Don't Judge The Altar Stone By Its Cover

Ciborowski and Nash, in their 2026 reply to Pearce et al., replot the dry pXRF of the Altar Stone’s upper surface against Salisbury Museum sample 2010K.240, the palm-sized chip taken from the underside in 1844. They find offsets in P, Zn, Mn, K, Ca, and to a lesser extent Fe, Ba and Sr, “that – at face value – would preclude a genetic link between the two.”

Face value is doing a lot of work. The Altar Stone is not a homogeneous brick. It is a 4.9 × 1 × 0.5 m slab of cross-bedded micaceous sandstone. Bevins et al. (2023a) already treated top-versus-bottom disagreement as something a bed is allowed to do. This note is about that, and about what sedimentary layering can and cannot own.

What kind of rock it is

The published description is consistent across Ixer and Turner (2006), Bevins et al. (2020) and the 2023 authenticity paper. Fine- to very-fine-grained, well sorted, grey-green. Detrital muscovite defines a depositional fabric. Opaque heavy minerals — zircon, tourmaline, Ti-oxides — concentrate in thin laminae. Those laminae, in thin section, define faint unidirectional ripple cross-lamination. No fossils, no bioturbation, no cleavage. Bevins et al. (2023b) read that as a post-Caledonian, non-marine sandstone, more likely fluvial than marine, from a bed originally thicker than 50 cm, tabular rather than channelised, with joints spaced on the order of the slab’s 5 m length.

Two later cements fill the pores: baryte (early, burial-diagenetic) and calcite (later, after quartz overgrowths and compaction). Kaolinite is also a pore-filling cement. Those three phases are how the stone is recognised. They are not detrital grains. They grew in the ground after the sand was deposited.

So there are already two clocks in the rock, and they do not have to agree.

• Depositional: millimetre-scale ripple laminae, muscovite flakes lying flat, heavy minerals hydraulically sorted into thin seams. Each ripple set is a pulse of current. A half-metre bed is a stack of those pulses, not a single pour.
• Diagenetic: baryte and calcite growing in pore space during burial. They can follow porosity and lamina-scale fabric, but they are not “sedimentary layers” in the depositional sense. They can be patchy along a bed and through its thickness.

You do not need a million years for the ripples. A current lays a lamina in minutes to hours; a 0.5 m tabular sandstone can be a flood, a season, or a stack of events over a longer interval. You do need burial time for the cements. Both leave a rock that is allowed to differ from the rain-washed top to the buried underside. That is ordinary Old Red Sandstone behaviour. It is what you would expect of half a metre of sandstone. It is not evidence of two lithologies.

The Salisbury specimen is from the bottom

That matters, because the comparison is only a top-versus-bottom test if 2010K.240 really came from the underside. The label says it did. I have set out the excavation on this blog before (The Altar Stone Sample Provenance; Who was Captain Beamish; The Source of the Altar Stone Fragment).

The Salisbury Museum label, as Simon Spencer and I read it, is:

Portion of the underpart of the Altar Stone at Stonehenge – taken by Mr Brown of Amesbury while excavating in the summer of 1844 to ascertain if any interment there – no traces of such discovered – The search was made at the request of a Swedish gentleman who was deputed by an Antiquarian Society of that Sweden to obtain the skeletons. The relic agrees with the particulars I had from Mr Brown March 19 1845 RHB

A second, damaged label adds that the Altar Stone is “about 18 inches in the gr(ound).” Eighteen inches is 0.46 m: the thickness of the slab. The piece is being described as coming from the buried underpart, not from a dressed end of the upper face.

Joseph Browne’s account to Thurnam, published in the Wiltshire Archaeological and Natural History Magazine, is the excavation. Captain Beamish, an officer from Devonport staying at the George, dug about eight feet square and six feet deep “in front of the altar-stone… digging backward some little distance under it.” He was looking for a burial, not sampling the rain-washed top. I have argued that this is Richard Beamish (1798–1873), formerly a Captain in the Grenadier Guards. The identification of the man is probable rather than proved. The geometry of the hole is not in doubt: they went under the stone.

