The Fish Stone Alignment.  Powys.


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Synopsis.

Appendix 1.  Why the Solstices and Equinoxes do not divide the Year equally.

Appendix 2.  Is this Actually an Alignment ?

The Fish Stone is a large standing stone situated in a meadow beside the Usk to the west of Crickhowell. Grid Reference SO 1829-1986, Latitude: 51.871305N  Longitude: 3.188221W.  Coflein says that it might have been used as a mediaeval boundary marker, but that does not imply that the stone was erected during the mediaeval period.  I will assume that it is a genuine Bronze Age megalith, which is what it looks like.  This site contains more information.

Synopsis.  It is argued that the Fish Stone was erected with the intention of marking the equinoctial quarter days of the year.  A search of the internet (e.g. 'Fish Stone equinox') does not produce any evidence that this idea has been suggested previously, so this might be a novel discovery. It is proposed that from the stone, the 'equinoctial' sunset was seen to occur on the summit of the nearby Tor y Foel, and that when this was seen, the bronze-age observer had identified the equinox.  Azimuth and altitude angles for the proposed alignment to Tor y Foel are derived from the OS 1:50,000 map of the area, and from the latter the
declination and azimuth of the equinoctial sunset is calculated.  These are compared with the declination of the equinox (0) and the azimuth of the alignment measured from the map.  The calculated historic sunset azimuth exceeds the observed topographical value.  This finding is consistent with the proposal put forward by Alexander Thom that such an error should be expected, and when found is an indication that "...we know we are thinking along the right lines".  (Thom, 1 p 107).  A number of alternative meanings of 'equinox' are considered, and the effect that differing definitions might have on the alignment are discussed.  It has been established by Thom and others that relatively short stone-rows can act as markers of astronomical events.  It is argued here that a single stone can also act in this way when it is located in a suitable environment.

I visited the site in May 2016 while on a stone-hunting expedition in the Usk Valley.  I had previously taken an interest in the Grey Hill (Gwent) stone circle and stone-row, and had assessed that site from an archaeoastronomical point of view.  My mind was focused on ideas developed by Alexander Thom, (Refs 1, 2) who describes numerous sites where a stone-row 'points to' a more distant foresight, and the alignment between the site of the row and the distant foresight has astronomical significance, perhaps being the direction (azimuth) of a solsticial sunrise or sunset.  This idea is discussed further below.

Since the Fish Stone is an isolated megalith, it cannot be classed among this type of alignment - it is not part of a row, and in itself points nowhere.  However, the location is overlooked by a distant mountain (Tor y Foel, 551m) in a most suggestive way, and I commented to a friend while photographing Fig 2 that if I had been a bronze-age stone man I would have placed a second stone where I was then standing.  When I photographed Fig 2, I was aware that I was imposing on the site an interpretation which could be entirely false, and when I later showed the picture to a friend, his immediate response was "It depends where you stand", which is of course true - I create the 'alignment' by my choice of viewpoint, which is by no means determined by the Fish Stone, or by those who erected it.  But I will argue that it is suggested by the environment.

fishstone penmyarth

Fig. 1.  The Fish Stone.
At the time of the visit it did not occur to me that this could actually be a real alignment, and although the suggestiveness of Fig 2 lodged in my mind,  I was so much influenced by Thom's ideas that I did not immediately follow up the idea.  On my return home I drew a line on the map and found that the line between the stone and the summit of  Tor y Foel is a little south of west, too far south, I thought, to qualify the 'alignment' as being toward the equinoctial sunset.  It took several days before these observations crystallised in my mind sufficiently for me to return to the idea. This was my thought experiment:-

We assume that the observer stands immediately in front of the stone and looks towards Tor y Foel, and that the stone has been positioned such that on the evening of the spring or autumn equinox the sun is seen to set on the summit as illustrated in Fig 2. We calculate the declination  of the sunset at an appropriate historic period, and compare it with that of the equinox, which is 0deg. If they agree, we say that our assumption about the function of the stone is correct.  To calculate the historic declination we need to know the altitude angle of the summit as viewed from the stone, since the higher this is, the further to the south the sunset will occur; the sun descends on a line inclined downward to the right, and the higher the summit, the further to the left (i.e. at a smaller azimuth angle) the sunset will be (Fig 3).  Comparison of  declinations allows us to calculate azimuth error, and also the error in the timing of the equinox as indicated by the alignment.

