Thanks Hermione

There were so many suggestions on ancient lengths and weights (which we now know were wrong) that it was possible to write a convincing theory in 1872.

I am not convinced that the weight of the ball was an Egyptian mina, or that it was a granite ball, but neither possibility rules out my 6/pi hypothesis.

Unfortunately we don't know the volume of the the stone ball from which we could then calculate its true volumetric diameter, and also the specific gravity from its weight.

It seems remiss that the volume of the ball was not determined because the specific gravity would have aided identification. The stone ball is now referred to as a basalt ball.

The volume of the ball could be determined by measuring the volume of water it displaces.

In practice the volume of water displaced by the stone ball could be determined from the weight of the water displaced having determined the specific gravity of the water at the temperature of the test.

The minimum diameter is 2.65 inches and the maximum is 2.88 inches, so the mean is 2.765 inches. The mean of 2.765 inches is not likely to be the true volumetric diameter, but may be fairly close.

6/pi for the radius corresponds to 12/pi for the diameter:
12/pi digits equates to 3 and 18/22 digits or 3.8181.. digit using decimals ie 3.82 digits.

3.82 digits equates to 2.81 inches, close to the mean, so the hypothesis is tenable.

The sarcophagus has an internal volume corresponding to a sphere with a radius of 35 digits, with the volume of the sphere apparently translated into linear dimensions. As such the designer may have made a block of basalt equal to the volume of a sphere with a radius of 6/pi digits. If this was the case then the volume of the basalt ball would be very close to 190.6 cubic centimetres, perhaps within 2 cubic centimetres.

If the volume of the ball proved to precisely 190.6 cubic centimetres then the true volumetric diameter would be 71.4 millimetres or 3.82 digits, as calculated from the pi approximation of 22/7. The sg would then be the weight of 539.282 grams divided by 190.6 cubic centimetre which is an sg of 2.83 (to 2 decimal places).

If the ball is damaged, as suggested in the article, then there is a question mark over the size of the ball, but perhaps many balls were weighed in the balance in a search for a ball close to a rectilinear basalt standard based on the volume of a sphere with a radius of 6/pi digits.


Mark



Edited 2 time(s). Last edit at 04/12/2018 03:57PM by Mark Heaton.