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    Re: Sun Moon Lunars to 155 degrees
    From: Brad Morris
    Date: 2010 Apr 1, 17:04 -0700

    Hi Bill

    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.

    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???? :-)

    Best Regards
    Brad


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