*CURIOUS SYSTEMS OF NOTATION.*

and market. Although our calculations are universally made in the decimal system, none of our tables of weights and measures are decimal in any one of their subdivisions. In all departments of trade the current prices have been derived from a process of successive halvings. The shopman reckons by halves, quarters, eighths, sixteenths, and thirty-seconds, and not by fifths or tenths. The yardstick is divided in its practical use into halves, quarters, eighths, etc., by successive bisections. Even the sixteenth of a unit is more commonly used in trade than the tenth. In the stock-exchange, shares change in price by eighths of a dollar, and not by tenths. Even with our decimal system of money, we require coins for half and quarter of a dollar for practical use in trading. Almost the entire price-list of our stores advances and recedes by these fractions of a unit formed by successive bisections.

The attempt by the French to compel the use of the decimal system shows the difficulty of such an undertaking. Popular necessities compelled the introduction of binal divisions. The prices of their money and stock markets are still frequently quoted in quarters and eighths. The attempt to divide time decimally was a failure. After trying to give to their decimal metrology a universal application, they have been compelled to modify it in many of their weights and measures. From the inherent defects of a ten scale, all attempts to introduce an international decimal system of weights and measures have met with strong opposition.

The decimal system, then, appears to be ill adapted both to arithmetical calculation and to the practical needs of trade. Since the principle of the Hindoo notation is one of universal applicability, its merits do not arise from the number which happens to be used as its radix. One number, however, may be better for that purpose than another; and attempts have been made to supply the place of ten with numbers claimed to be more suitable. New systems have been elaborated and offered as substitutes for the one now in use. There is probably no one, except perhaps the authors of these new systems, who supposes that any of these, however theoretically perfect, will ever supersede our common decimal system. Yet these new systems of notation are not without a theoretical interest, for some of them are certainly better than the system which we are compelled to use. A brief statement of some of these curious systems will enable the reader to understand the advantages and disadvantages of our own.

The first and most noted is the binary system, first brought to the notice of Europeans by Leibnitz. He esteemed it so highly that he zealously urged its adoption. He claimed that its superiority to the decimal system was so great that time would be saved by reducing the decimal expressions of a problem to a binary form, performing the calculation, and then restoring the answer to the decimal notation. A short description of the system will show the peculiarities upon which this claim was founded: In the Hindoo notation the number of signifi-