The Oriental tradesman does not deign to perplex himself by a process of mental arithmetic; he seizes his abacus, prepares it by a tilt, makes a few rapid, clicking movements and his calculations are completed. We always look with some slight contempt upon this method of calculation, but a little experience and investigation would tend to transform this contempt into admiration, for it may be safely asserted that even the simplest of all arithmetical operations, the abacus, possesses distinctive advantages over the mental or figuring process. In competition in simple addition between a “lightning calculator” and an ordinary Japanese small tradesman, the Japanese would easily win the contest. Blaise Pascal, the wonderful Frenchman, who discovered the theorem in conic sections, or Pascal’s hexogram, was not only one of the foremost mathematicians of his day but also excelled in mechanics; when he was nineteen years old he produced the first machine for the carrying of tens and the first arithmetical machine, as we know it, was invented by him about 1641. This was the first calculating machine made with dials. The same principle, that of using discs with figures on their peripheries, is employed in present-day calculating machines. Among these are numbering machines of all kinds, speedometers, cyclometers and counters used on printing presses. [Illustration: A MODERN BOOKKEEPING MACHINE, USED FOR LEDGER POSTING AND STATEMENT MAKING It has seventeen “banks” or rows of keys, is electrically operated, and automatically adds, subtracts, and computes balances. _Courtesy of the Burroughs Adding Machine Company._] Who Discovered the Slide Rule Principle? It was early in the seventeenth century that Napier, a native of Naples, invented the first actual mechanical means of calculating. He arranged strips of bone, on which were figures, so that they could be brought into various fixed combinations. The instrument was called “Napier’s rod” or “Napier’s bones.” It was the beginning of the slide rule, which has been found of invaluable aid to accountants and engineers. One trouble with all these contrivances was that, although they aided man to figure, they offered no means of making a record of the work. The man who used these machines had no way of checking his work to know if it was right unless he did it all over again. The first machine to perform multiplication by means of successive additions was invented by Leibnitz in the year 1671 and completed in 1694. It employed the principle of the “stepped reckoner.” This model was kept first at Göttingen and afterward at Hanover, but it did not act efficiently, as the gears were not cut with sufficient accuracy. This was long before the days of accurate machine tools.