As in the case of the common cubit, two-thirds of the royal cubit were taken for the royal foot = 13·76 inches, a measure which when cubed will be seen to be the source of our Imperial system of weights and measures.
The inconvenience of a cubit of 7 palms is increased when two-thirds of it are taken for the foot; this foot, being 4-2/3 palms or 18-2/3 digits, was possibly divided for popular use into 16 digits, if it were ever in popular use. For scientific and probably for popular use it appears to have been divided into 2 feet = 10·32 inches. This may be inferred from the division of the degrees, attributed to Eratosthenes (third century B.C.), into 700 stadia, each 600 of these feet. Probably 700 is a round number, for, on the basis of this foot, the degree would be 706·8 stadia.
Three centuries later Pliny gave the base of the Great Pyramid a length of 883 feet. The modern measurement being 760 feet = 9120 inches, we have 9120/883 = 10·328 as the length of the foot in Pliny’s account, a length differing by less than 1/100 inch from that of the half-cubit.
The investigations of Fréret, Jomard, Letronne and other mathematicians led them to the conclusion that the ancient Egyptians had surveyed their land so exactly as to know its dimensions to a cubit near, and that certainly at some unknown time they had measured an arc of the meridian and established their measures on the basis of the meridian degree with no less exactness than has been done in modern times.
I have put aside all attempts, often connected with theology, to show that the base of the Great Pyramid was 220 double cubits (of 2 × 20·61 inches), the same number as the yards in an Elizabethan furlong, or that its other dimensions were intended to hand down the English inch, or the gallon, or the squaring of the circle, or the laws of harmonic progression.
3. THE GREAT ASSYRIAN OR PERSIAN CUBIT (_c._ 700 B.C.)
The Egyptian idea of increasing the cubit appears to have also seized the Assyrian monarchy many centuries later. It was increased to 8 palms, as different from those of the Egyptian royal cubit as these were from those of the meridian cubit.
18·24 Egyptian common cubit 6 palms of 3·08 in. 24 digits 20·64 „ royal „ 7 „ of 2·95 in. 28 „ 25·26 Assyrian „ 8 „ of 3·16 in. 32 „