Samuel Morland

Very few people can afford to be poor.
George Bernard Shaw

Portrait of Sir Samuel Morland, by Peter Lely
Portrait of Sir Samuel Morland, by Peter Lely

The English polymath Samuel Morland invented in the early 1660s a total of three calculating machines: one for multiplication and division, one for trigonometry, and one for addition and subtraction. Morland’s calculating machines were simple but became rather popular and London instrument-makers were still selling Morland’s calculators as late as 1710.

Samuel Morland entered government service in 1653 when he was chosen to accompany a British diplomatic mission to the court of Sweden’s Queen Christina. Christina of Sweden was a noted patron of the sciences, and it was most likely at her court that Morland first became acquainted with the calculating machine of Blaise Pascal, who in 1652 placed at Queen’s disposal an example. This is probably the most important reason, why Morland became interested in the construction of calculating devices.

In his book, The description and use of two arithmetick instruments (published in 1673 in London), Morland described two invented by him calculating devices, which are working without charging the memory, disturbing the mind, or exposing the operations to any uncertainty. This is the first book on a calculator, written in English, and the first separate work on the subject after Napier’s Rabdologiae. The book may also be considered the first comprehensive book in computer literature, as Blaise Pascal published nothing about his own machine, except one 18-page pamphlet in 1644.

The description and use of two arithmetick instruments of Morland
The description and use of two arithmetick instruments of Morland

The Machina Nova Cyclologica Pro Multiplicatione of Morland

It seems the first calculating machine of Morland, devised probably in 1664, was so so-called multiplication machine, based on the principle of Napier’s bones. The device was described in the above-mentioned book of Morland under the name Machina Nova Cyclologica Pro Multiplicatione (A New Multiplying Instrument).

The sketch of the multiplication machine of Morland from his book <em>The description and use of two arithmetick instruments</em> (© United States Library of Congress)
The sketch of the multiplication machine of Morland from his book The description and use of two arithmetick instruments (© United States Library of Congress)

Morland ordered manufacturing of the device to the famous English mechanics Henri Sutton (London instrument-maker, active mainly between 1650 and 1661) and Samuel Knibb (1625-1674), and the particular machine, shown here, was donated by Morland himself to Grand Duke Cosimo III de’ Medici in 1679. The dedication to the Grand Duke contains an obvious error: it gives 1666 as the year of invention and 1664 as the year of manufacturing. Let’s examine the construction of the multiplication machine.

The multiplication machine of Morland (© Museo Galileo, Florence)
The multiplication machine of Morland, inside the case (© Museo Galileo, Florence)

In fact, the multiplication machine of Morland simplifies only the intermediate products, using the principle of Napier’s rods. There is no automatic or mechanical carry mechanism provided.

The device is made of silver, gilt, and silvered brass, wood, and crystal. The dimensions are 18 x 55.5 cm.

The digits from the ten Napier’s rods are inscribed across the periphery of 10 thin metal disks in such a manner, that units and tens of the rods are placed on the opposite ends of the circle (see the lower images for a closer view of the mechanism). There are two rows of axes in the device, the upper axes are fixed, while the lower can be rotated. In the row of windows, placed between the two axes can be set numbers, thus it serves as a mechanical memory. To perform a multiplication, the appropriate disk must be removed from the upper fixed axis and to be mounted to the lower working axis. Each of the lower axes is attached to a small pinion in the body of the machine, and this pinion is engaged with a toothed strip. This strip can be moved in the horizontal direction by means of the key, which can be seen in the lower right part of the lower figure, and its movement is marked by an arrow, which can be moved across a scale.

The multiplication machine of Morland , without the case (© Museo Galileo, Florence)
The multiplication machine of Morland, without the case (© Museo Galileo, Florence)

When the appropriate disks are set (according to the digits of the multiplicand), the lower part of the machine is covered by a lid, which has windows. The key must be rotated by the operator until the arrow comes to the digit of the multiplier on the scale, and during this rotation, the toothed strip will move and rotate the pinions, engaged with it. Thus in the lower row of windows can be seen the product. If the factors are multi-digital, then these actions must be repeated until all digits will be used.

For example, to multiply 23 by 7, the user would first take the discs for 2 and 3, place them on the central posts and close the door so that in the window the number 23 appears (3 in the left-most window and 2 in the left side of the second pair of windows). Then the user would turn the key until the pin on the slider scale pointed to 7. Each time the key is turned the discs are rotated once, which advances the display of the multiplication table for the selected numbers (2 and 3) by one. The windows are constructed so that a number on the leftmost edge of one disc appears next to the number on the rightmost edge of the next disc. The final answer must be obtained by adding the adjacent numbers in the windows, either with pen and paper or, as the inventor suggested, with the help of his instrument for addition. So, to finish the example, after discs 2 and 3 have been rotated 7 times, the numbers in the display window would read: 1 4 2 1. The final result is found by adding the adjacent digits to give 161.

The Machina Cyclologica Trigonometrica of Morland

Most probably in 1664, Samuel Morland invented a device, that can be used for trigonometric calculations, which he called the Machina Cyclologica Trigonometrica. The device was built in 1670 by John Marke (Maker of mathematical and astronomical instruments active in London between 1665 and 1679. Marke worked with Henry Sutton and succeeded him in 1665.) Materials used: silvered brass and silver, dimensions: 330×275 mm. The instrument is housed in an ebony case with a lid and engraved plate.

Trigonometric machine of Morland
Machina Cyclologica Trigonometrica of Morland (© Museo Galileo, Florence)

The trigonometric calculator of Morland allowed the operator to perform trigonometry by drawing out a problem and measuring the solution as with drawing instruments but without the need for pen and paper. It was a set of three rulers set into a divided circle that could be moved about using dials to form a triangle of any shape.

The device was used for determining the value of a trigonometric function (sine and cosine) of a known angle or, vice versa, for finding the value of an angle when its function is known. The instrument consists of a rectangular box holding a disk with a toothed circumference. At the center of the disk are mounted compasses with a fixed arm and a mobile arm rotating with the disk itself. Below are two smaller disks. The left-hand one shows the angle values. Its index is connected to the toothed circumference of the large disk and completes one revolution for every 30° traveled by the mobile compass arm. The right-hand disk shows the linear sine values. Its index is connected to the mobile horizontal rod on the upper half of the box and completes one revolution for every 25 units traveled by the rod on the side channels. The numbering of the horizontal rod and vertical channels basically represents the sine grid or reduction quadrant.

The machine for addition and subtraction of Samuel Morland

The adding machine of Samuel Morland (presented in the book as A new and most useful instrument for addition and subtraction of pounds, shillings, pence, and farthings…) was devised probably in 1665-1666, as four examples of the device survive to our time. The largest models can add up to one million, in either decimals or pounds, shillings, and pence.

The device (materials used are silver and brass), presented a true pocket calculator, measuring only 4 by 3 inches and less than a quarter of an inch thick (122 x 71 x 8 mm), weight 230 g. On page 12 of the book, Morland advertises that the instruments may be ordered from Humphry Adamson, living at Jonas Moore’s house in the Tower (Sir Jonas Moore was an English mathematician, surveyor, ordnance officer, and patron of astronomy, who warmly recommended the machines of Morland). Humphr(e)y Adamson was a very skillful English clock- and instrument-maker.

Morland's Adding Machine
Morland’s Adding Machine (© Science Museum Group Collection)

On the lid of the device are mounted 8 pairs of graduated dials. The scales of the dials are inscribed on the ring around them. The lower three scales are divided into 4, 12, and 20 parts and are inscribed and used for calculations in the English currency units of the 17th century—guinea (which was equal to 20 shillings), shilling (which was equal to 12 pennies), and penny (which was equal to 4 farthings). The upper five big dials have decimal scales and are inscribed with words unit, tens, hundreds, thousands, tenth.

Across the periphery of each big dial are made openings, according to the scale of the dial—4, 10, 12, or 20. In these openings can be put a stylus, and the dial can be rotated. During this rotation, in a little window in the upper part of each scale can be seen the appropriate number. Below each window is mounted a stop-pin, which is used for limiting the rotation during the adding operation. Over each big dial is mounted a smaller one, which serves as a counter to the revolutions of the big dial. For that purpose is used one-toothed gearing—the lower dial has one tooth, while the upper dial has ten teeth, so making a full revolution of the lower dial has as a result 1/10 revolution of the upper one.

Morland's Adding Machine, close view
Morland’s Adding Machine, close view (© Science Museum Group Collection)

The adding operation is performed by rotating the appropriate dials in the clockwise direction, pushing the stylus into the opening against the appropriate number, and turning the dial until the stylus will be stopped by the stop-pin. The subtraction can be done by rotating dials in the counter-clockwise direction, pushing the stylus in the opening below the window, and rotating the dial until it moves below the appropriate number.

The machine doesn’t have a tens carry mechanism, and this made it useless for practical needs. On 16 April 1668 Morland first printed short descriptions of his two adding devices in the London Gazette—As would now be expected, the adding instrument made its way into the pockets of modern young gentlemen (at a price of £3 10s).

Despite the excellent workmanship of the arithmetic devices of Morland, they were not very useful for practical needs, moreover, some of his contemporaries were not so fascinated by their usefulness also. Samuel Pepys (formerly Morland’s tutee at Cambridge from 1650, who did not think much of Morland) wrote in his 1667-8 years diary, that the machine of Morland is very pretty, but not very useful, while the famous scientist Robert Hooke, wrote in his diary for 31 January 1673: Saw Sir S. Morland’s Arithmetic engine Very Silly. The machines of Morland were, however, appreciated by King Charles II and Cosimo III de’ Medici, Grand Duke of Tuscany, which was more important for Morland as a typical courtier–inventor.

Portrait of Sir Samuel Morland, line engraving by P. Lombart from portrait by P. Lely

Biography of Samuel Morland

Samuel Morland was born in 1625 at Sulhamstead Bannister, near Reading in Berkshire, England. He was the son of Rev. Thomas Morland, a rector of the local parish church.

Morland entered Winchester School in Hampshire in 1638, and in May 1644, as a sizar (i.e. paying no fees but instead doing basic menial labor for the college between his studies) at Magdalene College, Cambridge. In 1649 he was elected a fellow of the society, and stayed there until 1653, but took no degree. While in College, Morland devoted much time to the study of mathematics, but he also became an accomplished Latinist and was proficient in Greek, Hebrew, and French (then the language of culture and diplomacy).

For the latter half of his time at university, Morland was a noted supporter of the Parliamentarian Party, and, from 1647 onward, he took part in student politics. In November 1653, he was included in the retinue of the English lawyer, writer, and parliamentarian Bulstrode Whitelocke, on an embassy to the Queen of Sweden for the purpose of concluding a military alliance. Whitelocke describes him as a very civil man and an excellent scholar; modest and respectful; perfect in the Latin tongue; an ingenious mechanist.

Morland as young
Samuel Morland a young

Upon his return from Sweden in July 1654, Morland was appointed as an assistant to John Thurloe, the secretary of the Lord Protector Oliver Cromwell. Later Cromwell appointed him as “commissioner extraordinary for the distribution of the collected moneys” and one of the clerks of the signet. In May 1655, Morland was sent by Cromwell to the King of France and to the Duke of Savoy to remonstrate with him on cruelties inflicted by him upon the sect of Waldenses or Vaudois, which had strongly excited the English public. Morland remained, for some time, in Geneva as an English resident, and his actions were highly appreciated after his return to England in December 1655.

Upon his return to England, Morland became intimately associated with the Government of the Commonwealth and he became a witness to several not-so-legitimate actions of his magnates, e.g. of Dr. Hewitt’s being “trepanned to death” in June 1658 by Thurloe and his agents. The most remarkable intrigue, however, which came to his knowledge was the so-called Sir Richard Willis’s Plot from the beginning of 1659. Its object was to induce King Charles II and his brother to effect a landing on the Sussex Coast, under the pretense of meeting their adherents and putting them both to death the moment they disembarked. This plot is said to have formed the subject of a conference between Cromwell, Thurloe, and Willis at Thurloe’s office, and the conversation was overheard by Morland, who pretended to be asleep at his desk. From this time, Morland endeavored to promote the Restoration and warned the King about the plot. In justifying to himself the abandonment of his former principles and associates, he observes that avarice could not be his object, as he was, at this time, living in greater plenty than he ever did after the Restoration, having a house well furnished, an establishment of servants, a coach, & co, and £1,000 a year to support all this, with several hundred pounds of ready money, and a beautiful young woman to his wife for a companion (in 1657, Morland married Susanne, daughter of Daniel de Milleville, Baron of Boissay in Normandy).

Sir Samuel Morland, painting from 1660-1661, artist Samuel Cooper
Sir Samuel Morland, painting from 1660-1661, artist Samuel Cooper

Morland officially joined the King’s party in May 1660, when in departed to Breda, bringing with him letters and notes of importance. The King welcomed him graciously and publicly acknowledged the services he had rendered for some years past, making him liberal promises of “future preferment” but these were, for the most part, unfulfilled. On 18 July 1660, Morland was made a baronet, being described as of Sulhamstead Bannister, although it does not appear very clear whether he was in possession of any considerable property in the parish. He was also made a Gentleman of the Privy Chamber; but this appointment, he says, was rather expensive than profitable, as he was obliged to spend £450 in two days on attending the ceremonies accompanying the coronation. He, indeed, obtained a pension of £500 from the post office, but his embarrassments obliged him to sell it, and, returning to his mathematical studies, he endeavored, by various experiments and the construction of machines, to earn a livelihood. But the King’s gratitude went no further. Morland was extravagant, sold his pension, wasted the proceeds in France, and ended as a beggar.

In 1666, Morland obtained, in conjunction with Richard Wigmore, Robert Lindsey, and Thomas Culpeper, a probably remunerative patent “for making metal fire-hearths”. From correspondence between Morland and Dr. Pell, it appears that about this same time (1666), the former had intended to publish a work “On the Quadrature of Curvilinear Spaces” and had actually proceeded to print part of it, but was happily persuaded, by Pell, to lay it aside. In carrying out his experiments in hydrostatics and hydraulics, Morland encountered many difficulties as a consequence of their expense. In December 1672, the King granted to him the sum of £260 to defray the charges of about five hundred looking-glasses “to be by him provided and set up in Olive wood frames for our special use and service,” as well as an annuity of £300 “in consideration of his keeping and maintaining in constant repair a certain private printing press… which by our Especial Order and Appointment he hath lately erected and set up”.

In 1681, Morland was appointed “magister mechanicorum” to the King, who, in recognition of his ingenuity, presented him with a medallion portrait of himself, set in diamonds, together with a medal as “an honorable badge of his signal loyalty”. In October 1684, the King advanced him £200 and, a year later, Morland received a similar sum by way of “bounty”.  According to his own account, his mechanical experiments pleased the King’s fancy; but when he had spent £500 or £1,000 upon them, he received sometimes only half, and sometimes only a third, of the cost.

In 1682, Charles II sent him to France “about the King’s waterworks,” but there also he seems to have lost more than he gained. On his return, King James II restored to him his pensions, which had been, for some reason, withdrawn and, likewise, granted him part of the arrears, but Morland was never repaid the expenses of the engine which he had constructed for bringing water from Blackmore Park, near Winkfield, to the top of Windsor Castle. In 1686, Morland was corresponding with Pepys about the new naval gun-carriages. In 1687, his pension was paid down to Lady Day 1689.

In 1689, Morland addressed a long letter to Archbishop Tenison, giving an account of his life, and concluding with a declaration that his only wish was to retire and spend his life “in Christian solitude”; and he begs the primate’s “helping hand to have his condition truly represented to his Majesty.” Tenison probably did something for him, as there is a letter of thanks for “favours and acts of charity,” dated 5 March 1695. The errors of his life were probably considerable, as he speaks of having been, at one time, excommunicated; but some of his writings show that he was a sincere penitent, particularly ‘The Urim of Conscience’ (1695), written, as the title says, “in blindness and retirement.”

Anne Fielding, Lady Morland
Anne Fielding, Lady Morland, third wife of Sir Samuel Morland

Morland married four times but was definitely not happy in his family life. In 1657 he married the Huguenot Susanne de Milleville, the beautiful daughter of Daniel de Milleville, seigneur de Boissay, Commissaire du roi au syndic provincial de Normandie, and Catherine de la Wespierre, his wife. They had three children (one son, Samuel), but Susanne died in 1668, when she returned with the children to France, mortally ill with dropsy (In his Sep. 1667 diary Samuel Pepys mentioned that they went to King’s Play House and …Here we saw Madam Morland, who is grown mighty fat but is very comely.)

Morland married secondly, on 26 October 1670, in Westminster Abbey, Carola Harsnett (1651-1674), daughter of Sir Roger Harsnett, knight. They had two children, but Carola died on 10 October 1674, aged 22. Morland married thirdly, on 10 November 1676, in Westminster Abbey, Anne Fielding (1661-1680), third daughter of George Fielding of Solihull, Warwickshire, by Mary, second daughter of Sir Thomas Shirley, knight, of Wiston, Sussex (Anne died on 20 February 1680, aged 19, leaving no issue). Lastly, Morland married, at the Knightsbridge Chapel, Middlesex, on 1 February 1687, Mary Ayliffe, a woman of low origin and infamous character, from whom he obtained a divorce for adultery on 16 July the following year.

Morland lost his sight about three years before his death. He died on 30 December 1695 and was buried in the Hammersmith Chapel on 6 January 1696. He must have been in an extremely weak condition, as he was unable to sign his will. By it, he disinherited his only son, Samuel (died Nov. 1716), who was the second and last baronet of the family, as the reason for this appears from a passage in a letter “I have been, in my youthful days, very undutiful to my parents, for which God has given me a son, altogether void of filial respect or natural affection”.

Charles Cotterell

You can easily judge the character of a man by how he treats those who can do nothing for him.
Malcolm Forbes

Cotterell Portrait

In 1667, Sir Charles Cotterell, an English courtier and translator, suggested a calculating instrument, called Arithmetical Compendium (Instrument for Arithmetick). It was a combination of Napier’s Bones with a bead-type abacus, used to avoid writing down the partial products of multiplication using the rods. In fact, Cotterell’s idea was popularized several years later, circa 1670, when Robert Jole (Jole was a scientific instrument maker, brother in the Clockmakers’ Company, who was active in London between 1664 and 1704), produced his version of the device.

Cotterell most probably knew and was influenced by Samuel Morland, who devised in the 1660s a total of three calculating machines, which were presented to King Charles II and the general audience.

Arithmetical Compendium of Cotterell
Arithmetical Compendium of Charles Cotterell (© National Museums Scotland)

The calculating instrument of Cotterell has a boxwood case (size: 184 mm x 59 mm x 19 mm, weight: 0.13 kg), and was made of brass (binding pieces), glass, iron, engraved paper, and vellum. There is a separate silvered brass tool, for pushing beads and lifting out rods.

Arithmetical Compendium of Cotterell
Arithmetical Compendium of Charles Cotterell in its boxwood case (© National Museums Scotland)

The user of Cotterell’s device would slide a window up and down to expose different parts of the times table, reading off the multiplicand on the edge of the instrument frame.

The box is inscribed with the text The Index of ye Quotient The Index of ye Multiplier Divisor Multiplic and The Fore Rule. The separate brass tool is inscribed with the text Robert Jole att ye Crowne Nere ye new Exchainge fecit.

Biography of Charles Cotterell

Charles Cotterell, portrait from 1660
Charles Cotterell, portrait from 1660 by Sir Peter Lely

Charles Cotterell (or Cottrell) was born on 7 April 1615 in Wilsford, Lincolnshire, England, and was baptized there two days later. He was the only son (there were four daughters) of Sir Clement Cotterell (1585–1631) and Anne Alleyne (d. 1660, an heiress and daughter of Henry Alleyne of Wilsford), who married in 1606.

Sir Clement Cotterell was appointed as muster-master of Buckinghamshire in 1616 and groom-porter to King James I in 1619, and was knighted in 1620. He was a Vice-Admiral of Lincolnshire from 1620 to 1631. In 1621, he was elected Member of Parliament for Grantham. In 1624 he was elected Member of Parliament again.

Charles Cotterell attended Queens’ College, Cambridge, from 1629 until 1632, but did not take any degree. In June 1632 he began touring Europe with aristocratic friends. Shortly after returning to England in 1634 he was engaged to take the Earl of Pembroke’s sons Charles and Philip Herbert on their travels. Though the tour was marred by the death of Charles, Cotterell entered Pembroke’s service on his return in 1636. Cotterell served the Earl of Pembroke under courtly and military service in the Cavalier army until knighted in Oxford in 1645.

In the early 1640s Cotterell served in the privy chamber troop against the Scots, and his real opportunity for advancement came with the death in July 1641 of the King’s master of the ceremonies, Sir John Finet. Sir Balthasar Gerbier had the reversion to Finet’s place and Cotterell replaced him as assistant master on 30 July. In December 1643 he was promoted to the rank of major and, having fought at Edgehill, at both battles of Newbury, and at Alresford, was knighted in Oxford on 21 March 1645.

The Cotterell Family, painted by Dutch artist Jan Mytens in 1657
The Cotterell Family, painted by Dutch artist Jan Mytens (Anne Cotterell obviously is missing, because she was left at nurse in England). The painting is said to be made in 1658, but this is very unlikely, because Cotterell’s wife Frances died in 1657, while their eldest daughter Frances died in December 1653.

In Oxford, Cotterell collaborated with William Aylesbury in translating Davila’s Storia delle guerre civile (published in 1647) from Italian. at the request of the king. In March 1649, after the king’s execution, Cotterell (along with his wife and elder daughter Frances (or Frank), born in 1646, as their infant daughter, Anne, born in 1648, remained in England), accompanied Aylesbury and the Duke of Buckingham into exile in Antwerp.

By 1652 Cotterell had moved to The Hague as steward to Elizabeth Stuart, Queen of Bohemia, while completing a translation of La Calprenède’s Cassandre. After resigning his stewardship in September 1655, Cotterell was appointed an adviser to the Duke of Gloucester, under whom he fought in three campaigns in Flanders.

In the summer of 1642, Charles Cotterell married Frances West (1621–1657), daughter of Edward West of Marsworth, Buckinghamshire, and half-sister of the architect Roger Pratt. They had three daughters and two sons: Frances (Frank), their eldest daughter, born in 1846, died on 31 December 1653; Anne Dormer (Cottrell) (1648-1695); Clement (1650-1672), their eldest son, was killed in a naval engagement against the Dutch at the Battle of Southwold Bay, in May 1672; Elizabeth Trumbull (Cottrell) (1652-1704); Charles Lodowick (1654–1710), followed his father as Master of the Ceremonies.

Sir Charles Cotterell by Robert Williams
Sir Charles Cotterell, by Robert Williams (© National Portrait Gallery, London)

On 29 May 1660, Cotterell returned with the royal party to London, with his children but without his wife Frances, who died around 1657, and was sworn Master of the Ceremonies on 5 June. The pursuit of a young widow, Anne Owen, led Cotterell to form a friendship with Katherine Phillips, whose husband was the Member of Parliament for Cardigan. Phillips was a young poet known in her salon as Orinda. Cotterell became a major figure in Orinda’s literary circle, and later took Phillips’s seat in Parliament from 1663 until 1678.

Sir Charles Cotterell resigned his seat as Master of the Ceremonies on 27 December 1686, in favor of his son Charles Lodowick. In 1693 he published a translation The Spiritual Year, a Spanish devotional tract.

Cotterell seems to have been well regarded by those who knew him. For example, the diarist and naval administrator Samuel Pepys described him as “ingenious”. The Italian historian and satirist Gregorio Leti lavished praise on him, believing he represented everything that any court in the world could seek in a master of ceremonies, describing him as “of kind disposition, soft and gentle, assiduous in his visits, of wise counsel, exemplary lifestyle, and the best conversation”.

After a sickness of some ten days, Charles Cotterell died at 6 p.m. on 7 June 1701 at his home in St Martin’s Lane, Westminster.

Salomon de Caus

Three Rules of Work: Out of clutter find simplicity; From discord find harmony; In the middle of difficulty lies opportunity.
Albert Einstein

Salomon de Caus

Jean Salomon de Caus was a French Huguenot engineer and scientist, who spent all his life moving across Europe. He worked as a hydraulic engineer and architect under Louis XIII from 1623 till his death in Paris in 1626. de Caus also was in service of the Prince of Wales and designed gardens in England, that of Somerset House among them. Salomon de Caus also designed the Hortus Palatinus, or Garden of the Palatinate, in Heidelberg, Germany (from 1614 till 1620 he was an engineer to the Elector Palatine, Frederick, at Heidelberg).