The 1958 Atkinson photographs of the exposed Altar Stone show the break, and a space of the right size and shape for the Salisbury chip, with a similar loose fragment still there. I cannot be 100% certain without a refit, which will not be allowed. It is physical corroboration of the label, not a closed proof. Taken together — underpart, 18 inches in the ground, a six-foot hole dug back under the slab, and a matching scar on the underside — 2010K.240 is from the bottom of the rock as it lies. Bevins et al. (2023a) already thought their option (i), that the chip came from the north-eastern end of the upper face, was “unlikely given the detail on the sample’s label.” The Beamish excavation makes that still less likely. The live option is (ii): composition through the 0.5 m.

What the pXRF actually sees

The Niton used an 8 mm spot. That is already many laminae in one reading. It is not the whole 0.5 m bed.

Critical penetration depth matters more. For light elements, Bevins et al. (2023a) cite Potts and Sargent (2022) for the depth from which fluorescent X-rays escape: Si and Al less than 15 µm, K and Ca about 50 µm — shallow enough to sit inside the zone affected by surface weathering and leaching. In the same paragraph, without a second citation, they extend the same logic to heavier elements: about 250 µm for Fe, about 2 mm for Sr, Rb and Zr, and about 4 mm for Ba. Calcium on the exposed top is therefore a measurement of a skin. Barium sees a few millimetres. Neither sees through the slab.

Comparing the dry upper face to 2010K.240 is comparing a weathered, rain-washed surface, analysed to a depth of tens of micrometres for the light elements, with a museum chip from the underside, analysed dry, on unlabelled faces, not on the cut. They are not two whole-rock analyses of a homogeneous stone.

The upper face already varies along its length

Three patches of the Altar Stone are accessible: Areas A, B and C. The 2022 dry campaign in the 2023b spreadsheet (mmc2) has five spots on A, five on B, and ten on C. Means in ppm:

	n	Ba	Sr	Zr	Ti	Ca	Fe
Area A, dry top	5	5093	148	410	3799	13269	13983
Area B, dry top	5	2680	120	407	3480	15408	14061
Area C, dry top	10	1426	95	252	2403	15834	13734
2010K.240, underside	10	1163	116	342	3035	107085	10698

2022 dry readings only, from Bevins et al. 2023b mmc2. 2010K.240 is labelled Wilts 277 Amesbury in the file. n is the number of spots in that campaign.

Figure 1. Mean Ba and Zr from the 2022 dry pXRF. Barium falls along the slab from Area A to Area C; 2010K.240 sits with Area C. Zirconium, a heavy-mineral proxy, is also lower in Area C. That is a sedimentological signal on the upper face, not only a weathering skin.

Barium on the accessible top falls from about 5100 ppm in Area A to about 1400 in Area C. 2010K.240, at about 1160, sits with Area C. That is exactly what Bevins et al. (2023a) said: the underside chip matches the low-Ba end of the upper face. Zirconium and titanium fall in the same direction. Those two are hosted in heavy-mineral laminae, not in baryte. So the along-strike gradient is not only cement. Area C is a slightly cleaner, less heavy-mineral-rich package as well as a baryte-poorer one.

Calcium does not follow that gradient. Areas A, B and C are all around 13,000–16,000 ppm Ca on the dry top. 2010K.240 is around 107,000. FN593, the Roman-context chip, is around 75,000. MS3, a Hawley chip from near Stone 1, is around 17,600 — with the leached top, not with the underside. That split is leaching of calcite from the rain-washed face, just as Bevins et al. (2022, 2023a) argued. It is not the same pattern as the Ba–Zr gradient along the slab.

