Thanks for link for all to see Smyth's survey so all can check the incredible precision of the external dimensions as framed by the edges of the sarcophagus.

Also, you would be right to be careful not to go for the 22/7 ratio rather than the 8/9 ratio because a particular feature of the sarcophagus is elegant using the 8/9 ratio. I think the designer was rather like an engineer, comfortable with approximations, so would not necessarily exclude the 8/9 ratio just because it does not give a perfect answer when applied to a circle with a diameter of 280 cubits compared to the area using 22/7, but I have not actually proved the 22/7 ratio was used to calculate the area of a circle, as you well know.

I also agree that the nature of the concavities does not give the impression of a scientific model, but the designer may have had a technique to determine the precise volume such as the level of sand required to fill the concavities, checked and rechecked during the grinding out process in a horizontal orientation.

It is a simple matter matter to double the volume of the interior on the assumption that the external height was 2 cubits and that the base was 1/6 times the external height because the external area must then be exactly 5/3 times the internal area as defined by the edges.
As ratios:
5 x 1 for external = 2 x (3 x 5/6) for double internal

Petrie did not determine the length and breadth defined by the edges only the mean planes after taking into account the concavities.

The external length framed by the edges has a theoretical length of 89.99 inches if the volume is doubled. Smyth determined at 90.01 inches so a difference of just 0.02 inches, as calculated for a cubit of 20.63 inches.

The external width has a theoretical breadth of 38.71 inches if the volume is doubled. Smyth determined the external width as 38.72 inches so a difference of 0.01 inches.

The external height has a theoretical height of 41.26 inches as 2 cubits of 20.63 inches. Smyth determined as 41.72 inches so a difference of 0.01 inches.

Few can measure, mark and cut to to a hundredth of inch having seen an engineer's ruler with such tiny divisions.

The sarcophagus was made very precisely indeed if this was the model. Any mistake could not be polished out as this would have resulted in a difference from the intended dimensions, so the saw error of 0.1 inches had to remain.

The theoretical thickness of the sides is 8.10 digits or 5.97 inches. Smyth got a mean of 5.99 inches.

Khufu's sarcophagus may have been the first granite sarcophagus, but the walls of the King's Chamber prove that the masons could achieve flat surfaces, as do the internal surfaces of the sarcophagus itself, so the concavities of the external surfaces were certainly intended especially as it would have been possible to finish off as flat planes if that was the specification.

The volume of a sphere with a diameter of 22/7 cubits converts to 2339.6 litres for a cubit of 524 millimetres (20.63 inches) as calculated using the Pi approximation 22/7.

Petrie determined the true external volume as 2335.7 litres from mean planes and 2336.6 litres using calipers, so a mean of 2336.15 litres

Smyth determined the true volume as 2344.9 litres by just using the figures he highlighted in bold.

The mean of Smyth and Petrie is 2340.5 litres which is within a litre of the proposed model.

The exterior certainly has two hypothetical models of volume which are well supported by the measurements.

The required reduction in volume between the two models is 15.5 litres so not just an egg cup full.

Smyth's determinations were approximations, but his measurements correspond to a reduction of 12.3 litres.

Don't forget Smyth had been a professor of astronomy for about 20 years when he measured the sarcophagus, and his survey was probably the most precise determination of an archaeological object that had ever been undertaken, as at 1865.

The theoretical external length, taking into account the concavities, is 89.81 inches for a cubit of 20.63 inches. Smyth determined as 89.71 inches and Petrie determined as 89.62 inches, so all measurements support the models very precisely indeed.

Mark



Edited 2 time(s). Last edit at 11/09/2019 05:35PM by Mark Heaton.