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Navigation in the Neolithic Retrospective Part II

MEGALITHIC AIDS

TO

NAVIGATION

Revised 1988

By P.B. Davidson

© Copyright 1988-2009

Privately Circulated

Scanned to OCR 2009

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MEGALITHIC AIDS TO NAVIGATION

Part A. Sea Passages

There are, along the Western Coasts of Britain and France, a collection of Neolithicstructures which the Victorians styled Rude Stone Monuments and which nowadayswe tend to style Megalithic.

Stonehenge, and the lines at Carnac in Brittany are the best known of these; therehave been numerous speculations about their origins and purposes; from Druidtemples to Egyptian star observatories and worse!

Alexander Thom, Professor Emeritus of Engineering at Oxford, who died last year(1987), aged 92, spent much time from the 1930’s surveying these Megalithic sites.He was a first class surveyor, the quality of his observation cannot be questioned (norequalled in practice), he surveyed with his son Alistair widely throughout Britain; hisfirst book, Megalithic sites in Britain in 1967, completely changed the archaeologicalview of the Neolithic in Britain.

That is to say it created a deep schism; the archaeological view that the noble, butilliterate, savage was incapable of the intellectual and mathematical observation anddata storage required of him by Thom’s theories.

For Thom said three things in effect; 1, that there was a standard unit of length (TheMegalithic Yard of 0.83m) used in setting out the stone circles from NorthernScotland to Brittany; 2, that in many cases an alignment of two or more stones couldbe related to particular first magnitude stars, the solar calendar points and the limitingdeclinations of the moon; and 3, that the limiting declinations of the moon weremeasured with such precision that eclipses could be predicted.

Having given the matter a lot of thought over the last 20 years, I have the opinion thatthe debate will only be resolved by careful reappraisal of Thom’s data; that three newconcepts have to be presented and taken together; but each concept comes from adifferent discipline; one must be as much interested in the logical rules we shouldapply in such a case as in the problem itself.

Let me put some facts before you; taking the Lake District as our starting point. Thomsurveyed the Stone Circle at Castle Rigg, near Keswick; you will observe thegeometry of his proposed construction of the circle and the panorama of thesurrounding hills providing the opportunity for observing throughout the year thevariation in declination of the rising and setting of sun and moon. (Fig. 1)

Cumbria has many other stone circles and megaliths and you will get some idea howthey are distributed. The mountainous centrepiece provides a volcanic outcrop, thesource of polished stone axes found throughout Britain but particularly on the otherside of England in East Yorkshire; Group VI in the classification used by Cumminsand others in P.P.S.

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It seemed reasonable to use the concept of Site Catchment Areas (SCA) for theexploitation of these stone axes to suggest some social structure at the time. There issome evidence for axe factories, where stone polishing took place, but little evidenceof habitation and no particular direct association between stone circles and axes.However you will see that each SCA has its source in the mountains, its axe factorynearer the coast and a stone circle or similar alignment.

Several of these alignments surveyed by Thom were for not very convincing stellar orsolar events. Perhaps they could be better interpreted as route indicators; there seemedto be one or two that could indicate inland routes. However it was only when thatroute indication, in many cases, was taken down to the adjacent sandy beach that theidea came alive.

You will see that for the Irish Sea Cumbria provided three route indications; pursuingthe idea in Galloway four more, and North Wales two more. In the event there aresome 32 from the Hebrides to the mouth of the Loire; and none that point the wrongway. Let us look at the evidence.

Langdale Axes

Manby in CW2 (1964) identifies the location not only of Group VI axes in Cumbriabut the location of part—finished axes, or roughouts, and the axe “factories’ in whichthey were worked. The roughouts are found along the routes that lead to Yorkshireand Humberside and provide an indication not only of the routes, but the suggestionthat the axes were being polished as the purveyors moved; suggesting perhaps theoperation of a transhumance route. There are five axe factories on Scafell and theLangdales for roughing out axes, but the finishing work seems to have been donelower down. These sites are at Portinscale near Keswick, at Gosforth, Edenside andDrigg in Eskdale, at Millom, and at Stainton—in_Furness. Concentrations ofroughout axes also suggest axe factories in the vicinity of Penrith, of Carlisle and ofSilloth on the coast.

If we look at the Site catchment Areas of these axe factories, we see that they eachcontain a stone circle (or two in some cases) and that they are each able easily toexploit a particular part of the outcrop on Scafell and the Langdales. While there areno circles associated with Silloth or Carlisle, there are two in the vicinity of Penrithand, although somewhat farther removed from the Langdales than the other areas, wemay consider it as one of the group.

So we have five Site Catchment Areas in a ring around Cumbria, each with at leastone axe factory and one or more stone circles. These circles are all identified in Thom1967; some of them have alignments and we should see what information we mayobtain from them: - Castle Rigg (L1/1 – see Thom 1967) we will for the momentclassify as an observatory for sun and moon and deal with it later. It has, however,one alignment to an outlier that does not fit the observatory; it does suggest a dry shodroute to the Penrith area.

Long Meg (L1/7) on the River Eden is a large circle with a large outlier (Long Meg)and a small subsidiary circle. Thom suggests a solar alignment for each of these, but

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we should note that the alignment to Long Meg is also for Scafell and provides adryshod route to the axe factories. Perhaps it is for both, but we shall return to thatsubject.

Burnmoor (L1/6) is a collection of five circles, two of which are some distance fromthe other three. Thom suggests a variety of solar, lunar and stellar alignments foralignments circle to circle. If, however, we confine ourselves to the alignments of thetwo circles adjacent to the principal circle, we have two bearings (azimuth) of 311.9°and 292.3°. These do seem to point in the general direction of the areas of Galloway,also much occupied by Late Neolithic people. Is it possible that they were used, as wehave suggested for dry shod land routes, for sea crossings? and, if so, how would ithave been done? and what advantage would it have provided?

On its own, of course, this pair of alignments can demonstrate nothing, but let usmake the proposition and see whether the proposition is supported from otherlocations. The proposition is that for sea crossings an inland alignment bearing,transferred to the adjacent shore will provide a viable sea route to another viablebeach and Site Catchment Area associated with the Axe trade. We shall come back totechnique and utility but broadly we are suggesting they learned the succession ofstars setting on the inland alignment and used that at sea.

Sunkenkirk (L1/3) has an alignment with a bearing of 308.8° which, if treated in thesame way as those at Burnmoor, suggests a similar landfall in Galloway.

Giants Graves (L1/11) on the sea shore near Millom is an alignment of three stoneswith a bearing of 210.8°. We shall see that this also fits the seagoing propositiongiving a landfall in Red Wharf Bay in Anglesey.

Seascale (L1/10) a small circle close by the shore with an outlier gives at 354° abearing for the Point of Air near Prestatyn in Clwydd.

By describing the region of Cumbria in this way, as a group of Site Catchment Areasexploiting the stone outcrops for axes, we have provided a basis for describing similarareas and extended our proposition to include a definition of the use of alignments forsea crossings. (Fig. 2)

Galloway

Three of our suggested sea crossings from Cumbria are towards Galloway; let ustherefore look at Site Catchment Areas there too.

In Galloway there are no axe factories; there are circles and alignments; and, what wehave not so far encountered, Megalithic graves. We shall need to study thedistribution of these in due course.

For our immediate purpose we can identify three site catchment areas based on thedistribution of circles, graves and alignments; we shall call them Cree, the Macharsand Ballantrae. We should probably also define one for the peninsula or the Westernshore of Luce bay; we will call it Logan.

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The Cree peninsula contains three stone circles and three megalithic graves but is alsothe part of the coast indicated by the more northerly alignments from Eskdale; thealignment fits completely our proposition. There, if we look at the alignments in theCree peninsula, we find indications of two dryshod land routes and two for seacrossings.

The circle at Cambret Moor (G4/12) has two alignments; at 254.3° (for which there isno obvious objective) and at 296.7° which indicates a dry shod route over the moor tothe alignment on the coast at Ballantrae. The circle at Cauldside (G4/14) has threealignments, of which for 78.2° there is no obvious objective; the alignment at 59.5°,however, indicates a dry shod route to the East having its termination at the largecircle at Dumfries, Twelve Apostles (G6/1). The third alignment at 156.8° I take to bea sea crossing to the coast of Clwydd near the point of Air. The third circle in Cree,Kirkmabreck (G4/13) has an alignment of 5.9° and I take that to be a sea crossing tothe Isle of Man, as it marks quite precisely the Eastern side of the headland Point ofAyre.

We shall discuss elsewhere the sea level in Neolithic times but it does seem to havebeen lower than it is today. This would have appreciably altered the shoreline in thisarea; we have shown these sea crossings starting and finishing at the 10 metre (5fathom) line.

The Site Catchment Area of Ballantrae probably includes a couple of graves and thecircle at Laggan garth (G3/3); we will note this as an observatory site and return to itlater. On the coast, however, is the alignment Ballantrae (G1/4), which preciselyterminates the alignment from Cambret Moor (G4/12). The alignment itself is for11.8°, indicating a route along the coast to Ardrossen.

Perhaps we should pause at this point to consider where this is leading us; theproposition that alignments may show a dry shod route or a sea crossing is leading usto define quite a coherent route to the North and to extend the network in otherdirections. This is beginning to seem reasonable; the routes fit the Site Catchmentareas and the Topography. In particular the indicated landfall at Androssan fits into apattern of Prehistoric trade routes into Scotland. Sir Lindsay Scott in PPS Vol.XVII(1951) “The colonisation of Scotland in the second Milleniurn BC” indicates theBlack Cart Pass, running inland from this part of the coast as a natural route leadingthrough various Glens to the North and East. Which brings us back to Luce Bay andthe Machars. The other alignment from Eskdale indicates the area of Logan on LuceBay, but the alignment on 308.8° indicates the Eastern shore of Luce Bay; the generalvicinity of Monterith Bay. There is one alignment in the Machars and it is close toMonterith Bay; it is Drumtrodden G3/12 with a bearing of 223°.

