Stone 62 - Spotting Its Source

Ciborowski and Nash’s reply to Pearce et al. includes a worked example on Stone 62. It does not propose a new source for the stone. It raises a methods question: how a geochemical similarity ranking should be read when it disagrees with a first-order petrographic observation, namely whether the rock is spotted.

The arithmetic-method discussion is in The Numbers Ain’t Enough and The Numbers Talk Back. This note is only the Stone 62 example, and only the spotting.

Stone 62

Stone 62 is a shaped, unspotted dolerite pillar in the bluestone circle. Pearce, Bevins and Ixer (2022) analysed it by portable XRF, compared it with Preseli dolerite outcrops, and matched it petrographically to sample PGDF24 from Garn Ddu Fach. Carn Ddafad-las is the same intrusion and a looser chemical envelope. That paper also showed that the Waun Mawn dolerites go to Cerrig Lladron, not to Stone 62.

The published source, as of 2022, is therefore an unspotted outcrop at the eastern end of the ridge. Carn Goedog is the spotted-dolerite source proposed for a different group of Stonehenge stones. The two outcrops are not interchangeable.

The tors

Carn Goedog sits on the north side of the ridge. The unspotted Group 2 sources used in the 2014 classification are other named outcrops: Cerrigmarchogion 1.7 km to the west (Stone 45), and Garn Ddu Fach 2.3 km to the east (Stone 62), with Carn Ddafad-las 460 m west of Garn Ddu Fach on the same intrusion. Craig Talfynydd, the other 2014 Group 2 candidate, is south of Carn Goedog. Waun Mawn is 6.9 km west of Garn Ddu Fach; its dolerites go to Cerrig Lladron, not to Stone 62.

The papers already treat these as separate tors. A similarity ranking that places Carn Goedog first for an unspotted pillar is matching a different outcrop, not a lateral change of texture on the same crag.

Click to embiggen

• Named dolerite tors on Mynydd Preseli.
• Red: Group 1 spotted (Carn Goedog).
• Orange filled: Group 3 spotted (Carn Breseb, Carn Gyfrwy, vicinity of Carn Alw).
• Orange open: Carn Menyn, spotted dolerite but not a 2014 Group 3 outcrop.
• Blue filled squares: Group 2 unspotted (Cerrigmarchogion, Craig Talfynydd, Garn Ddu Fach, Carn Ddafad-las).
• Blue open square: Cerrig Lladron, the Waun Mawn source, not in the 2014 Group 2 list.
• Carn Goedog to Garn Ddu Fach is 2.3 km; Carn Goedog to Cerrigmarchogion is 1.7 km. Craig Talfynydd* is placed in OS kilometre square SN1231.
• Basemap OpenStreetMap / OpenTopoMap. Groups 1–3 after Bevins, Ixer and Pearce 2014; Stone 62 after Pearce et al. 2022.

The similarity ranking

Ciborowski and Nash took Pearce et al.’s Preseli pXRF numbers and applied their arithmetic similarity method as a worked example. The ranking depended on which Stone 62 dataset they used:

Stone 62 dataset	1st	2nd	3rd
In situ analyses	Garn Ddu Fach	—	Carn Ddafad-las
1980s core	Carn Goedog	Carn Ddafad-las	Garn Ddu Fach

The in situ ranking agrees with Pearce et al. (2022). The core ranking does not. That is the result Pearce et al. (2026) discuss.

Petrography

Ciborowski and Nash number Pearce et al.’s conclusions and answer them in order. Their point 7 is this sentence, given as Pearce’s:

The calculation approach fails to take into account even the most basic petrographic observations, which in the case of Stone 62 at Stonehenge shows that it is a non-spotted dolerite, hence cannot be sourced from a spotted dolerite source such as Carn Goedog.

Whether a Preseli dolerite is spotted is a field observation. The white spots have been used as a discriminant since Thomas. Spotting can be uneven within a sill, so a sparsely spotted face is not automatically a different magma. Stone 62, however, is unspotted, and Garn Ddu Fach is an unspotted outcrop to which it has already been matched on chemistry and thin section.

Ciborowski and Nash state that they did not assign a source. They ranked a worked example. That is how the paper is framed. The core ranking still places Carn Goedog first for an unspotted pillar. If the method is used as a provenance tool, that ranking needs to be read against the petrography, which is the limit they state in general.

Source

Stone 62’s published source remains Garn Ddu Fach (Pearce et al. 2022). Ciborowski and Nash did not overturn that, and they say they were not trying to. On the in situ data their method already agreed with Garn Ddu Fach. The core ranking is the result that sits at odds with the spotting. Pearce et al. (2026) treat that as a methods point: similarity calculated from the geochemistry should not be taken in isolation from the petrography.

The arithmetic method can still be a useful ranking tool if it is used alongside those observations rather than instead of them.

References

• Bevins, R. E., Ixer, R. A. and 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.
• Ciborowski, T. J. R. and Nash, D. J. 2026. “Defining similarity: An arithmetic method for archaeological source provenance targeting using geochemical data.” Journal of Archaeological Science: Reports 69: 105513. https://doi.org/10.1016/j.jasrep.2025.105513
• Ciborowski, T. J. R. and Nash, D. J. 2026. “Arithmetic methods for exploring archaeological source provenance using geochemistry – A reply to Pearce et al.” Journal of Archaeological Science: Reports 75: 106012. https://doi.org/10.1016/j.jasrep.2026.106012
• Pearce, N. J. G., Bevins, R. E. and Ixer, R. A. 2022. “Portable XRF investigation of Stonehenge Stone 62 and potential source dolerite outcrops in the Mynydd Preseli, west Wales.” Journal of Archaeological Science: Reports 44: 103525. https://doi.org/10.1016/j.jasrep.2022.103525
• Pearce, N. J. G., Bevins, R. E., Ixer, R. A. and Pirrie, D. 2026. “Arithmetic approaches alone are inadequate in defining similarity: A comment on Ciborowski and Nash 2026.” Journal of Archaeological Science: Reports: 105874. https://doi.org/10.1016/j.jasrep.2026.105874

The Altar Stone Zircons, One Sample at a Time

The previous post treated a sentence in Ciborowski and Nash’s reply to Pearce et al. as a live problem for the Sarclet zircon match. The sentence is still the least hedged claim in that paper. The question it raises is still the right question. What it is not, once the grains are tested rather than the histograms inspected, is evidence that the Altar Stone is not from northeast Scotland.

