These are continuing tales of our pre-historic ancestors and their work in observational astronomy. You will remember Eos, the brilliant teenage boy, who had left his home village to study astronomy with a group of experts known as “The Elders”. He had spent five years with them, and now, aged eighteen he had been invited to join a special group planning a very large and impressive new series of astronomical constructions much further south.
1. Pre-Historic Stone Constructions
The History of Cogito
One of The Elders, Cogito, came with Eos to the village. He was made very welcome, but Eos was too shy to reveal his nickname, “Old Wilderness”. All his colleagues and students called him this, on account of his travels to the wildest and most remote parts of the island. He had made important astronomical discoveries in his youth. He knew that North and South, East and West were the same everywhere, as were the equinoxes and solstices.
However, he was convinced that some astronomical events did vary, depending on where you made the observations. He guessed that the sun rose higher in the sky the further you were to the south. Also, he thought that there were differences in the star pattern the further north you went. The only way to resolve these issues was to check them by observation and measurement.
He had made a bold plan to carry a chain of measurements across the island until he reached the far north and could go no further. Then he would turn round, continuing the measurements, and travel as far south as he could. It would involve a lot of travelling and some hardship. He had spent so much time in wild and lonely places that the nickname, “Old Wilderness” was one of awe and respect rather than amusement. Cogito had invited young Eos to travel with him, for several months, as his assistant, because it was impossible to do the measurements on his own. This would provide Eos with valuable practical experience of new regions, as well as taking part in a piece of original research.
2. A Simple Demonstration of Variation in Shadow Length
To decide on how high the sun rose, from the length of its shadow, he needed to measure it at some fixed time of year. There were only four times in the year which you could be certain about; the equinoxes and solstices, the cardinal dates. (2) It wasn’t really practicable to wait around for these events to occur, otherwise, it would take a lifetime to get any results. His plan was to travel north, and when it got near one of the cardinal dates, to stop, set everything up and make the observation on the correct day. Then they would travel on again.
The other important piece of standardisation was the use of the same portable staff (2) to create the shadow each time. The toe dug into the soil to keep it steady and the wide foot stopped it from going in too far. It was made of yew wood, reddish in colour, tough but springy, fine grained and capable of taking a surface polish. It had been carefully smoothed with stones and finally waxed with beeswax.
The staff was not only used as a shadow pole, but also a sighting pole, by means of a hole in the bulbous tip. (2) Finally it was used for record–keeping. It was such a vital piece of equipment that young Eos also carried an identical staff, in the hope that at least one would survive the journey and be brought safe home.
In an earlier essay, (Pre-Historic Science) I discussed briefly the problem of record–keeping in a period when writing and numerals had not yet been invented. I thought, perhaps, the answer was some form of tallying, because there is evidence that this may have been used as far back as the Palaeolithic period.
Cogito needed to record four sets of observations; sun shadow length at (i) the summer solstice, (ii) the winter solstice, (iii) the equinox, and (iv) a star sighting. He planned to record them vertically down the staff in four different positions, shown in Figure 3. The summer solstice column was symbolised by a larger circle, and on the opposite side, the winter solstice column by a smaller circle. The equinox column was between them, shown by a barred circle, and the star column was an asterisk.
The four columns are shown “unwrapped”, to the right of the staff head. In case any reader thinks this seems extremely advanced for a pre-historic person, it is only an extension of the idea of binding four tally sticks together with a leather thong.
3. Details of the “Old Wilderness” Staff
Those with a mathematical mind will already have realised that, if the angle of elevation of the sun is less than 45 degrees, the shadow will be longer than the staff itself, and it would be impossible to record its length. Cogito knew this already, and carried a set of thin leather thongs or cords in his knapsack.
When measuring the length of the sun’s shadow, his companion pushed a peg into the ground, at the shadow tip, slipped a loop round the peg and took the other end of the leather cord to the staff. He then doubled the cord, so he was using half of the true shadow-length. He placed one end of the cord against the incised ring of the foot, stretched the cord up the staff and made a nick in the wood of the correct column with a sharp flint knife.
There was one final piece of information needed on the recording staff. The complex astronomical information was simply defined by the columns, but how to describe where, geographically, they were done? Cogito thought that ten locations would be sufficient between their starting point, and the far north coast. He planned to choose locations that were memorable in some way.
Our distant ancestors made a far greater use of the power of memory for recording information than we would be capable of today. Writing and numbers have spoiled us. For Cogito and Eos, remembering geographical locations, even many years later would be child’s play.
The places were recorded on the staff with a tally-mark. 1 was /, 2 was // up to, 5 a hand V. Then 6 was V/, 7 was V//, up to VV, two hands or ten. Afterwards, Cogito would remember exactly where V/, for example, was located. In my first essay on this topic, (Pre-Historic Science), I was deliberately vague about geography, because it was unimportant to the issues, but here it is essential and I include a specially prepared map, (Figure 4). The modern names used would have been unknown to Cogito, except for the river-names which are believed to be very ancient.
A. ROSEBERRY TOPPING
In the end, Cogito’s journey needed only eight locations for astronomical observations. They left home in late winter, headed north-east towards the block of the North York Moors, crossing the rivers Wharfe and Ouse on the way there. The peak of Roseberry Topping (5) came into view, and they chose a high, but level spot among the hills with a good view to the south. The weather was bright and frosty, and there were still patches of snow among the hills, particularly in the north-facing hollows. (5)
4. Cogito’s Journey North
They planned to observe the Spring Equinox from here. During the first day they set up the staff and observed the movement of its shadow to establish the positions of the four points of the compass. During the night they observed the position of Polaris, (the Pole Star) as a further check on the North/South line.
5. Roseberry Topping in Late Winter
They got a few hours sleep and then waited to observe the sunrise over the North Sea horizon. It was just south of the East /West line. Cogito and Eos had a little competition to guess how many days to the Equinox; Cogito thought three days, while Eos guessed four days. They were both wrong; it was only two days away.
At noon on the day of the Spring Equinox, they measured the length of the staff shadow, and marked its half length in the “equinox column”. As soon as the sun had set, and the stars were clearly visible, they did a sighting on the angle of Polaris. This would not change during the night so they did it early on and had a good night’s sleep.
Cogito lay on his back, supporting his head with a board on a rock, so that he was looking towards Polaris. Eos took the sighting staff and moved it so that Cogito could see Polaris through the hole at the top. When Cogito was satisfied, Eos took a cord and measured the distance between the staff and Cogito’s eye. This distance was recorded on the “star column” of the staff. It was not necessary to halve the value, as will be explained later.
6. Cogito Takes a Sighting of Polaris
The two companions discussed what they had seen on the hills. They were above a steep escarpment of the moors which dropped away, giving a good view of the plain below, and the river Tees flowing in a graceful curve towards the North Sea. The peak reminded Cogito of the curve of a young girl’s breast. (5) The discussion helped fix the details of the place in their memory.
[In case the reader should think my imagination is a little overheated, many hill-tops in Britain had names referring to breasts – the Paps (Breasts) of Jura in the Hebrides, or Cioch-na-Oighe (kee och na hoy) on the Isle of Arran, whose Scots Gaelic name translates into English as "the Maiden's Breast". I suspect the name "Roseberry Topping" is very recent, and perhaps a drawing-room version of a more ancient name.]
Next day they packed up and came down off the hills with their equipment. In those days, crossing rivers was a major undertaking, as most of them were bordered by swamps and water meadows. Generally, the two men kept to the higher, better drained land, but occasionally they had no choice and must cross a river.
Cogito had planned for this and they carried a coracle. This was a simple kind of boat. Its great virtue was that it was extremely light, so the burden of carrying it was not too great. It had a circular wooden frame of light, twisted willow wands. A network of further willow wands was woven on this. Overall it was covered in leather sheets, stitched together.
7. A Modern Version of the Ancient Coracle
It was not highly waterproof but it was perfectly effective for the time needed for a river crossing. It had another great virtue. At night it could be turned upside down so the two men could sleep under it. It protected them from wind and rain during the night.
Cogito planned to get to the far northern coast in time for the summer solstice. The overland route from Roseberry Topping in North Yorkshire, to Duncansby Head is about 490 miles (780 Km) and they had a quarter of the year, or about 90 days to achieve it. This means they had to average about 5 ½ miles (9 Km) a day, which is quite a modest target. It is possible to keep up a walk at 4 miles per hour on a hard level surface. However, they would rarely have this luxury. The calculation did not take into account delays due to illness, injury, or holdups caused by floods or heavily swollen rivers.