The bearing of 223° from Monreith Bay takes us through seas clear of the tide racesof the North Channel to the Mouth of the Boyne; than which there is no moreimportant area of Neolithic settlement. The pattern is developing and gainingcredibility; we must state all the evidence before attempting to quantify ourconfidence in it. (Fig. 3)

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Gwynedd

Looking South from Cumbria, indeed following the suggested sea passage of 210.8°from Millom, we come to the District of Gwynedd (otherwise Anglesey andCaernarven). The bearing of 210.8° takes us into the centre of Red Wharf Bay inAnglesey; an area rich in Megalithic graves and standing stones. Anglesey probablyrepresents three Site Catchment Areas; Red Wharf Bay, Holyhead and Newborough.If, as seems probable, sea levels were some 30 ft lower than present day, Menai Straitmay well not have existed and the southern end, Newborough Warren, and theNorthern end, Penmaenmawr, both substantial sandy beaches.

Penmaenmawr is the important Site Catchment Area as it contains the Craig Llwydaxe factory (Group VII). Nearby is a stone circle, Penmaenmawr W211. This circlehas two outliers giving bearings of 18.6° and 240.9°. From the beach at Penmaermawrthe bearing of 18.6° leads to the mouth of the Esk in Cumbria; the objective of thebearing 240.9° is not so obvious, but from the beach at Newborough Warren wouldlead to the Irish Coast near Wexford. As an entry point to Ireland that is not veryobvious; a rather featureless coast not marked by prehistoric remains, but we shallconsider it again in the section on Dyfed.

On the western edge of the Penmaermawr area are a pair of henges; unusual in that atthe entrance to one is buried a stone axe and at the entrance to the other a beaker. Thisdedication to each of two important artefacts does suggest their purpose as tradingmarts. However, from Llandegài runs a prehistoric route, its course described byGresham and Irvine in Antiquity Vol.XXXVII (1963). The route crosses the riverConway and the Dee, over the Berwyn Mountains and eventually to the Severn,where we find a site catchment area centred on the Clun Forest in Shropshire and richin flint axe working sites.

Along this prehistoric route and on the Berwyn Mountain, and where anotherprehistoric track runs up from the coast at Ardudwy, will be found the stone circleMoel Ty Ucha (W5/1). Associated with it is a circle across the river Dee, Twyfos(W5/2). Noel Ty Ucha has an outlier, giving a bearing of 17.6° with a distantforesight of a prominent hill. The bearing indicates a nearby crossing of the Dee andleads to a standing stone on the hill just west of the Penbedw circle in Ciwyd. So thiscircle looks like an important signpost on an important axe route.

Returning to the West we find an important Site Catchment Area at the southern endof the Lleyn peninsula; there are two axe factories and five graves, two of which areat opposite ends of Porth Neigwl. We shall see that an alignment in Dyfed leads to itacross the bay. (Fig. 4)

Dyfed

Let us move South to the other Welsh peninsula; here we find a similar prehistoricregion; similar but, once again, with substantial peculiarities dictated in part at leastby the topography.

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South West of Carmarthen and adjacent to the Pendine Sands we find a self-containedSite Catchment Area with a similar distribution of graves and standing stones to thatwhich we have already observed. The same is true of the Gower peninsula; and in thiscase one of two beaches is the landfall for an indicated sea route from Cornwall. Wecan identify other areas on the Western end of the peninsula; at the southern end of St.Brides Bay and West of Fishguard, but neither is central to our argument.

The activity is in this region more concentrated than we have come across before; itconcerns the region North and South of Prescelly Mountain. On the north coast wehave one sheltered bay at Newport, to which we shall transfer the alignments relevantto sea travel. To the South of the mountain we have a difficulty; there are prehistoricremains but they have been much despoiled. The description of what was there in1910 and was then known to have been there is described by Bushell “Among thePrescelly Circles” in Arch. Cambrensis, 6th Series Vol.XI. We have put thisinformation as best we can on the grid system.

In this same vicinity we also have reference to the location of the source of theStonehenge Blue stones. This is given by Thomas in Antiquaries Journal, Vol.3, 1923.His assessment .. “the three main varieties of bluestone (spotted dolerite [prescilite] ,shyolite and volcanic ash) were matched exactly by the outcrops ... brought togetherby glacial action with a small area on the South East slopes near Cilmaen - Llwyd.We have shown this as the regional “axe factory” on the map; the concentration ofcircles close to it is remarkable. We shall put further consideration of these circlesaside until we consider from all the regions the characteristics of what we haveloosely called “observatories”.

In the area south of Prescelly there remains a small circle with outliers at Gors Fawr,W9/2, and also described by Bushell. Perhaps the small size of the stones has savedthem from destruction. We give a survey of the outliers of this circle which we madein 1971 and which we believe provides a key clue to the use we have been suggestingfor these alignments. Of the six bearings that we recorded, only one (242°) has noobvious objective, though its projection does reach the coast by a dry shod route in thevicinity of the Site catchment area at the Southern end of St. Brides Bay. One other(103.5°) indicates a dry-shod route to the Afon Cynin (and thence to the SiteCatchment area SW of Carmarthen) and it is also accurately marked at that point by astanding stone.

The remaining four bearings (291.5°, 307.5°, 8° and 14°) become interesting if takenas sea bearings from the beach at Newport. The bearings 8° and 14° mark the beachon the Lleyn peninsula.

Thom 1967 describes an alignment of large stones at a site north west of Prescelly,Parc y merw, W9/7, with a bearing of 301.4° indicating either Mt Leinster or thenorthern setting of the Moor; now here we have a bearing on either side and we aresuggesting them as navigation routes. We shall need to look at the landfalls in Irelandagain; for the moment we can say that. 291.5° leads to the Wicklow shore atessentially the same place as the bearing 240.9° from Gwynedd. The bearing 307.5°leads to a part of the coast at the northern end of the Wicklow mountains.

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So the region Dyfed and Newport Bay in particular fits the proposition we have beendeveloping. (Fig. 5)

Cornwall

To the South again, Cornwall as a region shows much the same pattern of SiteCatchment areas with axe factories and sea routes. We are setting on one side forconsideration under “observatories” the circles on Bodmin Moor, solely for the reasonthat they do stand apart in type and location. We must also note the isles of Scilly,rich in graves of various types; too many for the amount of land now visible.Crawford, in a paper on Lyonesse in Antiquity, Vol.1 (1927), discusses the change ofsea level and concludes that it must have been some 30 ft. lower.

The peninsula of Penwith is densely populated with standing stones, circles, gravesand what are there called Quoits (or Dolmen in France). One cannot, with certainty,separate site catchment areas for this but we might say there is the southern half,running from Sennen to Penzance and including the source (probably submerged) ofGroup I stone axes; and the northern half, mostly on high ground leading in the Eastto St. Ives and including there the source of Group II stone axes. Group III stone axesat Marazion might have been exploited by either.

We shall see that one of the sea routes indicated from Brittany leads to Mount’s Bay.But the interesting sea route from this area is one indicated by the stone circle NineMaidens, S1/11, on a bearing of 332.7°. This bearing, taken from the only possiblebeach, at St. Ives, indicates a landfall in Ireland at Tramore. This bearing follows allthe rules we have proposed so far, but it surprises by the length of the sea passage(250 km). It may find support from the association of Tramore with Scilly and Penrithas the only areas in which Passage graves are found.

Which leaves two areas to the East. The area around Camborne includes the axefactory at Cam Brea, the source of Group XVI stone axes; it is a good representationof a self-contained collection of stones and graves. Then we come to the area inlandand south of Padstow; with a north-facing beach at Trevose. There is a collection ofprehistoric graves between the beach and Trevose Head; there are several coastalgraves, but the main group are 10 km to the south; and that includes the importantalignment Nine Maidens, S1/9. This is a line of nine large stones on a bearing of26.3°, with the Eastern end of a prominent hill precisely marked by the alignment.Now this bearing from Trevose beach leads to the Port Eynon Point (very precisely) atthe western end of Port Eynon Bay in Gower. So that the headland, on arrival, mustbe very similar to that shown by the alignment. We shall evaluate this alignment withthe others; we have identified fourteen from Wigtown to St. Ives. (Fig. 6)

Brittany

And so we come to Brittany. Which presents us with two problems; an “embarras derichesse” of menhirs, dolmen, allee couverte, alignments and so on; and the lack of agood “corpus”. As elsewhere we have noted the main centres of population andavoided analysis in the terms of this study; so we have noted for the moment the

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“observatory” of Carnac and the inland settlements, of Muir de Bretagne, and ofLandes de Lanvin. We note also the source of three types of stone axe and show themon the map; Type A from Seledin near Plussulien, a site that was worked for athousand years and whose products are found throughout France; Type B from anunidentified area in the Montagnes Noires found only in Southern Finistere andMorbihan; Type C from an outcrop near Plenven, now destroyed by quarrying andfound both in Southern Finistere and Morbihan and across France; and Fibrolite,occurring as loose stones in fields and essentially in Finistere north of Brest.

Burl has recently published “Megalithic Brittany” (Thomas & Hudson 1985) which,although not a true Corpus, does go to some trouble to identify the exact location andnature of prehistoric monuments, including museums and similar related items. Wehave used Burl’s reference numbers, located them on the Carte de France 1/100,000of Institut Geographique National; and we use the rectilinear grid of this series.

While Thom has made important studies of the observatories at Carnac, I know of nosurvey of alignments by him or anyone else in the rest of Brittany. The record of thesealignments is therefore my own; the surveying was done in 1975, using a plane tableand elevating alidade with orientation on local features identifiable from the Carte deFrance 1/100,000, being typically churches and water towers (chateaux d’eau).

The alignments surveyed at Brignogan, at Plozevet, and at Guilvinec have not beenchecked; none of them was surveyed with any objective in mind and those atGuilvinec are marked on my survey notes as “rough”. Their consistency, therefore,with the pattern already found is impressive. The sites at Erdeven and on the seawardside of Presque’isle de Quiberon were re—surveyed in 1985 and the originalmeasurements confirmed.

My identification of Site Catchment Areas is therefore confined to the coast startingon the North coast of Brittany at Lannion (Cote du Nord). I have not surveyed; partlybecause the rocky coastline, even allowing for a prehistoric shore on the l0m line,made a suitable beach improbable. Next along the coast is the large passage grave siteof Barnenez, which appears to stand much on its own in a similarly rocky coast.