The claim

Ciborowski, T. J. R. and Nash, D. J. 2026. “Arithmetic Methods for Exploring Archaeological Source Provenance Using Geochemistry – A Reply to Pearce et al.” Journal of Archaeological Science: Reports 75: 106012. https://doi.org/10.1016/j.jasrep.2026.106012

In the course of a methods defence, discussing someone else’s data, they write:

“...the more valid conclusion that may be drawn from the U-Pb zircon data in Clarke et al. (2024) is that, even with five comparator analyses, none of the individual ‘Altar Stone’ samples look anything like the Orcadian Basin in terms of U-Pb zircon geochronology. This observation alone suggests that the Altar Stone is not from northeast Scotland.”

That is not a caveat about an arithmetic similarity method. It is a provenance conclusion. It is built on their Fig. 3: three sparse age histograms for the Altar Stone debitage thin sections (2010K.240, FN593, MS3) set against five histograms for Strachan et al. (2021)’s Orcadian Basin samples, all binned at 50 Myr. The eye is invited to see disagreement within each group, and therefore to treat the resemblance between the two pooled signatures in Clarke et al. (2024) as an artefact of averaging.

Clarke et al. (2026), “From Highlands to Henge,” does not answer this. Its Methods section states that it uses “the reported Altar Stone zircon U–Pb concordia dates from Clarke et al. (2024), which are compiled from three thin sections: MS3, 2010k.240 and FN593.” The celebrated Sarclet result (p = 0.96) is a match between one individual outcrop and that three-sample pool. The timeline rules out a considered rejection: Highlands-to-Henge was accepted on 2 May 2026; the Ciborowski and Nash reply was not accepted until 11 August 2026.

So the critique was unanswered in the journals. That much of the previous post stands. The natural next test, as that post said, was to rerun the Sarclet comparison three times — MS3 alone, FN593 alone, 2010K.240 alone — on the published grain lists. That test is sitting in the supplementary tables. This post reports it.

Why the question was fair

Pooling is not automatically wrong. If three fragments are pieces of the same sandstone, combining their zircon ages is the statistically honest thing to do: Clarke et al. (2024) recovered only 56 concordant grains across the three thin sections (24 from MS3, 17 from 2010K.240, 15 from FN593). Vermeesch (2004) is the usual reference for why that is a small sample. To be 95% sure of not missing a 5% age fraction in a worst-case population, 117 grains are wanted. Fifty-six is already thin; fifteen is a sketch.

Clarke et al. (2024) were explicit about the constraint, and about the three sections: “The total concordant analyses used in this work is thus 56 over 3 thin sections, each showing no discernible provenance differences.” They also noted that they analysed every zircon grain within the spatial limit of the technique in the sections. There is no larger Altar Stone zircon list waiting in a drawer. The stone itself is not available for destructive sampling.

The fair part of Ciborowski and Nash’s argument is therefore this: if the three fragments do disagree with one another, pooling them can manufacture a basin-level resemblance that no individual piece actually has. And if that is so, matching the pool to Sarclet does not tell you that any physical fragment of the Altar Stone looks like Sarclet. That is a real detrital-zircon methods worry. It is not settled by asserting, as Clarke et al. (2024) did, that the differences were not discernible. It is settled by testing them.

Visual comparison of n = 15 histograms is not that test.

What was done

The grain lists are the same ones used for the July 2026 independent audit of Clarke et al. (2026)’s Sarclet claim:

• Altar Stone: Clarke et al. (2024), Nature Supplementary Information 1, sheet “A) Zircon U–Pb.” Concordant grains defined as those with absolute discordance ≤ 10%, matching the published total of 56 (24 + 17 + 15). Age used: Concordia Age (Ma), as specified by Clarke et al. (2026).
• Orcadian Basin: Strachan et al. (2021), Supplementary Table B. Concordant grains are those classified by the authors as S or Y (detrital concordant / youngest detrital concordant). Age used: their Preferred Age (Ma). Locality counts: Sarclet 44, Braemore 42, Kirtomy 46, Portskerra 46, Watch Hill 34.

The statistic is a two-sample Kolmogorov–Smirnov test (scipy.stats.ks_2samp, two-sided). That is the same point-estimate KS used in the July audit, not Clarke et al.’s uncertainty-weighted Monte Carlo variant (Guynn and Gehrels 2010), which is why the pooled Sarclet p-value here is 0.865 rather than the published 0.96. The gap is documented; it does not change pass/fail at p = 0.05, and it does not change the ranking of localities. A p-value above 0.05 means the test cannot reject the hypothesis that the two age lists were drawn from the same parent. It is not a proof of identity, especially at these sample sizes. It is the right instrument for Ciborowski and Nash’s claim, which is a claim of dissimilarity.

The July audit already showed that, on the pooled Altar Stone list, Sarclet, Braemore, Kirtomy and Portskerra are all statistically indistinguishable from the Altar Stone, and that Braemore matches at least as well as Sarclet under every discordance threshold tested. This post asks a different question: do the three fragments still look like one another, and does each of them still look like Sarclet, once the pool is taken apart?

The three fragments do not disagree with each other

Ciborowski and Nash’s Fig. 3A is drawn so that 2010K.240, FN593 and MS3 appear to have different shapes. FN593 in particular looks younger: its mean concordia age is 1310 Ma against 1516 Ma for MS3 and 1490 Ma for 2010K.240. That offset is real. It is also what a 15-grain subsample of a Mesoproterozoic-dominated sandstone is allowed to do.

