Therefore, if we add 1/5 to 20·628 inches,
4·126
———
we have 24·754
as Newton's determination of the length of the Sacred Cubit.
Newton's determinations are therefore—
Length of Sacred Cubit 24·754 inches.
" Cubit of Memphis 20·628 "
The cubit measured by Mersennus (see p. 362, vol. ii. Life at the Pyramids) was 23-1/4 Paris inches, and Mr. Greaves estimated the Paris foot as equal to 1·068 of the English foot; therefore 23·25 + 1·068=24·831 was the length of this cubit, if we take Greaves' proportion of the Paris to the English foot; but by the more exact determination of the proportion of the Paris to the English foot made at the Ordnance Survey Office, Southampton, it is found to be as 1 to 1·06576 and 23·25 + 1·06576=24·780 English inches, which differs only in excess ·026 from the length of the Sacred Cubit determined by Newton.
The double Royal Cubit of Karnak, which is in the British Museum, was found by Sir Henry James to measure 41·398 inches; the length of the single cubit was therefore 20·699 inches, and differs only in excess ·071 inches from the length of the cubit of Memphis, as determined by Newton.
It will be observed that the lengths of the cubits derived by Newton from the length of the King's chamber are shorter than the measured lengths of the cubits which have come down to us. But if
we add 1/5 or = 4·140 to the length of the
Karnak cubit = 20·699,
———
we have 24·839 for the Sacred Cubit.
The one measured by Mersennus = 24·780 and the
———
mean of the two = 24·810, whilst the
length derived by Newton was = 24·754, showing
———
a difference of only ·056 between the
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length of the Sacred Cubit derived from the actual lengths of the two cubits which have come down to us, and the length of the Sacred Cubit derived by Newton from the length of the King's chamber.
The method adopted by Professor P. Smyth, to find the length of the Sacred Cubit, in p. 458, vol. ii. Life at the Pyramids, is also wrong in principle. He has no right to take the means between the limits of approach, or to say that the Sacred Cubit was, according to Sir Isaac Newton, 25·07 inches, when, as I have shown in his own words, Sir Isaac says it was 24·754 inches.