At Brignogan, however, we have a characteristic Site Catchment Area and apromising beach in the Grève de Goulven, particularly at the l0m line. On theheadland north of Brignogan Plage is a large “Christianised” Menhir, near thelighthouse. We identified to the S. East a smaller menhir that provided a good sight ofthe large menhir; that gives a bearing of 329° and leads to Newlyn in Mount’s Bay. Ithought there was a second alignment from this small menhir to a prominent naturaloutcrop of le Garo with a bearing of 39°.0 Burl records another menhir south west ofBrignogan at Kervizour (F81b in Burl) that appears from the map to give the samebearing. That needs to be checked, but if confirmed leads to Poole Bay and the mouthof the R. Avon. There is evidence too of a lower level for the shoreline; the passagegrave (F70a) is recorded and illustrated by Burl as being submerged at low tide.

In North West Finistere we find a Site Catchment area centred on the naturaloccurrence of Fibrolite stone axes. On the mainland the record is mainly of large andisolated menhir, but on the coast are two islands with a number of substantial passagegraves; at I Guernioc (F52) and at I Came (F51). At both these sites there is a

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presumption of a lower level for the shoreline; Burl comments on I Guernioc that ‘...once a low hill joined to the Mainland’. That implies at least the 5m line.

In the Baie de Douarnenez we find the peninsula of Camaret on which there are stillsome stone rows, but we have not surveyed them: but on the south side of the Bay wehave the peninsula leading to the Pointe du Raz on which we can identify a SiteCatchment Area. There is a collection of Graves on the northern side; but on the shoreof the southern side, on the Baie D’Audierne, there is a large and very flat menhir,south of Plozevet Pouldreuzic (F86a). This flatness is sufficient to give a good bearingof 173.5°. I think some foresight may have gone, which is a pity as one would like tobe quite sure of the prehistoric intention of the alignment, since it suggests a sea routeright across the Bay of Biscay to a beach in the vicinity of Picos de Europa, a passageof 485 km. This menhir is in close proximity to an area rich in graves, generallydescribed by Jacques Briand in describing the grave at Kersandy in l’ArchitectureMegalithique (1977); he notes also the abundant local working of flint from local“rognons de silex”.

In the South Western corner of Finistere, in the general area inland from Pen Marchwe have a considerable concentration; centrally there were stone rows (F80), nowmuch despoiled. On the southern coast East of Guilvinec near Lohan I recorded in1975 two alignments which I described as “rough” but which should be includedbecause they appear to be part of the network of sea bearings. They are (F76)Lechiagat, Lehan, which Burl describes as “this broad granite slab stands in marshyterrain . . .”, and my comment in my survey notes was “... is just behind the sanddunes and is flat pointing out to sea. At the position where the tip cuts the horizonthere is a natural rocky area but too (un)impressive to give a bearing better than ± 5;”and (F90a) Le Ruen of which Burl says “This is a remarkable jagged pillar of granite,S.5m high with its broad S face toward the sea” and my survey notes say “... is also aflat and large stone but points roughly E-W. There is no obvious sighting platformclose to”. The prehistoric sea line would have been 1 or 2 km farther out and no doubtthe position of these stones would have been more sure. However, that at (F90a) leadsus to the coast at Erdeven, avoiding many rocks and other hazards. The alignment atF76 would give a land­fall near Lacanau (Landes).

The Carnac district is so dominated by the stone rows and other elements of the“observatory” that few eyes are turned either to Erdeven or to the Cote Sauvage onthe Presqu’île de Quiberon, but that is where we find two more areas with this samecombination of alignment and beach. Near Erdeven there is an alignment of eightstones (CA187b), these are large and some are thrown down, the whole is in a clumpof gorse. However one can obtain a bearing; it gives us another location in the vicinityof Picos de Europa.

Finally there are a group of five stones of fair size, not recorded by Burl on thesouthern end of the Cote Sauvage. The northerly stone is seen to clip the horizonwhen viewed from three of the others. The remaining stone, large though it is, seemsto be something other. From these three stones we obtain bearings which we shall seehelp, with the others we have noted in Southern Brittany, to create an extension of thenetwork of sea passages round the Bay of Biscay to the Northern Coast of Spain. Itreally is quite remarkable! (Fig. 7)

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Biscay

The sea passages suggested by the alignments in Brittany surprise by the length ofpassage implied across open seas notorious even today for foul weather. We shallconsider separately whether techniques existed for navigating over this distance; as tothe dangers of the open sea, they may well be a lot less, particularly in a small boat,than tidal and cross currents near rocks and headlands.

We have extended our study round the shores of the Bay of Biscay, to the extent thatwe can suggest a feasible pattern of sea passages. While we have followed theconstraints of our proposition, we do not have as much data for Aquitaine (Landes) orfor Catalonia (Northern Spain); we do have, however, pairs of bearings indicating thesame landfall. We have had to make some assumptions; in particular that the sailingpoint from Quiberon is a stand off in the lee of Belle-Isle to clear the smallarchipelago of Islands. One of these suggests a landing on the coast at Lacanau, asdoes the rough bearing from Guilvinec in Southern Finistere; the closest prehistoricremains I am aware of is at Le Gurp some 40 km. north. However, the line fromQuiberon is a very precise one.

The other two bearings from Quiberon (with the stand-off) lead to the coast north ofSable d’Olonne. This coast is marked by a dolmen and a menhir, but we cannot tellhow much a lower sea level would have altered the coastline.

Inland from Sable d’Olonne, however, is a Site Catchment Area of various substantialdolmen and two alignments; further inland in the Vendee are various graves. The areafits the pattern and one of the alignments gives a good alignment for Bilbao; the othercannot easily be measured because one large stone is wired off and the other, behindthe Mairie, is no longer visible from the first. I have measured as best I can from themap, and only included it because it also suggests a landing at St. Vincente de laBarquera.

The two landfalls in Spain are “where we might expect them to be”; that at Bilbaobeing the gateway to the Valley of the Ebro and Catalonia; that at St. Vincente de laBarquera to Leon and Portugal. Both routes would be much aided by the Picos deEuropa, mountains whose height in metres we have indicated would provide a goodlandfall from 100 km and more to seaward. The suggestion lacks the precision of therest of the proposition, but contains sufficient merit to be made. (Fig. 8)

Hebrides

There remains one other region that displays the same pattern of prehistoric sitecatchment areas connected by alignments indicating sea passages; that is theHebrides.

The sea distances involved in crossing the Clyde Estuary from Galloway to Arran andKintyre are short and not notably hazardous. Arran and Kintyre are typical of theSite Catchment Areas we have been studying. To the north we find another aroundKilmartin and we shall look again at that in “Observatories”. Beyond that we come tothe open waters of the Minch and on the island of Mull we find again our alignment

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and a beach. Mull should probably be regarded as two areas, North and South,however most of the other islands are of a size where the coast line defines thecatchment area.

The alignment of 334° from Mull leads to the Eastern coast of North Uist, rich instanding stones and graves. There is an associated alignment at 342°, suggesting theroute to Canna (adjacent to Rhum); this may be a passage or it may be an ancillary tothe route to N. Uist.

Most of the alignments in the Outer Hebrides we propose to deal with under“Observatories” but we should note two particular areas. To the North we find thearea of Callanish on Lewis; manifestly an observatory, but on the Eastern shore analignment on the mainland mountain of Suilven. This bearing at 98.3° leads to a pointof entry to Sutherland, the Eastern side of which is an important catchment area. Farto the south, indeed on the most southerly island of Berneray, is an alignment shownby Thom H6/5 at 342° to Hecla is probably a reverse bearing from an adjacent beachto the large beach in Northern Ireland at Coleraine; the point of entry to the largesettlements of Tyrone.

Three other bearings we should note. From Brevig H6/3 on the Eastern shore of Barraa bearing of 135° leading to Coil. From Coil’s adjacent island Tiree the bearing ofTiree S M4/2 of 190.2° to the beach at ~‘4alin in N. Ireland.

From Islay, Thom in JHA Vol.5, Pt.I 1974, notes a secondary alignment at Ballinabythat from the adjacent beach at Machir Bay indicates the entry to Loch Foyle. (Fig. 9)

Ireland

Let us draw all this together by looking at the map of Ireland and observing therelationship between the suggested sea passages across the Irish Sea and the pattern ofprehistoric settlement.

The map we have used is enlarged from that in a paper by M. Davies in AntiquariesJournal Vol.25 (1945) and the suggested sea passages added. Davies, in her paper, isconcerned to show that there were sea lanes across the Irish Sea and that they wereinfluenced by the terrain and vegetation on the one hand and by the strong tidalcurrents on headlands and in the North Channel; but she is not specific, as we havebeen, about the sea passages.

It will be seen from the map that the points of entry to Ireland that this paper proposesare very relevant to the settlement pattern on both sides of the sea. Let us look at themfrom the South.

Tramore. The bearing from St. Ives leads to Tramore bay on the coast south ofWaterford. The graves concentrated here are known as “passage graves”; they do notoccur elsewhere in Ireland; they do not occur elsewhere in Britain except in the ScillyIsles and Cornwall.

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Wexford. Two bearings lead to the coast north of Wexford harbour; from NewportBay in Dyfed and from Newborough Warren in Anglesey. The coast here is open, butchanging sea levels may have revealed an island offshore; based on the present 5fathom line, these bearings would have lead north and south of the Island. As a pointof entry to Ireland it would have lead to the settlements in the South and West.

Arklow. The more northerly bearing from Newport Bay leads to the open shore Southof Arklow, between Ballymoney and Courtown. It will be remembered that these twobearings from Newport lie to North and South of Mt. Leinster; and so too would theroutes inland; this northerly one leading to the settlements West of the WicklowMountains.

Drogheda. The bearing from Galloway leads to the open shore just south of the mouthof the Boyne; from which point of entry it is a short distance to the large collection ofgraves dominated by New Grange. A point of entry might be expected, in this regionbecause of the typographic similarity of the Court cairns in Northern Ireland andSouth West Scotland.

We have shown no points of entry on the North Channel. There is one candidate; thealignment from Ballochray in Kintyre (Thom A.4/4) does give a bearing on RathlinIsland off Ballycastle bay on the North Coast of Antrim. Despite the strong prehistoricpresence in that area, we have not included it; preferring to treat it under“observatories”.

