Mesolithic dates at Stonehenge and the bluestone quarries

Trench 1 at Carn Goedog in 2016, viewed from the south (photograph by Adam Stanford). Pearson, Mike Parker, Josh Pollard, Colin Richards, Kate Welham, Chris Casswell, Charles French, and others, ‘Megalith Quarries for Stonehenge’s Bluestones’, Antiquity, 93 (2019), 45–62 http://dx.doi.org/10.15184/aqy.2018.111

Every so often someone rediscovers that Mesolithic radiocarbon dates keep appearing in the Stonehenge story — beneath the old car park, at Craig Rhos-y-Felin, at Carn Goedog — and presents this as an anomaly the discipline has declined to confront.

The dates are real. They are also all published, most of them in the same reports that establish the Neolithic chronology, and those reports are considerably more candid about the awkwardness than the rediscoverers tend to notice. What follows sets out what has actually been dated, at what depth, in what context, and on what material, because that is where the argument lives.

Two things emerged from doing this carefully that I had not expected. "Mesolithic" is doing far too much work as a single category: the Early Mesolithic and Late Mesolithic material at these sites occur in different kinds of context and mean different things. And the single find most often offered as a bridge between Stonehenge and the quarries — a rhyolite fragment in a car park pit — comes from a layer that was never radiocarbon dated.

Declaration: I am a co-author on Bevins et al. (2025), cited below, and have published separately on the glacial transport question.

The car park pits: what was actually found

Faith and Lance Vatcher excavated the car park extension between 7 February and 18 March 1966, ahead of works by the then Ministry of Public Buildings and Works (trench C82). Three circular holes appeared as the surface was cleaned down to chalk, in a line running roughly east–west on the 315ft contour, with a fourth, irregular disturbance further west. Centre to centre, A to B is 9.75m and B to C is 12.29m, with a further 13.72m from A to the irregular feature.

All three held large posts. The post in A was about 66cm across at 75cm depth, B about the same, C between 61 and 83cm. Holes A and B had recesses cut into the chalk on their south-east sides that the Vatchers read as seats for wedging timbers, and in B the section cut clean across traces of two such timbers running from the side of the hole to the side of the post. Both B and C had material accumulated on the base before the post went in — a 5cm scatter of soil in B, five thin layers in C — so the holes stood open for a while after being dug. Pit C did not show a clear postpipe; a post may have slipped out when the timber was largely rotten.

The Vatchers assumed a Late Neolithic date. What changed that was Susan Limbrey's charcoal identification: predominantly pine, a species not expected on the chalk in the Late Neolithic. That identification is what prompted the submission of two samples for dating.

One correction is due here. Allen states that all the material submitted to Limbrey was pine. Her own appendix to the Vatcher report says most of it was, and records that two samples from Hole C contained Rosaceae of "Crataegus type" — hawthorn, apple or whitebeam — alongside the pine. The pine dominates, but it is not the only species present, and arguments about deliberate selection of timber should be built on the appendix rather than the summary.

Allen's Table 3 in Stonehenge in its Landscape is worth reproducing, because it contains detail that rarely travels:

Feature	Diam (m)	Depth (m)	Flint	Rhyolite chip	Charcoal	Decayed wood	Burnt bone	Antler pick marks	Lab no	Determination	Calibration
Treehole	2.5	0.71	–	–	–	–	–	–	–	–	–
Pit A	1.93	1.34	–	–	Yes	Possibly	–	Yes	HAR-455	9130±180 BP	8820–7730 cal BC
Pit B	1.27–1.47	1.27	–	–	Yes	Yes	Yes (1)	Yes	HAR-456	8090±140 BP	7480–6590 cal BC
Pit C	1.52–1.77	1.55	Yes	–	Yes	Yes	–	Yes	–	–	–
Pit 9580	1.9	1.3	Yes (4)	Yes (1)	Yes	–	–	–	see below

Three points follow that the popular summaries lose.

Only two of the Vatcher pits were dated. Pit C has no determination at all. The commonly quoted range for the car park posts — "8500 to 7000 BC", or Allen's own summary phrasing of 8500–7650 cal BC — characterises the complex; it is not a set of measurements. The two determinations calibrate to 8820–7730 and 7480–6590 cal BC. HAR-456's range falls entirely outside Allen's summary range, and both carry large errors (±180 and ±140 BP) typical of their vintage. Anyone building an argument on tight chronological coincidence between these posts and something else should look at those error terms first.

All three postpits show antler pick marks. The Vatchers put it as "apparently dug out with antler picks", so this is an inference from tool marks rather than a recovered tool. It is not a chronological argument either — antler picks are ubiquitous in the Neolithic — but it does establish that these were deliberately excavated features rather than natural hollows.

The relationship to Stonehenge is undetermined, and Allen says so. He notes that the pits' span is too great for them to have supported horizontal members, that they are more likely individual uprights, and that the line of poles may represent formal display of some kind predating Stonehenge by over four millennia. Whether the five features were contemporaneous cannot be confirmed on radiocarbon grounds — his words, not a sceptic's.

It is worth registering that the 1973 report predates the radiocarbon dates entirely. The Vatchers had no pottery and no absolute dating, judged the holes Neolithic on morphology, and closed by endorsing C.A. Newham's argument that the three lined up with solar and lunar setting phenomena viewed from the Four Stations and the Heel Stone — which would have required posts standing some 30ft above ground. The Mesolithic determinations arrived afterwards and removed the frame the excavators had published in. That is worth remembering when the car park posts are pressed into service as evidence of continuity with the monument: the one published attempt to connect them to Stonehenge directly was made on the assumption that they were four thousand years younger than they are.

Pit 9580, and the rhyolite fragment

This find carries almost the whole weight of the Mesolithic-Stonehenge argument, so it deserves the full sequence.

Pit 9580 was recorded by Wessex Archaeology in 1988–9 (Martin Trott's unpublished notes, synthesised by Allen). The original feature was a circular hole cut into soft weathered chalk, about 1m across and 1.3m deep, filled with horizontally bedded layers of clean chalk rubble (contexts 9587–9592). Allen reads the horizontal bedding and clean chalky character as deliberate backfilling rather than natural silting.

At a later date the pit was widened — a probable recut — producing a broad shallow pit about 1.9m across and only 0.7m deep, with its own primary (9588), secondary (9585) and tertiary (9581–2) fills. Allen's reading is that the feature was originally a postpit like the others, and was subsequently partially backfilled, altered and redesigned, possibly because a post was removed and the hole had to be enlarged to free it.

