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    Re: Reliable Index Correction to a Tenth Minute of Arc
    From: Brad Morris
    Date: 2010 Feb 18, 14:21 -0500

    Hi Bill

     

    At Lunch, I took the following 10 readings, first off, then on, then off, etc.  Vernier Type Sextant, 10x Scope;  Upper and Lower limbs of the Sun brought into contact.  Apparent SD for today, 18Feb2010, is 32 minutes 21.8 seconds (source: http://sob.nao-rozhen.org/content/apparent-solar-diameter-and-basic-heliographic-data-2010 )

    Reading

    Off

    Decimal⁰

    Reading

    On

    Decimal⁰

    1

    32

    20

    -0.53889

    2

    32

    40

    0.54444

    3

    33

    10

    -0.55278

    4

    32

    20

    0.53889

    5

    33

    0

    -0.55000

    6

    33

    10

    0.55278

    7

    32

    30

    -0.54167

    8

    32

    40

    0.54444

    9

    32

    20

    -0.53889

    10

    32

    40

    0.54444

    From these 10 readings we can readily create 9 index error measurements.  That is, we can group 1+2, 3+4, 5+6, 7+8 and 9+10.  Additionally, we can easily see our way to group 2+3, 4+5, 6+7 and 8+9, as any of these pairs would be a natural pairing in that the on/off arc reading follows each other.

     

    Here are the 9 index error measurements

     

    Group

    Decimal⁰

    degrees

    minutes

    seconds

    on/off

    1+2

    0.00556

    0

    0

    20

    on

    3+4

    -0.01389

    0

    0

    50

    off

    5+6

    0.00278

    0

    0

    10

    on

    7+8

    0.00278

    0

    0

    10

    on

    9+10

    0.00556

    0

    0

    20

    on

    2+3

    -0.00833

    0

    0

    30

    off

    4+5

    -0.01111

    0

    0

    40

    off

    6+7

    0.01111

    0

    0

    40

    on

    8+9

    0.00556

    0

    0

    20

    on

     

     

    The average of these 9 index error measurements is 0 arc seconds, with a standard deviation of 31.6 arc seconds. 

     

    Extending the group/pair concept, we can permute every On the Arc against every Off the Arc reading.  That is, I can pair 1 with 2,4,6,8 and 10.  Next pair 3 with 2,4,6,8 and 10. Etc, yielding 25 IE measurements.  In this case the average of all permutations is 2 arc seconds, with a standard deviation of 26.9 arc seconds.

     

    The IE equal to zero outcome is a function of properly setting up the sextant in the first place.  The sextant was carefully set to read zero when the index mirror angle is zero.  Of course, I did not get 1/10 minute (6 seconds) every time.  That wasn’t possible as the smallest division on my vernier is 10 seconds.  Nor did I get 10 seconds every time (although clearly sometimes). 

     

    For this reason, I don’t bother to check my IE before and after a round of sights.  Firstly, I find this same result every time I make a serious attempt to measure the IE.  Secondly, I treat my sextant with kid gloves (in a gentle fashion for those not familiar with American slang).  Essentially, as Frank has noted in his high magnification IE trick, the IE is stable for metal sextants.  I have found the same thing and count on it.

     

    No need to warm up the congratulation machine Bill.  However, I would claim a very small IE for my sextant, certainly less than 6 seconds!

     

    Best Regards

    Brad

     

    Bill, you wrote:

    if they can get the same result within a tenth of a minute each time, I will be among the first to congratulate their instrument.

    Kind regards

    Bill Morris
    Pukenui
    New Zealand

     


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    "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."
       
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