Editors Bit

This is a Mike Frost issue, with 4 of his stories this time.  Thanks Mike for all your hard work in researching all these items.  The one I was most interested in is, “The Maunder Minimum” and its link to global warming.  Perhaps I should lay my cards on the table to start with and say I think most of what is said about global warming is just hot air and really bad science.  The Al Gore film “An Inconvenient Truth” has most climate scientists rolling their eyes sky-wards, the film’s purpose was to scare the living daylights out of people.  Even though he “isn’t technically lying” most of the scenarios he describes won’t happen or have “...any basis in physical reality in any reasonable time frame.  No climate model shows them happening” says Nathan Myhrvoid, a scientist who worked at Cambridge.
The problem is that all current climate models are crude both in time and space.  There are enormous amounts of natural phenomena they can’t handle, giant storms and hurricanes are examples.  One problem is that the way the software grids the planet it map the weather, the grids are at present too large to capture the start of storms, so they don’t register.  Only when computers get much more powerful and the mapping grids get much smaller will better weather prediction happen.  And if you can’t tell what will happen next week what chance have you for 20—30 years in the future?
There are other problems with the global warming debate.  One is the misplaced emphasis on carbon dioxide as the main greenhouse gas.  The major greenhouse gas is water vapour and current climate models can’t handle the complex mix of vapour and various types of clouds.  Hopefully this will be resolved in about 10 years as the software develops along with faster computers.
In the 1960’s it was excepted that the world was heading for a new ice age as overall temperatures fell.  Now 50 years later we are all going to roast!  It is now believed that the cooling in the 50’s and 60’s was caused by heavy practicalities in the air which caused a dimming of the sun.  Now that we have stared to clean up our act, the warming may be due to the cleaner air.
Carbon dioxide levels now are about 380 parts per million, up from 280 a century ago.  If the levels of carbon dioxide had fallen much more, plants would start to struggle to survive as they need carbon dioxide to make the sugars to grow.  20,000 years ago carbon dioxide levels were low and sea levels were low; trees were in a near state asphyxiation.  But 80 million years ago the levels of carbon dioxide were near 1,000 ppm with temperature levels only slightly higher than today.  The same level of concentration, in fact, as the new regulations for energy efficient office buildings!
The levels of carbon dioxide in the atmosphere don’t necessarily mirror human activity.  Ice cap evidence shows that over the past hundred thousand years, levels have risen after a rise in temperature, not the other way round.  2000 years ago the Romans invaded Britain, would the sun loving Italians have bothered to conquer a wet and cold country?  They were able to plant vineyards as far north as York.  Both York and Lincoln (both old Roman cities) have streets named Vine Street in them, where do you think they got that name from?
Also in the north the Vikings were sailing across the North Atlantic finding first Iceland and a little later, a bit further over, a green land covered in lush vegetation.  A little later still they sailed onto Newfoundland and Canada and the States.  This would have only been possible in warm conditions and settled weather of barmy summer days.  How much sea ice then covered the Arctic ocean?  Was the famed North West Passage wide open then?  We can measure the amount of ice on a permanent ice shelf like the Greenland ice cap, but we have no way of knowing how much ice covered the arctic ocean back then, as the Vikings had inconveniently not launched any mapping satellites!
The problem is the rate of change, there is nothing special about today’s levels of carbon dioxide, temperature, or sea level, only it’s increasing to fast for animals and plants, ie. the biosphere, to cope.  Since the last ice age the oceans have risen 425 feet and covered a huge amount of land, most of that rise was in the first thousand years and in the last century have only risen 8”.  We cannot be complacence where the lives of all our children are at risk.  We all must do our bit to help our planet.
Ivor Clarke Ed

