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 system of weights and measures proposed to conform with it. New methods of dividing time, the sphere, the barometer and thermometer, were also proposed. A description, however, of so much of the system as relates 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 sixteen 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:
1  2  3  4  5  6  7  
an  de  ti  go  su  by  ra  
8  9  (10)  (11)  (12)  (13)  (14)  
me  ni  ko  hu  vy  la  po  
(15)  10  11  12  20  21  30  
fy  ton  tonan  tonde  deton  detonan  titon  
40  50  100  101  102  120  135  
goton  suton  san  sanan  sande  sandeton  santitonsu  

The new name "ton" given to 10 furnishes the system with its name of tonal. 0 was called "noll." 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 by 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 fractions in common use, which require from four to seven places of decimals, would occupy only one or two when written in the tonal scale, as the following table will show: