This is a sort of pendicle to my previous post about the partial solar eclipse during the Battle of Isandlwana in 1879. I wanted to give a better impression of how minimal that 56% eclipse actually was, when compared to the “darkness during daytime” of a total solar eclipse, so I decided I’d plot some comparative light curves.
This involved a couple of simplifying assumptions—I’ve made the moon and sun exactly the same size, and I haven’t simulated the effect of limb darkening. This latter effect is due to the fact that the rim of the solar disc is slightly dimmer than the central portion, but it’s really only relevant during an annular eclipse, or the final moments of a total eclipse or very extreme partial eclipse.
So it was just a matter of calculating the yellow area below, technically known as a lune, for any given degree of offset between the centres of the grey disc and the yellow disc it is partially obscuring.
This turns out to involve a bit of a bonkers formula, but it gets considerably simpler when the two discs are the same diameter.
Knowing that the illuminance from the overhead sun in a clear sky is normally about 100,000 lux, I could then compare the light from the partially obscured sun with a range of other outdoor illuminants.
So I’ve plotted illuminance on the left vertical axis of my diagram above, from 100,000 lux (unobscured direct sunlight) down to 0.1 lux, which is in the ballpark of full moonlight. The scale is logarithmic, because that’s how our eyes and brains interpret light. We perceive equal ratios of illuminance as equal increments—a shift from 1,000 lux to 10,000 lux feels about the same as a shift from 10,000 lux to 100,000 lux. The magnitude scale by which astronomers measure the brightness of stars is also logarithmic—a star of first magnitude is shedding about 2.512 times more light than one of second magnitude, which is putting out 2.512 times more than one of third magnitude, and so on.*
There’s no horizontal timescale, because that varies a bit from eclipse to eclipse. The full width should come in somewhere between two and two-and-a-half hours.
Drawn across my diagram are some approximate thresholds for various kinds of outdoor brightness. A light overcast has very little effect on the day’s illuminance, a dense overcast has a noticeable effect, and if you’re under a really thick cumulonimbus storm cloud you’ll be turning on your car headlights. At which point, the daylight is a thousand times dimmer than bright sunshine.
When the sun sets, we enter civil twilight, which continues until civil dusk, when the sun is six degrees below the horizon. It’s called civil because it has relevance to civil authorities, the organizations that supply services to citizens. During civil twilight, it’s possible to carry on outdoor activities without artificial lighting, so that’s something civil authorities like to know about. You can also still read outdoors, if the print isn’t too small.
But by the time you get down to the brightest full moonlight, at about 0.2 lux, most people will struggle to read anything but a newspaper headline, and will be well on the way to losing colour vision (though it’s not entirely gone).
So that seems like a useful range within which to discuss how dark it gets during an eclipse.
At right of my chart, I’ve marked up the area of the solar disc that’s equivalent to the various illuminants. But once we get down to 100 lux, which would equate to 0.1% of the solar disc, the rough edges of the lunar disc become evident—the remaining solar crescent breaks up into segments, shining between the lunar mountains. This appearance is called Baily’s Beads, in honour of the astronomer Francis Baily. Here’s what they look like:
During a total eclipse, this appearance lasts for just a few seconds before the sun is completely obscured. At which point, it doesn’t get completely dark. Not only do we receive light from the solar corona, but we also have light coming in from the sky beyond the edges of the eclipse shadow, producing a glow of dim daylight along the horizon. So totality bottoms out at around 5 lux, equivalent to the darkest stages of civil twilight, but more than ten times brighter than the full moon.
With that explanation out of the way, let me just repost my graph here, to save you a bit of scrolling:
Click to enlarge
Notice how rapidly the illuminance falls around the central phase of the total eclipse. It drops more than a hundredfold in the last minute before totality, and leaves us in incontrovertibly dark surroundings.
But look at the broad “wings” of the eclipse curves. For something approaching an hour at start and finish, the illuminance changes only slightly, and very slowly, as the moon creeps across the margins of the solar disc. For most of that period, our pupils can easily adjust so that the light reaching our retinas doesn’t change at all. Anyone with normal pupillary responses, starting from the constricted pupils of full daylight, can easily double their pupil diameter, and therefore compensate for at least a four-fold change in brightness.
The 95% eclipse light curve drops out of this range, but never comes close to matching the final plummet of a total eclipse. Our brains are still happy that the 5,000 lux at the maximum of a 95% eclipse is bright daylight—it certainly never gets to any point we’d remotely consider dark. But the final change is fairly rapid, and it perhaps represents a point at which a lot of people might notice a change in the brightness of the environment. (I looked for, but could not detect, such a change from the recent 90% eclipse in eastern Scotland.)
Now look at the curve corresponding to the 56% eclipse at Isandlwana. It never even dips into “light overcast” territory, and never leaves the “pupillary compensation” zone. Which is why I doubt if it was ever noticeable on the battlefield.
* Why is there such a weird ratio in the stellar magnitude scale? The number is called Pogson’s ratio, in honour of the nineteenth-century astronomer Norman Pogson, who first suggested it. Astronomers at that time were still using the stellar magnitude scale from Ptolemy’s second-century Almagest star catalogue. But they had discovered, by using filters to reduce the brightness of one star to match that of a dimmer one, that the magnitude scale was operating in a logarithmic way, as I’ve described above. Pogson pointed out that a first-magnitude star was putting out about a hundred times more light than a sixth-magnitude star, and proposed that the magnitude scale be defined according to that ratio. So the ratio of brightness corresponding to a one-magnitude difference is the fifth root of 100—an irrational number equal to 2.511886431…
Ninety-one, ninety-two percent it’s going to be at peak, so it’s pretty significant. There’s a debate on whether we’ll see any dimming of the daylight, but perhaps we will, perhaps we won’t.
As this post goes live, on 12 August 2026, here in Scotland we’re just a few hours away from the event depicted and described above—a fairly dramatic partial solar eclipse.
Across most of Europe, West Africa, Arctic Russia, Canada and New England the moon will fall into an imperfect alignment with the sun, partially obscuring its disc. In a narrow band at the core of that broad area, the lunar-solar alignment will be perfect, and a total solar eclipse will occur. That’ll be visible only in limited parts of Siberia, the Arctic Ocean, East Greenland, west Iceland, the North Atlantic and Spain. (For more on the geometry of solar eclipses, see my post about Annular Solar Eclipses.)
But I wanted to pick up on something you may have found quite striking in Eric Walker’s short interview above—despite more than 90% of the solar disc being obscured, he said it’s debatable whether we’ll notice any diminution of daylight. How can that be? Your solar panels will certainly notice a 90% fall in illumination.
But the human eye is extremely adaptable to varying lighting conditions—there’s about a hundred-fold difference between bright sunlight and good indoor illumination, for instance, but we only ever notice the difference when we make an abrupt transition from one to the other. And the change in illumination during a partial eclipse is usually anything but abrupt—it can take an hour or more for the moon to crawl in from the edge of the solar disc to a central position.
The illuminance we receive from direct sunlight is about 100,000 lux. The illuminance under an overcast sky can be anything from 30,000 lux (a light cloud layer) down to 1,000 lux (a heavy overcast). A 90% partial eclipse will reduce the illuminance until it bottoms out at a pretty bright 10,000 lux, well within the range our eyes and brains have evolved to compensate for. But for such extreme partial eclipses, there is also an issue of rate of change. While the moon must move a long way across the solar disc to reduce its visible area by half, it doesn’t need to move so far to reduce that visible area by half again, and even less far to halve the area of the now quite slim visible crescent. And so on. So when a partial eclipse gets close to being total, there’s a period of relatively rapid dimming (and then brightening) around the time of maximum eclipse. And that might be noticeable to observers who are looking out for it, when an eclipse covers more than 90% of the sun’s disc. So, yes, there’s room for debate about what we’ll actually be able to see.
Which brings me to the Battle of Isandlwana*, which took place during the Anglo-Zulu War, on 22 January 1879. It was a massive defeat and humiliation for the British, during which 20,000 Zulu warriors surprised, overwhelmed, and almost entirely wiped out 1,800 British soldiers.
A partial solar eclipse occurred during the battle and, even by the standards of internet discussion, a truly colossal amount of garbage has been written about the eclipse’s supposed effect on the battlefield. A brief search of the internet will turn up stories of the battle being fought under “surreal light” or “apocalyptic gloom”, or even in “eerie darkness”. The onset of this darkness is often portrayed as being sudden. And I’ve seen it suggested that this “gloom” made it difficult for the British to select targets for their Martini-Henry rifles as the Zulus rushed towards them.
The main problem here is that many people, including Anglo-Zulu War historians, don’t appreciate the very dramatic difference between a total solar eclipse and a partial solar eclipse. They transfer the obvious and rapid darkening that everyone knows happens during a total eclipse (which lasts a few minutes at most) to the generally almost imperceptible change in illumination caused by a partial eclipse. And they also imagine that this darkness falls abruptly, and prevails during the entire duration of any solar eclipse. But the very striking fact is that every adult, everywhere, has lived through multiple partial solar eclipses, generally without noticing. At any given spot on the Earth’s surface, a partial solar eclipse occurs on an average of once every 2.6 years, and about a third of those eclipses will obscure more than half the solar disc.† How many of those do you remember? How often did you stumble to a halt in the street as the sky grew suddenly and unexpectedly dark? Yes, exactly.
