Journal of the Anthropological Institute of Great Britain and Ireland, 27 (1898), 194–203 + Plate XIII
{194}
Ancient Measures in Pre-Historic Monuments. By A. L. Lewis, F.C.A., Treasurer, Anthropological Institute.
[with plate xiii.]
I have no doubt that all who may listen to or read this paper are more or less acquainted with the account given by our much-lamented colleague, the late Mr. J. T. Bent, of the ruined cities of Mashonaland, and with the remarkable series of measurements found in them by Mr. R. M. W. Swan, but it is necessary that I should recapitulate the principal facts which bear upon the subject now to be considered. The largest ruins, it will be remembered, consist of a building known as the great Zimbabwe, constructed of small-squared stones without mortar, with herring-bone and other decorations on some parts of the walls, and containing a large and a small round tower, which, when complete, were probably solid cones of dry masonry; and of a fortress on a hill between 600 and 700 yards north from the Zimbabwe, which also contains what appears to have been a temple. There are other ruins of a similar description at Matindele and on the Lundi river, besides numerous smaller forts. At all the larger buildings there are indications of sun-worship or observance and of star-worship or observance, the character of which may be most readily gathered from the following extracts from Mr. Swan’s chapter on orientation and measurement.
Having described various methods of ascertaining the length of a year by observing the position of the sun relatively to the equator or amongst the stars he says:—“At Zimbabwe all these methods seem to have been used, and to do so does not necessarily imply more astronomical knowledge than is possessed by the peasantry in any of the more secluded districts of Europe, where watches are not much used, and where almanacks are not read, but where the people have the habit of telling the time of the day and of the year by the motions of the sun and of the stars, for, to an agricultural people, the change in position of the sun in summer and winter is as obvious as the seasons themselves, and the variation of the times of rising of the stars with the seasons can as little escape observation.”
“Zimbabwe is in south latitude 20° 16′ 30″, and the sun, when rising there at the summer solstice, would bear east 25° south were the horizon level, but Mount Varoma interposes itself between the temple and the rising sun at this time, so that the sun attains an altitude of 5° before its rays reach the temple, then its amplitude will be more nearly 24°, and a line {195} produced in this direction from the altar will pass across the doorway of the sacred enclosure, where the curve of the wall changes its radius, and, roughly speaking, through the middle of the chevron pattern; the same line drawn in an opposite direction for 73 feet would fall on a tall monolith which we there found lying by its well-built foundation … this monolith was sufficiently tall to receive the rays of the sun when it rose over Mount Varoma, and the shadow of a monolith erected on the wall would fall on it at the same time, thus marking with great accuracy the occurrence of the solstice.”
The points of sun-rising and setting at the summer and winter solstices are further distinguished in the various buildings by the positions of the decorative patterns on the outside walls, of which full particulars are given by Mr. Swan. The indications of star-worship or observance are of a very similar nature: some of them are as follows:—
The apparently irregular outline of the enclosing wall is really composed of a number of arcs of circles differing in radius, and the centre of each of these arcs, where altars were usually placed, has had a doorway or some other means of marking out the meridian placed north of it. “True north of the centre of the greater round tower we have a doorway in the wall of the sacred enclosure … the part of the great outer wall north of the tower seems also to have been marked, for about this point we found a great step constructed on its top about 5 feet high. Above the temple at the east end of the fortress on the hill a cliff rises perpendicularly for 50 feet, and poised on its top there stands a most remarkable great rock, which may once have been an object of veneration to the worshippers in the temple beneath it; it forms one of the highest points on the hill; a line drawn true south from this rock and produced 680 yards would pass through the doorway in the great temple and fall on the altar in the centre of the decorated arc. Until this line suggested itself we were puzzled to account for the peculiar character of the doorway.”
“Every point from which northern stars could have been observed has been used for this purpose, and there is no temple there from which northern stars were not observed, while at the same time the openly displayed southern sky has been left unregarcled; this of course points to a northern origin for the people, and suggests that before they came to Zimbabwe they had acquired the habit of observing certain stars … It seems a plausible supposition that, while the great temple itself was devoted to solar and analogous forms of worship, the little circular or partly circular temples within its walls … were dedicated to the cult of particular stars.”