Coleraine. The only point of entry on the north coast seems to be the bay of Coleraine.For this there are two bearings; from Berneray and from Islay. As a point of entry theroute leads either to the extensive settlements of Tyrone or to the settlements ofAntrim and the axe factory of Tievebulliagh. Taken with the routes between regionson the West cost of England and Wales that we have discussed in some detail, theresult is a remarkably coherent network of sea communications.

Discussion of sea passages (Fig.10)

By itself this theory only makes matters worse; the suggestion is that we have aconsistent network of route indicators across open sea of varying length from 50 kmto 350 km. Consistently the passages are from sandy beach to sandy beach andavoiding areas of strong tides, and between one area with Neolithic association andanother.

M. Davis went some way with this idea in 1946 and 1947 in J. Soc. Ant., (the map ofthe Irish Sea is taken from her paper with my sea passages overlaid). So perhaps allwe are lacking is some evidence that sea going craft were available and that theycould develop a technique for sailing out of sight of land in choppy seas. We have noboats in the Archaeological record, but there are several sea passages of 40—50 kmthat were regularly made (because the archaeological record is contin­uous at bothends); Scilly Isles, Channel Isles, Pentland Firth to Orkney, the Minch to theHebrides, Straits of Dover and a passage to Ireland. They moved the Stonehengeblue— stones from Prescelly in South Wales and that had to include the constructionand navigation of a very heavy raft across the British channel. They had to be sailors

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to that degree. The archaeological evidence is discussed in “Man and the Sea” byPhilip Banbury.

But what use were the alignments? The best suggestion seems to be the analogy of theSouth Pacific Islanders described in Lewis’s “We the Navigators” who were able tosail in low tech boats some 300 miles or so using star settings, the set of the swell andso on. This view has recently been reinforced by Sean McCrail in discussing preRoman traffic across the English Channel.

So we have cleared up a lot of the isolated alignments by this theory; but you will seewe are also suggesting a regional grouping of sea passages; indeed the organisationalfeature that all passages are indicated from one end only. And in each region with seapassages there is a site specialising in the observation of limiting declinations of sunand moon.

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Part B. Observatories

By associating these observatories with sea passages we are suggesting that they mayhave been associated with navigation; with the prediction of tides. We saw that thesea passages avoided bad tidal streams, but with the sailing technology onlydeveloping there will be particular advan­tage in knowing when the shortest neap tidewould be.

The observatories seem to show a progression through three main phases; those likeCastle Rigg (Galloway, Callanish, Stonehenge I) that from a centre observed themovement along the horizon; those where the observer had to move along a welldefined path for the moon rise or moon set to be observed in a particular notch; andthe observatory at Carnac where a large central monolith could be observedthroughout the North West and South Western sectors.

Thom developed his survey of these observatories on how well they could havedefined the ecliptic (e) the inclina­tion of the orbit of the moon to the ecliptic (t), thesemidiameter of the moon - (s) and the lunar wobble of 9’ (~ ). What he did not dowas to observe that by continuously observing (at Carnac) both northerly andsoutherly sectors the elliptical orbit of the moon could be determined by measuringthe variation of parallax. All these lunar variations affect the state of the tide and Ihave shown (using Thom’s data) that they could be laid out on the rows at Carnac andhave provided an enormous tide table.

In considering the site catchment areas concerned with the Stone axe trade we notedthat these could be assembled into regions that are geographically independent. Inthese regions we set aside particular sites of circles and alignments as “observatories”.Let us look more closely at what we mean.

The regions are all connected by our network of sea passages identified by a stonealignment, an adjacent sandy beach; the indication being of a satisfactory sea passageto a target sandy beach also associated as a point of entry to a Neolithic area. Theregions that originate sea passages are from South to North: - Brittany, Cornwall,Dyfed, Gwynedd, Cumbria, Galloway, Argyll, Hebrides.

There are others that do not; Ireland, for instance; Yorkshire; Northumbria; EastAnglia.

Each of these regions, with the exception of Gwynedd, contain one “observatory” siteat least; though all are of various types and complexity. With two exceptions no othercoastal region has an “observatory” site. Let us look at the exceptions: - Gwynedd.There is only one site, W2/1 Penmaenmawr in the region. Without too muchanticipation of our argument, this is a “late” site so that for most of the period theregion depended on sea passages controlled from other regions. We cannot be tooprecise about early or late sites, at any rate at this stage, but by “early” we might meanlarge undressed stones, and by “late” we might mean small stones in specialisedgeometric arrays and association with beakers.

Caithness, Orkney and Shetland. This region, dominated by difficult sea passages,(but from the archaeological record, sea passages that were made in the period), is

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only indirectly linked to the other eight regions. But we must include it and its two“observatory” sites of N1/1 Mid Clyth (and other stone row sites in the district) andthe ring of Brodgar in Orkney.

Stonehenge is clearly in the category of “observatory” but the regional associationwith the other seafaring regions is less direct. The bluestones came from Prescelly;and we identify a sea passage from Brignogan in Brittany to Poole Bay. Theassociation of Stonehenge with seafaring must rest on its position in the region ofSouthern England; the distribution map of Stone Axes (Clough & Cummins 1979) inSouthern England is suggestive of a coastal traffic along the south coast and intoSouthern Essex.

So we have nine regions with observatories, and at the same time an active interest inseafaring. On top of the support for seafaring between regions, we can now say thatthere is a strong support for observatories being associated with seafaring.

What then are these observatories and how could they have assisted the seafarer?

There seem to me to be two principle techniques that would develop from thewidespread observation of stars and moon needed for navigation. Very quickly theywould observe the association of springs and neaps with the phases of the moon. Itwould take a lot longer to unravel the complex­ities of the tides and of associatingthem with the eccentricity of the lunar(?) orbit and the 9’ perturbation of the lunarorbit. Over a protracted period they would observe that the stars precessed. That beingso, we must expect a variety of sites reflecting this developing set of ideas; we wouldexpect not only development at a site but between sites and regions.

Tides themselves are directly proportional to tidal currents; it is this aspect whichmakes them of such concern to primitive navigators.

The site at Castle Rigg L1/1 in Cumberland is a useful model of the primaryobservatory of sun and moon; we reproduce the panorama from Thom 1966 (page 2).The panorama of the bowl of hills surrounding the site enables an opinion to be madeon the uses to which the site may have been put. However, Thom (1967) lists herelimiting declinations for Sun at +24.3 and Moon at —29.8.

In Galloway the site Laggangarn G3/3 is similar in the type of observation that maybe made; various solar calendar lines are also possible but limiting declinations are forSun -23.7 and moon at -30.4 and -19.6.

In Dyfed we have a problem; there were several major sites south of the PrescellyMountains but they have essentially been destroyed. These circles are close by thelocation from which the bluestones were sent to Stonehenge. The identification of thesource of bluestones “from a small area on the South East slopes (of Prescelly) at Cil-maen-Llwyd” will be found in Antiquaries Journal Vol.3, 1923. A review of thecircles and alignments from this area, dating from about 1910, is by Rev. W. DeneBushell, FSA, “Among the Prescelly Circles” in Archaeologia Cambrensis 6th Series,Vol.XI. We have located these sites on an enlarged part of the 1” 0.S. Sheet 139; butthe alignments and so on given by Bushell are based on stellar alignments and even inhis day they were much depleted. Gors Fawr W9/2 he includes and is intact and we

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have referred to earlier. For the rest we must content ourselves with the category“observatory”.

There is however one precise observation in Dyfed to which we have already referred;Parc y Merw W917. This is a large stone, long alignment indicating the northernslopes of Mt. Leinster and one of the limiting declinations of the moon. Preciselythough this line is indicated, it raises the question of how it could have been observed.The moon sets on this line once every 18.6 years; the period over which the StoneAxe trade ran was between 1000 and 1500 years; we have only between 50 and 80opportunities to make the observation; but only very occasionally is the moon settingactually on the limit of its orbit; the setting on the day preceding and succeeding thelimiting day will be substantially short. We might suppose that by chance the moon isactually observed on one of the occasions when it is truly at its limit; that that isrecorded by an alignment and the repeat performance awaited; but for any useful datato be obtained about the behaviour of the moon a technique has to be devised forestimating, from the shortfall on the days before and after, by how much the limitingposition should be increased. Thom suggests that, if such precise observations aremade, there must have been devised an offset technique (he uses the phrase “a stakemethod”) and that from the parabolic approximation to the lunar movement over thosetwo days there is a characteristic offset dimension for each site, C, for which weshould require some evidence if a precise lunar observation is to be presumed.

The region of Cornwall has on Bodmin Moor a site, the Hurlers S1/1, which appearsto concentrate on the alignment of circumpolar stars; an interest stimulated perhaps bythe observation from the sea route indicated by S1/9 (Nine Maidens) that the starDeneb set on that line. Beyond that speculation we find (outside Cornwell) the siteMerrivale S2/2 on Dartmoor that does show evidence for the extrapolation length C.This site was surveyed by Wood & Penny and reported in Nature, Vol.275, 1975. Thisreport is worth reading for a description and survey not performed by Thom, and forits compact description of the importance and use of extrapolation.

Between two stone circles on the moor some 50m apart there is the opportunity toobserve the setting of sun and moon behind a ridge on which there are two distinctivenotches, between the limits of the ecliptic (midsummer sun set) and the limitingdeclination (e + i) of the moon. Across this viewing platform are two double rows ofstones and a third shorter row. Wood & Penny show that these rows can be interpretedas a device for calculating the extra­polation and for storing the information for aperiod of one to two years about the maximum of the 18.6 year cycle.

Turning now to Scotland. There is an observatory at Callanish in the Hebrides, thatdoes not have evidence of extrapolation but is more comprehensive than the sites wehave so far noted.

There are, however, three observatories in which there is evidence for theextrapolation length and upon which much of the argument for observation of the 9’perturbation rests. The most southerly of these is at Temple Wood A2/8 nearLochgilphead in Argyll. There are in the region a number of sites that individuallyindicate a particular position on sun and moon but at Temple Wood are a series ofstones arid circles arranged so that, by moving along a sequence of them, the setting

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of the moon behind a particular profile of the hills can be observed very preciselyaround one or more of its limiting declinations, much as at Merrivale.

The diagrams of this observatory are from Thom, 1971, and show clearly theopportunity for the observer to traverse but give no indication of how (or whether)extrapolation was carried out.