The Data.  (Taken from the OS map Sheet 161. Fig 4)  

The line from the Fish Stone to the summit of  Tor y Foel is inclined 3 degrees south of the OS gridlines.  Applying a correction of 1deg for the angle between the grid and true north gives the
azimuth of the alignment as 266
(+/-0.25).

Distance to summit:  136.0mm on map, corresponding to 6.80km (+/-50m)


Height of summit: 551m (+/-0.5m)

Height of ground at Fish Stone: 80m +/- 2m.  Add 2m for height of observer's eye to give 82m

Altitude angle of summit (h):- Thom gives this formula, which takes into consideration the curvature of the earth, and the effect of atmospheric refraction:- h = H/c - c*(1 - 2k)/2R
where:
h is in radians
H = difference in height =
551 - 82 = 469m,
c = distance = 6800m
k = coefficient of refraction of air = 0.075
R = radius of curvature of earth = 6365*10^3m at this latitude.

From which h = 3.92


Note that arctan(( 551 - 82)/6800) = 3.95, which is slightly greater, as would be expected since the surface of the earth is not in fact flat, and consequently distant hills tend to sink below horizons.

If it is assumed (Case 1) that the moment of interest is the moment when the edge of the disc of the setting sun just touches the summit, then 0.25 (half the 'diameter' of the sun) must be added.  The altitude of the setting sun is then 4.17. Alternatively (Case 2), if the moment of sunset is that when the disc just disappears, then the altitude is 3.67
.   These values are too large for the effect of atmospheric refraction on the apparent altitude of the sun to be worth considering.

Using an equation given by Thom, the declinations of the alignment in these 2 cases are found to be +0.816
and +0.422 respectively (0 expected), while the azimuths of the equinoctial sunsets at this site turn out to be 264.67 and 265.3 .  Already it is clear that the figures are close to the expected values, particularly if the sunset is interpreted as the moment when the sun completely disappears (Case 2):- declination 0.42 vs 0, azimuth 266 vs 265.3.   Although the 'errors' are small, they exceed the estimated error of measurement, and are larger than would be expected; the error in azimuth (0.7) exceeds the diameter of the solar disc (~0.5), and would be noticeable in practice. The errors therefore need to be explained, and will be discussed further below. At this location, the sunset will have the measured azimuth of 266 one day after the equinox, so the site could could yield the equinox with this degree of precision.  However, before we can pass judgment on this, we must look more closely at what our bronze-age astronomer might actually have been trying to achieve, and in particular what his notion of an 'equinox' might be. Hitherto we have simply assumed that he or she would understand the term as we do, but this is unsustainable.

Fishstone Penmyarth Powys

Fig. 2. Equinoctial Sunset on the supposed Alignment.




Fig 3.  Sunset on Hills of different Height.  
The higher the hill, the smaller
is the setting azimuth (more southward - to the left). 
fishstone alignment

Fig 4.  The 1:50,000 OS map Sheet 161.  Gliffaes Stone centre, Fish Stone right.

So what exactly is an equinox ? Or perhaps we might ask "what idea might have existed in the mind of a bronze-age community which corresponds to our idea of an equinox ?"  The modern astronomical definition of the equinoxes is that they are the moments in the year when the centre of the sun is on the plane of the earth's equator.  Such a definition is of course meaningless in this historic context, so we may fall back on such ideas as the first day of Spring or Autumn, the time of year at which day and night are of equal length, or the two days which are half-way between the summer and winter solstices, thereby providing a way of quartering the year, or the day on which the sun rises and sets in exactly opposite directions (i.e. east and west respectively).  The first two ideas are reasons why a bronze age community might take an interest in the equinoxes; a harbinger of coming summer or winter would be of great importance to a community which lived outdoors and earned its living by directly exploiting the gifts of nature.  The last two ideas provide ways of determining when the 'equinoxes' occur.