The determinations, from Allen's Table 4, are all on Pinus charcoal:

Fill	Context	Depth (m)	Lab ref	Determination	Calibration
Tertiary	9582	0.25–0.35	OxA-4220	8400±100 BP	7580–7090 cal BC
'Recut': secondary	9585	c. 0.40	OxA-4219	8520±80 BP	7700–7420 cal BC
'Recut': base of secondary	9585	0.57	GU-5109	8880±80 BP	8090–7690 cal BC

Context 9581 does not appear. The soil monolith sampled the secondary fill and the tertiary sequence, but Allen states that samples of the upper tertiary fill — 9581 — were not taken. The rhyolite fragment, 62g, sat at 0.2m depth in 9581.

That disposes of the strongest version of the sceptical reading. Brian John has argued that the rhyolite must be Mesolithic because a Mesolithic determination came from the tertiary fill, and that the layer is essentially homogeneous with no stratigraphic break to justify a later intrusion. But 8400±100 BP is from 9582, a different context 5–15cm deeper, and 9581 is undated. The date and the find are not in the same layer.

Allen's own reasoning about the fragment is also partly circular, and he does not quite acknowledge it. He treats the rhyolite as indicating that 9581 is contemporary with the dressing of the bluestones, then cites 9581's phase 3 attribution when discussing the environmental sequence. Scaife does the same in his pollen report within the same chapter. If that were the whole argument it would not be worth much.

It is not the whole argument. The molluscan evidence stands independently:

• Local mollusc zone 1 (chalk backfill and primary recut fills): dominated by shade-loving species, the Zonitids and the Punctum group, with Ena montana and Euconulus fulvus indicating mature ancient woodland with some leaf litter.
• Zone 2 (recut secondary fill 9585): gradual increase in open-country species, decline in E. fulvus, absence of E. montana, Pupilla muscorum and Helicella itala present. Open woodland with grass.
• Zone 3 (tertiary fills 9581, 9582): Allen describes a distinct break rather than a transition. Rapid increase in open country species, marked decline in shade-loving elements, P. muscorum superabundant at 82%, low overall diversity.

The decisive independent detail is that this Pupilla superabundance is mirrored in Evans's ditch zone F at Stonehenge, which is stratigraphically phase 3 within the Stonehenge Ditch. That correlation owes nothing to the rhyolite. Scaife's pollen sequence shows the same break at 360mm, between PAZ1 and PAZ2. Allen concludes that there is a hiatus of about five millennia in the pit's environmental record — Boreal woodland below, Sub-boreal open grassland above, the Atlantic simply unrepresented.

So the chip comes from an undated context, at the top of a reworked pit, on the far side of a break independently attested by snails and pollen and independently correlated to the Stonehenge Ditch. It sits 0.2m below the modern surface, in an area where W.E.V. Young recovered further pieces of both bluestone and sarsen, including several mauls, from the car park in 1935.

Why the fragment has been set aside

The fragment has never, as far as I can establish, been characterised petrographically. It does not appear in the provenancing literature. My reading is that it has been treated as intrusive and not diagnostic, and passed over on that basis.

That judgement looks sound, and the distribution across the car park features supports it. Of the five, only pit 9580 produced any bluestone. The three postpits whose timbers rotted in situ, and the treehole, produced none — and those are the features that were dug once and left. Pit 9580 is the one that was dug, deliberately backfilled, widened, and refilled, with its uppermost fill 0.2m below a surface that has since been ploughed, landscaped, tarmacked and stripped. The bluestone appears in the disturbed feature and nowhere else.

There is a useful control on how far small bluestone debris travels in such deposits: when Aubrey Hole 7 was re-excavated in 2008 it produced 63 fragments of bluestone and 455 of sarsen, despite having already been excavated and backfilled twice, and detailed analysis showed all the bluestone to be chippings rather than clasts. A single 62g chip near the top of a recut pit in the Stonehenge landscape is an unremarkable object.

But it is worth being honest about the shape of the reasoning, because it is the same shape I have just criticised in Allen. The standing position in the literature is that no bluestone debris from the Stonehenge landscape has been found in a securely pre-3000 BCE archaeological or natural context. In this one instance that claim rests partly on the assumption that the fragment is intrusive, rather than on an analysis that establishes it. The assumption is well founded, and the stratigraphy carries the argument without any help from the stone — but it is an assumption.

It could be closed. Bevins et al. (2025) set out the diagnostic criteria for Craig Rhos-y-Felin rhyolite: needle-like stilpnomelane crystals lying along and overlying a strong foliation, with secondary chlorite and titanite and partially resorbed primary zircon — the only documented occurrence of stilpnomelane in a foliated rhyolite anywhere in Wales, and not found elsewhere in north Pembrokeshire despite examination of hundreds of samples. Geochemically, Craig Rhos-y-Felin rhyolites all carry less than 500 ppm Zr and a Zr/Th ratio of about 20, against ratios above 40 for many other north Pembrokeshire rhyolites. Every piece of foliated rhyolite debitage so far analysed from Stonehenge — the Newall boulder, Cunnington's 1880s collection, the Open University samples used by Thorpe et al. — plots inside that field.

Portable XRF is non-destructive. If the fragment survives in an accessible archive, an afternoon's work would convert an assumption into a measurement. There is a prior question too, and a cheaper one: the identification as "rhyolite" comes from a field record in unpublished notes, and has never been checked by a petrographer. Whether the object is rhyolite at all is the first thing anyone should establish.

None of which changes the conclusion. It would simply put it on a different footing.

Craig Rhos-y-Felin: the sequence

Rhosyfelin has about 2m of stratigraphy on the west side of the outcrop, running from the Early Mesolithic to the medieval period on a bed of glacial till.

Four Early Mesolithic hearths were set sequentially into the top of a large dug pit. Eight determinations on carbonised hazelnut shell and roundwood:

Context	Date cal BC	Date BP	Sample	Material
111	8550–8330	9229±21	SUERC-50761	Nutshell, Corylus
106	8530–8280	9157±40	OxA-30507	Nutshell, Corylus
100	8290–7970	8984±47	SUERC-51164	Roundwood, Corylus
102	8290–7970	8970±45	OxA-30548	Roundwood, Corylus
102	8240–7850	8890±40	OxA-30549	Roundwood, Corylus
111	8210–7960	8888±21	SUERC-50760	Roundwood, Corylus
106	8210–7790	8851±44	SUERC-51165	Roundwood, Corylus
100	8210–7790	8848±37	OxA-30506	Roundwood, Corylus

Note the sample selection: hazelnut shell and roundwood throughout, both short-lived, minimising the old-wood offset. This is deliberate and it matters. When the same project dates oak charcoal — buried soil 098, at 7540–7300 and 7460–7180 cal BC — the material could be centuries older than its context of deposition. Any argument leaning on precise coincidence between determinations needs to know which kind of sample it is leaning on.

