Welcome to the NavList Message Boards.


A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

Add Images & Files
    Latitudes through double altitudes revisited (Bowditch & Benj. Peirce)
    From: Joel Silverberg
    Date: 2007 Apr 18, 14:07 -0700

    I posted a notice on NavList earlier asking for assistance in
    deciphering the mathemtics behind the method for determining the
    latitude from measuring the altitude of the sun at two different times
    and noting the elapsed time behind the observations.
    Frank Reed was kind enough to direct me to a mid-nineteenth century
    treatise on spherical trigonometry written by Benjamin Peirce:  a
    friend, student and colleague of Nathaniel Bowditch (and Henry
    Ingersoll Bowditch, Nathaniel's son, according the the history of
    mathematics archives at the University of  St Andrews, Scotland).
    Thank you, Frank.   Peirce's treatise is a most remarkable resource,
    and I am looking forward to reading the work in its entirety over the
    I have tried to organize, clarify,  illustrate, and describe Peirce's
    explanation of the derivation of Bowditch's method  and have provided
    a link to my notes below.
    I would also like to thank George Huxtable for providing a scanned
    copy of Cotter's explanation of Ivory's method.  The methods are
    virtually identical, but I found Cotter's diagrams and Cotter's
    notation to be extremely difficult to follow.  For me, at least, they
    clouded and obscured what was going on, rather than explained what was
    happening. I have not had the time to see if Ivory's original
    presentation to the Royal Society is on the web, but I'd be interested
    to see how Ivory explained things.
    I would also like to acknowledge the usefullness of the program
    "Spherical Easel" by David Austin and William Dickinson for preparing
    the diagrams that accompany this explanation.  This program is
    available as a java applet or as a downloadable program at no cost
    from http://merganser.math.gvsu.edu/easel/
    To see Bowditch's original Rules click on the links
    To see my illustrated explanation of Benjamin Peirce's Derivations of
    Bowditch's Rules click on
    1825 edition of Nathaniel Bowditch's New American Practical Navigator
    (pages 247 through 249).
    1845 edition of Benjamin Peirce's Elementary Treatise on Plane and
    Spherical Trigonometry (p. 133,134)
    both accessible  via books.google.com
    Have fun,
    To post to this group, send email to NavList@fer3.com
    To unsubscribe, send email to NavList-unsubscribe@fer3.com

    Browse Files

    Drop Files


    What is NavList?

    Join NavList

    (please, no nicknames or handles)
    Do you want to receive all group messages by email?
    Yes No

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

    Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.

    Email Settings

    Posting Code:

    Custom Index

    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site