Pyramid Quest (33 page)

The length of a royal cubit, or simply a cubit, is variously given as about 523 to 526 millimeters (very nearly 524 mm, according to K. P. Johnson, 1998, 1999, and Flinders Petrie, cited in Stecchini, 1971, p. 315); “in the neighborhood of 52.3 cm” (according to Herz-Fischler, 2000, p. 12); 52.5 centimeters (according to Herz-Fischler, 2000, p. 176); 523.55 millimeters (according to Borchardt, as cited in Herz-Fischler, 2000, p. 192, n. 10). Petrie (1883, p. 181) says, “On the whole we may take 20.626 ± .01 [inches, or 523.748 mm] as the original value [of the cubit].” Kingsland (1932, p. 113) adopts “for the most part” 20.612 British inches [523.5448 mm] as the value of the “Egyptian cubit.” Stecchini (1971, p. 320), however, based on studying the monuments and various ancient measuring rods, concludes that there were actually three values for the cubit (royal cubit) in use in ancient Egypt, measuring, respectively, 524.1483 millimeters, 525.0000 millimeters, and 526.3231 millimeters. According to Stecchini, the first value is the standard for the dimensions of the Great Pyramid, while the third value is the standard for the dimensions of the coffer in the Great Pyramid. The second value was the standard used for the dimensions of the Second (Khafre) Giza Pyramid (Stecchini, 1971, p. 320).

Using Stecchini’s value of 524.1483 millimeters for the cubit, a 440-cubit base is equal to 230.625 meters, and a 280-cubit height is equal to 146.762 meters. Using Kingsland’s value of 523.5448 millimeters for the cubit, a 440-cubit base is equal to 230.3597 meters, and a 280-cubit height is equal to 146.5925 meters.

The Cole Survey (1925) is the most recent and most definitive survey of the Great Pyramid. Based on this survey, the lengths of the four sides of the Great Pyramid, along with the corner-to-corner lengths, are as follows.

The foregoing values are the actual lengths of the base sides, as measured by the Cole Survey, upon the socle (base or platform upon which the casing stones sit).

Pochan (1978, p. 10) cites the following values and attributions for the height of the platform at the top of the Great Pyramid above the base: 139.40 meters (Petrie), 139.117 meters (Jean Marie Joseph Coutelle, a member of Napoleon’s expedition to Egypt; Tompkins, 1971, p. 44), and 138.30 meters (Edmé-François Jomard, another member of Napoleon’s expedition; Tompkins, 1971, p. 44) and the length of a side of the platform as 11.7 meters (Petrie) or 9.96 meters (Coutelle) (note that all four sides are not necessarily the same length). As late as the early seventeenth century, the sides of the platform may have been only about 5 meters long (Pochan, 1978, p. 6), indicating that some of the top of the structure has been lost since then.

The Great Pyramid currently contains 203 courses of blocks. It is generally believed that it originally had 7 or 8 more courses, for a total of 210 or 211; presumably this is based on the concept that it came to a full point rather than ending in a platform. Some authors, such as Pochan (1978, p. 1) suggest that the pyramid originally was comprised of 210 courses, since 210 is a product of the first four prime numbers, namely 2 × 3 × 5 × 7. Today the Great Pyramid ends in a rough platform, approximately 25 to 30 feet on the side (Bonwick, 1877, p. 19), composed of limestone blocks (as used to build the rest if the pyramid’s core), the tops of which are coarse and uneven. In 1874 the astronomers Sir David Gill and Professor Watson erected a steel mast on the top of the summit (DeSalvo, 2003, p. 10). Most researchers believe that the Great Pyramid came to a point at its summit and was capped with a pyramidion; some, however, disagree and contend: “It is certain that the Great Pyramid never ended in a point and was never capped with a pyramidion” (Pochan, 1978, p. 6; see also similar comments cited by Bonwick, 1877, p. 19). Pochan (1978, p. 245) cites Diodorus Siculus as saying that the Great Pyramid was intact in his day (first century B.C.) but ended in a platform 6 cubits (about 3 meters) long. The top platform of the Great Pyramid is today noticeably non-square (see aerial photo in DeSalvo, 2003, p. 10). It forms a distinct rectangle, and some researchers have suggested that perhaps it never held a pyramidion because a square-based pyramidion would not fit properly. Of course, it seems that a rectangular-based pyramidion could have been manufactured to specification so as to fit the platform.

