The teeth of the racks representing the multiples of the digits were arranged in groups of units and tens. For instance: 4 × 6 = 24, the rack representing the multiple of 4 × 6 would have two gear teeth in the tens place and four gear teeth in the units place, and likewise for the eighty other combinations. Adding the multiples of the digits by overlapping the orders was accomplished by a very simple means, the arrangement of the racks being such that as the carriage was moved from left to right the numeral wheel pinions would move over the units rack teeth of a multiplying rack of one order and the tens rack teeth of a multiplying rack in the next lower order. By close examination the reader will note from the drawings that the lower one of the sets of multiplying gear racks shown on the drum B, to the left in Fig. 4, is the series of one times the nine digits, the next set or series of racks above are the multiplying racks for the multiples of two, the lowest rack in that series having but two teeth, the next higher rack four teeth, the next rack six and the next eight. So far no multiple of two has amounted to more than a units ordinal place, therefore these racks operate on a lower-order numeral wheel, and are all placed to the right of the center on the drum B, but the next rack above for adding the multiple of two times five requires that one shall be added to a higher order, and is therefore placed on the left side of the center of the drum. Thus it will be noted that by reading the number of teeth on the right of each rack as units and those on the left as tens, that running anti-clockwise around the drum, each series of multiplying racks show multiples of the digits from one to four, it being obvious that the racks for adding the multiples of the higher digits are on the opposite side of the drums. From the layout of the racks it is also obvious that the starting or normal position of the carriage would be with the numeral wheel pinions of each order in the center of each drum, so that as the carriage is moved to the right the units wheel will receive movement from the units teeth of the rack on the units drum, while the tens wheel will receive movement from the units teeth of the tens drum and the tens teeth of the units drum, and so on with the higher wheels, as each numeral wheel pinion except the units passes from the center of one drum to the center of the next lower and engages such teeth as may be presented. Each of the drums B are independently mounted on the pivot shaft C, and are provided with the hand-operating setting-racks I and E, co-acting with the gears R and D, to help in bringing the proper racks into engageable positions with the pinions of the accumulator numeral or total wheels. The hand-knob G, Fig. 4, and the gears f, fast to a common shaft, furnish a means for operating the whole series of drums when the right multiple series of racks of each drum have been brought into position.