The book Les Raisons des Forces Mouvantes avec diverses machines tant utiles que plaisantes of de Caus
The book Les Raisons des Forces Mouvantes avec diverses machines tant utiles que plaisantes of de Caus

In 1615, de Caus published the book Les Raisons des Forces Mouvantes avec diverses machines tant utiles que plaisantes (The reasons for moving forces with various machines as useful as pleasant). It was an engineering treatise, which incorporated mechanical fountains, musical instruments, and other automata. His interest in these mechanical devices may have been influenced by the recovery of ancient texts by Heron of Alexandria around this time.

A water-driven organ, designed by de Caus for Hortus Palatinus
A water-driven organ, designed by de Caus for Hortus Palatinus

In his book, de Caus described an organ (see the upper image) in which a pegged cylinder, turned by a water wheel, activated levers that triggered bellows to force air through pipes.

A notable piece of work of de Caus was an automaton that had singing birds (see the picture below), directly influenced by a design by Heron. The birds flutter and chirp while an owl turns slowly toward them. When the intimidating owl faces the birds, they fall silent, but as he turns away, they resume their ruckus.

A water-driven singing bird automaton, designed by de Caus
A water-driven singing bird automaton, designed by de Caus
Another automaton of de Caus, a water-driven swan
Another automaton of de Caus, a water-driven swan

De Caus’s treatise also contains meticulous accounts of the mechanisms of hydraulic grottoes (small caves or caverns). In one (see the image below), Galatea rides astride a big seashell drawn by two dolphins. Behind her, Cyclops has put his club aside to play on a flageolet, while sheep gambol about. The mechanism is made entirely of wood, driven by two waterwheels, that are put in motion by jets of water from two pipes that emerge from a common reservoir. The pipes have valves that open and close alternately by means of a system of counterpoises so that the wheelwork turns one way and then the other as Galatea and her dolphins move back and forth across the scene. A third water wheel, through a train of gear wheels, drives a pinned barrel that is in turn connected with the keys of the flageolet.

Another automaton of Salomon de Caus, a hydraulic grotto
Another automaton of Salomon de Caus, a hydraulic grotto

Biography of Salomon de Caus

Salomon de Caus
Jean Salomon de Caus was born in 1576 in Dieppe, Normandy, into a Protestant family. The whole family moved to England, where Salomon obtained his education, studying painting, ancient languages, and mathematics. He was interested in engineering and architecture and studied ancient curiosities, such as the statue of Memnon and the Archite pigeons.

From 1595 till 1598 de Caus visited Italy, where he observed the garden of Bernardo Buontalenti in Pratolino in Florence with the mechanical arts and the Villa d’Este at Tivoli, near Rome. Inspired by Buontalenti he designed several gardens and related structures fountains, grottos, and machinery.

From 1600 till 1608 de Caus was an engineer (from 1605 “ingéniaire à la fontaine artificielle et en toutes autres choses que luy seront commandées”) at the court of the Austrian Archduke Albert VII of Habsburg, governor of the Netherlands, and his wife Isabella in Brussels.

During 1608 and 1609 de Caus was in London to teach drawing to Prince Henry, Prince of Wales, and to Princess Elizabeth, then continued his service at the court of King Charles I. Together with the architect Constantino de’ Servi he built water features and a picture gallery in Richmond Palace. De Caus built also gardens in Greenwich Park, Wilton House near Salisbury in Wiltshire, Hatfield House in Salisbury, and Somerset House (London), as well as some work in Richmond park, Gorhamburry, Camden House in Kensington.

In 1614, through the intervention of Princess Elizabeth Stuart, who had married Prince Elector Palatine, he answered the call to Heidelberg, to serve as the architect and engineer of Elector Friedrich V. De Caus was the architect of the part built under Frederick V at the Castle of Heidelberg. He was also the architect of Elisabethentors and the designer of Hortus Palatinus. This work occupied De Caus for some years and was not completed when, but he published in 1620 his complete designs in a work entitled Hortus Palatinus a Friderico Rege Boemiæ Electore Palatino Heidelbergæ exstructus.

He left Heidelberg for Rouen, then to Paris, in 1620, because of the war, to start in the service of Louis XIII, who employed him as “Engineer et architecte du Roy” (engineer and architect to the king) and was among others responsible for the sanitation and fountains.

Salomon’s brother, Isaac de Caus (1590–1648), also an engineer and landscape architect, is the creator of Hortus Penbrochianus (Wilton House) in 1615. Isaac also created several automata, similar to these of his brother, such as the water-powered machinery that counterfeited singing birds in Dieppe in 1617. In 1644 Isaac de Caus published a book, Nouvelle invention de level l’eau plus hault que sa source avec quelques machines mouvantes par le moyen de l’eau, et un discours de la conduite d’icelle, with print designs, which seem to have been taken directly from Salomon.

On 16 April 1606, Salomon de Caus married Esther Picart. On 24 February 1607, was born their son Guillaume.

Salomon de Caus died on 28 February 1626, in Paris, and was buried in cimetière de la Trinité.

William Pratt

The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.
G. K. Chesterton

The title page of Arithmeticall Jewell of William Pratt from 1617
The title page of Arithmeticall Jewell of William Pratt

A simple calculating device with the fancy name Arithmetical Jewell was designed by William Pratt in the middle 1610s, and described in the book of the same name (The Arithmeticall Jewell: or the use of a small Table Whereby is speedily wrought, as well all Arithmetical workes in whole Numbers, as all fractional operations, without fraction or reduction. Invented by William Pratt. Published by his Maiesties privilege, granted to the inventor, under the Great Seale of England), published in 1617 in London.

William Pratt, in association with John Harpur and Jeremy Drury, received a patent (privilege) on 27 March 1616, for the sole making of a table for casting accounts. The patent was for making a device “by which all questions arithmetical may be resolved without the use of pen or compters [counters]”. On 4 April 1616, the three men obtained a privilege for printing a book explaining an “instrument or table for cyfering and casting of accomptes”. Soon thereafter, the partners fell out, and published competing manuals of instruction: Harpur entered his in the Stationers’ Register on 8 March 1617, and Pratt on 21 June 1617.

The Arithmetical Jewell of Pratt is an instrument with a flat grid of semi-circular, rotating brass wedges, devised to facilitate addition, subtraction, multiplication, division, and the extraction of roots.

William Pratt was a mathematical practitioner and a member of the active circle of London’s mathematical teachers, close to the famous Gresham College, where the logarithms of Napier were popularized at that time.

The drawing of Arithmeticall Jewell of William Pratt from 1617
The drawing of Arithmetical Jewell of William Pratt from his book

Pratt’s device was nothing more than a rudimentary mechanical reconfiguration of the conventional reckoning technique: a portable, fancier, and gentlemanly adaptation of the century-old techniques of calculation like plume (manual calculations) and jetons of the abacus. With the exception here that you did not need paper to inscribe, for instance, the carry-over numbers of an addition; one could instead, using a small metallic stylus, “inscribe” them on the instrument’s appropriate sectors of brass. The reckoning method, nonetheless, was precisely the same as the plume and jetons.

The Arithmetical Jewell comprises two ivory-faced wooden tablets, with dimensions 122 mm x 65 mm x 5 mm each, put in tooled leather binding, 5″ x 3″, with a brass stylus 5 inches long. The weight of the device is only 0.14 kg. One tablet (below in the picture) has 14 columns, each with small brass parallel sectors, made from brass (copper, zinc alloy). The other has seven pairs of columns for laying out astronomical fractions to the base 60. Numbers are put in by moving the flags to reveal dots. Sums are then worked out with a pen and paper.

The Arithmeticall Jewell of William Pratt (© National Museums Scotland)
The Arithmetical Jewell of William Pratt (© National Museums Scotland)

There is a later account for Arithmetical Jewell by the English antiquary, natural philosopher, and writer John Aubrey (1626–1697):
Dr Pell told me, that one Jeremiah Grinken [a mathematical instrument maker] frequented Mr Gunters Lectures at Gresham College: He used an Instrument called a Mathematicall Jewell, by which he did speedily performe all Operations in Arithmeticke, without writing any figures, by little sectors of brasse [or some semi-circles] that did turn every one of them upon a Center. The Doctor has the booke… he told me, he thought his name is [William] Pratt.

Arithmetical Jewel in Science Museum Group Collection
The Arithmetical Jewell of William Pratt (© Science Museum Group Collection,

Jorge Luis Borges

I had found my religion: nothing seemed more important to me than a book. I saw the library as a temple.
Jean-Paul Sartre

Jorge Luis Borges
Jorge Francisco Isidoro Luis Borges Acevedo (24 August 1899 – 14 June 1986)

In 1939 the famous Argentine writer and librarian Jorge Luis Borges published in Buenos Aires an essay entitled La bibliotheca total (The Total Library), describing his fantasy of an all-encompassing archive or universal library.

A universal library is supposed to contain all existing information, all books, all works (regardless of format), or even all possible works. The Great Library of Alexandria is generally regarded as the first library approaching universality, in the classical sense, i.e containing all existing at the moment knowledge. It is estimated that at one time, this library contained between 30 and 70 percent of all works in existence. Universal libraries are often assumed to have a complete set of useful features (such as finding aids, translation tools, alternative formats, etc.)

As a phrase, the “universal library” can be traced back to 1545, when the Swiss scientist Conrad Gessner (1515-1565) published his Bibliotheca universalis. At the end of the 19th century, with the development of technologies, machines, and human imagination, appeared the idea of the device of a library which is universal in the sense that it not only contains all existing written works, but all possible written works. This idea appeared in Kurd Lasswitz’s 1901 story “The Universal Library” (Die Universalbibliothek), and was later developed by Borges.

In 1941, Borges enhanced his idea in the short story “The Library of Babel” (La biblioteca de Babel), conceiving of a universe in the form of a vast library containing all possible 410-page books of a certain format and character set.

Borges’ story of a universe in the form of a library, or an imaginary universal library, has been viewed as a fictional or philosophical predictor of characteristics and criticisms of the Internet.

The narrator of “The Library of Babel” describes how his universe consists of an endless expanse of interlocking hexagonal rooms, each of which contains the bare necessities for human survival—and four walls of bookshelves. Though the order and content of the books are random and apparently completely meaningless, the inhabitants believe that the books contain every possible ordering of just a few basic characters (letters, spaces and punctuation marks). Though the majority of the books in this universe are pure gibberish, the library also must contain, somewhere, every coherent book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books. The narrator notes that the library must contain all useful information, including predictions of the future, biographies of any person, and translations of every book in all languages. Conversely, for many of the texts some language could be devised that would make it readable with any of a vast number of different contents.

Despite — indeed, because of — this glut of information, all books are totally useless to the reader, leaving the librarians in a state of suicidal despair. However, Borges speculates on the existence of the Crimson Hexagon, containing a book that contains the log of all the other books; the librarian who reads it is akin to God.

Now, it seems we have already the device, which can create the Universal Library, and this is the computer. We still have not provided this device with the tools (intellect in the form of software, and some hardware resources) needed for the creation of this library, but sometime or another, this will happen.

Caroline Winter

Once made equal to man, the woman becomes his superior.

On 12 April 1859, a certain mysterious person, named C. Winter, of Piqua, from the county of Miami and the State of Ohio, received the 3-page US patent №23637 for Improved Adding-Machine, which was the fourth in the USA keyboard adder, after the machines of Parmelee, Castle and Nutz, and seventh in the world, after the machines of White, Torchi, and Schwilgué.

What makes this simple adding machine (in fact, a single column adding device. i.e. suitable for adding columns of numbers) a remarkable one is the fact, that (according to my personal investigation) its constructor is a woman, thus this machine is the first and the only mechanical calculator, devised by a woman. This remarkable lady was Caroline Winter from Piqua, a small town on the Great Miami River in southwest Ohio, developed along with the Miami and Erie Canal construction between 1825 and 1845.

Patent drawing of Caroline Winter's machine
Patent drawing of Caroline Winter’s machine (US patent No. 23637)

Almost nothing is known about the inventor of this machine—Caroline Winter. She was mentioned in the business directories for Piqua in 1859-60 and 1860-61 as the owner of a general store in the town. There is a tombstone in the Piqua’s Cedar Hill Cemetery of Caroline Winters, born in 1816, died on 8 Jan 1899 in Lima, Allen County, Ohio, at the home of her daughter—Amelia (Winters) Stein (1848-1932).

