14xi50
-2-
T e r n a r y s e r i e s :
_ = 1/3 ···················· .3333 ···················· 9
_ = 1/6 ···················· .1667 ···················· 8
_ = 1/12···················· .0833 ···················· 8
_ = 1/24···················· .0417 ···················· 6
_ = 1/48···················· .0208 ···················· 1
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The binary series is the main system, the ternary apparently being
used in conjunction with the binary to give a quicker approximation where
a reasonable standard of accuracy is required.
The lowest 4 or 5 values generally appear to be used only to show
small excesses over zero or whole numbers, and are not combined with
other terms to express larger fractions.
The work of adding together quantities involving multiple fractions,
especially when they include both binary and ternary terms, must have
been rather laborious, and cant help thinking that it must often have
been simpler to throw the whole "total" back in the pot and measure it
out again.
For instance in HT 123-124 the sum of the terms with L90 appears to
be:-
8 ¼ = decimal 8.2500
8 ¼ = 8.2500
4 1/3 plus 1/12(?)=4.4167
4 ¼ = 4.2500
4 1/6 = 25.1667
The expected total would be 1/6, but is apparently written here
as 3/16, a near approximation which might suggest re-measuring rather
than simple addition.
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I had already jotted down this synopsis of the A fractional values
when I turned over the page to the Linear B terms and was surprised to
see that they are for the most part nearly identical with the A fractions,
and that your calculated ratios largely correspond with the suggested
A values:-
1. 'Liquid' measure.
_ = ¼ of the unit measure, corresponds to the A fraction _ = ¼ .
_ or _ = 1/24 of the unit measure, corresponds to the A fraction
_ = 1/24.
_ = 1/96 of the unit measure probably represents, as you say, a cup,
It is small a term to be conveniently represented as a normal
fraction, though 1/96 might theoretically be the smallest fraction
in the ternary series, which we would expect to be repre-
sented by _-_ in A.
2. 'Dry' measure.
_ = 1/10 (?) of the unit measure, is indicated by the equivalent
of the A fraction 1/12 , the nearest approximation.
_ and _ , 1/60 and 1/240 of the unit measure, are shared with
the 'liquid' measure, and evidently have the same values as in the
latter, even though the fractional sequence is illogical when you
consider the 'dry' measure by itself.