Bevins already floated two live options

The authenticity paper is not silent about this. Noting that 2010K.240 sits chemically with Area C despite being labelled as coming from the underside, Bevins et al. (2023a) set out two explanations: either the chip came from the low-Ba, north-eastern end of the slab — which they call unlikely given the label — or composition varies vertically through the 0.5 m thickness, in which case, absent a full-thickness transect, "the extent of any compositional variation throughout it remains unknown."

That is option (ii): vertical composition through the bed. They make the same point for baryte itself, allowing that the lower modal baryte in 2010K.240 (0.13% against 0.29–0.80% in the six debitage sections) could equally reflect dispersed cement or a real variation through the bed's thickness.

They still call 2010K.240 the go-to proxy. They do not treat the Ba mismatch as a different rock. They treat it as an unsampled thickness. If the chip is from the bottom, as the Beamish excavation says, that thickness is the comparison we actually have.

The rest of the pXRF suite

Ciborowski and Nash’s unused plots are P, Zn and Mn. The 2023b spreadsheet is a full Niton TestAllGeo export, not a high-Z extract. Bevins et al. (2022) already listed the wider published set in their Table 4, pooled across debitage. I split that spreadsheet sample by sample, five spots each on MS3 and FN593, twenty on 2010K.240, twenty dry in situ spots on the Altar Stone in 2022.

One clerical wrinkle in that twenty is worth a sentence, since a careful reader will find it. Ten of those spots were logged in November 2021, LOCATION field reading "Wilts 277" on every row. The other ten were logged on one afternoon in July 2022, sample name unchanged at "Wilts 277 Amesbury" throughout — but the LOCATION field ticks up, one integer per reading, "Wilts 277" through "Wilts 286," every 2.5 minutes. Read on its own, that column looks like nine other specimens. Read against the November session, where the same field sat still for ten straight readings on the same chip, it reads instead as what it almost certainly is: a LOCATION field that incremented while the sample itself did not. Quandoque bonus dormitat Homerus — even the careful nod. The sample column is the one set deliberately for each reading, and it never leaves Wilts 277 across all twenty spots; that is the set used throughout this table.

The table below is that split: every element in the 2022 Table 4 set, means in ppm, Welch t p against the 2022 dry upper face. n detected is in brackets where it is below the number of spots. An asterisk is p < 0.05. n = 5 on the chips is small, and this is many tests; the pattern is the offsets, not any one p-value. Cd (~72,000–79,000 ppm) and Sc (~11,000–12,000 ppm) are Niton junk and are omitted.

Element	MS3 n=5	FN593 n=5	2010K.240 n=20	AS 2022 dry n=20	MS3 p	FN593 p	2010K.240 p
Mg	9574 (3)	8500 (2)	10596 (7)	7014 (8)	0.30	0.53	0.021*
Al	55765	45129	36809	27240	<0.001*	0.002*	0.028*
Si	326206	241077	247621	197198	<0.001*	0.28	0.069
P	2025 (3)	2313 (4)	531 (14)	3027 (19)	0.019*	<0.001*	<0.001*
K	9894	7331	6581	10765	0.39	<0.001*	<0.001*
Ca	17606	74919	102482	15086	0.42	0.008*	<0.001*
Ti	4050	3918	3217	3021	0.001*	0.27	0.44
V	59	62 (4)	45 (14)	46 (19)	0.055	0.032*	0.80
Cr	52	78	61	56	0.40	0.25	0.34
Mn	585	749	978	616	0.56	0.005*	<0.001*
Fe	16663	15346	11173	13878	0.049*	0.10	<0.001*
Ni	82	87	73	64 (16)	0.022*	0.031*	0.20
Cu	39	32	42 (18)	25 (16)	0.22	0.18	0.20
Zn	60	53	44	97	<0.001*	<0.001*	<0.001*
Rb	32	28	25	27	0.08	0.38	0.027*
Sr	125	122	119	114	0.16	0.19	0.44
Zr	381	399	364	331	0.65	0.33	0.49
Nb	13	13	12	12	0.25	0.25	0.79
Mo	8.9 (4)	6.1	5.7 (16)	5.7 (11)	0.40	0.42	0.89
Ba	4027	4416	1223	2656	0.002*	<0.001*	0.001*
Pb	31	37	46	37	0.09	0.96	0.09
Th	9.4	8.9	7.3	7.0	0.002*	0.005*	0.64
U	6.3	7.8 (4)	7.3 (10)	7.5 (15)	0.10	0.79	0.65