The published verdict on Mesolithic quarrying is short and unambiguous: the only artefact from the entire hearth sequence was a single tiny flint flake, and there was no evidence of any Mesolithic quarrying or working of rhyolite at the outcrop.

The quarry-associated features sit in the Neolithic occupation layer above (059 = 159), dated by two hazelnut shells to 3620–3360 and 3500–3120 cal BC. The prone monolith and its platform are Early Bronze Age, later than 2140–1950 cal BC.

Early Mesolithic, Late Mesolithic: an important distinction

Both quarry reports use "Mesolithic" as a single label, and this obscures something. Sorting the determinations by period changes the picture.

Early Mesolithic material (9th–7th millennia BC) at the quarries occurs in four places: Rhosyfelin's hearths and buried soil; Rhosyfelin's two orthostat-setting pits (110 and 116: 7940–7650, 8280–7970, 8190–7680 cal BC); Carn Goedog's central hearth (7190–6840 cal BC, OxA-31823); and two Carn Goedog platform-related contexts (176 at 7590–7380, OxA-35184; 130 at 6760–6530, OxA-35157).

Late Mesolithic and transitional material (6th–5th millennia BC) occurs somewhere quite different — overwhelmingly in redeposited and alluvial contexts:

Site	Context	Date cal BC	Date BP	Sample
Carn Goedog	171, middle ditch fill (east)	5470–5230	6359±33	OxA-35156
Carn Goedog	171, middle ditch fill (east)	4910–4690	5910±45	OxA-35396
Carn Goedog	128, upper ditch fill (west)	4530–4360	5619±34	OxA-35153
Carn Goedog	135, middle ditch fill (west)	4450–4330	5521±34	OxA-35155
Carn Goedog	128, upper ditch fill (west)	4230–3960	5236±34	OxA-35395
Rhosyfelin	164, platform fill	5226–5011	6182±35	OxA-35149
Rhosyfelin	164, platform fill	4907–4723	5940±33	OxA-35150
Rhosyfelin	153, palaeochannel basal fill	5800–5640	6833±40	OxA-32021
Rhosyfelin	153, palaeochannel basal fill	5620–5460	6543±37	OxA-32022
Rhosyfelin	069	5210–4950	6114±31	SUERC-46204

This matters for two reasons.

First, Parker Pearson et al. describe the ditch-129 dates as Mesolithic in their running text. They are — but Late Mesolithic, not the Early Mesolithic of the central hearth. Anyone repeating the phrase "Mesolithic hearths at both quarries with the same chronology" is conflating determinations two thousand years apart.

Second, the ditch dates make the residuality reading close to inevitable. Ditch 129 was cut through a podzol and backfilled with rubble and the iron-rich lower B horizon material dug out to make it. Charcoal in redeposited soil dates the soil's accumulated carbon, not the digging. The one determination in that ditch that does date the event — 3020–2880 cal BC, OxA-35154, from the middle fill — is Neolithic and matches the platform.

Paired dates: the residuality signature

The cleanest way to see the problem is to look at contexts that produced more than one determination:

• Carn Goedog central hearth (106): 7190–6840 cal BC and 2890–2630 cal BC. Four millennia apart, from one hearth set in a gap where a slab had been lifted out of the platform.
• Carn Goedog platform sediment (176): 7590–7380 cal BC and 3940–3690 cal BC.
• Carn Goedog sediment above platform (130): 6760–6530 cal BC and cal AD 1520–modern.
• Carn Goedog pillar recess (119): 2130–1900 cal BC and cal AD 1680–1940.
• Rhosyfelin Early Bronze Age platform (115): 2140–1950 and 2200–1980 cal BC and 4330–4050 cal BC.
• Rhosyfelin Iron Age pit (047): 3095–2925 and 2840–2495 cal BC — Neolithic hazelnut shell in an Iron Age feature.

This is what a landscape with long occupation and a lot of soil movement produces. The chronological model published for Rhosyfelin (Hamilton, in Parker Pearson et al. 2015, fig. 7) colour-codes the determinations inconsistent with the stratigraphy, separating suspected later contaminants from suspected residual material. The disagreements are the subject of the figure, not something concealed beneath it.

Note the direction the argument runs. A "take every date at face value" rule applied consistently would put megalith erection at Rhosyfelin in the Early Mesolithic and Neolithic activity in an Iron Age pit and early modern charcoal in a Bronze Age recess. Applied selectively, it produces whichever period the author started with.

Where the argument still has soft ground

Two things should be conceded rather than argued around.

The orthostat pits at Rhosyfelin are the weak joint. One of the two orthostats interpreted as a fulcrum for moving monoliths was set into a larger Early Mesolithic pit containing the sequence of hearths. John, Elis-Gruffydd and Downes have pressed exactly here, objecting that the stratigraphic separation is asserted rather than demonstrated. They are entitled to press. The residuality reading for contexts 110 and 116 is an interpretation, and its warrant is the wider stratigraphic model rather than a directly observed cut. The Neolithic case at Rhosyfelin does not depend on these two features — it rests on the dated occupation layer beside the recess, and on two stone wedges found in situ within the joints around a pillar next to that recess — but the orthostat pits should not be cited as though they were secure.

Some of the 2019 language outran its data. The claim in that paper that the quarry evidence conclusively invalidates glacial transport was stronger than what the excavation alone could show. The case against glacial transport has since been made properly and on other grounds — provenancing of the Newall boulder, the sarsen sourcing, the absence of glacial deposits or of spotted dolerite erratics east of Narberth, the Altar Stone's Orcadian source — but a quarry excavation does not by itself settle a question about ice.

What should be resisted is the idea that these soft spots help an early chronology. They do not. The glacial argument and the Mesolithic-quarrying argument are incompatible: one holds that nobody quarried anything, the other requires that somebody did, four thousand years earlier than the excavators say. Neither supports the other.

What would count as evidence

The Neolithic case at Carn Goedog does not rest on charcoal. It rests on recesses in the rock face with fresh surfaces where pillars are absent and no trace of those pillars in the rubble below; an artificial platform of split slabs pressed into the underlying sediment by something heavy; fifteen wedge-profiled coarse stone tools of imported mudstone and sandstone with flake scars and battered terminals; and two recorded instances of joint-widening on the outcrop itself. At Rhosyfelin it includes wedges left in situ in the joints beside the extraction niche. The charcoal dates the soils these things sit on and in.

