Pyramid Quest (16 page)

Hodges realized that the Egyptians had figured out something that Archimedes later immortalized and every sapper officer knew from experience: a few levers with a few men can lift crushingly huge weights. During his wartime service, Hodges had often watched as four sappers pumping two simple lever jacks readily and quickly raised the end of a 30-ton Bailey bridge to place rollers or permanent bearing plates under the lifted end. The handle on jacks the sappers employed raised the bridge about ⅓ inch with each stroke, then caught on a ratchet to hold the slightly higher weight in place. Another stroke, another ⅓ inch, and in a matter of minutes, four men could boost the bridge upward inch by inch and foot by foot.

The Egyptians, as far as we know, lacked the ratchet, but they could gain the same advantage by packing materials in under the block. Say, for example, two levers were inserted under the end of a typical 2½-ton pyramid building block. One or two men on each lever pushed down, raised the end of the block a short distance, and inserted a piece of wood into the space between the block and the surface it was sitting on. The same procedure of jacking and packing was followed on the other end of the block. Again and again, the block was jacked and packed. Do this enough times, and the block rises to the next course of stone, where it can be moved horizontally—again with the levers—onto the higher surface. The crew removes the now-freed packing, puts the levers under the block yet again, raises it the first increment, and puts some of the packing underneath. Again and again the process is repeated. This would work, as the sides of the unfinished pyramid courses formed a series of steps. Working in a finely tuned rhythm, Hodges figured that a crew of four could boost a typical building block halfway up the pyramid in a day’s work.

Hodges experimented with various kinds of levers, and he favored a design that looked something like a club-footed hockey stick, with the weight-bearing lower end sheathed in copper to add strength. Julian Keable, Hodges’s editor, preferred a straight lever; it lacked the obvious weak point in the bend of the curved lever. Whichever design the Egyptians may have used, the basic physical principles remain the same.

The exceptionally large, very heavy pieces of stone used in the Great Pyramid pose no stumbling block to the lever theory. A heavier stone is also a larger stone; that many more men can find foothold around the load and work their levers. Forty levers manned by one or two workers apiece could lift even the 50-ton, or more, red granite blocks that roofed the Relieving Chambers.

One of the fascinating aspects of the lever strategy is that it eliminates ramps or scaffolding. The pyramid itself becomes the platform on which the men work as they raise the stone blocks from one level to the next. When they put the last stone in place, they simply pick up their tools and go home. There was no ancillary structure left to remove. As soon as the pyramid is done, the project is finished.

Curiously, Hodges’s idea fits with Herodotus’s description that “they [the pyramid builders] raised the remaining stones by machines made of short pieces of wood” and “they removed the machine, which was only one and portable, to each range in succession, whenever they wished to raise the stone higher.”

Of course, lifting the stones is only part of the challenge of building a pyramid. The builders had to be sure that they were raising the right shape into the sky. They wanted to know that when they were finished, they could step back and see the shape they intended, not that of a collapsed angel-food cake.

Fashioning the right shape began with leveling the ground to create a flat, firm base in the bedrock. The first step was marking the approximate directions and length of each of the four sides. The builders then probably selected one side as a baseline and set their men to work cutting a broad, level track about 6 feet wide and at least 50 feet longer than the approximately 756-foot eventual length of the Great Pyramid’s side. As the baseline was cut, the builders could measure the level with the same principle masons and carpenters use today: checking the horizontal against a liquid. As you probably know, a level uses a bubble in a heavy liquid to indicate the horizontal. If the level is off, the bubble moves to one side or the other, depending on the direction of slope from the horizontal. The ancient Egyptians could have exploited a similar principle by building a narrow channel about one foot wide and 50 feet long and filling it with water—whose surface is, of course, level. Stones were placed at each end of the channel just flush with the surface of the water. Two men carrying flat-topped rods of exactly equal length placed the butts of the rods on the stones in the water, while other men with the rods of the same type and length set them at approximately equal intervals along the baseline. A worker sighting along the rods could use the level established by the two rods in the water to determine the amount of rock that needed to be removed farther down the line to make the base level. Although the work of removing the bedrock with the tools the Egyptians had to work with was difficult indeed, repeated rechecking allowed them to establish the level precisely.

With the baseline cut and level, the time came to determine the orientation and length of each of the four sides. One way to do this would be to determine the center point of the baseline, establish the true north-south axis of the pyramid, and orient the site plan so that the axis crossed at the center point. This orientation determined the rest of the square, which had to be marked before the real work could begin.

The square began by setting two right angles at the center point of the baseline. Three cords of at least 50 feet in length were set out, each from the center point marked into the rock. One followed the north-south axis exactly, the other two what would be the halves of the side. The builders marked the cords at exactly the same distance from the center point and placed the side cords as close to a right angle as eyeballing could make them. Next they measured the angle of the hypotenuse of the triangles formed between the marks on the side cords and the mark on the axis cord and adjusted the side cords until the hypotenuses were equal and both angles truly 90°. The same procedure was used to determine the right angles at the corners of the baseline, then around the remaining three sides of what would be the pyramid. Most likely, the pyramid builders placed sighting stones away from the corners but in line with the sides. This allowed them to check the right angles even when the original corners were covered with masonry and no longer visible.

The next task was determining the length of the baseline side, a solution that probably proved to be relatively simple. It could have been a matter of taking two rods of exactly the same length and laying them end to end over and over again until the predetermined length was reached. Most likely the rods were capped with metal to lessen wear and tear; they could also be filed to achieve exactness in length. Wooden measuring rods are known from the New Kingdom, although there is no evidence of their use in the Old Kingdom. Still, the solution is so simple and obvious that the ancient Egyptians were likely to have had such devices.

