In the recent past we have seen electronic computers develop from monsters such as ENIAC in the mid-forties to the incredibly small microchip of today. But there have also been some very large and very complex mechanical calculators. This chapter gives a brief survey of both areas.

Various mechanical aids to computation have been used since the early civilisations. In China, calculations were performed by means of counting rods on squared boards from about the tenth century BC, and the modern Chinese abacus (suan pan) was developed by the 16th century. The Japanese soroban was standardised by decree of the present Emperor Hirohito in 1930. The soroban is still used extensively, although it is now being rapidly overtaken by electronic calculators. Comparable types of abacus were used in ancient Greece and the Roman Empire, and the Russian schyoty is still used widely.

The first major advance beyond abacus-type devices was achieved by the Scottish mathematician John Napier (1550–1617). He published his invention of logarithms in 1614 and then, despite advanced age and poor health, he set about devising further aids to computation. In the last year of his life he published a small book Rabdologiae, in which he described several aids to computation. The only one to become popular was his numbering rods (‘Napier’s bones’), which are a trivial aid to multiplication. He also invented binary arithmetic, as far as square root extraction, but he described his Promptuary as his most important idea. This is a sophisticated device for multiplication of numbers with up to ten digits each, although it still required some mental arithmetic to handle carried figures.

The first known automatic calculating machine, in which carries were handled mechanically, was constructed by the German theologian and astronomer Wilhelm Schickard (1592–1635) in 1623. His machine added and subtracted numbers with up to six digits each, but unfortunately it remained little known.

Other machines were built by the French mathematician Blaise Pascal (1623–1662) in 1642 and the universal genius Gottfried Wilhelm Leibniz (1646–1716) in 1672, Pascal’s machine aroused very widespread interest, for demonstrating that some actions which had been regarded as characteristic of human reason could also he performed by a machine. Pascal appears to have sold 40 or 50 such adding machines — but they were intellectual curiosities rather than practically useful calculating machines.

The first commercially successful calculating machine, the Arithmometer of Thomas of Colmar, was manufactured in Alsace. He constructed the prototype in 1820, and a few thousand were produced. The Arithmometer is much less sophisticated than Leibniz’s machine of 1672, but it can perform the four arithmetic operations, and imitations continued to be manufactured until the 1920s.

A major advance in the theory and construction of calculating machines was made by the English mathematician Charles Babbage (1791–1871). He made a detailed study of mathematical, astronomical and navigational tables, and the many errors which he found stimulated him to invent his first Difference Engine in 1821. That was a multiple adding machine designed to compute and print tables. He worked on the Difference Engine from 1822 to 1833 when government support ceased and the one-tenth of the Difference Engine which he assembled in 1833 was a technological triumph, which still works perfectly.

In 1834 Babbage went far beyond the concept of the Difference Engine by inventing the first version of his Analytical Engine. He developed that concept in a prolonged creative frenzy, and by 1836 his designs included all of the fundamental components of general computers — input and output devices, control, store and mill for arithmetic operations. He adopted punched cards as the principal medium for input, output and storage, but he also designed printing, typing and curve-drawing mechanisms. The instructions were to be supplied as chains of cards, with provision for conditional branching; so that his Engine was indeed a computer, and not just a calculator. By 1836, Babbage realised that such an Engine was not confined to arithmetic, but could be used as a general symbol manipulator. He considered many possible bases for arithmetic, but settled upon decimal arithmetic as the most convenient for use in a mechanical computer.

In 1833 Augusta Ada Byron (1815–1852, later Countess of Lovelace), then aged 17, visited Babbage with her mother and was profoundly impressed by him and by the fragment of the Difference Engine. Babbage had recently suffered the deaths of his wife, several of their children and his father, and Ada became a substitute daughter for him. In 1842 Menabrea, who later became Prime Minister of Italy, published a brief but clear report of Babbage’s ideas on programming the Analytical Engine. Ada was persuaded to translate that paper from French to English, and then at Babbage’s suggestion she added notes which were several times as long as the original. Her paper was published in 1843 and it remained (until recent years) the fullest published account of Babbage’s ideas. After that scientific triumph Ada’s health collapsed, and Babbage was profoundly affected by her death, in tragic circumstances, at the age of 36. In recent years she has become renowned as the patron saint of computer programming.