An equivalent Mesolithic case would need equivalent things — extraction features stratified within or beneath the Early Mesolithic horizons, quarrying tools in Mesolithic contexts, dolerite or rhyolite working debris in the hearth layers. At Rhosyfelin the hearth sequence produced one small flint flake. That absence is the argument, and it is a strong one.

The Atlantic gap, and Blick Mead

One further thing falls out of reading Allen properly. Writing in 1995, he observed that nowhere in the pit 9580 sequence is the Atlantic — later Mesolithic — represented, and that there was then a complete absence of datable late Mesolithic activity in the Stonehenge area. He was careful to add that this might reflect the pattern of fieldwork rather than past human behaviour.

He was right to hedge. Blick Mead, at the spring below Vespasian's Camp about 2km east of Stonehenge, has since produced tens of thousands of struck flints, an aurochs-dominated faunal assemblage, and a radiocarbon sequence running from the eighth millennium down to roughly 4200–4000 BC — among the latest Mesolithic determinations from anywhere in England. The gap Allen identified has been substantially filled by a site nobody had excavated when he wrote.

This is the useful frame for all of it. Mesolithic material keeps appearing near Stonehenge and at Preseli crags because these were long-used Mesolithic landscapes. Sheltered outcrops beside water and open downland beside springs are exactly where that use is visible. Finding traces of it under a place later monumentalised is the expected result, not the anomaly.

The short version

At the quarries, Early Mesolithic material lies stratigraphically below the extraction features or appears as residual charcoal in disturbed contexts, and the Late Mesolithic material appears almost exclusively in redeposited ditch fills and alluvium. At Stonehenge, the Mesolithic features are 200m from the monument and four millennia earlier than anything proposed for it. The one find offered as a bridge between the two comes from an undated layer above a five-millennium environmental hiatus, in the top of a pit that had been dug, backfilled, widened and refilled.

A radiocarbon determination tells you when an organism stopped exchanging carbon. Establishing what it dates — which event, which deposit, which act — is a separate exercise, and it is most of the discipline.

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Sources

• Allen, M.J. 1995. Before Stonehenge, in R.M.J. Cleal, K.E. Walker & R. Montague, Stonehenge in its Landscape: twentieth-century excavations (English Heritage Archaeological Report 10): 41–62. Includes Scaife's pollen report and Table 4.
• Vatcher, L. & Vatcher, F. 1973. Excavation of three post-holes in Stonehenge car park. WANHM 68 (Part B: Archaeology and Local History): 57–63. Includes Limbrey's charcoal identification appendix. Scanned at the Biodiversity Heritage Library
• Parker Pearson, M. et al. 2015. Craig Rhos-y-felin: a Welsh bluestone megalith quarry for Stonehenge. Antiquity 89: 1331–52. Open access: doi.org/10.15184/aqy.2015.177
• Parker Pearson, M. et al. 2019. Megalith quarries for Stonehenge's bluestones. Antiquity 93: 45–62.
• Parker Pearson, M. et al. 2022. Reconstructing extraction techniques at Stonehenge's bluestone megalith quarries in the Preseli hills of west Wales. JAS: Reports 46: 103697.
• Bevins, R.E., Pearce, N.J.G., Ixer, R.A., Scourse, J., Daw, T., Parker Pearson, M., Pitts, M., Field, D., Pirrie, D., Saunders, I. & Power, M. 2025. The enigmatic 'Newall boulder' excavated at Stonehenge in 1924: new data and correcting the record. JAS: Reports 66: 105303. Open access: doi.org/10.1016/j.jasrep.2025.105303
• Bevins, R.E. et al. 2023. Lithological description and provenancing of a collection of bluestones from excavations at Stonehenge by William Hawley in 1924. Geoarchaeology 38: 771–85.
• Darvill, T., Marshall, P., Parker Pearson, M. & Wainwright, G. 2012. Stonehenge remodelled. Antiquity 86: 1021–40.
• Jacques, D. & Phillips, T. 2014. Mesolithic settlement near Stonehenge: excavations at Blick Mead, Vespasian's Camp, Amesbury. WANHM 107: 7–27.
• Ixer, R.A. & Bevins, R.E. 2011. Craig Rhos-y-felin, Pont Saeson is the dominant source of the Stonehenge rhyolitic 'debitage'. Archaeology in Wales 50: 21–31.
• John, B.S., Elis-Gruffydd, D. & Downes, J. 2015a. Quaternary events at Craig Rhosyfelin, Pembrokeshire. Quaternary Newsletter 137: 16–32.
• John, B.S., Elis-Gruffydd, D. & Downes, J. 2015b. Observations on the supposed 'Neolithic bluestone quarry' at Craig Rhosyfelin, Pembrokeshire. Archaeology in Wales 54: 139–48.

Distance Without Discrimination

 

A review of Resolving the Geochemical Provenance of Stonehenge Bluestones: A Sample-Size-Independent Multivariate Framework (G. W. Taylor, June 2026)

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Taylor's paper, DOI:10.13140/RG.2.2.17039.96164 , sets out to demonstrate that the Stonehenge bluestones are geochemically identical to outcrops in the Mynydd Preseli, using rare earth element (REE) ratio data and three complementary techniques: PERMANOVA, SIMPER, and Euclidean nearest-neighbour distance mapping. It is generous with its data. Table 1 gives the full REE ratio matrix for all forty-two analyses, Table 2 the complete pairwise PERMANOVA output, and Table 3 the entire 20 × 22 distance matrix with nearest-neighbour assignments. That openness makes a substantive review possible, and everything below is derived from those three tables and from the published source of the underlying measurements.

The conclusion the paper reaches is, in outline, correct. The problem is that the method used to reach it cannot distinguish that conclusion from its opposite — and the paper's own data, read against their source, contain the demonstration.

1. What the paper argues

The argument runs in three stages.

A global PERMANOVA on the pooled data fails to reject the null hypothesis of no difference between Stonehenge and Welsh samples (p = 0.85, pseudo-F = 0.074). The author treats this as positive support for common origin. Because the pairwise PERMANOVA matrix contains a handful of rejections, and because archaeological sample sizes are small, those pairwise results are judged unreliable and set aside.

To bypass the sample-size problem, all Stonehenge analyses are pooled into one group and all Welsh analyses into another, and SIMPER is used to compare group means. The means agree closely across all twelve ratios — La/Lu at 15.2 against 15.3, La/Yb at 2.12 against 2.12 — which is presented as demonstrating homogeneity.

Finally, Euclidean distances are computed between every Stonehenge analysis and every Welsh analysis. Several minima are very small, and these are offered as sample-level confirmation, with the two smallest presented as headline results.

