Hi Robin,

My recollection of Smyth's survey around the plug block was that he thought he may not have accomplished it very accurately, so I compared to Petrie's determination.

From memory Petrie's determination was precisely the same as Smyth's determination accurate to a small fraction of an inch.

It should be remembered that Petrie wanted a rigorous set of measurements connecting the exterior to the interior, and did not rely on any of Smyth's measurements.

Petrie drew attention to supposed errors in Smyth's measurements regarding the length of the ascending passage, but Petrie measured in a different way. I think I was able to understand both surveys and found a very close reconciliation.

Theorists have taken Petrie's determination of the length of the Ascending Passage as 75 cubits, which, in my opinion, is nonsense. This is the length of the projection onto the floor of the Descending Passage.

In my opinion the intended level at the top of the Great Step on the axis was 82 cubits or 2296 digits, with the top of the step actually having a deliberate slope equal to the cotangent of 112 with the width of the gallery equal to 112 digits.

The bottom of the Great Step on the axis is 48 digits lower at 2248 digits.

The length of the gallery's floor is 88 cubits with vertical difference of 39 cubits, so the level at the foot of the gallery is 1156 digits.

Petrie measured the Ascending Passage and the Grand Gallery as one, and his level at the foot of the gallery is actually above the floor. I plotted all of Petrie's offsets. In round figures Petrie measured offsets from an angle of 26 degrees 16 minutes, but the angle is actually about 26 degrees 21 minutes based on Petrie's offsets.

From Smyth's measurements the rise of the Grand Gallery is 1092.13 digits or 39.00 cubits for a cubit of 20.61 inches. Petrie's measurements correspond to a rise of 1091.97 digits or 39.00 cubits for a cubit of 20.61 inches, but actually approximately 39.1 cubits because his starting point was about 2 inches above the floor

In my opinion the length of the Ascending Passage was close to 2097 digits including the projection onto the floor of the descending passage (72 cubits plus an irregular 80.78 digits taking the perpendicular height of the entrance passage as 64.1 digits.

The slope of the Ascending Passage is the tangent of 176/360 bearing out the length of 360/5 cubits, so the level at the intersection of the projection is precisely 235 digits.

There is an error in Petrie's table of measurements on levels, as apparent from reading the text. I went to UCL to read an original edition of Petrie (1883) in 2003, and there was certainly an error.
It is not 179.9 inches, but 172.9 inches which passes a simple geometric test, so 234.9 digits, close to my model of 235 digits.

I calculated that the length from the true intersection point to the face of the pyramid as 1512 digits assuming the face of the Great Step is in the plane of the east-west axis.

On this basis the intended level at the entrance as a projection of the entrance passage is 908.75 digits which corresponds to 25.5 cubits (714 digits) from the north edge of the base square.

Petrie determined the height at the entrance as 668.2 inches so 907.8 inches, but I think this may have a slight error as Petrie's base-line may not have been exactly the same as the original base line.

I think we can rely on Petrie's survey. Smyth did not make a connection to the exterior of the pyramid, but we can use Smyth's measurements by finding a rigorous connection to Petrie's station marks.

The differences between Smyth and Petrie are extremely small.

Curiously, the length of the entrance passage is close to 100 x 56.25 digits, the width is close to 56.25 digits, and the slope of the upper section of the entrance passage is very close to the seked of (56.25)/4 palms which is 56.25 in digits.

Mark



Edited 2 time(s). Last edit at 10/16/2020 12:36PM by Mark Heaton.