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This is intended for George, Fred, or someone otherwise familiar
with short methods for clearing Lunar Distances, or in the use
and construction of tables of Proportional Logarithms.

I am currently working on a previously undiscussed short
clearing method, circa 1820, which I intend to post, however,
am having some difficulties is verifying the accuracy of
certain included tables which depend on the use of
proportional logarithms.

A Table III, supposedly entered with the Sun's Apparent Altitude,
produces a logarithm employed in calculating a "second correction".
This tabular, value is stated as the summation of the log sin 30-deg
+ log cos Apparent Altitude + proportional  log of the Altitude
Correction (parallax - refraction). At small values of Altitude
Correction, say in the order of 1-minute or less, I am unable to
accurately replicate the tabular values presented, while at larger
values acceptable coincidence can be demonstrated. For example ...

At 30-deg Apparent Altitude, and tabulated Sun's Correction
as 1m-30sec, the referenced Table III produces a log of 1.7115.
My calculation is log sine 30 = 9.6990 + log cos 30 = 9.9375 +
pl 1-30 = 2.0792, for a correction log of 1.7157. This is not an
earth shaking difference at 30-deg, however, as the altitude
becomes greater, and the correction therefore less,
the difference becomes greater and the result questionable.

A similar table published for the Moon, where altitude
corrections are significantly larger, utilizing the same deriving
formula, works out with amazing accuracy.

I am using proportional logarithm tables dating back to 1828,
all British, i.e., Norie's, and find no difference in entries at small
values. Were there other, perhaps American tables published,
circa 1820, am I having a "senior moment", are there other forms
of pl tables, or are proportional logs simply not accurate enough
at small values.

   

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