At Brogar in Orkney we have a similar configuration; it is complex but essentially thesequence of observations is performed by moving along a slightly raised ridge.

The diagrams of this observatory are from Thom, 1978. However Thom’s finalanalysis of Temple Wood and Brogar are set out in J.H.A. Archaeoastronomy, No. 7,1984. (Fig.11)

However, on the mainland of Caithness at Mid Clyth we have not only an observatoryof this type but a configur­ation which is called “Stone Rows” or fans; a number ofrows of fairly small stones are laid out in the shape of a narrow fan. The radius of thefan is identified as the extrapolation length C and the distance between stonesprovides a measure of the correction that must be applied to the limiting positionsobserved on successive days, to determine the true limit. There are, in close proximityin northern Caithness, four of these “stone rows”; suggesting certainly a speciality ofthe district, but probably its genesis and development. The criterion that theobservatory sites were used to measure accurately the limiting declina­tion of themoon turns on the need for an extrapolation technique; and the intellectual attainmentof that tech­nique must rank very high. The essentials are specified in Thom 1971; wereproduce his diagram and nomenclature for the “2 stake method”. The observerplaces a stake d to mark the maximum declination on successive nights; from the mostadvanced stake (L) and that preceding it CR) he has to determine by how much thestake must be advanced (YL) to give the maximum. He needs to know the value (G)of the stake movement corresponding to the declination deficiency half a lunar daybefore and after the maximum; a variable but constant for a particular maximum.

The essential relationship is then

(Fig.12)

Now the geometry of the stone rows is such that they permit the calculation of thisrelationship; we reproduce from Thom 1971 the observatory and stone rows at MidClyth N1/1 in Caithness and the essential geometry of the rows.

(Fig.13)

In considering the stone rows or fans we should include Stonehenge. Thedevelopment of Stonehenge passes in 500 or more years through various phases ofrebuilding that must represent in some way the development of skills in astronomicalobservation. In the “entrance” through which is observed the rising sun over the heelstone a pattern of post holes has been excavated that is fan shaped. No particularattribution is made for this “fan” but may well be the result of some series ofobservations made and is perhaps associated with the origin of the stone fans laterused for extrapolation.

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Finally we come, way down South, to Brittany and to the very complex array ofstones around Carnac. Thom has identified two lunar observatories (Thom & Thom1978); one based on the menhir Le Menec; and a much larger one based on the GrandMenhir brisee at Lochmaraquier. It is sometimes protested that the Grand Menhir wasnever erected; but there was certainly the other one available; in any event there mayhave been some tree or temporary wooden structure in anticipation of the stone. Thescope of the other stones in the district do tend to encourage the idea that the mainobservatory was operated.

The smaller observatory at Le Menec is probably the key to the problem; being thefirst occasion that the North West and South West sectors are viewed on the same £ore— sight. From this “pilot’ study the technical prize would be appreciated andwould justify the large expenditure on the Grand menhir and its observatory.

Here we find, as in Caithness, stone rows set out fan—shaped and based on theextrapolation length G for the Grand menhir; there are two fans, for the alignments onQuiberon, and for the northern sector. The novel feature at Carnac, however, is theenormous stone rows at Kermario and Kerlescan. But it is with the rows at Le Menecthat we shall be concerned.

So you will see that we have eleven observatories and they develop in theircomplexity through at least three technical phases;

a) Fixed alignments on specific lunar, solar, or stellar positions. There arefive of these: - The Hurlers on Bodmin Moor, Prescelly, Castle Rigg,Laggangarn and Callanish.

b) Offset alignments with indication of C for the site. There are three:Merrivale on Dartmoor, Temple Wood and Brodgar in Orkney.

c) Offset alignments with fans of stone rows. There are three:Stonehenge, Caithness and Carnac.

I think that we have just about completed this very complex jigsaw puzzle; with themost advanced observations they were competent to comprehend the details of lunarmovement and to relate it to the tides. But to do that we have to consider the role ofthe Carnac observatory in some detail.

I wrote a paper ten years ago, suggesting that the Alignments at Le Menec usedfortnightly observations of the lunar declination on Le Grand Menhir to predict thefine movement of the tides. That paper only has validity when taken as part of thewider subject of navigation.

That paper comprises the remainder of this part. It is a complex argument and I thinkthat, in order to keep the argument clear, it is helpful to summarise the stages that leadup to the Carnac observatory.

The site at Le Menec (Carnac), then, is the end product of a long period ofobservation which is represented by the periods:—

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1. Determination of lunar and solar limiting positions by fixedalignments.

2. Refinement of limiting positions by defining a traversing platform toobserve the changing position for a period either side of the limit.

3. Calculating from these traverse positions what the limiting positionwould be, by using the stone fans.

4. Increasing the number of traverse positions so that the whole range oflunar movement may be observed; making those observations for the(e + i) and the (e — i) sectors; scaling both to one range, using stonefans; relating the change in those measurements to a measurement oftides on the same set of stone rows.

Components of a Tide Predictor

The pattern of tidal currents around the shores of Western Europe are extremelycomplex (Ref.4). Around head­lands and in other special situations they may wellreach proportions that make small boat sailing unsafe. Even when the chosen courseavoids such danger areas there is generally a pattern of tidal currents, varying andchanging with the tide, of strength 1 to 2 knots and causing sub­stantial drift. Thesetidal currents, however, are approxi­mately proportioned to the height of the tide. Bychoosing neap tides rather than springs to make a voyage, tidal currents can be morethan halved. It is to obtain this advantage that, we suggest, tide predictors weredeveloped.

The components of the tides are of great complexity but from the equator. Variationsof lunar parallax can be measured and provide a measure of apogee and perigee. It iswith the making of this measurement that we suggest the lunar observatories wereconcerned and that they developed a simple way of regularly doing so.

Consider now the motion of the moon relative to the sun. The sun moves in theecliptic plane. Its declination varying through one year from +e to —e (where e = 23°53.4 in 1700 BC) and so determining the seasons. The moon moves in an orbitinclined at an angle to the ecliptic plane so that we shall observe a declination varyingthrough one month from +E to —E. Now E varies between the value (e±i) (where 15° 8.7’ in 1700 BC) through the 18.6 year cycle; the maximum value of E is reachedin a cycle of 27.2 days so we may observe +E and —E once every 13 or 14 days.

The moon is also moving round its elliptic path and taking 27.5 days to do it. It willpass through its closest position to the earth (perigee) and its farthest position(apogee) every 13 or 14 days. So we see that apogee and perigee precess at the rate of0.3 days relative to the cycle of declination maxima. If we were to measure monthlythe limiting declination we should eventually identify the elliptic motion, as shown byvariations of parallax but it would take many years. If, however, we measure thelimiting declination fortnightly we shall see that ÷E differs from —E due to the effectof parallax and shall be able to identify the period in a much shorter time.

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The effect is shown diagrammatically on Fig. 14.

Parallax (P) varies by ± 3.8’ about a mean of 57’, while the moon’s semi—diameter(S) varies by ~ 1.0’ about a mean of

15.7’. Clearly if measurement is being made of one edge of the moon the variation insemi—diameter must be added or subtracted from the parallax as may be appropriate.The effect is always to provide a variation in the apparent altitude of the horizon. It isthe effect of the variation in altitude on the relationship between azimuth anddeclina­tion with which we are concerned. The variation of the angle of the moon’sorbit to that of the sun by the 9’ “wobble” with a period of 173 days provides a furthereffect on tidal range.

Having decided, however, that these necessary effects can be observed, we have toconsider to what use they would have been put. How would the correlation betweentidal measurement and lunar observation have been made? Regular observationswould be made at least twice per lunar month and the full cycle of effects would notbe apparent for 18.6 years. We are looking for some data storage system with at least460 components in it.

The Observatory at Carnac

The alignments described by Professor Thom (Ref. 9,10, 11) based upon the use of LeGrand Menhir Brisee at Locmaraquier provide the opportunities for observation thatwould be required for a tide predictor. The observatory consists of the Grand Menhirused as a foresight for all observations; of two viewing sectors for the range ofdec­lination ±(e ± i); and of the alignments of Le Menec. Let us start with the latter.

(A) The Alignments at Le Menec

The geometry of Le Menec is shown (after Thom & Thom J.H.A. Vol.3 Pt.1) inFig.15. It has the following curious and interesting properties:—

a) At each end the rows terminate in a modified circle with typical parameters inmegalithic yards and defined by Pythagorean triangles in the same integerunits.

b) Twelve long rows of stones between the circles that are all spaced (orprobably originally were) at 5my apart.

c) The rows of stones taper in an unusual way being in two connected groups sothat at each end they are separated by an integer series of distances in my. Thesignifi­cance of this is discussed below.

Thom (J.H.A. Vol.3 Pt.3) has shown how this alignment could be used directly to findand store the extrapolation distance and suggests that it is a more sophisticated

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successor to the original stone row sectors. One may deduce also from his Table 3(Thom & Thom J.H.A. Vol.3 Pt.1), that there are approximately the same number ofstones in each row. The exact numbers are shown in Fig.15. The number from Rows,X, XI and XII of 458 gives us a suggestion for the use of the rows. Thom points outthat the ratio of the width of the rows at the narrow end to those at the wide end are inthe ratios of C for the large and small standstills. We have, therefore, to consider asone possibility that they moved from one end to the other through half the 18.6 yearcycle (230 lunations). To move therefore over 460 stones and back in the 18.6 yearswould suggest 2 observations per lunar month (i.e. full and no moon). 458 stoneswould give a resting point in each circle to complete the cycle. Stone rows I to VIII,however, have fewer than 458 stones. The number is, however, roughly made up if,when the tapered West end is reached, the extra periods are counted by going up anddown these last stones to reach the circle. One would presume the use of alternatestones on the outward and inward journey.

(B) The Observation Sectors

However to make use of the observatory all the time and not just at the ~standstills asThom assumes, implies that the foresight at Locmaraquier can be observed at alltimes. There is no problem in the south west sector from Quiberon to St. Pierre but theNorth West sector is undulatory and now covered by scrub and trees that make directobservation impossible.

