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William Baffin's story, as introduced to us by Tony Scorer, has rather taken
my fancy, and I have done a bit more reading, in case it interests  those
who enjoy nautical history; it will bore those that don't..

Tony has quoted from "The Voyages of William Baffin, 1612-1622" by Clements
R Markham (Hakluyt Society, 1881). Markham has taken his account from an
immense collection of travel tales, "Purchas, his Pilgrimes", or "Hakluytus
Posthumus", of the 1620s. Fortunately, that collection was republished by
Maclehose around 1910, in 20 volumes, and Baffin is mostly in vol 14. That's
probably more accessible, in a library, than the Hakluyt Society volume,
which is rather scarce.

I recommend both the Purchas set and its predecessor, "Hakluyt's Voyages" of
1600, which is a set of 10 volumes, also published by Maclehose in the early
1900s. They are both sets of "travellers' tales", from the Elizabethan era
and before, and make for fascinating browsing, to anyone interested in early
maritime history.

Now for Baffin.

Let's start at his end. After his Arctic voyaging ended, Baffin was one of a
party attacking an Arab castle, and "went out with his geometricall
instruments", in order to take measurements of the castle walls, "the better
to level his peace". He must have been in charge of the artillery. No doubt
he presented a conspicuous target, and as a result was shot by the
defenders. So died Baffin, a martyr to geometry.

Tony has enlightened us about two attempted measurements of longitude. The
first, in 1612, used a North-South line set up on land. Although in theory
that method could have made possible a precise timing of the Moon, in
practice it was so far out that the resulting long., if it had been properly
calculated, would have been far East of Greenwich, not far West! That error
Baffin seems to have covered up with some convenient confusion, as Tony has
shown.

For that 1612 observation, Baffin quotes deductions "by mine ephemerides",
without stating what that ephemeris was. We presume it was Searle's, which
he quoted for his 1615 observations, as Searle's ephemeris covered both
those years.

In a second attempt, in 1615, Baffin attempts another longitude by timing
the Moon's transit across his North-South meridian, from on board ship, a
far more error-prone process than from on land. He tells us he used his
"instrument of variation" to do that job. He had made several measurements
of magnetic variation, presumably with some sort of compass. Any attempt to
determine the meridian direction by magnetic means would be doomed to
failure, as being hopelessly inaccurate for the job, especially in view of
his far-North latitude. Nevertheless, the result ended up with a spot-on
result for his longitude, presumably by good luck rather than by good
management. We can only wonder at how he did it.

==========================
Some astronomy.

Next, I have to report on my look into John Searle's "Ephemeris from 1609 to
1617...". Unfortunately, this could only be a fleeting visit to the library,
so my job has only been half done, and I'll have to go back. Clearly, Searle
was writing for astrologers rather than for navigators. It wasn't as simple
a job as I expected.

What Baffin needed to know was the hour, in Apparent Time at London, at
which the Moon was predicted to cross the Meridian of London, on the same
day that he measured the corresponding Local Apparent Time in Greenland of
the Moon crossing the meridian there. He also needed to know how fast that
prediction was changing, from one day to the next. So I have extracted
Searle's prediction for the day of Baffin's two observations (9 July 1612
and 22 July 1615 by Julian calendar; or 19 July 1612 and 2 August 1615 by
our modern calendar) and for the preceding day and the following one.

Unfortunately, Searle didn't provide the information in the form that Baffin
needed. The table shows, for each day, the "daily motions of the planets",
ets. Presumably this is the prediction at (apparent) noon at London, but he
doesn't say so. (It could possibly have been at midnight, but I rather doubt
it). It gives a value , for the Sun, Moon, and 5 planets, measured not in
degrees and minutes, but in signs (of the zodiac) degrees, and minutes. Each
of the signs is exactly 30 degrees wide (there are 12) and it isn't hard to
convert those values to degrees, by adding the appropriate multiple of 30.
We need none of the planetary information.

But here I start to get a bit out of my depth. Judging by other almanacs I
have seen, it's only ecliptic longitudes, not right-ascensions, that are
measured in that way (in signs +degrees), because the zodiacal divisions are
defined to be around the ecliptic, not around the equator. Presumably, then
the numbers predicted  by Searle are all ecliptic longitudes, not
right-ascensions. To predict the time differences between Sun and Moon
crossing the meridian, it's the difference in their right-ascensions that's
needed, not the difference in ecliptic longitudes. Does that make sense to
others?