Babbage designed a succession of Analytical Engines from 1834 to 1848, and from 1856 onwards he attempted to construct simplified versions. However, he had not succeeded in completing more than some fragments before he died on 18 October 1871 at the age of 79. He was largely forgotten after his death.

Babbage’s youngest son Henry Prevost Babbage (1824–1918) attempted to continue work on the Analytical Engine. In 1879 he assembled six fragments of the Difference Engine; and in 1910 he completed the construction of the arithmetic ‘mill’ and printing mechanism, for the Analytical Engine.

During Charles Babbage’s lifetime the British Museum refused to accept the fragments of his incomplete Engines, which he had recommended to be displayed there. However, the Science Museum in London now displays some fragments of Babbage’s Engines amongst its greatest treasures.

New Zealand too has its Babbage connections. Charles Babbage’s two elder sons migrated to South Australia in 1849 and 1851, and many descendants now live in New Zealand and Australia. Some of them have large collections of relics of Charles Babbage, including many hundreds of letters and other documents, portraits, books, diplomas, medals et cetera. In particular, the Babbage family in Auckland hold one of the six fragments of the Difference Engine assembled in 1879, and two letters from Augusta Ada to Babbage. Several museums and libraries hold further Babbage material; the Babbage Collection at the Wanganui Regional Museum includes the manuscript of Charles Babbage’s remarkable memoir Passages from the Life of a Philosopher (London 1864), the Reed Collection of rare books and manuscripts in Dunedin Public Library includes ten letters from Babbage, and the George Grey Collection in Auckland Public Library includes three letters from Babbage to his younger friend Sir George Grey.

The first working Difference Engine was completed in 1853, by the Swedish publisher Georg Scheutz and his son the engineer Edvard Scheutz. It was much smaller than Babbage’s very ambitious design, but it did work fairly successfully, printing some mathematical and actuarial tables. The Scheutzes were advised not to exhibit their machine in England, since it might have provoked Babbage to quarrel with them. But on the contrary, Babbage behaved with noble generosity to the Scheutzes, who stayed as guests at his home in London. He wrote articles and gave speeches about the Scheutz Difference Engine, and arranged for gold medals and other honours to be awarded to them. The Babbage family in Auckland hold secretarial copies of letters written by Georg and Edvard Scheutz, warmly thanking Babbage for his truly noble efforts on their behalf.

Later, a few other Difference Engines were made. In contrast to such digital calculators, which give exact results, there were developed a wide variety of analogue calculators, whose results are limited in accuracy by errors of measurement. Six years after John Napier published his book on logarithms, Richard Gunter produced an analogue device for approximating multiplication and division. Scales of logarithms were engraved on rules, so that physical addition of lengths corresponded to addition of logarithms, and hence to multiplication. Such slide rules were used very extensively, until the development of electronic pocket calculators.

The Scottish physicist William Thomson (later Lord Kelvin, 1824–1907) invented in 1880 his differential analyser, a mechanical analogue computer for modelling physical processes. Variable quantities were represented by rotations of shafts, and those rotating shafts could be connected by mechanical devices for addition, subtraction, multiplication (by a constant) and integration. The first practical differential analyser was made by the American scientist Vannevar Bush, at Massachusetts Institute of Technology in 1930.

The English chemist Douglas Hartree got a demonstration model constructed from Meccano parts, at the University of Manchester in 1934. That model proved to be practically useful, and several other differential analysers were subsequently made from Meccano parts. The second such MecFrom Monsters To Micros 27 cano machine was made at Cambridge in 1935, for the chemist Lennard-Jones. In 1948 the radio-physicist Dr Harry Whale from Auckland University College was on leave at Cambridge University Computing Laboratory. He persuaded the New Zealand High Commissioner to buy that Meccano differential analyser for 100 pounds, and for several years Dr Whale used it in his research on radiophysics at Auckland University College. That second Meccano differential analyser is now displayed at the Museum of Transport and Technology in Auckland.