Pair	D	p	At p = 0.05
MS3 vs 2010K.240	0.292	0.290	indistinguishable
MS3 vs FN593	0.292	0.345	indistinguishable
2010K.240 vs FN593	0.267	0.529	indistinguishable

Clarke et al. (2024)’s “no discernible provenance differences” survives a formal test of the same 56 grains. The histograms “looking different” is sampling noise. There is no statistical licence, on these lists, to treat the three fragments as internally inconsistent groups whose disagreements are being smoothed away by pooling.

Each fragment still matches Sarclet

That was the test that would have carried the aggregation critique through into the specific result this blog has used. It does not.

Figure 1. Cumulative U–Pb age distributions for the three Altar Stone thin sections, the pooled 56-grain list, and Strachan et al. (2021) Sarclet (RS-ORS-18-17). Concordant grains only. The three fragments scatter around the Sarclet curve; they do not peel away from it. FN593’s younger mean is visible as a steeper early rise, and is still within what a 15-grain draw from the same parent can produce.

• 
  

  Figure 2. Each fragment against Sarclet and Braemore, the two strongest Caithness matches in the July audit. No panel shows a fragment sitting off both curves.

  Fragment	n	Mean age (Ma)	vs Sarclet p	vs Braemore p
  MS3	24	1515.5	0.445	0.691
  2010K.240	17	1490.2	0.600	0.694
  FN593	15	1309.9	0.610	0.271
  Pooled	56	1452.7	0.865	0.889

  All three fragments remain indistinguishable from Sarclet. Two of the three are a closer match to Braemore than to Sarclet — the same ranking the July audit found on the pool. FN593, the fragment whose histogram looks most unlike the others, is if anything the closest of the three to Sarclet on this test (p = 0.610).

  The full fragment-by-locality matrix is below. A p-value above 0.05 means the test cannot reject a shared parent. The only fail in the whole table is 2010K.240 versus Kirtomy, at p = 0.049 — a hair below the line, with n = 17. FN593 versus Watch Hill (p = 0.051) sits a hair above it. That is not a pattern of three samples pointing in different directions. It is a pattern of three small samples sitting inside the same Caithness neighbourhood.

  Sample	Braemore	Kirtomy	Portskerra	Sarclet	Watch Hill
  MS3	0.691	0.093	0.514	0.445	0.456
  2010K.240	0.694	0.049	0.680	0.600	0.389
  FN593	0.271	0.549	0.079	0.610	0.051
  Pooled	0.889	0.266	0.293	0.865	0.163

  FN593 is worth a separate sentence on identity rather than on ages. It is excavated debitage from a Roman context at Stonehenge (SH08 Context 16). Bevins et al. (2023, Table 1) give FN593 as the corrected designation: the same piece was mislabelled FN573 in Ixer et al. (2019) and in Bevins et al. (2020, 2022). It is not a purposive sample from the monolith. 2010K.240 is the 1844 underside piece. MS3 is further debitage, from near Stone 1 in Hawley’s excavations. If one of these were a different sandstone, the three-way split is exactly where that would have shown up. It does not.

  The five Orcadian samples do not “disagree with each other” either

  Ciborowski and Nash’s second limb is that Strachan et al. (2021)’s five Old Red Sandstone samples, “separated by 1000s of metres of stratigraphy and from across 100s of km²,” record mutual dissimilarities, “likely the product of a changing sedimentary input into the evolving basin.” Changing input across a basin is expected geology. It is not, by itself, a reason to distrust a match to one of those samples. And on a KS test, the five samples mostly do not disagree:

  Pair	D	p	At p = 0.05
  Braemore vs Sarclet	0.127	0.825	same
  Braemore vs Portskerra	0.135	0.753	same
  Kirtomy vs Sarclet	0.176	0.419	same
  Braemore vs Kirtomy	0.214	0.221	same
  Braemore vs Watch Hill	0.238	0.196	same
  Portskerra vs Sarclet	0.233	0.142	same
  Portskerra vs Watch Hill	0.266	0.101	same
  Sarclet vs Watch Hill	0.273	0.092	same
  Kirtomy vs Portskerra	0.304	0.028	different
  Kirtomy vs Watch Hill	0.367	0.007	different

  Eight of ten pairs cannot reject a shared parent. The two that can both involve Kirtomy. That is a modest, geographically intelligible amount of intra-basin variation. It is not five signatures pointing at five different places. It is also why matching a pooled Altar Stone list to a pooled “Orcadian Basin” signature, as Clarke et al. (2024) first did, is the weaker comparison, and why matching it to individual outcrops, as Clarke et al. (2026) then did, is the stronger one. Ciborowski and Nash are right that the 2024 basin-level pool is a blunt instrument. They are not right that taking it apart removes northeast Scotland.

  What this does not show

  Three limits, all real.

  Uncorrected pairwise tests. This post reports 28 pairwise KS comparisons (3 fragment pairs, 15 fragment-versus-locality, 10 locality pairs) at α = 0.05 with no multiple-comparison correction. Three of those 28 fall at or below 0.05 — 2010K.240 versus Kirtomy, Kirtomy versus Portskerra, Kirtomy versus Watch Hill — which is about what chance would produce across that many tests even if every list were drawn from the same parent. The argument does not rest on those three rejects. It rests on the failure of Ciborowski and Nash’s dissimilarity claim: the three fragments do not reject one another, and none of them rejects Sarclet. Those are the tests the critique asked for. Naming the multiple-testing issue does not change them.

  Low power. A 15-grain list cannot strongly prove identity. Failure to reject a shared parent at n = 15 versus n = 44 is weaker than a high-n match, and would often fail to detect a moderate difference. That limit cuts one way: it stops anyone from reading p = 0.610 as “FN593 is Sarclet.” It does not cut the other way. Ciborowski and Nash’s claim was the stronger one — “none look anything like.” A KS test of the same grains they plotted does not support that claim. You cannot look at n = 15 histograms and declare dissimilarity when the formal test says p = 0.61.

