Are Britain's ancient sites lined up more than chance allows? I mapped 50,822 churches, barrows, standing stones, stone circles, hillforts and holy wells, counted every straight line through them in four landscapes, and asked how many lines random points would give.
On 30 June 1921 Alfred Watkins, a Hereford businessman, photographer and antiquarian, was in the hills near Blackwardine in Herefordshire when, as he told it, he saw old sites falling into line across the landscape: a church, a mound, a camp on a hill, a standing stone. He went home, ruled straight lines across his Ordnance Survey maps, and found more. In The Old Straight Track (1925) he argued that these "leys" were the sighted trackways of prehistoric Britain, marked by mounds, beacons, moats and mark stones.
Archaeologists were not persuaded, then or since. In the 1960s and 1970s the idea came back in a new form: leys as lines of earth energy, promoted by John Michell's The View Over Atlantis (1969), which also gave us the Saint Michael's line, a long alignment of hilltop sites dedicated to the archangel from Cornwall towards Norfolk. In 1980 the statistician Simon Broadbent asked the question that matters most in a paper called "Simulating the Ley Hunter": how many alignments would you expect if the sites were not lined up at all?
This page asks the same question with today's open data. I put 50,822 old sites in Britain on one map, counted every straight line of three, four, five and more of them in four landscapes that ley hunters made famous, and compared each count with the same number of points scattered at random. I have tried to be fair to the idea. The answer is plain, though, and it is worth seeing why.
Each dot is one site: a church or chapel (any date, from Wikidata), a barrow or cairn, a standing stone or other megalith, a stone circle, a hillfort, or a holy well. Pick a landscape to see the straight lines of four or more sites that my count finds there, drawn in ochre. Then switch to Random points: the same number of points scattered at random over the same land, with the lines that they make, in teal. You can also follow the Saint Michael's line and the line G. H. Piper described in 1882.
Before looking at real sites, it helps to see what random points do. Below is a square 40 km across, the size of each of my sample landscapes. Scatter some points in it at random and the box draws every straight line of four or more of them: lines between 1 and 20 km long, with every point within half the corridor width of the line between the two end points. Push the sliders.
0 lines of four or more points, drawn
The number of lines grows much faster than the number of points. A set of four points needs one pair to define the line and two more that happen to fall inside its narrow corridor, so the expected count rises roughly with the fourth power of the number of points and the square of the corridor width. Double the points and you get about 16 times as many four-point lines; double the corridor width and you get 4 times as many. With 200 random points in my 40 km square and a 100 m corridor, the formula expects about 1,472 lines of three, 130 of four and 8 of five. That is the heart of Broadbent's point and of Tom Williamson and Liz Bellamy's book Ley Lines in Question (1983): in a landscape as crowded with old sites as Britain's, lines are unavoidable.
Now the real thing. I took four landscapes, each a 40 km square (West Penwith is smaller, because the sea is in the way): Watkins's own Herefordshire, around Hereford and Blackwardine; West Penwith, the tip of Cornwall that John Michell surveyed for leys in the 1970s; the chalk of Wiltshire from Avebury to Stonehenge; and the country around Cambridge, the subject of Watkins's last book. Barrow cemeteries and town churches would otherwise count many times over, so I first grouped sites into places: anything within 250 m of a place's first site joins it. Then I counted every line of three, four, five and six places, and did the same for random points, 300 times over for each test.
I used two kinds of random points. The first scatters points evenly over the same land. The second keeps the real pattern but nudges every real place up to 1 km in a random direction, which keeps the clusters (the valleys, the villages, the barrow-strewn downs) and breaks up any exact lines. If ancient builders had set out sites on deliberate straight lines, the real count should beat both.
In all four landscapes the real sites make more lines than evenly scattered points: between 1.5 and 5.4 times as many lines of four. In Herefordshire I count 759 lines of four places, against an average of 494 from even scatter (95% of runs between 368 and 689). Taken alone, that would look like a discovery.
It is not, because real sites are not scattered evenly. Churches sit in villages and towns, villages sit along rivers and roads, and barrows crowd onto chalk ridges. Crowding raises the local density, and the number of lines rises with density much faster than the density itself. Against random points that keep the real crowding, the real counts sit between 0.94 and 1.14 times the average, and in all 4 landscapes inside the range that chance gives. Herefordshire's 759 compares with 721 on average from the nudged sites (95% of runs between 577 and 952).
The real landscapes are full of straight lines. Random points that crowd where the real sites crowd draw just as many.