With the square marked and the baseline now level, the procedure of rough cutting followed by water leveling and sighting along the rods could be repeated around the three remaining sides of the pyramid site. This work began at the level established by the baseline, so that the whole square was brought to that one level. When this work was finished, the four sides had been leveled and measured, yet within lay them nearly 13 acres of rough, ragged bedrock. Leveling this part of the site became the next task, one that must have taken a great many men months to complete. And in a sense, they did not finish the task. One rocky prominence, which extends two dozen feet upward from the base, remains under the pyramid. Containing the lower portion of the Descending Passage, as well as the Subterranean Chamber and the Grotto, it was left in place, probably for important religious reasons (we will explore these further in chapter 6).

Even with the base squared and much of the underlying site leveled, the Egyptians faced the challenge of putting all those many block of stones in the right place. Stepped pyramids like Djoser’s at Saqqara were erected essentially by starting at the center and raising a core that was wider at the bottom and narrower at the top for stability. The outer layers leaned in against the core and acted as buttresses to hold it in place. The core rose faster than the outer layers, so that the center of pyramid was reaching into the sky sooner than the exterior faces. Some Egyptologists have argued that the Old Kingdom builders erected the core of the Great Pyramid in the same way, then evened up the outer walls to give a smoothly sloping outward appearance. Engineer Peter Hodges doesn’t think so, and I agree. Squaring off a stepped pyramid after the fact would have made it very difficult to ensure that the corners rose as they must to place the apex directly over the center of the pyramid. Building instead course by course and completing each tier in turn would make it easier to verify the building.

Once again, this approach fits with Herodotus’s account: “This pyramid was built thus: in the form of steps, which some call crossae [tiers], some bomides [terraces].” In other words, the builders laid one course completely, then set the next course atop it. They worked not from the center out but from the bottom up.

Each course in the Great Pyramid is a square that sits atop the slightly larger square of the course beneath it, center aligned to center. Put another way, each course angles precisely in from the course below it. The angle is the key. If it’s right, the pyramid is on track; if it’s off, there’s trouble that gets worse, course by course. One solution to the problem of setting each course at the correct angle is to raise the corners first, then fill in the straight reaches between the corners. The pyramid builders must have laid the four corner blocks of each course and checked the angles before laying the rest of that course and moving to the next course above, beginning again at the corners. Probably the pyramid builders used a plumb frame to check the corner angle, a triangular frame constructed to the correct 52° angle and equipped with a plumbing device to ensure vertical accuracy.

It was also possible to double-check the positioning of each corner by sighting from outside the pyramid. Because of the pyramid’s geometry, the corner hip line (where two adjoining sides meet) looks vertical to an observer standing opposite the hip and looking toward the pyramid. Old Kingdom engineers could sight the corner hip lines from the pyramid’s base against a vertical marker. If the corners were all rising vertically at the same angle to the horizontal, then the four would meet at the apex. If one of the hips was off, that corner could be adjusted before the structure reached any higher. As long as each step was parallel, equal, on the correct gradient, and straight along its hip line, the shape was guaranteed to grow into a correct pyramid.

An advantage to this approach is economy of effort. Setting the corner stones for each course was a demanding task; the stone had to be set in by a precise distance in two directions to maintain the hip line. But, since the Great Pyramid has 200 courses and four corners to each course, precision alignment of a total of 800 stones determined the shape of the entire structure. The 100,000 facing blocks lined up behind the corners, while the remainder of the pyramid—over 2 million pieces of stone—consisted principally of fill that required vastly less precision and care. The Egyptians put their effort where it showed, and economized on the hidden rest.

Besides pointing to the use of levers and the course-by-course construction of the Great Pyramid, Herodotus reported that it took 20 years to build the structure. A great many writers have argued that this is far too fast a pace, particularly when the project included the vast ramps thought to be necessary. Peter Hodges again disagrees. He calculated that 125 teams of men working 350 days a year could raise the Great Pyramid in 17 years.

After all stones were lifted and placed, a final step remained—the white limestone facing that once graced the surface of the Great Pyramid and turned it into a shining mountain under the midday sun. Many writers have assumed that the facing stones were cut to a sloping angle on the ground, then raised into place from the bottom to the top to encase the completed pyramid core. There is a better alternative, however, one that Hodges favored. As he saw it, rectangular blocks of white limestone were laid as the outward-facing stones in each course in the rising pyramid. When the topmost course was finished, masons working with hammers and chisels trimmed the white limestone blocks by cutting off the protruding step each block formed and smoothing the surface to the pyramid’s 52° slope. This work began from the top of the pyramid. The masons could stand on the step of the course below as they trimmed one course, then move down yet another course to work on the one that had just served as the platform for their work. Trimming, Hodges calculates, would have taken three years, which adds up to the 20 Herodotus reported.

Circumstantial evidence supports this idea. By Hodges’s calculations, trimming the Great Pyramid would have produced 56,000 tons of stone dust and chips. Archaeologists Michael and Angela Jones found large quantities of chips—including chips of Tura limestone, the very stone used for the casing—at the base of the Great Pyramid during their excavation of the nearby Temple of Isis. And the trimming method fits with Herodotus. “The highest parts of it, therefore, were first finished,” he writes, “and afterward they completed the parts next following, but last of all they finished the parts on the ground, and that were lowest.”