  Sarclet is not unique. The July audit already found that Braemore matches the pooled Altar Stone at least as well as Sarclet at every discordance threshold from 5% to 20%, and that Watch Hill, present in the same Strachan et al. (2021) dataset and unmentioned by Clarke et al. (2026), also clears p = 0.05. The three-way split does not change that. The group-level result is a Caithness neighbourhood (Sarclet, Braemore, Kirtomy, Portskerra), not a single harbour. Formation identity is still not facies identity: Sarclet and Braemore are mapped as Lower Old Red Sandstone, while the Altar Stone’s published description is of a flagstone-like facies developed principally in the Middle ORS. That distinction was in the screening paper and remains the reason East Caithness is a search area, not a quarry identification.

  Zircon is not the whole Scottish case. Even if the three-way split had gone the other way, “not from northeast Scotland” would not follow from “this zircon comparison is weaker than advertised.” Clarke et al. (2024) also have Laurentian-facing detrital ages, mid-Ordovician apatite and rutile overprinted by Grampian (~460 Ma) magmatism, and Lu–Hf. Bevins et al. (2020, 2023, 2024) have the mineralogical package — diagenetic baryte, calcite cement, tosudite, scarce K-feldspar — that already pushed the stone out of Anglo-Welsh ORS and off Mainland Orkney. The Ba/Rb stream-sediment screen does not use the zircon data at all. Ciborowski and Nash’s sentence asks one comparison to carry a conclusion that several independent lines are already carrying.

  The rest of the reply, in this light

  Two other Altar Stone points in the same paper should be kept in their place.

  Ciborowski and Nash replot Bevins et al. (2023) pXRF data to argue that sample 2010K.240 does not sit on the in-situ Altar Stone array for P, Zn, Mn, K and Ca, and that Bevins et al. did not discuss Mn, Zn or P despite treating Mn and Zn as usable provenance indicators elsewhere. Bevins et al. (2023) had already attributed the Ca offset to leaching of calcite cement, the Fe offset to an Fe-oxide film on the exposed upper surface, and the Ba–Sr range to variable baryte. Those are arguments about a recumbent, partly buried, partly weathered slab, not a confession that 2010K.240 is a different rock. The unused Mn–Zn–P plots are a fairer, narrower jab than the zircon sentence. They are not a disproof of the 1844 label, and they are not a disproof of the petrography: baryte, kaolinite, calcite cement, and the heavier elements still match. The zircon result above is consistent with 2010K.240 being what the label says it is. It cannot prove the label; it can stop the ages being used as if they already disproved it.

  Bevins et al. (2024), Was the Stonehenge Altar Stone from Orkney?, is not a rival “not Scotland” paper. It excludes the sampled Mainland Orkney formations on K-feldspar, tosudite and baryte. That removes the islands. It leaves Caithness and the rest of the mainland basin where Clarke et al. (2024, 2026) put them.

  What this means for the East Caithness screen

  Section 3.5 of the screening paper cited Clarke et al. (2026)’s Sarclet result as independent corroboration: two methods sharing no data, assumptions, or statistical framework, converging within about 10 km. The previous post said that corroborating value now rested on a comparison whose Altar Stone side had not been tested sample-by-sample, and that §3.5 should be caveated accordingly.

  The caveat that survives is the one the July audit already required: Sarclet is one of several statistically indistinguishable Caithness matches, not a unique p = 0.96 pin, and the Altar Stone side of Clarke et al. (2026) is still a 56-grain pool. The caveat that does not survive is the one Ciborowski and Nash’s sentence would have forced — that the zircon convergence might be an aggregation artefact, and that the independent-convergence argument might need to be withdrawn.

  It does not need to be withdrawn. The three-way split, now run on the published grains, does not pull the fragments apart from one another or off Sarclet and Braemore. The stream-sediment result never depended on the zircon data being sound. The zircon result, tested the way the critique asked, still points at the same stretch of East Caithness coast.

  State of the debate

  Year	Paper	Main development
  2024	Clarke et al., Nature	Orcadian Basin proposed as Altar Stone source, via pooled zircon, apatite and rutile. Three thin sections described as showing no discernible provenance differences (n = 56).
  2024	Bevins et al., JAS Rep.	Mainland Orkney excluded on mineralogy (K-feldspar, tosudite, baryte). Mainland basin left open.
  June 2026	Clarke et al., J. Quaternary Sci.	Sarclet identified as strongest individual-outcrop zircon match (p = 0.96); Altar Stone side left pooled. Braemore, Kirtomy and Portskerra also compatible.
  June 2026	Pearce et al., JAS Rep.	Comment on Ciborowski and Nash’s arithmetic similarity method. Does not itself address the Altar Stone zircon pooling.
  July 2026	Daw, sarsen.org	East Caithness Ba/Rb screen; cites Sarclet as independent corroboration. Independent KS audit: group-level match real; Sarclet not uniquely strongest.
  September 2026	Ciborowski & Nash, JAS Rep.	Reply to Pearce et al. Side argument: disaggregated zircon histograms “look nothing like” the Orcadian Basin, therefore not northeast Scotland.
  September 2026	This post	Three-way KS split of the published grains: fragments indistinguishable from each other; each indistinguishable from Sarclet and Braemore. Aggregation artefact not found. “Not from northeast Scotland” does not follow.

  Bottom line

  The aggregation worry was legitimate and, in the journals, unanswered. The observation it was built on does not survive a formal test of the same grains. That is the opposite of a kill-shot on northeast Scotland, and it is the opposite of a reason to retire the zircon convergence.

  Ciborowski and Nash’s sentence is the overreach. The histograms were the wrong instrument. The grains, taken one sample at a time, still look like Caithness.