Stated at its strongest, the argument is: three methods at three different scales all fail to find a difference, so there is no difference to find.

2. The data are from Bevins, Pearce and Ixer (2021), uncited

The paper does not say where its measurements come from. They can be identified exactly.

Taylor's Table 1 consists of twelve ratios, La divided by each of the other REE. Taking sample CGD1 from Table 2 of Bevins et al. (2021) — La 3.36, Ce 9.05, Pr 1.42, Nd 7.50, Sm 2.42, Eu 0.97, Gd 2.75, Tb 0.50, Dy 3.30, Ho 0.65, Er 1.78, Yb 1.71, Lu 0.24 ppm — and performing those divisions reproduces Taylor's row to every reported digit:

Ratio	Computed from Bevins et al. (2021)	Taylor Table 1
La/Ce	0.371271	0.371271
La/Pr	2.366197	2.366197
La/Nd	0.448000	0.448
La/Sm	1.388430	1.38843
La/Eu	3.463918	3.463918
La/Gd	1.221818	1.221818
La/Tb	6.720000	6.72
La/Dy	1.018182	1.018182
La/Ho	5.169231	5.169231
La/Er	1.887640	1.88764
La/Yb	1.964912	1.964912
La/Lu	14.000000	14

The same reconstruction succeeds for OU10, OU10 rpt, PCM7 and PCM7 rpt. Taylor's entire dataset is the REE table of Bevins et al. (2021), converted to La/X ratios.

That paper appears nowhere in Taylor's bibliography, which cites three methodological references (Clarke, 1993; Anderson, 2001; Gower, 1966) and no archaeological or geological source at all. The dataset represents years of laboratory work, sample access negotiated with the Natural History Museum and the Salisbury and South Wiltshire Museum, and analytical development at Aberystwyth. It should be cited.

Two errors follow from the missing attribution. Taylor's Table 1 caption describes the measurements as LA-ICP-MS data. Bevins et al. (2021) used solution nebulisation ICP-MS on acid-digested bulk powders — a different technique producing a different kind of measurement. And the ratios are described as "mineral element proportionality ratios"; they are ratios of whole-rock elemental concentrations, and carry no information about mineral proportions.

3. The groups are sampling categories, not geochemical ones

Taylor's group codes — PO1, SLF1, SODC1, SOF1, SLF2v, SLF2vi, PO2ii, PO2iii, PO2iv, PO3, SLF3 — have no stated derivation. They are Bevins et al.'s group numbers prefixed with their Sample source field:

Taylor code	Bevins group	Bevins sample source	n
PO1	Preseli Group 1	Preseli outcrop	3
SLF1	Stonehenge Group 1	Stonehenge Landscape fragment	7
SODC1	Stonehenge Group 1	Stonehenge orthostat drill core	4
SOF1	Stonehenge Group 1	Stonehenge orthostat fragment	1

Bevins et al.'s Stonehenge Group 1 is a single population of twelve analyses, argued on REE grounds to derive from one intrusive body and attributed to Carn Goedog. Taylor has divided it into three separate "geochemical groups" according to whether each sample was a drill core, a chip off an orthostat, or a surface find from the Stonehenge Landscape — and then run PERMANOVA between them.

This explains the two singleton groups. SOF1 contains one analysis because exactly one Group 1 sample happened to be an orthostat fragment (SH67); SLF2vi contains one for the same reason. These are not rare geological units. They are the intersection of a geochemical group with a collection method.

The scheme is also applied inconsistently: SLF2v contains a drill core (SH62), and SLF3 contains three orthostat fragments, which suggests labels carried down from the first row of each sorted block rather than a deliberate classification.

4. Twelve Welsh analyses and one Stonehenge analysis have been removed

Bevins et al. (2021) report 32 Preseli analyses and 23 Stonehenge analyses. Taylor uses 20 and 22 respectively. The omissions are unstated, and they are not random.

Dropped from the Welsh set: all four Group 2i samples (PCP12, PCS13, PCTF14, PCA15), together with PCM6, PMB9, PMB10, PCB16, PCB19, PCGF27, PCGF27 rpt and PCAW47.

Group 2i matters more than any other. Its distinctive concave-down, MREE-enriched patterns are what allow Bevins et al. to exclude Craig Talfynydd, Carn Sian, Carn Arthur and Carn Bica as sources for any Stonehenge dolerite. It is the clearest discriminating result in the source paper, and it is the one group removed in its entirety.

The twenty retained Welsh analyses span La from 3.04 to 4.26 ppm. All twelve dropped analyses fall outside that band — eight above it, four below. The retained set is, exactly, the central twenty of thirty-two by REE abundance.

Dropped from the Stonehenge set: SH42, at 5.50 ppm La the most REE-rich Stonehenge analysis, and the single sample that Bevins et al. identify as falling outside the envelope of the Preseli patterns in their Fig. 4.

No reason is given for any of this. Whatever the cause, the effect is that both tails were removed from the Welsh distribution and the one non-conforming Stonehenge analysis was removed from the other, before a test for homogeneity was run.

5. The conclusion is almost certainly right

It is worth being clear about this before going further. That the great majority of the Stonehenge bluestones derive from the Mynydd Preseli has been the settled position since Thomas (1923), and successive work by Bevins, Ixer, Pearce and colleagues has narrowed several lithologies to individual outcrops, with excavation at Carn Goedog recovering a Neolithic quarry (Parker Pearson et al., 2019). Nobody reading this review needs persuading of the Preseli connection.

That is precisely why the paper repays close reading. We already know the answer. A method applied to a case with a known answer, which cannot recover that answer reliably, has been shown not to work — and the demonstration is far cleaner than it would be on an open question. What follows is not a defence of some rival provenance. It is an argument that this framework would have produced the same confident result had the stones come from anywhere.

6. What a provenance method has to demonstrate

A geochemical fingerprint is only useful if it discriminates. Showing that a Stonehenge sample resembles a Welsh outcrop establishes nothing on its own; the question is always whether it resembles that outcrop more than it resembles the alternatives, and by a margin larger than the measurement error.

Two requirements follow:

1. A comparison set. At least one candidate source outside the favoured region, so that a match can be shown to be selective rather than universal.
2. A resolution limit. An estimate of how much two measurements of the same rock differ, so that "close" can be distinguished from "indistinguishable given the noise."

The paper meets neither. No non-Welsh source appears anywhere, so the specificity of the match is never tested. And no error estimate is offered — the framework is presented as a way of avoiding variance estimates rather than as a way of quantifying them.