No doubt, Caroline Winter devised this machine to facilitate the tedious calculations in her store and trade business, as it is specified in the patent “It will be perceived that by the use of this machine figures may be added rapidly and always with perfect correctness.” Interestingly, the witnesses of her patent—Augustin Thoma and John B. Larger probably also significantly contributed to the creation of her machine. Note: Both of them were emigrants from Germany, as it was a large part of Piqua’s population in the middle of the 19th century. Caroline Winter was most probably also an emigrant from Germany because, in the United States Index to Passenger Arrivals, we can find two records (from 1833 and 1835) for women named Caroline Winter arriving in the USA from Germany.

John B. (Baptiste) Larger was a wealthy Piqua merchant (b. 1828 in Fellering, Departement du Haut-Rhin, Alsace, France), who unfortunately get killed young, when in early 1862 volunteered 32nd Regiment of Ohio Infantry to take part in Civil War, and was shot by a sniper in May 1862, while in camp.

Augustin (August, Augustus) Thoma (b. 3 Aug 1819 in Kappel (Lenzkirch), Baden, Germany, d. 30 Dec 1899 in Piqua, OH) was the founder of a successful jeweler’s business in Piqua (est. 1838), which was conducted by his descendants and survived up to 2010. He landed in New York at the age of 13 in 1832, served as an apprentice to a watchmaker, learned the trade, and in 1838 moved to Piqua to found his own jewelry business. Admittedly, Thoma was not only a good jeweler and merchant, but also a skillful instrument maker, and civic leader. He is a holder of three US patents—for a Jewelers Tool (pat. №67462 from 1867-08-06), for a Watch Jeweling Tool (№70049 from 1867-10-22), and for a Watch Maker Tool (№120618 from 1871-11-07), so we could easily imagine, that he was somehow involved in the construction of the Winter’s machine. Interestingly, Thoma had a daughter, named Caroline.

Winter's Keyboard Adder
Front view of the machine of Winter (© 2009 by Auction Team Breker, Koeln, Germany,

In contrast to the first US keyboard calculating machines (these of Parmelee and Castle), the machine of Caroline Winter survived to the present, in the form of the Original U.S. Patent Model (up to 1880, the Patent Office required inventors to submit a model with their patent application). At the beginning of our century, the device was a property of Auction Team Breker, Koeln, Germany (see the photos below) and was restored and sold in an auction in 2009 for $46480 to Arithmeum Museum in Bonn, Germany (I guess Auction Team Breker could eventually get a much better price if they knew my assumption that this is the first (and only) mechanical calculator, devised by a woman 🙂 Arithmeum recently uploaded a 3D animated video made by a student of Computer Science, showing the functionality of the machine in detail and also giving an impression of its operation and aesthetics (see Arithmeum video on Winter’s machine).

The size of the machine is 27 x 22 x 25 cm. The box is made from oak, with ivory key taps and two dial faces on the plate on top of the registers. The base part of the internal calculating mechanism is the big ratchet wheel (marked with K on the patent drawing), which is provided with 100 teeth, a smaller ratchet wheel (n, for counting hundreds), bevel-wheels j and i, pawls s and z, cord o, and pulley P. The dial plate on top of the box has two dials: a big dial B, divided into 100 divisions, and a smaller dial for counting hundreds C, which is within the big dial, and is divided into 6 divisions, thus the calculating capacity of the machine is up to 699.

Winter's adding machine 1859 rear view
Rear view of the machine of Winter (© 2009 by Auction Team Breker, Cologne, Germany,

The device has a resetting mechanism, presented by the lever (marked with c), which has its fulcrum at c’, slotted to embrace the shaft h, having a groove around it at the point of contact with the lever. d represents a spring secured to lever c, which serves to raise it again after being depressed.

The adding device of Caroline Winter doesn’t have a tens carry mechanism, and in fact, it doesn’t need it, because the smaller ratchet wheel (counting hundreds), rotates simultaneously with (and proportionally to) the bigger ratchet wheel (counting 1-99). However, when adding multidigit numbers, tens carry operations must be done manually, as it is described in the patent application.

Winter machine’s use of an elementary switching latch mechanism is characteristic since this mechanism had only been used in very few calculating machines before, for example, those made by Jean-Baptiste Schwilgué.

Blaise Pascal

I’ll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is — oh dear! I shall never get to twenty at that rate!
Alice in Wonderland, by Lewis Carroll

Blaise Pascal
Blaise Pascal (1623-1662)

The Roulette ou Roue Paschaline (celebrated as Pascaline in France and abroad) of the great french scientist Blaise Pascal was for more than three centuries considered the first mechanical calculator in the world, as the Rechenuhr of Wilhelm Schickard was not widely known until the late 1950s. Pascal most probably didn’t know anything about Schickard’s machine. It is more likely Pascal to have read the Annus Positionum Mathematicarum, or Problemata (courses covering geometry, arithmetic, and optics) of Dutch Jesuit mathematician Jan Ciermans (1602-1648), who mentioned in his courses, that there is a method with rotuli (normally rolls of parchment for writing upon, but could also intend the more modern diminutive for rota i.e. little wheels) with pointers, which enables multiplication and division to be done with a little twist, so the calculation is shown without error.

In 1639 Étienne Pascal, the father of Blaise Pascal was appointed by the Cardinal de Richelieu as Commissaire député par sa Majesté en la Haute Normandie (financial assistant to the intendant Claude de Paris) in Rouen, capital of the Normandy province. Étienne Pascal arrived in the city of Rouen in January 1640. He was a meticulous, forthright, and honest man, and spent a considerable amount of his time completing arithmetic calculations for taxes. The task of calculating enormous amounts of numbers in millions of deniers, sols, and livres necessitated ultimately the help of his son Blaise and one of his cousins’ sons, Florin Perrier (1605-1672), who would soon marry Blaise’s sister Gilberte.

Étienne was buried with work and he and his helpers were often up until two or three o’clock in the morning, figuring and refiguring the ever-rising tax levies. They used initially only manual calculations and an abacus (counting boards), but in 1642 the Blaise started to design a calculating machine. The first variant of the machine was ready the next year, and the young genius continued his work on improving his calculating machine.

In his later pamphlet (Advis necessaire) Pascal asserted: …For the rest, if at any time you have thought of the invention of machines, I can readily persuade you that the form of the instrument, in the state in which it is at present, is not the first attempt that I have made on that subject. I began my project with a machine very different from this both in material and in form, which (although it would have pleased many) did not give me entire satisfaction. The result was that in altering it gradually I unknowingly made a second type, in which I still found inconveniences to which I would not agree. In order to find a remedy, I have devised a third, which works by springs and which is very simple in construction. It is that one which, as I have just said, I have operated many times, at the request of many persons, and which is still in perfect condition. Nevertheless, in constantly perfecting it, I have found reasons to change it, and finally recognizing in all these reasons, whether of difficulty of operation, or in the roughness of its movements, or in the disposition to get out of order too easily by weather or by transportation, I have had the patience to make as many as fifty models, wholly different, some of wood, some of ivory and ebony, and others of copper, before having arrived at the accomplishment of this machine which I now make known. Although it is composed of many different small parts, as you can see, at the same time it is so solid that, after the experience of which I have spoken before, I assure you that all the jarring that it receives in transportation, however far, will not disarrange it.

The first several copies (certainly made by a local clockmaker in Rouen, it was a time when clocks and clockwork were celebrated, with even the Universe being considered, at least metaphorically, as being a form of clockwork) of the machine didn’t satisfy the inventor. Meanwhile, in 1643, it happened an event, which almost manage to give up Pascal from the machine. A clockmaker from Rouen dared, (according to the words of the offended inventor, who named no name—whether he knew it is unknown), to make a beautiful, but absolutely useless for work copy of the machine. Let’s look again at how is describing this event Pascal himself in his pamphlet (Advis necessaire):
…Dear reader, I have good reason to give you this last advice, after having seen with my own eyes a wrong production of my idea by a workman of the city of Rouen, a clockmaker by profession, who, from a simple description which had been given him of my first model, which I had made some months previously, had the presumption, to undertake to make another; and what is more, by another type of movement. Since the good man has no other talent than that of handling his tools skillfully and has no knowledge of geometry and mechanics (although he is very skillful in his art and also very industrious in many things which are not related to it), he made only a useless piece, apparently true, polished and well filed on the outside, but so wholly imperfect on the inside that it was of no use. Because of its novelty alone, it was not without value to those who did not understand about it; and, notwithstanding all these essential defects which trial shows, it found in the same city a place in a collector’s cabinet which is filled with many other rare and curious pieces. The appearance of that small abortion displeased me to the last degree and so cooled the ardor with which I had worked to the accomplishment of my model, that I at once discharged all my workmen, resolved to give up entirely my enterprise because of the just apprehension that many others would feel a similar boldness and that the false copies which they would produce of this new idea would only ruin its value at its beginning and its usefulness to the public. But, some time afterward, Monseigneur le Chancelier, having deigned to examine my first model and to give testimony of the regard which he held for that invention, commanded me to perfect it. In order to eliminate the fear which held me back for some time, it pleased him to check the evil at its root, and to prevent the course it could take in prejudicing my reputation and inconveniencing the public. This was shown in the kindness that he did in granting me an unusual privilege, and which stamped out with their birth all those illegitimate abortions which might be produced by others than by the legitimate alliance of the theory with art.

Later on, however, friends of Pascal presented to the Chancellor of France, Pierre Seguier (1588–1672), a prototype of the calculating machine. Seguier admired the invention and encouraged Pascal to resume the development. In 1645 Pascal wrote a dedicatory letter at the beginning of his pamphlet (the above-mentioned Advis necessaire) describing the machine (actually advertising the machine, as almost nothing is mentioned about its construction and operation) (see the letter and the pamphlet of Pascal), and donated a copy of the machine to the Chancellor (still preserved in CNAM, Paris). The text concluded that the machine could be seen in operation and purchased at the residence of Prof. Gilles de Roberval (Roberval was a friend of Étienne Pascal). This is the only preserved description of the device from the inventor.
The Chancellor Seguier continued to support Pascal and on 22 May 1649, by royal decree, signed by Louis XIV of France, Pascal received a patent (or privilege as it then was called) on the arithmetical machine, according to which the main invention and movement are this, that every wheel and axis, moving to the 10 digits, will force the next to move to 1 digit and it is prohibited to make copies not only of the machine of Pascal, but also of any other calculating machine, without permission of Pascal. It is prohibited for foreigners to sell such machines in France, even if they are manufactured abroad. The violators of the privilege will have to pay a penalty of 3 thousand livres (see the Privilege of Pascal).
The privilege again (as the Advise) mentions that Pascal has already produced fifty somewhat different prototypes. Moreover, the patent was awarded gratis and did not specify an expiration time, which was rather an unusual affair. It seems Pascal was an authentic favorite of the french crown 🙂

It seems later Pascal wanted to manufacture his machines as a full-scale business enterprise, but it proved too costly, and he didn’t manage to make money from this privilege. It’s not known how many machines were sold but the total was probably no more than ten or fifteen. Price may have been the main issue here, though accounts vary significantly, from the Jesuit mathematician François’s 100 livres to Tallemant de Réaux’s 400 livres and Balthasar Gerbier’s 500 livres (let’s mention, that 100 livres were enough to keep a seventeenth-century Frenchman in modest comfort for a year).

Pascal continued to experiment, constructing a lot of variants of the machine (later on called the Pascaline or Pascalene). He worked so hard on this machine, it is said, that his mind was disturbed (avoir latête démontée) for the next three years. According to his sister Gilberte, the young inventor’s exhaustion did not come from the labor he put into designing the machine, but rather in trying to make the Rouen artisans understand what it was all about.

Pascal decided to test the reliability of the machine, sending a copy on a long journey with carriage (from Rouen to Clermont and back, some one thousand kilometers) and the machine returned in perfect condition. Later he wrote: “Although [the Pascaline] is composed of many different small parts, as you can see, at the same time it is so solid that, after the experience of which I have spoken before of [‘carrying the instrument over more than two hundred and fifty leagues of road, without its showing any damage’], I assure that the jarring that it receives in transportation, however far, will not disarrange it.

Actually, the mechanism for tens carry is not very reliable and the machine has to be in a position, near to horizontal, in order to work reliably, and sometimes, a hit to the box can cause unwanted carry to be performed.