The north west sector covers the declination range (e ~ i) and the limiting values areprecisely identified by observation points at Kervilor and Kerran though there alsoappear to be longer range viewing stations at Le Moustoir and Crac’h. There are anumber of “Rude stone monuments” within the sector, all of which are placed inpositions of some eminence. These positions between them provide a series ofviewing platforms that cover the whole sector albeit with the inconvenience of havingto move back or forward to the next platform.

The suggestion should be carefully checked but from a computer programmedeveloped to develop map sections from the viewing point to the foresight it doesseem that the sector can be largely covered by viewing platforms at Kervjlor andCrac’h. Between these two runs the river Crac’h and to cover this there seem to be ashort and a long viewing platform; the short based on Kerran and rising to Le ChatNoir; the long based on Le Moustoir and rising to La Madelajne and Marie Roch.

Thom (J.H.A. Vol.3 Pt.3) calculates that the values for 4Gsub0 for Kerran andKervilor are approximately the same and those for Quiberon and St. Pierre areapproximately four times and double respectively. If the data, not only for the extremepositions but for the full width of the sectors, are to be transferred to a data store theywould have to be adjusted. There is a line from Kerran to Kervilor along whichthroughout the cycle 4Gsub0 would be constant (or nearly so). Values from thesouth—west sector would then need to be reduced to give 4Gsub0 = constant in thesame way. Alterna­tively, they might have used the changing value from Quiberon toSt. Pierre as the standard. In that case Kervilor would stand at one end •of a similarnorth—west sector line that would in practice run to Crac’h. It looks as if this latterproposal is the more likely. Though “standardisation” of values for the observingplatforms in the north—west sector would still be needed to this line.

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To Operate the Tide Predictor (Fig.16)

The observation has been made that there are enough stones in each of the rows at LeMenec for some information to be placed on them twice a month for the whole 18.6year cycle. Our hypothesis starts from this possibility. Namely, that starting at thewestern end of the Le Menec alignments information is brought from the observationsectors concern­ing each limiting declination maxima. We suggested in the lastparagraph that the information would be “standardised” to permit comparison ofobservations from both sectors. We can consider, as Thom in effect does, that the LeMenec alignments are a model in “my” of the measurements made in the field of“rods” (1 rod = 2½ my). Any arrangement of stones used for the determination ofdeclination maxima must be large enough to accommodate the maximum daily stakemovement possible. This figure is 4G. The mean values of 4G; 4Gsub0, are given inJ.H.A. Vol.3 Pt.3. The value for Crac’h is extrapolated from that for Kerran in thefollowing table. The maximum and minimum values of 4G at any time are 4Gsub0 (1± 4a) where a is the eccentricity of the moon’s orbit and given in J.H.A. Vol.3 Pt.3 as0.0548. These limiting values have also been shown in the Table I.

We see that at both the major and minor standstills the maximum value of 4G comesclose to the width of the rows in my; 122my at the west end and 77my at the east. Thetaper of the rows is about right for the use of the rows on a calendar basis throughoutthe 18.6 year cycle. The major standstill would occur at the west end, the minor at theeast.

The quadratic relationship is translated by Thom into giving each row an integer value(Table II) which will be the value of yL to be added to the advanced stake to indicatethe declination maximum.

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In making successive observations of declination maxima in alternate sectors we areobserving the variations in apparent altitude of the horizon caused by the moon’sparallax and therefore of the moon’s distance from the earth. The mean value ho is aconstant that is allowed for by Thom in this calculation of declination from observedazimuths. The mean value ho is 57.7’ and the extreme values are 53.9’ and 61.5’Ref.8 (p.76). The ratio of h to change in declination lies between 0.91 and 1.0 and isassumed with sufficient accuracy to be 1. We are trying, therefore, to observe a rangeof variation in declination of 7.6’. The ground movement corresponding to 1’ ofdeclination depends upon both the distance from the foresight D and on the variationof azimuth with declination.

From Table III showing ground offsets for 1’ declina­tion we see that the maximumrange of parallax would show up on the rows at Le Menec as approximately (4.2 x7.6) = 30my. When successive observations are apogee and perigee, successive valueswill be 30my apart; midway between they will be equal.

By choosing the observation platforms that we have, we find that there is somethinglike a constant offset per unit of declination throughout the width of both sectors. Inthat this simplified the rules for operating the predictor, it gives some support to theassumption that these were the observation lines used. It is unlikely to have beendeduced as such.

The technique suggested makes~ no allowance for the large variation of C betweenapogee and perigee. In practice the “error” of not allowing for this variation is, by themethod suggested, to increase the separation across the rows at the extreme values. Atperigee, G max, the correct value of C will be used, but at apogee, C mm, the methodsuggested will choose too high a row number; giving too large a value for perigee andtoo small a value for apogee. As the position for perigee was smaller in any case thanthe value for perigee the error magnifies the separation.

While the technique proposed would work well near the major and minor standstillswhen the change of declination of the maxima from month to month is quite small, itneeds to be shown that a simple technique was available for the rest of the periodwhen the monthly declination change is substantial. The calculations used in Ref. 8and elsewhere are based on the use of a parabolic function close to the maximum. Therest of the cycle can be treated as a linear function connecting these parabolas.

We showed earlier that the number of stones in the rows suggests that a calendar waskept by moving on two stones at each full or no moon with an “end play” by movingup and down the rows to the west end circle. As this progression is developed notonly will the effects of parallax on successive measurements be observed, but twoother effects will be observed. The 9’ “wobble” will become apparent as a sinusoidalmovement of the mean position of the stakes with an amplitude of 36my and a period•of 173.3 days or 6 lunations. There will also be an initially small but steadilyincreasing shift of the observations as the declination maxima move away from thestandstill. At some point a new observation point must be chosen or a correctionmade.

Parallax takes up 47my and the 9’ “wobble” 36my of the width of the rows which atthe major standstill is 122my wide. This leaves 39my for drift from the standstill

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before a correction need be made, but it will be 264 days or 9 lunations before it isnecessary. Assuming that the rest of the cycle until 9 lunations before the nextstandstill is approximated by a linear function the correction needed would besomething like l5my each for 23 lunations followed by 3Omy for each of 51 lunationsand 23 at l5my. Possibly the correction would have been approximated by moving theposition back one row or two rows as appropriate. It does suggest a simple andworkable technique.

Such a display of the movements of the moon on the alignments of Le Menec wouldneed to have been complemented by a display also on the stones of the height of thetide. There is no way of checking that, but we would note that the three other sets ofstone rows away from the Carnac area are at Endevon, S.W. Finistere and Camaret(opposite Brest) which may suggest repeat displays of lunar position and tide in theadjacent areas that we have associated with sea passages.

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Part C. Logical Inference

Elaborate theories such as Thom’s (or my own) have to stand the test of logicalanalysis; and Thom was immedi­ately aware of the need to do that. In asserting thatthere was a quantum of length inherent in his observations he persuaded the Oxfordstatistician Broadbent to develop a method for identifying quanta. One of the moreamusing facets of the argument has been the perplexity of the statisticians in beingunable to handle the question; its highlight being a special meeting of the RoyalSociety in which Prof. Kendal gave a memorable discourse on “hunting Quanta”!)

The ideas of sea passages and of Carnac as a tide table I had developed by 1975, but itis only in the last couple of years that I have understood how they should beevaluated.

This new approach involves a logical system that is concerned with the choice of thehypothesis best supported by the data, rather than the extent to which data supports agiven hypothesis. While the concept is not new its use has in recent years beenadvocated by Hacking (1975) and Edwards (1972). I propose to base my commentson these two books, particularly on Edwards’s use of the statistical concept ofLikelihood as applied to scientific inference.

I have adapted what Edwards has to say, I trust without Bowdlerising it, to a simpleset of criteria suitable for making an everyday judgement between hypotheses.

For a statistical model I have taken the Jigsaw puzzle and applied to the criteria ofacceptance the simple test of “go/nogo” as if it were an Engineer’s gauge; that if thepiece is right all the parameters will be “go”; if any one is “nogo” then that hypothesisfails, must be amended or rejected.

We are impressed if two pieces of a jigsaw puzzle fit together; we are impressed if akey fits a lock; we are impressed if a coin being tossed always comes down heads.Can we find some method to quantify the feeling we have of being impressed? Howmany coincidences do we need to accept that the hypothesis is supported by the data?

Let us start by tossing a coin. We shall be making a series of trials in which we mayget heads (success) or tails (failure); if we make n trials then r of them will besuccesses and (n—r) will be failures.

This is a binomial trial: the precise statement is that, with the given hypothesis p, theprobability of obtaining a particular result R is given by:

In the problem we are discussing we are not trying to estimate a value; of decidingwhether a given result fits a hypothesis or not. Our concern is to choose the besthypothesis from the results we have; are the results R better supported by hypothesispsub1 or psub2.

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Edwards defines the likelihood function L(p/R) as proportional to P(R/p); this is thefunction by which we optimise p given results R. Because it happens to be the ratio ofLikelihood that we compare, it is arithmetically desirable to take logs; this functionLn [L(p/R)] Edwards calls “Support” and uses the symbol S. We are, in practice,always concerned with differences of support between one proposition and another.

The outcome is a superb arithmetic simplification and great logical clarity.

We get, in general

S(p) = Ln [L(p/r)J = Ln [P(R/p)} + k and we can forget k as we are only interested indifferences of Support

and in the binominal case

S(p) = r Ln p + (n—r) Ln (l—p)

The Measure of Support

Let us continue to consider the coin that, being tossed, always comes heads; we willrelate this to the Jigsaw puzzle subsequently.

We have tossed n times and r times it has come heads; we shall get a series of resultsas we continue to toss. How often should we do it? When will the Support for thehypothesis be strong enough?

With the coin, and many other~ problems of the go/no go variety, we are reallyconsidering the choice between two hypotheses; the coin has a head and a tail and isotherwise normal, or the coin has two heads.

In the case of a normal coin p = ½, but if the coin has two heads p = 1.

We can simplify the calculation again

S(½) = r Ln ½ + (n—r) Ln ½ = ~n Ln2

5(1) = r Lnl = (n—r) Ln 0 =

In the special case where the coin always comes heads

= r and S(1) =0 (I take it that Limit pLnp = 0 as p tends to 0) and of course when n~ rthe hypothesis fails.

