A difference of 0.1 inches is the difference between a good surveyor and an excellent surveyor.

Measurements in inches below.

Ratios are multiplied by 1000 to aid comparison:

Model: area equal to a circle with a diameter of 2.5 cubits as calculated from 22/7

D1/D2 = Internal length / Internal width (irregular dimensions governed by the diagonal D9 of 4 cubits)

D1/D2 = (105 + 15/16 digits) / (36 + 1/3 digits), 77.93 inches / 26.73 inches (Smyth), 78.06 inches / 26.81 inches (Petrie)

D1/D2 x 1,000 = 2,915.7 (22/7 model), 2,915.5 (Smyth), 2,911.6 (Petrie)

Smyth closer than Petrie for the 22/7 model

D1/D2 x 1,000 = 2,886 (8/9 model), 2,916 (Smyth), 2,912 (Petrie)

The idea of the 8/9 RMP model is tenable but much more likely to have been 22/7 or another close approximation to pi.

Petrie closer than Smyth for the 8/9 model

Model: Volume of sphere with a diameter if 2.5 cubits

volume = 4/3 x radius of 1.25 cubits x area of circle with a diameter of 2.5 cubits

internal depth = 4/3 x 1.25 =1.666... cubits

intended diagonal 4 cubits

D9/D3 = Internal diagonal / Internal depth

D9/D3 = 4 cubits /(1 + 2/3 cubits) = 2.4 (exactly)

D9/D3 = 112 digits / (46 + 2/3 digits), 82.39 inches / 34.34 inches (Smyth), 82.54 inches / 34.42 inches (Petrie)

D9/D3 x 1,000 = 2,400 (model), 2399.2 (Smyth), 2,397.9 (Petrie)

(Values for D9 calculated from measurements of D1 and D2 as perfect rectangle)

Smyth closer than Petrie.

Model of external volume double internal volume:

Unfortunately Petrie did not report the dimensions framed by the edges of the sarcophagus.

(Petrie determined the mean external dimensions which were irregular dimensions taking into account irregular concavities.)

Smyth reported the dimensions framed by the edges of the sarcophagus.

D5/D7 = External length / External height

D5/D7 = (122 + 1/7 digits) / 56 digits, 90.01 inches / 41.27 inches (Smyth)

D5/D7 x 1000 = 2181.1 (model), 2181.0 (Smyth)

D7/D6 = External height / External width

D7/D6 = 56 digits / (52 + 6/11 digits), 41.27 inches / 38.72 inches (Smyth)

D7/D6 x 1000 = 1065.7 (model), 1065.9 (Smyth)

D5/D6 = External length / External width

D5/D6 = (122 + 1/7 digits) / (52 + 6/11 digits), 90.01 inches / 38.72 inches (Smyth)

D5/D6 x 1000 = 2324.5 (model), 2324.6 (Smyth)

The ratios bear out the proposed model, most precisely so.

Smyth calibrated all his measuring rods against the standard British Yard presented to Scotland.

The standard British Yard had been checked against two platinum standards of the French metre.

There has been no significant change in the length of either the French metre or the British Yard so Smyth's measurements can be converted as 25.4 millimetres to an inch.

It was much easier to make exterior than interior.

Estimates of length of cubit from Smyth's measuremements:

D5 equivalent to a cubit of 20.635 inches

D6 equivalent to a cubit of 20.635 inches

D7 equivalent to a cubit of 20.635 inches (D7 is 2 cubits)

Three dimensions and three estimates of length of cubit precisely the same.

The sarcophagus was made with extraordinary precision. Dimensions are consistent to far better than 0.1 inches in the proposed model.

Unfortunately Smyth and Petrie didn't know how to judge their measurements using ratios.

Smyth had been handling high precision measuring equipment as a professional astronomer for nearly 30 years when he surveyed the sarcophagus.

Egyptologists have accepted Petrie's judgement on the sarcophagus as poorly made.

Mark

Edited 7 time(s). Last edit at 12/10/2019 03:43PM by Mark Heaton.