Kanga Wrote:

> > The seked is calculated from the vertical and
> > horizontal components of the GG and AP, but
> these are difficult to establish, as Legon has shown.
> >
> > Based on Petrie's measures, Legon suggested
> that the heights of the GG and AP are 39c and 33c
> > respectively, but that their runs are not whole
> > cubits. Rather, their sloping lengths are whole
> > numbers of cubits, 88c and 75c respectively.
>
> Thinking more about this, this is not quite right.
> The GG has whole cubit run and rise values, so the
> seked is fairly easy to calculate for a competent
> mathematician.

Upon careful analysis, even this is seen not to be correct. The height of the GG is NOT exactly 39 cubits as Legon asserted.

The height of the GG is given by the difference in elevation between the top and bottom of the GG floor. Now, the bottom of the GG is marked by the joint in the floor where the GG meets the AP, directly below the north wall of the GG. The elevation of this joint is 41c 2½p, and coincides with the top of course 24, whose elevation Petrie gives as 852.7". (I am using a cubit of 20.62".)

However, neither Legon nor Petrie gave the elevation for the top of the GG, the point where the GG meets the Great Step, and this is the point where an anomaly arises. Gantenbrink gives a plausible analysis of the elevation of the ceiling of the horizontal passage as 84 cubits above the base. The height of the passage is 2 cubits, making the floor of the horizontal passage, and the floor of the King's Chamber itself, 82 cubits above the base. This whole cubit value is consistent with Petrie's determination of this floor level as the "half area level" as it gives a sqrt2 value of 140/99.

On p. 75 of Pyrs. and Temples, Petrie states:

"The ramps along the sides, where they join this great step, are very irregular. Their top surfaces slope away downwards toward the side walls; thus the E. ramp top varies from 13.20 to 12.18 below the step from E. to W., and the W. ramp top from 12.82 to 12.2 (?) from W. to E. At present, moreover, the ends of the ramps are parted away from the face of the step by .30 on E. and .44 on W., an amount which has been duly subtracted from my length measures of the gallery. Beside this, the top of the step itself, though, straight, is far from level, the W. side being about 1.0 higher than the E. side. And the sloping floor seems to be also out of level by an equal amount in the opposite direction; since on the half width of the step (i.e., between the ramps) the height of the step face is 34.92 or 35.0 on E., and 35.80 or 35.85 on W."

[www.ronaldbirdsall.com]

34.92" or 35.0" on E. = 11.86 to 11.88 palms; 35.80" or 35.85" on W. = 12.15 to 12.17 p. So, presumably the height of the Great Step is 12 palms (1c 5p), a whole number of palms. This makes the elevation of the top of the GG 82c - 1c 5p = 80 cubits 2 palms. The height of the GG then becomes 80c 2p -41c 2½p = 38c 6½p, making the slope 545:1,106, and from this the seked can be worked out.

(545:1,106 = 26° 13' 57". Compare this with Petrie's calculated slope of 26°16' 40".)

The height of the Ascending Passage is still 33 cubits, but the horizontal remains uncertain.

Hail Atlantis.