Ley hunters often argued that the real leys were prehistoric and that churches only came later, built on older sacred spots. So I also ran the test with prehistoric places alone. West Penwith gives the most interesting result: 103 lines of four prehistoric places, against 19.2 from even scatter and 35.5 when I draw the same number of places at random from all the real places in Penwith. But the nudged version of the prehistoric sites themselves gives 76.1, and the real count is beaten or matched in 14% of those runs. Penwith's barrows, quoits and stones cluster together, largely apart from the churches, so a random draw of places misses their crowding; keep the crowding and the excess goes. In Wiltshire the prehistoric count is enormous, because barrow groups are dense there, and it too sits within the clustered chance range.
The lines that the computer finds are worth a look on the map. The longest real line in West Penwith runs for 18.8 km from Ballowall Barrow on the coast west of St Just, through Chûn Quoit, Mên Scryfa and four barrows, to St Ia's church in St Ives: 8 places, just the sort of line a ley hunter would be proud of. The longest line in Herefordshire is made of 7 churches and chapels, most of them in Hereford itself, among them a United Reformed church and an almshouse chapel. A line-finder does not care how old a site is, and nor did some of the leys.
Williamson and Bellamy's sharpest point was that Britain is so full of old sites that almost any line will clip a few. With my data and a strict tolerance, the effect depends a great deal on where you draw. I dropped 1,000 straight 20 km lines at random over the land of Great Britain and of each landscape and counted sites within 50 m of each line.
Across Britain a random 20 km line passes within 50 m of 0.38 sites on average, and 2.1% of lines pass three or more. On the Wiltshire chalk, 21% do. My data hold only six kinds of site, and only those that Wikidata, OpenStreetMap and the Atlas record. Watkins also counted mounds, moats, beacons, mark stones and castles, and a pencil line 1 mm wide on a map at one inch to the mile already covers about 63 m of ground. With every extra kind of mark point and every extra metre of tolerance, the count of chance lines climbs, as the curve above shows.
The English Saint Michael's line, first described by John Michell in 1969, runs east-north-east from St Michael's Mount in Cornwall through hilltop sites linked to the archangel, among them St Michael de Rupe on Brent Tor, Creech St Michael, Burrow Mump and St Michael's church on Glastonbury Tor, to the Norfolk coast. I drew it as the straight line from St Michael's Mount through the church on Glastonbury Tor and carried it on until it leaves Britain. It runs 572.3 km on a bearing of 61.4 degrees and meets the east coast 1.1 km from Gorleston-on-Sea in Norfolk.
The named sites in between do lie close to it: Burrow Mump church 230 m away, Creech St Michael 242 m, and Brent Tor church 1,311 m. Then I counted every site within 1 km of the line, leaving out anything within 1 km of the two points that define it, and compared the count with 2,000 copies of the same line rotated by up to 20 degrees and shifted sideways by up to 80 km.
Within 1 km, the real line passes 393 sites; a moved line of the same length would pass 344 on average, which puts the real line at the 74th percentile. It does better on prehistoric sites (193 against 90, the 94th percentile), mainly because it crosses the barrow country of Wessex, and on churches dedicated to St Michael (16 against 9.2, the 93th percentile). Neither passes the usual 95% bar, and I ran several comparisons, so one or two near misses are to be expected. At a tighter 100 m, the line passes 25 sites against 35 expected: fewer than an average moved line.
So the Saint Michael's line is a good line, chosen by someone who knew where the archangel's hilltop churches are, and it runs through a part of England unusually rich in barrows. It is not an exceptional one.
Watkins cited an earlier observation by G. H. Piper, read to the Woolhope Naturalists' Field Club in 1882: a line from the Skirrid mountain north to Arthur's Stone "would pass over the camp and southernmost point of Hatterall Hill, Oldcastle, Longtown Castle, and Urishay and Snodhill castles." I drew it from the Ordnance Survey's point for Ysgyryd Fawr to Arthur's Stone near Dorstone, 24.9 km. The places Piper named lie between 143 m and 1,908 m from the line.
Castles, a hamlet and a hill within a few hundred metres to two kilometres of a 25 km line is not a strong test of anything: the line was drawn after looking at the map, and the tolerance is generous. In my own data only 1 site lies within 50 m of the line (the church at Clodock); the same line dropped at random over the surrounding land passes 1.0 sites on average.