It would have been surprising if all this activity on computers and computing had not had an impact on the workforce, and indeed it did. The first significant use of automation in the manufacturing process came as early as about 1730, when the French mechanic Falcon invented a loom controlled by punched cards, which proved to be moderately successful. At the end of the 18th century the French engineer Joseph Marie Jacquard improved Falcon’s loom greatly, so that extremely intricate fabrics could be woven under the control of punched cards. Jacquard looms were used very extensively; and indeed some are still operating in New Zealand.

Punched cards, of course, went on to bigger and better things. By 1880, the United States Census Bureau had found that conventional methods were inadequate for processing their census data, and the Bureau arranged a competition for new techniques to be used for the 1890 census. The contest was won by Herman Hollerith who applied cards punched with simple binary data, with electrical machines for counting holes on cards and for sorting cards according to those holes. Hollerith’s system was very successful in processing the United States census for 1890 and 1900, and the Russian census for 1897. Many governmental and commercial organisations thereafter used punched card machinery for statistical and accounting work. For example, in 1929 New Zealand Railways installed an advanced punched-card system for its accounting. During the first half of the twentieth century a great variety of machines were manufactured to punch and print decimal data on cards, and later alphabetic and other characters. Machines were used to add and subtract decimal numbers on cards, and by the 1930s machines could multiply numbers on cards.

We have almost reached the end of the mechanical calculator saga, but before leaving there are two further New Zealand connections worth mentioning.

The first concerns a New Zealander whose achievements are much neglected. Leslie John Comrie was born at Pukekohe in 1893, and he graduated MA (with honours in Chemistry) at Auckland University College in 1916. From 1925 until his death in 1950 he was the undisputed world leader in scientific computing. He did not invent new computing machinery, having taken heed of Babbage’s difficulties, but he devised ways to exploit commercially available calculating machinery for scientific computation. In 1926 he became Deputy Director of the Nautical Almanac Office at Greenwich, and in 1930 he became its Director. He invented the first computing laboratory, producing the Nautical Almanac by punched-card machinery designed for accounting work.

In 1930 Comrie discovered that a National Accounting machine could be perverted to purposes never intended by its makers, and misused as a Babbage Difference Engine. Thereafter he applied Babbage’s ideas, using such machines to print mathematical tables of quite unprecedented accuracy; and conversely he used Difference Engines to detect an enormous number of errors in existing tables. In 1938 he founded the Scientific Computing Service Ltd in London, as the first computing agency. Through that firm he had immense influence on the development of scientific computing, and many scientists were inspired by him to create computing laboratories in Europe and the United States. Cornrie’s firm is still operating in London.

The second concerns two New Zealanders. In 1879 a Mr Ekberg patented a multiple adding machine, for use at racecourses. As each customer placed a bet, the operator pressed a pedal to add that bet into an accumulator for the chosen horse, and also into an overall accumulator for all horses. A clerk then used logarithm tables to calculate the dividends.

Within months, such totalisators dominated racecourse meetings throughout New Zealand and Australia. Indeed, before the end of the 1880 season, two operators of a totalisator were serving gaol sentences, after having been detected in attempts to cheat their customers! The Museum of Transport and Technology in Auckland displays such a foot-operated machine.

George Julius (1873–1946, later Sir George), son of Archbishop Julius, graduated as BSc from Canterbury University College in 1896. He spent most of his career in Australia, founding CSIRO in 1926 and remaining its head until 1946. In 1908 he invented an automatic totalisator and his firm Automatic Totalisators Ltd built the first such automatic totalisator in 1913, at Ellerslie Racecourse in Auckland. That machine accumulated bets on up to 30 horses and recorded the overall total, with 30 input devices operating independently. The early models were entirely mechanical and were operated by the muscles of the operators pulling levers to issue tickets, and logarithm tables were still used to calculate the dividends. Later models incorporated an increasing amount of electrical operation, with division mechanisms for computing the dividends.

