We move four beads to the left on the thousands-wire, eight on the hundreds-wire, two on the tens-wire, and seven on the units-wire; and we read, four thousand eight hundred and twenty-seven. This number is written by placing the numbers on the same line and in the mutually relative order determined by the symbolic positions for the decimal relations, 4827. We can do the same with the date of our present year, writing the figures on the left-hand side of the paper as indicated: 1917. Let us compose 2049 on the symbolic number frame. Two of the thousand-beads are moved to the left, four of the ten-beads, and nine of the unit-beads. On the hundreds-wire there is nothing. Here we have a good demonstration of the function of zero, which is to occupy the places that are empty on this chart. Similarly, to form the number 4700 on the frame, four Tlie bead material used for addition and subtraction.