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George:

My 1839 edition of Norie's contains a Table XXXV - it is entitled "To
correct the apparent distance of the Moon from the Sun, a Star & etc. for
the effects of Paralax and refraction" with entries against Apparent
Distance across the top and Paralax in Altitude or Distance down the
side; this Table covers distances to 120-degrees. My 1889 edition of
Norie's contains a Table XXXV, but only covers distances to 30-degrees. I
will not open these books as necessary for copying, but would be pleased
to provide specific entries - if you could copy the work forms indicated
in your posting, I would also be glad to comment.
                                        Henry

ps My 1902 copy of Norie's Tables alone no longer includes the XXXV

On Mon, 2 Aug 2004 10:40:04 +0100 George Huxtable
 writes:
> This is a request for some help, please, because my own knowledge and
> information has run out here.
>
> I am following the navigation practices of a captain in the
> Greenland
> Whaling, who accasionally used lunar distances to determine his
> longitude.
>
> I have copies of a pamphlet he carried, dated 1816, which was
> produced by
> J.W.Norie, which had the usual extravagantly-long title of those
> times, as-
> "Formulae for finding the longitude, in which a method invented by
> Mendoza
> Rios is used for clearing the observed distances from the effects of
> refraction and parallax, with rules for working the observations.".
>
> It seems that this consisted of a pad of blank forms for the
> navigator to
> fill in, preceded by a couple of  pages of explanation about how to
> do it.
> I have copies of some of these completed forms from various whaling
> voyages, and am attempting to work backwards to discover how the job
> was
> done, in detail.
>
> I have found no more than a mention of Mendoza's method in Cotter's
> "History of Nautical Astronomy", and no details about that method.
> From
> Norie's explanation it appears to be an approximate method rather
> than a
> rigorous one (though that doesn't necessarily detract from its
> accuracy).
>
> A footnote after the explanation states "N.B. In the above Rules,
> the
> numbers refer to the Tables in Norie's Epitome or Nautical Tables."
> I have
> my own copy of Norie's, but this dates from much later, 1900, while
> its
> bound-in tables date from as late as 1914. Even at such a late date,
> this
> includes tables for working a lunar distance, but unfortunately not
> the
> tables required for Mendoza's method, which had by then long been
> superceded. Nor does my copy of Raper's (of 1864) seem to carry any
> equivalent tables. So I'm stuck, rather.
>
> The vital table that's missing from that later Norie's is Table XXXV
> (=35);
> in my edition the tables go straight from XXXIV (=34) to XXXVI
> (=36). A
> handwritten note on the Mendoza explanation seems to imply that
> Mackay's
> table LXXII (=72) corresponds, but I don't have a copy of Mackay.
> The
> Mendoza-method explanation about using table XXXV states- "Enter
> Table
> XXXV. with the apparent distance at the top, and the Moon's
> correction in
> the side column, the corresponding number will be the third
> correction;  in
> the same column, and opposite the difference in corrections, will be
> found
> the fourth correction."
>
> Another Norie table required was table XXX (=30), stated to
> correspond to
> Mackay table IX (=9). This was described as for the "proportional
> logarithm
> of the Moon's correction". In my more modern Norie's, table XXX has
> become
> simply a table of the Moon's correction, with no mention of
> proportional
> logarithms, but as proportional logarithms still remain, as table
> XXXIV
> (=34), by combining two lookups one can get the required answer. So
> that's
> a problem that can be bypassed.
>
> It's likely that the Bodleian Library will have copies of those
> earlier
> Norie's, but usually they are very stuffy about photocopying pages
> from
> their older texts.
>
> So here is my request. I'm asking any Nav-L member who may possess
> (or have
> access to) a copy of Norie's that's old enough to contain Table XXXV
> if
> they would kindly let me know how many pages it covers (to assess
> the size
> of the problem). If it's only a page or two, then if anyone is in a
> position to make a scan and send it to me as a fax or off-list
> attachment,
> I would be most grateful. Alternatively, similar information about
> Mackay's
> table LXXII (=72) would be equally welcome.
>
> These difficulties exist only in the section of Norie's pamphlet
> which
> deals with clearing the apparent lunar distance, by Mendoza's
> method; the
> rest explains itself well.
>
> For those that are interested, here's a transcript of that section
> from
> Norie's pamphlet, about Mendoza's method-
>
> ==============================
>
> "To find the true Distance.
>
> 1. Add together the apparent distance and apparent altitudes, and
> take half
> their sum; the difference between the half sum and the Sun or Star's
> apparent altitude call the first remainder: and the difference
> between the
> half sum and the Moon's apparent altitude call the second remainder.
>
> 2. Add together the log sine of the apparent distance; the log.
> co-sine of
> the Moon's apparent altitude: the log.secant of the half sum; the
> log
> co-secant of the first remainder; the proportional logarithm of the
> Moon's
> correction (XXX) and the constant logarithm 9.6990: their sum,
> rejecting
> the tens in the index, will be the proportional logarithm of the
> first
> correction.
>
> 3. Add together, the log. sine of the apparent distance (already
> found;)
> the log. co-sine of the Sun or Star's apparent altitude; the log
> secant of
> the half sum (already found;) the log. co-secant of the second
> remainder;
> the proportional logarithm of the Sun or Star's correction; and the
> constant logarithm 9.6990: their sum, rejecting the tens in the
> index, will
> be the proportional logarithm of the second correction. [A footnote
> states-
> (The sun's correction is the difference of the refraction and
> parallax in
> altitude.  (IV,  VI) The star's correction is the refraction in
> altitude
> (IV)).]
>
> 4. The difference between the first correction and the correction of
> the
> Moon's altitude call the difference of corrections.
> Enter Table XXXV, with the apparent distance at the top, and the
> Moon's
> correction in the side column, the corresponding number will be the
> third
> correction; in the same column, and opposite the difference of
> corrections,
> will be found the fourth correction.
>
> 5. Subtract the sum of the Moon's correction, and the second and
> fourth
> corrections from the apparent distance; to the remainder add the Sun
> or
> Star's correction, and the first and third corrections; their sum
> will be
> the true distance."
>
> ===================
>
> To me, Mendoza's appears to be a remarkably complex and long-winded
> method,
> even though it avoided the necessity for using long 5-figure or
> 6-figure
> logarithm tables. It's not surprising that it failed to survive, in
> competition with (say) Thomson's Lunar and Horary Tables.
>
> In analysing these whaling journals, I could, of course, choose to
> use
> another method for clearing the lunar distance, one for which all
> the
> required information was readily available. But I would prefer to
> follow,
> if possible, exactly the same steps that were taken by this
> navigator.
>
> George.
>
> ================================================================
> contact George Huxtable by email at george@huxtable.u-net.com, by
> phone at
> 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1
> Sandy
> Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
> ================================================================
>

   

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