Precession had an effect on the orientation of the pyramids, which were aligned with remarkable accuracy. The eastern and western sides of the "Great" Pyramid (the pyramid of Khufu) run almost exactly due north and south: in fact, they point only 330 and 150 seconds west of north. (330 seconds is less than one-tenth of a degree.) The other two sides are even more accurate: they point 148 and 117 seconds south of west. The errors here are all clockwise. We have the following table for the errors in orientation of third- and fourth~dynasty pyramids. (A negative error is counterclockwise.) The dates listed are the beginnings of the reigns of the pharaohs to whom the pyramids are attributed.
Pyramid at Maidum 0.5o 2637 B.C. "Bent" pyramid at Dahshur 0.2o 2613 B.C. Pyramid of Khufu at Giza <0.1o 2589 B.C. Pyramid of Khafre at Giza 0.1o 2558 B.C Pyramid of Menkaure at Giza -0.2o 2530 B.C.Clearly the orientation is turning steadily counterclockwise as the years pass, though Khafre's pyramid does not quite fit the pattern. Is this a coincidence, or is there a reason for it?
Let us consider how the Egyptians could have oriented the pyramids. They must have started by finding north or south-east and west are simply the directions midway between them and cannot be found directly. To find north or south accurately we must use the stars; the sun is too big and too bright to yield an accurate result. I describe one way in which north can be found on page 26. Another way would be to bisect the angle between the directions in which a star rises and sets, taking care that the horizon heights are the same at the two points, perhaps by building an accurately leveled wall some distance north of the observer and using this as a horizon. All these methods are long and complicated, but once north has been found at some place, all four directions are known. Having found east and west we can wait until we see a star that rises due east or sets due west. Now if we want to find the cardinal directions at some other place we need not go through the long process of finding north again; we simply watch for our star. If the Egyptians used this method to orient the pyramids, this means that for each pyramid they established the east-west alignment first and obtained the north-south alignment from it. This agrees with the fact that the east-west directions in Khufu's pyramid are more accurate than the north-south directions. More important - as the years pass, precession will cause the direction in which our star rises or sets to change, and so the orientation will change, as shown in the table. In fact, there is a star, namely beta Scorpii, whose rising~directions at the various dates agree precisely with the orientation of all the pyramids listed above, except Khafre's; this pyramid is aligned on the direction in which beta Scorpii sets [110].
Revised 13 April 1996.