If that's right, to get the timing information that's needed, we have to
convert the position (ecliptic longitude, ecliptic latitude) of the Sun and
Moon into equatorial coordinates (right ascension, declination). For
Baffin's purpose, the declinations aren't required.

Conversion involves using the Meeus formula 13.3, with the inclination of
the Earth's axis i = 23.489 degrees (as it was then).-

Tan (RA) = (sin long cos 23.489- tan lat sin 23.489) / cos long

That's simple, for the Sun, because the ecliptic lat of the Sun is always
zero, as near as dammit. There are some tables in Searle, and one of them
may be for making that conversion. I will have to check.

For the Moon, which can wander about 5 degrees away from the ecliptic (in
ecliptic latitude), converting to right-ascension has to be somewhat more
compicated. Another column in Searle's daily table predicts the longitude of
the Moon's ascending node, which again has to be converted from signs to
degrees. As I see it, the Moon's ecliptic latitude can be deduced by taking
the sine of-
(Moon's long. - long of Moon's ascending node),
and multiplying that by the tilt of the Moon's orbit, of about 5.13 degrees.
(Was that tilt significantly different then?)

Is that correct? There may perhaps be a table in Searle for doing that job.

Note that this is a simplification of the truth: in reality, hundreds of
additional terms perturbing the motion of the Earth-Moon system, quite
unknown to Searle and to Baffin, should be allowed for.

Then you can use that ecliptic latitude in the Meeus formula 13.3, as above,
with the long, to get the Moon's RA.

Having obtained the RAs of the Sun and Moon at noon that day, if you take
the difference, that will give the hour-angle between the two, at London
noon: that is , the HA of the Moon, at noon by the Sun.  But still, that
isn't what Baffin needed. He needed the HA between Moon and Sun, at the
moment that the Moon, not the Sun, crosses the Meridian. This could come
from an interpolation, making the doubtful assumption that everything is
changing linearly, by taking HA Moon at noon on successive days, thus
finding the rate of change. Dividing the Moon HA by that daily change, and
multiplying by 360, should (I think) provide HA Sun at the moment the Moon's
meridian passage at London..

A few questions arise. Have I got that convoluted procedure right? Is there
a shortcut to bypass some of it? Would Baffin have gone through that same
procedure before announcing the time at London of Moon's meridian passage?
Somehow, I doubt it.

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

Here are the values from Searle's ephemeris. Because tables often come
across badly in emailese, I have simply listed consecutive values for the
three dates. Values given in "signs" have been converted to degrees by
adding the appropriate multiple of 30.

1612.
Julian dates July 8, July 9, July 10.
Corresponding modern-calendar dates July 18, July 19, July 20.
Ecliptic longitudes-
Sun                    115d 55', 116d 52', 117d 49'
Moon                357d 14', 009d 21', 021d 39'
Ascending node 058d 31', 058d 28', 058d 26'

From these figures, Baffin has deduced that moon's meridian passage at
London on 9 July was 4h 25m 34s, and that the moone's motion that day was
12d 07', or 48 minutes 29 seconds, wrongly stating that "the Moone cometh to
the meridian sooner that day then she did the day before"

1615
Julian dates June 21, June 22, June 23
Corresponding modern-calendar dates July 1, July 2, July 3
Ecliptic longitudes-
Sun                    099d 01', 099d 58', 100d 55'
Moon                158d 51', 171d 12', 183d 50'
Ascending node 031d 26', 031d 23', 031d 19'

[note that the Moon long of 158d 51' was written in my notes as 168d 51',
which is clearly wrong, and must be an transcription error of Searle's or,
more likely, mine. One of my tasks is to check it. The value of 158d 51' is,
for now, a presumption.]

Baffin has deduced that moon's meridian passage at London at 22 June was at
4h 54m 30s, and uses in this case "the moones ordinary mean motion, which is
12 degrees, which is in tyme 48 minits ...". That, in itself, seems to be a
doubtful assumption. At least, in 1615 he got the direction of the motion
right that time, in saying- "if the moone be on the meridian at 12 a clock
this day, tomorrow it will be 48 minites past 12."

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

I now doubt if Baffin made ANY correct deductions from his ephemeris. There
may be more to say after another library visit.

Baffin has been highly regarded as being the first mariner to attempt real
lunar observations. Tony's study, however, indicates feet of clay.

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

   

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