Proceedings of the Society of Biblical Archaeology

May i] PROCEEDINGS. [1894.

wholenumbers,* andon division by ^ starting from 1 or -| ; only
in cases of necessity using the cumbrous systemof reduction to
a greatest commonmeasure.

For* it is only naturalthat"yr" was preferred in the table, but

^ + i was a recognised equivalentof -- in the division of fractions

by that number(seePI. XIX, No. 61, a).

Eisenlohrshowsthatthe Egyptian scribefirst tookthosefractions

of which the denominators weredivisibleby 3, and treatedthem as

multiplesof 1 1 —-I using the formula f=|+ £; then thoseof which

the denominators weredivisibleby 5 (excluding thosealreadydealt
withon the f system, suchas T',), andtreatedthemas multiples of
.}, using the formula \ = \ + TV-
Thensimilarlyhe applied the formulae = + t1 g
TT — a ~ ft e
(Js was treated as a multiple of -j^, not of -J ; jV which, as a multiple
of f, should have yieldedT'T + t^t, wasmore convenientlybroken
up into ,V + 4V , so also Ai a multiple of \, into 7V + ri„, instead
of A + ih\
Thedivisionby the 18 prime numbersafter 11 (excepting 23,!
for which 1 — 1 offered the best solution)was expressed, not in
\a na
2, but in 3 or 4 terms. J
It is worth notingthat howevermanyfractionsthere maybe,
the first is always of higher value than £ of the corresponding
division of 2, or, as Eisenlohr expressesit, " the first fraction is
always selected so that when multiplied by the divisor of 2 it
producesmorethan1, generally i-J, or more thanthat"
To proceed to the text, the first entryis :—

H p TJ " rflh ^ >» T "

nas sen khent khemt ra...? sen

* As when j|nof 95 was required,

380 = 4 x 95

••.Thsof95-*•

+ With regardto this number, see the correction, Commentar,p. 294, l. 2

J Sec Commentar, p 33, for the details.

203