Welcome to the NavList Message Boards.

NavList:

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

Compose Your Message

Message:αβγ
Message:abc
Add Images & Files
    Name or NavList Code:
    Email:
       
    Reply
    Certain Errors in "Certaine Errors".
    From: Herbert Prinz
    Date: 2007 Dec 10, 10:35 -0500

    Garry and George have been puzzling over the inner workings of Wright's
    geometrical method for finding GCD. It's based on an analemma, whereby
    various orthogonal projections are sitting on top of each other. To add
    a little confusion, some lines are shifted around, other ones are reused
    for more than one purpose, all in an effort to minimize the effort of
    plotting.
    
    E is London, N is Jerusalem, F and O are the projections of these places
    onto the equatorial plane. FO can be constructed from the known
    latitudes and longitudes by means of projections into the respective
    meridional planes. In trapezoid FONE, EN is the chord of the required
    distance. EF and NO are parallel to each other and perpendicular to FO.
    FE = sin(Lat(London)) and NO = sin(Lat(Jerusalem)). The trapezoid FONE
    can thus be broken down into a rectangle FONN* and a right triangle NN*E
    with the right angle at N*. The rectangle is of no interest, only the
    triangle gets drawn as PFQ, with right angle at F.
    
    The recipe is actually explained for "him who desireth a
    demonstration",  but there are two small errors in the example for
    London and Jerusalem, which may confuse the issue:
    
    1. Read "[make] EQ equal to NO" instead of "PQ equal to NO". (This is
    mentioned in the errata.)
    2. In the corresponding diagram, the point Q is supposed to be a member
    of the line EF; not of FO, as it is drawn. The line from P to Q should
    thus meet the line EF in Q. (This is not mentioned in the errata. It may
    be just a flaw in the printing of the copy at hand.)
    
    I hope everything falls into place now. If not, I may try to come up
    with a 3-dimensional diagram of what's going on.
    
    Analemmata have been employed since antiquity to solve problems in
    spherical astronomy. They are orthographic projections. Their purpose
    was to convert problems of spherical trigonometry into ones of plane
    trig. The latter could be solved numerically by means of proportions.
    For a long time, this was the only way of expressing trigonometric
    equations. The analemma also found direct use in geometrical
    construction, e.g. of sun dials.
    
    Lacaille proposed a graphical method applying an analemma for the the
    reduction of time sights and lunar distances as late as 1761. At that
    time the moon predictions were still the limiting factor of accuracy in
    solving the longitude problem. After the introduction of Mayer's tables,
    graphical reduction was no longer adequate. I would not say that it
    disappeared. It pops up now and then in lifeboat navigation and the
    like. Other projections (e.g. stereographic) have been suggested since
    for graphical or mechanical methods with little success.
    
    Herbert Prinz
    
    --~--~---------~--~----~------------~-------~--~----~
    To post to this group, send email to NavList@fer3.com
    To , send email to NavList-@fer3.com
    -~----------~----~----~----~------~----~------~--~---
    
    

       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    Get a NavList ID Code

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

    A NavList ID Code guarantees your identity in NavList posts and allows faster posting of messages.

    Retrieve a NavList ID Code

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

    Email Settings

    NavList ID Code:

    Custom Index

    Subject:
    Author:
    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