Introduction

In the collection of the National Museum of Scotland in Edinburgh is an unusual artefact; a block of limestone, roughly hewn and damaged in places, and weighing around half a metric ton. The stone is of remarkable historic and scientific significance. Around 2,600 B.C.2 it was cut from the bedrock, shaped and sized in the RA-Aw quarries, now known as the Tura quarries (they are still accessible in the hills overlooking the east side of the Nile valley just south of modern day Cairo). The stone was then transported 15 km across the river valley to the largest pyramid ever built in Egypt, the Great Pyramid of pharaoh Khufu at Giza, where it was raised and placed on its outer face.

Incredibly, a written record of the journey these stones took to Giza has survived.3 In 2013 fragments of a 4th Dynasty papyrus from the 26th or 27th year of the reign of pharaoh Khufu were recovered from the Wadi al-Jarf on the west coast of the Red Sea, where an Old Kingdom port is being excavated. The papyrus fragments that the joint Franco-Egyptian team4 uncovered turned out to be the oldest ever found. Furthermore, the hieroglyphs written on one of them describe the transportation of stone blocks from the Tura quarries, across the Nile to the Pyramid of Khufu at Giza. As the high quality stone from the Tura quarry was reserved for use on the outer faces of the pyramids, the stones they described moving were surely casing blocks, and the stone in Edinburgh could therefore be one that was transported by the team described in the text.

The so-called ‘Journal of Merer’ on the papyrus dates from the end of Khufu’s reign, when the casing stones were being added to the almost-complete pyramid. Merer was the leader of a ‘phyle’ of approximately 200 workers in a team called MA-wrrt, a name which remains enigmatic. The journal records the following events:5

‛Day 26. Inspector Merer sailed with his team from Tura [south]; loaded with stones for the Horizon of Khufu;6 passed the night at the Lake of Khufu.

Day 27. Sailed from the Lake of Khufu; navigated to the Horizon of Khufu, loaded with stones; passed the night at the Horizon of Khufu.

Day 28. Sailed from the Horizon of Khufu in the morning; navigated back up the river to Tura [south].

Day 29. Inspector Merer spent the day collecting stones in Tura south; passed the night at Tura south.’

The content of this papyrus then is a daily diary of work carried out by Inspector Merer and his team during the construction of the Great Pyramid of Giza. It describes events just like the ones that would have brought the Edinburgh stone to Giza. It is incredibly fortuitous to have recovered this papyrus, but information regarding the stone is not only derived from ancient texts. Archaeological information about the Ancient Egyptians and their construction methods can also be derived from examining the stone itself. The Ancient Egyptian monument on which it was placed and the tools and techniques they used to build it also provide valuable information about the Old Kingdom culture and the technologies it developed.

In April of 2013 I was able to carry out a study of the casing stone in Edinburgh with permission granted by National Museums Scotland.7 That study yielded new data, new architectural information, and improved understanding of an issue of more profound cultural significance.

In this article I summarize the motivations of the man who had the stone brought to Edinburgh in 1872, Charles Piazzi Smyth, and critique his own analysis of the stone.8 I show that when more appropriately investigated, the stone reveals significant information about its original position on the outside of the Great Pyramid, as well as information regarding the Ancient Egyptians’ own systems of measurement. Finally, I address the symbolic significance of the principal dimensions of this stone, and the monument on which it was placed. I explain how the dimensions and proportions of the block and the building were most likely related to the geometric proportions of a circle, and I explain what this architectural symbolism would have meant to the Ancient Egyptians. This phenomenon was the issue which first attracted the English Egyptologist Flinders Petrie to study the architecture of Egypt and the Giza necropolis in particular. He addressed it at length in his report of his 1883 survey of Giza.9 Here I offer additional explanation to clarify aspects of this long standing investigation.

The Giza Casing Stone

The casing stone addressed by this study is NMS collection museum catalogue number A.1955.176. We studied and took measurements of this piece in the museum storerooms in April 2013. Casing stones have an angled front face that formed the flat outer surface of the pyramids and I was interested to establish if its face slope matched the angles calculated elsewhere for the Great Pyramid of Giza, from the building itself, and from surviving casings stones. The casing stones are trapezoidal in form when viewed from the side, as opposed to core blocks which were most likely left roughly hewn and approximately cuboid.10 If the slope of any casing stone’s outer face is accurately known then the side slope of all of the pyramid’s faces are known, and so these casing stones are of particular interest to archaeologists studying pyramid architecture, as was the case with Smyth and Petrie.

Based on the type of limestone used and its associated architectural function, this casing block was most likely mined at the Tura quarries on the east side of the Nile around 46 centuries ago, carefully shaped with copper tools, shipped across the river to Giza on the west bank, dragged up to the pyramid construction site on a wooden sled, and lifted into place on the outside of the Old Kingdom pyramid of pharaoh Khufu using methods that remain obscure. Its outer face may have been worked again in-situ to ensure it was finished flush with the rest of the pyramid’s external surface.

