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    Lunar Distance and Tides
    From: Gordon Talge
    Date: 2000 Sep 10, 12:31 PM

    I have three or four old navigation books that explain "Lunar
    Distance". You need a book written before about 1900. I have
    a 1916 Bowditch and all references to lunar distance and the
    accompanying tables have been dropped.
    
    The best explanation I have is in a 1844 copy of J.W. Norie's
    "Practical Navigation". It has a chapter on how to use Hadley's
    Sextant for taking lunar distance and how to find longitude
    by lunar observation.
    
    -- On another note, there is a neat way to figure tide. I don't
    know how accurate it is compared to "modern" methods but it
    may be useful.
    
    This is from J.W. Norie 1844.
    
    1) To find the Leap Year.
    
    Rule. Divide the given year by 4, and if there be no remainder, it is
    leap year; but if 1, 2, or 3 remain, they shew that it is so many years
    after leap year.
    Example. The year 1846, divided by 4, gives 461 and the remainder 2,
    which
    shews that it is the second year after leap year.
    
    ( Note this is not exactly correct, because  by this method 1800 would
    be
    a leap year which it is not, but it will work for  almost all years.)
    
    2) To find the Epact.
    
    Rule: Divide the given year by 19; multiply the remainder by 11, and the
    product will be the Epact, if it does not exceed 29; but if it does,
    divide
    the product by 30, and the last remainder will be the Epact.
    
    Example: Epact for 1846. 1846, divided by 19, gives 97 for the quotient,
    and
    3 for the remainder, which is multiplied by 11, gives 33; this, divided
    by 30,
    gives the quotient 1, and the remainder 3; which is the Epact for the
    year 1846.
    
    3) To find the Epact for Number for any given Month.
    
    Rule. Divide the number of days contained in the preceding months,
    reckoning from the beginning of January, by 29.5, or rather 29.53 ( the
    period of
    a mean lunation in days and decimal parts), and the nearest whole number
    to the
    remainder is the Epact, or Number for the Month required.
    
    Example: Epact for September.
    The days contained between the beginning of January and the beginning of
    September are 243; this number, divided by 29.53, gives the quotient 8,
    and the remainder 6.76, or 7 nearly, which is the Epact for September.
    
    
    Common   yrs.    Leap Yrs:
    
    Jan   0          0
    Feb   1          2
    Mar   0          1
    Apr   1          2
    May   2          3
    June  3          4
    July  4          5
    Aug   5          6
    Sept  7          8
    Oct   7          8
    Nov   9         10
    Dec   9         10
    
    
    To Find the Moon's Age.
    
    Rule. To the Epact of the Year add the Number for the Month, and
    the day of the month: the sum, if it does not exceed 30, is the moon's
    age; but if it does, subtract 30 from it, and the remainder will be the
    moon's age.
    
    
    Example. moon's age on July 17th, 1847.
    
    19)1847(97
        171
        ---
        137
        133
        ---
          4
         11
        ---
    30) 44 (1
        30
        ---
    The Epact for 1847=14
        ---
    
    Epact for 1847 ........................ 14
    Number for the month.................... 4
    Day of the month........................17
                                            ---
                                            35
                                            30
                                            --
    The moon's age...........................5 Days
    
    
    
    
    4) To Find the Time of the Moon's Passage over the meridian
    
    Rule. Multiply the moon's age by 4, and divide the product by 5; the
    quotient will be the hours, and the remainder, multiplied by 12,
    the minutes, past noon that the moon comes to the meridian. Or multiply
    the moon's age by 8, and point off the right-hand figure; then the
    left-hand
    figure or figures will be the hours, and the product of the right-hand
    figure by 6, the minutes, past noon of the moon's meridian passage. If
    the
    hours exceed 12, subtract that time from them, and the remainder will be
    the
    time of the moon's passage over the meridian after midnight.
    
    
    Example I. moon's meridian passage, July 7th 1846.
    
    Epact for 1846..................3
    Number for the month............4
    Day of the month................7
                                  ----
    Moon's age                     14 days
    ----------------------------------------------------------
    
    Moon's age 14 Days
                4
               ---
              5)56
              ------
              11. 1
                 12
            ----------------
      Moon's passage over meridian 11h 12m P.M.
    