Although Cogito had none of this mathematical information, he knew they must cover a reasonable distance every day, around 12-15 miles (19-24 Km) to achieve his target, and they moved accordingly, at a steady but unhurried pace.
Roseberry Topping to Hexham
Once they were off the hill, they planned to follow the valley of the River Tees upstream. The lower stretches were wide and the flat country on either side was swampy and full of reed-beds, so they kept to higher ground. When they reached Upper Teesdale, the river was much shallower and the bottom was rocky. It was easy to get to the edge of the river and launch the coracle, so they crossed the Tees, and turned north into the rolling heather moorland of the Pennine Hills.
8. The River Tees near Middleton
Although there were no peaks on their northward route, the heather moorland was high up and gave wide views in all directions. If they could be transported into our present age they would find the region largely unchanged. The North Durham Moors are one of the wildest parts of England.
The route descended steeply towards the flat, sloping, boulder-strewn rocks of the River Wear, where the coracle was launched again. The ascent up the far bank was very steep and they were forced to stop to regain their breath. Another stretch of rolling moorland lay in front of them, before they reached the pleasant meadows bordering the River Tyne.
9. Busy Paddling the Coracle
They decided to make camp on the old river terraces, high above the waters. They only planned to take a sighting of the Pole Star during the night. The process was quite easy, so they had done a sighting each time they camped for the night. They did not want to confuse the records on the staff so Cogito kept records on a separate stick. It was as he expected. The further north they went the higher the Pole Star appeared in the night sky.
Hexham to Melrose
The River Tyne was deep and wide at Hexham (10) and they planned to cross it and follow the River North Tyne on the other bank. They walked upstream for a mile or so, launched the coracle, and went with the current, paddling to the left and moving gradually nearer to the north shore. Eventually they were slowed by reed-beds and the effect of the current slackened. They were able to make slow progress through the reeds until they could reach a firm bank and climb out.
10. The River Tyne near Hexham
Cogito and Eos followed the North Tyne, then the River Rede, and finally the River Coquet to its source in the moorlands of the Cheviot Hills. Once over the top it was downhill to the River Teviot which they crossed and continued to the River Tweed. They walked steadily upstream looking out for the characteristic set of triple hills. (11)
C. MELROSE AND THE EILDON HILLS
These triple mounts are now called the Eildon Hills, (pronounced eel don), but the Romans knew them as Trimontium, “the three hills”. Both Cogito and Eos liked this spot on the banks of the Tweed, and were inclined to linger there, but they had only done three of the eight projected sites, and it was important to move on, once they had done their night time observation of the Pole Star.
11. The Eildon Hills near Melrose
12. From the North York Moors to the River Tweed
Melrose to Bathgate
Cogito knew many of the places they travelled through from previous journeys and reports by other astronomers. He remembered a place nicknamed, “Between Two Seas”, which was the next objective. Leaving “The Three Hills”, they travelled along the valley of the Tweed upstream until they were opposite a smaller river, the Leithen Water.
They crossed the Tweed and followed the Leithen Water until they reached a small oval shaped lake, Portmore Loch, below a minor peak. They climbed this peak, which gave a good view of the distant Pentland Hills. They noted the highest point of the Pentlands, the Scald Law (1898 feet or 578 metres) and made directly for it. From the top of it they could see down into the plain. Their destination was a small hill about ten miles away in a north-westerly direction.
D. BATHGATE- CAIRNPAPPLE HILL
This small mount was Cairnpapple Hill, a modest elevation which had great geographical significance for Cogito, because from the top you could look east and see the Firth of Forth, that great arm of the North Sea. Look west and you could see the River Clyde with its estuary leading into the Irish Sea, hence its nickname, “Between Two Seas”. They had travelled there, not because Cogito was an enthusiastic geographer, but because it was a sacred ceremonial site. That was why Cogito had found it so easily because he was remembering detailed instructions given him by an older astronomer, some years ago.
When Cogito and Eos arrived at the site they found a group of astronomer-priests already there. They greeted both of them warmly, and when Cogito showed them his equipment and explained his mission they realised that he was one of their own kind, keepers of the mysteries of the heavens.
13. The Chambered Mound on Cairnpapple Hill
Today, there is a large mound containing a megalithic chambered vault within, (13), but in Cogito’s time it was much plainer. It is close to the modern town of Bathgate. For fuller details of Cairnpapple, see the notes and references at the end.
The astronomer-priests took Cogito and his companion for a celebratory meal and asked them to stay with them for a few days. When Cogito explained about his aim to reach the north coast by midsummer, the eldest of their hosts re-assured them. He would provide guides to get them to the next destination, Oban, by the shortest route. This was to be of tremendous value to Cogito and Eos, as they discovered later.
They were very interested in Cogito’s measurements of the position of the Pole Star. For anyone who did not travel widely, the idea came as something of a surprise. It had not occurred to them that the stars showed any motion, other than the nightly rotation which was common knowledge.
Cogito’s Pole Star Sightings
As Cogito had proved with his regular measurements, the further north you go, the higher the Pole Star appears in the night sky. We have to remember that all of our modern concepts were unknown to him and the others. He did not know that the earth is a sphere, or that day and night are the result of its rotation. Neither did he know that the North Pole of the rotating earth pointed at the Pole Star, which explained why the stars seemed to rotate around it during the night.
Let us look at Cogito’s achievements from a modern standpoint. We now imagine the earth as ringed by Lines of Latitude, based on the angle from the centre. (14) The Pole Star has an angle of elevation of 90 degrees at North Pole, or in other words it is directly overhead. The angle at the equator is zero degrees. We can work out the latitude of any place in the Northern Hemisphere, by simply measuring the angle of elevation of the Pole Star during the night.
The British Isles lie roughly between Latitude 50 and Latitude 60 degrees. (14) Cogito’s first location, Roseberry Topping, is near the village of Great Ayton, (Latitude 54o 30/ N). His last location on the northern journey would be Duncansby Head, (58o 39/ N). Thus he was attempting to measure a difference of 58o 39/ -54o 30/ or 4o 9/. We now examine the feasibility with some trigonometry in Figure 15.
14. The Latitude of the British Isles
Definitions (h = height of eye above ground level, 20 cm, S = height of staff from foot to sighting hole, 2 metres, or 200 cm, d1 = measured distance in cm, from staff to eye at Location 1, d2 = measured distance, in cm, at Location 8)
15. The Trigonometrical Basis of Star Observations
In triangle ABE, angle ABE = 90o, therefore Tan angle AEB = AB/BE
Therefore BE = AB/ Tan angle AEB = (s-h)/Tan 54o 30/ = 180/1.402 = 128.4 cm.
In triangle CDE, angle CDE = 90o, therefore Tan angle CED = CD/DE
Therefore DE = CD/ Tan angle CED = (s-h)/Tan 58o 39/ = 180/1.641 = 109.7 cm.
So these early astronomers would have detected a difference of 18.7 cm between their initial sighting and the final one. Even the change from one location to the next would also be apparent to them. As explained, Cogito kept records of the star sightings on a separate tally stick. It was turning out as he expected.
Bathgate to Oban
The party of six left the Cairnpapple Astronomers’ Group with many calls of farewell, and exhortations to return soon. There were two senior astronomers, and two apprentices who wanted to help by carrying everything. They travelled due west over the gently rolling country to Dumbarton. They crossed the River Clyde to the south side, before it widened into the great Firth or estuary. The massive block of the Dumbarton Rock (16) dominated the northern shore.
16. Dumbarton Rock in the Firth of Clyde
Cogito had worried about how a party of six was going to manage in a coracle only capable of carrying two men. All became clear. One of the senior astronomers carried a ceremonial ox-horn trumpet. (17) At the Clyde crossing he sounded the trumpet several times and a wooden boat arrived a few minutes later. They all got in and were rowed to the far shore. The boatmen were extremely respectful of the two astronomers and treated them as men of importance. This pattern of behaviour, Cogito learned, was customary.