NASA’s eclipse data for the Isandlwana date show that this was an annular solar eclipse with a track much farther north than Isandlwana—so only a moderate partial eclipse occurred over the battlefield. For more information, I zoomed in on their map until I could identify the car park at the Isandlwana battlefield site, and requested data for that location. Here’s what I got:
In the details above, eclipse magnitude is the proportion of the sun’s diameter covered by the moon. Eclipse obscuration is the fractional area covered by the moon, and it’s the number relevant to how much light we receive—only a little over half the sun was obscured. (This geometrical difference between magnitude and obscuration is another fine source of confusion for those writing about this eclipse.) Here’s a simulation of what it looked like on the day:
With such a fat crescent, there’s no issue here of an episode of rapid dimming and brightening around the time of maximum eclipse. Given that the change in lighting happened slowly over a period of more than an hour, and that the fall in illumination could be completely compensated for by a millimetric dilation of everyone’s pupils, it’s difficult to see how it would even have been noticeable, let alone “surreal”, “apocalyptic” or “eerie”. And, indeed, the eclipse seems to have gone essentially unremarked in the region at the time. At nearby Rorke’s Drift, for instance, where British and colonial troops were busily setting up defences and assessing sightlines during the entire duration of the eclipse, no-one seems to have registered any change in illumination.
NASA gives its precise eclipse timings in Universal Time, which corresponds to Greenwich Mean Time. In 1879 there was no standard time zone operating in South Africa, so Local Mean Time (based on the position of the sun) was in use. Isandlwana’s longitude of 30.652°E gives us a Local Mean Time two hours and a couple of minutes ahead of Greenwich, so it’s easy enough to convert NASA’s timings. Here’s the progress of the eclipse according to Isandlwana LMT:
But no-one’s watches seem to have been synchronized on the day, and there are some fairly gross disagreements about the timing of some events during and after the battle. And the British forces might well have carried the local time with them from Natal when they moved eastwards to invade Zululand. So if we’re trying to compare eclipse events to the imprecise local timings we have from the battlefield, the best we can say is that the eclipse started around 13:00 hours, reached its modest maximum at about 14:30, and ended around 16:00.
If you care to look at Smith’s essay, you’ll see that a lot of madly complicated things were going on as the Zulus moved towards the British encampment. But at about 13:00 the Zulus of the central group became pinned down by “withering fire” from an infantry line deployed to protect the camp. This lasted about half an hour, while two Zulu “horns” swept around the infantry line and invaded the camp at 13:30, by which time the infantry had begun retiring towards the camp. There was then chaotic fighting among the tents, and by 14:00 British survivors were fleeing towards the Buffalo River.
So the volley fire directed from the infantry line towards the approaching Zulus happened just as the first tiny rim of the sun was disappearing, and the chaotic fighting in the camp ensued when the eclipse was not much more advanced. The maximum eclipse was only reached during various last-stand actions among the British survivors.
No-one on the Isandlwana battlefield made any observation consistent with this partial eclipse—understandably so, since they were all a bit busy.
According to P.S. Thompson, writing in Historia (2007) 52: 172-217, the solar eclipse on the battlefield wasn’t even mentioned in military histories until 1963, in Rupert Furneaux’s The Zulu War: Isandhlwana and Rorke’s Drift. Thompson, though, seems to impose his own understanding of how eclipses work, claiming that Furneaux “say[s] that it plunged the battlefield into darkness for three hours (p 79)”. Furneaux said no such thing. On page 79 he writes only that:
… at 1:02 P.M. the sunlight began to fade. During the next three hours, while the battle of Isandhlwana was being fought, the moon passed between the earth and the sun, causing a partial eclipse.
Later (page 96) he writes:
The sound of firing died away, the cloud of white smoke that, together with the eclipse, had drawn a dark pall over the scene of death, drifted slowly away.
This mention of smoke is really important. The Martini-Henry rifle used black powder and produced a lot of smoke, particularly during volley firing. There are reported occasions during the Zulu War when British rifle smoke grew so thick that firing needed to be halted to allow visibility to improve. And the camp itself is another potential source of smoke—when a relief force arrived (too late) they found many of the tents burned.
But a number of reports from the battlefield, mentioning transient darkness, have been shoehorned into the “eclipse darkening” narrative.
The sun turned black in the middle of the battle; we could still see it over us, or we should have thought we had been fighting till evening. Then we got into the camp and there was a great deal of smoke and firing. Afterwards the sun came out bright again.
But this occurred before the warrior had even reached the camp, so very early in the eclipse. The sun would in any case never “turn black” during this eclipse, but the quotation has been constantly misunderstood. It sounds, instead, like a description of a frighteningly dim solar disc seen through clouds of dense smoke—a sight that has become unfortunately familiar during the wildfire season of 2026.
Another Zulu warrior makes this clear:
The tumult and the firing was wonderful, every warrior shouted “Usutu!” as he killed anyone, and the sun got very dark like night with the smoke.
In her History of the Zulu War and its Origin (1880) Frances Colenso provided another witness statement that’s sometimes invoked as evidence of “eclipse darkening”. An officer in the relief force, still some distance from the camp, is quoted as saying:
There certainly were some tents standing then, but seemed very few, and away to the left front of the camp there was some smoke, though not much, and it was high up, just as if there had been musketry fire and the smoke had floated away; but there was certainly no musketry fire going on then. A few seconds afterwards a sergeant . . . . said: ‘There go the guns, sir.’ I could see the smoke, but we could hear nothing. In a few seconds we distinctly saw the guns fired again, one after the other, sharp. This was done several times—a pause, and then a flash—flash! The sun was shining on the camp at the time, and then the camp looked dark, just as if a shadow was passing over it. The guns did not fire after that, and in a few minutes all the tents had disappeared.
But eclipses don’t produce localized, transient areas of darkness the size of a military camp. Smoke from gunfire and burning tents might.
In an article entitled “The Sun Turned Black”, for the Journal of the Anglo Zulu War Historical Society, Ian Knight cites the recollection of a trooper some distance from Isandlwana as supporting evidence for a noticeable eclipse darkening:
Trooper Fred Symons of the Natal Carbineers, out at Mangeni [Falls] with Lord Chelmsford, was almost alone in recalling a strange, still, oppressive gloom—all characteristics of a partial degree of black-out—and felt a ‘presentiment that something was going to happen either to us or those at the tents.’
One can’t help but feel that this speaks more of Symons’s state of mind than anything to do with an actual eclipse.
A strange thing happened at this time. I was walking with Sir Theophilus Shepstone outside Utrecht‡, discussing the situation, when suddenly it became dark, and for a moment neither of us realised that it was a total eclipse of the sun. When we did he said “Struben this may have a strange effect on the Zulus, who are superstitious”. Next day we heard of the disaster at Isandhlwana and he said to some old Kaffirs who came to hear news “Umtwan ami u fele, George ugwazile.” “My child is dead, George is stabbed,” and he was quite overcome.
There was, of course, no total eclipse of the sun anywhere in the world that day; nor, as I’ve described, is “sudden darkness” a feature of partial eclipses. (The eclipse took an hour and twenty-five minutes to reach a maximum of 58% in Utrecht.) Struben was writing thirty years after the event, and long after Shepstone’s death, and it has the feel of a tale that grew in the telling.
Do you need more reassurance that the eclipse had no effect on visibility during the battle? Here’s Pat Rundgren’s personal report, from the battlefield itself:
Much has been made of the eclipse of the sun that took place on the day of the battle, and the “surreal light” that it allegedly cast on the proceedings. It has become part of the superstitious folk-lore associated with this most inauspicious day for the British. Yet I personally have witnessed three x 60% eclipses at Isandlwana in my 20 years on the battlefields,§ and I have to say that I wouldn’t have known that one was taking place without (a) being told so and (b) without dark glasses. On those three occasions it made no noticeable difference to the light.
The battlefield is now a poignant place, dotted with white cairns marking the places where British soldiers fell.
It wasn’t until 1999 that a memorial was built to honour the Zulus who died opposing the British invaders of their territory.
* In older texts, the name is given as Isandhlwana, but that central “h” is now deprecated. In Zulu, it’s properly spelled iSandlwana, “i” being a locative prefix, indicating “place of”. Sandlwana is the Zulu name for the reticulum, the second stomach of a cow. The reticulum has a complex honeycomb pattern to its interior, reminiscent of the eroded surface of the rocky outcrop that towers over the battlefield in the picture above. (For much more on all that, see another of Ian Knight’s articles for the Journal of the Anglo Zulu War Historical Society.) † Why don’t half of partial eclipses obscure 50% or more of the sun? Because the curved rim of the lunar disc has to intrude more than halfway across the solar disc in order to block off half its light. ‡ Shepstone had been responsible for the British annexation of the Transvaal in 1877. His son, George, died at Isandlwana. Utrecht (the one in South Africa!) was at that time the seat of the British adminstration of the Transvaal. § Rundgren was writing in 2020, so I believe these would be the eclipses of 21 June 2001, 4 December 2002, and 26 February 2017. Though this last one fell somewhat short of 60% magnitude, the other two were significantly greater than 60%.
In Part One of this series of posts, I left you with the animation above, showing how our view of the Moon shifts subtly during the course of a month. Part One explained why this happens, so you might want to look at that before you continue here.
As I described last time, what’s going on in the animation (prepared, as ever, using Celestia) is that the Moon is librating in longitude (that is, east-west) by up to eight degrees, while librating in latitude (north-south) by close to seven degrees. The two periods of oscillation are not identical, so the wobble during the course of a month is not quite repeated in the following month—it takes six years to return to (approximately) the same pattern of oscillation.
