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    Re: Longitude by observation of the Sun, 19th Century
    From: Frank Reed
    Date: 2013 Jun 13, 10:34 -0700

    Jacques, you wrote:
    ""haversine formula" = "Borda formula" "

    Yes, thank you. I discuss the merits of the cosine/fundamental formula versus the haversine/Borda formula quite regularly in classes and other presentations, so I am happy to have more names to apply to them to get the point across. Here's a thought: I would bet a dollar I am the only person on the planet who has written out this comparison of spherical trig equations longhand on a chalkboard (yes, chalk) in front a room full of students in the past six months!

    You also wrote:
    "but it is true that in french logarithmes tables, you dont find a table giving the nat or log of function "versine" ou "haversine" ".

    Got it. And I just want to make sure we're clear that those 'haversine' tables which appear much later in compilations like Bowditch c.1905 are not directly connected with this calculation which was the standard time sight computation for over a century. The later 'hav' tables are interesting in their own right, and they did become somewhat popular.

    You wrote:
    ""cosine formula" = "fundamental formula" in France."

    Thanks. And in future references, I will try to use a mixed description of it so we have a somewhat more internationalized language for the discussion. Maybe the "fundamental or cosine formula of spherical trigonometry" and also the "haversine or Borda formula".

    I am attaching an annotated image of a page from the back of a logbook showing a lunar being worked up to get a longitude. The date is March 27, 1825. Note that we can spot the signature pattern of the "haversine/Borda" calculation both in the clearing of the lunar (to get Greenwich Apparent Time) and in working the time sight (to get Local Apparent Time). I've discussed this "scrap paper" caulction quite a few times before in NavList messages, and if anyone is interested, I can direct you to a detailed analysis of every little figure on the page. On the other hand, that might spoil the fun!

    -FER


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