Equinoctial alignments are much less commonly found at megalithic sites than are solsticial alignments, and for good reasons.  The day of the winter solstice, for example, can easily be found by observing the point on the south-westerly horizon at which the sun sets around midwinter.  As the solstice approaches, the setting azimuth moves steadily toward the south, then slows to a stop on the evening of the solstice itself.  On days after the solstice, the setting point moves steadily back again towards the north. The day of the midwinter solstice is thus clearly indicated by the maximum southerly movement of the setting sun (Footnote 4).  The winter solstice sunrise can be used in a similar way, the position of sunrise again moves southward, reaches its maximum southward position on the morning of the solstice, and then moves north again on successively later mornings.  The summer solstice can be found in a similar way, except that now the northward progress of the sunrise or sunset reaches its maximum extent on the day of the solstice .  A clear horizon, and clear weather are needed, but otherwise the observations are extremely simple, and the movement of the sun might well attract the notice of anyone who lives an outdoor life. The equinoxes are more difficult however, since there is no reversal of movement of the direction of sunrise or sunset.  Around the spring equinox the points of sunrise and sunset move continuously northward, while at the autumn equinox the movement is steadily southward.  How then can the days of the equinoxes be determined ?

Several techniques might be used, the appeal of each can be judged by what prior knowledge is required, and the complexity of the concepts involved, and of the practical technique.   It is likely that our putative astronomer will have already found the days of the summer and winter solstices, or at least one of these, so it would then be simple to adopt one of these techniques:-

1) If only one solstice is known, (found as described above) the duration of the year can be found by counting days from one occurrence of that particular solstice to the next.  From this the other solstice can be found by dividing the day-count by 2, and the equinoxes, now more properly termed quarter-days, could be found by dividing by 2 again.  The basic concept here is simply the quartering of the year, using one solstice as the calendrical reference point. In order to avoid confusion, in what follows I shall reserve the word 'equinox' for the moments when the sun is in the plane of the terrestrial equator, and will refer to days such as those discussed here as EQDs - equinoctial quarter days, or simply 'quarter days'.

2) If both solstices have been found by observation, the spring quarter day could be found as the mid-point in time between midwinter and midsummer, while the autumn quarter day is the mid-point between midsummer and the next midwinter.  

For reasons which are discussed later, these two techniques will yield different alignments for the spring and autumn quarter days.  If we surmise that a single alignment is required for both, one of the following techniques can be used:-

3)  If both solstices are known, a temporary marker could be erected for the spring quarter day, and another for the autumn quarter day, found as in (2).  The permanent megalith could then be erected midway between these positions.  The days on which the sun set on the alignment would not be neither of the mathematical quarter days, but a  day or two from each.

4) Thom discusses the megalithic calendar in Chapter 9 of reference 1.  He describes a method for finding the EQDs that requires that the length of the year be known, and therefore that at least one solstice has been found. The alignment to one EQD is found approximately by casual observation or guesswork, and the proposed observation point is marked on the estimated day by a temporary marker.  Half a year later (determined by a day-count) the observation point for the other EQD  is similarly marked, using the same foresight. The observation point for the true EQDs, which will be the location of the megalith, is then midway between the two temporary markers.  Greater precision or confidence can be achieved by refining this mark during the succeeding half-year.  Essentially, this techniques finds a single alignment to two sunsets which are in the same direction at times exactly half a year apart.  Necessarily this technique will produce an alignment which is correct for both EQDs.  It seems to me that this method is less obvious than the previous three, requiring greater conceptual insight.  