Christopher Columbus’s Eclipses

By Mike Frost

I wanted to expand on some comments that I made when I gave the society “A Brief History of Astronomical Timekeeping” as a substitute speaker in May.  In that talk I tried to illustrate some of the ways in which astronomers hundreds of years ago were able to use events in the sky to tell the time absolutely, independent of the observer’s location on Earth.  This was not an academic exercise.  One of the driving forces behind the development of astronomy was navigation, and the timing of the same event for different locations allowed the calculation of longitude, the most difficult basic challenge of navigation, and one which occupied navigators up until the mid-eighteenth century.  As you’ll know if you have read Dava Sobel’s excellent book “Longitude”, the solution developed by John Harrison, the marine chronometer, was non-astronomical.  However you might be surprised to learn that sound astronomical solutions to the longitude problem had already been around for centuries; indeed, for millennia.
I gave two examples of astronomical timekeeping techniques which would have been achievable with the earliest telescopes.  First, eclipses and transits of the Moons of Jupiter.  Actually, as experienced Jupiter observers in the society pointed out, the best events of all to time are shadow transits, when Jupiter’s moons move into the planet’s shadow. A second possibility I suggested was the regular dips in the brightness of the star Algol, caused (we now know) by the transit of a companion star across the face of the main star in the Algol system.
Both these methods work in principle, but neither seems to have been used before the telescopic age.  The moons of Jupiter are just visible to the naked eye of an extremely acute observer, but they do not seem to have been noticed prior to Galileo’s telescopic observations.  The variability of Algol was probably known prior to the invention of the telescope, as the name Algol comes from “Al Ghoul”, the Arabic for “Demon Star”; but it is arguable whether the naked eye could discern the star’s variability in enough detail to be able to give accurate timings at different locations around the world.
However there is one technique which was available to, and used by, astronomers all the way back to the classical era.  This was the observation of eclipses of the Moon; that is to say, the passage of the Moon into the Earth’s shadow.  This is a dramatic and easily observable event which is visible from an entire hemisphere of the Earth, and the progression of the eclipse can be timed accurately with the use of cross-staffs and other pre-telescopic surveying equipment, and timers such as hour-glasses.  For example, Samuel Foster and his co-observers John Twysden and John Palmer made excellent, detailed, accurate observations of the lunar eclipse of November 30th 1638, from New House Coventry, without the use of telescopes.
But how can you use a lunar eclipse to calculate your longitude?  Let me give you an example from personal experience.  In 1989, I was working in Cleveland, Ohio, in the eastern United States.  On August 17th 1989, I attended an open-air concert in the Blossom music centre, a lovely open air venue in open country to the south of the city.  It’s the summer home of the Cleveland Orchestra, but also hosts a variety of other events throughout the summer.  I went to see a lot of concerts during 1989, both classical and popular.  On August 17th, the featured act were Anderson, Bruford, Wakeman, Howe – you may know them better as 80% of the 1970’s prog-rock group “Yes”, but for contractual reasons in 1989 they couldn’t call themselves that (Geoff Squire, the other 20% of Yes, objected, I think).  Lead singer Jon Anderson announced to the audience, in his broad Lancastrian accent, “We’ve got a great light show for you tonight – we’ve organised an eclipse of the Moon!”
Obviously, I was watching the eclipse as much as I was listening to the concert!  I estimated the mid-point of the eclipse to be 9:30 PM.  Here’s the interesting bit – my boss was watching the same event from his back garden in Bilton, Warwickshire, and he estimated the middle of the eclipse to be 2:30 AM. But we had both seen the same event at exactly the same time.  When we compared notes the next day, we realised we had proof that Ohio is five time zones to the west of Warwickshire.
We were by no means the first people to carry out this experiment!  For example, the eclipse of Nov 30th 1638 was also observed by Jeremiah Horrocks, from Much Hoole, Lancashire; and by his cousin, Thomas Horrocks, who had recently arrived at Quidnick, in the newly established colony of “Rhode Island and the Providence Plantations” in New England.  Thomas sent his timings back to Jeremiah in England, and Jeremiah used them to calculate the longitude of Quidnick – arguably the first determination of the longitude of any location in New England. 
The technique had even been known in classical times.  On September 20th 331 B.C., a lunar eclipse was observed by the army of Alexander the Great, encamped near Arbela in Mesopotamia (modern-day Iraq).  Alexander saw the eclipse begin two hours after sunset, but at Carthage, in modern-day Tunisia, the eclipse began as the Sun was setting.  Claudius Ptolemy and Pliny the Elder both reported the event, and inferred that the two hour difference indicated how far Carthage was west of Mesopotamia.  Each hour of time difference corresponded to 15 degrees of longitude.
So when Christopher Columbus made his voyages to discover the New World, he knew, having read Ptolemy, that if he was able to observe a lunar eclipse, he would have a technique for calculating his longitude, independent of the everyday dead reckoning which he recorded in his ship’s log (of course, lunar eclipses happen so infrequently that they cannot be used for everyday navigation).  Columbus took with him an almanac produced by the German astronomer and astrologer Regiomontanus (the nom-de-plume of Johannes Muller, from the Bavarian town of Konigsberg), which predicted lunar eclipses for the period 1475-1508.
Indeed, contemporary sources tell us that Columbus observed two lunar eclipses on his voyages to the New World.  The first lunar eclipse was on his maiden voyage to the West Indies, and took place on September 14th 1494.  Columbus observed it from near the Island of Hispaniola (Espanola) which is today shared between the Dominican Republic and Haiti.
The second eclipse is rather better known.  It occurred on Columbus’s fourth and final voyage, on February 29th 1504.  The fourth voyage was not Columbus’s most successful.  Columbus had a cool reception from the colony he had founded at Santo Domingo, Hispaniola.  His boats sailed into a fearsome storm in the western Caribbean, and the remains of the fleet suffered shipworm as he explored the West Indies.  On June 25th 1503, Columbus was forced to beach his last two vessels on Jamaica, and spent the winter there in St. Anne’s Bay.
Initially, the party was made welcome by the natives.  But as the weeks drew by they began to outstay their welcome.  Columbus’s sailors mutinied and began to steal provisions which the locals had previously traded for trinkets.  By the end of February the natives were beginning to be restless. 
Columbus had a trump card up his sleeve. Muller’s almanac predicted a lunar eclipse for February 29th.  Don’t forget though that this was before the laws of planetary and lunar motion were well-understood, and so the predictions were unreliable.  Nonetheless, Columbus was a desperate man prepared to take desperate actions.  Three days before February 29th, he told the local leaders that God, with whom he was in regular personal contact, had become displeased with their lack of co-operation, and would show his displeasure by eclipsing the Moon on the evening of the 29th