I find no sign, in any of my four landscapes or on the Saint Michael's line, that old sites in Britain are lined up more than chance allows once you allow for where they cluster. That matches what Broadbent, Williamson and Bellamy and others concluded decades ago, now with tens of thousands of sites and open data that anyone can check.
That is not the same as saying straight lines meant nothing to the people who built these sites. Some prehistoric monuments are straight on purpose: stone rows, the long ditches called cursuses, avenues to henges, and barrows set along ridges in rows. Roman roads are famously straight. Those are lines of a few hundred metres to a few kilometres, visible on the ground and dated. Leys are different: long lines drawn on a map between sites of very different ages, from prehistoric barrows to recent chapels, and a map with enough dots on it will always give you some.
Watkins comes out of this rather well as a person. He looked hard at his own landscape, photographed it, and wrote down what he saw so that others could check. The checking just took a computer.
Sites. Churches and chapels: every Wikidata item in the United Kingdom that is a church building, with coordinates (35,298 in Great Britain after merging). These are of all dates, from Saxon to modern, because Wikidata does not give a reliable founding date for most of them; Watkins and later ley hunters also used churches of any date on the assumption that they stood on older sites. Barrows and cairns, megaliths and standing stones, and stone circles come from OpenStreetMap and Wikidata, cleaned for my earlier projects Barrows of Europe, Megalith Highway and Same Shape, Different Millennia. Hillforts come from the Atlas of Hillforts of Britain and Ireland. Holy wells are those marked as holy in OpenStreetMap and Wikidata, from my Holy Wells project. Records within 50 m of each other, or sharing a Wikidata item, are merged into one site: 55,563 records became 50,822 sites. Coverage is uneven: Wikidata holds many scheduled monuments, so barrows are thickest where they were listed in detail, as in Wessex, and some famous sites are missing, including Arthur's Stone in Herefordshire, which I placed from its Wikipedia article. Not every Wikidata church is placed precisely: 1,378 have coordinates given to three decimal places (about 100 m) and 152 to two or fewer.
Places. To stop barrow cemeteries and town-centre churches counting many times over, sites are grouped into places in a fixed order (prehistoric first, then wells, then churches): each site joins the first place whose first site is within 250 m, or starts a new place. Britain has 41,920 places.
Alignments. A line of k places is a set of k places whose two outer places are between 1 and 20 km apart and whose other places all lie within 50 m (a 100 m corridor) of the straight segment between them, measured on the British National Grid. Each pair of end places with m places inside its corridor contributes C(m, k minus 2) lines of k. I count lines of 3, 4, 5 and 6, and also show corridors of 50, 200 and 400 m. Maps show only the longest maximal lines (lines not contained in a longer one).
Chance. For each landscape and set of places I made 300 random versions with the same number of points: even scatter over the land in the same box (Natural Earth 10 m coastline), the real places each moved up to 1 km in a random direction (staying on land), and, for prehistoric or church places, the same number drawn at random from all real places in the landscape. For uniform points the expected number of lines of k has a simple form: the number of pairs, times C(N minus 2, k minus 2), times the average of (w d / A) to the power k minus 2 over pairs between 1 and 20 km apart, where w is the corridor width, d the pair distance and A the area. My simulations match it closely (for 400 points, 2,106 lines of four simulated against 2,105 from the formula).
Named lines. The Saint Michael's line runs from St Michael's Mount through St Michael's church on Glastonbury Tor (Wikidata coordinates) to the east coast. That is my choice of definition: the line is described in different ways by different writers. Counts leave out sites within 1 km of these two anchors. Moved copies are rotated about the line's midpoint by up to 20 degrees and shifted by up to 80 km, and kept only if at least half their length is over land; rates are per 100 km over land. Piper's line runs from the Ordnance Survey Open Names point for Ysgyryd Fawr (a name position, not the summit) to Arthur's Stone. I take his "camp" on Hatterall Hill to be Pen Twyn hillfort at the hill's southern end; that is my reading. The sources of every named point are in data/named_points.csv.
Limits. This is a test of six kinds of site in open data, not of every mark point a ley hunter might use. A different corridor, length range or set of landscapes would give different counts, though the comparison with chance is what matters and it holds at every width I tried for even scatter. The nudged-points test is deliberately strict: it keeps clustering at scales above 1 km, so it cannot tell clustering from lines that run along a ridge or valley. A line of sites along a ridge is a real pattern, but it is a pattern of the ground, not evidence of a planned ley.
Related: Within Sight (could hillforts see each other?), How Roman is your road? (straight lines that really were planned), Holy Wells.