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Thanks to Paul Hirose for a useful contribution to this discussion. In
particular, his quotation from Bowditch 1984 Vol 1 is very relevant, and I
repeat it here.

>"An investigation by the Carnegie Institution of Washington showed
>that of 5,000 measurements of dip at sea, no value differed from the
>tabulated value by more than 2.5', except for one difference of 10.6'.
>Extreme values of more than 30' have been reported and even values of
>several DEGREES have been encountered in polar regions."

In my recent mailing on sextant sight accuracy, the section dealing with
horizon refraction commented on Jim Manzari's analysis as follows-

"For the Manzari approach to be workable, horizon refraction effects have
to be of two distinct kinds; those that are major, rare, and obvious, and
those that are totally negligible: nothing in between. Does he, or anyone
else have evidence to support this unlikely contention?".

Well, here I have to concede that the passage to which Paul Hirose has
drawn attention does indeed provide significant evidence in that direction,
in favour of what I had called Manzari's "unlikely contention". It would be
interesting to read the Carnegie report that was referred to, if anyone can
provide a reference to it.

Dutton (1968)  refers to a correction that could be made to the dip
resulting from sea-air temperature difference as follows-

"The Japanese Hydrographic Office, by considerable empiric testing, found
the value to be 0.11 minutes per degree Fahrenheit.; other values, ranging
up to 0.21 per degree Fahrenheit, have been suggested.  ...When the
Japanese value of 0.11 was applied to several hundred observations made
along the Atlantic coast between the Virgin Islands and New England
throughout a year, it proved to be generally satisfactory and improved some
98 per cent of the observations."

It would be interesting to see further details of those observations.
However, one might infer that if making this air-sea temperature correction
really did improve 98% of the observations, then-
1) It seems likely that refraction near the horizon must have been the
major error remaining, after all other corrections had been made.
2) The correction must have been a reasonable approximation to the effect
being corrected.

Perhaps other readers can inform us what is the likely range of air-sea
temprature differences at sea, the air temperature being measured near to
the eye-height of the observer, the sea temperature near the surface, from
the cooling-water intake or with a bucket. My rather uninformed guess would
be that a range of 0 to 25 degrees Fahrenheit (0 to 14 Celsius) in the
difference (air - sea) would be rather conservative, and this would
translate, according to the Japanese assumption, into a range of 2.75
minutes of arc correction.

Presumably, standard values for dip include a correction for horizon
refraction which is based on an average value of this temperature
difference. In that case, if no correction is made for air-sea difference
(which is probably true for all of us) a resulting scatter up to 1.4
minutes either side of this average would not be surprising.

So, not an overwhelming effect, this horizon refraction, but by no means
negligible either. When other observing conditions are good (calm sea,
clear horizon) then it may well be the dominant error remaining.

It may be useful for navigators to be aware of the sign of the
temperature-difference correction. Assuming the air is warmer than the sea,
then the horizon is raised and the dip is decreased, compared with its
standard value. Trouble is, until we know what air-sea temperature diffence
the standard dip correction has been calculated for, we can't properly
allow for changes.

Please note that I am NOT proposing that we should all arm ourselves with
buckets and thermometers and make such corrections. It's just worth
thinking seriously about what errors remain when we have made as accurate
an altitude observation as we can, and corrected it as well as we can.

MEASURING DAY-TO-DAY CHANGES IN DIP.

Both Paul and I have suggested that measurements could be made with a
theodolite from shore. But for any reader who is fortunate enough to have a
view of the open sea from his window, useful observations might be made
with much simpler gear than that, needing no theodolite. All it would need
is for a vertical scale to be made by sticking a vertical measuring-tape to
the inside of his window, and a post to be placed, say 10 metres away,
towards the sea. Knock a nail horizontally into the side of the post, at a
height where, when seen from a convenient height within the window, it
aligns with the horizon, more or less. If in tidal waters, note a mark on
the shore that the waves just lap, somewhere near mid-tide.

Now, whenever the tide is at or within a few inches of that mark (which
gives four possible shots per day) and when a clear horizon can be seen,
then line your eye up with the nail and the horizon, and note the
corresponding reading on the scale. Note the air temperature outside, too.
The sea temperature could be monitored from time to time, but won't change
quickly.

The most useful observations would be made from a residence close to the
sea, within say 100 or 200 metres, as the aim is to gauge refraction over
sea, not refraction over land. It would be best if the elevation was no
higher than a ship's bridge, preferably less. And a view directly out to
open sea, rather than out through a creek or over a harbour, would give the
best approximation to the seagoing conditions we wish to simulate.

With the dimensions I have suggested, a change in dip by one minute would
shift the reading on the scale by 2.9 mm, so day-to-day variations, if they
are of the magnitude suggested in the section above, should be readily
discernible, and might make an interesting plot against time.  Trouble is,
the unaided eye can only resolve a minute of arc or so. An improvement
would be a small telescope or binocular which can be fixed to a frame and
jacked vertically up and down against a scale. How about it, anyone?
Unfortunately, not me, as I live 80 miles from the sea, which in Britain is
nearly as far as it's possible to get.

George Huxtable.


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george@huxtable.u-net.com
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel, or fax, to 01865 820222 or (int.) +44 1865 820222.
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