And this shimmying around has implications for what the Earth looks like in the Moon’s sky. It doesn’t hang immobile over the lunar surface, as is often suggested in popular science and science fiction writing, but oscillates slowly around a mean position, moving up to eight degrees either side of that central point on an east-west axis, and almost seven degrees either side of it on a north-south axis.
I’ve used Celestia to assemble an animation of all this, adding some captions to explain what’s going on:
And all that movement means that there’s a fairly wide area of the Moon’s surface on which the Earth can be seen to rise and set, once a month. Here’s a view from the Moon’s south pole, speeded up a million times to fit a year into thirty seconds:
This also means that the point on the Moon’s surface at which the Earth is directly overhead (the sub-Earth point) roams quite widely, making a tour of several hundred kilometres every month, at a slow walking pace. Here’s six years’ worth of its travels across the centre of the Moon’s Earth-facing hemisphere, around a region appropriate called the Sinus Medii (“Central Bay”):
The centre of this pattern defines the zero points of lunar latitude and longitude—it’s the average sub-Earth point, even though the Earth is almost never directly overhead there.
For scale and context, here’s the same track superimposed on the disc of the full Moon at mean libration—that is, centred at zero latitude and longitude:
Any location within that red rectangle of sub-Earth points will, at some time, have the Earth directly overhead; and will, therefore, be momentarily at the centre of the Moon’s disc as seen from Earth. Around the rim of the Moon, I’ve shaded what I’ll call the libration zone in pale orange. This is the part of the Moon’s surface that will tilt in and out of view as the Moon librates (and where the Earth will be seen to rise and set each month). It looks tiny, doesn’t it? But that’s because we always see it at a very oblique angle. We can get a truer impression of its extent by using a different map projection, which preserves areas at the expense of distorting shapes. Here’s the Moon flattened out in a Lambert equal area projection:
The entire near side is contained within the red circle, which marks the 90° east and west meridians. Now you can also see the parts of the far side which tilt into view as the Moon librates, and from which some future astronaut might therefore be able to catch a monthly glimpse of the Earth. (I’ve trimmed off most of the far side beyond the libration zone—it would be grossly distorted in this projection.)
Overall, the libration zone covers about 18% of the Moon’s surface, or just under seven million square kilometres.
The detail at the north and south poles is difficult to make out in this sort of global photomosaic, because the shadows are always long at the lunar poles. So I had a bit of fun preparing polar shaded relief maps from elevation data—the apparent illumination shown below is impossible on the real Moon. Here’s the north pole:
Let’s go back to a more conventional view of the Moon, now. Here’s the lunar disc as we’d see it when the sub-Earth point is at its farthest excursion to the southwest:
The libration zone has disappeared in the northeast, but we now have a better view of the near side libration zone in the southwest, as well as a glimpse into the far side libration zone.
Let’s zoom in. Here’s the view of the southwest lunar disc at mean libration:
A couple of mountain ranges are just visible at the edge of the disc—the Montes Rook and Montes Cordillera. Now here’s the view of the same area under the most favourable libration conditions:
A grey lava plain on the lunar far side is just peeping into view! Despite its location beyond 90° west lunar longitude, it’s called Mare Orientale, the Eastern Sea, because it’s on the eastern side of the lunar disc as viewed from Earth. It was named in 1906 by Julius Franz, using photographs taken by Edward Holden at the Lick Observatory during the 1890s.
Until the second half of the twentieth century, our only glimpse of the lunar far side was courtesy of these lunar librations; which also, as you can see, improved our view of the extreme margins of the near side. But not only did we need to wait for a favourable libration (which might take six years to recur), we also needed to wait for favourable lighting conditions during the libration—preferably low sunlight to emphasize topography.
I’ve already mentioned that libration in latitude and longitude have different periods of oscillation, and now we need to introduce a third out-of-synch oscillation—the illumination cycle, corresponding to the phases of the Moon. Below, I’ve plotted some sine waves, reflecting these three cycles during the course of a year:
Click to enlarge
All the cycles are synchronized at the start of the year. In blue is the draconic month, of 27.2122 days, reflecting the length of a cycle of latitude libration. In red is the anomalistic month (27.5545 days) of longitude libration. As previously described, these are slowly diverging and won’t align again for six years. But in green is the synodic* month, the lunar illumination cycle (29.5305 days), which very quickly gets out of phase with the other cycles, but then comes back towards alignment in the course of a year.
All this means that there is at best just one night a year during which a favourable libration is combined with favourable illumination. During the first half of the twentieth century, astronomers (many of them amateurs) would wait with fingers crossed for a clear night on one of these rare occasions, during which they might glimpse and map some new feature of the lunar far side.
On 8 November 1965, for instance, a group of British amateurs took advantage of a favourable libration to observe the crater Caramuel† (now officially known as Einstein). Photographs were taken, but sketches made by skilled observers could often capture more detail, taking advantage of moments of excellent seeing. Below are a photograph, a sketch, and a rectified sketch by David A. Allen—the latter being a revision of the original sketch to simulate a view from directly overhead.
Professional astronomers, meanwhile, had come up with a neat trick to produce photographs of libration zone features as if viewed from overhead. They projected photographs of the Moon on to a white sphere, which they then photographed from the side. A compilation of these images was used in the creation of the Rectified Lunar Atlas (1963).
William Hartmann prepares to photograph a side view of a lunar image projected on to a white sphere
But this was the last gasp of Earth-based Moon mapping. The Lunar Orbiter missions commenced in 1963, with the aim of mapping the Moon photographically in preparation for a manned landing. The first three missions concentrated on potential landing sites, but Lunar Orbiter 4 had a more general mapping remit. And here’s its view of Caramuel / Einstein, obtained in 1967:‡
I’m going to visit this topic one more time, when I’ll write about the photographs of the Earth that the Apollo astronauts took from the surface of the Moon.
* Some day I’ll write a post explaining the strange names of the various kinds of month. † This name was bestowed by amateur observer H. Percy Wilkins, who had mapped the crater during the 1950s. The name honoured the philosopher and mathematician Juan Caramuel y Lobkowitz, Bishop of Vigevano. ‡ The sketches and photographs all have north at the bottom, as was customary at the time, because observers were using astronomical telescopes with inverting lens systems.
That the world ocean is a continuous body of water with relatively free interchange between its parts is of fundamental importance to oceanography. Because it covers more than two-thirds of the earth’s surface, a map of the world ocean is essentially a world map. On ordinary world maps the interruptions forming the edges of the map are often placed in the oceans to show the continents to best advantage. If, on the other hand, oceanographic conditions as a whole are to be shown, it is desirable to have the map interrupted within the land masses and the world ocean shown as a unit.
A while ago, I posted an appreciative review of Helen Czerski’s Blue Machine—but I didn’t mention its (UK) cover image. So here, belatedly, is my dissertation on what’s going on with that cover, which features one of my favourite map projections.
The layout of the map is so unfamiliar, and the contrast of the cover image so low, that at first it’s possible to mistake it for something quite abstract—some swirling gold lines against a meaningless blotch of blue. But there are labels, and with their aid you can pick out Antarctica, Africa, Europe, Greenland, Australia … and the hideously contorted coastlines of the Americas and Asia.
This is a map designed to show the world ocean as single continuous entity, created by the geophysicist/oceanographer Athelstan Spilhaus. Spilhaus had been creating map projections of this sort since 1942, but this one comes from his Atlas of the World with Geophysical Boundaries (1991), and is probably the most well-known.
Of all the world maps you’ve seen, probably most follow the plan that Spilhaus calls two singular point interruption, using the north and south poles as the singular points. The spherical surface of the Earth is, figuratively, slit open along a meridian of longitude from one pole to the other, and then flattened according to some carefully worked-out mathematical transformation.
Often, the meridian of interruption is at 180°, so that the Greenwich meridian lies in the centre of the map, like this:
Click to enlarge
If you’re interested in displaying the Earth’s landmasses, then it’s pleasant happenstance that the 180° meridian passes through very little land, but it does slice right through the middle of one of my favourite islands, Wrangel, in the Russian Arctic:
From there, it crosses the Chukchi Peninsula in the Russian Far East and passes through three Fijian islands before arriving in Antarctica.
It’s impossible to find a meridian that completely avoids land north of Antarctica, but 168°45′W does a pretty good job. It passes through the Bering Strait just east of the Diomede Islands, shaves past just a couple of hundred metres west of Fairway Rock, then crosses the eastern end of St Lawrence Island in the Bering Sea, and the western end of Umnak Island in the Aleutians. Beyond that, it manages to cross the entire Pacific without touching land before arriving in the deep embayment of the Ross Sea in Antarctica. The resulting world map is centred on 11°15′E, the so-called “Florence meridian” (which passes through the Italian city of Florence), proposed by the German historian Arno Peters.
Click to enlarge
But if you’re interested in the nations of the Pacific, world maps based on the Florence meridian have the same problem as the Greenwich meridian—chopping that ocean in half and consigning it to the peripheries. Splitting the world along the 30°W meridian provides a reasonable solution, without dividing too much land:
Click to enlarge
and if you’re interested in the geographical relationships of the Americas, you can place them centre-frame by cutting along the 90°E meridian, albeit at the expense of splitting Asia in half:
Click to enlarge
Once the Earth’s surface has been sliced open in this way, there are many ways of “flattening” it into a global map. The projection I’ve used above was created in the 1970s, by Arthur H. Robinson for Rand McNally. It’s not very fashionable these days, but I like it.
Here’s another thing you can do once you’ve split the Earth’s surface along the 180° meridian. This one was developed in 1929 by Oscar S. Adams, in a mathematical paper for the U.S. Coast and Geodetic Survey. It can take various forms, but what’s shown below is usually called “Adams World in a Square II”:
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At left, I’ve shown the line of the split along the 180° meridian; at right is what Adams did with it, opening out the point where the equator crosses the meridian (marked with a red dot) to form two corners of a square, with the poles at the other two corners. He had designed his map to be conformal, like the more familiar Mercator projection—that is, it preserves angles and shapes locally, at the expense of gross changes in scale as one approaches the edges of the map. The scale tends towards infinity at the corners of the Adams map, just as it does at the top and bottom of Mercator’s. It was primarily a neat mathematical exercise, and the Adams projection is not much seen in the wild.
Spilhaus adopted* the Adams II projection for his project of showing the world’s oceans as a single, continuous body of water. He did this by finding a 180° great-circle arc (analogous to a meridian of longitude, but not connecting the poles) that is confined almost entirely to land. It starts in China, at 30°N 115°E, and ends in Argentina, at 30°S 65°W. It crosses the “world ocean” at its narrowest point, the 85-kilometre-wide Bering Strait, which links the Pacific and Arctic Oceans. The line’s centre point is in Canada, just north of the border with the USA, at 49°34′N, 113°03′W.
Here’s how that works out:
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But Spilhaus orientated his map like this:
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The map edges are almost entirely land, becoming grossly distorted at the corners. But there are little isolated corners of ocean that have been chopped off, which I’ve marked in pale blue—the Sea of Okhotsk and the Yellow Sea along the top edge; the Gulf of Panama and a little rim of Pacific Ocean at left; the western Caribbean at the bottom.
But this is where things get clever, because Spilhaus’s map is tileable. After a 90° rotation, we can fit the bottom of the map to its left edge, and the top of the map to its right edge. Like this:
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I’ve now shown how the cut-off bodies of water, in pale blue, have been reunited with their parent oceans. By slightly extending Spilhaus’s square map to include these areas, we can produce a map of the whole ocean as a single entity.
Given that our interest is in the ocean, we can trim off the hugely distorted continental corners of the map. At which point it makes sense to rotate things back to the orientation of the parent Adams projection, like this:
If you scroll up to the top of this post, you’ll see that the map used by Czerski’s UK publishers, Transworld, corresponds to the left side of the projection I’ve laid out above. The cover image is, in fact, credited to John Nelson of Esri. It’s a slight adaptation of his “Cool and Warm Currents” map (it superimposes gold on both his cool and warm currents). You can find the original on his “Spilhaus? More Like Thrillhaus” blog post here.
Addendum: Since I mentioned that this map projection conserves shape locally, while distorting scale globally, I thought I’d show you an illustration of how that works:
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Every green circle above is 200 kilometres in diameter. You can see how the eastern and western sides of the Pacific, and the western side of the South Atlantic, are magnified when compared to the more centrally placed Indian Ocean, and the Southern Ocean around Antarctica.
Falling to with our hoes again, we worked singly, or together, as occasion required, until “Nooning Time” came. The period, so called by the planters, embraced about three hours in the middle of the day; during which it was so excessively hot, in this still, brooding valley, shut out from the Trades, and only open toward the leeward side of the island, that labour in the sun was out of the question. To use a hyperbolical phrase of Shorty’s, “It was ’ot enough to melt the nose h’off a brass monkey.”
Herman Melville: Omoo
When the Boon Companion and I travelled to the Marquesas and the Society Islands, back in 2017, I carried along Herman Melville’s semi-autobiographical narratives,Typee (1846) and Omoo (1847). The quotation above is Melville’s description of farming on an island he calls Imeeo—presumably a reference to Eimeo, another name for Mo’orea in the Society Islands. You can see its characteristic skyline, silhouetted against the tropical sunset clouds, in this view from Tahiti:
As the humid noonday heat in Tahiti nudged over 30°C, we could sympathize with Melville’s Nooning Time rest period, but were amused by how very different his brass monkey weather was from the modern interpretation of the phrase.
A decade later, a reference to brass monkeys and cold weather turns up in the diary of Charles A. Abbey, a teenage seaman crossing the Atlantic in the clipper Charmer (“a very fine crew & no Chinamen”). Abbey’s diaries, written between 1856 and 1860, were annotated and published in 1937, and deserve an extensive footnote*, if not an entire other post. He is often misquoted, or at least paraphrased, even by the Oxford English Dictionary, so here’s what he actually wrote on 16 January 1857, in all its erratic and near-incomprehensible glory:
Boo! Boo! Boo! Whew aint it a blowing “Jehosaphat Bumstead” & cold,” it would freeze the tail off from a braſs monkey.
(See my footnote for a partial explanation.)
Wikipedia has a whole list of nineteenth-century references to brass monkeys suffering under various extreme conditions, gleaned from the Australian government’s excellent newspaper archive at Trove. There are winds that would blow the nose off, or shave the whiskers off, a brass monkey; and people who could talk the tail off a brass monkey.
So the nineteenth-century brass monkey seems to have been an epitome of robustness under the onslaught of heat, cold, winds, and even loquacity. And as late as 1947 W.E. Johns, in his short story “An Oriental Assignment”, had a character remark that a situation was distressing enough to break the heart of a brass monkey. It evidently took a while for common usage to settle on cold as the standard simian stressor, and even longer to decide on which peripheral appendage was at risk. Here’s a screenshot of the Google Ngram for a selection of cold-related phrases (click on the graph to see the original Ngram):
The monkey’s ears and tail were deemed most imperilled, at least in published English, until about 1960, when the now-familiar “balls” usage became the dominant form. And the OED’s first citation for the coy expression brass monkey weather, meaning “very cold”, dates from 1981.
Which brings us, with weary inevitability, to this piece of nonsense, which was doing the rounds long before social media was invented, but has been popularized by it:
(origin unknown)
(If anyone can tell me where the photograph was taken, I’ll gladly acknowledge the source. And perhaps phone up the people responsible for the sign.)
I remember how I first encountered this bit of folk etymology back in the late 1970s, and how thrilled I was for all of five seconds before thinking Hang on a minute, though… The story is, alas, a product of the CANOE, the mythical Committee to Ascribe a Nautical Origin to Everything. While English is replete with phrases that do originate from the long maritime traditions of the UK and USA, this just isn’t one of them. Here’s why:
Neither the Oxford English Dictionary nor Admiral Smyth’s Sailor’s Word-Book (1867) offers any support for the usage of the word monkey in reference to a frame or tray supporting cannonballs.
These spherical iron objects were referred to as round shot, not balls.
They were generally kept below decks in shot lockers. When they were required for immediate use they were set, singly, into wooden or iron frames called shot garlands, either along the ship’s rail or around the hatches.
Only an actual idiot would pile up round shot in the way illustrated, on the deck of a ship that could roll or heel dramatically on heavy seas or under strong winds.
Only an actual idiot would leave iron shot exposed to the elements on deck for any longer than necessary. There were already enough problems with rust (which would be intermittently chipped off by the gunners), just because of humid conditions.
And, if all that isn’t enough, the physics doesn’t remotely hold up. Admiralty Brass (which contains a smidgen of tin to improve its resistance to seawater corrosion) contracts by a linear factor of about 0.00002 per Celsius degree. Cast iron contracts by about half as much. So if the temperature were to fall by 100°C, from a sweltering 40°C to a life-threatening -60°C, the mismatch in contraction between iron and brass would amount to 0.001, or just 0.1%.
As a concrete example, let’s take a couple of 32-pound iron round shot, diameter about 15cm, and set them in a brass frame, like so:
(I’ve “designed” the frame to be open at the bottom, because only an actual idiot would want to leave their iron shot sitting in a puddle of rain or seawater.) While the pair span 30 centimetres, the important part is where they’re in tight contact with the frame, about 25 centimetres wide in my design. Under the ludicrous change in temperature I’ve just described, the frame will squeeze in, relative to the shot, by a quarter of a millimetre overall, lifting them an eighth of a millimetre off the deck. Which is way below the tolerance with which round shot were made—any stack rendered unstable by such a minute change in size would have been impossible to assemble in the first place, because of the variation in size of the round shot themselves.
* Charles Augustus Abbey was born in New York in 1841, and began his maritime career in 1856, as a seaman on the clipper Surprise. He served for eight years on clippers, before returning to the USA to take up a post as Third Lieutenant in the Revenue Cutter Service—his commission was signed by Abraham Lincoln. While serving on the clippers he kept a diary, which was discovered by his family some time after his death. Extracts were assembled and annotated by Lieutenant Commander Harpur Gosnell, and published in a limited edition in 1937, entitled Before the Mast in the Clippers. This was republished by Dover in 1989, which is how I came to pick up my copy in the McMaster University bookshop. Gosnell enhances the narrative with maps, diagrams, historical detail and biographical chapters, interspersed between the sections devoted to the diary entries, which are presented “exactly as written, with no corrections or omissions”. Hence, then, the missing apostrophe and redundant quotation mark in the quotation above. The underlined “Jehosaphat Bumstead” is a mystery to me—there seems to be no record of the phrase beyond this quotation. And notice that Abbey wrote the word brass using the “long s”, bra∫s, which was rendered typographically as braſs. (See my post about the long s here.) This was quite a dated usage, having been abandoned by most printers at the start of the nineteenth century.
