47 Highpoint,
North Hill,
Highgate,
LONDON, N.6.
4 December 1950.
Mr. Emmett L. Bennett Jr,
Box 1967,
Yale Station,
New Haven, Conn.
Dear Bennett,
I've been thinking some more about the points raised in your article
in the AJA, and I'd like to set down a few more miscellaneous comments.
I hope you don't mind this deluge of paper, but I'm not saving up my ideas
for any future publication, and it's probably simplest to pass them on
in discussion to you, when you can either use them or discard them in your
own more intensive work on the problem (- which I hope will continue, be-
cause I'm looking to you to find the eventual answer !). Well, here
goes:-
FRACTIONS AND FRACTIONAL UNITS
(i) On second thoughts, it's probably best to regard _ as an ideogram,
1/120 th of the unit value, and not to try and explain its shape as a
normal fraction.
_ , on the other hand, I'd prefer to regard as 1/8 of _. I'm not
quite sure for the reason for your suggesting 1/12 : is it the occurrence
of _3, _6 and _1 , which might suggest the various amounts of mate-
rial necessary to make 1, 2 and 4 articles respectively? There may be
something in that, but wouldn't one expect _ 9 to figure as well ?
(ii) If _-_-_ is in fact the correct order of the 'ternary' splittings,
one might explain them in a way that hadn't occurred to me at the time of
my last letter: that is, that _ can be regarded as twice _ ( _ ), and
_ as twice _ ( _ ).
(iii) I spent a few hours wondering if there was any chance of establishing,
within very broad limits, the actual physical values of the B measuring
units, especially in the 'weight' series.
The most useful way of studying various possibilities seems to be to
plot on a sheet of logarithmic graph-paper (at least 5 cycles required):
a) The values and ratios of contemporary and classical systems.
b) The values of Minoan and Mycenaean weights and ingots which have
actually been found.
The logarithmic scale has the advantage that you can scale off on a
strip of paper the suggested _ system of ratios 30.4.8 = 960.1 , or
what have you, and slide them up and down over the graph to test alterna-
tive 'fits'.
The crucial question seems to be whether we assume that the ingots
on the Knossos account (which weigh on the average a little under _ 1),
are of the same size as the most common Aegean ingot size (a little under
30 kg, or 1 talent), or whether they are considerably lighter, so that the
'normal' ingots (and the Knossos gypsum octopus-weight of 28.6 kg)
represent a multiple of _ 1 , say 2, 4 or 6.
On the whole I think the first alternative is the best one to start
with. This gives us the following table:-
Fractional unit metrical Avoirdupois Equivalent
_ 28.5kg 63 lbs 1 talent
_ 1/30 950g 2.1 lbs 2 minas
_ ¼ 238g 8.4 ozs 1 mina
_ 1/8 30g 1.1 oz