The angle of inclination of the original sides, covered with their casing stones, of the Great Pyramid is a matter of uncertainty. Petrie (1885, p. 12) gives values that he measured on the few remaining in-place casing stones on the north face, as well as fragments found around the north face; he also gives one value for a casing stone on the south face. For the north face, Petrie’s measurements range from 51° 44’ 11” ± 23” (51.736° when converted to decimal form) to 51° 53’ 20” ± 1’ (51.889°), and for the south face he gives a value of 51° 57’ 30” ± 20” (51.958°). As the north face mean, Petrie gives the value 51° 50’ 40” ± 1’ 5” (51.844°). Petrie (1885, p. 13) concludes: “On the whole, we probably cannot do better than take 51° 52’ ± 02’ [51.866°] as the nearest approximation to the mean angle of the Pyramid, allowing some weight to the South side.” Assuming that the Great Pyramid originally came to a point at the top, Petrie (1885, p. 13) continues: “The mean base being 9068.8 ± .5 inches [230.3475 meters] this yields a height of 5776.0 ± 7.0 inches [146.7104 meters].”

Herz-Fischler (2000, p. 11) adopts the following values for his analyses and calculations: length of side: 230.4 meters; angle of inclination of the sides: 51.844°. From these, assuming that the pyramid came to a point, he calculates an original height of 146.6 meters. On the basis of these measurements, Herz-Fischler (2000, pp. 26-27) gives the following values for various relevant features of the Great Pyramid: the length of the diagonal line that connects two opposite corners of the base, 325.8 meters; the apothem, a line that connects the summit, vertex, or top point of the pyramid to a point at the base in the middle of one of the triangular faces, 186.5 meters; the arris, the line connecting the vertex or top of the pyramid to a corner, 219.2 meters; the angle of inclination of the arris relative to the level of the horizontal, 42.0°; the angle between an arris and a base line of the pyramid, 58.3°; the angle between adjacent faces, known as the dihedral angle, 112.4°; the area of each face, 21,481 square meters; the total surface area of the four faces plus the base, 139,008 square meters; and the volume of the Great Pyramid is 2,594,482 cubic meters. To this we can add that the area of the four sides, which would have originally been covered with the casing stones, is 85,924 square meters, and the area covered by the base of the Great Pyramid is 53,084 square meters.

There are four corner sockets carved into the bedrock, one at each corner of the Great Pyramid (see Petrie, 1885; Cole, 1925; Davidson and Aldersmith, 1924; and especially Kingsland, 1932, pp. 15-19, where the sockets are photographically illustrated—they are currently not as easily defined in the bedrock as in Kingsland’s time). At times, these sockets have been misinterpreted as defining the original four corners of the Great Pyramid, but this was not the case. The sockets are located at varying distances from both the true corners of the Great Pyramid and the edge of the base or platform underlying the casing stones of the Great Pyramid. Thus, the northern border of the northeast socket is about 85 centimeters north of the northeast corner of the Great Pyramid, whereas the northern border of the northwest socket is about 75 centimeters north of the northwest corner, according to the Cole Survey (1925). The depth of the sockets below the average level of the platform (base) of the Great Pyramid varies from 56.84 centimeters in the southwest socket to 104.69 centimeters in the southeast socket (Kingsland, 1932, p. 15). There is no certainty as to the purpose of the corner sockets, but one suggestion is that they were used to establish the original diagonals of the Great Pyramid (Kingsland, 1932, p. 16). Petrie (1885, plate 7) suggested that at the corners of the pyramid the corner casing stones did not sit on the platform or base as elsewhere but rather extended down to the bedrock and “locked” into the sockets, and the pavement here would then abut up against the sides of the corner casing stones. This is a hypothetical suggestion, however; other researchers have challenged it. Kingsland (1932, p. 18) writes: “If the angle [of the casing stone] were carried down right to the bottom of the Socket Hole it would not, even then—according to Sir Flinders Petrie’s measurements—reach the outer edge of the Socket.”