17. The Senior Priest-Astronomer’s Trumpet
The Argyll landscape (18) is dissected by deep sea-lochs which run a long way inland. Road travel requires long detours. It is much easier to cross the lochs by ferry. Even today, with fast motor transport, the ferries still remain a vital part of travel in this part of Britain, and visitors learn to plan their routes to take advantage of the convenience of ferries. (19)
18. Route from the Tweed into Argyll
I add a personal recollection here. Wishing to cross Loch Linnhe from east to west, by the Corran Ferry, which saves a 25 mile (40 Km) detour, I arrived in the car park just as the ferry was about to leave. I was prepared to wait for the next east/west crossing, in about twenty minutes, when the ferryman beckoned to me from a hundred yards away. I drove over to the gates which had been re-opened. Having driven on board, the ferryman explained, “I got them to squeeze up a bit for you.” This was an illustration of the generosity and flexibility of the men who run these services, principally for the benefit of local people.
19. The Modern Corran Ferry Crossing Loch Linnhe
Cogito’s group crossed the Firth of Clyde from Gourock to Dunoon on the Cowal Peninsula, and took the road which climbs up Glen Lean, through the Benmore Forest. This road descends to cross round the heads of Loch Striven, and Loch Ruel. Up another hill road and down the other side brought them to the eastern shore of Loch Fyne. The trumpet summoned the ferryman, who carried them respectfully to the western shore. The senior astronomers were keen to show their visitors the region between Loch Fyne and the open sea by the Sound of Jura.
20. Loch Fyne, Argyll, Scotland
The whole area was being developed as a religious ceremonial landscape. When it was complete, it consisted of stone circles, burial chambers, tumuli or mounds, carved stones, standing stones, and cursi or linear earthworks. Overall, it was a very ambitious undertaking. Many of the elements of this ceremonial landscape exist to this day, especially the Temple Wood site, marked “TW” on Figure 18.
21. The Temple Wood Stone Circle, Argyll, Scotland
Cogito and Eos were introduced to the Temple Wood Group of astronomer-priests, and they spent several days being shown around, and discussing astronomical issues. Eventually, Cogito explained that they needed to move on, if they were to reach the north coast by midsummer. The astronomers from the Cairnpapple Astronomers’ Group also made their farewells as they were returning home. As a parting gift, they presented Cogito with an ox-horn trumpet, with which to summon the ferryman.
E. OBAN – STRONTOILLER
Once Cogito and Eos were free again, they set a cracking pace and by nightfall they had arrived in the settlement at Oban, which was right on the sea coast. They did a night time measurement of the angle of the Pole Star. Next day, having questioned the local people, they located the sacred sie at Strontoiller, (21) which was inland, about four miles east of the Oban settlement.
Today, there is a circle of thirty-one boulders, about 60 feet (20 metres) in diameter and a single standing stone, (22) which is 12 feet or 4 metres high. The construction dates from the second millennium BC, but in Cogito’s day there was none of this, although it was already a sacred site.
22. The Strontoiller Stone Circle near Oban, Argyll
23. The Strontoiller Standing Stone
Oban to Inverness
Cogito and Eos set off early because they wanted to cover ground now. They were to travel up the east side of the Linnhe Loch to its head. Within four miles they came to the Connel Ferry, and Cogito sounded his trumpet for the first time. The ferryman was polite but did not show the awed respect accorded the Cairnpapple astronomers. Cogito thought it was probably the absence of a retinue. By evening they had reached the settlement at the head of the Linnhe Loch. Several millennia later, in the 18 C, this was to be called Fort William. Their route now was to take them up Glen More (the Great Glen).
The big advantage was that the journey was inland, their course was dead straight, the sea lochs and ferries were miles away to the west and Cogito expected to make good progress. The Great Glen, we now know, is a giant geological fault. It is filled with a series of lochs, the most famous of which is Loch Ness. (24) They followed the line of the lakes (25) and within a few days reached Inverness, “where Loch Ness meets the sea”.
24. Heading North to Inverness
25. Oban to Inverness via the Great Glen
26. The Moray Firth
From above Inverness, they could see a great stretch of enclosed water, the Moray Firth, (pronounced murry) trending north-eastwards to the open sea. Their goal was a sacred site at Clava, a few miles east of the settlement at Inverness. Today the area has a fascinating collection of chambered cairns and circles of standing stones, but none of this was in evidence in Cogito’s time. It all came in much later developments.
It may be wondered why Cogito and Eos did not simply camp in the most convenient place and take their measurements. The truth was that Cogito was not simply an early scientist, he was also a priest, and this trip was more akin to a pilgrimage than an astronomical field trip. Though we call him an astronomer, he was much more of an astrologer, and much of his measurement would be used to justify the belief systems of his people. He, and Eos, wanted to remember all his measuring sites and he chose places that had a religious significance as well as being visually memorable.
27. The Clava Site near Inverness
Inverness to Suilven
Heading westwards, they followed the southern shore of Beauly Firth, (pronounced bew lee) and turned north-westwards to Strathpeffer. The place-names are Scots Gaelic, or anglicised versions of them, in much of the Highlands. A “strath” is a wide flat valley, while a “glen” is narrow and steep-sided. “Inver” names mean a confluence of waters, either two rivers, or a river and the sea. They walked on into Strath More, (“big wide valley”) and down on to head of Loch Broom, a sea loch, of the western coast. They kept to its eastern shore, until, a few miles beyond the Ullapool settlement, it suddenly increased in width four times. At this point, they turned north-east and headed up the valley until they arrived at Knockan, a settlement among the lakes of a small plateau. The region is now known as Assynt, (ass int).
28. Route from Inverness to Duncansby Head via Suilven
29. Knockan near Suilven
The little plateau is surrounded by a series of peaks like Cul Beag, (little bottom), Cul Mhor, (big bottom), Ben More Assynt, (big mountain of Assynt) and Suilven (pillar mountain). Cogito’s original plan was to climb to the top of Suilven (seel ven) at 2, 785 feet (732 metres) to make his astronomical observations. He had only heard about Pillar Mountain, but now he saw it, the thing looked formidable, (30).
The approach march would be across a boggy region of lochans, (small lochs) (31) before they even got to the foot of the mountain itself. Time was pressing, and Cogito made a decision which he explained to Eos. They would abandon the original idea of climbing Suilven, and instead climb Cul Mhor, which they could see from Knockan, was only a couple of miles away across fairly easy ground.
What Cogito did not know, with his change of plan, was that Cul Mhor was actually higher than Suilven, at 2, 786 feet (849 metres). He was, of course, correct in thinking that it was much nearer and a much easier climb.
Cogito and Eos planned to spend the night on the mountain top, as it was good weather and near midsummer. They set out in early evening, and crossed the stony moorland leading to the foot of the mountain, (32). By the time they reached the boulder field, (33) they began to wonder if a night on the summit was such a good idea.
As they came nearer the twin peaks of Cul Mhor, (34) they had to decide which of the two to ascend. They chose the right-hand one, which was the higher of the two. The summit boulder field was a tangle of large boulders, often with flat faces. They tried pulling and arranging these to form a pair of flat couches. When the light finally faded, (around ten at night) and the stars were bright, they did a sighting on the Pole Star.
Having spent an uncomfortable night, they decided to descend from the summit into the flatter country below. They would make a record of the noon solar angle from a more comfortable position in the heather. Cogito had realised that, although the nearer you were to midsummer the higher the noonday sun rose, it also seemed that the further north you went the lower the noonday sun tended to rise. It was all still rather confusing, and further observations were needed.
Suilven to Duncansby Head
As Cogito and Eos left the beautiful Knockan plateau, with the twin peaks of Cul Mhor in the distance, it was in the knowledge that this was the last leg of the northward journey. They travelled north for a few miles, and worked their way round Loch Urigill and Loch Borralan till they were headed south eastwards down Strath Oykel. Their principal direction was north-east but this route avoided the mountains and many lochs that blocked their way to the north, (36).
Strath Oykel (37, 38) was a typical wide valley with gentle slopes and a meandering salmon river flowing to the sea at Dornoch Firth.
36. The Mountains beyond Knockan
They left Strath Oykel and turned due north up the Achany Glen, making for Strath Vagastie. The bulk of Ben Loyal (39) loomed over them as they skirted the western side of Loch Loyal., and in a few miles, came down to the north coast at the Kyle of Tongue, (40). The Kyle is a sea loch running inland for seven miles, in a north/south direction, while the coast trends east west. Following the coast eastwards, Cogito and Eos travelled through the flat landscape of the Sutherland plateau. It was the northern part of the “Flow Country” region of peat moorland, (41).