For these methods to be viable, in addition to the ability to find the solstices, we must credit our astronomer with the ability to count up to 365, perhaps by cutting notches on a stick, and also sufficient arithmetic skill to halve such a number.  Primitive division by 2 might be achieved by dividing the notches roughly into two groups, which are then adjusted for equality (plus or minus 1) by trial and error.  Nothing more than counting is required, but we could imagine fierce sectarian disputes arising from the question of how to attribute the two integer 'halves' of 365 (i.e. 182 and 183) to the two parts of the year.

Clearly these techniques imply different definitions of the concept of an equinox, which is closer to that of a quarter day.  Do these different definitions mean that different days, azimuths, or declinations are implied ?  Is a different alignment required in the different cases ? In fact these three techniques do not give the same days for the EQDs, and, moreover, none of them agrees with our modern equinoxes, and they all require subtly different alignments. This will influence our opinion of the accuracy of the observed alignment, and our interpretation of the 'errors' mentioned above.

This discussion reveals that a megalithic marker for the equinoctial quarter days is superfluous in a strictly practical sense; the quarter days can be found without the alignment simply by computation if a solstice is known, and that is presupposed (but see Footnote 3). Thus none of the alignments produced by these techniques represent a way of determining the equinox or quarter day, but merely a way of marking it once it has been found by computation; epistomologically, an EQD alignment has a different significance from that of a solsticial alignment. This lack of practical necessity probably explains the scarcity of equinoctial alignments, and suggests that where they are found they served some other purpose - possibly ritual or cultic, or to demonstrate the power of a priestly astronomer caste.  Perhaps these stones were intended to be the focus of socially important rituals having something in common with the observation of the new moon in relation to Ramadan (Fig 5).


Fig. 5.  The phases of the moon are routinely predicted, but observation has greater social or religious significance, and a large telescope, though unnecessary, is impressive.

The reason for this lack of agreement is that the orbit of the earth is elliptical, not truly circular.  During northern hemisphere winter the earth is closer to the sun than during the summer, the actual day of closest approach (the perihelion) being in the first week of January.  When the earth is closer to the sun it moves more quickly, and the angular progression of the earth in its orbit is then quicker.  It follows that the winter half of the orbit (in terms of angle) is completed in a shorter time than the summer half.   The span of days from autumn to spring equinox is shorter than that from spring to autumn equinox; the spring equinox appears earlier in the year than the mid-time between the solstices.  Correspondingly, the autumn equinox is later than its quarter-day, but not by the same amount, and this latter discrepancy means that a single alignment will not serve for both quarter days.  This is explained and illustrated in greater detail in Appendix 1. 

Thom acknowledges that the displacement of the quarter days from the equinoxes is a feature of the technique he describes (method 4 above). He says that there will be a characteristic 'error' in bronze-age 'equinoctial' alignments which, if present, is an indication that the alignment has been correctly interpreted as a genuine (if misguided) attempt at the equinox.  He estimates that the quarter days found by his technique will correspond to a declination of +0.5, rather than the 0 of the true equinox; we have found the declination at the Fish Stone alignment to be +0.41, which is very close to that predicted by Thom.  At the site of the Fish Stone, a declination of +0.5 corresponds to an azimuth of 266.15, while 266 has been measured.  Thom predicts that the EQD will be 1 day late using his method, which we agree with.  The other methods (mentioned above) for calculating the EQDs give similar results - mainly yielding a declination in the region of 0.54; they are discussed In Appendix 1. 


Appendix 1.  Why the Solstices and Equinoxes do not divide the Year equally.