We’re all familiar with the fact that the Moon always turns the same side towards the Earth, meaning that we can only ever see one hemisphere, the so-called near side. It wasn’t until 1959 that we got a view of the far side, when the Soviet spacecraft Luna 3 sent back a few grainy black and white photographs.
And pretty much everyone understands that the reason for this is that the Moon takes the same time to turn on its axis as it does to revolve around the Earth. Like this:
The red side is the far side of my model Moon, and an observer on the blue Earth in the centre can only ever see the white near side.
Well, not quite. We can actually catch glimpses of the lunar far side, from here on Earth, because of a phenomenon called lunar libration. Which is what this post is about.
Libration is a rocking motion—the word comes from Latin libra, a set of balance scales. (Which should be familiar from the zodiacal constellation Libra, The Scales.) So to librate is to rock back and forth like a disturbed set of scales, and the Moon appears to do exactly that when viewed from the Earth, so we can glimpse a little rim of the far side from time to time.
The Moon’s rotation rate and axial inclination do vary a little, responding to the gravitational tug of the Sun and planets, but this physical libration accounts for very little of the apparent rocking motion we observe. Almost all of it is optical libration—arising from our changing angle of view as the Earth rotates and the Moon revolves around it.
The first category of optical libration I want to describe is diurnal libration, so-called because it is usually observed by a single observer during the course of a day. Or, to be more accurate, half a day, between moonrise and moonset. During that period, the Earth’s rotation carries a Moon-watcher through an arc that can span, at maximum, the entire width of the Earth. This change in vantage point allows us to peek a little way around the trailing hemisphere of the Moon, and then a little way around the leading hemisphere. Here’s a madly out-of-proportion diagram showing how that works:
This lets us see, at maximum, about three-quarters of a degree into the lunar far side. Here’s a little animation of how our perspective of the moon shifts during such conditions:
It looks fairly impressive, but remember that this is actually happening over the course of about twelve hours—and that for most observers (for instance, those at high latitudes), most of the time, the effect is considerably less than what’s shown.
While the animation shows our viewpoint shifting in lunar longitude, as it would appear for a single observer between moonrise and moonset, there’s also a two-observer form of diurnal libration that shifts in latitude. An observer in high northern latitudes can see a little way over the Moon’s north pole, while an observer in high southern latitudes can see a little way over the Moon’s south pole. They could take simultaneous photographs, compare them, and infer something like this:
But there are a couple of more significant effects contributing to lunar libration. The first is libration in longitude, which arises because the Moon’s orbit is not perfectly circular. It moves around the Earth in an ellipse, and moves faster when it is closest to the Earth.
Here’s the ideal situation, a circular orbit with constant angular velocity, as depicted earlier in this post:
I’ve shown my little diagrammatic Moon at four equally spaced times during its orbit, and added a couple of time-ticks between each of those stages. Each tick corresponds to a 30° rotation of the Moon, over about 2.3 days.
But here, in exaggerated form, is what really happens:
The Earth is no longer at the centre of a circular orbit, but rather at one focus of an ellipse. And while the Moon is rotating at constant velocity, it’s whooshing past the Earth at its closest approach, and dilly-dallying at its farthest excursion. The combination of these two facts means that we can see a little way into the Moon’s far side on its trailing hemisphere as it recedes from us, and a see a corresponding distance into the leading hemisphere as it approaches us.
Here’s an animation, 24 seconds long, of what we’d see in this scenario.
The centre of the white near side is marked with a red dot. My toy moon has no axial inclination (its equator is marked in red), and it’s in a strongly elliptical orbit. The orbital plane is also marked in red, spanning the field of view.
The animation starts with a full moon at closest approach (perigee), after which it initially recedes quickly, giving a good view into the eastern far side, before slowing down as it approaches its greatest distance (apogee). Then it accelerates towards us again, and we can see a little way into the western rim of the far side before it returns to perigee.
The Moon’s orbit is much less elliptical than my model above, but we can still see a little way into the far side as it moves from perigee to apogee and back again. The shape of the lunar ellipse varies, as I’ve described in detail in a previous post, but the maximum libration in longitude is about 8°, like this:
We also see libration in latitude, because the Moon’s rotation axis is tilted relative to its orbital plane. Here’s an exaggerated diagram of that situation, viewed from the side:
When the lunar north pole is tilted towards us, we can see a little way into the northern part of the far side. Half an orbit later, with the north pole tilted away from us, we can see into the southern part of the far side. Here’s another brief animation showing how that works:
The simulated Moon is in a circular orbit, but its axis is strongly tilted, as we can see from the angle of the equator in the opening frames. First, it nods its northern pole towards us, and then half an orbit later, its southern pole.
The real Moon is less strongly tilted, but we can nevertheless see almost seven degrees into the far side over its north and south poles during the course of one orbit, like this:
The real moon, of course, experiences libration in longitude and latitude simultaneously. Here’s a 52-second animation of what that looks like, using real orbital data:
This combination of libration in longitude and latitude, combined with diurnal libration, means that from here on Earth we can actually see 59% of the surface of the Moon, although some of that is seen only glancingly and occasionally.
You might think that’s a pretty gross and obvious behaviour, but bear in mind it happens over the course of an entire month, and that our naked-eye view of the Moon doesn’t let us see much detail, as I described in a previous post. So it seems that for most of human history these librations went entirely unnoticed. It wasn’t until the middle of the seventeenth century, when people started trying to map the Moon using the recently invented telescope, that they noticed that something odd was happening around the edges of the lunar disc, with features popping in and out of visibility. I’ll write more about that in another post.
If the Moon’s perigee and axial tilt remained fixed in space, the lolloping motion in the video above would repeat over and over again in the same pattern. But the Moon’s orbit is complicated. The perigee shifts continuously in one direction, and the lunar axis precesses constantly in the opposite direction. So libration in longitude has an oscillation period of 27.55 days (the length of an anomalistic month), while libration in latitude ticks along at a faster rate, completing a cycle in 27.21 days (the duration of the draconic month). So every month produces a slightly different, and steadily evolving, mix of longitude and latitude libration, until the pattern starts to repeat after 2190.35 days, or almost exactly six years. And I’ll write more about that, too, when I return to this topic later.
Back in 2001, the Boon Companion and I drove from the town of Victoria Falls in Zimbabwe to Kasane Airport in Botswana. As we completed the border formalities at the Kazungula Road checkpoint, I was aware that, less than a mile to our north, in the middle of the Zambezi River, was a very strange international border. But there wasn’t going to be anything to see, and we had a plane to catch, so we never made the short detour to visit it. Do I regret that? Only a tiny bit.
At the point on the Zambezi where it’s joined by the Chobe River, four international borders converge—those separating Botswana, Namibia, Zambia and Zimbabwe. All four of these borders were established more than a century ago, during Africa’s colonial era, and they’ve survived without major revisions since then. But, until recently, no-one has been able to say with any certainty what happens where they all meet up in the middle of the Zambezi.
The boundary between Zambia and Zimbabwe was drawn when these countries were the British colonies of Northern and Southern Rhodesia. Its course is a little complicated farther downstream, but in our area of interest it’s very simple—it follows the medium filum (that is, the centre line) of the Zambezi.
The British also drew the line between Botswana (at that time, the British Protectorate of Bechuanaland) and Zimbabwe (Southern Rhodesia). As the border approaches the Zambezi from the south, it follows the line of an old road, which is now marked by a series of white-painted boundary posts.
Namibia’s borders with Zambia and Botswana required a bit of international diplomacy, however. The colony of German South West Africa, which would eventually become Namibia, had negotiated ownership of the Caprivi Strip, a long geographical salient (visible in the map at the head of this post) which gives access to the Zambezi River at its confluence with the Chobe River. Since both Britain and Germany wanted to be able to move boats on these rivers, the borders were deemed to lie along the middle of the main navigable channels. That’s a common solution when international boundaries involve waterways, and it has its own bit of legal jargon—the centre of the navigable channel is called the thalweg, a German word (with now outdated spelling) meaning “valley way”.
The problematic area, where these well-defined boundaries converge, is only a couple of hundred metres long, and a few tens of metres wide. At most map scales it can be treated as a single point (as at the head of the post), and is therefore often referred to as a quadripoint (where four borders meet), the very rare big brother of the common tripoint, which involves only three borders.
But here’s the situation as it pertained when the Boon Companion and I passed by:
The thalweg of the upper Zambezi is very unlikely to align and merge perfectly with the midline of the lower Zambezi. It’s unknown what happens to the Chobe thalweg after its waters emerge into the Zambezi. And the Botswana-Zimbabwe border has only ever been defined up to the Zambezi shoreline—what route does it take into the middle of the river?
To make this a true quadripoint would require an agreement between all four states, resolving these issues. Absent such an agreement, the real state of affairs was going to be that there were two tripoints in the middle of the Zambezi, in one of two configurations:
There could be various kinks and curves involved, but these are the only two topological possibilities. And at the time the Boon Companion and I drove past, no-one knew whether the short international border between these two tripoints was between Botswana and Zambia, or between Namibia and Zimbabwe—just that such a thing almost certainly existed, that it was going to be the only line along which the two countries involved touched each other, and that it was going to be very short indeed.
