The pace was also divided into quarters (palmipes) of a foot and a palm.
The foot was divided into 16 digits or into 12 inches (pollices). Roman dominion over Greece and Egypt led to some modifications, probably local, in measures of distance. There was a Roman schœnus of 4 miles, and the mile was divided, sometimes into 10 Olympic stadia, sometimes into 8 Pythic stadia of 500 feet or 100 paces.
It will be seen that the English mile was originally 5000 Roman feet, and then 5000 English feet, before being fixed at its present length of 5280 feet or 1760 yards.
2. The Egyptian Royal Cubit (c. 4000 B.C.)
The possession of a geodesic cubit, 1/4 of the fathom which was 1/1000 of the meridian mile, did not satisfy the astrolatric priesthood of Egypt. Under their influence another cubit, of 7 palms = 20·64 inches, became the official measure of Egypt, and it was used in the planning of the monuments, always excepting the outside plan of the Great Pyramid.
What could have been the reason for this change, from the scientifically excellent and fairly convenient common cubit to this less convenient length, and for bringing the inconvenient number seven into the divisions and making both palms and digits different in length from those of the common cubit?
No valid reason can be found other than the desire to institute, by the side of the common cubit in which the 6 palms and 24 digits corresponded to the watches and hours of the day, a sacred cubit in which the 7 palms would correspond to the seven planets or to the week of seven days, and the 28 digits to the vulgar lunar month of four weeks of seven days.[[2]] Among us, at the present day, astrology is far from being dead; the days still bear the names of the seven planets ruling successively the first hour of the days named respectively after them; we call, however unconsciously, men’s temperaments or characters according to the mercurial, jovial, saturnine and other influences of the planets which rule the hour of birth. It is not for us then to criticise severely the pious desire of a learned priesthood or of a theocratic king to institute a sacred standard of linear measure with divisions corresponding in number to the seven planets which ruled the destinies of man, whose influence ruled them through the Christian middle ages, which at the present day still rule the world in the minds of the great majority of mankind. The royal or sacred cubit became the official cubit of the Eastern great kingdoms, the common or meridian cubit being also used, not only for ordinary purposes, but sometimes along with it. Thus, the external dimensions of the Great Pyramid are in common cubits, while the unit of its internal dimensions is the royal cubit, perhaps recently established at the time of the building.[[3]] And centuries after the institution of the royal cubit, the meridian cubit became the standard of the Greeks.
The question naturally arises—Why was the royal cubit not formed by simply adding a seventh palm to the common cubit, a palm of the same length, = 3·04 inches, as the six others? This would have given a new cubit of 18·24 × 7/6 = 21·28 inches, instead of 20·64 inches in 7 palms of 2·95 inches. And it will be seen that this was actually done, fifty centuries later, by the caliph Al-Mamūn.
The answer I venture to give is, that the royal cubit was intended to be, not only by its division a homage to the seven planets, but also, by its increase of length, a symbol of the proportion of latitude to longitude at some Egyptian observatory.
Possibly it was a practical commemoration of the art of determining longitude. On this hypothesis the new cubit was made as much longer than the old cubit as the mean degree of latitude is longer than the degree of longitude in 29° N., at an observatory about 50 meridian miles south of the Pyramids. In that parallel, the proportion of the degree of longitude to the degree of latitude is 1 : 1·13, or as 18·24 to 20·64.