The History of Calculating Machines (page 2)

Since the earliest times, scientists, engineers, mathematicians, accountants and tax collectors have needed to carry out mathematical calculations as part of their job. While mental arithmetic, fingers, paper and pencil or papyrus and quills can be used for simple addition, subtraction, multiplication and division, there soon becomes a need to use some form of calculating machine to solve more complex problems involving larger numbers. This is a second page listing of some of the main inventions created to simplify the process of mathematical calculation. Visit page 1 for the earlier machines.

The first calculator that was produced commercially was the Pascaline or Pascal’s Arithmetic Machine. Wilhelm Schickard (1592 – 1635) had designed a Calculating Clock the Rechenuhr in 1623, but it was not widely known about until the 1950’s, so the Pascaline was therefore considered to be the first mechanical calculator.

How the Pascaline works by MechanicalComputing

The Pascaline was designed by the French mathematician and physicist Blaise Pascal (1623 – 1662). In 1642 he started designing a calculating machine in order to assist his father as a supervisor of taxes in Rouen. After 3 years work the final version of the machine was produced in 1645. Over the following 10 years over 50 of the calculating machines were manufactured. The design of the Pascaline would eventually lead to later calculators such as Gottfried Leibenz wheels 1671 and Thomas Colmar arithmometer in 1820.



Cylindre de Leibniz animé
The Leibniz wheel mechanism

Another calculating machine that expanded on the design of the Pascaline was the Leibniz Wheel. This was designed and built in 1673 by the German mathematician Gottfried Willhelm von Leibniz (1646 – 1716). After becoming acquainted with Pascal’s calculating machine, the Pascaline, he decided to improve the design so that multiplication and division could also be carried out. To perform multiplication and division he designed a stepped drum

Leibniz Stepped Reckoner
The Stepped Reckoner

mechanism or the Leibniz wheel. This was a drum with teeth of varying lengths around the drum. As the drum rotated the teeth meshed with teeth on a counting wheel that was was moved along the length of the drum to carry out the calculations. In 1676 Leibniz demonstrated a small working model of an arithmetic machine using several of his Leibniz wheels, however it wasn’t until 1694 that a full working Stepped Reckoner was manufactured. 


Le Chevalier Thomas de Colmar

Charles Xavier Thamas, de Colmar

With the industrial revolution the need for a reliable calculator in the office environment was needed. The Arithmometer was invented in 1820 by Charles Xavier Thomas (1785 – 1870) from Colmar in France, later known as Charles Xavier Thomas, de Colmar. In 1851 the Arithmometer was first successfully commercial mechanical calculator produced. By 1914 copies of the Arithmometer were being manufactured by approximately 20 European companies.

How the Arithmometer works - Valéry Monnier









Jacquard loom punch cards

Joseph Marie Jacquard (1752 – 1834) was French weaver and merchant. He designed a weaving loom in 1801 that made use of punched cards to control the pattern of the longitudinal warp threads. This allowed complex patterns to be woven by unskilled workers. He later developed his loom with the punched cards joined to form a continuous loop. The concept of punched cards to store information was adopted and in use until the early 1970’s.

A Jacquard loom using punched card system at Paisley Museum 

The mathematician, Charles Babbage (1791 – 1871) used a punched card system for the design of his Analytical Engine in 1833. The Analytical Engine almost completed in 1840 is considered to be the first general purpose computer machine.

Babbage Difference Engine

Babbage Difference Engine

Charles Babbage is probably better known for designing his Difference Engine rather than his Analytical Engine mentioned above. He started work on his first Difference Engine in 1820, designed to calculate polynomial functions and print out the results as a table. The project was abandoned when Government funding was cut in 1842 due to the cost of producing the high quality and precision of the components for the engine. Work had already been halted on the construction of the engine and Babbage had turned his attention to the Analytical Engine. With the successful completion of the Analytical Engine in 1840, Babbage started work on the design on an improved Difference Engine. In 1849 he had completed the design of the new Difference Engine. The Difference Engine was never constructed in Babbage’s lifetime and it was only in 1985 that the Museum of Science in London constructed a working engine from his original design drawings.  

Charles Babbage 1871

Babbage's Difference Engine No. 2 - Wired















image of hydraulic integrator from russian magazine science and life
Hydraulic Integrator

Vladimir Sergeevich Lukyanov (1902-1980) a Russian Soviet scientist and doctor of technical services proposed a fundamentally new way of mechanising the calculations of unsteady processes in 1934. In 1936 the world’s first hydro-mechanical analogue computer was produced. The Lukyanova Hydraulic Integrator was developed to solve partial differential equations. The changes in water levels in the machine were marked on a graph paper attached to measuring tubes (piezometers), which produced a curved graph.

It was not just the Soviet Union that used water in computing. William Philips (1914 – 1975) was an engineer and economist born in New Zealand. After World War II he studied economics at the London School of Economics. While studying he used his previous training as an engineer to develop the Monetary National Income Analogue Computer, (MONIAC) in 1949. The Phillips machine consisted of transparent plastic tanks and pipes, fastened to a wooden frame. The computer demonstrated how the UK national economy worked using coloured water to represent the flow of money within the economy. The machine did have limitations as there was no provision for inflation or swings in the credit cycle.


Phillips Hydraulic Computer (MONIAC)

By the 1940’s electronic digital programmable computers were beginning to take over from the mechanical, clockwork and hydraulic calculators of previous eras. One of the better know computers was the Colossus developed between 1943 and 1945. The Colossus used vacuum tubes, (thermionic valves) to carry out Boolean and counting operations. The Colossus was developed by Tommy Flowers (1905 – 1998) for codebreaking during WW II. Allen Coombs (1911 – 1995) was the principle designer for improved Colossus Mark II in 1944.


Frontal view of the reconstructed Colossus at The National Museum of Computing, Bletchley Park

Frontal view of the reconstructed Colossus

The post war years saw an increase in the number electronic computers being developed for different commercial applications. In 1946 the Electronic Numerical Integrator and computer (ENIAC) was designed by John Mauchly and J. Presper Eckert. In the same year the Small Scale Experimental Machine (SSEM) was built at Victoria University of Manchester. The Electronic Discrete Variable Computer (EDVAC) in 1952 was the first mainframe that used magnetic tapes. In 1953 IBM produced the IBM 702, which also used magnetic tapes. Between 1953 and 1969 IBM produced the first mass-produced IBM 650. British Ferranti Ltd. produced the Ferranti Pegasus 1 in 1956, followed in 1959 by the Ferranti Pegasus 2. All these early machines were all mainframe computers. It wasn’t until 1981 that the IBM Personal computer model 5150 made computer technology mainstream.

The 1980’s was a major turning point for calculating machines. This decade saw the widespread use of desktop business computer and the slide rule in use since the 17th century was replaced by the pocket calculator.  More details of calculating machines including modern computer software can be found on my page about maths tools.



Sources used and further reading

    A brief History of Computing

The History of Calculating Machines Timeline

Gizmodo UK - The History of Early Computing Machines

The Museum of HP Calculators

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Web page last updated  24 February 2019

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