with an index, which may be slid in the direction of its length, and by means of which we can enter any number we choose. Each button is connected by a pendent wire, with a ten-toothed pinion, below the tablet. By the side of each of the pinions is a cylinder with a horizontal axis, the length of which is the same with that of the grooving above it. Each of the cylinders bears projecting, upon half the circumference, nine nerves of successively increasing length, from 1⁄10 to 9⁄10 the length, and the motion of each cylinder is commanded by a horizontal shaft, which is turned by a crank. The cylinders make a revolution with each turn of the crank, but the pinions advance, each only according to the number of teeth marked by the corresponding index. Pinions mounted on the same axis with the index transmit the motion to the figure-bearing wheels of the reproducer, which is placed under a metallic plate, prolonging the first one. Each turn of the crank produces the successive terms of an arithmetical progression. Suppose we wish to multiply 37,456 by 435. We bring down to zero the figures opposite the openings in the reproducer by means of an effacer, which is to be described. We write on the tablet the number 37,456; then turn the crank five times, when we will be able to read through the opening the product of 37,456 by 5; to get the product by 35, we would have to turn 35 times, but for an ingenious disposition by which we push the whole apparatus a notch to the right, and turn three times, which gives the product we are seeking; then pushing another notch to the right, and turning four times, we have the product by 435. The function of the reverser may be best explained by a comparison. Suppose a carriage of two wheels and an axle-tree, and a person is riding upon it holding an opened umbrella. As long as the umbrella is held straight over the middle of the axle, it does not move; incline it over one of the wheels, it begins to revolve; incline it over the other wheel, it will turn in the contrary direction, while the carriage will be all the time going straight ahead. In the arithmometer, the wheels of our carriage are replaced by twin-pinions and the umbrella by the figure-bearing wheel of the reproducer. By pushing on a little lever, we bring whichever pinion we desire into gear with the figure-bearing wheel, so that each turn of the crank—it always turning in the same direction—brings successively before the openings numbers increasing or decreasing in an arithmetical progression, of which the common difference is marked on the abacus of the tablet.
Lastly, the effacer illustrates the advantage that may be drawn from a broken tooth. Below each figure-bearing wheel is found, solid with it, another smaller toothed wheel in which the tooth corresponding with the below the peep-hole is suppressed. A roweled button pushes along a rack, that keeps the wheel turning, till the moment when the is to appear before the opening. The operation is performed with extreme rapidity, and is one among many admirable details in the per-
