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    Re: Was Bowditch Table 15, now confused
    From: Trevor Kenchington
    Date: 2005 Jan 29, 01:34 -0400

    Bill,
    
    > The "relative to sensible horizon" portion is where I begin to lose it.
    > Relative is, well, relative.
    
    
    "Relative" seems like a poor choice of words. The plane of the oil in an
    artificial horizon is parallel to the plane of the sensible horizon.
    That is the key point. Or rather, what is really key is that both of
    those (plus the geoidal horizon) are parallel to the celestial horizon.
    
    > Observations of a body from plate of
    > mercury/oil at sea level, on deck, on the ground at 700 ft above sea level,
    > or on a stool at 703 ft above sea level will give the same results (noting
    > the approx. 700 feet is insignificant relative to the radius of the Earth
    > and resolution of the system).  Correct?
    
    
    Yes.
    
    Even the radius of the Earth, which is to say the distance between the
    celestial and geoidal horizons, is immaterial to a navigator for this
    purpose if you are observing a star and it is only a big deal if you are
    observing the Moon. (Hence the parallax corrections.) The distance
    between the geoidal and sensible horizons, which is approximately the
    same as the height of eye, is of no navigational significance at all.
    Ditto for the distance between the geoidal horizon and the surface of
    the fluid in an artificial horizon.
    
    
    > Stated in my words (don't you just love active listening) if a pool of
    > mercury/oil is 6 feet above water level, the plane it describes is the
    > sensible horizon--same as an eye at 6 ft.
    
    
    No. The sensible horizon passes through the eye of the observer, by
    definition. That can be at any height above the surface of sea or lake,
    from zero to thousands of feet. But the artificial horizon's surface
    will only coincide with the sensible horizon if the observer brings his
    eye (and so the sensible horizon) into line with the surface of the fluid.
    
    > Now the wrinkle.  If an eye is 6 ft above sea level, I apply a dip
    > correction as I can see farther over the horizon--put another way the
    > observed object appears higher than it would from sea level.  Yet I do not
    > apply dip just because the a blue water tide is up 2 feet--the observed
    > horizon went up along with my eye level (noting again the 2 feet is
    > insignificant relative to the radius of the Earth and resolution of the
    > system).
    
    
    Whether you correct your height of eye, and hence dip, for the rise of
    tide depends on whether you are standing on a boat (which rises with the
    water, maintaining the same height of eye) or on shore. If the latter,
    then as the tide rises, your height of eye decreases -- assuming that
    you don't get bored waiting and walk to higher ground to get a cup of
    coffee.
    
    > When using an artificial horizon the liquid is my sea level and my horizon
    > (observed angle is 2X when the observed body is factored in) so I do NOT
    > apply dip.  Elevation of the pool of liquid and actual sea level is
    > insignificant for practical purposes as noted above.
    
    
    NO. You could place the artificial horizon in the bottom of a deep
    valley and take your observation while standing on a high mountain
    (difficult to achieve in practice!) and you still would not correct for dip.
    
    It is not the height of the observer above the surface of the fluid but
    the geometry of the observation which determines whether a dip
    correction is needed.
    
    With a natural sea horizon, we attempt to measure the angle between the
    celestial body and our sensible horizon. However, we cannot detect the
    sensible horizon, so we have to use the visible horizon. Then we have to
    correct the angle for the difference between those two horizons. that
    angle is dip.
    
    With an artificial horizon, we measure twice the angle between the
    celestial body and the horizontal surface defined by the fluid in the
    artificial horizon (and then halve it). The light rays from the
    celestial object must strike all horizontal planes at the same angle
    (since those planes are all parallel to one another) so the angle
    between the celestial body and the horizontal surface defined by the
    fluid is identical to the angle between the celestial body and the
    sensible horizon. The visible horizon is nowhere involved in that
    geometry and thus dip is irrelevant.
    
    > Which brings us to a bubble level fitted to a sextant.  If I calibrate it so
    > the bubble is centered while a natural sea horizon is aligned on both sides
    > of the horizon mirror at almanac STP (discounting index error) while it is 6
    > ft. above the water level, I would have to take dip into account in
    > subsequent observations when using it on land.  Yes no?
    
    
    I have no experience of bubble attachments. However, I would think it a
    bit pointless to set up the attachment so that the bubble is centred
    when the telescope is angled downwards towards a visible horizon. That
    seems to negate half the point of using a bubble.
    
    
    Trevor Kenchington
    
    
    --
    Trevor J. Kenchington PhD                         Gadus{at}iStar.ca
    Gadus Associates,                                 Office(902) 889-9250
    R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
    Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555
    
                         Science Serving the Fisheries
                          http://home.istar.ca/~gadus
    
    
    

       
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