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Arthur Pearson has made an interesting response to my posting on anomalous
dip, confirming it to be an important matter from his own
observations.Jared Sherman is surprised that such an effect could be
routinely ignored.

Arthur quotes Bowditch as follows-

Bowditch also states that "The effect is greater as the temperature
>difference increases." He notes that studies attempting to derive a
>correction factor based on the sea-air temperature difference "differ
>considerably". However, he summarizes the range of results and reports
>"the average of these [studies] is about 0.16' per degree Fahrenheit
>(0.28' per degree Celsius).  Thus, the correction is about one-sixth of
>a minute per degree Fahrenheit, or one minute per each six degrees."

It's easy to see why there might be such conflict between observers as
Bowditch reports. We are considering the bending of a light-ray which skims
past the wave-tops at a tangent to the sea surface and then rises to reach
the height-of-eye of the observer, so it's never more than a few feet above
the sea. This ray gets curved according to the vertical temperature
gradient. How can we guess what that temperature gradient might be?
Mariners tried to allow for it by measuring the air temperature at the
level of the observer's viewpoint (A), and drawing a bucketful of seawater
to measure the water surface temperature (B).

The temperature of the air just above the water surface will presumably be
somewhere between A and B, but it's likely to be greatly affected by
low-level air turbulence from the wind, and by disturbance of the
sea-surface, which will both affect the temperature gradient. The gradient
will presumably be greatest under glassy-calm conditions, which is when a
mirage (an extreme case of anomalous dip) is likely to be seen at the
horizon, if there are any objects beyond the horizon to show them up.

Anomalous dip is also likely to occur when air, heated by a tropical Sun
shining on desert sands, blows across a nearby stretch of water. Also above
coral shoals, when awash and heated by the Sun. These may be the reasons
why the Red Sea has always been regarded as a haunt of anomalous dips.

So it's going to be hard to find a trustworthy rule that preducts value for
dip under a wide range of climatic conditions.

In the past, I suspect, many a duff sextant measurement has been blamed on
"anomalous dip", which provided a convenient scapegoat. But it was never
easy to assess the dip when out of sight of land, because there was no
independent way to discover a ship's true position, in the ocean (how
different things are now!).

Fred Hebard added, about Bowditch 1966-

> One interesting point was that
>measurements of three or four bodies more-or-less equidistant in
>azimuth would cancel the deleterious effects of anomalous dip.  Another
>was that backsights of an object combined with normal sights would
>allow one to estimate the magnitude of anomalous dip.

This is, of course quite true. However, anomalous dip effects are
presumably driven by the heat of the Sun to a great extent, and probably
affect Sun altitudes much more than stars. (and we have only one Sun in the
sky, and dip may change over the day}. It's another argument for using
stars for position, rather than the Sun.

The "backsight" proposal is fair enough, but with a normal sextant this
method can only be used when the Sun is more than 60 degrees up. When it
is, you can take its altitude in the normal way, then turn round and
measure it up from the opposite horizon, when it will be above-and-behind
your head. The difference between the sum of these two altitudes and 180
deg will be twice the dip.

====================

Thanks to Fred for providing data of his land-based observations, which any
sextant observer would be proud of. It would be interesting to compare
those figures with what Fred could get out of shore-based observations up
from a horizon, or those taken in real-life from a small boat.

It's notable that much of the scatter in Fred's positions occurs in his
altitudes of the Moon. Is Fred taking all the minor corrections for the
Moon into account, such as augmentation of semidiameter, reduction of
parallax, I wonder? Normally, one would only bother with such matters when
seeking the ultimate precision of a lunar, but Fred is achieving such
remarkably consistent answers that it may be worthwhile taking these minor
matters into account.

George Huxtable.

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contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
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