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Thanks to the collaboration of MANY listmembers, I now have a printed copy
of Table XXXV, that I needed from Norie's. In fact, I could have got it
through several different channels. What I printed out in the end came via
Paul Hirose's "back-door" entry into the Mystic Seaport digitised version
of Norie's. And I will look forward to the photocopied version, with its
extra information, arriving by US post from Bruce Stark. But no more help
now, please: I now have just what I need.

I've said it (or something like it) before, but the level of helpfulness
between members on the Nav-L list is remarkable, and satisfying. Doesn't it
work well? Nobody is trying to make anything out of it, members freely
offer what they have to meet the needs of others, no questions asked. (Pure
Socialism in action, I might add, if only to tease Americans...)

====================

There's a little curiosity about that Table XXXV, that I can only guess at,
but someone else (such as Frank) may know more about.

Frank Reed has written-

"But you don't really need the original. As I noted on this list two months
ago, Table XXXV is nothing more than a tabulation of the quantity
(1/2)*cot(d)*x^2 where d is the lunar distance, and x is the other angle (either
correction). That's all it is! ...

...the corrected distance  d' is found from the uncorrected
distance d via
   d' = d + A*dh1 + B*dh2 + Q.
That's two terms that depend linearly on the altitude corrections, dh1 and
dh2, and one term that depends quadratically on dh1 (other quadratic terms are
not necessary because they're very small). Details on tha A and B factors at
the link above, but for now it's worth knowing that Q is given by
   Q = (1/2)*cot(d)*dh1^2*(1 - A^2).
If you multiply this out, you find that you have two terms:
   Q = (1/2)*cot(d)*dh1^2  -  (1/2)*cot(d)*(dh1*A)^2.
So this means that we can get Q by entering a table of (1/2)*cot(d)*x^2 twice
--once with the Moon's altitude correction and then again with the Moon's
linear term which we have already calculated."

Table XXXV has columns labelled "APPARENT DISTANCE" (lunar distance of
course) from 10 deg to 120 deg, and rows labelled "Par. in alt. or dist."
in arc-minutes (5 to 62). The numbers in the table are corrections in
seconds.

As Frank points out, you have to look up this table with two different
values of that "par. in alt. or dist.", but the same lunar distance, and
take the difference between the two corrections that are found.

The curiosity is this- If you follow a row of this table, through
successively increasing values of lunar distance, the corrections decrease
(as you might expect) as you approach a lunar distance of 90deg and are
exactly zero for all rows at 90deg lunar distance. Then something funny
happens. At the next value of lunar distance (which is 95deg) all the rows
show a sudden jump in the value of the correction, by 20 seconds or nearly
so, which is completely unphysical and could never happen in that way in
real life. Then, as the lunar distance increases further, these values in
succeeding columns gradually fall, in some cases to near-zero.

I think what's happening may be this. The corrections, for distances above
90 deg, would become negative. In Norie's day, navigators had a hatred and
fear of negative numbers, and particularly of adding and (even worse)
subtracting negative numbers. Nowadays, schoolkids are familiar with such
concepts and techniques (though perhaps some of that fear remains).

So the jump of 20 sec seems to be one of Norie's "table tricks". To avoid
negative numbers, where the corrections would be negative he adds 20 sec to
ensure they are always positive. And because the overall correction is made
by subtracting one table-entry from another (in the same lunar distance
column) he could have added any number he liked to all the entries in a
column and the result of the subtraction would be the same. Clever, indeed,
but a user might get in a mess if he tried interpolating between lunar
distances of 90 deg and 95 deg, where that jump occurs.

There's a further minor-matter arises, in which any members who has access
to a pre-1828 version of Norie's may be able to help. In Norie's 1816 text
about Mendoza's method, which I quoted earlier, He mentions adding "the
proportional logarithm of the Moon's correction (XXX)". In my own, early
20th century edition of Norie's, table XXX just gives the Moon correction,
in minutes and seconds, not the proportional log. of that correction. This
presents no real problem, because there's a table of proportional logs
elsewhere, so the required number can be found by a two-step procedure.

It seems that even as early as 1828 (in the Mystic version), Norie's table
XXX was the same as in mine. So I ask if anyone can tell me if, in  an
earlier version of Norie's, (perhaps in the edition current in 1816) table
XXX contains the Moon correction in minutes and seconds, or whether it
contains the proportional log of that correction, so the step in Mendoza's
method can be mode in one go. Conceivably, it might offer columns for both.

Perhaps I have simply misunderstood Norie's text about the Mendoza method,
and he intendedd a two-step lookup from the start.

Please don't send me copies of that table XXX: just a few words about what
it contains, is all I am after.

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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