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More about Sumner's observation in 1837.

Jim Thompson said-

>He was pretty damn gutsy to have sailed ENE in poor
>visibility toward the rocks, assuming that his longtitude was west of
>Small's Light.  When Small's Light popped out of the mist, he must have been
>both immensely relieved and incredibly gratified.

Jim says "in poor visibility", and "out of the mist". He may know more than
I do. All I have to go on at present is Cotter's account of the event, with
a copy of Sumner's chart and some quotes from Sumner's text. But I find no
mention there of "in the mist". Indeed, Cotter managed a Sun altitude at 10
am, and to do that he would need a clear horizon, several miles away.

Cotter's plan was not then particurly "gutsy" in my view, but it was
logical. As the Smalls rocks were well marked, except in thick weather it
would be quite safe to approach them as Sumner did in the prevailing
Southeasterly gale, knowing he could always bear away when the light-tower
was sighted. He might well first sight the Welsh coast (near Milford Haven
entrance), which was a few miles further on. What he was trying to do was
to keep up to windward as far as he possibly could until he knew exactly
where he was, to be sure he could keep clear of the rocks off the Southeast
corner of Ireland, which was a lee shore. Prudent, yes. Inventive,
certainly. "Gutsy", no.

So, when Jim says- "It will make an interesting lecture, if I
>can reduce the elements sufficiently to lay terms and spice it up with
>information and graphics about a shipboard navigator's life in those
>days.", I hope he won't spice it up any more than is justified.

Jim said-

>If that old DR latitude was way off, then his longtitude was too -- which
>was one of the points that navigators in those days might not have
>appreciated, because they did not commonly understand the concept of a
>celestial LOP.

Well, that's the whole point, really. Sumner had shown that WHATEVER his DR
latitude was,  based on an old noon Sun several days earlier, he simply HAD
to be on the oblique position line he had calculated entirely from the one
Sun observation made at 10am on that day.

It's true that navigators "did not commonly understand the concept of a
celestial LOP", but they were certainly aware that the longitude they
derived from a "time sight" was crucially dependent on knowing an accurate
latitude.

There were several ways of deriving the longitude from a time-sight and the
latitude, but what he probably would use would be-

cos (P/2) = sqrt( sin s sin (s - ZX) / (sin PZ sin PX))

where P is the local hour angle, ZX is the Sun's zenith distance, PZ is the
co-lat, PX is the polar distance, and s = 1/2 (ZX + PZ + PX) .

It's an interesting question, why it had to wait until 1837 before mariners
had the commonsense to realise that an oblique position line could be drawn
from a single altitude of any body with a known position in the sky.
Looking back, it seems such an obvious step. I hope the new book on "Line
of Position Navigation" will go some way to enlighten us.

George Huxtable.




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