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Brad and I are in agreement about his assessment for GMT of Bayley's 
observation, using Frank Reed's lunar calculator.

And I presume that that calculator, in its Moon position predictions, 
allows for changes in Equation of Time, since 1773.

The only thing I would quibble with, slightly, is the height-of-eye, to use 
for estimating dip (which is largely irrelevant for the lunar part of the 
calculation, anyway) if the dip hasn't already been allowed for. I obtained 
a height of 18 feet for the poop above the waterline, +5 feet for the 
observer, so 23 feet all told.

He arrives at GMT = 15 hr, 48min, 17 sec for the lunar observation. That 
seems reasonable.

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

Now we come to the calculation of LAT = Local Apparent Time, which 
presumably was obtained from the Sun altitude. Again, as Brad recognises, 
there are unknowns here, as to what, if any, corrections have been made 
before being tabulated by Bayly. Those corrections matter more in this part 
of the calculation than for the lunar itself . Brad assumes that all 
corrections have been made, and the tabulated value represents true 
corrected altitude of the Sun's centre. I have some doubta about that, but 
will await hard evidence, one way or the other.

As usual Brad will expect a few quibbles from me, none of which are very 
material.

The declination is given at Greenwich noon. As the Greenwich time of the 
observation was nearly four hours later, the declinations for that noon and 
the next day's noon need to be proportioned accordingly, and I suggest that 
dec. at the moment should be reduced to N17º 5' 52". Does Brad agree?

What will also be needed from the tables is the equation of time. 
Proportioned in the same way, I would make that 5min 36 sec (to add to 
apparent time to get mean time).

=================
| Using
| (1) declination from the 1773 Nautical almanac N 17 degrees 8 minutes 8 
seconds
| (2) the sun's semi-diameter from the 1773 Nautical Almanac as 15 minutes 
49.5 seconds
| (3) the sun's altitude AS GIVEN IN THE LOG 5 degrees 41 minutes 45 
seconds
| (4) and the latitude S20 degrees 49 minutes
| I get LAT to be 06-54-00.  This is a time in the morning, consistent with 
our large distance
| and a waning moon.  Now I ask you, is that the right altitude?  Or the 
right time?

=======================
from George-
I agree with that Local Apparent Time, with only trivial differences. And 
it sounds reasonable, also. From within the tropics, sunrise will always be 
close to a local time of 6am, and the Sun had only risen through 5 degrees 
and-a-bit.  That low Sun altitude, by the way, with its rather uncertain 
refraction, was the weakest point of this whole operation.

What Brad should do next, is to correct that local apparent time to local 
mean time, and find out how much that differed from the GMT from the lunar. 
That difference, converted to degrees, is the longitude from Greenwich. I 
think he will find it corresponds well to the value calculated by Bayly, 
which was the number-he-first-though-of, before this rather circular 
calculation. If we discover more about Bayly's tabulated Sun altitude, that 
may allow us to fine-tune things further.

Of course, all we have done here is to reproduce Bayly's own calculations, 
using modern arithmetic technology. We don't know how good his longitude 
actually was. He didn't carry GPS, to check it against. That lunar was all 
he had to go on. However, we might be able to check it against Wales' 
observations, if he observed for longitude on the same day, as the two 
ships were sailing in company.

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

An interesting check to make would be to work the set of lunars at the foot 
of the page, which were taken in a harbour with a longitude that is 
precisely known today.

George.


contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 

   

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