Forty-four centuries later, the stone was found in the mounds of debris on the north side of the Great Pyramid of Khufu by Waynman Dixon in 1872. Its original architectural position on the pyramid was unknown at the time it was collected from the site. Dixon was an English engineer who carried out investigative work at Giza for Charles Piazzi Smyth.11 At the time, Smyth was Astronomer Royal for Scotland, based in Edinburgh, where he carried out research into many different scientific and historical issues.

Almost all of these casing stones were stripped off the pyramid in the ancient past as they were made from high quality stone and were useful for building the city of Cairo and for producing limestone mortar. Only a few oversized base level casing stones remain in situ at the Great Pyramid. The example in the NMS collection found by Waynman Dixon is not from the base level and is therefore unique in several respects.

Its arrival on the British Isles was reported in Nature, 26th December 1872, pp. 146-149, and The Graphic of 7th December 1872, pp. 530 and 545, where it was illustrated along with several other artefacts found in and around the Great Pyramid, including a stone ball, the remains of two copper tools, and a wooden shaft. Smyth published the stone’s primary dimensions and an analysis of those dimensions, but he did not investigate the piece with respect to Ancient Egyptian standards, methods and systems, and so he reached no significant historical conclusions. Although large parts of the stone are broken off and missing, its overall rectilinear dimensions can be reconstructed from the surviving material, with a margin of error of +/- 5 mm, as follows:

65 cm wide

52 cm in height

93 cm from front to rear at the base

51 cm from front to rear on the top.

A large section of the back and lower rear face of the stone is broken away and so its approximate weight is calculated to be around 500 kg.

Although it remains in one solid piece, the casing stone is substantially chipped around the edges and corners, probably due to having been pushed down the pyramid in the ancient past. Three all-important worked flat faces are partially intact and in good condition in places, a fact that was also noted by Smyth. These three surfaces are the flat base, the sloped front face and the flat top. This means that fairly accurate measurement of its original, intended primary dimensions, and its intended slope angle, can be made; something that Smyth achieved and we were able to repeat.

Our angular measurements showed that within our margins of error (+/- 0.25°), the face of the stone, when compared to the upper and lower flat surfaces, and hence the horizon, is at the correct angle known for the Great Pyramid’s faces, of around 51.84 degrees.12 The limestone of the block is still surprisingly bright in color, almost silvery, particularly the limestone dust that has accumulated on the surface over time. The Tura limestone from south of Cairo is thought to have been utilized because it is a light colored stone suitable for the outer faces of monuments. These two facts; the slope angle and the geological material, indicate that the NMS stone is a genuine Giza casing stone, and is the same stone studied by Smyth over one hundred years ago.

Authentically sized standard cubit replicas were also used to measure the incline of the stone’s face (Fig. 2). We simulated using the seked slope measuring method devised by the Ancient Egyptians themselves to check the face. The cubits were employed on the basis that practical experimental archaeology, using techniques from the ancient past, often reveals aspects of materials that otherwise remain hidden. During the Old Kingdom the Ancient Egyptian cubit standard was 52.37 cm long +/- 2 mm.13 This value was very consistently maintained with only a couple of millimeters of variation, particularly when it was utilized to build monumental architecture during the Old Kingdom. The standard cubit was subdivided into 7 palms of 4 digits each, giving 28 digits in total. This cubit was known as the mH nswt, written as follows meaning the royal, pharaonic or official cubit.

The slope measurement system employed by the Ancient Egyptians was a ‘rise and run’ method known as the ‘seked’ system, written as follows sqd . Textual evidence of the use of this system dates back to the Middle Kingdom. Angular slope measurement was made by measuring the linear horizontal offset, in palms, for each 1-cubit vertical rise. For example, a cubit has 7 palms, so a seked of 7 is 45 degrees.

The known seked of the Great Pyramid equates to 5 1/2 palms. Before we started the study this value was marked off on one cubit to be held along the horizontal top surface, while the other was to be set vertically, at right angles to the first. This formed a right angled triangle with a hypotenuse sloped at a seked of 5 1/2. This seked corresponds to 51.84 degrees from the horizontal, the known ‘pyramid angle’. During this measurement it immediately became apparent that the triangle fitted the sloped face and the block precisely, not just in slope but in height, and so indicated that the casing stone was exactly 1 cubit thick in height, something that was not noted by Smyth (Fig. 3). Why did Smyth not notice this fundamental relationship ? Going by Smyth’s publications this was because he was pre-occupied with the width of the stone, from side to side, as his own now-falsified theories were focused on measurements along that axis as of potential significance. It nevertheless seems strange that Smyth should not have noted that the height was 1 Egyptian cubit, but solid information regarding the real cubit standard and measurement techniques used by the Ancient Egyptians was not readily available during his lifetime, and the issue of measurement standards remained confused in several important respects.

Analysis of the thickness/height of the casing stone

Heavy though this casing stone is, it is small compared to the giant sloped stones still in place along the northern side of the base of the Great Pyramid. Most of the fine Tura casing stones were stripped off the Great Pyramid and recycled to build Cairo during the medieval period, but a few of the huge base row remain in place, where they were protected under mounds of fragmented stone that gathered along the edges of the pyramid over the centuries. Given the discrepancy in size between the surviving Giza base stones and the smaller stone in Edinburgh, the first question I addressed was whether or not this smaller stone was actually from the Great Pyramid at all, or if it came from one of the similarly proportioned queens pyramids nearby. They were constructed at the same time as the Great Pyramid (or shortly after) around 2,550 B.C., and to the same slope angle,14 but were built using casing blocks of around this smaller size.

