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 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.  But such men experience no difficulty whatever in performing their mental computations in the decimal system; and they acquire through constant practice such quickness and accuracy of calculation, that it is difficult to see how octonary reckoning would materially assist them.  Altogether, the reasons that have in the past been adduced in favour of this form of arithmetic seem trivial.  There is no record of any tribe that ever counted by eights, nor is there the slightest likelihood that such a system could ever meet with any general favour.  It is said that the ancient Saxons used the octonary system,[220] but how, or for what purposes, is not stated.  It is not to be supposed that this was the common system of counting, for it is well known that the decimal scale was in use as far back as the evidence of language will take us.  But the field of speculation into which one is led by the octonary scale has proved most attractive to some, and the conclusion has been soberly reached, that in the history of the Aryan race the octonary was to be regarded as the predecessor of the decimal scale.  In support of this theory no direct evidence is brought forward, but certain verbal resemblances.  Those ignes fatuii of the philologist are made to perform the duty of supporting an hypothesis which would never have existed but for their own treacherous suggestions.  Here is one of the most attractive of them: