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THE POPULAR SCIENCE MONTHLY.

correspondingly lessened. The mental work in using it would not probably be more than half that called for by our notation, while the number of places of figures required would be only slightly greater. The year 1878 would also be expressed by four figures, 3536, in the eight scale. Its fractions would be much simpler than those of the decimal system. They would differ very little from those of the sixteen scale.

The merits of the octonary scale have long attracted the attention of those interested in the subject of numerical notation. Charles XII. of Sweden seriously proposed introducing it in his kingdom. He commissioned Swedenborg to prepare the necessary details of a plan for establishing it. It is said that a complete system was elaborated, but the attempt to introduce it was prevented by the death of the king. No record of the system has been preserved.

But a complete octonary system has been elaborated, and a description of it was read by its author before one of our scientific associations about twenty years ago. In many respects, the details of it resemble those of the tonal system, which, in point of time, it preceded. New names were supplied for the digits as follows:

1 2 3 4 5 6 7 10 11 12
un du the fo pa se ki unty unty un unty du
20 30 31 50 100 200 1000
duty thety thety un paty under duder untyder
10000 100000
unsen untysen

The names of the larger numbers were made by compounding those of the smaller. Thus the present year, 3536, would be called thetyder pader thety se.

The octonary, like the tonal and quaternary scales, is without doubt admirably adapted to a natural system of weights and measures, and it is not without interest from a theoretical point of view. The disadvantages of the decimal system are clearly great, but the projects of those who expect to subvert it, with its immense store of arithmetical tables and formulas, are of course chimerical in the last degree. The author of the octonary system, just described, declared that the change involved no real difficulty, and that the national Government had only to will it, in order to bring the octonary scale into general use in one or two generations. But although the introduction of this or any other numerical scale in the place of the decimal is a dream without any probability of fulfillment, there can be no question that, theoretically, the octonary system of notation would be a vast improvement upon the one now in use, the basis of which was ignorantly bequeathed to us by our savage and barbarous ancestors.