CURIOUS SYSTEMS OF NOTATION. 423 



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 bisec- 

 tions. 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 com- 

 pelled 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 arith- 

 metical 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 elabo- 

 rated and offered as substitutes for the one now in use. There is prob- 

 ably 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 no- 

 tation are not without a theoretical interest, for some of them are cer- 

 tainly 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 cal- 

 culation, 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- 