{196} Respecting the subject more immediately before us, that of measurement, Mr. Swan says:—“The diameter of the great tower seems to have represented the unit of measure in the construction of the curves of the outer walls, and of all the regularly curved inner walls in the great temple, and in all the well built temples in Mashonaland; the diameter of the great tower at its base is 17·17 feet or 10 cubits (of 20·62 inches), and this is exactly equal to the circumference of the little tower.”
On examining the radii and diameters of the various curves in the walls of the different buildings explored, Mr. Swan has found and given particulars of—
3 instances where the measurement is 17·17 feet.
3 instances where the measurement is double that, namely, 34·34 feet.
7 instances where the measurement is 54 feet.
3 instances where the measurement is half that, namely, 27 feet.
3 instances where the measurement is
1074/5
feet or practically twice 54 feet.
2 instances where the measurement is 169·3 feet, and 1 instance where it is half that or 841/2 feet.
The diameter of the great tower is, as has already been stated, 17·17 feet, and that distance (including its double 34·34 feet) is found in six other instances. That distance, multiplied by 3·14, which is the ratio of circumference to diameter, equals 54 feet, and there are thirteen instances in which the 54 feet, or their half, or their double occur. When multiplied by 3·142 the 17·17 feet amount to 169·3 feet, and of this, or its half, three instances occur. Thus there are twenty-two cases in which the measurements appear to be based on the diameter of the great tower, and these include nearly all the cases in which satisfactory measurements can be obtained; in those places where none of these measurements are found there seems always to have been some special reason for the exception. Mr. Swan says :—“The only interesting mathematical fact which seems to have been embodied in the architecture of the temples is the ratio of diameter to circumference, and it may have had an occult significance in the peculiar form of nature worship which was practised there; we do not suppose that it was intended to symbolise anything of an astronomical nature, and it is extremely improbable that the builders of Zimbabwe had any notion of mathematical astronomy, for their astronomy was purely empirical, and amounted merely to an observation of the more obvious motions of the heavenly bodies;1 when the minds {197} of men were first interested in geometry it would at once occur to them that there must be some constant ratio between the circumference of a circle and its diameter, and they would easily discover what this ratio was, and they may have considered this discovery so important and significant that they desired to express it in their architecture.”
1 I have quoted Mr. Swan’s own words upon this subject because they express very clearly some conclusions I had myself arrived at from other data.
If the builders of the Zimbabwe really had this purpose in view it must be confessed that they chose a more complicated manner of expression than might have been expected, but it does seem that certain definite measurements do occur so frequently in and about these structures that their occurrence cannot be a mere coincidence, but must be the result of a system of some kind.
It is a long distance to Great Britain from Mashonaland, or even from Arabia, which Mr. Bent thinks (with much reason) to have been the fatherland of the builders of the Mashonaland monuments, but I can find many instances of peculiarities of position and measurement in connection with our own stone circles, which are the same in principle and often in detail as those observed in South Africa by Mr. Swan.
I have already drawn attention in numerous papers read before the British Association, the Anthropological Institute, and various archæological societies, to the connection of our circles with the rising sun, and in some cases with the northern stars, by means of menhirs, hills like Mount Varoma, or “remarkable great rocks” somewhat like that on the cliff above the temple at Zimbabwe, and I shall therefore confine my remarks on the present occasion to coincidences of measurement.
It is only within the last few months that Mr. C. W. Dymond, C.E., F.S.A., has published the final results of his very careful and precise measurements of the important group of megalithic monuments at Stanton Drew, seven miles south from Bristol, and has thereby given us the means of accurately comparing another set of measurements.
The Stanton Drew group consists of six items, namely, three circles of different sizes, two of which have short avenues attached to them, one group of three stones known as the “Cove,” two stones in another direction, and a solitary stone called “Hauteville’s Quoit.” Of these the Cove, the central circle, and the north-eastern circle are in a straight line in one direction; and the Quoit, the central circle, and the south-western circle are in a straight line in another direction. Some people regard these lines as accidental coincidences, but the {198} chances are at least 100 to 1 against either of them happening accidentally, and perhaps 10,000 to 1 against both of them occurring in a group of only six items; the existence of similar lines in connection with other circles proves that they were intentional, and this proof is still further sustained by the proportioned diameters and distances.
