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    Re: Brown-Nassau slide rule for clearing lunars
    From: Frank Reed
    Date: 2015 Oct 28, 01:12 -0700

    No, Francis, as we've discussed before, a two arcminute error in the process of clearing lunars is totally unacceptable except for a gross check. And it would have been unacceptable in 1775, too.

    By the way, you mentioned "hours" of work clearing lunars in the days of Maskelyne. This is often misunderstood. In the brief period from about 1763 to 1767, a small handful of British navigators tried out Tobias Mayer's tables as compiled in Maskelyne's "British Mariner's Guide". This process was much more complicated than simply clearing lunars and took four hours or so. That's because they were calculating the almanac data for the Moon itself, a long and laborious process. The small slice of this computation that consisted of actually clearing the observed distance required something like 20 minutes. After 1767, when the Nautical Almanac was first published with its tables of pre-computed lunar distances, lunars were routinely worked in less than 20 minutes, probably as little as 10 minutes in later decades, in the hands of a lunarian with some experience and computational facility. These were computations accurate to roughly 0.1 minutes of arc in most cases.

    If you want to work lunars by slide rule, you should be working with the mathematics of the series methods. This is exactly what I wrote up in my "Easy Lunars" essay here almost a dozen years ago: go here to read it. Sean recently provided a link to that, too. In a series method, the calculations require only two to three significant figures in the computation. This is reasonably well suited to slide rule work, if you're so inclined.

    Frank Reed

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