40. The Kyle of Tongue
41. The Flow Country of Lakes and Peat Bogs
The north-flowing rivers from the Flow Country were low at this time of year, so Cogito and Eos were able to ford them easily on foot, without recourse to the coracle. Although they were keen to know how near they were to the time of summer solstice, there was no easy way to do this. Unlike the equinoxes, where they could see how close the sunrise was to the east-west line, at the solstice the sun’s noon shadow changed very slowly. They had to measure it for several days, on either side of the actual day.
Cogito was worried that they might miss the actual solstice, which would be a pity, after a long journey like this. They moved as quickly as they could, taking advantage of the very long days of sunlight (around 20 hours) and making do with a few hours of sleep.
H. DUNCANSBY HEAD
Finally, they reached the place described to Cogito years ago, and remembered now. “The land is very flat in all directions; there are no trees, and much heather. The sea cliffs are very high and are vertical. Off the coast to the north is a whole collection of flat islands.”
42. The Sea Cliffs and Stacks of Duncansby Head
Cogito recited his memory to Eos, who pointed out the details of the cliff landscape before them, (42). The Orkney Island of Stroma showed as a thick black line, two and a half miles from where they stood on the cliffs of the mainland. The modern names of some of the islands are shown in Figure 44.
John O’ Groats is one of the most famous Scottish place names, but it has only been called this since the fifteenth century. King James IV of Scotland had recently acquired the Orkney Isles, and in 1496, granted a charter to a Dutchman, Jan de Groot and his two brothers, to run a ferry between the mainland and the islands.
43. The Island of Stroma in the Pentland Firth
44. The more southerly Orkney Islands with distances in miles
Waiting for the Solstice
Now they had arrived, Cogito and Eos set up camp on the flat ground well away from the cliffs. They spent a day establishing a north/south line and an east/west line. The absence of trees had been anticipated by Cogito, and when they were in Strath Oykel he had cut a set of light willow wands and bound them together with a leather cord. They carefully marked the length of the noon shadow of the measuring staff, and settled down for a few gentle days of rest.
It was clear that the length of the staff shadow, at noon, was still shortening, as the sun rose higher. After six days the shadow length remained steady; so they must be near the solstice.
After another four days the shadow lengthened almost imperceptibly. They had caught the solstice, and Cogito could confidently mark the “half-shadow length” on his recording staff. When they made sightings on the Pole Star it was against a very brightly lit night sky, (45). The sun was clearly only just below the horizon.
45. The stars are barely visible at 3.00 am in July
While waiting for the solstice, they amused themselves by catching sea fish and an occasional eider duck, (46). The fish they roasted on hot coals, already prepared, but the ducks they carefully plucked, so that they could save the eider down in a thin leather bag. This down could be made up into a winter jacket at some later stage. The eider duck meat tasted rather fishy compared with the freshwater ducks they normally caught, but they both had healthy appetites and welcomed any meal.
Readers may have wondered about how Cogito and Eos managed for food. They both carried small bows and arrows and were excellent marksmen. They killed birds like rooks and starlings, which they roasted on hot coals. There were no rabbits, chickens or pigeons, as these were introduced into Britain at a much later period in history. Hares were common, but very wary and difficult to stalk. Ptarmigan, woodcock and quail were present but needed patience, on open moorland or in woodland.
46. Eider Ducks in the Northern Seas
Deer were common but too big and inconvenient to skin and cook. Mallard ducks were plentiful among the reed fringed shores of rivers, and the coracle provided an excellent hide to approach close enough to shoot them, (47). Fish, like trout, could be tickled by hand from the rivers, and carp or pike near the surface were vulnerable to arrows. Sea fish could be caught on a line, with a baited hook. Along the shore there were shellfish to collect and both men were skilled at gathering edible roots, and fleshy stems, as well as fruits and nuts in season.
47. Mallard Ducks in Freshwater
Barter and Trade
They also traded with the local people they met along the way. A small portion of pork from a wild-boar kill or a joint of venison (deer meat) made a welcome change. They also obtained cereal food like bread or porridge. Cogito and Eos were both skilled flint-knappers and they carried collections of flint arrow-heads and spear points ready for trade, (48). These were always an acceptable basis for barter with any group they met.
48. Trade Goods Carried for Barter
As explained earlier, astronomer-priests like Cogito were held in great awe and reverence. As wise men, they would be asked to heal any sick people, and Eos had developed a skill in this direction. Grateful patients would offer gifts to them and food was always an acceptable present for men on the move. Both Cogito and Eos also made small votive objects or religious items, (49), and these were always available, either for barter, or as parting gifts to a generous benefactor.
As Figure 49 shows, votive carvings were found all over Europe. The so-called, “Willendorf Venus” is from German-speaking Central Europe, the carved ivory figurine of the Buren Man is from Siberia, and the mysterious objects found in the Skara Brae excavations are from the far north of Scotland.
In case this should sound too fanciful to a modern secular audience of readers, there is still an extensive trade in religious objects of all kinds, among Greek Orthodox, Roman Catholics, Hindus, and Buddhist peoples. It is only in the secular Protestant West that these practices seem strange.
Similarly, among modern professional doctors, we know that the most popular ones are those valued for skills like sympathy, listening, and calmness. They have a quality that makes the patient feel better, before any drug has been prescribed, or any surgical procedure has been tried. In an old phrase, “they have healing hands”, and this is true of nurses as well as doctors. Young Eos had, as I suggest, this quality, which made him a welcome visitor.
49. Votives from Different Parts of Europe
Language and Communication
At the time that Cogito and Eos were travelling through northern England and Scotland, there was no universal language in Britain. The Celts had not left Central Europe, from their centre in Hallstadt, now in the region of the German-speaking peoples. The two travellers made continual use of gesture and mime to speak to strangers, as did most other people of those times. When this is a common experience, people become experts in non-verbal communication.
As an illustration, I repeat an anecdote from a book, which I am now unable to trace. In the later years of the nineteenth century, in the American west, a Native American tracker was employed to assist the local military authorities. He was accompanied by a translator who spoke English. When asked what he had found, the tracker did not speak, but moved his right hand up and down in a wave motion, and brought his left hand across it. “Down at the ford of the river…” the tracker held up four fingers and rocked his flat hand up and down, “there were four horses crossing.” He held up three fingers, tapped the hair on his head, and rocked his flat hand with the thumb close to his fingers, (50). “There were three riderless bay horses.” He cupped his hand to his mouth. “They stopped to drink.”
He held up one finger, tapped a white feather on his clothing, and rocked his hand with the thumb sticking up. “There was a grey horse with a rider.” All these gestures were made with a continuous gentle flowing motion so that the tracker conveyed his findings more rapidly than the translator could turn them in English.
50. Non-Verbal Communication
THE SUN’S PATH IN THE HEAVENS
Short Northern Nights
As Cogito and Eos moved north-eastwards towards their destination on the north coast of Scotland, they became increasingly aware of the shortness of the night. The sun rose closer to the north each day, and what seemed earlier and earlier in the morning. They had no way of measuring the time of day, but sunrise was about 02.00 hours. Similarly, the sun set very late in the day and closer and closer to north. Sunset was at about 22.00 hours, so their night was only about four hours long.
They were physically active with continual walking and needed a good night’s sleep so they had to retire for the night while it was still light, and resist the habit of rising as soon as the sun was up. Cogito had been puzzling about this, and he imagined that if they went far enough to the north, the sun would not rise or set, and there would be no night, because it would always be above the horizon, (51). He had a vague recollection from many years ago, probably when he was a child, of a much-travelled visitor who spoke of, “The Land of the Midnight Sun”. The phrase had stuck in his head.
Earth’s Axial Tilt
With our modern knowledge of the relationship between the earth and the sun, it can help to understand some of the observations and difficulties experienced by these pre-historic astronomers. We know that the earth goes round the sun in an orbit which nearly, but not quite, circular. If we printed an accurate diagram of the orbit as a circle across a sheet of A4 paper, the difference between the “long” and “short” axis is about one millimetre.
51. Solar Motion in High Northern Latitudes
As the earth traces out its orbit around the sun as a plane, like a flat circular plate, it also spins on its axis. If the spinning axis was at 90 degrees to the plate, every day and every night would be exactly 12 hours each, everywhere on earth, and there would be no seasons. It is the fact that that the axis is tilted at 23.5 degrees to the vertical, (52) that creates the seasons and produces some of the puzzling apparent motions of the sun observed by Cogito.