The complete Bevins et al. (2022) Table 4 element set, split from 2023b mmc2. Order is atomic number, as in that table.

What this shows, once the chips are named rather than pooled:

• The high-Z framework (Sr, Zr, Nb, U, Pb) still says one sandstone. That is the 2022 linking result, now visible chip by chip, including the underside piece.
• Ba and Ca split the chips by cement, not by lithology. The underside (2010K.240) is baryte-poor and calcite-rich. FN593, buried in a Roman context, is calcite-rich like the underside. MS3 is calcite-poor like the rain-washed top, and baryte-rich. That is a leached-skin plus patchy-cement pattern, sampled in different places.
• The light and mid-Z offsets Ciborowski and Nash plotted for 2010K.240 (P, Zn, Mn, K) are real against the dry top. They are not unique to the Salisbury chip. Zn and P reject for MS3 and FN593 as well. Al rejects for all three. If those offsets made 2010K.240 a different rock, they would make the Hawley and Roman chips different rocks too. They have not been read that way, and the petrography does not support it.
• This is the same family of surface-versus-interior differences Bevins et al. (2023a) already framed as leaching, baryte and an Fe-oxide film — now seen across the whole published element list, not only the selected plots. Whether any remaining light-element offset is lamina chemistry through the bed is the open question. It is not a missing column.

What layering explains well

Barium. Baryte is a dispersed pore-filling cement. Modal baryte already ranges 0.13–0.80 % across pieces of the same sandstone. pXRF Ba on the dry top ranges from about 1350 ppm in Area C to about 5600 in Area A. A chip from a baryte-poor lamina-package, or from a baryte-poor level in the 0.5 m, will not sit on the baryte-rich end of the upper-face array. That is Bevins’s option (ii). It is also why 2010K.240 need not fall “convincingly on the strongly correlated Altar Stone array” on a Ba–Sr plot: the array is the weathered top, along-strike; the chip is a different level in the bed.

Calcium. Calcite cement is 12.6–18.8 modal % in the sections. The dry top has lost most of it from the outer 50 µm that the Ca X-rays actually sample. The underside chip has not. FN593 behaves like the underside; MS3 behaves like the top. That is a sampling-depth and weathering story sitting on top of whatever vertical cement variation the bed already had.

Zirconium, titanium, and the “framework feel.” Heavy-mineral laminae are a defining structure of this sandstone. Hit a zircon- and opaque-rich seam and Zr and Ti rise; hit a cleaner ripple and they fall. Area C is lower in both than Areas A and B. 2010K.240 sits between them. Bevins et al. (2023a) say the range in Zr, U and Th “largely reflect minor variations in … zircon … most likely related to the abundance of heavy mineral laminae.” That is depositional heterogeneity, millimetre to centimetre scale, stacked through half a metre.

What layering does not automatically own

Iron. Bevins prefer an Fe-oxide skin on the exposed top. Fe X-rays come from about 250 µm. A reddish film contributes out of proportion. 2010K.240 looks unoxidised and reads lower Fe. Areas A, B and C are similar to one another in Fe, which is not the Ba–Zr along-strike pattern. Surface alteration is the better first explanation. Layering is not required.

