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THE MULTIPLE STONE
ROWS OF CAITHNESS AND SUTHERLAND INTRODUCTION Previous articles in the Bulletin have described the distribution and plans of the various settings of fanshaped stone rows which are known to exist in Caithness and Sutherland. In recent years more of these megalithic sites have been discovered, and undoubtedly there are yet more to be found. The greater the number of such sites from which evidence may be gleaned perhaps the nearer we may come to understanding the reason for their construction. All the evidence which has been accumulated on these sites is based upon what can be found on the surface and from the surrounding topography. None has been excavated apart from the burial cist at Garrywhin, and that gives no further information on the rest of the site. The only theory which has been published on the purpose of these stone alignments is that of Professor Thom (Thom 1971). Of necessity, the explanation is couched in mathematical terms although this does not mean that the builders of the rows had the same mathematical knowledge that we have today. It is quite possible for the rows to have been set up solely by observation and experiment without any knowledge of the underlying mathematics. The purpose of this article is to attempt an explanation of Thom's theory without any mathematics but with the use of a few simple observations and measurements which could have been made easily by prehistoric man. THE MOVEMENTS OF THE SUN In order to understand the movements of the moon, as seen from the earth, it is best to consider first of ail what happens to the sun over a period of one year. The diagram of Fig. 7(a) represents the horizon opened out so as to be seen as a straight line and the corresponding true bearings, or azimuths, are such that E , S and W are represented by 90^{o 180o and 270o respectively. }Commencing the solar cycle at the summer solstice (midsummer) the sun will be seen to rise above the horizon in Caithness approximately in the NE at 2.55 a.m.. (G.M.T.) and it then rises in the sky until at midday it is in the S at an angular height of 55.5o above the horizon. It then gradually falls as it moves further along the horizon to set in the NW at 9.09 p. m. (G.M.T.). Its total time in the sky above the horizon at this time of year is thus just over 18 hours. As the year progresses from midsummer to midwinter the rising and setting points both gradually move further south each day until at the winter solstice it rises in the SE at 8.45 a.m. and sets in the SW at 3.11 p.m. It is then in the sky for only nearly six and a half hours, and at noon rises to an angular height of only 7.5o above the horizon. These are the extreme rising and setting points of the sun which occur at the summer and winter solstices round about the 22nd June and 21st December each year. Midway between these points we have the autumn and spring equinoxes on about the 22nd September and 20th March when the sun is halfway through its travels and it rises in the E and sets in the W. The complete solar cycle as described takes a period of one year from one summer solstice to the next, and each year the cycle is repeated. To anyone living in the country, away from tall buildings and having an unobstructed view of the distant horizon this daily movement of the sun is noticeably visible. Such would have been the case for megalithic man long before the days of cities and the obstructions of multistorey buildings. On a particular day each year, the sun would be seen to rise and set over the same horizon features when viewed from a given place. Using this phenomena it would be a simple matter to construct an accurate calendar of significant days in the year by using markers to indicate the direction of the rising or setting sun on the horizon. Such markers could have been wooden posts or large stones used as backsights and perhaps a significant feature such as a notch between two hills on the horizon as a foresight. THE MOVEMENTS OF THE MOON Whilst the sun appears from the earth to pass through a single cycle of movements which are repeated annually, the movements of the moon are much more complex. Not only does it have a 'monthly' cycle of about 28 days, but it also has a further cycle of 18.6 years added to which is another small variation over a period of 173.3 days. Each of these effects is well known to astronomers and today can be explained mathematically if required. Without the use of any mathematics these effects con be seen in the rising and setting of the moon solely by observation. It is quite easy to observe effects without having an understanding of why they take place. The modern use of mathematics merely helps in the understanding. (Any child can learn to ride a bicycle without a mathematical understanding of the gyroscopic forces which keep it upright.) A comparison of the movements of the moon with those of the sun is given in the diagram of Fig. 7 (b). At the beginning of a particular lunar month the moon will rise at the point A on the horizon and set at B. Two weeks later the rising and setting points will both have moved south gradually each day to C and D. It will then gradually move back along the horizon to rise at A and set at B again at the commencement of the next monthly period. Thus the pattern of movement of the moon in one month is similar to that of the sun in one year. However, over a much longer period of 9.3 years the extremities of the moon's monthly rising points will have changed from A and C to E and G. The corresponding extreme positions of the setting points will have moved to F and H. When the limits of rising are at A and C the moon is said to be at its 'minor standstill' and when rising between E and G it is at its 'major standstill'. At the minor standstill the altitude of the mean at its highest point in the sky varies between 50.5o and 12.5o whereas at the major standstill the variation ranges between 60.5oand 2. 5o in Caithness. OBSERVING THE MOON There is little difficulty in observing the rising and setting of the sun. Assuming a cloudless horizon, it can always be seen. If the extremities of its position, on the day of the solstices cannot be measured due to cloud on one day its movement along the horizon will make little difference if on observation is made on the following day, since its position on the horizon changes only very slowly at this time of the year. The error will thus be very small. When making observations on the moon however, the situation is somewhat more difficult for the followings reasons:
OBSERVATION OF MOONSET suppose that the moon is setting at one of the standstill positions H, D, B or F as in diagram Fig. 7(b). Using a distant point on the horizon, such as a notch between two hills, as a foresight a marker may be set in the ground to indicate the direction or azimuth so that the marker, foresight and setting moon are all in 1ine. If this is done one day before the standstill as in the diagram of Fig. 8(a) and the first marker is fixed in the ground, then on the next day the second marker would be placed further to the left. On the third day the moon would be moving back along the horizon again and so a third marker placed in the ground would then have to be placed to the right of that for the second day. Markers have now been placed in the ground in a straight line for the three successive days covering the standstill. Unfortunately, because of the rate at which the setting point moves along the horizon each day, the second marker may not quite coincide with the most northerly orbit of the moon. It would therefore be necessary to add an extra marker at X to indicate the true maximum position. The question then arises as to how it would be possible to find the extra distance, Y, (known as the extrapolation distance) between the markers 2 and X. Professor Thorn (Thom 1971) suggests that the stone rows were used for this purpose. WHAT THE OBSERVERS WOULD HAVE FOUND If successive monthly measurements had been made with the moon at one of the standstill positions the observers would have found that although the positions of the three markers would be slightly different each month one measurement would remain unchanged. That is the distance between marker 2 and the midpoint between markers 1 and 3. This distance is constant for a particular site and is dependant upon the distance to the foresight. Thom calls this distance 4G. The extrapolation distance, y, will of course vary from month to month as also will the distance between markers 1 and 3. This distance Thom calls 4m. HOW THE STONE ROWS WERE USED Diagram Fig. 8(c) shows a fanshaped setting of stone rows having a radius of 4G (the distance between marker 2 and the midpoint of markers 1 and 3). The stones are set in the base of the fan at the intersections of the radial lines and the radial arcs as shown. It is only necessary for the stones to extend over a radial length of G from the base and a circumferential distance G along it. The distance 4m between markers 1 and 3 is now measured with a rope which is then folded Into four to give a length m. This distance is now measured from the base of the fan radially to give the length AB on the fan. The rope is then bent around the stone, at B to give a further length m equal to BC. This is again repeated at C and D until the rope comes out again at A. Since the distance DA is less than BC the total distance ABCDA around the stones is less than the length of rope and so there is a piece of rope left over. The amount left over is equal to the extrapolation length, y, between the second marker and the required marker position at X. The above method is shown by Professor Thom, using a mathematical analysis, to give exactly the amount which is required to be added to the second marker. As in discovering the constant distance, 4G, by observation, the stone row method would have had to be discovered experimentally by observers working at these sites over a very long period of years. There are other slight variations on the method by which the stone rows could have been used to determine the position of the marker at X but the above is perhaps the easiest to understand. EVIDENCE FROM THE SITES With a modern knowledge of astronomy, and the use of mathematics which is available to us today, it is relatively easy to calculate the value of G for a particular site. Megalithic man would, of course, have had to find it experimentally. Thom's evidence for the use of the fanshaped rows is based upon the four Caithness sites given in the following table. For a fan to have the ideal shape for extrapolation purposes it should have a radius equal to 4G, the lengths of the rows and the base of the fan should both be equal to G. The method of calculating G in the table is that given by Thom (Thom 1971, 85) but modified by Heggie (Heggie 1972, 48). All dimensions are given in metres. ^{ }
With only 14 stones visible at Camster, it is difficult to accept the accuracy of the dimensions of the fan with any certainty. There may be many more stones buried. beneath the peat and excavation might show this site to be more extensive than it appears. The base of the sector is only about 30%, the length of the rows 60% and the radius 81% of the required values. Nevertheless, the fan would still have been useable without too much loss of accuracy. The lengths of the rows and the base of the fan at Yarrows is again too short, but almost certainly stones have been removed from this site. The exact radius of the fan is somewhat open to doubt. Ruggles (Ruggles and Whittle 1981, 193) suggests that the rows may be parallel, although a bestfit analysis of his small scale plan suggests a possible radius of only about 130m. With so many stones missing from the above two sites it is very difficult to draw definite conclusions. The radius of the Dirlot site is very close to the value of 4G and the length and base of the rows would be more than adequate. Dirlot could have been used satisfactorily for extrapolation purposes. The dimensions given for Mid Clyth are those of the main sector whose centre line is almost clue north and south. The length and base of the rows are very close to the value of G. The radius, on the other hand, is somewhat less then 4G. In fact it is only 65% of the required value. Despite this shortcoming, the error in determining the required extrapolation distance would not be very great and the Mid Clyth site could be used satisfactorily. Although a number of writers have expressed doubts about Thom's theory of the stone rows it is the only theory which has so far been published to explain their purpose. Of the four sites used to substantiate the theory the two best preserved, Dirlot and Mid Clyth, give the most convincing results. Camster and Yarrows which are less complete are not quite convincing. Now that so many other sites are known it is necessary that their dimensions also be checked against the use of possible foresights for lunar observation and the appropriate value of G. ^{ }REFERENCES