52. Axial Tilt of the Earth at Midsummer.
Apparent Solar Motions
We can look at the apparent solar motions in terms of the only two natural time periods available to ancient astronomers; the day and the year. Daily apparent motions are roughly circular, because they are mainly due to the earth’s rotation on its axis. Yearly apparent motions are linear, because they are due to the earth’s orbit around the sun. (The word “apparent” is used here because the sun only appears to move, it is actually the complex motion of the earth which creates this effect.)
In the absence of accurate calendars the yearly solar motion can only be described in terms of the four accurately known dates; the two equinoxes and the two solstices. Without accurate clocks, the daily solar motion can only be described in terms of the angle of elevation of the sun shown by a shadow, with noon as the only fixed time.
In examining the daily and yearly solar motions the main variable is latitude, and five regions have been selected, as indicated in Figure 53.
53. Angular Basis of Regions of Latitude
Horizon Views of Sunrise and Noon
We can extend the observations of ancient European astronomers like Cogito, illustrated in Figure 54, into regions he never knew. However, the simple horizon view proves inadequate to describe the very high and very low latitudes.
54. Yearly Solar Motions in Northern Regions
For example, north of the Arctic Circle, there is no sunrise for the summer months as the sun never goes below the horizon. In winter, the sun never rises above the horizon. Near the equator, the solar motions are so great that the horizon view is again inadequate.
Zenith Views of Sunrise and Noon
An alternative way of visualising the three-dimensional motions in two dimensions is to use a “zenith view”. The zenith is the point immediately above the observer’s head, and the horizon is a circle. This is the view obtained by the observer lying flat on his back and gazing into the heavens. Two important circles have the zenith as centre. The smaller one is at an elevation of 66.5 degrees, and the larger is at an elevation of 23.5 degrees. The principle by which these circles are constructed is shown in Figure 55
55. Elevation Circles Imposed on Zenithal View
As said earlier, yearly solar motion can only be described in terms of the four accurately known dates; the two equinoxes and the two solstices. We return to this idea to deepen our mathematical understanding of the process. To avoid encumbering the narrative, the detailed mathematical arguments are given in a separate document.
The Relationship between Solar Elevation and Latitude
As indicated earlier, five latitude regions have been chosen, to show where Cogito’s measurements fit within the quadrant between the Pole and the Equator. Se is solar elevation at noon, L is latitude, and 23.5 is the earth’s angle of axial tilt.
On Midsummer’s Day, Se = 90 + 23.5 –L. or Se = 113.5 –L.
On Midwinter’s Day, Se = 90 – 23.5 –L. or Se = 66.5 –L
At the Equinoxes, Se = 90-L
We can use the equations above to construct Table 1 with Se values, for the five latitudes, and four times of year.
TABLE 1 SOLAR ELEVATION, Se, at noon
|North Pole||90 deg N||-23.5 degrees (below horizon)||0 degrees (at the horizon)||23.5 degrees|
|Arctic Circle||66.5 deg N||0 degrees (at the horizon)||23.5 degrees||47 degrees|
|North Region||55 deg N||11.5 degrees||35 degrees||58.5 degrees|
|Tropic of Cancer||23.5 deg N||43 degrees||66.5 degrees||90 degrees (overhead)|
|Equator||0 deg N||66.5 degrees||90 degrees (overhead)||113.5 degrees (below equator)|
|Tropic of Capricorn||-23.5 deg (23.5 deg S)||90 degrees (overhead)||113.5 degrees (below equator)|
The linear graphs in Figure 56 show how the sun’s noon elevation varies with the latitude of the observer, at the midsummer solstice, the two equinoxes and the midwinter solstice. At any latitude the midsummer values are highest and the midwinter ones are lowest.
56 Simple Linear Graphs of Table 1
Yearly Variation in Solar Elevation
However, we are principally interested in how solar elevation varies during the course of a year, and the data from Table 1 can be arranged to demonstrate this. Figure 57 shows the yearly graphs for the three northernmost latitudes.
57 Inverted V Graphs of Table 1
The apparently simple inverted V graphs give clues as to their true nature. Although there are only four positions on the x-axis, each graph has two identical values on the y-axis, (at the equinoxes) and the higher and lower y values, (the solstices) are symmetrically placed, above and below. This suggests the graph is not linear but a sine curve.
It is not possible to plot a sine function on the co-ordinates of Figure 57 because there are only four intervals on the x-axis. A newly-designed x-axis, for “a”, the times of the year, runs from 0 to 360, with intervals as simple multiples of fifteen. Thus, 0 represents the vernal equinox, 90 the summer solstice, 180 the autumnal equinox, 270 the winter solstice, and 360 the vernal equinox again.
This choice of x-axis values greatly simplifies the equations describing various sine functions. Purely co-incidentally, the x-axis values are close to the actual days of the year, which are, of course, either 365 or 366. Investigating this sine function, we discover.that the equations for the noon solar elevation, Se, of the five latitude regions, was given by a simple general formula.
Se = (23.5 Sin a) + (90 – L), where L is the latitude, and a is the time of the year, as defined above.
The yearly solar motions are shown in Figure 58, for six latitude positions, five of which would have been unkown to Cogito and Eos.
58. Sine Curves of Yearly Solar Motion
We can pick out a number of simple issues from Figure 58. At the North Pole, the noon sun dips below the horizon at the autumn equinox and does not re-appear again until he spring equinox. At the Arctic Circle, the noon sun touches the horizon at the winter solstice but does not dip below it.
Egypt and Babylon
As we know, Cogito’s observations were made high up in northern latitudes, but his contemporary Egyptian and Babylonian astronomers lived much nearer the Equator. Ancient Babylon lies on latitude 32 degrees, between the rivers Tigris and Euphrates, in what is now Iran. The ancient Greek name for the region is Mesopotamia, (“between the rivers”). The Tropic of Cancer is about 700 miles, (1, 120 Km.) on the Persian Gulf, and a long way from the Babylonian’s normal observation sites.
By contrast, ancient Egypt was a very large region and lay roughly between Latitude 20 and Latitude 30 degrees, and the Tropic of Cancer, (latitude 23.5 degrees N), lies about forty miles, (64 Km.), south of the city of Aswan. The northward-flowing River Nile provided an easy way for astronomers to move by boat, (59), across a wide range of latitudes.
59. Travel by Boat in Ancient Egypt
Figure 58 shows that, at the Equator, the noon sun is overhead only twice during the year, at the two equinoxes. Along the Tropic of Cancer, the noon sun is overhead only once in the year, at the summer solstice. Similarly, along the Tropic of Capricorn, the noon sun is overhead only once in the year, at the (northern) winter solstice.
If we imagine the Equator, and the two Tropics, Cancer and Capricorn, unrolled into a rectangular strip, with three parallel straight lines, we can show how the overhead noon sun gradually shifts during the course of a year. (Figure 60) This is the hottest solar radiation because the sun’s rays strike flat on to the earth. As may be expected, the relationship between solar elevation, Se, and the time of year, a, involves a sine curve.
Thus, Se = 23.5 sine a
60. The Path of the Overhead Sun between the Tropics
The word, “tropic” for the two latitudes parallel to the Equator, comes from the Greek word, “tropikos” meaning “to turn” because the apparent northward motion of the overhead sun, on 21 June, turns at the Tropic of Cancer, and begins to move south. It continues southward for six months, and then turns north on 21 December, at the Tropic of Capricorn. “Tropical” has now come to mean, “climatically hot”, typical of the weather between the two Tropics.
61. Rising and Setting of Pole Star to Establish E/W Line
Cogito’s Egyptian counterpart, (61) is better dressed, but does not seem to be as well-equipped. His sighting-staff looks rather crude, and there is no indication on the ground of a socket or hole to ensure that he will measure the rising and setting lines from exactly the same spot. He also has the advantage of a scribe and a written language to record his observations.
Sunrise and Sunset
Having examined the nature of apparent solar motions through the year, at different latitudes, we now turn to a detailed examination of daily solar motions. We need to look at the variation in solar elevation, Se, with respect to the compass bearing, b, and time of day, t. These latter two variables are exactly parallel to each other, so that bearing, 090o is also 06.00 hours, and bearing 180o is 12.00 hours. It is most convenient to use b as the x-axis because it simplifies subsequent equations. This variation of Se, with respect to b, can be examined for different latitudes and different times of year.
We begin with Cogito’s observation region, around latitude 55o N, and choose the equinoxes, because we know that sunrise is due east and sunset is due west. At sunrise and sunset the solar elevation is zero. Also we know that the solar elevation at noon is 35o (from Table 1) so a simple table can be constructed to display the three known positions, and a fourth estimated one.
