Page:Popular Science Monthly Volume 49.djvu/206

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Set-offs you call them! To me it seems that the inconveniences outweigh the conveniences.

But surely you can not deny those enormous evils entailed by our present mixed system which the proposed change would exclude.

I demur to your assertion. I have shown you that the mixed system would in large part remain. You can not get rid of the established divisions of the circle and the points of the compass. You can not escape from those quarters which the order of Nature in several ways forces on us. You can not change the divisions of the year and the day and the hour. It is impossible to avoid all these incongruities by your method, but there is another method by which they may be avoided.

You astonish me. What else is possible?

I will tell you. We agree in condemning the existing arrangements under which our scheme of numeration and our modes of calculation based on it proceed in one way, while our various measures of length, area, capacity, weight, value, proceed in other ways. Doubtless, the two methods of procedure should be unified; but how? You assume that, as a matter of course, the measure system should be made to agree with the numeration system; but it may be contended that, conversely, the numeration system should be made to agree with the measure system—with the dominant measure system, I mean.

I do not see how that can be done.

Perhaps you will see if you join me in looking back upon the origins of these systems. Unable to count by giving a name to each additional unit, men fell into the habit of counting by groups of units and compound groups. Ten is a bundle of fingers, as you may still see in the Roman numerals, where the joined fingers of one hand and the joined fingers of the two hands are symbolized. Then, above these, the numbering was continued by counting two tens, three tens, four tens, etc., or 20, 30, 40 as we call them, until ten bundles of ten had been reached. Proceeding similarly, these compound bundles of tens, called hundreds, were accumulated until there came a doubly compound bundle of a thousand; and so on. Now, this process of counting by groups and compound groups, tied together by names, is equally practicable with other groups than 10. We may form our numerical system by taking a group of 12, then 12 groups of 12, then 12 of these compound groups; and so on as before. The 12-gi'oup has an enormous advantage over the 10-group. Ten is divisible only by 5 and 2. Twelve is divisible by 2, 3, 4, and 6. If the fifth in the one case and the sixth in the other be eliminated as of no great use, it remains that the one group has three times the divisibility of the other. Doubtless it is this great divisibility which has made men in such various cases fall into the habit of dividing into twelfths. For beyond the 12 divisions of the zodiac and the originally associated twelvemonth, and beyond the twelfths of the day, and beyond those fourths—submultiples of 12—which in sundry cases Nature insists upon and which in so many cases are adopted in trade, we have 12 ounces to the pound troy, 12 inches to the foot, 12 lines to the inch, 12 sacks to the last; and of multiples of 12 we have 24 grains to the pennyweight, 24 sheets to the quire. Moreover, large sales of small articles are habitually made by the gross (12 times 12) and great gross (12 x 12 x 12). Again, we have made our multiplication table go up to 12 times 12, and we habitually talk of dozens. Now,