, we find the fuller expressions, "by the mark one," "by the mark two,"
and so on, as far as the depth requires. This example also suggests the
older and far more widely diffused method of reckoning time at sea by
bells; a system in which "one bell," "two bells," "three bells," etc., mark
the passage of time for the sailor as distinctly as the hands of the clock
could do it. Other examples of a similar nature will readily suggest
themselves to the mind.
Two possible number systems that have, for purely theoretical reasons,
attracted much attention, are the octonary and the duodecimal systems. In
favour of the octonary system it is urged that 8 is an exact power of 2; or
in other words, a large number of repeated halves can be taken with 8 as a
starting-point, without producing a fractional result. With 8 as a base we
should obtain by successive halvings, 4, 2, 1. A similar process in our
decimal scale gives 5, 2-1/2, 1-1/4. All this is undeniably true, but,
granting the argument up to this point, one is then tempted to ask "What
of it?" A certain degree of simplicity would thereby be introduced into
the Theory of Numbers; but the only persons sufficiently interested in this
branch of mathematics to appreciate the benefit thus obtained are already
trained mathematicians, who are concerned rather with the pure science
involved, than with reckoning on any special base. A slightly increased
simplicity would appear in the work of stockbrokers, and others who reckon
extensively by quarters, eighths, and sixteenths.
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