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On 5 Jun 2003, at 16:46, Ken Muldrew wrote:

> I would really like to gain an appreciation of the mechanical aspects
> of the calculation, as it was done ca. 1800. I know that they used
> Merrifield's approximate method for clearing the lunar distance, using
> calculated altitudes of the moon and star (with a double altitude of
> the sun to establish latitude).

Sorry for following up my own post but it seems I was mistaken in
thinking that Merrifield's approximate method was used by these
explorers as it wasn't developed until about 50 years later (Cotter, A
History of Nautical Astronomy, 1968). Jeff Godfred apparently uses
William Hall's approximate method in his Northwest Journal article on
David Thompson, although this method was only published in 1903.
It doesn't much matter if one is using a calculator, but in order to get
a feeling for the difficulty and time required to do the calculation, the
actual method needs to be used.

Cotter says that two approximate methods (the first due to Lyons
and the second due to Dunthorne) were published in the original
Nautical Almanac. A brief description of Dunthorne's method is
given in Cotter and I am also slogging through a paper by Mendoza
from the Philosophical Transaction of the Royal Society published in
1797 where 40 exact methods are given and about 10 pages,
generously sprinkled with algebra, are devoted to approximate
methods. If anyone knows of other sources for the approximate
methods used ca. 1800 (especially those discussed in Robertson's
text, Elements of Navigation, as Thompson was known to have
possessed a copy) I would be very grateful for suggestions.

Ken Muldrew

   

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