The diameters of the circles are:—
North-east circle, 97 feet, or 100 of an ancient foot of 11·64 inches.
South-west circle, 145 feet, or 150 of an ancient foot of 11·64 inches (within 6 inches).
Great central circle, 368 feet, or 380 of an ancient foot of 11·64 inches (within 71/2 inches).
The length of the straight line from the centre of the “Cove,” through that of the great circle to the centre of the north-eastern circle is 1,367 feet 8 inches, or not quite 1,410 of the foot of 11·64 inches, that is (within a working error of 8 inches (+) per 100 feet) 14 diameters of the north-eastern circle.
The length of the straight line from the centre of the great circle to Hauteville’s Quoit is 1,856 feet, or 1,9131/2 of the foot of 11·64 inches, that is (within a working error of 9 inches (+) per 100 feet) nineteen diameters of the north-eastern circle, or five diameters of the great circle. And I may remark that this point is the nearest to the great circle which brings in the diameters of both circles. This in my opinion tends to show that the position of Hauteville’s Quoit was intentional and not accidental.
The length of the straight line from the centre of the southwestern circle through that of the great circle to Hauteville’s Quoit is 2,5672 feet, or 2,647 of the foot of 11·64 inches, that is (within a working error of 4 inches (–) per 100 feet) seven diameters of the great circle.
The distance from the two stones to the centre of the great circle is 3,305 feet,1 or 3,4071/4 of the foot of 11·64 inches, that is (within a working error of 5 inches (–) per 100 feet) nine diameters of the great circle.
1 In his first publication Mr. Dymond stated this distance at 3,293 feet, and that from the great circle to Hauteville’s Quoit at 1,852 feet only. If Mr. Dymond, notwithstanding his engineering skill and modern appliances, found mismeasurements in his own work we need not be surprised at finding fractional working errors in the measurements of those who set up these monuments so many centuries ago.
We find, therefore, that the diameters of the circles are in the relative proportions of 5, 71/2, and 19, that the diameter of the smallest circle is repeated fourteen times and nineteen times in other measurements, and that the diameter of the largest circle {199} is repeated five, seven, and nine times in other measurements. These latter coincidences are not mentioned in Mr. Dymond’s bookC.W. Dymond, The Ancient Remains at Stanton Drew (Bristol, 1896), but have been deduced by me from his measurements, and there may be yet others which I have not discovered.
Five, seven, fourteen (which is twice seven), nine and nineteen are all more or less significant numbers. Nine is frequently associated with the stone circles, many of which are called “Nine stones,” though they have originally consisted of more than that number; those who resorted to the Men-an-tol in Cornwall to heal their ailments passed through the hole in the stone nine times. Nineteen is the lunar cycle, the number of years in which it was thought the sun and moon returned to the same relative place in the heavens, and allusions to it have already been suspected in circles formed of nineteen stones. In connection with this number I must remind you of the oft-quoted extract from Hecatæus,1 given by Diodorus Siculus, respecting the island of the Hyperboreans, where Apollo (or the sun) had a stately grove and renowned temple of a round form, beautified with many rich gifts, and of which he says farther, “that in this island the moon seems near the earth, that certain eminences of a terrestrial form are seen in it, that the god visits the island once in the course of nineteen years, in which period the stars complete their revolution, and that for this reason the Greeks distinguish the cycle of nineteen years by the name of the greater year.” There is little doubt that the island referred to was Great Britain, and the temple has been thought to be that at Abury, but Stanton Drew, though much smaller, is far more accessible from the sea, and therefore more likely to have been known to casual visitors, and the embodiment of the number nineteen in its measurements makes its identity with the temple of Hecatæus very probable.
1 It is not certain whether this is Hecatæus of Abdera, who lived in the fourth century b.c., or Hecatæus of Miletus, who lived in the sixth century b.c.