It took a surprisingly long time for this situation to sort itself out. Back in 1915, Germany had lost control of South West Africa, which was transferred to the administration of South Africa. So for the next 45 years all four territories involved in the “quadripoint” were part of the British Commonwealth, and no-one seems to have paid much attention to the issue. Things began to change in the 1960s, however, as African nations began, one by one, to gain independence from the colonial powers. South Africa became a republic in 1961, retaining control of South West Africa; Zambia gained independence in 1964; a minority white government in Southern Rhodesia made a Unilateral Declaration of Independence (as just plain Rhodesia) in 1965; Bechuanaland became the Republic of Botswana in 1966. And amidst all those events, Botswana and Zambia began running a ferry service across the Zambezi, right through the middle of the unresolved border area.
Both South Africa and Rhodesia claimed that the ferry crossed illegally through their territory, and that it was being used to supply arms to revolutionary forces operating within South West Africa and Rhodesia. Shots were fired, and in 1979 a ferry was sunk by Rhodesian forces.
Things quietened down for a while after that—Rhodesian elections in 1980 led to the formation of the Republic of Zimbabwe; and UN pressure on South Africa was leading to the slow transformation of South West Africa into the independent Republic of Namibia. The ferries continued to run—in 2001, a pair of large pontoon barges were moving 70-tonne loads back and forth across the river, taking care never to drift downstream into incontrovertible Zimbabwean territory.
But political strife returned at the start of the millennium. While the Boon Companion and I were passing through, Botswana and Zambia were already in discussion about replacing the ferries with a bridge. This was a Big Deal, because it had the potential to pull a good chunk of the trade along the African North-South Corridor away from Zimbabwe. So President Robert Mugabe of Zimbabwe opposed the bridge construction, on the grounds that a straight crossing would inevitably encroach on Zimbabwean territory. But, after much to-ing and fro-ing, and with development costs secured, Zambia and Botswana cut the Gordian knot:
We approached Namibia and asked that the bridge pass through their territory and they agreed.
Indeed, Namibia seems to have gone further in their cooperation. The African Development Fund’s Project Appraisal Report for the bridge, dated October 2011, shows how the proposed bridge takes a long upstream curve, so as to avoid encroaching on the Zimbabwean border, which has been drawn as a direct extension of the land border. But the Namibian border with Botswana is shown to abandon the thalweg of the Chobe and tilt upstream, opening up a short midstream section of border between Botswana and Zambia, through which the bridge passes!
I’ve so far found no record of how that agreement was reached, but it seems to be official enough to have found its way into the US Department of State’s Large Scale International Boundaries (LSIB) geospatial dataset, which I’ve used below to update my map and show the course of the bridge, which opened in May 2021.
That 150-metre stretch of river is the only place at which the countries of Zambia and Botswana come into contact with each other. Making it (by one criterion at least) the shortest international border in the world.
By another criterion, it doesn’t quite hold the record—and that’s the topic for another post.
Galileo Galilei, Third Letter On Sunspots (1 December 1612)
As this post goes live, the seasons have just turned on Saturn. The autumnal equinox for its northern hemisphere came on 6 May 2025, and its north pole is now moving into a period of darkness that will last for 13½ years. After that, it will tilt towards the sun again, and enjoy 15½ years of uninterrupted daylight.*
I can plot the Saturnian latitude at which the sun is overhead on any given date, like this:
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As on Earth, the sun roams back and forth across the equator during the course of a Saturnian year. Because the axial tilt of Saturn is 26.7°, that’s how far the sun strays north and south.† It crossed into the northern hemisphere on 10 August 2009; it will return from its excursion south of the equator on 22 January 2039. The asymmetrical 15½:13½ seasonal split between north and south is easily discernable on the chart.
On 6 May 2025, as on the other equinox dates listed above, the sun shone down precisely above Saturn’s equator—which meant that it also illuminated Saturn’s rings edge-on, giving them minimal illumination.
And, because the Earth always stays close to the sun in Saturn’s sky, we are treated to an edge-on view of Saturn’s rings during the Saturnian equinoxes.
But, because the Earth can stray as much as six degrees either side of the sun, as seen from Saturn, the dates of our edge-on views don’t correspond precisely to the Saturnian equinoxes. I can make this clearer with another chart, adding the latitude at which the Earth is overhead to my plot of solar latitudes:
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That sinusoidal green line, marking the Earth’s latitude, cycles around the solar latitude with a period of 378 days—the extra 13 days beyond the length of a calendar year are the time it takes the Earth to catch up with Saturn’s own, slow movement around the sun.
It’s perhaps a little puzzling why the amplitude of the oscillation in Earth latitude is maximal during the equinoxes, as sun and Earth cross the Saturnian equator, and damps down to almost zero at the solstices, when the sun and Earth reach their maximum Saturnian latitude. But a couple of views of Saturn at different seasons will give the explanation.
Here’s a view from the dark, far side of Saturn during its northern summer solstice, looking towards the sun, with Earth’s orbit marked in red.
With Saturn’s rotation axis tilted towards the sun, the Earth’s orbit runs more or less parallel to Saturn’s lines of latitude, and the Earth’s latitude always closely matches that of the sun.
Contrast that with the situation during the northern autumnal equinox:
With Saturn’s axis tilted sideways relative to the direction to the sun, Earth moves back and forth at an angle to Saturn’s lines of latitude, alternately increasing and decreasing its latitude by several degrees.
Now let’s zoom in on the chart for the current equinox.
Click to enlarge
The Earth’s oscillation in latitude actually carried it across the Saturnian equator some time before the equinox on 6 May 2025. This event is called a ring plane crossing, and it happened on 23 March 2025. That’s the time at which we, here on Earth, had an edge-on view of Saturn’s rings—at which point, being less than a kilometre thick, they became invisible even to powerful telescopes.
Between 23 March and 6 May, there was another complication. During that period the Earth had a sliver of a view of the south side of the rings; but the sun was still illuminating the north side. Our usual view of the rings is in bright reflected light from their illuminated surface—but they’re much dimmer in transmitted light, something we only experience around the time of ring plane crossings.
For several weeks either side of that period of abnormal illumination, the rings are still hard to see because of the narrow viewing angle, particularly for small telescopes. And for this particular ring plane crossing, there was another complication—Saturn was very close to the sun, as seen from Earth, and so the event was difficult to observe.
But notice what happens towards the end of 2025—Earth oscillates back towards the Saturnian equator again, reaching its closest on 23 November. It’s not quite a ring plane crossing, but it’s close. And Saturn will be in a much more favourable position in the night sky, far from the sun. It will appear ringless to anyone with a small telescope.
That excursion back to the equator raises an immediate question. Can the Earth ever actually recross the Saturnian equator? It sure can. Here’s the situation around the 2039 equinox, as the sun cross the equator from south to north:
Click to enlarge
The Earth makes its first ring plane crossing on 15 October 2038, well before the sun reaches the equator on 22 Jan 2039, by which time the Earth is starting to drop southwards again. It crosses the Saturnian equator from north to south on 2 April 2039 and then crosses back again on 9 July 2039. These triplets of ring plane crossings are actually relatively common, slightly outnumbering the single crossings. (Note that a doublet is impossible—the Earth always has to end up on the opposite side of the equator from where it started.)
We can get a better handle on how these triple crossings occur by looking down on the solar system from above:
Click to enlarge
In this diagram, Earth and Saturn are moving around the sun in an anticlockwise direction. The intersection between Saturn’s ring plane and the Earth’s orbital plane is a line, which sweeps upwards across the diagram as Saturn moves along its orbit. The Earth’s first crossing of the ring plane occurs when the Earth is moving in the opposite direction to the ring plane’s motion. But it then sweeps around the sun and overtakes the slowly moving ring plane for its second crossing. Finally, as the Earth begins to turn back around the sun to complete its orbit, the ring plane catches up with it, and a third crossing occurs.
The ring plane takes a year to cross the width of Earth’s orbit, and that’s why three ring plane crossings are the maximum possible during any given Saturnian equinox—there’s no time for the Earth to “go around again” and catch up with the ring plane for a second time.
So why is all this relevant to Galileo Galilei?
Galileo was the first person to see Saturn’s rings, in 1610. The combination of poor telescope optics and the completely unfamiliar idea of a planet with rings, led Galileo to interpret what he saw like this‡:
Saturn is not single but a composite of three, which seem to touch each other and never change their relative position and never move among themselves or change
(The inset is Galileo’s drawing of what he had seen.)
But, having observed this constant triple appearance of Saturn for a couple of years, in December 1612 Galileo reported:
I found it solitary, without the presence of the accompanying stars and in the highest degree round and terminated like Jupiter, and thus it continues to remain. Now what is to be said concerning such a strange metamorphosis? Have the two minor stars been consumed after the manner of solar spots? Have they disappeared and suddenly fled? Has Saturn devoured his own sons?
But now we know the answer to Galileo’s puzzle. He had begun observing Saturn during the closing years of its northern summer. The autumnal equinox came on 30 December 1612, and Earth made its single ring plane crossing on 17 February 1613. No wonder Galileo’s mysterious “accompanying stars” had disappeared!
Of course, after a few months, Galileo was able to report that the “two little lateral stars” had reappeared, and by 1616, with the ring plane more open, he was able to make another sketch, and write that he:
… saw it with two mitres in place of the round stars which reduced it to the figure of an olive. However the middle ball was quite easily seen distinct and particularly two obscure spots placed in the middle of the attachments of the mitres or if we choose to say of the ears.
I don’t know about you, but I want to shout with frustration at the fact that Galileo got so close, but never knew the truth. It wasn’t until 1655, thirteen years after Galileo’s death, that Christaan Huygens first hazarded the idea that Saturn might be surrounded by a ring.