The almanac predictions were, fortunately, correct.  As the evening of February 29th progressed, the Earth’s shadow began to swallow the Moon.  The Jamaicans had probably seen lunar eclipses before, but were dumbstruck by Columbus’s ability to produce one on demand.  As the eclipse progressed, the moon became, in Columbus’s words “inflamed with wrath”, an apt description for the coppery hue associated with totality.  The locals were terrified. “With great howling and lamentation [they] came running from every direction to the ship, laden with provisions, praying to the Admiral to intercede with his God on their behalf”.  Columbus withdrew to his quarters, waiting until just before the end of totality before emerging to tell the native chiefs that God had decided to give them a second chance.  Columbus’s ploy was a success.  He and his crew encountered no further problems before the arrival of a relief vessel from Hispaniola on June 29th 1504.
The story has been re-told many times in fiction.  Among others, the heroes of Mark Twain’s A Connecticut Yankee in King Arthur’s Court and H. Rider Haggard’s King Solomon’s Mines use prior knowledge of eclipses to extract themselves from perilous situations, (as indeed did comic book hero Tintin in one of his adventures Ed.) although in both these cases the eclipses are total solar eclipses.  Indeed, the plot device of a convenient solar eclipse is pretty much a cliché these days.
However, as I prepared the talk in May, I began to think about the story a little more.  And the more I thought, the more I worried.  Here’s the problem – Columbus wasn’t supposed to be in the West Indies.  You may remember the purpose of the visit was to find a western route to the East Indies, present day Indonesia.  And the lunar eclipse wasn’t visible from Indonesia!  So why did he think he was going to see it? 
Well, there are a number of complications. Muller’s predictions were not accurate, for a start. More importantly, Columbus knew that he had not reached the East Indies, and never claimed to have done so.  What is a matter of great dispute, both at the time, and to historians ever since, was how far west Columbus believed he had sailed. 
Let me make this clear.  Columbus’s observations of lunar eclipses gave him two opportunities to establish his longitude absolutely at two separate occasions during his expeditions, completely independent of longitude estimates made by conventional means such as dead reckoning.  And this is also regardless of how accurate the predictions of Regiomontanus were; because once Columbus returned to Europe, he could compare his own eclipse timings with the timings made by astronomers in Europe, rendering Muller’s predictions irrelevant.
So it is of great interest to find out exactly how Columbus described his eclipse observations. Unfortunately, the sources are inconclusive.  During my research I found an online transcript of a talk given in 1997 by Keith. A. Pickering to the Society for the History of Discoveries (an American Society) and the Hakluyt Society (its British equivalent, named for Richard Hakluyt, a collector and editor of narratives of expeditions who lived from 1552-1616). Mr. Pickering, an American historian of science, has analysed the contemporary sources, and attempted to reconcile all the evidence from the navigational logs and the accounts of the eclipses.
Let us start with the first lunar eclipse, in 1494. There are a number of accounts:
Antonio Gallo of Genoa reported in a fragmentary biography in c.1497, “He declared also from the observation of his people that that when in the year of our Lord 1494 there appeared an eclipse in the month of September, it was seen in Espanola four hours before that it was visible in Spain”
Columbus’s son Fernando wrote a biography of his father, in which he said “On September 15th [sic] by the mercy of God they sighted an island which lies off the Eastern end of Espanola ... in the middle of a great storm he anchored behind this island ... That night he observed an eclipse of the moon and was able to determine a difference in time of about five hours and twenty three minutes between that place and Cadiz”
Columbus himself reported, in his Libro de Profecias (Book of Prophecies), “In the year 1494, when I was at the island of Saona, which is at the eastern end of the Island of Hispaniola, there was an eclipse of the moon on 14th September, and it was found that there was a difference from there to the Cape of St Vincent in Portugal of five hours and more than one half”
Columbus, again, writing to King Ferdinand and Queen Isabela on July 7th 1503, “In the year ninety-four, I navigated in twenty four degrees to the westward of nine hours, and I cannot be in error because there was an eclipse”
Bartolome Las Casas’s Historia de las Indias quotes Columbus, “From the end of Cuba (that is seen in Hispaniola), which was called the End of the East, and by another name Alpha and Omega, he sailed westward from the southern part, until he passed by the end of ten hours on the sphere, in such a way that when the sun set to him, it was two hours rising to those that lived in Cadiz, in Spain: and he says that there cannot be any error, because there was an eclipse of the moon in the 14th September, and he was well prepared with instruments and the sky was very clear that night.”
Las Casas reports the same story later in his history, except that this time he says Columbus was 5 hrs 23 minutes west of Cadiz.
I’m sure you’ll agree these are a frustrating and contradictory set of accounts!  There are no actual timings for the eclipse, and no indications whether the calculated time differences are using Muller’s predictions for Europe or actual observations there.  The calculated longititude for Saona varies wildly – from 60° degrees West of Cadiz (4 hrs) to a whopping 150° degrees West (10 hrs).  In reality Cadiz is 6° degrees West of Greenwich, the Cape of St Vincent 9° deg W, Saona 68° deg W and St Anne’s Bay 77° deg W, so that the longitude difference between Cadiz and Saona is 62° degrees – 4 hours and 10 minutes in time.
Additionally, the supplementary detail provided by those who were actually at Saona arouses suspicion.  Fernando Columbus reported that their ship arrived at Saona on the day of the eclipse during a storm; his father says that they observed a lunar eclipse from Saona in clear skies.  Could they both have been right?  Well yes, it’s possible – but is it likely?  (It doesn’t help that they also disagree by a day over the date of the eclipse). 
Mr. Pickering provides one account of the 1504 eclipse, by Columbus himself, which I quoted from earlier.  Columbus’s calculation of longitude for this eclipse was 7 hrs 15 minutes west of Cadiz.  The actual longitude difference is 71° degrees, or 4 hrs 44 minutes in time.
So what is going on?  Some authors have tried to explain the discrepancies as computational errors, but this seems a little far-fetched.  There is I think a more likely explanation – Columbus fudged his numbers.
There is a popular view of Christopher Columbus as a visionary who argued against those who thought the world was flat.  This is a long way from historical reality.  On the contrary, in the fifteenth century most educated people knew that the Earth was spherical, and indeed the Earth’s radius was known with reasonable accuracy.  The man in error was Columbus himself, who believed, incorrectly, that the planet’s radius was much smaller than conventional wisdom.  This was why he, against the common wisdom, thought it might be possible to sail west to the Indies – he was convinced they were much closer than everyone else believed, and within reach of the ill-equipped ships of the day: he was wrong.  When he finally found a royal house willing to fund his voyages, Ferdinand and Isabella of Spain, they granted him dominion over “the Ocean sea in the vicinity of the Indies”.  So it was very much in Columbus’s interests to convince everyone – and perhaps to convince himself – that he had sailed much further west than in reality.
Mr. Pickering and other authors have analysed Columbus’s (now incomplete) ship’s log, and found faults with his conventional navigational abilities. Perhaps his lunar eclipse observations were similarly flawed.  Maybe he never saw the eclipse of 1494, because of the storm that day, and simply made up timings to bolster his belief as to his true longitude. And given the huge amount by which the calculated longitude in 1504 differs from reality, can we trust his account of this eclipse in all its entertaining detail?
Many works of fiction have been inspired by the lunar eclipse of Feb 29th 1504.  And I wonder if Columbus’s own account is just as fictional as all the others.