The Pascaline soon become well-known in France and abroad. The first public description was in 1652, in the newspaper Muse Historique. The machine was demonstrated to the public in Paris. Pierre de Ferval, a family friend and a mathematics professor at the Royal College of France, agreed to demonstrate the device to prospective customers in his apartment at the College Maitre Gervais every Saturday morning and afternoon. Pascal went to work writing advertising flyers for the invention and asked a friend, the poet Charles Vion Dalibray, to compose a publicity sonnet. The Polish queen Marie Louise de Gonzague, a high-ranking and keen patron of sciences, asked to buy two copies (her secretary Pierre Des Noyers already had a copy, and Polish monarchs were so fascinated by the device, that they wanted to buy two more). Another fan of science, Swedish queen Christina desired a copy to be granted to her. Pascal satisfied their desire (the device for queen Christina was sent together with a short manual), but soon after this lost his interest and abandoned his occasions with the calculation machine until the end of his short life.

A Pascaline from 1652
A Pascaline from 1652 (© Musée des Arts et Métiers, Paris)

Of some 50 constructed Pascalines, only 8-9 survived to the present day and can be seen in private or museum collections (4 in CNAM, Paris, 2 in a museum in Clermont, and several in private collections, e.g. in IBM).

The first copies of the machine were with five digital positions. Later on, Pascal manufactured machines with 6, 8, and even 10 digital positions. Some of the machines are entirely decimal (i.e. the scales are divided into 10 parts), and others are destined for monetary calculations and have scales with 12 and 20 parts (according to french monetary units: 1 sol = 12 deniers, 1 livre = 20 sols).

The dimensions of the brass box of the machine (for 8 digital positions variant) are 35.1/12.8/8.8 cm. The input wheels are divided by 10, 12, or 20 spokes, depending on the scale. The spokes are used for rotating the wheels by means of a pin or stylus. The stylus rotates the wheel until it gets to an unmovable stop, fixed to the lower part of the lid. The result can be seen in the row of windows in the upper part, where is placed a plate, which can be moved upwards and downwards, allowing to be seen the upper or lower row of digits, used for addition or subtraction.

Let’s examine the principle of action of the mechanism, using the lower sketch.

A sketch of the calculating mechanism of Pascalene
A sketch of the calculating mechanism of Pascalene

The input wheels (used for entering numbers) are smooth wheels, across which periphery are made openings. Counter-wheels are crown-wheels, i.e. they have openings with attached pins across the periphery.

The movement is transferred from the input wheel (marked with N in the sketch), which can be rotated by the operator by means of a stylus, over the counter, which consists of four crown-wheels (marked with B1, B2, B3, and B4), pinion-wheel (K), and mechanism for tens carry (C), to the digital drum (I), which digits can be seen in the windows of the lid.

The tens carry mechanism (called by Pascal sautoir), works in this way:
On the counter-wheel of the junior digital positions (B1) are mounted two pins (C1), which during the rotating of the wheel around its axis (A1) will engage the teeth of the fork (M), placed on the edge of the 2-legs rod (D1). This rod can be rotated around the axis (A2) of the senior digital position, and the fork has a tongue (E) with a spring. When during the rotating of the axis (A1) the wheel (B1) reaches the position, according to the digit 6, then pins (C1) will engage with the teeth of the fork, and at the moment, when the wheel moves from 9 to 0, then the fork will slide off from the engagement and will drop down, pushing the tongue. It will push the counter wheel (B2) of the senior position one step forward (i.e. will rotate it together with the axis (A2) to the appropriate angle. The rod (L), which has a special tooth, will serve as a stop, and will prevent the rotating of the wheel (B1) during the raising of the fork. The tens carry mechanism of Pascal has an advantage, compared e.g. to this of Schickard’s Calculating Clock, because it is needed only a small force for transferring the motion between adjacent wheels. This advantage, however, is paid for by some shortcomings—during the carrying is produced a noise, and if the box is hit, may occur unwanted carrying.

The wheels of the calculating mechanism are rotating only in one direction and there are no intermediate wheels provided (designated to reverse the direction of the rotation). This means, that the machine can work only as an adding device, and subtraction must be done by means of an arithmetical operation, known as a complement to 9. This inconvenience can be avoided by adding additional intermediate gear-wheels in the mechanism, but Pascal, as well as all the next inventors of calculating machines (Leibniz, Lepine, Leupold, etc.), didn’t want to complicate the mechanism and didn’t provide such a possibility.

The rotating of the wheels is transferred via the mechanism to the digital cylinders, which can be seen in the windows (see the photo below).

A view to the digital cylinders of Pascaline
A view to the digital cylinders of Pascaline

On the surface of cylinders are inscribed 2 rows of digits in this way, that the pairs are complemented to 9, for example, if the upper digit is 1, the lower is 8. On the lid is mounted a plate (marked with 2 in the lower sketch), which can be moved upwards and downwards and by means of this plate, the upper row of digits must be shown during the subtraction, while the lower one—is during the addition. If we rotate the wheels, we will notice that the digits of the lower row are changing in ascending order (from 0 to 9), while the digits of the upper row are changing in descending order (from 9 to 0).

Zeroing of the mechanism can be done by rotating of the wheels by means of the stylus in such a way, that between the two starting spokes (marked on the wheel) to be seen 9 (see the lower sketch). At this moment the digits of the lower row will be 0, while the upper digits will be 9 (or 12 or 20, for sols and deniers) (see the lower sketch). The manuscript Usage de la machine (this is the earliest known manuscript for Pascaline, from the 18th century. The first part of this document is a manual for an accountant and describes how to perform addition, subtraction, multiplication, and division.) gives the following method:
“Before starting a calculus, you shift the sliding cover that lays over the display windows toward the edge of the machine. Then you have to set the marked spokes in order to read “0” on all the drums. This is done by setting the stylus in between the spokes that are marked with white paper and by turning the wheel until the needle stops it. This brings for each wheel the highest digit the drum can have, that is to say, “9” for all the wheels devoted to the “Livres”, “19” on the “sols” wheel, and “11” on the “deniers” wheel. Then you turn the last wheel on the right of only one position […] afterward all the drums will display “0”.”

Zeroing of the mechanism of Pascaline
Zeroing of the mechanism of Pascaline

An instruction for work with the machine from Pascal didn’t survive to the present day, so different sources described different ways of manipulation. I will describe a way, which is optimal as a number of operations, needed for performing calculations. To use this way, however, the operator must know the multiplication table (during the multiplication operation), and be able to determine a complement to 9 for digits (for division and subtraction). This is an easy task even for 8 years old children now, but not for the men of the 17th century. Of course, the calculations can be done without following the two upper-mentioned requirements, but it will be necessary more attention and additional movements of the wheels.

First, let’s make an addition, for example, 64 + 83. We have to put the stylus between the spokes of the units wheels, against 4, and to rotate the wheel to the stop. In the lower row of windows (the upper was hidden by the plate) we will see 4. Then we rotate the wheels of the tens in the same way to 6. Then we have to enter the second addend, 83, and we will see the result, 147, meanwhile, one carry will be performed.

The subtraction will be a little more difficult and will require not only rotating but some mental work. Let’s make, for example, 182–93.

After zeroing the mechanism (to see 000 in the lower windows), the plate of the windows must be moved to the lower position, and at this moment in the windows can be seen the number 999. Then the minuend is entered as a complement to 9, i.e. the units-wheel is rotated for 7, the tens-wheel for 1, and the hundreds-wheel to 8 (the complement to 9 of 182 is 817). As the upper row of digits actually is moved to descending order, thus we have made a subtraction 999-817 and the result is 182 (see the lower sketch).

Subtraction with the Pascaline (first phase)
Subtraction with the Pascaline (first phase)

Then must be entered the subtrahend (93), making a subtraction 182–93 (during rotating of the wheels two carries will happen—during the entering of the units (3), the units wheel will come to 9, and a carry to the tens-wheel wheel will be done, moving the tens-wheel to 7; then during the entering of 9 to the tens-wheel, it will be rotated to 8, and a carry will be transferred to the hundreds-wheel, making it to show 0). So, we have the right result 182–93=089 (see the lower sketch).

Subtraction with the Pascaline (second phase)
Subtraction with the Pascaline (second phase)

It wasn’t that difficult, but the operator must be able to determine the complement to 9 of a number.

To be able to use the fastest way for multiplication, the operator must know (or use) a multiplication table. Let’s make the multiplication 24 x 38. First, we have to multiply (mentally or looking at the table) units of the multiplicand to the units of the multiplier (8 x 4 = 32) and enter the result 32 in the mechanism (see the lower sketch).

Multiplication with the Pascaline (first phase)
Multiplication with the Pascaline (first phase)

Then we have to multiply units of the multiplier to the tens of the multiplicand (8 x 2 =16), but to enter the result (16) not in the right-most digital positions (for units and tens), but in the next (the positions for tens and hundreds). This we will have the result 192 (32 + 160) (see the lower sketch).

Multiplication with the Pascaline (second phase)
Multiplication with the Pascaline (second phase)

Then we have to repeat the same operation for the multiplication of the units of the multiplicand to the tens of the multiplier (3 x 4 =12) and for the multiplication of the tens of the multiplier to the tens of the multiplicand (3 x 2 = 6), entering the intermediate results into wheels of tens and hundreds (12), and into the hundreds and thousands (06). We have the right result (912) (see the lower sketch).

Multiplication with the Pascaline (third phase)
Multiplication with the Pascaline (third phase)

The division with the Pascaline can be done in a way, similar to the manual division of the numbers—first, we have to separate the dividend into 2 parts (according to the value of the divisor). Then we have to perform consecutive subtractions of the divisor from the selected part of the dividend until the remainder will become smaller than the part. At this moment we have to write down the number of subtractions, this will be the first digit of the result. Then we have to attach to the remainder (if any) 1 or more digits from the remained part of the dividend and start again the consecutive subtractions until we receive the second digit of the result and to continue this operation again and again until the last digit of the dividend will be used. In the end, we will have the remainder of the division in the windows, while the result will be written.

It’s quite obvious, that the work with the Pascaline is not very easy, but the machine is completely usable for simple calculations.

Some people at the time almost suggest Pascal was in possession of some kind of magical powers during his work on Pascaline. e.g. in Entretien avec M. de Sacy: It was common knowledge that [Pascal] seemed able to animate copper, and to give to brass the power of thought. Little unthinking wheels, each rimmed with then ten digits, were so arranged by him that they could give accounts even to the most reasonable persons, and he could in a sense make dumb machines speak.

Pierre Petit (1617–1687)—a French scholar and an inventor of a tool with Napier’s rods wrote: I find that since the invention of logarithms and rabdology, nothing of significance occurred regarding the practice of numbers other than Monsieur Pascal’s instrument. It is a device truly invented with as much success and speculation as his author has intelligence and knowledge. It consists, however, in a number of wheels, springs, and movements, and one needs the head and hands of a good clockmaker to understand how it works and to manufacture it, as well as the skills and knowledge of a good arithmetician to operate it. [For all these reasons], one fears that its use will never become widespread and that instead of being employed in financial bureaux and regional administrations to calculate taxes, or in merchant offices to compute their rules of discount and company, [the machine] will be stored in cabinets and libraries, there to be admired.

Admittedly, not all impressions from Pascal’s contemporaries were positive. Some were unfavorable, such as the October 1648 letter of the English gentleman traveler Balthasar Gerbier to Samuel Hartlib. Gerbier came upon Pascaline not long after a model in wood was finished, and thought it resembled something invented in England 30 years earlier. (Gerbier most likely meant William Pratt’s Arithmetical Jewel from 1616, a simple calculating instrument, that was nothing more than a variant of the common abacus). Gerbier though found many problems with Pascaline.

First, its user had to be knowledgeable in arithmetic, which ran contrary to Pascal’s rhetorical stance. Multiplications and divisions were complicated and it even took two Pascalines to make a simple rule of three. Gerbier also found Pascaline rather big (two feet in length, 9 inches broad), heavy, difficult to move, expensive (50 pistoles, or 500 lives), and useless to anyone who would like to learn the art of arithmetic. In other words, Gerbier did not admire this mechanical contraption supposed to “think” by itself. He ended his letter to Hartlib quoting a former ruler of Netherlands: Infine a Rare Invention farre saught, and deare baught: putt them jn the Storre house was the old Prince of Orange wont to saye and lett us proceede on the ordinary readdy way.

Pascaline was described in many other sources also, e.g. in the 18th century books of Jean Gaffin Gallon—Machines et inventions approuvées par l’Academie Royale des Sciences, depuis son établissment jusqu’a présent; avec leur description (see description of Pascaline from Gallon).

Jacques de Vaucanson

My second machine, or automaton, is a duck… The duck stretches out its neck to take corn out of your hand; it swallows it, digests it, and discharges it digested by the usual passage.
Jacques Vaucanson, letter to Abbe´ Desfontaines, 1738

Jacques de Vaucanson
Jacques de Vaucanson (1709-1782)

Jacques de Vaucanson (1709-1782) was a great French engineer and one of the significant inventors of the 18th century, who is primarily credited with creating the world’s first “true” robots in the early 1730s, as well as for creating the first completely automated loom, and the first all-metal lathe in late 1740s.