Table 2 SOLAR ELEVATION AT THE EQUINOX (Latitude 55o North)
TIME OF DAY
Time in hours, t
Bearing In Degrees, b
|Solar elevation, Se, degrees||
Looking at the data we see the classic evidence of a sine curve, that is, two identical values on the y-axis, (at zero) with a higher and a lower value symmetrically placed, above and below this. The higher value is 35o and the unknown lower value is estimated to be -35o, that is, 35o below the horizon.
From Table 2 we can derive an equation, Sed = 35 sin (b-90) where Sed is the daily solar elevation and b is the bearing in degrees. Figure 62 is the graphical display of this sine function.
62. Sine Function of Sed
at the Equinoxes
It is reasonable to suppose that this sine function is basic to latitude 55oN, and that the curve is simply displaced upwards for the midsummer solstice, and downwards for the midwinter solstice. The only useful datum for the solstices is the noon elevation.
At the equinox, the noon elevation is 35o, and at the summer solstice it is 58.5o, a difference of 23.5o. Hence the equation for the summer solstice is SSed = 35 sin (b-90) +23.5.
For the winter solstice, the equation is WSed = 35 sin (b-90)-23.5
These equations are displayed in Figure 63
63. Sine Functions of Sed
at the Equinoxes and Solstices
This information now enables us to predict events like sunrise and sunset with great accuracy. Examining figure 63, it is clear that on Midsummer’s Day the sun rises close to bearing 045o (due north-east) and this will be at 03.00 hours. Similarly, it sets close to bearing 315o (due north-west), at 21.00 hours.
By contrast, on Midwinter’s Day the sun rises close to bearing 135o (due south-east) at 09.00 hours, and sets close to bearing 225o (due south-west), at 15.00 hours.
The general equation, Sed = (90-L) sin (b-90) where L
latitude, can be used to find the time and bearing of sunrise and sunset for the equinoxes, and solstices at any latitude.
Zenithal View of Solar Motion
It has already been explained that this view of the heavens is the most realistic, as the zenith is directly overhead, and the horizon is the circumference of a flat circular plane. Figure 64 shows how an observer at latitude 55oN, lying on his back, would see the movement of the sun during the course of a single day.
64. Complete Equinoctal and Solstitial Daily Solar Motions
The sine functions in Figure 63 were plotted on “Excel” using axial co-ordinates instead of Cartesian ones to give a zenithal viewpoint, (Figure 64). The figure is somewhat theoretical, as it displays the complete solar motions, above and below the horizon, and clearly, the “below horizon” part is not observable. The circuit for midsummer shows the distinct “cardioid nick” pointing southwards (180o). This is less pronounced in the equinoctial circuit, and apparently absent from the midwinter circuit.
Figure 65 gives a more realistic zenithal viewpoint, because the “below horizon” part is omitted. The black circle for the horizon is now the outermost ring. The only source of inaccuracy is that 0 and 360 should correspond, but here they do not and there is an extra unnecessary sector of 30o.
65. Daytime Equinoctal and Solstitial Solar Motions
The “hand-drawn” zenithal view in Figure 66 is more accurate, but there is very little difference, as the reader will note.
The points of the graph were found by taking 30o intervals of bearings, and marking the elevation angle on it, from a scale drawn on the N/S axis. When the points are connected up they show a roughly circular shape with a “nick” which faces south. This shape approximates to a well-known geometrical figure known as a “cardioid” or heart-shape. A true cardioid results from the interaction of two circles of equal size. As this is not the case here, the solar paths are not precisely true cardioids.
66. Zenith View of Solar Motions during a Single Day
THE MYSTERY OF LATITUDE
Cogito had confirmed that the further north you go, the higher the elevation of the Pole Star, but he had only measured this between Northern England and the far north of Scotland. He did not know what happened beyond the Arctic Circle, nor as far north as the Pole; neither did he know what happened at the Tropic of Cancer or the Equator.
Nevertheless, he did understand the idea of “elevation” and guessed that there must be a cold, northerly place where it was at a maximum, that is, directly overhead. Also there must be a hot, southerly place where it was at a minimum, that is, right on the horizon. Lacking the concept of a spherical earth, it was difficult for him to explain the observations of changes in Pole Star elevation.
Figure 67 tries to show a flat earth view of Pole Star elevation. The unknown cold region is indicated by blue ripples and the unknown hot region by red ripples. The narrow region of Cogito’s observations (between 54 and 58 degrees of latitude) is shown in the pink sector (between 50 and 60 degrees of latitude).
67 A Possible Prehistoric Impression
It is quite possible that some prehistoric genius saw that the quadrant (from overhead to the horizon) visualised on a flat earth, (67) might just as easily be a
real quadrant of a spherical earth on which we lived. If the sun and moon were round, might that be true of the earth as well?
We often find in our reading, that the ancient Greeks of the classical period, (first millennium BC), seem to have been the first to have discovered everything. It is more correct to state that the ancient Greeks were the first to write down their discoveries in a language that we can now translate and understand. Those Greeks were undoubtedly intelligent, but no more intelligent than the best minds in other societies of the time.
A Spherical Earth
We may guess that an important discovery like the sphericity of the earth was made very much earlier than the first records show.
68. The Familiar Spherical Earth
It was probably made independently in several other cultures who took a detailed interest in astronomy. This is a usual experience in the history of scientific discoveries.
This particular discovery is first attributed to the Greek mathematician, Pythagoras, in the sixth century BC, so it is reasonable to assume that idea was around in Greece, and other societies, for several centuries before this. This takes us into the period of our hero, Cogito. Indeed, the whole mystery of the meaning of latitude is the major piece of evidence for the fact that the earth is a sphere.
Other evidences include, (i) the obvious curvature of the oceans whereby the masthead of a tall ship appears before the hull, (ii) the curved shadow of the earth moving across the moon in the frequent lunar eclipses, and (iii) the roundness of the moon and sun.
69. Greeks Meditate on the Setting Sun
We know that the Greeks (69) derived some of their astronomy from the Egyptians and the Babylonians, who gave us our present system of measuring angles from a circle of 360 degrees.
Cogito understood the idea of angles as did most ancient peoples. It is highly unlikely that they used a 360 degree circle, but it is probable that they had devised a method of dividing up a circle or a quadrant into a number of equal sized sectors. The measurements on Cogito’s recording staff were capable of being converted into angles. Using modern trigonometry, when e is the angle of elevation, S is the length of the staff, and m is the length marked on the staff, we find Tan e = S/2m.
What Cogito, or some of his contemporaries, had realised was that measuring the angle of elevation of the Pole Star was a way of determining how far north you were. Mathematically, latitude, L, = e
Solar Belief Systems
We must remember that, despite the previous mathematical and scientific discussion, the movement of the sun in prehistoric times was hedged round with religious and mythological beliefs. The ancient Greek myths are the most familiar to us, especially the God, Apollo, who drove the four horses which pulled the sun’s chariot across the heavens each day. (See the illustration by Odilon Redon in my earlier essay, “Pre-Historic Science.)
It is likely that they, and all their contemporary astronomers in other societies of the time, shared the belief systems of their own people regarding the sun and its movements.
70. Scandinavian Horse and Solar Chariot
Many other cultures also saw the sun as a chariot, and nearer the home of Cogito and Eos, the Scandinavian peoples used symbolic solar chariots in their worship, (70,71).
71. Symbolic Solar Chariot
The curious object in Figure 71 was obviously incapable of wheeled movement but it is a kind of personification of a wheeled chariot, and somehow more dramatic and more real than an actual chariot. Sun symbolism was refined from a chariot into images as simple as a rotating wheel (72).
72. Scandinavian Solar Symbol
The Celtic peoples also displayed wheels as solar symbols in their artwork, (73) but in Cogito’s day, they had not yet made the journey from their Central European base in modern Austria and Germany across the sea to ancient Britain.
73. A Celtic Solar Symbol
The wheel or circle as a as a solar symbol probably goes back well into the Neolithic period and was to survive to the present day. All over Britain there are stones carved with “cup and ring” markings, (74, 75). We still do not know whether they were carved at the time the megalithic monuments were erected, or whether they were cut much later.
74. Cup and Ring-Marked Stones in Northumberland
75. Detail Drawing of Cup and Ring-Marks
Eventually these old pre-Celtic symbols carved on stones were adopted by the incoming Celts and, after many centuries, were ultimately transmuted into Christian symbols, (76).