    Example II. Moon's passage Oct 23d, 1848?
    
    Epact for 1848..............25
    Number of Month..............8
    Day of Month............... 23
                              -----
                                56
                                30
                               ----
    Moon's Age .................26 days.
    ----------------------------------------------
    
    Moon's age .............. 26 days
                              .8
                             ----------
                              20.8
                                .6
                            ------------
    Moon's passes meridian ...... 20h.48m P.M.
                           or 8h. 48m. A.M.
    
    
    5) To find the Time of High Water at any Place on any given Day
    of the Moon's Age.
    
    Rule. To the time of the moon's meridian passage on the given day,
    add the time of high water at the given place on the full and change
    days
    (taken from Table LVII); their sum is the time of high water at the
    place,
    past noon, on the given day. If this sum exceed 12 hours 24 minutes,
    which is about the interval between each succeeding tide, subtract 12
    hours
    24 minutes from it; or if it exceed 24 hours 48 minutes, subtract 24
    hours 48
    minutes from it, and the remainder will be the time of high water in the
    afternoon of the given day.*
    
    * It is to be observed that the above method gives the times of high
    water in
    solar or apparent time, to which therefore the equation of time (taken
    from
    Page 1. of the Month in the Nautical Almanac), should be applied, to
    reduce
    them to mean time.
    
    Example I: Time of high water at London, June 10th 1848.
    
    Epact for 1848.........25
    Number for June.........4
    Day of Month...........10
                         --------
                           39
                           30
                        --------
    Moon's age..............9 days
    
    
    Moon's age June 10th, 1848............9 days
                                          4
                                        -------
                                       5)36 (1
                                       ----------
    Moon's meridian passage.......      7h.12m
    Time at London(Table LVII)          2   7
                                        -------------
    High Water at London.................9 19 P.M.
    
    ------------------------------------------------------------
    
    Example II. High Water in the Downs, Sept 25th 1847?
    
    Epact for 1847............14
    Number for Sept............7
    Day of Month..............25
                            --------
                              46
                              30
                             -----
    Moon's age................16 days
    
    
    
    Moon's  age Sept. 25th, 1847........ 16 days
                                          .8
                                         ----------
    Moon's meridian passage.............12h. 48m.
    Time at Downs(Table LVII)            11  15
                                        --------
                                        24    3
    subtract the time of a tide         12   24
                                      ------------
    High water in the Downs             11  39 P.M.
    
    -------------------------------------------------------------------
    
    The times of high water were given in Bowditch upto about 1925, maybe
    even until the 1930s. I know that in the 1943 and later editions this
    info was dropped.
    
    The  1916 edition of Bowditch lists Pt. Fermin, San Pedro Bay:
    Lighthouse
    at 33d 42' 14" N and 118d 17' 41" W and a   H.W. of 9h 36m
    
    Pt Loma: Lighthouse 32d 39' 48" N and 117d 14' 37" W with a H.W. of
    9h 29m
    
    In England Lizard Pt: W. lighthouse  49d 57' 40" N and   5d 12' 06" W
    with a H.W. of 4h 45m
    
    -----------------------
    Norie explains two  more methods which are more elaborate using a
    Nautical Almanac for the meridian passage and taking into account
    the observers longitude and the semi diameter of the moon.
    
    -- Gordon
    
    
    
    
    
    
    
    --
                                  ,,,
                                 (. .)
    +-------------------------ooO-(_)-Ooo-----------------------+
    | Gordon Talge WB6YKK                 e-mail: gtalge{at}pe.net |
    | Department of Mathematics  __       Long Beach, CA        |
    | Wilson High School        / /    __  _  _  _  _ __  __    |
    | (o-    Debian / GNU /    / /__  / / / \// //_// \ \/ /    |
    | //\                     /____/ /_/ /_/\/ /___/  /_/\_\    |
    | v_/_   The Choice of the GNU Generation                   |
    |                      .oooO                                |
    |    - E Aho Laula -    (  )   Oooo. - Wider is Better -    |
    + -----------------------\ (---(  )-------------------------+
                              \_)  ) /
                                  (_/
    

       
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