P. B. Davidson. Navigation in the Neolithic86 Supporting Paper III Le Menec as Tide Predictor Rev2011

7/27/2019 P. B. Davidson. Navigation in the Neolithic86 Supporting Paper III Le Menec as Tide Predictor Rev2011

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Peter Davidson 1986 - 2010

MEGALITHIC NAVIGATION 1986 - SUPPORT PAPER III (Rev2 2011)

Alignments at Le Menec as a Tide Predictor

This paper is reproduced without alteration from a paper submitted to JHA in 1976.The first part concerned the alignments between sandy beaches; the second part is

included here.

Components of a Tide Predictor

The patterns of tidal currents around the shores of Western Europe are extremely

complex (Ref.4). Around headlands and in other special situations they may well

reach proportions that make small boat sailing unsafe. Even when the chosen course

avoids 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. These

tidal currents, however, are approximately proportioned to the height of the tide. By

choosing neap tides rather than springs to make a voyage, tidal currents can be more

then halved. It is to obtain this advantage that, we suggest, tide predictors were

developed.

It can also be no accident that the earliest and most elaborate of these tide predictors

fringe the Golfe du Morbihan, where the changes in tidal effects through antiquity

must have been quite startling as the sea-level rose in the Holocene period. (dpd)

The components of the tides are of great complexity but the mathematics of the matter

need not concern us here. It is certain that the setting up of a tide predictor by

Neolithic people would only have been possible by a series of pragmatic observations.

It becomes a requirement of the hypothesis that such a step-by-step approach was

possible. We shall see that several substantial intellectual innovations were needed;

such as the method for measuring the moons limiting declination by calculating the

offset required. However, in the end the predictor had to demonstrate a simple

correlation between the measurement made of the position of the moon and of the

height of the tide.

The tidal components that concern us arise from the relative positions of sun andmoon and their distances from the earth at the time. We shall confine this note to

identifying these components and describing how they might have been measured.

The association of the phases of the moon with the height of the tide is the effect most

likely to have been observed; spring tides are associated with full and new moon and

neap tides with the quarter moons. It soon becomes clear that there is also a seasonal

effect due to the earths position relative to the sun. This shows up as an accentuation

of the difference between springs and neaps at the equinoxes compared to at the

solstices. Neither of these effects requires sophisticated astronomical observation and

little by way of administration to confirm the correlation. It would leave unexplained,

however, substantial variations in the levels of both springs and neaps.


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Fig II

Some idea of the magnitude of these effects is exemplified in Fig. II where the

limiting tides are shown for a year at Oban and the relationship of these to the lunar

quarters and to the equinoxes. The timing of apogee and perigee is also shown to

complete the picture (but will differ somewhat for Brittany dpd).

It is the distance of the moon from the earth that provides the further majorcomponent of the tides. The moon in its elliptical orbit round the earth with the earth

at one focus of the ellipse varies substantially in distance from the closest point

(perigee) to its farthest (apogee). The distance of the moon from the earth is such

however that substantial parallax (in which the edges of the moon appear in different

locations from more than one vantage points dpd) occurs in latitudes away from the

equator. Variations of lunar parallax can be measured and provide a measure of

apogee and perigee. It is with the making of this measurement that we suggest the

lunar observatories were (demonstrably) concerned and that their users developed a

simple way of regularly doing so.

Consider now the motion of the moon relative to the sun. The sun moves in what istermed the ecliptic plane. Its declination through one year from +e to -e (where the

amount termed e = 23deg 53.4 was true in 1700 BC) and so determining the seasons.

The moon moves in an orbit inclined at an angle to the ecliptic plane so that we shall

observe a declination varying through one month from +E to -E. Now the variable

called E varies between the value (e i) (where i = 5deg 8.7 in l700BC) through the

18.6 year cycle. The maximum value of E is reached in 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 (ecliptic? dpd) path and taking 27.5 days to

do it. It will pass 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 (bythe extrapolation distance dpd) at the rate of 0.3 days relative to the cycle of

declination maxima, while E varies relatively slowly taking l3.6 years for the

complete cycle.


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If we were to measure monthly the limiting declination we should eventually identify

the elliptic motion, as shown by variations of parallax, but it would take many years.

If, however, we measure the limiting declination fortnightly we shall see that +E

differs from -E due to the effect of parallax and we shall be able to identify the period

in a much shorter time.