In Fig. 6 the eccentricity of the earth's orbit is greatly exaggerated.  The winter solstice is shown as occurring before perihelion, which is true at present.  When the earth E is closer to the sun it moves more quickly in its orbit.  The winter half of the orbit (in terms of angle) from autumn equinox (AE) to spring equinox (SE) via the winter solstice WS and perihelion (P) is therefore completed more quickly than  the summer 'half' from SE to AE via SS and A.    Similarly the first half of the year from winter (WS) to summer (SS) via SE is completed more quickly than the later half of the year from summer to winter via A and AE.  In this case the difference is less pronounced.


Fig 6.  How the solstices and equinoxes divide the earth's orbit.

Using modern data for the solstices and equinoxes from winter 2015 to winter 2016, we can draw up the following tables which illustrates this.


In Table 1, columns 1 and 2 identify the times of solstices and equinoxes in 2015 and 2016.  In column 3, days are counted to the events, referenced from the 2015 autumn equinox.  The period from autumn to spring equinox can be said to be the winter 'half' of the year, but in fact it contains
only 178.8 days, leaving 186.5 days (i.e. 365.25 - 178.8)  for the remaining summer 'half' of the year, a difference of 7.7 days.   In column 4 the reference date is the 2015 winter solstice.  This column shows how the solstices divide the year more equally.  The summer solstice occurs after 181.8 days, which is the duration of the first 'half' of the year, while the period from summer to winter solstice (the second 'half') contains 183.5 days, a difference of 1.65 days.

1.   Event 2.   Time of Event 3. Days Referenced to 2015 Autumn Equinox 4.  Days Referenced to 2015 Winter Solstice  
Comment
Autumn Equinox 2015  8.20
23/09/2015
 
0
Winter Solstice 2015 04.48    22/12/2015 89.8 0

Spring Equinox 2016 04.30
20/03/2016

178.8
(Midpoint =  182.6)
89
Col 3 Spring Equinox is 3.8 days before mid-point 
Summer Solstice 2016 22.34
20/06/2016
271.6
181.8
(Midpoint =  182.6)
Col 4 Summer Solstice is 0.8 days before mid-point
Autumn Equinox 14.21
22/09/2016
365.25 275.45

Winter Solstice 2016 11.00
21/12/2016

365.25

Table 1.  The solstices and equinoxes do not divide the year equally,
but the solstices divide the year into more equal 'halves' than the equinoxes do.  

Table 2 compares the results obtained by Methods 1 and 2 for calculating the EQDs with the true astronomical equinoxes.  In both cases the spring EQD is late, and the autumn EQD is early, but Method 2, based on observations of both solstices yields EQDs which are closer to the equinoxes than does Method 1.

1.   Event 2.   Time of Event 4.   Events Referenced to 2015 Winter Solstice  (Days)
5.   Method 1.  All Quarter Days mark true quarters of the year based on observed winter solstices alone.
6.   Method 2.  Equinoctial Quarter Days calculated as mid-points between solstices; both solstices observed.   Comment
Winter Solstice 2015 04.48    22/12/2015 0
0
WS is determined by observation
0
WS is determined by observation
Spring Equinox 2016 04.30
20/03/2016

89
91.3
Estimated SE is 2.3 days late
90.9
Estimated SE is 1.9 days late
Both methods give the spring EQD late
Summer Solstice 2016 22.34
20/06/2016

181.8

182.6
Estimated SS is 1.8 days late
181.8
SS is determined by observation
Method 1 estimates the summer solstice late
Autumn Equinox 14.21
22/09/2016
275.45
273.9
Estimated AE is 1.55 days early
273.5
Estimated AE is 1.9 days early
Both methods give the autumn EQD early
Winter Solstice 2016 11.00
21/12/2016
365.25 362.5
WS is determined by observation
362.5
WS is determined by observation

Table 2.  Comparison between Methods 1 and 2 for calculating quarter days.  
Days are referenced to the 2015 Winter Solstice.  Both methods yield spring EQD later and autumn EQD earlier than the corresponding equinoxes.

Historic values for this type of data can be derived in several different ways.  
Here is one...