By the 1960s some electromechanical totalisators accepted input from 400 independent devices operating asynchronously. Such machines were not merely physically the largest calculating machines built by then, but they did have quite substantial computational capacity. Not until the late 1960s did electronic computers begin to supplant electromechanical totalisators; and Julius’s firm still dominates that curious industry. It is interesting to reflect that probably the largest mechanical calculators ever to be built will have been used in a sporting activity.

The chief impetus for the development of electronic computers came from the desire to break German ciphers and the construction of ballistic tables.

In the 1920s a German firm began manufacturing ENIGMA machines, for enciphering and deciphering messages. ENIGMA contained adjustable drums for setting the cipher key, such that almost ten billion different cipher keys could be used; and hence the German government felt that messages sent through ENIGMA were quite secure against decipherment. Accordingly, German military and governmental messages were broadcast openly in ENIGMA ciphers, and hence monitors were able to record the enciphered messages.

In 1932 the Polish General Staff engaged three mathematicians, Marian Rejewski, Jerzy Rozycki and Henryk Zygalski, to work on the ENIGMA ciphers. Mathematical logic was developed very largely by Polish mathematicians between the two World Wars; and Rejewski and his colleagues succeeded in cracking the ENIGMA ciphers by applying mathematical logic. In 1938 six electromechanical devices, called ‘Bombas’ were designed and constructed to assist them in finding ENIGMA keys. Those ‘Bombas’ were probably the most complicated machines that had ever been constructed by then. The Nazi plans for the conquest of Poland were learned from deciphered ENIGMA messages, and accordingly in July 1939 the Polish intelligence agency passed all information about ENIGMA to the British and French intelligence services. The three mathematicians were evacuated to southern France and then to England, and all traces of the work done in Poland on decipherment of ENIGMA were destroyed. Hence, the Germans continued to broadcast ENIGMA messages openly.

On the basis of that Polish work, the British intelligence service created an institution at Bletchley Park, which succeeded in deciphering enormous quantities of German messages, including Hitler’s dispatches to his generals. That entire project was kept totally secret until 1974, yet the limited information released by the British government since then indicates that Bletchley Park was one of the most important aspects of World War Two.

Bletchley Park owed much to the English mathematician Alan Turing (1912–1954). He made a major contribution to mathematical logic in 1936 when he postulated a very simple type of machine for manipulating symbols. In modern terms, he showed that any calculating device with a conditional branching facility (an if-statement), and with potentially unlimited storage, is a completely general computer, capable of performing any well-defined transformation of symbols. He also proved that no program could possibly perform certain hypothetical types of computation. Turing’s work has had much influence on later development of computer hardware and software.

At Bletchley Park from 1939 to 1943, Turing led a team of scientists who extended greatly the Polish work on the mathematical analysis of ENIGMA ciphers, and who constructed very elaborate electromechanical devices to assist in that task. In 1945, at the National Physical Laboratory, he designed, in remarkably full detail, a very powerful electronic computer which he called ACE (Automatic Computing Engine). COLOSSUS, now generally regarded as the first true electronic computer, also grew out of Bletchley Park activities. In 1943 the German military command began using the Geheimschreiber, a machine much more advanced than ENIGMA, for enciphering their messages. At Bletchley Park the mathematician MHA Newman and the engineers T Flowers, SW Broadhurst and WW Chandler designed an electronic machine, enormously larger and more intricate than any attempted previously, to crack the new ciphers. The engineers accomplished miracles to get the first COLOSSUS working in December 1943. COLOSSUS had 1500 thermionic valves, and it read paper tape at 5000 characters per second! (When the reader was tested at 7000 characters per second, shreds of paper tape got embedded in the walls.) That first COLOSSUS was immensely successful in cracking the German ciphers.

