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The Pascaline by Blaise Pascal, around 1650

In the run-up to the re-opening of the Mathematisch-Physikalischer Salon on April 14, 2013, we will be posting details on this site each month, showcasing a masterpiece of science and craftsmanship from our collection. The feature will include background information on the object’s history within the collection, its function, and use. The first such highlight is Blaise Pascal’s mechanical calculator, dubbed the Pascaline, dating from around 1650.

  • Mechanical calculator

    This machine is one of the oldest surviving mechanical calculators in the world. It was designed by the famous French mathematician, philosopher, and theologian Blaise Pascal (1623–1662). Only a handful of the arithmetic machines that Pascal built survive today – this ten-digit version in the Royal Cabinet’s collection is the only one held in a public collection outside France and the largest of its kind.

  • Functions

    The primary function of Pascal’s calculators was addition. The spoked wheels on the Pascaline’s top were used to programme the device. Each wheel represents a particular digit – ones, tens, hundreds, etc. The numbers to be added are entered into the appropriate digit-dials. A stylus was placed in the space between the spokes that corresponded to the desired figure and the wheel turned until a metal stop was reached, just as in the rotary dial of an old telephone.

    The inner mechanism consists of a series of straight-toothed bevel gears (an adaptation of a lantern gear), with backstop pawls between each one so they could only turn in one direction. This system was connected to output drums which rotate to show the desired number in the output window above each dial. To add two figures, the user simply entered them one after another via the input dials and the result would appear in the display windows above.

    To solve the problem of the carryover (e.g. of 1 from the ones to the tens position), Pascal invented a carry mechanism cleverly activated by a series of pins, levers, and spring-loaded pawls that connect each accumulator with the next higher ordered digit. This mechanism also works across several digits, necessary, for instance, in the addition of 999 and 1.

    The Dresden machine was clearly intended for calculating sums of money. Above the two last wheels on the right (in modern terms the equivalent to the two digits after the decimal point) are the words ‘deniers’ and ‘sols’, old French monetary units: there were 12 deniers to a sol, and 20 sols to a livre (pound).

  • Presentation

    In collaboration with HTV Dresden (University of Applied Sciences), the Royal Cabinet of Mathematical and Physical Instruments has constructed an interactive digital version of the ‘Pascaline’. Visitors to the Royal Cabinet will be able to marvel at the historical device and make calculations of their own on a digital replica directly beside it. The film above offers a foretaste.