As we toss our coin that always comes heads the support for the hypothesis that it isdouble-header increases with the number of throws. S= n Ln2 or S = 0.7n

Edwards is at pains to emphasise that each experimenter has to establish his owncriteria for accepting the importance of a given magnitude of 5; he does suggest auseful peg on which to hang our hat.

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(Fig. 17(a))

So if we have tossed three heads in succession we would have S = 2.1 for thedouble—headed coin and that support would be about the same as “the result beingsignificant at the 95% level”. But they are not the same statement and we must notconfuse them; we do have a basis for our Support system.

The Jigsaw Puzzle

A coin being tossed is one, readily comprehended, example of a family of systemsthat are concerned with a go/no go test; it does or it does not happen; there is nointermediate state of perhaps, perhaps not. Many problems are like this; fitting a pieceof a jigsaw certainly is; but we do now have to detach our mind from the coin to thesystem of which it is part.

Let us say that if we apply a go/no go test and it always gives the result go or no go,then we have a measure of support for the system. The tests do not have to besequenced in time; they do have to be independent.

In fitting two pieces of Jigsaw together we are matching two complex curves (asregards shape); each variable of one must be matched by the corresponding variableof the other with a more or less uniform tolerance between them.

How many dimensions are needed to define an irregular curve? Let us simplify thequestion to that of a spigot or socket of moderately regular shape as the basic elementof fitting one piece of a Jigsaw into another.

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Let us restrict this shape to the minimum requirement of three arcs of circles, each ofdifferent radius and angle. Two co-ordinates are required to define the centre of thearc. There is a radius R and two angles w, and w2. Fig. 17 ( b)

The three arcs of the spigot join at their ends and the one is tangential to the other. Sixvariables are needed (ab), (cd), (ef), to define the three centres of arc. We then need todefine one radius and two angles, say w1 and w4. (Fig.17(c))

(the angles w2 and w3 are defined by the other variables).

To define a simple spigot of 3 arcs we need 9 variables and for each additional arc weneed an extra 2 variables. So when we have a fit at least 9 variables agree.

More variables are needed to define the pattern match; we can define a point on theshape by one angle and a colour change by the points of intersection on the shape (w5& w6) and the colour on either side (C1 & C2) presents a further feature ofimportance.

In matching shapes the choice is binomial (either/or). In the case of colour we couldhave the choice of several; the choice would be multinomial. In the case of m possiblevalues where correct value always arises the support is

S = n Ln m

We now have a second measure of our Scale of Support. The interpolation is arbitrarybut we might set ourselves the following criteria:

match

We may elaborate this scale with experience; for some my measure of support will betoo cautious, for others too optimistic; it will depend on the problem and the cost ofbeing wrong.

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The measure is however a precise statement of the data and its support of theproposition.

The Megalithic Yard

Before returning to the question of what inference to place on our observations of seapassage indicators, we must look at two examples to do with the claim that there is aunit of measurement, the megalithic yard (MY) of O.83m and its related measure, themegalithic rod of 2½ MY; the statistical model of the Jigsaw puzzle that we have setup is so directly related to this problem and it will provide two further items in ourScale of Support.

Thom’s surveys of stone rings suggests that in addition to circular rings there aresome more elaborate rings which he calls Type A and Type B. The geometry heproposes for Type B is typified by his survey of Black Marsh, Shropshire D2/2; it isbased on circular arcs. The construction for the shape given in Thom (1967) p.28 isdefined by the coordinates of an equilateral triangle and requires six variables. Thecircle of stones consists of 36 stones whose position is defined by 36 x 2 = 72variables. Perhaps not all the stones may be judged to be correctly placed and we maywish to eliminate them, or we may choose a “fit” of the stone to the geometry.However we use our judgement on that, if the 36 stones are a fit to the curve then weshould have n = 72 less the degrees of freedom used in defining the curve, or n = 72— 6 = 66, and S = 66 Ln 2 = 46.

In this case, however, an alternative design was suggested by Angell (1978) where hesuggests that Type A and Type B circles may be drawn by a construction employingthree pegs and a rope of constant length. We have done some calculations using suchan “Angeli shape” for the example he quotes for Black Marsh, Shropshire, D2/2, andwe find ourselves with a construction similar to that for ellipses. The triangle of pegshas sides of 5 MR, 3.5 MR and 3.5 MR, and a cord length of 17 MR. However for thisconstruction the vertices of the triangle (six variables) and the cord length (onevariable) — seven variables in all — have had to be specified. For the construction asa whole we can calculate the support for the design on the same basis as for Thom’sdesign but we would need to go back to the site survey to obtain a meaningfuljudgment of the difference of support for the two hypotheses.

Avebury. The enormous circle at Avebury is of a shape quite unlike any other; it isalso much damaged. However, from the 44 or more stones (or whose position isknown) Thom has prepared an accurate survey and proposed a complex curve to fitthem. This work is described in (Thom 1967) but a further survey, confirmation of theproposed curve and a precise calculation of MY is described in (JHA, Vol.7, Pt.3,

No.10, 1976). The diagram is reproduced from Thom (1967).

The construction of the ring is based on the setting out of a “Pythagorean” triangle ofsides 30, 40, 50 MR, and radii of arcs 80, 104, 300. Seven circular arcs are thusdefined and 44 stones lie on them ± 2 ft (or thereabouts, which will do for our presentassessment). Now this again is a very close analogue of the support for the fit of twopieces of Jigsaw.

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We need three points (six dimensions) to define the arc of a circle; we have 44 stonesdefined by 88 dimensions. However for the Construction as a whole 13 points havehad to be specified (A B C D E F C H J K L M S). So that for the construction as awhole we have 44 stones (88 dimensions) with 13 x 2 degrees of freedom used in theconstruction.

So: S = 2 x (44 — 13) Ln 2 = 54

Thom maintained that the strongest argument for the use of the megalithic yard (androd) was the layout of Avebury. We could of course try other constructions; or moreprofit­ably try different values of MY from 2.72 ft. Thom, how­ever, notes that for anincrease of only 0.01 ft to 2.73 ft the curve fits none of the stones.

We can extend this argument to Carnac and so on and we shall no doubt be able tomodify and improve our inference from the data of Thom’s surveys. Here we areprimarily concerned with the proposal of navigation aids.

Assessment of Sea Passages

Now that we have introduced the Method of Likelihood for assessing the fit of piecesin a Jigsaw and established criteria for making that assessment we can use the sametechnique to assess the suggestion in Part A of this paper that there are a number ofindicators of sea passages from sandy beach to sandy beach between areas ofNeolithic settlement and avoiding the worst of the tidal currents.

The observations of Part A are repeated in Table A, showing not only the bearing butthe length of passage. To assess the support the data provide for any hypothesis weneed to construct a statistical model and then to apply our data to it.

From any of the beaches with indicated passages there is a seaward arc within whichwe would have considered a possible passage. At the far shore there may, usually willbe, more than one sandy beach with neolithic associations which we would haveaccepted as the objective of an indicated passage. It will be adequate for thisassessment, I think, if we simplify the calculation as follows:

Suppose the alignment to give an indication to within 1°;Suppose that each beach on the far shore to subtend 5° at the starting beach.

Then of the seaward arc, an arc 5 x (the number of target beaches)° would give asuccess; the rest of the arc a failure. We have described a binominal trial and may usethe techniques described earlier in this section.

It is useful to be specific about the statistical model; we have a bag with “balls” in it.Some of the balls are red (target beaches) and some black; some we can feel have arough surface (sea passages) and some smooth. We draw from the bag a roughsurfaced ball and observe its colour. If the outcome of the trial is that all the roughballs withdrawn are red then we have the outcome of one of the go/nogo trials weproposed.

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In this case in the support function

S(p) = Ln p + (n — r) Ln (1 — p)

we have the value for p the ratio of the arc subtended by the target beaches divided bythe seaward arc. This hypo­thesis we compare in the first instance with the hypothesisthat the indicated passages occur at random (p = ½).

For each trial of the hypothesis we use one of the indicated passages; which bydefinition are “successes” so that in each case r = n = 1.

We show in Table IV our assessment for each passage of seaward arc; the possiblebeaches; and the possible arc. From some beaches there is more than one indicatedpassage in which case r = n = 2 or more.

The support for the hypothesis is about S = 30 which is very convincing even thoughone might question some of the assumptions such as the extent of the possible arc.The support is spread remarkably evenly; each of the three main regions Brittany (8.3)Hebrides (10.7) and Western Britain (11.0) providing similar support. We have alsoshown the support contributed by passages of different length each length providingsimilar support.

We can and should construct further hypotheses from the data of sea passages butthey must, I think, take into account a variety of archaeological judgments on thetypology of the monuments and artefacts at each site and they will succeed as thesupport for them is substantially better than for that described here.

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Part D. Reflections

It is twenty years since Alexander Thom published his Megalithic Sites in Britain. Itwas a book that had an immediate fascination; the technical quality of his work wasobviously of a very high standard but he had become involved in a multidisciplineproblem of some complexity. The Engineer as Surveyor involved in an archaeologicalproblem in which the civil engineering problems were of surprising magnitude, foundthe immediate need for the Astronomer and for the Statistician to provide the solutionof a novel problem.

If controversy has not raged continuously since then it has indeed created someschism in archaeology and puzzlement amongst the statisticians. The archaeologist isreluctant to grant skills of observation, mensuration and information storage toprimitive and illiterate people; perhaps not giving them enough credit for engineeringand nautical skills inherent in the record and for the remarkable act of intellect at theend of the period in the discovery of bronze.

My appreciation of the doubts and problems of the Statistician have developed overthe past ten years with my understanding of this problem. An innate objection to someof the constraints of the statistician lurked at the back of my mind for many years butit was not until I came serendipitously on Edwards’s “Likelihood” in 1972 that I wasable to put my thoughts in order. -

Edwards’s book and Hacking’s gave some limited insight into the logical difficultiesof statistics and scientific inference. The key, of course, is the emphasis that Edwardsplaces on developing the ideas of R.F. Fisher on likelihood; that statistics forwhatever useful reasons in the 1930’s proved something of a dead-end inconcentrating on “significance testing”; that for many problems in science the criteriawas not the question of how probably the facts fitted a given hypothesis but whichhypothesis best fitted the facts.