In the United States two differential analysers had been installed at the Moore School of Engineering at the University of Pennsylvania in the 1930s. By 1942, those analogue computers could no longer cope with United States Army demands for artillery tables. The physicist John Mauchly and the engineer J Presper Eckert proceeded to design electronic replacements for various mechanical parts in order to speed up the operation; and they wound up by constructing a purely electronic digital computer with no moving parts at all (apart from a card reader and card punch).

The resulting Electronic Numerical Integrator and Computer (ENIAC), which operated from 1946 to 1955, was an incredibly ambitious machine. It occupied a large hall, it contained well over 19,000 thermionic valves, and it used over 200 kilowatts of power. Yet had storage capacity for only 20 variables, each of ten decimal digits, plus a few hundred constants set by hand-operated rotary switches. ENIAC was not programmed in the modern sense of the word, since it had been designed to emulate mechanical differential analysers. Rather, it was set up for any specific computation by the very laborious method of connecting conducting cables between thousands of sockets.

ENIAC was triumphantly successful — anything done by a mechanical differential analyser could be done by ENIAC in a thousandth of the time, and to much greater accuracy. Moreover, ENIAC was not only a digital electronic calculator, but it had evolved into a general-purpose computer with conditional branching facilities, and with potentially unlimited capacity available through punched cards.

In July 1944, the ENIAC team decided to start designing EDVAC, as a very much more powerful machine to succeed ENIAC. Late in 1944 they were joined by the eminent Hungarian-American mathematician John von Neumann (1903–1957), and he crystallized the various ideas for EDVAC into the concept of a general-purpose computer. As with Babbage’s design of 110 years previously there were a control device, input devices, a store, an arithmetic unit and output devices. Moreover, the store could contain the program to be executed, as well as numerical data (as in Turing’s paper of 1936). In order to operate at high speed, the computer should be made from electronic components. Almost every computer built since ENIAC has conformed to this general pattern, known as the von Neumann type computer.

In 1946 the plans for EDVAC were effectively publicized through a series of lectures given at the Moore School of Engineering. By the time that EDVAC eventually became operational in 1951, several stored-program electronic computers had been constructed in England, Australia and the United States.

The first stored-program electronic computer to operate, (apart from an extremely small test model at the University of Manchester) appears to have been the EDSAC, made by Maurice V Wilkes and his colleagues at Cambridge University. Wilkes had attended the Moore School lectures in 1946, and he designed EDSAC as a simplified model of EDVAC. EDSAC stored 512 35-bit words in mercury delay lines, it incorporated about 3000 thermionic valves, and it used a paper tape reader and punch. EDSAC provided a scientific computing service very successfully, from May 1949 to July 1958. A particularly valuable part of the EDSAC laboratory was the library of mathematical sub-routines developed by Wilkes, David J Wheeler and Stanley Gill, which had been very thoroughly documented.

The development of EDSAC had been supported by the English catering firm of J Lyons & Co Ltd; which operated the chain of Lyons Tea Shops. The LEO computer, a commercial version of EDSAC, began doing clerical computing for J Lyons & Co Ltd in 1951. That was the first recorded use of a commercial data-processing computer, the forerunner of the many thousands in use today.

In most forms of technological innovation, once the new technology has become established, its scale has grown exponentially with time, typically doubling about every ten to twenty years. After several such doublings the technology has usually settled down to a steadier state, or even started to decrease, as with railways.

For computers, the doubling period has typically been about two years, not 20! That estimate applies to most aspects by which merit can be measured — for example, cheapness, speed, capacity, compactness, reliability, convenience and economy of operation. This growth shows no signs of settling down to a steadier state: rather, during recent years, the doubling period has tended to decrease to about 1.5 years.

About 40 years have elapsed since the era of COLOSSUS and ENIAC, when computer technology became established. Accordingly, computer technology has been developed through about 20 doubling periods — giving a factor of approximately one million. And indeed it can plausibly be asserted that current computers are about a million times as good as the earliest specimens. Many readers will own microcomputers which are many times as powerful as COLOSSUS or ENIAC. No end to that progress can yet be seen, as long as humans are available to assist computers in designing and constructing the next generation of computers.