Manganese, zinc and phosphorus. These are the offsets Ciborowski and Nash flag as unused in the 2023a plots. Bevins do not assign them to bedding. The sample-by-sample split shows they are real against the dry top, and that Zn and P reject for MS3 and FN593 as well as for 2010K.240. That could be surface alteration, pXRF matrix effects on a weathered face, phosphate in a biofilm, or real lamina chemistry. There is no thickness transect, so there is no licence to pick. Ciborowski and Nash are right that the 2023a paper does not mention them. They are not right that an unexplained offset, at face value, precludes a genetic link — and they are not right that the offset is unique to the underside chip. An unassigned element is not a second lithology.

Potassium is in the same bin. Bevins relate light-element offsets to surface leaching. K X-rays, like Ca, come from about 50 µm. A weathered mica-clay skin can move K without the interior of the bed having changed.

Two heterogeneities, not one argument

It helps to keep them apart, because they are easy to mash into a single “the chemistry doesn’t match” sentence.

Pattern	Seen in	Likely cause
Ba, Sr, Zr, Ti fall from Area A to Area C	Along the 5 m upper face	Sedimentology plus patchy baryte: different packages in the cross-bedded sandstone
Ca high in 2010K.240 and FN593, low on the dry top and in MS3	Top versus protected chips	Leached calcite from the rain-washed skin (Ca sees ~50 µm)
Fe higher on the top than in 2010K.240	Top versus underside	Fe-oxide film; Fe sees ~250 µm
Mn, Zn, P, K, Al offsets	All three fragments versus dry top, not only 2010K.240	Not assigned to bedding. Alteration, matrix, or lamina chemistry; no transect

Layering is a plausible and published cause of top-versus-bottom differences, especially for cement-hosted Ba and Ca and for heavy-mineral Zr–Ti. It does not have to carry Fe. It has not been shown to carry Mn, Zn and P, and those three reject for more than the underside chip. Open is not “different rock.”

What this does to the bivariate-plot argument

Ciborowski and Nash’s point about selective plots is fair as a methods complaint. Pearce et al. asked for bivariate plots; Ciborowski and Nash showed the unused ones. The unused Mn–Zn–P panels are a narrower, better point than dropping 2010K.240 from the Scottish comparison.

What the plots cannot do, once the stone is read as a bed, is treat the dry upper face as the composition of the Altar Stone and the underside chip as a candidate source that fails to match it. That is comparing one weathered horizon to one other horizon in a 0.5 m cross-bedded sandstone whose own upper face already spans 1400–5100 ppm Ba. The debitage chips span that range too: MS3 and FN593 are baryte-richer than Area C; 2010K.240 is baryte-poorer. High-Z elements that live in the framework (Sr, Zr, Nb, U, Pb) do not reject a match, chip by chip. The light-element offsets that look damning for the underside piece also reject for the other two fragments. Modal mineralogy, minus the baryte abundance, puts 2010K.240 with the other Altar Stone sections.

A genetic link is a petrographic claim about one sandstone. It is not a claim that every 8 mm spot on every face will plot on the same line.

What this does not do

It does not prove that 2010K.240 came from a particular level in the bed. Bevins said the extent of vertical variation remains unknown without a thickness transect. That is still true and the Altar Stone will not be drilled for a sample.

It does not make sedimentary layering the explanation of every offset. Fe still looks like a skin. Mn, Zn and P are still unassigned.

Heterogeneity of the monolith is a fact about the stone at Stonehenge. It does not, by itself, name a quarry. That is a different question, settled by clays, zircons, and outcrop, not by whether Area A and the underside agree in barium.

It does not require anyone to drop 2010K.240 from the zircon list. The 1844 label, the Beamish hole under the slab, the ripple fabric, the calcite–baryte–kaolinite mineralogy, and the high-Z match still say it is the Altar Stone. A baryte-poor, calcite-rich chip from the underside is what a heterogeneous bed is expected to produce.

