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    Re: Was this optical instrument designed for celestial navigation?
    From: Frank Reed
    Date: 2016 Feb 3, 14:40 -0800

    John Morris, you wrote:
    "I did celestial nav when I was X0/navigator of a USN ship."

    Nice. :)

    And you added:
    "I avoided planets because additional corrections were needed."

    Not really. Maybe you're remembering the Moon, which has more corrections and more paperwork.

    You also wrote:
    "We were never taught about horizon dip."

    Certainly, and without doubt, you were taught about horizon dip. But I think what's going on here is that you're remembering a bit hazily and connecting up dip with a "dip meter", like the historical example you've been discussing. The dip of the horizon is just the standard "height of eye" correction, and it is quite easy to estimate from a simple rule (no, David, not just for the test!):

    • dip in minutes of arc is nearly equal to square root of height of eye in feet.

    This approximation and the tables for dip (which are only slightly more accurate, multiplying square root of height of eye by 0.97) are more than adequate for most celestial navigation. We apply it to every sight. But dip is slightly variable. It depends on atmospheric conditions, and it is the largest source of error in celestial navigation for a decent observer with a good sextant. Unfortunately, dip varies in a fashion that is not normally amenable to correction by additional tables or equations. In principle, such corrections can be made. The theory and physics are sound and straight-forward but atmospheric conditions in practice are not so predictable. Instead, as an alternative, at various times in the history of navigation, attempts have been made to measure the dip directly using a device like a dip meter. By measuring the angle across the sky from horizon to horizon and comparing to 180° a dip meter can directly measure the normal dip (which we can calculate from that simple rule) and it also picks up the small variations on top of normal dip which are sometimes called anomalous dip. Such direct measurements can be extremely useful in circumstances where dip is severely affected by atmospheric conditions, for example, in the Arctic. 

    Dip is a simple thing, and a necessary correction in celestial navigation when the horizon is used as a reference. You certainly used it your USN experience years ago. But anomalous dip is something rarely considered, and it required either special equations and tables (and good luck) or direct measurement with something like a dip meter.

    Here's something else to ponder... (for general consideration now, not just specific to John's dip question):
    There's another way to think about dip. Imagine the Moon smoothed out... mountains and craters all leveled until it becomes a perfect sphere. If you stand on its surface, it has a certain angular "dip" of its horizon dependent on the observer's height. But if you launch yourself upward off the surface, the dip will grow and grow until eventually the Moon appears as an 'orb' in the sky behind you and eventually becomes smaller and smaller --just a 'circle' in the sky, much as it appears from here on Earth. At that point, we can measure its semi-diameter with a sextant. But really there is a continuity here. Dip and SD are two ends of the same spectrum. And that applies here on Earth. The Earth has a certain angular "semi-diameter" when we stand on its surface. Its SD is nearly 90 degrees; the Earth occupies nearly 180 degrees of our field of view. That "nearly 90" is reduced by that small angular value that we call dip. So then, we have a simple equation:

    SD = 90° - dip.

    This relationship applies at any height of eye whether 50 feet or 50,000 miles. It is more natural to think in terms of the dip angle at low observer altitudes and the SD (semi-diameter) at great distances, but they are literally two sides of the same equation. Just another way of thinking about things...

    Frank Reed
    Conanicut Island USA

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