76. Evolution of the Celtic Wheel-head Cross
Note that the principal design in Figure 76 is one of those classic, “psychologically reversing images” or “ambiguous figures” of which deskarati’s founder is so fond, (77). Is it four black spots in a white circle, or a white cross patee against a black background?
77. Ambiguous Figure
The deletion of a small part of the design to make a white cross patee on a black ground, (78) should remove the ambiguity, but curiously it seems only to emphasize the missing part.
78. A White Cross Patee
The Flat Earth Society
I first became aware of the intellectual difficulties of proving that the earth was a sphere as an undergraduate in the 1950s, and I record a personal recollection here. As in many university towns, there was a flourishing inter-collegiate debating rivalry, and there was a formal competition system within the University of London, at that period.
From time to time, I received personal invitations to speak at private debates that were outside this competition structure, and this was just such an invitation. The motion for debate was, “This House believes that the earth is flat”, and the principal speaker in favour, was to be a member of the Flat Earth Society. I had been asked to oppose the motion, and my hosts were the College of Estate Management.
I should explain that many of the students of this college were the sons of very well-to-do families who owned large estates in Britain and abroad. They sent their sons to CEM to learn the economics and practicalities of running their own estates or managing those of other wealthy people.
When I arrived at CEM for the debate, I was introduced to the speaker from the Flat Earth Society. He was a tall man, in his sixties, gentle and courteous with a quiet speaking voice. We quickly realised that he was OK for an uninterrupted lecture but would probably be upset by the rough and tumble of student debating with interruptions, barracking and points of order.
Consequently we treated him very gently when he introduced the motion. When I spoke, I included the points mentioned previously, on the obvious curvature of the oceans, so the masthead of a ship appears before the hull, the curved shadow of the earth moving across the moon in the lunar eclipses, the comparable roundness of the moon and sun, and finished with a clincher.
In 1957 the Russians had fired Vostok 1 into space and it circled the earth bleeping plaintively. Yuri Gagarin first went into orbit in his capsule on 12 April 1961, and at this distance in time I can’t remember whether this debate, (about 1960 or early 1961) was before or after his epic flight. (We now know why Yuri was chosen over other candidates. He was a small man; he fitted easily into the Mini-sized capsule, among all the hardware. Sadly, Yuri was killed in a plane crash in 1968 at the early age of 34 in training for another mission. He was, reputedly, a nice modest man and we salute his memory.)
79. Student Debates
It was only later when the Flat Earth man began to reply to our case that the thing began to come apart. He explained that the earth was not completely flat; it had a slight curvature. This shows why a ship’s masthead appears first over the horizon. One by one he answered our points and explained that Vostok and the capsules had indeed gone round the earth, and seen the curvature, but they were travelling round an upturned bowl, not a sphere. Remember that at this period, so-called space travel was only at the thickness of the peel from the orange. The beautiful and unequivocal view of the earth from space seen in Figure 68 was still some years away.
In trying to restore the case for a spherical earth, we were reduced finicky arguments. The actual curve of the oceans was measurable; if the middle of a mile-long, straight steel girder touched the sea, it would be off the water by four inches at each end. All the areas of the earth had been mapped; they would only fit to the surface of a sphere. To my surprise, it was clear that we had failed to demolish the flat earth case. The contest was nowhere as unequal as I had supposed.
At the end, the students had to vote on the arguments they had heard. In my opinion, the flat earth motion had not been defeated, and modern science had failed to prove its argument. Unfairly, as is often the case, the majority voted for a round earth.
We parted company amicably with the flat earth man, who courteously declined an invitation to dine after the debate, and we set off to an excellent meal in a local restaurant, as guests of the CEM Debating Society.
I realised that the discovery, by the ancients, of the earth as a sphere, was a far greater intellectual breakthrough than I had thought. The powerful argument, from the elevation of the Pole Star with latitude, had not occurred to me then. Cogito, and his wilderness travels across the north of Britain, had realised an important truth about the nature of the earth.
80. The Return Journey- Part One
Cogito and Eos return
Now their main mission was accomplished Cogito and Eos planned to return by the quickest route (80) to the home village of Eos, in the north of England. After this, they had to make a long journey south to the great plain in the chalk country. They might be able to get there before the autumn equinox, but Cogito thought it was too far for them to manage this. His plan was to travel down the east coast of Scotland, which had fewer mountains and fewer sea lochs to negotiate than the west coast.
81. Helmsdale River
They left the north coast at Duncansby Head and kept to the coast, down to the settlement at Wick, and then after several days they crossed the Helmsdale River, (81). Their route along the coast was blocked, after several days march, by a large estuary, the Dornoch Firth. There was no need to sound their ceremonial trumpet as they could see the ferry approaching the north shore, and there were people waiting there to cross.
82. The Cromarty Firth
Once ashore, they set off for the next estuary, the Cromarty Firth, (82), which was only a few miles away across low hills. This time they did not cross the Firth, over to the Black Isle, but marched west along the north shore to the settlement at Dingwall, and then over the hills to Beauly, (bew lee) This was familiar ground as they had passed through Beauly on the way west from Inverness, across to Suilven. They went from Beauly to Inverness, and turned south down the Great Glen as quickly as possible.
Cogito had explained to Eos, that he wanted to avoid the groups they had met on the way north, because this would delay them considerably. They could not avoid Beauly and Inverness, because of simple geography and he was reconciled to meeting familiar faces all the way down the Great Glen.
83. The Return Journey- Part Two
However, they would take a different route over the mountains to avoid the western sea lochs and get to the River Forth more directly. Eos knew he had spent some time discussing routes with well-travelled traders, and had committed all this to memory. As it was still midsummer, the mountain routes would be quite sensible for them.
84. Glen Coe
They had come down the Great Glen to the head of the Linnhe Loch at Fort William, (83) and continued south along its eastern shore to Ballachulish, where they struck inland. The route lay through the narrow, and gloomy confines of Glen Coe, (84) and out on to the Rannoch Moor, (85) a wide plain of bogs and lochans, reminding them of the western Highlands. From here, their way was south through the Black Mount, with more bogs and lochans, to the small settlement at Tyndrum.
85. Rannoch Moor,
They then turned south-east into much easier country, along the wide valley of Strath Fillan, and they camped beside Loch Fillan, (86).
86. Loch Fillan
Next day they moved east along Glen Dochart, climbing a few miles over the hills to the head of Loch Earn, and a more mountainous region. From here, their route was due south to the pleasant valley of Strathyre, eventually turning south-east, through the mountains of the Trossachs, (87) to the settlement at Callander.
87. The Trossachs
Continuing south-east they left the mountains, and entered much flatter country around the River Forth, which they crossed near Stirling.
Although Cogito had explained that he wanted to avoid delays due to socialising, as much as possible, he felt they could not reasonably ignore the astronomers’ group from Cairnpapple Hill. As they had been so kind to them in providing hospitality, an escort, and a ceremonial trumpet, the least they could do was call in on their way home. Eos agreed that courtesy demanded a return visit.
The country, southward from the River Forth crossing, was made of gently rolling hills, and easy walking for Cogito and Eos. The main problem was to find Cairnpapple Hill again, because when they left there, with the escort party, they had travelled eastwards to the River Clyde. Fortunately, the astronomers were widely known about in the area, and it was only necessary to make general enquiries in the settlements they passed, to be given friendly and enthusiastic directions.
As explained earlier, it was only a modest elevation, but had the nickname, “Between Two Seas”, because from the top you could see both the Firth of Forth to the east, and the River Clyde to the west. We know that the hill was in use as a sacred site from the late Neolithic period onwards. The archaeologists, Ann MacSween and Mick Sharp, say of Cairnpapple, “It is an exposed vantage point, but the panorama is spectacular…It would have been an ideal spot from which to observe the rising and setting of the sun and moon in all seasons,” (pages 178-179). See “References” at the end for fuller details. The site today is open to the public, including the internal megalithic burial chamber.
As Cogito and Eos neared the site, they were met by one of the boys who had been part of their escort party to Argyll. The news of their coming had been carried by word of mouth, by other travellers in the same general direction. They got to the hill, on a bright evening under a lowering cloudy sky, (88).
The two travelling astronomers found they were guests of honour at a feast of the whole community. They stayed with the people for several days, giving Cogito and Eos a chance to explain what they had discovered about the mystery of latitude and the elevation of the Pole Star.
Before leaving, Cogito had explained that they wanted to head for Northern England by a different route from their northward journey. The ostensible reason he gave was to learn more of the routes in the region, rather than to avoid too many social events.