Sources / Further Reading

“The Navigational Mysteries and Fraudulent Longitudes of Christopher Columbus”, Keith. A. Pickering, 1997

“NASA Five Millennium Canon of Lunar Eclipse: -1999 to +3000 (2000 BCE to 3000 CE)”, Fred Espenak and Jean Meeus (NASA/TP-20090214172, Jan 2009). Plates 422 and 423 give the circumstances for Columbus’s two lunar eclipses.


The Maunder Minimum

By Mike Frost

On July 2nd 1651, John Twysden, observing from the Northamptonshire village of Easton Maudit, saw something bizarre. “Upon Tuesday the second of July in the year 1651, about eight of the clock at night, at Easton in Northamptonshire, under the elevation of the North Pole 52d. 15 min., I saw in the body of the Sun (through an excellent Tellescope whose Glasses were very clean) a very dark round spot in diameter about 12 part of the Sun’s diameter diameter, which to my sight appeared still in the same place for a matter of 9 or 10 min through thin clouds often interposed, and hindered me from the sight of the Sun for a short time.  The left margine of the Sun was very uneven, and tooth’d in the manner of a Saw, as in the adjoining Scheme.”

Twysden was observing the setting sun (not something I would ever recommend to anyone, unless it was by projection).  Mark Edwards has entered the timings into his planetarium program and assures me that the Sun was virtually on the horizon.  Twysden drew the sketch below showing a solar image distorted in the sawtooth manner he describes.  We have no idea what it was that Twysden actually saw, but it is most unlikely that his spot really was on the solar surface; perhaps something terrestrial in the far distance got in the way.
What is of more interest to me today is Twysden’s thoughts on what he might have seen. “I conceive that it was one of those spots which Galileus, Scheinerus, Hevelius and others have observed. For I cannot suspect Mercury in that place.”  Twysden correctly ruled out a transit of Mercury (which in any case would be minuscule in apparent size); Venus would be a little larger, about a thirtieth of the diameter of the Sun, but definitely didn’t transit the Sun in 1651.
No, what fascinates me is that John Twysden considers the possibility he might have seen a sunspot.  But didn’t he know what sunspots looked like?  Sunspots are much, much smaller in size than the substantial object drawn by Twysden; yet he gives serious consideration to the possibility that a sunspot is what he saw.  He can’t have been much of a solar observer, can he, if he had never even seen a sunspot?
Well, interestingly, John Twysden probably did know the Sun quite well.  He had observed a deep partial solar eclipse, in July 1639, and he left behind estimates of the latitude of various places he had visited in France, which he calculated from observations of solar altitude. But he might never have seen a sunspot.  Why? Because he lived during the Maunder Minimum – a period of around sixty years during which there were almost no spots on the Sun.

* * * * * * * *

First things first.  Who was Maunder?
His full name was Edward Walter Maunder and he lived between 1851 and 1928.  He was employed at the Royal Greenwich Observatory, and was arguably the first astrophysicist to work there, using a spectroscope to analyse the light of stars.  However, at the beginning of Maunder’s career, spectroscopy was still in its infancy, and so his main object of study was the brightest star of them all, the Sun.  (Additionally, but not relevant to this article, Maunder was one of the co-founders of the British Astronomical Association).
Maunder was very interested in sunspots, and kept records of their appearance on the Sun, day-by-day, for several years.  At that time, it was known that the number of spots varied over a cycle of approximately eleven years; this had first been pointed out by Heinrich Schwabe in 1843. As a result of his investigations, Maunder also discovered that the location of sunspots varied, over the same eleven year period.
In 1904 Maunder announced the existence of a “butterfly diagram”.  This plotted, for the first time, the latitude of all observed sunspots, from the year 1874 onwards.  The graph is quite dramatic.  At the beginning of the solar cycle, sunspots appear at very high latitudes (northerly and southerly).  The latitude of spots gradually declines through the course of the solar cycle.
Maunder was naturally interested to know how long back the periodicity lasted.  Was the eleven-year cycle a permanent feature of the Sun, or could it display other periodicity?  He searched back through historical records, which extended back to the beginning of the seventeenth century, when people like Galileo and Scheiner first began to record them.  Obviously the earliest records were less complete, but there were enough records to be able to give him three centuries of data, to which we have now added another century.
Maunder found that the length of the solar cycle could vary, irregularly, between about ten and fourteen years.  But, to his surprise, he also found that the size of the solar cycle, the number of sunspots in a cycle, varied by a much larger factor.  Over a standard eleven year cycle in recent years, we have observed around 40,000 – 50,000.  But during the period 1645-1675, the total number of sunspots reported was just 50.  Fifty sunspots in thirty years!  The observing record probably isn’t absolutely complete so there may be a little under-reporting, but not by a factor of a thousand.