Jacques Vaucanson was the tenth child of a poor glove-maker from Grenoble. As a little boy, Jacques quickly revealed his talent by fixing the watches and clock mechanisms of his neighbors, constructing a clock and a small automaton-priests that duplicated a few of the ecclesiastical offices. Therefore, his family initially wanted Jacques to become a clockmaker but was forced in 1715 to send him to study at the Jesuit school in Grenoble (now Lycée Stendhal). In 1725 Vaucanson took orders and joined the Les Ordre des Minimes in Lyon. In 1728 Vaucanson decided to leave the monastery to devote himself to his mechanical interests and departed to Paris, where he remained until 1731. There he studied medicine and anatomy at the Jardin du Roi, being encouraged and supported by the Parisian financier Samuel Bernard (1651-1739), one of the wealthiest men of his time.

In 1731 Vaucanson left Paris for Rouen, where he met the famous surgeon and anatomist Claude-Nicolas Le Cat (1700-1768), whose own interests in replicating human anatomical forms and movements likely stimulated Vaucanson to begin work on his first automaton. Later Vaucanson met another famous French surgeon and economist, François Quesnay (1694-1774), who also encouraged him to create artificial creatures in order to put in evidence most of the human or animal biological functions. Thus the young Vaucanson decided to further develop his knowledge in anatomy by making living anatomies.

In 1732 Vaucanson traveled around France exhibiting his first automaton which he described as “a self-moving physical machine containing many automata, which imitate the natural functions of several animals by the action of fire, air, and water.”

In 1733, Vaucanson signed a contract to build and exhibit another automaton with Jean Colvée (1696-1750), a man of the cloth whose interests included chemistry, natural history, geography, and various business ventures. In 1736 however, having squandered funds supplied by Colvée, Vaucanson signed an agreement with a Parisian gentleman, Jean Marguin, to build an automated flute player in exchange for financial support—Marguin would retain one-third ownership of the completed automaton and receive half the money taken in when it was exhibited. Thus Vaucanson devoted himself to his first android musician, The Flute Player, which he finished in 1737, and demonstrated to the French Academie in April 1738. Later in 1738, he opened an exhibition to the public first at the fair of Saint-Germain, then in a rented hall, the grand salle des quatre saisons at the Hôtel de Longueville in Paris, in which presented initially only The Flute Player, but at the end of the year added two other automata, the Duck and the Tambourine Player.

Vaucanson 3 Automata
The Flute Player, the Duck, and the Tambourine Player. From the prospectus of the 1738 exhibition of Vaucanson’s automata, Vaucanson, Le Mecanisme du fluteur automate.

Despite the substantial admission ticket (three livres, a week’s salary for a worker at that time), the exhibition was a triumph. In addition to making money, the three automata captured the fancy of Voltaire, who celebrated Vaucanson as Prometheus’s rival and persuaded Frederick the Great to invite their maker to join his court, but the inventor denied it, because Louis XV also supported him. When the visitors decreased Vaucanson started a triumphant wide tour through France, and then to Italy and England.

The Flute Player was a life-size (178 cm tall) figure of a shepherd, dressed in a savage, that played the transverse flute and had a repertoire of twelve songs (in the nearby image you can see the inner workings of Vaucanson’s flute player). The tune was played on a real instrument, a mechanism moves the lips and fingers of the player and pumps air through his mouth. The fingers are carved in wood with a piece of leather at the point where they cover the holes. The entire figure is made of wood with the exception of the arms which are made of cardboard.

The Flute Player was seated on a rock put on a pedestal, like a statue. The case, enclosing a large part of the weight engine mechanism, housed a wooden cylinder (56 cm in diameter and 83 cm in length), which turned on its axis. Covered with tiny protrusions, it sent impulses to fifteen levers, which controlled, by means of chains and strings, the output of the air supply, the movements of the lips, the tongue as well as the articulation of the fingers.

The flute player of Vaucanson
The Flute Player of Vaucanson

In the same 1738 Vaucanson presented The Flute Player to the French Academy of Science. For this occasion, he wrote a lengthy report—a dissertation entitled “Mechanism of the automaton flute player” (“Mécanisme du flûteur automate”), carefully describing how his automaton can play exactly like an alive person. These were the Academy’s conclusions: The Academy has heard the reading of a dissertation written by M. Jacques de Vaucanson. This dissertation included the description of a wooden statue playing the transverse flute, copied from the marble fauna of Coysevox. Twelve different tunes are played with a precision which merited the public attention, and to which many members of the Academy were witnesses. The Academy has judged that this machine was extremely ingenious; that the creator must have employed simple and new means, both to give the necessary movements to the fingers of this figure and to modify the wind that enters the flute by increasing or diminishing the speed according to the different sounds, by varying the position of the lips, by moving a valve which gives the functions of a tongue, and, at last, by imitating with art all that the human being is obliged to do. Moreover, M. Jacques de Vaucanson’s dissertation had all the clarity and precision of which this machine is capable, which proves both the intelligence of the creator and his extensive knowledge of all the mechanical parts.

As we already mentioned, in the same 1738, Vaucanson created two additional automatons, The Tambourine Player and The Digesting Duck (Canard Digérateur), which is considered his masterpiece.

There is very little information on The Tambourine Player. The automaton stood on its pedestal, like The Flute Player. The Tambourine Player was a life-sized man dressed like a Provençal shepherd, who could play 20 different tunes on the flute of Provence (also called galoubet) with one hand, and on the tambourine with the other hand with all the precision and perfection of a skillful musician. It must have been equipped with a very complex mechanism, because it could play two different musical instruments and, according to Vaucanson, the galoubet was the “most unrewarding and inexact instrument that exists.” Besides, he made the following note: “A curious discovery about the building of this automaton is that the galoubet is one of the most tiring instruments for the chest because muscles must sometimes make an effort equivalent to 56 pounds…”.

The Digesting Duck was Vaucanson’s masterpiece, and it was a very remarkable machine for its time. Interestingly, in 1733, several years before Vaucanson, a similar automaton was presented to the Paris Academy of Sciences by a mechanician named Maillard. Maillard’s Cygne artificiel (artificial swan) sported a mechanical paddle wheel and gears to navigate through the water while turning its head from side to side, reproducing the motion of a swimming duck. The device was described in Gallon’s “Cygne artificiel,” Machines, 7 vols., from 1735.

The Digesting Duck of Vaucanson
The Digesting Duck of Vaucanson

Vaucanson’s Duck was made of gilded copper and had over 400 moving parts, and could quack, flap its wings, drink water, digest grain, and defecate like a living duck. Although Vaucanson’s duck supposedly demonstrated digestion accurately, his duck actually contained a hidden compartment of “digested food”, so that what the duck defecated was not the same as what it ate. Although such “frauds” were sometimes controversial, they were common enough because such scientific demonstrations were needed to entertain the wealthy and powerful to attract their patronage. Vaucanson is credited as having invented the world’s first flexible rubber tube while in the process of building the duck’s intestines. Thanks to the open structure of its abdomen, the audience could even follow the digestive process from the throat to the sphincter which ejected a sort of green gruel.

Vaucanson provided his own description of his duck: …a duck, in which I show the mechanism of the viscera employed in the functions of drinking, eating, and digestion; the way in which all the parts required for these actions function together is imitated precisely: the duck extends its neck to take the grain out of the hand, it swallows it, digests it and expels it completely digested through the usual channels; all the movements of the duck, which swallows precipitously and which works its throat still more quickly to pass the food into its stomach, are copied from nature; the food is digested in the stomach as it is in real animals, by dissolution and not by trituration, as a number of physicists have claimed it; but this is what I intend to demonstrate and show upon that occasion. The material digested in the stomach passes through tubes, as it does through the entrails in the animal, to the anus, where there is a sphincter to allow its release.
I do not claim that this digestion is perfect digestion, able to make blood and nourishing particles to nurture the animal; to reproach me for this, I think, would show bad grace. I only claim to imitate the mechanics of this action in three parts which are: firstly, swallowing the grain; secondly, macerating, cooking, or dissolving it; thirdly, expelling it in a markedly changed state.
However, the three acts needed means, and perhaps these means will deserve some attention from the persons who would demand more accuracy. They will see the expedients that we used to make the artificial duck take the grain, suck it up into its stomach, and there, in a little space, build a chemical laboratory, to break down the main integral parts from it, and make it go out with no limit, through some convolutions of pipes, at an all opposed end of its body.
I think that attentive people will understand the difficulty to make my automaton perform so many different movements; for instance, when it rises up onto its feet, and it steers its neck to the right and to the left. They will know all the changes of the different fulcrums; they will even see that what acted as a fulcrum for a mobile part, becomes then mobile on this part which becomes fixed itself. At last, they will discover an infinity of mechanical combinations.

At the time, mechanical creatures were somewhat of a fad in Europe, but most could be classified as toys, and de Vaucanson’s creations were recognized as being revolutionary in their mechanical life-like sophistication. In spite of the considerable success of his three automata, Vaucanson tired of them quickly and sold them in 1743 to some entrepreneurs from Lyon, who toured with them for nearly a decade, showing them throughout Europe. Admission was always charged at these exhibitions and the automata appear to have brought in considerable revenue. Unfortunately, none of this survived to the present time. The musician automatons were lost or destroyed at the beginning of the 19th century, while the duck burnt in a museum in Krakow, Poland in 1889. For nearly 40 years, however, until his death in 1782, Vaucanson worked on the plan to make “an automaton’s face which would closely imitate the animal processes by its movements: blood circulation, breathing, digestion, the set of muscles, tendons, nerves, and so far…”

In 1741 Vaucanson was appointed by Cardinal André-Hercule de Fleury, chief minister of Louis XV, as inspector of the manufacture of silk in France. He was charged with undertaking reforms in the silk manufacturing process because at the time, the French weaving industry had fallen behind that of England. In 1742 Vaucanson promoted wide-ranging changes for the automation of the weaving process. Between 1745 and 1750, he created the world’s first completely automated loom, drawing on the work of Basile Bouchon and Jean Falcon, who he probably knew from his life in Lyon in the 1720s. However, Vaucanson’s loom was not successful, his proposals were not well received by weavers, who pelted him with stones in the street and eventually lead to strikes and social unrest in Lyon.

A reconstruction of Vaucanson's loom (© CNAM, Paris)
A reconstruction of Vaucanson’s loom (© CNAM, Paris)

In the mechanism of Vaucanson’s loom, the hooks that were to lift the warp threads were selected by long pins or needles, which were pressed against a sheet of punched paper, that was draped around a perforated cylinder. Specifically, each hook passed at a right angle through an eyelet of a needle. When the cylinder was pressed against the array of needles, some of the needles, pressing against the solid paper, would move forward, which in turn would tilt the corresponding hooks. The hooks that were tilted would not be raised, so the warp threads that were snagged by those hooks would remain in place; however, the hooks that were not tilted, would be raised, and the warp threads that were snagged by those hooks would also be raised. By placing his mechanism above the loom, Vaucanson eliminated the complicated system of weights and cords (tail cords, pulley box, etc.) that had been used to select which warp threads were to be raised during weaving. Vaucanson also added a ratchet mechanism to advance the punched paper each time the cylinder was pushed against the row of hooks.

The idea behind the loom of Vaucanson was ingenious and technically sound, the prototypes also worked reasonably well. The problem, though, was that the metal cylinders were expensive and difficult to produce. Moreover, by their very nature, they could only be used for making images that involved regularly repeated designs. Obviously, by switching to new cylinders it is possible to produce designs of open-ended variety, but in practice, the switching over of cylinders proved too time-consuming and laborious. A few examples of the loom went into production, but it never really caught on and was soon discontinued.

Moreover, in 1741 Vaucanson commenced a project, to construct an automaton figure that simulated in its movements the animal functions, the circulation of the blood, respiration, digestion, the operation of muscles, tendons, nerves, etc. However, this was a too ambitious project. In 1762, he began to work on the more modest project of a machine, that would simulate just the circulation of the blood, using rubber tubes for veins. But this project, too, remained unrealized, because of inadequacies in contemporary rubber technology.