The declination of the sun (
δʘ) can be estimated for any day in the year using this formula ( ref 3):
... (Eq 1)
The various symbols have the following meanings:-
 -23.44
       Declination at the moment of the winter solstice.  23.44 is the present-day obliquity of the ecliptic (ob).
0.0167           Eccentricity of the earth's orbit (ε)
365.24        Number of days in a year (y)
360             Number of degrees in a circle
N               Days after 1st January
(N + 10)     Days after the winter solstice, taken to be 21st Dec; Jan 1 is 10 days after the solstice at present.
(N - 2)        Days after the perihelion, taken to be 2nd Jan.
 
The following additional symbols will be used below
Ns             Days after the winter solstice.
Nsp           Days between solstice and perihelion (+12 at present).

Clearly (N + 10) = Ns, and (N - 2) = (Ns - Nsp)

Using radian measure, and referencing the day-count to the solstice gives this:-

sin(δʘ) = sin(-ob).cos{2π.Ns/y + 2ε.sin(2π.(Ns - Nsp)/y)} .... (eq. 2)
 
If this is written as sin(δʘ) = A.cos(B), it is evident that, since δʘ is zero at the equinoxes, and +/-A at the solstices, these events can be found by determining values of Ns for which B (i.e. 2(π.Ns + ε.sin(Ns - Nsp))/y) evaluates to  π/2, π, /2 and 2π.  I have written software which finds the events in this way, and which also uses eqn 2 to find δʘ on specified numbers of days before or after the equinoxes.  Such values of δʘ serve as estimates for the declinations implied by the various ways mentioned above of calculating the quarter days, and can be compared with the measured declination implied by the site.  The software permits historically correct values of ε, ob and sp to be used.  We also need a historic value of Nsp.  It is usually estimated that the perihelion is 1 day later every 60 years, implying that in BC1800 (a rough guess as to the likely period of the erection of the Fish Stone) it was 63 days earlier than at present.  For our historical estimates we therefore take Nsp to be 12 - 63 = -51 days.  

In the screenshot (Fig 7) panel 3 shows calculated number of days to the various seasonal events represented as number of days counted from the winter solstice of 1801BC; these include the true equinoxes of 1800BC.  In panel 4 the quarter days are calculated as equal divisions of the year (corresponding to method 1), together with their declinations. All events other than the winter solstice (which is the reference point) differ slightly from the 'true' day-counts.  Panel 5 shows similar data when both solstices are true, and the EQDs are calculated as mid-way between them (method 2).  These results largely agree with Thom's estimate for his method (method 4) in that the declinations are mainly not significantly different from 0.5
.  An exception occurs in the case of the spring EQD of method 2 (panel 5).  Here a difference of 1 day in the date results in a significant increase in declination.  For this data, method 3 would give the mean declination of  0.69.

Fig. 8 shows results for equal division calculations at other dates.  This gives a very good match for 2400BC.


Fig 7.  Software Screenshot 1800BC.



Fig. 8.  Alternative Dates.


Appendix 2.  Is this Actually an Alignment ?

