CURIOUS SYSTEMS OF NOTATION. 



425 



of the Tonal System. He published an account of it about twenty- 

 years ago. It was carefully elaborated in all its parts, and a new sys- 

 tem of weights and measures proposed to conform with it. New meth- 

 ods of dividing time, the sphere, the barometer and thermometer, were 

 also proposed. A description, however, of so much of the system as re- 

 lates to the notation is all that is required for our present purpose. 

 The tonal system requires fifteen digits in addition to zero. Six new 

 symbols were accordingly invented to represent the numbers, from ten 

 to fifteen inclusive. New names were given to all the digits, in order 

 to avoid confusion in using the new system. The reader may find it 

 difficult to shift the symbols from their ordinary values to tonal ones ; 

 but, if it be borne in mind that 11 represents not ten and one but six- 

 teen and one, 22 twice sixteen and two, 100 the square of sixteen, and 

 that a similar change of value obtains with all the figures, the difficulty 

 will disappear. The tonal figures below are printed in heavier type 

 than the corresponding decimal ones, but the six new symbols are 

 omitted. 



The names and figures in this curious notation are as follows : 



The new name " ton " given to 10 furnishes the system with its 

 name of tonal. was called " noil." The names of the figures above 

 10 were formed by simple combinations of the names of the digits. The 

 present year, 1878, would be represented bj' 756 in this system, and 

 be called rasan suton by. A lady 35 years old would be only 23 were 

 the tonal system in use, and the grave author of the scheme called 

 attention to this fact in an ingenious endeavor to make the better half 

 of mankind warm advocates of the tonal counting. 



However strange and fanciful this system may seem, its theoretical 

 advantages are many and valuable. Its radix is susceptible of indefinite 

 bisections, and is also a square and a fourth power. The vulgar frac- 

 tions in common use, which require from four to seven places of deci- 

 mals, would occupy only one or two when written in the tonal scale, as 

 the following table will show : 