Jacques de Vaucanson was one of the significant inventors of the 18th century. In 1740 he demonstrated a clockwork-powered carriage. He is known as the builder of one of the first all-metal slide rest lathes (in 1750), the precursor of the machine tools that will be developed during the 19th century. He was also one of the first, who used rubber in his machines. In 1770 he developed the first western chain drive, which is used in silk reeling and throwing mills.

Biography of Jacques de Vaucanson

Jacques de Vaucanson (1709-1782)
Jacques de Vaucanson (1709-1782)

Born as Jacques Vocanson (the particle de was added to his name in 1746 when he was made a member of the Académie des Sciences) on 24 February 1709 in the French town of Grenoble, he was the tenth child of the poor glove-maker Jacques Vocanson, born in Toulouse, and his wife Dorothée La Croix.

From an early age, Jacques quickly revealed his talent by fixing the watches and clock mechanisms of his neighbors, constructing a clock and a small automaton-priests that duplicated a few of the ecclesiastical offices. Therefore, his family initially wanted Jacques to become a clock-maker but was forced in 1715 to send him to study at the Jesuit school in Grenoble (now Lycée Stendhal), then in Collège de Juilly from 1717 to 1722. In 1725, influenced by his mother, Vaucanson took orders and joined the Les Ordre des Minimes in Lyon.

There is an interesting legend for Vaucanson from this period: It seems despite his interest to follow a course of religious studies, Vaucanson retained his interest in mechanical devices, because in 1727, being just 18 years of age, he was given his own workshop in Lyon, and a grant from a nobleman to construct a set of machines. In the same 1727, there was a visit from one of the governing heads of Les Ordre des Minimes. Vaucanson decided to make some automata, which would serve dinner and clear the tables for the visiting politicians. However, one government official declared that he thought Vaucanson’s tendencies “profane”, and ordered that his workshop be destroyed.

Vaucanson's house, 51 rue de Charonne, 11th arrondissement, Paris
Vaucanson’s house, 51 rue de Charonne, 11th arrondissement, Paris, a photo from May 1889

Around 1730 a big influence on young Vaucanson appeared to apply Claude-Nicolas Le Cat (1700–1768), an eminent French surgeon and science communicator, who taught him anatomy, wherefore it became easier to construct devices that would mimic biological functions.

Jacques de Vaucanson married to Madeleine Rey on 8 August 1753, in Paris. They had one daughter, Angélique Victoire de Vaucanson (7 November 1753 – 15 August 1820).

Toward the end of his life, Vaucanson collected his own and others’ inventions in what became in 1794 the Conservatoire des Arts et Métiers (Conservatory of Arts and Trades) in Paris; it was there that Joseph-Marie Jacquard found his automatic loom.

Jacques de Vaucanson died aged 73 years old on 21 November 1782 in his house, 51 rue de Charonne, 11th arrondissement, Paris.

Luigi Torchi

Acknowledgement to my correspondent Mr. Silvio Hénin, Milan, Italy, for his pioneering work on Torchi’s calculating machine.
Georgi Dalakov

The machine of the Italian Luigi Torchi from Milan was the first full-keyboard/direct multiplication machine in the world, moreover, it was the first practical keyboard calculator, as the earlier key-driven adding machine, described by the English engineer James White, seems to remain only on paper. Some 40 years will be needed for the direct multiplication machine to be reinvented by the American Edmund Barbour in 1872.

In 19th century, in Milan operated the R.I. Istituto Lombardo Veneto di Scienze, Arti e Lettere (Royal Imperial Lombard-Venetian Institute of Sciences, Arts and Letters), founded by Napoleon in 1797. Among the initiatives of this body, there was the institution of the Premj d’Industria (Prizes for Industry), awarded every year to those entrepreneurs and firms that achieved distinction in their areas of activity. In 1834 the Golden Medal was awarded to the local carpenter Luigi Torchi for the invention and construction of a Macchina pei Conteggi (counting machine). In charge of the assignment were the mathematician Gabrio Piola and the astronomer Francesco Carlini.

The Acts of the Solemn Distribution of Prizes include:
A young carpenter named Louigi Torchi… with no more than a tincture in the science of numbers, driven only by the strength of his ingenuity, imagined and performed with the petty means that he had at his disposal, pieces of wood and iron wire, a species of that machine which will perform the arithmetic operations, which first imagined Pascal, and after him few other mechanical and mathematical disciples…

In the following years, the arithmetic machine enjoyed a high local reputation, to the point that Torchi’s name was listed among the “Italians distinguished in science, literature, and the arts”.

Francesco Carlini was so enthusiastic about Torchi’s machine to ask the Government for an appropriation to build a more reliable metal model for the activities of the Brera’s Astronomical Observatory. On 6 May 1840, the Government confirmed the authorization with the following letter: “The Government authorizes the direction of the Imperial Royal Observatory to build the machine for counting, imagined by the carpenter Torchi, for the amount of 1000 Lire.” Carlini summoned Torchi: “I invite you to meet me in order to take the concert and fix the price”. At this point the story seems to come to an end, every trace of the machine is lost and we do not know if Torchi replied to Carlini’s letter or ever accepted the proposal, but it seems the improved metal exemplar was never built.

Thirty-two years later, in 1872, the famous Italian astronomer Giovanni Schiaparelli (who first described the canals on Mars) examined what remained of Torchi’s machine and found it “lacking many pieces, almost all the front part containing the device for the preparation [the keyboard] and the reading of the results is missing”. Schiaparelli concluded that “the completion and repair require not only to examine the machine to get an idea of the nature of its mechanism but also a long and expensive work of a clever craftsman”.

The ingenuity of Luigi Torchi revealed itself in another instance. In 1835 he invented a horse-less cart, exploiting the energy of the water stream, that moved along the canal towing-path, dragging the barge. An experiment was performed in October 1835 in the presence of H. M. the Viceroy: the boat and the barge went along a 212 meters stretch in 13 minutes and 25 seconds (0.948 Km/h). For this achievement, in 1837 Torchi was awarded another prize by the Institute, the Silver Medal. The fame of this invention spread as far as France, as it can be read in an article in the Mémorial encyclopédique et progressif des connaissances. Another known to us invention of Torchi is an improved “pendulum level” from 1858.

Almost nothing has been published on the mechanism of Torchi’s calculator. Most of the sources available just praise the machine, e.g. in Piola and Carlini’s report of the award: “It [the machine] responds to the touch of the keys [performing] the first three arithmetical operations with such a rapidity that the most experienced [human] computer cannot match its speed”, and also “it is especially of great help when several multiplications should be carried out, where a factor remains constant, as for proportionate shares, to reduce weights and measures of one country into another’s and it is useful to relieve the painful work of the [human] computers of tables.”

Only two documents propose a more thorough description of Torchi’s calculator, perhaps both by the same author; one is the hand-written Report of the Award Committee, and the second is an article published in the journal “La Fama” in 1836, where we can find the description of the operations and the only known picture of the machine (see the sketch below). The Report of the Award Committee includes: This combination of a constant and a variable number within certain limits, can be obtained by toothed sprockets and it is amazing to observe their particular configuration and bizarre teeth pattern. In spite of the poverty of the descriptions, two important features strike the attention: it was a “full-keyboard calculator” and it performed multiplication “instantaneously”.

The calculating machine of Luiggi Torchi
The calculating machine of Luigi Torchi (© Biblioteca Braidense, Milan, Italy)

Unless the fortuitous discovery of other documents or, almost impossible, of the machine or of parts of it, we cannot draw any definitive conclusion on the principle of operation of the Torchi’s contrivance and its innovative value. The lack of information may be attributable to Torchi himself, who would not have allowed any accurate inspection of his calculator to avoid possible plagiarism. In those times a craftsman was hardly protected from copies and Torchi’s bent on secrecy seems thus understandable.

The latest documented news about Luigi Torchi is the 1858 article about the pendulum level, written by Angelo Parrocchetti and Schiaparelli’s notes of 1872. If in nearly forty years since the prize, nothing more was recorded about the calculating machine and its inventor, one should think of a serious reason.

Why was the metal prototype never built? We can imagine that maybe the calculator was not as reliable as the enthusiastic descriptions bring us to understand?! Or maybe Torchi himself was not self-confident enough to work with different technology and with greater precision, and yet he was a carpenter, while the experience of a watchmaker or a scientific instruments maker was more appropriate?! Or maybe, finally, the inventor claimed more than the promised 1000 Lire?!

What happened to the prototype of his calculator? We know that it was probably exhibited in the Palace of Science and Arts of Brera from 1834 to 1837. It was then brought back to Torchi’s workshop, to be found again at the Brera Palace in 1872, when it was examined by Schiaparelli. We can imagine that, by that time very damaged and built with perishable material, it did not survive longer.

Strangely, almost nothing is known about this remarkable inventor—Luigi Torchi, except that he was born in 1812 and worked at the southern borders of the city of Milan (he lived in Borgo San Gottardo n° 1023, a neighborhood in Milan) as a mill carpenter. Torchi probably died before 1872. The exact details of his death have not been found in the city archives in Milan, as well as those relating to his origins, so probably Torchi was born and died far from the Lombard capital.

1. S. Hénin, La macchina calcolatrice del falegname Luigi Torchi, PRISTEM Lettera Matematica, Luglio 2008
2. S. Hénin, Two Early Italian Key-driven Calculators, IEEE Annals of the History of Computing, 2010. n. 1

Jean-Baptiste Schwilgue

Acknowledgement to my correspondent Mr. Denis Roegel, Professor at Loria, France, for his important works on Schwilgué’s calculating machines.
Georgi Dalakov

Portrait of Jean-Baptiste Schwilgué
Jean-Baptiste Schwilgué (1776-1856)

In 1844 the French engineer Jean-Baptiste Schwilgué from Strasbourg, together with his son Charles-Maximilien, patented a key-driven calculating machine, which seems to be the third key-driven machine in the world, after these of James White and Luigi Torchi, but was certainly the first popular keyboard calculator. Similar machines will be invented and manufactured by many inventors in the next 60 years. Moreover, several years later Schwilgué devised a bigger specialized calculating machine.

Additionneur Schwilgué (Schwilgué’s Adder)

Before starting the creation of his calculating machines, Schwilgué made a number of preliminary studies years before, such as a design of the computus mechanism (Easter computation) in 1816, of which he built a prototype in 1821. This mechanism, whose whereabouts are now unknown, could compute Easter following the complex Gregorian rule. The astronomical part is unusually accurate: it indicates leap years, equinoxes, and much more astronomical data.

Schwilgué himself was trained as a clockmaker, but also became a professor of mathematics, weights and measures controller, and an industry man, whose particular focus was on improving scales. After the completion of his famous astronomical clock of Strasbourg Cathedral in the early 1840s and following a change in the French patent laws, Schwilgué, with or without his son, patented several inventions, including the above-mentioned small adding machine. This machine appeared in the 1846 catalog of Schwilgué’s tower clock company, but was most probably devised some 10 years ago, in the middle 1830s.

The key adder of Schwilgué, a device from 1846 ((© Historical Museum Strasbourg)
The key adder of Schwilgué, a device from 1846, carrying the Nr. 15 (© Historical Museum Strasbourg)

As of now, several copies of the machine are known: one is in a private collection (Boutry-Ungerer family), one (dated 1846) in the Strasbourg Historical Museum (the machine (see the upper image) is in a poor state and carries the Nr. 15), and one (dated 1851) is in the collections of the Swiss Federal Institute of Technology in Zurich (see the lower images).

The calculating machine of Schwilgué in Zurich (Courtesy of the Swiss Federal Institute of Technology)
The calculating machine of Schwilgué in Zurich (Courtesy of the Swiss Federal Institute of Technology)
A side view of the Schwilgué's machine in Zurich (Courtesy of the Swiss Federal Institute of Technology)
A side view of Schwilgué’s machine in Zurich (Courtesy of the Swiss Federal Institute of Technology)

Like other machines of this kind (so-called single-column adders), the device of Schwilgué was intended to add a single digit at a time, i.e. the unit column is entered first, then the tens, the hundreds, the thousands, and so on, certainly rather cumbersome task (as every partial sum had to be recorded on paper and the sum eventually performed), which greatly limits the usefulness of such devices.

The inside of calculating machine of Schwilgué in Zurich (Courtesy of the Swiss Federal Institute of Technology and Mr. Denis Roegel)
The inside of calculating machine of Schwilgué in Zurich (Courtesy of the Swiss Federal Institute of Technology and Mr. Denis Roegel)
Under the top plate of calculating machine of Schwilgué (Courtesy of the Swiss Federal Institute of Technology and Mr. Denis Roegel)
Under the top plate of calculating machine of Schwilgué (Courtesy of the Swiss Federal Institute of Technology and Mr. Denis Roegel)

In closed status, the machine is a box with nine numbered keys, an opening showing two or three digits in two parts, and two knurled knobs. It is 25.5 cm long, 13.6 cm wide, and 9.5 cm tall (without the knobs), weight 3.3 kg. The inside of one of the machines is almost identical to the patent drawing (see the next figure).

