# Mechanical calculation

In the 17th and 18th centuries, clockwork and precision engineering made it possible to build devices that could add and subtract at the turn of a dial. The designs of these adding machines differed in important ways. They both inspired more complex work, like that of Charles Babbage and Konrad Zuse, and made it possible to mass produce devices to aid in everyday arithmetic.

Image 1 Pascal adding machine with gears, mid 20th century (Wh.4404). Image © the Whipple Museum.
Image 2 Burkhardt Arithmometer, c.1890 (Wh.3767). Image © the Whipple Museum.
Image 3 Brunsviga, c.1895 (Wh.6032). Image © the Whipple Museum.

### Entering the age of machines

The Enlightenment G  development of gear-driven mechanisms captured the popular imagination and inspired the design of amazing new machines. Devices known as 'automata', which often mimicked humans or animals, were invented by clockmakers to entertain the ruling classes and so win their favour. Amongst the most famous and advanced automata were a writing boy, various musicians, and a digesting duck capable of eating kernels of grain before metabolizing and defecating them.

A century earlier, John Napier XR  had been restricted to paper or ivory to build calculating tools. But by the 17th century, the growing popularity of clocks and associated mechanisms meant that knowledge and working examples of gears, levers, cams, pulleys, and cranks were in wide circulation, offering exciting new possibilities for the automation of calculation.

### Blaise Pascal

The world's first mechanical calculator is usually attributed to the precocious French polymath, Blaise Pascal XR  (1623-1662). Motivated by the tedium of adding up long columns of tax figures for his father, the young Pascal designed a gear and dial based machine for addition (Image 1). Pascal's first machine was completed in 1642, and he would go on to produce some 50 more during his unfortunately short life.

Pascal's device allowed the 'carrying' of numbers from one gear to another: when, for example, 3 was added to 7, the mechanism caused a 1 to appear in the appropriate place. However, the addition of large numbers required the carrying across of numerous places, and necessitated a much greater force than could be provided by hand.

Countryman Rene Grillet, a Royal watchmaker, and Englishman Samuel Morland XR  both invented machines incorporating Pascal's dials alongside Napier's rods, but these had no mechanical carry mechanism. The problem of the carry was deferred until engineering advances caught up.

### Leibniz and the stepped drum

Wilhelm Gottfried von Leibniz XR  (1646-1716), known for his creation of calculus alongside Isaac Newton XR , began working on his own calculating device in the 1670s. He was interested in automating not only addition and subtraction but multiplication, division, and even taking square roots.

His device, known as the 'stepped reckoner', used large stepped drums that meshed with secondary gears. One would slide the gear along an axle and it would mesh with a different number of teeth depending on its position. Turning the crank would cause all of the drums to rotate and add into counters, and one could multiply by simply cranking the desired number of times.

This design was also used in the first mechanical cipher, which Leibniz built a semi-operational model of and demonstrated before the Royal Society G  on a trip to England in 1672. A later working model was recently uncovered after being lost for 200 years.

Although Leibniz described the principles for his machine as early as the 1670s, it was a long time before they were applied to a practical design that could be marketed. Charles Xavier Thomas de Colmar used Leibniz's design to invent a machine known as an arithmometer. These bulky desktop machines, like the later Burkhardt example shown here (Image 2), were awkward to use but helped establish a market for mechanical calculating devices.

In 1873, Willgodt Theophil Odhner, a Swedish émigré living in Russia, drew up a practical, affordable, and efficient adaptation of Leibniz's machine that was suitable for mass production. The German firm of Grimme, Natalis & Co. bought out Odhner's German plant and secured manufacturing rights in 1892, creating the 'Brunsviga' brand.

Its flagship machine (Image 3) can mechanically calculate sums using a complex system of pinwheels coupled with geared carry mechanisms and a counter. Users would input numbers and turn the handle clockwise for addition and multiplication or anti-clockwise for subtraction and division. The owner of the Whipple Museum's example was George Udny Yule, appointed as Cambridge's first University Lecturer in Statistics in 1912.

Mikey McGovern

Mikey McGovern, 'Mechanical calculation', Explore Whipple Collections, Whipple Museum of the History of Science, University of Cambridge, [http://www.hps.cam.ac.uk/whipple/explore/calculatingdevices/mechanicalcalculation/]