Answer
:
There were 100
pints of wine in the cask, and on
thirty
occasions John
the Cellarer had stolen a pint and replaced it with a pint of
water.
After the first theft the wine left in the cask would be
99 pints; after
the second theft the wine in the cask would be 9801/100 pints (the
square
of 99 divided by 100); after the third theft there would remain
970299/10000 (the cube of 99 divided by the square of 100); after the
fourth theft there would remain the fourth power of 99 divided by the
cube of 100; and after the thirtieth theft there would remain in the
cask
the thirtieth power of 99 divided by the twentyninth power of
100.
This
by the ordinary method of calculation gives us a number composed of 59
figures to be divided by a number composed of 58 figures!
But by the
use
of logarithms it may be quickly ascertained that the required quantity
is
very nearly 7397/100 pints of wine left in the cask.
Consequently the
cellarer stole nearly 26.03 pints.
The monks doubtless omitted the
answer
for the reason that they had no tables of logarithms, and did not care
to
face the task of making that long and tedious calculation in order to
get
the quantity "to a nicety," as the wily cellarer had stipulated.
By a simplified
process of calculation, I have
ascertained
that the exact
quantity of wine stolen would be
26.0299626611719577269984907683285057747323737647323555652999
pints.
A man who would
involve the monastery in a
fraction of
fiftyeight
decimals deserved severe punishment.