88. Evening on Cairnpapple Hill
He had a clear idea of where he wanted to go, because he was reasonably familiar with the area, and as his escort discovered, he would brook no opposition or accept any suggestions. Eos had found Cogito an easy-going companion and this determination and inflexibility was new to him.
The party left Cairnpapple and headed due south to the River Clyde, which they crossed near Carstairs. (89). At this point the escorting party bade them farewell as they crossed the river in their coracle. Once they were gone, Cogito relaxed and Eos was alone again with his cheerful and optimistic leader. They were now moving south-eastwards, through Biggar, and along the Biggar Water, a tributary of the River Tweed. When they reached the Tweed they followed its south bank to Innerleithen.
89. The Return Journey- Part Three
This was where they had crossed the Tweed going northwards. Now they headed due south, up over the hills to Ettrick, and on to Eskdalemuir. It was a very lonely spot and they found no settlements and met no people on their travels. Cogito seemed to relish the loneliness and Eos could see why he was called, “Old Wilderness”.
Their route took them south-eastwards along Eskdale to Langholm, and Longtown, among the flat lands around the Solway Firth. On reaching the settlement at Carlisle they were able to barter for some fresh food. Their next objective was the Eden Valley, a region now familiar to both Cogito and Eos. They should be back to the home village of Eos in just a few days.
REFERENCES AND ILLUSTRATIONS
A. “THE FABER ATLAS”, edited by D J Sinclair, Geo, Oxford, 1961.
The atlas contains maps of the physical geography of the world, and some of the Scotland plates have been modified from the originals, to illustrate the travels of the pre-historic surveyors, described in this series of essays.
B. “INTRODUCTION TO ASTRONOMY” by Cecilia Payne-Gaposchkin, University Paperbacks, 1961
This is an excellent guide to a whole series of astronomical concepts and it is well illustrated. Historical astronomy is well covered and I have found many of the ideas and information presented there were invaluable in writing this essay.
C. “PREHISTORIC SCOTLAND” by Ann MacSween and Mick Sharp, Batsford, 1989
This book is an excellent, authoritative and well-illustrated gazeteer of most of the most important pre-historic sites in Scotland.
There is a short, two-page, account of the archaeology of Cairnpapple Hill, and its full complex history, unravelled by the distinguished British archaeologist, Stuart Piggott during the 1940s. The other sites mentioned in this essay, like Temple Wood, Clava, and Strontoiller are also fully described.
1. Pre-Historic Stone Constructions (“Celtic Britain” Homer Sykes, Cassell, 1997)
2. A Simple Demonstration of Variation in Shadow Length (Author)
3. Details of the “Old Wilderness” Staff (Author)
4. Cogito’s Journey North (Author)
5. Roseberry Topping in Late Winter (google images)
6. Cogito Takes a Sighting of Polaris (Author)
7. A Modern Version of the Ancient Coracle (“Encyclopaedia of Ships and Seafaring”, editor Peter Kemp, Reference International, 1980)
8. The River Tees near Middleton (“Wainwright on the Pennine Way”, photographs by Derry Brabbs, Michael Joseph, 1985)
9. Busy Paddling the Coracle (“Scotland’s First Settlers”, by Caroline Wickham-Jones, drawings by Alan Braby, Batsford, 1994)
10. The River Tyne near Hexham (google images)
11. The Eildon Hills near Melrose (google images)
12. From the North York Moors to the River Tweed
13. The Chambered Mound on Cairnpapple Hill (google images)
14. The Latitude of the British Isles (Author)
15. The Trigonometrical Basis of Star Observations (Author)
16. Dumbarton Rock in the Firth of Clyde (by Joe Porter, via google images)
17. The Senior Priest-Astronomer’s Trumpet (After a google image)
18. Route from the Tweed into Argyll (Author)
19. The Modern Corran Ferry Crossing Loch Linnhe (google images)
20. Loch Fyne, Argyll, Scotland (google images)
21. The Temple Wood Stone Circle, Argyll, Scotland (google images)
22. The Strontoiller Stone Circle near Oban, Argyll (google images)
23. The Strontoiller Standing Stone (google images)
24. Oban to Inverness via the Great Glen (Author)
25. Heading North to Inverness (google images)
26. The Moray Firth (google images)
27. The Clava Site near Inverness (google images)
28. Route from Inverness to Duncansby Head via Suilven (Author)
29. Knockan near Suilven (google images)
30. Aerial View of Suilven (google images)
31. Suilven and its Lochans, from Stac Pollaidh (google images)
32. The Approach to Cul Mhor (Author)
33. The Boulder Field on Cul Mhor (Author)
34. The Twin Peaks of Cul Mhor (Author)
35. The Summit Boulder Field (Author)
36. The Mountains beyond Knockan (google image)
37. The Wide Valley of Strath Oykel (google image)
38. The Oykel – a Salmon River (google image)
39. Ben Loyal, Sutherland, NW Highlands of Scotland (google image)
40. The Kyle of Tongue (google image)
41. The Flow Country of Lakes and Peat Bogs (google image)
42. The Sea Cliffs and Stacks of Duncansby Head (google image)
43. The Island of Stroma in the Pentland Firth (Author)
44. The more southerly Orkney Islands (After a diagram in “John O’ Groats” by Bill Mowat, published locally in Caithness)
45. The stars are barely visible at 3.00 am in July (Author)
46. Eider Ducks in the Northern Seas (google image)
47. Mallard Ducks in Freshwater (google image)
48. Trade Goods Carried for Barter (google images)
49. Votives from Different Parts of Europe (“Life in Prehistoric Times” by Linda Gamlin, Readers’ Digest 1997, and “Prehistoric Orkney” Anna Ritchie, Batsford, 1995)
50. Non-Verbal Communication (Author)
51. Solar Motion in High Northern Latitudes (Author)
52. Axial Tilt of the Earth at Midsummer (Author)
53. Angular Basis of Regions of Latitude (Author)
54. Yearly Solar Motions in Northern Regions (Author)
55. Elevation Circles Imposed on Zenithal View (Author)
56 Simple Linear Graphs of Table 1 (Author)
57 Inverted V Graphs of Table 1 (Author)
58. Sine Curves of Yearly Solar Motion (Author)
59. Travel by Boat in Ancient Egypt (“Pyramids” by Anne Millard, Kingfisher, 1996)
60. The Path of the Overhead Sun between the Tropics (Author)
61. Rising and Setting of Pole Star to Establish E/W Line (Millard, op. cit)
62. Sine Function of Sed
at the Equinoxes (Author)
63. Sine Functions of Sed
at the Equinoxes and Solstices (Author)
64. Complete Equinoctal and Solstitial Daily Solar Motions (Author)
65. Daytime Equinoctal and Solstitial Solar Motions (Author)
66. Zenith View of Solar Motions during a Single Day (Author)
67 A Possible Prehistoric Impression (Author)
68. The Familiar Spherical Earth (google image)
69. Greeks Meditate on the Setting Sun (“Symbolism” by Michael Gibson, Tashen, 1999)
70. Scandinavian Horse and Solar Chariot (“An Illustrated Encyclopaedia of Traditional Symbols” by JC Cooper, Thames and Hudson, 1984)
71. Symbolic Solar Chariot (“Larousse Encyclopedia of Mythology” general editor, Hamlyn, 1969)
72. Scandinavian Solar Symbol (Larousse, op. cit)
73. A Celtic Solar Symbol (“Celtic Art” by I M Stead, British Museum, 1985)
74. Cup and Ring-Marked Stones in Northumberland (? “Northumberland” ?)
75. Detail Drawing of Cup and Ring-Marks (? “Northumberland – A Sense of Place”?)
76. Evolution of the Celtic Wheel-head Cross (Author, with crosses from “Exploring Celtic Britain” by Denise Stobie, Collins & Brown, 1999)
77. Ambiguous Figure (Author)
78. A White Cross Patee (Author)
79. Student Debates (Author)
80. The Return Journey- Part One (Author)
81. Helmsdale River (google image)
82. The Cromarty Firth
83. The Return Journey- Part Two (Author)
84. Glen Coe (google image)
85. Rannoch Moor (google image)
86. Loch Fillan (google image)
87. The Trossachs (google image)
88. Evening on Cairnpapple Hill (google image)
89. The Return Journey- Part Three (Author)
90. Home Ground in the North Country (Sykes, op. cit)