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    Re: Back sights
    From: George Huxtable
    Date: 2010 Mar 24, 19:48 -0000

    Brad's arguments are at fault here, and Bill Noyce is right.
    Earlier, Brad referred us to Hans Heynau's website, at-
    which shows two sketches, 5a and 5b, of the light paths for fore and back 
    These sketches correctly show a difference in the angles of the light path 
    between the two mirrors, with respect to the frame, in the two cases. 
    Indeed, that simply has to be so, because when making a back observation, 
    the fore horizon mirror remains in place, and would otherwise block the 
    light path to the back horizon mirror. I don't know what that angle 
    difference needs to be, but let's just guess at 10º.
    Brad correctly points out that a zenith star has to be seen at 90º on the 
    scale, in both fore view and back view, so the index arm and index mirror 
    must stay unaltered, with respect to the frame, in the two modes.. But how 
    can this fit in with the light path between the relevant mirrors differing 
    by 10º? Answer: the whole instrument has to be tilted quite differently, 
    with respect to the horizontal, when making a back observation. If the 
    whole octant is rotated anticlockwise through 10º, that will return the 
    zenith star to the centre of the view from the back horizon mirror. The 
    resulting tilt of the frame isn't shown on Heynau's sketch 5b, so it's a 
    bit misleading in that respect. And next, the back horizon mirror needs to 
    be so angled to the frame that when the frame is tilted by that 10º angle, 
    and the horizon appears in view, the twice-reflected zenith star appears to 
    be aligned with it.
    I suggest that if Brad makes himself a more careful drawing than that 
    sketch, and sets up the angles with a protractor, it will become obvious. 
    What's bugging him is, perhaps, the notion that the inverted A-frame of a 
    sextant/octant must be somehow balanced, in the nodding direction, about 
    the vertical, but there is no such requirement; neither in fore 
    observations or back observations. It just depends how the geometry of the 
    mirrors has been designed and set up.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message ----- 
    From: "Brad Morris" 
    Sent: Wednesday, March 24, 2010 3:36 PM
    Subject: [NavList] Re: Back sights
    | Hi Bill
    | Angle of incidence = angle of reflection for planar mirrors.
    | If the paths are not parallel from either of the horizon mirrors to the 
    index mirror, then the angle of the beam out of the index mirror will be 
    different for the non-parallel paths from horizon mirrors to index mirror. 
    Since non-parallel paths will not place the object on the horizon (or the 
    star on the limb of the moon) for the same indication of the nonius of the 
    vernier to the arc, a different reading will be had once the contact is 
    made.  There is only one index arm, one index mirror and one arc.  The 
    angular setting must therefore be the same (excluding index error), to 
    achieve the same reading for the same angle, with both foresight and 
    backsight observations.
    | In other words, set the nonius of the vernier to 90 degrees.  Assume 
    index error for both the foresight and backsight to be zero.  Now observe a 
    zenith star using the backsight and foresight observation.  For both 
    observations, the index arm does not move.  Yet how can this be read as 90 
    degrees, if the optical path from the foresight horizon mirror is not 
    parallel to the optical path of the backsight horizon mirror.
    | I think the paths to be parallel, with an offset between them.  This 
    means that the optical paths strike the index mirror in different 
    locations.  However, since the index mirror is a planar surface, then the 
    angle of incidence and angle of reflection are the same.
    | Best Regards
    | Brad
    | From: navlist-bounce@fer3.com [mailto:navlist-bounce@fer3.com] 
    On Behalf Of Bill Noyce
    | Sent: Wednesday, March 24, 2010 11:21 AM
    | To: NavList@fer3.com
    | Subject: [NavList] Re: Back sights
    | I don't think the optical paths need to be parallel for the fore-sight 
    and the back-sight. The only requirement for the scale to read right is for 
    the back-horizon mirror to be at an angle of 90 degrees from the 
    fore-horizon mirror. It can then be placed almost anywhere, as long as the 
    back peephole then allows the index mirror to be seen in the back-horizon 
    mirror. Remember that the genius of the octant (and sextant) is that it 
    measures the angular difference between the horizon mirror and the index 
    mirror, regardless of how the instrument is oriented.
    | -- Bill N.
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