Instead of using eighty-one multiplying gear racks for each order as in the Barbour patent, Bollee used but two gear racks for each order; one for adding the units and the other for adding the tens; these racks operate vertically and are marked respectively Bb and Bc. (See Fig. 3.) The racks are frictionally held against gravity in the permanent framework of the machine, and are moved up and down by contact at each end, received from above by bar Ie, and from below by pins of varying length set in the movable plates Ab. The bar Ie forms part of a reciprocating frame which moves vertically and in which are slidably mounted the pin plates Ab. These plates are what Bollee called his “mechanical multiplication tables.” The arrangement of the pins and their lengths are such as to give degrees of additive movement to the units and tens gear racks equal to the multiplying racks in the Barbour multiplier. The pin plates are moved by the hand-knobs Ab², and the plate shown in Fig. 3 is positioned for multiples of nine. The means for setting the multiples correspond to the index hand-knob of the Barbour machine, and consists of the crank Am, which, when operated, shifts the whole series of plates laterally. A graduated dial serves the operator to set the multiple that the multiplicand, set by the positioning of the plates, is to be multiplied by. The accumulator mechanism is mounted in a reciprocating frame which moves horizontally, causing the gears of the numeral wheels to engage first the units racks on their upstroke under action of the pins, and then the tens racks on their down-stroke under the action of the top bar of the vertically moving frame, the downward motion, of course, being regulated by the upward movement it receives from the pin that forces it up. As may be noted in Fig. 1, the multiplying plates are held in a laterally movable carriage that is shifted through the turning of the multiplier factor setting hand crank Am, by means of the rack and pinion action. This gearing is such that each revolution moves the multiplying plates under a higher or lower series of orders, thus allowing the multiples of a higher or lower order series to be added in the process of multiplication or subtracted in division, as the case may be. Although the Bollee machine is reputed to be a practical machine, as is attested from the models on exhibit in the Museum of Des Arts and Metiers of Paris in France, it was never manufactured and placed on the market. [Sidenote: _Bollee’s principle commercialized_] Bollee’s principle has, however, been commercialized by a Swiss manufacturer in a machine made and sold under the trade name of “The Millionaire,” the U. S. patents of which were applied for and issued to Steiger.