In cubing the new foot, which was
estimated at .978728 of an English foot, or 11.744736 English inches,
an arithmetical error of an unit happened in the fourth column of
decimals, and was repeated in another line in the sixth column, so as
to make the result one ten thousandth and one millionth of a foot too
much. The thousandth part of this error (about one ten millionth of
a foot) consequently fell on the metre of measure, the ounce weight,
and the unit of money. In the last it made a difference of about the
twenty-fifth part of a grain Troy, in weight, or the ninety-third of
a cent in value. As it happened, this error was on the favorable
side, so that the detection of it approximates our estimate of the
new unit exactly that much nearer to the old, and reduces the
difference between them to 34, instead of 38 hundredths of a grain
Troy; that is to say, the money unit instead of 375.64 Troy grains of
pure silver, as established heretofore, will now be 375.98934306
grains, as far as our knowledge of the length of the second pendulum
enables us to judge; and the current of authorities since Sir Isaac
Newton's time, gives reason to believe that his estimate is more
probably above than below the truth, consequently future corrections
of it will bring the estimate of the new unit still nearer to the
old.
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