The Master of the Mint knows that two coins are never
exactly equal in weight, although he strives by improving machinery and
processes to make the differences as small as possible. When the utmost
care is taken, the finest balances which have been constructed can weigh 1
lb. of a metal with an uncertainty less than the hundredth part of a
grain. In other words, the weight is not accurate, but the inaccuracy is
very small. No person is so stupid as not to feel sure that the height of
a man he sees is between 3 ft. and 9 ft.; some are able by the eye to
estimate the height as between 5 ft. 6 in. and 5 ft. 8 in.; measurement
may show it to be between 5 ft. 6 in. and 5 ft. 7 in., but to go closer
than that requires many precautions. Training in observation and the use
of delicate instruments thus narrow the limits of approximation. Similarly
with regard to space and time, there are instruments with which one
millionth of an inch, or of a second, can be measured, but even this
approximation, although far closer than is ever practically necessary, is
not accuracy. In the statement of measurements there is no meaning in more
than six significant figures, and only the most careful observations can
be trusted so far. The height of Mount Everest is given as 29,002 feet;
but here the fifth figure is meaningless, the height of that mountain not
being known so accurately that two feet more or less would be detected.
Similarly, the radius of the earth is sometimes given as 3963.
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