But perhaps we should give someone who spent not a little of his time in New Zealand the last word. In the early 1860s Samuel Butler, living in his hut on Mesopotamia sheep station by the upper Rangitata River, was studying Charles Darwin’s The Origin of Species (London 1859), and he wrote a series of Darwinian essays which were published in The Press, in Christchurch. Those essays evolved into The Book of the Machines, which forms the core of Erewhon (London 1872); the major literary and philosophical work written, partly at least, in New Zealand.

In The Book of the Machines, an Erewhonian philosopher considers the implications of humanity’s dependence upon machines.

It can be answered that even though machines should hear never so well and speak never so wisely, they will still always do the one or the other for our advantage, not their own; that man will still he the ruling spirit and the machine the servant … so that instead of being likely to be developed into a higher kind of life than man’s they owe their very existence and progress to their power of ministering to human wants, and must therefore both now and ever be man’s inferiors.

Are we not ourselves creating our successors in the supremacy of the earth? Daily adding to the beauty and delicacy of their organization, daily giving them more skill and supplying more and more 35 of that self-regulating, self-acting power which will be better than any intellect?

This is all very well. But the servant glides by imperceptible approaches into the master; and we have come to such a pass that, even now, man must suffer terribly on ceasing to benefit the machines.

Complex now, but how much simpler and more intelligibly organised may it not become in another 100,000 years? or in 20,000? For man at present believes that his interest lies in that direction; he spends an incalculable amount of labour and time and thought in making machines breed always better and better; …

As we contemplate the future we can be sure that Butler’s time span is going to be considerably shortened. But this is leading us into areas to be looked at in later chapters of the book. Let us leave it there for the moment.

Chapter 2: From monsters to micros

Anonymous (signed A. A. L; i.e. Augusta Ada Lovelace), ‘Sketch of the Analytical Engine invented by Charles Babbage Esq; by LF Menabrea of Turin. Officer of the Military Engineers; from the Bihliothèque Universelle de Geneve. October 1842, No. 82. With notes upon the Memoir by the Translator’, Taylor’s Scientific Memoirs, 3 (1843)

Beard, Maston & Pearcey, Trevor, ‘The genesis of an early stored-program computer: CSIRAC’. Annals of the History of Computing, 6 (1984)

Bromley, Allan G, ‘Charles Babbage’s Analytical Engine’, Annals of the History of Computing, 4 (1982)

Butler, Samuel, Erewhon, or, Over the Range, London, Chapman & Hall, 1872

Hawkins, William F, ‘The first calculating machine (John Napier, 1617)’, The New Zealand Mathematical Society Newsletter, 16 (1979), Supplement

Hodges, Andrew, Alan Turing: the Enigma, London, Burnett Books, 1983

Lavington, Simon H, Early British Computers, Manchester University Press, 1980

Mackie, W, A Noble Breed: The Auckland Racing Club, 1874–1974, Auckland, Wilson & Horton, 1975

Merzbach, Uta C, Georg Scheutz and the First Printing Calculator, Smithsonian Studies in History and Technology, No. 36, Washington DC; 1977

Metropolis, N & Worlton, WJ, ‘A trilogy of errors in the history of computing’, Proc. First U.S.A.-Japan Computer Conf., 3–5 Oct. 1972, Tokyo., AFIPS Inc; Montvale NJ, 1972

Randell, Brian (editor), The Origins of Digital Computers: Selected Papers (third edition), Berlin, Springer-Verlag, 1982

Rejewski, Marian, ‘How Polish mathematicians broke the ENIGMA cipher’, Annals of the History of Computing, 3 (1981). Translated from the Polish original, published in Annals of the Polish Mathematical Society, Series 2, Wiadomósci Matematyczne, 23 (1980)

Stewart, David & Minto, Walter, An Account of the Life, Writings and Inventions of John Napier of Merchiston, R Morrison, Perth, 1787

Tee, Garry John, ‘The pioneering women mathematicians’, Mathematical Chronicle 10 (1981), Reprinted in The Mathematical Intelligencer 5 (4) (1983)