I have mentioned my doubts concerning this already.  My thoughts on archaoastronomical alignments have been much influenced by Alexander Thom.  In  Megalithic Sites in Britain (Ref 1) he describes a class of alignment which I will designate 'Stone-Row with Distant Foresight' or SRDF. The archetype for this type of alignment is that at Ballochroy, Mull of Kintyre (Fig.9).  Thom describes a short stone-row, less than 10m in extent, which, he says, 'points' to a foresight which is 19 miles distant.  The proposed alignment is between the site of the row, and a mountain on a distant island.  This long baseline allows of great precision, and is a characteristic of all of the alignments of this class which he considers.  To gain a feel for the significance of this type of situation, consider the following.  Let the breadth of one of the stones be 0.7m, and the overall length of the row be 10m.  Then the uncertainty in the direction in which the row 'points' is of the order of arctan(0.7/10) = 4 , or 8 solar 'diameters'. This is very imprecise.  If, however, the baseline is extended to 19 miles (30km) the uncertainty is reduced to arctan(0.7/30,000) = 1.33*10^-3 or 5 seconds of arc.  This is 1/376 of the 'diameter' of the sun.  The SRDF type of alignment is thus hyper-precise.  Where the stonerow allows a distant horizon feature to be identified unambiguously, one can expect the rising or setting sun to coincide with that feature with a precision which is much smaller than the apparent diameter of the sun.  Put another way, if the stonerow was constructed with this kind of intention, it could easily be located with sufficient accuracy for the visual effect to be pleasingly precise.  If an error of 1/10 of the sun's diameter (0.05 ) is acceptable, there will be a tolerance in the placing of the row of +/-13m (30,000*tan(0.05) = 26).  The row itself could thus be constructed quite carelessly, and questions concerning the breadth of the stones, or whether they lie in a truly straight line are of no consequence, provided only that they point unambiguously to the intended distant foresight. Thom Ballochroy

Fig 9.  The Ballochroy Alignment. From Thom (1).
Ideally such a row should contain at least three stones.  If a single stone (such as the Fish Stone) is erected in a given landscape there will inevitably be any number of features in the landscape to which the stone might refer; a single stone gives no sense of direction and points nowhere in particular.  Two stones do give a sense of direction, but this might be spurious, and not intended by the designer.  It will always be possible to draw a line through two points, but since such a line will always be present whether it is intended or not, such a line does not clearly signify "I am pointing somewhere, follow me". However, three or more stones will not define a line unless they have been deliberately placed in line, and such deliberate action on the part of the designer of a site can legitimately be interpreted by the modern observer as having a definite significance; when it is found it invites the response "where are you pointing ?"  

How, then, can we justify interpreting the Fish Stone as a pointer to Tor y Foel which acts as the foresight of an astronomical alignment ? 
 The answer to this is quite simply that the location of this monolith is deeply suggestive of such an interpretation.  Here, the Usk flows in a deep valley whose steep sides constrain the eye to follow the course of the river, which in this location is east-west; in all other directions the eye meets a dense wall of wooded hillside, and that is true even in the easterly direction.  Only in the direction of the summit (to the west) is there a clear outward view.  Of course we should not assume that the location was always so densely wooded as it is now, but the constraints of the steep valley can be relied upon, and the northern side of the valley in particular has the appearance of being a primordial forest - too steep to have been cleared and cultivated in any period.  If we ask the question - which is always legitimate concerning such sites - "why here ?" a moment's appraisal of the locale will inevitably draw the eye towards Tor y Foel, as Fig 2 clearly illustrates. A three-stone row would explicitly point to the summit, but my argument is that in this location there is no need for such a row, or for such explicitness; there can be no ambiguity about the intended target, and a single stone will serve.  The only doubt is whether such an alignment is actually intended, or whether the 'alignment' is completely fortuitous, the stone having been erected in this location for some completely different purpose.  Ultimately the "why here ?" question can only be answered by the investigator's own feeling for the site, and whatever rational arguments he or she puts forward to support his point of view.  Thom contributed the important idea that often megalithic sites reach out to distant natural (or sometimes artificial) features of the environment, and incorporate them into the mechanics of their workings.  It now seems that more local landscape features (such as a few hundred metres of a riverbank) must be considered to be structural and functional parts of a megalithic site, equal in importance to the stones themselves.  The significance of a megalithic site is likely to be missed if either the local or more distant features of the setting (or both) are ignored (Fig 1, Fig 10 - below).

At this point one might mention the Gliffaes stone.  This lies a little less than 3km to the WNW of the Fish Stone (see map); it is in an elevated, open setting, and is not intervisible with the Fish Stone.  Again Tor y Foel is visible, now at a smaller azimuth, but there is a relatively low horizon all around, and there seems to be no reason for looking especially in that direction.  The function of this almost equally impressive monument, and its relationship (if any) with the Fish Stone
or with the horizon is difficult to imagine.  Here we have an example which paradoxically, in a negative sense, supports my interpretation of the Fish Stone.  Setting is everything; when you have it, it strikes you immediately; when it is lacking you know that also.  If there is a reason to assert that this stone refers to Tor y Foel I have not yet found it.