  Methods, for anyone who wants to rerun it

  Two-sample Kolmogorov–Smirnov tests were computed in Python with scipy.stats.ks_2samp (two-sided). Altar Stone ages: Concordia Age (Ma), grains with |Disc (%)| ≤ 10 from Clarke et al. (2024) SI 1. Orcadian ages: Preferred Age (Ma), grains grouped S or Y in Strachan et al. (2021) Supplementary Table B. Locality codes: RS-ORS-18-14 Watch Hill, 18-15 Kirtomy, 18-16 Portskerra, 18-17 Sarclet, 18-18 Braemore. Cumulative plots are empirical distribution functions, not kernel density estimates, so that each step is a grain. The extracted grain lists used here are those already archived with the July 2026 Clarke et al. (2026) KS audit.

  References

  • Bevins, R. E., Pearce, N. J. G., Pirrie, D., Ixer, R. A., Hillier, S., Turner, P. and Power, M. 2023. “Assessing the authenticity of a sample taken from the Altar Stone at Stonehenge in 1844 using portable XRF and automated SEM-EDS.” Journal of Archaeological Science: Reports 49: 103973. https://doi.org/10.1016/j.jasrep.2023.103973
  • Bevins, R. E., Pearce, N. J. G., Hillier, S., Pirrie, D., Ixer, R. A., Andò, S., Barbarano, M., Power, M. and Turner, P. 2024. “Was the Stonehenge Altar Stone from Orkney? Investigating the mineralogy and geochemistry of Orcadian Old Red sandstones and Neolithic circle monuments.” Journal of Archaeological Science: Reports 58: 104738. https://doi.org/10.1016/j.jasrep.2024.104738
  • Ciborowski, T. J. R. and Nash, D. J. 2026. “Arithmetic methods for exploring archaeological source provenance using geochemistry – A reply to Pearce et al.” Journal of Archaeological Science: Reports 75: 106012. https://doi.org/10.1016/j.jasrep.2026.106012
  • Clarke, A. J. I., Kirkland, C. L., Bevins, R. E., Pearce, N. J. G., Glorie, S. and Ixer, R. A. 2024. “A Scottish provenance for the Altar Stone of Stonehenge.” Nature 632: 570–575. https://doi.org/10.1038/s41586-024-07652-1
  • Clarke, A. J. I., Veness, R. L. J., Kirkland, C. L., Clark, C. D., Gandy, N., Emery, A., Bradley, S. L., Ely, J. C. and Ignéczi, Á. 2026. “From Highlands to Henge: Refining the Provenance and Transport Pathways of Stonehenge’s Altar Stone.” Journal of Quaternary Science 41: 888–895. https://doi.org/10.1002/jqs.70080
  • Daw, T. 2026. “A Multi-Element Geochemical Screen, Verified Against Bedrock Geology, for the Source of the Stonehenge Altar Stone Within the Orcadian Basin.” sarsen.org, 2 July 2026. https://www.sarsen.org/2026/07/a-multi-element-geochemical-screen.html
  • Daw, T. 2026. “Not From Northeast Scotland At All.” sarsen.org, 3 September 2026. https://www.sarsen.org/2026/09/not-from-northeast-scotland-at-all.html
  • Guynn, J. and Gehrels, G. 2010. “Comparison of detrital zircon age distributions using the K-S test.” University of Arizona LaserChron Center.
  • Pearce, N. J. G., Bevins, R. E., Ixer, R. A. and Pirrie, D. 2026. “Arithmetic approaches alone are inadequate in defining similarity: A comment on Ciborowski and Nash 2026.” Journal of Archaeological Science: Reports: 105874. https://doi.org/10.1016/j.jasrep.2026.105874
  • Strachan, R. A., Olierook, H. K. H. and Kirkland, C. L. 2021. “Evidence from the U-Pb-Hf signatures of detrital zircons for a Baltican provenance for basal Old Red Sandstone successions, northern Scottish Caledonides.” Journal of the Geological Society 178: jgs2020-241. https://doi.org/10.1144/jgs2020-241
  • Vermeesch, P. 2004. “How many grains are needed for a provenance study?” Earth and Planetary Science Letters 224: 441–451. https://doi.org/10.1016/j.epsl.2004.05.037

Not From Northeast Scotland At All

A bold claim buried inside a methods dispute — and what happens when you check whether the follow-up paper answered it

Ciborowski and Nash's reply to Pearce et al. (2026) is, on its face, a defence of an arithmetic similarity method against a comment paper — the subject of the previous post. But in the course of that defence, almost as a side point in their Altar Stone discussion, the authors make one of the more consequential claims to appear anywhere in this literature. Discussing the U–Pb zircon evidence behind Clarke et al. (2024)'s Scottish attribution, they write:

"...the more valid conclusion that may be drawn from the U-Pb zircon data in Clarke et al. (2024) is that, even with five comparator analyses, none of the individual 'Altar Stone' samples look anything like the Orcadian Basin in terms of U-Pb zircon geochronology. This observation alone suggests that the Altar Stone is not from northeast Scotland.

That is the least hedged sentence in the entire reply. Everywhere else, Ciborowski and Nash are careful to say their arithmetic method makes no provenance determinations of its own. Here, discussing someone else's data, they drop that caveat and state a direct conclusion: on their reading, the Altar Stone may not be from the Orcadian Basin, or northeast Scotland, at all.

The argument

Clarke et al. (2024)'s Scottish attribution rests on comparing a U–Pb zircon age signature for "the Altar Stone" against a signature for "the Orcadian Basin." Both are aggregates. The Altar Stone signature is a pooled dataset built from three separate debitage samples — 2010K.240, FN593 and MS3. The Orcadian Basin signature is a pooled dataset built from five separate Old Red Sandstone samples (Strachan et al. 2021's RS-ORS-14 to RS-ORS-18), drawn from different formations spanning thousands of metres of stratigraphy across hundreds of square kilometres.

Ciborowski and Nash break both pools back into their constituent samples. Their finding: the three individual "Altar Stone" samples show different age-distribution shapes from each other, and the five individual "Orcadian Basin" samples likewise disagree with each other. If a pooled Altar Stone signature only resembles a pooled Orcadian Basin signature because averaging together internally inconsistent groups smooths out their disagreements, the resemblance between the two pooled signatures may not indicate a shared origin at all — it may simply be an artefact of aggregation.