As a bonus, here’s a quick little (38 seconds) video of Saturn during the 2038-2039 triple ring crossing, produced using (as ever) Celestia. Events are speeded up by a factor of a million, so you’ll notice a constant flicker as some of Saturn’s satellites (and their shadows) come and go.
* Like Earth, Saturn pursues a slightly elliptical orbit around the sun. It’s a little closer to the sun, and moving slightly faster, during its northern-hemisphere winter. Which means that summer lasts longer in the northern hemisphere than in the southern. † Latitudes plotted here are planetocentric—the angle between Saturn’s equatorial plane and a line connecting its centre to the sun (or Earth). Strictly speaking, the sun (or Earth) is not directly overhead at points on the planet’s surface corresponding to this latitude, because Saturn is significantly oblate, so that its surface isn’t orientated at right angles to lines radiating outwards from its centre, except at the poles and equator. Latitudes of Saturn’s surface features (cloud bands) are usually given in planetographic coordinates. The difference between planetocentric and planetographic is the same as that between geocentric and geodetic, which apply specifically to the Earth. For a detailed discussion of that topic, see my post “Finding Apollo Trajectory Data”. ‡ This, and subsequent translated quotations, comes from Partridge & Whitaker, “Galileo’s Work on Saturn’s Rings” Popular Astronomy (1895) 3: 408-14
Quae vero post aequinoctium, vel in ipso aequinoctio, suum plenilunium habet, in hac absque ulla dubietate, quia primi mensis est, et antiquos pascha celebrare solitos, et nos, ubi Dominica dies advenerit, celebrare debere noscendum est.
(But that moon which is full after the equinox, or at the very time of the equinox, belongs to the first month, and on that day, without a doubt, we must understand that the ancients were wont to celebrate the Passover; and that we also ought to keep Easter when the Sunday comes.)
Saint Ceolfrid, above, is lecturing King Nechtan on the correct way of calculating the date of Easter, and emphasizing a deep connection to the Jewish festival of Passover, or Pesach, of which more later.*
As this post goes live, we’re about to see a slightly unusual Easter Sunday, on 20 April 2025. But before I explain what’s unusual about it, some preamble is required.
There are two broad groups of Christian churches: the Orthodox Churches, which trace their practices back to the Patriarchs of the Byzantine Empire; and the Western Churches (including Roman Catholicism and the various kinds of Protestantism), whose practices descend from the Popes of the Western Roman Empire. It’s probably fairly common knowledge that Orthodox holy days occur on different dates from their Western equivalents—Orthodox Christmas, for instance, which is celebrated on 7 January, rather than the date familiar in the West, 25 December. And many people are probably aware that the difference of 13 days is because of a difference in ecclesiastical calendars—the Western Churches use the Gregorian calendar, established in 1582 by Pope Gregory (which is also in widespread civil use); the Orthodox Churches, for ecclesiastical purposes, use the older, Julian calendar, established by Julius Caesar in 45 BC. And those two calendars have drifted apart, over the centuries, because the Julian calendar has observed leap years that have been omitted by the Gregorian calendar. For much more on that process of divergence, see my post “February 30th”.
So. We might naively expect that there would be a fixed 13-day difference between the dates of the Western Easter and its Orthodox equivalent, Pascha. But, as my fifty-year chart of Easter/Pascha Sundays at the head of this post shows, while Pascha is typically later than Easter, both festivals vary in date from year to year (which is why they’re called “movable feasts”), and sometimes they stray far enough towards each other that the Easter dates of the two traditions coincide—which I’ve circled in red. This happens in 2025, and on fifteen other occasions during that specific fifty-year span.
In this post, I propose to explain why that it is, and also to account for the obvious, if intermittent, periodicity of those red-circled coincidences.
The reason the date of Easter leaps around in the way it does is because, as Ceolfrid summarizes at the head of this post, Easter is tied both to the season of the year and to the phase of the moon. And the reason for that is because, as he wrote, Christian Easter is linked to the Jewish Passover celebration. The Biblical accounts of Jesus’ resurrection after crucifixion make it clear that it occurred a few days after Passover. And by “Passover” the authors of the Gospels meant not the modern Jewish Passover holiday period, but specifically the date of 14 Nisan in the Jewish calendar.
The Jewish calendar is lunisolar, which is to say it takes account both of the seasons, and of the phases of the moon. Because the period from one full moon to the next is an awkward 29.5 days, lunisolar calendars accommodate this by alternating between months of 29 and 30 days. And because twelve lunar cycles, or lunations, add up to only 354 days, an extra month, called an embolismic month, is added from time to time so that the average length of a year works out to match the 365¼-day cycle of the seasons.
Nisan is the first month of spring. Like all Jewish calendar months, it begins and ends (approximately) with a new moon. So 14 Nisan corresponds (approximately) to the first full moon of spring—which is why Ceolfrid is so interested in the timing of the [spring] equinox and the full moon.
Come the spring, early Christians used to just check with their Jewish neighbours for the date of Passover, and celebrate accordingly. But by the time of the Council of Nicaea in 325 BC, there was a feeling (though by no means universal) that Christians should be coming up with their own way of setting a date for Easter. The debate over how exactly that should be done went on, at times venomously, for centuries, and eventually settled on the definition given by Ceolfrid at the head of this post—the first Sunday after the first full moon, on or after the vernal equinox. (Which is to say, the March equinox, but this debate was taking place exclusively in the northern hemisphere.)
So the ecclesiastical calendar that determines the date of Easter is a lunisolar calendar, just like the Jewish one. And the backward drift of the lunar months relative to the seasons, followed by the corrective lurch of an embolismic month, is why the date of Easter jumps around from year to year.
But it’s not an astronomical calendar—it doesn’t reflect the exact timings of the equinox, or of the full moon. Instead, what’s used is a fixed date for the “ecclesiastical equinox”, 21 March; and a set of calculations, referred to as the computus, which determines the date of the “ecclesiastical full moon”. The ecclesiastical full moon of interest is the one that falls within the 29-day period from 21 March to 18 April, inclusive—this calculated full moon is called the Paschal Full Moon†; and, for brevity, I’m going to refer to the prescribed period in which it occurs as the Paschal lunation.
The computus used at the time of Ceolfrid was a fairly simple one based on the fact that 235 lunations are very similar in duration to 19 years. This is the Metonic Cycle, which I described in more detail in my post about Blue Moons. When Pope Gregory introduced the Gregorian calendar in 1582, his astronomers also tweaked the computus, which was beginning to get out of phase with the real lunations—with the result that the Western Paschal Full Moon aligns pretty well (within in a day or so) with the astronomical full moon, whereas the Orthodox Paschal Full Moon, using the earlier computus, has continued to drift, and is now running about four days late.
Time for a chart. Here are the Paschal Full Moons, according to the Western computus, for the years 2001 to 2050, compared to the actual astronomical full moon dates.
Click to enlarge
I’ve also plotted the boundaries of the Paschal lunation. You can see that the Western computus generates Paschal Full Moons that match the real full moon pretty well, while keeping them constrained within the 29-day period of the Paschal lunation. But notice the years 2019 and 2038‡, in which the astronomical full moon occurs on 21 March, Greenwich time, but the computus places its calculated full moon on 20 March, too early for the Paschal lunation, so that the Paschal Full Moon is delayed until 18 April.
Notice also, the prominent diagonal trend in full moons at three-year intervals. This is a product of the 11-day mismatch, already alluded to, between the duration of 12 lunations and one calendar year, which means that full moons come about 11 days earlier each year.
It is impossible for three 11-day backward jumps to be accommodated within the 29-day Paschal lunation. On the third backward step, the full moon will necessarily fall before the equinox, and the Paschal Full Moon will occur one lunation later. Two backward jumps of 11 days, followed by a forward jump of one lunation minus 11 days, means that, after three years, the Paschal Full Moon will have moved backwards in the calendar by three or four days. (Though, on occasion, the computus produces only a two-day leap, as between 18 April 2019 and 16 April 2022.) This is the diagonal trend that’s so striking in the chart above, and it will be important in explaining the repeating coincidences between Western Easter and Orthodox Pascha.
To the chart above, I can now add the dates of Easter Sunday associated with each Paschal Full Moon:
Click to enlarge
Easter Sundays can occur as early as the day after the Paschal Full Moon, if that falls on a Saturday; but can be a maximum of seven days after the Paschal Full Moon, if that falls on a Sunday. This means the earliest possible date for Easter is 22 March, if the Paschal Full Moon falls on a 21 March that is also a Saturday. There’s no such event on my chart—the last time it happened was in 1818. The latest possible date for Easter is 25 April, seven days after the end of the Paschal lunation. You can see one of those in 2038, when the Paschal Full Moon falls on Sunday 18 April, with Easter on the following Sunday.
You’ll see I’ve also added diagonal lines marking the “trajectory” of Sunday from year to year. Because 52 weeks add up to one day less than the length of a 365-day calendar year, the days of the week move one day earlier each year, and two days earlier if there has been a leap day. This extra regression every four years accounts for the kinks in the “Sunday trajectory” lines.
The movement of Sunday to earlier dates, year on year, almost matches the three-year regression of the Paschal Full Moon I’ve been discussing, but is slightly faster. So the Paschal Full Moon and Easter Sunday slowly converge on each other. In 2030, for example, the Paschal Full Moon falls on Wednesday 17 April, with Easter on Sunday 21 April. After three years, in 2033, the Paschal Full Moon fall three days earlier, on 14 April, but an intervening leap year means that Sunday comes four days earlier, so that the Paschal Full Moon is now on a Thursday. Another leap year in 2036, and the Paschal Full Moon is on a Friday. No leap year before 2039 … still on a Friday. But then it’s on a Saturday in 2042; and in 2045 the convergence is complete—the Paschal Full Moon falls in a Sunday, and Easter leaps away to the following Sunday. This slow convergence will also be relevant to the runs of Easter/Pascha coincidences.