—— ‘Two New Zealand mathematicians’ (LJ Comrie & AC Aitken), First Australian Conference on the History of Mathematics, Department of Mathematics, Monash University, Clayton, Victoria, 1981

—— ‘The heritage of Charles Babbage in Australasia’, Annals of the History of Computing, 5 (1983), Reprinted in The Word Te Reo (August 1983)

—— ‘Charles Babbage (1791–1871) and his New Zealand connections’, In Search of New Zealand’s Scientific Heritage, Bulletin 21, The Royal Society of New Zealand, Wellington 1984

Wilkes, Maurice V; Wheeler, David J & Gill, Stanley, The Preparation of Programs for an Electronic Digital Computer, Cambridge, Mass, Addison-Wesley Press, 1951. Facsimile edition by Tomash Publishers, Los Angles/San Francisco, 1982

References

Anonymous (signed A. A. L; i.e. Augusta Ada Lovelace), ‘Sketch of the Analytical Engine invented by Charles Babbage Esq; by LF Menabrea of Turin. Officer of the Military Engineers; from the Bihliothèque Universelle de Geneve. October 1842, No. 82. With notes upon the Memoir by the Translator’, Taylor’s Scientific Memoirs, 3 (1843)

Beard, Maston & Pearcey, Trevor, ‘The genesis of an early stored-program computer: CSIRAC’. Annals of the History of Computing, 6 (1984)

Bromley, Allan G, ‘Charles Babbage’s Analytical Engine’, Annals of the History of Computing, 4 (1982)

Butler, Samuel, Erewhon, or, Over the Range, London, Chapman & Hall, 1872

Hawkins, William F, ‘The first calculating machine (John Napier, 1617)’, The New Zealand Mathematical Society Newsletter, 16 (1979), Supplement

Hodges, Andrew, Alan Turing: the Enigma, London, Burnett Books, 1983

Lavington, Simon H, Early British Computers, Manchester University Press, 1980

Mackie, W, A Noble Breed: The Auckland Racing Club, 1874–1974, Auckland, Wilson & Horton, 1975

Merzbach, Uta C, Georg Scheutz and the First Printing Calculator, Smithsonian Studies in History and Technology, No. 36, Washington DC; 1977

Metropolis, N & Worlton, WJ, ‘A trilogy of errors in the history of computing’, Proc. First U.S.A.-Japan Computer Conf., 3–5 Oct. 1972, Tokyo., AFIPS Inc; Montvale NJ, 1972

Randell, Brian (editor), The Origins of Digital Computers: Selected Papers (third edition), Berlin, Springer-Verlag, 1982

Rejewski, Marian, ‘How Polish mathematicians broke the ENIGMA cipher’, Annals of the History of Computing, 3 (1981). Translated from the Polish original, published in Annals of the Polish Mathematical Society, Series 2, Wiadomósci Matematyczne, 23 (1980)

Stewart, David & Minto, Walter, An Account of the Life, Writings and Inventions of John Napier of Merchiston, R Morrison, Perth, 1787

Tee, Garry John, ‘The pioneering women mathematicians’, Mathematical Chronicle 10 (1981), Reprinted in The Mathematical Intelligencer 5 (4) (1983)

—— ‘Two New Zealand mathematicians’ (LJ Comrie & AC Aitken), First Australian Conference on the History of Mathematics, Department of Mathematics, Monash University, Clayton, Victoria, 1981

—— ‘The heritage of Charles Babbage in Australasia’, Annals of the History of Computing, 5 (1983), Reprinted in The Word Te Reo (August 1983)

—— ‘Charles Babbage (1791–1871) and his New Zealand connections’, In Search of New Zealand’s Scientific Heritage, Bulletin 21, The Royal Society of New Zealand, Wellington 1984

Wilkes, Maurice V; Wheeler, David J & Gill, Stanley, The Preparation of Programs for an Electronic Digital Computer, Cambridge, Mass, Addison-Wesley Press, 1951. Facsimile edition by Tomash Publishers, Los Angles/San Francisco, 1982