The patent drawing of the calculating machine of Schwilgué
The patent drawing of the small calculating machine of Schwilgué

Schwilgué’s machine has three main functions: addition, carrying, and setting.

The upper figure shows figures I, II, III, and IV of Schwilgué’s patent. Figure IV shows how the keys operate. Each key can move downward by an amount corresponding to its value and moves the wheel G, but only when the key is released. (Schwilgué stated, however, that this can be changed, to work on key pressing). This wheel meshes with wheel H (horizontal in Figure III), and the unit wheel moves counterclockwise by as many digits as the pressed key. The unit wheel is the wheel on the right of Figure II. It contains each digit three times.

The units and tens wheels can be set using the knurled knobs, so that before an addition the openings would show 00. On the Zurich machine, resetting the wheels is made easier by pins located under the wheels. When the knobs are pushed downwards, R or U disengage, but the pins are put in the way of stops so that one merely has to turn the knobs until it is no longer possible.

It may seem surprising to see such an invention, long after more sophisticated calculating machines such as Thomas’s Arithmometre (1820), or even the Roth machine (1841). It must, however, be understood that Schwilgué’s machine was never meant as a general adding machine.

Schwilgué, who had obtained a number of patents since the 1820s, was no doubt well aware of Thomas’s machine and other general calculating machines. We know, for instance, that Schwilgué had a copy of the description of Roth’s machines, as well as a copy of a history of calculating instruments published in 1843 by Olivier. It is possible that these articles were an incentive for Schwilgué to build his calculating machine, or they may have been part of his research for his own machine.

Unlike that of the general-purpose calculating machines, Schwilgué’s purpose was to ease a particular operation, the hand checking of addition. In these cases, only small values were handled, and Schwilgué didn’t bother to build a machine with 10-digit inputs, although it could probably have been done with his carrying mechanism. Instead, Schwilgué could see that the existing machines, although powerful in principle, were of little use for everyday accounting. Schwilgué’s machine was designed to fill that gap by using keys to input numbers. Schwilgué could see their potential, even though he never claimed to have invented the keyboard, as keyboards already existed on musical instruments.

The calculating machine of Schwilgué has several other interesting features (some are mentioned only in the patent):
The one, that has already been mentioned, is the use of a clock escapement-like way of adding the carry, although Schwilgué never qualified it that way. This feature seems also present on Schilt’s machine.

The patent drawing also shows that the keyed figures are only taken into account when the keys are released. However, Schwilgué stated explicitly that both are possible, either upon pressing or upon release and that the patent covers both.

Schwilgué also mentioned an interesting feature which he called “tout ou rien” (all or nothing). Besides the name, which alludes to binary logic and may have been borrowed from Julien Le Roy in the context of repeating watches that had to ring all chimes or none, it was here an optional feature ensuring that a digit was only taken into account when the key had been completely pressed. However, according to Schwilgué, this was not really needed as one learned quickly to operate the machine and not to make mistakes. A similar safety measure was introduced as late as 1913 in the ill-fated E-model of the Comptometer of Dor Felt. On that, an automatic blocking device prevents errors and forces the operator to repeat pressing a key that was not adequately depressed.

Schwilgué’s Calculator of Sequences

It is known also, that in the middle 1840s Schwilgué constructed a bigger specialized calculating machine, a solid brass device with 36 result wheels, kept now in the collection of Historical Museum Strasbourg (see the lower photo). This machine was advertised at “300 to 400” francs in 1846 (about three months’ salary for a common laborer of the period), and at “400 to 500” francs in 1847, but it seems unlikely that any was sold because it was too specialized.

Schwilgué's Calculator of Sequences (© Historical Museum Strasbourg)
Schwilgué’s Calculator of Sequences (© Historical Museum Strasbourg)

This specialized machine had a single purpose—to calculate multiples of some value using additions, and on 12 digits (i.e. the machine works with 12-digit integers, and it computes their multiples in sequence). In the 1830s and 1840s Schwilgué made several gear-cutting machines, which position is given by angles at regular intervals. To be able to calculate the angles with a large accuracy, Schwilgué wanted to compute the fractions 1/p, 2/p, 3/p…, p/p on 12 places. Thus the output of the calculating machine (values were copied on paper) can be used as an input for the gear-cutting machine.

The machine is a weight-driven device with a modular design and includes 12 almost identical blocks (one for each place), a command arbor, and a command block. A crank is provided (normally not used), for rewinding the machine and clearing carries.

Once the machine is rewound, a detent is shifted and the mechanism does one addition, then stops. This operation is repeated until the machine is rewound. After each computation, the values are copied on paper.

The command block is similar to a striking clock with two 54-teeth wheels, a pinion of 9 leaves, a second wheel of 47 teeth, and a double threaded worm. The weight is attached to a string that is wound around a drum driving one of the 54 teeth wheels, and this wheel meshes with the second 54 teeth wheel, as well as with the pinion. The second 54 teeth wheel drives the command arbor. The pinion drives the second wheel and the worm which leads to a brake and an arm stopped by the detent. When the detent is released, the arm is freed and the mechanism turns, until the detent again meets a notch on the 54 teeth wheel of the command arbor. There is also a notch in the other 54 teeth wheel, and the two work together as in common striking clocks.

Schwilgué's bigger calculating machine (© Denis Roegel)
Schwilgué’s bigger calculating machine (© Denis Roegel)

When the command block is triggered, the 54 teeth wheels perform one turn and so does the command arbor. This arbor is tangent to the 12 blocks and carries 24 arms, organized helically, two per block. It is a natural consequence of the relative position of the blocks, of the arbor, and of the need to sequentialize the additions at each place: first the units, then the tens, etc. The arrangement of the computing blocks dictates the structure of the command arbor.

Each block displays three digits and the three sets of 12 digits represent three 12-digit numbers. One is a simple counter, and it will show 000000000000, 000000000001, 000000000002, etc. The other is a constant and will never change during an operation. It will for instance store a value such as 076923076923 for 1=13. The third one will merely show the multiples of the constant. There are therefore two independent, but synchronous, functions: the counter, and the multiple. These functions are synchronous so that one value (the counter) could serve as an entry to the second (the multiple). In the case of the counter, the machine has to add one to the units, and to propagate the carries. In the case of the constant, the constant must be added to the stored sum, and carries have to be propagated. Each of these two functions is obtained by two arms of the command arbor. One arm is for incrementing the counter, the other is for adding one digit of the constant to one digit of the sum.

The prototype of the machine was probably constructed in 1844, but the earliest known plans are from 1846. Later the machine seems to have slightly evolved and the above-mentioned device follows plans dated 1852.

Schwilgue’s bigger machine should be remembered as an exceptional example of his engineering genius and as a rare example of an early specialized calculator, full of subtle features.

Biography of Jean-Baptiste Schwilgué

Jean-Baptiste Schwilgué, portrait by Gabriel-Christophe Guérin from 1843
Jean-Baptiste Schwilgué, portrait by Gabriel-Christophe Guérin from 1843

Jean-Baptiste Sosime Schwilgue was born on 18 Dec. 1776 in Strasbourg, France, in a house located at the intersection of rue Brûlée and rue de la Comédie. He was the second son of the civil servant François-Antoine Schwilgue (1749-1815) and Jeanne Courteaux (1750-1784). François-Antoine was native from Thann in Grand Est (Schwilgue (or Schwilcke) family settled in Thann centuries ago), and came to Strasbourg to serve as valet de chambre in l’Intendance royale d’Alsace à Strasbourg. Jeanne Courteaux was native from de Solgne (Moselle). Jean-Baptiste had an elder brother, Charles Joseph Antoine, born on 10 Oct. 1774, who became a doctor and professor of medicine in Paris, but died only 33 years old on 7 Feb. 1808. His mother Jeanne also died young on 13 April 1784, when Jean-Baptiste was only 8, and his father married second time in June 1785 to Marie-Anne Kauffeisen (1746-1809).

As a boy, Jean-Baptiste showed great interest in mechanics, and with the help of the simplest tools available to him, he produced various machines and instruments, by which he made special improvements that he had conceived. He was very fond of looking at the Strasbourg Cathedral astronomical clock, made in the 1570s by Konrad Dasypodius (1532-1600), and often stood for hours before it, thinking about putting this highly sophisticated watch (which at the time was very badly or not at all functional anymore), again in the workable state.

In 1789, after the outbreak of the French Revolution, the father of Jean-Baptiste lost his position and moved from Strasbourg to Sélestat (Schlestadt), Alsace (he died there on 14 Feb. 1815), where Jean-Baptiste continued his studies, devoting himself, especially to mathematics. Besides his studies, he learned the art of watch-making, entering a watch-making shop as an apprentice.

Anne Marie Thérèse Hihn-Schwilgué
Anne Marie ‘Thérèse’ Hihn-Schwilgué

In 1796 Jean-Baptiste became self-employed and married Anne Marie “Thérèse” Hihn (1778-1851, see the nearby image), a daughter of the confectioner Charles Hihn and Thérèse Baldenberger, on 25 April in Sélestat.

Eight children, three boys and five girls, were born from this marriage: Marie Thérèse (1797-1848), Jean-Baptiste (1798-1855), Charles-Maximilien (1800-1861), Françoise (1802-1806), Louise (1804-1864), Adélaïde (Adèle) (1806-1850), Sébastien “Alexandre” (1811-1836), and Marie “Clémentine” Emilie (1812-1878).

In 1807 Jean-Baptiste was appointed official at the district’s office of Sélestat (he was the town clockmaker and verifier of weights and measurements), and also a professor of mathematics at the local college, which he retained until he moved to Strasbourg in 1827. In the meantime, he was always occupied with the Strasbourg astronomical clock, and around 1820 he invented a mechanical church calendar with a precise determination of the movable festivals according to the Gregorian. This church calendar, which he had carried out in a smaller model (15×20 cm), he brought to the French Academy of Sciences in 1821, and even presented it personally to King Louis XVIII.

The third astronomical clock of Strasbourg Cathedral
The third astronomical clock of Strasbourg Cathedral

The masterpiece of Schwilgué’s life was the third astronomical clock of Cathédrale Notre-Dame de Strasbourg. As early as 1827, Schwilgué had submitted to the city council of Strasbourg a report on the condition of the clock, together with three proposals on the repair of the same; the first two, while retaining certain parts of the old clock, and the third, for a completely new clock. But it was not until 1836, after lengthy negotiations, that the city council of Strasbourg came to a final decision on the restoration of the clock, and was only approved by the higher administrative authority at the beginning of 1838. As the agreement was signed in May 1838, in June, Schwilgué set to work on the new clock. Together with his son Charles and his apprentices and later partners—brothers Albert and Theodor Ungerer, he was able to finish this assignment in July 1842. On 2 October 1842, on the occasion of the 10th Congress of Sciences in France in Strasbourg, the clock was set in motion for the first time, and Schwilgué was congratulated on all sides for the great success of the work which he had undertaken. In November 1842, a large banquet was held in his honor, and on 31 December 1842, a grand feast with a solemn parade through the town to commemorate the fortunate prosperity of the work erected by Schwilgué.

In 1835 Schwilgue was appointed Knight of the Legion of Honour and in 1853 on a report of the Minister of Education and Religious Affairs he obtained the rank of Officer of the Legion of Honour.

Jean-Baptiste Sosime Schwilgue died 79 years old on 5 December 1856 in Strasbourg (see below the gravestone of Jean-Baptiste Schwilgué and his wife Anne Marie “Thérèse” Hihn). His son Charles inherited his father in the workshop (and in 1857 wrote a book about his famous father, named Notice sur la vie, les travaux et les ouvrages de mon pere, J. B. Schwilgue), but in 1858 he was paralyzed by a stroke, and died three years later.

The gravestone of Jean-Baptiste Schwilgué and his wife Anne Marie "Thérèse" Hihn in Strasbourg
The gravestone of Jean-Baptiste Schwilgué and his wife Anne Marie ‘Thérèse’ Hihn in Strasbourg

Denis Roegel: An Early (1844) Key-Driven Adding Machine, IEEE Annals of the History of Computing, vol. 30, №1, pp. 59-65, January-March 2008)