I can plot the Paschal Moons and Pascha dates from the Orthodox computus on my same chart, if I mark Julian dates on the right side:
Click to enlarge
The earliest and latest dates for Paschal Full Moons, and the latest date for Pascha, are exactly the same in the Julian calendar, just time-shifted by 13 days relative to the Gregorian dates. And notice how poorly the Orthodox computus tracks the real astronomical full moon, occurring four or five days later. But we can see exactly the same three-year recurring patterns in Paschal Full Moon and Pascha dates as were evident in the Western computus, and exactly the same convergence between Paschal Full Moon and Pascha Sunday.
So, finally, I can plot both Easter and Pascha on the same chart:
Click to enlarge
I’ve removed the astronomical full moons, but retained the other details. The Easter/Pascha coincidences now appear as red/blue rosettes, where the two symbols are superimposed.
The earliest possible Easter/Pascha coincidence is if Easter occurs on 22 March (Julian), 4 April (Gregorian), which is the earliest possible Pascha date. One of those occurred in 2010. The latest possible coincidence occurs if Pascha falls on 12 April (Julian), 25 April (Gregorian), which is the last possible Easter date—and we have one of those on the chart, too, in 2038.
Within this three-week period when Easter/Pascha coincidences are possible (4 April to 25 April), there’s another rule in operation. Because the Orthodox Paschal Full Moon always falls four or five days after the astronomical full moon, and the Western Paschal Full Moon tracks the astronomical full moon pretty well, we’ll only ever get a coincidence if Western Paschal Full Moon falls early in the week (Sunday, Monday, Tuesday), leaving enough “calendar room” for the Orthodox Paschal Full Moon to occur later the same week.
But in years like 2042, for example, when the Western Paschal Full Moon falls on Saturday, 5 April, with Easter the following day, the Orthodox Paschal Full Moon is pushed into the following week, and Pascha occurs the week after Easter.
So there are three possibilities:
Easter occurs before 4 April, and Pascha is four or five weeks later, after the next astronomical full moon
Easter falls between 4 and 25 April, but late in the week, and Pascha follows a week later
Easter falls between 4 and 25 April, early in the week, and there’s an Easter/Pascha coincidence
Finally, there’s that three-year cycle after which Easter and Pascha return to almost the same position in the calendar, but three days earlier, and Sunday migrates three or four days earlier in the same time period. So once an Easter/Pascha coincidence occurs, it tends to return three years later on a slightly earlier date. You can see that the coincidence we’re about to have on 20 April 2025 will return on 16 April 2028, 13 April 2031, 9 April 2034, and 5 April 2037—after which Easter occurs too early, on 1 April, and Pascha leaps forward to 6 May.
So that’s one way these runs of Easter/Pascha coincidences can end—when the repeating sequences creep so early that the Easter falls before 4 April.
The other way these runs end is if the gap between Western Paschal Full Moon and Easter Sunday dwindles below four days, so that there’s no room to fit an Orthodox Paschal Full Moon into the gap. That happens with the run of Easter/Pascha coincidences in 2011, 2014 and 2017. It starts with the Western Paschal Full Moon on a Sunday, affording plenty of room for the Orthodox Paschal Full Moon to fit in five days later. By 2017, Western Paschal Full Moon is on a Tuesday and the Orthodox Paschal Full Moon, four days later, is on Saturday. And in 2020 the sequence breaks, because Western Paschal Full Moon is on a Wednesday, and Orthodox Paschal Full Moon is on Easter Sunday, pushing Pascha a week later.
So that’s the story for this year’s Easter/Pascha coincidence. Mark your diaries for the next one, on 16 April 2028.
* Ceolfrid’s letter comes down to us because it’s quoted by Saint (“The Venerable”) Bede in his book Historia Ecclesiastica Gentis Anglorum (“Ecclesiastical History of the English People“), Book V, Chapter XXI (731 AD). Bede was a pupil of Ceolfrid’s. Ceolfrid uses the Latin word Pascha indiscriminately to refer to the Jewish Passover and Christian Easter. The translation I’ve used, by A.M. Sellar (1907), carefully separates the two meanings.
†Paschal means “pertaining to Easter”. It derives from Hebrew Pesach, “Passover”, which became Pascha in Latin and Greek. The Greek version gave its name to the Orthodox Easter festival; the Latin to the names for Easter in various Romance languages: Pasqua in Spanish, Pâques in French, for instance. Bede (see note above) wrote that the English name, Easter, came from a pagan goddess of the Spring, Eostre, who had given her name to the lunar month in which Christians now celebrated Easter. But in Stations of the Sun, Ronald Hutton suggests that it’s just as likely that Anglo-Saxon Estor-monath meant something like “month of opening” or “month of beginning” (Spring being considered the start of the year), and that Bede’s otherwise unattested Eostre either never existed, or was the name of a dawn-goddess, like Greek Eos, who was unrelated to springtime in general and the name of the month in particular.
‡ Notice that 2019 and 2038 are 19 years apart—this is the Metonic Cycle, on which the computus is based. If you scan across my chart, you’ll see how full moons fall on, or near, the same date at 19-year intervals.
A while ago I treated you to a dissertation entitled “Does The Sun Set On The British Empire?”, and concluded that it doesn’t. The UK’s widely scattered overseas territories, sparse though they are, mean that the sun is still always shining, somewhere in the world, over British territory.
The most important territories in maintaining this late-empire sunlight are the Pitcairn Islands, in the Pacific, and the British Indian Ocean Territory, in the Indian Ocean. To illustrate that, I offered the sunlight chart below, showing how Pitcairn and BIOT catch the sunlight when it’s dark in the UK.
Click to enlarge
In fact, as my map at the head of this post shows, BIOT is pivotal. There, I’ve plotted the distribution of light and darkness, across the globe, at 02:15 Greenwich Mean Time, during the June solstice of 2024.*
And here’s the situation at the December solstice:
Click to enlarge
Just after the sun sets in Pitcairn, it’s dark over every British territory except BIOT.
I’m revisiting the situation because the UK government has announced plans to hand over sovereignty of the Chagos Archipelago, which houses BIOT, to Mauritius. The announcement was made in October 2024, but the original agreement has now been contested by a new government in Mauritius. And the situation is further complicated by the fact that BIOT houses a large US military base on the island of Diego Garcia, so the new Trump administration also has a say in the process. (Meanwhile, the unfortunate Chagossians, evicted from their homeland in 1968 to make way for the military base, have so far been given no voice in the negotiations.)
The current proposal suggests that the military base would be maintained under a long-term lease agreement, in which case British sovereignty would be lost, and BIOT would cease to exist. At that point, the role of easternmost British territory would fall to the Sovereign Base Areas (SBAs), in Cyprus.
The SBAs are worth a few paragraphs, both because they’re relatively obscure, and because their existence, as sovereign military territories, perhaps has some slight relevance to how the situation on Diego Garcia might play out, should the Trump administration raise strong objections to the current plan.
The SBAs came into existence when Cyprus gained its independence from the UK in 1960. Under the Treaty of Establishment, the UK retained sovereignty over about 250 square kilometres of the island, in two separate areas—the Western Sovereign Base Area of Akrotiri, and the Eastern Sovereign Base Area of Dhekelia. These have extremely complicated boundaries, designed to avoid Cypriot settlements while including British military establishments. The Eastern SBA contains three Cypriot enclaves—the towns of Ormideia and Xylotymbou, and the area surrounding the Dhekelia power station (which is crossed by a British road). It also features a long northward extension along the road to the village of Ayios Nikolaos, which now houses a signals intelligence unit.
And the whole border situation became even more complicated after the Turkish invasion of Cyprus in 1974, which has left the island traversed by a UN buffer zone. British territory, including the Ayios Nikolaos road, forms part of the buffer zone. Elsewhere, the Turkish-controlled town of Kokkina has its very own buffer zone. Here’s an overview map, followed by some detail of the SBAs:
(Interestingly, the British military settlements within the SBAs are referred to as cantonments, a military term which, to me at least, has something of a colonial ring to it, given its association with British rule in India.)
The relevance, here, to the current situation of Diego Garcia, is because the UK government made plans to hand the SBAs back to Cyprus in 1974, but were persuaded to retain sovereignty by the USA, which valued access to signals intelligence in the Eastern Mediterranean, as well as a convenient location from which to fly, among other things, U2 spy planes. The difference, of course, is that the Cypriot government appears to have been compliant with that arrangement, whereas it seems unlikely, at time of writing, that the Mauritians would agree to such a deal.
We’ll see how it goes. Meanwhile, I’ve plotted another sunrise/sunset graph, showing how sunlight is handed off between the two key players in the absence of BIOT:
Click to enlarge
(For my sunlight calculation, I’ve plugged in the latitude and longitude of the easternmost part of the Eastern SBA—Ayios Nikolaos.)
It’s close—in June there’s less than an hour when it’s dark in both Pitcairn and the SBAs. But, if BIOT goes, when the sun sets on Pitcairn, it will also set on (what’s left of) the British Empire.
* I haven’t plotted British Antarctic Territory, because territorial claims in Antarctica are in abeyance under the Antarctic Treaty.