* * * * * * * *

The Maunder Minimum would be of great interest to solar physicists, even if there had been no noticeable effects on Earth.  But the sixty or so years of the Maunder Minimum were probably England’s coldest decades since reliable records began (again, let’s take this as about 1600).  During the winter the River Thames froze over at least eight times, and Frost Fairs were held on the river.  The harshest winter of all was 1683-4, when a severe frost from late December to early February led to the Thames freezing for two months.
There is some indication that the Maunder Minimum was the coldest portion of a much longer cold snap, dubbed the “little ice age” which lasted from the thirteenth to the seventeenth century, but meteorological records are not as complete before the seventeenth century; sunspot records, of course, are non-existent. The best way of judging the climate indirectly is to look at the width of tree rings, which tells us nothing about sunspot numbers.

The Maunder minimum is the most extreme example of sunspot depletion during the last 400 years, but there are other cycles where the sunspot numbers were smaller.  In particular, the cycles during the early decades of the nineteenth century (to be more precise, 1790-1830) were also deficient in sunspots.  This period is called the Dalton minimum, in honour of the chemist, John Dalton, who is primarily known for his atomic theory of matter, but was also a meteorologist.  Dalton lived from 1766-1844, so his academic career spanned the Dalton minimum.
The Dalton Minimum also coincided with bitterly cold winters in England.  This was the time when Charles Dickens (1812-1870) was a child, and his descriptions of the English winter have given us our notion of what an English winter should be like – blizzards, snowdrifts, ice skating – which bear little resemblance to the rather miserable, wet winters that we have enjoyed recently.  The Thames froze over in 1788, 1793 and 1814.  The Frost Fair of 1814, when an elephant crossed the frozen river at Blackfriars, was the last of the Dalton minimum, and perhaps the last ever, as the old London Bridge was demolished a few years later.  Even if the cold temperatures of the Dalton minimum return again in future, there is no longer a constriction on the river for ice to form around.
So, the Maunder Minimum was a period of sixty years or so with very few sunspots – and very cold climate.  The Dalton Minimum was a period of forty years or so with fewer sunspots than normal – and a cold climate.
But isn’t our climate supposed to have been getting hotter during recent history?

* * * * * * * *

Man-made climate change, as you well know, is considered one of the greatest threats to civilisation as we know it.  As far as I can see, there is incontrovertible evidence that the activities of mankind – in particular, the burning of fossil fuels - have been steadily increasing the proportion of carbon dioxide and other greenhouse gases in our atmosphere.  We can see it on historical timescales in ice-cores dug up in the Antarctic, we can see it on a year-by-year basis by direct measurement.  The rate has been increasing steadily as the world industrialises, but nonetheless increases in greenhouse gases can be seen through human history.
So why did the temperature dip during the Maunder Minimum?
Well, we have to be careful not to overstate the case.  The meteorological record is only conclusive in Europe, and possibly North America; elsewhere records are sketchier, but, arguably, do not indicate that temperature drops were quite as radical as in Europe.  Also, the Dalton minimum overlapped with the explosion of the volcano Tambora in 1815, releasing vast amounts of dust into the atmosphere.
Nonetheless, even given these caveats, it seems clear that temperatures were, on average, lower during the Maunder and Dalton minima. So it seems reasonable to ask if the lack of sunspots could in some way be responsible for the change in climate.
The connection, if there is one, isn’t easy to understand.  It’s tempting to say that the reduction in the number of sunspots during the Maunder Minimum was due to variability in the Sun’s energy output.  Many other stars show huge variabilities in wattage, on timescales of days, years and even decades.  So why shouldn’t the Sun?
Well, it has to be said there is good evidence that the Sun is NOT variable.  In recent decades the solar flux has been measured with great accuracy, across several solar cycles, and has been found to vary by no more than enough to cause a fraction of a degree (0.2°deg C at most) of temperature variation on Earth.  Constancy on a timescale of years doesn’t rule out variability on a timescale of decades, but does suggest that the numbers of sunspots don’t directly correlate with the temperature.  Ice ages, I should also mention, are now thought to correlate with changes in the eccentricity of Earth’s orbit, and do not show evidence for solar variability on scales of tens of thousands of years.
But let’s play Devil’s advocate.  Something had to cause the decades of cold weather during the Maunder Minimum.  Let’s assume that the climate and the lack of sunspots during the Maunder Minimum were due to a common cause – solar variability on a timescale of decades, perhaps.  Let’s also assume that this correlation extends in the opposite direction; the Earth gets hotter when the solar cycles are more active.
Well, this is where it gets interesting – because the last few solar cycles have been the most active ever observed.
Could it be that the major cause of global warming isn’t human intervention at all – but solar variability?!
It’s a contentious statement to make, isn’t it! Global warming has become such an emotive and vital issue that genuine, disinterested, debate is difficult.