The second gap can be closed from the source data, and doing so is the substance of the next section.

7. The replicates give the resolution limit directly

Bevins et al. (2021) include three analytical replicate pairs: OU10 and OU10 rpt, PCM7 and PCM7 rpt, PCGF27 and PCGF27 rpt. Each pair is one rock analysed twice. Two of the pairs survive into Taylor's dataset; the third was among the samples dropped.

Two measurements of one rock should, if the method has any resolving power, be closer to each other than either is to a genuinely different rock. The distance between replicates is therefore an estimate of the method's noise floor. Computing Taylor's metric on the Bevins concentrations gives it exactly:

Replicate pair	Euclidean distance	In Taylor's dataset?
PCGF27 / PCGF27 rpt	0.1475	dropped
OU10 / OU10 rpt	0.1909	retained
PCM7 / PCM7 rpt	0.2952	retained

Now set those against the paper's results.

The headline match is smaller than the noise floor. The abstract, methodology and conclusion all cite OU11 to CGD2 at d = 0.143 as the exemplary near-zero pairing. Every one of the three replicate distances exceeds it. A sample in this dataset sits further from itself than the flagship match sits from its claimed source.

Most of the reported matches fall inside the noise floor. Of the twenty-two nearest-neighbour distances in Taylor's "Closest Euclidean" row, thirteen are below 0.295 and four are below 0.191. For these the assignment carries no information.

The replicates disagree with each other about provenance. OU10 and OU10 rpt are one stone:

Analysis	Nearest Welsh outcrop	Group	d	Runner-up	Group	d
OU10	CGD2	PO1	0.203463	PCM30	PO3	0.317994
OU10 rpt	PCM30	PO3	0.222013	CGD2	PO1	0.345259

The same physical stone is assigned to Carn Goedog on one analytical run and to a Group 3 locality on the other. On Taylor's Fig. 1 these are different red boxes. The ranking is reversed by the difference between two analyses of one rock.

The Welsh-side replicate behaves the same way. Against SH33, PCM7 rpt ranks first at 0.196369 while PCM7 — the same rock — ranks fifth at 0.422311, behind PCM31, PCGF29 and PCM32.

It is worth being precise about the cause. OU10 and OU10 rpt differ in La by 3.63 against 3.67 ppm, about one percent, and both report Lu as 0.24. That one percent alone shifts La/Lu by 0.167, which supplies 76% of the squared distance between them. The noise floor here is substantially an artefact of two-significant-figure reporting of the heavy REE, amplified by the choice to divide by them.

The margins between competing sources are far smaller than the noise. SH62 is 0.550687 from PCDL25 and 0.561924 from PCAW49 — a separation of 0.011, a twentieth of the OU10 replicate distance. SH61 sits 0.023 from a decision between PCC11 and PCAW49. SH37 has four candidates within 0.08 of one another, spanning two different Welsh groups. Every assignment in Table 3 is a coin toss.

8. The assignments against the published attributions

Reading the bottom rows of Taylor's Table 3 produces the paper's actual provenance result: each Stonehenge analysis matched to a Welsh source. Compared with Bevins et al. (2021):

Carn Goedog. Bevins et al. assign twelve Stonehenge analyses to Group 1, sourced to Carn Goedog and corroborated by excavation of a Neolithic quarry there. Taylor's nearest-neighbour method sends four of the twelve to PO1. The other eight go to Carn Ddafad-las, the ground between Cerrigmarchogion and Mynydd Bach, and Group 3 outcrops.

SH45. The strongest positive attribution in Bevins et al. (2021) is SH45 to Preseli Group 2iii, the Cerrigmarchogion samples, described as a near-identical REE composition. Taylor's matrix assigns SH45 to PCC11 at d = 0.5404, with PCM2 — the nearest Group 2iii sample retained — next at 0.5735. The margin is 0.033, a ninth of the OU10 replicate distance. The method gets the source paper's cleanest result wrong, by a margin well inside its own noise.

Group 2iv. Bevins et al. explicitly exclude the outcrops between Cerrigmarchogion and Mynydd Bach as a source for any Stonehenge Group 2 dolerite. Two of Taylor's tightest matches — SH33 at 0.1964 and OU19A at 0.2328 — are both to PCM7 rpt, which belongs to that group.

Group 2v. SH62 and OU6 form one Stonehenge group in Bevins et al., linked by a shared marked positive Eu anomaly and tentatively associated with Carn Ddafad-las and Garn Ddu Fach. Taylor sends SH62 to PCDL25 at Carn Ddafad-las — agreeing with Bevins, but by a margin of 0.011 over the runner-up — and sends OU6 to PCM3 at Cerrigmarchogion, some eight kilometres west.

The spotted / non-spotted test. Bevins et al.'s Groups 1 and 3 are spotted dolerite; Group 2 is non-spotted. The distinction is visible without instruments. Seven of Taylor's twenty-two assignments cross it: six spotted Stonehenge analyses (OU8, OU12, OU14, OU19A, SH33, SH67) are sent to non-spotted Preseli sources, and one non-spotted stone (SH45) to a spotted one. No statistics are needed to see that these attributions cannot be right.

Reading Taylor's Table 3 alongside the published attributions is the most direct test available of whether the framework works, and it fails it in every case where the two make comparable claims.

9. What the distances are actually measuring

The methodology states that the distances are computed on normalised REE ratios. They are not. The calculation reproduces exactly from the untransformed values: taking OU11 and CGD2 and summing squared differences across all twelve ratios gives 0.020460, whose square root is 0.14304 — the reported 0.143. Full working is in the appendix.

This matters because the twelve variables are on wildly different scales. Across the dataset La/Lu ranges from about 13.8 to 16.8, a spread of 3.1, while La/Ce ranges from 0.355 to 0.407, a spread of 0.05. In an unstandardised Euclidean distance each variable contributes as the square of its difference, so La/Ce can contribute at most about 0.0025 to a squared distance while La/Lu can contribute over 9.

Decomposing the largest distance in the matrix, SH49 to PCDL26 at 3.7325: La/Lu supplies 75.5% of the squared distance, La/Tb a further 13.0%, La/Ho 6.1%. Three of the twelve variables account for 94.6% of the result. The remaining nine are, for practical purposes, absent. The twelve-variable multivariate distance is largely a single-variable comparison of La/Lu, dressed in twelve dimensions.

Three further problems attach to the variable set.

No chondrite normalisation. Bevins et al. work throughout with chondrite-normalised patterns, which removes the Oddo–Harkins alternation whereby even-atomic-number REE are roughly ten times more abundant than their odd-numbered neighbours. What remains after normalisation is the shape of the pattern, which is where the petrogenetic information lies. Taylor's raw La/X ratios retain the alternation, so a substantial part of what the distances measure is the periodic-table artefact that normalisation exists to remove.

