*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 construction of the abacus. In each case its origin was due to the habit or practise 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 transferred 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 mathematicians 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

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