Fig III

The effect is shown diagrammatically on Fig III. Parallax (P) varies by 3.8 about a

mean of 57, while the moons 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 in

semi-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 is

the effect of the variation in altitude on the relationship between azimuth and

declination with which we are concerned.


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The variation of the angle of the moons orbit to that of the sun provides a further

effect on tidal range, but this 9 wobble while being observed was not likely to have

produced a recognisable tidal effect.

Having decided, however, that these necessary effects can be observed, we have to

consider to what use they would have been put. How would the correlation betweentidal measurement and lunar observation have been made? Regular observations

would be made at least twice per lunar month and the full cycle of effects would not

be apparent for 18.6 years. We are therefore looking for some data storage system

with at least 460 components in it.

The Observatory at Carnac

The alignments described by Professor Thom (Ref. 9,10,11) based upon the use of Le

Grand Menhir Bris at Locmaraquier provide the opportunities for observation that

would be required for a tide predictor. The observatory consists of the Grand Menhir

used as a foresight for all observations; of two viewing sectors for the range ofdeclination (e 1); and of the alignments of Le Menec. Let us start with the latter.

(A) Les Alignments du Menec

The geometry of le Menec is shown (after Thom Ref.l0) in Fig. V. It has the following

curious and interesting properties:-

a) At each end the rows terminate in a modified circle with typical parameters in

megalithic yards (denoted my, but the argument would be true regardless of the

arguable case for the existence of a universal megalithic yard dpd) and defined by

Pythagorean triangles in the same integer units.

b) There are twelve long rows of stones between the circles that are all spaced (or

probably originally were) at 5my apart.

c) The rows of stones taper in an unusual way being in two connected groups so

that at each end they are separated by an integer series of distances in my. The

significance of this is discussed below.

Fig V Layout of Rows at le Menec


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Thom (Ref. 11) has shown how this alignment could be used directly to find and store

the extrapolation distance and suggests that it is a more sophisticated successor to the

original stone row sectors. One may deduce also from his Table 3 (Ref.10), that there

are approximately the same number of stones in each row. The exact numbers are

shown in Fig. V.

The number from Rows, X, XI and XII of 458 gives us a suggestion for the use of the

rows. Thom points out that the ratio of the width of the rows at the narrow end to

those at the wide end are in the ratio of G for the large and small standstill We have,

therefore, to consider as one possibility that they moved from one end to the other

through half the 18.6 year cycle (230 lunations).

To move therefore over 460 stones and back in the in the 18.6 years would suggest 2

observations per lunar month (i.e. full and no moon). 458 stones would 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 might have been counted by going up and downthese last stones to reach the circle. One would presume the use of alternate stones on

the outward and inward journey.

This is, however, only a persuasive idea only if it leads on to solving some of our

riddles. At least we can regard it as having the prime requirements for a data storage

system for our tide predictor.

(B) The Observation Sectors

The north-west sector covers the declination range (e + i) and the limiting values are

precisely identified by observation points at Kervilor and Kerran, though there also

appear to be longer range viewing stations at le Moustoir and Crach. There are a

number of Rude Stone Monuments within the sector, all of which are placed in

positions of some eminence.

We show in Appendix I that these positions between them provide a series of viewing

platforms that cover the whole sector, albeit with the small inconvenience of having to

move back or forward to the next platform.

The south-west sector covers the declination range (e i) and the limiting values are

defined at Quiberon and by a position close to the stone sectors at St. Pierre. It seemsthat continuous observation was possible through the sector along the coast, however,

no other stones are known in this area.

Professor Thom (Ref.1l) calculates that the values for 4G for Kerran and Kervilor are

approximately the same and those for Quiberon and St. Pierre are approximately four

times and double respectively. If the data, not only for the extreme positions but for

the full width of the sectors, are to be captured by the data store they would have to be

adjusted. There is a line from Kerran to Kervilor along which throughout the cycle

4G0 would be constant (or nearly so).

Values from the south-west sector would then need to be reduced to give 4G0 =constant in the same way. Alternatively, they might have used the changing value

from Quiberon to St. Pierre as the standard. In that case Kervilor would stand at one

end of a similar north-west sector line that would in practice run to Crach. It looks as


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if this latter proposal is the more likely, though standardisation of values for the

observing platforms in the north-west sector would still be needed to this line.

