Drill 13 holes 1/2-inch deep with your 1/8-inch bit in each 15-inch board. Space the holes 1 inch apart, leaving 1 inch from the two outside holes to the ends of the boards.
Lay the two 15-inch boards flat, parallel, spaced 7 inches apart and with the holes facing each other. Thread five beads onto each dowel and glue the ends of the dowels into the holes. Set the 7-inch boards between the 15-inch boards at right angles so they are flush with the ends of the boards. Screw through the 15-inch boards, using one screw for each corner. These boards will keep your abacus square and sturdy while the glue dries.
Group four beads on each dowel against one 15-inch board, and the fifth bead against the other 15-inch board. Place a 14-inch board flat on top of the dowels so they're perpendicular to each other, 2 inches away from the 15-inch board with the single beads. Glue this 14-inch board to the dowels and the second 14-inch board to the dowels on the opposite side of the first. These two boards keep the groups of beads separated during arithmetic calculations.