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Responding to Arthur Pearson, I said-

>>I'm a bit puzzled when Arthur says-

>>>(in my case, I interpolated within the hour for GHA, and within the 12
>>>hour period for Dec)

>>That is almost certainly adequate for Dec of the Sun, which varies slowly
>>and smoothly, >>but almost certainly inadequate for the Dec of the Moon,
>>which changes MUCH faster! As >>the nautical almanac provides Dec at
>>1-hour intervals, why didn't Arthur interpolate >>between those? Or was
>>he using a different almanac with more condensed data? If so, I >>suggest
>>they were inadequate for his purpose.

Arthur replied-

>With respect to my interpolations, I reexamined my spreadsheet and
>should correct myself. I interpolated only sun declination within a 12
>hour period. Sun GHA, moon GHA and moon declination are all interpolated
>within a 1 hour range. I got the idea for the 12 hour interpolation from
>George's annotations to the "Astronomical Notebook" that Lewis received
>from Patterson which state that Lewis' almanac only gave right ascension
>and declination sun and moon at 12 hour intervals. I started out to
>recreate this methodology but lost my nerve for all but sun declination.


Well, Arthur Pearson is right. Early Nautical Almanacs, from the first one
in 1767, gave Moon declination at 12-hour intervals, Noon and midnight. And
just making an ordinary linear interpolation for times within this 12-hour
interval gives rise to a worst-case interpolation error of around 4
arc-minutes in the Moon's declination. That is sufficiently accurate that a
calculated altitude based on that dec. will not affect the accuracy of
clearing the lunar distance. No doubt, that's why Maskelyne chose a 12-hour
interval for the tabulation of Moon dec. and Right Ascension.

Arthur's stated procedure of interpolating within a 12-hour interval
between tabulations would in fact have been satisfactory, even though, as
it turned out, his chosen Moon dec tabulations were only 1 hour apart.

Sun positions, in Dec and Right Ascension, were tabulated every day at
Noon, which was quite good enough in view of the slower and more orderly
motion of the Sun

Today, with the quantities tabulated every hour, we can achieve a much
greater accuracy, but it's not really necessary for the purpose of clearing
the lunar distance. As Arthur pointed out, this part of the operation is
rather forgiving.

George Huxtable.

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george@huxtable.u-net.com
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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