To Operate the Tide Predictor

The observation has been made that there are enough stones in each of the rows at Le

Menec for some information to be placed on them twice a month for the whole 18.6

year cycle. Our hypothesis starts from this possibility. Namely, that starting at the

western end of the le Menec alignments information is brought from the observation

sectors concerning each limiting declination maxima. We suggested in the last

paragraph that the information would be standardised to permit comparison of

observations from both sectors. We can consider (if we wish dpd), as Professor Thom

in effect does, that the le Menec alignments are a model in my of the measurements

made in the field of rods (1 rod = 2 my) any arrangement of stones used for the

determination of declination maxima must be large enough to accommodate the

maximum daily stake movement (so-called dpd) possible. This figure is 4G. Themean values of 4G; 4G0, are given in (Ref. 11).

The value for Crach is extrapolated from that for Kerran in the following table. The

maximum and minimum values of 4G at any time are 4G0 (1 4a) where a is the

eccentricity of the moons orbit and given in (Ref.11) as 0.0548. These limiting values

have also been shown in the Table III.

We see that at both the major and minor standstills the maximum value of 4G comes

close to the width of the rows in my; 122my at the west end and 77my at the east. The

taper of the rows is about right for the use of the rows on a calendar basis throughout

the 18.6 year cycle. The major standstill would occur at the west end, the minor at the

east.

At each declination maximum the following procedure is suggested (the nomenclature

of Fig. III and IV is consistent with Professor Thoms calculations though varies from

it to clarify the nature of the succession of observations):

a) Using the marker stone for the observation platform chosen, the stakepositions for the observations either side of the maximum are measured as y1 and y2

in rods.


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b) These values are then transferred to the stone rows at le Menec as y1 and y2

my

c) From Row 1 in Fig. V, y2 is offset as is Fig. IV. The value (y1-y2) in Ref. 11

and elsewhere in Thom), is offset from Row XII as in Fig. IV.

d) The amount by which the stake 2 must be advanced to find the position of the

maximum yL is a function of the row number nearest to (y1 - y2).e) This value is deducted from the position of y2 to find y3. It is the pattern

traced by successive values of y3 that is seen to be correlated with the height of the

tides.

We shall discuss below this correlation of y3 with tide but first it is necessary to say

more about the derivation of y3; Ref.11 page 157 describes a correlation between the

row number and the slope of the rows in the western half of the rows at Le Menec. It

observes that due to the varied spacing of the rows an integer value may be given to

each row that is proportional to the square of the distance from the northern row AB.

The same relationship does not appear to apply to the rows in the eastern half

although a similar taper continues. However the matter was arrived at, we may acceptthe integer values of the rows as follows:

Now the maximum value of yL occurs when y1 = y2 and has the value G. This varies

from 31 rods at the west end to 20 rods at the east. At the west end the value of

yL x 2 gives the value of (y2 y3) in my at the east end a factor of 2 rather than2 would be more suitable. Perhaps the factor changed at the knee. We shall see

however that great precision was not needed.

The Data Displayed

In Fig. III symbols y1, y2, y3 have each been given a second suffix N or S to denote

that the observation is made in the north-west or south-west sector, we shall extend

this to imply that second suffixes odd numbers are north-western and. even numbers

are south-western.

In making successive observations of declination minima in alternate sectors we areobserving the variations in apparent altitude of the horizon caused by the moons

parallax and therefore of the moon a distance from the earth. The mean value ho is a

constant that is allowed for by Professor Thom in this calculation of declination from

observed azimuths. The mean value h0 is 57.7 and the extreme values are 53.9 and

61.5 Ref.8 (p.78). The ratio of h to change in declination lies between 0.91 and 1.0

and is assumed with sufficient accuracy to be 1. We are trying, therefore, to observe a

range of variation in declination of 7.6. The ground movement corresponding to 1 arc

minute of declination depends U~0fl both the distance from the foresight D and on the

variation of azimuth with dec1ination .


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From Table V showing ground offsets for 1 declination we see that the maximum

range of parallax would show up on the rows at le Menec as approximately (4.2 x 7.6)= 30my. When successive observations are apogee and perigee, successive values of

y3 will be 30 my apart; midway between, they will be equal.

By choosing the lines that we have, we find that there is something like a constant

offset per unit of declination throughout the width of both sectors. In that this

simplified the rules for operating the predictor, it gives some support to the

assumption that these were the observation lines used. It is unlikely to have been

deduced as such.

