i68 Science
simplified his work. He knew that f+jfe made 11 unit-fractions
each ^, and that 4 more were required to complete the whole,
yet he made no attempt to evolve any notation to express the
11 unit-fractions as }J. To him, it was a collection of 11 unit-
fractions. The first examples of mixed fractions are not found
until Demotic times. Thus: cmy \ ^ part, which makes 2 parts
of 5 of the houses', which is merely another way of writing f.
The limitations of this notation made necessary the use of
special tables. For measuring out grain, a unit (bekaf), approxi-
mately a bushel, was in use. This was divided into fractional
parts |, |, |, jjj, ^ and ^ each with its own name, and at some
64 if
FIG. i.
stage identified with a part of the picture of the magic eye of
Horus, which (according to the ancient myth) was torn in
pieces by the wicked Set. Fractions below ^ were expressed
in terms of the TO (^ part of the bekat). The Egyptian never
used any other fractional parts, but if in the course of his work
he wished to express a fraction such as ) he immediately reduced
it to a series of dimidiated parts, as above. In the same way
to-day, we should not write ^ ton, but express it in cwt., qrs,
and Ib.
A table was then drawn up, expressing the various fractions
of the htkat in terms of the recognized units. Two examples
from such a table may be given:
4 tfkat = ik+s? and 4^ ro
& hekat = and