The body of the Great Pyramid as measured above, at least as far as can be observed around the four sides as preserved today, sits on a platform (base or socle, referred to as a “pavement” in Cole, 1925) composed of fine white limestone similar or identical to that used in the casing stones. The distance from the bottom edge of the casing stones to the edge of the platform averages about 40 centimeters, but varies, “being 38 centimetres on the western side, 42 centimetres on the northern side, and 48 centimetres on the eastern side, at the places where it could be measured” (Cole, 1925, p. 1; see also Kingsland, 1932, p. 20). Not enough remained on the southern side to measure. Cole (1925, p. 5) reports that “the pavement is practically flat, but has a very slight slope of about 15 millimetres up from the N.W. corner to the S.E. corner.” According to the calculations of Kingsland (1932, p. 19), the highest point of the platform is 2.15 centimeters above the lowest point, and this is over an area of 13 acres. The top surface of the platform (pavement) is about 60.4 meters above mean sea level, as measured at Alexandria (Cole, 1925).

The thickness of this platform is 55 centimeters or 21.6 inches, according to Fix (1978, p. 247) or 21½ inches, according to Kingsland (1932, p. 19). According to Pochan (1978, p. 12), the thickness of the platform (which Pochan refers to as the “socle”) is “0.525 m. (exactly 1 cubit).” Generally, when people talk about the height of the Great Pyramid, they are referring to the height above the base, or platform; in some cases, however, the height of the platform may be included, and thus they are referring to the height of the Great Pyramid above the bedrock. Herz-Fischler (2000), for instance, never takes the thickness of the platform into account in his various calculations and evaluations of theories related to the dimensions of the Great Pyramid.

The core masonry of the Great Pyramid is slightly indented, hollowed, or concave on each of the four major sides. This means that, in terms of the core masonry as exposed today, the Great Pyramid can be considered to actually have eight sides instead of four, in that each of the four major sides is divided in half. This hollowing or concavity is very subtle, however, and is rarely seen either in person or on photographs. If the conditions of light are just right, it can be seen quite dramatically, especially from the air, as is captured in an often-reproduced photograph first published by Groves and McCrindle (1926; for republications of the original, see for instance, Davidson, 1934; Haberman, 1935; Lepre, 1990; Pochan, 1978; Temple, 2000; Tompkins, 1971). It appears on all four faces. Petrie measured this hollowing during his survey of the Great Pyramid in 1880-1882 (originally published in Petrie, 1883, and quoted in Pochan, 1978, p. 114; see also Davidson and Aldersmith, 1924) and estimated that the hollowing consisted of a “concavity” or “indentation” in the amount of approximately 37 inches (0.94 meters) from a perfectly straight line along the base of the north side (Pochan, 1978, p. 114); Pochan (1978, p. 234) gives the value of 0.92 meters for the hollowing, meaning that the two planes of each “face” of the Great Pyramid meet at an angle of about 27’ (about 0.45°) different from a perfectly flat plane. Petrie (1883) and (Kingsland, 1932, p. 26) believed that only the core of the pyramid had the hollowing effect, and the facing blocks were thicker in the middle of each of the four main sides and thinned toward the edges such that the final four faces of the pyramid were perfectly flat. Pochan (1978, pp. 132-133) and Davidson and Aldersmith (1924), in contrast, believe that the hollowing effect was present in the facing itself. This hollowing-in of the sides of the Great Pyramid alters the length of the perimeter of the structure, and the amount by which it is altered was referred to as the “displacement factor” by Davidson (Davidson and Aldersmith, 1924, n.d., p. 124; Kingsland, 1932, pp. 26, 57-58). Davidson utilized his so-called displacement factor in interpreting the Great Pyramid as encoding all sorts of scientific data, from the exact length of the year and the precessional cycle to the dimensions and shape of the earth’s orbit (see Davidson and Aldersmith, n.d., pp. 124-137). For Davison, the displacement factor was also important in his prophetic interpretations of the Great Pyramid: “The Great Pyramid’s Displacement Factor, 286, is the Key Number to the understanding of the Great Pyramid’s Prophecy” (Davidson, [1931?], p. 1).

On the basis of an interpretation that the hollowing of the sides of the Great Pyramid was reflected in the final casing limestone, in September 1935 Pochan (see Pochan, 1978, pp. 230-233) introduced the concept that has seen become known as the “flash” phenomenon or effect. On the equinoctial day, at sunrise the sun’s rays would be so aligned that they would illuminate the western side of the southern (or northern; it should work on both façades) façade of the Great Pyramid, while the eastern side would remain in shadow. This effect, Pochan believed, would be visible for four or five minutes in the morning, until the eastern side was also illuminated such that the entire façade would be in light. At sunset, the phenomenon would be reversed, the western side first going into shadow while the eastern remained illuminated for some minutes still as the sun continued to set. According to Pochan (1978, p. 232),