Fig IV


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The technique suggested and set out in Fig. IV makes no allowance for the large

variation of G between apogee and perigee. In practice the error of not allowing for

this variation is, by the method suggested, to increase the separation across the rows at

the extreme values. At perigee, G max, the correct value of G will be used, but at

apogee, G min, the method suggested will choose too high a row number. This givestoo large a value for y1 and too small a value for y3. As y3 for apogee was smaller in

any case than the value of y3 for perigee the error magnifies the separation. If (y1 -

y2) approaches 4G then the error is 0, but increases until y1 = y2, when it will be l7

my (the difference between choosing row XII instead of row VIII).

While the technique proposed would work well near the major and minor standstills,

when the change of declination of the maxima from month to month is quite small, it

needs to be shown that a simple technique was available for the rest of the period

when the monthly declination change is substantial. The calculations used in Ref. 8

and elsewhere are based on the use of a parabolic function close to the maximum. The

rest of the cycle can be treated as a linear function connecting these parabolas.

At the major standstill let us suppose that the sequence of observations is started from

the circle at the west end of the rows. The first declination maximum after the

standstill will be the start of the calendar; the starting point the stones on the eastern

boundary of the circle; y2 offset from the point where the circle cuts the sloping line

of stones, close to the end of Row VIII. The maximum value for y3 from this point is

47my, and equals the maximum range of values of y3 if the moon is at apogee, and

the error of not using G mm (described above) is maximum.

We showed earlier that the number of stones in the rows suggests that a calendar was

kept by moving on two stones at each full or no moon with an end play by moving

up and down the rows to the west end circle. As this progression is developed not only

will the effects of parallax on successive measurements be observed, but two other

effects will be observed. The 9 wobble will become apparent as sinusoidal

movement 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 steadily

increasing shift of the observations as the declination maxima move away from the

standstill. At some point a new observation point must be chosen or a correction

made.

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

before a correction need be made, but it will be 264 days or 9 lunations before it is

necessary. Assuming that the rest of the cycle until 9 lunations before the next

standstill is approximated by a linear function the correction needed would be

something like 15my each for 23 lunations followed by 30my for each of 51 lunations

and 23 at l5my. Possibly the correction would have been approximated by moving the

position of y3 back one row or two rows as appropriate. It does suggest a simple and

workable technique.


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Discussion of the Hypothesis

In setting up a complex hypothesis as we have done in this note there is a real danger

of appearing to assert some item that is only a supposition. If the major feature of the

hypothesis is asserted (that navigators needed tide predictors), then it is a fact that a

tide predictor will have certain features, (methods of observing limiting declinationsof the moon).

It is not necessary to assume each particular aspects of how it was done (that stakes

were used, or that a distance was offset from one line or another). It is necessary

however, to explore the practicality of the method proposed in order to establish that

the hypothesis does not fail for some negative reason, (that they had to possess a piece

of knowledge manifestly impossible). Clearly they did not need to be aware of the

astronomical trigonometry behind it, which is adduced here to explain why certain

physical dimensions are encountered.

Unfortunately we do not possess a statistical technique for evaluating complexhypotheses and it is necessary to apply subjective tests to the hypothesis (is it

reasonable, or practical, or consistent with some pattern of behaviour). It is for that

reason that a way in which the stones could have been used has been described. We

are suggesting that each step had a simplicity about it, could have been arrived at on

its own and that when the steps were put together the whole system remained simple

and practical. Perhaps Occam would have approved!

Let us therefore consider some of the features that would have, or could have been

associated with the possession of a lunar observatory for tidal prediction.

Essentially there would have had to be some measure of the tide, probably also set out

on the calendar of the stone rows, from the observation of which the correlation with

the stake positions would have been deduced. How it was done need not concern us,

the requirements are simple administration. We would expect, however, to find some

evidence of stones in the water from which the tide could be measured, We would

expect to find it sheltered from the open sea and close to the alignments.

There are, in fact, two candidates; the extension of the stone rows at St. Pierre de

Quiberon, at one time observed on the foreshore; and the stone circle of er Lannic at

the entrance to the Golfe du Morbihan. There is a presumption of sea level change in

the area in since the neolithic for which the semi submerged circle at er Lannic is, inparticular, assumed to provide evidence. If this is the sole evidence perhaps it should

be reconsidered as the circle has many of the requirements of a tide gauge. The stone

rows at St. Pierre (St-Pierre-Quiberon Alignement dpd) are incomplete but they

would have had the merit of convenient access to the alignments.

Once the twin solar and lunar observatory had been completed and operated through a

few cycles it should have become clear that reliable tidal prediction could be made

many months in advance. Precise measurement at the major standstill could provide a

reference point for this tidal calendar.