Does the newer paper answer this?

The obvious question is whether Clarke et al.'s more recent paper — Clarke et al. (2026), "From Highlands to Henge," which refines the search to individual candidate outcrops within the Orcadian Basin and reports Sarclet as the strongest statistical match (p = 0.96) — addresses this aggregation problem. It does not. Checking the paper directly, its Methods section states:

"We use the reported Altar Stone zircon U–Pb concordia dates from Clarke et al. (2024), which are compiled from three thin sections: MS3, 2010k.240 and FN593."

The refinement in the 2026 paper is entirely on the source side of the comparison: instead of testing one basin-level "Orcadian Basin" aggregate, it tests five individual outcrop samples (Sarclet, Braemore, Kirtomy, Portskerra, New Aberdour) separately against the Altar Stone. But the Altar Stone side of every one of those five comparisons is still the same pooled, three-sample aggregate from 2024 — the exact aggregate Ciborowski and Nash's reply argues conceals internal disagreement. The celebrated Sarclet result (p = 0.96) is a match between one individual outcrop and an unexamined pool of three debitage samples, not a match against any single physical fragment of the Altar Stone.

This is not a case of Clarke et al. considering the aggregation critique and rejecting it. The timeline rules that out: "From Highlands to Henge" was accepted for publication on 2 May 2026, while the Ciborowski and Nash reply was not accepted until 11 August 2026. The critique postdates the paper it would apply to. As things stand, it is simply unanswered.

What this means for the East Caithness screening work

The Ba/Rb stream-sediment screen published on this blog cites the Sarclet zircon match as independent corroboration: two methods sharing no data, assumptions, or statistical framework converging within about 10 km of one another. That convergence claim is unaffected in its own terms — the stream-sediment screen does not depend on the zircon data being sound. But the corroborating value of the zircon match itself now rests on a result that a live, unaddressed critique says may be a statistical artefact of pooling three internally disagreeing samples. Section 3.5 of the screening paper should be caveated accordingly: the Sarclet convergence is worth noting, but it leans on a comparison whose Altar Stone side has not yet been tested sample-by-sample against Sarclet or any other candidate outcrop.

The natural next test, if the underlying per-sample zircon age data from Clarke et al. (2024) are available, is to rerun the Sarclet comparison three times — MS3 alone, FN593 alone, 2010K.240 alone — rather than pooled. If any individual sample still matches Sarclet at a comparable significance level, the convergence claim would be substantially strengthened. If none does, or if the three samples point in different directions, the aggregation critique would carry through into the specific result this blog has relied on, and the independent-convergence argument in the screening paper would need to be withdrawn or significantly qualified.

The rest of the reply, briefly

The remainder of Ciborowski and Nash's reply is a narrower methods dispute, covered in more detail in the previous post. In short: they concede three points to Pearce et al. (2026) — that rounding has an outsized effect on ratios calculated from silcrete's very low trace element concentrations, that the Certified Reference Materials used in the original sarsen analyses (Nash et al. 2020) were not ideal, and that weighting element ratios by analytical precision would improve their method. They dispute the framing of the rest of the comment as a straw man, defend the use of trace element/Zr ratios against raw concentrations for silcrete provenancing, and argue that Pearce, Bevins and Ixer's own past work (assigning non-spotted dolerite debitage to the spotted dolerite source Carn Goedog using geochemistry alone) is inconsistent with their criticism of a similar inference in Ciborowski and Nash's own paper regarding Stone 62.

State of the debate

Year	Paper	Main development
2020	Nash et al., Science Advances	West Woods proposed as sarsen source.
2024	Clarke et al., Nature	Orcadian Basin proposed as Altar Stone source, via pooled zircon comparison.
Early 2026	Ciborowski & Nash	Arithmetic similarity method proposed.
June 2026	Pearce et al.	Comment disputing the arithmetic method.
June 2026 (accepted 2 May)	Clarke et al., J. Quaternary Sci.	Sarclet identified as strongest individual-outcrop zircon match (p = 0.96); Altar Stone side of comparison left pooled.
July 2026	Daw	East Caithness Ba/Rb screen; cites Sarclet zircon match as independent corroboration.
September 2026	Ciborowski & Nash	Reply: disputes the comment's framing, and separately argues the disaggregated zircon evidence may not support a northeast Scotland source at all.

References

• Ciborowski, T. J. R., Nash, D. J. 2026. "Arithmetic Methods for Exploring Archaeological Source Provenance Using Geochemistry – A Reply to Pearce et al." Journal of Archaeological Science: Reports 75: 106012.
• Clarke, A. J. I., Kirkland, C. L., Bevins, R. E., Pearce, N. J. G., Glorie, S., Ixer, R. A. 2024. "A Scottish Provenance for the Altar Stone of Stonehenge." Nature 632: 570–575.
• Clarke, A. J. I., Veness, R. L. J., Kirkland, C. L., Clark, C. D., Gandy, N., Emery, A., Bradley, S. L., Ely, J. C., Ádám, I. 2026. "From Highlands to Henge: Refining the Provenance and Transport Pathways of Stonehenge's Altar Stone." Journal of Quaternary Science, 1–8.
• Daw, T. 2026. "A Multi-Element Geochemical Screen, Verified Against Bedrock Geology, for the Source of the Stonehenge Altar Stone Within the Orcadian Basin." sarsen.org.
• Pearce, N. J. G., Bevins, R. E., Ixer, R. A., Pirrie, D. 2026. "Arithmetic Approaches Alone Are Inadequate in Defining Similarity: A Comment on Ciborowski and Nash 2026." Journal of Archaeological Science: Reports: 105874.
• Strachan, R. A., Olierook, H. K. H., Kirkland, C. L. 2021. "Evidence from the U-Pb-Hf Signatures of Detrital Zircons for a Baltican Provenance for Basal Old Red Sandstone Successions, Northern Scottish Caledonides." Journal of the Geological Society 178.

