CALC ULA TING-MA CHINES. 



447 



plan of a quaternary arithmetic. Simon Stevin, of Bruges, had pre- 

 viously devised a system of duodecimal numeration like the one we 

 use in computing time and the degrees of the circle. The almost 

 unanimous choice of the number ten as the basis of numeration was 

 probably suggested by the ten fingers. 



Instead of increasing the height of our abacus by two squares to 

 explain the duodecimal system, let us put in its place a rectangle two 

 squares high and of any desired width. We shall then have the sys- 

 tem of binary numeration, and be able to write all the numbers with 

 only two figures, and 1. The numbers one, two, three, four, five, 



101 no 



Fia. 10.— The Binary Abacus. 



and six, may be formed on this system as in Fig. 10. This system 

 furnishes the explanation of the Chinese symbol " Je-Kim, or Book 

 of Mutations," which is attributed to the venerable Emperor Fo-Hi. 

 It is composed of sixty-four figures, each formed of six horizontal 

 lines written one over the other, some of them whole, others broken 

 in the middle. The whole lines represent units of different degrees, 

 rising from the lowest, and the broken lines zeros. 



OOOOOO 



000 001 



000 010 



000 011 



000 100 



000 101 



000 JIO 000 111 001 000 



Fig. 11.— The Nine First Characters op the Je-Kim. 