No sensitivity to the Eu anomaly. Eu/Eu* is a local deviation from the value interpolated between Sm and Gd, and it is the single most discriminating parameter in Bevins et al.'s Group 2 analysis — it is what links SH62 and OU6 to Carn Ddafad-las. La/Eu conflates that local deviation with the overall LREE-to-HREE slope. Taylor's variable set cannot see a Eu anomaly at all.

Induced correlation. All twelve variables share La as numerator. Dividing one quantity by twelve others induces strong correlation among the results by arithmetic alone (Chayes, 1949). The PCA reporting 87.47% of variance on the first component is not evidence that the projection is dependable; it is largely a measurement of that induced correlation. There is also an unresolved inconsistency: an unstandardised PCA on these ratios would place considerably more than 87% on PC1, so the PCA appears to have been run on the correlation matrix while the distances were not standardised at all. The two analyses are not on the same footing and cannot corroborate one another.

Ratios of compositional parts are in any case not amenable to ordinary Euclidean geometry; centred log-ratio transformation exists for exactly this case (Aitchison, 1986). Taylor's appendix presents the absence of transformation as a methodological virtue.

10. The PERMANOVA worked. Its results were discarded

This is the section a reviewer is most likely to get wrong, and the arithmetic repays care.

The pairwise matrix contains five p-values below 0.05. All five are discarded as artefacts of small sample sizes. Checking each against the group assignments of Bevins et al. (2021):

Rejection	p	Groups compared	Genuinely different?
SODC1 vs PO2ii	0.029	Stonehenge Gp 1 vs Preseli Gp 2ii	Yes
SODC1 vs SLF3	0.035	Stonehenge Gp 1 vs Stonehenge Gp 3	Yes
PO2ii vs PO3	0.020	Preseli Gp 2ii vs Preseli Gp 3	Yes
PO2ii vs SLF3	0.009	Preseli Gp 2ii vs Stonehenge Gp 3	Yes
PO2iv vs SLF3	0.009	Preseli Gp 2iv vs Stonehenge Gp 3	Yes

Five out of five. Not one false positive.

The non-rejections that matter also come out right. Preseli Group 1 against Stonehenge Group 1 — the Carn Goedog attribution — gives p = 0.972. Preseli Group 3 against Stonehenge Group 3 gives p = 0.178. Stonehenge Group 1 drill cores against Stonehenge Group 1 landscape fragments, which are the same population divided by collection method, give p = 0.184.

The test is underpowered and misses real differences: Preseli Group 1 against Preseli Group 3 fails to reject at p = 0.595 when it should not. But every difference it detected is real, and it recovered the published group structure wherever it had the samples to do so. Taylor deleted precisely the entries carrying the signal.

The showcase example the paper offers for discarding them is worth examining. It cites SOF1 against SODC1, where a pseudo-F of 5.317 accompanies a non-significant p of 0.197, as evidence that the pairwise results are unreliable. But SOF1 and SODC1 are both Stonehenge Group 1 — the same geochemical population, separated only by whether the sample was an orthostat fragment or a drill core. Failing to reject is the correct answer, and it says nothing about provenance. It is also an unavoidable answer: with group sizes of 1 and 4 there are only five distinct partitions of the data, so the smallest attainable p-value is 0.200, and 0.197 is the floor of the test.

That floor effect runs through every comparison involving the singleton groups. In a permutation test with group sizes n₁ and n₂ there are C(n₁+n₂, n₁) distinct partitions, and no p-value below 1/C(n₁+n₂, n₁) can be returned however large the true difference:

Comparison	Group sizes	Partitions	Minimum possible p	Reported p	Reported F
SOF1 vs SODC1	1, 4	5	0.200	0.197	5.317
SOF1 vs PO2iii	1, 3	4	0.250	0.245	37.24
SOF1 vs PO2iv	1, 3	4	0.250	0.251	92.41
SODC1 vs PO2ii	4, 3	35	0.029	0.029	16.3
SLF3 vs PO2ii	7, 3	120	0.008	0.009	9.532

The rows involving SOF1 and SLF2vi should be deleted rather than interpreted: PERMANOVA on a group of one has no within-group variance to estimate, and those groups exist only because of the sampling-category split described in section 3. The rows at the lower floor are the opposite case — the most extreme outcome the design permits, and correct.

The paper's diagnosis of the problem also needs correcting. It argues that a single critical F value of 2.1532 cannot apply to pairs of differing sizes because the degrees of freedom differ. The deeper point is that the pseudo-F in PERMANOVA does not follow an F distribution at all — that is the reason for permuting (Anderson, 2001). There is no critical F for any pair, at any sample size. The recommendation to work from permutation p-values is right; the reasoning offered for it is not.

11. Pooling for SIMPER

The SIMPER analysis pools all Stonehenge analyses into one group and all Welsh analyses into another, on the grounds that this removes small-sample noise. The paper's own Table 2 records Stonehenge Group 1 differing from Stonehenge Group 3, and Preseli Group 2ii differing from Preseli Group 3. Neither pool is internally homogeneous, by the paper's own test. Averaging each into a single mean profile produces two composite figures corresponding to no actual rock, whose agreement is guaranteed by the mixing rather than by shared origin.

The appendix result confirms it: a pooled pseudo-F of 0.074 means that variation between the two groups is about 7% of the variation within them. That is not a signature of common origin. It is a statement that the grouping explains essentially nothing, which is what happens when heterogeneous populations are pooled.

SIMPER (Clarke, 1993) is also built on Bray–Curtis dissimilarity, defined for abundance data; applied to element ratios it has no clear interpretation. The paper's own observation that the high-magnitude ratios dominate the dissimilarity profile is a symptom of this rather than a finding.

Underlying all of it is the load-bearing assumption that failing to reject H₀ is evidence for H₀. It is not, and the stated justification — that sample sizes are small and variances tight — describes the conditions under which a non-significant result is least informative.

12. Errors of fact

The text states that SH65 matches CGD1 at d = 0.1585. In Table 3 the distance from SH65 to CGD1 is 1.3004. The figure 0.1585 belongs to PCM30 — a different outcrop in a different group, and more than eight times nearer than CGD1. One of the paper's two headline pairings names the wrong source.

The note beneath Table 3 states that only two or three pairings reject the null hypothesis. Table 2 contains five p-values below 0.05, two of them within-side comparisons.

