Page:The Rhind Mathematical Papyrus, Volume I.pdf/47

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EGYPTIAN MEASURES^[1]

Measures of Capacity

The unit of volume or capacity, used especially in measuring grain, was the hekat, which can be determined as 292.24 cubic inches, or a little more than half a peck.^[2] This was divided into 320 parts called ro, but the Egyptians also used as fractions of a hekat the fractions whose denominators are powers of 2 down to ¹⁄₆₄, ¹⁄₆₄ of a hekat being 5 ro. This series of fractions was peculiarly adapted to multiplication by doubling or halving. They were written in a special notation and have been called “Horus eye” fractions (see Bibliography under Möller, 1911).^[3]

Besides using the “Horus eye” notation for parts of a hekat, the Egyptians had special hieratic signs for the numbers from 5 to 10 when used to express hekat. These signs seem to be ligatures of dots,^[4] the sign for 10 being a long vertical stroke, representing perhaps ten dots one above another. The Egyptians had also a peculiar way of writing an expression for a large quantity of grain (but, so far as I know,

↑ This discussion is conﬁned entirely to the subject as it is presented in the Rhind papyrus. A very elaborate study of Egyptian weights and measures was made by Griffith in 1892 (see Bibliography) and I have taken some statements from his article and checked many others by it, but for the most part my account is based on a study of the papyrus itself.
↑ See page 32. For some reason Peet calls the hekat a bushel, although he says that a hinu (¹⁄₁₀ of a hekat) was about 29.2 cubic inches (page 25). It is possible that he gets this word from Sethe, who uses the word Scheffel several times for hekat (1916, pages 74 and 80). Eisenlohr also uses the word Scheffel, but uses it for 10 hekat. Gunn calls the hekat a gallon (page 126), but the gallon is a liquid measure, at least in America, and for the same amount in dry measure it is better to say “half a peck,” unless we use the word hekat itself. A note by G. P. G. Sobhy in The Journal of Egyptian Archaeology, volume 10, pages 283-284, gives the hinu in litres as determined by several vases which are inscribed with their values, but there is a considerable variation in the results from these different vases, the value of a hinu varying from .4028 to .544, making the value of a hekat vary from 4.028 to 5.44 litres. As the litre is 61.023 cubic inches, 292.24 cubic inches would be 4.789 litres.
↑ In the Rhind papyrus when some calculation gives a portion of a hekat expressed in ordinary fractions, these are reduced first to ro, and then to the “Horus eye” fractions. See Problems 35, 37, 38, 69, and 70. In 69 and 70, “Horus eye” fractions are changed to ordinary form before multiplication, as if for purposes of multiplication the author thought of them as mere numbers. Generally the multiplications are carried through with the “Horus eye” forms.
↑ In hieroglyphic these dots may have been written as little circles (see Möller, 1909, volume 1, page 66).

[1] This discussion is conﬁned entirely to the subject as it is presented in the Rhind papyrus. A very elaborate study of Egyptian weights and measures was made by Griffith in 1892 (see Bibliography) and I have taken some statements from his article and checked many others by it, but for the most part my account is based on a study of the papyrus itself.

[2] See page 32. For some reason Peet calls the hekat a bushel, although he says that a hinu (¹⁄₁₀ of a hekat) was about 29.2 cubic inches (page 25). It is possible that he gets this word from Sethe, who uses the word Scheffel several times for hekat (1916, pages 74 and 80). Eisenlohr also uses the word Scheffel, but uses it for 10 hekat. Gunn calls the hekat a gallon (page 126), but the gallon is a liquid measure, at least in America, and for the same amount in dry measure it is better to say “half a peck,” unless we use the word hekat itself. A note by G. P. G. Sobhy in The Journal of Egyptian Archaeology, volume 10, pages 283-284, gives the hinu in litres as determined by several vases which are inscribed with their values, but there is a considerable variation in the results from these different vases, the value of a hinu varying from .4028 to .544, making the value of a hekat vary from 4.028 to 5.44 litres. As the litre is 61.023 cubic inches, 292.24 cubic inches would be 4.789 litres.

[3] In the Rhind papyrus when some calculation gives a portion of a hekat expressed in ordinary fractions, these are reduced first to ro, and then to the “Horus eye” fractions. See Problems 35, 37, 38, 69, and 70. In 69 and 70, “Horus eye” fractions are changed to ordinary form before multiplication, as if for purposes of multiplication the author thought of them as mere numbers. Generally the multiplications are carried through with the “Horus eye” forms.

[4] In hieroglyphic these dots may have been written as little circles (see Möller, 1909, volume 1, page 66).

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