Page:The Rhind Mathematical Papyrus, Volume I.pdf/48

 only in hieratic). The sign which represents a container of grain on its side, and forms a part of many words for different kinds of grain (see page 47) was also used in these expressions. When the amount was equal to or more than 100 hekat, this sign was written with the number of hundreds before it, and the signs for any smaller number of hekat next after it. Also 50 hekat and 25 hekat were put down as $1/undefined$ and $1/undefined$. The number of whole hekat was followed by “Horus eye” fractions and by ro and fractions of a ro. In the case of 2, 3, or 4 ro the sign for the word ro was written under the number, while this sign without a number stood for 1 ro, and the fractions of a ro came after the sign.

Furthermore the Egyptians had not only the system of a simple hekat and its parts and multiples, but also systems of a double hekat and a quadruple hekat with their parts and multiples, each part or multiple of a double hekat being twice the corresponding part or multiple of a simple hekat, and each part or multiple of a quadruple hekat four times the corresponding part or multiple of a simple hekat; and they had the peculiar way of writing an expression for a large quantity of grain in the double and quadruple systems that they used for simple hekat. The double hekat was indicated by doubling the vertical sign in the word for hekat and the quadruple hekat by introducing an additional grain sign with four grains over it, but when these signs are not given we cannot always be sure that the system indicated is the simple system. The quadruple hekat seems to have been called sometimes “a great hekat” (Griffith, volume 14, page 432), or “a great quadruple hekat” (Problem 68 ).

We get information as to the size of these various measures, and, in particular, of the hekat, from Problems 41-46, where the capacities of certain granaries are computed from their dimensions. Here the unit of length is the cubit (meh), supposed to be the royal cubit, equal to 20.62 inches. The author states that $2/3$ of a cubed cubit is the khar, and then