So here’s my position: –
Does human activity produce greenhouse gases? Yes, incontrovertibly.
Has this production been rising during recent history? Again, yes. 
Do greenhouse gases cause global warming to some degree? Again, yes. 
Does the Sun exhibit variability on timescales of decades? On the evidence of the Maunder Minimum – quite possibly. 
Does this lead to variability in the Earth’s climate? Again, the Maunder Minimum suggests yes.

And now the sixty-four thousand dollar question: - Is the climate variation due to solar variability more important than the variability due to human activity?

Well, that’s an interesting question, isn’t it? Because if all recorded climate change has been caused primarily by variation in the solar flux, why are we spending all this money on reducing carbon emissions?
Some comments before I answer my question.  First – if the Sun’s flux really is varying, it could go up or down, whereas net human contributions so far have all been in the direction of global warming.  Second – can we afford to bet the future of civilisation on a theory without a sound physical basis?  Probably not.  Third – the best models of global climate suggest that solar effects are less than human effects.  Do those same models retrospectively predict the Maunder Minimum?  I don’t know.
So here’s my answer. Is the climate variation due to solar variability more important than the variability due to human activity?  Answer – I don’t know.  But we might know soon.  The latest solar cycle has been notable so far for its almost complete lack of sunspots.  It might just be that we are in for another set of solar cycles without spots.  In which case perhaps – just perhaps - we might be due for another Maunder Minimum.
Global Warming, anyone?  Or Frost Fairs on the Thames?  We might just be about to find out.  My gut feeling is that human-caused global warming is the more significant effect. But if we do have a solar cycle with few or no sunspots, then we’ll have a much clearer idea of the relative sizes of variation due to human and solar effects.  Either the human effects on global warming have been over-estimated.  Or even a new Maunder Minimum won’t save us. 

Place your bets . . . .

Sources / Further Reading

Solar Impact, Kristina Grifantini (Sky and Telescope, March 2009, p.30)
Edward Walter Maunder FRAS (1851-1928): his life and times, Anthony J. Kinder (J.Br.Astron.Assoc. 118, 1, 2008, p.21)
John Twysden’s account of a spot on the Sun is appended to Samuel Foster’s “Observationes Eclipsum” in “Miscellanies, or mathematical lucubrations” Samuel Foster, ed. John Twysden (London, 1659) – St John’s College library, by kind permission of the Master and Fellows of St John’s College, Cambridge. I am very grateful to Jonathan Harrison of St John’s for scanning in Twysden’s diagram, after I had realised its significance.