The Numbers Talk Back

Ciborowski and Nash reply to the comment on their arithmetic similarity method

Following the June 2026 comment paper discussed in The Numbers Ain't Enough, the original authors have now published a formal reply in the same journal.

Ciborowski, T. J. R., and Nash, D. J. 2026. "Arithmetic Methods for Exploring Archaeological Source Provenance Using Geochemistry – A Reply to Pearce et al." Journal of Archaeological Science: Reports 75: 106012. 10.1016/j.jasrep.2026.106012

What the reply concedes

Ciborowski and Nash accept three of the points raised by Pearce et al. (2026):

• Low trace element concentrations in silcretes mean that rounding can have a disproportionate effect on the arithmetic method's results, and future users should build in an additional error tolerance for chemically "pure" materials.
• The Certified Reference Materials run alongside the original sarsen analyses (Nash et al., 2020) were not ideal, since no silcrete-specific CRM exists. Candidate substitutes are proposed: OREAS 21h, 22i, 293–297 and 299.
• Weighting each element ratio by its analytical precision, rather than treating all ratios equally in the geometric mean, is described as "a good one" that could improve the method, though it was not implemented in the original paper.

Where they push back

The reply rejects the framing of the comment on two main grounds.

Mischaracterisation of scope. Ciborowski and Nash argue that Pearce et al.'s title and introduction present the arithmetic method as a proposed replacement for petrography, when the original paper explicitly describes it as one tool to be used "in combination with other geochemical, petrographic and archaeological indicators." They also point out that both authors have never corresponded or presented at conferences with Pearce and co-authors, disputing the comment's suggestion that the method was developed to justify earlier use of element ratios in a separate dispute with Hancock et al. (2024) over Stonehenge sarsen sourcing.

Ratio versus concentration data. The reply restates the case for using trace element/Zr ratios rather than raw concentrations in silcrete provenancing: variable silicification and heavy-mineral laminae can alter absolute concentrations unpredictably, but not the ratios between non-Si elements. Ciborowski and Nash argue this problem does not shrink with sample size, contrary to a claim made in the comment about debitage-scale samples.

The Stone 62 / Carn Goedog exchange

Pearce et al. had argued that it is "obvious" the arithmetic method's identification of Carn Goedog as geochemically similar to Stone 62 cannot be correct, since Stone 62 is a non-spotted dolerite and Carn Goedog is a spotted dolerite outcrop. Ciborowski and Nash respond that:

• They did not propose Carn Goedog as the actual source of Stone 62 – only that it emerged as the closest geochemical match in a worked example demonstrating the method's mechanics.
• Bevins, Ixer and Pearce previously used geochemical data alone (Bevins et al., 2014) to assign non-spotted dolerite debitage samples from Stonehenge to Carn Goedog, a spotted dolerite source – the same type of inference the comment now characterises as untenable.

Rare earth elements and compatible elements

On the criticism that using a full suite of REE risks "swamping" other variation, the reply cites Nash et al. (2020)'s own dataset: at Totterdown Wood, REE/Zr ratios distinguish that outcrop from Stone 58, while at West Woods they do not – a distinction that would have been lost had REEs been excluded. On compatible elements, Ciborowski and Nash note that Worked Example 5 in the original paper did apply the two-step incompatible/compatible element procedure they recommend; it was omitted from the Preseli/Stone 62 example only because the method had already been demonstrated.

A reanalysis of the Altar Stone data

The most substantive new material in the reply concerns the Altar Stone. Ciborowski and Nash present bivariate plots (their Fig. 2) using Bevins et al. (2023) pXRF data comparing the Altar Stone with debitage sample 2010K.240 – the sample treated as a "go-to" proxy for the monolith in several subsequent papers, including Clarke et al. (2024)'s Scottish-provenance study. The plots show marked differences between the Altar Stone and 2010K.240 in P, Zn, Mn, K and Ca, which Bevins et al. (2023) do not address, despite Mn and Zn being described elsewhere by the same authors as reliably usable pXRF provenance indicators.

The reply also revisits the U–Pb zircon geochronology in Clarke et al. (2024). Broken down by individual sample rather than aggregated, the three debitage pieces attributed to the Altar Stone (2010K.240, FN593, MS3) show different age distributions from one another, and the five Orcadian Basin comparator samples show similarly wide internal variation. Ciborowski and Nash argue that once this aggregation is unpicked, the resemblance between the "Altar Stone" and "Orcadian Basin" signatures used to support the Scottish provenance is much less clear.

State of the debate

Year	Paper	Main development reported
2020	Nash et al., Science Advances	West Woods proposed as the source for most sarsens, using pXRF and statistical analysis.
2024–2025	Hancock et al., Archaeometry; Nash & Ciborowski reply	Re-examination of the Stone 58 data and methodological dispute.
Early 2026	Ciborowski & Nash	Arithmetic similarity method (geometric mean ΔEi/Zr) proposed.
June 2026	Pearce et al.	Comment arguing the arithmetic method is unreliable in isolation and mischaracterises provenance in its worked examples.
September 2026	Ciborowski & Nash	Reply: accepts three methodological refinements, disputes the framing of the comment, and reanalyses the Altar Stone/2010K.240 and Clarke et al. (2024) datasets.

Note on the paper

The reply is confined to the arithmetic similarity method and its worked examples; it does not itself propose a source for the Altar Stone or Stone 62, and both sides continue to agree that geochemical similarity calculations should not be used without petrographic and other corroborating evidence.

