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    Re: My Haversine Table...
    From: Greg B
    Date: 2014 Apr 22, 22:50 -0400
       Thank you! I use 'Libre Office Calc' a free ware clone of Excel.
    I'm doing a informational exchange at a pre-1840 rendezvous about
    the navigation of Lewis and Clark so I kind of went down the wrong path
    with my haversines so I think that I'm going to have to use ( i.e. talk about)
    what Frank pointed me toward: Bowditch - the 1807 edition; and it actually agrees
    pretty well with what I saw in the Lewis and Clark journals. Kind of unexpectedly
    I started thinking that I had seen some of this before ( Napier's Rules for rt. triangles
    etc, etc, ...) when I looked at a article on the Bygrave slide rule - I felt the math was familiar.
    I wonder if I'm loosing it or is the Bygrave solving using 
    Napier's Rules for rt. triangles?

    On 04/22/2014 09:31 AM, Andreas K wrote:

    Hi Greg,

    haversine is half of 2*sin^2(1/2*x). This versine equation was introduced to navigation, as far as I can see, by Cornelis Douwes 1747 with his method for finding latitude by two altitudes of the sun and the elapsed time. You can find the logs of this equation in the Tables Requisite 1767 and later. Here it is called "Log Rising". It was also used to determine the local apparent time using the formulae

    2*sin^2(1/2*LHA) = (cos(B-Dec) - sin(Alt))/(sin(B)*cos(Dec))
    with B=90?- Lat.

    An early table of haversine you can find in David Thomson's Lunar and Horary Tables 1831. Using the formulae

    sin^2(1/2*LHA) = (cos(1/2*(P + Lat + Alt))*sin(1/2*(P + Lat - Alt)))/(sin(P)*cos(Lat))
    with P=90?- Dec.

    For some years I made both tables very simple and quick with Excel (see att. files). Since then I used them with much fun and success. So I am curious what method you use to compute your tables!

    Kind regards

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    Linked File: http://www.fer3..com/arc/imgx/tr-59.pdf
    Attached File:

    (logsem2.pdf: Open and save or View online)

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