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
    or...
       
    Reply
    Re: The Bygrave Slide rule
    From: Brad Morris
    Date: 2009 May 29, 13:36 -0400

    I brought out the extended markings to help clarify the discussion!  I 
    realized that tan(89) does not equal the tan (91), yet the value denoted on 
    the scale is the same for either tan(89) and tan(91).  The same applies to 
    the outer scale, there is a sign change at 90 degrees, although the abs 
    values are the same.
    
    While I remain interested in resolving what the scales actually represent, I 
    don't know that we have enough information yet. Peter has essentially 
    utilized trigonometric identities to "flip the problem over".  Neither 
    argument is compelling enough to state, hey, that's the answer.  No argument 
    accounts for the absolute value, yet that must occur.  The scales are 
    logarithmic, yet there are no logarithms of negative numbers.
    
    Best Regards
    Brad
    
    
    
    
    -----Original Message-----
    From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of NavList@fer3.com
    Sent: Friday, May 29, 2009 5:46 AM
    To: NavList@fer3.com
    Subject: [NavList 8441] The Bygrave Slide rule
    
    
    Brad's point is interesting - he points out that the reversed 90-180 degree 
    markings on both scales show that the scales are logs of abs(tan) and 
    abs(cos) respectively. Maybe this is just a 'kludge' for the annoying fact 
    that logs of negative numbers don't exist. It's left to the user to sort out 
    the signs when using logs to work with mixed-sign numbers.
    
    However, I don't think Brad's point does impact on my postings, since it 
    applies whether or not the scales are 'thought of' as cotan/cos or 
    tan/secant.
    
    In effect all I am saying is that I found the references to cotangent scales 
    in the papers by Ron and Gary were counter-intuitive, and the alternative 
    tangent/secant interpretation was easier to grasp, so I thought it worth a 
    posting. If no-one else agrees with me then I will go back into my cave.
    
    I can't contribute an answer to Gary's puzzle about the apparent impossibility 
    of using the tangent/cosine method at the equinoxes (this puzzle is not 
    limited to the Bygrave solution). A quick look at the celestial triangle 
    tells me that if the sun is near the equator then the perpendicular from the 
    sun to the observers meridian is also near the equator, so the equation for 
    azimuth simplifies to tan(A)=tan(H)/cos(c), but this may already be what Gary 
    has rejected as not being very pretty. I wondered whether the discarded 
    azimuth in the alternative calculation might be a clue, but this is just 
    equivalent to swapping the observer with the sun. The altitude comes out the 
    same of course, but the discarded 'false' azimuth is then seen to be the 
    azimuth of the observer as seen from the sub-solar point, which isn't very 
    useful, even on March 21st.
    
    regards
    Peter M
    
    --------------------------------------------------------
    [Sent from archive by: peter.martinez-AT-btinternet.com]
    
    
    
    
    "Confidentiality and Privilege Notice
    The information transmitted by this electronic mail (and any attachments) is 
    being sent by or on behalf of Tactronics; it is intended for the exclusive 
    use of the addressee named above and may constitute information that is 
    privileged or confidential or otherwise legally exempt from disclosure. If 
    you are not the addressee or an employee or agent responsible for delivering 
    this message to same, you are not authorized to retain, read, copy or 
    disseminate this electronic mail (or any attachments) or any part thereof. If 
    you have received this electronic mail (and any attachments) in error, please 
    call us immediately and send written confirmation that same has been deleted 
    from your system. Thank you."
    
    --~--~---------~--~----~------------~-------~--~----~
    Navigation List archive: www.fer3.com/arc
    To post, email NavList@fer3.com
    To unsubscribe, email NavList-unsubscribe@fer3.com
    -~----------~----~----~----~------~----~------~--~---
    
    

       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    Join NavList

    Name:
    (please, no nicknames or handles)
    Email:
    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:

    Email Settings

    Posting 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