It is unnecessary to go into the history of the Hopkins Bookkeeping Machine to show the evolution of the Art relative to this class of machines, as the features that have made such a machine practical were developed by Hopkins himself, and at the present date there is none to dispute the title since his is the only machine having the required combination referred to. The scheme used by Hopkins for multiplication in his billing machine is, as stated, direct multiplication or that of adding the multiples of digits directly to the accumulator numeral wheels instead of pumping it into the accumulator wheels by repeated addition of the digits as is more commonly used. [Illustration: John Napier] The direct method of multiplying is old, as a matter of fact, the first mechanical means employed for multiplying worked by the direct method. But its combination with recording and typewriter mechanism invented by Hopkins was new. [Sidenote: _Napier’s bones first direct multiplier_] Napier, in 1620, laid the foundation of the mechanical method of direct multiplication when he invented his multiplying bones. The scheme of overlapping the ordinal places is shown in the diagonal lines used to separate units from the tens in each multiple of the nine digits (see illustration, page 179), thus providing a convenient means by which the ordinal values may be added together. [Sidenote: _First direct multiplying machine_] The first attempt to set Napier’s scheme to mechanism that would add and register the overlapping ordinal values was patented by E. D. Barbour in 1872. See reproduction of patent drawings on opposite page. THE BARBOUR MULTIPLIER The accumulator mechanism of the Barbour machine, including the numeral wheels and their devices for transferring the tens, is mounted in a sliding carriage at the top of the machine (see Fig. 1), which may be operated by the hand-knob. [Sidenote: Description of Barbour Multiplier] Extending through the bottom of the carriage are a series of pinions, one for each ordinal numeral wheel, and connected thereto by a ratchet and pawl action. The pinions are each so arranged as to be operative with a gear rack beneath the carriage when the carriage is slid back and forth. Thus the wheels received action from one direction of the motion of the carriage and remain idle during the movement in the other direction. The degree of motion so received would, of course, depend upon the number of teeth in the racks below encountered by the pinions. The gear racks employed by Barbour were numerous, one being provided for each multiple of the nine digits, arranged in groups constituting nine sets mounted on the drums marked B (see Fig. 4). Each of these sets contain nine mutilated gear racks, the arrangement of the teeth of which serve as the multiples of the digit they represent.