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.

Entering the age of machines

The Enlightenment 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 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.

On this page:

• Ball and spoke models
• Space-filling models
• Crystal lattice models

Dr. William A. R. Dillon Weston, a fungus expert at the University of Cambridge, demonstrated the structures of extremely small fungi using his own hand-made glass models. His models show fungi that cause diseases in plants, including the potato blight fungus and moulds found on bread and vegetables.

Fungi down the microscope

Trying to identify fungi and moulds that attack food crops can be a difficult task. The more quickly a type of fungus is identified, the more quickly the crops can be treated.

Dr. William Dillon Weston (1899-1953) was a mycologist (a fungus specialist) working for the Ministry of Fisheries in Cambridge in the 1930s. He came up with an inventive way to demonstrate what extremely small fungi looked like when viewed with a microscope. Instead of referring farmers to pictures of fungi, Dr. Dillon Weston made models of them using glass.

Dr. Dillon Weston's glass models were all made between 1936 and 1953. The particular fungi that he focused on were those that cause diseases in plants, which are normally only visible using a microscope. As well a being a useful demonstration tool, the models are also particularly beautiful.

Medical student Louis Auzoux was frustrated with the shortage of human corpses available for studying anatomy. Using his own secret papier-mâché mixture he developed 'dissectable' models, which could be used again and again. Later, he also created models of animals and plants.

Real corpses or models?

As a medical student in Paris, Louis Thomas Jérôme Auzoux (1797-1880) noticed that there was often a shortage of human remains available for doing human dissections. Dissections were an essential part of studying medicine. However, even if a body was available, it could only be used once before it began to decompose.

To deal with the shortage of bodies, Auzoux began producing accurate anatomical models that could be taken apart piece by piece.

The models were sturdy and inexpensive, especially when made with the secret papier-mâché mixture that Auzoux had developed. The mixture contained cork and clay as well as paper and glue.

Blaise Pascal

The world's first mechanical calculator is usually attributed to the precocious French polymath, Blaise Pascal (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 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 (1646-1716), known for his creation of calculus alongside Isaac Newton, 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 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.