What Mr. Dymond has done for Stanton Drew, Mr. Hansford Worth, C.E., of Plymouth, has done for the remains at Merivale Bridge, Dartmoor; that is, he has given us, for the first time, a thoroughly accurate plan of them. These remains consist of two double rows of stones, running from slightly north of east to slightly south of west; the southern lines extend beyond the northern lines at each end, but further at the west than at the east; the distance between the two sets of rows is greater at the west than at the east, and nothing seems more unlikely at first sight than any fixed measurement or proportion in the laying out of these lines. Starting, however, at the narrow or east end we find that the length of the overlap of the southern beyond {200} the northern lines is the same as the width between the two, while the distance between the eastern ends of the northern and southern rows (diagonally) is the same as the greatest width of the two rows from outside to outside at the west end, viz., 1,300 inches, or 100 of a foot of about 13 inches, which seems to have been the unit of measurement; the distance (diagonally) between the western ends of the northern and southern lines is 2,600 inches, or 200 units. In other words the longest side of the triangular ending of the lines at the east end is the same length as the shortest side, and half the length of the longest side of their triangular ending at the west end. The length of the southern beyond the northern lines is in the proportion of five at the western end to two at the eastern end; the length of the southern lines is 10,369 inches, or 797·6 (practically 800) of the 13-inch unit, that is, eight times the distance between the ends of the rows at the east end, and four times the distance between the ends of the rows at the west end. The length of the northern lines is 7,148 inches, or 549·8 units (practically 550). A “bird’s eye” view of these remains—a sort of “restoration” in fact—published in Rowe’s “Perambulation of Dartmoor,” 1830, depicts a circle at the eastern end of the northern lines, but Mr. Hansford Worth has satisfied himself that no such circle ever existed, and it may be considered certain that the eastern ends of the lines have not been interfered with. The western ends of both rows are represented in the same view as terminated by single stones somewhat taller than the rest, but these are not there now, nor can it be ascertained whether they ever existed; if they did they would bring the lines up to 800 units and about 552 units respectively, and there seems no reason to suppose that any other stones have been removed which would make any material alteration in the proportions stated. A small tumulus surrounded with stones stands across the southern lines very near their centre, it is in fact about 10 or 12 feet nearer the eastern than the western end, and anyone who objects to the idea that these lines were laid down by measurement is entitled to make the most of that difference; but I think it probable that this tumulus was made after the lines had been constructed, and that the exact middle of the lines was not ascertained by those who erected it. Besides the two double rows there are a circle of small stones and a menhir to the south of the western end of the lines; such measurements as can be deduced from them do not appear to be based on the same unit as those of the rows, but a straight line taken from the menhir through the centre of the circle due north would strike the western end of the northern lines and pass on to the {201} western extremity of Great Mis Tor. It seems probable therefore that the menhir and circle were set up at a later period than the rows, as they appear to have been set to them, but not at distances based on the same unit of measurement.
Our Journal for August, 1895, contains a paper in which, amongst other things, I have recorded a number of remarkable measurements and proportions in connection with five circles on Bodmin Moors in Cornwall, but, as the details are given in full in that paper, I need now only say that those circles, like the monuments we have been considering to-night, seem to have been arranged with much care and approximation to accuracy, for some purpose, or with some idea in view, which we are at present unable to ascertain.
The principal questions that we have to settle are, firstly, do the proportionate lengths and distances really exist? and secondly, if they do exist, are they the result of intention, or of accident?
As to the existence of the proportionate lengths and distances, I must point out that they are taken, not from my own measurements, but from the careful plans of skilled engineers and archæologists, most of whom have no sympathy with the use I am making of the facts they have recorded. My part in the matter has simply been the conception that the multiplication table might usefully be applied to their figures, and its application accordingly, with the results which I have now laid before you, and which can be checked by anybody.
If it be admitted that the proportionate lengths and distances do exist, it will be for everyone to form his own opinion as to whether they were intentionally arranged or whether they are all the result of mere blind chance. For myself, I admit it to be difficult to believe that these apparently rude constructions have in reality been very carefully measured and arranged, and it is only by degrees that I have come to find it many times less difficult to believe this than to retain the old trust in the working of accident and chance.