References

• Bevins, R. E., Ixer, R. A., Pearce, N. J. G. 2014. "Carn Goedog Is the Likely Major Source of Stonehenge Doleritic Bluestones." Journal of Archaeological Science 42: 179–193.
• Bevins, R. E., Pearce, N. J. G., Pirrie, D., Ixer, R. A., Hillier, S., Turner, P., Power, M. 2023. "Assessing the Authenticity of a Sample Taken from the Altar Stone at Stonehenge in 1844." Journal of Archaeological Science: Reports 49: 103973.
• Ciborowski, T. J. R., Nash, D. J. 2026. "Defining Similarity: An Arithmetic Method for Archaeological Source Provenance Targeting Using Geochemical Data." Journal of Archaeological Science: Reports 69: 105513.
• Ciborowski, T. J. R., Nash, D. J. 2026. "Arithmetic Methods for Exploring Archaeological Source Provenance Using Geochemistry – A Reply to Pearce et al." Journal of Archaeological Science: Reports 75: 106012. 10.1016/j.jasrep.2026.106012
• Clarke, A. J., Kirkland, C. L., Bevins, R. E., Pearce, N. J., Glorie, S., Ixer, R. A. 2024. "A Scottish Provenance for the Altar Stone of Stonehenge." Nature 632: 570–575.
• Hancock, R. G. V., et al. 2024. "Stonehenge Revisited: A Geochemical Approach to Interpreting the Geographical Source of Sarsen Stone #58." Archaeometry 67(1): 1–19.
• Nash, D. J., Ciborowski, T. J. R. 2025. "Comment on: Stonehenge Revisited." Archaeometry 67: 1423–1436.
• Nash, D. J., et al. 2020. "Origins of the Sarsen Megaliths at Stonehenge." Science Advances 6(31): eabc0133.
• Pearce, N. J. G., Bevins, R. E., Ixer, R. A. 2022. "Portable XRF Investigation of Stonehenge Stone 62 and Potential Source Dolerite Outcrops in the Mynydd Preseli." Journal of Archaeological Science: Reports 44: 103525.
• Pearce, N. J. G., Bevins, R. E., Ixer, R. A., Pirrie, D. 2026. "Arithmetic Approaches Alone Are Inadequate in Defining Similarity: A Comment on Ciborowski and Nash 2026." Journal of Archaeological Science: Reports: 105874.

Sarsens in Devon - A Gazetteer

 

https://devon-sarsens.netlify.app/ 

I was asked about Sarsens in Devon, and how unique the Shebbear two are. 

So here is the interactive Gazetteer - I hope it is interesting and informative.

A georeferenced plan of Stonehenge

 

https://timdaw37.github.io/stonehenge-plan/

I couldn't find an interactive georeferenced plan of Stonehenge so I've made one. It looks deceptively simple, deliberately, but it was very hard to make. Different historic plans vary. This one was tested against lidar and I think it's a pretty good match. Of course the real test would be to be on the ground rather than just relying on plans. 

Is the Bulford Post Alignment to the Midwinter Sunset?

Look along the posts: https://timdaw37.github.io/bulford-posts-3d/

Set Midwinter, Sunset, Full orb. Then Midsummer, Sunrise, First gleam. The question is which of those two pictures you trust.

Midwinter Sunset

Midsummer Sunrise

Stonehenge has the same argument. The axis works both ways, and for a generation the tourist photograph has been midsummer sunrise up the Avenue. Parker Pearson and others have put the weight on the other end: you walk in from the north-east and watch midwinter sunset drop through the Great Trilithon. Ruggles has been careful to say the architecture is precise enough to pick the solstice in space, and that first or last gleam is the closer convention, not that one festival owns the monument.

Harding, Leivers and Silva, in PAST 113, publish the Bulford posts as a solstitial pair — midsummer sunrise and midwinter sunset, about 120 m apart, around 2950 BC. Harding found the two structural pits first and only then asked what they pointed at. That is the right order. The question here is only which way the line is better.

The 3D model is the published plan, not the Wessex GNSS. From that plan the posts run 48.31° / 228.31° true. On Bulford’s own skyline, 2950 BC, the six like-for-like events are:

Event	Convention	Azimuth	Miss from the posts
Midwinter sunset	Full orb	228.55°	+0.23°
Midsummer sunrise	First gleam	48.90°	+0.58°
Midwinter sunset	Half orb	229.03°	+0.72°
Midsummer sunrise	Half orb	49.29°	+0.97°
Midwinter sunset	Last gleam	229.53°	+1.22°
Midsummer sunrise	Full orb	49.72°	+1.41°

Full orb at midwinter sunset is the closest of the six — a quarter of a degree, inside a solar radius. First gleam at midsummer is next, half a degree, one disc. The rest are worse.

Two warnings, which do not cancel the table.

You must not mix conventions. First gleam at one end and full orb at the other are different ways of watching. If the same limb is used both ways, winter last gleam is worse than summer first gleam. Reciprocity was never going to give a second bullseye on one straight line: refraction and the solar radius push rise and set apart, and the south-west horizon is not high enough to cancel that.

The picture also flatters the winter disc. The south-west skyline is a local rise at about 880 m, so the sun sitting on it looks planted. The north-east gleam is 5.7 km out. Your eye and the azimuth are not quite the same measurement.

Ruggles’ published rule of thumb is that claimed sightlines of half a degree and better in the old lists were the ones most easily explained as selection, that British prehistoric orientations show no evidence of precision much greater than about 1°, and that a couple of degrees is still a fair orientation in a group of sites (Ruggles 1984, 304–306; 1997, 207). On that scale the midwinter full-orb miss is allowed, the midsummer first-gleam miss is allowed, and neither is a prosecution. A single pair in a crowded pit field still has to beat coincidence.

We do not have the GNSS. Two independent digitising jobs of the PAST plan agree to 0.2 m, which is inside the pit and not the solar miss. The miss may move when the survey comes out. Until then, the model says: if you have to pick one, pick the sun standing on the south-west ridge at midwinter.

Have a go with the table in one hand and the model in the other.

Harding, P., Leivers, M. and Silva, F. 2026. A newly discovered solstitial post alignment in the Stonehenge landscape at Bulford. PAST 113, 2–5.

Ruggles, C.L.N. 1984. Megalithic Astronomy. BAR British Series 123. Oxford.

Ruggles, C.L.N. 1997. Astronomy and Stonehenge. Proceedings of the British Academy 92, 203–229.

3D plan: https://timdaw37.github.io/bulford-posts-3d/