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On 3 May 2004 at 18:16, Frank Reed wrote:

> George also wrote:
> "I don't know anything about Witchell's method"
>
>
> I bet you do, but you don't recognize it by name. You've got an old
> copy of Norie, don't you? If not, hit that link on the Mystic Seaport
> library web site. It's "Method III" in Norie, if I remember correctly.
> It's also in Moore and Bowditch.

In case anyone is interested, here is Witchell's method from Moore:

Witchell's Approximate Method for Clearing Lunar Distances:
From Moore - New Practical Navigator, 1798

First add the sun or star's and moon's apparent altitudes together,
and take half the sum; then subtract the less from the greater, and
take half the difference; then add together:
   The cotan of half the sum,
   The tan of half the difference, and
   The cotan of half the apparent distance,
Their sum, rejecting 20 in the index, will be the log tan of an angle
A.

Second, when the sun or star's altitude is greater than the moon's,
take the difference between A and half the apparent distance, but if
less, take their sum, then add together:
   The cotan of this sum or difference,
   The cotan of the sun or star's apparent altitude, and
   The proportional log of the correction of the sun or star's
altitude;
Their sum, rejecting 20 in the index, will be the proportional log of
the 1st correction.

Third, if the sum of A and half the apparent distance was taken in
the last article, take now their difference; but if their difference,
take now their sum. Then add together:
   The cotan of their sum or difference,
   The cotan of the moon's apparent altitude, and
   The proportional log of the correction of the moon's apparent
altitude.
Their sum, rejecting 20 in the index, will be the proportional log of
the 2nd correction.

Fourth, when A is less than half the apparent distance, the 1st
correction must be added to, and the 2nd correction subtracted from
the apparent distance; but when A is greater, their sum must be added
to the apparent distance, when the sun or star's altitude is less
than the moon's; but when the moon's altitude is less, their sum must
be subtracted to give the corrected distance.

Fifth, in table X, look for this last corrected distance in the top
column, and the correction of the moon's altitude in the left-hand
side column; take out the number of seconds that stand under the
former and opposite to the latter. Look again in the same table for
the corrected distance in the top column, and the principal effect of
the moon's parallax in the left hand side column, and take out the
number of seconds that stand under the former and opposite the
latter. The difference between these 2 numbers must be added to the
corrected distance if less than 90?, but subtracted from it if more
than 90?; the sum or difference will be the true distance.

[From Maskelyne's Tables Requisite:
Table X. Numbers to be subtracted from the Logarithms in Table IX,
when the Moon's Distance from the Sun is observed.
Table XI. Numbers to be subtracted from the Logarithms in Table IX,
when the Moon's Distance from a Star is observed.]

> And (of Thompson's method) George wrote:
> "This method adds three correction terms to the observed distance to
> clear it, just as Frank's method does. But his method appears to
> differ more from Frank's than he implies. From my limited
> understanding (it's all rather obscure) it appears that the first two
> of Thomson's terms relate only to the corrections due to Moon
> parallax" etc.
>
>
> It's just book-keeping. The differences among the various series
> methods usually amount to deciding how much of the altitude correction
> to "fold into" the calculation of the A and B factors.

Jan Kalidova has written about Thomson's method (you should be able
to find it by searching the NavL website). It appears this method is
unique in that Thomson cleared thousands of lunars using approximate
(1st term only, I think) and rigorous methods and created a table to
find the difference between the two for virtually any condition.

> And just to repeat for anyone who made it to the bottom of this post:
> Lunars are Easy! Now get out there and shoot some...

As an aside I'd like to thank Frank for his first post in this
thread. After reading it I stopped trying to get the star onto the
moon "live" and instead used both hands to steady the sextant while
rocking. It improved my accuracy by an order of magnitude (down to
0.1' for three lunars this past weekend). I'm starting to believe
this technique could work for land navigation (although it still
seems pretty unlikely on a boat).  ;-)



   \----------------------------+---------------------------------+
o_,
 O_/ \    Ken Muldrew, PhD      | Voice: (403) 220-5976           |
<\__/7
 <\__  \  Dept. of Cell Biology | Fax:   (403) 270-0617           |
  | /
  "\ L  | University of Calgary | kmuldrew@acs.ucalgary.ca        |
/ /
   <    +-----------------------+---------------------------------+ /
/
               Morning coffee recapitulate phylogeny               L/

   

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