6o8 THE POPULAR SCIENCE MONTHLY 



Thus, the decimal system was developed in language and in numeral 

 notation at the same time that it was being employed in the construc- 

 tion of the abacus. In each case its origin was due to the habit or prac- 

 tise among people of counting upon the ten fingers until they came by 

 custom to reckon in tens. In each case, however, the decimal system 

 was unwieldy in that it was built up upon a large number of words 

 and signs. It was the function of the abacus to make it simple by 

 reducing the number of signs. 



Since the Hindus employed the decimal system, so, on an Indian 

 counting device the counters in the second column had ten times the 

 value of those in the first; the ones in the third ten times the value of 

 those in the second, and one hundred times the value of the counters in 

 the first. It was necessary now for the Hindus to use only the signs 

 which in their present form are 1, 2, 3, 4, 5, 6, 7, 8, 9. Thus, 591 

 would be represented by 5 | 9 | 1. In like manner 501 would be 5 | | 1, 

 the middle space being vacant since there were only five hundreds and 

 one unit, but no tens. Among the Greeks it is probable that the same 

 method was worked out. In this manner the number signs could now 

 be attached to a definite place, and so had a definite place value. This 

 is the most important step which has ever been made in mathematical 

 science. 



But a difficulty arose when the calculation was transferred from the 

 abacus-board and became a written operation. 591 could be trans- 

 ferred without difficulty, since the digits by mere juxtaposition would 

 preserve their place value; but 5(0)1 taken from the abacus might be 

 51, since the vacant place was no longer indicated. Accordingly mathe- 

 maticians were led to invent a character to stand for the vacant space. 

 By so doing they perfected the system of place value, since they could 

 now show that even when there was no one of the nine numerals in a 

 particular place, the value of the place remained, and the values of the 

 adjoining places could be maintained. The invention of a symbol for 

 nothing is the crowning, transcendent achievement in the perfection of 

 the decimal system, and lies at the base of all subsequent arithmetical 

 progress. It is the peculiar triumph of the Hindu mathematicians to 

 have made this contribution to the science of number. 



A symbol for nothing was employed among the Chaldeans, but 

 merely for notation, and apparently never in calculating. In the 

 cuneiform incriptions it occurs as 



4- m 4- 



Among the Hindus it was at first a dot ( . ) . In this guise it was bor- 

 rowed by the Arabs, who still use it. Very soon, however, the Hindus 

 began to employ a circle, 0. The earliest known use is in an inscrip- 



