Finally, in the numerals used by the natives of the Marshall Islands, the following curiously irregular sequence also contains a single senary numeral:[216]
| 6. | thil thino | = 3 + 3. |
| 7. | thilthilim-thuon | = 6 + 1. |
| 8. | rua-li-dok | = 10 − 2. |
| 9. | ruathim-thuon | = 10 − 2 + 1. |
Many years ago a statement appeared which at once attracted attention and awakened curiosity. It was to the effect that the Maoris, the aboriginal inhabitants of New Zealand, used as the basis of their numeral system the number 11; and that the system was quite extensively developed, having simple words for 121 and 1331, i.e. for the square and cube of 11. No apparent reason existed for this anomaly, and the Maori scale was for a long time looked upon as something quite exceptional and outside all ordinary rules of number-system formation. But a closer and more accurate knowledge of the Maori language and customs served to correct the mistake, and to show that this system was a simple decimal system, and that the error arose from the following habit. Sometimes when counting a number of objects the Maoris would put aside 1 to represent each 10, and then those so set aside would afterward be counted to ascertain the number of tens in the heap. Early observers among this people, seeing them count 10 and then set aside 1, at the same time pronouncing the word tekau, imagined that this word meant 11, and that the ignorant savage was making use of this number as his base. This misconception found its way into the early New Zealand dictionary, but was corrected in later editions. It is here mentioned only because of the wide diffusion of the error, and the interest it has always excited.[217]
Aside from our common decimal scale, there exist in the English language other methods of counting, some of them formal enough to be dignified by the term system—as the sexagesimal method of measuring time and angular magnitude; and the duodecimal system of reckoning, so extensively used in buying and selling. Of these systems, other than decimal, two are noticed by Tylor,[218] and commented on at some length, as follows:
“One is the well-known dicing set, ace, deuce, tray, cater, cinque, size; thus size-ace is 6-1, cinques or sinks, double 5. These came to us from France, and correspond with the common French numerals, except ace, which is Latin as, a word of great philological interest, meaning ‘one.’ The other borrowed set is to be found in the Slang Dictionary. It appears that the English street-folk have adopted as a means of secret communication a set of Italian numerals from the organ-grinders and image-sellers, or by other ways through which Italian or Lingua Franca is brought into the low neighbourhoods of London. In so doing they have performed a philological operation not only curious but instructive. By copying such expressions as due soldi, tre soldi, as equivalent to ‘twopence,’ ‘threepence,’ the word saltee became a recognized slang term for ‘penny’; and pence are reckoned as follows:
One of these series simply adopts Italian numerals decimally. But 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:
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.