fourths, and, sometimes in subdividing the inch, one-hundred-and-twenty-eighths. To begin with, the existence of any such inherent tendency is quite open to discussion, but, without going into that, it is at least plain that it has never shown itself in the evolution of systems of weight and measure. In evidence of this the following tables of English measures of length and weight may be cited, and, that there may be no mistake, they are drawn from a text-book on arithmetic written by one of the most distinguished of England's nineteenth-century mathematicians:
| Length. | Weight. | ||
| 3 barleycorns are | 1 inch. | 27 13 12 |
1 dram. |
| 12 inches are | 1 foot. | 16 drams are | 1 ounce. |
| 3 feet are | 1 yard. | 16 ounces are | 1 pound. |
| 5-1/2 yards are | 1 pole. | 28 pounds are | 1 quarter. |
| 40 poles, or 220 yards, are | 1 furlong. | 4 quarters are | 1 hundredweight. |
| 8 furlongs, or 1,760 yards, are | 1 mile. | 20 hundredweights are | 1 ton. |
These are far from being complete, for two or three additional tables are necessary to fully exhibit the units and ratios for both length and weight, and they are even more irregular in construction than those shown above. In all, as well as in the English money units and denominations, there is no indication whatever of this "natural tendency" toward continual halving. It is a common practice, possibly growing out of a tendency in some degree natural, to continually bisect a single unit, and this is likely to be the case under any system of weights and measures, and to it there can be no sort of objection. It is important, however, to note that this is in no way related to the question of desirable or convenient ratios of units, and that it has practically no weight whatever as a criticism of the metric system.
But even if this were not true, it would weigh vastly more against the systems in customary use in England and America than against the metric system. What possible objection can there be to speaking of a half or a quarter or an eighth of a mile or rod or yard or inch, if one wishes to do so? And no more can there be to a half, quarter, eighth, or sixteenth of a kilometre, kilogramme, metre, gramme, centimetre, millimetre, etc., nor, again, to the use of such fractional parts as thirds, fifths, or sevenths, if they seem to be desirable. But to compare the two systems in this respect one should undertake such a problem as finding the value of a third, quarter, fifth, or eighth of a mile or a ton in rods, yards, feet, and inches, or hundredweight, pounds, ounces, drams, and grains, and then do the same thing in the metric system. The enormous superiority of the latter will at once be revealed.
On the other hand, it can not be denied that there is, and has been for many years, a strong tendency toward the decimal sub-
