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    Re: Lunar trouble, need help
    From: Frank Reed
    Date: 2008 Jul 01, 16:16 -0400

    Kent, you wrote:
    "The factor 60,35� has been provided to me from the Observatory in Stockholm 
    to be used with the true zenith altitudes for altitudes above approx. 10 
    degrees. The factor is taken from modern English litterature." 
    What color light? It's not often mentioned explicitly that this factor 
    applies only for one specific frequency in the visible spectrum. That's one 
    reason why two people can quote factors differing by an arcsecond and still 
    be technically correct. It's also why we shouldn't worry too much about the 
    tenths and hundredths of an arcsecond. And it's a big reason why we 
    shouldn't shoot lunars when the objects are below about ten degrees: the 
    stars and the limbs of the Sun and Moon are stretched out into colorful 
    bands at very low altitudes. Incidentally, I use 58" usually. 
    "Yes, this is correct. For altitudes below 20 degrees I use the formula
    defined by Smart." 
    Since you're modeling historical methods, you could just input the whole 
    refraction table as printed. Then the software would interpolate between 
    values much as a 19th century navigator would have done on paper. This 
    approach bypasses all this chatter about various formulae for different 
    altitudes. It's also a reasonable approach for a modern analysis. Sometimes 
    people doing these calculations obsess over the "Bennett" formula. This is 
    because we carry around "baggage" from the calculator era and the early 
    years of programming small computers. There's no real advantage to a short 
    formula today (except saving a few keystrokes). 
    And you wrote:
    "So again, what I have tried to achieve is a re-construction of how the LD�s 
    were measured and reduced in the old days (by Swedish navigators) and not 
    necessarily what will be achieved with todays know-how." 
    May I ask, what is your source material? Are you looking at old navigation 
    manuals and textbooks or old logbooks (or similar)? The textbooks tend to 
    focus on minor issues (like second-differences, and finding local time from 
    star altitudes, and correcting for the oblateness of the Earth) which were 
    almost entirely irrelevant in practical navigation. 
    "The first way is what I outlined and this way can be used for any celestial 
    body, incl. the sun and provides the local time (MT). The other method was 
    to use the sun for generating the local time by finding the sun�s apparent 
    time and correct it with the TE. This later method required (requires) less 
    calculations and was therefore probably preferred by navigators." 
    The general method (which you outlined previously) was also preferred by one 
    other group: sadistic navigation instructors! Seriously, by the second half 
    of the 19th century, very few navigators ever used lunars at sea, but many 
    studied them in schools and instructors used the arcane aspects of lunars as 
    a means of "spreading the curve" (as we would say today in education) or 
    more informally "separating the men from the boys." So an instructor might 
    teach this very involved method of getting local time and then put that on 
    an exam, just to see who was paying attention. Meanwhile, everyone knew that 
    local time was determined, almost without exception, by observations of the 
    Yet another reason some instructors and theoreticians emphasized the 
    possibility of getting local time from the stars is because it seemed "pure" 
    in a mathematical sense. If you take a lunar distance observation with a 
    star or planet, then surely you should get local time from that same body. 
    That sounds good "in theory." In fact, lunars with stars and planets were 
    nowhere near as common as Sun-Moon lunars. From my experience with logbooks, 
    I roughly estimate that around 80% of lunars were Sun-Moon observations. So 
    once again, the common method of finding local time was to measure the Sun's 
    altitude. In effect, it turns the sextant into a sundial. It's a simple 
    sight and a simple calculation. These sights were almost as common as Noon 
    Sun for latitude throughout the period from the late 18th century and into 
    the middle of the 20th century. 
    And you wrote:
    "Also keeping the local time with a watch was used but after what I have 
    gathered this was not a common method likely because watches were not good 
    enough. But this method, when working, was certainly much easier for the 
    navigator than the first method outlined by me." 
    Watches were not the issue. Plenty of good watches were widely available in 
    the period. The real problem with carrying local time on a watch is that you 
    have to correct it for the change in longitude since the last time sight. In 
    modern terms, it's a running fix problem. It's hard to guess how much time 
    since the last sight was considered acceptable historically, but a few hours 
    was certainly no problem and even twelve hours does not appear to have 
    caused much concern. 
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