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    Re: measuring Octant instrument error
    From: JC Sutherland
    Date: 2000 Sep 19, 7:31 PM

    Perhaps could add a little fuel to this discussion on octant calibration.
    Of course the final proof of the instrument calibration will be the accuracy of
    sights taken of the Sun etc as George Huxtable suggests. However this is the end
    point not the starting point of the exercise. All the corrections that we know
    and love,  necessary for a Sun sight e.g. Height of eye, Dip, Refraction
    Semi-diam, Irradiation,  all dilute the confidence in the calibration so
    obtained, A Sun sight also requires the use of Filters to reduce the glare and
    any refraction in them would be inseparable from the calibration.
    In my humble opinion it would be better to use the octant to measure the
    horizontal separation between selected pairs of stars in the night sky rather
    than the altitude of the Sun in daytime. This measurement can be compared
    directly with the 'book' value.
    By referring to a Star catalogue, pairs of bright stars having similar
    Declinations (within a degree or so) should be chosen in advance and a list made
    of (a) Their 'difference in SHA' and (b) their 'mean SHA'.
    To verify the whole scale of the instrument, collect values of 'Dif SHA' over as
    wide a range of angles as the octant can measure.(see below)
    To use suitable stars from the list,  calculate the time of the Meridian Passage
    of their 'mean SHA ' for the day you are going to observe. That is to say
    calculate the time of GHA Aries when the
                           'mean SHA' of the pair + 'GHA Aries' = 360 deg
    (About half of the list will have values of Mer.pass, that would put them in the
    daylight part of the sky at a that time, but these pairs can be put aside for use
    later on in the year).( Compare my Oct/May values)
    Select several pairs for increasingly later times during the night hours.
    The octant would be set up with the expected Angular separation of the chosen
    pair and the two stars observed  with the octant held horizontally. Any
    difference from the calculated value would be the error in the octant calibration
    
    Several angles on each pair would be measured and averaged,(just before to just
    after the calculated Meridian Pass) to ensure that the two stars of the pair will
    have the same Altitude.
    No correction will then be needed for Refraction.
    Using Stars of the same Declination  will ensure that their angular separation is
    the same as the difference in their SHA .
    No Horizon is necessary so the observations can be made anywhere and at any time
    there is a visible dark sky.
    No filters are needed on the octant and aligning two pinpoints of light is much
    easier than observing the edge of the Sun or Moon.
    Rocking the octant slightly will aid precise conjunction.
    The stars are not changing their separation so there is no hurry in taking the
    measurement
    There are very many pairs of stars to chose from and with practice it would be
    possible to use 'not so bright' stars, provided that one of the stars is easily
    found. The octant can be previously set with the expected angle, pointed at the
    brighter star and when it is properly horizontal the other should pop into view.
    I am not sure just how much tolerance in the declination of the pairs of  stars
    can be accepted but I guess a spherical trig calculation might be needed to
    determine their true separation if they differ in Declination by more than say
    about 5 degrees. However the familiar Sight Reduction formula or tabular methods
    could  be adapted for this purpose should it be necessary,
    I have roughly calculated with the aid of a spread sheet a few pairs of stars
    just to illustrate what I am talking about, I have used the short list of stars
    in the 1997 Nautical Almanac so to be any use the numbers would need to be
    recalculated using a current edition.
    
    TABLE HEADINGS
    NAME names of  stars in pairs, limited to those greater than -40 deg DEC
    DEC  approx  to show how similar they are. Decimal degrees.
    SHA   approx  sometimes =/- 360 deg needs to be applied to get Dif SHA.
    dif SHA Approx. Difference in SHA between the two stars. NOTE This value needs
    accurate recalculation as it is to be compared directly with the Octant
    measurement
    Mer Pas(OCT) ) Local Time when the two stars are horizontal and equally
    Mer Pas(MAY) ) spaced either side of the Southerly Meridian.
       It is the time when the GHA Aries = 360 - (mean SHA of the two    stars)
    tabled for two representative months of the year.
    
    
    NAME  DEC  SHA  dif SHA Mer Pas(OCT)Mer Pas(MAY
    
    Gienah S 17.5 176.2    13:00  23:00
    Zubenel' S 16.0 137.3  38.9
    
    Regulus N 12  207.9    13:00  23:00
    Rasalhague N 12.6 96.3  111.6
    
    Fomalhaut S 29.6 15.6    14:00  00
    Adhara S 29.0 255.4  120.2
    
    Gienah S 17.5 176.2    14:00  00
    Sabic  S 15.7 102.4  73.8
    
    Shaula S 37.1 96.6    15:00  01:00
    Menkent S 36.4 148.4  51.8
    
    Antares S 26.4 112.7    17:00  03:00
    Nunki  S 26.3 76.2  36.5
    
    Elnath N 28.6 278.5    02:00  12:00
    Alpheratz N 29.1 357.9  79.4
    
    Alpheratz N 29.1 357.9    03:00  13:00
    Pollux N 28  243.7  114.2
    
    Diphda S 18.0 349.1    05:00  16:00
    Sirius S 16.7 258.7  90.4
    
    Pollux N 28  243.7    06:00  16:00
    Elnath N 28.6 278.5  34.8
    
    Alphard S 8.7  218.1    07:00  17:00
    Rigel  S 8.2  281.4  63.3
    
    Sirius S 16.7 258.7    09:00  19:00
    Gienah S 17.5 176.2  82.5
    
    
    
    I dont know where Bill  lives or I would have set up the data to suit his
    location. These numbers are calculated for the Greenwich Meridian but they should
    not be very far wrong for any longitude if this is applied to adjust the times to
    GMT. The times only change slowly with date (about 4 mins a day) The times to the
    nearest hour on the first of the month
    
    Regards
    CLIVE
    
    
    

       
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