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    Re: lunars with and without altitudes
    From: Henry Halboth
    Date: 2006 Nov 14, 01:56 -0500
    Frank + George,
    Gentlemen, it would appear that you both ignore the fact that one of the observations in the Lunar set is also intended for the purpose of establishing the Local Apparent Time, for ultimate comparison with the GAT deduced from the GMT established by the distance cleared. An error in the Altitude or Latitude employed for that purpose will affect whatever accuracy in Longitude or Chronometer Error may be expected from the observations as a whole. The Latitude induced error, of course, being dependent on the distance off the Prime Vertical of the body employed for the purpose of establishing the LAT.
    In response to my previous comments, George has taken issue with my statement to the effect that computed altitudes were dependent upon knowledge of "position/time", but seems to go right on to prove my point by citing a prior knowledge of LAT to assist in the altitude computation. Now, I know of no watches that keep LAT, but it was not uncommon to take an earlier sight, as conditions might dictate, and by carefully noting the elapsed time and deduced difference of Longitude to the time of the distance observation, run an earlier established LAT up to the Lunar distance time; there does not appear to be any need to assume an LAT, or to iterate for Longitude. The accuracy here was, of course, dependent upon the accuracy of the reckoning between sights, as it would be in any running fix and, certainly, the elapsed time should be as short as possible. Regardless, I still consider simultaneous observation of all components entering into the Lunar distance observation to be conducive to the greater accuracy, other conditions being equal. Although the foregoing comments apply specifically to the Sun. it would appear more important that observations involving a star or planet be taken at the same time with no computation of altitudes, but that is probably a subject for later discussion. 
    As respects the use of series altitudes, as opposed to simultaneous observations, advocated by the learned gentlemen addressees, I can only say that this was the method employed by me when first attempting Lunars an awful long time ago and I find no great fault with such a procedure, but that I still must advocate simultaneous observation, if at all possible. I do not agree to the generality of inadequate manning, as most ocean going ships of a type likely to employ Lunars likely carried two mates, in addition to the Master, and in  the days before overtime there does not appear any reluctance to call out all hands to work the vessel. However, I know little of manning in general and do not press the point.
    It's now approaching 0300 hours and time to go to bed.
    ----- Original Message -----
    Sent: Sunday, November 12, 2006 12:21 AM
    Subject: [NavList 1677] Re: lunars with and without altitudes

    George you wrote:
    "However, one skilled man could do the whole job:
    any additional calculation, if the job was done systematically,
    involved no more than an extra bit of time-averaging. The most logical
    sequence was to take a star (or Sun) altitude, then a Moon altitude,
    then some lunar distances, then a Moon altitude, then a star altitude,
    in a regular time-sequence like clockwork, so that the averaged times
    for all three sets of measurements were the same. That was how a
    lightly-officered merchant vessel would proceed"
    It's also worth mentioning that this procedure was outlined in most of the early 19th century navigation manuals like Bowditch. Assistants were not necessary. Then again, they were usually available aboard smaller vessels. There was a lot of cheap labor.
    Also, it works really well in practice. If you've never tried it, it takes relatively little discipline to arrange the set of sights so that the altitude pairs average nicely to the same time as the average of the lunars.
    And you wrote:
    "Asking for the calculated altitude to be within four arc-minutes of
    the truth may be a bit over the top, but it's not entirely
    unreasonable. The biggest effect would be on the parallax correction
    for a high Moon at about the same azimuth as the relevant star. With
    such an error, the resulting error in the parallax correction could be
    no more than about 4 arc-sec."
    Within +/-4 minutes of arc for the altitudes is correct when the lunar distance is about 40 degrees. Just a reminder on the "ninety degree miracle" business from two years ago: if the lunar distance is near 90 degrees, the altitude of the Moon can be wrong by a whole degree or more and it will have no significant effect on clearing the lunar distance. The other altitude should still be accurate to +/- 6 minutes of arc. If the other object's altitude is being used for a time sight, too, then the observer should try for maximum accuracy when measuring that altitude.
    If the lunar distance is short, you have to be more careful in the altitude. At a distance of ten degrees, an error of one minute in either altitude will yield a tenth of a minute error in the clearing process.
    When calculating altitudes, if that's the better option, it's no problem to calculate to the nearest arc second but they can still be in error by several minutes of arc. In this case, the source of error is transferred from the altitudes to the two inputs that determine those calculated altitudes: the DR latitude and the local apparent time (which is secondarily dependent on the DR longitude).
    42.0N 87.7W, or 41.4N 72.1W.

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