I have tried in this paper to keep the factions in separate rooms while I negotiate withthem! Each part contains a major new concept that does need to be digested andaccepted on its own; and yet how shall we overcome incredulity without seeing thateach belongs as an essential part of the whole?

Part A is for the archaeologist; it takes up a theme of sea passages in Neolithic timespropounded by Davis in 1945 and 1946 and suggests a pattern of routes that accordswell with the settlement record. The test of credibility lies in the general region ofseamanship and navigation and here I have been very grateful for the recent (1983)work by Sean McGrail in presenting the professional’s view of what was, or couldhave been, done.

Archaeologists will rightly take exception to my lumping all Neolithic monumentstogether in a site catchment area; that was only a preliminary classification of themthat has led to the proposition of sea passages. The techniques for evaluating logicalinference put forward in Part C now needs to be developed to study the cluster ofmonuments in each Site Catchment Area and the relationships suggested by the seapassages; that will be a complex problem as the distri­bution patterns of stone axeshas demonstrated.

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Part B is for the Archaeo-astronomer; to suggest that the “observatories” so carefullysurveyed by Thom form a pattern linked geographically and probably operationally tothe seafaring regions. My particular contribution is to suggest that the enormousexpenditure of effort around Carnac was dedicated to the solution of a very pressingproblem (tidal currents) by the crowning glory of astronomical observation; that whenobserved at its limiting declination every fortnight (instead of every month) there wasanother anomalous movement (parallax) that accounted for much of the remainingtidal anomaly. The cost was high but the prize was great; using the network of seapassages each region could by a local calendar regularly updated know when the bestdates for sailing would occur.

I do not think we have had any better suggestion; I do not see the potential in all thateffort just to predict eclipses; even if they did, not so very many will occur tocorrespond with the limiting conditions measured.

Whether the argument that there was a unified unit of measurement (the megalithicyard) preceded or followed the success at Carnac is perhaps not important. That it didexist is the question behind all the debate. I am quite sure that it exists as a usefulunifying feature throughout the seafaring regions, in their observatories and in someplaces beyond that. But not all circles everywhere.

It is just this final question that lies behind Part C and has been the cause of thearguments among statisticians. I have not come across any appraisal of the logicalbasis of acceptance of the fit of one piece of a Jigsaw Puzzle to another; I believe myadaptation of the method of likelihood to doing that provides just the tool needed toexplore a great many problems concerned with getting the best fit of data to a curve.Carefully pursued in the way I have suggested I think you will find that argumentsabout whether and to what extent the megalithic yard was used will fall naturally intoplace.

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References

1. Manby, T.G. (1965) “The Distribution of Roughcut “Cumbrian” and relatedstone axes of Lake District origin in Northern England”. Trans. Cumb. &Westmoreland Antiquary & Archaeological Soc. Vol LXV new series,1965.

2. Davidson, I. (1983) “Site variability & prehistoric economy in Levante” in C.Bailey. Ed. Hunter-gatherer economy in prehistory. CUP.

3. Scott, Sir Lindsay (1951) “The colonisation of Scotland in the secondMillenium BC”. PPS. new series Vol XVII.

4. Davis, M. (1945) “Types of Megalithic Monument of the Irish Sea and NorthChannel Coastline; a study in distribution”. Antiquaries Journal XXV.

5. Davis, M. (1946) “Diffusion and Distribution patterns of the MegalithicMonuments of the Irish Sea and North Channel Coastline. Antiquaries JournalXXVI.

6. Clough, T.H.McK. & Cumins, W.A. Stone Axe Studies. CBA ResearchReport No.23.

7. Crawford, O.G.S. (1927) “Lyonesse”. Antiquity Vol.1.

8. Fowler, P. & Thomas, C. “Lyonesse revisited. The early walls of Scilly”.Antiquity Vol LIII.

9. Thomas, C. & Pool, P. (1964) The Principal Antiquities of the Lands EndDistrict. Cornwall Archaeological Society. Field Guide No.2.

10. Michell, J. (1974) The Old Stones of Lands End. Garnstone Press.

11. Ridgway, M.H. (1946) “Prehistoric Flint Workshop site near Abersoch,Caernarvonshire”. Arch.Camb. Vol XCIX Pt 1.

12. Lewis, J.B. (1971—2) “An account of the Penbedw Papers in the FlintshireRecord Office”. Flintshire Historical Society Vol 25.

13. Fox, Sir Cyril & Dickens, B. (1950) The Early Cultures of North WestEurope. H.M. Chadwick Memorial Studies.

14. Gresham, C.A. & Irvine, H.C. (1963) “Prehistoric routes across North Wales”.Antiquity XXXVII.

15. Lees, D. (1984) “The Sanctuary: A Neolithic Calendar?” Institute ofMathematics & its Applications Vol 20.

16. Lambrick, C. (1983) The Rollright Stones. Oxford Archaeological Unit.

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17. Joussaume, R. (1985) Des Dolmens pour les Morts. Flachette.

18. L’Architecture Megalithique. Colloque du 150~ anniversaire de laSociete Polymathique du Morbihan. (1977) Chateau Gaillard Vamey.

19. Lockyer, Sir Norman. (1906) Stonehenge and other British stonemonuments astronomically considered. McMillan.

20. Lockyer, Sir Norman. (1905) On the Observations of Stars made in someBritish Stone Circles — Preliminary note. Proc. Royal Soc. Vol 76—A.

21. Bushell, Rev. W.D. (1910) “Amongst the Prescelly Circles”. Arch.Cambrensis 6th series Vol XI.

22. Williams, C. et al (1963) Swansea Bay to Worms Head. Gower Society.

23. Wood, J.E. & Penny, A. (1975) “A Megalithic Observatory on Dartmoor”.Nature Vol 257. 18 Sep 1975.

24. — (1972) “Ancient Astronomy at the Royal Society”. Nature Vol 240. 29 Dec1972.

25. Angell, Ian O. (1978) ‘Megalithic Mathematics, Ancient Almanacs orNeolithic Nonsense”. The Institute of Mathematics and its Application”. Vol14. No 10.

26. Freeman, P.R. (1976) “A Bayesian Analysis of the Megalithic Yard”. Journalof the Royal Statistical Society A. Vol 139. Pt I.

27. Thom, A. (1955) A Statistical Examination of the Megalithic sites in Britain.Journal of the Royal Statistical Society. Vol 118 Pt III. 1955.

28. Thom, A. (1966) Megalithic Astronomy: Indications in Standing Stones.Vistas in Astronomy. Vol 7.

29. Thom, A. (1967) Megalithic Sites in Britain. Clarendon Press, 1967.

30. Thom, A. (1971) Megalithic Lunar Observatories. Clarendon Press, 1971.

31. Thom, A. & Thom, A.S. (1978) Megalithic Remains in Britain and Brittany.Clarendon Press, 1978.

32. Heggie, D.C. (1981) Megalithic Science. Thomas & Hudson, 1981.

33. Thom, A. & Thom, A.S. (1971) The Astronomical significance of the LargeCarnac Menhirs. Journal for the History of Astronomy. Vol 2, Pt 3, Oct.1971.

34. Thom, A. & Thom, A.S. (1972, Feb) The Carnac Alignments. Journal for theHistory of Astronomy, Vol 3, Pt 1, Feb.1972.

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35. Thom, A. & Thom, A.S. (1972 Oct) The Uses of the Alignments at Le MenecCarnac. Journal for the History of Astronomy, Vol 3, Pt 3, Oct.1972.

36. Thom, A., Thom, A.S. & Gowie, J.M. (1976) The Two Megalithic LunarObservatories at Carnac. Journal for the History of Astronomy, Vol 7, Pt 1,Feb.1976.

37. O’Nuallain, S. & Walsh, P. (1986) A reconsideration of the Tramorepassage—tombs. P.P.S. Vol 52, 1986.

38. Bambury, P. (1975) Man and the Sea. Book Club Associates, 1975.

39. McCrail, S. (1983) Cross Channel Seamanship & Naviga­tion in the late FirstMillenium B.C. Oxford Journal of Archaeology, Vol 2 No 3, Nov.1983.

40. Hacking, I. Logic of Statistical Inference. C.U.P. 1975.

41. Edwards, A.W.F. Likelihood. C.U.P. 1972.

Credits

At an early Stage I sought the opinion of Prof. Thom about these proposals His kindlyrebuff made me appreciate how substantial a burden of proof lay with the author; thishas delayed the paper - but probably improved the content.

I am indebted to Dr lain Davidson of the School of Archaeology & Prehistory at theUniversity of New England NSW, not only for his filial interest but for subt1y andeffectively acting as my tutor and for letting me give a 17 minute Sandwich Lecture tohis colleagues; a discipline that greatly clarified the presentation.

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Captions of Illustrations

Fig. 1 Castle Rigg Observatory

Fig. 2 Cumbria and the Langdale Axe Factories

Fig. 3 Galloway

Fig. 4 Gwynedd

Fig. 5 Dyfed

Fig. 6 Cornwall

Fig. 7 Brittany

Fig. 8 Biscay

Fig. 9 Hebrides

Fig. 10 Distribution of Megaliths and Sea Passages

Fig.11 Observations to Measure Parallax

Fig.12 Temple Wood & Brogar

Fig. 13 The 2-stake method

Fig.14 Mid Clyth

Fig.15 Layout of Rows at Le Menec

Fig.16 Carnac Observatory; the North West Sector

Fig.17 Jigsaw puzzle parameters

Fig. 18 Type A circle geometry

Fig.19 Avebury

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Fig. 1 Castle Rigg Observatory

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Fig. 2 Cumbria and the Langdale Axe Factories

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Fig. 3 Galloway

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Fig. 4 Gwynedd

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Fig. 5 Dyfed

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Fig. 6 Cornwall

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Fig. 7 Brittany

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Fig. 8 Biscay

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Fig. 9 Hebrides

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Fig. 10 Distribution of Megaliths and Sea Passages

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Fig.11 Temple Wood & Brogar

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Fig.12 The 2-stake method

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Fig. 13 Mid Clyth

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Fig.14 Observations to Measure Parallax

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Fig.15 Layout of Rows at Le Menec

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Fig.16 Carnac Observatory; the North West Sector

Fig.17 Jigsaw puzzle parameters

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Fig. 18 Type A circle geometry

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Fig.19 Avebury