Where that leaves the stone

The Altar Stone took time to become what it is: first as sand, in many current pulses, then as rock, as cements grew in the pores. Half a metre of that is not one number. The published pXRF already shows an along-strike gradient on the top, a leached calcite skin, a low-baryte underside chip that matches Area C, and heavy-mineral laminae strong enough to move Zr and Ti. Split sample by sample, the high-Z framework still matches; the light-element offsets Ciborowski and Nash plotted for 2010K.240 also appear on MS3 and FN593. That is a bed, sampled at the rain-washed top and, in 1844, from underneath. Treating those as two homogeneous compositions, and reading their disagreement as a broken genetic link, is the wrong comparison.

The measurement that would settle how much of the remaining offset is layering is a transect through the thickness. Until someone can make one, the honest position is Bevins et al. (2023a)’s second option, left open: composition may vary through the 0.5 m. That is the expected state of the rock. It is not a problem for the stone. It is a problem for anyone who needs it to be uniform.

Sources

Bevins, R. E., Pearce, N. J. G., Ixer, R. A., Hillier, S., Pirrie, D. and Turner, P. 2022. Linking derived debitage to the Stonehenge Altar Stone using portable X-ray fluorescence analysis. Mineralogical Magazine 86: 688–700.

Bevins, R. E., Pearce, N. J. G., Pirrie, D., Ixer, R. A., Hillier, S., Turner, P. and Power, M. 2023a. 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. (The two live options for Area C / vertical variation; Table 3 modal baryte; Fig. 5 ripple laminae.)

Bevins, R. E., Pearce, N. J. G., Ixer, R. A., Pirrie, D., Andò, S., Hillier, S., Turner, P. and Power, M. 2023b. The Stonehenge Altar Stone was probably not sourced from the Old Red Sandstone of the Anglo-Welsh Basin. Journal of Archaeological Science: Reports 51: 104215. Supplementary spreadsheet mmc2 (spot pXRF, including 2022 dry Areas A–C and Wilts 277).

Bevins, R. E., Pirrie, D., Ixer, R. A., O’Brien, H., Parker Pearson, M., Power, M. R. and Shail, R. K. 2020. Constraining the provenance of the Stonehenge ‘Altar Stone’: Evidence from automated mineralogy and U-Pb zircon age dating. Journal of Archaeological Science 120: 105188.

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. (Fig. 2 and the “preclude a genetic link” sentence.)

Ixer, R. A. and Turner, P. 2006. A detailed re-examination of the petrography of the Altar Stone and other non-sarsen sandstones from Stonehenge as a guide to their provenance. Wiltshire Archaeological and Natural History Magazine 99: 1–9.

Potts, P. J. and Sargent, M. 2022. In situ measurements using hand-held XRF spectrometers: a tutorial review. Journal of Analytical Atomic Spectrometry.

Daw, T. 2022. The Altar Stone Sample Provenance. sarsen.org. Label reading; Browne to Thurnam on Beamish digging under the slab.

Daw, T. 2023. Who was Captain Beamish, excavator of Stonehenge? sarsen.org.

Daw, T. 2024. The Source of the Altar Stone Fragment. sarsen.org. 1958 photograph of the underside scar.

Thurnam, J., quoting Joseph Browne, in Wiltshire Archaeological and Natural History Magazine 16: excavation “in front of the altar-stone… digging backward some little distance under it.” https://www.biodiversitylibrary.org/page/12541499

Area means in the first table are from the 2022 dry rows in mmc2 (Altar Stone '22 A/B/C; Wilts 277 Amesbury, n = 10). The named-chip tables use all twenty 2010K.240 spots in that spreadsheet. They are not the pooled wet-plus-dry averages in Bevins et al. 2023a Table 2.

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 from the one Stone 62 has been assigned to on direct evidence.

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. That uncertainty cuts against ranking Carn Goedog first for an unspotted pillar on chemistry alone, but it does not put Carn Goedog back in contention for Stone 62: the Garn Ddu Fach attribution rests on a direct chemical and thin-section match to the stone, not on an assumption that Carn Goedog is spotted throughout.

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.