Of course the further questions arise, “What do these arrangements mean?” and “Why should all this labour have been undertaken?” and I have been told, in effect, that unless the meaning of the facts can be explained their existence cannot be admitted. Of those who think thus I will ask in return, “Why did the builders of Stonehenge drag forty or fifty ‘bluestones’ of no inconsiderable weight from Wales, Devonshire or still further away, to Salisbury Plain?” “Why did the early inhabitants of Dartmoor set up a row of stones, nearly {202} two miles long, extending from a circle on one side of the river Erme to a tumulus on the other side of it ?” We cannot deny that these things were done, because most of the stones remain there to this day, but we do not know why they were done, and so it is with the measurements.
Finally, I have to point out that in each of the monuments I have spoken of the unit of measurement, if such there were, appears to have been different, which seems to indicate a separate influence, personal or otherwise, in the construction of each of them.
In setting up a number of stones in a large and regular circle there must at the very least have been the describing of a circle on the ground by means of a rope or pole, one end of which would be fixed to the centre, and the other taken round the circumference. In some cases this rope or pole may not have been, measured at all; in others, and especially where proportionate measurements were intended, it may have been very carefully measured by any unit that happened to be available. All the units I have spoken of were in use round about the Mediterranean from two to three thousand years ago, and may have come here at various times and in various ways, the first to be brought here being perhaps by no means the oldest; but it does not necessarily follow that the unit I have mentioned in each case was actually used; I can only say that it suits the measurement, by working out in even numbers, better than any other that I can find, but that I may not have exhausted them all. The unit of measurement is, however, quite a secondary thing, and can, perhaps, never be proved, but only inferred; the great point to be established is that some of these apparently rude structures were in reality laid out in careful proportion, for some purpose, or with some idea, which we may hope at some time or other to discover.
The President complimented Mr. Lewis on his paper. He quite agreed that the measurements cannot be accidental, but must have been intentional.
Dr. Garson remarked that the large temples, their positions, and measurements, were certainly not arrived at by chance, as can be seen by the orientation of Egyptian pyramids, temples, and some of the large temple remains, very probably of neolithic people. Professor Flinders Petrie observed this in this year’s discoveries.
Mr. Gomme begged to differ from Mr. Lewis. He wanted evidence on measures not fitting, as well as measures suiting this theory.
{203} Mr. Lewis said in reply to Mr. Gomme that there were doubtless many of the rude stone monuments in which proportion could not be traced, but that fact in no way interfered with the fact that in others proportion could be traced. Even where there were no means of tracing it, as for instance in a single circle with no measurements about it of which to make a comparison, the diameter might have been based upon some unit or other and carefully measured from it. He thanked the meeting for the manner in which his paper had been received.
Explanation of Plate XIII.
Stanton Drew reduced from Mr. Dymond’s plans to about 1 in 12,000. In consequence of the smallness of the scale the sizes of the Quoit, Cove, two detached stones and avenues are considerably exaggerated, and the circles are represented by continuous lines instead of separate stones, but the diameters of the circles and distances between them are carefully measured. The length of the line from the centre of the Cove through that of the great circle to the middle of the north-eastern circle is fourteen diameters of the north-eastern circle. The length of the straight line from the centre of the great circle to the Quoit is five diameters of the great circle or nineteen diameters of the north-eastern circle The length of the straight line from the centre of the south-western circle to the Quoit is seven diameters of the great circle, and the distance from the two stones to the centre of the great circle is nine diameters of the great circle (all within a working error of less than one per cent).
Merrivale reduced from Mr. Hansford Worth’s plan to about 1 in 3,000. In consequence of the smallness of the scale the stones are somewhat enlarged in size, but the lengths of the lines and distances between them are carefully measured. The distance from A to C (inside the lines) is the same as that from C to B. The distance from A to B is the same as that from B to E (outside the lines), which is half the distance from D to F, which latter is a quarter of the distance from F to B (the length of the longest line). The error of workmanship in these measurements is hardly distinguishable. There are some but circles, detached cairns, etc., which are not indicated here as they have no connection with the rows.