There remains in my mind some suspicion that my response to the Fish Stone is highly idiosyncratic.  Of eighteen pictures of the stone on this webpage, taken by different visitors to the site, only one apart from my own includes Tor y Foel in the background, and in that picture the possibility of an alignment has been ignored (Fig. 10 below).  I have not yet found any picture of the stone that emphasises the alignment in the manner of Fig. 2.  So is the magnetism that drew me to the viewpoint of Fig. 2 merely some spurious working of my own imagination ?  The only defence I can give is that, having read Thom, I have become trained in the habit of searching the skyline
when visiting a site.  Perhaps bronze-age astronomers did the same ...

fishstone penmyarth

Fig 10. The 'Alignment' has not been spotted.


References


1. Thom A, Megalithic Sites in Britain, Oxford University Press, (1967)

2.  Thom A, Megalithic Lunar Observatories, Oxford University Press, (1971).

3. https://en.wikipedia.org/wiki/Position_of_the_Sun

Notes.

1)Calculating Declination.  Thom (1967, p 17) gives:-
sin(δ)= sin(λ).sin(h) + cos(λ).cos(h).cos(A)

where h = horizon altitude (corrected for refraction if necessary), A = azimuth, λ= latitude of site.

This relationship arises from the geometric relationship between the co-ordinate systems used, and does not vary with historical epoch.  However, if it is used in relation to a solstice,
δ will be +/-ob (the obliquity of the ecliptic), whose historically correct value must be used.  In the case of the equinoxes the solar declination is 0 at all epochs.

2).
"Astronomer". I use this word to denote those supposed individuals in a Bronze Age community who were versed in lore related to standing stones and their alignments.  I imagine that this lore might relate to the seasons, and the movements of the sun, moon, and stars in particular, and possibly also to wider ideas concerning life, death, fertility, etc. Such 'astronomers' would, I suppose, be responsible for directing the erection of megalithic monuments, and subsequently using them. I use 'astronomer' in an ironic sense which has little to do with the concept of the modern professional astronomer.  'Priest' or 'shaman' might be alternative terms, but I feel that the assumption that megalithic alignments signify religious ideas, valid though it might be, is not relevant to the present discussion of the calendar.

3).  The moment of sunrise or sunset.  When I started to take an interest in this topic, it seemed to me that the image represented in Fig 2 was attractive - i.e. the moment of sunrise or sunset is the first moment when the horizon is tangential to the sun's disc.  However, when I actually began to observe such events, it was obvious that, except under unusual atmospheric conditions, directly viewing the sun's disc on the horizon was impossible - there was simply too much glare.  I have therefore more recently begun to assume that, for purely practical reasons concerned with naked-eye observations, the moments of sunrise and sunset can more realistically be considered to be the moments when the first or last glimpse of the sun's disc is seen.

4). Determination of a solstice.   The discussion presented here presupposes that a solstice could be found with a precision of 1 day.  But the technique which has been outlined has a major defect.  At the time of the solstices, the rate of change of sunrise or sunset azimuth with time is so low that several days must pass before the turning point of azimuth can be reliably identified.  The technique has a built-in uncertainty of +/-2 days at best.  This is illustrated here (Fig 18 & Discussion of Results).  The Grey Hill site can be interpreted as representing a modification of this technique, which allows the day of the solstice to be uniquely identified, but it is debatable whether this interpretation of  the Grey Hill alignment is convincing, or whether the suggested technique was ever in fact used, and therefore whether the day of a solstice could ever be known with a precision better than 2 days.  This observation extends the range of 'error' which might be expected in an equinoctial alignment.