Surviving casing stones still in place on the upper levels of pharaoh Khafre’s pyramid, however, demonstrate that smaller casing stones were also used near the peaks of the larger structures. As Lehner described with respect to the second Giza pyramid of Khafre,15 ‘the casing stones at the top of the pyramid are much smaller – about 1 cubit thick (c. 50 cm/20 in)’.

It was not just the casing stones that were smaller towards the summits of the pyramids. During his 1883 survey Flinders Petrie measured the height of every individual layer of the core blocks of the Great Pyramid, at the north-eastern, and south-western corners,16 from the base to the current summit. His data clearly show that as the summit is approached the height of the core layers tend closer and closer to 1 cubit in thickness.

The graph (Fig. 4) provides Petrie’s data in a format whereby the total volume of blocks set in place is plotted against the height or thickness of each layer, as the pyramid was built, from the ground level (left) to the summit (right). The layer heights clearly trended in cycles. This is most likely because the core blocks naturally varied in height due to the varying heights of the stratified layers of rock in the quarries. The stones could be excavated out in layers more easily if the natural stratigraphy was followed. They were then gathered and grouped on-site by size and sorted into a sequence each year, ready for the transportation workforce to become available. Although still unverified, it is though that the transportation teams worked on a seasonal basis and only became available once the agricultural work in the fields by the Nile was completed. When the transportation workforce arrived during the inundation, when agricultural work was impossible, the larger blocks would be sent up to the pyramid first, working down to smaller blocks as the teams tired towards the end of each construction season. The cycles apparent in the stone height dimensions on the graph therefore correspond to a period of one year, so that it would have taken around ten or eleven years to set the core block layers in place. The height of the fine Tura casing blocks would not necessarily have matched the roughly cut core blocks (which were quarried closer to the site) in size, but as the summit was approached it appears that more control and consistency was required over the form of each layer, perhaps because the elevation of the blocks became increasingly hazardous (Fig. 5). The reducing magnitude of the pyramidal form would also have been more sensitive to dimensional variations. As a result, smaller core and casing blocks were cut to size as the summit was completed, tending closer and closer to a precise 1-cubit thickness.

But why did sizing of stones so clearly stop at a 1-cubit minimum? One explanation derived from our experiment is that if pairs of cubits were used to measure out and then check slopes of casing stones using the seked system described above, then the blocks must be at least 1 cubit in height. Measurement from the top of the vertical cubit, at right angles horizontally towards the face, cannot be carried out if the stone is less than 1 cubit in height, because the horizontal cubit will not meet the top or front face of the stone.

Hypothetically, the quarry workers would typically have used pairs of cubits in large numbers for rapid every-day measurement of dimensions and angles, to cut the stones to the approximate size for transport, with occasional plumb bob checks. More accurate plumb-levelled angle measurement using cubits may have been reserved for the finishing of the casing stone faces after installation on the pyramid, using the methods shown in the diagrams and animations associated with this article. Triangular templates pre-cut to the correct angle may also have been used.17 These templates may have been 1 cubit in height if they were made using cubits, but in fact no such triangular tool has ever been recovered. The ease of manufacturing fairly accurate cubit measuring rules, by simply copying an existing cubit of known dimensions, is an important factor to consider when dealing with an industrial-scale quarry site which was producing enormous numbers of stones. Plumb bob tools that could be used in combination with cubits have been found, but it is perhaps unlikely that these were widely used in the quarry. It is likely that the cubit was the primary measurement tool for both linear and angular measurement used throughout the quarry, with more accurate finishing completed at Giza.

The stone in Edinburgh then is most likely a rare survivor; an upper level casing stone from the top of the north face of Khufu’s pyramid, perhaps dropped, lost or forgotten during removal in Antiquity or the medieval period. This stone, however, is not ‘approximately’ 1 cubit tall, it seems to be precisely 1 cubit tall. This level of precision would fit well with the exceptional standards of quality evidenced by the rest of the architectural and archaeological remains of the Great Pyramid, internally as well as externally. It is possible that several layers of the uppermost levels of casing stones of the Great Pyramid of Khufu were constructed to be precisely 1 cubit tall, to make finishing the peak of the pyramid a more controllable process and to ensure that high levels of precision could be maintained over the final form of the structure (Fig. 6). Despite some uncertainty over the exact metrical and construction methods used, it is possibly to say that the Edinburgh casing stone was originally placed near the summit of the monument.

As the stone’s outer dimensions are known, its original weight when placed there can also be calculated. Its volume when complete was first calculated and then multiplied by the known density of Tura limestone. This gives a result of 650 kg. This is significantly less than the 2.5 tons usually estimated for regular core blocks, but it remains a very substantial weight. We can only imagine the challenges involved when maneuvering the stone towards the outer edges of the upper levels of Khufu’s Great Pyramid, at a height approaching 146 meters over the desert below.