Gulliver and the Moons of Mars

By Mike Frost

Have you ever read Gulliver’s Travels, by Jonathan Swift?  It’s a well-known work, and if you haven’t read the book, you probably think you have a good idea of what happens in it.  It’s a children’s book, of course, in which the hero, Lemuel Gulliver, is ship-wrecked on an island of tiny people.   Right?
Well, up to a point, yes...  but that’s not a description that Swift himself would have agreed with.  First of all, Jonathan Swift did not write a novel for children.  On the contrary, he was a satirist, renowned for writing excoriating work which savaged the institutions of the time – government, church and social institutions.  In A Modest Proposal published 3 years after Gulliver’s Travels in 1729, the “modest proposal” is that the poor should sell their children for the rich to eat!
Moreover, Lilliput is only the first stop in Gulliver’s Travels.  Visitors to tourist attractions such as Gullivers World (which has, annoyingly, no apostrophe) might be surprised to learn that Lemuel Gulliver also visited a land of giants, Brobdingnag; and a land of talking horses, Houyhnhnms, and savages called Yahoos (and yes, that is where the web-site gets its name from).  Credit where credit is due - one recent re-telling of story does venture beyond Lilliput.  The 1996 version of Gulliver’s Travels, starring Ted Danson as Gulliver, stays creditably close to the original story, and also captures something of the essence of Swift’s original satire.
One episode in Gulliver’s Travels which the Danson movie brings to life is Gulliver’s visit to the flying island of Laputa.  In the novel, this is Gulliver’s third voyage (after Lilliput and Brobdingnag) to islands in the ocean to the east of Korea and Japan. Gulliver’s ship is raided by pirates, and Lemuel is cast adrift on the ocean on a small canoe.
He is making his way towards the island of Balnibarbi when, “...all of a Sudden [the Sun] became obscured, as I thought, in a Manner very different from what happens by the Interposition of a Cloud.  I turned back, and perceived a vast Opake Body between me and the Sun, moving forward towards the Island: It seemed to be about two Miles high, and hid the Sun six or seven Minutes ... I took out my Pocket-Perspective, and could plainly discover Numbers of People moving up and down the Sides of it.”
Gulliver hails the inhabitants of the flying island, and is winched aboard.  Laputa is a circular island four-and-a-half miles across, which is suspended above the ground because it contains a giant lodestone at its centre.  It serves as a roving capital for the island of Balnibarbi.  The male aristocrats of Laputa are intellectuals, who spend their time thinking to such an extent that they have to employ servants, flappers, to remind them when to listen and when to speak.  (The wives and daughters despair of their menfolk, and prefer if possible to spend their time landside.)  Among their many intellectual pursuits, the Laputans are astronomers:-
“They spend the greatest Part of their Lives in observing the celestial Bodies, which they do by the Assistance of Glasses, far excelling ours in Goodness. For, although their largest Telescopes do not exceed three Feet, they magnify much more than those of a Hundred with us, and shew the Stars with greater Clearness.  This Advantage hath enabled them to extend their Discoveries much farther than our Astronomers in Europe.  They have made a Catalogue of ten Thousand fixed stars, whereas the largest of ours do not contain above one third Part of that Number.  They have likewise discovered two lesser Stars, or Satellites, which revolve about Mars...”
Let’s leap forward one hundred and fifty years. In August 1877, the American astronomer Asaph Hall was observing with the world’s largest refracting telescope, the 66-cm telescope at the US Naval Observatory in Washington D.C..  Refractors are excellent for planetary observing, and so he turned the telescope to Mars, in an attempt to spot any satellites of the planet.  He caught a glimpse of two tiny moons, close to the planet.
Following a suggestion by a science master at Eton, the moons were named Phobos (fear) and Deimos (dread) after two spirits from the Iliad.  The moons’ origin is not well-understood; they may be captured asteroids, or they may have formed in orbit from the debris of previous larger satellites.  The orbit of Phobos is decaying, slowly spiralling inwards, and the gravity of Mars will tear the moon apart in a few tens of millions of years.
So, how did Jonathan Swift know about the Moons of Mars?  As you might expect, there have been some pretty crazy theories down the years, claiming that Swift was tapping into ancient knowledge, or extra-terrestrials - the usual suspects!  Well, if he was accessing knowledge not known to modern science, he wasn’t paying close attention.
Gulliver’s account continues “... the innermost is distant from the Centre of the primary Planet exactly three of his Diameters, and the outermost five; the former revolves in the Space of ten Hours, and the latter in Twenty-one and a Half; so that the Squares of their periodical Times, are very near in the same Proportion with the Cubes of their Distance from the Centre of Mars; which evidently shows them to be governed by the same Law of Gravitation, that influences the other heavenly Bodies”
Gulliver (and so Swift) is clearly familiar with Kepler’s third law of planetary motion, which, because of the sensational discoveries of Isaac Newton, was probably better known to the general populace in Swift’s day than it is now.  However, his “facts” about the Moons of Mars are completely wrong.  Phobos is 1.4 Martian diameters from the centre of the planet, Diemos 3.5 Martian diameters. The orbital period of Phobos is just short of 8 hours, that of Diemos 30 hours.
It’s most likely, of course, that Swift simply invented his Martian moons.  And there is a plausible aesthetic reason why he would choose two.  At the end of the seventeenth century, only three planets were known to have moons.  Earth had one, Jupiter four (all discovered by Galileo in 1610), and Saturn five (Titan, discovered by Huyghens in 1655 and Iapetus, Rhea, Dione and Tethys, discovered by Cassini between 1671 and 1684).
In Swift’s time, it seemed clear that satellites were scarce in the inner solar system, but common in the outer reaches.  So if Swift wanted to give some moons to a new planet, Mars, in between Earth and Jupiter, two was an obvious choice.  And by simple geometric progression, two moons go nicely between one (Earth) and four (Jupiter).
Jonathan Swift did eventually receive some recognition for his lucky guess, however.  Two features have been named on the surface of Deimos, both craters about 3km across.  Both are named for writers who speculated about moons of Mars prior to their discovery.  One is named after Voltaire – and the other is called Swift. Maybe one day Gulliver will visit!

The Pearson Papers

By Mike Frost
This is a real Boy’s Own story. Unfortunately it’s not one with a happy ending. Yet.

Many of you may have visited my website – for a long time there used to be a link from the Society’s home page.  I used it to advertise my astronomy talks so that people could check them out without me having to send details to them.
One of the side-effects, however, was that I would occasionally receive unsolicited email on subjects prompted by the website (in addition to the usual avalanche of spam).  Sometimes it would be an astronomy question from a student trying to answer homework questions (“Where is the Southern Cross?”).  I had an appreciative email from another Mike Frost, in Texas, and we had a short correspondence on the many achievements of our namesakes (world skydiving champion, Floridian stock-car racer, and best of all, executive producer of Neighbours).
Two emails stood out.  Justin O’Jack, a graduate student in Divinity from San Diego, wrote to ask me about the physics of the Glory, and to my astonishment provided documentary evidence that, confirming legend, Buddhists have indeed been known to jump off Himalayan mountains, “Into the Arms of Buddha” on encountering this extra-ordinary sky phenomenon.  And Karen Lockyer-Elmy, a young lady from America, wrote to tell me that she thought she was descended from Sir Norman Lockyer, Rugby’s greatest astronomer (so far).  I was able to tell her that Lockyer did indeed have a son who emigrated to America, and she should be very proud of her ancestor.
My website used to be located at members.aol.com/name. Unfortunately, in October last year AOL withdrew support for home pages.  I wasn’t sure what to do to replace it.  Bebo and Myspace weren’t really my scene; Facebook had a reputation for collecting too much information on its users.  I considered and rejected various home page sites.
Fortunately, friends helped me out.  Peta Jellis, originally of the Open University Astronomical Society, and now a member of Northamptonshire Astronomers, helped me to resurrect my home page at  www.mikefrost.info  Go on, take a look!  It looks a lot like my old website, only neater (this is due to Peta, who sets up websites as a hobby).
After several months floundering around, I finally had a website once more.  I was rather pleased.  Two weeks later, I received an email.  This is what it said:

“Dear Mr Frost,

I found your name from searching the internet and saw that you had given lectures on Rev Pearson of South Kilworth and his involvement with the [Royal] Astronomical Society.  My connection to him is that I grew up in his house, the Old Rectory at South Kilworth, living there from 1970 to 1974.
As a boy aged 11 in 1972, I found 18 old letters in a hidden room only accessible by a trap door in the ceiling of a passageway in the house.  The letters were hidden behind the trap door and it was only when I climbed up into the room and put the door down that these letters were revealed.
The letters date from August 1821 to April 1822 and are all from Rev Michael Ward to Rev Pearson and all associated with their work on Astronomy at the time.  They are all in great condition and legible, mainly addressed to South Kilworth but one addressed to East Sheen and a couple to Rev Pearson at the Astronomical Society in London.
Some of the letters include diagrams and tables and many refer to the challenges they were encountering in trying to calculate angles using logarithms.
My father kept the letters safely for the last 36 years and I have just re-discovered them.  I intend to make contact with the Royal Astronomical Society this coming Wednesday or Thursday and take them there for them to see as I live in USA and am only in the UK until next Friday.
If you can give me any advice or names of people I could contact who might be interested in these letters it would be very helpful.
You can contact me on this email or by mobile phone: [Numbers removed]

Oliver Johnson.”

How about that! 

Revd. William Pearson, The Rector of South Kilworth, was one of the co-founders of the Royal Astronomical Society – you might remember that I wrote about him in MIRA 71.  I have prepared a talk on Revd. Pearson, which I have promised to give to Leicester AS at some time in the future, but haven’t yet delivered to anyone.  And yet advertising the talk on my home page attracted this email, with its amazing story – just two weeks after I re-launched my website!
Of course, I replied to Oliver immediately. Sure I could give him a contact within the Royal Astronomical Society – Peter Hingley, the librarian of that organisation, who of course has spoken to our society on two occasions.

Part of the Old Rectory in South Kilworth

There was a problem, however. Peter was on holiday.  Oliver replied to me that he had contacted the RAS, quoting Peter’s name, and had been told that there was no-one available to meet him.  I emailed back to say that, if necessary, I was willing to travel down to London to view the letters and, if possible, photograph them.  This wasn’t at all convenient for me, as I was also planning to travel with work, but I felt that the opportunity had to be taken, if Peter Hingley wasn’t available.
In the end, we decided on a different course of action.  The RAS managed to contact Peter on his holidays, and Peter spoke to Oliver, who suggested leaving the manuscripts with relatives in England, who could bring them to the RAS at a later date.  I then called Oliver myself and spoke to him, thanking him for his efforts to bring the manuscripts to the people who would most appreciate them.
I was able to help Oliver in one other way. I passed on his email to Jacky Harrison, the current owner of the Old Rectory in South Kilworth. Jacky was as fascinated as I was by the story.  She remembered Oliver as a young boy from when she first visited the house, shortly after 1974.  She invited Oliver to come and visit South Kilworth, the next time he came to England.
I was of course very intrigued to know if Jacky was aware of the hidden room.  In my youth I was forever reading Famous Five and Secret Seven books in which the protagonists discovered hidden attics containing long lost treasure – but this was the first time I had come across a such an room in real life!  It would be great to report that Jacky had been unaware of the hidden attic in her house for 35 years – but, more prosaically, she did know of its existence.  Nonetheless, just to be certain, the next time Jacky’s son visited, she asked him to climb up and check it out, just in case there were any more letters that Oliver had failed to notice first time round.  Unfortunately, there was no more treasure to be discovered.
Jacky tells me that the hidden room is very small, more of a loft than an attic.  Only a small person could comfortably get inside and close the trap door behind them.  This was probably why the letters, hidden behind the trap door, were not discovered until the arrival of a daring and inquisitive small boy!

A satellitium, or clockwork model of the Galilean Moons of Jupiter

Of course, I was dying to read the letters.  From my telephone conversation with Oliver, I found out that the contents of the letters included references to a Mr. Fayrer.  This is probably the same Mr. Fayrer of Pentonville who built a satellitium, or clockwork model of the Galilean Moons of Jupiter, to Pearson’s design.  It was used to demonstrate the motion of the moons, their eclipses and transits, and may have featured in astronomical lectures by Pearson.  The satellitium still exists and is held by the Museum of Science at Oxford; Dr. Jim Bennett of that museum kindly demonstrated it to me (by appointment) when I visited the museum a few years ago, and we found to our delight that the satellitium was still in good working order.  There are unanswered questions as to just which Fayrer it was, as there were several instrument makers of that name in London, and I was hoping that Oliver’s treasure trove of letters would help me to answer the question.
Unfortunately, I have to report, the trail has unexpectedly run out.  Oliver has not responded to my recent emails, nor has he got back in touch with Peter Hingley.  We don’t know why.  We don’t know where the letters are now and we haven’t been able to see them.  It would be such a shame if these fascinating letters, which came to light in such an extraordinary way, did not find their way (perhaps as facsimiles or photographs) to the place where they belong – the library of the Royal Astronomical Society, Burlington House, Piccadilly.  I will keep you posted as to their whereabouts.
But I think I can draw a moral from this story. I had the chance to view these documents, in London, at just a few days notice, and passed that chance by for reasons of convenience and expedience.  Next time I get the chance to examine historically important letters found, by a small boy, hidden behind a trapdoor for a century and a half, I will say YES!!  And blow the inconvenience!