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    Re: Riddle of the Secant
    From: David Pike
    Date: 2026 Aug 10, 13:13 -0700

    Jacqueline Hardy you wrote:
    "As a young 2nd mate on a cargo ship, I used to take a sun amplitude and calculate the gyro error with the formula:

       sin(Amplitude) = sin(declination) * secant(latitude)
    And then an event happened and I stopped using the above formula and I used instead:
       sin(Ampl.) = sin(declination) / cos(latitude)

    What is this event ?
    How old am I ?"

    The two formulae are essentially the same, because secant(lat) = 1/cosine(lat).  However, the closer you get to the Pole, secant(lat) has a nasty habit of wandering off towards infinity.  This means that if you’re looking for gyro setting accuracy above 70N, you might run into the blank area in the mean differences column of Norrie’s Natural Secant Tables Page 358 (ish).  Therefore, I’m guessing the event was when commercial shipping exploitation of the Northwest and Northeast passages became a distinct possibility. 

    There must be many possibilities for this, but let’s take the
    first commercial cargo ship to sail through the Northwest Passage, the SS Manhattan in 1969.

    As to your age, that’s easy.  I’m told that no lady ever admits to being older than 40, so I must go for 39 and a half. 

    However, that would mean you were born in 1986, so we must seek a different route.  My father, who went to sea age 15 in 1929, was required fill in the time between finishing his apprenticeship and being old enough to hold a watch keeping certificate sailing as an AB.  In the 1930s that age was 21.  I doubt that’s changed much, and in the USA it might even be 22.

    Therefore, let’s assume you were 22 in 1969.  That would make you 126-69+22=79, three years younger than me.  Usual caveat applies.  I might be completely wrong, and often am.  DaveP

       
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