Figure 1 is an annotated reproduction of a published geological map of southwest Wales — its own legend refers to sources proposed by Thomas — presented without attribution. It is not the map from Bevins et al. (2021); its origin should be established and credited.

Separately, the submitted document contains material that reads as unedited drafting: passages addressed in the second person within a first-person paper, unrendered LaTeX in the body and appendix, two alternative titles both retained, and one sentence in the appendix describing an intention to draw the reader's attention away from a discrepancy in the author's own figure. That sentence cannot be what the author meant to publish, and should be removed.

13. What a working version would look like

The instinct behind the sample-level analysis is sound. Nearest-neighbour matching in geochemical space is a legitimate provenance technique, and preferring it to group-level tests when groups are small is a reasonable judgement. The execution is what fails. A version that would carry weight would need:

• Full attribution of the dataset to Bevins et al. (2021), with the analytical method correctly described.
• The complete dataset, including Group 2i and SH42. The samples that don't fit are the ones that establish resolution.
• Chondrite-normalised concentrations, centred-log-ratio transformed, rather than twelve raw ratios sharing a numerator.
• Standardisation before any distance is computed, so that all variables contribute and the result is not a proxy for La/Lu.
• Shape-sensitive parameters — Lan/Smn, Gdn/Ybn, Eu/Eu*, and the λ coefficients of O'Neill (2016) — rather than a set blind to the Eu anomaly.
• The published geochemical groups, not sampling categories. The pairwise structure is the provenance signal, and the rejections are the informative entries, because exclusion is what geochemistry can establish.
• Candidate sources outside Preseli, so that specificity can be demonstrated rather than assumed.
• A permutation null for the nearest-neighbour distances, answering whether the observed minima are smaller than would arise by chance from twenty candidate outcrops.
• The replicate distance reported as the resolution limit, with any assignment whose margin over the runner-up falls below it declared undetermined.

Applied honestly, that last step alone would leave most of the assignments in Table 3 unresolved. That is not a failure of the study; it is the correct result for this dataset, and stating it would be a genuine contribution.

14. Why this matters beyond one paper

Bevins et al.'s Fig. 4 shows the Stonehenge Group 1 and 3 REE patterns falling inside the envelope of the Preseli patterns, with one exception — SH42. They present this as consistency with a Preseli origin and as a limit on what REE alone can resolve, which is why the group definitions rest on compatible-element geochemistry (Bevins et al., 2014) and why the rhyolite work required zircon chemistry. Their section on sample sizes and analytical homogeneity states in advance that differences of ten percent to a factor of two are to be expected between Preseli field samples and Stonehenge drill cores, and that exact matching should not be looked for.

Taylor's headline result is that same overlap, with SH42 and Group 2i removed, restated as proof of identity and presented as a novel framework. The source paper's stated conclusion — that these data are consistent with Preseli origin but cannot on their own resolve outcrops — has been converted into its opposite by removing the uncertainty rather than by adding information.

The pattern is not unusual. "No statistically significant difference" is quietly doing the work of a positive finding across a good deal of provenance literature, and the smaller the sample the more confident the claim tends to become. The framework in this paper is an unusually explicit version of a common move: replacing tests that can fail with descriptive statistics that cannot, and describing the absence of an error estimate as independence from sample size.

The replicate check offers a cheap and general guard against it. Most analytical programmes run duplicates already — Bevins et al. ran three. Computing the distance between two analyses of the same sample, and refusing to report any assignment whose margin is smaller than that distance, costs nothing and would prevent a great deal of overclaiming. It is the one thing this paper's data do establish, and the source data supplied the means to establish it.

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Appendix: worked arithmetic

A1. Reproducing d(OU11, CGD2) from untransformed ratios.

Ratio	OU11	CGD2	Difference	Squared
La/Ce	0.382173	0.373181	0.008992	0.0000809
La/Pr	2.464567	2.409396	0.055171	0.0030438
La/Nd	0.473525	0.460256	0.013269	0.0001761
La/Sm	1.462617	1.436000	0.026617	0.0007085
La/Eu	3.556818	3.626263	−0.069445	0.0048226
La/Gd	1.298755	1.291367	0.007388	0.0000546
La/Tb	7.113636	7.039216	0.074420	0.0055383
La/Dy	1.046823	1.052786	−0.005963	0.0000356
La/Ho	5.396552	5.439394	−0.042842	0.0018354
La/Er	1.956250	1.983425	−0.027175	0.0007385
La/Yb	2.100671	2.124260	−0.023589	0.0005564
La/Lu	14.904760	14.958330	−0.053570	0.0028698
			Σ	0.0204605

√0.0204605 = 0.14304, matching the reported 0.143. The distances are computed on untransformed ratios, not normalised values.

A2. Decomposition of the largest distance, d(SH49, PCDL26) = 3.7325.

Ratio	Difference	Squared	% of total
La/Lu	3.24276	10.5155	75.5
La/Tb	1.34784	1.8167	13.0
La/Ho	0.92424	0.8542	6.1
La/Eu	0.51740	0.2677	1.9
La/Yb	0.38592	0.1489	1.1
La/Er	0.37596	0.1413	1.0
remaining six		0.1870	1.3
	Σ	13.9313

√13.9313 = 3.7325. Three variables account for 94.6% of the result.

A3. Replicate distances, computed from Bevins et al. (2021) Table 2.

Ratios were formed as in Taylor's Table 1 and the same untransformed Euclidean distance applied.

Pair	La (ppm)	Lu (ppm)	Δ(La/Lu)	Σ of squares	d
OU10 / OU10 rpt	3.63 / 3.67	0.24 / 0.24	0.16667	0.036440	0.1909
PCM7 / PCM7 rpt	3.04 / 3.10	0.21 / 0.21	0.28572	0.087112	0.2952
PCGF27 / PCGF27 rpt	5.16 / 5.20	0.32 / 0.32	0.12500	0.021750	0.1475

In each case the La/Lu term supplies the large majority of the total: 76%, 94% and 72% respectively. All three exceed the paper's headline match of d = 0.143.

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References

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Bevins, R.E., Ixer, R.A., Pearce, N.J.G., 2014. Carn Goedog is the likely major source of Stonehenge doleritic bluestones: evidence based on compatible element geochemistry and Principal Component Analysis. Journal of Archaeological Science 42, 179–193.

Bevins, R.E., Pearce, N.J.G., Ixer, R.A., 2021. Revisiting the provenance of the Stonehenge bluestones: Refining the provenance of the Group 2 non-spotted dolerites using rare earth element geochemistry. Journal of Archaeological Science: Reports 38, 103083. https://doi.org/10.1016/j.jasrep.2021.103083

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