t the
other, when it has reached 6, having had enough of novelty, makes 7 by 6-1,
and so forth. It is for no abstract reason that 6 is thus made the
turning-point, but simply because the costermonger is adding pence up to
the silver sixpence, and then adding pence again up to the shilling. Thus
our duodecimal coinage has led to the practice of counting by sixes, and
produced a philological curiosity, a real senary notation."

In addition to the two methods of counting here alluded to, another may be
mentioned, which is equally instructive as showing how readily any special
method of reckoning may be developed out of the needs arising in connection
with any special line of work. As is well known, it is the custom in ocean,
lake, and river navigation to measure soundings by the fathom. On the
Mississippi River, where constant vigilance is needed because of the rapid
shifting of sand-bars, a special sounding nomenclature has come into
vogue,[219] which the following terms will illustrate:

5 ft. = five feet.
6 ft. = six feet.
9 ft. = nine feet.
10-1/2 ft. = a quarter less twain; _i.e._ a quarter of a fathom less than 2.
12 ft. = mark twain.
13-1/2 ft. = a quarter twain.
16-1/2 ft. = a quarter less three.
18 ft. = mark three.
19-1/2 ft. = a quarter three.
24 ft. = deep four.

As the soundings are taken, the readings are called off in the manner
indicated in the table; 10-1/2 feet being "a quarter less twain," 12 feet
"mark twain," etc. Any sounding above "deep four" is reported as "no
bottom." In the Atlantic and Gulf waters on the coast of this country the
same system prevails, only it is extended to meet the requirements of the
deeper soundings there found, and instead of "six feet," "mark twain,"
etc., 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