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Brad deduced that Cook, in those North Atlantic crossings, 1764 to 1767,
was using incremental reckoning, not absolute reckoning.

Exactly so! His longitudes were obtained entirely by dead reckoning, from
his point of departure until he arrived at his destination. He would not
learn how to take a lunar until 1768. And he would not have a chronometer
until his second circumnavigation, 1772.

Cook was very pernickety about his dead reckoning. The log was streamed
regularly, each hour. Think about the manpower requirement of that. The
total complement of his brig was no more than 20, so 10 for each watch. It
seems to me that taking the log must call for two pairs of hands on the
poop, even with a bit of help from the helmsman there. So two men were
diverted from other ship's duties once an hour, for a job which must have
taken 10 minutes. Dead-reckoning, by later navigators that were less fussy,
would call for the log twice, or maybe just once, in a four-hour watch.

Each hour, the compass heading, in magnetic points or half-points (rarely
quarter-points) would be noted, as well as logged speed, probably on a
slate or else pegged-up on a traverse-board.

Then it was the navigator's job to integrate-up these 24 vectors, over a
day. This was an important part of his day's work, which called for the
traverse tables, designed for that job. Versions of those existed which
provided the vector sum in miles, and the course in degrees (magnetic). In
that form, it was then easy to allow for magnetic variation to get true
course and distance, providing  true Northing (in miles) and Westerly
departure (in miles) and then Westing (in minutes). That was then offset
from the position of the previous noon. And, as Brad has realised, any
error over a day simply accumulates with the next day, and so on. Little of
the working was shown on the log, and I haven't yet discovered if (and if
so, where) allowances were made for leeway, or for ocean currents, if
known.

After all that, it was a surprise for us to discover, when the landfall was
made at the end of the passage, that the log was consistently under-reading
the travelled distance by something like 5%. In each of those 7 crossings,
Cook was that much "ahead of his reckoning". That behaviour would usually
be attributed to the existence of ocean currents, but surprisingly, there
was no appreciable difference in that respect between Eastbound and
Westbound passages.

Presumably Cook simply accepted that consistent under-reading, and allowed
for it in his mind, without bothering to re-knot the log, or add a bit more
sand (or crushed eggshell) to his timing-glass. He would always start
sounding, as the voyage neared its end, well in time before landfall.

That may be a bit more than Brad asked for, or really wanted, but it shows
how badly navigators needed some way to determine the actual longitude they
had got to.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message -----
From: "Brad Morris" 
To: 
Sent: Saturday, March 20, 2010 5:35 PM
Subject: [NavList] Re: AW: Early lunars


Hi George

You wrote:
Even as late as 1767, such an experienced navigator as James Cook was not
noting his longitudes as from Greenwich, in his North Atlantic crossings.
They were always from the point from which he took his "departure" ...Never
from Greenwich, much to my surprise.

This means that he was using incremental reckoning, not absolute reckoning.
Truly interesting! The problem with this type of reckoning is the
accumulation of round-off.

Example:  I went west 1.234 degrees on day 1 and on day two, I went west
2.345 degrees. Since that is 'too many' digits to write, on day 1, I record
1.2 degrees and on day 2, I record 2.3 degrees.  How far west am I?
According to my records 3.5 degrees, when I actually went west 3.579
degrees.  Make this 1000 days, and you get the picture.

Cook was out exploring for years, if I have it right.  Therefore his
records must show a gradual shift in longitudes with respect to time.  Does
your research show this outcome?

Best Regards
Brad




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