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Brad wrote-

"The Nautical Almanac 1773, states that the Equation of Time for 4 August
1773 is ADD 5 minutes 36.4 seconds Additionally, we have 5.8 seconds from
noon to noon at Greenwich, this being 15-48-17 GMT, we must add  0.914
seconds."

All right until the last bit. Equation of Time is REDUCING, from 5 min 36.4
sec at Greenwich noon on 4 August, to 5min 30.6 sec on the 5th. Brad has
calculated the amount of the adjustment as 0.914 seconds correctly, for the
fraction of a day after Greenwich noon on the 4th, but has got its sign
wrong.

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

Further on, he wrote-

"Before we can jump to the time difference, we must calculate the GMT using
the corrected
sun's altitude and a corrected moon's altitude."

Clearing the lunar distance itself corrects for refraction and parallax of
both bodies. So to obtain GMT the corrections to make beforehand are for
index error, dip, and semidiameter: nothing more. As I keep on saying...

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

Brad should not be looking for exact correspondence between his own
calculations and those of Bayly. Via Frank's calculator, he has used a
precise modern ephemeris of the Moon, the position of which, back in 1773,
is known much better to us now than it was predicted in the 1773 almanac
that Bayly had to work from. We should expect to see discrepancies that can
reach an arc-minute or so in the lunar distance, or up to 30 minutes, or
thereabouts, in the resulting longitude.

A more interesting comparison would arise if Brad chose to work his lunar
distance, not using Frank's calculator, but instead using the 1773 almanac,
as Bayly had to do. All the necessary information is there. He should then
get exact correspondence with Bayly: any discrepancy should be due to
rounding errors, or to blunders. In that case, there would be no equation
of time correction to make, because the almanac in 1773 was working in
apparent time, not mean time.

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

May I clear up something I stated a couple of days ago, which was wrong (or
at least, misleading)?

I wrote- "If the resulting longitude does differ greatly from the presumed
value, then a reiteration is called for, because position changes affect
the clearing process (a bit)."

That was true only if the altitudes (and so, the corrections) were being
derived by calculation, taking an assumed (usually DR) position for the
observer.

However, if the altitudes are obtained by observation, as they presumably
were in all these cases we are considering, the altitudes are what they
are. Being measured, they do not depend on an assumed position of the
vessel. So no reiteration is called for. The question doesn't even arise.

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.

----- Original Message -----
From: "Brad Morris" 
To: 
Sent: Wednesday, March 31, 2010 1:47 AM
Subject: [NavList] Re: AW: Sun Moon Lunars to 155 degrees


Hi George

You wrote:
Where has equation of time got to?

It went missing through that hole in my head.  The Nautical Almanac 1773,
states that the Equation of Time for 4 August 1773 is ADD 5 minutes 36.4
seconds Additionally, we have 5.8 seconds from noon to noon at Greenwich,
this being 15-48-17 GMT, we must add  0.914 seconds

06-54-00         (LAT)
00-05-36.4      (EoT)
00-00-00.914  (EoT adjustment)


Thus we have 06-59-37.3 seconds, which I will round off to an even 37
seconds


15-48-17 (GMT from Frank's Online Calculator, using given altitudes)
06-59-37 (LMT From LAT using given sun altitude, sun semi-diameter and EoT)
-- -- -- -- -
08-48-40(time difference from Greenwich)

Convert to Arc

132d 10m 0s  West

Check by adding it to Cook's given longitude 227d 40m 30s East, yields 359d
50m 30s

There still is a missing 9 minutes and 30 seconds of longitude.

---------------------------------------------------------------------
Instead of using the altitude directly, I will correct it here for DIP and
by the
2010 Nautical Alamanc using the 0-10degree altitude correction tables.

Sun's altitude given by Cook as 5d 41m 45s  (actually, 5d 41 3/4m)
Dip correction for 24 feet is -4.8 minutes
Altitude correction for 5d 41m 45s is +7.2 minutes
So the altitude of the sun might be 5d 44m 19s

Using 5d 44m 19s, sun's declination of N17d 8m 8s and Cook's latitude of
S20d 49m, we
get LAT of  06-52-59, to which we will add the same EoT adjustments

06-52-59         (LAT)
00-05-36.4      (EoT)
00-00-00.914  (EoT adjustment)
--------------
06-57-36.3      (LMT)


Before we can jump to the time difference, we must calculate the GMT using
the corrected
sun's altitude and a corrected moon's altitude.  Again, using the modern
correction tables,
10d 31m 52s Moon's apparent altitude, dip correction of -4m48s, moon's HP
of 58.9 yields
an altitude correction of +6.4m, all in turn yielding a Moon's corrected
altitude of 10d 33m 28s.
Of course we could have used the 1773 NA Horizontal Parallax of 57' 09",
yielding a slightly
different alt corr'n +4.1m

Injecting this into Frank's online calculator with the parameters
Date 4-Aug-1773
Time 15-48-22 (NOTE: this bumped by 5 seconds since last time )
Sun's alt 5 degrees 44.3 minutes
Moon's alt 10 degrees 33.48minutes
DR Long 227 degrees 40.5 minutes EAST
DR Lat 20 degrees 49 minutes SOUTH
Temperature 76 degrees F
IC 0
HoE 24 feet, in deference to the consensus of opinion

Yields 0 error in lunar and 0.5 minutes of error in longitude

15-48-22 (GMT from Frank's Online Calculator, using given altitudes)
06-57-36 (LMT From LAT using given sun altitude, dip & alt correction)
-----------
08-50-46 (time difference from Greenwich)

Convert to Arc
132d 41m 30s WEST

As a check, add to Cook's given value of 227d 40m 30s EAST

yields 360 degrees 22 minutes 0 seconds.

This is 22 minutes too much.

---------------------------------------------
Of course we could have used the 1773 NA Horizontal Parallax of 57' 09",
yielding a slightly
different alt corr'n +4.1m yielding a final Moon Alt of 10d 31.2m.

Injecting that into Frank's online calculator requires that we revert to
15-48-17 for time.

15-48-17 (GMT)
06-57-36 (LMT From LAT using given sun altitude, dip & alt correction)
----------
08-50-41 (time difference from Greenwich)

Convert to arc

132d 40m 15s WEST

adding to 227d 40m 30s EAST, yields360d 20m 45s.

This is still 20minutes 45seconds too much.

-------------------------------------------------------------------------

Still no joy in the land of lunars!

Could it be that the altitudes given are actually in error?

Or am I still missing something!

Best Regards
Brad

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