We can therefore consider the possibility that the many sites on the western shores ofthe British Isles at which alignments for the major standstill are to be found is for this

reason. The counting for the calendar could be checked every 18 years and dates

supplied from Carnac for identifying particularly low tides for substantial periods in


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the future. Only the number of lunations ahead needed to be transmitted and the next

quarter moon selected locally using simpler observatories. Perhaps the widespread

uniformity of the unit of measurement should be associated with this notion of

dependence on Carnac for regular and vital information.

Finally one must look at other alignments in the Carnac area. There is the secondobservatory at Carnac based on the menhir at le Mario (Ref.l6). There are also the

alignments at Kermario, which Thom (Ref.l5) suggests may have been abandoned

because it was incorrectly conceived. The rows at the west end are, he suggests, a

means of measuring (2G - p). The east end appears to be a confusion between the

original rows tapering to a point and other rows superimposed. Perhaps the

importance of the value (2G-p) that we have suggested could give a clue in the future

to understanding the arrangements at Kermario.

APPENDIX I

The visibility of Le Grand Menhir Bris from the North-West Sector

The North-West sector of the observatory at Carnac is on undulating terrain with the

River Crach running across it. As a result Le Grand Menhir cannot be observed from

a continuous platform crossing the whole of the sector.

It is necessary to make a large number of map sections to find to what extent Le

Grand Menhir can be observed from the ground adjacent to the Rude Stone

Monuments in the sector. We have carried out a computerised study of these

sections, the result of which is given in table VI and Fig. VI.

The precision of the calculation is sufficient to indicate that there are viewing

platforms that traverse the whole sector and that each is marked by a Rude Stone

Monument at one end, as required by our hypothesis. The section allows for

curvature of the earth, but the contour values are those shown on the 1/25000 map and

may be as much as 1 metre in error. As direct observation is not possible at the

present time, an accurate survey of the contours is most desirable.

It will be seen from the map overlay Fig. VI the contour data has been measured for

each of 26 transverse sections. The transverse sections are identified by their distance

from Le Grand Menhir along the axis. Radial sections have been occupied from the

intersection with the transverse sections and the clearance of the sightline above thetransverse section recorded. Starting from each Rude Stone Monument it has been

possible to traverse along the transverse section metre by metre searching for zero or

negative clearance. The length of viewing platform is therefore the length along the

transverse section of this traverse and may not be the optimum path on the ground.

We can see from the table that the sector can be traversed by 4 or 5 platforms. Those

at Kervilor and Crach cover most of the sector and the remainder may be covered by

the sections 11 and 10 which is probably one platform, sections 22 and 20 and the

sections 6 and 5. At the northern end there seems to be plenty of viewing opportunity.


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REFERENCES

1. a) Ancient Astronomy at the Royal Society, Nature, December 29, 1972

b)Conference on Ancient Astronomy at the Royal Society, Journal for the

History of Astronomy, February 1973, Vol.4, Part I.

2. Types of Megalithic Monument of the Irish Sea and North Channel Coastline;

A study in distribution, M. Davies, Antiquaries Journal XXV (1945) 125-144

3. Diffusion and Distribution Patterns of the Megalithic Monuments

of the Irish Sea and North Channel Coastlands, H. Davies, Antiquaries Journal

XXVI(1946) 38-6O.

4. Reeds Nautical Almanac

5, Prehistoric Chamber Tombs of England and Wales, Glyn Daniell. ON?, 1950

6. We the Navigators. The Ancient Art of Landfinding in the Pacific,

David Lewis. Australian National University Press, 1972.

7. Megalithic Sites in Britain. A Thorn. Clarendon 1967

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No.5 October 1971

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Vol.3 Pt.3 No.8 October 1972

12. Reeds Nautical Almanac Various Years

13. The Kermario Alignments A. Thom and A.S. Thom

Journal for the History of Astronomy Vol.5 Part l No.12 February 1974

14. Megalithic Astronomy - A Prehistorians Comment. R. J. C.Atkinson

Journal for the History of Astronomy Vol.6 Pt.1 February 1975

15. The Kermario Alignments A. Thom and A.S. Thom

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16. The Two Megalithic Lunar Observatories at Carnac Alexander Thom,

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Documents

P. B. Davidson. Navigation in the Neolithic86 Supporting Paper III Le Menec as Tide Predictor Rev2011