond and one by Ramsden. These were similar to the two provided for
    Resolution. Additionally, we know that Resolution's officers had also,
    between them, at least three more (possibly four more) brass sextants of
    their own. If Adventure's officers had been able to muster a similar number
    between them, there would have been more than enough for measuring the
    lunar distance and the altitudes simultaneously, given three observers;
    which no doubt were available on such a well-manned vessel. I know nothing
    about any wooden octants aboard, but think it likely there would have been
    several, and these would probably be regarded as good enough for taking the
    altitudes.
    
    Bayly, in a letter to Banks about the third voyage, quoted in David vol 3,
    writes about the poor accuracy he found in the 15-inch Ramsden aboard
    Discovery, (which may well have been the same instrument used on Adventure
    in the second voyage) finding that it was producing longitude errors of
    sometimes more than a degree; "in consequence of which I made no other use
    of it during the remaining part of the voyage but to observe altitudes at
    the time of observing distances, as in that case a small error on altitude
    would seldom cause any effect in computing of the correction for parallax
    and refraction"
    
    Which appears to confirms that simultaneous measurement of altitudes with
    lunar distance, requiring three observers with three instruments, was the
    way the job was done. However, if necessary, the astronomers were capable
    of obtaining the altitudes of the bodies by calculation rather than
    observation, as Maskelyne had explained how to do so in his British
    Mariner's Guide of 1973.
    
    Now for Brad's comments about the various symbols that were placed by the
    lunar distance:  no doubt this will become clear once someone can get
    access to the relevant pages of the Second-voyage report.
    
    In the Third voyage, which also visited Ulietea and made observations over
    several days, there was a complex program of different observers (Cook and
    King)making simultaneous measurements of lunar distance with various
    sextants, which they then exchanged and remeasured (see page 43, third
    voyage). Four Ramsden sextants, a Dollond, and a Bird were compared in this
    way, so many different combinations of sextant and observer occurred, and
    provide some remarkable results, which are well worth a bit of scrutiny.
    
    But the point I wish to make is that the various instruments were marked by
    one set of code-letters in that table, and the observers by another set. I
    suspect that the symbols used against the lunar distance in the second
    voyage have a similar intention, even if we can't yet decode it.
    
    George.
    
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    =======================
    
    Brad wrote-
    
    It is also a possibility that we are being presented with averaged results,
    over individual or combined sextants.
    
    Bowditch recommends that "Whilst one person is observing the distance of
    the objects, two others ought to be observing the altitudes.  The
    chronometer should be placed near one of the observers, or put into the
    hands of a fourth person appointed to note the time; the observer who takes
    the angular distance giving previous notice to the others to be ready with
    their altitudes by the time he has finished his observation; which being
    done, the time, altitudes and distance should be carefully noted, and other
    sets of observations taken, which must be done within the space of 15
    minutes, and the mean of all these observations must be taken and worked as
    a single one".
    
    I think this advice is consistent with what we are seeing in the log, as
    tne log shows the "No. of Obs." in the 8th column.  We are seeing the
    result of multiple observations, averaged, to show the one distance
    recorded.  If Cook & Co used multiple observers or not is something hard to
    tell.
    
    Bowditch also offers this advice:
    "Method of taking a lunar observation by one observer.
    
    In case of not having a sufficient number of instruments or observers to
    take the altitudes, it has been customary to calculate them...These
    calculations are long...the following method of obtaining these altitudes
    is far more simple and sufficiently accurate.  This method depends on the
    supposition that the altitudes increase or decrease uniformly.
    
    Before you measure the distance of the bodies, take their altitudes, and
    note the times by a chronometer;  then measure the distance and note the
    time, (or you may measure a number of distances, and note the corresponding
    times, and take the mean of all the times and distances for the time and
    distance respectively;) after you have measured the distances, again
    measure the altitudes and note the times; then from the observed altitudes
    of either of the two observed altitudes of either of the objects, the
    sought altitude of that object may be found in the following manner:-
    
    Add together the proportional logarithm (Table XXII) of the variation of
    altitude of the object between the two times of observing the altitudes,
    and the prop. log. of the time elapsed between taking the first altitude
    and measuring the distance; from the sum subtract the prop. log. of the
    time elapsed between observing the two altitudes of that object; the
    remainder will be the prop. log. of the correction, to be applied to the
    first altitude, additive or subtractive, according as the altitude was
    increasing or decreasing ; to the altitude, thus corrected, apply the
    correction for dip of the horizon and semi-diameter, as usual"
    
    Whew! In other words, estimate the alitude of the objects at the time that
    the distance was measured by using proportional logarithms!
    
    If I recall properly, and there were only two octants on board, then it
    would not have been possible to simultaneously measure the altitudes of two
    objects AND the distance between them.  Further, for the example being
    worked for the distance in Ohamaneno Harbor, the sun's altitude could not
    be measured, the horizon was masked by the island.  So it is possible we
    are being presented with a mix of cases, sometimes with the altitudes being
    measured, sometimes with the altitudes being calculated.
    
    ----------------------------------
    
    From all of this, here is my first tentative assignment of the mark found
    by the distance, in column 3.  There are four mark types, "Cross", "Doubled
    Cross", "Dots" and "Blank".  Could these correspond to the types of
    altitude used in the distance calcuation.  That is: (1)Both altitudes
    measured, (2)Sun altitude measured Moon altitude calc'd, (3) Moon altitude
    measured Sun altitude calc'd, (4) both altitudes Calc'd.  Any takers????
    :-)
    
    
    
    
    

       
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